LMFDB - Embedded newform 1323.2.h.f.802.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.3
Root			$0.247934 + 0.429435i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.f.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.495868 q^{2} -1.75411 q^{4} +(1.84629 - 3.19787i) q^{5} -1.86155 q^{8} +O(q^{10})$	\(q+0.495868 q^{2} -1.75411 q^{4} +(1.84629 - 3.19787i) q^{5} -1.86155 q^{8} +(0.915516 - 1.58572i) q^{10} +(-0.446284 - 0.772987i) q^{11} +(-0.598355 - 1.03638i) q^{13} +2.58515 q^{16} +(-0.124991 + 0.216492i) q^{17} +(-1.40414 - 2.43204i) q^{19} +(-3.23860 + 5.60943i) q^{20} +(-0.221298 - 0.383300i) q^{22} +(1.23886 - 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +(-0.296705 - 0.513909i) q^{26} +(-2.07128 + 3.58755i) q^{29} -3.58515 q^{31} +5.00499 q^{32} +(-0.0619793 + 0.107351i) q^{34} +(-2.36568 - 4.09747i) q^{37} +(-0.696267 - 1.20597i) q^{38} +(-3.43695 + 5.95298i) q^{40} +(-2.39093 - 4.14121i) q^{41} +(-4.98928 + 8.64169i) q^{43} +(0.782834 + 1.35591i) q^{44} +(0.614310 - 1.06402i) q^{46} -10.1731 q^{47} +(-2.14095 - 3.70823i) q^{50} +(1.04958 + 1.81793i) q^{52} +(4.94465 - 8.56438i) q^{53} -3.29588 q^{55} +(-1.02708 + 1.77895i) q^{58} +1.81237 q^{59} -10.8041 q^{61} -1.77776 q^{62} -2.68848 q^{64} -4.41895 q^{65} +1.02937 q^{67} +(0.219249 - 0.379751i) q^{68} +4.94533 q^{71} +(0.915262 - 1.58528i) q^{73} +(-1.17306 - 2.03181i) q^{74} +(2.46302 + 4.26607i) q^{76} -1.79912 q^{79} +(4.77293 - 8.26696i) q^{80} +(-1.18559 - 2.05350i) q^{82} +(6.16156 - 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} +(-2.47403 + 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} +(-1.20370 - 2.08488i) q^{89} +(-2.17310 + 3.76392i) q^{92} -5.04450 q^{94} -10.3698 q^{95} +(-5.52210 + 9.56456i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 + 6 * q^8	$ 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8} + 7 q^{10} - 4 q^{11} + 8 q^{13} - 4 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 11 q^{26} - 7 q^{29} - 6 q^{31} - 4 q^{32} - 3 q^{34} + 20 q^{38} + 3 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 54 q^{47} - 19 q^{50} + 10 q^{52} + 21 q^{53} - 4 q^{55} - 10 q^{58} - 60 q^{59} - 28 q^{61} - 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} + 27 q^{68} + 6 q^{71} - 15 q^{73} + 36 q^{74} - 5 q^{76} + 8 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 28 q^{89} - 27 q^{92} - 6 q^{94} - 28 q^{95} + 12 q^{97}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 + 6 * q^8 + 7 * q^10 - 4 * q^11 + 8 * q^13 - 4 * q^16 + 12 * q^17 - q^19 + 5 * q^20 - q^22 - 3 * q^23 - q^25 + 11 * q^26 - 7 * q^29 - 6 * q^31 - 4 * q^32 - 3 * q^34 + 20 * q^38 + 3 * q^40 + 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 54 * q^47 - 19 * q^50 + 10 * q^52 + 21 * q^53 - 4 * q^55 - 10 * q^58 - 60 * q^59 - 28 * q^61 - 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 + 27 * q^68 + 6 * q^71 - 15 * q^73 + 36 * q^74 - 5 * q^76 + 8 * q^79 + 20 * q^80 + 5 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 28 * q^89 - 27 * q^92 - 6 * q^94 - 28 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.495868			0.350632			0.175316	−	0.984512i	$-0.443905\pi$
$2$	0.495868			0.350632			0.175316	+	0.984512i	$0.443905\pi$
$3$		0			0
$3$		0			0
$4$	−1.75411			−0.877057
$5$	1.84629	−	3.19787i	0.825686	−	1.43013i	−0.0757082	−	0.997130i	$-0.524122\pi$
$5$	1.84629	−	3.19787i	0.825686	−	1.43013i	0.901394	−	0.433000i	$-0.142545\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.86155			−0.658156
$9$		0			0
$10$	0.915516	−	1.58572i	0.289512	−	0.501449i
$11$	−0.446284	−	0.772987i	−0.134560	−	0.233064i	0.790869	−	0.611985i	$-0.209629\pi$
$11$	−0.446284	−	0.772987i	−0.134560	−	0.233064i	−0.925429	+	0.378921i	$0.876295\pi$
$12$		0			0
$13$	−0.598355	−	1.03638i	−0.165954	−	0.287441i	0.771040	−	0.636787i	$-0.219737\pi$
$13$	−0.598355	−	1.03638i	−0.165954	−	0.287441i	−0.936994	+	0.349346i	$0.886404\pi$
$14$		0			0
$15$		0			0
$16$	2.58515			0.646287
$17$	−0.124991	+	0.216492i	−0.0303149	+	0.0525069i	−0.880785	−	0.473517i	$-0.842984\pi$
$17$	−0.124991	+	0.216492i	−0.0303149	+	0.0525069i	0.850470	+	0.526024i	$0.176318\pi$
$18$		0			0
$19$	−1.40414	−	2.43204i	−0.322131	−	0.557948i	0.658796	−	0.752321i	$-0.271066\pi$
$19$	−1.40414	−	2.43204i	−0.322131	−	0.557948i	−0.980928	+	0.194374i	$0.937733\pi$
$20$	−3.23860	+	5.60943i	−0.724174	+	1.25431i
$21$		0			0
$22$	−0.221298	−	0.383300i	−0.0471809	−	0.0817198i
$23$	1.23886	−	2.14576i	0.258320	−	0.447423i	−0.707472	−	0.706741i	$-0.750165\pi$
$23$	1.23886	−	2.14576i	0.258320	−	0.447423i	0.965792	+	0.259318i	$0.0834979\pi$
$24$		0			0
$25$	−4.31757	−	7.47825i	−0.863514	−	1.49565i
$26$	−0.296705	−	0.513909i	−0.0581887	−	0.100786i
$27$		0			0
$28$		0			0
$29$	−2.07128	+	3.58755i	−0.384626	+	0.666192i	−0.991717	−	0.128440i	$-0.959003\pi$
$29$	−2.07128	+	3.58755i	−0.384626	+	0.666192i	0.607091	+	0.794632i	$0.292336\pi$
$30$		0			0
$31$	−3.58515			−0.643912			−0.321956	−	0.946755i	$-0.604340\pi$
$31$	−3.58515			−0.643912			−0.321956	+	0.946755i	$0.604340\pi$
$32$	5.00499			0.884765
$33$		0			0
$34$	−0.0619793	+	0.107351i	−0.0106294	+	0.0184106i
$35$		0			0
$36$		0			0
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	0.603389	−	0.797447i	$-0.293817\pi$
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	−0.992304	+	0.123826i	$0.960483\pi$
$38$	−0.696267	−	1.20597i	−0.112949	−	0.195634i
$39$		0			0
$40$	−3.43695	+	5.95298i	−0.543430	+	0.941249i
$41$	−2.39093	−	4.14121i	−0.373400	−	0.646748i	0.616686	−	0.787209i	$-0.288475\pi$
$41$	−2.39093	−	4.14121i	−0.373400	−	0.646748i	−0.990086	+	0.140461i	$0.955142\pi$
$42$		0			0
$43$	−4.98928	+	8.64169i	−0.760859	+	1.31785i	0.181550	+	0.983382i	$0.441889\pi$
$43$	−4.98928	+	8.64169i	−0.760859	+	1.31785i	−0.942408	+	0.334464i	$0.891445\pi$
$44$	0.782834	+	1.35591i	0.118017	+	0.204411i
$45$		0			0
$46$	0.614310	−	1.06402i	0.0905751	−	0.156881i
$47$	−10.1731			−1.48389			−0.741947	−	0.670459i	$-0.766097\pi$
$47$	−10.1731			−1.48389			−0.741947	+	0.670459i	$0.766097\pi$
$48$		0			0
$49$		0			0
$50$	−2.14095	−	3.70823i	−0.302776	−	0.524423i
$51$		0			0
$52$	1.04958	+	1.81793i	0.145551	+	0.252102i
$53$	4.94465	−	8.56438i	0.679199	−	1.17641i	−0.296023	−	0.955181i	$-0.595661\pi$
$53$	4.94465	−	8.56438i	0.679199	−	1.17641i	0.975222	−	0.221227i	$-0.0710061\pi$
$54$		0			0
$55$	−3.29588			−0.444416
$56$		0			0
$57$		0			0
$58$	−1.02708	+	1.77895i	−0.134862	+	0.233588i
$59$	1.81237			0.235951			0.117975	−	0.993017i	$-0.462360\pi$
$59$	1.81237			0.235951			0.117975	+	0.993017i	$0.462360\pi$
$60$		0			0
$61$	−10.8041			−1.38332			−0.691662	−	0.722221i	$-0.743121\pi$
$61$	−10.8041			−1.38332			−0.691662	+	0.722221i	$0.743121\pi$
$62$	−1.77776			−0.225776
$63$		0			0
$64$	−2.68848			−0.336060
$65$	−4.41895			−0.548103
$66$		0			0
$67$	1.02937			0.125757			0.0628787	−	0.998021i	$-0.479972\pi$
$67$	1.02937			0.125757			0.0628787	+	0.998021i	$0.479972\pi$
$68$	0.219249	−	0.379751i	0.0265879	−	0.0460516i
$69$		0			0
$70$		0			0
$71$	4.94533			0.586903			0.293451	−	0.955974i	$-0.405196\pi$
$71$	4.94533			0.586903			0.293451	+	0.955974i	$0.405196\pi$
$72$		0			0
$73$	0.915262	−	1.58528i	0.107123	−	0.185543i	−0.807480	−	0.589894i	$-0.799169\pi$
$73$	0.915262	−	1.58528i	0.107123	−	0.185543i	0.914604	+	0.404351i	$0.132503\pi$
$74$	−1.17306	−	2.03181i	−0.136366	−	0.236193i
$75$		0			0
$76$	2.46302	+	4.26607i	0.282527	+	0.489352i
$77$		0			0
$78$		0			0
$79$	−1.79912			−0.202417			−0.101209	−	0.994865i	$-0.532271\pi$
$79$	−1.79912			−0.202417			−0.101209	+	0.994865i	$0.532271\pi$
$80$	4.77293	−	8.26696i	0.533630	−	0.924274i
$81$		0			0
$82$	−1.18559	−	2.05350i	−0.130926	−	0.226771i
$83$	6.16156	−	10.6721i	0.676319	−	1.17142i	−0.299763	−	0.954014i	$-0.596908\pi$
$83$	6.16156	−	10.6721i	0.676319	−	1.17142i	0.976082	−	0.217405i	$-0.0697591\pi$
$84$		0			0
$85$	0.461541	+	0.799412i	0.0500611	+	0.0867084i
$86$	−2.47403	+	4.28514i	−0.266781	+	0.462079i
$87$		0			0
$88$	0.830779	+	1.43895i	0.0885613	+	0.153393i
$89$	−1.20370	−	2.08488i	−0.127592	−	0.220997i	0.795151	−	0.606412i	$-0.207392\pi$
$89$	−1.20370	−	2.08488i	−0.127592	−	0.220997i	−0.922743	+	0.385415i	$0.874058\pi$
$90$		0			0
$91$		0			0
$92$	−2.17310	+	3.76392i	−0.226561	+	0.392416i
$93$		0			0
$94$	−5.04450			−0.520300
$95$	−10.3698			−1.06392
$96$		0			0
$97$	−5.52210	+	9.56456i	−0.560684	+	0.971134i	0.436752	+	0.899582i	$0.356129\pi$
$97$	−5.52210	+	9.56456i	−0.560684	+	0.971134i	−0.997437	+	0.0715522i	$0.977205\pi$
$98$		0			0
$99$		0			0
$100$	7.57351	+	13.1177i	0.757351	+	1.31177i
$101$	1.29982	+	2.25136i	0.129337	+	0.224018i	0.923420	−	0.383791i	$-0.125382\pi$
$101$	1.29982	+	2.25136i	0.129337	+	0.224018i	−0.794083	+	0.607810i	$0.792048\pi$
$102$		0			0
$103$	4.85578	−	8.41045i	0.478454	−	0.828706i	−0.521241	−	0.853409i	$-0.674531\pi$
$103$	4.85578	−	8.41045i	0.478454	−	0.828706i	0.999695	+	0.0247032i	$0.00786408\pi$
$104$	1.11387	+	1.92927i	0.109224	+	0.189181i
$105$		0			0
$106$	2.45189	−	4.24680i	0.238149	−	0.412486i
$107$	5.45025	+	9.44012i	0.526896	+	0.912610i	0.999509	+	0.0313403i	$0.00997757\pi$
$107$	5.45025	+	9.44012i	0.526896	+	0.912610i	−0.472613	+	0.881270i	$0.656689\pi$
$108$		0			0
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	−0.912353	−	0.409404i	$-0.865737\pi$
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	0.810731	+	0.585419i	$0.199070\pi$
$110$	−1.63432			−0.155826
$111$		0			0
$112$		0			0
$113$	−7.91318	−	13.7060i	−0.744409	−	1.28935i	−0.950470	−	0.310816i	$-0.899398\pi$
$113$	−7.91318	−	13.7060i	−0.744409	−	1.28935i	0.206061	−	0.978539i	$-0.433935\pi$
$114$		0			0
$115$	−4.57458	−	7.92341i	−0.426582	−	0.738861i
$116$	3.63325	−	6.29298i	0.337339	−	0.584289i
$117$		0			0
$118$	0.898698			0.0827318
$119$		0			0
$120$		0			0
$121$	5.10166	−	8.83634i	0.463787	−	0.803303i
$122$	−5.35741			−0.485038
$123$		0			0
$124$	6.28876			0.564747
$125$	−13.4230			−1.20059
$126$		0			0
$127$	−1.26946			−0.112647			−0.0563233	−	0.998413i	$-0.517938\pi$
$127$	−1.26946			−0.112647			−0.0563233	+	0.998413i	$0.517938\pi$
$128$	−11.3431			−1.00260
$129$		0			0
$130$	−2.19122			−0.192182
$131$	7.51444	−	13.0154i	0.656540	−	1.13716i	−0.324965	−	0.945726i	$-0.605353\pi$
$131$	7.51444	−	13.0154i	0.656540	−	1.13716i	0.981505	−	0.191435i	$-0.0613140\pi$
$132$		0			0
$133$		0			0
$134$	0.510432			0.0440946
$135$		0			0
$136$	0.232677	−	0.403009i	0.0199519	−	0.0345577i
$137$	−0.244246	−	0.423047i	−0.0208674	−	0.0361433i	0.855403	−	0.517963i	$-0.173309\pi$
$137$	−0.244246	−	0.423047i	−0.0208674	−	0.0361433i	−0.876271	+	0.481819i	$0.839976\pi$
$138$		0			0
$139$	4.93487	+	8.54745i	0.418570	+	0.724985i	0.995796	−	0.0915997i	$-0.0291980\pi$
$139$	4.93487	+	8.54745i	0.418570	+	0.724985i	−0.577226	+	0.816585i	$0.695865\pi$
$140$		0			0
$141$		0			0
$142$	2.45223			0.205787
$143$	−0.534073	+	0.925042i	−0.0446614	+	0.0773559i
$144$		0			0
$145$	7.64835	+	13.2473i	0.635161	+	1.10013i
$146$	0.453849	−	0.786090i	0.0375609	−	0.0650573i
$147$		0			0
$148$	4.14967	+	7.18744i	0.341101	+	0.590804i
$149$	10.5120	−	18.2073i	0.861175	−	1.49160i	−0.00962096	−	0.999954i	$-0.503062\pi$
$149$	10.5120	−	18.2073i	0.861175	−	1.49160i	0.870796	−	0.491645i	$-0.163604\pi$
$150$		0			0
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	0.833930	−	0.551870i	$-0.186086\pi$
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	−0.894898	+	0.446270i	$0.852752\pi$
$152$	2.61387	+	4.52735i	0.212013	+	0.367217i
$153$		0			0
$154$		0			0
$155$	−6.61922	+	11.4648i	−0.531669	+	0.920877i
$156$		0			0
$157$	16.6796			1.33118			0.665590	−	0.746317i	$-0.268180\pi$
$157$	16.6796			1.33118			0.665590	+	0.746317i	$0.268180\pi$
$158$	−0.892128			−0.0709739
$159$		0			0
$160$	9.24065	−	16.0053i	0.730538	−	1.26533i
$161$		0			0
$162$		0			0
$163$	−3.34135	−	5.78738i	−0.261714	−	0.453303i	0.704983	−	0.709224i	$-0.250954\pi$
$163$	−3.34135	−	5.78738i	−0.261714	−	0.453303i	−0.966698	+	0.255921i	$0.917621\pi$
$164$	4.19396	+	7.26416i	0.327494	+	0.567236i
$165$		0			0
$166$	3.05532	−	5.29197i	0.237139	−	0.410737i
$167$	8.81549	+	15.2689i	0.682163	+	1.18154i	0.974319	+	0.225170i	$0.0722939\pi$
$167$	8.81549	+	15.2689i	0.682163	+	1.18154i	−0.292156	+	0.956371i	$0.594373\pi$
$168$		0			0
$169$	5.78394	−	10.0181i	0.444919	−	0.770622i
$170$	0.228863	+	0.396403i	0.0175530	+	0.0304027i
$171$		0			0
$172$	8.75178	−	15.1585i	0.667317	−	1.15583i
$173$	−3.88685			−0.295511			−0.147756	−	0.989024i	$-0.547205\pi$
$173$	−3.88685			−0.295511			−0.147756	+	0.989024i	$0.547205\pi$
$174$		0			0
$175$		0			0
$176$	−1.15371	−	1.99829i	−0.0869642	−	0.150626i
$177$		0			0
$178$	−0.596879	−	1.03382i	−0.0447380	−	0.0774884i
$179$	−3.66758	+	6.35244i	−0.274128	+	0.474804i	−0.969915	−	0.243445i	$-0.921723\pi$
$179$	−3.66758	+	6.35244i	−0.274128	+	0.474804i	0.695787	+	0.718248i	$0.255056\pi$
$180$		0			0
$181$	−11.2566			−0.836693			−0.418346	−	0.908288i	$-0.637390\pi$
$181$	−11.2566			−0.836693			−0.418346	+	0.908288i	$0.637390\pi$
$182$		0			0
$183$		0			0
$184$	−2.30619	+	3.99444i	−0.170015	+	0.294474i
$185$	−17.4709			−1.28449
$186$		0			0
$187$	0.223127			0.0163167
$188$	17.8447			1.30146
$189$		0			0
$190$	−5.14204			−0.373043
$191$	23.8459			1.72543			0.862715	−	0.505690i	$-0.168762\pi$
$191$	23.8459			1.72543			0.862715	+	0.505690i	$0.168762\pi$
$192$		0			0
$193$	5.93456			0.427179			0.213589	−	0.976924i	$-0.431485\pi$
$193$	5.93456			0.427179			0.213589	+	0.976924i	$0.431485\pi$
$194$	−2.73823	+	4.74276i	−0.196594	+	0.340510i
$195$		0			0
$196$		0			0
$197$	15.4682			1.10206			0.551032	−	0.834484i	$-0.314234\pi$
$197$	15.4682			1.10206			0.551032	+	0.834484i	$0.314234\pi$
$198$		0			0
$199$	−7.74818	+	13.4202i	−0.549254	+	0.951336i	0.449072	+	0.893496i	$0.351755\pi$
$199$	−7.74818	+	13.4202i	−0.549254	+	0.951336i	−0.998326	+	0.0578402i	$0.981579\pi$
$200$	8.03736	+	13.9211i	0.568327	+	0.984371i
$201$		0			0
$202$	0.644540	+	1.11638i	0.0453497	+	0.0785480i
$203$		0			0
$204$		0			0
$205$	−17.6574			−1.23325
$206$	2.40783	−	4.17048i	0.167761	−	0.290571i
$207$		0			0
$208$	−1.54684	−	2.67920i	−0.107254	−	0.185769i
$209$	−1.25329	+	2.17076i	−0.0866918	+	0.150155i
$210$		0			0
$211$	0.771898	+	1.33697i	0.0531397	+	0.0920406i	0.891372	−	0.453273i	$-0.149744\pi$
$211$	0.771898	+	1.33697i	0.0531397	+	0.0920406i	−0.838232	+	0.545314i	$0.816410\pi$
$212$	−8.67347	+	15.0229i	−0.595697	+	1.03178i
$213$		0			0
$214$	2.70261	+	4.68105i	0.184746	+	0.319990i
$215$	18.4233	+	31.9101i	1.25646	+	2.17625i
$216$		0			0
$217$		0			0
$218$	−0.526098	+	0.911229i	−0.0356319	+	0.0617162i
$219$		0			0
$220$	5.78135			0.389779
$221$	0.299157			0.0201235
$222$		0			0
$223$	2.72171	−	4.71414i	0.182259	−	0.315682i	−0.760390	−	0.649466i	$-0.774992\pi$
$223$	2.72171	−	4.71414i	0.182259	−	0.315682i	0.942649	+	0.333784i	$0.108326\pi$
$224$		0			0
$225$		0			0
$226$	−3.92389	−	6.79638i	−0.261014	−	0.452089i
$227$	8.03818	+	13.9225i	0.533513	+	0.924072i	0.999234	+	0.0391399i	$0.0124618\pi$
$227$	8.03818	+	13.9225i	0.533513	+	0.924072i	−0.465721	+	0.884932i	$0.654205\pi$
$228$		0			0
$229$	−4.98420	+	8.63289i	−0.329365	+	0.570477i	−0.982386	−	0.186863i	$-0.940168\pi$
$229$	−4.98420	+	8.63289i	−0.329365	+	0.570477i	0.653021	+	0.757340i	$0.273501\pi$
$230$	−2.26839	−	3.92897i	−0.149573	−	0.259068i
$231$		0			0
$232$	3.85578	−	6.67840i	0.253144	−	0.438458i
$233$	−8.27045	−	14.3248i	−0.541815	−	0.938451i	−0.998800	−	0.0489765i	$-0.984404\pi$
$233$	−8.27045	−	14.3248i	−0.541815	−	0.938451i	0.456985	−	0.889474i	$-0.348929\pi$
$234$		0			0
$235$	−18.7824	+	32.5321i	−1.22523	+	2.12216i
$236$	−3.17911			−0.206942
$237$		0			0
$238$		0			0
$239$	11.0119	+	19.0732i	0.712303	+	1.23375i	0.963990	+	0.265937i	$0.0856813\pi$
$239$	11.0119	+	19.0732i	0.712303	+	1.23375i	−0.251687	+	0.967809i	$0.580985\pi$
$240$		0			0
$241$	8.36004	+	14.4800i	0.538517	+	0.932739i	0.998984	+	0.0450623i	$0.0143486\pi$
$241$	8.36004	+	14.4800i	0.538517	+	0.932739i	−0.460467	+	0.887677i	$0.652318\pi$
$242$	2.52975	−	4.38166i	0.162619	−	0.281664i
$243$		0			0
$244$	18.9516			1.21325
$245$		0			0
$246$		0			0
$247$	−1.68035	+	2.91045i	−0.106918	+	0.185187i
$248$	6.67392			0.423794
$249$		0			0
$250$	−6.65606			−0.420966
$251$	−8.53099			−0.538471			−0.269236	−	0.963074i	$-0.586771\pi$
$251$	−8.53099			−0.538471			−0.269236	+	0.963074i	$0.586771\pi$
$252$		0			0
$253$	−2.21153			−0.139038
$254$	−0.629487			−0.0394975
$255$		0			0
$256$	−0.247722			−0.0154826
$257$	8.55986	−	14.8261i	0.533950	−	0.924828i	−0.465264	−	0.885172i	$-0.654041\pi$
$257$	8.55986	−	14.8261i	0.533950	−	0.924828i	0.999213	−	0.0396557i	$-0.0126261\pi$
$258$		0			0
$259$		0			0
$260$	7.75135			0.480718
$261$		0			0
$262$	3.72617	−	6.45392i	0.230204	−	0.398725i
$263$	10.2763	+	17.7991i	0.633666	+	1.09754i	0.986796	+	0.161967i	$0.0517838\pi$
$263$	10.2763	+	17.7991i	0.633666	+	1.09754i	−0.353130	+	0.935574i	$0.614883\pi$
$264$		0			0
$265$	−18.2585	−	31.6246i	−1.12161	−	1.94269i
$266$		0			0
$267$		0			0
$268$	−1.80563			−0.110297
$269$	9.92267	−	17.1866i	0.604996	−	1.04788i	−0.387057	−	0.922056i	$-0.626508\pi$
$269$	9.92267	−	17.1866i	0.604996	−	1.04788i	0.992052	−	0.125827i	$-0.0401585\pi$
$270$		0			0
$271$	−5.32056	−	9.21548i	−0.323201	−	0.559801i	0.657946	−	0.753065i	$-0.271426\pi$
$271$	−5.32056	−	9.21548i	−0.323201	−	0.559801i	−0.981147	+	0.193265i	$0.938092\pi$
$272$	−0.323121	+	0.559663i	−0.0195921	+	0.0339345i
$273$		0			0
$274$	−0.121114	−	0.209776i	−0.00731676	−	0.0126730i
$275$	−3.85373	+	6.67485i	−0.232388	+	0.402509i
$276$		0			0
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	0.949024	+	0.315205i	$0.102073\pi$
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	−0.201536	+	0.979481i	$0.564593\pi$
$278$	2.44705	+	4.23841i	0.146764	+	0.254203i
$279$		0			0
$280$		0			0
$281$	6.83733	−	11.8426i	0.407881	−	0.706470i	−0.586771	−	0.809753i	$-0.699601\pi$
$281$	6.83733	−	11.8426i	0.407881	−	0.706470i	0.994652	+	0.103282i	$0.0329346\pi$
$282$		0			0
$283$	−6.32179			−0.375791			−0.187896	−	0.982189i	$-0.560167\pi$
$283$	−6.32179			−0.375791			−0.187896	+	0.982189i	$0.560167\pi$
$284$	−8.67468			−0.514747
$285$		0			0
$286$	−0.264830	+	0.458699i	−0.0156597	+	0.0271234i
$287$		0			0
$288$		0			0
$289$	8.46875	+	14.6683i	0.498162	+	0.862842i
$290$	3.79257	+	6.56893i	0.222708	+	0.385741i
$291$		0			0
$292$	−1.60547	+	2.78076i	−0.0939533	+	0.162732i
$293$	−1.31508	−	2.27778i	−0.0768277	−	0.133069i	0.825052	−	0.565057i	$-0.191146\pi$
$293$	−1.31508	−	2.27778i	−0.0768277	−	0.133069i	−0.901880	+	0.431987i	$0.857812\pi$
$294$		0			0
$295$	3.34616	−	5.79573i	0.194821	−	0.337440i
$296$	4.40382	+	7.62764i	0.255967	+	0.443348i
$297$		0			0
$298$	5.21256	−	9.02841i	0.301955	−	0.523002i
$299$	−2.96511			−0.171477
$300$		0			0
$301$		0			0
$302$	−0.371500	−	0.643457i	−0.0213774	−	0.0370268i
$303$		0			0
$304$	−3.62990	−	6.28717i	−0.208189	−	0.360594i
$305$	−19.9475	+	34.5501i	−1.14219	+	1.97833i
$306$		0			0
$307$	2.79496			0.159517			0.0797583	−	0.996814i	$-0.474585\pi$
$307$	2.79496			0.159517			0.0797583	+	0.996814i	$0.474585\pi$
$308$		0			0
$309$		0			0
$310$	−3.28226	+	5.68504i	−0.186420	+	0.322889i
$311$	−15.1003			−0.856258			−0.428129	−	0.903718i	$-0.640827\pi$
$311$	−15.1003			−0.856258			−0.428129	+	0.903718i	$0.640827\pi$
$312$		0			0
$313$	25.4785			1.44013			0.720064	−	0.693908i	$-0.244112\pi$
$313$	25.4785			1.44013			0.720064	+	0.693908i	$0.244112\pi$
$314$	8.27090			0.466754
$315$		0			0
$316$	3.15587			0.177531
$317$	−32.5209			−1.82656			−0.913278	−	0.407337i	$-0.866457\pi$
$317$	−32.5209			−1.82656			−0.913278	+	0.407337i	$0.866457\pi$
$318$		0			0
$319$	3.69751			0.207021
$320$	−4.96372	+	8.59741i	−0.277480	+	0.480610i
$321$		0			0
$322$		0			0
$323$	0.702021			0.0390615
$324$		0			0
$325$	−5.16688	+	8.94931i	−0.286607	+	0.496418i
$326$	−1.65687	−	2.86978i	−0.0917654	−	0.158942i
$327$		0			0
$328$	4.45083	+	7.70906i	0.245756	+	0.425661i
$329$		0			0
$330$		0			0
$331$	18.0948			0.994582			0.497291	−	0.867584i	$-0.334328\pi$
$331$	18.0948			0.994582			0.497291	+	0.867584i	$0.334328\pi$
$332$	−10.8081	+	18.7201i	−0.593170	+	1.02740i
$333$		0			0
$334$	4.37132	+	7.57135i	0.239188	+	0.414286i
$335$	1.90051	−	3.29179i	0.103836	−	0.179850i
$336$		0			0
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	−0.974557	−	0.224139i	$-0.928043\pi$
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	0.293168	−	0.956061i	$-0.405290\pi$
$338$	2.86807	−	4.96765i	0.156003	−	0.270204i
$339$		0			0
$340$	−0.809596	−	1.40226i	−0.0439065	−	0.0760483i
$341$	1.59999	+	2.77127i	0.0866446	+	0.150073i
$342$		0			0
$343$		0			0
$344$	9.28778	−	16.0869i	0.500764	−	0.867348i
$345$		0			0
$346$	−1.92736			−0.103616
$347$	−10.7489			−0.577030			−0.288515	−	0.957475i	$-0.593162\pi$
$347$	−10.7489			−0.577030			−0.288515	+	0.957475i	$0.593162\pi$
$348$		0			0
$349$	1.64301	−	2.84577i	0.0879482	−	0.152331i	−0.818695	−	0.574228i	$-0.805302\pi$
$349$	1.64301	−	2.84577i	0.0879482	−	0.152331i	0.906644	+	0.421897i	$0.138636\pi$
$350$		0			0
$351$		0			0
$352$	−2.23365	−	3.86879i	−0.119054	−	0.206207i
$353$	−8.40960	−	14.5658i	−0.447598	−	0.775262i	0.550631	−	0.834748i	$-0.314387\pi$
$353$	−8.40960	−	14.5658i	−0.447598	−	0.775262i	−0.998229	+	0.0594866i	$0.981054\pi$
$354$		0			0
$355$	9.13051	−	15.8145i	0.484597	−	0.839347i
$356$	2.11144	+	3.65711i	0.111906	+	0.193827i
$357$		0			0
$358$	−1.81864	+	3.14997i	−0.0961180	+	0.166481i
$359$	−11.8921	−	20.5978i	−0.627642	−	1.08711i	−0.988024	−	0.154303i	$-0.950687\pi$
$359$	−11.8921	−	20.5978i	−0.627642	−	1.08711i	0.360382	−	0.932805i	$-0.382646\pi$
$360$		0			0
$361$	5.55680	−	9.62466i	0.292463	−	0.506561i
$362$	−5.58177			−0.293371
$363$		0			0
$364$		0			0
$365$	−3.37968	−	5.85377i	−0.176900	−	0.306401i
$366$		0			0
$367$	−0.344992	−	0.597544i	−0.0180084	−	0.0311915i	0.856881	−	0.515515i	$-0.172399\pi$
$367$	−0.344992	−	0.597544i	−0.0180084	−	0.0311915i	−0.874889	+	0.484323i	$0.839066\pi$
$368$	3.20263	−	5.54712i	0.166949	−	0.289164i
$369$		0			0
$370$	−8.66327			−0.450382
$371$		0			0
$372$		0			0
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	−0.813239	−	0.581929i	$-0.802298\pi$
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	0.910585	+	0.413321i	$0.135631\pi$
$374$	0.110642			0.00572114
$375$		0			0
$376$	18.9376			0.976634
$377$	4.95744			0.255321
$378$		0			0
$379$	32.8735			1.68860			0.844300	−	0.535872i	$-0.180017\pi$
$379$	32.8735			1.68860			0.844300	+	0.535872i	$0.180017\pi$
$380$	18.1898			0.933116
$381$		0			0
$382$	11.8244			0.604991
$383$	0.536335	−	0.928960i	0.0274055	−	0.0474676i	−0.851997	−	0.523546i	$-0.824609\pi$
$383$	0.536335	−	0.928960i	0.0274055	−	0.0474676i	0.879403	+	0.476078i	$0.157942\pi$
$384$		0			0
$385$		0			0
$386$	2.94276			0.149782
$387$		0			0
$388$	9.68640	−	16.7773i	0.491752	−	0.851740i
$389$	−11.8718	−	20.5626i	−0.601925	−	1.04256i	−0.992529	−	0.122006i	$-0.961067\pi$
$389$	−11.8718	−	20.5626i	−0.601925	−	1.04256i	0.390605	−	0.920559i	$-0.372266\pi$
$390$		0			0
$391$	0.309693	+	0.536405i	0.0156619	+	0.0271271i
$392$		0			0
$393$		0			0
$394$	7.67019			0.386419
$395$	−3.32170	+	5.75336i	−0.167133	+	0.289483i
$396$		0			0
$397$	0.0160489	+	0.0277975i	0.000805471	+	0.00139512i	0.866428	−	0.499302i	$-0.166410\pi$
$397$	0.0160489	+	0.0277975i	0.000805471	+	0.00139512i	−0.865622	+	0.500697i	$0.833077\pi$
$398$	−3.84208	+	6.65467i	−0.192586	+	0.333569i
$399$		0			0
$400$	−11.1616	−	19.3324i	−0.558078	−	0.966619i
$401$	12.2628	−	21.2398i	0.612374	−	1.06066i	−0.378465	−	0.925616i	$-0.623548\pi$
$401$	12.2628	−	21.2398i	0.612374	−	1.06066i	0.990839	−	0.135048i	$-0.0431188\pi$
$402$		0			0
$403$	2.14519	+	3.71558i	0.106860	+	0.185086i
$404$	−2.28004	−	3.94914i	−0.113436	−	0.196477i
$405$		0			0
$406$		0			0
$407$	−2.11153	+	3.65728i	−0.104665	+	0.181284i
$408$		0			0
$409$	−26.7897			−1.32467			−0.662333	−	0.749210i	$-0.730433\pi$
$409$	−26.7897			−1.32467			−0.662333	+	0.749210i	$0.730433\pi$
$410$	−8.75574			−0.432415
$411$		0			0
$412$	−8.51759	+	14.7529i	−0.419631	+	0.726823i
$413$		0			0
$414$		0			0
$415$	−22.7520	−	39.4077i	−1.11685	−	1.93445i
$416$	−2.99476	−	5.18708i	−0.146830	−	0.254317i
$417$		0			0
$418$	−0.621466	+	1.07641i	−0.0303969	+	0.0526490i
$419$	−10.5262	−	18.2320i	−0.514240	−	0.890689i	−0.999864	−	0.0165215i	$-0.994741\pi$
$419$	−10.5262	−	18.2320i	−0.514240	−	0.890689i	0.485624	−	0.874168i	$-0.338593\pi$
$420$		0			0
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	−0.988431	−	0.151672i	$-0.951534\pi$
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	0.625568	+	0.780170i	$0.284867\pi$
$422$	0.382760	+	0.662959i	0.0186325	+	0.0322724i
$423$		0			0
$424$	−9.20469	+	15.9430i	−0.447019	+	0.774260i
$425$	2.15864			0.104709
$426$		0			0
$427$		0			0
$428$	−9.56037	−	16.5590i	−0.462118	−	0.800412i
$429$		0			0
$430$	9.13554	+	15.8232i	0.440555	+	0.763064i
$431$	7.95192	−	13.7731i	0.383031	−	0.663428i	−0.608463	−	0.793582i	$-0.708214\pi$
$431$	7.95192	−	13.7731i	0.383031	−	0.663428i	0.991494	+	0.130154i	$0.0415471\pi$
$432$		0			0
$433$	16.3658			0.786490			0.393245	−	0.919434i	$-0.371352\pi$
$433$	16.3658			0.786490			0.393245	+	0.919434i	$0.371352\pi$
$434$		0			0
$435$		0			0
$436$	1.86105	−	3.22344i	0.0891282	−	0.154375i
$437$	−6.95811			−0.332851
$438$		0			0
$439$	15.5447			0.741909			0.370954	−	0.928651i	$-0.379031\pi$
$439$	15.5447			0.741909			0.370954	+	0.928651i	$0.379031\pi$
$440$	6.13543			0.292495
$441$		0			0
$442$	0.148343			0.00705594
$443$	−1.79005			−0.0850480			−0.0425240	−	0.999095i	$-0.513540\pi$
$443$	−1.79005			−0.0850480			−0.0425240	+	0.999095i	$0.513540\pi$
$444$		0			0
$445$	−8.88955			−0.421405
$446$	1.34961	−	2.33759i	0.0639058	−	0.110688i
$447$		0			0
$448$		0			0
$449$	−13.5666			−0.640250			−0.320125	−	0.947375i	$-0.603725\pi$
$449$	−13.5666			−0.640250			−0.320125	+	0.947375i	$0.603725\pi$
$450$		0			0
$451$	−2.13407	+	3.69631i	−0.100489	+	0.174053i
$452$	13.8806	+	24.0419i	0.652890	+	1.13084i
$453$		0			0
$454$	3.98588	+	6.90375i	0.187067	+	0.324009i
$455$		0			0
$456$		0			0
$457$	2.56917			0.120181			0.0600905	−	0.998193i	$-0.480861\pi$
$457$	2.56917			0.120181			0.0600905	+	0.998193i	$0.480861\pi$
$458$	−2.47151	+	4.28078i	−0.115486	+	0.200028i
$459$		0			0
$460$	8.02434	+	13.8986i	0.374137	+	0.648024i
$461$	18.0934	−	31.3388i	0.842695	−	1.45959i	−0.0449122	−	0.998991i	$-0.514301\pi$
$461$	18.0934	−	31.3388i	0.842695	−	1.45959i	0.887608	−	0.460600i	$-0.152366\pi$
$462$		0			0
$463$	8.19224	+	14.1894i	0.380726	+	0.659436i	0.991166	−	0.132626i	$-0.0423409\pi$
$463$	8.19224	+	14.1894i	0.380726	+	0.659436i	−0.610440	+	0.792062i	$0.709008\pi$
$464$	−5.35455	+	9.27436i	−0.248579	+	0.430551i
$465$		0			0
$466$	−4.10105	−	7.10323i	−0.189978	−	0.329051i
$467$	−4.35022	−	7.53480i	−0.201304	−	0.348669i	0.747645	−	0.664099i	$-0.231185\pi$
$467$	−4.35022	−	7.53480i	−0.201304	−	0.348669i	−0.948949	+	0.315430i	$0.897851\pi$
$468$		0			0
$469$		0			0
$470$	−9.31361	+	16.1316i	−0.429605	+	0.744097i
$471$		0			0
$472$	−3.37381			−0.155292
$473$	8.90655			0.409524
$474$		0			0
$475$	−12.1249	+	21.0010i	−0.556330	+	0.963591i
$476$		0			0
$477$		0			0
$478$	5.46047	+	9.45782i	0.249756	+	0.432591i
$479$	8.88370	+	15.3870i	0.405907	+	0.703051i	0.994427	−	0.105432i	$-0.0336224\pi$
$479$	8.88370	+	15.3870i	0.405907	+	0.703051i	−0.588520	+	0.808483i	$0.700289\pi$
$480$		0			0
$481$	−2.83103	+	4.90349i	−0.129084	+	0.223580i
$482$	4.14548	+	7.18018i	0.188821	+	0.327048i
$483$		0			0
$484$	−8.94890	+	15.4999i	−0.406768	+	0.704543i
$485$	20.3908	+	35.3179i	0.925898	+	1.60370i
$486$		0			0
$487$	8.32763	−	14.4239i	0.377361	−	0.653608i	−0.613316	−	0.789837i	$-0.710165\pi$
$487$	8.32763	−	14.4239i	0.377361	−	0.653608i	0.990677	+	0.136229i	$0.0434983\pi$
$488$	20.1123			0.910443
$489$		0			0
$490$		0			0
$491$	3.21021	+	5.56025i	0.144875	+	0.250930i	0.929326	−	0.369260i	$-0.120389\pi$
$491$	3.21021	+	5.56025i	0.144875	+	0.250930i	−0.784451	+	0.620190i	$0.787055\pi$
$492$		0			0
$493$	−0.517784	−	0.896827i	−0.0233198	−	0.0403911i
$494$	−0.833230	+	1.44320i	−0.0374888	+	0.0649325i
$495$		0			0
$496$	−9.26814			−0.416152
$497$		0			0
$498$		0			0
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	−0.963382	−	0.268134i	$-0.913593\pi$
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	0.713902	+	0.700246i	$0.246926\pi$
$500$	23.5456			1.05299
$501$		0			0
$502$	−4.23025			−0.188805
$503$	−17.7223			−0.790200			−0.395100	−	0.918638i	$-0.629290\pi$
$503$	−17.7223			−0.790200			−0.395100	+	0.918638i	$0.629290\pi$
$504$		0			0
$505$	9.59939			0.427167
$506$	−1.09663			−0.0487511
$507$		0			0
$508$	2.22678			0.0987976
$509$	−15.5411	+	26.9180i	−0.688848	+	1.19312i	0.283362	+	0.959013i	$0.408550\pi$
$509$	−15.5411	+	26.9180i	−0.688848	+	1.19312i	−0.972211	+	0.234107i	$0.924783\pi$
$510$		0			0
$511$		0			0
$512$	22.5634			0.997169
$513$		0			0
$514$	4.24456	−	7.35180i	0.187220	−	0.324274i
$515$	−17.9303	−	31.0563i	−0.790105	−	1.36850i
$516$		0			0
$517$	4.54008	+	7.86365i	0.199672	+	0.345843i
$518$		0			0
$519$		0			0
$520$	8.22608			0.360737
$521$	−2.37986	+	4.12203i	−0.104263	+	0.180590i	−0.913437	−	0.406980i	$-0.866582\pi$
$521$	−2.37986	+	4.12203i	−0.104263	+	0.180590i	0.809174	+	0.587570i	$0.199915\pi$
$522$		0			0
$523$	−20.1258	−	34.8588i	−0.880038	−	1.52427i	−0.851298	−	0.524683i	$-0.824184\pi$
$523$	−20.1258	−	34.8588i	−0.880038	−	1.52427i	−0.0287402	−	0.999587i	$-0.509150\pi$
$524$	−13.1812	+	22.8305i	−0.575823	+	0.997355i
$525$		0			0
$526$	5.09571	+	8.82602i	0.222183	+	0.384833i
$527$	0.448113	−	0.776154i	0.0195201	−	0.0338098i
$528$		0			0
$529$	8.43046	+	14.6020i	0.366542	+	0.634869i
$530$	−9.05381	−	15.6817i	−0.393272	−	0.681168i
$531$		0			0
$532$		0			0
$533$	−2.86125	+	4.95583i	−0.123935	+	0.214661i
$534$		0			0
$535$	40.2510			1.74020
$536$	−1.91622			−0.0827680
$537$		0			0
$538$	4.92033	−	8.52227i	0.212131	−	0.367421i
$539$		0			0
$540$		0			0
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	0.999775	+	0.0212301i	$0.00675826\pi$
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	−0.481502	+	0.876445i	$0.659908\pi$
$542$	−2.63830	−	4.56966i	−0.113325	−	0.196284i
$543$		0			0
$544$	−0.625580	+	1.08354i	−0.0268215	+	0.0464563i
$545$	3.91769	+	6.78564i	0.167815	+	0.290665i
$546$		0			0
$547$	−6.17751	+	10.6998i	−0.264131	+	0.457489i	−0.967336	−	0.253499i	$-0.918419\pi$
$547$	−6.17751	+	10.6998i	−0.264131	+	0.457489i	0.703204	+	0.710988i	$0.251752\pi$
$548$	0.428436	+	0.742073i	0.0183019	+	0.0316998i
$549$		0			0
$550$	−1.91094	+	3.30985i	−0.0814828	+	0.141132i
$551$	11.6334			0.495600
$552$		0			0
$553$		0			0
$554$	6.16893	+	10.6849i	0.262093	+	0.453958i
$555$		0			0
$556$	−8.65633	−	14.9932i	−0.367110	−	0.635853i
$557$	−4.03845	+	6.99479i	−0.171114	+	0.296379i	−0.938810	−	0.344436i	$-0.888070\pi$
$557$	−4.03845	+	6.99479i	−0.171114	+	0.296379i	0.767695	+	0.640815i	$0.221403\pi$
$558$		0			0
$559$	11.9415			0.505070
$560$		0			0
$561$		0			0
$562$	3.39041	−	5.87237i	0.143016	−	0.247711i
$563$	45.2127			1.90549			0.952744	−	0.303774i	$-0.0982467\pi$
$563$	45.2127			1.90549			0.952744	+	0.303774i	$0.0982467\pi$
$564$		0			0
$565$	−58.4401			−2.45859
$566$	−3.13477			−0.131764
$567$		0			0
$568$	−9.20596			−0.386274
$569$	−22.4299			−0.940309			−0.470155	−	0.882584i	$-0.655802\pi$
$569$	−22.4299			−0.940309			−0.470155	+	0.882584i	$0.655802\pi$
$570$		0			0
$571$	−21.8269			−0.913426			−0.456713	−	0.889614i	$-0.650973\pi$
$571$	−21.8269			−0.913426			−0.456713	+	0.889614i	$0.650973\pi$
$572$	0.936826	−	1.62263i	0.0391706	−	0.0678455i
$573$		0			0
$574$		0			0
$575$	−21.3954			−0.892251
$576$		0			0
$577$	16.1022	−	27.8898i	0.670342	−	1.16107i	−0.307465	−	0.951559i	$-0.599481\pi$
$577$	16.1022	−	27.8898i	0.670342	−	1.16107i	0.977807	−	0.209508i	$-0.0671861\pi$
$578$	4.19939	+	7.27355i	0.174671	+	0.302540i
$579$		0			0
$580$	−13.4161	−	23.2373i	−0.557072	−	0.964878i
$581$		0			0
$582$		0			0
$583$	−8.82687			−0.365571
$584$	−1.70380	+	2.95107i	−0.0705039	+	0.122116i
$585$		0			0
$586$	−0.652105	−	1.12948i	−0.0269382	−	0.0466584i
$587$	−9.72304	+	16.8408i	−0.401313	+	0.695094i	−0.993885	−	0.110424i	$-0.964779\pi$
$587$	−9.72304	+	16.8408i	−0.401313	+	0.695094i	0.592572	+	0.805518i	$0.298113\pi$
$588$		0			0
$589$	5.03404	+	8.71921i	0.207424	+	0.359269i
$590$	1.65926	−	2.87392i	0.0683105	−	0.118317i
$591$		0			0
$592$	−6.11563	−	10.5926i	−0.251351	−	0.435352i
$593$	−14.4202	−	24.9766i	−0.592168	−	1.02566i	−0.993940	−	0.109925i	$-0.964939\pi$
$593$	−14.4202	−	24.9766i	−0.592168	−	1.02566i	0.401772	−	0.915740i	$-0.368394\pi$
$594$		0			0
$595$		0			0
$596$	−18.4392	+	31.9377i	−0.755300	+	1.30822i
$597$		0			0
$598$	−1.47030			−0.0601252
$599$	46.9989			1.92032			0.960161	−	0.279447i	$-0.0901511\pi$
$599$	46.9989			1.92032			0.960161	+	0.279447i	$0.0901511\pi$
$600$		0			0
$601$	7.80843	−	13.5246i	0.318512	−	0.551680i	−0.661665	−	0.749799i	$-0.730150\pi$
$601$	7.80843	−	13.5246i	0.318512	−	0.551680i	0.980178	+	0.198119i	$0.0634834\pi$
$602$		0			0
$603$		0			0
$604$	1.31417	+	2.27620i	0.0534727	+	0.0926174i
$605$	−18.8383	−	32.6289i	−0.765885	−	1.32655i
$606$		0			0
$607$	−14.3266	+	24.8144i	−0.581500	+	1.00719i	0.413802	+	0.910367i	$0.364200\pi$
$607$	−14.3266	+	24.8144i	−0.581500	+	1.00719i	−0.995302	+	0.0968200i	$0.969133\pi$
$608$	−7.02769	−	12.1723i	−0.285010	−	0.493652i
$609$		0			0
$610$	−9.89134	+	17.1323i	−0.400489	+	0.693667i
$611$	6.08711	+	10.5432i	0.246258	+	0.426531i
$612$		0			0
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	−0.401220	−	0.915982i	$-0.631414\pi$
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	0.993873	−	0.110524i	$-0.0352529\pi$
$614$	1.38593			0.0559316
$615$		0			0
$616$		0			0
$617$	−2.06401	−	3.57497i	−0.0830938	−	0.143923i	0.821484	−	0.570232i	$-0.193147\pi$
$617$	−2.06401	−	3.57497i	−0.0830938	−	0.143923i	−0.904577	+	0.426310i	$0.859813\pi$
$618$		0			0
$619$	11.3565	+	19.6700i	0.456456	+	0.790605i	0.998771	−	0.0495708i	$-0.0157853\pi$
$619$	11.3565	+	19.6700i	0.456456	+	0.790605i	−0.542315	+	0.840175i	$0.682452\pi$
$620$	11.6109	−	20.1106i	0.466304	−	0.807662i
$621$		0			0
$622$	−7.48774			−0.300231
$623$		0			0
$624$		0			0
$625$	−3.19498	+	5.53387i	−0.127799	+	0.221355i
$626$	12.6340			0.504955
$627$		0			0
$628$	−29.2580			−1.16752
$629$	1.18276			0.0471597
$630$		0			0
$631$	−38.6411			−1.53828			−0.769138	−	0.639082i	$-0.779314\pi$
$631$	−38.6411			−1.53828			−0.769138	+	0.639082i	$0.779314\pi$
$632$	3.34915			0.133222
$633$		0			0
$634$	−16.1261			−0.640449
$635$	−2.34380	+	4.05958i	−0.0930107	+	0.161099i
$636$		0			0
$637$		0			0
$638$	1.83348			0.0725881
$639$		0			0
$640$	−20.9427	+	36.2737i	−0.827831	+	1.43385i
$641$	−14.2363	−	24.6580i	−0.562301	−	0.973933i	−0.997295	−	0.0735002i	$-0.976583\pi$
$641$	−14.2363	−	24.6580i	−0.562301	−	0.973933i	0.434995	−	0.900433i	$-0.356750\pi$
$642$		0			0
$643$	8.52125	+	14.7592i	0.336045	+	0.582048i	0.983685	−	0.179899i	$-0.0575771\pi$
$643$	8.52125	+	14.7592i	0.336045	+	0.582048i	−0.647640	+	0.761947i	$0.724244\pi$
$644$		0			0
$645$		0			0
$646$	0.348110			0.0136962
$647$	1.68809	−	2.92386i	0.0663657	−	0.114949i	−0.830933	−	0.556372i	$-0.812193\pi$
$647$	1.68809	−	2.92386i	0.0663657	−	0.114949i	0.897299	+	0.441423i	$0.145526\pi$
$648$		0			0
$649$	−0.808833	−	1.40094i	−0.0317495	−	0.0549917i
$650$	−2.56209	+	4.43768i	−0.100494	+	0.174060i
$651$		0			0
$652$	5.86110	+	10.1517i	0.229538	+	0.397572i
$653$	−9.17255	+	15.8873i	−0.358950	+	0.621719i	−0.987786	−	0.155819i	$-0.950198\pi$
$653$	−9.17255	+	15.8873i	−0.358950	+	0.621719i	0.628836	+	0.777538i	$0.283532\pi$
$654$		0			0
$655$	−27.7477	−	48.0604i	−1.08419	−	1.87787i
$656$	−6.18090	−	10.7056i	−0.241324	−	0.417985i
$657$		0			0
$658$		0			0
$659$	13.9248	−	24.1184i	0.542432	−	0.939519i	−0.456332	−	0.889810i	$-0.650837\pi$
$659$	13.9248	−	24.1184i	0.542432	−	0.939519i	0.998764	−	0.0497098i	$-0.0158297\pi$
$660$		0			0
$661$	−39.0141			−1.51747			−0.758737	−	0.651397i	$-0.774183\pi$
$661$	−39.0141			−1.51747			−0.758737	+	0.651397i	$0.774183\pi$
$662$	8.97265			0.348732
$663$		0			0
$664$	−11.4700	+	19.8667i	−0.445123	+	0.770976i
$665$		0			0
$666$		0			0
$667$	5.13203	+	8.88894i	0.198713	+	0.344181i
$668$	−15.4634	−	26.7834i	−0.598296	−	1.03628i
$669$		0			0
$670$	0.942405	−	1.63229i	0.0364083	−	0.0630610i
$671$	4.82170	+	8.35143i	0.186140	+	0.322404i
$672$		0			0
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.201014	−	0.979588i	$-0.435576\pi$
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.747841	−	0.663878i	$-0.231090\pi$
$674$	−6.20264	−	10.7433i	−0.238917	−	0.413816i
$675$		0			0
$676$	−10.1457	+	17.5729i	−0.390219	+	0.675879i
$677$	−23.3915			−0.899010			−0.449505	−	0.893278i	$-0.648400\pi$
$677$	−23.3915			−0.899010			−0.449505	+	0.893278i	$0.648400\pi$
$678$		0			0
$679$		0			0
$680$	−0.859180	−	1.48814i	−0.0329480	−	0.0570677i
$681$		0			0
$682$	0.793387	+	1.37419i	0.0303803	+	0.0526203i
$683$	15.1632	−	26.2634i	0.580204	−	1.00494i	−0.415251	−	0.909707i	$-0.636306\pi$
$683$	15.1632	−	26.2634i	0.580204	−	1.00494i	0.995455	−	0.0952356i	$-0.0303604\pi$
$684$		0			0
$685$	−1.80380			−0.0689196
$686$		0			0
$687$		0			0
$688$	−12.8980	+	22.3401i	−0.491733	+	0.851707i
$689$	−11.8346			−0.450863
$690$		0			0
$691$	4.11330			0.156477			0.0782387	−	0.996935i	$-0.475070\pi$
$691$	4.11330			0.156477			0.0782387	+	0.996935i	$0.475070\pi$
$692$	6.81797			0.259180
$693$		0			0
$694$	−5.33003			−0.202325
$695$	36.4448			1.38243
$696$		0			0
$697$	1.19538			0.0452784
$698$	0.814716	−	1.41113i	0.0308375	−	0.0534120i
$699$		0			0
$700$		0			0
$701$	−29.1835			−1.10225			−0.551123	−	0.834424i	$-0.685800\pi$
$701$	−29.1835			−1.10225			−0.551123	+	0.834424i	$0.685800\pi$
$702$		0			0
$703$	−6.64347	+	11.5068i	−0.250563	+	0.433988i
$704$	1.19983	+	2.07816i	0.0452202	+	0.0783236i
$705$		0			0
$706$	−4.17005	−	7.22274i	−0.156942	−	0.271831i
$707$		0			0
$708$		0			0
$709$	−42.4617			−1.59468			−0.797342	−	0.603528i	$-0.793761\pi$
$709$	−42.4617			−1.59468			−0.797342	+	0.603528i	$0.793761\pi$
$710$	4.52753	−	7.84192i	0.169915	−	0.294302i
$711$		0			0
$712$	2.24075	+	3.88109i	0.0839757	+	0.145450i
$713$	−4.44149	+	7.69288i	−0.166335	+	0.288101i
$714$		0			0
$715$	1.97211	+	3.41579i	0.0737526	+	0.127743i
$716$	6.43336	−	11.1429i	0.240426	−	0.416430i
$717$		0			0
$718$	−5.89692	−	10.2138i	−0.220071	−	0.381175i
$719$	−5.57126	−	9.64970i	−0.207773	−	0.359873i	0.743240	−	0.669025i	$-0.233288\pi$
$719$	−5.57126	−	9.64970i	−0.207773	−	0.359873i	−0.951013	+	0.309152i	$0.899955\pi$
$720$		0			0
$721$		0			0
$722$	2.75544	−	4.77256i	0.102547	−	0.177616i
$723$		0			0
$724$	19.7453			0.733828
$725$	35.7715			1.32852
$726$		0			0
$727$	14.3410	−	24.8393i	0.531878	−	0.921239i	−0.467430	−	0.884030i	$-0.654820\pi$
$727$	14.3410	−	24.8393i	0.531878	−	0.921239i	0.999308	−	0.0372089i	$-0.0118467\pi$
$728$		0			0
$729$		0			0
$730$	−1.67588	−	2.90270i	−0.0620269	−	0.107434i
$731$	−1.24724	−	2.16028i	−0.0461307	−	0.0799007i
$732$		0			0
$733$	−12.5264	+	21.6964i	−0.462674	+	0.801375i	−0.999093	−	0.0425768i	$-0.986443\pi$
$733$	−12.5264	+	21.6964i	−0.462674	+	0.801375i	0.536419	+	0.843952i	$0.319777\pi$
$734$	−0.171071	−	0.296303i	−0.00631433	−	0.0109367i
$735$		0			0
$736$	6.20047	−	10.7395i	0.228552	−	0.395864i
$737$	−0.459391	−	0.795689i	−0.0169219	−	0.0293096i
$738$		0			0
$739$	13.7608	−	23.8344i	0.506198	−	0.876761i	−0.493776	−	0.869589i	$-0.664384\pi$
$739$	13.7608	−	23.8344i	0.506198	−	0.876761i	0.999974	−	0.00717223i	$-0.00228301\pi$
$740$	30.6460			1.12657
$741$		0			0
$742$		0			0
$743$	7.00608	+	12.1349i	0.257028	+	0.445186i	0.965444	−	0.260609i	$-0.0839233\pi$
$743$	7.00608	+	12.1349i	0.257028	+	0.445186i	−0.708416	+	0.705795i	$0.750590\pi$
$744$		0			0
$745$	−38.8163	−	67.2318i	−1.42212	−	2.46318i
$746$	0.932261	−	1.61472i	0.0341325	−	0.0591192i
$747$		0			0
$748$	−0.391390			−0.0143106
$749$		0			0
$750$		0			0
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.215692	−	0.976461i	$-0.430799\pi$
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.737795	−	0.675025i	$-0.235867\pi$
$752$	−26.2989			−0.959021
$753$		0			0
$754$	2.45824			0.0895237
$755$	−5.53289			−0.201363
$756$		0			0
$757$	−43.3447			−1.57539			−0.787694	−	0.616066i	$-0.788725\pi$
$757$	−43.3447			−1.57539			−0.787694	+	0.616066i	$0.788725\pi$
$758$	16.3009			0.592077
$759$		0			0
$760$	19.3038			0.700223
$761$	8.62550	−	14.9398i	0.312674	−	0.541568i	−0.666266	−	0.745714i	$-0.732109\pi$
$761$	8.62550	−	14.9398i	0.312674	−	0.541568i	0.978940	+	0.204146i	$0.0654419\pi$
$762$		0			0
$763$		0			0
$764$	−41.8285			−1.51330
$765$		0			0
$766$	0.265952	−	0.460642i	0.00960922	−	0.0166437i
$767$	−1.08444	−	1.87831i	−0.0391570	−	0.0678218i
$768$		0			0
$769$	10.6727	+	18.4856i	0.384867	+	0.666609i	0.991751	−	0.128182i	$-0.0409141\pi$
$769$	10.6727	+	18.4856i	0.384867	+	0.666609i	−0.606884	+	0.794790i	$0.707581\pi$
$770$		0			0
$771$		0			0
$772$	−10.4099			−0.374660
$773$	−6.57357	+	11.3858i	−0.236435	+	0.409517i	−0.959689	−	0.281065i	$-0.909312\pi$
$773$	−6.57357	+	11.3858i	−0.236435	+	0.409517i	0.723254	+	0.690582i	$0.242646\pi$
$774$		0			0
$775$	15.4791	+	26.8106i	0.556027	+	0.963066i
$776$	10.2796	−	17.8049i	0.369018	−	0.639158i
$777$		0			0
$778$	−5.88685	−	10.1963i	−0.211054	−	0.365556i
$779$	−6.71439	+	11.6297i	−0.240568	+	0.416676i
$780$		0			0
$781$	−2.20702	−	3.82268i	−0.0789735	−	0.136786i
$782$	0.153567	+	0.265986i	0.00549155	+	0.00951164i
$783$		0			0
$784$		0			0
$785$	30.7954	−	53.3393i	1.09914	−	1.90376i
$786$		0			0
$787$	28.1301			1.00273			0.501364	−	0.865236i	$-0.332832\pi$
$787$	28.1301			1.00273			0.501364	+	0.865236i	$0.332832\pi$
$788$	−27.1330			−0.966573
$789$		0			0
$790$	−1.64713	+	2.85291i	−0.0586021	+	0.101502i
$791$		0			0
$792$		0			0
$793$	6.46470	+	11.1972i	0.229568	+	0.397624i
$794$	0.00795814	+	0.0137839i	0.000282424	+	0.000489172i
$795$		0			0
$796$	13.5912	−	23.5406i	0.481727	−	0.834376i
$797$	12.8683	+	22.2885i	0.455817	+	0.789499i	0.998735	−	0.0502873i	$-0.0160137\pi$
$797$	12.8683	+	22.2885i	0.455817	+	0.789499i	−0.542917	+	0.839786i	$0.682680\pi$
$798$		0			0
$799$	1.27155	−	2.20238i	0.0449841	−	0.0779147i
$800$	−21.6094	−	37.4285i	−0.764007	−	1.32330i
$801$		0			0
$802$	6.08073	−	10.5321i	0.214718	−	0.371902i
$803$	−1.63387			−0.0576580
$804$		0			0
$805$		0			0
$806$	1.06373	+	1.84244i	0.0374684	+	0.0648972i
$807$		0			0
$808$	−2.41968	−	4.19100i	−0.0851240	−	0.147439i
$809$	−15.9353	+	27.6007i	−0.560254	+	0.970388i	0.437220	+	0.899355i	$0.355963\pi$
$809$	−15.9353	+	27.6007i	−0.560254	+	0.970388i	−0.997474	+	0.0710338i	$0.977370\pi$
$810$		0			0
$811$	−43.3860			−1.52349			−0.761744	−	0.647878i	$-0.775657\pi$
$811$	−43.3860			−1.52349			−0.761744	+	0.647878i	$0.775657\pi$
$812$		0			0
$813$		0			0
$814$	−1.04704	+	1.81353i	−0.0366987	+	0.0635641i
$815$	−24.6764			−0.864375
$816$		0			0
$817$	28.0226			0.980385
$818$	−13.2842			−0.464470
$819$		0			0
$820$	30.9731			1.08163
$821$	16.3935			0.572139			0.286069	−	0.958209i	$-0.407651\pi$
$821$	16.3935			0.572139			0.286069	+	0.958209i	$0.407651\pi$
$822$		0			0
$823$	−26.3780			−0.919478			−0.459739	−	0.888054i	$-0.652057\pi$
$823$	−26.3780			−0.919478			−0.459739	+	0.888054i	$0.652057\pi$
$824$	−9.03925	+	15.6564i	−0.314897	+	0.545418i
$825$		0			0
$826$		0			0
$827$	−36.7225			−1.27697			−0.638484	−	0.769635i	$-0.720438\pi$
$827$	−36.7225			−1.27697			−0.638484	+	0.769635i	$0.720438\pi$
$828$		0			0
$829$	−12.1579	+	21.0581i	−0.422261	+	0.731377i	−0.996160	−	0.0875485i	$-0.972097\pi$
$829$	−12.1579	+	21.0581i	−0.422261	+	0.731377i	0.573899	+	0.818926i	$0.305430\pi$
$830$	−11.2820	−	19.5410i	−0.391604	−	0.678279i
$831$		0			0
$832$	1.60867	+	2.78629i	0.0557705	+	0.0965974i
$833$		0			0
$834$		0			0
$835$	65.1038			2.25301
$836$	2.19841	−	3.80776i	0.0760337	−	0.131694i
$837$		0			0
$838$	−5.21962	−	9.04065i	−0.180309	−	0.312304i
$839$	−12.8405	+	22.2404i	−0.443303	+	0.767824i	−0.997932	−	0.0642741i	$-0.979527\pi$
$839$	−12.8405	+	22.2404i	−0.443303	+	0.767824i	0.554629	+	0.832098i	$0.312860\pi$
$840$		0			0
$841$	5.91963	+	10.2531i	0.204125	+	0.353555i
$842$	−3.69190	+	6.39456i	−0.127231	+	0.220371i
$843$		0			0
$844$	−1.35400	−	2.34519i	−0.0466065	−	0.0807249i
$845$	−21.3577	−	36.9926i	−0.734726	−	1.27258i
$846$		0			0
$847$		0			0
$848$	12.7826	−	22.1402i	0.438958	−	0.760297i
$849$		0			0
$850$	1.07040			0.0367144
$851$	−11.7230			−0.401858
$852$		0			0
$853$	−14.4872	+	25.0925i	−0.496031	+	0.859150i	−0.999990	−	0.00457743i	$-0.998543\pi$
$853$	−14.4872	+	25.0925i	−0.496031	+	0.859150i	0.503959	+	0.863728i	$0.331876\pi$
$854$		0			0
$855$		0			0
$856$	−10.1459	−	17.5732i	−0.346780	−	0.600640i
$857$	12.6934	+	21.9856i	0.433598	+	0.751015i	0.997180	−	0.0750458i	$-0.0239103\pi$
$857$	12.6934	+	21.9856i	0.433598	+	0.751015i	−0.563582	+	0.826060i	$0.690577\pi$
$858$		0			0
$859$	−2.97891	+	5.15963i	−0.101639	+	0.176044i	−0.912360	−	0.409388i	$-0.865742\pi$
$859$	−2.97891	+	5.15963i	−0.101639	+	0.176044i	0.810721	+	0.585433i	$0.199075\pi$
$860$	−32.3166	−	55.9740i	−1.10199	−	1.90870i
$861$		0			0
$862$	3.94310	−	6.82966i	0.134303	−	0.232619i
$863$	−8.19545	−	14.1949i	−0.278977	−	0.483201i	0.692154	−	0.721750i	$-0.256662\pi$
$863$	−8.19545	−	14.1949i	−0.278977	−	0.483201i	−0.971131	+	0.238548i	$0.923328\pi$
$864$		0			0
$865$	−7.17624	+	12.4296i	−0.244000	+	0.422620i
$866$	8.11528			0.275768
$867$		0			0
$868$		0			0
$869$	0.802920	+	1.39070i	0.0272372	+	0.0471762i
$870$		0			0
$871$	−0.615929	−	1.06682i	−0.0208700	−	0.0361478i
$872$	1.97503	−	3.42086i	0.0668830	−	0.115845i
$873$		0			0
$874$	−3.45030			−0.116708
$875$		0			0
$876$		0			0
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	0.398295	+	0.917257i	$0.369602\pi$
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	−0.993516	+	0.113695i	$0.963731\pi$
$878$	7.70813			0.260137
$879$		0			0
$880$	−8.52033			−0.287220
$881$	26.2582			0.884661			0.442331	−	0.896852i	$-0.354152\pi$
$881$	26.2582			0.884661			0.442331	+	0.896852i	$0.354152\pi$
$882$		0			0
$883$	10.0087			0.336821			0.168410	−	0.985717i	$-0.446137\pi$
$883$	10.0087			0.336821			0.168410	+	0.985717i	$0.446137\pi$
$884$	−0.524756			−0.0176495
$885$		0			0
$886$	−0.887631			−0.0298205
$887$	7.95282	−	13.7747i	0.267030	−	0.462509i	−0.701064	−	0.713099i	$-0.747291\pi$
$887$	7.95282	−	13.7747i	0.267030	−	0.462509i	0.968093	+	0.250590i	$0.0806245\pi$
$888$		0			0
$889$		0			0
$890$	−4.40804			−0.147758
$891$		0			0
$892$	−4.77419	+	8.26914i	−0.159852	+	0.276871i
$893$	14.2844	+	24.7413i	0.478009	+	0.827935i
$894$		0			0
$895$	13.5428	+	23.4569i	0.452687	+	0.784077i
$896$		0			0
$897$		0			0
$898$	−6.72727			−0.224492
$899$	7.42583	−	12.8619i	0.247665	−	0.428969i
$900$		0			0
$901$	1.23608	+	2.14095i	0.0411797	+	0.0713253i
$902$	−1.05822	+	1.83288i	−0.0352348	+	0.0610284i
$903$		0			0
$904$	14.7307	+	25.5144i	0.489937	+	0.848597i
$905$	−20.7829	+	35.9970i	−0.690846	+	1.19658i
$906$		0			0
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	0.972311	−	0.233691i	$-0.0750804\pi$
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	−0.688538	+	0.725201i	$0.741747\pi$
$908$	−14.0999	−	24.4217i	−0.467922	−	0.810464i
$909$		0			0
$910$		0			0
$911$	−14.9435	+	25.8829i	−0.495099	+	0.857537i	−0.999984	−	0.00564955i	$-0.998202\pi$
$911$	−14.9435	+	25.8829i	−0.495099	+	0.857537i	0.504885	+	0.863187i	$0.331535\pi$
$912$		0			0
$913$	−10.9992			−0.364021
$914$	1.27397			0.0421393
$915$		0			0
$916$	8.74286	−	15.1431i	0.288872	−	0.500341i
$917$		0			0
$918$		0			0
$919$	11.8283	+	20.4873i	0.390181	+	0.675813i	0.992473	−	0.122462i	$-0.0390791\pi$
$919$	11.8283	+	20.4873i	0.390181	+	0.675813i	−0.602292	+	0.798276i	$0.705746\pi$
$920$	8.51579	+	14.7498i	0.280757	+	0.486286i
$921$		0			0
$922$	8.97196	−	15.5399i	0.295476	−	0.511779i
$923$	−2.95907	−	5.12525i	−0.0973989	−	0.168700i
$924$		0			0
$925$	−20.4280	+	35.3823i	−0.671667	+	1.16336i
$926$	4.06227	+	7.03606i	0.133495	+	0.231219i
$927$		0			0
$928$	−10.3667	+	17.9557i	−0.340304	+	0.589423i
$929$	12.6176			0.413970			0.206985	−	0.978344i	$-0.433635\pi$
$929$	12.6176			0.413970			0.206985	+	0.978344i	$0.433635\pi$
$930$		0			0
$931$		0			0
$932$	14.5073	+	25.1274i	0.475203	+	0.823075i
$933$		0			0
$934$	−2.15714	−	3.73627i	−0.0705836	−	0.122254i
$935$	0.411957	−	0.713530i	0.0134724	−	0.0233349i
$936$		0			0
$937$	26.3440			0.860622			0.430311	−	0.902681i	$-0.358404\pi$
$937$	26.3440			0.860622			0.430311	+	0.902681i	$0.358404\pi$
$938$		0			0
$939$		0			0
$940$	32.9465	−	57.0651i	1.07460	−	1.86126i
$941$	50.9397			1.66059			0.830294	−	0.557326i	$-0.188173\pi$
$941$	50.9397			1.66059			0.830294	+	0.557326i	$0.188173\pi$
$942$		0			0
$943$	−11.8481			−0.385827
$944$	4.68525			0.152492
$945$		0			0
$946$	4.41648			0.143592
$947$	−27.6798			−0.899474			−0.449737	−	0.893161i	$-0.648482\pi$
$947$	−27.6798			−0.899474			−0.449737	+	0.893161i	$0.648482\pi$
$948$		0			0
$949$	−2.19061			−0.0711102
$950$	−6.01236	+	10.4137i	−0.195067	+	0.337866i
$951$		0			0
$952$		0			0
$953$	27.4017			0.887628			0.443814	−	0.896119i	$-0.353625\pi$
$953$	27.4017			0.887628			0.443814	+	0.896119i	$0.353625\pi$
$954$		0			0
$955$	44.0265	−	76.2561i	1.42466	−	2.46759i
$956$	−19.3162	−	33.4567i	−0.624731	−	1.08207i
$957$		0			0
$958$	4.40515	+	7.62994i	0.142324	+	0.246512i
$959$		0			0
$960$		0			0
$961$	−18.1467			−0.585378
$962$	−1.40382	+	2.43149i	−0.0452610	+	0.0783943i
$963$		0			0
$964$	−14.6645	−	25.3996i	−0.472310	−	0.818066i
$965$	10.9569	−	18.9779i	0.352715	−	0.610921i
$966$		0			0
$967$	9.09069	+	15.7455i	0.292337	+	0.506342i	0.974362	−	0.224986i	$-0.0722338\pi$
$967$	9.09069	+	15.7455i	0.292337	+	0.506342i	−0.682025	+	0.731329i	$0.738900\pi$
$968$	−9.49698	+	16.4492i	−0.305244	+	0.528699i
$969$		0			0
$970$	10.1111	+	17.5130i	0.324649	+	0.562309i
$971$	19.7416	+	34.1935i	0.633538	+	1.09732i	0.986823	+	0.161804i	$0.0517313\pi$
$971$	19.7416	+	34.1935i	0.633538	+	1.09732i	−0.353285	+	0.935516i	$0.614935\pi$
$972$		0			0
$973$		0			0
$974$	4.12941	−	7.15234i	0.132315	−	0.229176i
$975$		0			0
$976$	−27.9302			−0.894024
$977$	−11.9156			−0.381215			−0.190608	−	0.981666i	$-0.561046\pi$
$977$	−11.9156			−0.381215			−0.190608	+	0.981666i	$0.561046\pi$
$978$		0			0
$979$	−1.07439	+	1.86090i	−0.0343376	+	0.0594745i
$980$		0			0
$981$		0			0
$982$	1.59184	+	2.75715i	0.0507977	+	0.0879842i
$983$	9.23896	+	16.0024i	0.294677	+	0.510396i	0.974910	−	0.222601i	$-0.0714546\pi$
$983$	9.23896	+	16.0024i	0.294677	+	0.510396i	−0.680233	+	0.732996i	$0.738121\pi$
$984$		0			0
$985$	28.5588	−	49.4653i	0.909959	−	1.57609i
$986$	−0.256752	−	0.444708i	−0.00817666	−	0.0141624i
$987$		0			0
$988$	2.94752	−	5.10525i	0.0937731	−	0.162420i
$989$	12.3620	+	21.4117i	0.393090	+	0.680851i
$990$		0			0
$991$	−6.34850	+	10.9959i	−0.201667	+	0.349297i	−0.949066	−	0.315079i	$-0.897969\pi$
$991$	−6.34850	+	10.9959i	−0.201667	+	0.349297i	0.747399	+	0.664376i	$0.231302\pi$
$992$	−17.9436			−0.569710
$993$		0			0
$994$		0			0
$995$	28.6108	+	49.5553i	0.907023	+	1.57101i
$996$		0			0
$997$	20.9767	+	36.3327i	0.664338	+	1.15067i	0.979464	+	0.201617i	$0.0646197\pi$
$997$	20.9767	+	36.3327i	0.664338	+	1.15067i	−0.315127	+	0.949050i	$0.602047\pi$
$998$	−2.76345	+	4.78644i	−0.0874755	+	0.151512i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.f.802.3		10
3.2	odd	2		441.2.h.f.214.3		10
7.2	even	3		1323.2.g.f.667.3		10
7.3	odd	6		1323.2.f.e.883.3		10
7.4	even	3		1323.2.f.f.883.3		10
7.5	odd	6		189.2.g.b.100.3		10
7.6	odd	2		189.2.h.b.46.3		10
9.4	even	3		1323.2.g.f.361.3		10
9.5	odd	6		441.2.g.f.67.3		10
21.2	odd	6		441.2.g.f.79.3		10
21.5	even	6		63.2.g.b.16.3	yes	10
21.11	odd	6		441.2.f.f.295.3		10
21.17	even	6		441.2.f.e.295.3		10
21.20	even	2		63.2.h.b.25.3	yes	10
28.19	even	6		3024.2.t.i.289.5		10
28.27	even	2		3024.2.q.i.2881.1		10
63.4	even	3		1323.2.f.f.442.3		10
63.5	even	6		63.2.h.b.58.3	yes	10
63.11	odd	6		3969.2.a.ba.1.3		5
63.13	odd	6		189.2.g.b.172.3		10
63.20	even	6		567.2.e.f.487.3		10
63.23	odd	6		441.2.h.f.373.3		10
63.25	even	3		3969.2.a.bb.1.3		5
63.31	odd	6		1323.2.f.e.442.3		10
63.32	odd	6		441.2.f.f.148.3		10
63.34	odd	6		567.2.e.e.487.3		10
63.38	even	6		3969.2.a.z.1.3		5
63.40	odd	6		189.2.h.b.37.3		10
63.41	even	6		63.2.g.b.4.3	✓	10
63.47	even	6		567.2.e.f.163.3		10
63.52	odd	6		3969.2.a.bc.1.3		5
63.58	even	3	inner	1323.2.h.f.226.3		10
63.59	even	6		441.2.f.e.148.3		10
63.61	odd	6		567.2.e.e.163.3		10
84.47	odd	6		1008.2.t.i.961.1		10
84.83	odd	2		1008.2.q.i.529.3		10
252.103	even	6		3024.2.q.i.2305.1		10
252.131	odd	6		1008.2.q.i.625.3		10
252.139	even	6		3024.2.t.i.1873.5		10
252.167	odd	6		1008.2.t.i.193.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	63.41	even	6
63.2.g.b.16.3	yes	10	21.5	even	6
63.2.h.b.25.3	yes	10	21.20	even	2
63.2.h.b.58.3	yes	10	63.5	even	6
189.2.g.b.100.3		10	7.5	odd	6
189.2.g.b.172.3		10	63.13	odd	6
189.2.h.b.37.3		10	63.40	odd	6
189.2.h.b.46.3		10	7.6	odd	2
441.2.f.e.148.3		10	63.59	even	6
441.2.f.e.295.3		10	21.17	even	6
441.2.f.f.148.3		10	63.32	odd	6
441.2.f.f.295.3		10	21.11	odd	6
441.2.g.f.67.3		10	9.5	odd	6
441.2.g.f.79.3		10	21.2	odd	6
441.2.h.f.214.3		10	3.2	odd	2
441.2.h.f.373.3		10	63.23	odd	6
567.2.e.e.163.3		10	63.61	odd	6
567.2.e.e.487.3		10	63.34	odd	6
567.2.e.f.163.3		10	63.47	even	6
567.2.e.f.487.3		10	63.20	even	6
1008.2.q.i.529.3		10	84.83	odd	2
1008.2.q.i.625.3		10	252.131	odd	6
1008.2.t.i.193.1		10	252.167	odd	6
1008.2.t.i.961.1		10	84.47	odd	6
1323.2.f.e.442.3		10	63.31	odd	6
1323.2.f.e.883.3		10	7.3	odd	6
1323.2.f.f.442.3		10	63.4	even	3
1323.2.f.f.883.3		10	7.4	even	3
1323.2.g.f.361.3		10	9.4	even	3
1323.2.g.f.667.3		10	7.2	even	3
1323.2.h.f.226.3		10	63.58	even	3	inner
1323.2.h.f.802.3		10	1.1	even	1	trivial
3024.2.q.i.2305.1		10	252.103	even	6
3024.2.q.i.2881.1		10	28.27	even	2
3024.2.t.i.289.5		10	28.19	even	6
3024.2.t.i.1873.5		10	252.139	even	6
3969.2.a.z.1.3		5	63.38	even	6
3969.2.a.ba.1.3		5	63.11	odd	6
3969.2.a.bb.1.3		5	63.25	even	3
3969.2.a.bc.1.3		5	63.52	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.495868 q^{2} -1.75411 q^{4} +(1.84629 - 3.19787i) q^{5} -1.86155 q^{8} +O(q^{10})\)	\(q+0.495868 q^{2} -1.75411 q^{4} +(1.84629 - 3.19787i) q^{5} -1.86155 q^{8} +(0.915516 - 1.58572i) q^{10} +(-0.446284 - 0.772987i) q^{11} +(-0.598355 - 1.03638i) q^{13} +2.58515 q^{16} +(-0.124991 + 0.216492i) q^{17} +(-1.40414 - 2.43204i) q^{19} +(-3.23860 + 5.60943i) q^{20} +(-0.221298 - 0.383300i) q^{22} +(1.23886 - 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +(-0.296705 - 0.513909i) q^{26} +(-2.07128 + 3.58755i) q^{29} -3.58515 q^{31} +5.00499 q^{32} +(-0.0619793 + 0.107351i) q^{34} +(-2.36568 - 4.09747i) q^{37} +(-0.696267 - 1.20597i) q^{38} +(-3.43695 + 5.95298i) q^{40} +(-2.39093 - 4.14121i) q^{41} +(-4.98928 + 8.64169i) q^{43} +(0.782834 + 1.35591i) q^{44} +(0.614310 - 1.06402i) q^{46} -10.1731 q^{47} +(-2.14095 - 3.70823i) q^{50} +(1.04958 + 1.81793i) q^{52} +(4.94465 - 8.56438i) q^{53} -3.29588 q^{55} +(-1.02708 + 1.77895i) q^{58} +1.81237 q^{59} -10.8041 q^{61} -1.77776 q^{62} -2.68848 q^{64} -4.41895 q^{65} +1.02937 q^{67} +(0.219249 - 0.379751i) q^{68} +4.94533 q^{71} +(0.915262 - 1.58528i) q^{73} +(-1.17306 - 2.03181i) q^{74} +(2.46302 + 4.26607i) q^{76} -1.79912 q^{79} +(4.77293 - 8.26696i) q^{80} +(-1.18559 - 2.05350i) q^{82} +(6.16156 - 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} +(-2.47403 + 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} +(-1.20370 - 2.08488i) q^{89} +(-2.17310 + 3.76392i) q^{92} -5.04450 q^{94} -10.3698 q^{95} +(-5.52210 + 9.56456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 + 6 * q^8	\( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8} + 7 q^{10} - 4 q^{11} + 8 q^{13} - 4 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 11 q^{26} - 7 q^{29} - 6 q^{31} - 4 q^{32} - 3 q^{34} + 20 q^{38} + 3 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 54 q^{47} - 19 q^{50} + 10 q^{52} + 21 q^{53} - 4 q^{55} - 10 q^{58} - 60 q^{59} - 28 q^{61} - 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} + 27 q^{68} + 6 q^{71} - 15 q^{73} + 36 q^{74} - 5 q^{76} + 8 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 28 q^{89} - 27 q^{92} - 6 q^{94} - 28 q^{95} + 12 q^{97}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 + 6 * q^8 + 7 * q^10 - 4 * q^11 + 8 * q^13 - 4 * q^16 + 12 * q^17 - q^19 + 5 * q^20 - q^22 - 3 * q^23 - q^25 + 11 * q^26 - 7 * q^29 - 6 * q^31 - 4 * q^32 - 3 * q^34 + 20 * q^38 + 3 * q^40 + 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 54 * q^47 - 19 * q^50 + 10 * q^52 + 21 * q^53 - 4 * q^55 - 10 * q^58 - 60 * q^59 - 28 * q^61 - 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 + 27 * q^68 + 6 * q^71 - 15 * q^73 + 36 * q^74 - 5 * q^76 + 8 * q^79 + 20 * q^80 + 5 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 28 * q^89 - 27 * q^92 - 6 * q^94 - 28 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more