LMFDB - Embedded newform 252.2.i.b.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(25,252)]

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, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.i (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			25.6
Root			$-1.58203 + 0.705117i$ of defining polynomial
Character	$\chi$	$=$	252.25
Dual form			252.2.i.b.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40166 + 1.01752i) q^{3} +(1.26013 - 2.18261i) q^{5} +(0.527655 - 2.59260i) q^{7} +(0.929318 + 2.85243i) q^{9} +O(q^{10})$	\(q+(1.40166 + 1.01752i) q^{3} +(1.26013 - 2.18261i) q^{5} +(0.527655 - 2.59260i) q^{7} +(0.929318 + 2.85243i) q^{9} +(0.687041 + 1.18999i) q^{11} +(-2.80008 - 4.84989i) q^{13} +(3.98712 - 1.77708i) q^{15} +(-2.69613 + 4.66983i) q^{17} +(2.44717 + 4.23863i) q^{19} +(3.37761 - 3.09705i) q^{21} +(-2.08765 + 3.61591i) q^{23} +(-0.675864 - 1.17063i) q^{25} +(-1.59981 + 4.94375i) q^{27} +(-1.56761 + 2.71518i) q^{29} +4.80121 q^{31} +(-0.247835 + 2.36704i) q^{33} +(-4.99373 - 4.41869i) q^{35} +(-2.69839 - 4.67374i) q^{37} +(1.01007 - 9.64704i) q^{39} +(-3.02991 - 5.24797i) q^{41} +(2.44717 - 4.23863i) q^{43} +(7.39682 + 1.56610i) q^{45} -5.65548 q^{47} +(-6.44316 - 2.73600i) q^{49} +(-8.53069 + 3.80217i) q^{51} +(-7.00281 + 12.1292i) q^{53} +3.46305 q^{55} +(-0.882764 + 8.43117i) q^{57} +14.2688 q^{59} -6.85721 q^{61} +(7.88558 - 0.904251i) q^{63} -14.1139 q^{65} -8.11356 q^{67} +(-6.60543 + 2.94407i) q^{69} -2.25704 q^{71} +(3.51456 - 6.08739i) q^{73} +(0.243803 - 2.32853i) q^{75} +(3.44769 - 1.15332i) q^{77} +2.75685 q^{79} +(-7.27273 + 5.30163i) q^{81} +(7.48876 - 12.9709i) q^{83} +(6.79495 + 11.7692i) q^{85} +(-4.95999 + 2.21069i) q^{87} +(2.75804 + 4.77707i) q^{89} +(-14.0513 + 4.70043i) q^{91} +(6.72968 + 4.88531i) q^{93} +12.3350 q^{95} +(0.894003 - 1.54846i) q^{97} +(-2.75589 + 3.06562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.40166	+	1.01752i	0.809251	+	0.587464i
$3$	1.40166	+	1.01752i	0.809251	+	0.587464i
$4$		0			0
$5$	1.26013	−	2.18261i	0.563548	−	0.976094i	−0.433635	−	0.901089i	$-0.642769\pi$
$5$	1.26013	−	2.18261i	0.563548	−	0.976094i	0.997183	−	0.0750053i	$-0.0238974\pi$
$6$		0			0
$7$	0.527655	−	2.59260i	0.199435	−	0.979911i
$7$	0.527655	−	2.59260i	0.199435	−	0.979911i
$8$		0			0
$9$	0.929318	+	2.85243i	0.309773	+	0.950811i
$10$		0			0
$11$	0.687041	+	1.18999i	0.207151	+	0.358796i	0.950816	−	0.309757i	$-0.100248\pi$
$11$	0.687041	+	1.18999i	0.207151	+	0.358796i	−0.743665	+	0.668552i	$0.766914\pi$
$12$		0			0
$13$	−2.80008	−	4.84989i	−0.776603	−	1.34512i	−0.933889	−	0.357563i	$-0.883608\pi$
$13$	−2.80008	−	4.84989i	−0.776603	−	1.34512i	0.157285	−	0.987553i	$-0.449726\pi$
$14$		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
$21$	3.37761	−	3.09705i	0.737055	−	0.675833i
$22$		0			0
$23$	−2.08765	+	3.61591i	−0.435304	+	0.753969i	−0.997320	−	0.0731570i	$-0.976693\pi$
$23$	−2.08765	+	3.61591i	−0.435304	+	0.753969i	0.562016	+	0.827126i	$0.310026\pi$
$24$		0			0
$25$	−0.675864	−	1.17063i	−0.135173	−	0.234126i
$26$		0			0
$27$	−1.59981	+	4.94375i	−0.307883	+	0.951424i
$28$		0			0
$29$	−1.56761	+	2.71518i	−0.291097	+	0.504195i	−0.974069	−	0.226249i	$-0.927354\pi$
$29$	−1.56761	+	2.71518i	−0.291097	+	0.504195i	0.682972	+	0.730444i	$0.260687\pi$
$30$		0			0
$31$	4.80121			0.862323			0.431161	−	0.902275i	$-0.358104\pi$
$31$	4.80121			0.862323			0.431161	+	0.902275i	$0.358104\pi$
$32$		0			0
$33$	−0.247835	+	2.36704i	−0.0431426	+	0.412049i
$34$		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
$39$	1.01007	−	9.64704i	0.161740	−	1.54476i
$40$		0			0
$41$	−3.02991	−	5.24797i	−0.473193	−	0.819595i	0.526336	−	0.850277i	$-0.323565\pi$
$41$	−3.02991	−	5.24797i	−0.473193	−	0.819595i	−0.999529	+	0.0306820i	$0.990232\pi$
$42$		0			0
$43$	2.44717	−	4.23863i	0.373190	−	0.646385i	−0.616864	−	0.787070i	$-0.711597\pi$
$43$	2.44717	−	4.23863i	0.373190	−	0.646385i	0.990054	+	0.140685i	$0.0449305\pi$
$44$		0			0
$45$	7.39682	+	1.56610i	1.10265	+	0.233460i
$46$		0			0
$47$	−5.65548			−0.824936			−0.412468	−	0.910972i	$-0.635333\pi$
$47$	−5.65548			−0.824936			−0.412468	+	0.910972i	$0.635333\pi$
$48$		0			0
$49$	−6.44316	−	2.73600i	−0.920451	−	0.390857i
$50$		0			0
$51$	−8.53069	+	3.80217i	−1.19454	+	0.532411i
$52$		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
$59$	14.2688			1.85765			0.928823	−	0.370524i	$-0.120822\pi$
$59$	14.2688			1.85765			0.928823	+	0.370524i	$0.120822\pi$
$60$		0			0
$61$	−6.85721			−0.877975			−0.438988	−	0.898493i	$-0.644663\pi$
$61$	−6.85721			−0.877975			−0.438988	+	0.898493i	$0.644663\pi$
$62$		0			0
$63$	7.88558	−	0.904251i	0.993489	−	0.113925i
$64$		0			0
$65$	−14.1139			−1.75061
$66$		0			0
$67$	−8.11356			−0.991229			−0.495615	−	0.868543i	$-0.665057\pi$
$67$	−8.11356			−0.991229			−0.495615	+	0.868543i	$0.665057\pi$
$68$		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
$75$	0.243803	−	2.32853i	0.0281520	−	0.268876i
$76$		0			0
$77$	3.44769	−	1.15332i	0.392901	−	0.131433i
$78$		0			0
$79$	2.75685			0.310170			0.155085	−	0.987901i	$-0.450435\pi$
$79$	2.75685			0.310170			0.155085	+	0.987901i	$0.450435\pi$
$80$		0			0
$81$	−7.27273	+	5.30163i	−0.808082	+	0.589070i
$82$		0			0
$83$	7.48876	−	12.9709i	0.821998	−	1.42374i	−0.0821933	−	0.996616i	$-0.526192\pi$
$83$	7.48876	−	12.9709i	0.821998	−	1.42374i	0.904192	−	0.427127i	$-0.140474\pi$
$84$		0			0
$85$	6.79495	+	11.7692i	0.737016	+	1.27655i
$86$		0			0
$87$	−4.95999	+	2.21069i	−0.531767	+	0.237011i
$88$		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
$93$	6.72968	+	4.88531i	0.697835	+	0.506583i
$94$		0			0
$95$	12.3350			1.26555
$96$		0			0
$97$	0.894003	−	1.54846i	0.0907722	−	0.157222i	−0.817064	−	0.576547i	$-0.804400\pi$
$97$	0.894003	−	1.54846i	0.0907722	−	0.157222i	0.907836	+	0.419325i	$0.137733\pi$
$98$		0			0
$99$	−2.75589	+	3.06562i	−0.276977	+	0.308106i
$100$		0			0
$101$	−6.69534	−	11.5967i	−0.666211	−	1.15391i	−0.978955	−	0.204074i	$-0.934582\pi$
$101$	−6.69534	−	11.5967i	−0.666211	−	1.15391i	0.312744	−	0.949837i	$-0.398752\pi$
$102$		0			0
$103$	−1.10164	+	1.90810i	−0.108548	+	0.188010i	−0.915182	−	0.403040i	$-0.867953\pi$
$103$	−1.10164	+	1.90810i	−0.108548	+	0.188010i	0.806634	+	0.591051i	$0.201287\pi$
$104$		0			0
$105$	−2.50343	−	11.2747i	−0.244310	−	1.10030i
$106$		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	0.876134	−	0.482067i	$-0.160114\pi$
$113$	0.218815	+	0.378999i	0.0205844	+	0.0356532i	−0.855550	+	0.517721i	$0.826781\pi$
$114$		0			0
$115$	5.26142	+	9.11304i	0.490630	+	0.849796i
$116$		0			0
$117$	11.2318	−	12.4941i	1.03838	−	1.15508i
$118$		0			0
$119$	10.6844	+	9.45404i	0.979435	+	0.866651i
$120$		0			0
$121$	4.55595	−	7.89113i	0.414177	−	0.717376i
$122$		0			0
$123$	1.09298	−	10.4389i	0.0985503	−	0.941241i
$124$		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
$129$	7.74299	−	3.45109i	0.681732	−	0.303851i
$130$		0			0
$131$	0.714865	−	1.23818i	0.0624580	−	0.108180i	−0.833106	−	0.553114i	$-0.813439\pi$
$131$	0.714865	−	1.23818i	0.0624580	−	0.108180i	0.895564	+	0.444934i	$0.146773\pi$
$132$		0			0
$133$	12.2803	−	4.10801i	1.06484	−	0.356210i
$134$		0			0
$135$	8.77431	+	9.72153i	0.755172	+	0.836696i
$136$		0			0
$137$	−5.59335	−	9.68796i	−0.477872	−	0.827698i	0.521806	−	0.853064i	$-0.325258\pi$
$137$	−5.59335	−	9.68796i	−0.477872	−	0.827698i	−0.999678	+	0.0253656i	$0.991925\pi$
$138$		0			0
$139$	7.87024	+	13.6317i	0.667545	+	1.15622i	0.978589	+	0.205826i	$0.0659881\pi$
$139$	7.87024	+	13.6317i	0.667545	+	1.15622i	−0.311044	+	0.950396i	$0.600679\pi$
$140$		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
$147$	−6.24721	−	10.3910i	−0.515261	−	0.857033i
$148$		0			0
$149$	−3.96513	+	6.86780i	−0.324836	+	0.562632i	−0.981479	−	0.191569i	$-0.938642\pi$
$149$	−3.96513	+	6.86780i	−0.324836	+	0.562632i	0.656643	+	0.754201i	$0.271976\pi$
$150$		0			0
$151$	5.39683	+	9.34758i	0.439188	+	0.760696i	0.997627	−	0.0688499i	$-0.0219329\pi$
$151$	5.39683	+	9.34758i	0.439188	+	0.760696i	−0.558439	+	0.829545i	$0.688600\pi$
$152$		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
$157$	21.1768			1.69009			0.845045	−	0.534695i	$-0.179574\pi$
$157$	21.1768			1.69009			0.845045	+	0.534695i	$0.179574\pi$
$158$		0			0
$159$	−22.1573	+	9.87561i	−1.75719	+	0.783187i
$160$		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
$165$	4.85403	+	3.52371i	0.377886	+	0.274321i
$166$		0			0
$167$	−7.71638	−	13.3652i	−0.597112	−	1.03423i	−0.993245	−	0.116035i	$-0.962982\pi$
$167$	−7.71638	−	13.3652i	−0.597112	−	1.03423i	0.396133	−	0.918193i	$-0.370352\pi$
$168$		0			0
$169$	−9.18094	+	15.9018i	−0.706226	+	1.22322i
$170$		0			0
$171$	−9.81620	+	10.9194i	−0.750663	+	0.835030i
$172$		0			0
$173$	20.3620			1.54809			0.774046	−	0.633129i	$-0.218230\pi$
$173$	20.3620			1.54809			0.774046	+	0.633129i	$0.218230\pi$
$174$		0			0
$175$	−3.39160	+	1.13456i	−0.256381	+	0.0857644i
$176$		0			0
$177$	20.0001	+	14.5188i	1.50330	+	1.09130i
$178$		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
$185$	−13.6013			−0.999987
$186$		0			0
$187$	−7.40940			−0.541829
$188$		0			0
$189$	11.9730	+	6.75625i	0.870909	+	0.491445i
$190$		0			0
$191$	−22.1987			−1.60624			−0.803120	−	0.595818i	$-0.796828\pi$
$191$	−22.1987			−1.60624			−0.803120	+	0.595818i	$0.796828\pi$
$192$		0			0
$193$	−26.6160			−1.91586			−0.957930	−	0.287002i	$-0.907342\pi$
$193$	−26.6160			−1.91586			−0.957930	+	0.287002i	$0.907342\pi$
$194$		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
$201$	−11.3725	−	8.25569i	−0.802153	−	0.582311i
$202$		0			0
$203$	6.21221	+	5.49686i	0.436012	+	0.385804i
$204$		0			0
$205$	−15.2724			−1.06667
$206$		0			0
$207$	−12.2542	−	2.59454i	−0.851727	−	0.180333i
$208$		0			0
$209$	−3.36262	+	5.82423i	−0.232597	+	0.402870i
$210$		0			0
$211$	−1.29535	−	2.24361i	−0.0891755	−	0.154456i	0.817987	−	0.575236i	$-0.195090\pi$
$211$	−1.29535	−	2.24361i	−0.0891755	−	0.154456i	−0.907163	+	0.420780i	$0.861757\pi$
$212$		0			0
$213$	−3.16361	−	2.29658i	−0.216767	−	0.157359i
$214$		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
$219$	11.1202	−	4.95635i	0.751437	−	0.334919i
$220$		0			0
$221$	30.1975			2.03131
$222$		0			0
$223$	−12.4029	+	21.4824i	−0.830556	+	1.43857i	0.0670411	+	0.997750i	$0.478644\pi$
$223$	−12.4029	+	21.4824i	−0.830556	+	1.43857i	−0.897598	+	0.440816i	$0.854689\pi$
$224$		0			0
$225$	2.71105	−	3.01574i	0.180737	−	0.201050i
$226$		0			0
$227$	−3.55125	−	6.15095i	−0.235705	−	0.408253i	0.723772	−	0.690039i	$-0.242407\pi$
$227$	−3.55125	−	6.15095i	−0.235705	−	0.408253i	−0.959477	+	0.281786i	$0.909073\pi$
$228$		0			0
$229$	3.23252	−	5.59889i	0.213611	−	0.369985i	−0.739231	−	0.673452i	$-0.764811\pi$
$229$	3.23252	−	5.59889i	0.213611	−	0.369985i	0.952842	+	0.303467i	$0.0981442\pi$
$230$		0			0
$231$	6.00602	+	1.89152i	0.395167	+	0.124453i
$232$		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	0.997759	+	0.0669138i	$0.0213152\pi$
$239$	8.60836	+	14.9101i	0.556828	+	0.964455i	−0.440930	+	0.897541i	$0.645351\pi$
$240$		0			0
$241$	−10.1106	−	17.5120i	−0.651279	−	1.12805i	−0.982813	−	0.184604i	$-0.940900\pi$
$241$	−10.1106	−	17.5120i	−0.651279	−	1.12805i	0.331534	−	0.943443i	$-0.392434\pi$
$242$		0			0
$243$	−15.5884	+	0.0309734i	−0.999998	+	0.00198694i
$244$		0			0
$245$	−14.0909	+	10.6152i	−0.900232	+	0.678180i
$246$		0			0
$247$	13.7046	−	23.7370i	0.872001	−	1.51035i
$248$		0			0
$249$	23.6949	−	10.5609i	1.50160	−	0.669271i
$250$		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
$255$	−2.45113	+	23.4104i	−0.153496	+	1.46602i
$256$		0			0
$257$	−3.07308	+	5.32274i	−0.191694	+	0.332023i	−0.945812	−	0.324716i	$-0.894731\pi$
$257$	−3.07308	+	5.32274i	−0.191694	+	0.332023i	0.754118	+	0.656739i	$0.228065\pi$
$258$		0			0
$259$	−13.5410	+	4.52971i	−0.841395	+	0.281463i
$260$		0			0
$261$	−9.20166	−	1.94823i	−0.569568	−	0.120592i
$262$		0			0
$263$	0.0824634	+	0.142831i	0.00508491	+	0.00880732i	0.868557	−	0.495590i	$-0.165048\pi$
$263$	0.0824634	+	0.142831i	0.00508491	+	0.00880732i	−0.863472	+	0.504397i	$0.831715\pi$
$264$		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
$273$	−24.4780	−	7.70902i	−1.48147	−	0.466571i
$274$		0			0
$275$	0.928693	−	1.60854i	0.0560023	−	0.0969988i
$276$		0			0
$277$	1.62954	+	2.82245i	0.0979096	+	0.169584i	0.910819	−	0.412805i	$-0.135451\pi$
$277$	1.62954	+	2.82245i	0.0979096	+	0.169584i	−0.812910	+	0.582390i	$0.802118\pi$
$278$		0			0
$279$	4.46185	+	13.6951i	0.267124	+	0.819906i
$280$		0			0
$281$	9.39147	−	16.2665i	0.560248	−	0.970379i	−0.437226	−	0.899352i	$-0.644039\pi$
$281$	9.39147	−	16.2665i	0.560248	−	0.970379i	0.997474	−	0.0710269i	$-0.0226276\pi$
$282$		0			0
$283$	−12.8370			−0.763078			−0.381539	−	0.924353i	$-0.624606\pi$
$283$	−12.8370			−0.763078			−0.381539	+	0.924353i	$0.624606\pi$
$284$		0			0
$285$	17.2896	+	12.5511i	1.02415	+	0.743464i
$286$		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
$291$	2.82867	−	1.26075i	0.165820	−	0.0739067i
$292$		0			0
$293$	−13.6293	−	23.6066i	−0.796230	−	1.37911i	−0.922055	−	0.387058i	$-0.873491\pi$
$293$	−13.6293	−	23.6066i	−0.796230	−	1.37911i	0.125825	−	0.992052i	$-0.459842\pi$
$294$		0			0
$295$	17.9806	−	31.1434i	1.04687	−	1.81324i
$296$		0			0
$297$	−6.98214	+	1.49280i	−0.405145	+	0.0866212i
$298$		0			0
$299$	23.3823			1.35224
$300$		0			0
$301$	−9.69781	−	8.58108i	−0.558972	−	0.494605i
$302$		0			0
$303$	2.41520	−	23.0672i	0.138749	−	1.32518i
$304$		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
$311$	−17.1783			−0.974094			−0.487047	−	0.873376i	$-0.661926\pi$
$311$	−17.1783			−0.974094			−0.487047	+	0.873376i	$0.661926\pi$
$312$		0			0
$313$	15.8645			0.896715			0.448358	−	0.893854i	$-0.352009\pi$
$313$	15.8645			0.896715			0.448358	+	0.893854i	$0.352009\pi$
$314$		0			0
$315$	7.96324	−	18.3506i	0.448678	−	1.03394i
$316$		0			0
$317$	−22.7252			−1.27638			−0.638188	−	0.769880i	$-0.720316\pi$
$317$	−22.7252			−1.27638			−0.638188	+	0.769880i	$0.720316\pi$
$318$		0			0
$319$	−4.30804			−0.241204
$320$		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
$327$	4.88340	−	2.17656i	0.270053	−	0.120364i
$328$		0			0
$329$	−2.98414	+	14.6624i	−0.164521	+	0.808364i
$330$		0			0
$331$	24.2281			1.33170			0.665848	−	0.746088i	$-0.268070\pi$
$331$	24.2281			1.33170			0.665848	+	0.746088i	$0.268070\pi$
$332$		0			0
$333$	10.8239	−	12.0404i	0.593145	−	0.659808i
$334$		0			0
$335$	−10.2242	+	17.7088i	−0.558605	+	0.967533i
$336$		0			0
$337$	−2.20181	−	3.81365i	−0.119940	−	0.207743i	0.799803	−	0.600262i	$-0.204937\pi$
$337$	−2.20181	−	3.81365i	−0.119940	−	0.207743i	−0.919744	+	0.392519i	$0.871604\pi$
$338$		0			0
$339$	−0.0789328	+	0.753877i	−0.00428704	+	0.0409450i
$340$		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
$345$	−1.89794	+	18.1270i	−0.102182	+	0.975925i
$346$		0			0
$347$	−12.2506			−0.657645			−0.328823	−	0.944392i	$-0.606652\pi$
$347$	−12.2506			−0.657645			−0.328823	+	0.944392i	$0.606652\pi$
$348$		0			0
$349$	7.19444	−	12.4611i	0.385110	−	0.667030i	−0.606675	−	0.794950i	$-0.707497\pi$
$349$	7.19444	−	12.4611i	0.385110	−	0.667030i	0.991784	+	0.127921i	$0.0408303\pi$
$350$		0			0
$351$	28.4562	−	6.08402i	1.51888	−	0.324741i
$352$		0			0
$353$	4.40835	+	7.63549i	0.234633	+	0.406396i	0.959166	−	0.282844i	$-0.0912779\pi$
$353$	4.40835	+	7.63549i	0.234633	+	0.406396i	−0.724533	+	0.689240i	$0.757945\pi$
$354$		0			0
$355$	−2.84417	+	4.92624i	−0.150953	+	0.261458i
$356$		0			0
$357$	5.35625	+	24.1229i	0.283483	+	1.27672i
$358$		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
$367$	3.45814	+	5.98967i	0.180513	+	0.312658i	0.942055	−	0.335457i	$-0.108891\pi$
$367$	3.45814	+	5.98967i	0.180513	+	0.312658i	−0.761542	+	0.648115i	$0.775557\pi$
$368$		0			0
$369$	12.1537	−	13.5197i	0.632697	−	0.703805i
$370$		0			0
$371$	27.7512	+	24.5556i	1.44077	+	1.27486i
$372$		0			0
$373$	11.9489	−	20.6961i	0.618691	−	1.07160i	−0.371034	−	0.928619i	$-0.620997\pi$
$373$	11.9489	−	20.6961i	0.618691	−	1.07160i	0.989725	−	0.142985i	$-0.0456701\pi$
$374$		0			0
$375$	12.8877	+	9.35567i	0.665520	+	0.483125i
$376$		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
$381$	−8.07299	−	5.86047i	−0.413592	−	0.300241i
$382$		0			0
$383$	−9.71507	+	16.8270i	−0.496417	+	0.859820i	−0.999991	−	0.00413220i	$-0.998685\pi$
$383$	−9.71507	+	16.8270i	−0.496417	+	0.859820i	0.503574	+	0.863952i	$0.332018\pi$
$384$		0			0
$385$	1.82730	−	8.97831i	0.0931277	−	0.457577i
$386$		0			0
$387$	14.3646	+	3.04136i	0.730194	+	0.154601i
$388$		0			0
$389$	16.3172	+	28.2623i	0.827317	+	1.43295i	0.900136	+	0.435610i	$0.143467\pi$
$389$	16.3172	+	28.2623i	0.827317	+	1.43295i	−0.0728190	+	0.997345i	$0.523200\pi$
$390$		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
$399$	21.3929	+	6.73741i	1.07098	+	0.337292i
$400$		0			0
$401$	12.3672	−	21.4207i	0.617591	−	1.06970i	−0.372333	−	0.928099i	$-0.621442\pi$
$401$	12.3672	−	21.4207i	0.617591	−	1.06970i	0.989924	−	0.141599i	$-0.0452245\pi$
$402$		0			0
$403$	−13.4438	−	23.2853i	−0.669683	−	1.15992i
$404$		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
$409$	−23.1499			−1.14469			−0.572344	−	0.820014i	$-0.693966\pi$
$409$	−23.1499			−1.14469			−0.572344	+	0.820014i	$0.693966\pi$
$410$		0			0
$411$	2.01768	−	19.2706i	0.0995247	−	0.950548i
$412$		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
$417$	−2.83902	+	27.1151i	−0.139027	+	1.32783i
$418$		0			0
$419$	−0.703260	−	1.21808i	−0.0343565	−	0.0595072i	0.848336	−	0.529458i	$-0.177605\pi$
$419$	−0.703260	−	1.21808i	−0.0343565	−	0.0595072i	−0.882692	+	0.469951i	$0.844271\pi$
$420$		0			0
$421$	−0.663904	+	1.14992i	−0.0323567	+	0.0560435i	−0.881750	−	0.471716i	$-0.843635\pi$
$421$	−0.663904	+	1.14992i	−0.0323567	+	0.0560435i	0.849394	+	0.527760i	$0.176968\pi$
$422$		0			0
$423$	−5.25574	−	16.1319i	−0.255543	−	0.784358i
$424$		0			0
$425$	7.28886			0.353562
$426$		0			0
$427$	−3.61824	+	17.7780i	−0.175099	+	0.860338i
$428$		0			0
$429$	12.1738	−	5.42594i	0.587759	−	0.261967i
$430$		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
$437$	−20.4353			−0.977554
$438$		0			0
$439$	−0.454645			−0.0216990			−0.0108495	−	0.999941i	$-0.503454\pi$
$439$	−0.454645			−0.0216990			−0.0108495	+	0.999941i	$0.503454\pi$
$440$		0			0
$441$	1.81651	−	20.9213i	0.0865003	−	0.996252i
$442$		0			0
$443$	18.6288			0.885083			0.442542	−	0.896748i	$-0.354077\pi$
$443$	18.6288			0.885083			0.442542	+	0.896748i	$0.354077\pi$
$444$		0			0
$445$	13.9020			0.659017
$446$		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
$453$	−1.94679	+	18.5935i	−0.0914681	+	0.873600i
$454$		0			0
$455$	−7.44727	+	36.5917i	−0.349134	+	1.71545i
$456$		0			0
$457$	29.3458			1.37274			0.686370	−	0.727252i	$-0.259203\pi$
$457$	29.3458			1.37274			0.686370	+	0.727252i	$0.259203\pi$
$458$		0			0
$459$	−18.7732	−	20.7998i	−0.876256	−	0.970851i
$460$		0			0
$461$	−12.6587	+	21.9254i	−0.589572	+	1.02117i	0.404716	+	0.914442i	$0.367370\pi$
$461$	−12.6587	+	21.9254i	−0.589572	+	1.02117i	−0.994288	+	0.106727i	$0.965963\pi$
$462$		0			0
$463$	−11.6503	−	20.1789i	−0.541435	−	0.937793i	−0.998822	−	0.0485250i	$-0.984548\pi$
$463$	−11.6503	−	20.1789i	−0.541435	−	0.937793i	0.457387	−	0.889268i	$-0.348785\pi$
$464$		0			0
$465$	19.1430	−	8.53214i	0.887736	−	0.395669i
$466$		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
$471$	29.6827	+	21.5477i	1.36771	+	0.992866i
$472$		0			0
$473$	6.72524			0.309227
$474$		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
$479$	−2.76946	−	4.79684i	−0.126540	−	0.219173i	0.795794	−	0.605567i	$-0.207054\pi$
$479$	−2.76946	−	4.79684i	−0.126540	−	0.219173i	−0.922334	+	0.386394i	$0.873720\pi$
$480$		0			0
$481$	−15.1114	+	26.1737i	−0.689021	+	1.19342i
$482$		0			0
$483$	4.14741	+	18.6787i	0.188714	+	0.849910i
$484$		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	0.545015	−	0.838426i	$-0.316524\pi$
$491$	−10.0509	−	17.4087i	−0.453590	−	0.785642i	−0.998606	+	0.0527842i	$0.983190\pi$
$492$		0			0
$493$	−8.45294	−	14.6409i	−0.380701	−	0.659394i
$494$		0			0
$495$	3.21828	+	9.87812i	0.144651	+	0.443988i
$496$		0			0
$497$	−1.19094	+	5.85160i	−0.0534209	+	0.262480i
$498$		0			0
$499$	−17.7587	+	30.7589i	−0.794987	+	1.37696i	0.127861	+	0.991792i	$0.459189\pi$
$499$	−17.7587	+	30.7589i	−0.794987	+	1.37696i	−0.922848	+	0.385166i	$0.874144\pi$
$500$		0			0
$501$	2.78352	−	26.5850i	0.124358	−	1.18773i
$502$		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
$507$	−29.0490	+	12.9473i	−1.29011	+	0.575009i
$508$		0			0
$509$	3.86723	−	6.69824i	0.171412	−	0.296894i	−0.767502	−	0.641047i	$-0.778500\pi$
$509$	3.86723	−	6.69824i	0.171412	−	0.296894i	0.938914	+	0.344153i	$0.111834\pi$
$510$		0			0
$511$	−13.9277	−	12.3239i	−0.616125	−	0.545177i
$512$		0			0
$513$	−24.8697	+	5.31721i	−1.09802	+	0.234761i
$514$		0			0
$515$	2.77642	+	4.80891i	0.122344	+	0.211906i
$516$		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
$525$	−5.90831	−	1.86075i	−0.257860	−	0.0812097i
$526$		0			0
$527$	−12.9447	+	22.4208i	−0.563879	+	0.976667i
$528$		0			0
$529$	2.78347	+	4.82110i	0.121020	+	0.209613i
$530$		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
$535$	24.8641			1.07497
$536$		0			0
$537$	9.64910	−	4.30065i	0.416389	−	0.185587i
$538$		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
$543$	14.0245	+	10.1809i	0.601851	+	0.436905i
$544$		0			0
$545$	−3.88977	−	6.73729i	−0.166620	−	0.288594i
$546$		0			0
$547$	−16.6136	+	28.7756i	−0.710347	+	1.23036i	0.254380	+	0.967104i	$0.418129\pi$
$547$	−16.6136	+	28.7756i	−0.710347	+	1.23036i	−0.964727	+	0.263253i	$0.915205\pi$
$548$		0			0
$549$	−6.37253	−	19.5597i	−0.271973	−	0.834788i
$550$		0			0
$551$	−15.3448			−0.653712
$552$		0			0
$553$	1.45467	−	7.14741i	0.0618587	−	0.303939i
$554$		0			0
$555$	−19.0644	−	13.8395i	−0.809240	−	0.587456i
$556$		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
$563$	−19.5118			−0.822326			−0.411163	−	0.911562i	$-0.634877\pi$
$563$	−19.5118			−0.822326			−0.411163	+	0.911562i	$0.634877\pi$
$564$		0			0
$565$	1.10294			0.0464012
$566$		0			0
$567$	9.90753	+	21.6527i	0.416077	+	0.909329i
$568$		0			0
$569$	7.18361			0.301153			0.150576	−	0.988598i	$-0.451887\pi$
$569$	7.18361			0.301153			0.150576	+	0.988598i	$0.451887\pi$
$570$		0			0
$571$	29.5773			1.23777			0.618886	−	0.785481i	$-0.287584\pi$
$571$	29.5773			1.23777			0.618886	+	0.785481i	$0.287584\pi$
$572$		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
$579$	−37.3066	−	27.0822i	−1.55041	−	1.12550i
$580$		0			0
$581$	−29.6769	−	26.2595i	−1.23121	−	1.08943i
$582$		0			0
$583$	−19.2449			−0.797042
$584$		0			0
$585$	−13.1163	−	40.2589i	−0.542292	−	1.66450i
$586$		0			0
$587$	14.4563	−	25.0391i	0.596677	−	1.03348i	−0.396630	−	0.917978i	$-0.629821\pi$
$587$	14.4563	−	25.0391i	0.596677	−	1.03348i	0.993308	−	0.115497i	$-0.0368461\pi$
$588$		0			0
$589$	11.7494	+	20.3505i	0.484125	+	0.838530i
$590$		0			0
$591$	14.2543	+	10.3477i	0.586343	+	0.425647i
$592$		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
$597$	−5.26001	+	2.34441i	−0.215278	+	0.0959504i
$598$		0			0
$599$	7.83304			0.320049			0.160025	−	0.987113i	$-0.448843\pi$
$599$	7.83304			0.320049			0.160025	+	0.987113i	$0.448843\pi$
$600$		0			0
$601$	−7.27021	+	12.5924i	−0.296558	+	0.513654i	−0.975346	−	0.220681i	$-0.929172\pi$
$601$	−7.27021	+	12.5924i	−0.296558	+	0.513654i	0.678788	+	0.734334i	$0.262505\pi$
$602$		0			0
$603$	−7.54008	−	23.1434i	−0.307056	−	0.942471i
$604$		0			0
$605$	−11.4822	−	19.8877i	−0.466817	−	0.808551i
$606$		0			0
$607$	15.2755	−	26.4579i	0.620013	−	1.07389i	−0.369470	−	0.929243i	$-0.620461\pi$
$607$	15.2755	−	26.4579i	0.620013	−	1.07389i	0.989483	−	0.144651i	$-0.0462060\pi$
$608$		0			0
$609$	3.11428	+	14.0258i	0.126197	+	0.568353i
$610$		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	0.910293	+	0.413964i	$0.135856\pi$
$617$	20.2106	+	35.0059i	0.813650	+	1.40928i	−0.0966430	+	0.995319i	$0.530811\pi$
$618$		0			0
$619$	9.05857	+	15.6899i	0.364095	+	0.630631i	0.988630	−	0.150366i	$-0.0480451\pi$
$619$	9.05857	+	15.6899i	0.364095	+	0.630631i	−0.624536	+	0.780996i	$0.714712\pi$
$620$		0			0
$621$	−14.5363	−	16.1055i	−0.583322	−	0.646293i
$622$		0			0
$623$	13.8403	−	4.62985i	0.554501	−	0.185491i
$624$		0			0
$625$	14.9657	−	25.9214i	0.598629	−	1.03686i
$626$		0			0
$627$	−10.6395	+	4.74208i	−0.424901	+	0.189380i
$628$		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
$633$	0.467269	−	4.46282i	0.0185723	−	0.177381i
$634$		0			0
$635$	−7.25783	+	12.5709i	−0.288018	+	0.498862i
$636$		0			0
$637$	4.77210	+	38.9096i	0.189077	+	1.54166i
$638$		0			0
$639$	−2.09751	−	6.43805i	−0.0829762	−	0.254685i
$640$		0			0
$641$	−11.0020	−	19.0561i	−0.434554	−	0.752669i	0.562705	−	0.826658i	$-0.309761\pi$
$641$	−11.0020	−	19.0561i	−0.434554	−	0.752669i	−0.997259	+	0.0739883i	$0.976427\pi$
$642$		0			0
$643$	13.1156	+	22.7170i	0.517230	+	0.895869i	0.999800	+	0.0200115i	$0.00637029\pi$
$643$	13.1156	+	22.7170i	0.517230	+	0.895869i	−0.482569	+	0.875858i	$0.660296\pi$
$644$		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
$651$	16.2166	−	14.8696i	0.635579	−	0.582786i
$652$		0			0
$653$	−6.83467	+	11.8380i	−0.267461	+	0.463257i	−0.968206	−	0.250156i	$-0.919518\pi$
$653$	−6.83467	+	11.8380i	−0.267461	+	0.463257i	0.700744	+	0.713413i	$0.252851\pi$
$654$		0			0
$655$	−1.80165	−	3.12054i	−0.0703962	−	0.121930i
$656$		0			0
$657$	20.6300	+	4.36791i	0.804853	+	0.170408i
$658$		0			0
$659$	−3.06683	+	5.31191i	−0.119467	+	0.206923i	−0.919557	−	0.392958i	$-0.871452\pi$
$659$	−3.06683	+	5.31191i	−0.119467	+	0.206923i	0.800090	+	0.599880i	$0.204785\pi$
$660$		0			0
$661$	−44.6236			−1.73566			−0.867828	−	0.496865i	$-0.834484\pi$
$661$	−44.6236			−1.73566			−0.867828	+	0.496865i	$0.834484\pi$
$662$		0			0
$663$	42.3268	+	30.7265i	1.64384	+	1.19332i
$664$		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
$669$	−39.2433	+	17.4909i	−1.51723	+	0.676238i
$670$		0			0
$671$	−4.71119	−	8.16001i	−0.181873	−	0.315014i
$672$		0			0
$673$	−16.3833	+	28.3767i	−0.631531	+	1.09384i	0.355708	+	0.934597i	$0.384240\pi$
$673$	−16.3833	+	28.3767i	−0.631531	+	1.09384i	−0.987239	+	0.159246i	$0.949094\pi$
$674$		0			0
$675$	6.86855	−	1.46852i	0.264371	−	0.0565232i
$676$		0			0
$677$	27.1527			1.04356			0.521782	−	0.853079i	$-0.325267\pi$
$677$	27.1527			1.04356			0.521782	+	0.853079i	$0.325267\pi$
$678$		0			0
$679$	−3.54281	−	3.13484i	−0.135961	−	0.120304i
$680$		0			0
$681$	1.28104	−	12.2350i	0.0490895	−	0.468847i
$682$		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
$689$	78.4338			2.98809
$690$		0			0
$691$	−12.7570			−0.485297			−0.242649	−	0.970114i	$-0.578016\pi$
$691$	−12.7570			−0.485297			−0.242649	+	0.970114i	$0.578016\pi$
$692$		0			0
$693$	6.49377	+	8.76250i	0.246678	+	0.332860i
$694$		0			0
$695$	39.6701			1.50477
$696$		0			0
$697$	32.6761			1.23770
$698$		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
$705$	−22.5491	+	10.0502i	−0.849248	+	0.378514i
$706$		0			0
$707$	−33.5984	+	11.2393i	−1.26360	+	0.422697i
$708$		0			0
$709$	−7.49104			−0.281332			−0.140666	−	0.990057i	$-0.544924\pi$
$709$	−7.49104			−0.281332			−0.140666	+	0.990057i	$0.544924\pi$
$710$		0			0
$711$	2.56199	+	7.86373i	0.0960822	+	0.294913i
$712$		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
$717$	−3.10528	+	29.6581i	−0.115969	+	1.10760i
$718$		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
$723$	3.64716	−	34.8336i	0.135639	−	1.29548i
$724$		0			0
$725$	4.23796			0.157394
$726$		0			0
$727$	8.01088	−	13.8753i	0.297107	−	0.514605i	−0.678366	−	0.734724i	$-0.737311\pi$
$727$	8.01088	−	13.8753i	0.297107	−	0.514605i	0.975473	+	0.220120i	$0.0706448\pi$
$728$		0			0
$729$	−21.8812	−	15.8181i	−0.810416	−	0.585855i
$730$		0			0
$731$	13.1958	+	22.8558i	0.488064	+	0.845351i
$732$		0			0
$733$	−14.8123	+	25.6556i	−0.547104	+	0.947611i	0.451368	+	0.892338i	$0.350936\pi$
$733$	−14.8123	+	25.6556i	−0.547104	+	0.947611i	−0.998471	+	0.0552733i	$0.982397\pi$
$734$		0			0
$735$	−30.5518	+	0.541247i	−1.12692	+	0.0199642i
$736$		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	0.742985	−	0.669308i	$-0.233410\pi$
$743$	−5.67364	−	9.82704i	−0.208146	−	0.360519i	−0.951130	+	0.308789i	$0.900076\pi$
$744$		0			0
$745$	9.99317	+	17.3087i	0.366121	+	0.634141i
$746$		0			0
$747$	43.9581	+	9.30707i	1.60834	+	0.340528i
$748$		0			0
$749$	24.7538	−	8.28063i	0.904485	−	0.302568i
$750$		0			0
$751$	−17.5928	+	30.4716i	−0.641970	+	1.11192i	0.343023	+	0.939327i	$0.388549\pi$
$751$	−17.5928	+	30.4716i	−0.641970	+	1.11192i	−0.984992	+	0.172597i	$0.944784\pi$
$752$		0			0
$753$	10.2632	+	7.45040i	0.374011	+	0.271508i
$754$		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
$759$	−8.04162	−	5.83770i	−0.291892	−	0.211895i
$760$		0			0
$761$	−5.72243	+	9.91155i	−0.207438	+	0.359293i	−0.950907	−	0.309477i	$-0.899846\pi$
$761$	−5.72243	+	9.91155i	−0.207438	+	0.359293i	0.743469	+	0.668771i	$0.233179\pi$
$762$		0			0
$763$	−6.11628	−	5.41197i	−0.221424	−	0.195927i
$764$		0			0
$765$	−27.2562	+	30.3195i	−0.985449	+	1.09620i
$766$		0			0
$767$	−39.9540	−	69.2023i	−1.44265	−	2.49875i
$768$		0			0
$769$	−14.9723	−	25.9328i	−0.539916	−	0.935162i	−0.998908	−	0.0467217i	$-0.985123\pi$
$769$	−14.9723	−	25.9328i	−0.539916	−	0.935162i	0.458992	−	0.888440i	$-0.348211\pi$
$770$		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
$777$	−23.5889	−	7.42903i	−0.846248	−	0.266515i
$778$		0			0
$779$	14.8295	−	25.6854i	0.531320	−	0.920274i
$780$		0			0
$781$	−1.55068	−	2.68586i	−0.0554877	−	0.0961075i
$782$		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
$787$	43.2074			1.54018			0.770089	−	0.637936i	$-0.220212\pi$
$787$	43.2074			1.54018			0.770089	+	0.637936i	$0.220212\pi$
$788$		0			0
$789$	−0.0297469	+	0.284108i	−0.00105902	+	0.0101145i
$790$		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
$795$	−6.36647	+	60.8053i	−0.225795	+	2.15654i
$796$		0			0
$797$	−8.34385	−	14.4520i	−0.295554	−	0.511915i	0.679559	−	0.733620i	$-0.262171\pi$
$797$	−8.34385	−	14.4520i	−0.295554	−	0.511915i	−0.975114	+	0.221706i	$0.928838\pi$
$798$		0			0
$799$	15.2479	−	26.4101i	0.539432	−	0.934323i
$800$		0			0
$801$	−11.0632	+	12.3065i	−0.390897	+	0.434830i
$802$		0			0
$803$	9.65858			0.340844
$804$		0			0
$805$	26.4027	−	8.83221i	0.930573	−	0.311295i
$806$		0			0
$807$	−5.90024	+	2.62977i	−0.207698	+	0.0925722i
$808$		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
$815$	2.70451			0.0947347
$816$		0			0
$817$	23.9546			0.838066
$818$		0			0
$819$	−26.4658	−	35.7122i	−0.924790	−	1.24788i
$820$		0			0
$821$	−25.2738			−0.882063			−0.441031	−	0.897492i	$-0.645387\pi$
$821$	−25.2738			−0.882063			−0.441031	+	0.897492i	$0.645387\pi$
$822$		0			0
$823$	8.88782			0.309810			0.154905	−	0.987929i	$-0.450493\pi$
$823$	8.88782			0.309810			0.154905	+	0.987929i	$0.450493\pi$
$824$		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
$831$	−0.587821	+	5.61421i	−0.0203913	+	0.194755i
$832$		0			0
$833$	30.1482	−	22.7119i	1.04457	−	0.786919i
$834$		0			0
$835$	−38.8946			−1.34600
$836$		0			0
$837$	−7.68101	+	23.7360i	−0.265494	+	0.820435i
$838$		0			0
$839$	−14.9632	+	25.9171i	−0.516588	+	0.894757i	0.483226	+	0.875496i	$0.339465\pi$
$839$	−14.9632	+	25.9171i	−0.516588	+	0.894757i	−0.999814	+	0.0192618i	$0.993868\pi$
$840$		0			0
$841$	9.58522	+	16.6021i	0.330525	+	0.572486i
$842$		0			0
$843$	29.7151	−	13.2442i	1.02344	−	0.456154i
$844$		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
$849$	−17.9931	−	13.0618i	−0.617522	−	0.448281i
$850$		0			0
$851$	22.5331			0.772425
$852$		0			0
$853$	6.46929	−	11.2051i	0.221504	−	0.383657i	−0.733761	−	0.679408i	$-0.762237\pi$
$853$	6.46929	−	11.2051i	0.221504	−	0.383657i	0.955265	+	0.295751i	$0.0955699\pi$
$854$		0			0
$855$	11.4632	+	35.1849i	0.392032	+	1.20330i
$856$		0			0
$857$	4.12252	+	7.14042i	0.140823	+	0.243912i	0.927807	−	0.373061i	$-0.121692\pi$
$857$	4.12252	+	7.14042i	0.140823	+	0.243912i	−0.786984	+	0.616973i	$0.788359\pi$
$858$		0			0
$859$	−1.73399	+	3.00336i	−0.0591630	+	0.102473i	−0.894090	−	0.447888i	$-0.852177\pi$
$859$	−1.73399	+	3.00336i	−0.0591630	+	0.102473i	0.834927	+	0.550361i	$0.185510\pi$
$860$		0			0
$861$	−26.4871	−	8.34177i	−0.902678	−	0.284287i
$862$		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
$871$	22.7186	+	39.3499i	0.769792	+	1.33332i
$872$		0			0
$873$	5.24768	+	1.11107i	0.177607	+	0.0376041i
$874$		0			0
$875$	4.85158	−	23.8379i	0.164013	−	0.805870i
$876$		0			0
$877$	−18.1880	+	31.5026i	−0.614166	+	1.06377i	0.376365	+	0.926472i	$0.377174\pi$
$877$	−18.1880	+	31.5026i	−0.614166	+	1.06377i	−0.990530	+	0.137295i	$0.956159\pi$
$878$		0			0
$879$	4.91646	−	46.9565i	0.165828	−	1.58380i
$880$		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
$885$	56.8917	−	25.3569i	1.91239	−	0.852363i
$886$		0			0
$887$	−22.0791	+	38.2421i	−0.741344	+	1.28405i	0.210539	+	0.977585i	$0.432478\pi$
$887$	−22.0791	+	38.2421i	−0.741344	+	1.28405i	−0.951883	+	0.306460i	$0.900855\pi$
$888$		0			0
$889$	−3.03907	+	14.9323i	−0.101927	+	0.500813i
$890$		0			0
$891$	−11.3056	−	5.01204i	−0.378751	−	0.167910i
$892$		0			0
$893$	−13.8399	−	23.9715i	−0.463136	−	0.802175i
$894$		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
$903$	−4.86167	−	21.8955i	−0.161786	−	0.728635i
$904$		0			0
$905$	12.6084	−	21.8384i	0.419118	−	0.725934i
$906$		0			0
$907$	−3.53884	−	6.12946i	−0.117505	−	0.203525i	0.801273	−	0.598299i	$-0.204156\pi$
$907$	−3.53884	−	6.12946i	−0.117505	−	0.203525i	−0.918778	+	0.394773i	$0.870823\pi$
$908$		0			0
$909$	26.8566	−	29.8750i	0.890777	−	0.990891i
$910$		0			0
$911$	−23.6764	+	41.0088i	−0.784435	+	1.35868i	0.144901	+	0.989446i	$0.453714\pi$
$911$	−23.6764	+	41.0088i	−0.784435	+	1.35868i	−0.929336	+	0.369235i	$0.879620\pi$
$912$		0			0
$913$	20.5804			0.681110
$914$		0			0
$915$	−27.3405	+	12.1858i	−0.903850	+	0.402851i
$916$		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
$921$	34.2879	+	24.8908i	1.12983	+	0.820181i
$922$		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
$927$	−6.46649	−	1.36912i	−0.212387	−	0.0449680i
$928$		0			0
$929$	−5.32221			−0.174616			−0.0873080	−	0.996181i	$-0.527826\pi$
$929$	−5.32221			−0.174616			−0.0873080	+	0.996181i	$0.527826\pi$
$930$		0			0
$931$	−4.17064	−	34.0056i	−0.136687	−	1.11449i
$932$		0			0
$933$	−24.0782	−	17.4792i	−0.788286	−	0.572245i
$934$		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
$941$	21.7637			0.709476			0.354738	−	0.934966i	$-0.384570\pi$
$941$	21.7637			0.709476			0.354738	+	0.934966i	$0.384570\pi$
$942$		0			0
$943$	25.3016			0.823932
$944$		0			0
$945$	29.8339	−	17.6187i	0.970495	−	0.573135i
$946$		0			0
$947$	−34.8784			−1.13339			−0.566697	−	0.823926i	$-0.691779\pi$
$947$	−34.8784			−1.13339			−0.566697	+	0.823926i	$0.691779\pi$
$948$		0			0
$949$	−39.3642			−1.27782
$950$		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
$957$	−6.03843	−	4.38351i	−0.195195	−	0.141699i
$958$		0			0
$959$	−28.0684	+	9.38941i	−0.906375	+	0.303200i
$960$		0			0
$961$	−7.94838			−0.256399
$962$		0			0
$963$	−19.7868	+	22.0106i	−0.637620	+	0.709282i
$964$		0			0
$965$	−33.5396	+	58.0924i	−1.07968	+	1.87006i
$966$		0			0
$967$	7.21327	+	12.4937i	0.231963	+	0.401772i	0.958386	−	0.285476i	$-0.0921518\pi$
$967$	7.21327	+	12.4937i	0.231963	+	0.401772i	−0.726423	+	0.687248i	$0.758819\pi$
$968$		0			0
$969$	−36.9921	−	26.8539i	−1.18836	−	0.862670i
$970$		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
$975$	−11.9758	+	5.33767i	−0.383532	+	0.170942i
$976$		0			0
$977$	−40.3733			−1.29166			−0.645829	−	0.763482i	$-0.723488\pi$
$977$	−40.3733			−1.29166			−0.645829	+	0.763482i	$0.723488\pi$
$978$		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
$983$	10.7299	+	18.5847i	0.342230	+	0.592759i	0.984846	−	0.173429i	$-0.0554846\pi$
$983$	10.7299	+	18.5847i	0.342230	+	0.592759i	−0.642617	+	0.766188i	$0.722151\pi$
$984$		0			0
$985$	12.8150	−	22.1962i	0.408319	−	0.707230i
$986$		0			0
$987$	−19.1020	+	17.5153i	−0.608023	+	0.557519i
$988$		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
$997$	−18.2204	−	31.5587i	−0.577047	−	0.999475i	−0.995816	−	0.0913822i	$-0.970871\pi$
$997$	−18.2204	−	31.5587i	−0.577047	−	0.999475i	0.418769	−	0.908093i	$-0.362462\pi$
$998$		0			0
$999$	27.4227	−	5.86305i	0.867616	−	0.185499i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.6	✓	14	1.1	even	1	trivial
252.2.i.b.121.6	yes	14	63.58	even	3	inner
252.2.l.b.193.2	yes	14	9.4	even	3
252.2.l.b.205.2	yes	14	7.2	even	3
756.2.i.b.37.1		14	63.23	odd	6
756.2.i.b.613.1		14	3.2	odd	2
756.2.l.b.289.7		14	21.2	odd	6
756.2.l.b.361.7		14	9.5	odd	6
1008.2.q.j.529.2		14	4.3	odd	2
1008.2.q.j.625.2		14	252.247	odd	6
1008.2.t.j.193.6		14	36.31	odd	6
1008.2.t.j.961.6		14	28.23	odd	6
1764.2.i.i.373.2		14	63.40	odd	6
1764.2.i.i.1537.2		14	7.6	odd	2
1764.2.j.g.589.5		14	63.4	even	3
1764.2.j.g.1177.5		14	7.4	even	3
1764.2.j.h.589.3		14	63.31	odd	6
1764.2.j.h.1177.3		14	7.3	odd	6
1764.2.l.i.949.6		14	63.13	odd	6
1764.2.l.i.961.6		14	7.5	odd	6
2268.2.k.e.1297.7		14	63.16	even	3
2268.2.k.e.1621.7		14	9.7	even	3
2268.2.k.f.1297.1		14	63.2	odd	6
2268.2.k.f.1621.1		14	9.2	odd	6
3024.2.q.j.2305.1		14	252.23	even	6
3024.2.q.j.2881.1		14	12.11	even	2
3024.2.t.j.289.7		14	84.23	even	6
3024.2.t.j.1873.7		14	36.23	even	6
5292.2.i.i.1549.7		14	63.5	even	6
5292.2.i.i.2125.7		14	21.20	even	2
5292.2.j.g.1765.7		14	63.59	even	6
5292.2.j.g.3529.7		14	21.17	even	6
5292.2.j.h.1765.1		14	63.32	odd	6
5292.2.j.h.3529.1		14	21.11	odd	6
5292.2.l.i.361.1		14	63.41	even	6
5292.2.l.i.3313.1		14	21.5	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40166 + 1.01752i) q^{3} +(1.26013 - 2.18261i) q^{5} +(0.527655 - 2.59260i) q^{7} +(0.929318 + 2.85243i) q^{9} +O(q^{10})\)	\(q+(1.40166 + 1.01752i) q^{3} +(1.26013 - 2.18261i) q^{5} +(0.527655 - 2.59260i) q^{7} +(0.929318 + 2.85243i) q^{9} +(0.687041 + 1.18999i) q^{11} +(-2.80008 - 4.84989i) q^{13} +(3.98712 - 1.77708i) q^{15} +(-2.69613 + 4.66983i) q^{17} +(2.44717 + 4.23863i) q^{19} +(3.37761 - 3.09705i) q^{21} +(-2.08765 + 3.61591i) q^{23} +(-0.675864 - 1.17063i) q^{25} +(-1.59981 + 4.94375i) q^{27} +(-1.56761 + 2.71518i) q^{29} +4.80121 q^{31} +(-0.247835 + 2.36704i) q^{33} +(-4.99373 - 4.41869i) q^{35} +(-2.69839 - 4.67374i) q^{37} +(1.01007 - 9.64704i) q^{39} +(-3.02991 - 5.24797i) q^{41} +(2.44717 - 4.23863i) q^{43} +(7.39682 + 1.56610i) q^{45} -5.65548 q^{47} +(-6.44316 - 2.73600i) q^{49} +(-8.53069 + 3.80217i) q^{51} +(-7.00281 + 12.1292i) q^{53} +3.46305 q^{55} +(-0.882764 + 8.43117i) q^{57} +14.2688 q^{59} -6.85721 q^{61} +(7.88558 - 0.904251i) q^{63} -14.1139 q^{65} -8.11356 q^{67} +(-6.60543 + 2.94407i) q^{69} -2.25704 q^{71} +(3.51456 - 6.08739i) q^{73} +(0.243803 - 2.32853i) q^{75} +(3.44769 - 1.15332i) q^{77} +2.75685 q^{79} +(-7.27273 + 5.30163i) q^{81} +(7.48876 - 12.9709i) q^{83} +(6.79495 + 11.7692i) q^{85} +(-4.95999 + 2.21069i) q^{87} +(2.75804 + 4.77707i) q^{89} +(-14.0513 + 4.70043i) q^{91} +(6.72968 + 4.88531i) q^{93} +12.3350 q^{95} +(0.894003 - 1.54846i) q^{97} +(-2.75589 + 3.06562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Introduction

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