LMFDB - Embedded newform 1323.2.h.f.802.2

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			802.2
Root			$-0.335166 - 0.580525i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.f.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.670333 q^{2} -1.55065 q^{4} +(-0.712469 + 1.23403i) q^{5} +2.38012 q^{8} +O(q^{10})$	\(q-0.670333 q^{2} -1.55065 q^{4} +(-0.712469 + 1.23403i) q^{5} +2.38012 q^{8} +(0.477591 - 0.827212i) q^{10} +(-2.46539 - 4.27018i) q^{11} +(1.37730 + 2.38556i) q^{13} +1.50584 q^{16} +(0.559839 - 0.969670i) q^{17} +(2.00752 + 3.47713i) q^{19} +(1.10479 - 1.91356i) q^{20} +(1.65263 + 2.86244i) q^{22} +(2.71830 - 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(-0.923251 - 1.59912i) q^{26} +(-3.40555 + 5.89858i) q^{29} -2.50584 q^{31} -5.76965 q^{32} +(-0.375279 + 0.650002i) q^{34} +(0.709787 + 1.22939i) q^{37} +(-1.34571 - 2.33083i) q^{38} +(-1.69576 + 2.93714i) q^{40} +(0.124384 + 0.215440i) q^{41} +(-0.498313 + 0.863104i) q^{43} +(3.82296 + 6.62156i) q^{44} +(-1.82217 + 3.15609i) q^{46} -9.47579 q^{47} +(-0.995294 - 1.72390i) q^{50} +(-2.13572 - 3.69917i) q^{52} +(0.410229 - 0.710537i) q^{53} +7.02604 q^{55} +(2.28285 - 3.95401i) q^{58} -6.58407 q^{59} -0.0752645 q^{61} +1.67974 q^{62} +0.855913 q^{64} -3.92514 q^{65} -12.5877 q^{67} +(-0.868117 + 1.50362i) q^{68} -0.0804951 q^{71} +(-5.34551 + 9.25869i) q^{73} +(-0.475793 - 0.824098i) q^{74} +(-3.11297 - 5.39183i) q^{76} -1.84491 q^{79} +(-1.07286 + 1.85825i) q^{80} +(-0.0833788 - 0.144416i) q^{82} +(-7.23583 + 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(0.334036 - 0.578567i) q^{86} +(-5.86792 - 10.1635i) q^{88} +(6.76292 + 11.7137i) q^{89} +(-4.21515 + 7.30085i) q^{92} +6.35193 q^{94} -5.72119 q^{95} +(-2.70160 + 4.67930i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.670333			−0.473997			−0.236998	−	0.971510i	$-0.576164\pi$
$2$	−0.670333			−0.473997			−0.236998	+	0.971510i	$0.576164\pi$
$3$		0			0
$3$		0			0
$4$	−1.55065			−0.775327
$5$	−0.712469	+	1.23403i	−0.318626	+	0.551876i	−0.980202	−	0.198002i	$-0.936555\pi$
$5$	−0.712469	+	1.23403i	−0.318626	+	0.551876i	0.661576	+	0.749878i	$0.269888\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.38012			0.841499
$9$		0			0
$10$	0.477591	−	0.827212i	0.151028	−	0.261587i
$11$	−2.46539	−	4.27018i	−0.743342	−	1.28751i	−0.950965	−	0.309297i	$-0.899906\pi$
$11$	−2.46539	−	4.27018i	−0.743342	−	1.28751i	0.207623	−	0.978209i	$-0.433427\pi$
$12$		0			0
$13$	1.37730	+	2.38556i	0.381995	+	0.661635i	0.991347	−	0.131265i	$-0.0419038\pi$
$13$	1.37730	+	2.38556i	0.381995	+	0.661635i	−0.609352	+	0.792900i	$0.708571\pi$
$14$		0			0
$15$		0			0
$16$	1.50584			0.376459
$17$	0.559839	−	0.969670i	0.135781	−	0.235180i	−0.790115	−	0.612959i	$-0.789979\pi$
$17$	0.559839	−	0.969670i	0.135781	−	0.235180i	0.925896	+	0.377780i	$0.123312\pi$
$18$		0			0
$19$	2.00752	+	3.47713i	0.460557	+	0.797709i	0.998989	−	0.0449606i	$-0.0143162\pi$
$19$	2.00752	+	3.47713i	0.460557	+	0.797709i	−0.538431	+	0.842669i	$0.680983\pi$
$20$	1.10479	−	1.91356i	0.247039	−	0.427884i
$21$		0			0
$22$	1.65263	+	2.86244i	0.352342	+	0.610274i
$23$	2.71830	−	4.70824i	0.566806	−	0.981736i	−0.430073	−	0.902794i	$-0.641512\pi$
$23$	2.71830	−	4.70824i	0.566806	−	0.981736i	0.996879	−	0.0789424i	$-0.0251543\pi$
$24$		0			0
$25$	1.48478	+	2.57171i	0.296955	+	0.514342i
$26$	−0.923251	−	1.59912i	−0.181064	−	0.313613i
$27$		0			0
$28$		0			0
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	0.354667	+	0.934993i	$0.384594\pi$
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	−0.987061	+	0.160346i	$0.948739\pi$
$30$		0			0
$31$	−2.50584			−0.450061			−0.225031	−	0.974352i	$-0.572248\pi$
$31$	−2.50584			−0.450061			−0.225031	+	0.974352i	$0.572248\pi$
$32$	−5.76965			−1.01994
$33$		0			0
$34$	−0.375279	+	0.650002i	−0.0643597	+	0.111474i
$35$		0			0
$36$		0			0
$37$	0.709787	+	1.22939i	0.116688	+	0.202110i	0.918453	−	0.395529i	$-0.129439\pi$
$37$	0.709787	+	1.22939i	0.116688	+	0.202110i	−0.801765	+	0.597639i	$0.796106\pi$
$38$	−1.34571	−	2.33083i	−0.218303	−	0.378111i
$39$		0			0
$40$	−1.69576	+	2.93714i	−0.268123	+	0.464403i
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	0.875575	−	0.483083i	$-0.160483\pi$
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	−0.856149	+	0.516729i	$0.827150\pi$
$42$		0			0
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	−0.901517	−	0.432743i	$-0.857546\pi$
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	0.825525	+	0.564365i	$0.190879\pi$
$44$	3.82296	+	6.62156i	0.576333	+	0.998238i
$45$		0			0
$46$	−1.82217	+	3.15609i	−0.268664	+	0.465340i
$47$	−9.47579			−1.38219			−0.691093	−	0.722766i	$-0.742871\pi$
$47$	−9.47579			−1.38219			−0.691093	+	0.722766i	$0.742871\pi$
$48$		0			0
$49$		0			0
$50$	−0.995294	−	1.72390i	−0.140756	−	0.243796i
$51$		0			0
$52$	−2.13572	−	3.69917i	−0.296171	−	0.512983i
$53$	0.410229	−	0.710537i	0.0563493	−	0.0975998i	−0.836475	−	0.548005i	$-0.815387\pi$
$53$	0.410229	−	0.710537i	0.0563493	−	0.0975998i	0.892824	+	0.450406i	$0.148721\pi$
$54$		0			0
$55$	7.02604			0.947392
$56$		0			0
$57$		0			0
$58$	2.28285	−	3.95401i	0.299753	−	0.519187i
$59$	−6.58407			−0.857173			−0.428586	−	0.903501i	$-0.640988\pi$
$59$	−6.58407			−0.857173			−0.428586	+	0.903501i	$0.640988\pi$
$60$		0			0
$61$	−0.0752645			−0.00963663			−0.00481831	−	0.999988i	$-0.501534\pi$
$61$	−0.0752645			−0.00963663			−0.00481831	+	0.999988i	$0.501534\pi$
$62$	1.67974			0.213328
$63$		0			0
$64$	0.855913			0.106989
$65$	−3.92514			−0.486854
$66$		0			0
$67$	−12.5877			−1.53783			−0.768916	−	0.639350i	$-0.779204\pi$
$67$	−12.5877			−1.53783			−0.768916	+	0.639350i	$0.779204\pi$
$68$	−0.868117	+	1.50362i	−0.105275	+	0.182341i
$69$		0			0
$70$		0			0
$71$	−0.0804951			−0.00955301			−0.00477651	−	0.999989i	$-0.501520\pi$
$71$	−0.0804951			−0.00955301			−0.00477651	+	0.999989i	$0.501520\pi$
$72$		0			0
$73$	−5.34551	+	9.25869i	−0.625644	+	1.08365i	0.362772	+	0.931878i	$0.381830\pi$
$73$	−5.34551	+	9.25869i	−0.625644	+	1.08365i	−0.988416	+	0.151769i	$0.951503\pi$
$74$	−0.475793	−	0.824098i	−0.0553098	−	0.0957995i
$75$		0			0
$76$	−3.11297	−	5.39183i	−0.357083	−	0.618485i
$77$		0			0
$78$		0			0
$79$	−1.84491			−0.207569			−0.103785	−	0.994600i	$-0.533095\pi$
$79$	−1.84491			−0.207569			−0.103785	+	0.994600i	$0.533095\pi$
$80$	−1.07286	+	1.85825i	−0.119950	+	0.207759i
$81$		0			0
$82$	−0.0833788	−	0.144416i	−0.00920765	−	0.0159481i
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	0.129088	+	0.991633i	$0.458795\pi$
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	−0.923323	+	0.384023i	$0.874538\pi$
$84$		0			0
$85$	0.797736	+	1.38172i	0.0865266	+	0.149868i
$86$	0.334036	−	0.578567i	0.0360200	−	0.0623885i
$87$		0			0
$88$	−5.86792	−	10.1635i	−0.625522	−	1.08344i
$89$	6.76292	+	11.7137i	0.716868	+	1.24165i	0.962235	+	0.272222i	$0.0877584\pi$
$89$	6.76292	+	11.7137i	0.716868	+	1.24165i	−0.245366	+	0.969430i	$0.578908\pi$
$90$		0			0
$91$		0			0
$92$	−4.21515	+	7.30085i	−0.439460	+	0.761167i
$93$		0			0
$94$	6.35193			0.655152
$95$	−5.72119			−0.586982
$96$		0			0
$97$	−2.70160	+	4.67930i	−0.274306	+	0.475111i	−0.969960	−	0.243266i	$-0.921781\pi$
$97$	−2.70160	+	4.67930i	−0.274306	+	0.475111i	0.695654	+	0.718377i	$0.255115\pi$
$98$		0			0
$99$		0			0
$100$	−2.30238	−	3.98783i	−0.230238	−	0.398783i
$101$	2.56770	+	4.44739i	0.255496	+	0.442531i	0.965030	−	0.262139i	$-0.0844280\pi$
$101$	2.56770	+	4.44739i	0.255496	+	0.442531i	−0.709534	+	0.704671i	$0.751095\pi$
$102$		0			0
$103$	−7.10561	+	12.3073i	−0.700137	+	1.21267i	0.268282	+	0.963341i	$0.413544\pi$
$103$	−7.10561	+	12.3073i	−0.700137	+	1.21267i	−0.968418	+	0.249332i	$0.919789\pi$
$104$	3.27814	+	5.67791i	0.321448	+	0.556765i
$105$		0			0
$106$	−0.274990	+	0.476296i	−0.0267094	+	0.0462620i
$107$	−3.83015	−	6.63401i	−0.370274	−	0.641334i	0.619333	−	0.785128i	$-0.287403\pi$
$107$	−3.83015	−	6.63401i	−0.370274	−	0.641334i	−0.989608	+	0.143794i	$0.954070\pi$
$108$		0			0
$109$	−0.849394	+	1.47119i	−0.0813572	+	0.140915i	−0.903833	−	0.427885i	$-0.859259\pi$
$109$	−0.849394	+	1.47119i	−0.0813572	+	0.140915i	0.822476	+	0.568800i	$0.192592\pi$
$110$	−4.70979			−0.449061
$111$		0			0
$112$		0			0
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	0.879807	−	0.475331i	$-0.157672\pi$
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	−0.851552	+	0.524270i	$0.824338\pi$
$114$		0			0
$115$	3.87341	+	6.70895i	0.361198	+	0.625613i
$116$	5.28083	−	9.14666i	0.490312	−	0.849246i
$117$		0			0
$118$	4.41352			0.406297
$119$		0			0
$120$		0			0
$121$	−6.65626	+	11.5290i	−0.605115	+	1.04809i
$122$	0.0504522			0.00456773
$123$		0			0
$124$	3.88569			0.348945
$125$	−11.3561			−1.01572
$126$		0			0
$127$	7.25977			0.644200			0.322100	−	0.946706i	$-0.395611\pi$
$127$	7.25977			0.644200			0.322100	+	0.946706i	$0.395611\pi$
$128$	10.9656			0.969227
$129$		0			0
$130$	2.63115			0.230767
$131$	10.2265	−	17.7128i	0.893492	−	1.54757i	0.0578326	−	0.998326i	$-0.481581\pi$
$131$	10.2265	−	17.7128i	0.893492	−	1.54757i	0.835660	−	0.549248i	$-0.185086\pi$
$132$		0			0
$133$		0			0
$134$	8.43794			0.728927
$135$		0			0
$136$	1.33248	−	2.30793i	0.114260	−	0.197903i
$137$	6.10581	+	10.5756i	0.521655	+	0.903532i	0.999683	+	0.0251879i	$0.00801840\pi$
$137$	6.10581	+	10.5756i	0.521655	+	0.903532i	−0.478028	+	0.878345i	$0.658648\pi$
$138$		0			0
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	0.913842	−	0.406071i	$-0.133101\pi$
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	−0.808588	+	0.588375i	$0.799768\pi$
$140$		0			0
$141$		0			0
$142$	0.0539585			0.00452810
$143$	6.79117	−	11.7626i	0.567906	−	0.983642i
$144$		0			0
$145$	−4.85269	−	8.40511i	−0.402994	−	0.698006i
$146$	3.58327	−	6.20640i	0.296553	−	0.513645i
$147$		0			0
$148$	−1.10063	−	1.90635i	−0.0904715	−	0.156701i
$149$	−4.27797	+	7.40966i	−0.350465	+	0.607023i	−0.986331	−	0.164777i	$-0.947310\pi$
$149$	−4.27797	+	7.40966i	−0.350465	+	0.607023i	0.635866	+	0.771799i	$0.280643\pi$
$150$		0			0
$151$	8.82962	+	15.2933i	0.718544	+	1.24455i	0.961577	+	0.274537i	$0.0885244\pi$
$151$	8.82962	+	15.2933i	0.718544	+	1.24455i	−0.243033	+	0.970018i	$0.578142\pi$
$152$	4.77814	+	8.27599i	0.387559	+	0.671271i
$153$		0			0
$154$		0			0
$155$	1.78533	−	3.09228i	0.143401	−	0.248378i
$156$		0			0
$157$	−6.32149			−0.504510			−0.252255	−	0.967661i	$-0.581172\pi$
$157$	−6.32149			−0.504510			−0.252255	+	0.967661i	$0.581172\pi$
$158$	1.23671			0.0983871
$159$		0			0
$160$	4.11070	−	7.11993i	0.324979	−	0.562880i
$161$		0			0
$162$		0			0
$163$	−4.01134	−	6.94784i	−0.314192	−	0.544197i	0.665073	−	0.746778i	$-0.268400\pi$
$163$	−4.01134	−	6.94784i	−0.314192	−	0.544197i	−0.979265	+	0.202581i	$0.935067\pi$
$164$	−0.192877	−	0.334073i	−0.0150612	−	0.0260867i
$165$		0			0
$166$	4.85041	−	8.40116i	0.376465	−	0.652057i
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	0.904132	−	0.427253i	$-0.140518\pi$
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	−0.822078	+	0.569375i	$0.807185\pi$
$168$		0			0
$169$	2.70608	−	4.68706i	0.208160	−	0.360543i
$170$	−0.534749	−	0.926212i	−0.0410133	−	0.0710372i
$171$		0			0
$172$	0.772712	−	1.33838i	0.0589187	−	0.102050i
$173$	−18.2881			−1.39042			−0.695208	−	0.718808i	$-0.744688\pi$
$173$	−18.2881			−1.39042			−0.695208	+	0.718808i	$0.744688\pi$
$174$		0			0
$175$		0			0
$176$	−3.71247	−	6.43018i	−0.279838	−	0.484693i
$177$		0			0
$178$	−4.53341	−	7.85209i	−0.339793	−	0.588539i
$179$	−3.81276	+	6.60389i	−0.284979	+	0.493598i	−0.972604	−	0.232468i	$-0.925320\pi$
$179$	−3.81276	+	6.60389i	−0.284979	+	0.493598i	0.687625	+	0.726066i	$0.258653\pi$
$180$		0			0
$181$	−15.5305			−1.15438			−0.577188	−	0.816611i	$-0.695850\pi$
$181$	−15.5305			−1.15438			−0.577188	+	0.816611i	$0.695850\pi$
$182$		0			0
$183$		0			0
$184$	6.46989	−	11.2062i	0.476967	−	0.826130i
$185$	−2.02280			−0.148719
$186$		0			0
$187$	−5.52088			−0.403727
$188$	14.6937			1.07165
$189$		0			0
$190$	3.83510			0.278227
$191$	−14.8325			−1.07324			−0.536620	−	0.843824i	$-0.680299\pi$
$191$	−14.8325			−1.07324			−0.536620	+	0.843824i	$0.680299\pi$
$192$		0			0
$193$	16.5677			1.19257			0.596286	−	0.802772i	$-0.296642\pi$
$193$	16.5677			1.19257			0.596286	+	0.802772i	$0.296642\pi$
$194$	1.81097	−	3.13669i	0.130020	−	0.225201i
$195$		0			0
$196$		0			0
$197$	4.03740			0.287653			0.143826	−	0.989603i	$-0.454059\pi$
$197$	4.03740			0.287653			0.143826	+	0.989603i	$0.454059\pi$
$198$		0			0
$199$	12.6407	−	21.8943i	0.896076	−	1.55205i	0.0636081	−	0.997975i	$-0.479739\pi$
$199$	12.6407	−	21.8943i	0.896076	−	1.55205i	0.832468	−	0.554074i	$-0.186927\pi$
$200$	3.53395	+	6.12097i	0.249888	+	0.432818i
$201$		0			0
$202$	−1.72121	−	2.98123i	−0.121104	−	0.209758i
$203$		0			0
$204$		0			0
$205$	−0.354480			−0.0247579
$206$	4.76312	−	8.24997i	0.331862	−	0.574803i
$207$		0			0
$208$	2.07399	+	3.59226i	0.143805	+	0.249078i
$209$	9.89864	−	17.1449i	0.684703	−	1.18594i
$210$		0			0
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	0.706961	−	0.707253i	$-0.250066\pi$
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	−0.965979	+	0.258619i	$0.916732\pi$
$212$	−0.636123	+	1.10180i	−0.0436891	+	0.0756718i
$213$		0			0
$214$	2.56747	+	4.44699i	0.175509	+	0.303990i
$215$	−0.710065	−	1.22987i	−0.0484261	−	0.0838764i
$216$		0			0
$217$		0			0
$218$	0.569377	−	0.986190i	0.0385631	−	0.0667932i
$219$		0			0
$220$	−10.8950			−0.734538
$221$	3.08427			0.207471
$222$		0			0
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	−0.997276	−	0.0737638i	$-0.976499\pi$
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	0.562519	+	0.826784i	$0.309832\pi$
$224$		0			0
$225$		0			0
$226$	−0.201335	−	0.348723i	−0.0133926	−	0.0231967i
$227$	14.4832	+	25.0857i	0.961286	+	1.66500i	0.719277	+	0.694723i	$0.244473\pi$
$227$	14.4832	+	25.0857i	0.961286	+	1.66500i	0.242009	+	0.970274i	$0.422194\pi$
$228$		0			0
$229$	7.71790	−	13.3678i	0.510013	−	0.883369i	−0.489919	−	0.871768i	$-0.662974\pi$
$229$	7.71790	−	13.3678i	0.510013	−	0.883369i	0.999933	−	0.0116012i	$-0.00369285\pi$
$230$	−2.59648	−	4.49723i	−0.171207	−	0.296538i
$231$		0			0
$232$	−8.10561	+	14.0393i	−0.532159	+	0.921727i
$233$	2.47324	+	4.28378i	0.162027	+	0.280640i	0.935596	−	0.353073i	$-0.114863\pi$
$233$	2.47324	+	4.28378i	0.162027	+	0.280640i	−0.773568	+	0.633713i	$0.781530\pi$
$234$		0			0
$235$	6.75121	−	11.6934i	0.440400	−	0.762795i
$236$	10.2096			0.664589
$237$		0			0
$238$		0			0
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	0.574523	−	0.818489i	$-0.305188\pi$
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	−0.996093	+	0.0883069i	$0.971854\pi$
$240$		0			0
$241$	7.29123	+	12.6288i	0.469670	+	0.813492i	0.999399	−	0.0346754i	$-0.0110397\pi$
$241$	7.29123	+	12.6288i	0.469670	+	0.813492i	−0.529729	+	0.848167i	$0.677706\pi$
$242$	4.46191	−	7.72826i	0.286823	−	0.496791i
$243$		0			0
$244$	0.116709			0.00747154
$245$		0			0
$246$		0			0
$247$	−5.52993	+	9.57812i	−0.351861	+	0.609441i
$248$	−5.96419			−0.378726
$249$		0			0
$250$	7.61238			0.481449
$251$	−14.0715			−0.888187			−0.444094	−	0.895980i	$-0.646474\pi$
$251$	−14.0715			−0.888187			−0.444094	+	0.895980i	$0.646474\pi$
$252$		0			0
$253$	−26.8067			−1.68532
$254$	−4.86646			−0.305349
$255$		0			0
$256$	−9.06240			−0.566400
$257$	4.18108	−	7.24184i	0.260808	−	0.451733i	−0.705649	−	0.708562i	$-0.749344\pi$
$257$	4.18108	−	7.24184i	0.260808	−	0.451733i	0.966457	+	0.256829i	$0.0826776\pi$
$258$		0			0
$259$		0			0
$260$	6.08653			0.377471
$261$		0			0
$262$	−6.85515	+	11.8735i	−0.423512	+	0.733545i
$263$	1.63533	+	2.83247i	0.100839	+	0.174658i	0.912030	−	0.410122i	$-0.134514\pi$
$263$	1.63533	+	2.83247i	0.100839	+	0.174658i	−0.811192	+	0.584780i	$0.801181\pi$
$264$		0			0
$265$	0.584551	+	1.01247i	0.0359087	+	0.0621956i
$266$		0			0
$267$		0			0
$268$	19.5192			1.19232
$269$	−7.69349	+	13.3255i	−0.469081	+	0.812471i	−0.999375	−	0.0353420i	$-0.988748\pi$
$269$	−7.69349	+	13.3255i	−0.469081	+	0.812471i	0.530295	+	0.847813i	$0.322081\pi$
$270$		0			0
$271$	−4.06308	−	7.03747i	−0.246815	−	0.427496i	0.715825	−	0.698279i	$-0.246051\pi$
$271$	−4.06308	−	7.03747i	−0.246815	−	0.427496i	−0.962640	+	0.270783i	$0.912717\pi$
$272$	0.843026	−	1.46016i	0.0511160	−	0.0885355i
$273$		0			0
$274$	−4.09293	−	7.08915i	−0.247263	−	0.428271i
$275$	7.32110	−	12.6805i	0.441479	−	0.764664i
$276$		0			0
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	0.605982	−	0.795478i	$-0.292780\pi$
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	−0.991895	+	0.127057i	$0.959447\pi$
$278$	−0.831826	−	1.44077i	−0.0498896	−	0.0864114i
$279$		0			0
$280$		0			0
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	−0.843620	−	0.536941i	$-0.819580\pi$
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	0.886815	+	0.462125i	$0.152913\pi$
$282$		0			0
$283$	17.4385			1.03661			0.518306	−	0.855195i	$-0.326563\pi$
$283$	17.4385			1.03661			0.518306	+	0.855195i	$0.326563\pi$
$284$	0.124820			0.00740671
$285$		0			0
$286$	−4.55234	+	7.88489i	−0.269186	+	0.466243i
$287$		0			0
$288$		0			0
$289$	7.87316	+	13.6367i	0.463127	+	0.802160i
$290$	3.25292	+	5.63422i	0.191018	+	0.330853i
$291$		0			0
$292$	8.28903	−	14.3570i	0.485079	−	0.840181i
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	0.838537	−	0.544845i	$-0.183412\pi$
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	−0.891118	+	0.453772i	$0.850078\pi$
$294$		0			0
$295$	4.69094	−	8.12495i	0.273117	−	0.473053i
$296$	1.68938	+	2.92609i	0.0981931	+	0.170075i
$297$		0			0
$298$	2.86766	−	4.96693i	0.166119	−	0.287727i
$299$	14.9757			0.866068
$300$		0			0
$301$		0			0
$302$	−5.91878	−	10.2516i	−0.340588	−	0.589915i
$303$		0			0
$304$	3.02300	+	5.23599i	0.173381	+	0.300305i
$305$	0.0536236	−	0.0928787i	0.00307048	−	0.00531822i
$306$		0			0
$307$	−1.06478			−0.0607699			−0.0303850	−	0.999538i	$-0.509673\pi$
$307$	−1.06478			−0.0607699			−0.0303850	+	0.999538i	$0.509673\pi$
$308$		0			0
$309$		0			0
$310$	−1.19676	+	2.07286i	−0.0679717	+	0.117730i
$311$	−16.9293			−0.959970			−0.479985	−	0.877277i	$-0.659358\pi$
$311$	−16.9293			−0.959970			−0.479985	+	0.877277i	$0.659358\pi$
$312$		0			0
$313$	8.27856			0.467932			0.233966	−	0.972245i	$-0.424830\pi$
$313$	8.27856			0.467932			0.233966	+	0.972245i	$0.424830\pi$
$314$	4.23750			0.239136
$315$		0			0
$316$	2.86082			0.160934
$317$	−6.54741			−0.367739			−0.183870	−	0.982951i	$-0.558862\pi$
$317$	−6.54741			−0.367739			−0.183870	+	0.982951i	$0.558862\pi$
$318$		0			0
$319$	33.5840			1.88034
$320$	−0.609811	+	1.05622i	−0.0340895	+	0.0590447i
$321$		0			0
$322$		0			0
$323$	4.49556			0.250140
$324$		0			0
$325$	−4.08997	+	7.08404i	−0.226871	+	0.392952i
$326$	2.68893	+	4.65736i	0.148926	+	0.257947i
$327$		0			0
$328$	0.296049	+	0.512773i	0.0163466	+	0.0283131i
$329$		0			0
$330$		0			0
$331$	−26.7258			−1.46899			−0.734493	−	0.678617i	$-0.762580\pi$
$331$	−26.7258			−1.46899			−0.734493	+	0.678617i	$0.762580\pi$
$332$	11.2203	−	19.4341i	0.615792	−	1.06658i
$333$		0			0
$334$	−0.710806	−	1.23115i	−0.0388936	−	0.0673657i
$335$	8.96834	−	15.5336i	0.489993	−	0.848692i
$336$		0			0
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	0.706694	−	0.707520i	$-0.250186\pi$
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	−0.966077	+	0.258255i	$0.916853\pi$
$338$	−1.81397	+	3.14189i	−0.0986670	+	0.170896i
$339$		0			0
$340$	−1.23701	−	2.14257i	−0.0670864	−	0.116197i
$341$	6.17786	+	10.7004i	0.334550	+	0.579457i
$342$		0			0
$343$		0			0
$344$	−1.18605	+	2.05429i	−0.0639473	+	0.110760i
$345$		0			0
$346$	12.2591			0.659053
$347$	18.7031			1.00404			0.502018	−	0.864857i	$-0.332591\pi$
$347$	18.7031			1.00404			0.502018	+	0.864857i	$0.332591\pi$
$348$		0			0
$349$	15.0542	−	26.0747i	0.805834	−	1.39574i	−0.109893	−	0.993943i	$-0.535051\pi$
$349$	15.0542	−	26.0747i	0.805834	−	1.39574i	0.915727	−	0.401801i	$-0.131616\pi$
$350$		0			0
$351$		0			0
$352$	14.2244	+	24.6374i	0.758164	+	1.31318i
$353$	−3.12966	−	5.42074i	−0.166575	−	0.288517i	0.770638	−	0.637273i	$-0.219938\pi$
$353$	−3.12966	−	5.42074i	−0.166575	−	0.288517i	−0.937214	+	0.348756i	$0.886604\pi$
$354$		0			0
$355$	0.0573502	−	0.0993335i	0.00304383	−	0.00527208i
$356$	−10.4870	−	18.1639i	−0.555807	−	0.962686i
$357$		0			0
$358$	2.55582	−	4.42680i	0.135079	−	0.233964i
$359$	5.09755	+	8.82921i	0.269038	+	0.465988i	0.968614	−	0.248571i	$-0.0799608\pi$
$359$	5.09755	+	8.82921i	0.269038	+	0.465988i	−0.699575	+	0.714559i	$0.746628\pi$
$360$		0			0
$361$	1.43970	−	2.49364i	0.0757739	−	0.131244i
$362$	10.4106			0.547171
$363$		0			0
$364$		0			0
$365$	−7.61701	−	13.1931i	−0.398693	−	0.690556i
$366$		0			0
$367$	−14.3278	−	24.8165i	−0.747906	−	1.29541i	−0.948824	−	0.315804i	$-0.897726\pi$
$367$	−14.3278	−	24.8165i	−0.747906	−	1.29541i	0.200918	−	0.979608i	$-0.435608\pi$
$368$	4.09332	−	7.08984i	0.213379	−	0.369584i
$369$		0			0
$370$	1.35595			0.0704926
$371$		0			0
$372$		0			0
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	−0.579421	−	0.815028i	$-0.696721\pi$
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	0.995546	+	0.0942796i	$0.0300548\pi$
$374$	3.70083			0.191365
$375$		0			0
$376$	−22.5535			−1.16311
$377$	−18.7619			−0.966286
$378$		0			0
$379$	−1.01893			−0.0523388			−0.0261694	−	0.999658i	$-0.508331\pi$
$379$	−1.01893			−0.0523388			−0.0261694	+	0.999658i	$0.508331\pi$
$380$	8.87158			0.455103
$381$		0			0
$382$	9.94270			0.508713
$383$	5.79327	−	10.0342i	0.296022	−	0.512725i	−0.679200	−	0.733953i	$-0.737673\pi$
$383$	5.79327	−	10.0342i	0.296022	−	0.512725i	0.975222	+	0.221228i	$0.0710065\pi$
$384$		0			0
$385$		0			0
$386$	−11.1059			−0.565275
$387$		0			0
$388$	4.18924	−	7.25598i	0.212677	−	0.368367i
$389$	8.90675	+	15.4270i	0.451590	+	0.782178i	0.998485	−	0.0550239i	$-0.0175235\pi$
$389$	8.90675	+	15.4270i	0.451590	+	0.782178i	−0.546895	+	0.837201i	$0.684190\pi$
$390$		0			0
$391$	−3.04363	−	5.27172i	−0.153923	−	0.266602i
$392$		0			0
$393$		0			0
$394$	−2.70640			−0.136346
$395$	1.31444	−	2.27668i	0.0661369	−	0.114552i
$396$		0			0
$397$	6.54229	+	11.3316i	0.328348	+	0.568715i	0.982184	−	0.187921i	$-0.0601748\pi$
$397$	6.54229	+	11.3316i	0.328348	+	0.568715i	−0.653836	+	0.756636i	$0.726841\pi$
$398$	−8.47348	+	14.6765i	−0.424737	+	0.735666i
$399$		0			0
$400$	2.23583	+	3.87257i	0.111792	+	0.193629i
$401$	7.05165	−	12.2138i	0.352143	−	0.609929i	−0.634482	−	0.772938i	$-0.718787\pi$
$401$	7.05165	−	12.2138i	0.352143	−	0.609929i	0.986625	+	0.163009i	$0.0521199\pi$
$402$		0			0
$403$	−3.45129	−	5.97782i	−0.171921	−	0.297776i
$404$	−3.98161	−	6.89636i	−0.198093	−	0.343107i
$405$		0			0
$406$		0			0
$407$	3.49980	−	6.06183i	0.173479	−	0.300474i
$408$		0			0
$409$	2.64599			0.130836			0.0654179	−	0.997858i	$-0.479162\pi$
$409$	2.64599			0.130836			0.0654179	+	0.997858i	$0.479162\pi$
$410$	0.237619			0.0117352
$411$		0			0
$412$	11.0183	−	19.0843i	0.542835	−	0.940217i
$413$		0			0
$414$		0			0
$415$	−10.3106	−	17.8585i	−0.506128	−	0.876639i
$416$	−7.94655	−	13.7638i	−0.389612	−	0.674827i
$417$		0			0
$418$	−6.63538	+	11.4928i	−0.324547	+	0.562132i
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	0.906700	+	0.421776i	$0.138593\pi$
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	−0.0880816	+	0.996113i	$0.528074\pi$
$420$		0			0
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	−0.918943	−	0.394390i	$-0.870956\pi$
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	0.801024	+	0.598633i	$0.204289\pi$
$422$	2.52210	+	4.36841i	0.122774	+	0.212651i
$423$		0			0
$424$	0.976394	−	1.69116i	0.0474179	−	0.0821302i
$425$	3.32495			0.161284
$426$		0			0
$427$		0			0
$428$	5.93923	+	10.2871i	0.287084	+	0.497244i
$429$		0			0
$430$	0.475980	+	0.824422i	0.0229538	+	0.0397571i
$431$	−17.6643	+	30.5954i	−0.850858	+	1.47373i	0.0295774	+	0.999562i	$0.490584\pi$
$431$	−17.6643	+	30.5954i	−0.850858	+	1.47373i	−0.880435	+	0.474166i	$0.842749\pi$
$432$		0			0
$433$	−5.47404			−0.263066			−0.131533	−	0.991312i	$-0.541990\pi$
$433$	−5.47404			−0.263066			−0.131533	+	0.991312i	$0.541990\pi$
$434$		0			0
$435$		0			0
$436$	1.31712	−	2.28131i	0.0630785	−	0.109255i
$437$	21.8282			1.04419
$438$		0			0
$439$	−6.39812			−0.305365			−0.152683	−	0.988275i	$-0.548791\pi$
$439$	−6.39812			−0.305365			−0.152683	+	0.988275i	$0.548791\pi$
$440$	16.7228			0.797229
$441$		0			0
$442$	−2.06749			−0.0983404
$443$	6.38682			0.303447			0.151723	−	0.988423i	$-0.451518\pi$
$443$	6.38682			0.303447			0.151723	+	0.988423i	$0.451518\pi$
$444$		0			0
$445$	−19.2735			−0.913650
$446$	4.35200	−	7.53789i	0.206073	−	0.356929i
$447$		0			0
$448$		0			0
$449$	11.7460			0.554327			0.277163	−	0.960823i	$-0.410606\pi$
$449$	11.7460			0.554327			0.277163	+	0.960823i	$0.410606\pi$
$450$		0			0
$451$	0.613311	−	1.06229i	0.0288797	−	0.0500210i
$452$	−0.465741	−	0.806687i	−0.0219066	−	0.0379434i
$453$		0			0
$454$	−9.70859	−	16.8158i	−0.455647	−	0.789203i
$455$		0			0
$456$		0			0
$457$	10.5224			0.492217			0.246108	−	0.969242i	$-0.420848\pi$
$457$	10.5224			0.492217			0.246108	+	0.969242i	$0.420848\pi$
$458$	−5.17356	+	8.96087i	−0.241745	+	0.418714i
$459$		0			0
$460$	−6.00633	−	10.4033i	−0.280046	−	0.485055i
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	−0.936657	−	0.350249i	$-0.886097\pi$
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	0.771653	+	0.636044i	$0.219430\pi$
$462$		0			0
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	0.942305	+	0.334755i	$0.108654\pi$
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	−0.181246	+	0.983438i	$0.558013\pi$
$464$	−5.12820	+	8.88230i	−0.238071	+	0.412350i
$465$		0			0
$466$	−1.65789	−	2.87156i	−0.0768004	−	0.133022i
$467$	1.96216	+	3.39856i	0.0907978	+	0.157266i	0.907847	−	0.419301i	$-0.137725\pi$
$467$	1.96216	+	3.39856i	0.0907978	+	0.157266i	−0.817049	+	0.576568i	$0.804392\pi$
$468$		0			0
$469$		0			0
$470$	−4.52555	+	7.83849i	−0.208748	+	0.361563i
$471$		0			0
$472$	−15.6709			−0.721310
$473$	4.91414			0.225952
$474$		0			0
$475$	−5.96145	+	10.3255i	−0.273530	+	0.473768i
$476$		0			0
$477$		0			0
$478$	4.36878	+	7.56694i	0.199823	+	0.346104i
$479$	−8.04324	−	13.9313i	−0.367505	−	0.636537i	0.621670	−	0.783279i	$-0.286455\pi$
$479$	−8.04324	−	13.9313i	−0.367505	−	0.636537i	−0.989175	+	0.146742i	$0.953121\pi$
$480$		0			0
$481$	−1.95518	+	3.38647i	−0.0891486	+	0.154410i
$482$	−4.88755	−	8.46549i	−0.222622	−	0.385592i
$483$		0			0
$484$	10.3216	−	17.8775i	0.469162	−	0.812612i
$485$	−3.84961	−	6.66771i	−0.174802	−	0.302765i
$486$		0			0
$487$	−1.75172	+	3.03407i	−0.0793781	+	0.137487i	−0.902982	−	0.429679i	$-0.858627\pi$
$487$	−1.75172	+	3.03407i	−0.0793781	+	0.137487i	0.823604	+	0.567166i	$0.191960\pi$
$488$	−0.179138			−0.00810921
$489$		0			0
$490$		0			0
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.787296	+	0.616575i	$0.211480\pi$
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.140321	+	0.990106i	$0.455186\pi$
$492$		0			0
$493$	3.81312	+	6.60452i	0.171734	+	0.297452i
$494$	3.70689	−	6.42053i	0.166781	−	0.288873i
$495$		0			0
$496$	−3.77338			−0.169430
$497$		0			0
$498$		0			0
$499$	−5.91486	+	10.2448i	−0.264785	+	0.458622i	−0.967507	−	0.252843i	$-0.918634\pi$
$499$	−5.91486	+	10.2448i	−0.264785	+	0.458622i	0.702722	+	0.711465i	$0.251968\pi$
$500$	17.6094			0.787517
$501$		0			0
$502$	9.43261			0.420998
$503$	21.8595			0.974665			0.487332	−	0.873217i	$-0.337970\pi$
$503$	21.8595			0.974665			0.487332	+	0.873217i	$0.337970\pi$
$504$		0			0
$505$	−7.31762			−0.325630
$506$	17.9694			0.798837
$507$		0			0
$508$	−11.2574			−0.499466
$509$	−8.44831	+	14.6329i	−0.374465	+	0.648592i	−0.990247	−	0.139324i	$-0.955507\pi$
$509$	−8.44831	+	14.6329i	−0.374465	+	0.648592i	0.615782	+	0.787917i	$0.288840\pi$
$510$		0			0
$511$		0			0
$512$	−15.8563			−0.700756
$513$		0			0
$514$	−2.80271	+	4.85444i	−0.123622	+	0.214120i
$515$	−10.1250	−	17.5371i	−0.446163	−	0.772777i
$516$		0			0
$517$	23.3615	+	40.4633i	1.02744	+	1.77957i
$518$		0			0
$519$		0			0
$520$	−9.34230			−0.409687
$521$	−17.2466	+	29.8720i	−0.755587	+	1.30872i	0.189495	+	0.981882i	$0.439315\pi$
$521$	−17.2466	+	29.8720i	−0.755587	+	1.30872i	−0.945082	+	0.326834i	$0.894018\pi$
$522$		0			0
$523$	−0.995615	−	1.72445i	−0.0435352	−	0.0754051i	0.843437	−	0.537229i	$-0.180529\pi$
$523$	−0.995615	−	1.72445i	−0.0435352	−	0.0754051i	−0.886972	+	0.461823i	$0.847195\pi$
$524$	−15.8577	+	27.4664i	−0.692749	+	1.19988i
$525$		0			0
$526$	−1.09622	−	1.89870i	−0.0477972	−	0.0827873i
$527$	−1.40287	+	2.42983i	−0.0611098	+	0.105845i
$528$		0			0
$529$	−3.27836	−	5.67829i	−0.142538	−	0.246882i
$530$	−0.391843	−	0.678693i	−0.0170206	−	0.0294805i
$531$		0			0
$532$		0			0
$533$	−0.342629	+	0.593452i	−0.0148409	+	0.0257052i
$534$		0			0
$535$	10.9154			0.471916
$536$	−29.9602			−1.29408
$537$		0			0
$538$	5.15720	−	8.93253i	0.222343	−	0.385109i
$539$		0			0
$540$		0			0
$541$	−15.0681	−	26.0988i	−0.647830	−	1.12207i	−0.983640	−	0.180145i	$-0.942343\pi$
$541$	−15.0681	−	26.0988i	−0.647830	−	1.12207i	0.335810	−	0.941930i	$-0.390990\pi$
$542$	2.72362	+	4.71745i	0.116989	+	0.202632i
$543$		0			0
$544$	−3.23008	+	5.59466i	−0.138488	+	0.239869i
$545$	−1.21033	−	2.09636i	−0.0518450	−	0.0897982i
$546$		0			0
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	−0.653792	−	0.756674i	$-0.726823\pi$
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	0.982195	+	0.187864i	$0.0601563\pi$
$548$	−9.46800	−	16.3991i	−0.404453	−	0.700533i
$549$		0			0
$550$	−4.90757	+	8.50016i	−0.209260	+	0.362448i
$551$	−27.3469			−1.16502
$552$		0			0
$553$		0			0
$554$	4.30546	+	7.45728i	0.182921	+	0.316829i
$555$		0			0
$556$	−1.92423	−	3.33287i	−0.0816056	−	0.141345i
$557$	11.6412	−	20.1631i	0.493252	−	0.854338i	−0.506718	−	0.862112i	$-0.669141\pi$
$557$	11.6412	−	20.1631i	0.493252	−	0.854338i	0.999970	+	0.00777438i	$0.00247469\pi$
$558$		0			0
$559$	−2.74531			−0.116114
$560$		0			0
$561$		0			0
$562$	−0.485375	+	0.840695i	−0.0204743	+	0.0354626i
$563$	4.55885			0.192133			0.0960663	−	0.995375i	$-0.469374\pi$
$563$	4.55885			0.192133			0.0960663	+	0.995375i	$0.469374\pi$
$564$		0			0
$565$	−0.855964			−0.0360107
$566$	−11.6896			−0.491351
$567$		0			0
$568$	−0.191588			−0.00803885
$569$	−18.1995			−0.762963			−0.381482	−	0.924376i	$-0.624586\pi$
$569$	−18.1995			−0.762963			−0.381482	+	0.924376i	$0.624586\pi$
$570$		0			0
$571$	−17.0455			−0.713332			−0.356666	−	0.934232i	$-0.616087\pi$
$571$	−17.0455			−0.713332			−0.356666	+	0.934232i	$0.616087\pi$
$572$	−10.5307	+	18.2398i	−0.440313	+	0.762644i
$573$		0			0
$574$		0			0
$575$	16.1443			0.673264
$576$		0			0
$577$	5.70473	−	9.88088i	0.237491	−	0.411346i	−0.722503	−	0.691368i	$-0.757008\pi$
$577$	5.70473	−	9.88088i	0.237491	−	0.411346i	0.959994	+	0.280022i	$0.0903417\pi$
$578$	−5.27764	−	9.14113i	−0.219521	−	0.380221i
$579$		0			0
$580$	7.52485	+	13.0334i	0.312452	+	0.541183i
$581$		0			0
$582$		0			0
$583$	−4.04549			−0.167547
$584$	−12.7229	+	22.0368i	−0.526479	+	0.911889i
$585$		0			0
$586$	0.603332	+	1.04500i	0.0249234	+	0.0431686i
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	−0.809190	−	0.587548i	$-0.800094\pi$
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	0.913426	+	0.407005i	$0.133427\pi$
$588$		0			0
$589$	−5.03052	−	8.71312i	−0.207279	−	0.359018i
$590$	−3.14449	+	5.44642i	−0.129457	+	0.224226i
$591$		0			0
$592$	1.06882	+	1.85126i	0.0439283	+	0.0760861i
$593$	−9.98892	−	17.3013i	−0.410196	−	0.710480i	0.584715	−	0.811239i	$-0.301206\pi$
$593$	−9.98892	−	17.3013i	−0.410196	−	0.710480i	−0.994911	+	0.100759i	$0.967873\pi$
$594$		0			0
$595$		0			0
$596$	6.63365	−	11.4898i	0.271725	−	0.470641i
$597$		0			0
$598$	−10.0387			−0.410513
$599$	−4.39321			−0.179502			−0.0897508	−	0.995964i	$-0.528607\pi$
$599$	−4.39321			−0.179502			−0.0897508	+	0.995964i	$0.528607\pi$
$600$		0			0
$601$	−12.1778	+	21.0926i	−0.496743	+	0.860385i	−0.999993	−	0.00375637i	$-0.998804\pi$
$601$	−12.1778	+	21.0926i	−0.496743	+	0.860385i	0.503250	+	0.864141i	$0.332138\pi$
$602$		0			0
$603$		0			0
$604$	−13.6917	−	23.7147i	−0.557107	−	0.964937i
$605$	−9.48476	−	16.4281i	−0.385610	−	0.667897i
$606$		0			0
$607$	6.56281	−	11.3671i	0.266376	−	0.461377i	−0.701547	−	0.712623i	$-0.747507\pi$
$607$	6.56281	−	11.3671i	0.266376	−	0.461377i	0.967923	+	0.251246i	$0.0808403\pi$
$608$	−11.5827	−	20.0618i	−0.469741	−	0.813615i
$609$		0			0
$610$	−0.0359456	+	0.0622597i	−0.00145540	+	0.00252082i
$611$	−13.0510	−	22.6051i	−0.527988	−	0.914502i
$612$		0			0
$613$	−23.2403	+	40.2534i	−0.938667	+	1.62582i	−0.170707	+	0.985322i	$0.554605\pi$
$613$	−23.2403	+	40.2534i	−0.938667	+	1.62582i	−0.767960	+	0.640497i	$0.778728\pi$
$614$	0.713754			0.0288048
$615$		0			0
$616$		0			0
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	−0.996416	−	0.0845873i	$-0.973043\pi$
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	0.424953	−	0.905215i	$-0.360291\pi$
$618$		0			0
$619$	15.9606	+	27.6446i	0.641511	+	1.11113i	0.985096	+	0.172008i	$0.0550254\pi$
$619$	15.9606	+	27.6446i	0.641511	+	1.11113i	−0.343585	+	0.939122i	$0.611641\pi$
$620$	−2.76843	+	4.79506i	−0.111183	+	0.192574i
$621$		0			0
$622$	11.3482			0.455023
$623$		0			0
$624$		0			0
$625$	0.666993	−	1.15527i	0.0266797	−	0.0462106i
$626$	−5.54939			−0.221798
$627$		0			0
$628$	9.80244			0.391160
$629$	1.58947			0.0633762
$630$		0			0
$631$	38.7184			1.54135			0.770677	−	0.637226i	$-0.219918\pi$
$631$	38.7184			1.54135			0.770677	+	0.637226i	$0.219918\pi$
$632$	−4.39112			−0.174669
$633$		0			0
$634$	4.38895			0.174307
$635$	−5.17236	+	8.95878i	−0.205259	+	0.355519i
$636$		0			0
$637$		0			0
$638$	−22.5124			−0.891276
$639$		0			0
$640$	−7.81261	+	13.5318i	−0.308821	+	0.534893i
$641$	−20.2001	−	34.9875i	−0.797854	−	1.38192i	−0.921011	−	0.389537i	$-0.872635\pi$
$641$	−20.2001	−	34.9875i	−0.797854	−	1.38192i	0.123157	−	0.992387i	$-0.460698\pi$
$642$		0			0
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	0.715400	−	0.698715i	$-0.246244\pi$
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	−0.962805	+	0.270198i	$0.912911\pi$
$644$		0			0
$645$		0			0
$646$	−3.01352			−0.118565
$647$	17.2774	−	29.9253i	0.679245	−	1.17649i	−0.295964	−	0.955199i	$-0.595641\pi$
$647$	17.2774	−	29.9253i	0.679245	−	1.17649i	0.975209	−	0.221287i	$-0.0710258\pi$
$648$		0			0
$649$	16.2323	+	28.1151i	0.637173	+	1.10362i
$650$	2.74164	−	4.74866i	0.107536	−	0.186258i
$651$		0			0
$652$	6.22019	+	10.7737i	0.243602	+	0.421930i
$653$	−11.1472	+	19.3075i	−0.436223	+	0.755560i	−0.997395	−	0.0721392i	$-0.977017\pi$
$653$	−11.1472	+	19.3075i	−0.436223	+	0.755560i	0.561172	+	0.827699i	$0.310351\pi$
$654$		0			0
$655$	14.5721	+	25.2396i	0.569379	+	0.986194i
$656$	0.187302	+	0.324417i	0.00731293	+	0.0126664i
$657$		0			0
$658$		0			0
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	−0.927217	−	0.374526i	$-0.877806\pi$
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	0.787957	+	0.615730i	$0.211139\pi$
$660$		0			0
$661$	−42.9060			−1.66885			−0.834425	−	0.551122i	$-0.814200\pi$
$661$	−42.9060			−1.66885			−0.834425	+	0.551122i	$0.814200\pi$
$662$	17.9152			0.696294
$663$		0			0
$664$	−17.2221	+	29.8296i	−0.668349	+	1.15761i
$665$		0			0
$666$		0			0
$667$	18.5146	+	32.0683i	0.716889	+	1.24169i
$668$	−1.64428	−	2.84798i	−0.0636191	−	0.110192i
$669$		0			0
$670$	−6.01177	+	10.4127i	−0.232255	+	0.402277i
$671$	0.185556	+	0.321392i	0.00716331	+	0.0124072i
$672$		0			0
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	0.232944	+	0.972490i	$0.425164\pi$
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	−0.958673	+	0.284510i	$0.908169\pi$
$674$	3.19188	+	5.52850i	0.122947	+	0.212950i
$675$		0			0
$676$	−4.19619	+	7.26801i	−0.161392	+	0.279539i
$677$	−26.3616			−1.01316			−0.506580	−	0.862193i	$-0.669090\pi$
$677$	−26.3616			−1.01316			−0.506580	+	0.862193i	$0.669090\pi$
$678$		0			0
$679$		0			0
$680$	1.89871	+	3.28866i	0.0728121	+	0.126114i
$681$		0			0
$682$	−4.14122	−	7.17280i	−0.158575	−	0.274661i
$683$	−1.96588	+	3.40500i	−0.0752222	+	0.130289i	−0.901183	−	0.433439i	$-0.857300\pi$
$683$	−1.96588	+	3.40500i	−0.0752222	+	0.130289i	0.825961	+	0.563728i	$0.190633\pi$
$684$		0			0
$685$	−17.4008			−0.664850
$686$		0			0
$687$		0			0
$688$	−0.750378	+	1.29969i	−0.0286079	+	0.0495503i
$689$	2.26004			0.0861006
$690$		0			0
$691$	−19.9010			−0.757072			−0.378536	−	0.925587i	$-0.623572\pi$
$691$	−19.9010			−0.757072			−0.378536	+	0.925587i	$0.623572\pi$
$692$	28.3585			1.07803
$693$		0			0
$694$	−12.5373			−0.475910
$695$	−3.53645			−0.134145
$696$		0			0
$697$	0.278541			0.0105505
$698$	−10.0913	+	17.4787i	−0.381963	+	0.661579i
$699$		0			0
$700$		0			0
$701$	−43.7908			−1.65396			−0.826979	−	0.562234i	$-0.809942\pi$
$701$	−43.7908			−1.65396			−0.826979	+	0.562234i	$0.809942\pi$
$702$		0			0
$703$	−2.84983	+	4.93604i	−0.107483	+	0.186166i
$704$	−2.11016	−	3.65490i	−0.0795295	−	0.137749i
$705$		0			0
$706$	2.09792	+	3.63370i	0.0789561	+	0.136756i
$707$		0			0
$708$		0			0
$709$	44.6344			1.67628			0.838139	−	0.545457i	$-0.183644\pi$
$709$	44.6344			1.67628			0.838139	+	0.545457i	$0.183644\pi$
$710$	−0.0384437	+	0.0665865i	−0.00144277	+	0.00249895i
$711$		0			0
$712$	16.0966	+	27.8801i	0.603244	+	1.04485i
$713$	−6.81163	+	11.7981i	−0.255097	+	0.441842i
$714$		0			0
$715$	9.67699	+	16.7610i	0.361899	+	0.626827i
$716$	5.91227	−	10.2403i	0.220952	−	0.382700i
$717$		0			0
$718$	−3.41705	−	5.91851i	−0.127523	−	0.220877i
$719$	−19.5096	−	33.7917i	−0.727586	−	1.26022i	−0.957901	−	0.287100i	$-0.907309\pi$
$719$	−19.5096	−	33.7917i	−0.727586	−	1.26022i	0.230315	−	0.973116i	$-0.426024\pi$
$720$		0			0
$721$		0			0
$722$	−0.965081	+	1.67157i	−0.0359166	+	0.0622094i
$723$		0			0
$724$	24.0825			0.895019
$725$	−20.2259			−0.751171
$726$		0			0
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	−0.578242	−	0.815865i	$-0.696261\pi$
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	0.995681	+	0.0928402i	$0.0295946\pi$
$728$		0			0
$729$		0			0
$730$	5.10593	+	8.84373i	0.188979	+	0.327321i
$731$	0.557951	+	0.966399i	0.0206366	+	0.0357436i
$732$		0			0
$733$	−0.448519	+	0.776858i	−0.0165664	+	0.0286939i	−0.874190	−	0.485584i	$-0.838607\pi$
$733$	−0.448519	+	0.776858i	−0.0165664	+	0.0286939i	0.857623	+	0.514278i	$0.171940\pi$
$734$	9.60441	+	16.6353i	0.354505	+	0.614021i
$735$		0			0
$736$	−15.6837	+	27.1649i	−0.578108	+	1.00131i
$737$	31.0335	+	53.7517i	1.14314	+	1.97997i
$738$		0			0
$739$	1.79032	−	3.10092i	0.0658578	−	0.114069i	−0.831216	−	0.555949i	$-0.812355\pi$
$739$	1.79032	−	3.10092i	0.0658578	−	0.114069i	0.897074	+	0.441880i	$0.145688\pi$
$740$	3.13667			0.115306
$741$		0			0
$742$		0			0
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.814493	+	0.580173i	$0.197015\pi$
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.0951977	+	0.995458i	$0.469652\pi$
$744$		0			0
$745$	−6.09583	−	10.5583i	−0.223334	−	0.386826i
$746$	−5.38726	+	9.33101i	−0.197242	+	0.341633i
$747$		0			0
$748$	8.56098			0.313020
$749$		0			0
$750$		0			0
$751$	21.4515	−	37.1551i	0.782776	−	1.35581i	−0.147543	−	0.989056i	$-0.547136\pi$
$751$	21.4515	−	37.1551i	0.782776	−	1.35581i	0.930319	−	0.366752i	$-0.119530\pi$
$752$	−14.2690			−0.520337
$753$		0			0
$754$	12.5767			0.458016
$755$	−25.1633			−0.915786
$756$		0			0
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$	0.683021			0.0248084
$759$		0			0
$760$	−13.6171			−0.493945
$761$	−20.3599	+	35.2643i	−0.738044	+	1.27833i	0.215330	+	0.976541i	$0.430917\pi$
$761$	−20.3599	+	35.2643i	−0.738044	+	1.27833i	−0.953375	+	0.301789i	$0.902416\pi$
$762$		0			0
$763$		0			0
$764$	23.0001			0.832113
$765$		0			0
$766$	−3.88342	+	6.72627i	−0.140313	+	0.243030i
$767$	−9.06826	−	15.7067i	−0.327436	−	0.567135i
$768$		0			0
$769$	−5.57381	−	9.65413i	−0.200997	−	0.348137i	0.747853	−	0.663864i	$-0.231085\pi$
$769$	−5.57381	−	9.65413i	−0.200997	−	0.348137i	−0.948850	+	0.315728i	$0.897751\pi$
$770$		0			0
$771$		0			0
$772$	−25.6908			−0.924633
$773$	−0.462831	+	0.801647i	−0.0166469	+	0.0288332i	−0.874229	−	0.485514i	$-0.838632\pi$
$773$	−0.462831	+	0.801647i	−0.0166469	+	0.0288332i	0.857582	+	0.514347i	$0.171966\pi$
$774$		0			0
$775$	−3.72061	−	6.44428i	−0.133648	−	0.231485i
$776$	−6.43012	+	11.1373i	−0.230828	+	0.399806i
$777$		0			0
$778$	−5.97049	−	10.3412i	−0.214052	−	0.370750i
$779$	−0.499408	+	0.865001i	−0.0178932	+	0.0309919i
$780$		0			0
$781$	0.198452	+	0.343728i	0.00710116	+	0.0122996i
$782$	2.04024	+	3.53381i	0.0729590	+	0.126369i
$783$		0			0
$784$		0			0
$785$	4.50386	−	7.80092i	0.160750	−	0.278427i
$786$		0			0
$787$	−23.0240			−0.820716			−0.410358	−	0.911925i	$-0.634596\pi$
$787$	−23.0240			−0.820716			−0.410358	+	0.911925i	$0.634596\pi$
$788$	−6.26061			−0.223025
$789$		0			0
$790$	−0.881115	+	1.52614i	−0.0313487	+	0.0542975i
$791$		0			0
$792$		0			0
$793$	−0.103662	−	0.179548i	−0.00368114	−	0.00637593i
$794$	−4.38551	−	7.59592i	−0.155636	−	0.269569i
$795$		0			0
$796$	−19.6014	+	33.9505i	−0.694752	+	1.20335i
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	0.994151	−	0.108000i	$-0.0344447\pi$
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	−0.590606	+	0.806960i	$0.701111\pi$
$798$		0			0
$799$	−5.30492	+	9.18839i	−0.187675	+	0.325062i
$800$	−8.56664	−	14.8379i	−0.302877	−	0.524598i
$801$		0			0
$802$	−4.72695	+	8.18732i	−0.166914	+	0.289104i
$803$	52.7150			1.86027
$804$		0			0
$805$		0			0
$806$	2.31352	+	4.00713i	0.0814901	+	0.141145i
$807$		0			0
$808$	6.11143	+	10.5853i	0.214999	+	0.372390i
$809$	−6.73753	+	11.6697i	−0.236879	+	0.410286i	−0.959817	−	0.280627i	$-0.909458\pi$
$809$	−6.73753	+	11.6697i	−0.236879	+	0.410286i	0.722938	+	0.690913i	$0.242791\pi$
$810$		0			0
$811$	30.7348			1.07924			0.539622	−	0.841907i	$-0.318567\pi$
$811$	30.7348			1.07924			0.539622	+	0.841907i	$0.318567\pi$
$812$		0			0
$813$		0			0
$814$	−2.34603	+	4.06344i	−0.0822283	+	0.142424i
$815$	11.4318			0.400439
$816$		0			0
$817$	−4.00150			−0.139995
$818$	−1.77369			−0.0620158
$819$		0			0
$820$	0.549675			0.0191955
$821$	16.9864			0.592829			0.296414	−	0.955059i	$-0.404209\pi$
$821$	16.9864			0.592829			0.296414	+	0.955059i	$0.404209\pi$
$822$		0			0
$823$	−18.5831			−0.647768			−0.323884	−	0.946097i	$-0.604989\pi$
$823$	−18.5831			−0.647768			−0.323884	+	0.946097i	$0.604989\pi$
$824$	−16.9122	+	29.2928i	−0.589164	+	1.02046i
$825$		0			0
$826$		0			0
$827$	−14.5419			−0.505670			−0.252835	−	0.967509i	$-0.581363\pi$
$827$	−14.5419			−0.505670			−0.252835	+	0.967509i	$0.581363\pi$
$828$		0			0
$829$	−4.78717	+	8.29161i	−0.166265	+	0.287980i	−0.937104	−	0.349051i	$-0.886504\pi$
$829$	−4.78717	+	8.29161i	−0.166265	+	0.287980i	0.770839	+	0.637030i	$0.219837\pi$
$830$	6.91154	+	11.9711i	0.239903	+	0.415524i
$831$		0			0
$832$	1.17885	+	2.04183i	0.0408693	+	0.0707877i
$833$		0			0
$834$		0			0
$835$	−3.02195			−0.104579
$836$	−15.3494	+	26.5859i	−0.530869	+	0.919492i
$837$		0			0
$838$	−11.2326	−	19.4554i	−0.388023	−	0.672075i
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	−0.222664	−	0.974895i	$-0.571475\pi$
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	0.955616	−	0.294615i	$-0.0951913\pi$
$840$		0			0
$841$	−8.69551	−	15.0611i	−0.299845	−	0.519347i
$842$	1.62187	−	2.80917i	0.0558934	−	0.0968103i
$843$		0			0
$844$	5.83428	+	10.1053i	0.200824	+	0.347838i
$845$	3.85599	+	6.67877i	0.132650	+	0.229757i
$846$		0			0
$847$		0			0
$848$	0.617738	−	1.06995i	0.0212132	−	0.0367423i
$849$		0			0
$850$	−2.22882			−0.0764479
$851$	7.71767			0.264558
$852$		0			0
$853$	−7.14039	+	12.3675i	−0.244482	+	0.423456i	−0.961986	−	0.273099i	$-0.911951\pi$
$853$	−7.14039	+	12.3675i	−0.244482	+	0.423456i	0.717504	+	0.696555i	$0.245285\pi$
$854$		0			0
$855$		0			0
$856$	−9.11621	−	15.7897i	−0.311586	−	0.539682i
$857$	−17.3895	−	30.1195i	−0.594013	−	1.02886i	−0.993685	−	0.112203i	$-0.964209\pi$
$857$	−17.3895	−	30.1195i	−0.594013	−	1.02886i	0.399672	−	0.916658i	$-0.369124\pi$
$858$		0			0
$859$	−6.32429	+	10.9540i	−0.215782	+	0.373745i	−0.953514	−	0.301348i	$-0.902563\pi$
$859$	−6.32429	+	10.9540i	−0.215782	+	0.373745i	0.737732	+	0.675093i	$0.235897\pi$
$860$	1.10107	+	1.90710i	0.0375460	+	0.0650316i
$861$		0			0
$862$	11.8409	−	20.5091i	0.403304	−	0.698543i
$863$	−13.2398	−	22.9321i	−0.450690	−	0.780617i	0.547739	−	0.836649i	$-0.315489\pi$
$863$	−13.2398	−	22.9321i	−0.450690	−	0.780617i	−0.998429	+	0.0560318i	$0.982155\pi$
$864$		0			0
$865$	13.0297	−	22.5681i	0.443022	−	0.767337i
$866$	3.66943			0.124692
$867$		0			0
$868$		0			0
$869$	4.54843	+	7.87811i	0.154295	+	0.267247i
$870$		0			0
$871$	−17.3371	−	30.0287i	−0.587444	−	1.01748i
$872$	−2.02166	+	3.50162i	−0.0684621	+	0.118580i
$873$		0			0
$874$	−14.6322			−0.494941
$875$		0			0
$876$		0			0
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	−0.999747	−	0.0224835i	$-0.992843\pi$
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	0.519345	+	0.854565i	$0.326176\pi$
$878$	4.28887			0.144742
$879$		0			0
$880$	10.5801			0.356654
$881$	−20.3637			−0.686071			−0.343036	−	0.939322i	$-0.611455\pi$
$881$	−20.3637			−0.686071			−0.343036	+	0.939322i	$0.611455\pi$
$882$		0			0
$883$	49.1950			1.65554			0.827772	−	0.561065i	$-0.189608\pi$
$883$	49.1950			1.65554			0.827772	+	0.561065i	$0.189608\pi$
$884$	−4.78264			−0.160858
$885$		0			0
$886$	−4.28129			−0.143833
$887$	2.10846	−	3.65196i	0.0707952	−	0.122621i	−0.828455	−	0.560056i	$-0.810780\pi$
$887$	2.10846	−	3.65196i	0.0707952	−	0.122621i	0.899250	+	0.437435i	$0.144113\pi$
$888$		0			0
$889$		0			0
$890$	12.9196			0.433067
$891$		0			0
$892$	10.0673	−	17.4371i	0.337078	−	0.583837i
$893$	−19.0229	−	32.9486i	−0.636576	−	1.10258i
$894$		0			0
$895$	−5.43294	−	9.41013i	−0.181603	−	0.314546i
$896$		0			0
$897$		0			0
$898$	−7.87371			−0.262749
$899$	8.53374	−	14.7809i	0.284616	−	0.492970i
$900$		0			0
$901$	−0.459325	−	0.795574i	−0.0153023	−	0.0265044i
$902$	−0.411122	+	0.712084i	−0.0136889	+	0.0237098i
$903$		0			0
$904$	0.714872	+	1.23819i	0.0237763	+	0.0411817i
$905$	11.0650	−	19.1652i	0.367814	−	0.637072i
$906$		0			0
$907$	−23.9925	−	41.5563i	−0.796659	−	1.37985i	−0.921780	−	0.387713i	$-0.873265\pi$
$907$	−23.9925	−	41.5563i	−0.796659	−	1.37985i	0.125121	−	0.992142i	$-0.460068\pi$
$908$	−22.4585	−	38.8993i	−0.745311	−	1.29092i
$909$		0			0
$910$		0			0
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	−0.570247	−	0.821474i	$-0.693152\pi$
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	0.996540	+	0.0831113i	$0.0264857\pi$
$912$		0			0
$913$	71.3565			2.36155
$914$	−7.05351			−0.233309
$915$		0			0
$916$	−11.9678	+	20.7288i	−0.395427	+	0.684900i
$917$		0			0
$918$		0			0
$919$	1.13478	+	1.96550i	0.0374330	+	0.0648359i	0.884135	−	0.467232i	$-0.154749\pi$
$919$	1.13478	+	1.96550i	0.0374330	+	0.0648359i	−0.846702	+	0.532068i	$0.821415\pi$
$920$	9.21919	+	15.9681i	0.303948	+	0.526453i
$921$		0			0
$922$	2.37484	−	4.11334i	0.0782111	−	0.135466i
$923$	−0.110866	−	0.192026i	−0.00364920	−	0.00632060i
$924$		0			0
$925$	−2.10775	+	3.65073i	−0.0693024	+	0.120035i
$926$	−10.9774	−	19.0134i	−0.360740	−	0.624819i
$927$		0			0
$928$	19.6488	−	34.0328i	0.645004	−	1.11718i
$929$	45.8496			1.50428			0.752138	−	0.659006i	$-0.229023\pi$
$929$	45.8496			1.50428			0.752138	+	0.659006i	$0.229023\pi$
$930$		0			0
$931$		0			0
$932$	−3.83514	−	6.64266i	−0.125624	−	0.217587i
$933$		0			0
$934$	−1.31530	−	2.27816i	−0.0430379	−	0.0745438i
$935$	3.93346	−	6.81294i	0.128638	−	0.222807i
$936$		0			0
$937$	56.2075			1.83622			0.918110	−	0.396325i	$-0.129715\pi$
$937$	56.2075			1.83622			0.918110	+	0.396325i	$0.129715\pi$
$938$		0			0
$939$		0			0
$940$	−10.4688	+	18.1325i	−0.341454	+	0.591416i
$941$	−35.2803			−1.15011			−0.575053	−	0.818116i	$-0.695018\pi$
$941$	−35.2803			−1.15011			−0.575053	+	0.818116i	$0.695018\pi$
$942$		0			0
$943$	1.35246			0.0440421
$944$	−9.91453			−0.322691
$945$		0			0
$946$	−3.29411			−0.107101
$947$	50.7130			1.64795			0.823976	−	0.566625i	$-0.191751\pi$
$947$	50.7130			1.64795			0.823976	+	0.566625i	$0.191751\pi$
$948$		0			0
$949$	−29.4495			−0.955972
$950$	3.99615	−	6.92154i	0.129652	−	0.224564i
$951$		0			0
$952$		0			0
$953$	−25.9988			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$953$	−25.9988			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$954$		0			0
$955$	10.5677	−	18.3038i	0.341962	−	0.592296i
$956$	10.1061	+	17.5043i	0.326855	+	0.566130i
$957$		0			0
$958$	5.39165	+	9.33861i	0.174196	+	0.301717i
$959$		0			0
$960$		0			0
$961$	−24.7208			−0.797445
$962$	1.31062	−	2.27006i	0.0422562	−	0.0731898i
$963$		0			0
$964$	−11.3062	−	19.5829i	−0.364148	−	0.630722i
$965$	−11.8040	+	20.4451i	−0.379984	+	0.658152i
$966$		0			0
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	0.578239	−	0.815867i	$-0.303740\pi$
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	−0.995681	+	0.0928360i	$0.970407\pi$
$968$	−15.8427	+	27.4404i	−0.509204	+	0.881967i
$969$		0			0
$970$	2.58052	+	4.46959i	0.0828554	+	0.143510i
$971$	−3.97206	−	6.87981i	−0.127469	−	0.220783i	0.795226	−	0.606313i	$-0.207352\pi$
$971$	−3.97206	−	6.87981i	−0.127469	−	0.220783i	−0.922696	+	0.385530i	$0.874019\pi$
$972$		0			0
$973$		0			0
$974$	1.17424	−	2.03384i	0.0376249	−	0.0651683i
$975$		0			0
$976$	−0.113336			−0.00362779
$977$	52.2548			1.67178			0.835889	−	0.548898i	$-0.184952\pi$
$977$	52.2548			1.67178			0.835889	+	0.548898i	$0.184952\pi$
$978$		0			0
$979$	33.3464	−	57.7577i	1.06576	−	1.84594i
$980$		0			0
$981$		0			0
$982$	−13.7784	−	23.8650i	−0.439688	−	0.761562i
$983$	19.4190	+	33.6346i	0.619369	+	1.07278i	0.989601	+	0.143839i	$0.0459448\pi$
$983$	19.4190	+	33.6346i	0.619369	+	1.07278i	−0.370232	+	0.928939i	$0.620722\pi$
$984$		0			0
$985$	−2.87652	+	4.98228i	−0.0916535	+	0.158749i
$986$	−2.55606	−	4.42722i	−0.0814015	−	0.140991i
$987$		0			0
$988$	8.57501	−	14.8524i	0.272807	−	0.472516i
$989$	2.70914	+	4.69236i	0.0861455	+	0.149208i
$990$		0			0
$991$	−15.4689	+	26.7929i	−0.491385	+	0.851104i	−0.999951	−	0.00991892i	$-0.996843\pi$
$991$	−15.4689	+	26.7929i	−0.491385	+	0.851104i	0.508565	+	0.861023i	$0.330176\pi$
$992$	14.4578			0.459036
$993$		0			0
$994$		0			0
$995$	18.0122	+	31.1981i	0.571025	+	0.989045i
$996$		0			0
$997$	23.5335	+	40.7612i	0.745313	+	1.29092i	0.950048	+	0.312103i	$0.101033\pi$
$997$	23.5335	+	40.7612i	0.745313	+	1.29092i	−0.204735	+	0.978817i	$0.565633\pi$
$998$	3.96492	−	6.86745i	0.125507	−	0.217385i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.f.802.2		10
3.2	odd	2		441.2.h.f.214.4		10
7.2	even	3		1323.2.g.f.667.4		10
7.3	odd	6		1323.2.f.e.883.4		10
7.4	even	3		1323.2.f.f.883.4		10
7.5	odd	6		189.2.g.b.100.4		10
7.6	odd	2		189.2.h.b.46.2		10
9.4	even	3		1323.2.g.f.361.4		10
9.5	odd	6		441.2.g.f.67.2		10
21.2	odd	6		441.2.g.f.79.2		10
21.5	even	6		63.2.g.b.16.2	yes	10
21.11	odd	6		441.2.f.f.295.2		10
21.17	even	6		441.2.f.e.295.2		10
21.20	even	2		63.2.h.b.25.4	yes	10
28.19	even	6		3024.2.t.i.289.1		10
28.27	even	2		3024.2.q.i.2881.5		10
63.4	even	3		1323.2.f.f.442.4		10
63.5	even	6		63.2.h.b.58.4	yes	10
63.11	odd	6		3969.2.a.ba.1.4		5
63.13	odd	6		189.2.g.b.172.4		10
63.20	even	6		567.2.e.f.487.2		10
63.23	odd	6		441.2.h.f.373.4		10
63.25	even	3		3969.2.a.bb.1.2		5
63.31	odd	6		1323.2.f.e.442.4		10
63.32	odd	6		441.2.f.f.148.2		10
63.34	odd	6		567.2.e.e.487.4		10
63.38	even	6		3969.2.a.z.1.4		5
63.40	odd	6		189.2.h.b.37.2		10
63.41	even	6		63.2.g.b.4.2	✓	10
63.47	even	6		567.2.e.f.163.2		10
63.52	odd	6		3969.2.a.bc.1.2		5
63.58	even	3	inner	1323.2.h.f.226.2		10
63.59	even	6		441.2.f.e.148.2		10
63.61	odd	6		567.2.e.e.163.4		10
84.47	odd	6		1008.2.t.i.961.4		10
84.83	odd	2		1008.2.q.i.529.1		10
252.103	even	6		3024.2.q.i.2305.5		10
252.131	odd	6		1008.2.q.i.625.1		10
252.139	even	6		3024.2.t.i.1873.1		10
252.167	odd	6		1008.2.t.i.193.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	63.41	even	6
63.2.g.b.16.2	yes	10	21.5	even	6
63.2.h.b.25.4	yes	10	21.20	even	2
63.2.h.b.58.4	yes	10	63.5	even	6
189.2.g.b.100.4		10	7.5	odd	6
189.2.g.b.172.4		10	63.13	odd	6
189.2.h.b.37.2		10	63.40	odd	6
189.2.h.b.46.2		10	7.6	odd	2
441.2.f.e.148.2		10	63.59	even	6
441.2.f.e.295.2		10	21.17	even	6
441.2.f.f.148.2		10	63.32	odd	6
441.2.f.f.295.2		10	21.11	odd	6
441.2.g.f.67.2		10	9.5	odd	6
441.2.g.f.79.2		10	21.2	odd	6
441.2.h.f.214.4		10	3.2	odd	2
441.2.h.f.373.4		10	63.23	odd	6
567.2.e.e.163.4		10	63.61	odd	6
567.2.e.e.487.4		10	63.34	odd	6
567.2.e.f.163.2		10	63.47	even	6
567.2.e.f.487.2		10	63.20	even	6
1008.2.q.i.529.1		10	84.83	odd	2
1008.2.q.i.625.1		10	252.131	odd	6
1008.2.t.i.193.4		10	252.167	odd	6
1008.2.t.i.961.4		10	84.47	odd	6
1323.2.f.e.442.4		10	63.31	odd	6
1323.2.f.e.883.4		10	7.3	odd	6
1323.2.f.f.442.4		10	63.4	even	3
1323.2.f.f.883.4		10	7.4	even	3
1323.2.g.f.361.4		10	9.4	even	3
1323.2.g.f.667.4		10	7.2	even	3
1323.2.h.f.226.2		10	63.58	even	3	inner
1323.2.h.f.802.2		10	1.1	even	1	trivial
3024.2.q.i.2305.5		10	252.103	even	6
3024.2.q.i.2881.5		10	28.27	even	2
3024.2.t.i.289.1		10	28.19	even	6
3024.2.t.i.1873.1		10	252.139	even	6
3969.2.a.z.1.4		5	63.38	even	6
3969.2.a.ba.1.4		5	63.11	odd	6
3969.2.a.bb.1.2		5	63.25	even	3
3969.2.a.bc.1.2		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)

\(f(q)\)	\(=\)	\(q-0.670333 q^{2} -1.55065 q^{4} +(-0.712469 + 1.23403i) q^{5} +2.38012 q^{8} +O(q^{10})\)	\(q-0.670333 q^{2} -1.55065 q^{4} +(-0.712469 + 1.23403i) q^{5} +2.38012 q^{8} +(0.477591 - 0.827212i) q^{10} +(-2.46539 - 4.27018i) q^{11} +(1.37730 + 2.38556i) q^{13} +1.50584 q^{16} +(0.559839 - 0.969670i) q^{17} +(2.00752 + 3.47713i) q^{19} +(1.10479 - 1.91356i) q^{20} +(1.65263 + 2.86244i) q^{22} +(2.71830 - 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(-0.923251 - 1.59912i) q^{26} +(-3.40555 + 5.89858i) q^{29} -2.50584 q^{31} -5.76965 q^{32} +(-0.375279 + 0.650002i) q^{34} +(0.709787 + 1.22939i) q^{37} +(-1.34571 - 2.33083i) q^{38} +(-1.69576 + 2.93714i) q^{40} +(0.124384 + 0.215440i) q^{41} +(-0.498313 + 0.863104i) q^{43} +(3.82296 + 6.62156i) q^{44} +(-1.82217 + 3.15609i) q^{46} -9.47579 q^{47} +(-0.995294 - 1.72390i) q^{50} +(-2.13572 - 3.69917i) q^{52} +(0.410229 - 0.710537i) q^{53} +7.02604 q^{55} +(2.28285 - 3.95401i) q^{58} -6.58407 q^{59} -0.0752645 q^{61} +1.67974 q^{62} +0.855913 q^{64} -3.92514 q^{65} -12.5877 q^{67} +(-0.868117 + 1.50362i) q^{68} -0.0804951 q^{71} +(-5.34551 + 9.25869i) q^{73} +(-0.475793 - 0.824098i) q^{74} +(-3.11297 - 5.39183i) q^{76} -1.84491 q^{79} +(-1.07286 + 1.85825i) q^{80} +(-0.0833788 - 0.144416i) q^{82} +(-7.23583 + 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(0.334036 - 0.578567i) q^{86} +(-5.86792 - 10.1635i) q^{88} +(6.76292 + 11.7137i) q^{89} +(-4.21515 + 7.30085i) q^{92} +6.35193 q^{94} -5.72119 q^{95} +(-2.70160 + 4.67930i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) \) 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

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Modular forms

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