LMFDB - Embedded newform 1080.2.d.g.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(109,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("1080.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.d (of order $2$, degree $1$, 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 3 x^{14} + 36 x^{13} - 78 x^{12} - 96 x^{11} + 1194 x^{10} + 1456 x^{9} + \cdots + 45658 $ x^16 - 3x^15 - 3x^14 + 36x^13 - 78x^12 - 96x^11 + 1194x^10 + 1456x^9 + 2243x^8 + 23019x^7 + 49749x^6 + 37798x^5 + 78784x^4 + 244612x^3 + 302532x^2 + 157882*x + 45658
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.9
Root			$-2.05868 - 0.306986i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.g.109.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.393855 - 1.35826i) q^{2} +(-1.68976 - 1.06992i) q^{4} +(-1.33104 - 1.79676i) q^{5} +4.27541i q^{7} +(-2.11875 + 1.87374i) q^{8} +O(q^{10})$	\(q+(0.393855 - 1.35826i) q^{2} +(-1.68976 - 1.06992i) q^{4} +(-1.33104 - 1.79676i) q^{5} +4.27541i q^{7} +(-2.11875 + 1.87374i) q^{8} +(-2.96471 + 1.10024i) q^{10} +0.381432i q^{11} +3.13006 q^{13} +(5.80712 + 1.68389i) q^{14} +(1.71055 + 3.61580i) q^{16} -3.34970i q^{17} +3.69099i q^{19} +(0.326748 + 4.46018i) q^{20} +(0.518086 + 0.150229i) q^{22} +8.20607i q^{23} +(-1.45667 + 4.78311i) q^{25} +(1.23279 - 4.25144i) q^{26} +(4.57433 - 7.22439i) q^{28} -2.98635i q^{29} -2.30924 q^{31} +(5.58492 - 0.899275i) q^{32} +(-4.54978 - 1.31930i) q^{34} +(7.68186 - 5.69073i) q^{35} +10.5781 q^{37} +(5.01334 + 1.45372i) q^{38} +(6.18679 + 1.31286i) q^{40} +4.98243 q^{41} +5.59564 q^{43} +(0.408101 - 0.644528i) q^{44} +(11.1460 + 3.23200i) q^{46} +5.88732i q^{47} -11.2791 q^{49} +(5.92300 + 3.86240i) q^{50} +(-5.28904 - 3.34891i) q^{52} +4.40820 q^{53} +(0.685342 - 0.507701i) q^{55} +(-8.01100 - 9.05851i) q^{56} +(-4.05625 - 1.17619i) q^{58} -5.51654i q^{59} +6.32959i q^{61} +(-0.909505 + 3.13655i) q^{62} +(0.978197 - 7.93997i) q^{64} +(-4.16623 - 5.62396i) q^{65} -12.6504 q^{67} +(-3.58391 + 5.66018i) q^{68} +(-4.70396 - 12.6753i) q^{70} +15.7805 q^{71} -1.92303i q^{73} +(4.16623 - 14.3678i) q^{74} +(3.94906 - 6.23687i) q^{76} -1.63078 q^{77} -12.3371 q^{79} +(4.21991 - 7.88622i) q^{80} +(1.96236 - 6.76746i) q^{82} -1.18214 q^{83} +(-6.01861 + 4.45859i) q^{85} +(2.20387 - 7.60035i) q^{86} +(-0.714705 - 0.808160i) q^{88} -11.8558 q^{89} +13.3823i q^{91} +(8.77982 - 13.8663i) q^{92} +(7.99652 + 2.31875i) q^{94} +(6.63181 - 4.91285i) q^{95} +7.71322i q^{97} +(-4.44233 + 15.3200i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8	$ 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8} + 5 q^{10} - 30 q^{16} - q^{20} - 22 q^{25} + 18 q^{32} - 4 q^{34} - 2 q^{35} + 56 q^{38} + 19 q^{40} + 40 q^{46} - 44 q^{49} - 27 q^{50} + 96 q^{53} + 34 q^{55} + 2 q^{62} - 6 q^{64} + 72 q^{68} - 7 q^{70} - 12 q^{77} + 4 q^{79} - 9 q^{80} + 64 q^{83} + 20 q^{92} - 20 q^{94} - 36 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8 + 5 * q^10 - 30 * q^16 - q^20 - 22 * q^25 + 18 * q^32 - 4 * q^34 - 2 * q^35 + 56 * q^38 + 19 * q^40 + 40 * q^46 - 44 * q^49 - 27 * q^50 + 96 * q^53 + 34 * q^55 + 2 * q^62 - 6 * q^64 + 72 * q^68 - 7 * q^70 - 12 * q^77 + 4 * q^79 - 9 * q^80 + 64 * q^83 + 20 * q^92 - 20 * q^94 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	0.393855	−	1.35826i	0.278498	−	0.960437i
$2$	0.393855	−	1.35826i	0.278498	−	0.960437i
$3$		0			0
$3$		0			0
$4$	−1.68976	−	1.06992i	−0.844878	−	0.534959i
$5$	−1.33104	−	1.79676i	−0.595259	−	0.803534i
$5$	−1.33104	−	1.79676i	−0.595259	−	0.803534i
$6$		0			0
$7$			4.27541i			1.61595i	0.589216	+	0.807976i	$0.299437\pi$
$7$			4.27541i			1.61595i	−0.589216	+	0.807976i	$0.700563\pi$
$8$	−2.11875	+	1.87374i	−0.749091	+	0.662467i
$9$		0			0
$10$	−2.96471	+	1.10024i	−0.937522	+	0.347926i
$11$			0.381432i			0.115006i	0.998345	+	0.0575031i	$0.0183139\pi$
$11$			0.381432i			0.115006i	−0.998345	+	0.0575031i	$0.981686\pi$
$12$		0			0
$13$	3.13006			0.868123			0.434061	−	0.900883i	$-0.357080\pi$
$13$	3.13006			0.868123			0.434061	+	0.900883i	$0.357080\pi$
$14$	5.80712	+	1.68389i	1.55202	+	0.450039i
$15$		0			0
$16$	1.71055	+	3.61580i	0.427638	+	0.903950i
$17$		−	3.34970i		−	0.812423i	−0.913779	−	0.406211i	$-0.866850\pi$
$17$		−	3.34970i		−	0.812423i	0.913779	−	0.406211i	$-0.133150\pi$
$18$		0			0
$19$			3.69099i			0.846771i	0.905950	+	0.423386i	$0.139158\pi$
$19$			3.69099i			0.846771i	−0.905950	+	0.423386i	$0.860842\pi$
$20$	0.326748	+	4.46018i	0.0730630	+	0.997327i
$21$		0			0
$22$	0.518086	+	0.150229i	0.110456	+	0.0320290i
$23$			8.20607i			1.71108i	0.517734	+	0.855542i	$0.326776\pi$
$23$			8.20607i			1.71108i	−0.517734	+	0.855542i	$0.673224\pi$
$24$		0			0
$25$	−1.45667	+	4.78311i	−0.291334	+	0.956621i
$26$	1.23279	−	4.25144i	0.241770	−	0.833777i
$27$		0			0
$28$	4.57433	−	7.22439i	0.864468	−	1.36528i
$29$		−	2.98635i		−	0.554551i	−0.960790	−	0.277276i	$-0.910569\pi$
$29$		−	2.98635i		−	0.554551i	0.960790	−	0.277276i	$-0.0894315\pi$
$30$		0			0
$31$	−2.30924			−0.414751			−0.207376	−	0.978261i	$-0.566492\pi$
$31$	−2.30924			−0.414751			−0.207376	+	0.978261i	$0.566492\pi$
$32$	5.58492	−	0.899275i	0.987283	−	0.158971i
$33$		0			0
$34$	−4.54978	−	1.31930i	−0.780281	−	0.226258i
$35$	7.68186	−	5.69073i	1.29847	−	0.961909i
$36$		0			0
$37$	10.5781			1.73903			0.869513	−	0.493911i	$-0.164433\pi$
$37$	10.5781			1.73903			0.869513	+	0.493911i	$0.164433\pi$
$38$	5.01334	+	1.45372i	0.813270	+	0.235824i
$39$		0			0
$40$	6.18679	+	1.31286i	0.978218	+	0.207581i
$41$	4.98243			0.778126			0.389063	−	0.921211i	$-0.372799\pi$
$41$	4.98243			0.778126			0.389063	+	0.921211i	$0.372799\pi$
$42$		0			0
$43$	5.59564			0.853327			0.426664	−	0.904410i	$-0.359689\pi$
$43$	5.59564			0.853327			0.426664	+	0.904410i	$0.359689\pi$
$44$	0.408101	−	0.644528i	0.0615236	−	0.0971662i
$45$		0			0
$46$	11.1460	+	3.23200i	1.64339	+	0.476533i
$47$			5.88732i			0.858753i	0.903126	+	0.429377i	$0.141267\pi$
$47$			5.88732i			0.858753i	−0.903126	+	0.429377i	$0.858733\pi$
$48$		0			0
$49$	−11.2791			−1.61130
$50$	5.92300	+	3.86240i	0.837638	+	0.546225i
$51$		0			0
$52$	−5.28904	−	3.34891i	−0.733458	−	0.464410i
$53$	4.40820			0.605513			0.302756	−	0.953068i	$-0.402093\pi$
$53$	4.40820			0.605513			0.302756	+	0.953068i	$0.402093\pi$
$54$		0			0
$55$	0.685342	−	0.507701i	0.0924114	−	0.0684584i
$56$	−8.01100	−	9.05851i	−1.07051	−	1.21049i
$57$		0			0
$58$	−4.05625	−	1.17619i	−0.532611	−	0.154441i
$59$		−	5.51654i		−	0.718192i	−0.933301	−	0.359096i	$-0.883085\pi$
$59$		−	5.51654i		−	0.718192i	0.933301	−	0.359096i	$-0.116915\pi$
$60$		0			0
$61$			6.32959i			0.810421i	0.914223	+	0.405210i	$0.132802\pi$
$61$			6.32959i			0.810421i	−0.914223	+	0.405210i	$0.867198\pi$
$62$	−0.909505	+	3.13655i	−0.115507	+	0.398342i
$63$		0			0
$64$	0.978197	−	7.93997i	0.122275	−	0.992496i
$65$	−4.16623	−	5.62396i	−0.516757	−	0.697566i
$66$		0			0
$67$	−12.6504			−1.54549			−0.772747	−	0.634714i	$-0.781118\pi$
$67$	−12.6504			−1.54549			−0.772747	+	0.634714i	$0.781118\pi$
$68$	−3.58391	+	5.66018i	−0.434613	+	0.686398i
$69$		0			0
$70$	−4.70396	−	12.6753i	−0.562231	−	1.51499i
$71$	15.7805			1.87280			0.936399	−	0.350937i	$-0.114137\pi$
$71$	15.7805			1.87280			0.936399	+	0.350937i	$0.114137\pi$
$72$		0			0
$73$		−	1.92303i		−	0.225073i	−0.993648	−	0.112537i	$-0.964102\pi$
$73$		−	1.92303i		−	0.225073i	0.993648	−	0.112537i	$-0.0358976\pi$
$74$	4.16623	−	14.3678i	0.484315	−	1.67022i
$75$		0			0
$76$	3.94906	−	6.23687i	0.452988	−	0.715418i
$77$	−1.63078			−0.185844
$78$		0			0
$79$	−12.3371			−1.38803			−0.694014	−	0.719962i	$-0.744159\pi$
$79$	−12.3371			−1.38803			−0.694014	+	0.719962i	$0.744159\pi$
$80$	4.21991	−	7.88622i	0.471800	−	0.881706i
$81$		0			0
$82$	1.96236	−	6.76746i	0.216706	−	0.747340i
$83$	−1.18214			−0.129757			−0.0648784	−	0.997893i	$-0.520666\pi$
$83$	−1.18214			−0.129757			−0.0648784	+	0.997893i	$0.520666\pi$
$84$		0			0
$85$	−6.01861	+	4.45859i	−0.652809	+	0.483602i
$86$	2.20387	−	7.60035i	0.237650	−	0.819567i
$87$		0			0
$88$	−0.714705	−	0.808160i	−0.0761878	−	0.0861501i
$89$	−11.8558			−1.25671			−0.628354	−	0.777927i	$-0.716271\pi$
$89$	−11.8558			−1.25671			−0.628354	+	0.777927i	$0.716271\pi$
$90$		0			0
$91$			13.3823i			1.40284i
$92$	8.77982	−	13.8663i	0.915359	−	1.44566i
$93$		0			0
$94$	7.99652	+	2.31875i	0.824778	+	0.239161i
$95$	6.63181	−	4.91285i	0.680410	−	0.504048i
$96$		0			0
$97$			7.71322i			0.783159i	0.920144	+	0.391579i	$0.128071\pi$
$97$			7.71322i			0.783159i	−0.920144	+	0.391579i	$0.871929\pi$
$98$	−4.44233	+	15.3200i	−0.448743	+	1.54755i
$99$		0			0
$100$	7.57895	−	6.52376i	0.757895	−	0.652376i
$101$			13.6859i			1.36180i	0.732377	+	0.680900i	$0.238411\pi$
$101$			13.6859i			1.36180i	−0.732377	+	0.680900i	$0.761589\pi$
$102$		0			0
$103$			17.2794i			1.70259i	0.524685	+	0.851297i	$0.324183\pi$
$103$			17.2794i			1.70259i	−0.524685	+	0.851297i	$0.675817\pi$
$104$	−6.63181	+	5.86492i	−0.650303	+	0.575103i
$105$		0			0
$106$	1.73619	−	5.98749i	0.168634	−	0.581557i
$107$	−4.36922			−0.422389			−0.211194	−	0.977444i	$-0.567735\pi$
$107$	−4.36922			−0.422389			−0.211194	+	0.977444i	$0.567735\pi$
$108$		0			0
$109$		−	11.6902i		−	1.11972i	−0.828588	−	0.559858i	$-0.810855\pi$
$109$		−	11.6902i		−	1.11972i	0.828588	−	0.559858i	$-0.189145\pi$
$110$	−0.419667	−	1.13083i	−0.0400136	−	0.107821i
$111$		0			0
$112$	−15.4590	+	7.31330i	−1.46074	+	0.691042i
$113$			1.60764i			0.151234i	0.997137	+	0.0756172i	$0.0240927\pi$
$113$			1.60764i			0.151234i	−0.997137	+	0.0756172i	$0.975907\pi$
$114$		0			0
$115$	14.7443	−	10.9226i	1.37491	−	1.01854i
$116$	−3.19515	+	5.04620i	−0.296662	+	0.468528i
$117$		0			0
$118$	−7.49291	−	2.17272i	−0.689778	−	0.200015i
$119$	14.3213			1.31284
$120$		0			0
$121$	10.8545			0.986774
$122$	8.59724	+	2.49294i	0.778358	+	0.225700i
$123$		0			0
$124$	3.90205	+	2.47069i	0.350414	+	0.221875i
$125$	10.5330	−	3.74921i	0.942097	−	0.335340i
$126$		0			0
$127$			0.236674i			0.0210014i	0.999945	+	0.0105007i	$0.00334255\pi$
$127$			0.236674i			0.0210014i	−0.999945	+	0.0105007i	$0.996657\pi$
$128$	−10.3993	−	4.45585i	−0.919177	−	0.393845i
$129$		0			0
$130$	−9.27971	+	3.44381i	−0.813884	+	0.302042i
$131$			8.02462i			0.701114i	0.936541	+	0.350557i	$0.114008\pi$
$131$			8.02462i			0.701114i	−0.936541	+	0.350557i	$0.885992\pi$
$132$		0			0
$133$	−15.7805			−1.36834
$134$	−4.98243	+	17.1826i	−0.430417	+	1.48435i
$135$		0			0
$136$	6.27648	+	7.09718i	0.538203	+	0.608579i
$137$			4.48654i			0.383311i	0.981462	+	0.191656i	$0.0613856\pi$
$137$			4.48654i			0.383311i	−0.981462	+	0.191656i	$0.938614\pi$
$138$		0			0
$139$		−	5.54603i		−	0.470408i	−0.971946	−	0.235204i	$-0.924424\pi$
$139$		−	5.54603i		−	0.470408i	0.971946	−	0.235204i	$-0.0755758\pi$
$140$	−19.0691	+	1.39698i	−1.61163	+	0.118066i
$141$		0			0
$142$	6.21523	−	21.4340i	0.521570	−	1.79870i
$143$			1.19391i			0.0998395i
$144$		0			0
$145$	−5.36574	+	3.97495i	−0.445601	+	0.330101i
$146$	−2.61197	−	0.757394i	−0.216169	−	0.0626824i
$147$		0			0
$148$	−17.8744	−	11.3177i	−1.46926	−	0.930307i
$149$			10.4259i			0.854124i	0.904222	+	0.427062i	$0.140451\pi$
$149$			10.4259i			0.854124i	−0.904222	+	0.427062i	$0.859549\pi$
$150$		0			0
$151$	16.2217			1.32010			0.660052	−	0.751220i	$-0.270534\pi$
$151$	16.2217			1.32010			0.660052	+	0.751220i	$0.270534\pi$
$152$	−6.91596	−	7.82028i	−0.560958	−	0.634309i
$153$		0			0
$154$	−0.642291	+	2.21503i	−0.0517573	+	0.178492i
$155$	3.07368	+	4.14914i	0.246884	+	0.333267i
$156$		0			0
$157$	16.3937			1.30836			0.654179	−	0.756339i	$-0.273014\pi$
$157$	16.3937			1.30836			0.654179	+	0.756339i	$0.273014\pi$
$158$	−4.85902	+	16.7570i	−0.386563	+	1.33311i
$159$		0			0
$160$	−9.04952	−	8.83777i	−0.715427	−	0.698687i
$161$	−35.0843			−2.76503
$162$		0			0
$163$	10.5781			0.828539			0.414269	−	0.910154i	$-0.364037\pi$
$163$	10.5781			0.828539			0.414269	+	0.910154i	$0.364037\pi$
$164$	−8.41910	−	5.33080i	−0.657421	−	0.416265i
$165$		0			0
$166$	−0.465593	+	1.60566i	−0.0361370	+	0.124623i
$167$			8.92917i			0.690960i	0.938426	+	0.345480i	$0.112284\pi$
$167$			8.92917i			0.690960i	−0.938426	+	0.345480i	$0.887716\pi$
$168$		0			0
$169$	−3.20272			−0.246363
$170$	3.68547	+	9.93089i	0.282663	+	0.761664i
$171$		0			0
$172$	−9.45527	−	5.98688i	−0.720958	−	0.456495i
$173$	−23.8777			−1.81539			−0.907694	−	0.419633i	$-0.862159\pi$
$173$	−23.8777			−1.81539			−0.907694	+	0.419633i	$0.862159\pi$
$174$		0			0
$175$	−20.4497	−	6.22786i	−1.54585	−	0.470782i
$176$	−1.37918	+	0.652460i	−0.103960	+	0.0491810i
$177$		0			0
$178$	−4.66945	+	16.1032i	−0.349990	+	1.20699i
$179$		−	5.40876i		−	0.404270i	−0.979358	−	0.202135i	$-0.935212\pi$
$179$		−	5.40876i		−	0.404270i	0.979358	−	0.202135i	$-0.0647879\pi$
$180$		0			0
$181$			18.7143i			1.39103i	0.718514	+	0.695513i	$0.244823\pi$
$181$			18.7143i			1.39103i	−0.718514	+	0.695513i	$0.755177\pi$
$182$	18.1766	+	5.27068i	1.34734	+	0.390689i
$183$		0			0
$184$	−15.3760	−	17.3866i	−1.13354	−	1.28176i
$185$	−14.0798	−	19.0062i	−1.03517	−	1.39737i
$186$		0			0
$187$	1.27769			0.0934337
$188$	6.29895	−	9.94813i	0.459398	−	0.725542i
$189$		0			0
$190$	−4.06097	−	10.9427i	−0.294614	−	0.793867i
$191$	6.87333			0.497337			0.248668	−	0.968589i	$-0.420007\pi$
$191$	6.87333			0.497337			0.248668	+	0.968589i	$0.420007\pi$
$192$		0			0
$193$			22.0920i			1.59021i	0.606469	+	0.795107i	$0.292586\pi$
$193$			22.0920i			1.59021i	−0.606469	+	0.795107i	$0.707414\pi$
$194$	10.4766	+	3.03789i	0.752175	+	0.218108i
$195$		0			0
$196$	19.0589	+	12.0677i	1.36135	+	0.861979i
$197$	−20.2935			−1.44585			−0.722924	−	0.690927i	$-0.757202\pi$
$197$	−20.2935			−1.44585			−0.722924	+	0.690927i	$0.757202\pi$
$198$		0			0
$199$	12.9391			0.917232			0.458616	−	0.888635i	$-0.348345\pi$
$199$	12.9391			0.917232			0.458616	+	0.888635i	$0.348345\pi$
$200$	−5.87597	−	12.8636i	−0.415494	−	0.909596i
$201$		0			0
$202$	18.5891	+	5.39027i	1.30792	+	0.379258i
$203$	12.7679			0.896128
$204$		0			0
$205$	−6.63181	−	8.95222i	−0.463186	−	0.625250i
$206$	23.4700	+	6.80560i	1.63523	+	0.474168i
$207$		0			0
$208$	5.35413	+	11.3177i	0.371242	+	0.784740i
$209$	−1.40786			−0.0973840
$210$		0			0
$211$		−	13.3313i		−	0.917762i	−0.888498	−	0.458881i	$-0.848250\pi$
$211$		−	13.3313i		−	0.917762i	0.888498	−	0.458881i	$-0.151750\pi$
$212$	−7.44878	−	4.71641i	−0.511584	−	0.323924i
$213$		0			0
$214$	−1.72084	+	5.93455i	−0.117634	+	0.405678i
$215$	−7.44802	−	10.0540i	−0.507950	−	0.685678i
$216$		0			0
$217$		−	9.87292i		−	0.670217i
$218$	−15.8783	−	4.60424i	−1.07542	−	0.311839i
$219$		0			0
$220$	−1.70126	+	0.124632i	−0.114699	+	0.00840270i
$221$		−	10.4848i		−	0.705282i
$222$		0			0
$223$		−	17.2794i		−	1.15712i	−0.815641	−	0.578558i	$-0.803616\pi$
$223$		−	17.2794i		−	1.15712i	0.815641	−	0.578558i	$-0.196384\pi$
$224$	3.84477	+	23.8778i	0.256889	+	1.59540i
$225$		0			0
$226$	2.18360	+	0.633179i	0.145251	+	0.0421184i
$227$	−19.0068			−1.26153			−0.630763	−	0.775975i	$-0.717258\pi$
$227$	−19.0068			−1.26153			−0.630763	+	0.775975i	$0.717258\pi$
$228$		0			0
$229$		−	4.60897i		−	0.304569i	−0.988337	−	0.152285i	$-0.951337\pi$
$229$		−	4.60897i		−	0.304569i	0.988337	−	0.152285i	$-0.0486630\pi$
$230$	−9.02863	−	24.3286i	−0.595330	−	1.60418i
$231$		0			0
$232$	5.59564	+	6.32733i	0.367372	+	0.415409i
$233$		−	11.7746i		−	0.771382i	−0.922628	−	0.385691i	$-0.873963\pi$
$233$		−	11.7746i		−	0.771382i	0.922628	−	0.385691i	$-0.126037\pi$
$234$		0			0
$235$	10.5781	−	7.83625i	0.690038	−	0.511180i
$236$	−5.90225	+	9.32161i	−0.384203	+	0.606785i
$237$		0			0
$238$	5.64054	−	19.4522i	0.365622	−	1.26090i
$239$	8.33246			0.538982			0.269491	−	0.963003i	$-0.413145\pi$
$239$	8.33246			0.538982			0.269491	+	0.963003i	$0.413145\pi$
$240$		0			0
$241$	−2.69630			−0.173684			−0.0868420	−	0.996222i	$-0.527678\pi$
$241$	−2.69630			−0.173684			−0.0868420	+	0.996222i	$0.527678\pi$
$242$	4.27511	−	14.7433i	0.274814	−	0.947734i
$243$		0			0
$244$	6.77214	−	10.6955i	0.433542	−	0.684707i
$245$	15.0129	+	20.2658i	0.959139	+	1.29473i
$246$		0			0
$247$			11.5530i			0.735101i
$248$	4.89269	−	4.32691i	0.310686	−	0.274759i
$249$		0			0
$250$	−0.943954	−	15.7832i	−0.0597009	−	0.998216i
$251$		−	30.2613i		−	1.91008i	−0.296478	−	0.955040i	$-0.595812\pi$
$251$		−	30.2613i		−	1.91008i	0.296478	−	0.955040i	$-0.404188\pi$
$252$		0			0
$253$	−3.13006			−0.196785
$254$	0.321466	+	0.0932154i	0.0201706	+	0.00584886i
$255$		0			0
$256$	−10.1480	+	12.3700i	−0.634252	+	0.773126i
$257$		−	11.5438i		−	0.720081i	−0.932937	−	0.360041i	$-0.882763\pi$
$257$		−	11.5438i		−	0.720081i	0.932937	−	0.360041i	$-0.117237\pi$
$258$		0			0
$259$			45.2256i			2.81018i
$260$	1.02274	+	13.9606i	0.0634277	+	0.865802i
$261$		0			0
$262$	10.8995	+	3.16054i	0.673376	+	0.195259i
$263$			13.6271i			0.840285i	0.907458	+	0.420142i	$0.138020\pi$
$263$			13.6271i			0.840285i	−0.907458	+	0.420142i	$0.861980\pi$
$264$		0			0
$265$	−5.86748	−	7.92046i	−0.360437	−	0.486550i
$266$	−6.21523	+	21.4340i	−0.381080	+	1.31421i
$267$		0			0
$268$	21.3761	+	13.5349i	1.30575	+	0.826776i
$269$		−	7.49843i		−	0.457187i	−0.973522	−	0.228594i	$-0.926587\pi$
$269$		−	7.49843i		−	0.457187i	0.973522	−	0.228594i	$-0.0734127\pi$
$270$		0			0
$271$	−8.00060			−0.486002			−0.243001	−	0.970026i	$-0.578132\pi$
$271$	−8.00060			−0.486002			−0.243001	+	0.970026i	$0.578132\pi$
$272$	12.1119	−	5.72984i	0.734390	−	0.347423i
$273$		0			0
$274$	6.09390	+	1.76705i	0.368146	+	0.106751i
$275$	−1.82443	−	0.555622i	−0.110017	−	0.0335053i
$276$		0			0
$277$	−3.74327			−0.224911			−0.112456	−	0.993657i	$-0.535872\pi$
$277$	−3.74327			−0.224911			−0.112456	+	0.993657i	$0.535872\pi$
$278$	−7.53297	−	2.18433i	−0.451797	−	0.131008i
$279$		0			0
$280$	−5.61300	+	26.4510i	−0.335441	+	1.58075i
$281$	3.52330			0.210182			0.105091	−	0.994463i	$-0.466487\pi$
$281$	3.52330			0.210182			0.105091	+	0.994463i	$0.466487\pi$
$282$		0			0
$283$	−6.20885			−0.369078			−0.184539	−	0.982825i	$-0.559079\pi$
$283$	−6.20885			−0.369078			−0.184539	+	0.982825i	$0.559079\pi$
$284$	−26.6652	−	16.8838i	−1.58229	−	1.00187i
$285$		0			0
$286$	1.62164	+	0.470226i	0.0958895	+	0.0278051i
$287$			21.3019i			1.25741i
$288$		0			0
$289$	5.77948			0.339969
$290$	3.28570	+	8.85364i	0.192943	+	0.519904i
$291$		0			0
$292$	−2.05748	+	3.24944i	−0.120405	+	0.190159i
$293$	18.6961			1.09224			0.546119	−	0.837707i	$-0.316104\pi$
$293$	18.6961			1.09224			0.546119	+	0.837707i	$0.316104\pi$
$294$		0			0
$295$	−9.91188	+	7.34273i	−0.577092	+	0.427510i
$296$	−22.4123	+	19.8206i	−1.30269	+	1.15205i
$297$		0			0
$298$	14.1611	+	4.10630i	0.820332	+	0.237872i
$299$			25.6855i			1.48543i
$300$		0			0
$301$			23.9236i			1.37894i
$302$	6.38901	−	22.0334i	0.367646	−	1.26788i
$303$		0			0
$304$	−13.3459	+	6.31363i	−0.765439	+	0.362111i
$305$	11.3727	−	8.42493i	0.651201	−	0.482410i
$306$		0			0
$307$	2.07234			0.118275			0.0591374	−	0.998250i	$-0.481165\pi$
$307$	2.07234			0.118275			0.0591374	+	0.998250i	$0.481165\pi$
$308$	2.75562	+	1.74480i	0.157016	+	0.0994192i
$309$		0			0
$310$	6.84620	−	2.54071i	0.388838	−	0.144303i
$311$	−25.7453			−1.45988			−0.729942	−	0.683509i	$-0.760453\pi$
$311$	−25.7453			−1.45988			−0.729942	+	0.683509i	$0.760453\pi$
$312$		0			0
$313$		−	13.6701i		−	0.772677i	−0.922357	−	0.386339i	$-0.873740\pi$
$313$		−	13.6701i		−	0.772677i	0.922357	−	0.386339i	$-0.126260\pi$
$314$	6.45674	−	22.2669i	0.364375	−	1.25660i
$315$		0			0
$316$	20.8466	+	13.1996i	1.17271	+	0.742538i
$317$	−24.9535			−1.40153			−0.700764	−	0.713393i	$-0.747158\pi$
$317$	−24.9535			−1.40153			−0.700764	+	0.713393i	$0.747158\pi$
$318$		0			0
$319$	1.13909			0.0637768
$320$	−15.5682	+	8.81083i	−0.870290	+	0.492540i
$321$		0			0
$322$	−13.8181	+	47.6536i	−0.770054	+	2.65563i
$323$	12.3637			0.687936
$324$		0			0
$325$	−4.55947	+	14.9714i	−0.252914	+	0.830465i
$326$	4.16623	−	14.3678i	0.230746	−	0.795759i
$327$		0			0
$328$	−10.5565	+	9.33579i	−0.582887	+	0.515483i
$329$	−25.1707			−1.38770
$330$		0			0
$331$			5.54603i			0.304837i	0.988316	+	0.152419i	$0.0487062\pi$
$331$			5.54603i			0.304837i	−0.988316	+	0.152419i	$0.951294\pi$
$332$	1.99753	+	1.26479i	0.109629	+	0.0694146i
$333$		0			0
$334$	12.1282	+	3.51680i	0.663623	+	0.192431i
$335$	16.8382	+	22.7297i	0.919969	+	1.24186i
$336$		0			0
$337$		−	13.9054i		−	0.757476i	−0.925504	−	0.378738i	$-0.876358\pi$
$337$		−	13.9054i		−	0.757476i	0.925504	−	0.378738i	$-0.123642\pi$
$338$	−1.26141	+	4.35014i	−0.0686116	+	0.236616i
$339$		0			0
$340$	14.9403	−	1.09451i	0.810251	−	0.0593581i
$341$		−	0.880818i		−	0.0476989i
$342$		0			0
$343$		−	18.2948i		−	0.987828i
$344$	−11.8558	+	10.4848i	−0.639220	+	0.565301i
$345$		0			0
$346$	−9.40436	+	32.4322i	−0.505582	+	1.74357i
$347$	−6.48876			−0.348335			−0.174168	−	0.984716i	$-0.555723\pi$
$347$	−6.48876			−0.348335			−0.174168	+	0.984716i	$0.555723\pi$
$348$		0			0
$349$		−	30.0107i		−	1.60644i	−0.595684	−	0.803219i	$-0.703119\pi$
$349$		−	30.0107i		−	1.60644i	0.595684	−	0.803219i	$-0.296881\pi$
$350$	−16.5133	+	25.3232i	−0.882673	+	1.35358i
$351$		0			0
$352$	0.343013	+	2.13027i	0.0182826	+	0.113544i
$353$		−	26.2378i		−	1.39650i	−0.715854	−	0.698250i	$-0.753963\pi$
$353$		−	26.2378i		−	1.39650i	0.715854	−	0.698250i	$-0.246037\pi$
$354$		0			0
$355$	−21.0044	−	28.3537i	−1.11480	−	1.50486i
$356$	20.0333	+	12.6847i	1.06177	+	0.672287i
$357$		0			0
$358$	−7.34652	−	2.13027i	−0.388276	−	0.112588i
$359$	−8.50573			−0.448915			−0.224458	−	0.974484i	$-0.572061\pi$
$359$	−8.50573			−0.448915			−0.224458	+	0.974484i	$0.572061\pi$
$360$		0			0
$361$	5.37659			0.282978
$362$	25.4190	+	7.37074i	1.33599	+	0.387398i
$363$		0			0
$364$	14.3179	−	22.6128i	0.750464	−	1.18523i
$365$	−3.45521	+	2.55962i	−0.180854	+	0.133977i
$366$		0			0
$367$		−	6.86938i		−	0.358579i	−0.983796	−	0.179289i	$-0.942620\pi$
$367$		−	6.86938i		−	0.358579i	0.983796	−	0.179289i	$-0.0573798\pi$
$368$	−29.6715	+	14.0369i	−1.54673	+	0.731724i
$369$		0			0
$370$	−31.3609	+	11.6384i	−1.63037	+	0.605052i
$371$			18.8468i			0.978479i
$372$		0			0
$373$	32.1742			1.66592			0.832958	−	0.553337i	$-0.186646\pi$
$373$	32.1742			1.66592			0.832958	+	0.553337i	$0.186646\pi$
$374$	0.503223	−	1.73543i	0.0260211	−	0.0897371i
$375$		0			0
$376$	−11.0313	−	12.4737i	−0.568896	−	0.643284i
$377$		−	9.34745i		−	0.481418i
$378$		0			0
$379$		−	15.2373i		−	0.782688i	−0.920244	−	0.391344i	$-0.872010\pi$
$379$		−	15.2373i		−	0.782688i	0.920244	−	0.391344i	$-0.127990\pi$
$380$	−16.4625	+	1.20602i	−0.844508	+	0.0618677i
$381$		0			0
$382$	2.70710	−	9.33579i	0.138507	−	0.477660i
$383$		−	3.27016i		−	0.167097i	−0.996504	−	0.0835486i	$-0.973375\pi$
$383$		−	3.27016i		−	0.167097i	0.996504	−	0.0835486i	$-0.0266254\pi$
$384$		0			0
$385$	2.17063	+	2.93011i	0.110626	+	0.149332i
$386$	30.0067	+	8.70104i	1.52730	+	0.442871i
$387$		0			0
$388$	8.25251	−	13.0335i	0.418958	−	0.661674i
$389$			29.1650i			1.47872i	0.673309	+	0.739361i	$0.264872\pi$
$389$			29.1650i			1.47872i	−0.673309	+	0.739361i	$0.735128\pi$
$390$		0			0
$391$	27.4879			1.39012
$392$	23.8976	−	21.1341i	1.20701	−	1.06743i
$393$		0			0
$394$	−7.99268	+	27.5638i	−0.402666	+	1.38865i
$395$	16.4211	+	22.1667i	0.826235	+	1.11533i
$396$		0			0
$397$	−26.9718			−1.35367			−0.676837	−	0.736133i	$-0.736650\pi$
$397$	−26.9718			−1.35367			−0.676837	+	0.736133i	$0.736650\pi$
$398$	5.09615	−	17.5748i	0.255447	−	0.880943i
$399$		0			0
$400$	−19.7865	+	2.91471i	−0.989324	+	0.145736i
$401$	6.39030			0.319116			0.159558	−	0.987189i	$-0.448993\pi$
$401$	6.39030			0.319116			0.159558	+	0.987189i	$0.448993\pi$
$402$		0			0
$403$	−7.22805			−0.360055
$404$	14.6428	−	23.1259i	0.728507	−	1.15055i
$405$		0			0
$406$	5.02869	−	17.3421i	0.249570	−	0.860674i
$407$			4.03482i			0.199999i
$408$		0			0
$409$	14.3411			0.709123			0.354562	−	0.935033i	$-0.384630\pi$
$409$	14.3411			0.709123			0.354562	+	0.935033i	$0.384630\pi$
$410$	−14.7714	+	5.48186i	−0.729510	+	0.270730i
$411$		0			0
$412$	18.4876	−	29.1980i	0.910817	−	1.43848i
$413$	23.5854			1.16056
$414$		0			0
$415$	1.57348	+	2.12402i	0.0772389	+	0.104264i
$416$	17.4811	−	2.81479i	0.857083	−	0.138006i
$417$		0			0
$418$	−0.554495	+	1.91225i	−0.0271212	+	0.0935312i
$419$		−	16.5213i		−	0.807116i	−0.914954	−	0.403558i	$-0.867773\pi$
$419$		−	16.5213i		−	0.807116i	0.914954	−	0.403558i	$-0.132227\pi$
$420$		0			0
$421$		−	35.2560i		−	1.71827i	−0.511747	−	0.859136i	$-0.671002\pi$
$421$		−	35.2560i		−	1.71827i	0.511747	−	0.859136i	$-0.328998\pi$
$422$	−18.1074	−	5.25059i	−0.881452	−	0.255595i
$423$		0			0
$424$	−9.33987	+	8.25982i	−0.453584	+	0.401132i
$425$	16.0220	+	4.87942i	0.777181	+	0.236687i
$426$		0			0
$427$	−27.0616			−1.30960
$428$	7.38292	+	4.67471i	0.356867	+	0.225961i
$429$		0			0
$430$	−16.5894	+	6.15654i	−0.800013	+	0.296895i
$431$	13.8383			0.666568			0.333284	−	0.942826i	$-0.391843\pi$
$431$	13.8383			0.666568			0.333284	+	0.942826i	$0.391843\pi$
$432$		0			0
$433$		−	3.38265i		−	0.162560i	−0.996691	−	0.0812799i	$-0.974099\pi$
$433$		−	3.38265i		−	0.162560i	0.996691	−	0.0812799i	$-0.0259008\pi$
$434$	−13.4100	−	3.88850i	−0.643702	−	0.186654i
$435$		0			0
$436$	−12.5075	+	19.7536i	−0.599003	+	0.946024i
$437$	−30.2885			−1.44890
$438$		0			0
$439$	24.9454			1.19058			0.595289	−	0.803512i	$-0.297038\pi$
$439$	24.9454			1.19058			0.595289	+	0.803512i	$0.297038\pi$
$440$	−0.500766	+	2.35984i	−0.0238731	+	0.112501i
$441$		0			0
$442$	−14.2411	−	4.12949i	−0.677379	−	0.196420i
$443$	−20.5705			−0.977333			−0.488667	−	0.872471i	$-0.662517\pi$
$443$	−20.5705			−0.977333			−0.488667	+	0.872471i	$0.662517\pi$
$444$		0			0
$445$	15.7805	+	21.3019i	0.748066	+	1.00981i
$446$	−23.4700	−	6.80560i	−1.11134	−	0.322254i
$447$		0			0
$448$	33.9466	+	4.18219i	1.60383	+	0.197590i
$449$	30.1531			1.42301			0.711506	−	0.702680i	$-0.248013\pi$
$449$	30.1531			1.42301			0.711506	+	0.702680i	$0.248013\pi$
$450$		0			0
$451$			1.90046i			0.0894893i
$452$	1.72005	−	2.71653i	0.0809042	−	0.127775i
$453$		0			0
$454$	−7.48593	+	25.8162i	−0.351332	+	1.21162i
$455$	24.0447	−	17.8123i	1.12723	−	0.835055i
$456$		0			0
$457$		−	11.8171i		−	0.552779i	−0.961046	−	0.276389i	$-0.910862\pi$
$457$		−	11.8171i		−	0.552779i	0.961046	−	0.276389i	$-0.0891379\pi$
$458$	−6.26019	−	1.81527i	−0.292519	−	0.0848218i
$459$		0			0
$460$	−36.6006	+	2.68131i	−1.70651	+	0.125017i
$461$		−	19.6586i		−	0.915593i	−0.889057	−	0.457797i	$-0.848639\pi$
$461$		−	19.6586i		−	0.915593i	0.889057	−	0.457797i	$-0.151361\pi$
$462$		0			0
$463$		−	12.4557i		−	0.578867i	−0.957198	−	0.289433i	$-0.906533\pi$
$463$		−	12.4557i		−	0.578867i	0.957198	−	0.289433i	$-0.0934668\pi$
$464$	10.7980	−	5.10830i	0.501287	−	0.237147i
$465$		0			0
$466$	−15.9930	−	4.63750i	−0.740864	−	0.214828i
$467$	−1.25941			−0.0582787			−0.0291394	−	0.999575i	$-0.509277\pi$
$467$	−1.25941			−0.0582787			−0.0291394	+	0.999575i	$0.509277\pi$
$468$		0			0
$469$		−	54.0857i		−	2.49744i
$470$	−6.47745	−	17.4542i	−0.298782	−	0.805100i
$471$		0			0
$472$	10.3366	+	11.6882i	0.475779	+	0.537991i
$473$			2.13436i			0.0981380i
$474$		0			0
$475$	−17.6544	−	5.37656i	−0.810039	−	0.246694i
$476$	−24.1996	−	15.3227i	−1.10919	−	0.702313i
$477$		0			0
$478$	3.28178	−	11.3177i	0.150105	−	0.517658i
$479$	7.44802			0.340309			0.170154	−	0.985417i	$-0.445573\pi$
$479$	7.44802			0.340309			0.170154	+	0.985417i	$0.445573\pi$
$480$		0			0
$481$	33.1100			1.50969
$482$	−1.06195	+	3.66228i	−0.0483706	+	0.166812i
$483$		0			0
$484$	−18.3415	−	11.6134i	−0.833703	−	0.527883i
$485$	13.8588	−	10.2666i	0.629295	−	0.466182i
$486$		0			0
$487$		−	14.9159i		−	0.675903i	−0.941163	−	0.337952i	$-0.890266\pi$
$487$		−	14.9159i		−	0.675903i	0.941163	−	0.337952i	$-0.109734\pi$
$488$	−11.8600	−	13.4108i	−0.536877	−	0.607079i
$489$		0			0
$490$	33.4392	−	12.4097i	1.51063	−	0.560612i
$491$		−	27.3930i		−	1.23623i	−0.786089	−	0.618113i	$-0.787897\pi$
$491$		−	27.3930i		−	1.23623i	0.786089	−	0.618113i	$-0.212103\pi$
$492$		0			0
$493$	−10.0034			−0.450530
$494$	15.6920	+	4.55022i	0.706018	+	0.204724i
$495$		0			0
$496$	−3.95007	−	8.34974i	−0.177363	−	0.374914i
$497$			67.4679i			3.02635i
$498$		0			0
$499$			13.6320i			0.610253i	0.952312	+	0.305127i	$0.0986988\pi$
$499$			13.6320i			0.610253i	−0.952312	+	0.305127i	$0.901301\pi$
$500$	−21.8095	−	4.93415i	−0.975350	−	0.220662i
$501$		0			0
$502$	−41.1029	−	11.9186i	−1.83451	−	0.531953i
$503$		−	26.2664i		−	1.17116i	−0.810615	−	0.585580i	$-0.800867\pi$
$503$		−	26.2664i		−	1.17116i	0.810615	−	0.585580i	$-0.199133\pi$
$504$		0			0
$505$	24.5903	−	18.2165i	1.09425	−	0.810623i
$506$	−1.23279	+	4.25144i	−0.0548042	+	0.189000i
$507$		0			0
$508$	0.253222	−	0.399922i	0.0112349	−	0.0177437i
$509$		−	7.43957i		−	0.329753i	−0.986314	−	0.164876i	$-0.947277\pi$
$509$		−	7.43957i		−	0.329753i	0.986314	−	0.164876i	$-0.0527226\pi$
$510$		0			0
$511$	8.22171			0.363707
$512$	12.8049	+	18.6557i	0.565901	+	0.824473i
$513$		0			0
$514$	−15.6795	−	4.54658i	−0.691593	−	0.200541i
$515$	31.0469	−	22.9996i	1.36809	−	1.01348i
$516$		0			0
$517$	−2.24561			−0.0987620
$518$	61.4282	+	17.8123i	2.69900	+	0.782629i
$519$		0			0
$520$	19.3650	+	4.10932i	0.849213	+	0.180206i
$521$	−9.91360			−0.434323			−0.217161	−	0.976136i	$-0.569680\pi$
$521$	−9.91360			−0.434323			−0.217161	+	0.976136i	$0.569680\pi$
$522$		0			0
$523$	−26.1386			−1.14296			−0.571480	−	0.820616i	$-0.693631\pi$
$523$	−26.1386			−1.14296			−0.571480	+	0.820616i	$0.693631\pi$
$524$	8.58569	−	13.5596i	0.375067	−	0.592356i
$525$		0			0
$526$	18.5092	+	5.36712i	0.807040	+	0.234017i
$527$			7.73526i			0.336953i
$528$		0			0
$529$	−44.3395			−1.92781
$530$	−13.0690	+	4.85007i	−0.567681	+	0.210674i
$531$		0			0
$532$	26.6652	+	16.8838i	1.15608	+	0.732006i
$533$	15.5953			0.675508
$534$		0			0
$535$	5.81560	+	7.85043i	0.251430	+	0.339404i
$536$	26.8031	−	23.7036i	1.15772	−	1.02384i
$537$		0			0
$538$	−10.1848	−	2.95330i	−0.439100	−	0.127326i
$539$		−	4.30221i		−	0.185309i
$540$		0			0
$541$			28.1143i			1.20873i	0.796708	+	0.604364i	$0.206573\pi$
$541$			28.1143i			1.20873i	−0.796708	+	0.604364i	$0.793427\pi$
$542$	−3.15108	+	10.8669i	−0.135350	+	0.466774i
$543$		0			0
$544$	−3.01231	−	18.7078i	−0.129152	−	0.802091i
$545$	−21.0044	+	15.5601i	−0.899731	+	0.666521i
$546$		0			0
$547$	35.2144			1.50566			0.752830	−	0.658215i	$-0.228688\pi$
$547$	35.2144			1.50566			0.752830	+	0.658215i	$0.228688\pi$
$548$	4.80023	−	7.58116i	0.205056	−	0.323851i
$549$		0			0
$550$	−1.47324	+	2.25922i	−0.0628193	+	0.0963336i
$551$	11.0226			0.469578
$552$		0			0
$553$		−	52.7459i		−	2.24298i
$554$	−1.47431	+	5.08434i	−0.0626373	+	0.216013i
$555$		0			0
$556$	−5.93380	+	9.37144i	−0.251649	+	0.397437i
$557$	11.9112			0.504694			0.252347	−	0.967637i	$-0.418798\pi$
$557$	11.9112			0.504694			0.252347	+	0.967637i	$0.418798\pi$
$558$		0			0
$559$	17.5147			0.740793
$560$	33.7168	+	18.0418i	1.42479	+	0.762406i
$561$		0			0
$562$	1.38767	−	4.78557i	0.0585353	−	0.201867i
$563$	25.8476			1.08934			0.544672	−	0.838649i	$-0.316654\pi$
$563$	25.8476			1.08934			0.544672	+	0.838649i	$0.316654\pi$
$564$		0			0
$565$	2.88855	−	2.13984i	0.121522	−	0.0900236i
$566$	−2.44539	+	8.43325i	−0.102787	+	0.354476i
$567$		0			0
$568$	−33.4349	+	29.5685i	−1.40290	+	1.24067i
$569$	−6.92460			−0.290294			−0.145147	−	0.989410i	$-0.546366\pi$
$569$	−6.92460			−0.290294			−0.145147	+	0.989410i	$0.546366\pi$
$570$		0			0
$571$		−	34.5498i		−	1.44586i	−0.690919	−	0.722932i	$-0.742794\pi$
$571$		−	34.5498i		−	1.44586i	0.690919	−	0.722932i	$-0.257206\pi$
$572$	1.27738	−	2.01741i	0.0534100	−	0.0843522i
$573$		0			0
$574$	28.9336	+	8.38988i	1.20767	+	0.350187i
$575$	−39.2505	−	11.9535i	−1.63686	−	0.498497i
$576$		0			0
$577$			38.5338i			1.60418i	0.597201	+	0.802092i	$0.296280\pi$
$577$			38.5338i			1.60418i	−0.597201	+	0.802092i	$0.703720\pi$
$578$	2.27628	−	7.85005i	0.0946807	−	0.326519i
$579$		0			0
$580$	13.3197	−	0.975783i	0.553069	−	0.0405172i
$581$		−	5.05413i		−	0.209681i
$582$		0			0
$583$			1.68143i			0.0696377i
$584$	3.60325	+	4.07441i	0.149104	+	0.168600i
$585$		0			0
$586$	7.36356	−	25.3942i	0.304186	−	1.04903i
$587$	−22.6932			−0.936650			−0.468325	−	0.883556i	$-0.655142\pi$
$587$	−22.6932			−0.936650			−0.468325	+	0.883556i	$0.655142\pi$
$588$		0			0
$589$		−	8.52337i		−	0.351199i
$590$	6.06951	+	16.3549i	0.249878	+	0.673321i
$591$		0			0
$592$	18.0943	+	38.2482i	0.743673	+	1.57199i
$593$			1.74206i			0.0715379i	0.999360	+	0.0357689i	$0.0113880\pi$
$593$			1.74206i			0.0715379i	−0.999360	+	0.0357689i	$0.988612\pi$
$594$		0			0
$595$	−19.0623	−	25.7320i	−0.781477	−	1.05491i
$596$	11.1549	−	17.6173i	0.456921	−	0.721631i
$597$		0			0
$598$	34.8876	+	10.1164i	1.42666	+	0.413689i
$599$	17.4129			0.711471			0.355736	−	0.934587i	$-0.384230\pi$
$599$	17.4129			0.711471			0.355736	+	0.934587i	$0.384230\pi$
$600$		0			0
$601$	44.8993			1.83148			0.915740	−	0.401770i	$-0.131605\pi$
$601$	44.8993			1.83148			0.915740	+	0.401770i	$0.131605\pi$
$602$	32.4946	+	9.42245i	1.32438	+	0.384030i
$603$		0			0
$604$	−27.4107	−	17.3559i	−1.11533	−	0.706202i
$605$	−14.4478	−	19.5029i	−0.587385	−	0.792906i
$606$		0			0
$607$		−	28.0915i		−	1.14020i	−0.821576	−	0.570099i	$-0.806905\pi$
$607$		−	28.0915i		−	1.14020i	0.821576	−	0.570099i	$-0.193095\pi$
$608$	3.31922	+	20.6139i	0.134612	+	0.836003i
$609$		0			0
$610$	−6.96405	−	18.7654i	−0.281966	−	0.759787i
$611$			18.4277i			0.745503i
$612$		0			0
$613$	−11.1913			−0.452012			−0.226006	−	0.974126i	$-0.572567\pi$
$613$	−11.1913			−0.452012			−0.226006	+	0.974126i	$0.572567\pi$
$614$	0.816203	−	2.81479i	0.0329393	−	0.113596i
$615$		0			0
$616$	3.45521	−	3.05565i	0.139214	−	0.123116i
$617$			32.4154i			1.30500i	0.757791	+	0.652498i	$0.226279\pi$
$617$			32.4154i			1.30500i	−0.757791	+	0.652498i	$0.773721\pi$
$618$		0			0
$619$			39.6795i			1.59486i	0.603415	+	0.797428i	$0.293806\pi$
$619$			39.6795i			1.59486i	−0.603415	+	0.797428i	$0.706194\pi$
$620$	−0.754538	−	10.2996i	−0.0303030	−	0.413643i
$621$		0			0
$622$	−10.1399	+	34.9690i	−0.406575	+	1.40213i
$623$		−	50.6882i		−	2.03078i
$624$		0			0
$625$	−20.7562	−	13.9348i	−0.830249	−	0.557393i
$626$	−18.5675	−	5.38402i	−0.742108	−	0.215189i
$627$		0			0
$628$	−27.7013	−	17.5399i	−1.10540	−	0.699918i
$629$		−	35.4334i		−	1.41282i
$630$		0			0
$631$	−41.0977			−1.63607			−0.818036	−	0.575167i	$-0.804937\pi$
$631$	−41.0977			−1.63607			−0.818036	+	0.575167i	$0.804937\pi$
$632$	26.1391	−	23.1164i	1.03976	−	0.919523i
$633$		0			0
$634$	−9.82807	+	33.8934i	−0.390323	+	1.34608i
$635$	0.425246	−	0.315023i	0.0168754	−	0.0125013i
$636$		0			0
$637$	−35.3042			−1.39880
$638$	0.448637	−	1.54718i	0.0177617	−	0.0612536i
$639$		0			0
$640$	5.83579	+	24.6159i	0.230680	+	0.973030i
$641$	23.2285			0.917470			0.458735	−	0.888573i	$-0.348303\pi$
$641$	23.2285			0.917470			0.458735	+	0.888573i	$0.348303\pi$
$642$		0			0
$643$	−39.7120			−1.56609			−0.783044	−	0.621967i	$-0.786334\pi$
$643$	−39.7120			−1.56609			−0.783044	+	0.621967i	$0.786334\pi$
$644$	59.2838	+	37.5373i	2.33611	+	1.47918i
$645$		0			0
$646$	4.86952	−	16.7932i	0.191589	−	0.660719i
$647$			29.2392i			1.14951i	0.818326	+	0.574755i	$0.194903\pi$
$647$			29.2392i			1.14951i	−0.818326	+	0.574755i	$0.805097\pi$
$648$		0			0
$649$	2.10419			0.0825966
$650$	18.5393	+	12.0895i	0.727173	+	0.474190i
$651$		0			0
$652$	−17.8744	−	11.3177i	−0.700014	−	0.443234i
$653$	37.9006			1.48316			0.741582	−	0.670862i	$-0.234076\pi$
$653$	37.9006			1.48316			0.741582	+	0.670862i	$0.234076\pi$
$654$		0			0
$655$	14.4183	−	10.6811i	0.563369	−	0.417344i
$656$	8.52271	+	18.0155i	0.332756	+	0.703387i
$657$		0			0
$658$	−9.91360	+	34.1884i	−0.386472	+	1.33280i
$659$		−	16.1193i		−	0.627918i	−0.949437	−	0.313959i	$-0.898345\pi$
$659$		−	16.1193i		−	0.627918i	0.949437	−	0.313959i	$-0.101655\pi$
$660$		0			0
$661$			17.1112i			0.665550i	0.943006	+	0.332775i	$0.107985\pi$
$661$			17.1112i			0.665550i	−0.943006	+	0.332775i	$0.892015\pi$
$662$	7.53297	+	2.18433i	0.292777	+	0.0848965i
$663$		0			0
$664$	2.50466	−	2.21503i	0.0971997	−	0.0859597i
$665$	21.0044	+	28.3537i	0.814517	+	1.09951i
$666$		0			0
$667$	24.5062			0.948883
$668$	9.55348	−	15.0881i	0.369635	−	0.583777i
$669$		0			0
$670$	37.5048	−	13.9185i	1.44894	−	0.537718i
$671$	−2.41431			−0.0932034
$672$		0			0
$673$			35.6654i			1.37480i	0.726279	+	0.687400i	$0.241248\pi$
$673$			35.6654i			1.37480i	−0.726279	+	0.687400i	$0.758752\pi$
$674$	−18.8872	−	5.47672i	−0.727507	−	0.210955i
$675$		0			0
$676$	5.41182	+	3.42665i	0.208147	+	0.131794i
$677$	19.0953			0.733894			0.366947	−	0.930242i	$-0.380403\pi$
$677$	19.0953			0.733894			0.366947	+	0.930242i	$0.380403\pi$
$678$		0			0
$679$	−32.9771			−1.26555
$680$	4.39768	−	20.7239i	0.168644	−	0.794726i
$681$		0			0
$682$	−1.19638	−	0.346915i	−0.0458118	−	0.0132840i
$683$	12.7051			0.486148			0.243074	−	0.970008i	$-0.421844\pi$
$683$	12.7051			0.486148			0.243074	+	0.970008i	$0.421844\pi$
$684$		0			0
$685$	8.06122	−	5.97176i	0.308004	−	0.228169i
$686$	−24.8492	−	7.20552i	−0.948747	−	0.275108i
$687$		0			0
$688$	9.57163	+	20.2327i	0.364915	+	0.771366i
$689$	13.7979			0.525659
$690$		0			0
$691$		−	6.25004i		−	0.237763i	−0.992908	−	0.118881i	$-0.962069\pi$
$691$		−	6.25004i		−	0.237763i	0.992908	−	0.118881i	$-0.0379308\pi$
$692$	40.3475	+	25.5472i	1.53378	+	0.971158i
$693$		0			0
$694$	−2.55563	+	8.81345i	−0.0970106	+	0.334554i
$695$	−9.96487	+	7.38198i	−0.377989	+	0.280014i
$696$		0			0
$697$		−	16.6897i		−	0.632167i
$698$	−40.7625	−	11.8199i	−1.54288	−	0.447389i
$699$		0			0
$700$	27.8917	+	32.4031i	1.05421	+	1.22472i
$701$			18.8640i			0.712484i	0.934394	+	0.356242i	$0.115942\pi$
$701$			18.8640i			0.712484i	−0.934394	+	0.356242i	$0.884058\pi$
$702$		0			0
$703$			39.0436i			1.47256i
$704$	3.02856	+	0.373116i	0.114143	+	0.0140623i
$705$		0			0
$706$	−35.6379	−	10.3339i	−1.34125	−	0.388922i
$707$	−58.5128			−2.20060
$708$		0			0
$709$		−	1.34976i		−	0.0506914i	−0.999679	−	0.0253457i	$-0.991931\pi$
$709$		−	1.34976i		−	0.0506914i	0.999679	−	0.0253457i	$-0.00806865\pi$
$710$	−46.7845	+	17.3623i	−1.75579	+	0.651595i
$711$		0			0
$712$	25.1194	−	22.2146i	0.941389	−	0.832528i
$713$		−	18.9497i		−	0.709674i
$714$		0			0
$715$	2.14516	−	1.58914i	0.0802244	−	0.0594303i
$716$	−5.78693	+	9.13949i	−0.216268	+	0.341559i
$717$		0			0
$718$	−3.35003	+	11.5530i	−0.125022	+	0.431155i
$719$	−31.5610			−1.17703			−0.588513	−	0.808488i	$-0.700286\pi$
$719$	−31.5610			−1.17703			−0.588513	+	0.808488i	$0.700286\pi$
$720$		0			0
$721$	−73.8766			−2.75131
$722$	2.11760	−	7.30282i	0.0788088	−	0.271783i
$723$		0			0
$724$	20.0228	−	31.6227i	0.744142	−	1.17525i
$725$	14.2840	+	4.35013i	0.530495	+	0.161560i
$726$		0			0
$727$		−	27.2812i		−	1.01181i	−0.862591	−	0.505903i	$-0.831159\pi$
$727$		−	27.2812i		−	1.01181i	0.862591	−	0.505903i	$-0.168841\pi$
$728$	−25.0749	−	28.3537i	−0.929338	−	1.05086i
$729$		0			0
$730$	2.11579	+	5.70120i	0.0783088	+	0.211011i
$731$		−	18.7437i		−	0.693263i
$732$		0			0
$733$	0.613208			0.0226493			0.0113247	−	0.999936i	$-0.496395\pi$
$733$	0.613208			0.0226493			0.0113247	+	0.999936i	$0.496395\pi$
$734$	−9.33042	−	2.70554i	−0.344392	−	0.0998634i
$735$		0			0
$736$	7.37951	+	45.8302i	0.272012	+	1.68932i
$737$		−	4.82528i		−	0.177741i
$738$		0			0
$739$			34.0881i			1.25395i	0.779039	+	0.626975i	$0.215707\pi$
$739$			34.0881i			1.25395i	−0.779039	+	0.626975i	$0.784293\pi$
$740$	3.45636	+	47.1802i	0.127058	+	1.73438i
$741$		0			0
$742$	25.5990	+	7.42293i	0.939767	+	0.272504i
$743$			7.90870i			0.290142i	0.989421	+	0.145071i	$0.0463411\pi$
$743$			7.90870i			0.290142i	−0.989421	+	0.145071i	$0.953659\pi$
$744$		0			0
$745$	18.7328	−	13.8773i	0.686318	−	0.508425i
$746$	12.6720	−	43.7010i	0.463954	−	1.60001i
$747$		0			0
$748$	−2.15898	−	1.36702i	−0.0789401	−	0.0499832i
$749$		−	18.6802i		−	0.682559i
$750$		0			0
$751$	10.5897			0.386422			0.193211	−	0.981157i	$-0.438110\pi$
$751$	10.5897			0.386422			0.193211	+	0.981157i	$0.438110\pi$
$752$	−21.2874	+	10.0706i	−0.776270	+	0.367235i
$753$		0			0
$754$	−12.6963	−	3.68154i	−0.462372	−	0.134074i
$755$	−21.5917	−	29.1465i	−0.785804	−	1.06075i
$756$		0			0
$757$	−32.5802			−1.18415			−0.592073	−	0.805884i	$-0.701690\pi$
$757$	−32.5802			−1.18415			−0.592073	+	0.805884i	$0.701690\pi$
$758$	−20.6963	−	6.00130i	−0.751723	−	0.217977i
$759$		0			0
$760$	−4.84574	+	22.8354i	−0.175774	+	0.828327i
$761$	33.4519			1.21263			0.606314	−	0.795225i	$-0.292647\pi$
$761$	33.4519			1.21263			0.606314	+	0.795225i	$0.292647\pi$
$762$		0			0
$763$	49.9803			1.80941
$764$	−11.6142	−	7.35390i	−0.420189	−	0.266055i
$765$		0			0
$766$	−4.44173	−	1.28797i	−0.160486	−	0.0465362i
$767$		−	17.2671i		−	0.623479i
$768$		0			0
$769$	−5.03867			−0.181699			−0.0908495	−	0.995865i	$-0.528958\pi$
$769$	−5.03867			−0.181699			−0.0908495	+	0.995865i	$0.528958\pi$
$770$	4.83478	−	1.79424i	0.174233	−	0.0646601i
$771$		0			0
$772$	23.6366	−	37.3300i	0.850700	−	1.34354i
$773$	−38.4946			−1.38455			−0.692277	−	0.721632i	$-0.743392\pi$
$773$	−38.4946			−1.38455			−0.692277	+	0.721632i	$0.743392\pi$
$774$		0			0
$775$	3.36380	−	11.0453i	0.120831	−	0.396760i
$776$	−14.4526	−	16.3424i	−0.518817	−	0.586657i
$777$		0			0
$778$	39.6137	+	11.4868i	1.42022	+	0.411821i
$779$			18.3901i			0.658894i
$780$		0			0
$781$			6.01919i			0.215383i
$782$	10.8263	−	37.3358i	0.387146	−	1.33513i
$783$		0			0
$784$	−19.2935	−	40.7829i	−0.689052	−	1.45653i
$785$	−21.8206	−	29.4555i	−0.778812	−	1.05131i
$786$		0			0
$787$	35.8000			1.27613			0.638066	−	0.769981i	$-0.279735\pi$
$787$	35.8000			1.27613			0.638066	+	0.769981i	$0.279735\pi$
$788$	34.2910	+	21.7123i	1.22157	+	0.773470i
$789$		0			0
$790$	36.5757	−	13.5737i	1.30131	−	0.482931i
$791$	−6.87333			−0.244387
$792$		0			0
$793$			19.8120i			0.703545i
$794$	−10.6230	+	36.6347i	−0.376995	+	1.30012i
$795$		0			0
$796$	−21.8640	−	13.8438i	−0.774949	−	0.490682i
$797$	−13.4741			−0.477278			−0.238639	−	0.971108i	$-0.576701\pi$
$797$	−13.4741			−0.477278			−0.238639	+	0.971108i	$0.576701\pi$
$798$		0			0
$799$	19.7208			0.697671
$800$	−3.83406	+	28.0232i	−0.135555	+	0.990770i
$801$		0			0
$802$	2.51685	−	8.67970i	0.0888732	−	0.306491i
$803$	0.733505			0.0258848
$804$		0			0
$805$	46.6985	+	63.0379i	1.64591	+	2.22179i
$806$	−2.84681	+	9.81759i	−0.100274	+	0.345810i
$807$		0			0
$808$	−25.6439	−	28.9970i	−0.902148	−	1.02011i
$809$	23.1772			0.814868			0.407434	−	0.913235i	$-0.366424\pi$
$809$	23.1772			0.814868			0.407434	+	0.913235i	$0.366424\pi$
$810$		0			0
$811$		−	3.64557i		−	0.128013i	−0.997949	−	0.0640066i	$-0.979612\pi$
$811$		−	3.64557i		−	0.128013i	0.997949	−	0.0640066i	$-0.0203879\pi$
$812$	−21.5746	−	13.6606i	−0.757119	−	0.479392i
$813$		0			0
$814$	5.48035	+	1.58914i	0.192086	+	0.0556992i
$815$	−14.0798	−	19.0062i	−0.493195	−	0.665759i
$816$		0			0
$817$			20.6535i			0.722573i
$818$	5.64833	−	19.4790i	0.197489	−	0.681068i
$819$		0			0
$820$	1.62800	+	22.2226i	0.0568522	+	0.776046i
$821$			32.8395i			1.14610i	0.819519	+	0.573052i	$0.194241\pi$
$821$			32.8395i			1.14610i	−0.819519	+	0.573052i	$0.805759\pi$
$822$		0			0
$823$		−	7.30498i		−	0.254636i	−0.991862	−	0.127318i	$-0.959363\pi$
$823$		−	7.30498i		−	0.254636i	0.991862	−	0.127318i	$-0.0406368\pi$
$824$	−32.3772	−	36.6108i	−1.12791	−	1.27540i
$825$		0			0
$826$	9.28925	−	32.0352i	0.323214	−	1.11465i
$827$	−12.2507			−0.425999			−0.212999	−	0.977052i	$-0.568323\pi$
$827$	−12.2507			−0.425999			−0.212999	+	0.977052i	$0.568323\pi$
$828$		0			0
$829$		−	28.1143i		−	0.976450i	−0.872718	−	0.488225i	$-0.837644\pi$
$829$		−	28.1143i		−	0.976450i	0.872718	−	0.488225i	$-0.162356\pi$
$830$	3.50470	−	1.30064i	0.121650	−	0.0451458i
$831$		0			0
$832$	3.06182	−	24.8526i	0.106149	−	0.861608i
$833$			37.7816i			1.30906i
$834$		0			0
$835$	16.0435	−	11.8851i	0.555210	−	0.411300i
$836$	2.37895	+	1.50630i	0.0822776	+	0.0520964i
$837$		0			0
$838$	−22.4402	−	6.50699i	−0.775184	−	0.224780i
$839$	−51.8712			−1.79079			−0.895396	−	0.445271i	$-0.853108\pi$
$839$	−51.8712			−1.79079			−0.895396	+	0.445271i	$0.853108\pi$
$840$		0			0
$841$	20.0817			0.692473
$842$	−47.8869	−	13.8858i	−1.65029	−	0.478535i
$843$		0			0
$844$	−14.2634	+	22.5266i	−0.490965	+	0.775397i
$845$	4.26295	+	5.75451i	0.146650	+	0.197961i
$846$		0			0
$847$			46.4074i			1.59458i
$848$	7.54045	+	15.9392i	0.258940	+	0.547353i
$849$		0			0
$850$	12.9379	−	19.8403i	0.443766	−	0.680516i
$851$			86.8044i			2.97562i
$852$		0			0
$853$	−1.22642			−0.0419917			−0.0209958	−	0.999780i	$-0.506684\pi$
$853$	−1.22642			−0.0419917			−0.0209958	+	0.999780i	$0.506684\pi$
$854$	−10.6583	+	36.7567i	−0.364721	+	1.25779i
$855$		0			0
$856$	9.25729	−	8.18679i	0.316407	−	0.279819i
$857$			14.7535i			0.503969i	0.967731	+	0.251985i	$0.0810832\pi$
$857$			14.7535i			0.503969i	−0.967731	+	0.251985i	$0.918917\pi$
$858$		0			0
$859$			34.8505i			1.18909i	0.804064	+	0.594543i	$0.202667\pi$
$859$			34.8505i			1.18909i	−0.804064	+	0.594543i	$0.797333\pi$
$860$	1.82836	+	24.9576i	0.0623467	+	0.851047i
$861$		0			0
$862$	5.45029	−	18.7961i	0.185638	−	0.640197i
$863$		−	22.4673i		−	0.764796i	−0.923998	−	0.382398i	$-0.875098\pi$
$863$		−	22.4673i		−	0.764796i	0.923998	−	0.382398i	$-0.124902\pi$
$864$		0			0
$865$	31.7821	+	42.9024i	1.08063	+	1.45873i
$866$	−4.59453	−	1.33227i	−0.156128	−	0.0452725i
$867$		0			0
$868$	−10.5632	+	16.6828i	−0.358539	+	0.566252i
$869$		−	4.70575i		−	0.159632i
$870$		0			0
$871$	−39.5966			−1.34168
$872$	21.9044	+	24.7686i	0.741776	+	0.838770i
$873$		0			0
$874$	−11.9293	+	41.1398i	−0.403514	+	1.39157i
$875$	16.0294	+	45.0327i	0.541893	+	1.52238i
$876$		0			0
$877$	24.8994			0.840794			0.420397	−	0.907340i	$-0.361891\pi$
$877$	24.8994			0.840794			0.420397	+	0.907340i	$0.361891\pi$
$878$	9.82486	−	33.8824i	0.331573	−	1.14347i
$879$		0			0
$880$	3.00806	+	1.60961i	0.101402	+	0.0542599i
$881$	33.6251			1.13286			0.566430	−	0.824110i	$-0.308324\pi$
$881$	33.6251			1.13286			0.566430	+	0.824110i	$0.308324\pi$
$882$		0			0
$883$	22.4338			0.754959			0.377479	−	0.926018i	$-0.376791\pi$
$883$	22.4338			0.754959			0.377479	+	0.926018i	$0.376791\pi$
$884$	−11.2179	+	17.7167i	−0.377297	+	0.595878i
$885$		0			0
$886$	−8.10179	+	27.9401i	−0.272185	+	0.938667i
$887$		−	15.8140i		−	0.530982i	−0.964113	−	0.265491i	$-0.914466\pi$
$887$		−	15.8140i		−	0.530982i	0.964113	−	0.265491i	$-0.0855341\pi$
$888$		0			0
$889$	−1.01188			−0.0339373
$890$	35.1488	−	13.0442i	1.17819	−	0.437241i
$891$		0			0
$892$	−18.4876	+	29.1980i	−0.619010	+	0.977622i
$893$	−21.7300			−0.727168
$894$		0			0
$895$	−9.71823	+	7.19927i	−0.324845	+	0.240645i
$896$	19.0506	−	44.4612i	0.636434	−	1.48534i
$897$		0			0
$898$	11.8760	−	40.9558i	0.396306	−	1.36671i
$899$			6.89619i			0.230001i
$900$		0			0
$901$		−	14.7662i		−	0.491932i
$902$	2.58133	+	0.748507i	0.0859488	+	0.0249226i
$903$		0			0
$904$	−3.01231	−	3.40619i	−0.100188	−	0.113288i
$905$	33.6251	−	24.9095i	1.11774	−	0.828020i
$906$		0			0
$907$	50.9545			1.69192			0.845959	−	0.533248i	$-0.179029\pi$
$907$	50.9545			1.69192			0.845959	+	0.533248i	$0.179029\pi$
$908$	32.1169	+	20.3357i	1.06584	+	0.674865i
$909$		0			0
$910$	−14.7237	−	39.6745i	−0.488086	−	1.31520i
$911$	−56.3302			−1.86630			−0.933151	−	0.359484i	$-0.882953\pi$
$911$	−56.3302			−1.86630			−0.933151	+	0.359484i	$0.882953\pi$
$912$		0			0
$913$		−	0.450907i		−	0.0149228i
$914$	−16.0507	−	4.65421i	−0.530909	−	0.153948i
$915$		0			0
$916$	−4.93122	+	7.78803i	−0.162932	+	0.257324i
$917$	−34.3085			−1.13297
$918$		0			0
$919$	4.37513			0.144322			0.0721611	−	0.997393i	$-0.477010\pi$
$919$	4.37513			0.144322			0.0721611	+	0.997393i	$0.477010\pi$
$920$	−10.7734	+	50.7692i	−0.355188	+	1.67381i
$921$		0			0
$922$	−26.7016	−	7.74265i	−0.879369	−	0.254991i
$923$	49.3939			1.62582
$924$		0			0
$925$	−15.4088	+	50.5961i	−0.506638	+	1.66359i
$926$	−16.9181	−	4.90575i	−0.555965	−	0.161213i
$927$		0			0
$928$	−2.68555	−	16.6785i	−0.0881575	−	0.547499i
$929$	23.4870			0.770583			0.385291	−	0.922795i	$-0.374101\pi$
$929$	23.4870			0.770583			0.385291	+	0.922795i	$0.374101\pi$
$930$		0			0
$931$		−	41.6310i		−	1.36440i
$932$	−12.5979	+	19.8963i	−0.412658	+	0.651724i
$933$		0			0
$934$	−0.496027	+	1.71062i	−0.0162305	+	0.0559730i
$935$	−1.70065	−	2.29569i	−0.0556172	−	0.0750771i
$936$		0			0
$937$		−	32.7647i		−	1.07038i	−0.844733	−	0.535189i	$-0.820241\pi$
$937$		−	32.7647i		−	1.07038i	0.844733	−	0.535189i	$-0.179759\pi$
$938$	−73.4625	−	21.3019i	−2.39864	−	0.695533i
$939$		0			0
$940$	−26.2585	+	1.92367i	−0.856458	+	0.0627431i
$941$			19.9859i			0.651521i	0.945452	+	0.325761i	$0.105620\pi$
$941$			19.9859i			0.651521i	−0.945452	+	0.325761i	$0.894380\pi$
$942$		0			0
$943$			40.8862i			1.33144i
$944$	19.9467	−	9.43632i	0.649210	−	0.307126i
$945$		0			0
$946$	2.89902	+	0.840629i	0.0942553	+	0.0273312i
$947$	25.6951			0.834979			0.417490	−	0.908682i	$-0.362910\pi$
$947$	25.6951			0.834979			0.417490	+	0.908682i	$0.362910\pi$
$948$		0			0
$949$		−	6.01919i		−	0.195391i
$950$	−14.2561	+	21.8617i	−0.462528	+	0.709288i
$951$		0			0
$952$	−30.3433	+	26.8345i	−0.983433	+	0.869710i
$953$			18.9877i			0.615073i	0.951536	+	0.307536i	$0.0995046\pi$
$953$			18.9877i			0.615073i	−0.951536	+	0.307536i	$0.900495\pi$
$954$		0			0
$955$	−9.14867	−	12.3497i	−0.296044	−	0.399627i
$956$	−14.0798	−	8.91505i	−0.455374	−	0.288333i
$957$		0			0
$958$	2.93344	−	10.1164i	0.0947752	−	0.326845i
$959$	−19.1818			−0.619412
$960$		0			0
$961$	−25.6674			−0.827982
$962$	13.0406	−	44.9721i	0.420444	−	1.44996i
$963$		0			0
$964$	4.55609	+	2.88482i	0.146742	+	0.0929138i
$965$	39.6939	−	29.4053i	1.27779	−	0.946589i
$966$		0			0
$967$			23.3552i			0.751053i	0.926812	+	0.375527i	$0.122538\pi$
$967$			23.3552i			0.751053i	−0.926812	+	0.375527i	$0.877462\pi$
$968$	−22.9980	+	20.3385i	−0.739183	+	0.653705i
$969$		0			0
$970$	−8.48638	−	22.8674i	−0.272481	−	0.734229i
$971$			24.6232i			0.790195i	0.918639	+	0.395097i	$0.129289\pi$
$971$			24.6232i			0.790195i	−0.918639	+	0.395097i	$0.870711\pi$
$972$		0			0
$973$	23.7115			0.760157
$974$	−20.2597	−	5.87470i	−0.649162	−	0.188238i
$975$		0			0
$976$	−22.8865	+	10.8271i	−0.732580	+	0.346566i
$977$		−	40.7010i		−	1.30214i	−0.759017	−	0.651071i	$-0.774320\pi$
$977$		−	40.7010i		−	1.30214i	0.759017	−	0.651071i	$-0.225680\pi$
$978$		0			0
$979$		−	4.52217i		−	0.144529i
$980$	−3.68542	−	50.3068i	−0.117726	−	1.60699i
$981$		0			0
$982$	−37.2068	−	10.7889i	−1.18732	−	0.344286i
$983$			5.81942i			0.185611i	0.995684	+	0.0928053i	$0.0295834\pi$
$983$			5.81942i			0.185611i	−0.995684	+	0.0928053i	$0.970417\pi$
$984$		0			0
$985$	27.0114	+	36.4624i	0.860654	+	1.16179i
$986$	−3.93989	+	13.5872i	−0.125472	+	0.432706i
$987$		0			0
$988$	12.3608	−	19.5218i	0.393249	−	0.621071i
$989$			45.9182i			1.46011i
$990$		0			0
$991$	−6.08446			−0.193279			−0.0966396	−	0.995319i	$-0.530809\pi$
$991$	−6.08446			−0.193279			−0.0966396	+	0.995319i	$0.530809\pi$
$992$	−12.8969	+	2.07664i	−0.409477	+	0.0659333i
$993$		0			0
$994$	91.6392	+	26.5726i	2.90662	+	0.842832i
$995$	−17.2225	−	23.2485i	−0.545990	−	0.737027i
$996$		0			0
$997$	−38.3958			−1.21601			−0.608003	−	0.793935i	$-0.708029\pi$
$997$	−38.3958			−1.21601			−0.608003	+	0.793935i	$0.708029\pi$
$998$	18.5159	+	5.36904i	0.586110	+	0.169954i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.d.g.109.9	✓	16
3.2	odd	2		1080.2.d.h.109.8	yes	16
4.3	odd	2		4320.2.d.g.3889.6		16
5.4	even	2		1080.2.d.h.109.7	yes	16
8.3	odd	2		4320.2.d.h.3889.11		16
8.5	even	2		1080.2.d.h.109.6	yes	16
12.11	even	2		4320.2.d.h.3889.12		16
15.14	odd	2	inner	1080.2.d.g.109.10	yes	16
20.19	odd	2		4320.2.d.h.3889.9		16
24.5	odd	2	inner	1080.2.d.g.109.11	yes	16
24.11	even	2		4320.2.d.g.3889.5		16
40.19	odd	2		4320.2.d.g.3889.8		16
40.29	even	2	inner	1080.2.d.g.109.12	yes	16
60.59	even	2		4320.2.d.g.3889.7		16
120.29	odd	2		1080.2.d.h.109.5	yes	16
120.59	even	2		4320.2.d.h.3889.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.d.g.109.9	✓	16	1.1	even	1	trivial
1080.2.d.g.109.10	yes	16	15.14	odd	2	inner
1080.2.d.g.109.11	yes	16	24.5	odd	2	inner
1080.2.d.g.109.12	yes	16	40.29	even	2	inner
1080.2.d.h.109.5	yes	16	120.29	odd	2
1080.2.d.h.109.6	yes	16	8.5	even	2
1080.2.d.h.109.7	yes	16	5.4	even	2
1080.2.d.h.109.8	yes	16	3.2	odd	2
4320.2.d.g.3889.5		16	24.11	even	2
4320.2.d.g.3889.6		16	4.3	odd	2
4320.2.d.g.3889.7		16	60.59	even	2
4320.2.d.g.3889.8		16	40.19	odd	2
4320.2.d.h.3889.9		16	20.19	odd	2
4320.2.d.h.3889.10		16	120.59	even	2
4320.2.d.h.3889.11		16	8.3	odd	2
4320.2.d.h.3889.12		16	12.11	even	2

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:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.393855 - 1.35826i) q^{2} +(-1.68976 - 1.06992i) q^{4} +(-1.33104 - 1.79676i) q^{5} +4.27541i q^{7} +(-2.11875 + 1.87374i) q^{8} +O(q^{10})\)	\(q+(0.393855 - 1.35826i) q^{2} +(-1.68976 - 1.06992i) q^{4} +(-1.33104 - 1.79676i) q^{5} +4.27541i q^{7} +(-2.11875 + 1.87374i) q^{8} +(-2.96471 + 1.10024i) q^{10} +0.381432i q^{11} +3.13006 q^{13} +(5.80712 + 1.68389i) q^{14} +(1.71055 + 3.61580i) q^{16} -3.34970i q^{17} +3.69099i q^{19} +(0.326748 + 4.46018i) q^{20} +(0.518086 + 0.150229i) q^{22} +8.20607i q^{23} +(-1.45667 + 4.78311i) q^{25} +(1.23279 - 4.25144i) q^{26} +(4.57433 - 7.22439i) q^{28} -2.98635i q^{29} -2.30924 q^{31} +(5.58492 - 0.899275i) q^{32} +(-4.54978 - 1.31930i) q^{34} +(7.68186 - 5.69073i) q^{35} +10.5781 q^{37} +(5.01334 + 1.45372i) q^{38} +(6.18679 + 1.31286i) q^{40} +4.98243 q^{41} +5.59564 q^{43} +(0.408101 - 0.644528i) q^{44} +(11.1460 + 3.23200i) q^{46} +5.88732i q^{47} -11.2791 q^{49} +(5.92300 + 3.86240i) q^{50} +(-5.28904 - 3.34891i) q^{52} +4.40820 q^{53} +(0.685342 - 0.507701i) q^{55} +(-8.01100 - 9.05851i) q^{56} +(-4.05625 - 1.17619i) q^{58} -5.51654i q^{59} +6.32959i q^{61} +(-0.909505 + 3.13655i) q^{62} +(0.978197 - 7.93997i) q^{64} +(-4.16623 - 5.62396i) q^{65} -12.6504 q^{67} +(-3.58391 + 5.66018i) q^{68} +(-4.70396 - 12.6753i) q^{70} +15.7805 q^{71} -1.92303i q^{73} +(4.16623 - 14.3678i) q^{74} +(3.94906 - 6.23687i) q^{76} -1.63078 q^{77} -12.3371 q^{79} +(4.21991 - 7.88622i) q^{80} +(1.96236 - 6.76746i) q^{82} -1.18214 q^{83} +(-6.01861 + 4.45859i) q^{85} +(2.20387 - 7.60035i) q^{86} +(-0.714705 - 0.808160i) q^{88} -11.8558 q^{89} +13.3823i q^{91} +(8.77982 - 13.8663i) q^{92} +(7.99652 + 2.31875i) q^{94} +(6.63181 - 4.91285i) q^{95} +7.71322i q^{97} +(-4.44233 + 15.3200i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8	\( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8} + 5 q^{10} - 30 q^{16} - q^{20} - 22 q^{25} + 18 q^{32} - 4 q^{34} - 2 q^{35} + 56 q^{38} + 19 q^{40} + 40 q^{46} - 44 q^{49} - 27 q^{50} + 96 q^{53} + 34 q^{55} + 2 q^{62} - 6 q^{64} + 72 q^{68} - 7 q^{70} - 12 q^{77} + 4 q^{79} - 9 q^{80} + 64 q^{83} + 20 q^{92} - 20 q^{94} - 36 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8 + 5 * q^10 - 30 * q^16 - q^20 - 22 * q^25 + 18 * q^32 - 4 * q^34 - 2 * q^35 + 56 * q^38 + 19 * q^40 + 40 * q^46 - 44 * q^49 - 27 * q^50 + 96 * q^53 + 34 * q^55 + 2 * q^62 - 6 * q^64 + 72 * q^68 - 7 * q^70 - 12 * q^77 + 4 * q^79 - 9 * q^80 + 64 * q^83 + 20 * q^92 - 20 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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