LMFDB - Embedded newform 108.2.i.a.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.3
Root			$1.16555 - 1.28120i$ of defining polynomial
Character	$\chi$	$=$	108.61
Dual form			108.2.i.a.85.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53346 - 0.805294i) q^{3} +(0.583982 + 3.31193i) q^{5} +(-1.47262 - 1.23568i) q^{7} +(1.70300 - 2.46977i) q^{9} +O(q^{10})$	\(q+(1.53346 - 0.805294i) q^{3} +(0.583982 + 3.31193i) q^{5} +(-1.47262 - 1.23568i) q^{7} +(1.70300 - 2.46977i) q^{9} +(0.352079 - 1.99674i) q^{11} +(-5.53134 - 2.01324i) q^{13} +(3.56259 + 4.60843i) q^{15} +(1.69713 + 2.93951i) q^{17} +(-0.0802464 + 0.138991i) q^{19} +(-3.25330 - 0.708969i) q^{21} +(-3.29370 + 2.76375i) q^{23} +(-5.92935 + 2.15811i) q^{25} +(0.622595 - 5.15872i) q^{27} +(-7.79349 + 2.83660i) q^{29} +(8.07924 - 6.77928i) q^{31} +(-1.06806 - 3.34545i) q^{33} +(3.23249 - 5.59884i) q^{35} +(2.17770 + 3.77190i) q^{37} +(-10.1034 + 1.36713i) q^{39} +(1.21218 + 0.441196i) q^{41} +(-1.25374 + 7.11032i) q^{43} +(9.17423 + 4.19792i) q^{45} +(0.0743444 + 0.0623824i) q^{47} +(-0.573816 - 3.25427i) q^{49} +(4.96964 + 3.14094i) q^{51} +12.8006 q^{53} +6.81866 q^{55} +(-0.0111262 + 0.277759i) q^{57} +(-0.422649 - 2.39696i) q^{59} +(4.41834 + 3.70742i) q^{61} +(-5.55973 + 1.53268i) q^{63} +(3.43751 - 19.4951i) q^{65} +(3.89658 + 1.41824i) q^{67} +(-2.82514 + 6.89050i) q^{69} +(-3.09944 - 5.36839i) q^{71} +(2.12803 - 3.68585i) q^{73} +(-7.35452 + 8.08425i) q^{75} +(-2.98581 + 2.50539i) q^{77} +(2.80608 - 1.02133i) q^{79} +(-3.19956 - 8.41206i) q^{81} +(-8.95967 + 3.26105i) q^{83} +(-8.74434 + 7.33737i) q^{85} +(-9.66672 + 10.6259i) q^{87} +(-0.821473 + 1.42283i) q^{89} +(5.65787 + 9.79971i) q^{91} +(6.92987 - 16.9019i) q^{93} +(-0.507190 - 0.184602i) q^{95} +(0.484584 - 2.74821i) q^{97} +(-4.33190 - 4.27001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 18 * q + 3 * q^5 + 6 * q^9	$ 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) $ 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	1.53346	−	0.805294i	0.885344	−	0.464937i
$3$	1.53346	−	0.805294i	0.885344	−	0.464937i
$4$		0			0
$5$	0.583982	+	3.31193i	0.261165	+	1.48114i	0.779738	+	0.626105i	$0.215352\pi$
$5$	0.583982	+	3.31193i	0.261165	+	1.48114i	−0.518574	+	0.855033i	$0.673537\pi$
$6$		0			0
$7$	−1.47262	−	1.23568i	−0.556600	−	0.467043i	0.320569	−	0.947225i	$-0.396126\pi$
$7$	−1.47262	−	1.23568i	−0.556600	−	0.467043i	−0.877169	+	0.480183i	$0.840570\pi$
$8$		0			0
$9$	1.70300	−	2.46977i	0.567668	−	0.823258i
$10$		0			0
$11$	0.352079	−	1.99674i	0.106156	−	0.602040i	−0.884597	−	0.466357i	$-0.845566\pi$
$11$	0.352079	−	1.99674i	0.106156	−	0.602040i	0.990752	−	0.135683i	$-0.0433227\pi$
$12$		0			0
$13$	−5.53134	−	2.01324i	−1.53412	−	0.558373i	−0.569493	−	0.821996i	$-0.692860\pi$
$13$	−5.53134	−	2.01324i	−1.53412	−	0.558373i	−0.964626	+	0.263623i	$0.915083\pi$
$14$		0			0
$15$	3.56259	+	4.60843i	0.919856	+	1.18989i
$16$		0			0
$17$	1.69713	+	2.93951i	0.411613	+	0.712935i	0.995066	−	0.0992115i	$-0.0316320\pi$
$17$	1.69713	+	2.93951i	0.411613	+	0.712935i	−0.583453	+	0.812147i	$0.698299\pi$
$18$		0			0
$19$	−0.0802464	+	0.138991i	−0.0184098	+	0.0318867i	−0.875084	−	0.483972i	$-0.839194\pi$
$19$	−0.0802464	+	0.138991i	−0.0184098	+	0.0318867i	0.856674	+	0.515859i	$0.172527\pi$
$20$		0			0
$21$	−3.25330	−	0.708969i	−0.709927	−	0.154710i
$22$		0			0
$23$	−3.29370	+	2.76375i	−0.686785	+	0.576281i	−0.917980	−	0.396626i	$-0.870181\pi$
$23$	−3.29370	+	2.76375i	−0.686785	+	0.576281i	0.231195	+	0.972907i	$0.425736\pi$
$24$		0			0
$25$	−5.92935	+	2.15811i	−1.18587	+	0.431622i
$26$		0			0
$27$	0.622595	−	5.15872i	0.119819	−	0.992796i
$28$		0			0
$29$	−7.79349	+	2.83660i	−1.44722	+	0.526743i	−0.941812	−	0.336140i	$-0.890878\pi$
$29$	−7.79349	+	2.83660i	−1.44722	+	0.526743i	−0.505403	+	0.862883i	$0.668656\pi$
$30$		0			0
$31$	8.07924	−	6.77928i	1.45107	−	1.21760i	0.519281	−	0.854603i	$-0.326200\pi$
$31$	8.07924	−	6.77928i	1.45107	−	1.21760i	0.931792	−	0.362992i	$-0.118245\pi$
$32$		0			0
$33$	−1.06806	−	3.34545i	−0.185926	−	0.582368i
$34$		0			0
$35$	3.23249	−	5.59884i	0.546390	−	0.946376i
$36$		0			0
$37$	2.17770	+	3.77190i	0.358012	+	0.620096i	0.987629	−	0.156810i	$-0.0501212\pi$
$37$	2.17770	+	3.77190i	0.358012	+	0.620096i	−0.629616	+	0.776906i	$0.716788\pi$
$38$		0			0
$39$	−10.1034	+	1.36713i	−1.61783	+	0.218915i
$40$		0			0
$41$	1.21218	+	0.441196i	0.189310	+	0.0689032i	0.434936	−	0.900462i	$-0.356771\pi$
$41$	1.21218	+	0.441196i	0.189310	+	0.0689032i	−0.245626	+	0.969365i	$0.578993\pi$
$42$		0			0
$43$	−1.25374	+	7.11032i	−0.191194	+	1.08431i	0.726542	+	0.687122i	$0.241126\pi$
$43$	−1.25374	+	7.11032i	−0.191194	+	1.08431i	−0.917736	+	0.397192i	$0.869985\pi$
$44$		0			0
$45$	9.17423	+	4.19792i	1.36761	+	0.625789i
$46$		0			0
$47$	0.0743444	+	0.0623824i	0.0108442	+	0.00909940i	0.648194	−	0.761476i	$-0.275525\pi$
$47$	0.0743444	+	0.0623824i	0.0108442	+	0.00909940i	−0.637349	+	0.770575i	$0.719969\pi$
$48$		0			0
$49$	−0.573816	−	3.25427i	−0.0819738	−	0.464896i
$50$		0			0
$51$	4.96964	+	3.14094i	0.695889	+	0.439819i
$52$		0			0
$53$	12.8006			1.75830			0.879152	−	0.476541i	$-0.158110\pi$
$53$	12.8006			1.75830			0.879152	+	0.476541i	$0.158110\pi$
$54$		0			0
$55$	6.81866			0.919428
$56$		0			0
$57$	−0.0111262	+	0.277759i	−0.00147370	+	0.0367901i
$58$		0			0
$59$	−0.422649	−	2.39696i	−0.0550242	−	0.312058i	0.944857	−	0.327484i	$-0.106201\pi$
$59$	−0.422649	−	2.39696i	−0.0550242	−	0.312058i	−0.999881	+	0.0154260i	$0.995090\pi$
$60$		0			0
$61$	4.41834	+	3.70742i	0.565710	+	0.474687i	0.880219	−	0.474567i	$-0.157395\pi$
$61$	4.41834	+	3.70742i	0.565710	+	0.474687i	−0.314509	+	0.949254i	$0.601840\pi$
$62$		0			0
$63$	−5.55973	+	1.53268i	−0.700460	+	0.193100i
$64$		0			0
$65$	3.43751	−	19.4951i	0.426371	−	2.41807i
$66$		0			0
$67$	3.89658	+	1.41824i	0.476043	+	0.173266i	0.568888	−	0.822415i	$-0.307374\pi$
$67$	3.89658	+	1.41824i	0.476043	+	0.173266i	−0.0928447	+	0.995681i	$0.529596\pi$
$68$		0			0
$69$	−2.82514	+	6.89050i	−0.340107	+	0.829518i
$70$		0			0
$71$	−3.09944	−	5.36839i	−0.367836	−	0.637111i	0.621391	−	0.783501i	$-0.286568\pi$
$71$	−3.09944	−	5.36839i	−0.367836	−	0.637111i	−0.989227	+	0.146390i	$0.953235\pi$
$72$		0			0
$73$	2.12803	−	3.68585i	0.249067	−	0.431396i	−0.714200	−	0.699941i	$-0.753209\pi$
$73$	2.12803	−	3.68585i	0.249067	−	0.431396i	0.963267	+	0.268545i	$0.0865428\pi$
$74$		0			0
$75$	−7.35452	+	8.08425i	−0.849227	+	0.933489i
$76$		0			0
$77$	−2.98581	+	2.50539i	−0.340264	+	0.285516i
$78$		0			0
$79$	2.80608	−	1.02133i	0.315708	−	0.114908i	−0.179306	−	0.983793i	$-0.557385\pi$
$79$	2.80608	−	1.02133i	0.315708	−	0.114908i	0.495014	+	0.868885i	$0.335163\pi$
$80$		0			0
$81$	−3.19956	−	8.41206i	−0.355507	−	0.934674i
$82$		0			0
$83$	−8.95967	+	3.26105i	−0.983451	+	0.357947i	−0.783181	−	0.621794i	$-0.786404\pi$
$83$	−8.95967	+	3.26105i	−0.983451	+	0.357947i	−0.200270	+	0.979741i	$0.564182\pi$
$84$		0			0
$85$	−8.74434	+	7.33737i	−0.948457	+	0.795850i
$86$		0			0
$87$	−9.66672	+	10.6259i	−1.03638	+	1.13921i
$88$		0			0
$89$	−0.821473	+	1.42283i	−0.0870760	+	0.150820i	−0.906274	−	0.422691i	$-0.861086\pi$
$89$	−0.821473	+	1.42283i	−0.0870760	+	0.150820i	0.819198	+	0.573511i	$0.194419\pi$
$90$		0			0
$91$	5.65787	+	9.79971i	0.593106	+	1.02729i
$92$		0			0
$93$	6.92987	−	16.9019i	0.718595	−	1.75265i
$94$		0			0
$95$	−0.507190	−	0.184602i	−0.0520366	−	0.0189398i
$96$		0			0
$97$	0.484584	−	2.74821i	0.0492021	−	0.279039i	−0.950274	−	0.311416i	$-0.899197\pi$
$97$	0.484584	−	2.74821i	0.0492021	−	0.279039i	0.999476	+	0.0323773i	$0.0103078\pi$
$98$		0			0
$99$	−4.33190	−	4.27001i	−0.435373	−	0.429152i
$100$		0			0
$101$	6.69442	+	5.61728i	0.666120	+	0.558941i	0.911914	−	0.410381i	$-0.134604\pi$
$101$	6.69442	+	5.61728i	0.666120	+	0.558941i	−0.245794	+	0.969322i	$0.579049\pi$
$102$		0			0
$103$	−0.935204	−	5.30381i	−0.0921484	−	0.522600i	−0.995584	−	0.0938756i	$-0.970074\pi$
$103$	−0.935204	−	5.30381i	−0.0921484	−	0.522600i	0.903436	−	0.428724i	$-0.141037\pi$
$104$		0			0
$105$	0.448187	−	11.1887i	0.0437386	−	1.09191i
$106$		0			0
$107$	−14.7899			−1.42979			−0.714896	−	0.699231i	$-0.753526\pi$
$107$	−14.7899			−1.42979			−0.714896	+	0.699231i	$0.753526\pi$
$108$		0			0
$109$	2.68614			0.257286			0.128643	−	0.991691i	$-0.458938\pi$
$109$	2.68614			0.257286			0.128643	+	0.991691i	$0.458938\pi$
$110$		0			0
$111$	6.37691	+	4.03036i	0.605269	+	0.382545i
$112$		0			0
$113$	2.31653	+	13.1377i	0.217921	+	1.23589i	0.875765	+	0.482738i	$0.160358\pi$
$113$	2.31653	+	13.1377i	0.217921	+	1.23589i	−0.657844	+	0.753154i	$0.728531\pi$
$114$		0			0
$115$	−11.0768	−	9.29453i	−1.03292	−	0.866719i
$116$		0			0
$117$	−14.3922	+	10.2326i	−1.33055	+	0.946004i
$118$		0			0
$119$	1.13306	−	6.42589i	0.103867	−	0.589061i
$120$		0			0
$121$	6.47361	+	2.35620i	0.588510	+	0.214200i
$122$		0			0
$123$	2.21412	−	0.299601i	0.199640	−	0.0270141i
$124$		0			0
$125$	−2.20259	−	3.81499i	−0.197005	−	0.341223i
$126$		0			0
$127$	−4.80710	+	8.32614i	−0.426561	+	0.738826i	−0.996565	−	0.0828165i	$-0.973608\pi$
$127$	−4.80710	+	8.32614i	−0.426561	+	0.738826i	0.570004	+	0.821642i	$0.306942\pi$
$128$		0			0
$129$	3.80334	+	11.9130i	0.334865	+	1.04888i
$130$		0			0
$131$	13.9408	−	11.6977i	1.21801	−	1.02203i	0.219085	−	0.975706i	$-0.429693\pi$
$131$	13.9408	−	11.6977i	1.21801	−	1.02203i	0.998926	−	0.0463275i	$-0.0147518\pi$
$132$		0			0
$133$	0.289921	−	0.105523i	0.0251393	−	0.00914996i
$134$		0			0
$135$	17.4489	−	0.950608i	1.50176	−	0.0818153i
$136$		0			0
$137$	−4.40892	+	1.60472i	−0.376679	+	0.137100i	−0.523420	−	0.852075i	$-0.675344\pi$
$137$	−4.40892	+	1.60472i	−0.376679	+	0.137100i	0.146740	+	0.989175i	$0.453122\pi$
$138$		0			0
$139$	−8.70983	+	7.30841i	−0.738758	+	0.619892i	−0.932504	−	0.361160i	$-0.882381\pi$
$139$	−8.70983	+	7.30841i	−0.738758	+	0.619892i	0.193746	+	0.981052i	$0.437936\pi$
$140$		0			0
$141$	0.164240	+	0.0357918i	0.0138315	+	0.00301421i
$142$		0			0
$143$	−5.96740	+	10.3358i	−0.499019	+	0.864326i
$144$		0			0
$145$	−13.9459	−	24.1549i	−1.15814	−	2.00596i
$146$		0			0
$147$	−3.50057	−	4.52821i	−0.288722	−	0.373481i
$148$		0			0
$149$	−7.18803	−	2.61623i	−0.588867	−	0.214330i	0.0303643	−	0.999539i	$-0.490333\pi$
$149$	−7.18803	−	2.61623i	−0.588867	−	0.214330i	−0.619231	+	0.785209i	$0.712555\pi$
$150$		0			0
$151$	2.09815	−	11.8992i	0.170745	−	0.968342i	−0.772197	−	0.635384i	$-0.780842\pi$
$151$	2.09815	−	11.8992i	0.170745	−	0.968342i	0.942941	−	0.332959i	$-0.108047\pi$
$152$		0			0
$153$	10.1501	+	0.814477i	0.820589	+	0.0658465i
$154$		0			0
$155$	27.1706	+	22.7989i	2.18240	+	1.83125i
$156$		0			0
$157$	−0.444027	−	2.51820i	−0.0354372	−	0.200974i	0.961949	−	0.273229i	$-0.0880917\pi$
$157$	−0.444027	−	2.51820i	−0.0354372	−	0.200974i	−0.997386	+	0.0722546i	$0.976981\pi$
$158$		0			0
$159$	19.6293	−	10.3083i	1.55670	−	0.817500i
$160$		0			0
$161$	8.26549			0.651412
$162$		0			0
$163$	−19.1557			−1.50039			−0.750195	−	0.661217i	$-0.770040\pi$
$163$	−19.1557			−1.50039			−0.750195	+	0.661217i	$0.770040\pi$
$164$		0			0
$165$	10.4561	−	5.49103i	0.814010	−	0.427476i
$166$		0			0
$167$	−3.46665	−	19.6603i	−0.268257	−	1.52136i	−0.759596	−	0.650395i	$-0.774603\pi$
$167$	−3.46665	−	19.6603i	−0.268257	−	1.52136i	0.491339	−	0.870969i	$-0.336508\pi$
$168$		0			0
$169$	16.5840	+	13.9156i	1.27569	+	1.07043i
$170$		0			0
$171$	0.206616	+	0.434892i	0.0158003	+	0.0332570i
$172$		0			0
$173$	−2.11783	+	12.0108i	−0.161016	+	0.913167i	0.792062	+	0.610441i	$0.209008\pi$
$173$	−2.11783	+	12.0108i	−0.161016	+	0.913167i	−0.953078	+	0.302726i	$0.902103\pi$
$174$		0			0
$175$	11.3984	+	4.14869i	0.861641	+	0.313612i
$176$		0			0
$177$	−2.57837	−	3.33529i	−0.193802	−	0.250696i
$178$		0			0
$179$	10.8419	+	18.7786i	0.810358	+	1.40358i	0.912613	+	0.408824i	$0.134061\pi$
$179$	10.8419	+	18.7786i	0.810358	+	1.40358i	−0.102255	+	0.994758i	$0.532606\pi$
$180$		0			0
$181$	2.99749	−	5.19181i	0.222802	−	0.385904i	−0.732856	−	0.680384i	$-0.761813\pi$
$181$	2.99749	−	5.19181i	0.222802	−	0.385904i	0.955658	+	0.294480i	$0.0951464\pi$
$182$		0			0
$183$	9.76091	+	2.12713i	0.721547	+	0.157242i
$184$		0			0
$185$	−11.2205	+	9.41512i	−0.824947	+	0.692213i
$186$		0			0
$187$	6.46696	−	2.35378i	0.472911	−	0.172125i
$188$		0			0
$189$	−7.29137	+	6.82753i	−0.530369	+	0.496629i
$190$		0			0
$191$	−17.9956	+	6.54987i	−1.30212	+	0.473932i	−0.897686	−	0.440636i	$-0.854753\pi$
$191$	−17.9956	+	6.54987i	−1.30212	+	0.473932i	−0.404432	+	0.914568i	$0.632531\pi$
$192$		0			0
$193$	−0.345033	+	0.289517i	−0.0248360	+	0.0208399i	−0.655121	−	0.755524i	$-0.727382\pi$
$193$	−0.345033	+	0.289517i	−0.0248360	+	0.0208399i	0.630285	+	0.776364i	$0.282938\pi$
$194$		0			0
$195$	−10.4280	−	32.6632i	−0.746764	−	2.33906i
$196$		0			0
$197$	−1.79534	+	3.10963i	−0.127913	+	0.221552i	−0.922868	−	0.385117i	$-0.874161\pi$
$197$	−1.79534	+	3.10963i	−0.127913	+	0.221552i	0.794955	+	0.606669i	$0.207494\pi$
$198$		0			0
$199$	−3.63803	−	6.30125i	−0.257893	−	0.446684i	0.707784	−	0.706429i	$-0.249695\pi$
$199$	−3.63803	−	6.30125i	−0.257893	−	0.446684i	−0.965677	+	0.259745i	$0.916362\pi$
$200$		0			0
$201$	7.11736	−	0.963079i	0.502020	−	0.0679303i
$202$		0			0
$203$	14.9820	+	5.45301i	1.05153	+	0.382726i
$204$		0			0
$205$	−0.753319	+	4.27229i	−0.0526141	+	0.298389i
$206$		0			0
$207$	1.21664	+	12.8414i	0.0845621	+	0.892537i
$208$		0			0
$209$	0.249275	+	0.209167i	0.0172427	+	0.0144684i
$210$		0			0
$211$	1.12702	+	6.39162i	0.0775870	+	0.440017i	0.998711	+	0.0507493i	$0.0161610\pi$
$211$	1.12702	+	6.39162i	0.0775870	+	0.440017i	−0.921124	+	0.389268i	$0.872728\pi$
$212$		0			0
$213$	−9.07601	−	5.73626i	−0.621878	−	0.393042i
$214$		0			0
$215$	−24.2810			−1.65595
$216$		0			0
$217$	−20.2747			−1.37634
$218$		0			0
$219$	0.295052	−	7.36579i	0.0199378	−	0.497734i
$220$		0			0
$221$	−3.46944	−	19.6762i	−0.233380	−	1.32356i
$222$		0			0
$223$	−11.3466	−	9.52092i	−0.759824	−	0.637568i	0.178257	−	0.983984i	$-0.442954\pi$
$223$	−11.3466	−	9.52092i	−0.759824	−	0.637568i	−0.938081	+	0.346416i	$0.887399\pi$
$224$		0			0
$225$	−4.76767	+	18.3194i	−0.317845	+	1.22130i
$226$		0			0
$227$	0.144137	−	0.817444i	0.00956673	−	0.0542556i	−0.979651	−	0.200710i	$-0.935675\pi$
$227$	0.144137	−	0.817444i	0.00956673	−	0.0542556i	0.989217	+	0.146454i	$0.0467862\pi$
$228$		0			0
$229$	−14.7280	−	5.36054i	−0.973251	−	0.354235i	−0.194039	−	0.980994i	$-0.562159\pi$
$229$	−14.7280	−	5.36054i	−0.973251	−	0.354235i	−0.779213	+	0.626759i	$0.784381\pi$
$230$		0			0
$231$	−2.56104	+	6.24637i	−0.168504	+	0.410981i
$232$		0			0
$233$	−7.29551	−	12.6362i	−0.477945	−	0.827824i	0.521736	−	0.853107i	$-0.325285\pi$
$233$	−7.29551	−	12.6362i	−0.477945	−	0.827824i	−0.999680	+	0.0252828i	$0.991951\pi$
$234$		0			0
$235$	−0.163190	+	0.282653i	−0.0106453	+	0.0184383i
$236$		0			0
$237$	3.48054	−	3.82588i	0.226085	−	0.248518i
$238$		0			0
$239$	6.75790	−	5.67056i	0.437133	−	0.366798i	−0.397503	−	0.917601i	$-0.630123\pi$
$239$	6.75790	−	5.67056i	0.437133	−	0.366798i	0.834635	+	0.550803i	$0.185679\pi$
$240$		0			0
$241$	12.7593	−	4.64402i	0.821901	−	0.299147i	0.103370	−	0.994643i	$-0.467037\pi$
$241$	12.7593	−	4.64402i	0.821901	−	0.299147i	0.718530	+	0.695496i	$0.244815\pi$
$242$		0			0
$243$	−11.6806	−	10.3230i	−0.749310	−	0.662220i
$244$		0			0
$245$	10.4428	−	3.80087i	0.667167	−	0.242829i
$246$		0			0
$247$	0.723693	−	0.607250i	0.0460475	−	0.0386384i
$248$		0			0
$249$	−11.1132	+	12.2159i	−0.704270	+	0.774149i
$250$		0			0
$251$	5.80404	−	10.0529i	0.366348	−	0.634533i	−0.622643	−	0.782506i	$-0.713941\pi$
$251$	5.80404	−	10.0529i	0.366348	−	0.634533i	0.988992	+	0.147972i	$0.0472746\pi$
$252$		0			0
$253$	4.35884	+	7.54973i	0.274038	+	0.474647i
$254$		0			0
$255$	−7.50036	+	18.2933i	−0.469691	+	1.14557i
$256$		0			0
$257$	−8.13448	−	2.96071i	−0.507415	−	0.184684i	0.0756113	−	0.997137i	$-0.475909\pi$
$257$	−8.13448	−	2.96071i	−0.507415	−	0.184684i	−0.583026	+	0.812454i	$0.698131\pi$
$258$		0			0
$259$	1.45391	−	8.24553i	0.0903415	−	0.512352i
$260$		0			0
$261$	−6.26659	+	24.0789i	−0.387892	+	1.49045i
$262$		0			0
$263$	11.0954	+	9.31017i	0.684173	+	0.574089i	0.917222	−	0.398375i	$-0.130426\pi$
$263$	11.0954	+	9.31017i	0.684173	+	0.574089i	−0.233049	+	0.972465i	$0.574870\pi$
$264$		0			0
$265$	7.47535	+	42.3948i	0.459207	+	2.60429i
$266$		0			0
$267$	−0.113898	+	2.84339i	−0.00697044	+	0.174012i
$268$		0			0
$269$	−14.3063			−0.872273			−0.436137	−	0.899880i	$-0.643654\pi$
$269$	−14.3063			−0.872273			−0.436137	+	0.899880i	$0.643654\pi$
$270$		0			0
$271$	9.43403			0.573077			0.286538	−	0.958069i	$-0.407495\pi$
$271$	9.43403			0.573077			0.286538	+	0.958069i	$0.407495\pi$
$272$		0			0
$273$	16.5678	+	10.4712i	1.00273	+	0.633748i
$274$		0			0
$275$	2.22158	+	12.5992i	0.133966	+	0.759761i
$276$		0			0
$277$	1.16538	+	0.977871i	0.0700210	+	0.0587546i	0.677126	−	0.735867i	$-0.263225\pi$
$277$	1.16538	+	0.977871i	0.0700210	+	0.0587546i	−0.607105	+	0.794621i	$0.707669\pi$
$278$		0			0
$279$	−2.98433	−	31.4990i	−0.178667	−	1.88580i
$280$		0			0
$281$	4.44941	−	25.2338i	0.265429	−	1.50532i	−0.502380	−	0.864647i	$-0.667542\pi$
$281$	4.44941	−	25.2338i	0.265429	−	1.50532i	0.767810	−	0.640678i	$-0.221347\pi$
$282$		0			0
$283$	−5.94272	−	2.16297i	−0.353258	−	0.128575i	0.159295	−	0.987231i	$-0.449078\pi$
$283$	−5.94272	−	2.16297i	−0.353258	−	0.128575i	−0.512553	+	0.858656i	$0.671300\pi$
$284$		0			0
$285$	−0.926414	+	0.125357i	−0.0548761	+	0.00742551i
$286$		0			0
$287$	−1.23990	−	2.14757i	−0.0731892	−	0.126767i
$288$		0			0
$289$	2.73953	−	4.74500i	0.161149	−	0.279118i
$290$		0			0
$291$	−1.47003	−	4.60451i	−0.0861746	−	0.269921i
$292$		0			0
$293$	16.9435	−	14.2173i	0.989851	−	0.830583i	0.00430446	−	0.999991i	$-0.498630\pi$
$293$	16.9435	−	14.2173i	0.989851	−	0.830583i	0.985546	+	0.169408i	$0.0541854\pi$
$294$		0			0
$295$	7.69174	−	2.79956i	0.447830	−	0.162997i
$296$		0			0
$297$	−10.0814	−	3.05944i	−0.584983	−	0.177527i
$298$		0			0
$299$	23.7827	−	8.65620i	1.37539	−	0.500601i
$300$		0			0
$301$	10.6324	−	8.92161i	0.612839	−	0.514233i
$302$		0			0
$303$	14.7892	+	3.22291i	0.849617	+	0.185151i
$304$		0			0
$305$	−9.69849	+	16.7983i	−0.555334	+	0.961866i
$306$		0			0
$307$	3.48009	+	6.02769i	0.198619	+	0.344019i	0.948081	−	0.318029i	$-0.103021\pi$
$307$	3.48009	+	6.02769i	0.198619	+	0.344019i	−0.749462	+	0.662048i	$0.769688\pi$
$308$		0			0
$309$	−5.70522	−	7.38006i	−0.324559	−	0.419837i
$310$		0			0
$311$	−8.99620	−	3.27435i	−0.510128	−	0.185671i	0.0741159	−	0.997250i	$-0.476387\pi$
$311$	−8.99620	−	3.27435i	−0.510128	−	0.185671i	−0.584244	+	0.811578i	$0.698609\pi$
$312$		0			0
$313$	2.12624	−	12.0585i	0.120182	−	0.681588i	−0.863871	−	0.503713i	$-0.831967\pi$
$313$	2.12624	−	12.0585i	0.120182	−	0.681588i	0.984053	−	0.177874i	$-0.0569221\pi$
$314$		0			0
$315$	−8.32291	−	17.5184i	−0.468943	−	0.987047i
$316$		0			0
$317$	−8.36450	−	7.01865i	−0.469797	−	0.394207i	0.376923	−	0.926244i	$-0.376982\pi$
$317$	−8.36450	−	7.01865i	−0.469797	−	0.394207i	−0.846721	+	0.532038i	$0.821426\pi$
$318$		0			0
$319$	2.92002	+	16.5603i	0.163490	+	0.927198i
$320$		0			0
$321$	−22.6797	+	11.9102i	−1.26586	+	0.664762i
$322$		0			0
$323$	−0.544753			−0.0303109
$324$		0			0
$325$	37.1421			2.06027
$326$		0			0
$327$	4.11909	−	2.16313i	0.227786	−	0.119622i
$328$		0			0
$329$	−0.0323968	−	0.183732i	−0.00178610	−	0.0101294i
$330$		0			0
$331$	16.0932	+	13.5038i	0.884560	+	0.742234i	0.967112	−	0.254353i	$-0.0818623\pi$
$331$	16.0932	+	13.5038i	0.884560	+	0.742234i	−0.0825512	+	0.996587i	$0.526307\pi$
$332$		0			0
$333$	13.0244	+	1.04511i	0.713731	+	0.0572719i
$334$		0			0
$335$	−2.42157	+	13.7334i	−0.132305	+	0.750337i
$336$		0			0
$337$	6.39458	+	2.32744i	0.348335	+	0.126784i	0.510262	−	0.860019i	$-0.329549\pi$
$337$	6.39458	+	2.32744i	0.348335	+	0.126784i	−0.161927	+	0.986803i	$0.551771\pi$
$338$		0			0
$339$	14.1320	+	18.2807i	0.767547	+	0.992870i
$340$		0			0
$341$	−10.6919	−	18.5190i	−0.579001	−	1.00286i
$342$		0			0
$343$	−9.90453	+	17.1552i	−0.534794	+	0.926291i
$344$		0			0
$345$	−24.4706	−	5.33272i	−1.31746	−	0.287104i
$346$		0			0
$347$	3.61225	−	3.03104i	0.193916	−	0.162715i	−0.540660	−	0.841241i	$-0.681826\pi$
$347$	3.61225	−	3.03104i	0.193916	−	0.162715i	0.734576	+	0.678526i	$0.237381\pi$
$348$		0			0
$349$	8.27656	−	3.01242i	0.443034	−	0.161251i	−0.110864	−	0.993836i	$-0.535362\pi$
$349$	8.27656	−	3.01242i	0.443034	−	0.161251i	0.553898	+	0.832584i	$0.313140\pi$
$350$		0			0
$351$	−13.8295	+	27.2812i	−0.738167	+	1.45616i
$352$		0			0
$353$	−16.4528	+	5.98832i	−0.875692	+	0.318726i	−0.740470	−	0.672089i	$-0.765397\pi$
$353$	−16.4528	+	5.98832i	−0.875692	+	0.318726i	−0.135222	+	0.990815i	$0.543175\pi$
$354$		0			0
$355$	15.9697	−	13.4002i	0.847584	−	0.711207i
$356$		0			0
$357$	−3.43723	−	10.7663i	−0.181918	−	0.569813i
$358$		0			0
$359$	9.44318	−	16.3561i	0.498392	−	0.863240i	−0.501606	−	0.865096i	$-0.667257\pi$
$359$	9.44318	−	16.3561i	0.498392	−	0.863240i	0.999998	+	0.00185580i	$0.000590721\pi$
$360$		0			0
$361$	9.48712	+	16.4322i	0.499322	+	0.864851i
$362$		0			0
$363$	11.8245	−	1.60002i	0.620623	−	0.0839791i
$364$		0			0
$365$	13.4500	+	4.89540i	0.704005	+	0.256237i
$366$		0			0
$367$	−2.38348	+	13.5174i	−0.124417	+	0.705602i	0.857236	+	0.514924i	$0.172180\pi$
$367$	−2.38348	+	13.5174i	−0.124417	+	0.705602i	−0.981653	+	0.190678i	$0.938931\pi$
$368$		0			0
$369$	3.15399	−	2.24244i	0.164190	−	0.116737i
$370$		0			0
$371$	−18.8505	−	15.8175i	−0.978671	−	0.821203i
$372$		0			0
$373$	−6.38785	−	36.2273i	−0.330751	−	1.87578i	−0.465723	−	0.884930i	$-0.654206\pi$
$373$	−6.38785	−	36.2273i	−0.330751	−	1.87578i	0.134973	−	0.990849i	$-0.456905\pi$
$374$		0			0
$375$	−6.44977	−	4.07641i	−0.333065	−	0.210505i
$376$		0			0
$377$	48.8192			2.51432
$378$		0			0
$379$	−28.9790			−1.48855			−0.744276	−	0.667872i	$-0.767205\pi$
$379$	−28.9790			−1.48855			−0.744276	+	0.667872i	$0.767205\pi$
$380$		0			0
$381$	−0.666508	+	16.6389i	−0.0341462	+	0.852439i
$382$		0			0
$383$	1.31770	+	7.47305i	0.0673313	+	0.381855i	0.999788	+	0.0205739i	$0.00654934\pi$
$383$	1.31770	+	7.47305i	0.0673313	+	0.381855i	−0.932457	+	0.361281i	$0.882340\pi$
$384$		0			0
$385$	−10.0413	−	8.42567i	−0.511753	−	0.429412i
$386$		0			0
$387$	15.4258	+	15.2054i	0.784135	+	0.772932i
$388$		0			0
$389$	−1.02208	+	5.79648i	−0.0518213	+	0.293893i	−0.999693	−	0.0247577i	$-0.992119\pi$
$389$	−1.02208	+	5.79648i	−0.0518213	+	0.293893i	0.947872	+	0.318651i	$0.103230\pi$
$390$		0			0
$391$	−13.7139	−	4.99145i	−0.693541	−	0.252428i
$392$		0			0
$393$	11.9575	−	29.1644i	0.603179	−	1.47115i
$394$		0			0
$395$	5.02126	+	8.69708i	0.252647	+	0.437597i
$396$		0			0
$397$	9.47451	−	16.4103i	0.475512	−	0.823611i	−0.524094	−	0.851660i	$-0.675596\pi$
$397$	9.47451	−	16.4103i	0.475512	−	0.823611i	0.999607	+	0.0280490i	$0.00892943\pi$
$398$		0			0
$399$	0.359605	−	0.395286i	0.0180028	−	0.0197891i
$400$		0			0
$401$	−16.2592	+	13.6431i	−0.811948	+	0.681305i	−0.951072	−	0.308970i	$-0.900016\pi$
$401$	−16.2592	+	13.6431i	−0.811948	+	0.681305i	0.139124	+	0.990275i	$0.455571\pi$
$402$		0			0
$403$	−58.3374	+	21.2331i	−2.90599	+	1.05769i
$404$		0			0
$405$	25.9916	−	15.5092i	1.29154	−	0.770658i
$406$		0			0
$407$	8.29822	−	3.02030i	0.411327	−	0.149711i
$408$		0			0
$409$	−9.81285	+	8.23396i	−0.485214	+	0.407143i	−0.852308	−	0.523041i	$-0.824797\pi$
$409$	−9.81285	+	8.23396i	−0.485214	+	0.407143i	0.367093	+	0.930184i	$0.380353\pi$
$410$		0			0
$411$	−5.46864	+	6.01125i	−0.269748	+	0.296513i
$412$		0			0
$413$	−2.33947	+	4.05208i	−0.115118	+	0.199390i
$414$		0			0
$415$	−16.0326	−	27.7694i	−0.787012	−	1.36314i
$416$		0			0
$417$	−7.47076	+	18.2211i	−0.365845	+	0.892293i
$418$		0			0
$419$	−25.6752	−	9.34502i	−1.25432	−	0.456534i	−0.372459	−	0.928049i	$-0.621485\pi$
$419$	−25.6752	−	9.34502i	−1.25432	−	0.456534i	−0.881858	+	0.471515i	$0.843707\pi$
$420$		0			0
$421$	−4.95468	+	28.0994i	−0.241476	+	1.36948i	0.587059	+	0.809544i	$0.300286\pi$
$421$	−4.95468	+	28.0994i	−0.241476	+	1.36948i	−0.828535	+	0.559937i	$0.810825\pi$
$422$		0			0
$423$	0.280679	−	0.0773764i	0.0136471	−	0.00376217i
$424$		0			0
$425$	−16.4066	−	13.7668i	−0.795839	−	0.667788i
$426$		0			0
$427$	−1.92536	−	10.9193i	−0.0931749	−	0.528421i
$428$		0			0
$429$	−0.827383	+	20.6551i	−0.0399464	+	0.997238i
$430$		0			0
$431$	3.44020			0.165709			0.0828544	−	0.996562i	$-0.473596\pi$
$431$	3.44020			0.165709			0.0828544	+	0.996562i	$0.473596\pi$
$432$		0			0
$433$	−1.84486			−0.0886584			−0.0443292	−	0.999017i	$-0.514115\pi$
$433$	−1.84486			−0.0886584			−0.0443292	+	0.999017i	$0.514115\pi$
$434$		0			0
$435$	−40.8373	−	25.8101i	−1.95800	−	1.23750i
$436$		0			0
$437$	−0.119827	−	0.679575i	−0.00573213	−	0.0325085i
$438$		0			0
$439$	4.15794	+	3.48892i	0.198447	+	0.166517i	0.736596	−	0.676333i	$-0.236432\pi$
$439$	4.15794	+	3.48892i	0.198447	+	0.166517i	−0.538149	+	0.842850i	$0.680876\pi$
$440$		0			0
$441$	−9.01453	−	4.12484i	−0.429263	−	0.196421i
$442$		0			0
$443$	−4.68017	+	26.5425i	−0.222361	+	1.26107i	0.645304	+	0.763926i	$0.276731\pi$
$443$	−4.68017	+	26.5425i	−0.222361	+	1.26107i	−0.867666	+	0.497148i	$0.834381\pi$
$444$		0			0
$445$	−5.19205	−	1.88975i	−0.246127	−	0.0895827i
$446$		0			0
$447$	−13.1294	+	1.77659i	−0.620999	+	0.0840300i
$448$		0			0
$449$	11.3097	+	19.5890i	0.533737	+	0.924460i	0.999223	+	0.0394051i	$0.0125463\pi$
$449$	11.3097	+	19.5890i	0.533737	+	0.924460i	−0.465486	+	0.885055i	$0.654120\pi$
$450$		0			0
$451$	1.30773	−	2.26506i	0.0615788	−	0.106658i
$452$		0			0
$453$	−6.36492	−	19.9366i	−0.299050	−	0.936702i
$454$		0			0
$455$	−29.1518	+	24.4613i	−1.36666	+	1.14676i
$456$		0			0
$457$	20.1532	−	7.33515i	0.942725	−	0.343124i	0.175484	−	0.984482i	$-0.443851\pi$
$457$	20.1532	−	7.33515i	0.942725	−	0.343124i	0.767242	+	0.641358i	$0.221629\pi$
$458$		0			0
$459$	16.2207	−	6.92487i	0.757118	−	0.323225i
$460$		0			0
$461$	−8.02648	+	2.92140i	−0.373830	+	0.136063i	−0.522101	−	0.852884i	$-0.674852\pi$
$461$	−8.02648	+	2.92140i	−0.373830	+	0.136063i	0.148271	+	0.988947i	$0.452629\pi$
$462$		0			0
$463$	3.27248	−	2.74593i	0.152085	−	0.127614i	−0.563570	−	0.826068i	$-0.690573\pi$
$463$	3.27248	−	2.74593i	0.152085	−	0.127614i	0.715655	+	0.698454i	$0.246128\pi$
$464$		0			0
$465$	60.0248	+	13.0808i	2.78359	+	0.606608i
$466$		0			0
$467$	4.12319	−	7.14157i	0.190798	−	0.330472i	−0.754717	−	0.656051i	$-0.772226\pi$
$467$	4.12319	−	7.14157i	0.190798	−	0.330472i	0.945515	+	0.325578i	$0.105559\pi$
$468$		0			0
$469$	−3.98571	−	6.90346i	−0.184043	−	0.318772i
$470$		0			0
$471$	−2.70879	−	3.50399i	−0.124815	−	0.161455i
$472$		0			0
$473$	13.7560	+	5.00679i	0.632504	+	0.230213i
$474$		0			0
$475$	0.175852	−	0.997306i	0.00806864	−	0.0457596i
$476$		0			0
$477$	21.7995	−	31.6147i	0.998133	−	1.44754i
$478$		0			0
$479$	−17.0611	−	14.3160i	−0.779541	−	0.654112i	0.163592	−	0.986528i	$-0.447692\pi$
$479$	−17.0611	−	14.3160i	−0.779541	−	0.654112i	−0.943133	+	0.332416i	$0.892136\pi$
$480$		0			0
$481$	−4.45189	−	25.2479i	−0.202989	−	1.15121i
$482$		0			0
$483$	12.6748	−	6.65615i	0.576724	−	0.302865i
$484$		0			0
$485$	9.38487			0.426145
$486$		0			0
$487$	36.7759			1.66647			0.833237	−	0.552916i	$-0.186485\pi$
$487$	36.7759			1.66647			0.833237	+	0.552916i	$0.186485\pi$
$488$		0			0
$489$	−29.3745	+	15.4260i	−1.32836	+	0.697586i
$490$		0			0
$491$	5.01904	+	28.4644i	0.226506	+	1.28458i	0.859785	+	0.510656i	$0.170597\pi$
$491$	5.01904	+	28.4644i	0.226506	+	1.28458i	−0.633279	+	0.773924i	$0.718291\pi$
$492$		0			0
$493$	−21.5647	−	18.0950i	−0.971227	−	0.814956i
$494$		0			0
$495$	11.6122	−	16.8405i	0.521930	−	0.756926i
$496$		0			0
$497$	−2.06929	+	11.7355i	−0.0928204	+	0.526411i
$498$		0			0
$499$	13.1940	+	4.80222i	0.590644	+	0.214977i	0.620013	−	0.784592i	$-0.287127\pi$
$499$	13.1940	+	4.80222i	0.590644	+	0.214977i	−0.0293684	+	0.999569i	$0.509350\pi$
$500$		0			0
$501$	−21.1483	−	27.3567i	−0.944838	−	1.22221i
$502$		0			0
$503$	10.4453	+	18.0917i	0.465731	+	0.806669i	0.999234	−	0.0391285i	$-0.0124582\pi$
$503$	10.4453	+	18.0917i	0.465731	+	0.806669i	−0.533503	+	0.845798i	$0.679125\pi$
$504$		0			0
$505$	−14.6946	+	25.4518i	−0.653902	+	1.13259i
$506$		0			0
$507$	36.6371	+	7.98409i	1.62711	+	0.354586i
$508$		0			0
$509$	−5.22308	+	4.38269i	−0.231509	+	0.194259i	−0.751161	−	0.660119i	$-0.770506\pi$
$509$	−5.22308	+	4.38269i	−0.231509	+	0.194259i	0.519652	+	0.854378i	$0.326062\pi$
$510$		0			0
$511$	−7.68831	+	2.79832i	−0.340111	+	0.123790i
$512$		0			0
$513$	0.667054	+	0.500504i	0.0294511	+	0.0220978i
$514$		0			0
$515$	17.0197	−	6.19465i	0.749976	−	0.272969i
$516$		0			0
$517$	0.150736	−	0.126483i	0.00662938	−	0.00556271i
$518$		0			0
$519$	6.42464	+	20.1236i	0.282010	+	0.883329i
$520$		0			0
$521$	−3.17259	+	5.49509i	−0.138994	+	0.240744i	−0.927116	−	0.374774i	$-0.877720\pi$
$521$	−3.17259	+	5.49509i	−0.138994	+	0.240744i	0.788122	+	0.615519i	$0.211053\pi$
$522$		0			0
$523$	22.3401	+	38.6942i	0.976864	+	1.69198i	0.673641	+	0.739059i	$0.264730\pi$
$523$	22.3401	+	38.6942i	0.976864	+	1.69198i	0.303224	+	0.952919i	$0.401937\pi$
$524$		0			0
$525$	20.8200	−	2.81724i	0.908658	−	0.122954i
$526$		0			0
$527$	33.6392	+	12.2437i	1.46535	+	0.533343i
$528$		0			0
$529$	−0.783712	+	4.44465i	−0.0340744	+	0.193246i
$530$		0			0
$531$	−6.63972	−	3.03818i	−0.288139	−	0.131846i
$532$		0			0
$533$	−5.81672	−	4.88081i	−0.251950	−	0.211411i
$534$		0			0
$535$	−8.63702	−	48.9830i	−0.373411	−	2.11772i
$536$		0			0
$537$	31.7479	+	20.0654i	1.37002	+	0.865887i
$538$		0			0
$539$	−6.69997			−0.288588
$540$		0			0
$541$	−11.3563			−0.488244			−0.244122	−	0.969745i	$-0.578500\pi$
$541$	−11.3563			−0.488244			−0.244122	+	0.969745i	$0.578500\pi$
$542$		0			0
$543$	0.415604	−	10.3753i	0.0178353	−	0.445246i
$544$		0			0
$545$	1.56866	+	8.89631i	0.0671940	+	0.381076i
$546$		0			0
$547$	0.0798430	+	0.0669963i	0.00341384	+	0.00286455i	0.644493	−	0.764610i	$-0.277069\pi$
$547$	0.0798430	+	0.0669963i	0.00341384	+	0.00286455i	−0.641079	+	0.767475i	$0.721513\pi$
$548$		0			0
$549$	16.6809	−	4.59853i	0.711925	−	0.196261i
$550$		0			0
$551$	0.231138	−	1.31085i	0.00984683	−	0.0558441i
$552$		0			0
$553$	−5.39433	−	1.96337i	−0.229390	−	0.0834912i
$554$		0			0
$555$	−9.62426	+	23.4735i	−0.408527	+	0.996395i
$556$		0			0
$557$	−13.7684	−	23.8476i	−0.583385	−	1.01045i	−0.995075	−	0.0991289i	$-0.968394\pi$
$557$	−13.7684	−	23.8476i	−0.583385	−	1.01045i	0.411689	−	0.911324i	$-0.364939\pi$
$558$		0			0
$559$	21.2497	−	36.8055i	0.898766	−	1.55671i
$560$		0			0
$561$	8.02134	−	8.81723i	0.338661	−	0.372264i
$562$		0			0
$563$	2.49216	−	2.09117i	0.105032	−	0.0881323i	−0.588759	−	0.808308i	$-0.700383\pi$
$563$	2.49216	−	2.09117i	0.105032	−	0.0881323i	0.693791	+	0.720176i	$0.255939\pi$
$564$		0			0
$565$	−42.1583	+	15.3444i	−1.77361	+	0.645543i
$566$		0			0
$567$	−5.68286	+	16.3414i	−0.238658	+	0.686276i
$568$		0			0
$569$	35.6272	−	12.9672i	1.49357	−	0.543615i	0.539183	−	0.842188i	$-0.318733\pi$
$569$	35.6272	−	12.9672i	1.49357	−	0.543615i	0.954387	+	0.298573i	$0.0965107\pi$
$570$		0			0
$571$	−22.5340	+	18.9082i	−0.943017	+	0.791285i	−0.978108	−	0.208099i	$-0.933272\pi$
$571$	−22.5340	+	18.9082i	−0.943017	+	0.791285i	0.0350911	+	0.999384i	$0.488828\pi$
$572$		0			0
$573$	−22.3210	+	24.5357i	−0.932474	+	1.02500i
$574$		0			0
$575$	13.5651	−	23.4954i	0.565703	−	0.979826i
$576$		0			0
$577$	13.3737	+	23.1640i	0.556755	+	0.964329i	0.997765	+	0.0668261i	$0.0212873\pi$
$577$	13.3737	+	23.1640i	0.556755	+	0.964329i	−0.441009	+	0.897503i	$0.645379\pi$
$578$		0			0
$579$	−0.295948	+	0.721815i	−0.0122992	+	0.0299976i
$580$		0			0
$581$	17.2238	+	6.26896i	0.714565	+	0.260080i
$582$		0			0
$583$	4.50684	−	25.5596i	0.186654	−	1.05857i
$584$		0			0
$585$	−42.2944	−	41.6901i	−1.74866	−	1.72367i
$586$		0			0
$587$	−36.3965	−	30.5403i	−1.50225	−	1.26053i	−0.877374	−	0.479807i	$-0.840707\pi$
$587$	−36.3965	−	30.5403i	−1.50225	−	1.26053i	−0.624872	−	0.780727i	$-0.714849\pi$
$588$		0			0
$589$	0.293929	+	1.66695i	0.0121111	+	0.0686856i
$590$		0			0
$591$	−0.248926	+	6.21427i	−0.0102394	+	0.255621i
$592$		0			0
$593$	9.40677			0.386290			0.193145	−	0.981170i	$-0.438131\pi$
$593$	9.40677			0.386290			0.193145	+	0.981170i	$0.438131\pi$
$594$		0			0
$595$	21.9438			0.899607
$596$		0			0
$597$	−10.6531	−	6.73304i	−0.436004	−	0.275565i
$598$		0			0
$599$	−0.615845	−	3.49263i	−0.0251628	−	0.142705i	0.969638	−	0.244544i	$-0.0786384\pi$
$599$	−0.615845	−	3.49263i	−0.0251628	−	0.142705i	−0.994801	+	0.101839i	$0.967527\pi$
$600$		0			0
$601$	−32.6268	−	27.3772i	−1.33088	−	1.11674i	−0.983872	−	0.178874i	$-0.942755\pi$
$601$	−32.6268	−	27.3772i	−1.33088	−	1.11674i	−0.347004	−	0.937864i	$-0.612801\pi$
$602$		0			0
$603$	10.1386	−	7.20841i	0.412877	−	0.293549i
$604$		0			0
$605$	−4.02309	+	22.8161i	−0.163562	+	0.927606i
$606$		0			0
$607$	10.2067	+	3.71493i	0.414277	+	0.150784i	0.540746	−	0.841186i	$-0.318142\pi$
$607$	10.2067	+	3.71493i	0.414277	+	0.150784i	−0.126469	+	0.991971i	$0.540364\pi$
$608$		0			0
$609$	27.3656	−	3.70295i	1.10891	−	0.150051i
$610$		0			0
$611$	−0.285633	−	0.494732i	−0.0115555	−	0.0200147i
$612$		0			0
$613$	−12.6149	+	21.8496i	−0.509510	+	0.882497i	0.490429	+	0.871481i	$0.336840\pi$
$613$	−12.6149	+	21.8496i	−0.509510	+	0.882497i	−0.999939	+	0.0110162i	$0.996493\pi$
$614$		0			0
$615$	2.28526	+	7.15803i	0.0921506	+	0.288639i
$616$		0			0
$617$	−6.59580	+	5.53453i	−0.265537	+	0.222812i	−0.765828	−	0.643045i	$-0.777671\pi$
$617$	−6.59580	+	5.53453i	−0.265537	+	0.222812i	0.500291	+	0.865857i	$0.333226\pi$
$618$		0			0
$619$	33.9476	−	12.3559i	1.36447	−	0.496626i	0.447036	−	0.894516i	$-0.352480\pi$
$619$	33.9476	−	12.3559i	1.36447	−	0.496626i	0.917433	+	0.397890i	$0.130257\pi$
$620$		0			0
$621$	12.2067	+	18.7120i	0.489840	+	0.750886i
$622$		0			0
$623$	2.96789	−	1.08022i	0.118906	−	0.0432782i
$624$		0			0
$625$	−12.8196	+	10.7569i	−0.512783	+	0.430276i
$626$		0			0
$627$	0.550695	+	0.120009i	0.0219926	+	0.00479271i
$628$		0			0
$629$	−7.39168	+	12.8028i	−0.294726	+	0.510480i
$630$		0			0
$631$	−0.0668013	−	0.115703i	−0.00265932	−	0.00460607i	0.864693	−	0.502301i	$-0.167513\pi$
$631$	−0.0668013	−	0.115703i	−0.00265932	−	0.00460607i	−0.867352	+	0.497695i	$0.834180\pi$
$632$		0			0
$633$	6.87537	+	8.89372i	0.273271	+	0.353494i
$634$		0			0
$635$	−30.3828	−	11.0584i	−1.20571	−	0.438841i
$636$		0			0
$637$	−3.37767	+	19.1557i	−0.133828	+	0.758978i
$638$		0			0
$639$	−18.5371	−	1.48747i	−0.733315	−	0.0588434i
$640$		0			0
$641$	−7.35762	−	6.17378i	−0.290609	−	0.243850i	0.485814	−	0.874062i	$-0.338523\pi$
$641$	−7.35762	−	6.17378i	−0.290609	−	0.243850i	−0.776423	+	0.630213i	$0.782968\pi$
$642$		0			0
$643$	2.18840	+	12.4110i	0.0863020	+	0.489443i	0.997068	+	0.0765200i	$0.0243809\pi$
$643$	2.18840	+	12.4110i	0.0863020	+	0.489443i	−0.910766	+	0.412923i	$0.864508\pi$
$644$		0			0
$645$	−37.2340	+	19.5534i	−1.46609	+	0.769913i
$646$		0			0
$647$	−21.0753			−0.828556			−0.414278	−	0.910150i	$-0.635966\pi$
$647$	−21.0753			−0.828556			−0.414278	+	0.910150i	$0.635966\pi$
$648$		0			0
$649$	−4.93491			−0.193712
$650$		0			0
$651$	−31.0904	+	16.3271i	−1.21853	+	0.639909i
$652$		0			0
$653$	5.40708	+	30.6650i	0.211595	+	1.20002i	0.886718	+	0.462311i	$0.152980\pi$
$653$	5.40708	+	30.6650i	0.211595	+	1.20002i	−0.675123	+	0.737705i	$0.735909\pi$
$654$		0			0
$655$	46.8831	+	39.3396i	1.83187	+	1.53712i
$656$		0			0
$657$	−5.47918	−	11.5328i	−0.213763	−	0.449936i
$658$		0			0
$659$	5.83780	−	33.1078i	0.227409	−	1.28970i	−0.630618	−	0.776093i	$-0.717199\pi$
$659$	5.83780	−	33.1078i	0.227409	−	1.28970i	0.858027	−	0.513605i	$-0.171690\pi$
$660$		0			0
$661$	34.5713	+	12.5829i	1.34467	+	0.489419i	0.911280	−	0.411788i	$-0.135095\pi$
$661$	34.5713	+	12.5829i	1.34467	+	0.489419i	0.433389	+	0.901207i	$0.357318\pi$
$662$		0			0
$663$	−21.1653	−	27.3787i	−0.821994	−	1.06330i
$664$		0			0
$665$	0.518791	+	0.898573i	0.0201179	+	0.0348452i
$666$		0			0
$667$	17.8298	−	30.8822i	0.690373	−	1.19576i
$668$		0			0
$669$	−25.0667	−	5.46262i	−0.969134	−	0.211197i
$670$		0			0
$671$	8.95837	−	7.51696i	0.345834	−	0.290189i
$672$		0			0
$673$	6.08175	−	2.21358i	0.234434	−	0.0853271i	−0.222132	−	0.975017i	$-0.571301\pi$
$673$	6.08175	−	2.21358i	0.234434	−	0.0853271i	0.456566	+	0.889690i	$0.349079\pi$
$674$		0			0
$675$	7.44149	+	31.9315i	0.286423	+	1.22904i
$676$		0			0
$677$	35.9751	−	13.0939i	1.38263	−	0.503238i	0.459659	−	0.888096i	$-0.347972\pi$
$677$	35.9751	−	13.0939i	1.38263	−	0.503238i	0.922976	+	0.384858i	$0.125749\pi$
$678$		0			0
$679$	−4.10952	+	3.44830i	−0.157709	+	0.132333i
$680$		0			0
$681$	−0.437253	−	1.36959i	−0.0167556	−	0.0524828i
$682$		0			0
$683$	13.7010	−	23.7309i	0.524255	−	0.908037i	−0.475346	−	0.879799i	$-0.657677\pi$
$683$	13.7010	−	23.7309i	0.524255	−	0.908037i	0.999601	−	0.0282377i	$-0.00898954\pi$
$684$		0			0
$685$	−7.88943	−	13.6649i	−0.301440	−	0.522109i
$686$		0			0
$687$	−26.9016	+	3.64016i	−1.02636	+	0.138881i
$688$		0			0
$689$	−70.8048	−	25.7708i	−2.69745	−	0.981790i
$690$		0			0
$691$	−3.49952	+	19.8468i	−0.133128	+	0.755007i	0.843017	+	0.537887i	$0.180777\pi$
$691$	−3.49952	+	19.8468i	−0.133128	+	0.755007i	−0.976145	+	0.217120i	$0.930334\pi$
$692$		0			0
$693$	1.10291	+	11.6410i	0.0418959	+	0.442203i
$694$		0			0
$695$	−29.2913	−	24.5783i	−1.11108	−	0.932309i
$696$		0			0
$697$	0.760316	+	4.31196i	0.0287990	+	0.163327i
$698$		0			0
$699$	−21.3632	−	13.5021i	−0.808031	−	0.510695i
$700$		0			0
$701$	−25.8155			−0.975036			−0.487518	−	0.873113i	$-0.662098\pi$
$701$	−25.8155			−0.975036			−0.487518	+	0.873113i	$0.662098\pi$
$702$		0			0
$703$	−0.699012			−0.0263637
$704$		0			0
$705$	−0.0226264	+	0.564854i	−0.000852160	+	0.0212736i
$706$		0			0
$707$	−2.91721	−	16.5443i	−0.109713	−	0.622212i
$708$		0			0
$709$	23.9831	+	20.1242i	0.900704	+	0.755780i	0.970328	−	0.241793i	$-0.0777355\pi$
$709$	23.9831	+	20.1242i	0.900704	+	0.755780i	−0.0696241	+	0.997573i	$0.522180\pi$
$710$		0			0
$711$	2.25631	−	8.66970i	0.0846182	−	0.325139i
$712$		0			0
$713$	−7.87440	+	44.6579i	−0.294898	+	1.67245i
$714$		0			0
$715$	−37.7164	−	13.7276i	−1.41051	−	0.513384i
$716$		0			0
$717$	5.79652	−	14.1377i	0.216475	−	0.527981i
$718$		0			0
$719$	18.9508	+	32.8237i	0.706744	+	1.22412i	0.966058	+	0.258324i	$0.0831702\pi$
$719$	18.9508	+	32.8237i	0.706744	+	1.22412i	−0.259314	+	0.965793i	$0.583496\pi$
$720$		0			0
$721$	−5.17659	+	8.96613i	−0.192786	+	0.333916i
$722$		0			0
$723$	15.8261	−	17.3964i	0.588580	−	0.646980i
$724$		0			0
$725$	40.0887	−	33.6384i	1.48886	−	1.24930i
$726$		0			0
$727$	−2.96307	+	1.07847i	−0.109894	+	0.0399982i	−0.396382	−	0.918086i	$-0.629734\pi$
$727$	−2.96307	+	1.07847i	−0.109894	+	0.0399982i	0.286488	+	0.958084i	$0.407512\pi$
$728$		0			0
$729$	−26.2247	−	6.42359i	−0.971287	−	0.237911i
$730$		0			0
$731$	−23.0286	+	8.38173i	−0.851744	+	0.310009i
$732$		0			0
$733$	30.8260	−	25.8661i	1.13858	−	0.955385i	0.139193	−	0.990265i	$-0.455549\pi$
$733$	30.8260	−	25.8661i	1.13858	−	0.955385i	0.999392	+	0.0348799i	$0.0111049\pi$
$734$		0			0
$735$	12.9528	−	14.2380i	0.477772	−	0.525178i
$736$		0			0
$737$	4.20376	−	7.28113i	0.154848	−	0.268204i
$738$		0			0
$739$	−5.71378	−	9.89656i	−0.210185	−	0.364051i	0.741587	−	0.670856i	$-0.234073\pi$
$739$	−5.71378	−	9.89656i	−0.210185	−	0.364051i	−0.951772	+	0.306805i	$0.900740\pi$
$740$		0			0
$741$	0.620739	−	1.51398i	0.0228034	−	0.0556174i
$742$		0			0
$743$	24.2580	+	8.82918i	0.889939	+	0.323911i	0.746214	−	0.665706i	$-0.231870\pi$
$743$	24.2580	+	8.82918i	0.889939	+	0.323911i	0.143725	+	0.989618i	$0.454092\pi$
$744$		0			0
$745$	4.46708	−	25.3341i	0.163661	−	0.928168i
$746$		0			0
$747$	−7.20428	+	27.6819i	−0.263591	+	1.01283i
$748$		0			0
$749$	21.7799	+	18.2755i	0.795821	+	0.667773i
$750$		0			0
$751$	5.82330	+	33.0256i	0.212495	+	1.20512i	0.885201	+	0.465209i	$0.154021\pi$
$751$	5.82330	+	33.0256i	0.212495	+	1.20512i	−0.672706	+	0.739910i	$0.734868\pi$
$752$		0			0
$753$	0.804735	−	20.0897i	0.0293262	−	0.732109i
$754$		0			0
$755$	40.6345			1.47884
$756$		0			0
$757$	−8.62121			−0.313343			−0.156672	−	0.987651i	$-0.550076\pi$
$757$	−8.62121			−0.313343			−0.156672	+	0.987651i	$0.550076\pi$
$758$		0			0
$759$	12.7639	+	8.06707i	0.463299	+	0.292816i
$760$		0			0
$761$	−6.56504	−	37.2322i	−0.237982	−	1.34967i	−0.836241	−	0.548362i	$-0.815251\pi$
$761$	−6.56504	−	37.2322i	−0.237982	−	1.34967i	0.598258	−	0.801303i	$-0.295860\pi$
$762$		0			0
$763$	−3.95568	−	3.31921i	−0.143205	−	0.120163i
$764$		0			0
$765$	3.23001	+	34.0921i	0.116781	+	1.23260i
$766$		0			0
$767$	−2.48785	+	14.1093i	−0.0898311	+	0.509457i
$768$		0			0
$769$	27.0932	+	9.86114i	0.977007	+	0.355602i	0.780676	−	0.624936i	$-0.214875\pi$
$769$	27.0932	+	9.86114i	0.977007	+	0.355602i	0.196331	+	0.980538i	$0.437097\pi$
$770$		0			0
$771$	−14.8581	+	2.01052i	−0.535103	+	0.0724070i
$772$		0			0
$773$	−18.9144	−	32.7607i	−0.680304	−	1.17832i	−0.974888	−	0.222695i	$-0.928514\pi$
$773$	−18.9144	−	32.7607i	−0.680304	−	1.17832i	0.294584	−	0.955626i	$-0.404819\pi$
$774$		0			0
$775$	−33.2742	+	57.6326i	−1.19525	+	2.07023i
$776$		0			0
$777$	−4.41056	−	13.8150i	−0.158228	−	0.495611i
$778$		0			0
$779$	−0.158595	+	0.133077i	−0.00568225	+	0.00476798i
$780$		0			0
$781$	−11.8105	+	4.29868i	−0.422614	+	0.153819i
$782$		0			0
$783$	9.78102	+	41.9705i	0.349545	+	1.49990i
$784$		0			0
$785$	8.08080	−	2.94117i	0.288416	−	0.104975i
$786$		0			0
$787$	25.9376	−	21.7643i	0.924577	−	0.775812i	−0.0502589	−	0.998736i	$-0.516005\pi$
$787$	25.9376	−	21.7643i	0.924577	−	0.775812i	0.974836	+	0.222924i	$0.0715602\pi$
$788$		0			0
$789$	24.5118	+	5.34170i	0.872644	+	0.190169i
$790$		0			0
$791$	12.8226	−	22.2094i	0.455919	−	0.789676i
$792$		0			0
$793$	−16.9754	−	29.4022i	−0.602814	−	1.04410i
$794$		0			0
$795$	45.6034	+	58.9909i	1.61739	+	2.09219i
$796$		0			0
$797$	49.7073	+	18.0920i	1.76072	+	0.640850i	0.999966	−	0.00818822i	$-0.00260642\pi$
$797$	49.7073	+	18.0920i	1.76072	+	0.640850i	0.760755	+	0.649039i	$0.224829\pi$
$798$		0			0
$799$	−0.0572017	+	0.324407i	−0.00202365	+	0.0114767i
$800$		0			0
$801$	2.11510	+	4.45194i	0.0747335	+	0.157302i
$802$		0			0
$803$	−6.61045	−	5.54683i	−0.233278	−	0.195743i
$804$		0			0
$805$	4.82690	+	27.3747i	0.170126	+	0.964831i
$806$		0			0
$807$	−21.9382	+	11.5208i	−0.772262	+	0.405552i
$808$		0			0
$809$	10.9680			0.385614			0.192807	−	0.981237i	$-0.438241\pi$
$809$	10.9680			0.385614			0.192807	+	0.981237i	$0.438241\pi$
$810$		0			0
$811$	6.54690			0.229893			0.114946	−	0.993372i	$-0.463330\pi$
$811$	6.54690			0.229893			0.114946	+	0.993372i	$0.463330\pi$
$812$		0			0
$813$	14.4667	−	7.59717i	0.507370	−	0.266444i
$814$		0			0
$815$	−11.1866	−	63.4422i	−0.391849	−	2.22228i
$816$		0			0
$817$	−0.887661	−	0.744836i	−0.0310553	−	0.0260585i
$818$		0			0
$819$	33.8384	+	2.71530i	1.18241	+	0.0948801i
$820$		0			0
$821$	−7.50955	+	42.5888i	−0.262085	+	1.48636i	0.515124	+	0.857116i	$0.327746\pi$
$821$	−7.50955	+	42.5888i	−0.262085	+	1.48636i	−0.777209	+	0.629243i	$0.783365\pi$
$822$		0			0
$823$	0.409020	+	0.148871i	0.0142575	+	0.00518931i	0.349139	−	0.937071i	$-0.386474\pi$
$823$	0.409020	+	0.148871i	0.0142575	+	0.00518931i	−0.334882	+	0.942260i	$0.608696\pi$
$824$		0			0
$825$	13.5528	+	17.5314i	0.471847	+	0.610364i
$826$		0			0
$827$	−8.70278	−	15.0737i	−0.302625	−	0.524162i	0.674105	−	0.738636i	$-0.264530\pi$
$827$	−8.70278	−	15.0737i	−0.302625	−	0.524162i	−0.976730	+	0.214474i	$0.931196\pi$
$828$		0			0
$829$	12.7891	−	22.1513i	0.444183	−	0.769348i	−0.553812	−	0.832642i	$-0.686827\pi$
$829$	12.7891	−	22.1513i	0.444183	−	0.769348i	0.997995	+	0.0632941i	$0.0201606\pi$
$830$		0			0
$831$	2.57454	+	0.561052i	0.0893098	+	0.0194627i
$832$		0			0
$833$	8.59213	−	7.20965i	0.297700	−	0.249800i
$834$		0			0
$835$	63.0892	−	22.9626i	2.18329	−	0.794653i
$836$		0			0
$837$	−29.9423	−	45.8993i	−1.03496	−	1.58651i
$838$		0			0
$839$	48.8836	−	17.7922i	1.68765	−	0.614254i	0.693322	−	0.720628i	$-0.256147\pi$
$839$	48.8836	−	17.7922i	1.68765	−	0.614254i	0.994326	+	0.106375i	$0.0339243\pi$
$840$		0			0
$841$	30.4769	−	25.5732i	1.05093	−	0.881834i
$842$		0			0
$843$	−13.4977	−	42.2782i	−0.464884	−	1.45614i
$844$		0			0
$845$	−36.4028	+	63.0515i	−1.25230	+	2.16904i
$846$		0			0
$847$	−6.62169	−	11.4691i	−0.227524	−	0.394083i
$848$		0			0
$849$	−10.8548	+	1.46880i	−0.372534	+	0.0504091i
$850$		0			0
$851$	−17.5973	−	6.40489i	−0.603227	−	0.219557i
$852$		0			0
$853$	−4.91369	+	27.8669i	−0.168242	+	0.954146i	0.777417	+	0.628985i	$0.216529\pi$
$853$	−4.91369	+	27.8669i	−0.168242	+	0.954146i	−0.945659	+	0.325161i	$0.894582\pi$
$854$		0			0
$855$	−1.31967	+	0.938266i	−0.0451318	+	0.0320880i
$856$		0			0
$857$	26.5795	+	22.3028i	0.907938	+	0.761850i	0.971726	−	0.236113i	$-0.0758737\pi$
$857$	26.5795	+	22.3028i	0.907938	+	0.761850i	−0.0637879	+	0.997963i	$0.520318\pi$
$858$		0			0
$859$	5.51676	+	31.2871i	0.188229	+	1.06750i	0.921736	+	0.387819i	$0.126771\pi$
$859$	5.51676	+	31.2871i	0.188229	+	1.06750i	−0.733506	+	0.679683i	$0.762118\pi$
$860$		0			0
$861$	−3.63077	−	2.29474i	−0.123736	−	0.0782044i
$862$		0			0
$863$	−31.0932			−1.05843			−0.529213	−	0.848489i	$-0.677513\pi$
$863$	−31.0932			−1.05843			−0.529213	+	0.848489i	$0.677513\pi$
$864$		0			0
$865$	−41.0158			−1.39458
$866$		0			0
$867$	0.379837	−	9.48240i	0.0129000	−	0.322039i
$868$		0			0
$869$	−1.05137	−	5.96259i	−0.0356651	−	0.202267i
$870$		0			0
$871$	−18.6981	−	15.6895i	−0.633560	−	0.531620i
$872$		0			0
$873$	−5.96222	−	5.87703i	−0.201790	−	0.198907i
$874$		0			0
$875$	−1.47052	+	8.33974i	−0.0497127	+	0.281935i
$876$		0			0
$877$	−50.1496	−	18.2530i	−1.69343	−	0.616359i	−0.698382	−	0.715725i	$-0.746096\pi$
$877$	−50.1496	−	18.2530i	−1.69343	−	0.616359i	−0.995051	+	0.0993659i	$0.968319\pi$
$878$		0			0
$879$	14.5331	−	35.4462i	0.490190	−	1.19557i
$880$		0			0
$881$	−6.55673	−	11.3566i	−0.220902	−	0.382613i	0.734180	−	0.678955i	$-0.237567\pi$
$881$	−6.55673	−	11.3566i	−0.220902	−	0.382613i	−0.955082	+	0.296341i	$0.904233\pi$
$882$		0			0
$883$	21.0350	−	36.4337i	0.707885	−	1.22609i	−0.257756	−	0.966210i	$-0.582983\pi$
$883$	21.0350	−	36.4337i	0.707885	−	1.22609i	0.965640	−	0.259882i	$-0.0836837\pi$
$884$		0			0
$885$	9.54050	−	10.4871i	0.320701	−	0.352521i
$886$		0			0
$887$	−44.7527	+	37.5520i	−1.50265	+	1.26087i	−0.625921	+	0.779887i	$0.715277\pi$
$887$	−44.7527	+	37.5520i	−1.50265	+	1.26087i	−0.876728	+	0.480986i	$0.840279\pi$
$888$		0			0
$889$	17.3675	−	6.32125i	0.582487	−	0.212008i
$890$		0			0
$891$	−17.9232	+	3.42697i	−0.600450	+	0.114808i
$892$		0			0
$893$	−0.0146364	+	0.00532723i	−0.000489790	+	0.000178269i
$894$		0			0
$895$	−55.8620	+	46.8738i	−1.86726	+	1.56682i
$896$		0			0
$897$	29.4991	−	32.4260i	0.984945	−	1.08267i
$898$		0			0
$899$	−43.7354	+	75.7519i	−1.45866	+	2.52647i
$900$		0			0
$901$	21.7243	+	37.6276i	0.723742	+	1.25356i
$902$		0			0
$903$	9.11979	−	22.2431i	0.303488	−	0.740205i
$904$		0			0
$905$	18.9454	+	6.89555i	0.629765	+	0.229216i
$906$		0			0
$907$	8.47053	−	48.0388i	0.281259	−	1.59510i	−0.437090	−	0.899418i	$-0.643991\pi$
$907$	8.47053	−	48.0388i	0.281259	−	1.59510i	0.718349	−	0.695683i	$-0.244898\pi$
$908$		0			0
$909$	25.2740	−	6.96744i	0.838287	−	0.231095i
$910$		0			0
$911$	18.5369	+	15.5543i	0.614153	+	0.515336i	0.895960	−	0.444135i	$-0.146489\pi$
$911$	18.5369	+	15.5543i	0.614153	+	0.515336i	−0.281806	+	0.959471i	$0.590934\pi$
$912$		0			0
$913$	3.35696	+	19.0383i	0.111099	+	0.630075i
$914$		0			0
$915$	−1.34470	+	33.5696i	−0.0444545	+	1.10978i
$916$		0			0
$917$	−34.9841			−1.15528
$918$		0			0
$919$	−42.7812			−1.41122			−0.705610	−	0.708600i	$-0.749327\pi$
$919$	−42.7812			−1.41122			−0.705610	+	0.708600i	$0.749327\pi$
$920$		0			0
$921$	10.1906	+	6.44073i	0.335793	+	0.212229i
$922$		0			0
$923$	6.33620	+	35.9344i	0.208558	+	1.18279i
$924$		0			0
$925$	−21.0525	−	17.6652i	−0.692203	−	0.580828i
$926$		0			0
$927$	−14.6919	−	6.72266i	−0.482544	−	0.220801i
$928$		0			0
$929$	0.529440	−	3.00260i	0.0173704	−	0.0985122i	−0.974890	−	0.222687i	$-0.928517\pi$
$929$	0.529440	−	3.00260i	0.0173704	−	0.0985122i	0.992260	+	0.124175i	$0.0396283\pi$
$930$		0			0
$931$	0.498361	+	0.181389i	0.0163331	+	0.00594477i
$932$		0			0
$933$	−16.4321	+	2.22350i	−0.537964	+	0.0727941i
$934$		0			0
$935$	11.5721	+	20.0435i	0.378449	+	0.655493i
$936$		0			0
$937$	−16.1594	+	27.9888i	−0.527903	+	0.914355i	0.471568	+	0.881830i	$0.343688\pi$
$937$	−16.1594	+	27.9888i	−0.527903	+	0.914355i	−0.999471	+	0.0325254i	$0.989645\pi$
$938$		0			0
$939$	−6.45014	−	20.2035i	−0.210492	−	0.659317i
$940$		0			0
$941$	12.1288	−	10.1773i	0.395389	−	0.331770i	−0.423319	−	0.905981i	$-0.639135\pi$
$941$	12.1288	−	10.1773i	0.395389	−	0.331770i	0.818708	+	0.574210i	$0.194691\pi$
$942$		0			0
$943$	−5.21190	+	1.89698i	−0.169723	+	0.0617741i
$944$		0			0
$945$	−26.8703	−	20.1613i	−0.874090	−	0.655848i
$946$		0			0
$947$	−17.9799	+	6.54414i	−0.584267	+	0.212656i	−0.617206	−	0.786802i	$-0.711736\pi$
$947$	−17.9799	+	6.54414i	−0.584267	+	0.212656i	0.0329390	+	0.999457i	$0.489513\pi$
$948$		0			0
$949$	−19.1914	+	16.1035i	−0.622978	+	0.522741i
$950$		0			0
$951$	−18.4787	−	4.02694i	−0.599213	−	0.130583i
$952$		0			0
$953$	14.7660	−	25.5755i	0.478319	−	0.828472i	−0.521372	−	0.853329i	$-0.674580\pi$
$953$	14.7660	−	25.5755i	0.478319	−	0.828472i	0.999691	+	0.0248569i	$0.00791302\pi$
$954$		0			0
$955$	−32.2018	−	55.7752i	−1.04203	−	1.80484i
$956$		0			0
$957$	17.8136	+	23.0431i	0.575833	+	0.744877i
$958$		0			0
$959$	8.47560	+	3.08486i	0.273691	+	0.0996155i
$960$		0			0
$961$	13.9323	−	79.0138i	0.449428	−	2.54883i
$962$		0			0
$963$	−25.1872	+	36.5276i	−0.811646	+	1.17709i
$964$		0			0
$965$	−1.16035	−	0.973650i	−0.0373530	−	0.0313429i
$966$		0			0
$967$	7.14971	+	40.5480i	0.229919	+	1.30394i	0.853055	+	0.521822i	$0.174747\pi$
$967$	7.14971	+	40.5480i	0.229919	+	1.30394i	−0.623135	+	0.782114i	$0.714141\pi$
$968$		0			0
$969$	−0.835357	+	0.438686i	−0.0268355	+	0.0140926i
$970$		0			0
$971$	−36.8784			−1.18348			−0.591742	−	0.806128i	$-0.701560\pi$
$971$	−36.8784			−1.18348			−0.591742	+	0.806128i	$0.701560\pi$
$972$		0			0
$973$	21.8572			0.700708
$974$		0			0
$975$	56.9559	−	29.9103i	1.82405	−	0.957896i
$976$		0			0
$977$	0.880454	+	4.99330i	0.0281682	+	0.159750i	0.995647	−	0.0932012i	$-0.0297100\pi$
$977$	0.880454	+	4.99330i	0.0281682	+	0.159750i	−0.967479	+	0.252951i	$0.918599\pi$
$978$		0			0
$979$	2.55180	+	2.14122i	0.0815560	+	0.0684336i
$980$		0			0
$981$	4.57451	−	6.63416i	0.146053	−	0.211813i
$982$		0			0
$983$	4.06602	−	23.0595i	0.129686	−	0.735485i	−0.848728	−	0.528830i	$-0.822631\pi$
$983$	4.06602	−	23.0595i	0.129686	−	0.735485i	0.978414	−	0.206655i	$-0.0662578\pi$
$984$		0			0
$985$	−11.3473	−	4.13008i	−0.361555	−	0.131595i
$986$		0			0
$987$	−0.197637	−	0.255656i	−0.00629086	−	0.00813762i
$988$		0			0
$989$	−15.5217	−	26.8843i	−0.493561	−	0.854872i
$990$		0			0
$991$	5.92671	−	10.2654i	0.188268	−	0.326090i	−0.756405	−	0.654104i	$-0.773046\pi$
$991$	5.92671	−	10.2654i	0.188268	−	0.326090i	0.944673	+	0.328014i	$0.106379\pi$
$992$		0			0
$993$	35.5527	+	7.74777i	1.12823	+	0.245868i
$994$		0			0
$995$	18.7447	−	15.7287i	0.594248	−	0.498633i
$996$		0			0
$997$	−38.3789	+	13.9688i	−1.21547	+	0.442396i	−0.868599	−	0.495516i	$-0.834979\pi$
$997$	−38.3789	+	13.9688i	−1.21547	+	0.442396i	−0.346873	+	0.937912i	$0.612757\pi$
$998$		0			0
$999$	20.8140	−	8.88580i	0.658525	−	0.281134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.i.a.61.3	✓	18
3.2	odd	2		324.2.i.a.181.1		18
4.3	odd	2		432.2.u.d.385.1		18
9.2	odd	6		972.2.i.b.865.3		18
9.4	even	3		972.2.i.a.217.3		18
9.5	odd	6		972.2.i.d.217.1		18
9.7	even	3		972.2.i.c.865.1		18
27.2	odd	18		2916.2.a.c.1.2		9
27.4	even	9	inner	108.2.i.a.85.3	yes	18
27.5	odd	18		972.2.i.d.757.1		18
27.7	even	9		2916.2.e.c.1945.2		18
27.11	odd	18		2916.2.e.d.973.8		18
27.13	even	9		972.2.i.c.109.1		18
27.14	odd	18		972.2.i.b.109.3		18
27.16	even	9		2916.2.e.c.973.2		18
27.20	odd	18		2916.2.e.d.1945.8		18
27.22	even	9		972.2.i.a.757.3		18
27.23	odd	18		324.2.i.a.145.1		18
27.25	even	9		2916.2.a.d.1.8		9
108.31	odd	18		432.2.u.d.193.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.61.3	✓	18	1.1	even	1	trivial
108.2.i.a.85.3	yes	18	27.4	even	9	inner
324.2.i.a.145.1		18	27.23	odd	18
324.2.i.a.181.1		18	3.2	odd	2
432.2.u.d.193.1		18	108.31	odd	18
432.2.u.d.385.1		18	4.3	odd	2
972.2.i.a.217.3		18	9.4	even	3
972.2.i.a.757.3		18	27.22	even	9
972.2.i.b.109.3		18	27.14	odd	18
972.2.i.b.865.3		18	9.2	odd	6
972.2.i.c.109.1		18	27.13	even	9
972.2.i.c.865.1		18	9.7	even	3
972.2.i.d.217.1		18	9.5	odd	6
972.2.i.d.757.1		18	27.5	odd	18
2916.2.a.c.1.2		9	27.2	odd	18
2916.2.a.d.1.8		9	27.25	even	9
2916.2.e.c.973.2		18	27.16	even	9
2916.2.e.c.1945.2		18	27.7	even	9
2916.2.e.d.973.8		18	27.11	odd	18
2916.2.e.d.1945.8		18	27.20	odd	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.53346 - 0.805294i) q^{3} +(0.583982 + 3.31193i) q^{5} +(-1.47262 - 1.23568i) q^{7} +(1.70300 - 2.46977i) q^{9} +O(q^{10})\)	\(q+(1.53346 - 0.805294i) q^{3} +(0.583982 + 3.31193i) q^{5} +(-1.47262 - 1.23568i) q^{7} +(1.70300 - 2.46977i) q^{9} +(0.352079 - 1.99674i) q^{11} +(-5.53134 - 2.01324i) q^{13} +(3.56259 + 4.60843i) q^{15} +(1.69713 + 2.93951i) q^{17} +(-0.0802464 + 0.138991i) q^{19} +(-3.25330 - 0.708969i) q^{21} +(-3.29370 + 2.76375i) q^{23} +(-5.92935 + 2.15811i) q^{25} +(0.622595 - 5.15872i) q^{27} +(-7.79349 + 2.83660i) q^{29} +(8.07924 - 6.77928i) q^{31} +(-1.06806 - 3.34545i) q^{33} +(3.23249 - 5.59884i) q^{35} +(2.17770 + 3.77190i) q^{37} +(-10.1034 + 1.36713i) q^{39} +(1.21218 + 0.441196i) q^{41} +(-1.25374 + 7.11032i) q^{43} +(9.17423 + 4.19792i) q^{45} +(0.0743444 + 0.0623824i) q^{47} +(-0.573816 - 3.25427i) q^{49} +(4.96964 + 3.14094i) q^{51} +12.8006 q^{53} +6.81866 q^{55} +(-0.0111262 + 0.277759i) q^{57} +(-0.422649 - 2.39696i) q^{59} +(4.41834 + 3.70742i) q^{61} +(-5.55973 + 1.53268i) q^{63} +(3.43751 - 19.4951i) q^{65} +(3.89658 + 1.41824i) q^{67} +(-2.82514 + 6.89050i) q^{69} +(-3.09944 - 5.36839i) q^{71} +(2.12803 - 3.68585i) q^{73} +(-7.35452 + 8.08425i) q^{75} +(-2.98581 + 2.50539i) q^{77} +(2.80608 - 1.02133i) q^{79} +(-3.19956 - 8.41206i) q^{81} +(-8.95967 + 3.26105i) q^{83} +(-8.74434 + 7.33737i) q^{85} +(-9.66672 + 10.6259i) q^{87} +(-0.821473 + 1.42283i) q^{89} +(5.65787 + 9.79971i) q^{91} +(6.92987 - 16.9019i) q^{93} +(-0.507190 - 0.184602i) q^{95} +(0.484584 - 2.74821i) q^{97} +(-4.33190 - 4.27001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 18 * q + 3 * q^5 + 6 * q^9	\( 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

Introduction

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