LMFDB - Embedded newform 252.2.l.b.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(193,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("252.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.l (of order $3$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.2
Root			$-1.58203 - 0.705117i$ of defining polynomial
Character	$\chi$	$=$	252.193
Dual form			252.2.l.b.205.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58203 - 0.705117i) q^{3} -2.52026 q^{5} +(1.98143 + 1.75326i) q^{7} +(2.00562 + 2.23103i) q^{9} +O(q^{10})$	\(q+(-1.58203 - 0.705117i) q^{3} -2.52026 q^{5} +(1.98143 + 1.75326i) q^{7} +(2.00562 + 2.23103i) q^{9} -1.37408 q^{11} +(-2.80008 + 4.84989i) q^{13} +(3.98712 + 1.77708i) q^{15} +(-2.69613 + 4.66983i) q^{17} +(2.44717 + 4.23863i) q^{19} +(-1.89842 - 4.17085i) q^{21} +4.17529 q^{23} +1.35173 q^{25} +(-1.59981 - 4.94375i) q^{27} +(-1.56761 - 2.71518i) q^{29} +(-2.40060 - 4.15797i) q^{31} +(2.17384 + 0.968889i) q^{33} +(-4.99373 - 4.41869i) q^{35} +(-2.69839 - 4.67374i) q^{37} +(7.84955 - 5.69827i) q^{39} +(-3.02991 + 5.24797i) q^{41} +(2.44717 + 4.23863i) q^{43} +(-5.05469 - 5.62278i) q^{45} +(2.82774 - 4.89779i) q^{47} +(0.852135 + 6.94794i) q^{49} +(7.55812 - 5.48671i) q^{51} +(-7.00281 + 12.1292i) q^{53} +3.46305 q^{55} +(-0.882764 - 8.43117i) q^{57} +(-7.13442 - 12.3572i) q^{59} +(3.42860 - 5.93852i) q^{61} +(0.0624137 + 7.93701i) q^{63} +(7.05695 - 12.2230i) q^{65} +(4.05678 + 7.02655i) q^{67} +(-6.60543 - 2.94407i) q^{69} -2.25704 q^{71} +(3.51456 - 6.08739i) q^{73} +(-2.13847 - 0.953127i) q^{75} +(-2.72265 - 2.40913i) q^{77} +(-1.37843 + 2.38750i) q^{79} +(-0.954983 + 8.94919i) q^{81} +(7.48876 + 12.9709i) q^{83} +(6.79495 - 11.7692i) q^{85} +(0.565480 + 5.40083i) q^{87} +(2.75804 + 4.77707i) q^{89} +(-14.0513 + 4.70043i) q^{91} +(0.865966 + 8.27073i) q^{93} +(-6.16752 - 10.6825i) q^{95} +(0.894003 + 1.54846i) q^{97} +(-2.75589 - 3.06562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−1.58203	−	0.705117i	−0.913384	−	0.407100i
$3$	−1.58203	−	0.705117i	−0.913384	−	0.407100i
$4$		0			0
$5$	−2.52026			−1.12710			−0.563548	−	0.826083i	$-0.690564\pi$
$5$	−2.52026			−1.12710			−0.563548	+	0.826083i	$0.690564\pi$
$6$		0			0
$7$	1.98143	+	1.75326i	0.748910	+	0.662671i
$7$	1.98143	+	1.75326i	0.748910	+	0.662671i
$8$		0			0
$9$	2.00562	+	2.23103i	0.668540	+	0.743676i
$10$		0			0
$11$	−1.37408			−0.414302			−0.207151	−	0.978309i	$-0.566419\pi$
$11$	−1.37408			−0.414302			−0.207151	+	0.978309i	$0.566419\pi$
$12$		0			0
$13$	−2.80008	+	4.84989i	−0.776603	+	1.34512i	0.157285	+	0.987553i	$0.449726\pi$
$13$	−2.80008	+	4.84989i	−0.776603	+	1.34512i	−0.933889	+	0.357563i	$0.883608\pi$
$14$		0			0
$15$	3.98712	+	1.77708i	1.02947	+	0.458840i
$16$		0			0
$17$	−2.69613	+	4.66983i	−0.653907	+	1.13260i	0.328260	+	0.944588i	$0.393538\pi$
$17$	−2.69613	+	4.66983i	−0.653907	+	1.13260i	−0.982167	+	0.188013i	$0.939795\pi$
$18$		0			0
$19$	2.44717	+	4.23863i	0.561420	+	0.972408i	0.997373	+	0.0724385i	$0.0230781\pi$
$19$	2.44717	+	4.23863i	0.561420	+	0.972408i	−0.435953	+	0.899969i	$0.643589\pi$
$20$		0			0
$21$	−1.89842	−	4.17085i	−0.414269	−	0.910154i
$22$		0			0
$23$	4.17529			0.870609			0.435304	−	0.900283i	$-0.356641\pi$
$23$	4.17529			0.870609			0.435304	+	0.900283i	$0.356641\pi$
$24$		0			0
$25$	1.35173			0.270346
$26$		0			0
$27$	−1.59981	−	4.94375i	−0.307883	−	0.951424i
$28$		0			0
$29$	−1.56761	−	2.71518i	−0.291097	−	0.504195i	0.682972	−	0.730444i	$-0.260687\pi$
$29$	−1.56761	−	2.71518i	−0.291097	−	0.504195i	−0.974069	+	0.226249i	$0.927354\pi$
$30$		0			0
$31$	−2.40060	−	4.15797i	−0.431161	−	0.746793i	0.565812	−	0.824534i	$-0.308563\pi$
$31$	−2.40060	−	4.15797i	−0.431161	−	0.746793i	−0.996974	+	0.0777407i	$0.975229\pi$
$32$		0			0
$33$	2.17384	+	0.968889i	0.378416	+	0.168662i
$34$		0			0
$35$	−4.99373	−	4.41869i	−0.844094	−	0.746894i
$36$		0			0
$37$	−2.69839	−	4.67374i	−0.443612	−	0.768359i	0.554342	−	0.832289i	$-0.312970\pi$
$37$	−2.69839	−	4.67374i	−0.443612	−	0.768359i	−0.997954	+	0.0639302i	$0.979637\pi$
$38$		0			0
$39$	7.84955	−	5.69827i	1.25693	−	0.912453i
$40$		0			0
$41$	−3.02991	+	5.24797i	−0.473193	+	0.819595i	−0.999529	−	0.0306820i	$-0.990232\pi$
$41$	−3.02991	+	5.24797i	−0.473193	+	0.819595i	0.526336	+	0.850277i	$0.323565\pi$
$42$		0			0
$43$	2.44717	+	4.23863i	0.373190	+	0.646385i	0.990054	−	0.140685i	$-0.0449305\pi$
$43$	2.44717	+	4.23863i	0.373190	+	0.646385i	−0.616864	+	0.787070i	$0.711597\pi$
$44$		0			0
$45$	−5.05469	−	5.62278i	−0.753509	−	0.838195i
$46$		0			0
$47$	2.82774	−	4.89779i	0.412468	−	0.714416i	−0.582691	−	0.812694i	$-0.698000\pi$
$47$	2.82774	−	4.89779i	0.412468	−	0.714416i	0.995159	+	0.0982782i	$0.0313335\pi$
$48$		0			0
$49$	0.852135	+	6.94794i	0.121734	+	0.992563i
$50$		0			0
$51$	7.55812	−	5.48671i	1.05835	−	0.768293i
$52$		0			0
$53$	−7.00281	+	12.1292i	−0.961910	+	1.66608i	−0.244214	+	0.969721i	$0.578530\pi$
$53$	−7.00281	+	12.1292i	−0.961910	+	1.66608i	−0.717696	+	0.696356i	$0.754803\pi$
$54$		0			0
$55$	3.46305			0.466958
$56$		0			0
$57$	−0.882764	−	8.43117i	−0.116925	−	1.11674i
$58$		0			0
$59$	−7.13442	−	12.3572i	−0.928823	−	1.60877i	−0.785294	−	0.619122i	$-0.787488\pi$
$59$	−7.13442	−	12.3572i	−0.928823	−	1.60877i	−0.143529	−	0.989646i	$-0.545845\pi$
$60$		0			0
$61$	3.42860	−	5.93852i	0.438988	−	0.760349i	−0.558624	−	0.829421i	$-0.688670\pi$
$61$	3.42860	−	5.93852i	0.438988	−	0.760349i	0.997612	+	0.0690720i	$0.0220038\pi$
$62$		0			0
$63$	0.0624137	+	7.93701i	0.00786338	+	0.999969i
$64$		0			0
$65$	7.05695	−	12.2230i	0.875307	−	1.51608i
$66$		0			0
$67$	4.05678	+	7.02655i	0.495615	+	0.858430i	0.999987	−	0.00505643i	$-0.00160952\pi$
$67$	4.05678	+	7.02655i	0.495615	+	0.858430i	−0.504373	+	0.863486i	$0.668276\pi$
$68$		0			0
$69$	−6.60543	−	2.94407i	−0.795200	−	0.354424i
$70$		0			0
$71$	−2.25704			−0.267861			−0.133931	−	0.990991i	$-0.542760\pi$
$71$	−2.25704			−0.267861			−0.133931	+	0.990991i	$0.542760\pi$
$72$		0			0
$73$	3.51456	−	6.08739i	0.411348	−	0.712475i	−0.583690	−	0.811977i	$-0.698392\pi$
$73$	3.51456	−	6.08739i	0.411348	−	0.712475i	0.995037	+	0.0995017i	$0.0317249\pi$
$74$		0			0
$75$	−2.13847	−	0.953127i	−0.246929	−	0.110058i
$76$		0			0
$77$	−2.72265	−	2.40913i	−0.310275	−	0.274546i
$78$		0			0
$79$	−1.37843	+	2.38750i	−0.155085	+	0.268615i	−0.933090	−	0.359643i	$-0.882898\pi$
$79$	−1.37843	+	2.38750i	−0.155085	+	0.268615i	0.778005	+	0.628258i	$0.216232\pi$
$80$		0			0
$81$	−0.954983	+	8.94919i	−0.106109	+	0.994354i
$82$		0			0
$83$	7.48876	+	12.9709i	0.821998	+	1.42374i	0.904192	+	0.427127i	$0.140474\pi$
$83$	7.48876	+	12.9709i	0.821998	+	1.42374i	−0.0821933	+	0.996616i	$0.526192\pi$
$84$		0			0
$85$	6.79495	−	11.7692i	0.737016	−	1.27655i
$86$		0			0
$87$	0.565480	+	5.40083i	0.0606258	+	0.579030i
$88$		0			0
$89$	2.75804	+	4.77707i	0.292352	+	0.506368i	0.974365	−	0.224971i	$-0.0722289\pi$
$89$	2.75804	+	4.77707i	0.292352	+	0.506368i	−0.682014	+	0.731339i	$0.738896\pi$
$90$		0			0
$91$	−14.0513	+	4.70043i	−1.47298	+	0.492739i
$92$		0			0
$93$	0.865966	+	8.27073i	0.0897965	+	0.857635i
$94$		0			0
$95$	−6.16752	−	10.6825i	−0.632774	−	1.09600i
$96$		0			0
$97$	0.894003	+	1.54846i	0.0907722	+	0.157222i	0.907836	−	0.419325i	$-0.137733\pi$
$97$	0.894003	+	1.54846i	0.0907722	+	0.157222i	−0.817064	+	0.576547i	$0.804400\pi$
$98$		0			0
$99$	−2.75589	−	3.06562i	−0.276977	−	0.308106i
$100$		0			0
$101$	13.3907			1.33242			0.666211	−	0.745763i	$-0.267915\pi$
$101$	13.3907			1.33242			0.666211	+	0.745763i	$0.267915\pi$
$102$		0			0
$103$	2.20328			0.217096			0.108548	−	0.994091i	$-0.465380\pi$
$103$	2.20328			0.217096			0.108548	+	0.994091i	$0.465380\pi$
$104$		0			0
$105$	4.78452	+	10.5116i	0.466921	+	1.02583i
$106$		0			0
$107$	4.93284	+	8.54392i	0.476875	+	0.825972i	0.999649	−	0.0264995i	$-0.00843603\pi$
$107$	4.93284	+	8.54392i	0.476875	+	0.825972i	−0.522774	+	0.852472i	$0.675103\pi$
$108$		0			0
$109$	1.54340	−	2.67325i	0.147831	−	0.256051i	−0.782595	−	0.622532i	$-0.786104\pi$
$109$	1.54340	−	2.67325i	0.147831	−	0.256051i	0.930426	+	0.366481i	$0.119438\pi$
$110$		0			0
$111$	0.973384	+	9.29667i	0.0923895	+	0.882401i
$112$		0			0
$113$	0.218815	−	0.378999i	0.0205844	−	0.0356532i	−0.855550	−	0.517721i	$-0.826781\pi$
$113$	0.218815	−	0.378999i	0.0205844	−	0.0356532i	0.876134	+	0.482067i	$0.160114\pi$
$114$		0			0
$115$	−10.5228			−0.981260
$116$		0			0
$117$	−16.4361	+	3.47996i	−1.51952	+	0.321722i
$118$		0			0
$119$	−13.5296	+	4.52592i	−1.24026	+	0.414891i
$120$		0			0
$121$	−9.11190			−0.828354
$122$		0			0
$123$	8.49384	−	6.16598i	0.765864	−	0.555968i
$124$		0			0
$125$	9.19461			0.822391
$126$		0			0
$127$	−5.75958			−0.511080			−0.255540	−	0.966798i	$-0.582253\pi$
$127$	−5.75958			−0.511080			−0.255540	+	0.966798i	$0.582253\pi$
$128$		0			0
$129$	−0.882764	−	8.43117i	−0.0777231	−	0.742323i
$130$		0			0
$131$	−1.42973			−0.124916			−0.0624580	−	0.998048i	$-0.519894\pi$
$131$	−1.42973			−0.124916			−0.0624580	+	0.998048i	$0.519894\pi$
$132$		0			0
$133$	−2.58253	+	12.6891i	−0.223934	+	1.10028i
$134$		0			0
$135$	4.03193	+	12.4595i	0.347014	+	1.07235i
$136$		0			0
$137$	11.1867			0.955744			0.477872	−	0.878430i	$-0.341408\pi$
$137$	11.1867			0.955744			0.477872	+	0.878430i	$0.341408\pi$
$138$		0			0
$139$	7.87024	−	13.6317i	0.667545	−	1.15622i	−0.311044	−	0.950396i	$-0.600679\pi$
$139$	7.87024	−	13.6317i	0.667545	−	1.15622i	0.978589	−	0.205826i	$-0.0659881\pi$
$140$		0			0
$141$	−7.92707	+	5.75454i	−0.667580	+	0.484620i
$142$		0			0
$143$	3.84755	−	6.66415i	0.321748	−	0.557284i
$144$		0			0
$145$	3.95078	+	6.84296i	0.328095	+	0.568277i
$146$		0			0
$147$	3.55101	−	11.5927i	0.292883	−	0.956148i
$148$		0			0
$149$	7.93026			0.649672			0.324836	−	0.945770i	$-0.394691\pi$
$149$	7.93026			0.649672			0.324836	+	0.945770i	$0.394691\pi$
$150$		0			0
$151$	−10.7937			−0.878376			−0.439188	−	0.898395i	$-0.644734\pi$
$151$	−10.7937			−0.878376			−0.439188	+	0.898395i	$0.644734\pi$
$152$		0			0
$153$	−15.8259	+	3.35076i	−1.27945	+	0.270893i
$154$		0			0
$155$	6.05016	+	10.4792i	0.485960	+	0.841708i
$156$		0			0
$157$	−10.5884	−	18.3396i	−0.845045	−	1.46366i	−0.885582	−	0.464483i	$-0.846240\pi$
$157$	−10.5884	−	18.3396i	−0.845045	−	1.46366i	0.0405373	−	0.999178i	$-0.487093\pi$
$158$		0			0
$159$	19.6312	−	14.2510i	1.55685	−	1.13017i
$160$		0			0
$161$	8.27305	+	7.32039i	0.652008	+	0.576927i
$162$		0			0
$163$	0.536552	+	0.929336i	0.0420260	+	0.0727912i	0.886273	−	0.463163i	$-0.153285\pi$
$163$	0.536552	+	0.929336i	0.0420260	+	0.0727912i	−0.844247	+	0.535954i	$0.819952\pi$
$164$		0			0
$165$	−5.47864	−	2.44186i	−0.426512	−	0.190098i
$166$		0			0
$167$	−7.71638	+	13.3652i	−0.597112	+	1.03423i	0.396133	+	0.918193i	$0.370352\pi$
$167$	−7.71638	+	13.3652i	−0.597112	+	1.03423i	−0.993245	+	0.116035i	$0.962982\pi$
$168$		0			0
$169$	−9.18094	−	15.9018i	−0.706226	−	1.22322i
$170$		0			0
$171$	−4.54841	+	13.9608i	−0.347825	+	1.06761i
$172$		0			0
$173$	−10.1810	+	17.6340i	−0.774046	+	1.34069i	0.161283	+	0.986908i	$0.448437\pi$
$173$	−10.1810	+	17.6340i	−0.774046	+	1.34069i	−0.935329	+	0.353779i	$0.884897\pi$
$174$		0			0
$175$	2.67835	+	2.36993i	0.202465	+	0.179150i
$176$		0			0
$177$	2.57359	+	24.5800i	0.193443	+	1.84755i
$178$		0			0
$179$	3.04960	−	5.28206i	0.227938	−	0.394800i	−0.729259	−	0.684238i	$-0.760135\pi$
$179$	3.04960	−	5.28206i	0.227938	−	0.394800i	0.957197	+	0.289438i	$0.0934684\pi$
$180$		0			0
$181$	10.0056			0.743714			0.371857	−	0.928290i	$-0.378721\pi$
$181$	10.0056			0.743714			0.371857	+	0.928290i	$0.378721\pi$
$182$		0			0
$183$	−9.61149	+	6.97733i	−0.710502	+	0.515779i
$184$		0			0
$185$	6.80065	+	11.7791i	0.499993	+	0.866014i
$186$		0			0
$187$	3.70470	−	6.41673i	0.270915	−	0.469238i
$188$		0			0
$189$	5.49778	−	12.6006i	0.399905	−	0.916557i
$190$		0			0
$191$	11.0993	−	19.2246i	0.803120	−	1.39104i	−0.114433	−	0.993431i	$-0.536505\pi$
$191$	11.0993	−	19.2246i	0.803120	−	1.39104i	0.917553	−	0.397613i	$-0.130161\pi$
$192$		0			0
$193$	13.3080	+	23.0501i	0.957930	+	1.65918i	0.727516	+	0.686091i	$0.240675\pi$
$193$	13.3080	+	23.0501i	0.957930	+	1.65918i	0.230414	+	0.973093i	$0.425992\pi$
$194$		0			0
$195$	−19.7829	+	14.3611i	−1.41668	+	1.02842i
$196$		0			0
$197$	10.1696			0.724551			0.362276	−	0.932071i	$-0.382000\pi$
$197$	10.1696			0.724551			0.362276	+	0.932071i	$0.382000\pi$
$198$		0			0
$199$	−1.66243	+	2.87941i	−0.117846	+	0.204116i	−0.918914	−	0.394458i	$-0.870932\pi$
$199$	−1.66243	+	2.87941i	−0.117846	+	0.204116i	0.801068	+	0.598574i	$0.204266\pi$
$200$		0			0
$201$	−1.46339	−	13.9767i	−0.103220	−	0.985840i
$202$		0			0
$203$	1.65431	−	8.12836i	0.116110	−	0.570499i
$204$		0			0
$205$	7.63618	−	13.2263i	0.533334	−	0.923762i
$206$		0			0
$207$	8.37405	+	9.31520i	0.582037	+	0.647451i
$208$		0			0
$209$	−3.36262	−	5.82423i	−0.232597	−	0.402870i
$210$		0			0
$211$	−1.29535	+	2.24361i	−0.0891755	+	0.154456i	−0.907163	−	0.420780i	$-0.861757\pi$
$211$	−1.29535	+	2.24361i	−0.0891755	+	0.154456i	0.817987	+	0.575236i	$0.195090\pi$
$212$		0			0
$213$	3.57070	+	1.59148i	0.244660	+	0.109046i
$214$		0			0
$215$	−6.16752	−	10.6825i	−0.420621	−	0.728538i
$216$		0			0
$217$	2.53338	−	12.4476i	0.171977	−	0.845000i
$218$		0			0
$219$	−9.85245	+	7.15224i	−0.665767	+	0.483304i
$220$		0			0
$221$	−15.0988	−	26.1518i	−1.01565	−	1.75916i
$222$		0			0
$223$	−12.4029	−	21.4824i	−0.830556	−	1.43857i	−0.897598	−	0.440816i	$-0.854689\pi$
$223$	−12.4029	−	21.4824i	−0.830556	−	1.43857i	0.0670411	−	0.997750i	$-0.478644\pi$
$224$		0			0
$225$	2.71105	+	3.01574i	0.180737	+	0.201050i
$226$		0			0
$227$	7.10251			0.471410			0.235705	−	0.971825i	$-0.424260\pi$
$227$	7.10251			0.471410			0.235705	+	0.971825i	$0.424260\pi$
$228$		0			0
$229$	−6.46504			−0.427222			−0.213611	−	0.976919i	$-0.568522\pi$
$229$	−6.46504			−0.427222			−0.213611	+	0.976919i	$0.568522\pi$
$230$		0			0
$231$	2.60859	+	5.73109i	0.171632	+	0.377078i
$232$		0			0
$233$	−4.42950	−	7.67212i	−0.290186	−	0.502617i	0.683667	−	0.729794i	$-0.260384\pi$
$233$	−4.42950	−	7.67212i	−0.290186	−	0.502617i	−0.973854	+	0.227177i	$0.927051\pi$
$234$		0			0
$235$	−7.12665	+	12.3437i	−0.464891	+	0.805215i
$236$		0			0
$237$	3.86418	−	2.80514i	0.251005	−	0.182214i
$238$		0			0
$239$	8.60836	−	14.9101i	0.556828	−	0.964455i	−0.440930	−	0.897541i	$-0.645351\pi$
$239$	8.60836	−	14.9101i	0.556828	−	0.964455i	0.997759	−	0.0669138i	$-0.0213152\pi$
$240$		0			0
$241$	20.2211			1.30256			0.651279	−	0.758839i	$-0.274233\pi$
$241$	20.2211			1.30256			0.651279	+	0.758839i	$0.274233\pi$
$242$		0			0
$243$	7.82104	−	13.4845i	0.501720	−	0.865030i
$244$		0			0
$245$	−2.14760	−	17.5106i	−0.137205	−	1.11871i
$246$		0			0
$247$	−27.4092			−1.74400
$248$		0			0
$249$	−2.70141	−	25.8008i	−0.171195	−	1.63506i
$250$		0			0
$251$	7.32214			0.462169			0.231085	−	0.972934i	$-0.425773\pi$
$251$	7.32214			0.462169			0.231085	+	0.972934i	$0.425773\pi$
$252$		0			0
$253$	−5.73720			−0.360695
$254$		0			0
$255$	−19.0485	+	13.8280i	−1.19286	+	0.865940i
$256$		0			0
$257$	6.14617			0.383387			0.191694	−	0.981455i	$-0.438602\pi$
$257$	6.14617			0.383387			0.191694	+	0.981455i	$0.438602\pi$
$258$		0			0
$259$	2.84764	−	13.9917i	0.176944	−	0.869401i
$260$		0			0
$261$	2.91361	−	8.94299i	0.180348	−	0.553557i
$262$		0			0
$263$	−0.164927			−0.0101698			−0.00508491	−	0.999987i	$-0.501619\pi$
$263$	−0.164927			−0.0101698			−0.00508491	+	0.999987i	$0.501619\pi$
$264$		0			0
$265$	17.6489	−	30.5689i	1.08417	−	1.87783i
$266$		0			0
$267$	−0.994903	−	9.50219i	−0.0608871	−	0.581525i
$268$		0			0
$269$	−1.86477	+	3.22988i	−0.113697	+	0.196929i	−0.917258	−	0.398293i	$-0.869603\pi$
$269$	−1.86477	+	3.22988i	−0.113697	+	0.196929i	0.803561	+	0.595222i	$0.202936\pi$
$270$		0			0
$271$	−0.393652	−	0.681825i	−0.0239127	−	0.0414179i	0.853821	−	0.520566i	$-0.174279\pi$
$271$	−0.393652	−	0.681825i	−0.0239127	−	0.0414179i	−0.877734	+	0.479148i	$0.840946\pi$
$272$		0			0
$273$	25.5439	+	2.47161i	1.54599	+	0.149588i
$274$		0			0
$275$	−1.85739			−0.112005
$276$		0			0
$277$	−3.25908			−0.195819			−0.0979096	−	0.995195i	$-0.531216\pi$
$277$	−3.25908			−0.195819			−0.0979096	+	0.995195i	$0.531216\pi$
$278$		0			0
$279$	4.46185	−	13.6951i	0.267124	−	0.819906i
$280$		0			0
$281$	9.39147	+	16.2665i	0.560248	+	0.970379i	0.997474	+	0.0710269i	$0.0226276\pi$
$281$	9.39147	+	16.2665i	0.560248	+	0.970379i	−0.437226	+	0.899352i	$0.644039\pi$
$282$		0			0
$283$	6.41848	+	11.1171i	0.381539	+	0.660845i	0.991282	−	0.131754i	$-0.0420608\pi$
$283$	6.41848	+	11.1171i	0.381539	+	0.660845i	−0.609743	+	0.792599i	$0.708727\pi$
$284$		0			0
$285$	2.22480	+	21.2488i	0.131786	+	1.25867i
$286$		0			0
$287$	−15.2046	+	5.08624i	−0.897501	+	0.300231i
$288$		0			0
$289$	−6.03821	−	10.4585i	−0.355189	−	0.615205i
$290$		0			0
$291$	−0.322492	−	3.08008i	−0.0189048	−	0.180557i
$292$		0			0
$293$	−13.6293	+	23.6066i	−0.796230	+	1.37911i	0.125825	+	0.992052i	$0.459842\pi$
$293$	−13.6293	+	23.6066i	−0.796230	+	1.37911i	−0.922055	+	0.387058i	$0.873491\pi$
$294$		0			0
$295$	17.9806	+	31.1434i	1.04687	+	1.81324i
$296$		0			0
$297$	2.19827	+	6.79312i	0.127556	+	0.394177i
$298$		0			0
$299$	−11.6912	+	20.2497i	−0.676118	+	1.17107i
$300$		0			0
$301$	−2.58253	+	12.6891i	−0.148854	+	0.731387i
$302$		0			0
$303$	−21.1844	−	9.44200i	−1.21701	−	0.542429i
$304$		0			0
$305$	−8.64098	+	14.9666i	−0.494781	+	0.856986i
$306$		0			0
$307$	24.4623			1.39614			0.698069	−	0.716030i	$-0.254043\pi$
$307$	24.4623			1.39614			0.698069	+	0.716030i	$0.254043\pi$
$308$		0			0
$309$	−3.48565	−	1.55357i	−0.198292	−	0.0883796i
$310$		0			0
$311$	8.58916	+	14.8769i	0.487047	+	0.843590i	0.999889	−	0.0148930i	$-0.00474075\pi$
$311$	8.58916	+	14.8769i	0.487047	+	0.843590i	−0.512842	+	0.858483i	$0.671407\pi$
$312$		0			0
$313$	−7.93226	+	13.7391i	−0.448358	+	0.776578i	−0.998279	−	0.0586380i	$-0.981324\pi$
$313$	−7.93226	+	13.7391i	−0.448358	+	0.776578i	0.549922	+	0.835216i	$0.314658\pi$
$314$		0			0
$315$	−0.157299	−	20.0034i	−0.00886279	−	1.12706i
$316$		0			0
$317$	11.3626	−	19.6806i	0.638188	−	1.10537i	−0.347642	−	0.937627i	$-0.613017\pi$
$317$	11.3626	−	19.6806i	0.638188	−	1.10537i	0.985830	−	0.167747i	$-0.0536492\pi$
$318$		0			0
$319$	2.15402	+	3.73088i	0.120602	+	0.208889i
$320$		0			0
$321$	−1.77941	−	16.9949i	−0.0993171	−	0.948565i
$322$		0			0
$323$	−26.3916			−1.46847
$324$		0			0
$325$	−3.78495	+	6.55573i	−0.209951	+	0.363646i
$326$		0			0
$327$	−4.32665	+	3.14087i	−0.239264	+	0.173691i
$328$		0			0
$329$	14.1901	−	4.74686i	0.782324	−	0.261703i
$330$		0			0
$331$	−12.1140	+	20.9821i	−0.665848	+	1.15328i	0.313207	+	0.949685i	$0.398597\pi$
$331$	−12.1140	+	20.9821i	−0.665848	+	1.15328i	−0.979055	+	0.203597i	$0.934737\pi$
$332$		0			0
$333$	5.01532	−	15.3939i	0.274838	−	0.843582i
$334$		0			0
$335$	−10.2242	−	17.7088i	−0.558605	−	0.967533i
$336$		0			0
$337$	−2.20181	+	3.81365i	−0.119940	+	0.207743i	−0.919744	−	0.392519i	$-0.871604\pi$
$337$	−2.20181	+	3.81365i	−0.119940	+	0.207743i	0.799803	+	0.600262i	$0.204937\pi$
$338$		0			0
$339$	−0.613410	+	0.445296i	−0.0333159	+	0.0241852i
$340$		0			0
$341$	3.29863	+	5.71339i	0.178631	+	0.309398i
$342$		0			0
$343$	−10.4931	+	15.2609i	−0.566575	+	0.824010i
$344$		0			0
$345$	16.6474	+	7.41983i	0.896267	+	0.399470i
$346$		0			0
$347$	6.12528	+	10.6093i	0.328823	+	0.569537i	0.982278	−	0.187427i	$-0.0600149\pi$
$347$	6.12528	+	10.6093i	0.328823	+	0.569537i	−0.653456	+	0.756965i	$0.726682\pi$
$348$		0			0
$349$	7.19444	+	12.4611i	0.385110	+	0.667030i	0.991784	−	0.127921i	$-0.0408303\pi$
$349$	7.19444	+	12.4611i	0.385110	+	0.667030i	−0.606675	+	0.794950i	$0.707497\pi$
$350$		0			0
$351$	28.4562	+	6.08402i	1.51888	+	0.324741i
$352$		0			0
$353$	−8.81670			−0.469266			−0.234633	−	0.972084i	$-0.575389\pi$
$353$	−8.81670			−0.469266			−0.234633	+	0.972084i	$0.575389\pi$
$354$		0			0
$355$	5.68834			0.301906
$356$		0			0
$357$	24.5955	+	2.37985i	1.30173	+	0.125955i
$358$		0			0
$359$	−3.04909	−	5.28118i	−0.160925	−	0.278730i	0.774276	−	0.632848i	$-0.218114\pi$
$359$	−3.04909	−	5.28118i	−0.160925	−	0.278730i	−0.935201	+	0.354118i	$0.884781\pi$
$360$		0			0
$361$	−2.47731	+	4.29083i	−0.130385	+	0.225833i
$362$		0			0
$363$	14.4153	+	6.42496i	0.756605	+	0.337223i
$364$		0			0
$365$	−8.85761	+	15.3418i	−0.463628	+	0.803028i
$366$		0			0
$367$	−6.91628			−0.361027			−0.180513	−	0.983573i	$-0.557776\pi$
$367$	−6.91628			−0.361027			−0.180513	+	0.983573i	$0.557776\pi$
$368$		0			0
$369$	−17.7852	+	3.76559i	−0.925862	+	0.196029i
$370$		0			0
$371$	−35.1413	+	11.7554i	−1.82445	+	0.610312i
$372$		0			0
$373$	−23.8978			−1.23738			−0.618691	−	0.785634i	$-0.712337\pi$
$373$	−23.8978			−1.23738			−0.618691	+	0.785634i	$0.712337\pi$
$374$		0			0
$375$	−14.5461	−	6.48328i	−0.751158	−	0.334795i
$376$		0			0
$377$	17.5577			0.904269
$378$		0			0
$379$	34.6719			1.78097			0.890487	−	0.455008i	$-0.150364\pi$
$379$	34.6719			1.78097			0.890487	+	0.455008i	$0.150364\pi$
$380$		0			0
$381$	9.11181	+	4.06118i	0.466812	+	0.208061i
$382$		0			0
$383$	19.4301			0.992834			0.496417	−	0.868084i	$-0.334649\pi$
$383$	19.4301			0.992834			0.496417	+	0.868084i	$0.334649\pi$
$384$		0			0
$385$	6.86179	+	6.07164i	0.349709	+	0.309439i
$386$		0			0
$387$	−4.54841	+	13.9608i	−0.231208	+	0.709667i
$388$		0			0
$389$	−32.6345			−1.65463			−0.827317	−	0.561736i	$-0.810134\pi$
$389$	−32.6345			−1.65463			−0.827317	+	0.561736i	$0.810134\pi$
$390$		0			0
$391$	−11.2571	+	19.4979i	−0.569297	+	0.986051i
$392$		0			0
$393$	2.26187	+	1.00813i	0.114096	+	0.0508533i
$394$		0			0
$395$	3.47400	−	6.01714i	0.174796	−	0.302755i
$396$		0			0
$397$	−3.11807	−	5.40065i	−0.156491	−	0.271051i	0.777110	−	0.629365i	$-0.216685\pi$
$397$	−3.11807	−	5.40065i	−0.156491	−	0.271051i	−0.933601	+	0.358314i	$0.883352\pi$
$398$		0			0
$399$	13.0329	−	18.2535i	0.652462	−	0.913818i
$400$		0			0
$401$	−24.7345			−1.23518			−0.617591	−	0.786500i	$-0.711891\pi$
$401$	−24.7345			−1.23518			−0.617591	+	0.786500i	$0.711891\pi$
$402$		0			0
$403$	26.8876			1.33937
$404$		0			0
$405$	2.40681	−	22.5543i	0.119595	−	1.12073i
$406$		0			0
$407$	3.70781	+	6.42211i	0.183789	+	0.318332i
$408$		0			0
$409$	11.5749	+	20.0484i	0.572344	+	0.991329i	0.996325	+	0.0856575i	$0.0272991\pi$
$409$	11.5749	+	20.0484i	0.572344	+	0.991329i	−0.423981	+	0.905671i	$0.639368\pi$
$410$		0			0
$411$	−17.6977	−	7.88793i	−0.872961	−	0.389083i
$412$		0			0
$413$	7.52903	−	36.9934i	0.370480	−	1.82033i
$414$		0			0
$415$	−18.8737	−	32.6901i	−0.926471	−	1.60470i
$416$		0			0
$417$	−22.0628	+	16.0162i	−1.08042	+	0.784317i
$418$		0			0
$419$	−0.703260	+	1.21808i	−0.0343565	+	0.0595072i	−0.882692	−	0.469951i	$-0.844271\pi$
$419$	−0.703260	+	1.21808i	−0.0343565	+	0.0595072i	0.848336	+	0.529458i	$0.177605\pi$
$420$		0			0
$421$	−0.663904	−	1.14992i	−0.0323567	−	0.0560435i	0.849394	−	0.527760i	$-0.176968\pi$
$421$	−0.663904	−	1.14992i	−0.0323567	−	0.0560435i	−0.881750	+	0.471716i	$0.843635\pi$
$422$		0			0
$423$	16.5985	−	3.51433i	0.807045	−	0.170873i
$424$		0			0
$425$	−3.64443	+	6.31234i	−0.176781	+	0.306193i
$426$		0			0
$427$	17.2053	−	5.75551i	0.832624	−	0.278529i
$428$		0			0
$429$	−10.7859	+	7.82989i	−0.520749	+	0.378031i
$430$		0			0
$431$	−2.83378	+	4.90825i	−0.136498	+	0.236422i	−0.926169	−	0.377109i	$-0.876918\pi$
$431$	−2.83378	+	4.90825i	−0.136498	+	0.236422i	0.789670	+	0.613531i	$0.210252\pi$
$432$		0			0
$433$	1.60371			0.0770696			0.0385348	−	0.999257i	$-0.487731\pi$
$433$	1.60371			0.0770696			0.0385348	+	0.999257i	$0.487731\pi$
$434$		0			0
$435$	−1.42516	−	13.6115i	−0.0683311	−	0.652622i
$436$		0			0
$437$	10.2177	+	17.6975i	0.488777	+	0.846587i
$438$		0			0
$439$	0.227323	−	0.393735i	0.0108495	−	0.0187919i	−0.860550	−	0.509367i	$-0.829880\pi$
$439$	0.227323	−	0.393735i	0.0108495	−	0.0187919i	0.871399	+	0.490575i	$0.163213\pi$
$440$		0			0
$441$	−13.7920	+	15.8361i	−0.656762	+	0.754098i
$442$		0			0
$443$	−9.31442	+	16.1331i	−0.442542	+	0.766505i	−0.997877	−	0.0651217i	$-0.979256\pi$
$443$	−9.31442	+	16.1331i	−0.442542	+	0.766505i	0.555336	+	0.831626i	$0.312590\pi$
$444$		0			0
$445$	−6.95099	−	12.0395i	−0.329508	−	0.570725i
$446$		0			0
$447$	−12.5459	−	5.59176i	−0.593400	−	0.264481i
$448$		0			0
$449$	−14.2330			−0.671696			−0.335848	−	0.941916i	$-0.609023\pi$
$449$	−14.2330			−0.671696			−0.335848	+	0.941916i	$0.609023\pi$
$450$		0			0
$451$	4.16335	−	7.21114i	0.196045	−	0.339559i
$452$		0			0
$453$	17.0759	+	7.61080i	0.802294	+	0.357586i
$454$		0			0
$455$	35.4130	−	11.8463i	1.66019	−	0.555364i
$456$		0			0
$457$	−14.6729	+	25.4142i	−0.686370	+	1.18883i	0.286634	+	0.958040i	$0.407464\pi$
$457$	−14.6729	+	25.4142i	−0.686370	+	1.18883i	−0.973004	+	0.230788i	$0.925870\pi$
$458$		0			0
$459$	27.3997	+	5.85814i	1.27891	+	0.273435i
$460$		0			0
$461$	−12.6587	−	21.9254i	−0.589572	−	1.02117i	−0.994288	−	0.106727i	$-0.965963\pi$
$461$	−12.6587	−	21.9254i	−0.589572	−	1.02117i	0.404716	−	0.914442i	$-0.367370\pi$
$462$		0			0
$463$	−11.6503	+	20.1789i	−0.541435	+	0.937793i	0.457387	+	0.889268i	$0.348785\pi$
$463$	−11.6503	+	20.1789i	−0.541435	+	0.937793i	−0.998822	+	0.0485250i	$0.984548\pi$
$464$		0			0
$465$	−2.18246	−	20.8444i	−0.101209	−	0.966637i
$466$		0			0
$467$	−20.8409	−	36.0976i	−0.964403	−	1.67040i	−0.711210	−	0.702980i	$-0.751852\pi$
$467$	−20.8409	−	36.0976i	−0.964403	−	1.67040i	−0.253194	−	0.967416i	$-0.581481\pi$
$468$		0			0
$469$	−4.28116	+	21.0352i	−0.197686	+	0.971316i
$470$		0			0
$471$	3.81953	+	36.4798i	0.175995	+	1.68090i
$472$		0			0
$473$	−3.36262	−	5.82423i	−0.154613	−	0.267798i
$474$		0			0
$475$	3.30791	+	5.72947i	0.151777	+	0.262886i
$476$		0			0
$477$	−41.1056	+	8.70313i	−1.88210	+	0.398489i
$478$		0			0
$479$	5.53891			0.253079			0.126540	−	0.991962i	$-0.459613\pi$
$479$	5.53891			0.253079			0.126540	+	0.991962i	$0.459613\pi$
$480$		0			0
$481$	30.2228			1.37804
$482$		0			0
$483$	−7.92646	−	17.4145i	−0.360666	−	0.792388i
$484$		0			0
$485$	−2.25312	−	3.90252i	−0.102309	−	0.177204i
$486$		0			0
$487$	12.3357	−	21.3661i	0.558985	−	0.968190i	−0.438597	−	0.898684i	$-0.644524\pi$
$487$	12.3357	−	21.3661i	0.558985	−	0.968190i	0.997582	−	0.0695061i	$-0.0221423\pi$
$488$		0			0
$489$	−0.193549	−	1.84857i	−0.00875261	−	0.0835951i
$490$		0			0
$491$	−10.0509	+	17.4087i	−0.453590	+	0.785642i	−0.998606	−	0.0527842i	$-0.983190\pi$
$491$	−10.0509	+	17.4087i	−0.453590	+	0.785642i	0.545015	+	0.838426i	$0.316524\pi$
$492$		0			0
$493$	16.9059			0.761402
$494$		0			0
$495$	6.94556	+	7.72617i	0.312180	+	0.347265i
$496$		0			0
$497$	−4.47217	−	3.95719i	−0.200604	−	0.177504i
$498$		0			0
$499$	35.5173			1.58997			0.794987	−	0.606627i	$-0.207478\pi$
$499$	35.5173			1.58997			0.794987	+	0.606627i	$0.207478\pi$
$500$		0			0
$501$	21.6315	−	15.7031i	0.966426	−	0.701563i
$502$		0			0
$503$	24.2236			1.08008			0.540039	−	0.841640i	$-0.318410\pi$
$503$	24.2236			1.08008			0.540039	+	0.841640i	$0.318410\pi$
$504$		0			0
$505$	−33.7480			−1.50177
$506$		0			0
$507$	3.31182	+	31.6308i	0.147083	+	1.40477i
$508$		0			0
$509$	−7.73446			−0.342824			−0.171412	−	0.985199i	$-0.554833\pi$
$509$	−7.73446			−0.342824			−0.171412	+	0.985199i	$0.554833\pi$
$510$		0			0
$511$	17.6366	−	5.89980i	0.780199	−	0.260992i
$512$		0			0
$513$	17.0397	−	18.8792i	0.752321	−	0.833536i
$514$		0			0
$515$	−5.55285			−0.244688
$516$		0			0
$517$	−3.88555	+	6.72997i	−0.170886	+	0.295984i
$518$		0			0
$519$	28.5406	−	20.7187i	1.25279	−	0.909448i
$520$		0			0
$521$	−14.9050	+	25.8161i	−0.652998	+	1.13103i	0.329394	+	0.944193i	$0.393156\pi$
$521$	−14.9050	+	25.8161i	−0.652998	+	1.13103i	−0.982392	+	0.186833i	$0.940178\pi$
$522$		0			0
$523$	−1.76218	−	3.05219i	−0.0770547	−	0.133463i	0.824923	−	0.565245i	$-0.191218\pi$
$523$	−1.76218	−	3.05219i	−0.0770547	−	0.133463i	−0.901978	+	0.431782i	$0.857885\pi$
$524$		0			0
$525$	−2.56615	−	5.63786i	−0.111996	−	0.246056i
$526$		0			0
$527$	25.8893			1.12776
$528$		0			0
$529$	−5.56693			−0.242040
$530$		0			0
$531$	13.2603	−	40.7009i	0.575448	−	1.76627i
$532$		0			0
$533$	−16.9680	−	29.3895i	−0.734967	−	1.27300i
$534$		0			0
$535$	−12.4320	−	21.5329i	−0.537484	−	0.930950i
$536$		0			0
$537$	−8.54902	+	6.20604i	−0.368918	+	0.267810i
$538$		0			0
$539$	−1.17090	−	9.54704i	−0.0504344	−	0.411220i
$540$		0			0
$541$	13.8435	+	23.9777i	0.595180	+	1.03088i	0.993521	+	0.113645i	$0.0362525\pi$
$541$	13.8435	+	23.9777i	0.595180	+	1.03088i	−0.398342	+	0.917237i	$0.630414\pi$
$542$		0			0
$543$	−15.8292	−	7.05515i	−0.679296	−	0.302766i
$544$		0			0
$545$	−3.88977	+	6.73729i	−0.166620	+	0.288594i
$546$		0			0
$547$	−16.6136	−	28.7756i	−0.710347	−	1.23036i	−0.964727	−	0.263253i	$-0.915205\pi$
$547$	−16.6136	−	28.7756i	−0.710347	−	1.23036i	0.254380	−	0.967104i	$-0.418129\pi$
$548$		0			0
$549$	20.1255	−	4.26109i	0.858934	−	0.181859i
$550$		0			0
$551$	7.67241	−	13.2890i	0.326856	−	0.566131i
$552$		0			0
$553$	−6.91718	+	2.31393i	−0.294148	+	0.0983983i
$554$		0			0
$555$	−2.45318	−	23.4300i	−0.104132	−	0.994550i
$556$		0			0
$557$	7.80873	−	13.5251i	0.330866	−	0.573078i	−0.651816	−	0.758378i	$-0.725992\pi$
$557$	7.80873	−	13.5251i	0.330866	−	0.573078i	0.982682	+	0.185300i	$0.0593257\pi$
$558$		0			0
$559$	−27.4092			−1.15928
$560$		0			0
$561$	−10.3855	+	7.53919i	−0.438476	+	0.318305i
$562$		0			0
$563$	9.75592	+	16.8977i	0.411163	+	0.712155i	0.995017	−	0.0997034i	$-0.0317894\pi$
$563$	9.75592	+	16.8977i	0.411163	+	0.712155i	−0.583854	+	0.811858i	$0.698456\pi$
$564$		0			0
$565$	−0.551472	+	0.955177i	−0.0232006	+	0.0401846i
$566$		0			0
$567$	−17.5825	+	16.0579i	−0.738396	+	0.674367i
$568$		0			0
$569$	−3.59181	+	6.22119i	−0.150576	+	0.260806i	−0.931439	−	0.363896i	$-0.881446\pi$
$569$	−3.59181	+	6.22119i	−0.150576	+	0.260806i	0.780863	+	0.624702i	$0.214780\pi$
$570$		0			0
$571$	−14.7886	−	25.6147i	−0.618886	−	1.07194i	−0.989689	−	0.143230i	$-0.954251\pi$
$571$	−14.7886	−	25.6147i	−0.618886	−	1.07194i	0.370804	−	0.928711i	$-0.379082\pi$
$572$		0			0
$573$	−31.1151	+	22.5875i	−1.29985	+	0.943607i
$574$		0			0
$575$	5.64386			0.235365
$576$		0			0
$577$	5.18911	−	8.98780i	0.216025	−	0.374167i	−0.737564	−	0.675277i	$-0.764024\pi$
$577$	5.18911	−	8.98780i	0.216025	−	0.374167i	0.953589	+	0.301110i	$0.0973573\pi$
$578$		0			0
$579$	−4.80057	−	45.8496i	−0.199505	−	1.90544i
$580$		0			0
$581$	−7.90297	+	38.8307i	−0.327870	+	1.61097i
$582$		0			0
$583$	9.62244	−	16.6666i	0.398521	−	0.690259i
$584$		0			0
$585$	41.4234	−	8.77041i	1.71265	−	0.362612i
$586$		0			0
$587$	14.4563	+	25.0391i	0.596677	+	1.03348i	0.993308	+	0.115497i	$0.0368461\pi$
$587$	14.4563	+	25.0391i	0.596677	+	1.03348i	−0.396630	+	0.917978i	$0.629821\pi$
$588$		0			0
$589$	11.7494	−	20.3505i	0.484125	−	0.838530i
$590$		0			0
$591$	−16.0885	−	7.17073i	−0.661793	−	0.294964i
$592$		0			0
$593$	−10.2645	−	17.7786i	−0.421512	−	0.730080i	0.574576	−	0.818451i	$-0.305167\pi$
$593$	−10.2645	−	17.7786i	−0.421512	−	0.730080i	−0.996088	+	0.0883714i	$0.971834\pi$
$594$		0			0
$595$	34.0982	−	11.4065i	1.39789	−	0.467622i
$596$		0			0
$597$	4.66032	−	3.38310i	0.190734	−	0.138461i
$598$		0			0
$599$	−3.91652	−	6.78361i	−0.160025	−	0.277171i	0.774853	−	0.632142i	$-0.217824\pi$
$599$	−3.91652	−	6.78361i	−0.160025	−	0.277171i	−0.934877	+	0.354971i	$0.884491\pi$
$600$		0			0
$601$	−7.27021	−	12.5924i	−0.296558	−	0.513654i	0.678788	−	0.734334i	$-0.262505\pi$
$601$	−7.27021	−	12.5924i	−0.296558	−	0.513654i	−0.975346	+	0.220681i	$0.929172\pi$
$602$		0			0
$603$	−7.54008	+	23.1434i	−0.307056	+	0.942471i
$604$		0			0
$605$	22.9644			0.933635
$606$		0			0
$607$	−30.5510			−1.24003			−0.620013	−	0.784592i	$-0.712873\pi$
$607$	−30.5510			−1.24003			−0.620013	+	0.784592i	$0.712873\pi$
$608$		0			0
$609$	−8.34861	+	11.6928i	−0.338303	+	0.473816i
$610$		0			0
$611$	15.8358	+	27.4284i	0.640648	+	1.10964i
$612$		0			0
$613$	−14.4646	+	25.0534i	−0.584220	+	1.01190i	0.410752	+	0.911747i	$0.365266\pi$
$613$	−14.4646	+	25.0534i	−0.584220	+	1.01190i	−0.994972	+	0.100152i	$0.968067\pi$
$614$		0			0
$615$	−21.4067	+	15.5399i	−0.863202	+	0.626629i
$616$		0			0
$617$	20.2106	−	35.0059i	0.813650	−	1.40928i	−0.0966430	−	0.995319i	$-0.530811\pi$
$617$	20.2106	−	35.0059i	0.813650	−	1.40928i	0.910293	−	0.413964i	$-0.135856\pi$
$618$		0			0
$619$	−18.1171			−0.728190			−0.364095	−	0.931362i	$-0.618622\pi$
$619$	−18.1171			−0.728190			−0.364095	+	0.931362i	$0.618622\pi$
$620$		0			0
$621$	−6.67966	−	20.6416i	−0.268046	−	0.828318i
$622$		0			0
$623$	−2.91059	+	14.3010i	−0.116610	+	0.572957i
$624$		0			0
$625$	−29.9315			−1.19726
$626$		0			0
$627$	1.21299	+	11.5851i	0.0484422	+	0.462665i
$628$		0			0
$629$	29.1008			1.16032
$630$		0			0
$631$	8.50373			0.338528			0.169264	−	0.985571i	$-0.445861\pi$
$631$	8.50373			0.338528			0.169264	+	0.985571i	$0.445861\pi$
$632$		0			0
$633$	3.63128	−	2.63608i	0.144331	−	0.104775i
$634$		0			0
$635$	14.5157			0.576036
$636$		0			0
$637$	−36.0828	−	15.3221i	−1.42965	−	0.607082i
$638$		0			0
$639$	−4.52676	−	5.03552i	−0.179076	−	0.199202i
$640$		0			0
$641$	22.0040			0.869108			0.434554	−	0.900646i	$-0.356906\pi$
$641$	22.0040			0.869108			0.434554	+	0.900646i	$0.356906\pi$
$642$		0			0
$643$	13.1156	−	22.7170i	0.517230	−	0.895869i	−0.482569	−	0.875858i	$-0.660296\pi$
$643$	13.1156	−	22.7170i	0.517230	−	0.895869i	0.999800	−	0.0200115i	$-0.00637029\pi$
$644$		0			0
$645$	2.22480	+	21.2488i	0.0876013	+	0.836669i
$646$		0			0
$647$	19.5845	−	33.9214i	0.769946	−	1.33359i	−0.167645	−	0.985847i	$-0.553616\pi$
$647$	19.5845	−	33.9214i	0.769946	−	1.33359i	0.937591	−	0.347739i	$-0.113050\pi$
$648$		0			0
$649$	9.80329	+	16.9798i	0.384813	+	0.666515i
$650$		0			0
$651$	−12.7849	+	17.9061i	−0.501080	+	0.701797i
$652$		0			0
$653$	13.6693			0.534923			0.267461	−	0.963569i	$-0.413815\pi$
$653$	13.6693			0.534923			0.267461	+	0.963569i	$0.413815\pi$
$654$		0			0
$655$	3.60329			0.140792
$656$		0			0
$657$	20.6300	−	4.36791i	0.804853	−	0.170408i
$658$		0			0
$659$	−3.06683	−	5.31191i	−0.119467	−	0.206923i	0.800090	−	0.599880i	$-0.204785\pi$
$659$	−3.06683	−	5.31191i	−0.119467	−	0.206923i	−0.919557	+	0.392958i	$0.871452\pi$
$660$		0			0
$661$	22.3118	+	38.6451i	0.867828	+	1.50312i	0.864212	+	0.503128i	$0.167818\pi$
$661$	22.3118	+	38.6451i	0.867828	+	1.50312i	0.00361604	+	0.999993i	$0.498849\pi$
$662$		0			0
$663$	5.44655	+	52.0193i	0.211526	+	2.02026i
$664$		0			0
$665$	6.50865	−	31.9798i	0.252395	−	1.24013i
$666$		0			0
$667$	−6.54522	−	11.3367i	−0.253432	−	0.438957i
$668$		0			0
$669$	4.47406	+	42.7312i	0.172977	+	1.65208i
$670$		0			0
$671$	−4.71119	+	8.16001i	−0.181873	+	0.315014i
$672$		0			0
$673$	−16.3833	−	28.3767i	−0.631531	−	1.09384i	−0.987239	−	0.159246i	$-0.949094\pi$
$673$	−16.3833	−	28.3767i	−0.631531	−	1.09384i	0.355708	−	0.934597i	$-0.384240\pi$
$674$		0			0
$675$	−2.16250	−	6.68260i	−0.0832348	−	0.257213i
$676$		0			0
$677$	−13.5764	+	23.5150i	−0.521782	+	0.903753i	0.477897	+	0.878416i	$0.341399\pi$
$677$	−13.5764	+	23.5150i	−0.521782	+	0.903753i	−0.999679	+	0.0253373i	$0.991934\pi$
$678$		0			0
$679$	−0.943451	+	4.63558i	−0.0362063	+	0.177897i
$680$		0			0
$681$	−11.2364	−	5.00810i	−0.430578	−	0.191911i
$682$		0			0
$683$	−19.0334	+	32.9668i	−0.728293	+	1.26144i	0.229312	+	0.973353i	$0.426353\pi$
$683$	−19.0334	+	32.9668i	−0.728293	+	1.26144i	−0.957604	+	0.288087i	$0.906981\pi$
$684$		0			0
$685$	−28.1934			−1.07721
$686$		0			0
$687$	10.2279	+	4.55861i	0.390217	+	0.173922i
$688$		0			0
$689$	−39.2169	−	67.9257i	−1.49405	−	2.58776i
$690$		0			0
$691$	6.37848	−	11.0478i	0.242649	−	0.420280i	−0.718819	−	0.695197i	$-0.755317\pi$
$691$	6.37848	−	11.0478i	0.242649	−	0.420280i	0.961468	+	0.274917i	$0.0886504\pi$
$692$		0			0
$693$	−0.0857615	−	10.9061i	−0.00325781	−	0.414289i
$694$		0			0
$695$	−19.8351	+	34.3554i	−0.752387	+	1.30317i
$696$		0			0
$697$	−16.3381	−	28.2984i	−0.618849	−	1.07188i
$698$		0			0
$699$	1.59784	+	15.2608i	0.0604360	+	0.577217i
$700$		0			0
$701$	40.6428			1.53506			0.767528	−	0.641015i	$-0.221486\pi$
$701$	40.6428			1.53506			0.767528	+	0.641015i	$0.221486\pi$
$702$		0			0
$703$	13.2068	−	22.8749i	0.498105	−	0.862744i
$704$		0			0
$705$	19.9783	−	14.5030i	0.752427	−	0.546213i
$706$		0			0
$707$	26.5327	+	23.4774i	0.997865	+	0.882958i
$708$		0			0
$709$	3.74552	−	6.48743i	0.140666	−	0.243640i	−0.787082	−	0.616849i	$-0.788409\pi$
$709$	3.74552	−	6.48743i	0.140666	−	0.243640i	0.927748	+	0.373208i	$0.121742\pi$
$710$		0			0
$711$	−8.09119	+	1.71311i	−0.303443	+	0.0642468i
$712$		0			0
$713$	−10.0232	−	17.3607i	−0.375373	−	0.650165i
$714$		0			0
$715$	−9.69683	+	16.7954i	−0.362641	+	0.628112i
$716$		0			0
$717$	−24.1320	+	17.5183i	−0.901227	+	0.654233i
$718$		0			0
$719$	−1.64056	−	2.84154i	−0.0611827	−	0.105972i	0.833812	−	0.552049i	$-0.186154\pi$
$719$	−1.64056	−	2.84154i	−0.0611827	−	0.105972i	−0.894994	+	0.446078i	$0.852821\pi$
$720$		0			0
$721$	4.36565	+	3.86293i	0.162585	+	0.143863i
$722$		0			0
$723$	−31.9904	−	14.2583i	−1.18973	−	0.530271i
$724$		0			0
$725$	−2.11898	−	3.67018i	−0.0786969	−	0.136307i
$726$		0			0
$727$	8.01088	+	13.8753i	0.297107	+	0.514605i	0.975473	−	0.220120i	$-0.0706448\pi$
$727$	8.01088	+	13.8753i	0.297107	+	0.514605i	−0.678366	+	0.734724i	$0.737311\pi$
$728$		0			0
$729$	−21.8812	+	15.8181i	−0.810416	+	0.585855i
$730$		0			0
$731$	−26.3916			−0.976127
$732$		0			0
$733$	29.6245			1.09421			0.547104	−	0.837065i	$-0.315730\pi$
$733$	29.6245			1.09421			0.547104	+	0.837065i	$0.315730\pi$
$734$		0			0
$735$	−8.94949	+	29.2166i	−0.330107	+	1.07767i
$736$		0			0
$737$	−5.57435	−	9.65506i	−0.205334	−	0.355649i
$738$		0			0
$739$	−22.2867	+	38.6017i	−0.819829	+	1.41998i	0.0859797	+	0.996297i	$0.472598\pi$
$739$	−22.2867	+	38.6017i	−0.819829	+	1.41998i	−0.905808	+	0.423688i	$0.860735\pi$
$740$		0			0
$741$	43.3620	+	19.3267i	1.59294	+	0.709983i
$742$		0			0
$743$	−5.67364	+	9.82704i	−0.208146	+	0.360519i	−0.951130	−	0.308789i	$-0.900076\pi$
$743$	−5.67364	+	9.82704i	−0.208146	+	0.360519i	0.742985	+	0.669308i	$0.233410\pi$
$744$		0			0
$745$	−19.9863			−0.732243
$746$		0			0
$747$	−13.9189	+	42.7224i	−0.509266	+	1.56313i
$748$		0			0
$749$	−5.20567	+	25.5777i	−0.190211	+	0.934591i
$750$		0			0
$751$	35.1856			1.28394			0.641970	−	0.766730i	$-0.278117\pi$
$751$	35.1856			1.28394			0.641970	+	0.766730i	$0.278117\pi$
$752$		0			0
$753$	−11.5838	−	5.16297i	−0.422138	−	0.188149i
$754$		0			0
$755$	27.2029			0.990014
$756$		0			0
$757$	40.9186			1.48721			0.743605	−	0.668619i	$-0.233114\pi$
$757$	40.9186			1.48721			0.743605	+	0.668619i	$0.233114\pi$
$758$		0			0
$759$	9.07640	+	4.04540i	0.329453	+	0.146839i
$760$		0			0
$761$	11.4449			0.414876			0.207438	−	0.978248i	$-0.433487\pi$
$761$	11.4449			0.414876			0.207438	+	0.978248i	$0.433487\pi$
$762$		0			0
$763$	7.74505	−	2.59087i	0.280390	−	0.0937957i
$764$		0			0
$765$	39.8855	−	8.44480i	1.44206	−	0.305322i
$766$		0			0
$767$	79.9079			2.88531
$768$		0			0
$769$	−14.9723	+	25.9328i	−0.539916	+	0.935162i	0.458992	+	0.888440i	$0.348211\pi$
$769$	−14.9723	+	25.9328i	−0.539916	+	0.935162i	−0.998908	+	0.0467217i	$0.985123\pi$
$770$		0			0
$771$	−9.72340	−	4.33377i	−0.350180	−	0.156077i
$772$		0			0
$773$	−3.96578	+	6.86893i	−0.142639	+	0.247058i	−0.928490	−	0.371358i	$-0.878892\pi$
$773$	−3.96578	+	6.86893i	−0.142639	+	0.247058i	0.785851	+	0.618416i	$0.212225\pi$
$774$		0			0
$775$	−3.24496	−	5.62044i	−0.116563	−	0.201892i
$776$		0			0
$777$	−14.3708	+	20.1273i	−0.515550	+	0.722063i
$778$		0			0
$779$	−29.6589			−1.06264
$780$		0			0
$781$	3.10136			0.110975
$782$		0			0
$783$	−10.9153	+	12.0936i	−0.390080	+	0.432190i
$784$		0			0
$785$	26.6855	+	46.2207i	0.952447	+	1.64969i
$786$		0			0
$787$	−21.6037	−	37.4187i	−0.770089	−	1.33383i	−0.937514	−	0.347949i	$-0.886878\pi$
$787$	−21.6037	−	37.4187i	−0.770089	−	1.33383i	0.167425	−	0.985885i	$-0.446455\pi$
$788$		0			0
$789$	0.260919	+	0.116293i	0.00928895	+	0.00414013i
$790$		0			0
$791$	1.09805	−	0.367320i	0.0390422	−	0.0130604i
$792$		0			0
$793$	19.2008	+	33.2567i	0.681839	+	1.18098i
$794$		0			0
$795$	−49.4757	+	35.9162i	−1.75472	+	1.27382i
$796$		0			0
$797$	−8.34385	+	14.4520i	−0.295554	+	0.511915i	−0.975114	−	0.221706i	$-0.928838\pi$
$797$	−8.34385	+	14.4520i	−0.295554	+	0.511915i	0.679559	+	0.733620i	$0.262171\pi$
$798$		0			0
$799$	15.2479	+	26.4101i	0.539432	+	0.934323i
$800$		0			0
$801$	−5.12619	+	15.7342i	−0.181125	+	0.555942i
$802$		0			0
$803$	−4.82929	+	8.36458i	−0.170422	+	0.295180i
$804$		0			0
$805$	−20.8503	−	18.4493i	−0.734876	−	0.650253i
$806$		0			0
$807$	5.22757	−	3.79488i	0.184019	−	0.133586i
$808$		0			0
$809$	−2.54846	+	4.41407i	−0.0895992	+	0.155190i	−0.907342	−	0.420394i	$-0.861892\pi$
$809$	−2.54846	+	4.41407i	−0.0895992	+	0.155190i	0.817743	+	0.575584i	$0.195225\pi$
$810$		0			0
$811$	10.2996			0.361666			0.180833	−	0.983514i	$-0.442121\pi$
$811$	10.2996			0.361666			0.180833	+	0.983514i	$0.442121\pi$
$812$		0			0
$813$	0.142001	+	1.35624i	0.00498021	+	0.0475653i
$814$		0			0
$815$	−1.35225	−	2.34217i	−0.0473674	−	0.0820427i
$816$		0			0
$817$	−11.9773	+	20.7453i	−0.419033	+	0.725787i
$818$		0			0
$819$	−38.6684	−	21.9216i	−1.35118	−	0.766002i
$820$		0			0
$821$	12.6369	−	21.8878i	0.441031	−	0.763889i	−0.556735	−	0.830690i	$-0.687946\pi$
$821$	12.6369	−	21.8878i	0.441031	−	0.763889i	0.997766	+	0.0668013i	$0.0212794\pi$
$822$		0			0
$823$	−4.44391	−	7.69707i	−0.154905	−	0.268303i	0.778120	−	0.628116i	$-0.216174\pi$
$823$	−4.44391	−	7.69707i	−0.154905	−	0.268303i	−0.933024	+	0.359813i	$0.882840\pi$
$824$		0			0
$825$	2.93843	+	1.30967i	0.102303	+	0.0455970i
$826$		0			0
$827$	−13.1680			−0.457895			−0.228947	−	0.973439i	$-0.573528\pi$
$827$	−13.1680			−0.457895			−0.228947	+	0.973439i	$0.573528\pi$
$828$		0			0
$829$	−11.3459	+	19.6516i	−0.394058	+	0.682529i	−0.992981	−	0.118278i	$-0.962263\pi$
$829$	−11.3459	+	19.6516i	−0.394058	+	0.682529i	0.598922	+	0.800807i	$0.295596\pi$
$830$		0			0
$831$	5.15596	+	2.29804i	0.178858	+	0.0797180i
$832$		0			0
$833$	−34.7432	−	14.7532i	−1.20378	−	0.511168i
$834$		0			0
$835$	19.4473	−	33.6838i	0.673002	−	1.16567i
$836$		0			0
$837$	−16.7154	+	18.5199i	−0.577770	+	0.640142i
$838$		0			0
$839$	−14.9632	−	25.9171i	−0.516588	−	0.894757i	−0.999814	−	0.0192618i	$-0.993868\pi$
$839$	−14.9632	−	25.9171i	−0.516588	−	0.894757i	0.483226	−	0.875496i	$-0.339465\pi$
$840$		0			0
$841$	9.58522	−	16.6021i	0.330525	−	0.572486i
$842$		0			0
$843$	−3.38777	−	32.3561i	−0.116681	−	1.11440i
$844$		0			0
$845$	23.1384	+	40.0768i	0.795984	+	1.37869i
$846$		0			0
$847$	−18.0546	−	15.9756i	−0.620363	−	0.548927i
$848$		0			0
$849$	−2.31533	−	22.1134i	−0.0794618	−	0.758930i
$850$		0			0
$851$	−11.2666	−	19.5142i	−0.386213	−	0.668940i
$852$		0			0
$853$	6.46929	+	11.2051i	0.221504	+	0.383657i	0.955265	−	0.295751i	$-0.0955699\pi$
$853$	6.46929	+	11.2051i	0.221504	+	0.383657i	−0.733761	+	0.679408i	$0.762237\pi$
$854$		0			0
$855$	11.4632	−	35.1849i	0.392032	−	1.20330i
$856$		0			0
$857$	−8.24505			−0.281645			−0.140823	−	0.990035i	$-0.544975\pi$
$857$	−8.24505			−0.281645			−0.140823	+	0.990035i	$0.544975\pi$
$858$		0			0
$859$	3.46798			0.118326			0.0591630	−	0.998248i	$-0.481157\pi$
$859$	3.46798			0.118326			0.0591630	+	0.998248i	$0.481157\pi$
$860$		0			0
$861$	27.6405	+	2.67448i	0.941987	+	0.0911459i
$862$		0			0
$863$	−0.256394	−	0.444087i	−0.00872775	−	0.0151169i	0.861629	−	0.507539i	$-0.169445\pi$
$863$	−0.256394	−	0.444087i	−0.00872775	−	0.0151169i	−0.870356	+	0.492423i	$0.836111\pi$
$864$		0			0
$865$	25.6588	−	44.4423i	0.872424	−	1.51108i
$866$		0			0
$867$	2.17815	+	20.8032i	0.0739739	+	0.706515i
$868$		0			0
$869$	1.89407	−	3.28063i	0.0642519	−	0.111288i
$870$		0			0
$871$	−45.4373			−1.53958
$872$		0			0
$873$	−1.66163	+	5.10016i	−0.0562375	+	0.172614i
$874$		0			0
$875$	18.2185	+	16.1206i	0.615897	+	0.544975i
$876$		0			0
$877$	36.3760			1.22833			0.614166	−	0.789177i	$-0.289493\pi$
$877$	36.3760			1.22833			0.614166	+	0.789177i	$0.289493\pi$
$878$		0			0
$879$	38.2073	−	27.7360i	1.28870	−	0.935513i
$880$		0			0
$881$	−23.3999			−0.788363			−0.394181	−	0.919033i	$-0.628972\pi$
$881$	−23.3999			−0.788363			−0.394181	+	0.919033i	$0.628972\pi$
$882$		0			0
$883$	−22.8345			−0.768442			−0.384221	−	0.923241i	$-0.625530\pi$
$883$	−22.8345			−0.768442			−0.384221	+	0.923241i	$0.625530\pi$
$884$		0			0
$885$	−6.48612	−	61.9481i	−0.218029	−	2.08236i
$886$		0			0
$887$	44.1582			1.48269			0.741344	−	0.671125i	$-0.234189\pi$
$887$	44.1582			1.48269			0.741344	+	0.671125i	$0.234189\pi$
$888$		0			0
$889$	−11.4122	−	10.0981i	−0.382753	−	0.338678i
$890$		0			0
$891$	1.31223	−	12.2969i	0.0439612	−	0.411963i
$892$		0			0
$893$	27.6799			0.926271
$894$		0			0
$895$	−7.68579	+	13.3122i	−0.256908	+	0.444977i
$896$		0			0
$897$	32.7742	−	23.7919i	1.09430	−	0.794389i
$898$		0			0
$899$	−7.52641	+	13.0361i	−0.251020	+	0.434779i
$900$		0			0
$901$	−37.7610	−	65.4039i	−1.25800	−	2.17892i
$902$		0			0
$903$	13.0329	−	18.2535i	0.433709	−	0.607438i
$904$		0			0
$905$	−25.2169			−0.838237
$906$		0			0
$907$	7.07769			0.235011			0.117505	−	0.993072i	$-0.462510\pi$
$907$	7.07769			0.235011			0.117505	+	0.993072i	$0.462510\pi$
$908$		0			0
$909$	26.8566	+	29.8750i	0.890777	+	0.990891i
$910$		0			0
$911$	−23.6764	−	41.0088i	−0.784435	−	1.35868i	−0.929336	−	0.369235i	$-0.879620\pi$
$911$	−23.6764	−	41.0088i	−0.784435	−	1.35868i	0.144901	−	0.989446i	$-0.453714\pi$
$912$		0			0
$913$	−10.2902	−	17.8231i	−0.340555	−	0.589859i
$914$		0			0
$915$	24.2235	−	17.5847i	0.800804	−	0.581332i
$916$		0			0
$917$	−2.83291	−	2.50669i	−0.0935509	−	0.0827783i
$918$		0			0
$919$	12.9752	+	22.4736i	0.428011	+	0.741337i	0.996696	−	0.0812182i	$-0.0258811\pi$
$919$	12.9752	+	22.4736i	0.428011	+	0.741337i	−0.568685	+	0.822555i	$0.692548\pi$
$920$		0			0
$921$	−38.7001	−	17.2488i	−1.27521	−	0.568368i
$922$		0			0
$923$	6.31990	−	10.9464i	0.208022	−	0.360305i
$924$		0			0
$925$	−3.64748	−	6.31763i	−0.119929	−	0.207722i
$926$		0			0
$927$	4.41894	+	4.91558i	0.145137	+	0.161449i
$928$		0			0
$929$	2.66110	−	4.60917i	0.0873080	−	0.151222i	−0.819064	−	0.573702i	$-0.805507\pi$
$929$	2.66110	−	4.60917i	0.0873080	−	0.151222i	0.906372	+	0.422480i	$0.138840\pi$
$930$		0			0
$931$	−27.3644	+	20.6147i	−0.896832	+	0.675619i
$932$		0			0
$933$	−3.09835	−	29.5920i	−0.101436	−	0.968798i
$934$		0			0
$935$	−9.33682	+	16.1719i	−0.305347	+	0.528876i
$936$		0			0
$937$	−30.4266			−0.993994			−0.496997	−	0.867752i	$-0.665564\pi$
$937$	−30.4266			−0.993994			−0.496997	+	0.867752i	$0.665564\pi$
$938$		0			0
$939$	22.2367	−	16.1424i	0.725667	−	0.526788i
$940$		0			0
$941$	−10.8818	−	18.8479i	−0.354738	−	0.614424i	0.632335	−	0.774695i	$-0.282097\pi$
$941$	−10.8818	−	18.8479i	−0.354738	−	0.614424i	−0.987073	+	0.160271i	$0.948763\pi$
$942$		0			0
$943$	−12.6508	+	21.9118i	−0.411966	+	0.713546i
$944$		0			0
$945$	−13.8559	+	31.7568i	−0.450731	+	1.03305i
$946$		0			0
$947$	17.4392	−	30.2055i	0.566697	−	0.981548i	−0.430192	−	0.902737i	$-0.641554\pi$
$947$	17.4392	−	30.2055i	0.566697	−	0.981548i	0.996890	−	0.0788112i	$-0.0251124\pi$
$948$		0			0
$949$	19.6821	+	34.0904i	0.638908	+	1.10662i
$950$		0			0
$951$	−31.8531	+	23.1233i	−1.03291	+	0.749825i
$952$		0			0
$953$	27.3744			0.886742			0.443371	−	0.896338i	$-0.353782\pi$
$953$	27.3744			0.886742			0.443371	+	0.896338i	$0.353782\pi$
$954$		0			0
$955$	−27.9732	+	48.4511i	−0.905193	+	1.56784i
$956$		0			0
$957$	−0.777016	−	7.42118i	−0.0251174	−	0.239893i
$958$		0			0
$959$	22.1657	+	19.6132i	0.715766	+	0.633344i
$960$		0			0
$961$	3.97419	−	6.88350i	0.128200	−	0.222048i
$962$		0			0
$963$	−9.16835	+	28.1412i	−0.295446	+	0.906836i
$964$		0			0
$965$	−33.5396	−	58.0924i	−1.07968	−	1.87006i
$966$		0			0
$967$	7.21327	−	12.4937i	0.231963	−	0.401772i	−0.726423	−	0.687248i	$-0.758819\pi$
$967$	7.21327	−	12.4937i	0.231963	−	0.401772i	0.958386	+	0.285476i	$0.0921518\pi$
$968$		0			0
$969$	41.7522	+	18.6091i	1.34127	+	0.597812i
$970$		0			0
$971$	−13.2592	−	22.9657i	−0.425509	−	0.737004i	0.570959	−	0.820979i	$-0.306572\pi$
$971$	−13.2592	−	22.9657i	−0.425509	−	0.737004i	−0.996468	+	0.0839752i	$0.973238\pi$
$972$		0			0
$973$	39.4942	−	13.2116i	1.26613	−	0.423544i
$974$		0			0
$975$	10.6105	−	7.70250i	0.339806	−	0.246678i
$976$		0			0
$977$	20.1867	+	34.9643i	0.645829	+	1.11861i	0.984109	+	0.177563i	$0.0568214\pi$
$977$	20.1867	+	34.9643i	0.645829	+	1.11861i	−0.338281	+	0.941045i	$0.609845\pi$
$978$		0			0
$979$	−3.78978	−	6.56408i	−0.121122	−	0.209789i
$980$		0			0
$981$	9.05957	−	1.91815i	0.289250	−	0.0612417i
$982$		0			0
$983$	−21.4597			−0.684459			−0.342230	−	0.939616i	$-0.611182\pi$
$983$	−21.4597			−0.684459			−0.342230	+	0.939616i	$0.611182\pi$
$984$		0			0
$985$	−25.6300			−0.816639
$986$		0			0
$987$	−25.7962	−	2.49602i	−0.821101	−	0.0794491i
$988$		0			0
$989$	10.2177	+	17.6975i	0.324903	+	0.562748i
$990$		0			0
$991$	7.25341	−	12.5633i	0.230412	−	0.399085i	−0.727517	−	0.686089i	$-0.759326\pi$
$991$	7.25341	−	12.5633i	0.230412	−	0.399085i	0.957929	+	0.287004i	$0.0926593\pi$
$992$		0			0
$993$	33.9596	−	24.6525i	1.07768	−	0.782323i
$994$		0			0
$995$	4.18975	−	7.25687i	0.132824	−	0.230058i
$996$		0			0
$997$	36.4409			1.15409			0.577047	−	0.816711i	$-0.304205\pi$
$997$	36.4409			1.15409			0.577047	+	0.816711i	$0.304205\pi$
$998$		0			0
$999$	−18.7889	+	20.8172i	−0.594454	+	0.658628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.l.b.193.2	yes	14
3.2	odd	2		756.2.l.b.361.7		14
4.3	odd	2		1008.2.t.j.193.6		14
7.2	even	3		252.2.i.b.121.6	yes	14
7.3	odd	6		1764.2.j.h.589.3		14
7.4	even	3		1764.2.j.g.589.5		14
7.5	odd	6		1764.2.i.i.373.2		14
7.6	odd	2		1764.2.l.i.949.6		14
9.2	odd	6		756.2.i.b.613.1		14
9.4	even	3		2268.2.k.e.1621.7		14
9.5	odd	6		2268.2.k.f.1621.1		14
9.7	even	3		252.2.i.b.25.6	✓	14
12.11	even	2		3024.2.t.j.1873.7		14
21.2	odd	6		756.2.i.b.37.1		14
21.5	even	6		5292.2.i.i.1549.7		14
21.11	odd	6		5292.2.j.h.1765.1		14
21.17	even	6		5292.2.j.g.1765.7		14
21.20	even	2		5292.2.l.i.361.1		14
28.23	odd	6		1008.2.q.j.625.2		14
36.7	odd	6		1008.2.q.j.529.2		14
36.11	even	6		3024.2.q.j.2881.1		14
63.2	odd	6		756.2.l.b.289.7		14
63.11	odd	6		5292.2.j.h.3529.1		14
63.16	even	3	inner	252.2.l.b.205.2	yes	14
63.20	even	6		5292.2.i.i.2125.7		14
63.23	odd	6		2268.2.k.f.1297.1		14
63.25	even	3		1764.2.j.g.1177.5		14
63.34	odd	6		1764.2.i.i.1537.2		14
63.38	even	6		5292.2.j.g.3529.7		14
63.47	even	6		5292.2.l.i.3313.1		14
63.52	odd	6		1764.2.j.h.1177.3		14
63.58	even	3		2268.2.k.e.1297.7		14
63.61	odd	6		1764.2.l.i.961.6		14
84.23	even	6		3024.2.q.j.2305.1		14
252.79	odd	6		1008.2.t.j.961.6		14
252.191	even	6		3024.2.t.j.289.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.6	✓	14	9.7	even	3
252.2.i.b.121.6	yes	14	7.2	even	3
252.2.l.b.193.2	yes	14	1.1	even	1	trivial
252.2.l.b.205.2	yes	14	63.16	even	3	inner
756.2.i.b.37.1		14	21.2	odd	6
756.2.i.b.613.1		14	9.2	odd	6
756.2.l.b.289.7		14	63.2	odd	6
756.2.l.b.361.7		14	3.2	odd	2
1008.2.q.j.529.2		14	36.7	odd	6
1008.2.q.j.625.2		14	28.23	odd	6
1008.2.t.j.193.6		14	4.3	odd	2
1008.2.t.j.961.6		14	252.79	odd	6
1764.2.i.i.373.2		14	7.5	odd	6
1764.2.i.i.1537.2		14	63.34	odd	6
1764.2.j.g.589.5		14	7.4	even	3
1764.2.j.g.1177.5		14	63.25	even	3
1764.2.j.h.589.3		14	7.3	odd	6
1764.2.j.h.1177.3		14	63.52	odd	6
1764.2.l.i.949.6		14	7.6	odd	2
1764.2.l.i.961.6		14	63.61	odd	6
2268.2.k.e.1297.7		14	63.58	even	3
2268.2.k.e.1621.7		14	9.4	even	3
2268.2.k.f.1297.1		14	63.23	odd	6
2268.2.k.f.1621.1		14	9.5	odd	6
3024.2.q.j.2305.1		14	84.23	even	6
3024.2.q.j.2881.1		14	36.11	even	6
3024.2.t.j.289.7		14	252.191	even	6
3024.2.t.j.1873.7		14	12.11	even	2
5292.2.i.i.1549.7		14	21.5	even	6
5292.2.i.i.2125.7		14	63.20	even	6
5292.2.j.g.1765.7		14	21.17	even	6
5292.2.j.g.3529.7		14	63.38	even	6
5292.2.j.h.1765.1		14	21.11	odd	6
5292.2.j.h.3529.1		14	63.11	odd	6
5292.2.l.i.361.1		14	21.20	even	2
5292.2.l.i.3313.1		14	63.47	even	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58203 - 0.705117i) q^{3} -2.52026 q^{5} +(1.98143 + 1.75326i) q^{7} +(2.00562 + 2.23103i) q^{9} +O(q^{10})\)	\(q+(-1.58203 - 0.705117i) q^{3} -2.52026 q^{5} +(1.98143 + 1.75326i) q^{7} +(2.00562 + 2.23103i) q^{9} -1.37408 q^{11} +(-2.80008 + 4.84989i) q^{13} +(3.98712 + 1.77708i) q^{15} +(-2.69613 + 4.66983i) q^{17} +(2.44717 + 4.23863i) q^{19} +(-1.89842 - 4.17085i) q^{21} +4.17529 q^{23} +1.35173 q^{25} +(-1.59981 - 4.94375i) q^{27} +(-1.56761 - 2.71518i) q^{29} +(-2.40060 - 4.15797i) q^{31} +(2.17384 + 0.968889i) q^{33} +(-4.99373 - 4.41869i) q^{35} +(-2.69839 - 4.67374i) q^{37} +(7.84955 - 5.69827i) q^{39} +(-3.02991 + 5.24797i) q^{41} +(2.44717 + 4.23863i) q^{43} +(-5.05469 - 5.62278i) q^{45} +(2.82774 - 4.89779i) q^{47} +(0.852135 + 6.94794i) q^{49} +(7.55812 - 5.48671i) q^{51} +(-7.00281 + 12.1292i) q^{53} +3.46305 q^{55} +(-0.882764 - 8.43117i) q^{57} +(-7.13442 - 12.3572i) q^{59} +(3.42860 - 5.93852i) q^{61} +(0.0624137 + 7.93701i) q^{63} +(7.05695 - 12.2230i) q^{65} +(4.05678 + 7.02655i) q^{67} +(-6.60543 - 2.94407i) q^{69} -2.25704 q^{71} +(3.51456 - 6.08739i) q^{73} +(-2.13847 - 0.953127i) q^{75} +(-2.72265 - 2.40913i) q^{77} +(-1.37843 + 2.38750i) q^{79} +(-0.954983 + 8.94919i) q^{81} +(7.48876 + 12.9709i) q^{83} +(6.79495 - 11.7692i) q^{85} +(0.565480 + 5.40083i) q^{87} +(2.75804 + 4.77707i) q^{89} +(-14.0513 + 4.70043i) q^{91} +(0.865966 + 8.27073i) q^{93} +(-6.16752 - 10.6825i) q^{95} +(0.894003 + 1.54846i) q^{97} +(-2.75589 - 3.06562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more