LMFDB - Embedded newform 648.2.t.a.397.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			397.7
Character	$\chi$	$=$	648.397
Dual form			648.2.t.a.253.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08004 - 0.912975i) q^{2} +(0.332954 + 1.97209i) q^{4} +(-0.114718 - 0.136716i) q^{5} +(2.42085 - 0.881117i) q^{7} +(1.44087 - 2.43391i) q^{8} +(-0.000918366 + 0.252392i) q^{10} +(0.599296 - 0.714213i) q^{11} +(-0.368417 + 0.0649618i) q^{13} +(-3.41904 - 1.25854i) q^{14} +(-3.77828 + 1.31323i) q^{16} +(2.26254 + 3.91883i) q^{17} +(1.97566 + 1.14065i) q^{19} +(0.231420 - 0.271754i) q^{20} +(-1.29932 + 0.224233i) q^{22} +(-4.40423 - 1.60301i) q^{23} +(0.862710 - 4.89267i) q^{25} +(0.457212 + 0.266194i) q^{26} +(2.54367 + 4.48076i) q^{28} +(1.58682 + 0.279799i) q^{29} +(8.17965 + 2.97715i) q^{31} +(5.27963 + 2.03114i) q^{32} +(1.13417 - 6.29812i) q^{34} +(-0.398177 - 0.229888i) q^{35} +(3.82721 - 2.20964i) q^{37} +(-1.09240 - 3.03566i) q^{38} +(-0.498046 + 0.0822239i) q^{40} +(-0.238139 - 1.35055i) q^{41} +(3.28437 - 3.91416i) q^{43} +(1.60803 + 0.944066i) q^{44} +(3.29322 + 5.75225i) q^{46} +(7.70413 - 2.80407i) q^{47} +(-0.278168 + 0.233411i) q^{49} +(-5.39864 + 4.49663i) q^{50} +(-0.250776 - 0.704922i) q^{52} -9.07829i q^{53} -0.166394 q^{55} +(1.34357 - 7.16169i) q^{56} +(-1.45837 - 1.75092i) q^{58} +(9.44865 + 11.2605i) q^{59} +(-5.07860 - 13.9533i) q^{61} +(-6.11625 - 10.6832i) q^{62} +(-3.84780 - 7.01387i) q^{64} +(0.0511453 + 0.0429160i) q^{65} +(-1.72274 + 0.303765i) q^{67} +(-6.97497 + 5.76672i) q^{68} +(0.220164 + 0.611813i) q^{70} +(-2.77372 - 4.80422i) q^{71} +(-4.77001 + 8.26190i) q^{73} +(-6.15087 - 1.10766i) q^{74} +(-1.59165 + 4.27595i) q^{76} +(0.821500 - 2.25705i) q^{77} +(-0.704340 + 3.99451i) q^{79} +(0.612976 + 0.365899i) q^{80} +(-0.975822 + 1.67606i) q^{82} +(15.0319 + 2.65052i) q^{83} +(0.276212 - 0.758885i) q^{85} +(-7.12077 + 1.22889i) q^{86} +(-0.874822 - 2.48772i) q^{88} +(-8.16359 + 14.1397i) q^{89} +(-0.834643 + 0.481881i) q^{91} +(1.69487 - 9.21926i) q^{92} +(-10.8808 - 4.00518i) q^{94} +(-0.0706993 - 0.400955i) q^{95} +(-8.94677 - 7.50723i) q^{97} +(0.513530 + 0.00186855i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.08004	−	0.912975i	−0.763701	−	0.645571i
$2$	−1.08004	−	0.912975i	−0.763701	−	0.645571i
$3$		0			0
$3$		0			0
$4$	0.332954	+	1.97209i	0.166477	+	0.986045i
$5$	−0.114718	−	0.136716i	−0.0513035	−	0.0611411i	0.739782	−	0.672846i	$-0.234928\pi$
$5$	−0.114718	−	0.136716i	−0.0513035	−	0.0611411i	−0.791086	+	0.611705i	$0.790484\pi$
$6$		0			0
$7$	2.42085	−	0.881117i	0.914995	−	0.333031i	0.158749	−	0.987319i	$-0.449254\pi$
$7$	2.42085	−	0.881117i	0.914995	−	0.333031i	0.756245	+	0.654288i	$0.227032\pi$
$8$	1.44087	−	2.43391i	0.509423	−	0.860516i
$9$		0			0
$10$	−0.000918366		0.252392i	−0.000290413		0.0798135i
$11$	0.599296	−	0.714213i	0.180695	−	0.215343i	−0.668093	−	0.744078i	$-0.732889\pi$
$11$	0.599296	−	0.714213i	0.180695	−	0.215343i	0.848787	+	0.528735i	$0.177333\pi$
$12$		0			0
$13$	−0.368417	+	0.0649618i	−0.102180	+	0.0180172i	−0.224505	−	0.974473i	$-0.572076\pi$
$13$	−0.368417	+	0.0649618i	−0.102180	+	0.0180172i	0.122324	+	0.992490i	$0.460965\pi$
$14$	−3.41904	−	1.25854i	−0.913777	−	0.336358i
$15$		0			0
$16$	−3.77828	+	1.31323i	−0.944571	+	0.328308i
$17$	2.26254	+	3.91883i	0.548746	+	0.950456i	0.998361	+	0.0572337i	$0.0182280\pi$
$17$	2.26254	+	3.91883i	0.548746	+	0.950456i	−0.449615	+	0.893223i	$0.648439\pi$
$18$		0			0
$19$	1.97566	+	1.14065i	0.453246	+	0.261682i	0.709200	−	0.705007i	$-0.249056\pi$
$19$	1.97566	+	1.14065i	0.453246	+	0.261682i	−0.255954	+	0.966689i	$0.582390\pi$
$20$	0.231420	−	0.271754i	0.0517470	−	0.0607661i
$21$		0			0
$22$	−1.29932	+	0.224233i	−0.277016	+	0.0478067i
$23$	−4.40423	−	1.60301i	−0.918345	−	0.334250i	−0.160765	−	0.986993i	$-0.551396\pi$
$23$	−4.40423	−	1.60301i	−0.918345	−	0.334250i	−0.757580	+	0.652742i	$0.773618\pi$
$24$		0			0
$25$	0.862710	−	4.89267i	0.172542	−	0.978534i
$26$	0.457212	+	0.266194i	0.0896666	+	0.0522050i
$27$		0			0
$28$	2.54367	+	4.48076i	0.480709	+	0.846785i
$29$	1.58682	+	0.279799i	0.294665	+	0.0519574i	0.319026	−	0.947746i	$-0.396644\pi$
$29$	1.58682	+	0.279799i	0.294665	+	0.0519574i	−0.0243613	+	0.999703i	$0.507755\pi$
$30$		0			0
$31$	8.17965	+	2.97715i	1.46911	+	0.534712i	0.947858	−	0.318692i	$-0.103244\pi$
$31$	8.17965	+	2.97715i	1.46911	+	0.534712i	0.521250	+	0.853404i	$0.325466\pi$
$32$	5.27963	+	2.03114i	0.933315	+	0.359059i
$33$		0			0
$34$	1.13417	−	6.29812i	0.194509	−	1.08012i
$35$	−0.398177	−	0.229888i	−0.0673043	−	0.0388581i
$36$		0			0
$37$	3.82721	−	2.20964i	0.629190	−	0.363263i	−0.151248	−	0.988496i	$-0.548329\pi$
$37$	3.82721	−	2.20964i	0.629190	−	0.363263i	0.780438	+	0.625233i	$0.214996\pi$
$38$	−1.09240	−	3.03566i	−0.177210	−	0.492449i
$39$		0			0
$40$	−0.498046	+	0.0822239i	−0.0787481	+	0.0130007i
$41$	−0.238139	−	1.35055i	−0.0371910	−	0.210921i	0.960549	−	0.278110i	$-0.0897080\pi$
$41$	−0.238139	−	1.35055i	−0.0371910	−	0.210921i	−0.997740	+	0.0671892i	$0.978597\pi$
$42$		0			0
$43$	3.28437	−	3.91416i	0.500862	−	0.596904i	−0.455083	−	0.890449i	$-0.650391\pi$
$43$	3.28437	−	3.91416i	0.500862	−	0.596904i	0.955945	+	0.293545i	$0.0948350\pi$
$44$	1.60803	+	0.944066i	0.242420	+	0.142323i
$45$		0			0
$46$	3.29322	+	5.75225i	0.485558	+	0.848124i
$47$	7.70413	−	2.80407i	1.12376	−	0.409016i	0.287738	−	0.957709i	$-0.407097\pi$
$47$	7.70413	−	2.80407i	1.12376	−	0.409016i	0.836024	+	0.548693i	$0.184874\pi$
$48$		0			0
$49$	−0.278168	+	0.233411i	−0.0397383	+	0.0333444i
$50$	−5.39864	+	4.49663i	−0.763483	+	0.635919i
$51$		0			0
$52$	−0.250776	−	0.704922i	−0.0347764	−	0.0977551i
$53$		−	9.07829i		−	1.24700i	−0.781824	−	0.623500i	$-0.785710\pi$
$53$		−	9.07829i		−	1.24700i	0.781824	−	0.623500i	$-0.214290\pi$
$54$		0			0
$55$	−0.166394			−0.0224366
$56$	1.34357	−	7.16169i	0.179541	−	0.957022i
$57$		0			0
$58$	−1.45837	−	1.75092i	−0.191494	−	0.229907i
$59$	9.44865	+	11.2605i	1.23011	+	1.46599i	0.837641	+	0.546222i	$0.183934\pi$
$59$	9.44865	+	11.2605i	1.23011	+	1.46599i	0.392469	+	0.919765i	$0.371621\pi$
$60$		0			0
$61$	−5.07860	−	13.9533i	−0.650247	−	1.78654i	−0.616827	−	0.787099i	$-0.711582\pi$
$61$	−5.07860	−	13.9533i	−0.650247	−	1.78654i	−0.0334206	−	0.999441i	$-0.510640\pi$
$62$	−6.11625	−	10.6832i	−0.776765	−	1.35677i
$63$		0			0
$64$	−3.84780	−	7.01387i	−0.480975	−	0.876734i
$65$	0.0511453	+	0.0429160i	0.00634380	+	0.00532308i
$66$		0			0
$67$	−1.72274	+	0.303765i	−0.210466	+	0.0371108i	−0.277887	−	0.960614i	$-0.589634\pi$
$67$	−1.72274	+	0.303765i	−0.210466	+	0.0371108i	0.0674209	+	0.997725i	$0.478523\pi$
$68$	−6.97497	+	5.76672i	−0.845840	+	0.699318i
$69$		0			0
$70$	0.220164	+	0.611813i	0.0263146	+	0.0731256i
$71$	−2.77372	−	4.80422i	−0.329180	−	0.570156i	0.653169	−	0.757212i	$-0.273439\pi$
$71$	−2.77372	−	4.80422i	−0.329180	−	0.570156i	−0.982349	+	0.187055i	$0.940106\pi$
$72$		0			0
$73$	−4.77001	+	8.26190i	−0.558287	+	0.966982i	0.439352	+	0.898315i	$0.355208\pi$
$73$	−4.77001	+	8.26190i	−0.558287	+	0.966982i	−0.997640	+	0.0686670i	$0.978125\pi$
$74$	−6.15087	−	1.10766i	−0.715024	−	0.128762i
$75$		0			0
$76$	−1.59165	+	4.27595i	−0.182575	+	0.490486i
$77$	0.821500	−	2.25705i	0.0936186	−	0.257215i
$78$		0			0
$79$	−0.704340	+	3.99451i	−0.0792444	+	0.449417i	0.919206	+	0.393776i	$0.128831\pi$
$79$	−0.704340	+	3.99451i	−0.0792444	+	0.449417i	−0.998451	+	0.0556413i	$0.982280\pi$
$80$	0.612976	+	0.365899i	0.0685328	+	0.0409088i
$81$		0			0
$82$	−0.975822	+	1.67606i	−0.107761	+	0.185090i
$83$	15.0319	+	2.65052i	1.64996	+	0.290933i	0.919813	−	0.392357i	$-0.128340\pi$
$83$	15.0319	+	2.65052i	1.64996	+	0.290933i	0.730148	+	0.683289i	$0.239451\pi$
$84$		0			0
$85$	0.276212	−	0.758885i	0.0299594	−	0.0823126i
$86$	−7.12077	+	1.22889i	−0.767852	+	0.132514i
$87$		0			0
$88$	−0.874822	−	2.48772i	−0.0932564	−	0.265191i
$89$	−8.16359	+	14.1397i	−0.865339	+	1.49881i	0.00137211	+	0.999999i	$0.499563\pi$
$89$	−8.16359	+	14.1397i	−0.865339	+	1.49881i	−0.866711	+	0.498811i	$0.833770\pi$
$90$		0			0
$91$	−0.834643	+	0.481881i	−0.0874943	+	0.0505149i
$92$	1.69487	−	9.21926i	0.176703	−	0.961175i
$93$		0			0
$94$	−10.8808	−	4.00518i	−1.12227	−	0.413102i
$95$	−0.0706993	−	0.400955i	−0.00725359	−	0.0411372i
$96$		0			0
$97$	−8.94677	−	7.50723i	−0.908407	−	0.762244i	0.0634084	−	0.997988i	$-0.479803\pi$
$97$	−8.94677	−	7.50723i	−0.908407	−	0.762244i	−0.971815	+	0.235744i	$0.924247\pi$
$98$	0.513530	+	0.00186855i	0.0518744	+	0.000188752i
$99$		0			0
$100$	9.93603	+	0.0723083i	0.993603	+	0.00723083i
$101$	−0.733566	−	2.01546i	−0.0729926	−	0.200545i	0.897831	−	0.440340i	$-0.145142\pi$
$101$	−0.733566	−	2.01546i	−0.0729926	−	0.200545i	−0.970824	+	0.239795i	$0.922920\pi$
$102$		0			0
$103$	8.97851	−	7.53386i	0.884679	−	0.742334i	−0.0824568	−	0.996595i	$-0.526277\pi$
$103$	8.97851	−	7.53386i	0.884679	−	0.742334i	0.967136	+	0.254261i	$0.0818322\pi$
$104$	−0.372729	+	0.990294i	−0.0365491	+	0.0971063i
$105$		0			0
$106$	−8.28825	+	9.80488i	−0.805026	+	0.952334i
$107$		−	7.40373i		−	0.715745i	−0.933770	−	0.357873i	$-0.883502\pi$
$107$		−	7.40373i		−	0.715745i	0.933770	−	0.357873i	$-0.116498\pi$
$108$		0			0
$109$		−	13.2321i		−	1.26741i	−0.773575	−	0.633704i	$-0.781534\pi$
$109$		−	13.2321i		−	1.26741i	0.773575	−	0.633704i	$-0.218466\pi$
$110$	0.179712	+	0.151914i	0.0171348	+	0.0144844i
$111$		0			0
$112$	−7.98954	+	6.50824i	−0.754941	+	0.614971i
$113$	7.02588	−	5.89541i	0.660939	−	0.554594i	−0.249429	−	0.968393i	$-0.580243\pi$
$113$	7.02588	−	5.89541i	0.660939	−	0.554594i	0.910368	+	0.413799i	$0.135799\pi$
$114$		0			0
$115$	0.286088	+	0.786020i	0.0266778	+	0.0732968i
$116$	−0.0234515	+	3.22251i	−0.00217741	+	0.299203i
$117$		0			0
$118$	0.0756404	−	20.7881i	0.00696326	−	1.91370i
$119$	8.93021	+	7.49334i	0.818631	+	0.686913i
$120$		0			0
$121$	1.75919	+	9.97684i	0.159926	+	0.906985i
$122$	−7.25397	+	19.7067i	−0.656744	+	1.78416i
$123$		0			0
$124$	−3.14776	+	17.1223i	−0.282677	+	1.53762i
$125$	−1.54067	+	0.889506i	−0.137802	+	0.0795598i
$126$		0			0
$127$	−9.58464	+	16.6011i	−0.850500	+	1.47311i	0.0302583	+	0.999542i	$0.490367\pi$
$127$	−9.58464	+	16.6011i	−0.850500	+	1.47311i	−0.880758	+	0.473567i	$0.842966\pi$
$128$	−2.24772	+	11.0882i	−0.198673	+	0.980066i
$129$		0			0
$130$	−0.0160575	−	0.0930453i	−0.00140834	−	0.00816061i
$131$	0.312406	−	0.858328i	0.0272950	−	0.0749924i	−0.925297	−	0.379244i	$-0.876184\pi$
$131$	0.312406	−	0.858328i	0.0272950	−	0.0749924i	0.952592	+	0.304252i	$0.0984063\pi$
$132$		0			0
$133$	5.78780	+	1.02055i	0.501866	+	0.0884926i
$134$	2.13795	+	1.24474i	0.184691	+	0.107529i
$135$		0			0
$136$	12.7981	+	0.139708i	1.09743	+	0.0119799i
$137$	−0.995947	+	5.64830i	−0.0850895	+	0.482566i	0.912248	+	0.409639i	$0.134345\pi$
$137$	−0.995947	+	5.64830i	−0.0850895	+	0.482566i	−0.997337	+	0.0729275i	$0.976766\pi$
$138$		0			0
$139$	−7.23743	+	19.8847i	−0.613871	+	1.68660i	0.107638	+	0.994190i	$0.465671\pi$
$139$	−7.23743	+	19.8847i	−0.613871	+	1.68660i	−0.721509	+	0.692406i	$0.756551\pi$
$140$	0.320785	−	0.861784i	0.0271113	−	0.0728340i
$141$		0			0
$142$	−1.39042	+	7.72107i	−0.116681	+	0.647938i
$143$	−0.174394	+	0.302060i	−0.0145836	+	0.0252595i
$144$		0			0
$145$	−0.143784	−	0.249041i	−0.0119406	−	0.0206817i
$146$	12.6947	−	4.56824i	1.05062	−	0.378071i
$147$		0			0
$148$	5.63190	+	6.81190i	0.462939	+	0.559935i
$149$	−7.83652	+	1.38179i	−0.641992	+	0.113201i	−0.485161	−	0.874425i	$-0.661239\pi$
$149$	−7.83652	+	1.38179i	−0.641992	+	0.113201i	−0.156831	+	0.987625i	$0.550128\pi$
$150$		0			0
$151$	−2.04551	−	1.71638i	−0.166461	−	0.139677i	0.555752	−	0.831348i	$-0.312430\pi$
$151$	−2.04551	−	1.71638i	−0.166461	−	0.139677i	−0.722213	+	0.691671i	$0.756875\pi$
$152$	5.62288	−	3.16504i	0.456076	−	0.256719i
$153$		0			0
$154$	−2.94788	+	1.68769i	−0.237547	+	0.135998i
$155$	−0.531330	−	1.45982i	−0.0426775	−	0.117255i
$156$		0			0
$157$	7.93100	+	9.45180i	0.632963	+	0.754336i	0.983241	−	0.182310i	$-0.0583574\pi$
$157$	7.93100	+	9.45180i	0.632963	+	0.754336i	−0.350278	+	0.936646i	$0.613913\pi$
$158$	4.40760	−	3.67117i	0.350650	−	0.292062i
$159$		0			0
$160$	−0.327980	−	0.954816i	−0.0259291	−	0.0754848i
$161$	−12.0744			−0.951597
$162$		0			0
$163$			13.6508i			1.06922i	0.845100	+	0.534608i	$0.179541\pi$
$163$			13.6508i			1.06922i	−0.845100	+	0.534608i	$0.820459\pi$
$164$	2.58412	−	0.919303i	0.201786	−	0.0717855i
$165$		0			0
$166$	−13.8151	−	16.5864i	−1.07226	−	1.28735i
$167$	3.21110	−	2.69443i	0.248482	−	0.208502i	−0.510036	−	0.860153i	$-0.670368\pi$
$167$	3.21110	−	2.69443i	0.248482	−	0.208502i	0.758519	+	0.651651i	$0.225924\pi$
$168$		0			0
$169$	−12.0845	+	4.39840i	−0.929576	+	0.338338i
$170$	−0.991161	+	0.567449i	−0.0760186	+	0.0435213i
$171$		0			0
$172$	8.81262	+	5.17384i	0.671956	+	0.394502i
$173$	−12.8781	+	15.3475i	−0.979103	+	1.16685i	0.00687524	+	0.999976i	$0.497812\pi$
$173$	−12.8781	+	15.3475i	−0.979103	+	1.16685i	−0.985978	+	0.166873i	$0.946633\pi$
$174$		0			0
$175$	−2.22253	−	12.6046i	−0.168007	−	0.952816i
$176$	−1.32638	+	3.48551i	−0.0999799	+	0.262730i
$177$		0			0
$178$	21.7262	−	7.81828i	1.62845	−	0.586005i
$179$	−6.96829	+	4.02315i	−0.520835	+	0.300704i	−0.737276	−	0.675592i	$-0.763888\pi$
$179$	−6.96829	+	4.02315i	−0.520835	+	0.300704i	0.216441	+	0.976296i	$0.430555\pi$
$180$		0			0
$181$	−6.99841	−	4.04053i	−0.520188	−	0.300331i	0.216824	−	0.976211i	$-0.430430\pi$
$181$	−6.99841	−	4.04053i	−0.520188	−	0.300331i	−0.737011	+	0.675880i	$0.763764\pi$
$182$	1.34139	+	0.241559i	0.0994304	+	0.0179055i
$183$		0			0
$184$	−10.2475	+	8.40976i	−0.755454	+	0.619976i
$185$	−0.741143	−	0.269754i	−0.0544899	−	0.0198327i
$186$		0			0
$187$	4.15481	+	0.732605i	0.303830	+	0.0535734i
$188$	8.09501	+	14.2596i	0.590389	+	1.03999i
$189$		0			0
$190$	−0.289705	+	0.497593i	−0.0210174	+	0.0360992i
$191$	−2.88972	+	16.3884i	−0.209093	+	1.18582i	0.681776	+	0.731561i	$0.261208\pi$
$191$	−2.88972	+	16.3884i	−0.209093	+	1.18582i	−0.890868	+	0.454262i	$0.849903\pi$
$192$		0			0
$193$	−0.775835	−	0.282381i	−0.0558458	−	0.0203262i	0.313946	−	0.949441i	$-0.398349\pi$
$193$	−0.775835	−	0.282381i	−0.0558458	−	0.0203262i	−0.369792	+	0.929115i	$0.620571\pi$
$194$	2.80892	+	16.2763i	0.201668	+	1.16857i
$195$		0			0
$196$	−0.552925	−	0.470858i	−0.0394946	−	0.0336327i
$197$	−13.0620	−	7.54137i	−0.930632	−	0.537301i	−0.0436205	−	0.999048i	$-0.513889\pi$
$197$	−13.0620	−	7.54137i	−0.930632	−	0.537301i	−0.887011	+	0.461748i	$0.847223\pi$
$198$		0			0
$199$	−7.77810	−	13.4721i	−0.551375	−	0.955009i	−0.998176	−	0.0603759i	$-0.980770\pi$
$199$	−7.77810	−	13.4721i	−0.551375	−	0.955009i	0.446801	−	0.894633i	$-0.352563\pi$
$200$	−10.6653	−	9.14944i	−0.754147	−	0.646963i
$201$		0			0
$202$	−1.04778	+	2.84649i	−0.0737218	+	0.200279i
$203$	4.08799	−	0.720823i	0.286921	−	0.0505918i
$204$		0			0
$205$	−0.157323	+	0.187490i	−0.0109879	+	0.0130949i
$206$	−16.5753	−	0.0603118i	−1.15486	−	0.00420212i
$207$		0			0
$208$	1.30667	−	0.729260i	0.0906015	−	0.0505651i
$209$	1.99867	−	0.727455i	0.138251	−	0.0503191i
$210$		0			0
$211$	−3.55232	−	4.23349i	−0.244552	−	0.291445i	0.629781	−	0.776773i	$-0.283145\pi$
$211$	−3.55232	−	4.23349i	−0.244552	−	0.291445i	−0.874332	+	0.485328i	$0.838700\pi$
$212$	17.9032	−	3.02265i	1.22960	−	0.207597i
$213$		0			0
$214$	−6.75942	+	7.99629i	−0.462064	+	0.546615i
$215$	−0.911903			−0.0621913
$216$		0			0
$217$	22.4249			1.52230
$218$	−12.0806	+	14.2912i	−0.818202	+	0.967920i
$219$		0			0
$220$	−0.0554016	−	0.328144i	−0.00373517	−	0.0221235i
$221$	−1.08813	−	1.29679i	−0.0731957	−	0.0872312i
$222$		0			0
$223$	4.91216	−	1.78788i	0.328942	−	0.119725i	−0.172269	−	0.985050i	$-0.555110\pi$
$223$	4.91216	−	1.78788i	0.328942	−	0.119725i	0.501212	+	0.865325i	$0.332888\pi$
$224$	14.5709	+	0.265119i	0.973556	+	0.0177140i
$225$		0			0
$226$	−12.9706	−	0.0471953i	−0.862789	−	0.00313938i
$227$	−5.65872	+	6.74381i	−0.375583	+	0.447602i	−0.920415	−	0.390943i	$-0.872149\pi$
$227$	−5.65872	+	6.74381i	−0.375583	+	0.447602i	0.544832	+	0.838545i	$0.316593\pi$
$228$		0			0
$229$	−8.50987	+	1.50052i	−0.562348	+	0.0991572i	−0.447594	−	0.894237i	$-0.647719\pi$
$229$	−8.50987	+	1.50052i	−0.562348	+	0.0991572i	−0.114754	+	0.993394i	$0.536608\pi$
$230$	0.408632	−	1.11012i	0.0269444	−	0.0731992i
$231$		0			0
$232$	2.96740	−	3.45902i	0.194820	−	0.227096i
$233$	0.420645	+	0.728579i	0.0275574	+	0.0477308i	0.879475	−	0.475945i	$-0.157894\pi$
$233$	0.420645	+	0.728579i	0.0275574	+	0.0477308i	−0.851918	+	0.523676i	$0.824560\pi$
$234$		0			0
$235$	−1.26716	−	0.731597i	−0.0826606	−	0.0477241i
$236$	−19.0607	+	22.3828i	−1.24075	+	1.45700i
$237$		0			0
$238$	−2.80372	−	16.2461i	−0.181738	−	1.05308i
$239$	−12.9749	−	4.72248i	−0.839276	−	0.305472i	−0.113616	−	0.993525i	$-0.536243\pi$
$239$	−12.9749	−	4.72248i	−0.839276	−	0.305472i	−0.725660	+	0.688053i	$0.758466\pi$
$240$		0			0
$241$	2.61837	−	14.8495i	0.168664	−	0.956542i	−0.776541	−	0.630066i	$-0.783028\pi$
$241$	2.61837	−	14.8495i	0.168664	−	0.956542i	0.945206	−	0.326476i	$-0.105861\pi$
$242$	7.20862	−	12.3814i	0.463387	−	0.795908i
$243$		0			0
$244$	25.8263	−	14.6613i	1.65336	−	0.938591i
$245$	0.0638218	+	0.0112535i	0.00407743	+	0.000718960i
$246$		0			0
$247$	−0.801963	−	0.291891i	−0.0510277	−	0.0185726i
$248$	19.0319	−	15.6188i	1.20853	−	0.991797i
$249$		0			0
$250$	2.47607	+	0.445894i	0.156601	+	0.0282008i
$251$	−9.73582	−	5.62098i	−0.614520	−	0.354793i	0.160213	−	0.987083i	$-0.448782\pi$
$251$	−9.73582	−	5.62098i	−0.614520	−	0.354793i	−0.774732	+	0.632289i	$0.782115\pi$
$252$		0			0
$253$	−3.78432	+	2.18488i	−0.237918	+	0.137362i
$254$	25.5081	−	9.17923i	1.60052	−	0.575956i
$255$		0			0
$256$	12.5509	−	9.92351i	0.784428	−	0.620220i
$257$	−1.23538	−	7.00619i	−0.0770609	−	0.437034i	−0.998789	−	0.0491976i	$-0.984334\pi$
$257$	−1.23538	−	7.00619i	−0.0770609	−	0.437034i	0.921728	−	0.387837i	$-0.126778\pi$
$258$		0			0
$259$	7.31815	−	8.72143i	0.454728	−	0.541923i
$260$	−0.0676053	+	0.115152i	−0.00419270	+	0.00714144i
$261$		0			0
$262$	−1.12104	+	0.641806i	−0.0692581	+	0.0396509i
$263$	18.0450	−	6.56783i	1.11270	−	0.404990i	0.280717	−	0.959790i	$-0.409428\pi$
$263$	18.0450	−	6.56783i	1.11270	−	0.404990i	0.831983	+	0.554801i	$0.187205\pi$
$264$		0			0
$265$	−1.24114	+	1.04144i	−0.0762429	+	0.0639754i
$266$	−5.31930	−	6.38635i	−0.326147	−	0.391572i
$267$		0			0
$268$	−1.17265	−	3.29626i	−0.0716307	−	0.201351i
$269$			16.5198i			1.00723i	0.863928	+	0.503616i	$0.167997\pi$
$269$			16.5198i			1.00723i	−0.863928	+	0.503616i	$0.832003\pi$
$270$		0			0
$271$	−1.17854			−0.0715913			−0.0357956	−	0.999359i	$-0.511397\pi$
$271$	−1.17854			−0.0715913			−0.0357956	+	0.999359i	$0.511397\pi$
$272$	−13.6948	−	11.8352i	−0.830372	−	0.717616i
$273$		0			0
$274$	6.23241	−	5.19109i	0.376514	−	0.313605i
$275$	−2.97739	−	3.54832i	−0.179543	−	0.213972i
$276$		0			0
$277$	7.87030	+	21.6235i	0.472880	+	1.29923i	0.915428	+	0.402483i	$0.131853\pi$
$277$	7.87030	+	21.6235i	0.472880	+	1.29923i	−0.442547	+	0.896745i	$0.645925\pi$
$278$	25.9709	−	14.8686i	1.55763	−	0.891757i
$279$		0			0
$280$	−1.13325	+	0.637889i	−0.0677244	+	0.0381212i
$281$	−16.4336	−	13.7895i	−0.980348	−	0.822610i	0.00379366	−	0.999993i	$-0.498792\pi$
$281$	−16.4336	−	13.7895i	−0.980348	−	0.822610i	−0.984142	+	0.177383i	$0.943237\pi$
$282$		0			0
$283$	0.339199	−	0.0598100i	0.0201633	−	0.00355534i	−0.163557	−	0.986534i	$-0.552297\pi$
$283$	0.339199	−	0.0598100i	0.0201633	−	0.00355534i	0.183721	+	0.982978i	$0.441186\pi$
$284$	8.55084	−	7.06961i	0.507399	−	0.419504i
$285$		0			0
$286$	0.464125	−	0.167018i	0.0274443	−	0.00987596i
$287$	−1.76649	−	3.05966i	−0.104273	−	0.180606i
$288$		0			0
$289$	−1.73816	+	3.01059i	−0.102245	+	0.177093i
$290$	−0.0720765	+	0.400244i	−0.00423248	+	0.0235032i
$291$		0			0
$292$	−17.8814	−	6.65606i	−1.04643	−	0.389516i
$293$	9.01139	−	24.7586i	0.526451	−	1.44641i	−0.336770	−	0.941587i	$-0.609335\pi$
$293$	9.01139	−	24.7586i	0.526451	−	1.44641i	0.863221	−	0.504826i	$-0.168443\pi$
$294$		0			0
$295$	0.455551	−	2.58356i	0.0265232	−	0.150420i
$296$	0.136442	−	12.4989i	0.00793051	−	0.726482i
$297$		0			0
$298$	9.72525	+	5.66216i	0.563369	+	0.328000i
$299$	1.72673	+	0.304468i	0.0998591	+	0.0176079i
$300$		0			0
$301$	4.50213	−	12.3695i	0.259499	−	0.712967i
$302$	0.642205	+	3.72125i	0.0369547	+	0.214134i
$303$		0			0
$304$	−8.96252	−	1.71519i	−0.514036	−	0.0983729i
$305$	−1.32503	+	2.29502i	−0.0758711	+	0.131413i
$306$		0			0
$307$	−14.2917	+	8.25134i	−0.815673	+	0.470929i	−0.848922	−	0.528518i	$-0.822748\pi$
$307$	−14.2917	+	8.25134i	−0.815673	+	0.470929i	0.0332493	+	0.999447i	$0.489414\pi$
$308$	4.72463	+	0.868578i	0.269211	+	0.0494918i
$309$		0			0
$310$	−0.758922	+	2.06175i	−0.0431039	+	0.117099i
$311$	−3.58763	−	20.3464i	−0.203436	−	1.15374i	−0.899882	−	0.436133i	$-0.856348\pi$
$311$	−3.58763	−	20.3464i	−0.203436	−	1.15374i	0.696447	−	0.717609i	$-0.254763\pi$
$312$		0			0
$313$	−9.65918	−	8.10501i	−0.545969	−	0.458122i	0.327604	−	0.944815i	$-0.393759\pi$
$313$	−9.65918	−	8.10501i	−0.545969	−	0.458122i	−0.873573	+	0.486693i	$0.838203\pi$
$314$	0.0634910	−	17.4491i	0.00358300	−	0.984709i
$315$		0			0
$316$	−8.11205	−	0.0590345i	−0.456338	−	0.00332095i
$317$	−4.18467	−	11.4973i	−0.235034	−	0.645752i	−0.999999	−	0.00167879i	$-0.999466\pi$
$317$	−4.18467	−	11.4973i	−0.235034	−	0.645752i	0.764964	−	0.644073i	$-0.222757\pi$
$318$		0			0
$319$	1.15081	−	0.965645i	0.0644331	−	0.0540658i
$320$	−0.517493	+	1.33067i	−0.0289288	+	0.0743868i
$321$		0			0
$322$	13.0408	+	11.0236i	0.726735	+	0.614323i
$323$			10.3230i			0.574388i
$324$		0			0
$325$			1.85859i			0.103096i
$326$	12.4629	−	14.7434i	0.690254	−	0.816561i
$327$		0			0
$328$	−3.63024	−	1.36636i	−0.200447	−	0.0754445i
$329$	16.1798	−	13.5765i	0.892022	−	0.748495i
$330$		0			0
$331$	6.93586	+	19.0561i	0.381230	+	1.04742i	0.970839	+	0.239731i	$0.0770593\pi$
$331$	6.93586	+	19.0561i	0.381230	+	1.04742i	−0.589610	+	0.807688i	$0.700718\pi$
$332$	−0.222154	+	30.5267i	−0.0121923	+	1.67537i
$333$		0			0
$334$	−5.92805	−	0.0215701i	−0.324369	−	0.00118026i
$335$	0.239159	+	0.200678i	0.0130666	+	0.0109642i
$336$		0			0
$337$	2.99094	+	16.9625i	0.162927	+	0.924006i	0.951176	+	0.308649i	$0.0998769\pi$
$337$	2.99094	+	16.9625i	0.162927	+	0.924006i	−0.788249	+	0.615357i	$0.789012\pi$
$338$	17.0673	+	6.28241i	0.928339	+	0.341718i
$339$		0			0
$340$	1.58856	+	0.292041i	0.0861515	+	0.0158381i
$341$	7.02835	−	4.05782i	0.380606	−	0.219743i
$342$		0			0
$343$	−9.48449	+	16.4276i	−0.512114	+	0.887008i
$344$	−4.79436	−	13.6336i	−0.258495	−	0.735076i
$345$		0			0
$346$	27.9207	−	4.81849i	1.50103	−	0.259043i
$347$	−2.18170	+	5.99416i	−0.117120	+	0.321783i	−0.984376	−	0.176078i	$-0.943659\pi$
$347$	−2.18170	+	5.99416i	−0.117120	+	0.321783i	0.867257	+	0.497861i	$0.165881\pi$
$348$		0			0
$349$	−13.1972	−	2.32702i	−0.706430	−	0.124563i	−0.191120	−	0.981567i	$-0.561212\pi$
$349$	−13.1972	−	2.32702i	−0.706430	−	0.124563i	−0.515310	+	0.857004i	$0.672323\pi$
$350$	−9.10725	+	15.6425i	−0.486803	+	0.836126i
$351$		0			0
$352$	4.61473	−	2.55352i	0.245966	−	0.136103i
$353$	1.95983	−	11.1147i	0.104311	−	0.591577i	−0.887182	−	0.461419i	$-0.847340\pi$
$353$	1.95983	−	11.1147i	0.104311	−	0.591577i	0.991493	−	0.130158i	$-0.0415484\pi$
$354$		0			0
$355$	−0.338617	+	0.930342i	−0.0179719	+	0.0493774i
$356$	−30.6030	−	11.3915i	−1.62195	−	0.603746i
$357$		0			0
$358$	11.1990	+	2.01674i	0.591888	+	0.106588i
$359$	13.5862	−	23.5320i	0.717053	−	1.24197i	−0.245109	−	0.969495i	$-0.578824\pi$
$359$	13.5862	−	23.5320i	0.717053	−	1.24197i	0.962162	−	0.272477i	$-0.0878428\pi$
$360$		0			0
$361$	−6.89786	−	11.9474i	−0.363045	−	0.628813i
$362$	3.86963	+	10.7533i	0.203383	+	0.565181i
$363$		0			0
$364$	−1.22821	−	1.48555i	−0.0643757	−	0.0778638i
$365$	1.67674	−	0.295654i	0.0877644	−	0.0154752i
$366$		0			0
$367$	17.5436	+	14.7209i	0.915771	+	0.768423i	0.973208	−	0.229926i	$-0.0738485\pi$
$367$	17.5436	+	14.7209i	0.915771	+	0.768423i	−0.0574375	+	0.998349i	$0.518293\pi$
$368$	18.7455	+	0.272851i	0.977179	+	0.0142234i
$369$		0			0
$370$	0.554182	+	0.967988i	0.0288105	+	0.0503233i
$371$	−7.99904	−	21.9772i	−0.415289	−	1.14100i
$372$		0			0
$373$	18.2082	+	21.6997i	0.942786	+	1.12357i	0.992183	+	0.124790i	$0.0398257\pi$
$373$	18.2082	+	21.6997i	0.942786	+	1.12357i	−0.0493967	+	0.998779i	$0.515730\pi$
$374$	−3.81849	−	4.58448i	−0.197450	−	0.237058i
$375$		0			0
$376$	4.27577	−	22.7914i	0.220506	−	1.17538i
$377$	−0.602788			−0.0310451
$378$		0			0
$379$		−	9.20463i		−	0.472810i	−0.971655	−	0.236405i	$-0.924031\pi$
$379$		−	9.20463i		−	0.472810i	0.971655	−	0.236405i	$-0.0759692\pi$
$380$	0.767181	−	0.272925i	0.0393556	−	0.0140008i
$381$		0			0
$382$	18.0832	−	15.0618i	0.925217	−	0.770630i
$383$	−18.0654	+	15.1587i	−0.923100	+	0.774573i	−0.974566	−	0.224102i	$-0.928055\pi$
$383$	−18.0654	+	15.1587i	−0.923100	+	0.774573i	0.0514658	+	0.998675i	$0.483611\pi$
$384$		0			0
$385$	−0.402815	+	0.146613i	−0.0205294	+	0.00747207i
$386$	0.580123	+	1.01330i	0.0295275	+	0.0515756i
$387$		0			0
$388$	11.8261	−	20.1434i	0.600378	−	1.02263i
$389$	−19.3453	+	23.0548i	−0.980844	+	1.16892i	0.00478250	+	0.999989i	$0.498478\pi$
$389$	−19.3453	+	23.0548i	−0.980844	+	1.16892i	−0.985627	+	0.168936i	$0.945967\pi$
$390$		0			0
$391$	−3.68282	−	20.8863i	−0.186248	−	1.05627i
$392$	0.167297	+	1.01335i	0.00844977	+	0.0511819i
$393$		0			0
$394$	7.22239	+	20.0703i	0.363859	+	1.01113i
$395$	0.626912	−	0.361948i	0.0315434	−	0.0182116i
$396$		0			0
$397$	−15.4854	−	8.94051i	−0.777191	−	0.448711i	0.0582431	−	0.998302i	$-0.481450\pi$
$397$	−15.4854	−	8.94051i	−0.777191	−	0.448711i	−0.835434	+	0.549591i	$0.814783\pi$
$398$	−3.89903	+	21.6515i	−0.195441	+	1.08529i
$399$		0			0
$400$	3.16564	+	19.6188i	0.158282	+	0.980942i
$401$	9.33220	+	3.39664i	0.466028	+	0.169620i	0.564352	−	0.825534i	$-0.309126\pi$
$401$	9.33220	+	3.39664i	0.466028	+	0.169620i	−0.0983243	+	0.995154i	$0.531348\pi$
$402$		0			0
$403$	−3.20692	−	0.565467i	−0.159748	−	0.0281679i
$404$	3.73042	−	2.11771i	0.185595	−	0.105360i
$405$		0			0
$406$	−5.07327	−	2.95372i	−0.251782	−	0.146590i
$407$	0.715477	−	4.05767i	0.0354649	−	0.201131i
$408$		0			0
$409$	−5.20287	−	1.89369i	−0.257265	−	0.0936369i	0.210168	−	0.977665i	$-0.432599\pi$
$409$	−5.20287	−	1.89369i	−0.257265	−	0.0936369i	−0.467433	+	0.884028i	$0.654821\pi$
$410$	0.341088	−	0.0588641i	0.0168451	−	0.00290709i
$411$		0			0
$412$	17.8469	+	15.1980i	0.879253	+	0.748752i
$413$	32.7955	+	18.9345i	1.61376	+	0.931706i
$414$		0			0
$415$	−1.36206	−	2.35915i	−0.0668608	−	0.115806i
$416$	−2.07705	−	0.405333i	−0.101836	−	0.0198731i
$417$		0			0
$418$	−2.82278	−	1.03905i	−0.138067	−	0.0508218i
$419$	4.02902	−	0.710424i	0.196830	−	0.0347065i	−0.0743638	−	0.997231i	$-0.523693\pi$
$419$	4.02902	−	0.710424i	0.196830	−	0.0347065i	0.271194	+	0.962525i	$0.412581\pi$
$420$		0			0
$421$	−15.7920	+	18.8201i	−0.769653	+	0.917237i	−0.998417	−	0.0562453i	$-0.982087\pi$
$421$	−15.7920	+	18.8201i	−0.769653	+	0.917237i	0.228764	+	0.973482i	$0.426532\pi$
$422$	−0.0284378	+	7.81549i	−0.00138433	+	0.380452i
$423$		0			0
$424$	−22.0957	−	13.0806i	−1.07306	−	0.635251i
$425$	21.1255	−	7.68904i	1.02474	−	0.372973i
$426$		0			0
$427$	−24.5890	−	29.3041i	−1.18995	−	1.41812i
$428$	14.6008	−	2.46510i	0.705757	−	0.119155i
$429$		0			0
$430$	0.984888	+	0.832545i	0.0474955	+	0.0401489i
$431$	−14.0058			−0.674635			−0.337318	−	0.941391i	$-0.609520\pi$
$431$	−14.0058			−0.674635			−0.337318	+	0.941391i	$0.609520\pi$
$432$		0			0
$433$	12.4899			0.600227			0.300113	−	0.953904i	$-0.402976\pi$
$433$	12.4899			0.600227			0.300113	+	0.953904i	$0.402976\pi$
$434$	−24.2197	−	20.4734i	−1.16258	−	0.982754i
$435$		0			0
$436$	26.0950	−	4.40569i	1.24972	−	0.210994i
$437$	−6.87277	−	8.19065i	−0.328769	−	0.391812i
$438$		0			0
$439$	−10.1446	+	3.69232i	−0.484174	+	0.176225i	−0.572562	−	0.819861i	$-0.694050\pi$
$439$	−10.1446	+	3.69232i	−0.484174	+	0.176225i	0.0883886	+	0.996086i	$0.471828\pi$
$440$	−0.239752	+	0.404988i	−0.0114297	+	0.0193070i
$441$		0			0
$442$	−0.00871096	+	2.39401i	−0.000414338	+	0.113872i
$443$	−18.6993	+	22.2849i	−0.888430	+	1.05879i	0.109469	+	0.993990i	$0.465085\pi$
$443$	−18.6993	+	22.2849i	−0.888430	+	1.05879i	−0.997898	+	0.0647991i	$0.979359\pi$
$444$		0			0
$445$	2.86963	−	0.505994i	0.136034	−	0.0239864i
$446$	−6.93759	−	2.55370i	−0.328504	−	0.120921i
$447$		0			0
$448$	−15.4950	−	13.5892i	−0.732070	−	0.642027i
$449$	15.0485	+	26.0648i	0.710184	+	1.23007i	0.964788	+	0.263029i	$0.0847216\pi$
$449$	15.0485	+	26.0648i	0.710184	+	1.23007i	−0.254604	+	0.967045i	$0.581945\pi$
$450$		0			0
$451$	−1.10730	−	0.639299i	−0.0521406	−	0.0301034i
$452$	13.9656	+	11.8928i	0.656886	+	0.559389i
$453$		0			0
$454$	12.2685	−	2.11728i	0.575792	−	0.0993687i
$455$	0.161629	+	0.0588282i	0.00757729	+	0.00275791i
$456$		0			0
$457$	2.71160	−	15.3782i	0.126843	−	0.719363i	−0.853353	−	0.521334i	$-0.825435\pi$
$457$	2.71160	−	15.3782i	0.126843	−	0.719363i	0.980196	−	0.198029i	$-0.0634542\pi$
$458$	10.5609	+	6.14868i	0.493479	+	0.287309i
$459$		0			0
$460$	−1.45485	+	0.825900i	−0.0678327	+	0.0385078i
$461$	12.7088	+	2.24090i	0.591908	+	0.104369i	0.461575	−	0.887101i	$-0.347284\pi$
$461$	12.7088	+	2.24090i	0.591908	+	0.104369i	0.130332	+	0.991470i	$0.458396\pi$
$462$		0			0
$463$	32.6243	+	11.8743i	1.51618	+	0.551845i	0.960191	−	0.279345i	$-0.0901172\pi$
$463$	32.6243	+	11.8743i	1.51618	+	0.551845i	0.555990	+	0.831189i	$0.312339\pi$
$464$	−6.36290	+	1.02670i	−0.295390	+	0.0476634i
$465$		0			0
$466$	0.210862	−	1.17093i	0.00976801	−	0.0542423i
$467$	−12.4213	−	7.17141i	−0.574787	−	0.331853i	0.184272	−	0.982875i	$-0.441007\pi$
$467$	−12.4213	−	7.17141i	−0.574787	−	0.331853i	−0.759059	+	0.651022i	$0.774341\pi$
$468$		0			0
$469$	−3.90284	+	2.25330i	−0.180216	+	0.104048i
$470$	0.700651	+	1.94704i	0.0323186	+	0.0898102i
$471$		0			0
$472$	41.0212	−	6.77230i	1.88815	−	0.311720i
$473$	−0.827235	−	4.69148i	−0.0380363	−	0.215715i
$474$		0			0
$475$	7.28522	−	8.68219i	0.334269	−	0.398366i
$476$	−11.8042	+	20.1061i	−0.541044	+	0.921563i
$477$		0			0
$478$	9.70185	+	16.9462i	0.443752	+	0.775101i
$479$	−0.567163	+	0.206430i	−0.0259143	+	0.00943204i	−0.354945	−	0.934887i	$-0.615500\pi$
$479$	−0.567163	+	0.206430i	−0.0259143	+	0.00943204i	0.329030	+	0.944319i	$0.393278\pi$
$480$		0			0
$481$	−1.26647	+	1.06269i	−0.0577459	+	0.0484546i
$482$	−16.3852	+	13.6475i	−0.746324	+	0.621627i
$483$		0			0
$484$	−19.0895	+	6.79110i	−0.867704	+	0.308686i
$485$			2.08438i			0.0946467i
$486$		0			0
$487$	−22.8735			−1.03650			−0.518249	−	0.855230i	$-0.673416\pi$
$487$	−22.8735			−1.03650			−0.518249	+	0.855230i	$0.673416\pi$
$488$	−41.2787	−	7.74406i	−1.86860	−	0.350557i
$489$		0			0
$490$	−0.0586557	−	0.0704219i	−0.00264979	−	0.00318134i
$491$	−5.76980	−	6.87618i	−0.260387	−	0.310318i	0.619973	−	0.784623i	$-0.287144\pi$
$491$	−5.76980	−	6.87618i	−0.260387	−	0.310318i	−0.880360	+	0.474306i	$0.842699\pi$
$492$		0			0
$493$	2.49376	+	6.85154i	0.112313	+	0.308578i
$494$	0.599660	+	1.04742i	0.0269800	+	0.0471259i
$495$		0			0
$496$	−34.8147	−	0.506747i	−1.56323	−	0.0227536i
$497$	−10.9478	−	9.18633i	−0.491078	−	0.412063i
$498$		0			0
$499$	43.2976	−	7.63454i	1.93827	−	0.341769i	0.938276	−	0.345886i	$-0.112422\pi$
$499$	43.2976	−	7.63454i	1.93827	−	0.341769i	0.999992	+	0.00411738i	$0.00131061\pi$
$500$	−2.26716	−	2.74217i	−0.101390	−	0.122634i
$501$		0			0
$502$	5.38322	+	14.9594i	0.240265	+	0.667671i
$503$	−8.29388	−	14.3654i	−0.369806	−	0.640523i	0.619729	−	0.784816i	$-0.287242\pi$
$503$	−8.29388	−	14.3654i	−0.369806	−	0.640523i	−0.989535	+	0.144293i	$0.953909\pi$
$504$		0			0
$505$	−0.191391	+	0.331499i	−0.00851679	+	0.0147515i
$506$	6.08195	+	1.09524i	0.270376	+	0.0486895i
$507$		0			0
$508$	−35.9301	−	13.3744i	−1.59414	−	0.593393i
$509$	−9.18363	+	25.2318i	−0.407057	+	1.11838i	0.551672	+	0.834061i	$0.313990\pi$
$509$	−9.18363	+	25.2318i	−0.407057	+	1.11838i	−0.958730	+	0.284320i	$0.908232\pi$
$510$		0			0
$511$	−4.26777	+	24.2037i	−0.188795	+	1.07071i
$512$	−22.6153	−	0.740862i	−0.999464	−	0.0327418i
$513$		0			0
$514$	−5.06222	+	8.69481i	−0.223285	+	0.383512i
$515$	−2.05999	−	0.363232i	−0.0907742	−	0.0160059i
$516$		0			0
$517$	2.61435	−	7.18286i	0.114979	−	0.315902i
$518$	−15.8663	+	2.73817i	−0.697126	+	0.120308i
$519$		0			0
$520$	0.178147	−	0.0626467i	0.00781228	−	0.00274724i
$521$	−1.11230	+	1.92655i	−0.0487306	+	0.0844039i	−0.889362	−	0.457204i	$-0.848851\pi$
$521$	−1.11230	+	1.92655i	−0.0487306	+	0.0844039i	0.840631	+	0.541608i	$0.182184\pi$
$522$		0			0
$523$	3.08920	−	1.78355i	0.135081	−	0.0779892i	−0.430937	−	0.902382i	$-0.641817\pi$
$523$	3.08920	−	1.78355i	0.135081	−	0.0779892i	0.566018	+	0.824393i	$0.308483\pi$
$524$	1.79672	+	0.330309i	0.0784899	+	0.0144296i
$525$		0			0
$526$	−25.4855	−	9.38111i	−1.11122	−	0.409036i
$527$	6.83983	+	38.7906i	0.297948	+	1.68974i
$528$		0			0
$529$	−0.791437	−	0.664094i	−0.0344103	−	0.0288737i
$530$	2.29129	+	0.00833720i	0.0995274	+	0.000362145i
$531$		0			0
$532$	−0.0855374	+	11.7539i	−0.00370852	+	0.509595i
$533$	0.175469	+	0.482096i	0.00760039	+	0.0208819i
$534$		0			0
$535$	−1.01220	+	0.849341i	−0.0437614	+	0.0367202i
$536$	−1.74290	+	4.63067i	−0.0752819	+	0.200015i
$537$		0			0
$538$	15.0822	−	17.8420i	0.650239	−	0.769224i
$539$			0.338554i			0.0145825i
$540$		0			0
$541$			16.0298i			0.689174i	0.938754	+	0.344587i	$0.111981\pi$
$541$			16.0298i			0.689174i	−0.938754	+	0.344587i	$0.888019\pi$
$542$	1.27287	+	1.07598i	0.0546743	+	0.0462172i
$543$		0			0
$544$	3.98566	+	25.2855i	0.170884	+	1.08411i
$545$	−1.80904	+	1.51796i	−0.0774907	+	0.0650224i
$546$		0			0
$547$	−11.0856	−	30.4574i	−0.473985	−	1.30226i	−0.914525	−	0.404530i	$-0.867435\pi$
$547$	−11.0856	−	30.4574i	−0.473985	−	1.30226i	0.440539	−	0.897733i	$-0.354787\pi$
$548$	−11.4706	−	0.0834756i	−0.489998	−	0.00356590i
$549$		0			0
$550$	−0.0238353	+	6.55059i	−0.00101634	+	0.279318i
$551$	2.81586	+	2.36279i	0.119960	+	0.100658i
$552$		0			0
$553$	1.81453	+	10.2907i	0.0771616	+	0.437605i
$554$	11.2415	−	30.5395i	0.477605	−	1.29750i
$555$		0			0
$556$	−41.6241	−	7.65219i	−1.76526	−	0.324525i
$557$	29.5913	−	17.0845i	1.25382	−	0.723895i	0.281956	−	0.959427i	$-0.409017\pi$
$557$	29.5913	−	17.0845i	1.25382	−	0.723895i	0.971867	+	0.235532i	$0.0756833\pi$
$558$		0			0
$559$	−0.955747	+	1.65540i	−0.0404238	+	0.0700160i
$560$	1.80632	+	0.345683i	0.0763311	+	0.0146078i
$561$		0			0
$562$	5.15948	+	29.8966i	0.217640	+	1.26111i
$563$	−2.63340	+	7.23520i	−0.110984	+	0.304927i	−0.982734	−	0.185025i	$-0.940763\pi$
$563$	−2.63340	+	7.23520i	−0.110984	+	0.304927i	0.871749	+	0.489952i	$0.162986\pi$
$564$		0			0
$565$	−1.61199	−	0.284237i	−0.0678169	−	0.0119580i
$566$	−0.420952	−	0.245084i	−0.0176939	−	0.0103016i
$567$		0			0
$568$	−15.6896	−	0.171273i	−0.658321	−	0.00718644i
$569$	−2.70678	+	15.3509i	−0.113474	+	0.643544i	0.874020	+	0.485890i	$0.161504\pi$
$569$	−2.70678	+	15.3509i	−0.113474	+	0.643544i	−0.987494	+	0.157654i	$0.949607\pi$
$570$		0			0
$571$	7.83178	−	21.5176i	0.327750	−	0.900485i	−0.660930	−	0.750447i	$-0.729838\pi$
$571$	7.83178	−	21.5176i	0.327750	−	0.900485i	0.988680	−	0.150038i	$-0.0479396\pi$
$572$	−0.653754	−	0.243349i	−0.0273348	−	0.0101749i
$573$		0			0
$574$	−0.885513	+	4.91730i	−0.0369606	+	0.205244i
$575$	−11.6426	+	20.1655i	−0.485528	+	0.840960i
$576$		0			0
$577$	13.3039	+	23.0431i	0.553850	+	0.959297i	0.997992	+	0.0633405i	$0.0201754\pi$
$577$	13.3039	+	23.0431i	0.553850	+	0.959297i	−0.444141	+	0.895957i	$0.646491\pi$
$578$	4.62587	−	1.66464i	0.192411	−	0.0692400i
$579$		0			0
$580$	0.443258	−	0.366474i	0.0184053	−	0.0152170i
$581$	38.7253	−	6.82831i	1.60660	−	0.283286i
$582$		0			0
$583$	−6.48384	−	5.44058i	−0.268533	−	0.225326i
$584$	13.2357	+	23.5140i	0.547699	+	0.973018i
$585$		0			0
$586$	−32.3366	+	18.5130i	−1.33581	+	0.764765i
$587$	−14.1595	−	38.9028i	−0.584424	−	1.60569i	−0.780537	−	0.625110i	$-0.785054\pi$
$587$	−14.1595	−	38.9028i	−0.584424	−	1.60569i	0.196113	−	0.980581i	$-0.437168\pi$
$588$		0			0
$589$	12.7643	+	15.2119i	0.525944	+	0.626795i
$590$	−2.85073	+	2.37443i	−0.117363	+	0.0977536i
$591$		0			0
$592$	−11.5585	+	13.3747i	−0.475052	+	0.549695i
$593$	12.1474			0.498833			0.249417	−	0.968396i	$-0.419761\pi$
$593$	12.1474			0.498833			0.249417	+	0.968396i	$0.419761\pi$
$594$		0			0
$595$		−	2.08052i		−	0.0852930i
$596$	−5.33421	−	14.9942i	−0.218498	−	0.614188i
$597$		0			0
$598$	−1.58695	−	1.90529i	−0.0648954	−	0.0779133i
$599$	−25.1300	+	21.0866i	−1.02679	+	0.861575i	−0.990465	−	0.137765i	$-0.956008\pi$
$599$	−25.1300	+	21.0866i	−1.02679	+	0.861575i	−0.0363204	+	0.999340i	$0.511564\pi$
$600$		0			0
$601$	26.6419	−	9.69685i	1.08674	−	0.395543i	0.264331	−	0.964432i	$-0.414849\pi$
$601$	26.6419	−	9.69685i	1.08674	−	0.395543i	0.822414	+	0.568889i	$0.192627\pi$
$602$	−16.1555	+	9.24917i	−0.658450	+	0.376968i
$603$		0			0
$604$	2.70380	−	4.60540i	0.110016	−	0.187391i
$605$	1.16218	−	1.38503i	0.0472493	−	0.0563095i
$606$		0			0
$607$	−0.218532	−	1.23936i	−0.00886995	−	0.0503040i	0.980052	−	0.198744i	$-0.0636861\pi$
$607$	−0.218532	−	1.23936i	−0.00886995	−	0.0503040i	−0.988921	+	0.148440i	$0.952575\pi$
$608$	8.11391	+	10.0350i	0.329063	+	0.406974i
$609$		0			0
$610$	3.52638	−	1.26898i	0.142779	−	0.0513797i
$611$	−2.65617	+	1.53354i	−0.107457	+	0.0620405i
$612$		0			0
$613$	27.4944	+	15.8739i	1.11049	+	0.641141i	0.938956	−	0.344038i	$-0.111795\pi$
$613$	27.4944	+	15.8739i	1.11049	+	0.641141i	0.171532	+	0.985179i	$0.445128\pi$
$614$	22.9689	+	4.13626i	0.926947	+	0.166926i
$615$		0			0
$616$	−4.30978	−	5.25157i	−0.173646	−	0.211592i
$617$	29.6509	+	10.7920i	1.19370	+	0.434471i	0.861021	−	0.508569i	$-0.169825\pi$
$617$	29.6509	+	10.7920i	1.19370	+	0.434471i	0.332679	+	0.943040i	$0.392047\pi$
$618$		0			0
$619$	29.3688	+	5.17850i	1.18043	+	0.208142i	0.729222	−	0.684277i	$-0.239882\pi$
$619$	29.3688	+	5.17850i	1.18043	+	0.208142i	0.451208	+	0.892419i	$0.350993\pi$
$620$	2.70199	−	1.53388i	0.108514	−	0.0616023i
$621$		0			0
$622$	−14.7010	+	25.2503i	−0.589458	+	1.01244i
$623$	−7.30404	+	41.4233i	−0.292630	+	1.65959i
$624$		0			0
$625$	−23.0443	−	8.38744i	−0.921772	−	0.335498i
$626$	3.03258	+	17.5723i	0.121206	+	0.702330i
$627$		0			0
$628$	−15.9991	+	18.7877i	−0.638435	+	0.749710i
$629$	17.3184	+	9.99880i	0.690531	+	0.398678i
$630$		0			0
$631$	−15.5109	−	26.8656i	−0.617478	−	1.06950i	−0.989944	−	0.141458i	$-0.954821\pi$
$631$	−15.5109	−	26.8656i	−0.617478	−	1.06950i	0.372466	−	0.928046i	$-0.378512\pi$
$632$	8.70740	+	7.46985i	0.346362	+	0.297135i
$633$		0			0
$634$	−5.97714	+	16.2380i	−0.237382	+	0.644892i
$635$	3.36916	−	0.594074i	0.133701	−	0.0235751i
$636$		0			0
$637$	0.0873191	−	0.104063i	0.00345971	−	0.00412312i
$638$	−2.12453	−	0.00773040i	−0.0841108	−	0.000306049i
$639$		0			0
$640$	1.77378	−	0.964715i	0.0701149	−	0.0381337i
$641$	−34.7901	+	12.6626i	−1.37413	+	0.500142i	−0.920393	−	0.390995i	$-0.872131\pi$
$641$	−34.7901	+	12.6626i	−1.37413	+	0.500142i	−0.453735	+	0.891137i	$0.649909\pi$
$642$		0			0
$643$	−21.1010	−	25.1472i	−0.832143	−	0.991710i	−0.999983	−	0.00589543i	$-0.998123\pi$
$643$	−21.1010	−	25.1472i	−0.832143	−	0.991710i	0.167839	−	0.985814i	$-0.446321\pi$
$644$	−4.02022	−	23.8118i	−0.158419	−	0.938317i
$645$		0			0
$646$	9.42465	−	11.1492i	0.370808	−	0.438660i
$647$	32.3509			1.27185			0.635923	−	0.771752i	$-0.280620\pi$
$647$	32.3509			1.27185			0.635923	+	0.771752i	$0.280620\pi$
$648$		0			0
$649$	13.7049			0.537965
$650$	1.69684	−	2.00734i	0.0665556	−	0.0787343i
$651$		0			0
$652$	−26.9207	+	4.54510i	−1.05430	+	0.178000i
$653$	−7.14706	−	8.51753i	−0.279686	−	0.333317i	0.607853	−	0.794050i	$-0.292031\pi$
$653$	−7.14706	−	8.51753i	−0.279686	−	0.333317i	−0.887539	+	0.460733i	$0.847587\pi$
$654$		0			0
$655$	−0.153185	+	0.0557549i	−0.00598545	+	0.00217852i
$656$	2.67334	+	4.79004i	0.104376	+	0.187020i
$657$		0			0
$658$	−29.8698	−	0.108685i	−1.16444	−	0.00423700i
$659$	21.7371	−	25.9052i	0.846757	−	1.00913i	−0.153025	−	0.988222i	$-0.548901\pi$
$659$	21.7371	−	25.9052i	0.846757	−	1.00913i	0.999782	−	0.0209028i	$-0.00665406\pi$
$660$		0			0
$661$	−26.9698	+	4.75551i	−1.04901	+	0.184968i	−0.671473	−	0.741029i	$-0.734338\pi$
$661$	−26.9698	+	4.75551i	−1.04901	+	0.184968i	−0.377532	+	0.925997i	$0.623227\pi$
$662$	9.90679	−	26.9136i	0.385038	−	1.04603i
$663$		0			0
$664$	28.1100	−	32.7671i	1.09088	−	1.27161i
$665$	−0.524441	−	0.908358i	−0.0203369	−	0.0352246i
$666$		0			0
$667$	−6.54020	−	3.77598i	−0.253237	−	0.146207i
$668$	6.38282	+	5.43546i	0.246959	+	0.210304i
$669$		0			0
$670$	−0.0750860	−	0.435085i	−0.00290082	−	0.0168088i
$671$	−13.0092	−	4.73497i	−0.502216	−	0.182792i
$672$		0			0
$673$	−3.55472	+	20.1598i	−0.137024	+	0.777103i	0.836404	+	0.548113i	$0.184654\pi$
$673$	−3.55472	+	20.1598i	−0.137024	+	0.777103i	−0.973429	+	0.228990i	$0.926458\pi$
$674$	12.2560	−	21.0508i	0.472083	−	0.810845i
$675$		0			0
$676$	−12.6976	−	22.3673i	−0.488370	−	0.860279i
$677$	32.7893	+	5.78165i	1.26020	+	0.222207i	0.763552	−	0.645747i	$-0.223454\pi$
$677$	32.7893	+	5.78165i	1.26020	+	0.222207i	0.496645	+	0.867954i	$0.334565\pi$
$678$		0			0
$679$	−28.2735	−	10.2907i	−1.08504	−	0.394922i
$680$	−1.44907	−	1.76573i	−0.0555693	−	0.0677125i
$681$		0			0
$682$	−11.2956	−	2.03412i	−0.432529	−	0.0778904i
$683$	11.8895	+	6.86440i	0.454939	+	0.262659i	0.709914	−	0.704289i	$-0.248734\pi$
$683$	11.8895	+	6.86440i	0.454939	+	0.262659i	−0.254975	+	0.966948i	$0.582067\pi$
$684$		0			0
$685$	0.886463	−	0.511800i	0.0338700	−	0.0195549i
$686$	25.2416	−	9.08331i	0.963728	−	0.346802i
$687$		0			0
$688$	−7.26909	+	19.1019i	−0.277131	+	0.728255i
$689$	0.589743	+	3.34460i	0.0224674	+	0.127419i
$690$		0			0
$691$	−16.4903	+	19.6524i	−0.627321	+	0.747612i	−0.982311	−	0.187258i	$-0.940040\pi$
$691$	−16.4903	+	19.6524i	−0.627321	+	0.747612i	0.354990	+	0.934870i	$0.384484\pi$
$692$	−34.5545	−	20.2867i	−1.31356	−	0.771187i
$693$		0			0
$694$	7.82883	−	4.48207i	0.297178	−	0.170137i
$695$	3.54881	−	1.29166i	0.134614	−	0.0489955i
$696$		0			0
$697$	4.75379	−	3.98890i	0.180063	−	0.151090i
$698$	12.1289	+	14.5620i	0.459087	+	0.551179i
$699$		0			0
$700$	24.1174	−	8.57976i	0.911550	−	0.324284i
$701$			0.366433i			0.0138400i	0.999976	+	0.00692000i	$0.00220272\pi$
$701$			0.366433i			0.0138400i	−0.999976	+	0.00692000i	$0.997797\pi$
$702$		0			0
$703$	10.0817			0.380237
$704$	−7.31537	−	1.45523i	−0.275708	−	0.0548462i
$705$		0			0
$706$	−12.2641	+	10.2150i	−0.461567	+	0.384447i
$707$	−3.55171	−	4.23276i	−0.133576	−	0.159189i
$708$		0			0
$709$	2.32486	+	6.38749i	0.0873118	+	0.239887i	0.975662	−	0.219279i	$-0.0703705\pi$
$709$	2.32486	+	6.38749i	0.0873118	+	0.239887i	−0.888350	+	0.459166i	$0.848148\pi$
$710$	1.21510	−	0.695654i	0.0456018	−	0.0261074i
$711$		0			0
$712$	22.6522	+	40.2429i	0.848926	+	1.50817i
$713$	−31.2526	−	26.2241i	−1.17042	−	0.982100i
$714$		0			0
$715$	0.0613024	−	0.0108093i	0.00229258	−	0.000404244i
$716$	−10.2541	−	12.4026i	−0.383215	−	0.463506i
$717$		0			0
$718$	−36.1577	+	13.0115i	−1.34939	+	0.485586i
$719$	6.07495	+	10.5221i	0.226558	+	0.392409i	0.956786	−	0.290794i	$-0.0939195\pi$
$719$	6.07495	+	10.5221i	0.226558	+	0.392409i	−0.730228	+	0.683203i	$0.760586\pi$
$720$		0			0
$721$	15.0974	−	26.1495i	0.562257	−	0.973857i
$722$	−3.45778	+	19.2012i	−0.128685	+	0.714596i
$723$		0			0
$724$	5.63815	−	15.1468i	0.209540	−	0.562927i
$725$	2.73793	−	7.52240i	0.101684	−	0.279375i
$726$		0			0
$727$	0.337498	−	1.91405i	0.0125171	−	0.0709881i	−0.977909	−	0.209029i	$-0.932970\pi$
$727$	0.337498	−	1.91405i	0.0125171	−	0.0709881i	0.990426	+	0.138041i	$0.0440807\pi$
$728$	−0.0297554	+	2.72577i	−0.00110281	+	0.101024i
$729$		0			0
$730$	−2.08086	−	1.21150i	−0.0770160	−	0.0448397i
$731$	22.7700	+	4.01496i	0.842177	+	0.148499i
$732$		0			0
$733$	14.2681	−	39.2014i	0.527006	−	1.44794i	−0.335572	−	0.942014i	$-0.608930\pi$
$733$	14.2681	−	39.2014i	0.527006	−	1.44794i	0.862579	−	0.505923i	$-0.168848\pi$
$734$	−5.50798	−	31.9160i	−0.203303	−	1.17804i
$735$		0			0
$736$	−19.9967	−	17.4089i	−0.737090	−	0.641700i
$737$	−0.815477	+	1.41245i	−0.0300385	+	0.0520282i
$738$		0			0
$739$	22.3170	−	12.8847i	0.820943	−	0.473971i	−0.0297988	−	0.999556i	$-0.509487\pi$
$739$	22.3170	−	12.8847i	0.820943	−	0.473971i	0.850741	+	0.525584i	$0.176153\pi$
$740$	0.285213	−	1.55142i	0.0104846	−	0.0570312i
$741$		0			0
$742$	−11.4254	+	31.0391i	−0.419438	+	1.13948i
$743$	0.466716	+	2.64688i	0.0171222	+	0.0971046i	0.992171	−	0.124885i	$-0.0398561\pi$
$743$	0.466716	+	2.64688i	0.0171222	+	0.0971046i	−0.975049	+	0.221989i	$0.928745\pi$
$744$		0			0
$745$	1.08790	+	0.912858i	0.0398576	+	0.0334445i
$746$	0.145765	−	40.0601i	0.00533682	−	1.46671i
$747$		0			0
$748$	−0.0614036	+	8.43759i	−0.00224514	+	0.308509i
$749$	−6.52355	−	17.9233i	−0.238365	−	0.654903i
$750$		0			0
$751$	−35.3934	+	29.6986i	−1.29153	+	1.08372i	−0.299982	+	0.953945i	$0.596981\pi$
$751$	−35.3934	+	29.6986i	−1.29153	+	1.08372i	−0.991544	+	0.129773i	$0.958575\pi$
$752$	−25.4260	+	20.7119i	−0.927190	+	0.755284i
$753$		0			0
$754$	0.651032	+	0.550330i	0.0237092	+	0.0200418i
$755$			0.476553i			0.0173435i
$756$		0			0
$757$		−	41.2974i		−	1.50098i	−0.660883	−	0.750489i	$-0.729818\pi$
$757$		−	41.2974i		−	1.50098i	0.660883	−	0.750489i	$-0.270182\pi$
$758$	−8.40360	+	9.94133i	−0.305232	+	0.361085i
$759$		0			0
$760$	−1.07776	−	0.405648i	−0.0390943	−	0.0147144i
$761$	−16.6555	+	13.9756i	−0.603762	+	0.506616i	−0.892652	−	0.450746i	$-0.851158\pi$
$761$	−16.6555	+	13.9756i	−0.603762	+	0.506616i	0.288891	+	0.957362i	$0.406714\pi$
$762$		0			0
$763$	−11.6591	−	32.0330i	−0.422086	−	1.15967i
$764$	−33.2816	−	0.242203i	−1.20408	−	0.00876258i
$765$		0			0
$766$	33.3508	+	0.121352i	1.20501	+	0.00438462i
$767$	−4.21254	−	3.53474i	−0.152106	−	0.127632i
$768$		0			0
$769$	4.86149	+	27.5709i	0.175310	+	0.994232i	0.937786	+	0.347215i	$0.112873\pi$
$769$	4.86149	+	27.5709i	0.175310	+	0.994232i	−0.762476	+	0.647017i	$0.776016\pi$
$770$	0.568908	+	0.209413i	0.0205020	+	0.00754672i
$771$		0			0
$772$	0.298563	−	1.62404i	0.0107455	−	0.0584504i
$773$	−23.6486	+	13.6535i	−0.850580	+	0.491083i	−0.860847	−	0.508864i	$-0.830065\pi$
$773$	−23.6486	+	13.6535i	−0.850580	+	0.491083i	0.0102662	+	0.999947i	$0.496732\pi$
$774$		0			0
$775$	21.6229	−	37.4519i	0.776717	−	1.34531i
$776$	−31.1630	+	10.9587i	−1.11869	+	0.393394i
$777$		0			0
$778$	41.9420	−	7.23826i	1.50370	−	0.259504i
$779$	1.07002	−	2.93986i	0.0383375	−	0.105331i
$780$		0			0
$781$	−5.09352	−	0.898125i	−0.182260	−	0.0321374i
$782$	−15.0911	+	25.9203i	−0.539656	+	0.926907i
$783$		0			0
$784$	0.744476	−	1.24719i	0.0265884	−	0.0445426i
$785$	0.382380	−	2.16858i	0.0136477	−	0.0774001i
$786$		0			0
$787$	−7.72182	+	21.2155i	−0.275253	+	0.756252i	0.722631	+	0.691234i	$0.242933\pi$
$787$	−7.72182	+	21.2155i	−0.275253	+	0.756252i	−0.997884	+	0.0650180i	$0.979290\pi$
$788$	10.5232	−	28.2705i	0.374874	−	1.00709i
$789$		0			0
$790$	−1.00754	−	0.181438i	−0.0358465	−	0.00645529i
$791$	11.8140	−	20.4625i	0.420059	−	0.727564i
$792$		0			0
$793$	2.77747	+	4.81073i	0.0986310	+	0.170834i
$794$	8.56234	+	23.7939i	0.303866	+	0.844412i
$795$		0			0
$796$	23.9784	−	19.8247i	0.849891	−	0.702668i
$797$	−19.2857	+	3.40058i	−0.683133	+	0.120455i	−0.504436	−	0.863449i	$-0.668299\pi$
$797$	−19.2857	+	3.40058i	−0.683133	+	0.120455i	−0.178697	+	0.983904i	$0.557188\pi$
$798$		0			0
$799$	28.4196	+	23.8469i	1.00541	+	0.843641i
$800$	14.4925	−	24.0792i	0.512387	−	0.851328i
$801$		0			0
$802$	−6.97806	−	12.1886i	−0.246404	−	0.430393i
$803$	3.04211	+	8.35812i	0.107354	+	0.294952i
$804$		0			0
$805$	1.38515	+	1.65076i	0.0488202	+	0.0581816i
$806$	2.94733	+	3.53856i	0.103815	+	0.124641i
$807$		0			0
$808$	−5.96241	−	1.11857i	−0.209757	−	0.0393513i
$809$	27.8483			0.979094			0.489547	−	0.871977i	$-0.337162\pi$
$809$	27.8483			0.979094			0.489547	+	0.871977i	$0.337162\pi$
$810$		0			0
$811$			7.82601i			0.274808i	0.990515	+	0.137404i	$0.0438759\pi$
$811$			7.82601i			0.274808i	−0.990515	+	0.137404i	$0.956124\pi$
$812$	2.78264	+	7.82188i	0.0976515	+	0.274494i
$813$		0			0
$814$	−4.47730	+	3.72922i	−0.156929	+	0.130709i
$815$	1.86628	−	1.56600i	0.0653730	−	0.0548545i
$816$		0			0
$817$	10.9535	−	3.98673i	0.383213	−	0.139478i
$818$	3.89039	+	6.79534i	0.136024	+	0.237593i
$819$		0			0
$820$	−0.422128	−	0.247829i	−0.0147414	−	0.00865457i
$821$	−9.82911	+	11.7139i	−0.343038	+	0.408817i	−0.909788	−	0.415073i	$-0.863756\pi$
$821$	−9.82911	+	11.7139i	−0.343038	+	0.408817i	0.566750	+	0.823890i	$0.308201\pi$
$822$		0			0
$823$	−4.11133	−	23.3165i	−0.143312	−	0.812763i	−0.968707	−	0.248207i	$-0.920159\pi$
$823$	−4.11133	−	23.3165i	−0.143312	−	0.812763i	0.825395	−	0.564556i	$-0.190953\pi$
$824$	−5.39988	−	32.7082i	−0.188114	−	1.13944i
$825$		0			0
$826$	−18.1336	−	50.3914i	−0.630949	−	1.75334i
$827$	−0.0403168	+	0.0232769i	−0.00140195	+	0.000809419i	−0.500701	−	0.865620i	$-0.666924\pi$
$827$	−0.0403168	+	0.0232769i	−0.00140195	+	0.000809419i	0.499299	+	0.866430i	$0.333591\pi$
$828$		0			0
$829$	6.44307	+	3.71991i	0.223777	+	0.129198i	0.607698	−	0.794168i	$-0.292093\pi$
$829$	6.44307	+	3.71991i	0.223777	+	0.129198i	−0.383921	+	0.923366i	$0.625426\pi$
$830$	−0.682776	+	3.79149i	−0.0236995	+	0.131605i
$831$		0			0
$832$	1.87323	+	2.33407i	0.0649426	+	0.0809193i
$833$	−1.54406	−	0.561994i	−0.0534987	−	0.0194719i
$834$		0			0
$835$	−0.736742	−	0.129908i	−0.0254960	−	0.00449564i
$836$	2.10007	+	3.69934i	0.0726325	+	0.127944i
$837$		0			0
$838$	−5.00008	−	2.91111i	−0.172725	−	0.100562i
$839$	3.69536	−	20.9574i	0.127578	−	0.723531i	−0.852165	−	0.523273i	$-0.824711\pi$
$839$	3.69536	−	20.9574i	0.127578	−	0.723531i	0.979743	−	0.200258i	$-0.0641780\pi$
$840$		0			0
$841$	−24.8114	−	9.03060i	−0.855565	−	0.311400i
$842$	34.2382	−	5.90874i	1.17993	−	0.203629i
$843$		0			0
$844$	7.16606	−	8.41505i	0.246666	−	0.289658i
$845$	1.98764	+	1.14756i	0.0683768	+	0.0394774i
$846$		0			0
$847$	13.0495	+	22.6024i	0.448385	+	0.776626i
$848$	11.9219	+	34.3004i	0.409399	+	1.17788i
$849$		0			0
$850$	−29.8362	−	10.9826i	−1.02337	−	0.376700i
$851$	−20.3980	+	3.59671i	−0.699234	+	0.123294i
$852$		0			0
$853$	11.8527	−	14.1255i	0.405829	−	0.483648i	−0.523959	−	0.851744i	$-0.675545\pi$
$853$	11.8527	−	14.1255i	0.405829	−	0.483648i	0.929788	+	0.368095i	$0.119990\pi$
$854$	−0.196846	+	54.0986i	−0.00673591	+	1.85122i
$855$		0			0
$856$	−18.0200	−	10.6678i	−0.615910	−	0.364617i
$857$	18.6167	−	6.77591i	0.635933	−	0.231461i	−0.00387866	−	0.999992i	$-0.501235\pi$
$857$	18.6167	−	6.77591i	0.635933	−	0.231461i	0.639812	+	0.768532i	$0.279012\pi$
$858$		0			0
$859$	−5.06270	−	6.03349i	−0.172737	−	0.205860i	0.672729	−	0.739889i	$-0.265122\pi$
$859$	−5.06270	−	6.03349i	−0.172737	−	0.205860i	−0.845466	+	0.534029i	$0.820677\pi$
$860$	−0.303622	−	1.79836i	−0.0103534	−	0.0613234i
$861$		0			0
$862$	15.1268	+	12.7869i	0.515219	+	0.435525i
$863$	3.41425			0.116222			0.0581111	−	0.998310i	$-0.481492\pi$
$863$	3.41425			0.116222			0.0581111	+	0.998310i	$0.481492\pi$
$864$		0			0
$865$	3.57559			0.121574
$866$	−13.4895	−	11.4030i	−0.458393	−	0.387489i
$867$		0			0
$868$	7.46646	+	44.2240i	0.253428	+	1.50106i
$869$	2.43082	+	2.89694i	0.0824600	+	0.0982720i
$870$		0			0
$871$	0.614953	−	0.223825i	0.0208369	−	0.00758401i
$872$	−32.2058	−	19.0657i	−1.09063	−	0.645648i
$873$		0			0
$874$	−0.0550194	+	15.1209i	−0.00186106	+	0.511471i
$875$	−2.94597	+	3.51087i	−0.0995919	+	0.118689i
$876$		0			0
$877$	−13.1746	+	2.32305i	−0.444876	+	0.0784437i	−0.391599	−	0.920136i	$-0.628078\pi$
$877$	−13.1746	+	2.32305i	−0.444876	+	0.0784437i	−0.0532774	+	0.998580i	$0.516967\pi$
$878$	14.3275	+	5.27389i	0.483529	+	0.177985i
$879$		0			0
$880$	0.628684	−	0.218514i	0.0211929	−	0.00736610i
$881$	−28.5441	−	49.4399i	−0.961676	−	1.66567i	−0.718292	−	0.695742i	$-0.755076\pi$
$881$	−28.5441	−	49.4399i	−0.961676	−	1.66567i	−0.243384	−	0.969930i	$-0.578257\pi$
$882$		0			0
$883$	17.0975	+	9.87122i	0.575375	+	0.332193i	0.759293	−	0.650749i	$-0.225545\pi$
$883$	17.0975	+	9.87122i	0.575375	+	0.332193i	−0.183918	+	0.982942i	$0.558878\pi$
$884$	2.19508	−	2.57766i	0.0738285	−	0.0866962i
$885$		0			0
$886$	40.5415	−	6.99655i	1.36202	−	0.235054i
$887$	53.6182	+	19.5154i	1.80032	+	0.655264i	0.998320	+	0.0579452i	$0.0184549\pi$
$887$	53.6182	+	19.5154i	1.80032	+	0.655264i	0.802004	+	0.597319i	$0.203767\pi$
$888$		0			0
$889$	−8.57547	+	48.6339i	−0.287612	+	1.63113i
$890$	−3.56127	−	2.07341i	−0.119374	−	0.0695010i
$891$		0			0
$892$	5.16138	+	9.09194i	0.172816	+	0.304421i
$893$	18.4192	+	3.24779i	0.616373	+	0.108683i
$894$		0			0
$895$	1.34942	+	0.491147i	0.0451060	+	0.0164172i
$896$	4.32858	+	28.8233i	0.144608	+	0.962919i
$897$		0			0
$898$	7.54357	−	41.8899i	0.251732	−	1.39788i
$899$	12.1466	+	7.01286i	0.405113	+	0.233892i
$900$		0			0
$901$	35.5763	−	20.5400i	1.18522	−	0.684286i
$902$	0.612257	+	1.70140i	0.0203859	+	0.0566504i
$903$		0			0
$904$	−4.22553	−	25.5948i	−0.140539	−	0.851272i
$905$	0.250440	+	1.42031i	0.00832490	+	0.0472128i
$906$		0			0
$907$	−15.5646	+	18.5491i	−0.516813	+	0.615914i	−0.959824	−	0.280602i	$-0.909466\pi$
$907$	−15.5646	+	18.5491i	−0.516813	+	0.615914i	0.443011	+	0.896516i	$0.353910\pi$
$908$	−15.1835	−	8.91414i	−0.503882	−	0.295826i
$909$		0			0
$910$	−0.120857	−	0.211100i	−0.00400636	−	0.00699790i
$911$	−21.3962	+	7.78758i	−0.708888	+	0.258014i	−0.671201	−	0.741275i	$-0.734221\pi$
$911$	−21.3962	+	7.78758i	−0.708888	+	0.258014i	−0.0376870	+	0.999290i	$0.511999\pi$
$912$		0			0
$913$	10.9016	−	9.14750i	0.360789	−	0.302738i
$914$	−16.9686	+	14.1334i	−0.561270	+	0.467492i
$915$		0			0
$916$	−5.79256	−	16.2826i	−0.191391	−	0.537993i
$917$		−	2.35315i		−	0.0777078i
$918$		0			0
$919$	3.40847			0.112435			0.0562174	−	0.998419i	$-0.482096\pi$
$919$	3.40847			0.112435			0.0562174	+	0.998419i	$0.482096\pi$
$920$	2.32532	+	0.436239i	0.0766634	+	0.0143824i
$921$		0			0
$922$	−11.6801	−	14.0231i	−0.384662	−	0.461825i
$923$	1.33398	+	1.58977i	0.0439084	+	0.0523279i
$924$		0			0
$925$	−7.50928	−	20.6316i	−0.246904	−	0.678362i
$926$	−24.3945	−	42.6098i	−0.801653	−	1.40025i
$927$		0			0
$928$	7.80951	+	4.70029i	0.256360	+	0.154295i
$929$	16.2267	+	13.6158i	0.532381	+	0.446721i	0.868923	−	0.494948i	$-0.164813\pi$
$929$	16.2267	+	13.6158i	0.532381	+	0.446721i	−0.336541	+	0.941669i	$0.609257\pi$
$930$		0			0
$931$	−0.815804	+	0.143848i	−0.0267369	+	0.00471443i
$932$	−1.29677	+	1.07213i	−0.0424771	+	0.0351189i
$933$		0			0
$934$	6.86807	+	19.0857i	0.224730	+	0.624502i
$935$	−0.376473	−	0.652071i	−0.0123120	−	0.0213250i
$936$		0			0
$937$	20.8301	−	36.0788i	0.680489	−	1.17864i	−0.294342	−	0.955700i	$-0.595101\pi$
$937$	20.8301	−	36.0788i	0.680489	−	1.17864i	0.974832	−	0.222942i	$-0.0715661\pi$
$938$	6.27241	+	1.12954i	0.204802	+	0.0368809i
$939$		0			0
$940$	1.02087	−	2.74255i	0.0332971	−	0.0894520i
$941$	−17.2670	+	47.4407i	−0.562888	+	1.54652i	0.252493	+	0.967599i	$0.418749\pi$
$941$	−17.2670	+	47.4407i	−0.562888	+	1.54652i	−0.815382	+	0.578924i	$0.803473\pi$
$942$		0			0
$943$	−1.11613	+	6.32988i	−0.0363461	+	0.206129i
$944$	−50.4873	−	30.1370i	−1.64322	−	0.980874i
$945$		0			0
$946$	−3.38976	+	5.82221i	−0.110211	+	0.189296i
$947$	38.1758	+	6.73142i	1.24055	+	0.218742i	0.755149	−	0.655553i	$-0.227564\pi$
$947$	38.1758	+	6.73142i	1.24055	+	0.218742i	0.485396	+	0.874294i	$0.338675\pi$
$948$		0			0
$949$	1.22064	−	3.35369i	0.0396238	−	0.108865i
$950$	−15.7949	+	2.72585i	−0.512455	+	0.0884382i
$951$		0			0
$952$	31.1053	−	10.9384i	1.00813	−	0.354516i
$953$	17.7159	−	30.6848i	0.573873	−	0.993977i	−0.422290	−	0.906461i	$-0.638774\pi$
$953$	17.7159	−	30.6848i	0.573873	−	0.993977i	0.996163	−	0.0875165i	$-0.0278931\pi$
$954$		0			0
$955$	2.57205	−	1.48498i	0.0832297	−	0.0480527i
$956$	4.99311	−	27.1600i	0.161489	−	0.878419i
$957$		0			0
$958$	0.801022	+	0.294853i	0.0258798	+	0.00952627i
$959$	2.56577	+	14.5512i	0.0828531	+	0.469883i
$960$		0			0
$961$	34.2959	+	28.7776i	1.10632	+	0.928311i
$962$	2.33804	+	0.00850730i	0.0753815	+	0.000274286i
$963$		0			0
$964$	30.1564	+	0.219460i	0.971272	+	0.00706832i
$965$	0.0503964	+	0.138463i	0.00162232	+	0.00445728i
$966$		0			0
$967$	−1.48262	+	1.24406i	−0.0476777	+	0.0400064i	−0.666315	−	0.745670i	$-0.732129\pi$
$967$	−1.48262	+	1.24406i	−0.0476777	+	0.0400064i	0.618637	+	0.785677i	$0.287685\pi$
$968$	26.8174	+	10.0936i	0.861945	+	0.324421i
$969$		0			0
$970$	1.90298	−	2.25120i	0.0611011	−	0.0722817i
$971$		−	30.4220i		−	0.976288i	−0.872763	−	0.488144i	$-0.837674\pi$
$971$		−	30.4220i		−	0.976288i	0.872763	−	0.488144i	$-0.162326\pi$
$972$		0			0
$973$			54.5148i			1.74766i
$974$	24.7042	+	20.8830i	0.791574	+	0.669133i
$975$		0			0
$976$	37.5123	+	46.0503i	1.20074	+	1.47403i
$977$	−2.40690	+	2.01963i	−0.0770035	+	0.0646136i	−0.680477	−	0.732769i	$-0.738227\pi$
$977$	−2.40690	+	2.01963i	−0.0770035	+	0.0646136i	0.603473	+	0.797383i	$0.293783\pi$
$978$		0			0
$979$	5.20639	+	14.3044i	0.166397	+	0.457172i
$980$	−0.000943217		0.129609i	−3.01300e−5		0.00414022i
$981$		0			0
$982$	−0.0461897	+	12.6942i	−0.00147397	+	0.405088i
$983$	−44.9828	−	37.7451i	−1.43473	−	1.20388i	−0.942850	−	0.333218i	$-0.891865\pi$
$983$	−44.9828	−	37.7451i	−1.43473	−	1.20388i	−0.491880	−	0.870663i	$-0.663690\pi$
$984$		0			0
$985$	0.467428	+	2.65092i	0.0148935	+	0.0844652i
$986$	3.56194	−	9.67664i	0.113435	−	0.308167i
$987$		0			0
$988$	0.308618	−	1.67873i	0.00981845	−	0.0534075i
$989$	−20.7395	+	11.9740i	−0.659479	+	0.380750i
$990$		0			0
$991$	10.3807	−	17.9799i	0.329754	−	0.571150i	−0.652709	−	0.757609i	$-0.726368\pi$
$991$	10.3807	−	17.9799i	0.329754	−	0.571150i	0.982463	+	0.186458i	$0.0597009\pi$
$992$	37.1385	+	32.3323i	1.17915	+	1.02655i
$993$		0			0
$994$	3.43717	+	19.9167i	0.109020	+	0.631718i
$995$	−0.949553	+	2.60888i	−0.0301029	+	0.0827069i
$996$		0			0
$997$	−32.5454	−	5.73863i	−1.03072	−	0.181744i	−0.367389	−	0.930067i	$-0.619748\pi$
$997$	−32.5454	−	5.73863i	−1.03072	−	0.181744i	−0.663335	+	0.748323i	$0.730859\pi$
$998$	−53.7331	−	31.2841i	−1.70089	−	0.990280i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.397.7		204
3.2	odd	2		216.2.t.a.133.28	yes	204
8.5	even	2	inner	648.2.t.a.397.30		204
12.11	even	2		864.2.bf.a.241.22		204
24.5	odd	2		216.2.t.a.133.5	yes	204
24.11	even	2		864.2.bf.a.241.13		204
27.13	even	9	inner	648.2.t.a.253.30		204
27.14	odd	18		216.2.t.a.13.5	✓	204
108.95	even	18		864.2.bf.a.337.13		204
216.13	even	18	inner	648.2.t.a.253.7		204
216.149	odd	18		216.2.t.a.13.28	yes	204
216.203	even	18		864.2.bf.a.337.22		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.5	✓	204	27.14	odd	18
216.2.t.a.13.28	yes	204	216.149	odd	18
216.2.t.a.133.5	yes	204	24.5	odd	2
216.2.t.a.133.28	yes	204	3.2	odd	2
648.2.t.a.253.7		204	216.13	even	18	inner
648.2.t.a.253.30		204	27.13	even	9	inner
648.2.t.a.397.7		204	1.1	even	1	trivial
648.2.t.a.397.30		204	8.5	even	2	inner
864.2.bf.a.241.13		204	24.11	even	2
864.2.bf.a.241.22		204	12.11	even	2
864.2.bf.a.337.13		204	108.95	even	18
864.2.bf.a.337.22		204	216.203	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08004 - 0.912975i) q^{2} +(0.332954 + 1.97209i) q^{4} +(-0.114718 - 0.136716i) q^{5} +(2.42085 - 0.881117i) q^{7} +(1.44087 - 2.43391i) q^{8} +(-0.000918366 + 0.252392i) q^{10} +(0.599296 - 0.714213i) q^{11} +(-0.368417 + 0.0649618i) q^{13} +(-3.41904 - 1.25854i) q^{14} +(-3.77828 + 1.31323i) q^{16} +(2.26254 + 3.91883i) q^{17} +(1.97566 + 1.14065i) q^{19} +(0.231420 - 0.271754i) q^{20} +(-1.29932 + 0.224233i) q^{22} +(-4.40423 - 1.60301i) q^{23} +(0.862710 - 4.89267i) q^{25} +(0.457212 + 0.266194i) q^{26} +(2.54367 + 4.48076i) q^{28} +(1.58682 + 0.279799i) q^{29} +(8.17965 + 2.97715i) q^{31} +(5.27963 + 2.03114i) q^{32} +(1.13417 - 6.29812i) q^{34} +(-0.398177 - 0.229888i) q^{35} +(3.82721 - 2.20964i) q^{37} +(-1.09240 - 3.03566i) q^{38} +(-0.498046 + 0.0822239i) q^{40} +(-0.238139 - 1.35055i) q^{41} +(3.28437 - 3.91416i) q^{43} +(1.60803 + 0.944066i) q^{44} +(3.29322 + 5.75225i) q^{46} +(7.70413 - 2.80407i) q^{47} +(-0.278168 + 0.233411i) q^{49} +(-5.39864 + 4.49663i) q^{50} +(-0.250776 - 0.704922i) q^{52} -9.07829i q^{53} -0.166394 q^{55} +(1.34357 - 7.16169i) q^{56} +(-1.45837 - 1.75092i) q^{58} +(9.44865 + 11.2605i) q^{59} +(-5.07860 - 13.9533i) q^{61} +(-6.11625 - 10.6832i) q^{62} +(-3.84780 - 7.01387i) q^{64} +(0.0511453 + 0.0429160i) q^{65} +(-1.72274 + 0.303765i) q^{67} +(-6.97497 + 5.76672i) q^{68} +(0.220164 + 0.611813i) q^{70} +(-2.77372 - 4.80422i) q^{71} +(-4.77001 + 8.26190i) q^{73} +(-6.15087 - 1.10766i) q^{74} +(-1.59165 + 4.27595i) q^{76} +(0.821500 - 2.25705i) q^{77} +(-0.704340 + 3.99451i) q^{79} +(0.612976 + 0.365899i) q^{80} +(-0.975822 + 1.67606i) q^{82} +(15.0319 + 2.65052i) q^{83} +(0.276212 - 0.758885i) q^{85} +(-7.12077 + 1.22889i) q^{86} +(-0.874822 - 2.48772i) q^{88} +(-8.16359 + 14.1397i) q^{89} +(-0.834643 + 0.481881i) q^{91} +(1.69487 - 9.21926i) q^{92} +(-10.8808 - 4.00518i) q^{94} +(-0.0706993 - 0.400955i) q^{95} +(-8.94677 - 7.50723i) q^{97} +(0.513530 + 0.00186855i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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