LMFDB - Embedded newform 1323.2.f.f.442.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (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:	$\Z[a_1, \ldots, a_{4}]$
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			442.3
Root			$0.247934 + 0.429435i$ of defining polynomial
Character	$\chi$	$=$	1323.442
Dual form			1323.2.f.f.883.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.247934 - 0.429435i) q^{2} +(0.877057 - 1.51911i) q^{4} +(1.84629 - 3.19787i) q^{5} -1.86155 q^{8} -1.83103 q^{10} +(-0.446284 - 0.772987i) q^{11} +(-0.598355 + 1.03638i) q^{13} +(-1.29257 - 2.23880i) q^{16} +0.249983 q^{17} +2.80827 q^{19} +(-3.23860 - 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(1.23886 - 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +0.593411 q^{26} +(-2.07128 - 3.58755i) q^{29} +(1.79257 - 3.10483i) q^{31} +(-2.50249 + 4.33444i) q^{32} +(-0.0619793 - 0.107351i) q^{34} +4.73136 q^{37} +(-0.696267 - 1.20597i) q^{38} +(-3.43695 + 5.95298i) q^{40} +(-2.39093 + 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} -1.56567 q^{44} -1.22862 q^{46} +(5.08653 + 8.81013i) q^{47} +(-2.14095 + 3.70823i) q^{50} +(1.04958 + 1.81793i) q^{52} -9.88929 q^{53} -3.29588 q^{55} +(-1.02708 + 1.77895i) q^{58} +(-0.906186 + 1.56956i) q^{59} +(5.40205 + 9.35663i) q^{61} -1.77776 q^{62} -2.68848 q^{64} +(2.20948 + 3.82692i) q^{65} +(-0.514685 + 0.891460i) q^{67} +(0.219249 - 0.379751i) q^{68} +4.94533 q^{71} -1.83052 q^{73} +(-1.17306 - 2.03181i) q^{74} +(2.46302 - 4.26607i) q^{76} +(0.899562 + 1.55809i) q^{79} -9.54586 q^{80} +2.37117 q^{82} +(6.16156 + 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(-2.47403 + 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} +2.40741 q^{89} +(-2.17310 - 3.76392i) q^{92} +(2.52225 - 4.36867i) q^{94} +(5.18489 - 8.98049i) q^{95} +(-5.52210 - 9.56456i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{8} - 14 q^{10} - 4 q^{11} + 8 q^{13} + 2 q^{16} - 24 q^{17} + 2 q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 22 q^{26} - 7 q^{29} + 3 q^{31} + 2 q^{32} - 3 q^{34}+ \cdots + 12 q^{97}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^8 - 14 * q^10 - 4 * q^11 + 8 * q^13 + 2 * q^16 - 24 * q^17 + 2 * q^19 + 5 * q^20 - q^22 - 3 * q^23 - q^25 - 22 * q^26 - 7 * q^29 + 3 * q^31 + 2 * q^32 - 3 * q^34 + 20 * q^38 + 3 * q^40 + 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 + 27 * q^47 - 19 * q^50 + 10 * q^52 - 42 * q^53 - 4 * q^55 - 10 * q^58 + 30 * q^59 + 14 * q^61 - 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 27 * q^68 + 6 * q^71 + 30 * q^73 + 36 * q^74 - 5 * q^76 - 4 * q^79 - 40 * q^80 - 10 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 56 * q^89 - 27 * q^92 + 3 * q^94 + 14 * q^95 + 12 * q^97

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.247934	−	0.429435i	−0.175316	−	0.303656i	0.764955	−	0.644084i	$-0.222761\pi$
$2$	−0.247934	−	0.429435i	−0.175316	−	0.303656i	−0.940271	+	0.340428i	$0.889428\pi$
$3$		0			0
$3$		0			0
$4$	0.877057	−	1.51911i	0.438529	−	0.759554i
$5$	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
$10$	−1.83103			−0.579023
$11$	−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	−0.936994	−	0.349346i	$-0.886404\pi$
$13$	−0.598355	+	1.03638i	−0.165954	+	0.287441i	0.771040	+	0.636787i	$0.219737\pi$
$14$		0			0
$15$		0			0
$16$	−1.29257	−	2.23880i	−0.323143	−	0.559701i
$17$	0.249983			0.0606298			0.0303149	−	0.999540i	$-0.490349\pi$
$17$	0.249983			0.0606298			0.0303149	+	0.999540i	$0.490349\pi$
$18$		0			0
$19$	2.80827			0.644262			0.322131	−	0.946695i	$-0.395601\pi$
$19$	2.80827			0.644262			0.322131	+	0.946695i	$0.395601\pi$
$20$	−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
$26$	0.593411			0.116377
$27$		0			0
$28$		0			0
$29$	−2.07128	−	3.58755i	−0.384626	−	0.666192i	0.607091	−	0.794632i	$-0.292336\pi$
$29$	−2.07128	−	3.58755i	−0.384626	−	0.666192i	−0.991717	+	0.128440i	$0.959003\pi$
$30$		0			0
$31$	1.79257	−	3.10483i	0.321956	−	0.557644i	−0.658936	−	0.752199i	$-0.728993\pi$
$31$	1.79257	−	3.10483i	0.321956	−	0.557644i	0.980892	+	0.194555i	$0.0623264\pi$
$32$	−2.50249	+	4.33444i	−0.442382	+	0.766229i
$33$		0			0
$34$	−0.0619793	−	0.107351i	−0.0106294	−	0.0184106i
$35$		0			0
$36$		0			0
$37$	4.73136			0.777830			0.388915	−	0.921274i	$-0.372850\pi$
$37$	4.73136			0.777830			0.388915	+	0.921274i	$0.372850\pi$
$38$	−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	−0.990086	−	0.140461i	$-0.955142\pi$
$41$	−2.39093	+	4.14121i	−0.373400	+	0.646748i	0.616686	+	0.787209i	$0.288475\pi$
$42$		0			0
$43$	−4.98928	−	8.64169i	−0.760859	−	1.31785i	−0.942408	−	0.334464i	$-0.891445\pi$
$43$	−4.98928	−	8.64169i	−0.760859	−	1.31785i	0.181550	−	0.983382i	$-0.441889\pi$
$44$	−1.56567			−0.236033
$45$		0			0
$46$	−1.22862			−0.181150
$47$	5.08653	+	8.81013i	0.741947	+	1.28509i	0.951608	+	0.307316i	$0.0994308\pi$
$47$	5.08653	+	8.81013i	0.741947	+	1.28509i	−0.209661	+	0.977774i	$0.567236\pi$
$48$		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
$53$	−9.88929			−1.35840			−0.679199	−	0.733954i	$-0.737673\pi$
$53$	−9.88929			−1.35840			−0.679199	+	0.733954i	$0.737673\pi$
$54$		0			0
$55$	−3.29588			−0.444416
$56$		0			0
$57$		0			0
$58$	−1.02708	+	1.77895i	−0.134862	+	0.233588i
$59$	−0.906186	+	1.56956i	−0.117975	+	0.204339i	−0.918965	−	0.394339i	$-0.870974\pi$
$59$	−0.906186	+	1.56956i	−0.117975	+	0.204339i	0.800990	+	0.598678i	$0.204307\pi$
$60$		0			0
$61$	5.40205	+	9.35663i	0.691662	+	1.19799i	0.971293	+	0.237886i	$0.0764546\pi$
$61$	5.40205	+	9.35663i	0.691662	+	1.19799i	−0.279631	+	0.960108i	$0.590212\pi$
$62$	−1.77776			−0.225776
$63$		0			0
$64$	−2.68848			−0.336060
$65$	2.20948	+	3.82692i	0.274052	+	0.474671i
$66$		0			0
$67$	−0.514685	+	0.891460i	−0.0628787	+	0.108909i	−0.895751	−	0.444556i	$-0.853361\pi$
$67$	−0.514685	+	0.891460i	−0.0628787	+	0.108909i	0.832872	+	0.553465i	$0.186695\pi$
$68$	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
$73$	−1.83052			−0.214247			−0.107123	−	0.994246i	$-0.534164\pi$
$73$	−1.83052			−0.214247			−0.107123	+	0.994246i	$0.534164\pi$
$74$	−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
$79$	0.899562	+	1.55809i	0.101209	+	0.175298i	0.912183	−	0.409783i	$-0.134396\pi$
$79$	0.899562	+	1.55809i	0.101209	+	0.175298i	−0.810974	+	0.585082i	$0.801062\pi$
$80$	−9.54586			−1.06726
$81$		0			0
$82$	2.37117			0.261852
$83$	6.16156	+	10.6721i	0.676319	+	1.17142i	0.976082	+	0.217405i	$0.0697591\pi$
$83$	6.16156	+	10.6721i	0.676319	+	1.17142i	−0.299763	+	0.954014i	$0.596908\pi$
$84$		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
$89$	2.40741			0.255185			0.127592	−	0.991827i	$-0.459275\pi$
$89$	2.40741			0.255185			0.127592	+	0.991827i	$0.459275\pi$
$90$		0			0
$91$		0			0
$92$	−2.17310	−	3.76392i	−0.226561	−	0.392416i
$93$		0			0
$94$	2.52225	−	4.36867i	0.260150	−	0.450593i
$95$	5.18489	−	8.98049i	0.531958	−	0.921379i
$96$		0			0
$97$	−5.52210	−	9.56456i	−0.560684	−	0.971134i	−0.997437	−	0.0715522i	$-0.977205\pi$
$97$	−5.52210	−	9.56456i	−0.560684	−	0.971134i	0.436752	−	0.899582i	$-0.356129\pi$
$98$		0			0
$99$		0			0
$100$	−15.1470			−1.51470
$101$	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
$107$	−10.9005			−1.05379			−0.526896	−	0.849930i	$-0.676644\pi$
$107$	−10.9005			−1.05379			−0.526896	+	0.849930i	$0.676644\pi$
$108$		0			0
$109$	2.12193			0.203244			0.101622	−	0.994823i	$-0.467597\pi$
$109$	2.12193			0.203244			0.101622	+	0.994823i	$0.467597\pi$
$110$	0.817161	+	1.41536i	0.0779132	+	0.134950i
$111$		0			0
$112$		0			0
$113$	−7.91318	+	13.7060i	−0.744409	+	1.28935i	0.206061	+	0.978539i	$0.433935\pi$
$113$	−7.91318	+	13.7060i	−0.744409	+	1.28935i	−0.950470	+	0.310816i	$0.899398\pi$
$114$		0			0
$115$	−4.57458	−	7.92341i	−0.426582	−	0.738861i
$116$	−7.26651			−0.674679
$117$		0			0
$118$	0.898698			0.0827318
$119$		0			0
$120$		0			0
$121$	5.10166	−	8.83634i	0.463787	−	0.803303i
$122$	2.67871	−	4.63966i	0.242519	−	0.420055i
$123$		0			0
$124$	−3.14438	−	5.44623i	−0.282374	−	0.489086i
$125$	−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	$0.517938\pi$
$128$	5.67155	+	9.82342i	0.501299	+	0.868275i
$129$		0			0
$130$	1.09561	−	1.89765i	0.0960912	−	0.166435i
$131$	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
$136$	−0.465355			−0.0399038
$137$	−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	−0.577226	−	0.816585i	$-0.695865\pi$
$139$	4.93487	−	8.54745i	0.418570	−	0.724985i	0.995796	+	0.0915997i	$0.0291980\pi$
$140$		0			0
$141$		0			0
$142$	−1.22612	−	2.12370i	−0.102893	−	0.178217i
$143$	1.06815			0.0893229
$144$		0			0
$145$	−15.2967			−1.27032
$146$	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	$0.852752\pi$
$152$	−5.22773			−0.424025
$153$		0			0
$154$		0			0
$155$	−6.61922	−	11.4648i	−0.531669	−	0.920877i
$156$		0			0
$157$	−8.33982	+	14.4450i	−0.665590	+	1.15284i	0.313535	+	0.949577i	$0.398487\pi$
$157$	−8.33982	+	14.4450i	−0.665590	+	1.15284i	−0.979125	+	0.203259i	$0.934847\pi$
$158$	0.446064	−	0.772606i	0.0354870	−	0.0614652i
$159$		0			0
$160$	9.24065	+	16.0053i	0.730538	+	1.26533i
$161$		0			0
$162$		0			0
$163$	6.68269			0.523429			0.261714	−	0.965145i	$-0.415712\pi$
$163$	6.68269			0.523429			0.261714	+	0.965145i	$0.415712\pi$
$164$	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	−0.292156	−	0.956371i	$-0.594373\pi$
$167$	8.81549	−	15.2689i	0.682163	−	1.18154i	0.974319	−	0.225170i	$-0.0722939\pi$
$168$		0			0
$169$	5.78394	+	10.0181i	0.444919	+	0.770622i
$170$	−0.457727			−0.0351061
$171$		0			0
$172$	−17.5036			−1.33463
$173$	1.94342	+	3.36611i	0.147756	+	0.255920i	0.930398	−	0.366552i	$-0.119462\pi$
$173$	1.94342	+	3.36611i	0.147756	+	0.255920i	−0.782642	+	0.622472i	$0.786128\pi$
$174$		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
$179$	7.33516			0.548256			0.274128	−	0.961693i	$-0.411611\pi$
$179$	7.33516			0.548256			0.274128	+	0.961693i	$0.411611\pi$
$180$		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
$185$	8.73545	−	15.1302i	0.642243	−	1.11240i
$186$		0			0
$187$	−0.111563	−	0.193234i	−0.00815833	−	0.0141306i
$188$	17.8447			1.30146
$189$		0			0
$190$	−5.14204			−0.373043
$191$	−11.9230	−	20.6512i	−0.862715	−	1.49427i	−0.869298	−	0.494288i	$-0.835429\pi$
$191$	−11.9230	−	20.6512i	−0.862715	−	1.49427i	0.00658302	−	0.999978i	$-0.497905\pi$
$192$		0			0
$193$	−2.96728	+	5.13948i	−0.213589	+	0.369948i	−0.952835	−	0.303488i	$-0.901849\pi$
$193$	−2.96728	+	5.13948i	−0.213589	+	0.369948i	0.739246	+	0.673436i	$0.235182\pi$
$194$	−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
$199$	15.4964			1.09851			0.549254	−	0.835655i	$-0.314912\pi$
$199$	15.4964			1.09851			0.549254	+	0.835655i	$0.314912\pi$
$200$	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
$205$	8.82870	+	15.2917i	0.616623	+	1.06802i
$206$	−4.81565			−0.335522
$207$		0			0
$208$	3.09367			0.214508
$209$	−1.25329	−	2.17076i	−0.0866918	−	0.150155i
$210$		0			0
$211$	0.771898	−	1.33697i	0.0531397	−	0.0920406i	−0.838232	−	0.545314i	$-0.816410\pi$
$211$	0.771898	−	1.33697i	0.0531397	−	0.0920406i	0.891372	+	0.453273i	$0.149744\pi$
$212$	−8.67347	+	15.0229i	−0.595697	+	1.03178i
$213$		0			0
$214$	2.70261	+	4.68105i	0.184746	+	0.319990i
$215$	−36.8467			−2.51292
$216$		0			0
$217$		0			0
$218$	−0.526098	−	0.911229i	−0.0356319	−	0.0617162i
$219$		0			0
$220$	−2.89068	+	5.00680i	−0.194889	+	0.337558i
$221$	−0.149579	+	0.259078i	−0.0100617	+	0.0174275i
$222$		0			0
$223$	2.72171	+	4.71414i	0.182259	+	0.315682i	0.942649	−	0.333784i	$-0.108326\pi$
$223$	2.72171	+	4.71414i	0.182259	+	0.315682i	−0.760390	+	0.649466i	$0.774992\pi$
$224$		0			0
$225$		0			0
$226$	7.84779			0.522027
$227$	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
$233$	16.5409			1.08363			0.541815	−	0.840498i	$-0.317737\pi$
$233$	16.5409			1.08363			0.541815	+	0.840498i	$0.317737\pi$
$234$		0			0
$235$	37.5648			2.45046
$236$	1.58955	+	2.75319i	0.103471	+	0.179217i
$237$		0			0
$238$		0			0
$239$	11.0119	−	19.0732i	0.712303	−	1.23375i	−0.251687	−	0.967809i	$-0.580985\pi$
$239$	11.0119	−	19.0732i	0.712303	−	1.23375i	0.963990	−	0.265937i	$-0.0856813\pi$
$240$		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	$0.652318\pi$
$242$	−5.05950			−0.325237
$243$		0			0
$244$	18.9516			1.21325
$245$		0			0
$246$		0			0
$247$	−1.68035	+	2.91045i	−0.106918	+	0.185187i
$248$	−3.33696	+	5.77978i	−0.211897	+	0.367017i
$249$		0			0
$250$	3.32803	+	5.76432i	0.210483	+	0.364568i
$251$	−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
$254$	0.314743	+	0.545151i	0.0197488	+	0.0342058i
$255$		0			0
$256$	0.123861	−	0.214533i	0.00774131	−	0.0134083i
$257$	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
$262$	−7.45235			−0.460408
$263$	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
$268$	0.902816	+	1.56372i	0.0551483	+	0.0955196i
$269$	−19.8453			−1.20999			−0.604996	−	0.796229i	$-0.706825\pi$
$269$	−19.8453			−1.20999			−0.604996	+	0.796229i	$0.706825\pi$
$270$		0			0
$271$	10.6411			0.646402			0.323201	−	0.946330i	$-0.395241\pi$
$271$	10.6411			0.646402			0.323201	+	0.946330i	$0.395241\pi$
$272$	−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	$0.564593\pi$
$278$	−4.89409			−0.293528
$279$		0			0
$280$		0			0
$281$	6.83733	+	11.8426i	0.407881	+	0.706470i	0.994652	−	0.103282i	$-0.0329346\pi$
$281$	6.83733	+	11.8426i	0.407881	+	0.706470i	−0.586771	+	0.809753i	$0.699601\pi$
$282$		0			0
$283$	3.16089	−	5.47483i	0.187896	−	0.325445i	−0.756653	−	0.653817i	$-0.773167\pi$
$283$	3.16089	−	5.47483i	0.187896	−	0.325445i	0.944548	+	0.328372i	$0.106500\pi$
$284$	4.33734	−	7.51249i	0.257374	−	0.445784i
$285$		0			0
$286$	−0.264830	−	0.458699i	−0.0156597	−	0.0271234i
$287$		0			0
$288$		0			0
$289$	−16.9375			−0.996324
$290$	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	−0.901880	−	0.431987i	$-0.857812\pi$
$293$	−1.31508	+	2.27778i	−0.0768277	+	0.133069i	0.825052	+	0.565057i	$0.191146\pi$
$294$		0			0
$295$	3.34616	+	5.79573i	0.194821	+	0.337440i
$296$	−8.80764			−0.511934
$297$		0			0
$298$	−10.4251			−0.603911
$299$	1.48255	+	2.56786i	0.0857384	+	0.148503i
$300$		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
$305$	39.8950			2.28438
$306$		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
$311$	7.55013	−	13.0772i	0.428129	−	0.741541i	−0.568578	−	0.822629i	$-0.692506\pi$
$311$	7.55013	−	13.0772i	0.428129	−	0.741541i	0.996707	+	0.0810885i	$0.0258396\pi$
$312$		0			0
$313$	−12.7392	−	22.0650i	−0.720064	−	1.24719i	−0.960974	−	0.276640i	$-0.910779\pi$
$313$	−12.7392	−	22.0650i	−0.720064	−	1.24719i	0.240910	−	0.970548i	$-0.422554\pi$
$314$	8.27090			0.466754
$315$		0			0
$316$	3.15587			0.177531
$317$	16.2605	+	28.1639i	0.913278	+	1.58184i	0.809403	+	0.587253i	$0.199791\pi$
$317$	16.2605	+	28.1639i	0.913278	+	1.58184i	0.103875	+	0.994590i	$0.466876\pi$
$318$		0			0
$319$	−1.84875	+	3.20214i	−0.103510	+	0.179285i
$320$	−4.96372	+	8.59741i	−0.277480	+	0.480610i
$321$		0			0
$322$		0			0
$323$	0.702021			0.0390615
$324$		0			0
$325$	10.3338			0.573214
$326$	−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
$331$	−9.04741	−	15.6706i	−0.497291	−	0.861333i	0.502704	−	0.864458i	$-0.332338\pi$
$331$	−9.04741	−	15.6706i	−0.497291	−	0.861333i	−0.999995	+	0.00312545i	$0.999005\pi$
$332$	21.6162			1.18634
$333$		0			0
$334$	−8.74264			−0.478376
$335$	1.90051	+	3.29179i	0.103836	+	0.179850i
$336$		0			0
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	0.293168	+	0.956061i	$0.405290\pi$
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	−0.974557	+	0.224139i	$0.928043\pi$
$338$	2.86807	−	4.96765i	0.156003	−	0.270204i
$339$		0			0
$340$	−0.809596	−	1.40226i	−0.0439065	−	0.0760483i
$341$	−3.19999			−0.173289
$342$		0			0
$343$		0			0
$344$	9.28778	+	16.0869i	0.500764	+	0.867348i
$345$		0			0
$346$	0.963682	−	1.66915i	0.0518078	−	0.0897338i
$347$	5.37444	−	9.30881i	0.288515	−	0.499723i	−0.684940	−	0.728599i	$-0.740172\pi$
$347$	5.37444	−	9.30881i	0.288515	−	0.499723i	0.973456	+	0.228876i	$0.0735051\pi$
$348$		0			0
$349$	1.64301	+	2.84577i	0.0879482	+	0.152331i	0.906644	−	0.421897i	$-0.138636\pi$
$349$	1.64301	+	2.84577i	0.0879482	+	0.152331i	−0.818695	+	0.574228i	$0.805302\pi$
$350$		0			0
$351$		0			0
$352$	4.46729			0.238107
$353$	−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
$359$	23.7842			1.25528			0.627642	−	0.778502i	$-0.284020\pi$
$359$	23.7842			1.25528			0.627642	+	0.778502i	$0.284020\pi$
$360$		0			0
$361$	−11.1136			−0.584926
$362$	2.79088	+	4.83395i	0.146686	+	0.254067i
$363$		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	$0.839066\pi$
$368$	−6.40526			−0.333897
$369$		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	$0.135631\pi$
$374$	−0.0553208	+	0.0958184i	−0.00286057	+	0.00495465i
$375$		0			0
$376$	−9.46882	−	16.4005i	−0.488317	−	0.845790i
$377$	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	$0.180017\pi$
$380$	−9.09489	−	15.7528i	−0.466558	−	0.808102i
$381$		0			0
$382$	−5.91222	+	10.2403i	−0.302495	+	0.523937i
$383$	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
$388$	−19.3728			−0.983505
$389$	−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
$394$	−3.83510	−	6.64258i	−0.193209	−	0.334648i
$395$	6.64340			0.334266
$396$		0			0
$397$	−0.0320978			−0.00161094			−0.000805471	−	1.00000i	$-0.500256\pi$
$397$	−0.0320978			−0.00161094			−0.000805471		1.00000i	$0.500256\pi$
$398$	−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
$404$	4.56007			0.226872
$405$		0			0
$406$		0			0
$407$	−2.11153	−	3.65728i	−0.104665	−	0.181284i
$408$		0			0
$409$	13.3948	−	23.2006i	0.662333	−	1.14719i	−0.317669	−	0.948202i	$-0.602900\pi$
$409$	13.3948	−	23.2006i	0.662333	−	1.14719i	0.980001	−	0.198992i	$-0.0637667\pi$
$410$	4.37787	−	7.58269i	0.216208	−	0.374483i
$411$		0			0
$412$	−8.51759	−	14.7529i	−0.419631	−	0.726823i
$413$		0			0
$414$		0			0
$415$	45.5041			2.23371
$416$	−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	0.485624	+	0.874168i	$0.338593\pi$
$419$	−10.5262	+	18.2320i	−0.514240	+	0.890689i	−0.999864	+	0.0165215i	$0.994741\pi$
$420$		0			0
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	0.625568	−	0.780170i	$-0.284867\pi$
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	−0.988431	+	0.151672i	$0.951534\pi$
$422$	−0.765520			−0.0372649
$423$		0			0
$424$	18.4094			0.894038
$425$	−1.07932	−	1.86944i	−0.0523547	−	0.0906809i
$426$		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
$431$	−15.9038			−0.766061			−0.383031	−	0.923736i	$-0.625120\pi$
$431$	−15.9038			−0.766061			−0.383031	+	0.923736i	$0.625120\pi$
$432$		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
$437$	3.47905	−	6.02590i	0.166426	−	0.288258i
$438$		0			0
$439$	−7.77236	−	13.4621i	−0.370954	−	0.642512i	0.618758	−	0.785582i	$-0.287636\pi$
$439$	−7.77236	−	13.4621i	−0.370954	−	0.642512i	−0.989713	+	0.143070i	$0.954303\pi$
$440$	6.13543			0.292495
$441$		0			0
$442$	0.148343			0.00705594
$443$	0.895027	+	1.55023i	0.0425240	+	0.0736537i	0.886504	−	0.462721i	$-0.153127\pi$
$443$	0.895027	+	1.55023i	0.0425240	+	0.0736537i	−0.843980	+	0.536375i	$0.819793\pi$
$444$		0			0
$445$	4.44477	−	7.69857i	0.210702	−	0.364947i
$446$	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
$451$	4.26814			0.200979
$452$	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
$457$	−1.28459	−	2.22497i	−0.0600905	−	0.104080i	0.834415	−	0.551136i	$-0.185806\pi$
$457$	−1.28459	−	2.22497i	−0.0600905	−	0.104080i	−0.894506	+	0.447057i	$0.852472\pi$
$458$	4.94301			0.230972
$459$		0			0
$460$	−16.0487			−0.748274
$461$	18.0934	+	31.3388i	0.842695	+	1.45959i	0.887608	+	0.460600i	$0.152366\pi$
$461$	18.0934	+	31.3388i	0.842695	+	1.45959i	−0.0449122	+	0.998991i	$0.514301\pi$
$462$		0			0
$463$	8.19224	−	14.1894i	0.380726	−	0.659436i	−0.610440	−	0.792062i	$-0.709008\pi$
$463$	8.19224	−	14.1894i	0.380726	−	0.659436i	0.991166	+	0.132626i	$0.0423409\pi$
$464$	−5.35455	+	9.27436i	−0.248579	+	0.430551i
$465$		0			0
$466$	−4.10105	−	7.10323i	−0.189978	−	0.329051i
$467$	8.70044			0.402608			0.201304	−	0.979529i	$-0.435482\pi$
$467$	8.70044			0.402608			0.201304	+	0.979529i	$0.435482\pi$
$468$		0			0
$469$		0			0
$470$	−9.31361	−	16.1316i	−0.429605	−	0.744097i
$471$		0			0
$472$	1.68691	−	2.92181i	0.0776462	−	0.134487i
$473$	−4.45328	+	7.71330i	−0.204762	+	0.354658i
$474$		0			0
$475$	−12.1249	−	21.0010i	−0.556330	−	0.963591i
$476$		0			0
$477$		0			0
$478$	−10.9209			−0.499513
$479$	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
$485$	−40.7816			−1.85180
$486$		0			0
$487$	−16.6553			−0.754722			−0.377361	−	0.926066i	$-0.623168\pi$
$487$	−16.6553			−0.754722			−0.377361	+	0.926066i	$0.623168\pi$
$488$	−10.0562	−	17.4178i	−0.455222	−	0.788467i
$489$		0			0
$490$		0			0
$491$	3.21021	−	5.56025i	0.144875	−	0.250930i	−0.784451	−	0.620190i	$-0.787055\pi$
$491$	3.21021	−	5.56025i	0.144875	−	0.250930i	0.929326	+	0.369260i	$0.120389\pi$
$492$		0			0
$493$	−0.517784	−	0.896827i	−0.0233198	−	0.0403911i
$494$	1.66646			0.0749776
$495$		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	$0.246926\pi$
$500$	−11.7728	+	20.3911i	−0.526495	+	0.911916i
$501$		0			0
$502$	2.11512	+	3.66350i	0.0944026	+	0.163510i
$503$	−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
$506$	0.548314	+	0.949708i	0.0243755	+	0.0422197i
$507$		0			0
$508$	−1.11339	+	1.92845i	−0.0493988	+	0.0855612i
$509$	−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
$514$	−8.48913			−0.374439
$515$	−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
$520$	−4.11304	−	7.12399i	−0.180369	−	0.312408i
$521$	4.75971			0.208527			0.104263	−	0.994550i	$-0.466751\pi$
$521$	4.75971			0.208527			0.104263	+	0.994550i	$0.466751\pi$
$522$		0			0
$523$	40.2515			1.76008			0.880038	−	0.474904i	$-0.157517\pi$
$523$	40.2515			1.76008			0.880038	+	0.474904i	$0.157517\pi$
$524$	−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
$530$	18.1076			0.786545
$531$		0			0
$532$		0			0
$533$	−2.86125	−	4.95583i	−0.123935	−	0.214661i
$534$		0			0
$535$	−20.1255	+	34.8584i	−0.870101	+	1.50706i
$536$	0.958109	−	1.65949i	0.0413840	−	0.0716792i
$537$		0			0
$538$	4.92033	+	8.52227i	0.212131	+	0.367421i
$539$		0			0
$540$		0			0
$541$	−24.1094			−1.03655			−0.518273	−	0.855215i	$-0.673425\pi$
$541$	−24.1094			−1.03655			−0.518273	+	0.855215i	$0.673425\pi$
$542$	−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	0.703204	−	0.710988i	$-0.251752\pi$
$547$	−6.17751	−	10.6998i	−0.264131	−	0.457489i	−0.967336	+	0.253499i	$0.918419\pi$
$548$	−0.856872			−0.0366038
$549$		0			0
$550$	3.82188			0.162966
$551$	−5.81671	−	10.0748i	−0.247800	−	0.429203i
$552$		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
$557$	8.07689			0.342229			0.171114	−	0.985251i	$-0.445263\pi$
$557$	8.07689			0.342229			0.171114	+	0.985251i	$0.445263\pi$
$558$		0			0
$559$	11.9415			0.505070
$560$		0			0
$561$		0			0
$562$	3.39041	−	5.87237i	0.143016	−	0.247711i
$563$	−22.6064	+	39.1554i	−0.952744	+	1.65020i	−0.213296	+	0.976988i	$0.568420\pi$
$563$	−22.6064	+	39.1554i	−0.952744	+	1.65020i	−0.739448	+	0.673214i	$0.764913\pi$
$564$		0			0
$565$	29.2200	+	50.6106i	1.22930	+	2.12920i
$566$	−3.13477			−0.131764
$567$		0			0
$568$	−9.20596			−0.386274
$569$	11.2149	+	19.4248i	0.470155	+	0.814332i	0.999418	−	0.0341263i	$-0.0108648\pi$
$569$	11.2149	+	19.4248i	0.470155	+	0.814332i	−0.529263	+	0.848458i	$0.677532\pi$
$570$		0			0
$571$	10.9134	−	18.9026i	0.456713	−	0.791050i	−0.542072	−	0.840332i	$-0.682360\pi$
$571$	10.9134	−	18.9026i	0.456713	−	0.791050i	0.998785	+	0.0492820i	$0.0156933\pi$
$572$	0.936826	−	1.62263i	0.0391706	−	0.0678455i
$573$		0			0
$574$		0			0
$575$	−21.3954			−0.892251
$576$		0			0
$577$	−32.2044			−1.34068			−0.670342	−	0.742052i	$-0.733853\pi$
$577$	−32.2044			−1.34068			−0.670342	+	0.742052i	$0.733853\pi$
$578$	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
$583$	4.41343	+	7.64429i	0.182786	+	0.316594i
$584$	3.40761			0.141008
$585$		0			0
$586$	1.30421			0.0538765
$587$	−9.72304	−	16.8408i	−0.401313	−	0.695094i	0.592572	−	0.805518i	$-0.298113\pi$
$587$	−9.72304	−	16.8408i	−0.401313	−	0.695094i	−0.993885	+	0.110424i	$0.964779\pi$
$588$		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
$593$	28.8405			1.18434			0.592168	−	0.805815i	$-0.298272\pi$
$593$	28.8405			1.18434			0.592168	+	0.805815i	$0.298272\pi$
$594$		0			0
$595$		0			0
$596$	−18.4392	−	31.9377i	−0.755300	−	1.30822i
$597$		0			0
$598$	0.735152	−	1.27332i	0.0300626	−	0.0520699i
$599$	−23.4994	+	40.7022i	−0.960161	+	1.66305i	−0.238072	+	0.971247i	$0.576516\pi$
$599$	−23.4994	+	40.7022i	−0.960161	+	1.66305i	−0.722089	+	0.691800i	$0.756818\pi$
$600$		0			0
$601$	7.80843	+	13.5246i	0.318512	+	0.551680i	0.980178	−	0.198119i	$-0.0634834\pi$
$601$	7.80843	+	13.5246i	0.318512	+	0.551680i	−0.661665	+	0.749799i	$0.730150\pi$
$602$		0			0
$603$		0			0
$604$	−2.62833			−0.106945
$605$	−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
$611$	−12.1742			−0.492516
$612$		0			0
$613$	−29.3468			−1.18531			−0.592653	−	0.805458i	$-0.701920\pi$
$613$	−29.3468			−1.18531			−0.592653	+	0.805458i	$0.701920\pi$
$614$	−0.692965	−	1.20025i	−0.0279658	−	0.0484382i
$615$		0			0
$616$		0			0
$617$	−2.06401	+	3.57497i	−0.0830938	+	0.143923i	−0.904577	−	0.426310i	$-0.859813\pi$
$617$	−2.06401	+	3.57497i	−0.0830938	+	0.143923i	0.821484	+	0.570232i	$0.193147\pi$
$618$		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	$0.682452\pi$
$620$	−23.2217			−0.932608
$621$		0			0
$622$	−7.48774			−0.300231
$623$		0			0
$624$		0			0
$625$	−3.19498	+	5.53387i	−0.127799	+	0.221355i
$626$	−6.31698	+	10.9413i	−0.252477	+	0.437304i
$627$		0			0
$628$	14.6290	+	25.3382i	0.583761	+	1.01110i
$629$	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	$0.779314\pi$
$632$	−1.67458	−	2.90045i	−0.0666110	−	0.115374i
$633$		0			0
$634$	8.06304	−	13.9656i	0.320224	−	0.554645i
$635$	−2.34380	+	4.05958i	−0.0930107	+	0.161099i
$636$		0			0
$637$		0			0
$638$	1.83348			0.0725881
$639$		0			0
$640$	41.8853			1.65566
$641$	−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	−0.647640	−	0.761947i	$-0.724244\pi$
$643$	8.52125	−	14.7592i	0.336045	−	0.582048i	0.983685	+	0.179899i	$0.0575771\pi$
$644$		0			0
$645$		0			0
$646$	−0.174055	−	0.301472i	−0.00684810	−	0.0118613i
$647$	−3.37618			−0.132731			−0.0663657	−	0.997795i	$-0.521140\pi$
$647$	−3.37618			−0.132731			−0.0663657	+	0.997795i	$0.521140\pi$
$648$		0			0
$649$	1.61767			0.0634989
$650$	−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
$656$	12.3618			0.482648
$657$		0			0
$658$		0			0
$659$	13.9248	+	24.1184i	0.542432	+	0.939519i	0.998764	+	0.0497098i	$0.0158297\pi$
$659$	13.9248	+	24.1184i	0.542432	+	0.939519i	−0.456332	+	0.889810i	$0.650837\pi$
$660$		0			0
$661$	19.5071	−	33.7872i	0.758737	−	1.31417i	−0.184758	−	0.982784i	$-0.559150\pi$
$661$	19.5071	−	33.7872i	0.758737	−	1.31417i	0.943495	−	0.331387i	$-0.107516\pi$
$662$	−4.48633	+	7.77054i	−0.174366	+	0.302011i
$663$		0			0
$664$	−11.4700	−	19.8667i	−0.445123	−	0.770976i
$665$		0			0
$666$		0			0
$667$	−10.2641			−0.397426
$668$	−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	0.747841	+	0.663878i	$0.231090\pi$
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.201014	+	0.979588i	$0.435576\pi$
$674$	12.4053			0.477833
$675$		0			0
$676$	20.2914			0.780438
$677$	11.6958	+	20.2577i	0.449505	+	0.778565i	0.998354	−	0.0573564i	$-0.0182671\pi$
$677$	11.6958	+	20.2577i	0.449505	+	0.778565i	−0.548849	+	0.835922i	$0.684934\pi$
$678$		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
$683$	−30.3264			−1.16041			−0.580204	−	0.814471i	$-0.697027\pi$
$683$	−30.3264			−1.16041			−0.580204	+	0.814471i	$0.697027\pi$
$684$		0			0
$685$	−1.80380			−0.0689196
$686$		0			0
$687$		0			0
$688$	−12.8980	+	22.3401i	−0.491733	+	0.851707i
$689$	5.91731	−	10.2491i	0.225432	−	0.390459i
$690$		0			0
$691$	−2.05665	−	3.56223i	−0.0782387	−	0.135513i	0.824251	−	0.566224i	$-0.191596\pi$
$691$	−2.05665	−	3.56223i	−0.0782387	−	0.135513i	−0.902490	+	0.430711i	$0.858263\pi$
$692$	6.81797			0.259180
$693$		0			0
$694$	−5.33003			−0.202325
$695$	−18.2224	−	31.5621i	−0.691215	−	1.19722i
$696$		0			0
$697$	−0.597691	+	1.03523i	−0.0226392	+	0.0392122i
$698$	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
$703$	13.2869			0.501127
$704$	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
$709$	21.2309	+	36.7729i	0.797342	+	1.38104i	0.921341	+	0.388755i	$0.127095\pi$
$709$	21.2309	+	36.7729i	0.797342	+	1.38104i	−0.123999	+	0.992282i	$0.539572\pi$
$710$	−9.05507			−0.339831
$711$		0			0
$712$	−4.48150			−0.167951
$713$	−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
$719$	11.1425			0.415546			0.207773	−	0.978177i	$-0.433379\pi$
$719$	11.1425			0.415546			0.207773	+	0.978177i	$0.433379\pi$
$720$		0			0
$721$		0			0
$722$	2.75544	+	4.77256i	0.102547	+	0.177616i
$723$		0			0
$724$	−9.87264	+	17.0999i	−0.366914	+	0.635513i
$725$	−17.8858	+	30.9790i	−0.664260	+	1.15053i
$726$		0			0
$727$	14.3410	+	24.8393i	0.531878	+	0.921239i	0.999308	+	0.0372089i	$0.0118467\pi$
$727$	14.3410	+	24.8393i	0.531878	+	0.921239i	−0.467430	+	0.884030i	$0.654820\pi$
$728$		0			0
$729$		0			0
$730$	3.35175			0.124054
$731$	−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
$737$	0.918782			0.0338438
$738$		0			0
$739$	−27.5216			−1.01240			−0.506198	−	0.862417i	$-0.668950\pi$
$739$	−27.5216			−1.01240			−0.506198	+	0.862417i	$0.668950\pi$
$740$	−15.3230	−	26.5402i	−0.563284	−	0.975637i
$741$		0			0
$742$		0			0
$743$	7.00608	−	12.1349i	0.257028	−	0.445186i	−0.708416	−	0.705795i	$-0.750590\pi$
$743$	7.00608	−	12.1349i	0.257028	−	0.445186i	0.965444	+	0.260609i	$0.0839233\pi$
$744$		0			0
$745$	−38.8163	−	67.2318i	−1.42212	−	2.46318i
$746$	−1.86452			−0.0682650
$747$		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	$-0.235867\pi$
$752$	13.1494	−	22.7755i	0.479511	−	0.830537i
$753$		0			0
$754$	−1.22912	−	2.12889i	−0.0447618	−	0.0775298i
$755$	−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	$0.788725\pi$
$758$	−8.15047	−	14.1170i	−0.296038	−	0.512753i
$759$		0			0
$760$	−9.65191	+	16.7176i	−0.350112	+	0.606411i
$761$	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
$766$	−0.531903			−0.0192184
$767$	−1.08444	−	1.87831i	−0.0391570	−	0.0678218i
$768$		0			0
$769$	10.6727	−	18.4856i	0.384867	−	0.666609i	−0.606884	−	0.794790i	$-0.707581\pi$
$769$	10.6727	−	18.4856i	0.384867	−	0.666609i	0.991751	+	0.128182i	$0.0409141\pi$
$770$		0			0
$771$		0			0
$772$	5.20495	+	9.01523i	0.187330	+	0.324465i
$773$	13.1471			0.472870			0.236435	−	0.971647i	$-0.424021\pi$
$773$	13.1471			0.472870			0.236435	+	0.971647i	$0.424021\pi$
$774$		0			0
$775$	−30.9583			−1.11205
$776$	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
$782$	−0.307134			−0.0109831
$783$		0			0
$784$		0			0
$785$	30.7954	+	53.3393i	1.09914	+	1.90376i
$786$		0			0
$787$	−14.0650	+	24.3614i	−0.501364	+	0.868389i	0.498634	+	0.866812i	$0.333835\pi$
$787$	−14.0650	+	24.3614i	−0.501364	+	0.868389i	−0.999999	+	0.00157623i	$0.999498\pi$
$788$	13.5665	−	23.4979i	0.483287	−	0.837077i
$789$		0			0
$790$	−1.64713	−	2.85291i	−0.0586021	−	0.101502i
$791$		0			0
$792$		0			0
$793$	−12.9294			−0.459136
$794$	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	−0.542917	−	0.839786i	$-0.682680\pi$
$797$	12.8683	−	22.2885i	0.455817	−	0.789499i	0.998735	+	0.0502873i	$0.0160137\pi$
$798$		0			0
$799$	1.27155	+	2.20238i	0.0449841	+	0.0779147i
$800$	43.2188			1.52801
$801$		0			0
$802$	−12.1615			−0.429436
$803$	0.816934	+	1.41497i	0.0288290	+	0.0499333i
$804$		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
$809$	31.8705			1.12051			0.560254	−	0.828321i	$-0.310704\pi$
$809$	31.8705			1.12051			0.560254	+	0.828321i	$0.310704\pi$
$810$		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
$815$	12.3382	−	21.3704i	0.432188	−	0.748571i
$816$		0			0
$817$	−14.0113	−	24.2682i	−0.490193	−	0.849039i
$818$	−13.2842			−0.464470
$819$		0			0
$820$	30.9731			1.08163
$821$	−8.19677	−	14.1972i	−0.286069	−	0.495487i	0.686799	−	0.726848i	$-0.259015\pi$
$821$	−8.19677	−	14.1972i	−0.286069	−	0.495487i	−0.972868	+	0.231361i	$0.925682\pi$
$822$		0			0
$823$	13.1890	−	22.8440i	0.459739	−	0.796292i	−0.539208	−	0.842173i	$-0.681276\pi$
$823$	13.1890	−	22.8440i	0.459739	−	0.796292i	0.998947	+	0.0458812i	$0.0146096\pi$
$824$	−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
$829$	24.3158			0.844522			0.422261	−	0.906474i	$-0.361237\pi$
$829$	24.3158			0.844522			0.422261	+	0.906474i	$0.361237\pi$
$830$	−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
$835$	−32.5519	−	56.3815i	−1.12650	−	1.95116i
$836$	−4.39682			−0.152067
$837$		0			0
$838$	10.4392			0.360618
$839$	−12.8405	−	22.2404i	−0.443303	−	0.767824i	0.554629	−	0.832098i	$-0.312860\pi$
$839$	−12.8405	−	22.2404i	−0.443303	−	0.767824i	−0.997932	+	0.0642741i	$0.979527\pi$
$840$		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
$845$	42.7153			1.46945
$846$		0			0
$847$		0			0
$848$	12.7826	+	22.1402i	0.438958	+	0.760297i
$849$		0			0
$850$	−0.535200	+	0.926994i	−0.0183572	+	0.0317956i
$851$	5.86148	−	10.1524i	0.200929	−	0.348019i
$852$		0			0
$853$	−14.4872	−	25.0925i	−0.496031	−	0.859150i	0.503959	−	0.863728i	$-0.331876\pi$
$853$	−14.4872	−	25.0925i	−0.496031	−	0.859150i	−0.999990	+	0.00457743i	$0.998543\pi$
$854$		0			0
$855$		0			0
$856$	20.2918			0.693559
$857$	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
$863$	16.3909			0.557953			0.278977	−	0.960298i	$-0.410005\pi$
$863$	16.3909			0.557953			0.278977	+	0.960298i	$0.410005\pi$
$864$		0			0
$865$	14.3525			0.487999
$866$	−4.05764	−	7.02804i	−0.137884	−	0.238822i
$867$		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
$872$	−3.95006			−0.133766
$873$		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	$0.963731\pi$
$878$	−3.85407	+	6.67544i	−0.130068	+	0.225285i
$879$		0			0
$880$	4.26017	+	7.37883i	0.143610	+	0.248740i
$881$	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	$0.446137\pi$
$884$	0.262378	+	0.454452i	0.00882473	+	0.0152849i
$885$		0			0
$886$	0.443815	−	0.768711i	0.0149103	−	0.0258253i
$887$	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
$892$	9.54838			0.319703
$893$	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
$898$	3.36364	+	5.82599i	0.112246	+	0.194416i
$899$	−14.8517			−0.495331
$900$		0			0
$901$	−2.47215			−0.0823594
$902$	−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	$0.741747\pi$
$908$	28.1998			0.935843
$909$		0			0
$910$		0			0
$911$	−14.9435	−	25.8829i	−0.495099	−	0.857537i	0.504885	−	0.863187i	$-0.331535\pi$
$911$	−14.9435	−	25.8829i	−0.495099	−	0.857537i	−0.999984	+	0.00564955i	$0.998202\pi$
$912$		0			0
$913$	5.49961	−	9.52561i	0.182011	−	0.315252i
$914$	−0.636986	+	1.10329i	−0.0210696	+	0.0364937i
$915$		0			0
$916$	8.74286	+	15.1431i	0.288872	+	0.500341i
$917$		0			0
$918$		0			0
$919$	−23.6567			−0.780362			−0.390181	−	0.920738i	$-0.627588\pi$
$919$	−23.6567			−0.780362			−0.390181	+	0.920738i	$0.627588\pi$
$920$	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
$926$	−8.12454			−0.266989
$927$		0			0
$928$	20.7334			0.680607
$929$	−6.30880	−	10.9272i	−0.206985	−	0.358509i	0.743778	−	0.668426i	$-0.233032\pi$
$929$	−6.30880	−	10.9272i	−0.206985	−	0.358509i	−0.950763	+	0.309918i	$0.899698\pi$
$930$		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
$935$	−0.823914			−0.0269449
$936$		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
$941$	−25.4699	+	44.1151i	−0.830294	+	1.43811i	0.0675118	+	0.997718i	$0.478494\pi$
$941$	−25.4699	+	44.1151i	−0.830294	+	1.43811i	−0.897805	+	0.440392i	$0.854839\pi$
$942$		0			0
$943$	5.92404	+	10.2607i	0.192913	+	0.334136i
$944$	4.68525			0.152492
$945$		0			0
$946$	4.41648			0.143592
$947$	13.8399	+	23.9714i	0.449737	+	0.778967i	0.998369	−	0.0570968i	$-0.0181844\pi$
$947$	13.8399	+	23.9714i	0.449737	+	0.778967i	−0.548632	+	0.836064i	$0.684851\pi$
$948$		0			0
$949$	1.09530	−	1.89712i	0.0355551	−	0.0615832i
$950$	−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
$955$	−88.0530			−2.84933
$956$	−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
$961$	9.07336	+	15.7155i	0.292689	+	0.506952i
$962$	2.80764			0.0905219
$963$		0			0
$964$	29.3289			0.944621
$965$	10.9569	+	18.9779i	0.352715	+	0.610921i
$966$		0			0
$967$	9.09069	−	15.7455i	0.292337	−	0.506342i	−0.682025	−	0.731329i	$-0.738900\pi$
$967$	9.09069	−	15.7455i	0.292337	−	0.506342i	0.974362	+	0.224986i	$0.0722338\pi$
$968$	−9.49698	+	16.4492i	−0.305244	+	0.528699i
$969$		0			0
$970$	10.1111	+	17.5130i	0.324649	+	0.562309i
$971$	−39.4832			−1.26708			−0.633538	−	0.773712i	$-0.718398\pi$
$971$	−39.4832			−1.26708			−0.633538	+	0.773712i	$0.718398\pi$
$972$		0			0
$973$		0			0
$974$	4.12941	+	7.15234i	0.132315	+	0.229176i
$975$		0			0
$976$	13.9651	−	24.1883i	0.447012	−	0.774248i
$977$	5.95782	−	10.3193i	0.190608	−	0.330142i	−0.754844	−	0.655904i	$-0.772288\pi$
$977$	5.95782	−	10.3193i	0.190608	−	0.330142i	0.945452	+	0.325762i	$0.105621\pi$
$978$		0			0
$979$	−1.07439	−	1.86090i	−0.0343376	−	0.0594745i
$980$		0			0
$981$		0			0
$982$	−3.18368			−0.101595
$983$	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
$989$	−24.7241			−0.786179
$990$		0			0
$991$	12.6970			0.403334			0.201667	−	0.979454i	$-0.435364\pi$
$991$	12.6970			0.403334			0.201667	+	0.979454i	$0.435364\pi$
$992$	8.97181	+	15.5396i	0.284855	+	0.493384i
$993$		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	$0.602047\pi$
$998$	5.52690			0.174951
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	21.5	even	6
63.2.g.b.16.3	yes	10	63.38	even	6
63.2.h.b.25.3	yes	10	63.47	even	6
63.2.h.b.58.3	yes	10	21.17	even	6
189.2.g.b.100.3		10	63.52	odd	6
189.2.g.b.172.3		10	7.5	odd	6
189.2.h.b.37.3		10	7.3	odd	6
189.2.h.b.46.3		10	63.61	odd	6
441.2.f.e.148.3		10	21.20	even	2
441.2.f.e.295.3		10	63.20	even	6
441.2.f.f.148.3		10	3.2	odd	2
441.2.f.f.295.3		10	9.2	odd	6
441.2.g.f.67.3		10	21.2	odd	6
441.2.g.f.79.3		10	63.11	odd	6
441.2.h.f.214.3		10	63.2	odd	6
441.2.h.f.373.3		10	21.11	odd	6
567.2.e.e.163.3		10	63.31	odd	6
567.2.e.e.487.3		10	63.40	odd	6
567.2.e.f.163.3		10	63.59	even	6
567.2.e.f.487.3		10	63.5	even	6
1008.2.q.i.529.3		10	252.47	odd	6
1008.2.q.i.625.3		10	84.59	odd	6
1008.2.t.i.193.1		10	84.47	odd	6
1008.2.t.i.961.1		10	252.227	odd	6
1323.2.f.e.442.3		10	7.6	odd	2
1323.2.f.e.883.3		10	63.34	odd	6
1323.2.f.f.442.3		10	1.1	even	1	trivial
1323.2.f.f.883.3		10	9.7	even	3	inner
1323.2.g.f.361.3		10	7.2	even	3
1323.2.g.f.667.3		10	63.25	even	3
1323.2.h.f.226.3		10	7.4	even	3
1323.2.h.f.802.3		10	63.16	even	3
3024.2.q.i.2305.1		10	28.3	even	6
3024.2.q.i.2881.1		10	252.187	even	6
3024.2.t.i.289.5		10	252.115	even	6
3024.2.t.i.1873.5		10	28.19	even	6
3969.2.a.z.1.3		5	63.41	even	6
3969.2.a.ba.1.3		5	9.5	odd	6
3969.2.a.bb.1.3		5	9.4	even	3
3969.2.a.bc.1.3		5	63.13	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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.247934 - 0.429435i) q^{2} +(0.877057 - 1.51911i) q^{4} +(1.84629 - 3.19787i) q^{5} -1.86155 q^{8} -1.83103 q^{10} +(-0.446284 - 0.772987i) q^{11} +(-0.598355 + 1.03638i) q^{13} +(-1.29257 - 2.23880i) q^{16} +0.249983 q^{17} +2.80827 q^{19} +(-3.23860 - 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(1.23886 - 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +0.593411 q^{26} +(-2.07128 - 3.58755i) q^{29} +(1.79257 - 3.10483i) q^{31} +(-2.50249 + 4.33444i) q^{32} +(-0.0619793 - 0.107351i) q^{34} +4.73136 q^{37} +(-0.696267 - 1.20597i) q^{38} +(-3.43695 + 5.95298i) q^{40} +(-2.39093 + 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} -1.56567 q^{44} -1.22862 q^{46} +(5.08653 + 8.81013i) q^{47} +(-2.14095 + 3.70823i) q^{50} +(1.04958 + 1.81793i) q^{52} -9.88929 q^{53} -3.29588 q^{55} +(-1.02708 + 1.77895i) q^{58} +(-0.906186 + 1.56956i) q^{59} +(5.40205 + 9.35663i) q^{61} -1.77776 q^{62} -2.68848 q^{64} +(2.20948 + 3.82692i) q^{65} +(-0.514685 + 0.891460i) q^{67} +(0.219249 - 0.379751i) q^{68} +4.94533 q^{71} -1.83052 q^{73} +(-1.17306 - 2.03181i) q^{74} +(2.46302 - 4.26607i) q^{76} +(0.899562 + 1.55809i) q^{79} -9.54586 q^{80} +2.37117 q^{82} +(6.16156 + 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(-2.47403 + 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} +2.40741 q^{89} +(-2.17310 - 3.76392i) q^{92} +(2.52225 - 4.36867i) q^{94} +(5.18489 - 8.98049i) q^{95} +(-5.52210 - 9.56456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{8} - 14 q^{10} - 4 q^{11} + 8 q^{13} + 2 q^{16} - 24 q^{17} + 2 q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 22 q^{26} - 7 q^{29} + 3 q^{31} + 2 q^{32} - 3 q^{34}+ \cdots + 12 q^{97}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^8 - 14 * q^10 - 4 * q^11 + 8 * q^13 + 2 * q^16 - 24 * q^17 + 2 * q^19 + 5 * q^20 - q^22 - 3 * q^23 - q^25 - 22 * q^26 - 7 * q^29 + 3 * q^31 + 2 * q^32 - 3 * q^34 + 20 * q^38 + 3 * q^40 + 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 + 27 * q^47 - 19 * q^50 + 10 * q^52 - 42 * q^53 - 4 * q^55 - 10 * q^58 + 30 * q^59 + 14 * q^61 - 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 27 * q^68 + 6 * q^71 + 30 * q^73 + 36 * q^74 - 5 * q^76 - 4 * q^79 - 40 * q^80 - 10 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 56 * q^89 - 27 * q^92 + 3 * q^94 + 14 * q^95 + 12 * q^97

Introduction

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