LMFDB - Embedded newform 176.4.m.b.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [176,4,Mod(49,176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("176.49"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(176, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	176.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.3843361610$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 $ x^8 - x^7 + 71x^6 - 141x^5 + 2911x^4 + 2710x^3 + 75340x^2 + 169400x + 5856400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			49.1
Root			$2.22300 + 6.84169i$ of defining polynomial
Character	$\chi$	$=$	176.49
Dual form			176.4.m.b.97.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.31989 - 4.59167i) q^{3} +(4.60996 - 14.1880i) q^{5} +(17.6106 - 12.7948i) q^{7} +(10.5141 + 32.3592i) q^{9} +(29.3767 - 21.6335i) q^{11} +(-13.6056 - 41.8736i) q^{13} +(-94.2810 + 68.4992i) q^{15} +(-7.69900 + 23.6951i) q^{17} +(17.7638 + 12.9061i) q^{19} -170.046 q^{21} -177.749 q^{23} +(-78.9203 - 57.3389i) q^{25} +(16.9569 - 52.1881i) q^{27} +(120.864 - 87.8130i) q^{29} +(-23.2207 - 71.4658i) q^{31} +(-284.992 + 1.83359i) q^{33} +(-100.349 - 308.842i) q^{35} +(-179.874 + 130.686i) q^{37} +(-106.284 + 327.109i) q^{39} +(204.779 + 148.781i) q^{41} -130.623 q^{43} +507.582 q^{45} +(403.775 + 293.360i) q^{47} +(40.4316 - 124.436i) q^{49} +(157.457 - 114.399i) q^{51} +(3.99933 + 12.3087i) q^{53} +(-171.511 - 516.526i) q^{55} +(-53.0044 - 163.131i) q^{57} +(28.7697 - 20.9024i) q^{59} +(166.357 - 511.995i) q^{61} +(599.190 + 435.337i) q^{63} -656.824 q^{65} +519.621 q^{67} +(1123.35 + 816.165i) q^{69} +(-24.2420 + 74.6091i) q^{71} +(-925.571 + 672.467i) q^{73} +(235.486 + 724.752i) q^{75} +(240.543 - 756.848i) q^{77} +(-238.730 - 734.735i) q^{79} +(396.416 - 288.013i) q^{81} +(-166.017 + 510.947i) q^{83} +(300.694 + 218.467i) q^{85} -1167.06 q^{87} +667.089 q^{89} +(-775.368 - 563.338i) q^{91} +(-181.395 + 558.278i) q^{93} +(265.003 - 192.536i) q^{95} +(-55.5161 - 170.861i) q^{97} +(1008.91 + 723.148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9} + 155 q^{11} + 7 q^{13} - 211 q^{15} + 161 q^{17} + 272 q^{19} - 50 q^{21} - 628 q^{23} - 17 q^{25} + 528 q^{27} + 33 q^{29} - 323 q^{31} - 1144 q^{33} + 697 q^{35}+ \cdots + 2213 q^{99}+O(q^{100}) $ 8 * q - 3 * q^3 + 5 * q^5 + q^7 - 21 * q^9 + 155 * q^11 + 7 * q^13 - 211 * q^15 + 161 * q^17 + 272 * q^19 - 50 * q^21 - 628 * q^23 - 17 * q^25 + 528 * q^27 + 33 * q^29 - 323 * q^31 - 1144 * q^33 + 697 * q^35 + 49 * q^37 - 391 * q^39 + 361 * q^41 - 1442 * q^43 + 2652 * q^45 + 1069 * q^47 - 709 * q^49 + 1332 * q^51 - 281 * q^53 + 7 * q^55 - 438 * q^57 + 128 * q^59 - 617 * q^61 - 694 * q^63 - 138 * q^65 - 578 * q^67 - 310 * q^69 - 115 * q^71 - 1487 * q^73 + 1852 * q^75 + 553 * q^77 - 71 * q^79 + 1630 * q^81 - 1942 * q^83 - 329 * q^85 - 2122 * q^87 - 2202 * q^89 - 4523 * q^91 + 6019 * q^93 + 793 * q^95 - 5128 * q^97 + 2213 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−6.31989	−	4.59167i	−1.21626	−	0.883667i	−0.220479	−	0.975392i	$-0.570762\pi$
$3$	−6.31989	−	4.59167i	−1.21626	−	0.883667i	−0.995784	+	0.0917244i	$0.970762\pi$
$4$		0			0
$5$	4.60996	−	14.1880i	0.412327	−	1.26901i	−0.502293	−	0.864698i	$-0.667510\pi$
$5$	4.60996	−	14.1880i	0.412327	−	1.26901i	0.914620	−	0.404315i	$-0.132490\pi$
$6$		0			0
$7$	17.6106	−	12.7948i	0.950881	−	0.690856i	−0.000134039	−	1.00000i	$-0.500043\pi$
$7$	17.6106	−	12.7948i	0.950881	−	0.690856i	0.951015	+	0.309144i	$0.100043\pi$
$8$		0			0
$9$	10.5141	+	32.3592i	0.389412	+	1.19849i
$10$		0			0
$11$	29.3767	−	21.6335i	0.805219	−	0.592978i
$11$	29.3767	−	21.6335i	0.805219	−	0.592978i
$12$		0			0
$13$	−13.6056	−	41.8736i	−0.290270	−	0.893358i	−0.984769	−	0.173865i	$-0.944374\pi$
$13$	−13.6056	−	41.8736i	−0.290270	−	0.893358i	0.694500	−	0.719493i	$-0.255626\pi$
$14$		0			0
$15$	−94.2810	+	68.4992i	−1.62288	+	1.17909i
$16$		0			0
$17$	−7.69900	+	23.6951i	−0.109840	+	0.338053i	−0.990836	−	0.135071i	$-0.956874\pi$
$17$	−7.69900	+	23.6951i	−0.109840	+	0.338053i	0.880996	+	0.473124i	$0.156874\pi$
$18$		0			0
$19$	17.7638	+	12.9061i	0.214489	+	0.155835i	0.689842	−	0.723960i	$-0.257680\pi$
$19$	17.7638	+	12.9061i	0.214489	+	0.155835i	−0.475353	+	0.879795i	$0.657680\pi$
$20$		0			0
$21$	−170.046			−1.76701
$22$		0			0
$23$	−177.749			−1.61145			−0.805723	−	0.592293i	$-0.798223\pi$
$23$	−177.749			−1.61145			−0.805723	+	0.592293i	$0.798223\pi$
$24$		0			0
$25$	−78.9203	−	57.3389i	−0.631362	−	0.458711i
$26$		0			0
$27$	16.9569	−	52.1881i	0.120865	−	0.371985i
$28$		0			0
$29$	120.864	−	87.8130i	0.773928	−	0.562292i	−0.129223	−	0.991616i	$-0.541248\pi$
$29$	120.864	−	87.8130i	0.773928	−	0.562292i	0.903151	+	0.429324i	$0.141248\pi$
$30$		0			0
$31$	−23.2207	−	71.4658i	−0.134534	−	0.414053i	0.860983	−	0.508633i	$-0.169849\pi$
$31$	−23.2207	−	71.4658i	−0.134534	−	0.414053i	−0.995517	+	0.0945803i	$0.969849\pi$
$32$		0			0
$33$	−284.992	+	1.83359i	−1.50335	+	0.00967232i
$34$		0			0
$35$	−100.349	−	308.842i	−0.484630	−	1.49154i
$36$		0			0
$37$	−179.874	+	130.686i	−0.799219	+	0.580667i	−0.910685	−	0.413102i	$-0.864445\pi$
$37$	−179.874	+	130.686i	−0.799219	+	0.580667i	0.111466	+	0.993768i	$0.464445\pi$
$38$		0			0
$39$	−106.284	+	327.109i	−0.436387	+	1.34306i
$40$		0			0
$41$	204.779	+	148.781i	0.780029	+	0.566724i	0.904988	−	0.425438i	$-0.139880\pi$
$41$	204.779	+	148.781i	0.780029	+	0.566724i	−0.124959	+	0.992162i	$0.539880\pi$
$42$		0			0
$43$	−130.623			−0.463253			−0.231626	−	0.972805i	$-0.574405\pi$
$43$	−130.623			−0.463253			−0.231626	+	0.972805i	$0.574405\pi$
$44$		0			0
$45$	507.582			1.68146
$46$		0			0
$47$	403.775	+	293.360i	1.25312	+	0.910445i	0.998399	−	0.0565693i	$-0.0180162\pi$
$47$	403.775	+	293.360i	1.25312	+	0.910445i	0.254722	+	0.967014i	$0.418016\pi$
$48$		0			0
$49$	40.4316	−	124.436i	0.117876	−	0.362786i
$50$		0			0
$51$	157.457	−	114.399i	0.432321	−	0.314100i
$52$		0			0
$53$	3.99933	+	12.3087i	0.0103651	+	0.0319005i	0.956105	−	0.293023i	$-0.0946613\pi$
$53$	3.99933	+	12.3087i	0.0103651	+	0.0319005i	−0.945740	+	0.324924i	$0.894661\pi$
$54$		0			0
$55$	−171.511	−	516.526i	−0.420483	−	1.26633i
$56$		0			0
$57$	−53.0044	−	163.131i	−0.123169	−	0.379074i
$58$		0			0
$59$	28.7697	−	20.9024i	0.0634831	−	0.0461232i	−0.555591	−	0.831456i	$-0.687508\pi$
$59$	28.7697	−	20.9024i	0.0634831	−	0.0461232i	0.619074	+	0.785332i	$0.287508\pi$
$60$		0			0
$61$	166.357	−	511.995i	0.349178	−	1.07466i	−0.610131	−	0.792301i	$-0.708883\pi$
$61$	166.357	−	511.995i	0.349178	−	1.07466i	0.959309	−	0.282359i	$-0.0911169\pi$
$62$		0			0
$63$	599.190	+	435.337i	1.19827	+	0.870592i
$64$		0			0
$65$	−656.824			−1.25337
$66$		0			0
$67$	519.621			0.947491			0.473745	−	0.880662i	$-0.342902\pi$
$67$	519.621			0.947491			0.473745	+	0.880662i	$0.342902\pi$
$68$		0			0
$69$	1123.35	+	816.165i	1.95994	+	1.42398i
$70$		0			0
$71$	−24.2420	+	74.6091i	−0.0405210	+	0.124711i	−0.969271	−	0.245997i	$-0.920885\pi$
$71$	−24.2420	+	74.6091i	−0.0405210	+	0.124711i	0.928750	+	0.370708i	$0.120885\pi$
$72$		0			0
$73$	−925.571	+	672.467i	−1.48397	+	1.07817i	−0.507722	+	0.861521i	$0.669512\pi$
$73$	−925.571	+	672.467i	−1.48397	+	1.07817i	−0.976250	+	0.216648i	$0.930488\pi$
$74$		0			0
$75$	235.486	+	724.752i	0.362555	+	1.11583i
$76$		0			0
$77$	240.543	−	756.848i	0.356005	−	1.12014i
$78$		0			0
$79$	−238.730	−	734.735i	−0.339990	−	1.04638i	−0.964212	−	0.265134i	$-0.914584\pi$
$79$	−238.730	−	734.735i	−0.339990	−	1.04638i	0.624222	−	0.781247i	$-0.285416\pi$
$80$		0			0
$81$	396.416	−	288.013i	0.543780	−	0.395079i
$82$		0			0
$83$	−166.017	+	510.947i	−0.219551	+	0.675708i	0.779248	+	0.626715i	$0.215601\pi$
$83$	−166.017	+	510.947i	−0.219551	+	0.675708i	−0.998799	+	0.0489926i	$0.984399\pi$
$84$		0			0
$85$	300.694	+	218.467i	0.383704	+	0.278777i
$86$		0			0
$87$	−1167.06			−1.43818
$88$		0			0
$89$	667.089			0.794509			0.397255	−	0.917708i	$-0.369963\pi$
$89$	667.089			0.794509			0.397255	+	0.917708i	$0.369963\pi$
$90$		0			0
$91$	−775.368	−	563.338i	−0.893194	−	0.648943i
$92$		0			0
$93$	−181.395	+	558.278i	−0.202256	+	0.622481i
$94$		0			0
$95$	265.003	−	192.536i	0.286197	−	0.207934i
$96$		0			0
$97$	−55.5161	−	170.861i	−0.0581114	−	0.178848i	0.917787	−	0.397072i	$-0.129974\pi$
$97$	−55.5161	−	170.861i	−0.0581114	−	0.178848i	−0.975899	+	0.218224i	$0.929974\pi$
$98$		0			0
$99$	1008.91	+	723.148i	1.02424	+	0.734132i
$100$		0			0
$101$	−126.924	−	390.633i	−0.125044	−	0.384846i	0.868865	−	0.495049i	$-0.164850\pi$
$101$	−126.924	−	390.633i	−0.125044	−	0.384846i	−0.993909	+	0.110203i	$0.964850\pi$
$102$		0			0
$103$	1106.46	−	803.890i	1.05847	−	0.769026i	0.0846679	−	0.996409i	$-0.473017\pi$
$103$	1106.46	−	803.890i	1.05847	−	0.769026i	0.973805	+	0.227383i	$0.0730171\pi$
$104$		0			0
$105$	−783.907	+	2412.62i	−0.728586	+	2.24236i
$106$		0			0
$107$	−319.756	−	232.317i	−0.288897	−	0.209896i	0.433892	−	0.900965i	$-0.357140\pi$
$107$	−319.756	−	232.317i	−0.288897	−	0.209896i	−0.722789	+	0.691069i	$0.757140\pi$
$108$		0			0
$109$	505.826			0.444490			0.222245	−	0.974991i	$-0.428662\pi$
$109$	505.826			0.444490			0.222245	+	0.974991i	$0.428662\pi$
$110$		0			0
$111$	1736.85			1.48518
$112$		0			0
$113$	−1243.96	−	903.793i	−1.03560	−	0.752404i	−0.0661744	−	0.997808i	$-0.521079\pi$
$113$	−1243.96	−	903.793i	−1.03560	−	0.752404i	−0.969421	+	0.245404i	$0.921079\pi$
$114$		0			0
$115$	−819.416	+	2521.90i	−0.664443	+	2.04494i
$116$		0			0
$117$	1211.95	−	880.530i	0.957645	−	0.695770i
$118$		0			0
$119$	167.591	+	515.791i	0.129101	+	0.397332i
$120$		0			0
$121$	394.980	−	1271.04i	0.296754	−	0.954954i
$122$		0			0
$123$	−611.031	−	1880.56i	−0.447925	−	1.37857i
$124$		0			0
$125$	331.285	−	240.693i	0.237048	−	0.172226i
$126$		0			0
$127$	215.487	−	663.202i	0.150562	−	0.463383i	−0.847122	−	0.531399i	$-0.821667\pi$
$127$	215.487	−	663.202i	0.150562	−	0.463383i	0.997684	+	0.0680154i	$0.0216667\pi$
$128$		0			0
$129$	825.525	+	599.779i	0.563437	+	0.409361i
$130$		0			0
$131$	259.910			0.173347			0.0866735	−	0.996237i	$-0.472376\pi$
$131$	259.910			0.173347			0.0866735	+	0.996237i	$0.472376\pi$
$132$		0			0
$133$	477.962			0.311613
$134$		0			0
$135$	−662.273	−	481.170i	−0.422218	−	0.306759i
$136$		0			0
$137$	−643.856	+	1981.58i	−0.401520	+	1.23575i	0.522245	+	0.852795i	$0.325094\pi$
$137$	−643.856	+	1981.58i	−0.401520	+	1.23575i	−0.923766	+	0.382958i	$0.874906\pi$
$138$		0			0
$139$	140.307	−	101.939i	0.0856163	−	0.0622039i	−0.544154	−	0.838986i	$-0.683149\pi$
$139$	140.307	−	101.939i	0.0856163	−	0.0622039i	0.629770	+	0.776782i	$0.283149\pi$
$140$		0			0
$141$	−1204.80	−	3708.00i	−0.719594	−	2.21468i
$142$		0			0
$143$	−1305.56	−	935.772i	−0.763473	−	0.547225i
$144$		0			0
$145$	−688.711	−	2119.63i	−0.394444	−	1.21397i
$146$		0			0
$147$	−826.891	+	600.772i	−0.463951	+	0.337080i
$148$		0			0
$149$	−138.766	+	427.077i	−0.0762961	+	0.234815i	−0.981930	−	0.189246i	$-0.939396\pi$
$149$	−138.766	+	427.077i	−0.0762961	+	0.234815i	0.905634	+	0.424061i	$0.139396\pi$
$150$		0			0
$151$	23.0859	+	16.7729i	0.0124418	+	0.00903947i	0.593989	−	0.804473i	$-0.297552\pi$
$151$	23.0859	+	16.7729i	0.0124418	+	0.00903947i	−0.581547	+	0.813513i	$0.697552\pi$
$152$		0			0
$153$	−847.702			−0.447926
$154$		0			0
$155$	−1121.00			−0.580910
$156$		0			0
$157$	−1394.63	−	1013.26i	−0.708941	−	0.515076i	0.173891	−	0.984765i	$-0.444366\pi$
$157$	−1394.63	−	1013.26i	−0.708941	−	0.515076i	−0.882832	+	0.469689i	$0.844366\pi$
$158$		0			0
$159$	31.2420	−	96.1531i	0.0155827	−	0.0479587i
$160$		0			0
$161$	−3130.26	+	2274.27i	−1.53229	+	1.11328i
$162$		0			0
$163$	−1025.39	−	3155.82i	−0.492727	−	1.51646i	−0.820470	−	0.571690i	$-0.806288\pi$
$163$	−1025.39	−	3155.82i	−0.492727	−	1.51646i	0.327743	−	0.944767i	$-0.393712\pi$
$164$		0			0
$165$	−1287.78	+	4051.91i	−0.607599	+	1.91176i
$166$		0			0
$167$	931.871	+	2868.00i	0.431799	+	1.32894i	0.896332	+	0.443384i	$0.146222\pi$
$167$	931.871	+	2868.00i	0.431799	+	1.32894i	−0.464533	+	0.885556i	$0.653778\pi$
$168$		0			0
$169$	209.120	−	151.934i	0.0951842	−	0.0691554i
$170$		0			0
$171$	−230.862	+	710.519i	−0.103242	+	0.317747i
$172$		0			0
$173$	1787.45	+	1298.66i	0.785534	+	0.570724i	0.906635	−	0.421917i	$-0.138643\pi$
$173$	1787.45	+	1298.66i	0.785534	+	0.570724i	−0.121101	+	0.992640i	$0.538643\pi$
$174$		0			0
$175$	−2123.47			−0.917254
$176$		0			0
$177$	−277.799			−0.117970
$178$		0			0
$179$	−1837.95	−	1335.35i	−0.767457	−	0.557590i	0.133731	−	0.991018i	$-0.457304\pi$
$179$	−1837.95	−	1335.35i	−0.767457	−	0.557590i	−0.901189	+	0.433427i	$0.857304\pi$
$180$		0			0
$181$	−192.961	+	593.873i	−0.0792413	+	0.243880i	−0.982828	−	0.184527i	$-0.940925\pi$
$181$	−192.961	+	593.873i	−0.0792413	+	0.243880i	0.903586	+	0.428406i	$0.140925\pi$
$182$		0			0
$183$	−3402.27	+	2471.89i	−1.37433	+	0.998512i
$184$		0			0
$185$	1024.96	+	3154.51i	0.407333	+	1.25364i
$186$		0			0
$187$	286.438	+	862.640i	0.112013	+	0.337340i
$188$		0			0
$189$	−369.116	−	1136.02i	−0.142059	−	0.437214i
$190$		0			0
$191$	−1087.48	+	790.100i	−0.411975	+	0.299317i	−0.774401	−	0.632695i	$-0.781949\pi$
$191$	−1087.48	+	790.100i	−0.411975	+	0.299317i	0.362426	+	0.932013i	$0.381949\pi$
$192$		0			0
$193$	1428.82	−	4397.46i	0.532895	−	1.64008i	−0.215258	−	0.976557i	$-0.569059\pi$
$193$	1428.82	−	4397.46i	0.532895	−	1.64008i	0.748154	−	0.663526i	$-0.230941\pi$
$194$		0			0
$195$	4151.06	+	3015.92i	1.52443	+	1.10756i
$196$		0			0
$197$	664.691			0.240392			0.120196	−	0.992750i	$-0.461648\pi$
$197$	664.691			0.240392			0.120196	+	0.992750i	$0.461648\pi$
$198$		0			0
$199$	3042.82			1.08392			0.541959	−	0.840405i	$-0.317683\pi$
$199$	3042.82			1.08392			0.541959	+	0.840405i	$0.317683\pi$
$200$		0			0
$201$	−3283.95	−	2385.93i	−1.15240	−	0.837266i
$202$		0			0
$203$	1004.93	−	3092.87i	0.347451	−	1.06934i
$204$		0			0
$205$	3054.93	−	2219.53i	1.04081	−	0.756190i
$206$		0			0
$207$	−1868.88	−	5751.81i	−0.627517	−	1.93130i
$208$		0			0
$209$	801.047	−	5.15380i	0.265118	−	0.00170572i
$210$		0			0
$211$	−800.851	−	2464.77i	−0.261293	−	0.804178i	−0.992524	−	0.122048i	$-0.961054\pi$
$211$	−800.851	−	2464.77i	−0.261293	−	0.804178i	0.731231	−	0.682130i	$-0.238946\pi$
$212$		0			0
$213$	495.787	−	360.210i	0.159487	−	0.115874i
$214$		0			0
$215$	−602.168	+	1853.28i	−0.191012	+	0.587873i
$216$		0			0
$217$	−1323.32	−	961.449i	−0.413977	−	0.300772i
$218$		0			0
$219$	8937.26			2.75764
$220$		0			0
$221$	1096.95			0.333886
$222$		0			0
$223$	2133.54	+	1550.11i	0.640684	+	0.465484i	0.860085	−	0.510150i	$-0.170410\pi$
$223$	2133.54	+	1550.11i	0.640684	+	0.465484i	−0.219401	+	0.975635i	$0.570410\pi$
$224$		0			0
$225$	1025.66	−	3156.66i	0.303900	−	0.935308i
$226$		0			0
$227$	202.796	−	147.340i	0.0592954	−	0.0430806i	−0.557743	−	0.830014i	$-0.688332\pi$
$227$	202.796	−	147.340i	0.0592954	−	0.0430806i	0.617038	+	0.786933i	$0.288332\pi$
$228$		0			0
$229$	556.018	+	1711.25i	0.160449	+	0.493810i	0.998672	−	0.0515169i	$-0.0164056\pi$
$229$	556.018	+	1711.25i	0.160449	+	0.493810i	−0.838224	+	0.545327i	$0.816406\pi$
$230$		0			0
$231$	−4995.40	+	3678.71i	−1.42283	+	1.04780i
$232$		0			0
$233$	982.821	+	3024.81i	0.276338	+	0.850481i	0.988862	+	0.148833i	$0.0475518\pi$
$233$	982.821	+	3024.81i	0.276338	+	0.850481i	−0.712524	+	0.701647i	$0.752448\pi$
$234$		0			0
$235$	6023.57	−	4376.38i	1.67206	−	1.21482i
$236$		0			0
$237$	−1864.91	+	5739.61i	−0.511135	+	1.57311i
$238$		0			0
$239$	4056.25	+	2947.04i	1.09781	+	0.797608i	0.980701	−	0.195511i	$-0.0626366\pi$
$239$	4056.25	+	2947.04i	1.09781	+	0.797608i	0.117111	+	0.993119i	$0.462637\pi$
$240$		0			0
$241$	6074.13			1.62352			0.811761	−	0.583990i	$-0.198509\pi$
$241$	6074.13			1.62352			0.811761	+	0.583990i	$0.198509\pi$
$242$		0			0
$243$	−5309.35			−1.40163
$244$		0			0
$245$	−1579.10	−	1147.29i	−0.411777	−	0.299173i
$246$		0			0
$247$	298.741	−	919.430i	0.0769572	−	0.236850i
$248$		0			0
$249$	3395.31	−	2466.84i	0.864132	−	0.627829i
$250$		0			0
$251$	1721.13	+	5297.09i	0.432816	+	1.33207i	0.895309	+	0.445447i	$0.146955\pi$
$251$	1721.13	+	5297.09i	0.432816	+	1.33207i	−0.462493	+	0.886623i	$0.653045\pi$
$252$		0			0
$253$	−5221.68	+	3845.34i	−1.29757	+	0.955552i
$254$		0			0
$255$	−897.224	−	2761.37i	−0.220339	−	0.678133i
$256$		0			0
$257$	4778.90	−	3472.08i	1.15992	−	0.842732i	0.170153	−	0.985418i	$-0.445574\pi$
$257$	4778.90	−	3472.08i	1.15992	−	0.842732i	0.989768	+	0.142685i	$0.0455737\pi$
$258$		0			0
$259$	−1495.58	+	4602.91i	−0.358805	+	1.10429i
$260$		0			0
$261$	4112.34	+	2987.79i	0.975277	+	0.708580i
$262$		0			0
$263$	6853.74			1.60692			0.803459	−	0.595360i	$-0.202991\pi$
$263$	6853.74			1.60692			0.803459	+	0.595360i	$0.202991\pi$
$264$		0			0
$265$	193.072			0.0447559
$266$		0			0
$267$	−4215.93	−	3063.05i	−0.966333	−	0.702082i
$268$		0			0
$269$	340.340	−	1047.46i	0.0771409	−	0.237415i	−0.905049	−	0.425308i	$-0.860166\pi$
$269$	340.340	−	1047.46i	0.0771409	−	0.237415i	0.982190	+	0.187893i	$0.0601657\pi$
$270$		0			0
$271$	−2080.54	+	1511.60i	−0.466362	+	0.338832i	−0.796022	−	0.605268i	$-0.793066\pi$
$271$	−2080.54	+	1511.60i	−0.466362	+	0.338832i	0.329660	+	0.944100i	$0.393066\pi$
$272$		0			0
$273$	2313.58	+	7120.46i	0.512909	+	1.57857i
$274$		0			0
$275$	−3558.86	+	22.8971i	−0.780390	+	0.00502090i
$276$		0			0
$277$	−2268.22	−	6980.85i	−0.492000	−	1.51422i	−0.821581	−	0.570092i	$-0.806908\pi$
$277$	−2268.22	−	6980.85i	−0.492000	−	1.51422i	0.329581	−	0.944127i	$-0.393092\pi$
$278$		0			0
$279$	2068.43	−	1502.80i	0.443848	−	0.322475i
$280$		0			0
$281$	−2315.45	+	7126.21i	−0.491559	+	1.51286i	0.330693	+	0.943738i	$0.392718\pi$
$281$	−2315.45	+	7126.21i	−0.491559	+	1.51286i	−0.822252	+	0.569124i	$0.807282\pi$
$282$		0			0
$283$	−5253.84	−	3817.14i	−1.10356	−	0.801785i	−0.121925	−	0.992539i	$-0.538907\pi$
$283$	−5253.84	−	3817.14i	−1.10356	−	0.801785i	−0.981638	+	0.190754i	$0.938907\pi$
$284$		0			0
$285$	−2558.85			−0.531835
$286$		0			0
$287$	5509.91			1.13324
$288$		0			0
$289$	3472.52	+	2522.93i	0.706802	+	0.513522i
$290$		0			0
$291$	−433.681	+	1334.73i	−0.0873638	+	0.268878i
$292$		0			0
$293$	2172.11	−	1578.13i	0.433092	−	0.314660i	−0.349792	−	0.936827i	$-0.613748\pi$
$293$	2172.11	−	1578.13i	0.433092	−	0.314660i	0.782884	+	0.622168i	$0.213748\pi$
$294$		0			0
$295$	−163.936	−	504.544i	−0.0323551	−	0.0995787i
$296$		0			0
$297$	−630.874	−	1899.95i	−0.123256	−	0.371200i
$298$		0			0
$299$	2418.38	+	7443.00i	0.467754	+	1.43960i
$300$		0			0
$301$	−2300.35	+	1671.30i	−0.440498	+	0.320041i
$302$		0			0
$303$	−991.509	+	3051.55i	−0.187989	+	0.578571i
$304$		0			0
$305$	−6497.28	−	4720.55i	−1.21978	−	0.886223i
$306$		0			0
$307$	−8331.66			−1.54890			−0.774451	−	0.632633i	$-0.781974\pi$
$307$	−8331.66			−1.54890			−0.774451	+	0.632633i	$0.781974\pi$
$308$		0			0
$309$	−10683.9			−1.96695
$310$		0			0
$311$	−4061.55	−	2950.89i	−0.740545	−	0.538037i	0.152337	−	0.988329i	$-0.451320\pi$
$311$	−4061.55	−	2950.89i	−0.740545	−	0.538037i	−0.892882	+	0.450292i	$0.851320\pi$
$312$		0			0
$313$	933.873	−	2874.16i	0.168644	−	0.519033i	−0.830642	−	0.556807i	$-0.812026\pi$
$313$	933.873	−	2874.16i	0.168644	−	0.519033i	0.999286	+	0.0377733i	$0.0120265\pi$
$314$		0			0
$315$	8938.80	−	6494.42i	1.59887	−	1.16165i
$316$		0			0
$317$	−3257.08	−	10024.3i	−0.577085	−	1.77609i	−0.628966	−	0.777433i	$-0.716522\pi$
$317$	−3257.08	−	10024.3i	−0.577085	−	1.77609i	0.0518809	−	0.998653i	$-0.483478\pi$
$318$		0			0
$319$	1650.88	−	5194.37i	0.289755	−	0.911690i
$320$		0			0
$321$	954.104	+	2936.43i	0.165897	+	0.510578i
$322$		0			0
$323$	−442.576	+	321.550i	−0.0762402	+	0.0553917i
$324$		0			0
$325$	−1327.23	+	4084.81i	−0.226528	+	0.697183i
$326$		0			0
$327$	−3196.77	−	2322.59i	−0.540617	−	0.392781i
$328$		0			0
$329$	10864.2			1.82055
$330$		0			0
$331$	−309.871			−0.0514563			−0.0257281	−	0.999669i	$-0.508190\pi$
$331$	−309.871			−0.0514563			−0.0257281	+	0.999669i	$0.508190\pi$
$332$		0			0
$333$	−6120.11	−	4446.52i	−1.00715	−	0.731736i
$334$		0			0
$335$	2395.43	−	7372.39i	0.390676	−	1.20238i
$336$		0			0
$337$	−9032.40	+	6562.42i	−1.46002	+	1.06076i	−0.476659	+	0.879088i	$0.658152\pi$
$337$	−9032.40	+	6562.42i	−1.46002	+	1.06076i	−0.983358	+	0.181677i	$0.941848\pi$
$338$		0			0
$339$	3711.80	+	11423.7i	0.594682	+	1.83024i
$340$		0			0
$341$	−2228.20	−	1597.08i	−0.353854	−	0.253627i
$342$		0			0
$343$	1427.13	+	4392.25i	0.224658	+	0.691425i
$344$		0			0
$345$	16758.4	−	12175.7i	2.61519	−	1.90005i
$346$		0			0
$347$	−777.327	+	2392.37i	−0.120257	+	0.370112i	−0.993007	−	0.118055i	$-0.962334\pi$
$347$	−777.327	+	2392.37i	−0.120257	+	0.370112i	0.872750	+	0.488167i	$0.162334\pi$
$348$		0			0
$349$	9203.85	+	6686.99i	1.41166	+	1.02563i	0.993078	+	0.117457i	$0.0374744\pi$
$349$	9203.85	+	6686.99i	1.41166	+	1.02563i	0.418587	+	0.908177i	$0.362526\pi$
$350$		0			0
$351$	−2416.01			−0.367400
$352$		0			0
$353$	6210.08			0.936343			0.468172	−	0.883638i	$-0.344913\pi$
$353$	6210.08			0.936343			0.468172	+	0.883638i	$0.344913\pi$
$354$		0			0
$355$	946.799	+	687.889i	0.141552	+	0.102843i
$356$		0			0
$357$	1309.19	−	4029.27i	0.194088	−	0.597343i
$358$		0			0
$359$	−2012.43	+	1462.12i	−0.295856	+	0.214952i	−0.725804	−	0.687902i	$-0.758532\pi$
$359$	−2012.43	+	1462.12i	−0.295856	+	0.214952i	0.429948	+	0.902854i	$0.358532\pi$
$360$		0			0
$361$	−1970.56	−	6064.77i	−0.287296	−	0.884207i
$362$		0			0
$363$	−8332.44	+	6219.24i	−1.20479	+	0.899244i
$364$		0			0
$365$	5274.11	+	16232.0i	0.756328	+	2.32774i
$366$		0			0
$367$	5436.21	−	3949.64i	0.773209	−	0.561770i	−0.129724	−	0.991550i	$-0.541409\pi$
$367$	5436.21	−	3949.64i	0.773209	−	0.561770i	0.902933	+	0.429781i	$0.141409\pi$
$368$		0			0
$369$	−2661.35	+	8190.80i	−0.375459	+	1.15554i
$370$		0			0
$371$	227.918	+	165.592i	0.0318946	+	0.0231728i
$372$		0			0
$373$	−8614.37			−1.19580			−0.597902	−	0.801569i	$-0.703999\pi$
$373$	−8614.37			−1.19580			−0.597902	+	0.801569i	$0.703999\pi$
$374$		0			0
$375$	−3198.87			−0.440503
$376$		0			0
$377$	−5321.47	−	3866.28i	−0.726976	−	0.528179i
$378$		0			0
$379$	2474.95	−	7617.10i	0.335434	−	1.03236i	−0.631074	−	0.775723i	$-0.717386\pi$
$379$	2474.95	−	7617.10i	0.335434	−	1.03236i	0.966508	−	0.256637i	$-0.0826144\pi$
$380$		0			0
$381$	−4407.06	+	3201.92i	−0.592600	+	0.430549i
$382$		0			0
$383$	−2475.83	−	7619.82i	−0.330310	−	1.01659i	−0.968986	−	0.247115i	$-0.920517\pi$
$383$	−2475.83	−	7619.82i	−0.330310	−	1.01659i	0.638676	−	0.769476i	$-0.279483\pi$
$384$		0			0
$385$	−9629.27	−	6901.86i	−1.27468	−	0.913639i
$386$		0			0
$387$	−1373.39	−	4226.86i	−0.180396	−	0.555203i
$388$		0			0
$389$	−6496.09	+	4719.68i	−0.846696	+	0.615160i	−0.924233	−	0.381829i	$-0.875294\pi$
$389$	−6496.09	+	4719.68i	−0.846696	+	0.615160i	0.0775373	+	0.996989i	$0.475294\pi$
$390$		0			0
$391$	1368.49	−	4211.78i	0.177001	−	0.544754i
$392$		0			0
$393$	−1642.60	−	1193.42i	−0.210836	−	0.153181i
$394$		0			0
$395$	−11524.9			−1.46806
$396$		0			0
$397$	4435.00			0.560670			0.280335	−	0.959902i	$-0.409554\pi$
$397$	4435.00			0.560670			0.280335	+	0.959902i	$0.409554\pi$
$398$		0			0
$399$	−3020.67	−	2194.64i	−0.379004	−	0.275363i
$400$		0			0
$401$	−1214.19	+	3736.90i	−0.151207	+	0.465366i	−0.997757	−	0.0669429i	$-0.978675\pi$
$401$	−1214.19	+	3736.90i	−0.151207	+	0.465366i	0.846550	+	0.532309i	$0.178675\pi$
$402$		0			0
$403$	−2676.60	+	1944.67i	−0.330847	+	0.240374i
$404$		0			0
$405$	−2258.86	−	6952.07i	−0.277145	−	0.852965i
$406$		0			0
$407$	−2456.90	+	7730.44i	−0.299223	+	0.941483i
$408$		0			0
$409$	−4500.59	−	13851.4i	−0.544107	−	1.67459i	−0.723103	−	0.690740i	$-0.757285\pi$
$409$	−4500.59	−	13851.4i	−0.544107	−	1.67459i	0.178996	−	0.983850i	$-0.442715\pi$
$410$		0			0
$411$	13167.9	−	9567.02i	1.58035	−	1.14819i
$412$		0			0
$413$	239.208	−	736.208i	0.0285004	−	0.0877153i
$414$		0			0
$415$	6483.98	+	4710.89i	0.766955	+	0.557225i
$416$		0			0
$417$	−1354.79			−0.159099
$418$		0			0
$419$	−4028.77			−0.469734			−0.234867	−	0.972028i	$-0.575465\pi$
$419$	−4028.77			−0.469734			−0.234867	+	0.972028i	$0.575465\pi$
$420$		0			0
$421$	6898.98	+	5012.40i	0.798659	+	0.580260i	0.910521	−	0.413464i	$-0.135681\pi$
$421$	6898.98	+	5012.40i	0.798659	+	0.580260i	−0.111861	+	0.993724i	$0.535681\pi$
$422$		0			0
$423$	−5247.54	+	16150.3i	−0.603177	+	1.85639i
$424$		0			0
$425$	1966.26	−	1428.57i	0.224418	−	0.163049i
$426$		0			0
$427$	−3621.24	−	11145.0i	−0.410408	−	1.26310i
$428$		0			0
$429$	3954.25	+	11908.7i	0.445019	+	1.34023i
$430$		0			0
$431$	−4145.53	−	12758.6i	−0.463302	−	1.42590i	−0.861105	−	0.508427i	$-0.830227\pi$
$431$	−4145.53	−	12758.6i	−0.463302	−	1.42590i	0.397803	−	0.917471i	$-0.369773\pi$
$432$		0			0
$433$	−3343.11	+	2428.91i	−0.371038	+	0.269575i	−0.757641	−	0.652671i	$-0.773648\pi$
$433$	−3343.11	+	2428.91i	−0.371038	+	0.269575i	0.386603	+	0.922246i	$0.373648\pi$
$434$		0			0
$435$	−5380.08	+	16558.2i	−0.593000	+	1.82507i
$436$		0			0
$437$	−3157.50	−	2294.06i	−0.345637	−	0.251120i
$438$		0			0
$439$	−3358.46			−0.365126			−0.182563	−	0.983194i	$-0.558439\pi$
$439$	−3358.46			−0.365126			−0.182563	+	0.983194i	$0.558439\pi$
$440$		0			0
$441$	4451.74			0.480698
$442$		0			0
$443$	−357.383	−	259.654i	−0.0383290	−	0.0278477i	0.568456	−	0.822714i	$-0.307541\pi$
$443$	−357.383	−	259.654i	−0.0383290	−	0.0278477i	−0.606785	+	0.794866i	$0.707541\pi$
$444$		0			0
$445$	3075.25	−	9464.66i	0.327598	−	1.00824i
$446$		0			0
$447$	2837.98	−	2061.91i	0.300295	−	0.218177i
$448$		0			0
$449$	−126.227	−	388.486i	−0.0132673	−	0.0408325i	0.944204	−	0.329362i	$-0.106834\pi$
$449$	−126.227	−	388.486i	−0.0132673	−	0.0408325i	−0.957471	+	0.288530i	$0.906834\pi$
$450$		0			0
$451$	9234.40	−	59.4126i	0.964148	−	0.00620317i
$452$		0			0
$453$	−68.8849	−	212.006i	−0.00714458	−	0.0219888i
$454$		0			0
$455$	−11567.0	+	8403.95i	−1.19181	+	0.865897i
$456$		0			0
$457$	470.585	−	1448.31i	0.0481686	−	0.148248i	−0.924079	−	0.382201i	$-0.875166\pi$
$457$	470.585	−	1448.31i	0.0481686	−	0.148248i	0.972248	+	0.233953i	$0.0751663\pi$
$458$		0			0
$459$	1106.05	+	803.592i	0.112475	+	0.0817178i
$460$		0			0
$461$	−13861.4			−1.40041			−0.700203	−	0.713944i	$-0.746907\pi$
$461$	−13861.4			−1.40041			−0.700203	+	0.713944i	$0.746907\pi$
$462$		0			0
$463$	6502.26			0.652669			0.326334	−	0.945254i	$-0.394186\pi$
$463$	6502.26			0.652669			0.326334	+	0.945254i	$0.394186\pi$
$464$		0			0
$465$	7084.62	+	5147.27i	0.706540	+	0.513331i
$466$		0			0
$467$	−131.015	+	403.223i	−0.0129821	+	0.0399548i	−0.957338	−	0.288971i	$-0.906687\pi$
$467$	−131.015	+	403.223i	−0.0129821	+	0.0399548i	0.944356	+	0.328926i	$0.106687\pi$
$468$		0			0
$469$	9150.83	−	6648.46i	0.900951	−	0.654579i
$470$		0			0
$471$	4161.37	+	12807.4i	0.407104	+	1.25294i
$472$		0			0
$473$	−3837.28	+	2825.84i	−0.373020	+	0.274699i
$474$		0			0
$475$	−661.898	−	2037.11i	−0.0639368	−	0.196777i
$476$		0			0
$477$	−356.249	+	258.830i	−0.0341961	+	0.0248449i
$478$		0			0
$479$	−1408.29	+	4334.29i	−0.134335	+	0.413442i	−0.995486	−	0.0949081i	$-0.969744\pi$
$479$	−1408.29	+	4334.29i	−0.134335	+	0.413442i	0.861151	+	0.508350i	$0.169744\pi$
$480$		0			0
$481$	7919.59	+	5753.92i	0.750732	+	0.545439i
$482$		0			0
$483$	30225.6			2.84744
$484$		0			0
$485$	−2680.10			−0.250922
$486$		0			0
$487$	−5427.63	−	3943.41i	−0.505030	−	0.366926i	0.305905	−	0.952062i	$-0.401041\pi$
$487$	−5427.63	−	3943.41i	−0.505030	−	0.366926i	−0.810935	+	0.585136i	$0.801041\pi$
$488$		0			0
$489$	−8010.13	+	24652.6i	−0.740758	+	2.27982i
$490$		0			0
$491$	11753.1	−	8539.14i	1.08027	−	0.784859i	0.102537	−	0.994729i	$-0.467304\pi$
$491$	11753.1	−	8539.14i	1.08027	−	0.784859i	0.977729	+	0.209870i	$0.0673040\pi$
$492$		0			0
$493$	1150.20	+	3539.96i	0.105076	+	0.323391i
$494$		0			0
$495$	14911.1	−	10980.8i	1.35394	−	0.997070i
$496$		0			0
$497$	527.695	+	1624.08i	0.0476265	+	0.146579i
$498$		0			0
$499$	−7847.09	+	5701.24i	−0.703976	+	0.511468i	−0.881225	−	0.472698i	$-0.843280\pi$
$499$	−7847.09	+	5701.24i	−0.703976	+	0.511468i	0.177249	+	0.984166i	$0.443280\pi$
$500$		0			0
$501$	7279.61	−	22404.3i	0.649159	−	1.99791i
$502$		0			0
$503$	12707.4	+	9232.43i	1.12643	+	0.818397i	0.985171	−	0.171576i	$-0.0548859\pi$
$503$	12707.4	+	9232.43i	1.12643	+	0.818397i	0.141256	+	0.989973i	$0.454886\pi$
$504$		0			0
$505$	−6127.41			−0.539933
$506$		0			0
$507$	−2019.25			−0.176879
$508$		0			0
$509$	1192.56	+	866.443i	0.103849	+	0.0754507i	0.638498	−	0.769624i	$-0.279556\pi$
$509$	1192.56	+	866.443i	0.103849	+	0.0754507i	−0.534649	+	0.845074i	$0.679556\pi$
$510$		0			0
$511$	−7695.74	+	23685.0i	−0.666222	+	2.05042i
$512$		0			0
$513$	974.766	−	708.209i	0.0838928	−	0.0609517i
$514$		0			0
$515$	−6304.85	−	19404.3i	−0.539466	−	1.66031i
$516$		0			0
$517$	18208.0	−	117.147i	1.54891	−	0.00996542i
$518$		0			0
$519$	−5333.48	−	16414.8i	−0.451086	−	1.38830i
$520$		0			0
$521$	7501.89	−	5450.44i	0.630832	−	0.458326i	−0.225856	−	0.974161i	$-0.572518\pi$
$521$	7501.89	−	5450.44i	0.630832	−	0.458326i	0.856688	+	0.515834i	$0.172518\pi$
$522$		0			0
$523$	1311.01	−	4034.86i	0.109610	−	0.337346i	−0.881174	−	0.472791i	$-0.843246\pi$
$523$	1311.01	−	4034.86i	0.109610	−	0.337346i	0.990785	+	0.135445i	$0.0432464\pi$
$524$		0			0
$525$	13420.1	+	9750.28i	1.11562	+	0.810547i
$526$		0			0
$527$	1872.17			0.154749
$528$		0			0
$529$	19427.7			1.59676
$530$		0			0
$531$	978.875	+	711.194i	0.0799992	+	0.0581228i
$532$		0			0
$533$	3443.86	−	10599.1i	0.279869	−	0.861348i
$534$		0			0
$535$	−4770.17	+	3465.73i	−0.385481	+	0.280068i
$536$		0			0
$537$	5484.16	+	16878.5i	0.440706	+	1.35635i
$538$		0			0
$539$	−1504.24	−	4530.19i	−0.120208	−	0.362020i
$540$		0			0
$541$	−2014.87	−	6201.13i	−0.160122	−	0.492805i	0.838522	−	0.544868i	$-0.183420\pi$
$541$	−2014.87	−	6201.13i	−0.160122	−	0.492805i	−0.998644	+	0.0520633i	$0.983420\pi$
$542$		0			0
$543$	3946.36	−	2867.20i	0.311887	−	0.226599i
$544$		0			0
$545$	2331.84	−	7176.66i	0.183275	−	0.564063i
$546$		0			0
$547$	5154.07	+	3744.65i	0.402874	+	0.292705i	0.770711	−	0.637185i	$-0.219901\pi$
$547$	5154.07	+	3744.65i	0.402874	+	0.292705i	−0.367836	+	0.929890i	$0.619901\pi$
$548$		0			0
$549$	18316.8			1.42394
$550$		0			0
$551$	3280.33			0.253624
$552$		0			0
$553$	−13605.0	−	9884.59i	−1.04619	−	0.760100i
$554$		0			0
$555$	8006.81	−	24642.4i	0.612379	−	1.88471i
$556$		0			0
$557$	−4938.23	+	3587.84i	−0.375655	+	0.272929i	−0.759552	−	0.650447i	$-0.774582\pi$
$557$	−4938.23	+	3587.84i	−0.375655	+	0.272929i	0.383897	+	0.923376i	$0.374582\pi$
$558$		0			0
$559$	1777.20	+	5469.67i	0.134468	+	0.413851i
$560$		0			0
$561$	2150.70	−	6767.02i	0.161859	−	0.509276i
$562$		0			0
$563$	4200.34	+	12927.3i	0.314429	+	0.967711i	0.975989	+	0.217820i	$0.0698945\pi$
$563$	4200.34	+	12927.3i	0.314429	+	0.967711i	−0.661561	+	0.749892i	$0.730106\pi$
$564$		0			0
$565$	−18557.6	+	13482.9i	−1.38181	+	1.00395i
$566$		0			0
$567$	3296.03	−	10144.1i	0.244127	−	0.751347i
$568$		0			0
$569$	−13913.1	−	10108.5i	−1.02508	−	0.744761i	−0.0577589	−	0.998331i	$-0.518395\pi$
$569$	−13913.1	−	10108.5i	−1.02508	−	0.744761i	−0.967317	+	0.253569i	$0.918395\pi$
$570$		0			0
$571$	−2475.65			−0.181441			−0.0907203	−	0.995876i	$-0.528917\pi$
$571$	−2475.65			−0.181441			−0.0907203	+	0.995876i	$0.528917\pi$
$572$		0			0
$573$	10500.6			0.765567
$574$		0			0
$575$	14028.0	+	10191.9i	1.01741	+	0.739188i
$576$		0			0
$577$	−6285.32	+	19344.2i	−0.453485	+	1.39568i	0.419419	+	0.907793i	$0.362234\pi$
$577$	−6285.32	+	19344.2i	−0.453485	+	1.39568i	−0.872904	+	0.487892i	$0.837766\pi$
$578$		0			0
$579$	−29221.7	+	21230.8i	−2.09743	+	1.52387i
$580$		0			0
$581$	3613.83	+	11122.2i	0.258050	+	0.794196i
$582$		0			0
$583$	383.767	+	275.068i	0.0272625	+	0.0195406i
$584$		0			0
$585$	−6905.94	−	21254.3i	−0.488078	−	1.50215i
$586$		0			0
$587$	−11988.4	+	8710.07i	−0.842953	+	0.612441i	−0.923194	−	0.384334i	$-0.874431\pi$
$587$	−11988.4	+	8710.07i	−0.842953	+	0.612441i	0.0802411	+	0.996775i	$0.474431\pi$
$588$		0			0
$589$	509.862	−	1569.19i	0.0356681	−	0.109775i
$590$		0			0
$591$	−4200.77	−	3052.04i	−0.292380	−	0.212427i
$592$		0			0
$593$	11123.2			0.770281			0.385140	−	0.922858i	$-0.374153\pi$
$593$	11123.2			0.770281			0.385140	+	0.922858i	$0.374153\pi$
$594$		0			0
$595$	8090.63			0.557451
$596$		0			0
$597$	−19230.3	−	13971.6i	−1.31833	−	0.957824i
$598$		0			0
$599$	−2560.26	+	7879.67i	−0.174640	+	0.537487i	−0.999617	−	0.0276796i	$-0.991188\pi$
$599$	−2560.26	+	7879.67i	−0.174640	+	0.537487i	0.824977	+	0.565167i	$0.191188\pi$
$600$		0			0
$601$	−22101.0	+	16057.3i	−1.50003	+	1.08984i	−0.529660	+	0.848210i	$0.677680\pi$
$601$	−22101.0	+	16057.3i	−1.50003	+	1.08984i	−0.970370	+	0.241625i	$0.922320\pi$
$602$		0			0
$603$	5463.37	+	16814.5i	0.368965	+	1.13556i
$604$		0			0
$605$	−16212.7	−	11463.4i	−1.08949	−	0.770338i
$606$		0			0
$607$	−5045.53	−	15528.6i	−0.337384	−	1.03836i	−0.965536	−	0.260270i	$-0.916188\pi$
$607$	−5045.53	−	15528.6i	−0.337384	−	1.03836i	0.628152	−	0.778091i	$-0.283812\pi$
$608$		0			0
$609$	−20552.5	+	14932.3i	−1.36754	+	0.993574i
$610$		0			0
$611$	6790.45	−	20898.9i	0.449611	−	1.38376i
$612$		0			0
$613$	17009.8	+	12358.4i	1.12075	+	0.814274i	0.984323	−	0.176376i	$-0.0564374\pi$
$613$	17009.8	+	12358.4i	1.12075	+	0.814274i	0.136429	+	0.990650i	$0.456437\pi$
$614$		0			0
$615$	−29498.2			−1.93412
$616$		0			0
$617$	871.824			0.0568854			0.0284427	−	0.999595i	$-0.490945\pi$
$617$	871.824			0.0568854			0.0284427	+	0.999595i	$0.490945\pi$
$618$		0			0
$619$	7602.75	+	5523.72i	0.493668	+	0.358671i	0.806593	−	0.591107i	$-0.201309\pi$
$619$	7602.75	+	5523.72i	0.493668	+	0.358671i	−0.312925	+	0.949778i	$0.601309\pi$
$620$		0			0
$621$	−3014.08	+	9276.38i	−0.194768	+	0.599434i
$622$		0			0
$623$	11747.8	−	8535.29i	0.755484	−	0.548891i
$624$		0			0
$625$	−5655.84	−	17406.9i	−0.361974	−	1.11404i
$626$		0			0
$627$	−5086.19	−	3645.57i	−0.323960	−	0.232201i
$628$		0			0
$629$	−1711.77	−	5268.28i	−0.108510	−	0.333959i
$630$		0			0
$631$	−11759.8	+	8544.01i	−0.741919	+	0.539036i	−0.893311	−	0.449438i	$-0.851624\pi$
$631$	−11759.8	+	8544.01i	−0.741919	+	0.539036i	0.151393	+	0.988474i	$0.451624\pi$
$632$		0			0
$633$	−6256.10	+	19254.3i	−0.392824	+	1.20899i
$634$		0			0
$635$	−8416.12	−	6114.67i	−0.525958	−	0.382131i
$636$		0			0
$637$	−5760.67			−0.358314
$638$		0			0
$639$	−2669.17			−0.165244
$640$		0			0
$641$	9238.70	+	6712.31i	0.569277	+	0.413604i	0.834843	−	0.550489i	$-0.185559\pi$
$641$	9238.70	+	6712.31i	0.569277	+	0.413604i	−0.265565	+	0.964093i	$0.585559\pi$
$642$		0			0
$643$	−7407.11	+	22796.7i	−0.454289	+	1.39816i	0.417679	+	0.908595i	$0.362844\pi$
$643$	−7407.11	+	22796.7i	−0.454289	+	1.39816i	−0.871968	+	0.489563i	$0.837156\pi$
$644$		0			0
$645$	12315.3	−	8947.58i	0.751805	−	0.546218i
$646$		0			0
$647$	−2569.24	−	7907.32i	−0.156117	−	0.480478i	0.842156	−	0.539234i	$-0.181286\pi$
$647$	−2569.24	−	7907.32i	−0.156117	−	0.480478i	−0.998272	+	0.0587569i	$0.981286\pi$
$648$		0			0
$649$	392.966	−	1236.44i	0.0237677	−	0.0747833i
$650$		0			0
$651$	3948.59	+	12152.5i	0.237723	+	0.731635i
$652$		0			0
$653$	24334.7	−	17680.2i	1.45833	−	1.05954i	0.474536	−	0.880236i	$-0.342616\pi$
$653$	24334.7	−	17680.2i	1.45833	−	1.05954i	0.983794	−	0.179303i	$-0.0573843\pi$
$654$		0			0
$655$	1198.17	−	3687.60i	0.0714757	−	0.219980i
$656$		0			0
$657$	−31492.1	−	22880.3i	−1.87005	−	1.35867i
$658$		0			0
$659$	10041.6			0.593572			0.296786	−	0.954944i	$-0.404085\pi$
$659$	10041.6			0.593572			0.296786	+	0.954944i	$0.404085\pi$
$660$		0			0
$661$	1402.50			0.0825281			0.0412640	−	0.999148i	$-0.486862\pi$
$661$	1402.50			0.0825281			0.0412640	+	0.999148i	$0.486862\pi$
$662$		0			0
$663$	−6932.60	−	5036.83i	−0.406093	−	0.295044i
$664$		0			0
$665$	2203.39	−	6781.32i	0.128487	−	0.395441i
$666$		0			0
$667$	−21483.5	+	15608.7i	−1.24714	+	0.906102i
$668$		0			0
$669$	−6366.17	−	19593.1i	−0.367908	−	1.13230i
$670$		0			0
$671$	−6189.24	−	18639.6i	−0.356085	−	1.07239i
$672$		0			0
$673$	6299.43	+	19387.7i	0.360810	+	1.11046i	0.952563	+	0.304341i	$0.0984361\pi$
$673$	6299.43	+	19387.7i	0.360810	+	1.11046i	−0.591753	+	0.806119i	$0.701564\pi$
$674$		0			0
$675$	−4330.65	+	3146.40i	−0.246944	+	0.179415i
$676$		0			0
$677$	−2282.09	+	7023.55i	−0.129554	+	0.398725i	−0.994703	−	0.102789i	$-0.967223\pi$
$677$	−2282.09	+	7023.55i	−0.129554	+	0.398725i	0.865149	+	0.501514i	$0.167223\pi$
$678$		0			0
$679$	−3163.81	−	2298.64i	−0.178815	−	0.129917i
$680$		0			0
$681$	−1958.19			−0.110188
$682$		0			0
$683$	25844.0			1.44787			0.723935	−	0.689868i	$-0.242332\pi$
$683$	25844.0			1.44787			0.723935	+	0.689868i	$0.242332\pi$
$684$		0			0
$685$	25146.5	+	18270.0i	1.40263	+	1.01907i
$686$		0			0
$687$	4343.51	−	13368.0i	0.241216	−	0.742386i
$688$		0			0
$689$	460.996	−	334.933i	0.0254899	−	0.0185195i
$690$		0			0
$691$	−2607.73	−	8025.78i	−0.143564	−	0.441845i	0.853259	−	0.521487i	$-0.174622\pi$
$691$	−2607.73	−	8025.78i	−0.143564	−	0.441845i	−0.996824	+	0.0796417i	$0.974622\pi$
$692$		0			0
$693$	27020.1	−	173.843i	1.48111	−	0.00952920i
$694$		0			0
$695$	−799.499	−	2460.60i	−0.0436356	−	0.134296i
$696$		0			0
$697$	−5101.98	+	3706.80i	−0.277261	+	0.201442i
$698$		0			0
$699$	7677.62	−	23629.3i	0.415442	−	1.27860i
$700$		0			0
$701$	10503.8	+	7631.43i	0.565937	+	0.411177i	0.833627	−	0.552328i	$-0.186260\pi$
$701$	10503.8	+	7631.43i	0.565937	+	0.411177i	−0.267690	+	0.963505i	$0.586260\pi$
$702$		0			0
$703$	−4881.90			−0.261912
$704$		0			0
$705$	−58163.2			−3.10717
$706$		0			0
$707$	−7233.28	−	5255.29i	−0.384775	−	0.279555i
$708$		0			0
$709$	−5537.15	+	17041.6i	−0.293303	+	0.902695i	0.690483	+	0.723349i	$0.257398\pi$
$709$	−5537.15	+	17041.6i	−0.293303	+	0.902695i	−0.983786	+	0.179346i	$0.942602\pi$
$710$		0			0
$711$	21265.4	−	15450.2i	1.12168	−	0.814948i
$712$		0			0
$713$	4127.45	+	12703.0i	0.216794	+	0.667224i
$714$		0			0
$715$	−19295.3	+	14209.4i	−1.00924	+	0.743220i
$716$		0			0
$717$	−12103.2	−	37250.0i	−0.630410	−	1.94020i
$718$		0			0
$719$	2845.59	−	2067.45i	0.147598	−	0.107236i	−0.511536	−	0.859262i	$-0.670923\pi$
$719$	2845.59	−	2067.45i	0.147598	−	0.107236i	0.659133	+	0.752026i	$0.270923\pi$
$720$		0			0
$721$	9199.75	−	28313.9i	0.475196	−	1.46250i
$722$		0			0
$723$	−38387.8	−	27890.4i	−1.97463	−	1.43465i
$724$		0			0
$725$	−14573.7			−0.746559
$726$		0			0
$727$	29438.9			1.50183			0.750913	−	0.660401i	$-0.229614\pi$
$727$	29438.9			1.50183			0.750913	+	0.660401i	$0.229614\pi$
$728$		0			0
$729$	22851.3	+	16602.5i	1.16097	+	0.843492i
$730$		0			0
$731$	1005.67	−	3095.13i	0.0508837	−	0.156604i
$732$		0			0
$733$	−2779.70	+	2019.57i	−0.140069	+	0.101766i	−0.655613	−	0.755097i	$-0.727590\pi$
$733$	−2779.70	+	2019.57i	−0.140069	+	0.101766i	0.515544	+	0.856863i	$0.327590\pi$
$734$		0			0
$735$	4711.81	+	14501.5i	0.236459	+	0.727747i
$736$		0			0
$737$	15264.8	−	11241.3i	0.762937	−	0.561841i
$738$		0			0
$739$	10383.5	+	31957.2i	0.516866	+	1.59075i	0.779861	+	0.625953i	$0.215290\pi$
$739$	10383.5	+	31957.2i	0.516866	+	1.59075i	−0.262995	+	0.964797i	$0.584710\pi$
$740$		0			0
$741$	−6109.73	+	4438.98i	−0.302897	+	0.220067i
$742$		0			0
$743$	368.875	−	1135.28i	0.0182136	−	0.0560557i	−0.941537	−	0.336911i	$-0.890618\pi$
$743$	368.875	−	1135.28i	0.0182136	−	0.0560557i	0.959750	+	0.280855i	$0.0906180\pi$
$744$		0			0
$745$	5419.66	+	3937.61i	0.266525	+	0.193641i
$746$		0			0
$747$	−18279.4			−0.895324
$748$		0			0
$749$	−8603.54			−0.419715
$750$		0			0
$751$	19828.5	+	14406.2i	0.963451	+	0.699988i	0.953950	−	0.299967i	$-0.0969755\pi$
$751$	19828.5	+	14406.2i	0.963451	+	0.699988i	0.00950152	+	0.999955i	$0.496976\pi$
$752$		0			0
$753$	13445.1	−	41379.9i	0.650688	−	2.00261i
$754$		0			0
$755$	344.399	−	250.221i	0.0166013	−	0.0120615i
$756$		0			0
$757$	3338.57	+	10275.0i	0.160294	+	0.493333i	0.998659	−	0.0517762i	$-0.0164882\pi$
$757$	3338.57	+	10275.0i	0.160294	+	0.493333i	−0.838365	+	0.545109i	$0.816488\pi$
$758$		0			0
$759$	50657.0	−	325.918i	2.42257	−	0.0155864i
$760$		0			0
$761$	2526.49	+	7775.75i	0.120349	+	0.370395i	0.993025	−	0.117904i	$-0.0376175\pi$
$761$	2526.49	+	7775.75i	0.120349	+	0.370395i	−0.872676	+	0.488299i	$0.837617\pi$
$762$		0			0
$763$	8907.88	−	6471.96i	0.422657	−	0.307078i
$764$		0			0
$765$	−3907.87	+	12027.2i	−0.184692	+	0.568424i
$766$		0			0
$767$	−1266.69	−	920.304i	−0.0596317	−	0.0433250i
$768$		0			0
$769$	−28895.9			−1.35502			−0.677511	−	0.735513i	$-0.736941\pi$
$769$	−28895.9			−1.35502			−0.677511	+	0.735513i	$0.736941\pi$
$770$		0			0
$771$	−46144.8			−2.15547
$772$		0			0
$773$	14559.7	+	10578.3i	0.677460	+	0.492203i	0.872514	−	0.488589i	$-0.162488\pi$
$773$	14559.7	+	10578.3i	0.677460	+	0.492203i	−0.195054	+	0.980792i	$0.562488\pi$
$774$		0			0
$775$	−2265.19	+	6971.55i	−0.104991	+	0.323130i
$776$		0			0
$777$	30586.9	−	22222.7i	1.41223	−	1.02604i
$778$		0			0
$779$	1717.47	+	5285.83i	0.0789919	+	0.243112i
$780$		0			0
$781$	901.910	+	2716.21i	0.0413225	+	0.124448i
$782$		0			0
$783$	−2533.30	−	7796.71i	−0.115623	−	0.355851i
$784$		0			0
$785$	−20805.3	+	15115.9i	−0.945954	+	0.687276i
$786$		0			0
$787$	4906.17	−	15099.6i	0.222219	−	0.683918i	−0.776343	−	0.630310i	$-0.782928\pi$
$787$	4906.17	−	15099.6i	0.222219	−	0.683918i	0.998562	−	0.0536084i	$-0.0170723\pi$
$788$		0			0
$789$	−43314.9	−	31470.1i	−1.95444	−	1.41998i
$790$		0			0
$791$	−33470.8			−1.50453
$792$		0			0
$793$	−23702.5			−1.06141
$794$		0			0
$795$	−1220.19	−	886.523i	−0.0544350	−	0.0395494i
$796$		0			0
$797$	5098.07	−	15690.2i	0.226578	−	0.697336i	−0.771549	−	0.636170i	$-0.780518\pi$
$797$	5098.07	−	15690.2i	0.226578	−	0.697336i	0.998128	−	0.0611668i	$-0.0194822\pi$
$798$		0			0
$799$	−10059.9	+	7308.91i	−0.445422	+	0.323618i
$800$		0			0
$801$	7013.87	+	21586.5i	0.309392	+	0.952210i
$802$		0			0
$803$	−12642.4	+	39778.2i	−0.555591	+	1.74812i
$804$		0			0
$805$	17836.9	+	54896.4i	0.780955	+	2.40353i
$806$		0			0
$807$	−6960.50	+	5057.10i	−0.303620	+	0.220593i
$808$		0			0
$809$	−2812.97	+	8657.42i	−0.122248	+	0.376241i	−0.993390	−	0.114791i	$-0.963380\pi$
$809$	−2812.97	+	8657.42i	−0.122248	+	0.376241i	0.871142	+	0.491032i	$0.163380\pi$
$810$		0			0
$811$	29590.8	+	21499.0i	1.28123	+	0.930865i	0.999589	−	0.0286567i	$-0.00912297\pi$
$811$	29590.8	+	21499.0i	1.28123	+	0.930865i	0.281636	+	0.959521i	$0.409123\pi$
$812$		0			0
$813$	20089.6			0.866633
$814$		0			0
$815$	−49501.7			−2.12757
$816$		0			0
$817$	−2320.36	−	1685.84i	−0.0993626	−	0.0721912i
$818$		0			0
$819$	10076.8	−	31013.3i	0.429930	−	1.32319i
$820$		0			0
$821$	2948.23	−	2142.01i	0.125328	−	0.0910558i	−0.523356	−	0.852114i	$-0.675320\pi$
$821$	2948.23	−	2142.01i	0.125328	−	0.0910558i	0.648683	+	0.761059i	$0.275320\pi$
$822$		0			0
$823$	5221.12	+	16068.9i	0.221138	+	0.680593i	0.998661	+	0.0517380i	$0.0164761\pi$
$823$	5221.12	+	16068.9i	0.221138	+	0.680593i	−0.777523	+	0.628855i	$0.783524\pi$
$824$		0			0
$825$	22596.7	+	16196.4i	0.953597	+	0.683499i
$826$		0			0
$827$	11983.1	+	36880.1i	0.503860	+	1.55072i	0.802678	+	0.596413i	$0.203408\pi$
$827$	11983.1	+	36880.1i	0.503860	+	1.55072i	−0.298817	+	0.954310i	$0.596592\pi$
$828$		0			0
$829$	10027.2	−	7285.20i	0.420096	−	0.305218i	−0.357580	−	0.933882i	$-0.616398\pi$
$829$	10027.2	−	7285.20i	0.420096	−	0.305218i	0.777677	+	0.628665i	$0.216398\pi$
$830$		0			0
$831$	−17718.9	+	54533.1i	−0.739665	+	2.27645i
$832$		0			0
$833$	2637.23	+	1916.06i	0.109694	+	0.0796970i
$834$		0			0
$835$	44987.1			1.86448
$836$		0			0
$837$	−4123.41			−0.170282
$838$		0			0
$839$	19872.6	+	14438.3i	0.817732	+	0.594117i	0.916062	−	0.401037i	$-0.131350\pi$
$839$	19872.6	+	14438.3i	0.817732	+	0.594117i	−0.0983299	+	0.995154i	$0.531350\pi$
$840$		0			0
$841$	−639.584	+	1968.44i	−0.0262243	+	0.0807100i
$842$		0			0
$843$	47354.6	−	34405.1i	1.93473	−	1.40566i
$844$		0			0
$845$	−1191.61	−	3667.40i	−0.0485120	−	0.149305i
$846$		0			0
$847$	−9306.97	−	27437.5i	−0.377557	−	1.11306i
$848$		0			0
$849$	15676.7	+	48247.8i	0.633712	+	1.95036i
$850$		0			0
$851$	31972.4	−	23229.3i	1.28790	−	0.935712i
$852$		0			0
$853$	−3772.37	+	11610.1i	−0.151422	+	0.466030i	−0.997781	−	0.0665834i	$-0.978790\pi$
$853$	−3772.37	+	11610.1i	−0.151422	+	0.466030i	0.846358	+	0.532614i	$0.178790\pi$
$854$		0			0
$855$	9016.57	+	6550.92i	0.360655	+	0.262031i
$856$		0			0
$857$	7281.72			0.290244			0.145122	−	0.989414i	$-0.453643\pi$
$857$	7281.72			0.290244			0.145122	+	0.989414i	$0.453643\pi$
$858$		0			0
$859$	−5927.39			−0.235437			−0.117718	−	0.993047i	$-0.537558\pi$
$859$	−5927.39			−0.235437			−0.117718	+	0.993047i	$0.537558\pi$
$860$		0			0
$861$	−34822.0	−	25299.7i	−1.37832	−	1.00141i
$862$		0			0
$863$	11916.3	−	36674.5i	0.470028	−	1.44660i	−0.382518	−	0.923948i	$-0.624943\pi$
$863$	11916.3	−	36674.5i	0.470028	−	1.44660i	0.852547	−	0.522651i	$-0.175057\pi$
$864$		0			0
$865$	26665.4	−	19373.6i	1.04815	−	0.761527i
$866$		0			0
$867$	−10361.5	−	31889.3i	−0.405875	−	1.24916i
$868$		0			0
$869$	−22908.0	−	16419.5i	−0.894247	−	0.640959i
$870$		0			0
$871$	−7069.75	−	21758.4i	−0.275028	−	0.846449i
$872$		0			0
$873$	4945.22	−	3592.91i	0.191719	−	0.139292i
$874$		0			0
$875$	2754.49	−	8477.46i	0.106422	−	0.327532i
$876$		0			0
$877$	−23067.2	−	16759.3i	−0.888170	−	0.645293i	0.0472301	−	0.998884i	$-0.484961\pi$
$877$	−23067.2	−	16759.3i	−0.888170	−	0.645293i	−0.935400	+	0.353591i	$0.884961\pi$
$878$		0			0
$879$	−20973.7			−0.804809
$880$		0			0
$881$	40747.6			1.55826			0.779128	−	0.626865i	$-0.215662\pi$
$881$	40747.6			1.55826			0.779128	+	0.626865i	$0.215662\pi$
$882$		0			0
$883$	−2908.89	−	2113.43i	−0.110863	−	0.0805467i	0.530972	−	0.847389i	$-0.321827\pi$
$883$	−2908.89	−	2113.43i	−0.110863	−	0.0805467i	−0.641835	+	0.766842i	$0.721827\pi$
$884$		0			0
$885$	−1280.64	+	3941.41i	−0.0486421	+	0.149705i
$886$		0			0
$887$	−6241.81	+	4534.94i	−0.236279	+	0.171667i	−0.699624	−	0.714511i	$-0.746649\pi$
$887$	−6241.81	+	4534.94i	−0.236279	+	0.171667i	0.463345	+	0.886178i	$0.346649\pi$
$888$		0			0
$889$	−4690.70	−	14436.5i	−0.176964	−	0.544639i
$890$		0			0
$891$	5414.64	−	17036.7i	0.203588	−	0.640575i
$892$		0			0
$893$	3386.43	+	10422.4i	0.126901	+	0.390561i
$894$		0			0
$895$	−27418.8	+	19920.9i	−1.02403	+	0.744003i
$896$		0			0
$897$	18891.9	−	58143.4i	0.703214	−	2.16427i
$898$		0			0
$899$	−9082.17	−	6598.58i	−0.336938	−	0.244800i
$900$		0			0
$901$	−322.446			−0.0119226
$902$		0			0
$903$	22212.0			0.818571
$904$		0			0
$905$	7536.32	+	5475.46i	0.276813	+	0.201117i
$906$		0			0
$907$	10418.1	−	32063.6i	0.381398	−	1.17382i	−0.557662	−	0.830068i	$-0.688302\pi$
$907$	10418.1	−	32063.6i	0.381398	−	1.17382i	0.939060	−	0.343753i	$-0.111698\pi$
$908$		0			0
$909$	11306.1	−	8214.33i	0.412539	−	0.299727i
$910$		0			0
$911$	−4644.75	−	14295.1i	−0.168922	−	0.519887i	0.830382	−	0.557194i	$-0.188122\pi$
$911$	−4644.75	−	14295.1i	−0.168922	−	0.519887i	−0.999304	+	0.0373070i	$0.988122\pi$
$912$		0			0
$913$	6176.57	+	18601.5i	0.223894	+	0.674281i
$914$		0			0
$915$	19386.9	+	59666.7i	0.700449	+	2.15576i
$916$		0			0
$917$	4577.16	−	3325.50i	0.164832	−	0.119758i
$918$		0			0
$919$	5281.31	−	16254.2i	0.189570	−	0.583435i	−0.810428	−	0.585839i	$-0.800765\pi$
$919$	5281.31	−	16254.2i	0.189570	−	0.583435i	0.999997	+	0.00240379i	$0.000765151\pi$
$920$		0			0
$921$	52655.2	+	38256.3i	1.88387	+	1.36871i
$922$		0			0
$923$	3453.98			0.123173
$924$		0			0
$925$	21689.1			0.770955
$926$		0			0
$927$	37646.7	+	27351.9i	1.33385	+	0.969099i
$928$		0			0
$929$	4066.74	−	12516.1i	0.143623	−	0.442025i	−0.853209	−	0.521570i	$-0.825347\pi$
$929$	4066.74	−	12516.1i	0.143623	−	0.442025i	0.996831	+	0.0795446i	$0.0253466\pi$
$930$		0			0
$931$	2324.20	−	1688.63i	0.0818182	−	0.0594444i
$932$		0			0
$933$	12119.0	+	37298.6i	0.425252	+	1.30879i
$934$		0			0
$935$	13559.6	−	87.2401i	0.474274	−	0.00305140i
$936$		0			0
$937$	1253.46	+	3857.76i	0.0437021	+	0.134501i	0.970527	−	0.240993i	$-0.0774731\pi$
$937$	1253.46	+	3857.76i	0.0437021	+	0.134501i	−0.926825	+	0.375494i	$0.877473\pi$
$938$		0			0
$939$	−19099.2	+	13876.4i	−0.663768	+	0.482256i
$940$		0			0
$941$	10320.4	−	31763.0i	0.357531	−	1.10037i	−0.596996	−	0.802244i	$-0.703639\pi$
$941$	10320.4	−	31763.0i	0.357531	−	1.10037i	0.954527	−	0.298123i	$-0.0963607\pi$
$942$		0			0
$943$	−36399.3	−	26445.7i	−1.25697	−	0.913245i
$944$		0			0
$945$	−17819.5			−0.613405
$946$		0			0
$947$	−25660.8			−0.880533			−0.440267	−	0.897867i	$-0.645116\pi$
$947$	−25660.8			−0.880533			−0.440267	+	0.897867i	$0.645116\pi$
$948$		0			0
$949$	40751.6	+	29607.8i	1.39394	+	1.01276i
$950$		0			0
$951$	−25443.7	+	78307.8i	−0.867581	+	2.67014i
$952$		0			0
$953$	−39522.7	+	28714.9i	−1.34341	+	0.976042i	−0.344096	+	0.938935i	$0.611815\pi$
$953$	−39522.7	+	28714.9i	−1.34341	+	0.976042i	−0.999311	+	0.0371079i	$0.988185\pi$
$954$		0			0
$955$	6196.70	+	19071.5i	0.209969	+	0.646218i
$956$		0			0
$957$	−34284.3	+	25247.6i	−1.15805	+	0.852809i
$958$		0			0
$959$	14015.4	+	43134.8i	0.471929	+	1.45245i
$960$		0			0
$961$	19533.3	−	14191.7i	0.655677	−	0.476377i
$962$		0			0
$963$	4155.61	−	12789.7i	0.139058	−	0.427976i
$964$		0			0
$965$	−55804.3	−	40544.2i	−1.86156	−	1.35250i
$966$		0			0
$967$	48861.8			1.62491			0.812456	−	0.583023i	$-0.198130\pi$
$967$	48861.8			1.62491			0.812456	+	0.583023i	$0.198130\pi$
$968$		0			0
$969$	4273.48			0.141676
$970$		0			0
$971$	28224.6	+	20506.4i	0.932822	+	0.677735i	0.946682	−	0.322169i	$-0.104412\pi$
$971$	28224.6	+	20506.4i	0.932822	+	0.677735i	−0.0138603	+	0.999904i	$0.504412\pi$
$972$		0			0
$973$	1166.59	−	3590.40i	0.0384370	−	0.118297i
$974$		0			0
$975$	27144.1	−	19721.3i	0.891596	−	0.647782i
$976$		0			0
$977$	−5875.16	−	18081.9i	−0.192388	−	0.592109i	−0.999997	−	0.00239112i	$-0.999239\pi$
$977$	−5875.16	−	18081.9i	−0.192388	−	0.592109i	0.807609	−	0.589718i	$-0.200761\pi$
$978$		0			0
$979$	19596.9	−	14431.5i	0.639754	−	0.471126i
$980$		0			0
$981$	5318.33	+	16368.1i	0.173090	+	0.532716i
$982$		0			0
$983$	−6025.47	+	4377.76i	−0.195506	+	0.142044i	−0.681232	−	0.732068i	$-0.738555\pi$
$983$	−6025.47	+	4377.76i	−0.195506	+	0.142044i	0.485726	+	0.874111i	$0.338555\pi$
$984$		0			0
$985$	3064.20	−	9430.63i	0.0991202	−	0.305061i
$986$		0			0
$987$	−68660.5	−	49884.8i	−2.21427	−	1.60876i
$988$		0			0
$989$	23218.2			0.746506
$990$		0			0
$991$	−5313.37			−0.170318			−0.0851588	−	0.996367i	$-0.527140\pi$
$991$	−5313.37			−0.170318			−0.0851588	+	0.996367i	$0.527140\pi$
$992$		0			0
$993$	1958.35	+	1422.82i	0.0625844	+	0.0454702i
$994$		0			0
$995$	14027.3	−	43171.5i	0.446929	−	1.37551i
$996$		0			0
$997$	−43301.8	+	31460.6i	−1.37551	+	0.999365i	−0.378223	+	0.925714i	$0.623465\pi$
$997$	−43301.8	+	31460.6i	−1.37551	+	0.999365i	−0.997284	+	0.0736504i	$0.976535\pi$
$998$		0			0
$999$	3770.14	+	11603.3i	0.119401	+	0.367480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.b.49.1		8
4.3	odd	2		22.4.c.b.5.2	✓	8
11.3	even	5		1936.4.a.bn.1.4		4
11.8	odd	10		1936.4.a.bm.1.4		4
11.9	even	5	inner	176.4.m.b.97.1		8
12.11	even	2		198.4.f.d.181.1		8
44.3	odd	10		242.4.a.n.1.1		4
44.7	even	10		242.4.c.n.3.1		8
44.15	odd	10		242.4.c.r.3.1		8
44.19	even	10		242.4.a.o.1.1		4
44.27	odd	10		242.4.c.r.81.1		8
44.31	odd	10		22.4.c.b.9.2	yes	8
44.35	even	10		242.4.c.q.9.2		8
44.39	even	10		242.4.c.n.81.1		8
44.43	even	2		242.4.c.q.27.2		8
132.47	even	10		2178.4.a.by.1.1		4
132.107	odd	10		2178.4.a.bt.1.1		4
132.119	even	10		198.4.f.d.163.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.5.2	✓	8	4.3	odd	2
22.4.c.b.9.2	yes	8	44.31	odd	10
176.4.m.b.49.1		8	1.1	even	1	trivial
176.4.m.b.97.1		8	11.9	even	5	inner
198.4.f.d.163.1		8	132.119	even	10
198.4.f.d.181.1		8	12.11	even	2
242.4.a.n.1.1		4	44.3	odd	10
242.4.a.o.1.1		4	44.19	even	10
242.4.c.n.3.1		8	44.7	even	10
242.4.c.n.81.1		8	44.39	even	10
242.4.c.q.9.2		8	44.35	even	10
242.4.c.q.27.2		8	44.43	even	2
242.4.c.r.3.1		8	44.15	odd	10
242.4.c.r.81.1		8	44.27	odd	10
1936.4.a.bm.1.4		4	11.8	odd	10
1936.4.a.bn.1.4		4	11.3	even	5
2178.4.a.bt.1.1		4	132.107	odd	10
2178.4.a.by.1.1		4	132.47	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	176.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.31989 - 4.59167i) q^{3} +(4.60996 - 14.1880i) q^{5} +(17.6106 - 12.7948i) q^{7} +(10.5141 + 32.3592i) q^{9} +(29.3767 - 21.6335i) q^{11} +(-13.6056 - 41.8736i) q^{13} +(-94.2810 + 68.4992i) q^{15} +(-7.69900 + 23.6951i) q^{17} +(17.7638 + 12.9061i) q^{19} -170.046 q^{21} -177.749 q^{23} +(-78.9203 - 57.3389i) q^{25} +(16.9569 - 52.1881i) q^{27} +(120.864 - 87.8130i) q^{29} +(-23.2207 - 71.4658i) q^{31} +(-284.992 + 1.83359i) q^{33} +(-100.349 - 308.842i) q^{35} +(-179.874 + 130.686i) q^{37} +(-106.284 + 327.109i) q^{39} +(204.779 + 148.781i) q^{41} -130.623 q^{43} +507.582 q^{45} +(403.775 + 293.360i) q^{47} +(40.4316 - 124.436i) q^{49} +(157.457 - 114.399i) q^{51} +(3.99933 + 12.3087i) q^{53} +(-171.511 - 516.526i) q^{55} +(-53.0044 - 163.131i) q^{57} +(28.7697 - 20.9024i) q^{59} +(166.357 - 511.995i) q^{61} +(599.190 + 435.337i) q^{63} -656.824 q^{65} +519.621 q^{67} +(1123.35 + 816.165i) q^{69} +(-24.2420 + 74.6091i) q^{71} +(-925.571 + 672.467i) q^{73} +(235.486 + 724.752i) q^{75} +(240.543 - 756.848i) q^{77} +(-238.730 - 734.735i) q^{79} +(396.416 - 288.013i) q^{81} +(-166.017 + 510.947i) q^{83} +(300.694 + 218.467i) q^{85} -1167.06 q^{87} +667.089 q^{89} +(-775.368 - 563.338i) q^{91} +(-181.395 + 558.278i) q^{93} +(265.003 - 192.536i) q^{95} +(-55.5161 - 170.861i) q^{97} +(1008.91 + 723.148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9} + 155 q^{11} + 7 q^{13} - 211 q^{15} + 161 q^{17} + 272 q^{19} - 50 q^{21} - 628 q^{23} - 17 q^{25} + 528 q^{27} + 33 q^{29} - 323 q^{31} - 1144 q^{33} + 697 q^{35}+ \cdots + 2213 q^{99}+O(q^{100}) \) 8 * q - 3 * q^3 + 5 * q^5 + q^7 - 21 * q^9 + 155 * q^11 + 7 * q^13 - 211 * q^15 + 161 * q^17 + 272 * q^19 - 50 * q^21 - 628 * q^23 - 17 * q^25 + 528 * q^27 + 33 * q^29 - 323 * q^31 - 1144 * q^33 + 697 * q^35 + 49 * q^37 - 391 * q^39 + 361 * q^41 - 1442 * q^43 + 2652 * q^45 + 1069 * q^47 - 709 * q^49 + 1332 * q^51 - 281 * q^53 + 7 * q^55 - 438 * q^57 + 128 * q^59 - 617 * q^61 - 694 * q^63 - 138 * q^65 - 578 * q^67 - 310 * q^69 - 115 * q^71 - 1487 * q^73 + 1852 * q^75 + 553 * q^77 - 71 * q^79 + 1630 * q^81 - 1942 * q^83 - 329 * q^85 - 2122 * q^87 - 2202 * q^89 - 4523 * q^91 + 6019 * q^93 + 793 * q^95 - 5128 * q^97 + 2213 * q^99

Introduction

L-functions

Modular forms

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Database

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