LMFDB - Embedded newform 176.4.m.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,4,Mod(49,176)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.3843361610$
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			97.1
Root			$2.22300 - 6.84169i$ of defining polynomial
Character	$\chi$	$=$	176.97
Dual form			176.4.m.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.31989 + 4.59167i) q^{3} +(4.60996 + 14.1880i) q^{5} +(17.6106 + 12.7948i) q^{7} +(10.5141 - 32.3592i) q^{9} +O(q^{10})$	\(q+(-6.31989 + 4.59167i) q^{3} +(4.60996 + 14.1880i) q^{5} +(17.6106 + 12.7948i) q^{7} +(10.5141 - 32.3592i) q^{9} +(29.3767 + 21.6335i) q^{11} +(-13.6056 + 41.8736i) q^{13} +(-94.2810 - 68.4992i) q^{15} +(-7.69900 - 23.6951i) q^{17} +(17.7638 - 12.9061i) q^{19} -170.046 q^{21} -177.749 q^{23} +(-78.9203 + 57.3389i) q^{25} +(16.9569 + 52.1881i) q^{27} +(120.864 + 87.8130i) q^{29} +(-23.2207 + 71.4658i) q^{31} +(-284.992 - 1.83359i) q^{33} +(-100.349 + 308.842i) q^{35} +(-179.874 - 130.686i) q^{37} +(-106.284 - 327.109i) q^{39} +(204.779 - 148.781i) q^{41} -130.623 q^{43} +507.582 q^{45} +(403.775 - 293.360i) q^{47} +(40.4316 + 124.436i) q^{49} +(157.457 + 114.399i) q^{51} +(3.99933 - 12.3087i) q^{53} +(-171.511 + 516.526i) q^{55} +(-53.0044 + 163.131i) q^{57} +(28.7697 + 20.9024i) q^{59} +(166.357 + 511.995i) q^{61} +(599.190 - 435.337i) q^{63} -656.824 q^{65} +519.621 q^{67} +(1123.35 - 816.165i) q^{69} +(-24.2420 - 74.6091i) q^{71} +(-925.571 - 672.467i) q^{73} +(235.486 - 724.752i) q^{75} +(240.543 + 756.848i) q^{77} +(-238.730 + 734.735i) q^{79} +(396.416 + 288.013i) q^{81} +(-166.017 - 510.947i) q^{83} +(300.694 - 218.467i) q^{85} -1167.06 q^{87} +667.089 q^{89} +(-775.368 + 563.338i) q^{91} +(-181.395 - 558.278i) q^{93} +(265.003 + 192.536i) q^{95} +(-55.5161 + 170.861i) q^{97} +(1008.91 - 723.148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9}+O(q^{10}) $ 8 * q - 3 * q^3 + 5 * q^5 + q^7 - 21 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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	−0.995784	−	0.0917244i	$-0.970762\pi$
$3$	−6.31989	+	4.59167i	−1.21626	+	0.883667i	−0.220479	+	0.975392i	$0.570762\pi$
$4$		0			0
$5$	4.60996	+	14.1880i	0.412327	+	1.26901i	0.914620	+	0.404315i	$0.132490\pi$
$5$	4.60996	+	14.1880i	0.412327	+	1.26901i	−0.502293	+	0.864698i	$0.667510\pi$
$6$		0			0
$7$	17.6106	+	12.7948i	0.950881	+	0.690856i	0.951015	−	0.309144i	$-0.100043\pi$
$7$	17.6106	+	12.7948i	0.950881	+	0.690856i	−0.000134039		1.00000i	$0.500043\pi$
$8$		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	0.694500	+	0.719493i	$0.255626\pi$
$13$	−13.6056	+	41.8736i	−0.290270	+	0.893358i	−0.984769	+	0.173865i	$0.944374\pi$
$14$		0			0
$15$	−94.2810	−	68.4992i	−1.62288	−	1.17909i
$16$		0			0
$17$	−7.69900	−	23.6951i	−0.109840	−	0.338053i	0.880996	−	0.473124i	$-0.156874\pi$
$17$	−7.69900	−	23.6951i	−0.109840	−	0.338053i	−0.990836	+	0.135071i	$0.956874\pi$
$18$		0			0
$19$	17.7638	−	12.9061i	0.214489	−	0.155835i	−0.475353	−	0.879795i	$-0.657680\pi$
$19$	17.7638	−	12.9061i	0.214489	−	0.155835i	0.689842	+	0.723960i	$0.257680\pi$
$20$		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	0.903151	−	0.429324i	$-0.141248\pi$
$29$	120.864	+	87.8130i	0.773928	+	0.562292i	−0.129223	+	0.991616i	$0.541248\pi$
$30$		0			0
$31$	−23.2207	+	71.4658i	−0.134534	+	0.414053i	−0.995517	−	0.0945803i	$-0.969849\pi$
$31$	−23.2207	+	71.4658i	−0.134534	+	0.414053i	0.860983	+	0.508633i	$0.169849\pi$
$32$		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	0.111466	−	0.993768i	$-0.464445\pi$
$37$	−179.874	−	130.686i	−0.799219	−	0.580667i	−0.910685	+	0.413102i	$0.864445\pi$
$38$		0			0
$39$	−106.284	−	327.109i	−0.436387	−	1.34306i
$40$		0			0
$41$	204.779	−	148.781i	0.780029	−	0.566724i	−0.124959	−	0.992162i	$-0.539880\pi$
$41$	204.779	−	148.781i	0.780029	−	0.566724i	0.904988	+	0.425438i	$0.139880\pi$
$42$		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	0.254722	−	0.967014i	$-0.418016\pi$
$47$	403.775	−	293.360i	1.25312	−	0.910445i	0.998399	+	0.0565693i	$0.0180162\pi$
$48$		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	−0.945740	−	0.324924i	$-0.894661\pi$
$53$	3.99933	−	12.3087i	0.0103651	−	0.0319005i	0.956105	+	0.293023i	$0.0946613\pi$
$54$		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	0.619074	−	0.785332i	$-0.287508\pi$
$59$	28.7697	+	20.9024i	0.0634831	+	0.0461232i	−0.555591	+	0.831456i	$0.687508\pi$
$60$		0			0
$61$	166.357	+	511.995i	0.349178	+	1.07466i	0.959309	+	0.282359i	$0.0911169\pi$
$61$	166.357	+	511.995i	0.349178	+	1.07466i	−0.610131	+	0.792301i	$0.708883\pi$
$62$		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	0.928750	−	0.370708i	$-0.120885\pi$
$71$	−24.2420	−	74.6091i	−0.0405210	−	0.124711i	−0.969271	+	0.245997i	$0.920885\pi$
$72$		0			0
$73$	−925.571	−	672.467i	−1.48397	−	1.07817i	−0.976250	−	0.216648i	$-0.930488\pi$
$73$	−925.571	−	672.467i	−1.48397	−	1.07817i	−0.507722	−	0.861521i	$-0.669512\pi$
$74$		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	0.624222	+	0.781247i	$0.285416\pi$
$79$	−238.730	+	734.735i	−0.339990	+	1.04638i	−0.964212	+	0.265134i	$0.914584\pi$
$80$		0			0
$81$	396.416	+	288.013i	0.543780	+	0.395079i
$82$		0			0
$83$	−166.017	−	510.947i	−0.219551	−	0.675708i	−0.998799	−	0.0489926i	$-0.984399\pi$
$83$	−166.017	−	510.947i	−0.219551	−	0.675708i	0.779248	−	0.626715i	$-0.215601\pi$
$84$		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	−0.975899	−	0.218224i	$-0.929974\pi$
$97$	−55.5161	+	170.861i	−0.0581114	+	0.178848i	0.917787	+	0.397072i	$0.129974\pi$
$98$		0			0
$99$	1008.91	−	723.148i	1.02424	−	0.734132i
$100$		0			0
$101$	−126.924	+	390.633i	−0.125044	+	0.384846i	−0.993909	−	0.110203i	$-0.964850\pi$
$101$	−126.924	+	390.633i	−0.125044	+	0.384846i	0.868865	+	0.495049i	$0.164850\pi$
$102$		0			0
$103$	1106.46	+	803.890i	1.05847	+	0.769026i	0.973805	−	0.227383i	$-0.0730171\pi$
$103$	1106.46	+	803.890i	1.05847	+	0.769026i	0.0846679	+	0.996409i	$0.473017\pi$
$104$		0			0
$105$	−783.907	−	2412.62i	−0.728586	−	2.24236i
$106$		0			0
$107$	−319.756	+	232.317i	−0.288897	+	0.209896i	−0.722789	−	0.691069i	$-0.757140\pi$
$107$	−319.756	+	232.317i	−0.288897	+	0.209896i	0.433892	+	0.900965i	$0.357140\pi$
$108$		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	−0.969421	−	0.245404i	$-0.921079\pi$
$113$	−1243.96	+	903.793i	−1.03560	+	0.752404i	−0.0661744	+	0.997808i	$0.521079\pi$
$114$		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	0.997684	−	0.0680154i	$-0.0216667\pi$
$127$	215.487	+	663.202i	0.150562	+	0.463383i	−0.847122	+	0.531399i	$0.821667\pi$
$128$		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	−0.923766	−	0.382958i	$-0.874906\pi$
$137$	−643.856	−	1981.58i	−0.401520	−	1.23575i	0.522245	−	0.852795i	$-0.325094\pi$
$138$		0			0
$139$	140.307	+	101.939i	0.0856163	+	0.0622039i	0.629770	−	0.776782i	$-0.283149\pi$
$139$	140.307	+	101.939i	0.0856163	+	0.0622039i	−0.544154	+	0.838986i	$0.683149\pi$
$140$		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	0.905634	−	0.424061i	$-0.139396\pi$
$149$	−138.766	−	427.077i	−0.0762961	−	0.234815i	−0.981930	+	0.189246i	$0.939396\pi$
$150$		0			0
$151$	23.0859	−	16.7729i	0.0124418	−	0.00903947i	−0.581547	−	0.813513i	$-0.697552\pi$
$151$	23.0859	−	16.7729i	0.0124418	−	0.00903947i	0.593989	+	0.804473i	$0.297552\pi$
$152$		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	−0.882832	−	0.469689i	$-0.844366\pi$
$157$	−1394.63	+	1013.26i	−0.708941	+	0.515076i	0.173891	+	0.984765i	$0.444366\pi$
$158$		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	0.327743	+	0.944767i	$0.393712\pi$
$163$	−1025.39	+	3155.82i	−0.492727	+	1.51646i	−0.820470	+	0.571690i	$0.806288\pi$
$164$		0			0
$165$	−1287.78	−	4051.91i	−0.607599	−	1.91176i
$166$		0			0
$167$	931.871	−	2868.00i	0.431799	−	1.32894i	−0.464533	−	0.885556i	$-0.653778\pi$
$167$	931.871	−	2868.00i	0.431799	−	1.32894i	0.896332	−	0.443384i	$-0.146222\pi$
$168$		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	−0.121101	−	0.992640i	$-0.538643\pi$
$173$	1787.45	−	1298.66i	0.785534	−	0.570724i	0.906635	+	0.421917i	$0.138643\pi$
$174$		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	−0.901189	−	0.433427i	$-0.857304\pi$
$179$	−1837.95	+	1335.35i	−0.767457	+	0.557590i	0.133731	+	0.991018i	$0.457304\pi$
$180$		0			0
$181$	−192.961	−	593.873i	−0.0792413	−	0.243880i	0.903586	−	0.428406i	$-0.140925\pi$
$181$	−192.961	−	593.873i	−0.0792413	−	0.243880i	−0.982828	+	0.184527i	$0.940925\pi$
$182$		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	0.362426	−	0.932013i	$-0.381949\pi$
$191$	−1087.48	−	790.100i	−0.411975	−	0.299317i	−0.774401	+	0.632695i	$0.781949\pi$
$192$		0			0
$193$	1428.82	+	4397.46i	0.532895	+	1.64008i	0.748154	+	0.663526i	$0.230941\pi$
$193$	1428.82	+	4397.46i	0.532895	+	1.64008i	−0.215258	+	0.976557i	$0.569059\pi$
$194$		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	0.731231	+	0.682130i	$0.238946\pi$
$211$	−800.851	+	2464.77i	−0.261293	+	0.804178i	−0.992524	+	0.122048i	$0.961054\pi$
$212$		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	−0.219401	−	0.975635i	$-0.570410\pi$
$223$	2133.54	−	1550.11i	0.640684	−	0.465484i	0.860085	+	0.510150i	$0.170410\pi$
$224$		0			0
$225$	1025.66	+	3156.66i	0.303900	+	0.935308i
$226$		0			0
$227$	202.796	+	147.340i	0.0592954	+	0.0430806i	0.617038	−	0.786933i	$-0.288332\pi$
$227$	202.796	+	147.340i	0.0592954	+	0.0430806i	−0.557743	+	0.830014i	$0.688332\pi$
$228$		0			0
$229$	556.018	−	1711.25i	0.160449	−	0.493810i	−0.838224	−	0.545327i	$-0.816406\pi$
$229$	556.018	−	1711.25i	0.160449	−	0.493810i	0.998672	+	0.0515169i	$0.0164056\pi$
$230$		0			0
$231$	−4995.40	−	3678.71i	−1.42283	−	1.04780i
$232$		0			0
$233$	982.821	−	3024.81i	0.276338	−	0.850481i	−0.712524	−	0.701647i	$-0.752448\pi$
$233$	982.821	−	3024.81i	0.276338	−	0.850481i	0.988862	−	0.148833i	$-0.0475518\pi$
$234$		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	0.117111	−	0.993119i	$-0.462637\pi$
$239$	4056.25	−	2947.04i	1.09781	−	0.797608i	0.980701	+	0.195511i	$0.0626366\pi$
$240$		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	−0.462493	−	0.886623i	$-0.653045\pi$
$251$	1721.13	−	5297.09i	0.432816	−	1.33207i	0.895309	−	0.445447i	$-0.146955\pi$
$252$		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	0.989768	−	0.142685i	$-0.0455737\pi$
$257$	4778.90	+	3472.08i	1.15992	+	0.842732i	0.170153	+	0.985418i	$0.445574\pi$
$258$		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	0.982190	−	0.187893i	$-0.0601657\pi$
$269$	340.340	+	1047.46i	0.0771409	+	0.237415i	−0.905049	+	0.425308i	$0.860166\pi$
$270$		0			0
$271$	−2080.54	−	1511.60i	−0.466362	−	0.338832i	0.329660	−	0.944100i	$-0.393066\pi$
$271$	−2080.54	−	1511.60i	−0.466362	−	0.338832i	−0.796022	+	0.605268i	$0.793066\pi$
$272$		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	0.329581	+	0.944127i	$0.393092\pi$
$277$	−2268.22	+	6980.85i	−0.492000	+	1.51422i	−0.821581	+	0.570092i	$0.806908\pi$
$278$		0			0
$279$	2068.43	+	1502.80i	0.443848	+	0.322475i
$280$		0			0
$281$	−2315.45	−	7126.21i	−0.491559	−	1.51286i	−0.822252	−	0.569124i	$-0.807282\pi$
$281$	−2315.45	−	7126.21i	−0.491559	−	1.51286i	0.330693	−	0.943738i	$-0.392718\pi$
$282$		0			0
$283$	−5253.84	+	3817.14i	−1.10356	+	0.801785i	−0.981638	−	0.190754i	$-0.938907\pi$
$283$	−5253.84	+	3817.14i	−1.10356	+	0.801785i	−0.121925	+	0.992539i	$0.538907\pi$
$284$		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	0.782884	−	0.622168i	$-0.213748\pi$
$293$	2172.11	+	1578.13i	0.433092	+	0.314660i	−0.349792	+	0.936827i	$0.613748\pi$
$294$		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	−0.892882	−	0.450292i	$-0.851320\pi$
$311$	−4061.55	+	2950.89i	−0.740545	+	0.538037i	0.152337	+	0.988329i	$0.451320\pi$
$312$		0			0
$313$	933.873	+	2874.16i	0.168644	+	0.519033i	0.999286	−	0.0377733i	$-0.0120265\pi$
$313$	933.873	+	2874.16i	0.168644	+	0.519033i	−0.830642	+	0.556807i	$0.812026\pi$
$314$		0			0
$315$	8938.80	+	6494.42i	1.59887	+	1.16165i
$316$		0			0
$317$	−3257.08	+	10024.3i	−0.577085	+	1.77609i	0.0518809	+	0.998653i	$0.483478\pi$
$317$	−3257.08	+	10024.3i	−0.577085	+	1.77609i	−0.628966	+	0.777433i	$0.716522\pi$
$318$		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	−0.983358	−	0.181677i	$-0.941848\pi$
$337$	−9032.40	−	6562.42i	−1.46002	−	1.06076i	−0.476659	−	0.879088i	$-0.658152\pi$
$338$		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	0.872750	−	0.488167i	$-0.162334\pi$
$347$	−777.327	−	2392.37i	−0.120257	−	0.370112i	−0.993007	+	0.118055i	$0.962334\pi$
$348$		0			0
$349$	9203.85	−	6686.99i	1.41166	−	1.02563i	0.418587	−	0.908177i	$-0.362526\pi$
$349$	9203.85	−	6686.99i	1.41166	−	1.02563i	0.993078	−	0.117457i	$-0.0374744\pi$
$350$		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	0.429948	−	0.902854i	$-0.358532\pi$
$359$	−2012.43	−	1462.12i	−0.295856	−	0.214952i	−0.725804	+	0.687902i	$0.758532\pi$
$360$		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	0.902933	−	0.429781i	$-0.141409\pi$
$367$	5436.21	+	3949.64i	0.773209	+	0.561770i	−0.129724	+	0.991550i	$0.541409\pi$
$368$		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	0.966508	+	0.256637i	$0.0826144\pi$
$379$	2474.95	+	7617.10i	0.335434	+	1.03236i	−0.631074	+	0.775723i	$0.717386\pi$
$380$		0			0
$381$	−4407.06	−	3201.92i	−0.592600	−	0.430549i
$382$		0			0
$383$	−2475.83	+	7619.82i	−0.330310	+	1.01659i	0.638676	+	0.769476i	$0.279483\pi$
$383$	−2475.83	+	7619.82i	−0.330310	+	1.01659i	−0.968986	+	0.247115i	$0.920517\pi$
$384$		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	0.0775373	−	0.996989i	$-0.475294\pi$
$389$	−6496.09	−	4719.68i	−0.846696	−	0.615160i	−0.924233	+	0.381829i	$0.875294\pi$
$390$		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	0.846550	−	0.532309i	$-0.178675\pi$
$401$	−1214.19	−	3736.90i	−0.151207	−	0.465366i	−0.997757	+	0.0669429i	$0.978675\pi$
$402$		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	0.178996	+	0.983850i	$0.442715\pi$
$409$	−4500.59	+	13851.4i	−0.544107	+	1.67459i	−0.723103	+	0.690740i	$0.757285\pi$
$410$		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	−0.111861	−	0.993724i	$-0.535681\pi$
$421$	6898.98	−	5012.40i	0.798659	−	0.580260i	0.910521	+	0.413464i	$0.135681\pi$
$422$		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	0.397803	+	0.917471i	$0.369773\pi$
$431$	−4145.53	+	12758.6i	−0.463302	+	1.42590i	−0.861105	+	0.508427i	$0.830227\pi$
$432$		0			0
$433$	−3343.11	−	2428.91i	−0.371038	−	0.269575i	0.386603	−	0.922246i	$-0.373648\pi$
$433$	−3343.11	−	2428.91i	−0.371038	−	0.269575i	−0.757641	+	0.652671i	$0.773648\pi$
$434$		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	−0.606785	−	0.794866i	$-0.707541\pi$
$443$	−357.383	+	259.654i	−0.0383290	+	0.0278477i	0.568456	+	0.822714i	$0.307541\pi$
$444$		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	−0.957471	−	0.288530i	$-0.906834\pi$
$449$	−126.227	+	388.486i	−0.0132673	+	0.0408325i	0.944204	+	0.329362i	$0.106834\pi$
$450$		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	0.972248	−	0.233953i	$-0.0751663\pi$
$457$	470.585	+	1448.31i	0.0481686	+	0.148248i	−0.924079	+	0.382201i	$0.875166\pi$
$458$		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	0.944356	−	0.328926i	$-0.106687\pi$
$467$	−131.015	−	403.223i	−0.0129821	−	0.0399548i	−0.957338	+	0.288971i	$0.906687\pi$
$468$		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	0.861151	−	0.508350i	$-0.169744\pi$
$479$	−1408.29	−	4334.29i	−0.134335	−	0.413442i	−0.995486	+	0.0949081i	$0.969744\pi$
$480$		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	−0.810935	−	0.585136i	$-0.801041\pi$
$487$	−5427.63	+	3943.41i	−0.505030	+	0.366926i	0.305905	+	0.952062i	$0.401041\pi$
$488$		0			0
$489$	−8010.13	−	24652.6i	−0.740758	−	2.27982i
$490$		0			0
$491$	11753.1	+	8539.14i	1.08027	+	0.784859i	0.977729	−	0.209870i	$-0.0673040\pi$
$491$	11753.1	+	8539.14i	1.08027	+	0.784859i	0.102537	+	0.994729i	$0.467304\pi$
$492$		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	0.177249	−	0.984166i	$-0.443280\pi$
$499$	−7847.09	−	5701.24i	−0.703976	−	0.511468i	−0.881225	+	0.472698i	$0.843280\pi$
$500$		0			0
$501$	7279.61	+	22404.3i	0.649159	+	1.99791i
$502$		0			0
$503$	12707.4	−	9232.43i	1.12643	−	0.818397i	0.141256	−	0.989973i	$-0.454886\pi$
$503$	12707.4	−	9232.43i	1.12643	−	0.818397i	0.985171	+	0.171576i	$0.0548859\pi$
$504$		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	−0.534649	−	0.845074i	$-0.679556\pi$
$509$	1192.56	−	866.443i	0.103849	−	0.0754507i	0.638498	+	0.769624i	$0.279556\pi$
$510$		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	0.856688	−	0.515834i	$-0.172518\pi$
$521$	7501.89	+	5450.44i	0.630832	+	0.458326i	−0.225856	+	0.974161i	$0.572518\pi$
$522$		0			0
$523$	1311.01	+	4034.86i	0.109610	+	0.337346i	0.990785	−	0.135445i	$-0.0432464\pi$
$523$	1311.01	+	4034.86i	0.109610	+	0.337346i	−0.881174	+	0.472791i	$0.843246\pi$
$524$		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	−0.998644	−	0.0520633i	$-0.983420\pi$
$541$	−2014.87	+	6201.13i	−0.160122	+	0.492805i	0.838522	+	0.544868i	$0.183420\pi$
$542$		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	−0.367836	−	0.929890i	$-0.619901\pi$
$547$	5154.07	−	3744.65i	0.402874	−	0.292705i	0.770711	+	0.637185i	$0.219901\pi$
$548$		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	0.383897	−	0.923376i	$-0.374582\pi$
$557$	−4938.23	−	3587.84i	−0.375655	−	0.272929i	−0.759552	+	0.650447i	$0.774582\pi$
$558$		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	−0.661561	−	0.749892i	$-0.730106\pi$
$563$	4200.34	−	12927.3i	0.314429	−	0.967711i	0.975989	−	0.217820i	$-0.0698945\pi$
$564$		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	−0.967317	−	0.253569i	$-0.918395\pi$
$569$	−13913.1	+	10108.5i	−1.02508	+	0.744761i	−0.0577589	+	0.998331i	$0.518395\pi$
$570$		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	−0.872904	−	0.487892i	$-0.837766\pi$
$577$	−6285.32	−	19344.2i	−0.453485	−	1.39568i	0.419419	−	0.907793i	$-0.362234\pi$
$578$		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	0.0802411	−	0.996775i	$-0.474431\pi$
$587$	−11988.4	−	8710.07i	−0.842953	−	0.612441i	−0.923194	+	0.384334i	$0.874431\pi$
$588$		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	0.824977	−	0.565167i	$-0.191188\pi$
$599$	−2560.26	−	7879.67i	−0.174640	−	0.537487i	−0.999617	+	0.0276796i	$0.991188\pi$
$600$		0			0
$601$	−22101.0	−	16057.3i	−1.50003	−	1.08984i	−0.970370	−	0.241625i	$-0.922320\pi$
$601$	−22101.0	−	16057.3i	−1.50003	−	1.08984i	−0.529660	−	0.848210i	$-0.677680\pi$
$602$		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	0.628152	+	0.778091i	$0.283812\pi$
$607$	−5045.53	+	15528.6i	−0.337384	+	1.03836i	−0.965536	+	0.260270i	$0.916188\pi$
$608$		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	0.136429	−	0.990650i	$-0.456437\pi$
$613$	17009.8	−	12358.4i	1.12075	−	0.814274i	0.984323	+	0.176376i	$0.0564374\pi$
$614$		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	−0.312925	−	0.949778i	$-0.601309\pi$
$619$	7602.75	−	5523.72i	0.493668	−	0.358671i	0.806593	+	0.591107i	$0.201309\pi$
$620$		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	0.151393	−	0.988474i	$-0.451624\pi$
$631$	−11759.8	−	8544.01i	−0.741919	−	0.539036i	−0.893311	+	0.449438i	$0.851624\pi$
$632$		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	−0.265565	−	0.964093i	$-0.585559\pi$
$641$	9238.70	−	6712.31i	0.569277	−	0.413604i	0.834843	+	0.550489i	$0.185559\pi$
$642$		0			0
$643$	−7407.11	−	22796.7i	−0.454289	−	1.39816i	−0.871968	−	0.489563i	$-0.837156\pi$
$643$	−7407.11	−	22796.7i	−0.454289	−	1.39816i	0.417679	−	0.908595i	$-0.362844\pi$
$644$		0			0
$645$	12315.3	+	8947.58i	0.751805	+	0.546218i
$646$		0			0
$647$	−2569.24	+	7907.32i	−0.156117	+	0.480478i	−0.998272	−	0.0587569i	$-0.981286\pi$
$647$	−2569.24	+	7907.32i	−0.156117	+	0.480478i	0.842156	+	0.539234i	$0.181286\pi$
$648$		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	0.983794	+	0.179303i	$0.0573843\pi$
$653$	24334.7	+	17680.2i	1.45833	+	1.05954i	0.474536	+	0.880236i	$0.342616\pi$
$654$		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	−0.591753	−	0.806119i	$-0.701564\pi$
$673$	6299.43	−	19387.7i	0.360810	−	1.11046i	0.952563	−	0.304341i	$-0.0984361\pi$
$674$		0			0
$675$	−4330.65	−	3146.40i	−0.246944	−	0.179415i
$676$		0			0
$677$	−2282.09	−	7023.55i	−0.129554	−	0.398725i	0.865149	−	0.501514i	$-0.167223\pi$
$677$	−2282.09	−	7023.55i	−0.129554	−	0.398725i	−0.994703	+	0.102789i	$0.967223\pi$
$678$		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	−0.996824	−	0.0796417i	$-0.974622\pi$
$691$	−2607.73	+	8025.78i	−0.143564	+	0.441845i	0.853259	+	0.521487i	$0.174622\pi$
$692$		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	−0.267690	−	0.963505i	$-0.586260\pi$
$701$	10503.8	−	7631.43i	0.565937	−	0.411177i	0.833627	+	0.552328i	$0.186260\pi$
$702$		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	−0.983786	−	0.179346i	$-0.942602\pi$
$709$	−5537.15	−	17041.6i	−0.293303	−	0.902695i	0.690483	−	0.723349i	$-0.257398\pi$
$710$		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	0.659133	−	0.752026i	$-0.270923\pi$
$719$	2845.59	+	2067.45i	0.147598	+	0.107236i	−0.511536	+	0.859262i	$0.670923\pi$
$720$		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	0.515544	−	0.856863i	$-0.327590\pi$
$733$	−2779.70	−	2019.57i	−0.140069	−	0.101766i	−0.655613	+	0.755097i	$0.727590\pi$
$734$		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	−0.262995	−	0.964797i	$-0.584710\pi$
$739$	10383.5	−	31957.2i	0.516866	−	1.59075i	0.779861	−	0.625953i	$-0.215290\pi$
$740$		0			0
$741$	−6109.73	−	4438.98i	−0.302897	−	0.220067i
$742$		0			0
$743$	368.875	+	1135.28i	0.0182136	+	0.0560557i	0.959750	−	0.280855i	$-0.0906180\pi$
$743$	368.875	+	1135.28i	0.0182136	+	0.0560557i	−0.941537	+	0.336911i	$0.890618\pi$
$744$		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	0.00950152	−	0.999955i	$-0.496976\pi$
$751$	19828.5	−	14406.2i	0.963451	−	0.699988i	0.953950	+	0.299967i	$0.0969755\pi$
$752$		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	−0.838365	−	0.545109i	$-0.816488\pi$
$757$	3338.57	−	10275.0i	0.160294	−	0.493333i	0.998659	+	0.0517762i	$0.0164882\pi$
$758$		0			0
$759$	50657.0	+	325.918i	2.42257	+	0.0155864i
$760$		0			0
$761$	2526.49	−	7775.75i	0.120349	−	0.370395i	−0.872676	−	0.488299i	$-0.837617\pi$
$761$	2526.49	−	7775.75i	0.120349	−	0.370395i	0.993025	+	0.117904i	$0.0376175\pi$
$762$		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	−0.195054	−	0.980792i	$-0.562488\pi$
$773$	14559.7	−	10578.3i	0.677460	−	0.492203i	0.872514	+	0.488589i	$0.162488\pi$
$774$		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	0.998562	+	0.0536084i	$0.0170723\pi$
$787$	4906.17	+	15099.6i	0.222219	+	0.683918i	−0.776343	+	0.630310i	$0.782928\pi$
$788$		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	0.998128	+	0.0611668i	$0.0194822\pi$
$797$	5098.07	+	15690.2i	0.226578	+	0.697336i	−0.771549	+	0.636170i	$0.780518\pi$
$798$		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	0.871142	−	0.491032i	$-0.163380\pi$
$809$	−2812.97	−	8657.42i	−0.122248	−	0.376241i	−0.993390	+	0.114791i	$0.963380\pi$
$810$		0			0
$811$	29590.8	−	21499.0i	1.28123	−	0.930865i	0.281636	−	0.959521i	$-0.409123\pi$
$811$	29590.8	−	21499.0i	1.28123	−	0.930865i	0.999589	+	0.0286567i	$0.00912297\pi$
$812$		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	0.648683	−	0.761059i	$-0.275320\pi$
$821$	2948.23	+	2142.01i	0.125328	+	0.0910558i	−0.523356	+	0.852114i	$0.675320\pi$
$822$		0			0
$823$	5221.12	−	16068.9i	0.221138	−	0.680593i	−0.777523	−	0.628855i	$-0.783524\pi$
$823$	5221.12	−	16068.9i	0.221138	−	0.680593i	0.998661	−	0.0517380i	$-0.0164761\pi$
$824$		0			0
$825$	22596.7	−	16196.4i	0.953597	−	0.683499i
$826$		0			0
$827$	11983.1	−	36880.1i	0.503860	−	1.55072i	−0.298817	−	0.954310i	$-0.596592\pi$
$827$	11983.1	−	36880.1i	0.503860	−	1.55072i	0.802678	−	0.596413i	$-0.203408\pi$
$828$		0			0
$829$	10027.2	+	7285.20i	0.420096	+	0.305218i	0.777677	−	0.628665i	$-0.216398\pi$
$829$	10027.2	+	7285.20i	0.420096	+	0.305218i	−0.357580	+	0.933882i	$0.616398\pi$
$830$		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	−0.0983299	−	0.995154i	$-0.531350\pi$
$839$	19872.6	−	14438.3i	0.817732	−	0.594117i	0.916062	+	0.401037i	$0.131350\pi$
$840$		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	0.846358	−	0.532614i	$-0.178790\pi$
$853$	−3772.37	−	11610.1i	−0.151422	−	0.466030i	−0.997781	+	0.0665834i	$0.978790\pi$
$854$		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	0.852547	+	0.522651i	$0.175057\pi$
$863$	11916.3	+	36674.5i	0.470028	+	1.44660i	−0.382518	+	0.923948i	$0.624943\pi$
$864$		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	−0.935400	−	0.353591i	$-0.884961\pi$
$877$	−23067.2	+	16759.3i	−0.888170	+	0.645293i	0.0472301	+	0.998884i	$0.484961\pi$
$878$		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	−0.641835	−	0.766842i	$-0.721827\pi$
$883$	−2908.89	+	2113.43i	−0.110863	+	0.0805467i	0.530972	+	0.847389i	$0.321827\pi$
$884$		0			0
$885$	−1280.64	−	3941.41i	−0.0486421	−	0.149705i
$886$		0			0
$887$	−6241.81	−	4534.94i	−0.236279	−	0.171667i	0.463345	−	0.886178i	$-0.346649\pi$
$887$	−6241.81	−	4534.94i	−0.236279	−	0.171667i	−0.699624	+	0.714511i	$0.746649\pi$
$888$		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	0.939060	+	0.343753i	$0.111698\pi$
$907$	10418.1	+	32063.6i	0.381398	+	1.17382i	−0.557662	+	0.830068i	$0.688302\pi$
$908$		0			0
$909$	11306.1	+	8214.33i	0.412539	+	0.299727i
$910$		0			0
$911$	−4644.75	+	14295.1i	−0.168922	+	0.519887i	−0.999304	−	0.0373070i	$-0.988122\pi$
$911$	−4644.75	+	14295.1i	−0.168922	+	0.519887i	0.830382	+	0.557194i	$0.188122\pi$
$912$		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	0.999997	−	0.00240379i	$-0.000765151\pi$
$919$	5281.31	+	16254.2i	0.189570	+	0.583435i	−0.810428	+	0.585839i	$0.800765\pi$
$920$		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	0.996831	−	0.0795446i	$-0.0253466\pi$
$929$	4066.74	+	12516.1i	0.143623	+	0.442025i	−0.853209	+	0.521570i	$0.825347\pi$
$930$		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	−0.926825	−	0.375494i	$-0.877473\pi$
$937$	1253.46	−	3857.76i	0.0437021	−	0.134501i	0.970527	+	0.240993i	$0.0774731\pi$
$938$		0			0
$939$	−19099.2	−	13876.4i	−0.663768	−	0.482256i
$940$		0			0
$941$	10320.4	+	31763.0i	0.357531	+	1.10037i	0.954527	+	0.298123i	$0.0963607\pi$
$941$	10320.4	+	31763.0i	0.357531	+	1.10037i	−0.596996	+	0.802244i	$0.703639\pi$
$942$		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	−0.999311	−	0.0371079i	$-0.988185\pi$
$953$	−39522.7	−	28714.9i	−1.34341	−	0.976042i	−0.344096	−	0.938935i	$-0.611815\pi$
$954$		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	−0.0138603	−	0.999904i	$-0.504412\pi$
$971$	28224.6	−	20506.4i	0.932822	−	0.677735i	0.946682	+	0.322169i	$0.104412\pi$
$972$		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	0.807609	+	0.589718i	$0.200761\pi$
$977$	−5875.16	+	18081.9i	−0.192388	+	0.592109i	−0.999997	+	0.00239112i	$0.999239\pi$
$978$		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	0.485726	−	0.874111i	$-0.338555\pi$
$983$	−6025.47	−	4377.76i	−0.195506	−	0.142044i	−0.681232	+	0.732068i	$0.738555\pi$
$984$		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	−0.997284	−	0.0736504i	$-0.976535\pi$
$997$	−43301.8	−	31460.6i	−1.37551	−	0.999365i	−0.378223	−	0.925714i	$-0.623465\pi$
$998$		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.97.1		8
4.3	odd	2		22.4.c.b.9.2	yes	8
11.4	even	5		1936.4.a.bn.1.4		4
11.5	even	5	inner	176.4.m.b.49.1		8
11.7	odd	10		1936.4.a.bm.1.4		4
12.11	even	2		198.4.f.d.163.1		8
44.3	odd	10		242.4.c.r.81.1		8
44.7	even	10		242.4.a.o.1.1		4
44.15	odd	10		242.4.a.n.1.1		4
44.19	even	10		242.4.c.n.81.1		8
44.27	odd	10		22.4.c.b.5.2	✓	8
44.31	odd	10		242.4.c.r.3.1		8
44.35	even	10		242.4.c.n.3.1		8
44.39	even	10		242.4.c.q.27.2		8
44.43	even	2		242.4.c.q.9.2		8
132.59	even	10		2178.4.a.by.1.1		4
132.71	even	10		198.4.f.d.181.1		8
132.95	odd	10		2178.4.a.bt.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.5.2	✓	8	44.27	odd	10
22.4.c.b.9.2	yes	8	4.3	odd	2
176.4.m.b.49.1		8	11.5	even	5	inner
176.4.m.b.97.1		8	1.1	even	1	trivial
198.4.f.d.163.1		8	12.11	even	2
198.4.f.d.181.1		8	132.71	even	10
242.4.a.n.1.1		4	44.15	odd	10
242.4.a.o.1.1		4	44.7	even	10
242.4.c.n.3.1		8	44.35	even	10
242.4.c.n.81.1		8	44.19	even	10
242.4.c.q.9.2		8	44.43	even	2
242.4.c.q.27.2		8	44.39	even	10
242.4.c.r.3.1		8	44.31	odd	10
242.4.c.r.81.1		8	44.3	odd	10
1936.4.a.bm.1.4		4	11.7	odd	10
1936.4.a.bn.1.4		4	11.4	even	5
2178.4.a.bt.1.1		4	132.95	odd	10
2178.4.a.by.1.1		4	132.59	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-6.31989 + 4.59167i) q^{3} +(4.60996 + 14.1880i) q^{5} +(17.6106 + 12.7948i) q^{7} +(10.5141 - 32.3592i) q^{9} +O(q^{10})\)	\(q+(-6.31989 + 4.59167i) q^{3} +(4.60996 + 14.1880i) q^{5} +(17.6106 + 12.7948i) q^{7} +(10.5141 - 32.3592i) q^{9} +(29.3767 + 21.6335i) q^{11} +(-13.6056 + 41.8736i) q^{13} +(-94.2810 - 68.4992i) q^{15} +(-7.69900 - 23.6951i) q^{17} +(17.7638 - 12.9061i) q^{19} -170.046 q^{21} -177.749 q^{23} +(-78.9203 + 57.3389i) q^{25} +(16.9569 + 52.1881i) q^{27} +(120.864 + 87.8130i) q^{29} +(-23.2207 + 71.4658i) q^{31} +(-284.992 - 1.83359i) q^{33} +(-100.349 + 308.842i) q^{35} +(-179.874 - 130.686i) q^{37} +(-106.284 - 327.109i) q^{39} +(204.779 - 148.781i) q^{41} -130.623 q^{43} +507.582 q^{45} +(403.775 - 293.360i) q^{47} +(40.4316 + 124.436i) q^{49} +(157.457 + 114.399i) q^{51} +(3.99933 - 12.3087i) q^{53} +(-171.511 + 516.526i) q^{55} +(-53.0044 + 163.131i) q^{57} +(28.7697 + 20.9024i) q^{59} +(166.357 + 511.995i) q^{61} +(599.190 - 435.337i) q^{63} -656.824 q^{65} +519.621 q^{67} +(1123.35 - 816.165i) q^{69} +(-24.2420 - 74.6091i) q^{71} +(-925.571 - 672.467i) q^{73} +(235.486 - 724.752i) q^{75} +(240.543 + 756.848i) q^{77} +(-238.730 + 734.735i) q^{79} +(396.416 + 288.013i) q^{81} +(-166.017 - 510.947i) q^{83} +(300.694 - 218.467i) q^{85} -1167.06 q^{87} +667.089 q^{89} +(-775.368 + 563.338i) q^{91} +(-181.395 - 558.278i) q^{93} +(265.003 + 192.536i) q^{95} +(-55.5161 + 170.861i) q^{97} +(1008.91 - 723.148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9}+O(q^{10}) \) 8 * q - 3 * q^3 + 5 * q^5 + q^7 - 21 * q^9	\( 8 q - 3 q^{3} + 5 q^{5} + q^{7} - 21 q^{9} + 155 q^{11} + 7 q^{13} - 211 q^{15} + 161 q^{17} + 272 q^{19} - 50 q^{21} - 628 q^{23} - 17 q^{25} + 528 q^{27} + 33 q^{29} - 323 q^{31} - 1144 q^{33} + 697 q^{35} + 49 q^{37} - 391 q^{39} + 361 q^{41} - 1442 q^{43} + 2652 q^{45} + 1069 q^{47} - 709 q^{49} + 1332 q^{51} - 281 q^{53} + 7 q^{55} - 438 q^{57} + 128 q^{59} - 617 q^{61} - 694 q^{63} - 138 q^{65} - 578 q^{67} - 310 q^{69} - 115 q^{71} - 1487 q^{73} + 1852 q^{75} + 553 q^{77} - 71 q^{79} + 1630 q^{81} - 1942 q^{83} - 329 q^{85} - 2122 q^{87} - 2202 q^{89} - 4523 q^{91} + 6019 q^{93} + 793 q^{95} - 5128 q^{97} + 2213 q^{99}+O(q^{100}) \) 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

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