LMFDB - Embedded newform 351.2.h.a.334.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(289,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.h (of order $3$, degree $2$, 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			334.12
Character	$\chi$	$=$	351.334
Dual form			351.2.h.a.289.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.65628 q^{2} +5.05585 q^{4} +(-0.324360 + 0.561808i) q^{5} +(-0.773958 + 1.34053i) q^{7} +8.11720 q^{8} +(-0.861592 + 1.49232i) q^{10} -5.07008 q^{11} +(-0.445184 - 3.57796i) q^{13} +(-2.05585 + 3.56084i) q^{14} +11.4499 q^{16} +(0.103828 + 0.179835i) q^{17} +(-1.79488 - 3.10883i) q^{19} +(-1.63991 + 2.84041i) q^{20} -13.4676 q^{22} +(-1.60137 - 2.77365i) q^{23} +(2.28958 + 3.96567i) q^{25} +(-1.18254 - 9.50408i) q^{26} +(-3.91301 + 6.77754i) q^{28} +6.83026 q^{29} +(1.58024 - 2.73705i) q^{31} +14.1798 q^{32} +(0.275796 + 0.477692i) q^{34} +(-0.502082 - 0.869631i) q^{35} +(-4.71300 + 8.16316i) q^{37} +(-4.76772 - 8.25793i) q^{38} +(-2.63289 + 4.56031i) q^{40} +(-4.30114 - 7.44979i) q^{41} +(-2.99929 + 5.19492i) q^{43} -25.6335 q^{44} +(-4.25368 - 7.36759i) q^{46} +(1.42859 + 2.47438i) q^{47} +(2.30198 + 3.98714i) q^{49} +(6.08178 + 10.5340i) q^{50} +(-2.25078 - 18.0896i) q^{52} +2.48667 q^{53} +(1.64453 - 2.84841i) q^{55} +(-6.28237 + 10.8814i) q^{56} +18.1431 q^{58} +2.98403 q^{59} +(-4.02238 + 6.96697i) q^{61} +(4.19756 - 7.27038i) q^{62} +14.7657 q^{64} +(2.15453 + 0.910439i) q^{65} +(-2.47432 - 4.28565i) q^{67} +(0.524937 + 0.909217i) q^{68} +(-1.33367 - 2.30999i) q^{70} +(0.787066 + 1.36324i) q^{71} +3.03817 q^{73} +(-12.5191 + 21.6837i) q^{74} +(-9.07465 - 15.7178i) q^{76} +(3.92403 - 6.79661i) q^{77} +(3.23418 + 5.60177i) q^{79} +(-3.71389 + 6.43264i) q^{80} +(-11.4251 - 19.7888i) q^{82} +(-1.24623 - 2.15854i) q^{83} -0.134710 q^{85} +(-7.96696 + 13.7992i) q^{86} -41.1548 q^{88} +(1.76275 - 3.05317i) q^{89} +(5.14094 + 2.17241i) q^{91} +(-8.09626 - 14.0231i) q^{92} +(3.79473 + 6.57267i) q^{94} +2.32875 q^{95} +(4.69325 - 8.12894i) q^{97} +(6.11471 + 10.5910i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 18 q^{4} + 2 q^{5} + 3 q^{7} + 18 q^{8} - 6 q^{11} - 2 q^{14} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 11 q^{20} - 18 q^{22} - 17 q^{23} - 6 q^{25} + 12 q^{26} + 24 q^{29} - 6 q^{31} + 38 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.65628			1.87828			0.939138	−	0.343539i	$-0.111626\pi$
$2$	2.65628			1.87828			0.939138	+	0.343539i	$0.111626\pi$
$3$		0			0
$3$		0			0
$4$	5.05585			2.52792
$5$	−0.324360	+	0.561808i	−0.145058	+	0.251248i	−0.929395	−	0.369088i	$-0.879670\pi$
$5$	−0.324360	+	0.561808i	−0.145058	+	0.251248i	0.784336	+	0.620336i	$0.213004\pi$
$6$		0			0
$7$	−0.773958	+	1.34053i	−0.292529	+	0.506674i	−0.974407	−	0.224791i	$-0.927830\pi$
$7$	−0.773958	+	1.34053i	−0.292529	+	0.506674i	0.681878	+	0.731466i	$0.261163\pi$
$8$	8.11720			2.86986
$9$		0			0
$10$	−0.861592	+	1.49232i	−0.272459	+	0.471913i
$11$	−5.07008			−1.52869			−0.764343	−	0.644810i	$-0.776937\pi$
$11$	−5.07008			−1.52869			−0.764343	+	0.644810i	$0.776937\pi$
$12$		0			0
$13$	−0.445184	−	3.57796i	−0.123472	−	0.992348i
$13$	−0.445184	−	3.57796i	−0.123472	−	0.992348i
$14$	−2.05585	+	3.56084i	−0.549450	+	0.951675i
$15$		0			0
$16$	11.4499			2.86247
$17$	0.103828	+	0.179835i	0.0251819	+	0.0436163i	0.878342	−	0.478033i	$-0.158650\pi$
$17$	0.103828	+	0.179835i	0.0251819	+	0.0436163i	−0.853160	+	0.521650i	$0.825317\pi$
$18$		0			0
$19$	−1.79488	−	3.10883i	−0.411774	−	0.713214i	0.583310	−	0.812250i	$-0.301757\pi$
$19$	−1.79488	−	3.10883i	−0.411774	−	0.713214i	−0.995084	+	0.0990360i	$0.968424\pi$
$20$	−1.63991	+	2.84041i	−0.366696	+	0.635136i
$21$		0			0
$22$	−13.4676			−2.87130
$23$	−1.60137	−	2.77365i	−0.333908	−	0.578345i	0.649367	−	0.760475i	$-0.275034\pi$
$23$	−1.60137	−	2.77365i	−0.333908	−	0.578345i	−0.983274	+	0.182130i	$0.941701\pi$
$24$		0			0
$25$	2.28958	+	3.96567i	0.457916	+	0.793134i
$26$	−1.18254	−	9.50408i	−0.231914	−	1.86390i
$27$		0			0
$28$	−3.91301	+	6.77754i	−0.739490	+	1.28083i
$29$	6.83026			1.26835			0.634173	−	0.773191i	$-0.281341\pi$
$29$	6.83026			1.26835			0.634173	+	0.773191i	$0.281341\pi$
$30$		0			0
$31$	1.58024	−	2.73705i	0.283819	−	0.491589i	−0.688503	−	0.725233i	$-0.741732\pi$
$31$	1.58024	−	2.73705i	0.283819	−	0.491589i	0.972322	+	0.233645i	$0.0750653\pi$
$32$	14.1798			2.50665
$33$		0			0
$34$	0.275796	+	0.477692i	0.0472986	+	0.0819235i
$35$	−0.502082	−	0.869631i	−0.0848673	−	0.146995i
$36$		0			0
$37$	−4.71300	+	8.16316i	−0.774813	+	1.34202i	0.160087	+	0.987103i	$0.448823\pi$
$37$	−4.71300	+	8.16316i	−0.774813	+	1.34202i	−0.934900	+	0.354912i	$0.884511\pi$
$38$	−4.76772	−	8.25793i	−0.773426	−	1.33961i
$39$		0			0
$40$	−2.63289	+	4.56031i	−0.416297	+	0.721048i
$41$	−4.30114	−	7.44979i	−0.671725	−	1.16346i	−0.977415	−	0.211331i	$-0.932220\pi$
$41$	−4.30114	−	7.44979i	−0.671725	−	1.16346i	0.305689	−	0.952131i	$-0.401113\pi$
$42$		0			0
$43$	−2.99929	+	5.19492i	−0.457387	+	0.792217i	−0.998822	−	0.0485254i	$-0.984548\pi$
$43$	−2.99929	+	5.19492i	−0.457387	+	0.792217i	0.541435	+	0.840743i	$0.317881\pi$
$44$	−25.6335			−3.86440
$45$		0			0
$46$	−4.25368	−	7.36759i	−0.627171	−	1.08629i
$47$	1.42859	+	2.47438i	0.208381	+	0.360926i	0.951205	−	0.308561i	$-0.0998474\pi$
$47$	1.42859	+	2.47438i	0.208381	+	0.360926i	−0.742824	+	0.669487i	$0.766514\pi$
$48$		0			0
$49$	2.30198	+	3.98714i	0.328854	+	0.569592i
$50$	6.08178	+	10.5340i	0.860093	+	1.48973i
$51$		0			0
$52$	−2.25078	−	18.0896i	−0.312128	−	2.50858i
$53$	2.48667			0.341571			0.170786	−	0.985308i	$-0.445369\pi$
$53$	2.48667			0.341571			0.170786	+	0.985308i	$0.445369\pi$
$54$		0			0
$55$	1.64453	−	2.84841i	0.221748	−	0.384079i
$56$	−6.28237	+	10.8814i	−0.839517	+	1.45409i
$57$		0			0
$58$	18.1431			2.38231
$59$	2.98403			0.388487			0.194244	−	0.980953i	$-0.437775\pi$
$59$	2.98403			0.388487			0.194244	+	0.980953i	$0.437775\pi$
$60$		0			0
$61$	−4.02238	+	6.96697i	−0.515013	+	0.892029i	0.484835	+	0.874606i	$0.338880\pi$
$61$	−4.02238	+	6.96697i	−0.515013	+	0.892029i	−0.999848	+	0.0174233i	$0.994454\pi$
$62$	4.19756	−	7.27038i	0.533090	−	0.923339i
$63$		0			0
$64$	14.7657			1.84572
$65$	2.15453	+	0.910439i	0.267236	+	0.112926i
$66$		0			0
$67$	−2.47432	−	4.28565i	−0.302286	−	0.523575i	0.674367	−	0.738396i	$-0.264417\pi$
$67$	−2.47432	−	4.28565i	−0.302286	−	0.523575i	−0.976653	+	0.214821i	$0.931083\pi$
$68$	0.524937	+	0.909217i	0.0636579	+	0.110259i
$69$		0			0
$70$	−1.33367	−	2.30999i	−0.159404	−	0.276096i
$71$	0.787066	+	1.36324i	0.0934076	+	0.161787i	0.908943	−	0.416921i	$-0.136891\pi$
$71$	0.787066	+	1.36324i	0.0934076	+	0.161787i	−0.815535	+	0.578707i	$0.803557\pi$
$72$		0			0
$73$	3.03817			0.355591			0.177796	−	0.984067i	$-0.443103\pi$
$73$	3.03817			0.355591			0.177796	+	0.984067i	$0.443103\pi$
$74$	−12.5191	+	21.6837i	−1.45531	+	2.52068i
$75$		0			0
$76$	−9.07465	−	15.7178i	−1.04093	−	1.80295i
$77$	3.92403	−	6.79661i	0.447184	−	0.774546i
$78$		0			0
$79$	3.23418	+	5.60177i	0.363874	+	0.630248i	0.988595	−	0.150600i	$-0.0481205\pi$
$79$	3.23418	+	5.60177i	0.363874	+	0.630248i	−0.624721	+	0.780848i	$0.714787\pi$
$80$	−3.71389	+	6.43264i	−0.415225	+	0.719191i
$81$		0			0
$82$	−11.4251	−	19.7888i	−1.26169	−	2.18530i
$83$	−1.24623	−	2.15854i	−0.136792	−	0.236931i	0.789489	−	0.613765i	$-0.210346\pi$
$83$	−1.24623	−	2.15854i	−0.136792	−	0.236931i	−0.926281	+	0.376835i	$0.877013\pi$
$84$		0			0
$85$	−0.134710			−0.0146114
$86$	−7.96696	+	13.7992i	−0.859099	+	1.48800i
$87$		0			0
$88$	−41.1548			−4.38712
$89$	1.76275	−	3.05317i	0.186851	−	0.323635i	−0.757348	−	0.653012i	$-0.773505\pi$
$89$	1.76275	−	3.05317i	0.186851	−	0.323635i	0.944199	+	0.329376i	$0.106839\pi$
$90$		0			0
$91$	5.14094	+	2.17241i	0.538916	+	0.227730i
$92$	−8.09626	−	14.0231i	−0.844093	−	1.46201i
$93$		0			0
$94$	3.79473	+	6.57267i	0.391397	+	0.677919i
$95$	2.32875			0.238925
$96$		0			0
$97$	4.69325	−	8.12894i	0.476527	−	0.825369i	−0.523111	−	0.852265i	$-0.675229\pi$
$97$	4.69325	−	8.12894i	0.476527	−	0.825369i	0.999638	+	0.0268952i	$0.00856206\pi$
$98$	6.11471	+	10.5910i	0.617679	+	1.06985i
$99$		0			0
$100$	11.5758	+	20.0498i	1.15758	+	2.00498i
$101$	4.18722			0.416644			0.208322	−	0.978060i	$-0.433200\pi$
$101$	4.18722			0.416644			0.208322	+	0.978060i	$0.433200\pi$
$102$		0			0
$103$	2.03207	−	3.51965i	0.200226	−	0.346801i	−0.748375	−	0.663275i	$-0.769166\pi$
$103$	2.03207	−	3.51965i	0.200226	−	0.346801i	0.948601	+	0.316474i	$0.102499\pi$
$104$	−3.61365	−	29.0430i	−0.354348	−	2.84790i
$105$		0			0
$106$	6.60532			0.641565
$107$	−5.05806	+	8.76081i	−0.488981	+	0.846940i	−0.999920	−	0.0126775i	$-0.995965\pi$
$107$	−5.05806	+	8.76081i	−0.488981	+	0.846940i	0.510939	+	0.859617i	$0.329298\pi$
$108$		0			0
$109$	−4.37589			−0.419134			−0.209567	−	0.977794i	$-0.567205\pi$
$109$	−4.37589			−0.419134			−0.209567	+	0.977794i	$0.567205\pi$
$110$	4.36834	−	7.56619i	0.416505	−	0.721407i
$111$		0			0
$112$	−8.86174	+	15.3490i	−0.837355	+	1.45034i
$113$	13.4142			1.26190			0.630951	−	0.775823i	$-0.282665\pi$
$113$	13.4142			1.26190			0.630951	+	0.775823i	$0.282665\pi$
$114$		0			0
$115$	2.07767			0.193744
$116$	34.5327			3.20628
$117$		0			0
$118$	7.92642			0.729686
$119$	−0.321433			−0.0294657
$120$		0			0
$121$	14.7057			1.33688
$122$	−10.6846	+	18.5062i	−0.967337	+	1.67548i
$123$		0			0
$124$	7.98943	−	13.8381i	0.717472	−	1.24270i
$125$	−6.21419			−0.555814
$126$		0			0
$127$	6.23233	−	10.7947i	0.553029	−	0.957875i	−0.445024	−	0.895518i	$-0.646805\pi$
$127$	6.23233	−	10.7947i	0.553029	−	0.957875i	0.998054	−	0.0623567i	$-0.0198617\pi$
$128$	10.8624			0.960113
$129$		0			0
$130$	5.72304	+	2.41839i	0.501943	+	0.212106i
$131$	−9.84851	+	17.0581i	−0.860468	+	1.49037i	0.0110094	+	0.999939i	$0.496496\pi$
$131$	−9.84851	+	17.0581i	−0.860468	+	1.49037i	−0.871478	+	0.490435i	$0.836838\pi$
$132$		0			0
$133$	5.55665			0.481823
$134$	−6.57250	−	11.3839i	−0.567777	−	0.983419i
$135$		0			0
$136$	0.842789	+	1.45975i	0.0722686	+	0.125173i
$137$	7.09825	−	12.2945i	0.606444	−	1.05039i	−0.385377	−	0.922759i	$-0.625929\pi$
$137$	7.09825	−	12.2945i	0.606444	−	1.05039i	0.991821	−	0.127633i	$-0.0407380\pi$
$138$		0			0
$139$	3.49371			0.296333			0.148166	−	0.988962i	$-0.452663\pi$
$139$	3.49371			0.296333			0.148166	+	0.988962i	$0.452663\pi$
$140$	−2.53845	−	4.39672i	−0.214538	−	0.371591i
$141$		0			0
$142$	2.09067	+	3.62115i	0.175445	+	0.303880i
$143$	2.25712	+	18.1405i	0.188750	+	1.51699i
$144$		0			0
$145$	−2.21546	+	3.83729i	−0.183984	+	0.318670i
$146$	8.07025			0.667899
$147$		0			0
$148$	−23.8282	+	41.2717i	−1.95867	+	3.39251i
$149$	12.3716			1.01352			0.506761	−	0.862087i	$-0.330843\pi$
$149$	12.3716			1.01352			0.506761	+	0.862087i	$0.330843\pi$
$150$		0			0
$151$	0.517479	+	0.896300i	0.0421118	+	0.0729398i	0.886313	−	0.463087i	$-0.153258\pi$
$151$	0.517479	+	0.896300i	0.0421118	+	0.0729398i	−0.844201	+	0.536026i	$0.819925\pi$
$152$	−14.5694	−	25.2350i	−1.18174	−	2.04683i
$153$		0			0
$154$	10.4233	−	18.0537i	0.839936	−	1.45481i
$155$	1.02513	+	1.77558i	0.0823405	+	0.142618i
$156$		0			0
$157$	0.504491	−	0.873804i	0.0402628	−	0.0697372i	−0.845192	−	0.534463i	$-0.820514\pi$
$157$	0.504491	−	0.873804i	0.0402628	−	0.0697372i	0.885455	+	0.464726i	$0.153847\pi$
$158$	8.59091	+	14.8799i	0.683456	+	1.18378i
$159$		0			0
$160$	−4.59935	+	7.96631i	−0.363611	+	0.629792i
$161$	4.95756			0.390710
$162$		0			0
$163$	−3.52876	−	6.11200i	−0.276394	−	0.478728i	0.694092	−	0.719886i	$-0.255806\pi$
$163$	−3.52876	−	6.11200i	−0.276394	−	0.478728i	−0.970486	+	0.241158i	$0.922473\pi$
$164$	−21.7459	−	37.6650i	−1.69807	−	2.94114i
$165$		0			0
$166$	−3.31035	−	5.73370i	−0.256933	−	0.445021i
$167$	−9.22813	−	15.9836i	−0.714094	−	1.23685i	−0.963308	−	0.268398i	$-0.913506\pi$
$167$	−9.22813	−	15.9836i	−0.714094	−	1.23685i	0.249214	−	0.968448i	$-0.419828\pi$
$168$		0			0
$169$	−12.6036	+	3.18571i	−0.969509	+	0.245054i
$170$	−0.357828			−0.0274442
$171$		0			0
$172$	−15.1639	+	26.2647i	−1.15624	+	2.00266i
$173$	0.879831	−	1.52391i	0.0668923	−	0.115861i	−0.830640	−	0.556811i	$-0.812025\pi$
$173$	0.879831	−	1.52391i	0.0668923	−	0.115861i	0.897532	+	0.440950i	$0.145358\pi$
$174$		0			0
$175$	−7.08816			−0.535814
$176$	−58.0519			−4.37582
$177$		0			0
$178$	4.68236	−	8.11009i	0.350958	−	0.607877i
$179$	4.63867	−	8.03441i	0.346711	−	0.600520i	−0.638952	−	0.769246i	$-0.720632\pi$
$179$	4.63867	−	8.03441i	0.346711	−	0.600520i	0.985663	+	0.168726i	$0.0539653\pi$
$180$		0			0
$181$	−17.7014			−1.31574			−0.657868	−	0.753133i	$-0.728541\pi$
$181$	−17.7014			−1.31574			−0.657868	+	0.753133i	$0.728541\pi$
$182$	13.6558	+	5.77053i	1.01223	+	0.427740i
$183$		0			0
$184$	−12.9986	−	22.5142i	−0.958269	−	1.65977i
$185$	−3.05742	−	5.29560i	−0.224786	−	0.389341i
$186$		0			0
$187$	−0.526414	−	0.911776i	−0.0384952	−	0.0666757i
$188$	7.22271	+	12.5101i	0.526771	+	0.912393i
$189$		0			0
$190$	6.18583			0.448767
$191$	0.271844	−	0.470847i	0.0196699	−	0.0340693i	−0.856023	−	0.516938i	$-0.827072\pi$
$191$	0.271844	−	0.470847i	0.0196699	−	0.0340693i	0.875693	+	0.482869i	$0.160405\pi$
$192$		0			0
$193$	12.3513	+	21.3931i	0.889065	+	1.53991i	0.840982	+	0.541063i	$0.181978\pi$
$193$	12.3513	+	21.3931i	0.889065	+	1.53991i	0.0480832	+	0.998843i	$0.484689\pi$
$194$	12.4666	−	21.5928i	0.895050	−	1.55027i
$195$		0			0
$196$	11.6384	+	20.1584i	0.831318	+	1.43988i
$197$	−9.01337	+	15.6116i	−0.642176	+	1.11228i	0.342770	+	0.939419i	$0.388635\pi$
$197$	−9.01337	+	15.6116i	−0.642176	+	1.11228i	−0.984946	+	0.172863i	$0.944698\pi$
$198$		0			0
$199$	−8.59093	−	14.8799i	−0.608995	−	1.05481i	−0.991406	−	0.130818i	$-0.958240\pi$
$199$	−8.59093	−	14.8799i	−0.608995	−	1.05481i	0.382412	−	0.923992i	$-0.375094\pi$
$200$	18.5850	+	32.1901i	1.31416	+	2.27619i
$201$		0			0
$202$	11.1225			0.782573
$203$	−5.28633	+	9.15620i	−0.371028	+	0.642639i
$204$		0			0
$205$	5.58047			0.389757
$206$	5.39775	−	9.34918i	0.376079	−	0.651388i
$207$		0			0
$208$	−5.09731	−	40.9673i	−0.353435	−	2.84057i
$209$	9.10019	+	15.7620i	0.629473	+	1.09028i
$210$		0			0
$211$	−1.35161	−	2.34105i	−0.0930483	−	0.161164i	0.815744	−	0.578413i	$-0.196328\pi$
$211$	−1.35161	−	2.34105i	−0.0930483	−	0.161164i	−0.908792	+	0.417249i	$0.862994\pi$
$212$	12.5722			0.863465
$213$		0			0
$214$	−13.4356	+	23.2712i	−0.918441	+	1.59079i
$215$	−1.94570	−	3.37004i	−0.132695	−	0.229835i
$216$		0			0
$217$	2.44607	+	4.23672i	0.166050	+	0.287607i
$218$	−11.6236			−0.787250
$219$		0			0
$220$	8.31449	−	14.4011i	0.560563	−	0.970923i
$221$	0.597219	−	0.451551i	0.0401733	−	0.0303746i
$222$		0			0
$223$	5.22419			0.349838			0.174919	−	0.984583i	$-0.444034\pi$
$223$	5.22419			0.349838			0.174919	+	0.984583i	$0.444034\pi$
$224$	−10.9746	+	19.0085i	−0.733268	+	1.27006i
$225$		0			0
$226$	35.6319			2.37020
$227$	−2.78555	+	4.82471i	−0.184883	+	0.320227i	−0.943537	−	0.331267i	$-0.892524\pi$
$227$	−2.78555	+	4.82471i	−0.184883	+	0.320227i	0.758654	+	0.651494i	$0.225857\pi$
$228$		0			0
$229$	11.4445	−	19.8225i	0.756276	−	1.30991i	−0.188461	−	0.982081i	$-0.560350\pi$
$229$	11.4445	−	19.8225i	0.756276	−	1.30991i	0.944737	−	0.327828i	$-0.106317\pi$
$230$	5.51889			0.363905
$231$		0			0
$232$	55.4425			3.63998
$233$	−15.4122			−1.00969			−0.504844	−	0.863211i	$-0.668450\pi$
$233$	−15.4122			−1.00969			−0.504844	+	0.863211i	$0.668450\pi$
$234$		0			0
$235$	−1.85350			−0.120909
$236$	15.0868			0.982066
$237$		0			0
$238$	−0.853817			−0.0553447
$239$	5.97112	−	10.3423i	0.386240	−	0.668987i	−0.605701	−	0.795693i	$-0.707107\pi$
$239$	5.97112	−	10.3423i	0.386240	−	0.668987i	0.991940	+	0.126706i	$0.0404404\pi$
$240$		0			0
$241$	8.91315	−	15.4380i	0.574146	−	0.994450i	−0.421988	−	0.906602i	$-0.638667\pi$
$241$	8.91315	−	15.4380i	0.574146	−	0.994450i	0.996134	−	0.0878488i	$-0.0279992\pi$
$242$	39.0625			2.51103
$243$		0			0
$244$	−20.3365	+	35.2239i	−1.30191	+	2.25498i
$245$	−2.98668			−0.190812
$246$		0			0
$247$	−10.3242	+	7.80602i	−0.656914	+	0.496685i
$248$	12.8271	−	22.2172i	0.814521	−	1.41079i
$249$		0			0
$250$	−16.5067			−1.04397
$251$	−0.779623	−	1.35035i	−0.0492094	−	0.0852331i	0.840372	−	0.542011i	$-0.182337\pi$
$251$	−0.779623	−	1.35035i	−0.0492094	−	0.0852331i	−0.889581	+	0.456778i	$0.849003\pi$
$252$		0			0
$253$	8.11905	+	14.0626i	0.510440	+	0.884108i
$254$	16.5548	−	28.6738i	1.03874	−	1.79915i
$255$		0			0
$256$	−0.677748			−0.0423593
$257$	9.90154	+	17.1500i	0.617641	+	1.06979i	0.989915	+	0.141663i	$0.0452450\pi$
$257$	9.90154	+	17.1500i	0.617641	+	1.06979i	−0.372274	+	0.928123i	$0.621422\pi$
$258$		0			0
$259$	−7.29533	−	12.6359i	−0.453310	−	0.785156i
$260$	10.8930	+	4.60304i	0.675553	+	0.285469i
$261$		0			0
$262$	−26.1604	+	45.3112i	−1.61620	+	2.79934i
$263$	−16.3224			−1.00648			−0.503241	−	0.864146i	$-0.667859\pi$
$263$	−16.3224			−1.00648			−0.503241	+	0.864146i	$0.667859\pi$
$264$		0			0
$265$	−0.806578	+	1.39703i	−0.0495477	+	0.0858191i
$266$	14.7601			0.904997
$267$		0			0
$268$	−12.5098	−	21.6676i	−0.764157	−	1.32356i
$269$	−15.1854	−	26.3019i	−0.925870	−	1.60365i	−0.790156	−	0.612906i	$-0.790000\pi$
$269$	−15.1854	−	26.3019i	−0.925870	−	1.60365i	−0.135714	−	0.990748i	$-0.543333\pi$
$270$		0			0
$271$	−11.5518	+	20.0082i	−0.701719	+	1.21541i	0.266143	+	0.963933i	$0.414251\pi$
$271$	−11.5518	+	20.0082i	−0.701719	+	1.21541i	−0.967863	+	0.251480i	$0.919083\pi$
$272$	1.18882	+	2.05909i	0.0720825	+	0.124851i
$273$		0			0
$274$	18.8550	−	32.6578i	1.13907	−	1.97293i
$275$	−11.6084	−	20.1063i	−0.700010	−	1.21245i
$276$		0			0
$277$	6.84420	−	11.8545i	0.411228	−	0.712268i	−0.583796	−	0.811900i	$-0.698433\pi$
$277$	6.84420	−	11.8545i	0.411228	−	0.712268i	0.995024	+	0.0996320i	$0.0317665\pi$
$278$	9.28030			0.556595
$279$		0			0
$280$	−4.07550	−	7.05897i	−0.243558	−	0.421854i
$281$	13.2269	+	22.9096i	0.789049	+	1.36667i	0.926550	+	0.376171i	$0.122760\pi$
$281$	13.2269	+	22.9096i	0.789049	+	1.36667i	−0.137501	+	0.990502i	$0.543907\pi$
$282$		0			0
$283$	−3.30018	−	5.71608i	−0.196175	−	0.339786i	0.751110	−	0.660177i	$-0.229519\pi$
$283$	−3.30018	−	5.71608i	−0.196175	−	0.339786i	−0.947285	+	0.320392i	$0.896185\pi$
$284$	3.97929	+	6.89233i	0.236127	+	0.408984i
$285$		0			0
$286$	5.99555	+	48.1864i	0.354524	+	2.84932i
$287$	13.3156			0.785996
$288$		0			0
$289$	8.47844	−	14.6851i	0.498732	−	0.863829i
$290$	−5.88490	+	10.1929i	−0.345573	+	0.598550i
$291$		0			0
$292$	15.3605			0.898907
$293$	0.494901			0.0289124			0.0144562	−	0.999896i	$-0.495398\pi$
$293$	0.494901			0.0289124			0.0144562	+	0.999896i	$0.495398\pi$
$294$		0			0
$295$	−0.967898	+	1.67645i	−0.0563532	+	0.0976066i
$296$	−38.2564	+	66.2620i	−2.22361	+	3.85140i
$297$		0			0
$298$	32.8625			1.90367
$299$	−9.21110	+	6.96441i	−0.532691	+	0.402762i
$300$		0			0
$301$	−4.64264	−	8.04129i	−0.267597	−	0.463492i
$302$	1.37457	+	2.38083i	0.0790977	+	0.137001i
$303$		0			0
$304$	−20.5512	−	35.5957i	−1.17869	−	2.04156i
$305$	−2.60940	−	4.51961i	−0.149414	−	0.258792i
$306$		0			0
$307$	3.08744			0.176210			0.0881048	−	0.996111i	$-0.471919\pi$
$307$	3.08744			0.176210			0.0881048	+	0.996111i	$0.471919\pi$
$308$	19.8393	−	34.3626i	1.13045	−	1.95799i
$309$		0			0
$310$	2.72304	+	4.71644i	0.154658	+	0.267876i
$311$	−4.13808	+	7.16736i	−0.234649	+	0.406424i	−0.959171	−	0.282828i	$-0.908727\pi$
$311$	−4.13808	+	7.16736i	−0.234649	+	0.406424i	0.724522	+	0.689252i	$0.242061\pi$
$312$		0			0
$313$	14.4586	+	25.0429i	0.817246	+	1.41551i	0.907704	+	0.419611i	$0.137833\pi$
$313$	14.4586	+	25.0429i	0.817246	+	1.41551i	−0.0904586	+	0.995900i	$0.528833\pi$
$314$	1.34007	−	2.32107i	0.0756246	−	0.130986i
$315$		0			0
$316$	16.3515	+	28.3217i	0.919846	+	1.59322i
$317$	1.41121	+	2.44429i	0.0792615	+	0.137285i	0.902932	−	0.429784i	$-0.141410\pi$
$317$	1.41121	+	2.44429i	0.0792615	+	0.137285i	−0.823670	+	0.567069i	$0.808077\pi$
$318$		0			0
$319$	−34.6299			−1.93890
$320$	−4.78941	+	8.29551i	−0.267736	+	0.463733i
$321$		0			0
$322$	13.1687			0.733862
$323$	0.372717	−	0.645564i	0.0207385	−	0.0359202i
$324$		0			0
$325$	13.1697	−	9.95749i	0.730525	−	0.552342i
$326$	−9.37340	−	16.2352i	−0.519144	−	0.899185i
$327$		0			0
$328$	−34.9132	−	60.4715i	−1.92776	−	3.33898i
$329$	−4.42266			−0.243829
$330$		0			0
$331$	6.07904	−	10.5292i	0.334134	−	0.578737i	−0.649184	−	0.760631i	$-0.724889\pi$
$331$	6.07904	−	10.5292i	0.334134	−	0.578737i	0.983318	+	0.181894i	$0.0582228\pi$
$332$	−6.30077	−	10.9133i	−0.345800	−	0.598943i
$333$		0			0
$334$	−24.5125	−	42.4569i	−1.34127	−	2.32314i
$335$	3.21028			0.175396
$336$		0			0
$337$	−10.2611	+	17.7727i	−0.558956	+	0.968139i	0.438628	+	0.898668i	$0.355464\pi$
$337$	−10.2611	+	17.7727i	−0.558956	+	0.968139i	−0.997584	+	0.0694709i	$0.977869\pi$
$338$	−33.4788	+	8.46214i	−1.82101	+	0.460280i
$339$		0			0
$340$	−0.681073			−0.0369364
$341$	−8.01192	+	13.8771i	−0.433870	+	0.751484i
$342$		0			0
$343$	−17.9619			−0.969854
$344$	−24.3458	+	42.1682i	−1.31264	+	2.27355i
$345$		0			0
$346$	2.33708	−	4.04794i	0.125642	−	0.217619i
$347$	−21.6959			−1.16470			−0.582348	−	0.812940i	$-0.697866\pi$
$347$	−21.6959			−1.16470			−0.582348	+	0.812940i	$0.697866\pi$
$348$		0			0
$349$	−34.4486			−1.84399			−0.921995	−	0.387201i	$-0.873442\pi$
$349$	−34.4486			−1.84399			−0.921995	+	0.387201i	$0.873442\pi$
$350$	−18.8282			−1.00641
$351$		0			0
$352$	−71.8926			−3.83189
$353$	1.42723			0.0759639			0.0379819	−	0.999278i	$-0.487907\pi$
$353$	1.42723			0.0759639			0.0379819	+	0.999278i	$0.487907\pi$
$354$		0			0
$355$	−1.02117			−0.0541981
$356$	8.91218	−	15.4364i	0.472345	−	0.818125i
$357$		0			0
$358$	12.3216	−	21.3417i	0.651218	−	1.12794i
$359$	−8.30365			−0.438250			−0.219125	−	0.975697i	$-0.570320\pi$
$359$	−8.30365			−0.438250			−0.219125	+	0.975697i	$0.570320\pi$
$360$		0			0
$361$	3.05680	−	5.29453i	0.160884	−	0.278659i
$362$	−47.0200			−2.47132
$363$		0			0
$364$	25.9918	+	10.9834i	1.36234	+	0.575684i
$365$	−0.985461	+	1.70687i	−0.0515814	+	0.0893416i
$366$		0			0
$367$	−30.9192			−1.61397			−0.806984	−	0.590573i	$-0.798902\pi$
$367$	−30.9192			−1.61397			−0.806984	+	0.590573i	$0.798902\pi$
$368$	−18.3355	−	31.7580i	−0.955802	−	1.65550i
$369$		0			0
$370$	−8.12137	−	14.0666i	−0.422210	−	0.731289i
$371$	−1.92458	+	3.33347i	−0.0999193	+	0.173065i
$372$		0			0
$373$	14.2576			0.738230			0.369115	−	0.929384i	$-0.379661\pi$
$373$	14.2576			0.738230			0.369115	+	0.929384i	$0.379661\pi$
$374$	−1.39831	−	2.42194i	−0.0723047	−	0.125235i
$375$		0			0
$376$	11.5961	+	20.0851i	0.598024	+	1.03581i
$377$	−3.04072	−	24.4384i	−0.156605	−	1.25864i
$378$		0			0
$379$	3.17631	−	5.50154i	0.163156	−	0.282595i	−0.772843	−	0.634598i	$-0.781166\pi$
$379$	3.17631	−	5.50154i	0.163156	−	0.282595i	0.935999	+	0.352003i	$0.114499\pi$
$380$	11.7738			0.603984
$381$		0			0
$382$	0.722094	−	1.25070i	0.0369455	−	0.0639915i
$383$	−29.1159			−1.48775			−0.743877	−	0.668316i	$-0.767015\pi$
$383$	−29.1159			−1.48775			−0.743877	+	0.668316i	$0.767015\pi$
$384$		0			0
$385$	2.54559	+	4.40910i	0.129735	+	0.224708i
$386$	32.8085	+	56.8261i	1.66991	+	2.89237i
$387$		0			0
$388$	23.7283	−	41.0987i	1.20462	−	2.08647i
$389$	−15.8354	−	27.4277i	−0.802887	−	1.39064i	−0.917708	−	0.397255i	$-0.869963\pi$
$389$	−15.8354	−	27.4277i	−0.802887	−	1.39064i	0.114821	−	0.993386i	$-0.463371\pi$
$390$		0			0
$391$	0.332532	−	0.575962i	0.0168169	−	0.0291277i
$392$	18.6856	+	32.3644i	0.943766	+	1.63465i
$393$		0			0
$394$	−23.9421	+	41.4689i	−1.20618	+	2.08917i
$395$	−4.19616			−0.211132
$396$		0			0
$397$	7.89246	+	13.6701i	0.396111	+	0.686085i	0.993242	−	0.116059i	$-0.0370261\pi$
$397$	7.89246	+	13.6701i	0.396111	+	0.686085i	−0.597131	+	0.802144i	$0.703693\pi$
$398$	−22.8199	−	39.5253i	−1.14386	−	1.98122i
$399$		0			0
$400$	26.2155	+	45.4065i	1.31077	+	2.27033i
$401$	−0.379497	−	0.657309i	−0.0189512	−	0.0328244i	0.856394	−	0.516322i	$-0.172699\pi$
$401$	−0.379497	−	0.657309i	−0.0189512	−	0.0328244i	−0.875345	+	0.483498i	$0.839366\pi$
$402$		0			0
$403$	−10.4966	−	4.43553i	−0.522871	−	0.220950i
$404$	21.1700			1.05324
$405$		0			0
$406$	−14.0420	+	24.3215i	−0.696893	+	1.20705i
$407$	23.8953	−	41.3879i	1.18445	−	2.05152i
$408$		0			0
$409$	−26.9714			−1.33365			−0.666824	−	0.745215i	$-0.732347\pi$
$409$	−26.9714			−1.33365			−0.666824	+	0.745215i	$0.732347\pi$
$410$	14.8233			0.732071
$411$		0			0
$412$	10.2738	−	17.7948i	0.506155	−	0.876686i
$413$	−2.30951	+	4.00019i	−0.113644	+	0.196836i
$414$		0			0
$415$	1.61691			0.0793712
$416$	−6.31262	−	50.7347i	−0.309501	−	2.48747i
$417$		0			0
$418$	24.1727	+	41.8683i	1.18233	+	2.04785i
$419$	5.30079	+	9.18123i	0.258960	+	0.448533i	0.965964	−	0.258678i	$-0.0832867\pi$
$419$	5.30079	+	9.18123i	0.258960	+	0.448533i	−0.707003	+	0.707210i	$0.749953\pi$
$420$		0			0
$421$	−8.35573	−	14.4725i	−0.407233	−	0.705349i	0.587345	−	0.809336i	$-0.300173\pi$
$421$	−8.35573	−	14.4725i	−0.407233	−	0.705349i	−0.994579	+	0.103988i	$0.966840\pi$
$422$	−3.59025	−	6.21849i	−0.174771	−	0.302711i
$423$		0			0
$424$	20.1848			0.980262
$425$	−0.475444	+	0.823492i	−0.0230624	+	0.0399452i
$426$		0			0
$427$	−6.22631	−	10.7843i	−0.301312	−	0.521888i
$428$	−25.5728	+	44.2933i	−1.23611	+	2.14100i
$429$		0			0
$430$	−5.16832	−	8.95180i	−0.249239	−	0.431694i
$431$	4.15171	−	7.19098i	0.199981	−	0.346377i	−0.748541	−	0.663089i	$-0.769245\pi$
$431$	4.15171	−	7.19098i	0.199981	−	0.346377i	0.948522	+	0.316711i	$0.102579\pi$
$432$		0			0
$433$	0.0394092	+	0.0682587i	0.00189388	+	0.00328030i	0.866971	−	0.498359i	$-0.166064\pi$
$433$	0.0394092	+	0.0682587i	0.00189388	+	0.00328030i	−0.865077	+	0.501639i	$0.832730\pi$
$434$	6.49746	+	11.2539i	0.311888	+	0.540206i
$435$		0			0
$436$	−22.1238			−1.05954
$437$	−5.74852	+	9.95673i	−0.274989	+	0.476295i
$438$		0			0
$439$	25.7420			1.22860			0.614298	−	0.789074i	$-0.289439\pi$
$439$	25.7420			1.22860			0.614298	+	0.789074i	$0.289439\pi$
$440$	13.3490	−	23.1211i	0.636387	−	1.10226i
$441$		0			0
$442$	1.58638	−	1.19945i	0.0754566	−	0.0570519i
$443$	14.1715	+	24.5458i	0.673309	+	1.16621i	0.976960	+	0.213422i	$0.0684609\pi$
$443$	14.1715	+	24.5458i	0.673309	+	1.16621i	−0.303651	+	0.952783i	$0.598206\pi$
$444$		0			0
$445$	1.14353	+	1.98065i	0.0542085	+	0.0938919i
$446$	13.8769			0.657092
$447$		0			0
$448$	−11.4281	+	19.7940i	−0.539925	+	0.935178i
$449$	−2.18709	−	3.78815i	−0.103215	−	0.178774i	0.809792	−	0.586716i	$-0.199580\pi$
$449$	−2.18709	−	3.78815i	−0.103215	−	0.178774i	−0.913008	+	0.407943i	$0.866246\pi$
$450$		0			0
$451$	21.8071	+	37.7710i	1.02686	+	1.77857i
$452$	67.8201			3.18999
$453$		0			0
$454$	−7.39920	+	12.8158i	−0.347262	+	0.601475i
$455$	−2.88799	+	2.18358i	−0.135391	+	0.102368i
$456$		0			0
$457$	−13.5568			−0.634161			−0.317080	−	0.948399i	$-0.602703\pi$
$457$	−13.5568			−0.634161			−0.317080	+	0.948399i	$0.602703\pi$
$458$	30.3999	−	52.6542i	1.42050	−	2.46037i
$459$		0			0
$460$	10.5044			0.489770
$461$	1.00295	−	1.73716i	0.0467120	−	0.0809076i	−0.841724	−	0.539908i	$-0.818459\pi$
$461$	1.00295	−	1.73716i	0.0467120	−	0.0809076i	0.888436	+	0.459000i	$0.151792\pi$
$462$		0			0
$463$	−20.7451	+	35.9315i	−0.964104	+	1.66988i	−0.252102	+	0.967701i	$0.581122\pi$
$463$	−20.7451	+	35.9315i	−0.964104	+	1.66988i	−0.712002	+	0.702177i	$0.752211\pi$
$464$	78.2057			3.63061
$465$		0			0
$466$	−40.9392			−1.89647
$467$	25.0664			1.15993			0.579967	−	0.814640i	$-0.303065\pi$
$467$	25.0664			1.15993			0.579967	+	0.814640i	$0.303065\pi$
$468$		0			0
$469$	7.66008			0.353710
$470$	−4.92344			−0.227101
$471$		0			0
$472$	24.2219			1.11490
$473$	15.2066	−	26.3386i	0.699201	−	1.21105i
$474$		0			0
$475$	8.21906	−	14.2358i	0.377116	−	0.653184i
$476$	−1.62512			−0.0744870
$477$		0			0
$478$	15.8610	−	27.4720i	0.725465	−	1.25654i
$479$	6.11222			0.279274			0.139637	−	0.990203i	$-0.455406\pi$
$479$	6.11222			0.279274			0.139637	+	0.990203i	$0.455406\pi$
$480$		0			0
$481$	31.3056	+	13.2288i	1.42741	+	0.603183i
$482$	23.6759	−	41.0078i	1.07841	−	1.86785i
$483$		0			0
$484$	74.3497			3.37953
$485$	3.04460	+	5.27341i	0.138248	+	0.239453i
$486$		0			0
$487$	−5.55082	−	9.61430i	−0.251532	−	0.435666i	0.712416	−	0.701757i	$-0.247601\pi$
$487$	−5.55082	−	9.61430i	−0.251532	−	0.435666i	−0.963948	+	0.266092i	$0.914268\pi$
$488$	−32.6505	+	56.5523i	−1.47802	+	2.56000i
$489$		0			0
$490$	−7.93346			−0.358397
$491$	1.13858	+	1.97207i	0.0513832	+	0.0889984i	0.890573	−	0.454840i	$-0.150304\pi$
$491$	1.13858	+	1.97207i	0.0513832	+	0.0889984i	−0.839190	+	0.543839i	$0.816970\pi$
$492$		0			0
$493$	0.709169	+	1.22832i	0.0319394	+	0.0553206i
$494$	−27.4240	+	20.7350i	−1.23387	+	0.932912i
$495$		0			0
$496$	18.0935	−	31.3389i	0.812424	−	1.40716i
$497$	−2.43662			−0.109298
$498$		0			0
$499$	−5.67665	+	9.83225i	−0.254122	+	0.440152i	−0.964657	−	0.263510i	$-0.915120\pi$
$499$	−5.67665	+	9.83225i	−0.254122	+	0.440152i	0.710535	+	0.703662i	$0.248453\pi$
$500$	−31.4180			−1.40506
$501$		0			0
$502$	−2.07090	−	3.58690i	−0.0924288	−	0.160091i
$503$	17.2266	+	29.8374i	0.768097	+	1.33038i	0.938594	+	0.345025i	$0.112129\pi$
$503$	17.2266	+	29.8374i	0.768097	+	1.33038i	−0.170497	+	0.985358i	$0.554537\pi$
$504$		0			0
$505$	−1.35817	+	2.35241i	−0.0604377	+	0.104681i
$506$	21.5665	+	37.3543i	0.958748	+	1.66060i
$507$		0			0
$508$	31.5097	−	54.5764i	1.39802	−	2.42144i
$509$	0.684664	+	1.18587i	0.0303472	+	0.0525629i	0.880800	−	0.473488i	$-0.157005\pi$
$509$	0.684664	+	1.18587i	0.0303472	+	0.0525629i	−0.850453	+	0.526051i	$0.823672\pi$
$510$		0			0
$511$	−2.35142	+	4.07278i	−0.104021	+	0.180169i
$512$	−23.5252			−1.03968
$513$		0			0
$514$	26.3013	+	45.5552i	1.16010	+	2.00935i
$515$	1.31824	+	2.28326i	0.0580887	+	0.100613i
$516$		0			0
$517$	−7.24304	−	12.5453i	−0.318549	−	0.551743i
$518$	−19.3785	−	33.5645i	−0.851441	−	1.47474i
$519$		0			0
$520$	17.4887	+	7.39022i	0.766931	+	0.324082i
$521$	4.08021			0.178757			0.0893785	−	0.995998i	$-0.471512\pi$
$521$	4.08021			0.178757			0.0893785	+	0.995998i	$0.471512\pi$
$522$		0			0
$523$	3.04053	−	5.26635i	0.132953	−	0.230281i	−0.791861	−	0.610702i	$-0.790887\pi$
$523$	3.04053	−	5.26635i	0.132953	−	0.230281i	0.924814	+	0.380420i	$0.124221\pi$
$524$	−49.7926	+	86.2432i	−2.17520	+	3.76755i
$525$		0			0
$526$	−43.3570			−1.89045
$527$	0.656289			0.0285884
$528$		0			0
$529$	6.37126	−	11.0353i	0.277011	−	0.479798i
$530$	−2.14250	+	3.71092i	−0.0930642	+	0.161192i
$531$		0			0
$532$	28.0936			1.21801
$533$	−24.7403	+	18.7058i	−1.07162	+	0.810240i
$534$		0			0
$535$	−3.28126	−	5.68331i	−0.141861	−	0.245711i
$536$	−20.0845	−	34.7875i	−0.867520	−	1.50259i
$537$		0			0
$538$	−40.3367	−	69.8653i	−1.73904	−	3.01211i
$539$	−11.6712	−	20.2151i	−0.502714	−	0.870727i
$540$		0			0
$541$	−25.5909			−1.10024			−0.550120	−	0.835086i	$-0.685418\pi$
$541$	−25.5909			−1.10024			−0.550120	+	0.835086i	$0.685418\pi$
$542$	−30.6847	+	53.1475i	−1.31802	+	2.28288i
$543$		0			0
$544$	1.47225	+	2.55002i	0.0631223	+	0.109331i
$545$	1.41936	−	2.45841i	0.0607988	−	0.105307i
$546$		0			0
$547$	−11.9024	−	20.6155i	−0.508909	−	0.881457i	−0.999947	−	0.0103185i	$-0.996715\pi$
$547$	−11.9024	−	20.6155i	−0.508909	−	0.881457i	0.491037	−	0.871139i	$-0.336618\pi$
$548$	35.8876	−	62.1592i	1.53304	−	2.65531i
$549$		0			0
$550$	−30.8351	−	53.4079i	−1.31481	−	2.27732i
$551$	−12.2595	−	21.2341i	−0.522272	−	0.904602i
$552$		0			0
$553$	−10.0125			−0.425774
$554$	18.1802	−	31.4889i	0.772401	−	1.33784i
$555$		0			0
$556$	17.6637			0.749107
$557$	−11.0730	+	19.1790i	−0.469178	+	0.812639i	−0.999379	−	0.0352323i	$-0.988783\pi$
$557$	−11.0730	+	19.1790i	−0.469178	+	0.812639i	0.530202	+	0.847872i	$0.322116\pi$
$558$		0			0
$559$	19.9224	+	8.41863i	0.842630	+	0.356070i
$560$	−5.74878	−	9.95719i	−0.242930	−	0.420768i
$561$		0			0
$562$	35.1343	+	60.8544i	1.48205	+	2.56699i
$563$	20.7225			0.873347			0.436674	−	0.899620i	$-0.356156\pi$
$563$	20.7225			0.873347			0.436674	+	0.899620i	$0.356156\pi$
$564$		0			0
$565$	−4.35103	+	7.53620i	−0.183049	+	0.317050i
$566$	−8.76621	−	15.1835i	−0.368471	−	0.638211i
$567$		0			0
$568$	6.38877	+	11.0657i	0.268067	+	0.464306i
$569$	44.5426			1.86732			0.933661	−	0.358159i	$-0.116595\pi$
$569$	44.5426			1.86732			0.933661	+	0.358159i	$0.116595\pi$
$570$		0			0
$571$	16.8188	−	29.1310i	0.703845	−	1.21910i	−0.263261	−	0.964725i	$-0.584798\pi$
$571$	16.8188	−	29.1310i	0.703845	−	1.21910i	0.967107	−	0.254371i	$-0.0818685\pi$
$572$	11.4117	+	91.7158i	0.477145	+	3.83483i
$573$		0			0
$574$	35.3700			1.47632
$575$	7.33291	−	12.7010i	0.305804	−	0.529667i
$576$		0			0
$577$	30.4547			1.26784			0.633922	−	0.773397i	$-0.281444\pi$
$577$	30.4547			1.26784			0.633922	+	0.773397i	$0.281444\pi$
$578$	22.5211	−	39.0078i	0.936756	−	1.62251i
$579$		0			0
$580$	−11.2010	+	19.4008i	−0.465098	+	0.805573i
$581$	3.85813			0.160062
$582$		0			0
$583$	−12.6076			−0.522155
$584$	24.6615			1.02050
$585$		0			0
$586$	1.31460			0.0543055
$587$	−42.0287			−1.73471			−0.867354	−	0.497691i	$-0.834181\pi$
$587$	−42.0287			−1.73471			−0.867354	+	0.497691i	$0.834181\pi$
$588$		0			0
$589$	−11.3453			−0.467477
$590$	−2.57101	+	4.45313i	−0.105847	+	0.183332i
$591$		0			0
$592$	−53.9634	+	93.4673i	−2.21788	+	3.84148i
$593$	6.55587			0.269217			0.134609	−	0.990899i	$-0.457022\pi$
$593$	6.55587			0.269217			0.134609	+	0.990899i	$0.457022\pi$
$594$		0			0
$595$	0.104260	−	0.180583i	0.00427424	−	0.00740320i
$596$	62.5489			2.56210
$597$		0			0
$598$	−24.4673	+	18.4994i	−1.00054	+	0.756499i
$599$	−11.5220	+	19.9566i	−0.470774	+	0.815405i	−0.999441	−	0.0334242i	$-0.989359\pi$
$599$	−11.5220	+	19.9566i	−0.470774	+	0.815405i	0.528667	+	0.848829i	$0.322692\pi$
$600$		0			0
$601$	5.81390			0.237154			0.118577	−	0.992945i	$-0.462167\pi$
$601$	5.81390			0.237154			0.118577	+	0.992945i	$0.462167\pi$
$602$	−12.3322	−	21.3600i	−0.502622	−	0.870567i
$603$		0			0
$604$	2.61629	+	4.53155i	0.106455	+	0.184386i
$605$	−4.76994	+	8.26177i	−0.193925	+	0.335889i
$606$		0			0
$607$	32.8020			1.33139			0.665696	−	0.746223i	$-0.268135\pi$
$607$	32.8020			1.33139			0.665696	+	0.746223i	$0.268135\pi$
$608$	−25.4510	−	44.0825i	−1.03218	−	1.78778i
$609$		0			0
$610$	−6.93130	−	12.0054i	−0.280640	−	0.486083i
$611$	8.21727	−	6.21298i	0.332435	−	0.251350i
$612$		0			0
$613$	1.48010	−	2.56360i	0.0597805	−	0.103543i	−0.834586	−	0.550877i	$-0.814293\pi$
$613$	1.48010	−	2.56360i	0.0597805	−	0.103543i	0.894367	+	0.447334i	$0.147627\pi$
$614$	8.20112			0.330970
$615$		0			0
$616$	31.8521	−	55.1695i	1.28336	−	2.22284i
$617$	45.4995			1.83174			0.915871	−	0.401472i	$-0.131501\pi$
$617$	45.4995			1.83174			0.915871	+	0.401472i	$0.131501\pi$
$618$		0			0
$619$	24.4251	+	42.3055i	0.981728	+	1.70040i	0.655659	+	0.755057i	$0.272391\pi$
$619$	24.4251	+	42.3055i	0.981728	+	1.70040i	0.326069	+	0.945346i	$0.394276\pi$
$620$	5.18290	+	8.97705i	0.208150	+	0.360527i
$621$		0			0
$622$	−10.9919	+	19.0385i	−0.440735	+	0.763376i
$623$	2.72859	+	4.72605i	0.109318	+	0.189345i
$624$		0			0
$625$	−9.43227	+	16.3372i	−0.377291	+	0.653487i
$626$	38.4060	+	66.5212i	1.53501	+	2.65872i
$627$		0			0
$628$	2.55063	−	4.41782i	0.101781	−	0.176290i
$629$	−1.95736			−0.0780450
$630$		0			0
$631$	−10.2771	−	17.8004i	−0.409123	−	0.708622i	0.585669	−	0.810551i	$-0.300832\pi$
$631$	−10.2771	−	17.8004i	−0.409123	−	0.708622i	−0.994792	+	0.101929i	$0.967499\pi$
$632$	26.2525	+	45.4707i	1.04427	+	1.80873i
$633$		0			0
$634$	3.74858	+	6.49273i	0.148875	+	0.257859i
$635$	4.04303	+	7.00274i	0.160443	+	0.277895i
$636$		0			0
$637$	13.2410	−	10.0114i	0.524629	−	0.396666i
$638$	−91.9869			−3.64180
$639$		0			0
$640$	−3.52334	+	6.10260i	−0.139272	+	0.241227i
$641$	2.91485	−	5.04866i	0.115129	−	0.199410i	−0.802702	−	0.596380i	$-0.796605\pi$
$641$	2.91485	−	5.04866i	0.115129	−	0.199410i	0.917832	+	0.396970i	$0.129938\pi$
$642$		0			0
$643$	44.2628			1.74555			0.872777	−	0.488119i	$-0.162317\pi$
$643$	44.2628			1.74555			0.872777	+	0.488119i	$0.162317\pi$
$644$	25.0647			0.987686
$645$		0			0
$646$	0.990041	−	1.71480i	0.0389527	−	0.0674680i
$647$	−8.63857	+	14.9624i	−0.339617	+	0.588234i	−0.984361	−	0.176165i	$-0.943631\pi$
$647$	−8.63857	+	14.9624i	−0.339617	+	0.588234i	0.644744	+	0.764399i	$0.276964\pi$
$648$		0			0
$649$	−15.1292			−0.593875
$650$	34.9826	−	26.4499i	1.37213	−	1.03745i
$651$		0			0
$652$	−17.8409	−	30.9013i	−0.698703	−	1.21019i
$653$	−3.47689	−	6.02216i	−0.136061	−	0.235665i	0.789941	−	0.613183i	$-0.210111\pi$
$653$	−3.47689	−	6.02216i	−0.136061	−	0.235665i	−0.926002	+	0.377518i	$0.876778\pi$
$654$		0			0
$655$	−6.38892	−	11.0659i	−0.249636	−	0.432382i
$656$	−49.2476	−	85.2994i	−1.92280	−	3.33038i
$657$		0			0
$658$	−11.7479			−0.457979
$659$	8.92277	−	15.4547i	0.347582	−	0.602030i	−0.638237	−	0.769840i	$-0.720336\pi$
$659$	8.92277	−	15.4547i	0.347582	−	0.602030i	0.985819	+	0.167810i	$0.0536695\pi$
$660$		0			0
$661$	2.20696	+	3.82256i	0.0858407	+	0.148680i	0.905749	−	0.423814i	$-0.139309\pi$
$661$	2.20696	+	3.82256i	0.0858407	+	0.148680i	−0.819908	+	0.572495i	$0.805976\pi$
$662$	16.1477	−	27.9686i	0.627596	−	1.08703i
$663$		0			0
$664$	−10.1159	−	17.5213i	−0.392574	−	0.679959i
$665$	−1.80236	+	3.12177i	−0.0698924	+	0.121057i
$666$		0			0
$667$	−10.9377	−	18.9447i	−0.423511	−	0.733542i
$668$	−46.6560	−	80.8105i	−1.80517	−	3.12665i
$669$		0			0
$670$	8.52742			0.329443
$671$	20.3938	−	35.3231i	0.787293	−	1.36363i
$672$		0			0
$673$	28.2309			1.08822			0.544110	−	0.839014i	$-0.316867\pi$
$673$	28.2309			1.08822			0.544110	+	0.839014i	$0.316867\pi$
$674$	−27.2563	+	47.2093i	−1.04987	+	1.81843i
$675$		0			0
$676$	−63.7220	+	16.1064i	−2.45085	+	0.619478i
$677$	6.30338	+	10.9178i	0.242259	+	0.419604i	0.961357	−	0.275304i	$-0.0887784\pi$
$677$	6.30338	+	10.9178i	0.242259	+	0.419604i	−0.719099	+	0.694908i	$0.755445\pi$
$678$		0			0
$679$	7.26475	+	12.5829i	0.278796	+	0.482888i
$680$	−1.09347			−0.0419326
$681$		0			0
$682$	−21.2819	+	36.8614i	−0.814927	+	1.41150i
$683$	12.3897	+	21.4597i	0.474081	+	0.821132i	0.999560	−	0.0296749i	$-0.00944720\pi$
$683$	12.3897	+	21.4597i	0.474081	+	0.821132i	−0.525479	+	0.850807i	$0.676114\pi$
$684$		0			0
$685$	4.60477	+	7.97570i	0.175939	+	0.304736i
$686$	−47.7120			−1.82165
$687$		0			0
$688$	−34.3415	+	59.4812i	−1.30926	+	2.26770i
$689$	−1.10703	−	8.89723i	−0.0421744	−	0.338957i
$690$		0			0
$691$	16.8086			0.639430			0.319715	−	0.947514i	$-0.396413\pi$
$691$	16.8086			0.639430			0.319715	+	0.947514i	$0.396413\pi$
$692$	4.44829	−	7.70466i	0.169099	−	0.292887i
$693$		0			0
$694$	−57.6304			−2.18762
$695$	−1.13322	+	1.96280i	−0.0429855	+	0.0744531i
$696$		0			0
$697$	0.893154	−	1.54699i	0.0338306	−	0.0585964i
$698$	−91.5052			−3.46352
$699$		0			0
$700$	−35.8366			−1.35450
$701$	−11.1825			−0.422358			−0.211179	−	0.977447i	$-0.567730\pi$
$701$	−11.1825			−0.422358			−0.211179	+	0.977447i	$0.567730\pi$
$702$		0			0
$703$	33.8371			1.27619
$704$	−74.8634			−2.82152
$705$		0			0
$706$	3.79113			0.142681
$707$	−3.24073	+	5.61312i	−0.121880	+	0.211103i
$708$		0			0
$709$	13.1682	−	22.8079i	0.494541	−	0.856570i	−0.505439	−	0.862862i	$-0.668670\pi$
$709$	13.1682	−	22.8079i	0.494541	−	0.856570i	0.999980	+	0.00629240i	$0.00200295\pi$
$710$	−2.71252			−0.101799
$711$		0			0
$712$	14.3086	−	24.7832i	0.536237	−	0.928789i
$713$	−10.1221			−0.379077
$714$		0			0
$715$	−10.9236	−	4.61600i	−0.408520	−	0.172629i
$716$	23.4524	−	40.6208i	0.876458	−	1.51807i
$717$		0			0
$718$	−22.0569			−0.823154
$719$	7.74314	+	13.4115i	0.288770	+	0.500165i	0.973516	−	0.228617i	$-0.0734203\pi$
$719$	7.74314	+	13.4115i	0.288770	+	0.500165i	−0.684746	+	0.728782i	$0.740087\pi$
$720$		0			0
$721$	3.14547	+	5.44812i	0.117143	+	0.202898i
$722$	8.11972	−	14.0638i	0.302185	−	0.523399i
$723$		0			0
$724$	−89.4956			−3.32608
$725$	15.6384	+	27.0866i	0.580797	+	1.00597i
$726$		0			0
$727$	11.8967	+	20.6057i	0.441225	+	0.764225i	0.997781	−	0.0665857i	$-0.0212106\pi$
$727$	11.8967	+	20.6057i	0.441225	+	0.764225i	−0.556555	+	0.830811i	$0.687877\pi$
$728$	41.7300	+	17.6339i	1.54662	+	0.653554i
$729$		0			0
$730$	−2.61767	+	4.53393i	−0.0968842	+	0.167808i
$731$	−1.24563			−0.0460715
$732$		0			0
$733$	2.12642	−	3.68306i	0.0785410	−	0.136037i	−0.824080	−	0.566474i	$-0.808307\pi$
$733$	2.12642	−	3.68306i	0.0785410	−	0.136037i	0.902621	+	0.430437i	$0.141641\pi$
$734$	−82.1302			−3.03148
$735$		0			0
$736$	−22.7070	−	39.3297i	−0.836991	−	1.44971i
$737$	12.5450	+	21.7286i	0.462101	+	0.800382i
$738$		0			0
$739$	−2.29397	+	3.97326i	−0.0843849	+	0.146159i	−0.905129	−	0.425137i	$-0.860226\pi$
$739$	−2.29397	+	3.97326i	−0.0843849	+	0.146159i	0.820744	+	0.571296i	$0.193559\pi$
$740$	−15.4578	−	26.7738i	−0.568241	−	0.984223i
$741$		0			0
$742$	−5.11224	+	8.85465i	−0.187676	+	0.325065i
$743$	11.1086	+	19.2406i	0.407533	+	0.705868i	0.994613	−	0.103661i	$-0.0330557\pi$
$743$	11.1086	+	19.2406i	0.407533	+	0.705868i	−0.587079	+	0.809529i	$0.699722\pi$
$744$		0			0
$745$	−4.01285	+	6.95046i	−0.147020	+	0.254645i
$746$	37.8722			1.38660
$747$		0			0
$748$	−2.66147	−	4.60980i	−0.0973129	−	0.168551i
$749$	−7.82945	−	13.5610i	−0.286082	−	0.495508i
$750$		0			0
$751$	4.83340	+	8.37170i	0.176373	+	0.305488i	0.940636	−	0.339418i	$-0.110230\pi$
$751$	4.83340	+	8.37170i	0.176373	+	0.305488i	−0.764262	+	0.644905i	$0.776897\pi$
$752$	16.3572	+	28.3314i	0.596484	+	1.03314i
$753$		0			0
$754$	−8.07703	−	64.9153i	−0.294148	−	2.36408i
$755$	−0.671398			−0.0244347
$756$		0			0
$757$	9.26864	−	16.0538i	0.336875	−	0.583484i	−0.646969	−	0.762517i	$-0.723964\pi$
$757$	9.26864	−	16.0538i	0.336875	−	0.583484i	0.983843	+	0.179033i	$0.0572968\pi$
$758$	8.43719	−	14.6136i	0.306453	−	0.530791i
$759$		0			0
$760$	18.9029			0.685682
$761$	−23.1466			−0.839065			−0.419533	−	0.907740i	$-0.637806\pi$
$761$	−23.1466			−0.839065			−0.419533	+	0.907740i	$0.637806\pi$
$762$		0			0
$763$	3.38675	−	5.86603i	0.122609	−	0.212365i
$764$	1.37440	−	2.38053i	0.0497240	−	0.0861245i
$765$		0			0
$766$	−77.3402			−2.79442
$767$	−1.32844	−	10.6767i	−0.0479673	−	0.385514i
$768$		0			0
$769$	−20.9179	−	36.2309i	−0.754318	−	1.30652i	−0.945712	−	0.325005i	$-0.894634\pi$
$769$	−20.9179	−	36.2309i	−0.754318	−	1.30652i	0.191394	−	0.981513i	$-0.438699\pi$
$770$	6.76182	+	11.7118i	0.243679	+	0.422065i
$771$		0			0
$772$	62.4462	+	108.160i	2.24749	+	3.89277i
$773$	8.76453	+	15.1806i	0.315238	+	0.546009i	0.979488	−	0.201502i	$-0.0645823\pi$
$773$	8.76453	+	15.1806i	0.315238	+	0.546009i	−0.664250	+	0.747511i	$0.731249\pi$
$774$		0			0
$775$	14.4723			0.519861
$776$	38.0960	−	65.9843i	1.36757	−	2.36870i
$777$		0			0
$778$	−42.0634	−	72.8559i	−1.50804	−	2.61201i
$779$	−15.4401	+	26.7430i	−0.553198	+	0.958168i
$780$		0			0
$781$	−3.99049	−	6.91173i	−0.142791	−	0.247321i
$782$	0.883299	−	1.52992i	0.0315867	−	0.0547098i
$783$		0			0
$784$	26.3574	+	45.6524i	0.941336	+	1.63044i
$785$	0.327273	+	0.566854i	0.0116809	+	0.0202319i
$786$		0			0
$787$	−19.5951			−0.698489			−0.349245	−	0.937032i	$-0.613562\pi$
$787$	−19.5951			−0.698489			−0.349245	+	0.937032i	$0.613562\pi$
$788$	−45.5702	+	78.9300i	−1.62337	+	2.81176i
$789$		0			0
$790$	−11.1462			−0.396564
$791$	−10.3820	+	17.9822i	−0.369142	+	0.639373i
$792$		0			0
$793$	26.7182	+	11.2903i	0.948793	+	0.400932i
$794$	20.9646	+	36.3118i	0.744006	+	1.28866i
$795$		0			0
$796$	−43.4344	−	75.2306i	−1.53949	−	2.66648i
$797$	10.7281			0.380010			0.190005	−	0.981783i	$-0.439150\pi$
$797$	10.7281			0.380010			0.190005	+	0.981783i	$0.439150\pi$
$798$		0			0
$799$	−0.296653	+	0.513819i	−0.0104948	+	0.0181776i
$800$	32.4658	+	56.2323i	1.14784	+	1.98811i
$801$		0			0
$802$	−1.00805	−	1.74600i	−0.0355956	−	0.0616534i
$803$	−15.4038			−0.543587
$804$		0			0
$805$	−1.60803	+	2.78519i	−0.0566757	+	0.0981652i
$806$	−27.8818	−	11.7820i	−0.982096	−	0.415005i
$807$		0			0
$808$	33.9885			1.19571
$809$	21.3013	−	36.8949i	0.748914	−	1.29716i	−0.199430	−	0.979912i	$-0.563909\pi$
$809$	21.3013	−	36.8949i	0.748914	−	1.29716i	0.948344	−	0.317245i	$-0.102758\pi$
$810$		0			0
$811$	−12.5260			−0.439847			−0.219923	−	0.975517i	$-0.570581\pi$
$811$	−12.5260			−0.439847			−0.219923	+	0.975517i	$0.570581\pi$
$812$	−26.7269	+	46.2923i	−0.937930	+	1.62454i
$813$		0			0
$814$	63.4727	−	109.938i	2.22472	−	3.85332i
$815$	4.57836			0.160373
$816$		0			0
$817$	21.5335			0.753360
$818$	−71.6436			−2.50496
$819$		0			0
$820$	28.2140			0.985276
$821$	−38.9488			−1.35932			−0.679661	−	0.733527i	$-0.737873\pi$
$821$	−38.9488			−1.35932			−0.679661	+	0.733527i	$0.737873\pi$
$822$		0			0
$823$	39.5846			1.37983			0.689916	−	0.723890i	$-0.257648\pi$
$823$	39.5846			1.37983			0.689916	+	0.723890i	$0.257648\pi$
$824$	16.4947	−	28.5697i	0.574620	−	0.995271i
$825$		0			0
$826$	−6.13472	+	10.6256i	−0.213454	+	0.369713i
$827$	19.0344			0.661890			0.330945	−	0.943650i	$-0.392633\pi$
$827$	19.0344			0.661890			0.330945	+	0.943650i	$0.392633\pi$
$828$		0			0
$829$	−5.06015	+	8.76445i	−0.175746	+	0.304402i	−0.940419	−	0.340017i	$-0.889567\pi$
$829$	−5.06015	+	8.76445i	−0.175746	+	0.304402i	0.764673	+	0.644419i	$0.222901\pi$
$830$	4.29498			0.149081
$831$		0			0
$832$	−6.57348	−	52.8312i	−0.227894	−	1.83159i
$833$	−0.478018	+	0.827951i	−0.0165623	+	0.0286868i
$834$		0			0
$835$	11.9729			0.414341
$836$	46.0092	+	79.6902i	1.59126	+	2.75614i
$837$		0			0
$838$	14.0804	+	24.3880i	0.486399	+	0.842468i
$839$	13.6152	−	23.5823i	0.470050	−	0.814151i	−0.529363	−	0.848395i	$-0.677569\pi$
$839$	13.6152	−	23.5823i	0.470050	−	0.814151i	0.999413	+	0.0342445i	$0.0109025\pi$
$840$		0			0
$841$	17.6524			0.608703
$842$	−22.1952	−	38.4432i	−0.764897	−	1.32484i
$843$		0			0
$844$	−6.83351	−	11.8360i	−0.235219	−	0.407411i
$845$	2.29836	−	8.11413i	0.0790658	−	0.279135i
$846$		0			0
$847$	−11.3816	+	19.7135i	−0.391076	+	0.677363i
$848$	28.4722			0.977738
$849$		0			0
$850$	−1.26291	+	2.18743i	−0.0433176	+	0.0750282i
$851$	30.1890			1.03486
$852$		0			0
$853$	−4.43767	−	7.68627i	−0.151943	−	0.263173i	0.779999	−	0.625781i	$-0.215220\pi$
$853$	−4.43767	−	7.68627i	−0.151943	−	0.263173i	−0.931942	+	0.362608i	$0.881886\pi$
$854$	−16.5388	−	28.6461i	−0.565948	−	0.980250i
$855$		0			0
$856$	−41.0572	+	71.1132i	−1.40331	+	2.43060i
$857$	18.5179	+	32.0740i	0.632560	+	1.09563i	0.987027	+	0.160557i	$0.0513291\pi$
$857$	18.5179	+	32.0740i	0.632560	+	1.09563i	−0.354467	+	0.935069i	$0.615338\pi$
$858$		0			0
$859$	−23.2978	+	40.3530i	−0.794912	+	1.37683i	0.127983	+	0.991776i	$0.459150\pi$
$859$	−23.2978	+	40.3530i	−0.794912	+	1.37683i	−0.922895	+	0.385052i	$0.874184\pi$
$860$	−9.83714	−	17.0384i	−0.335444	−	0.581006i
$861$		0			0
$862$	11.0281	−	19.1013i	0.375620	−	0.650593i
$863$	38.8584			1.32275			0.661377	−	0.750053i	$-0.269972\pi$
$863$	38.8584			1.32275			0.661377	+	0.750053i	$0.269972\pi$
$864$		0			0
$865$	0.570764	+	0.988591i	0.0194065	+	0.0336131i
$866$	0.104682	+	0.181315i	0.00355724	+	0.00616132i
$867$		0			0
$868$	12.3670	+	21.4202i	0.419762	+	0.727050i
$869$	−16.3976	−	28.4014i	−0.556249	−	0.963452i
$870$		0			0
$871$	−14.2324	+	10.7609i	−0.482245	+	0.364620i
$872$	−35.5199			−1.20286
$873$		0			0
$874$	−15.2697	+	26.4479i	−0.516506	+	0.894614i
$875$	4.80952	−	8.33034i	0.162592	−	0.281617i
$876$		0			0
$877$	−16.2126			−0.547460			−0.273730	−	0.961807i	$-0.588258\pi$
$877$	−16.2126			−0.547460			−0.273730	+	0.961807i	$0.588258\pi$
$878$	68.3780			2.30764
$879$		0			0
$880$	18.8297	−	32.6140i	0.634749	−	1.09942i
$881$	17.4979	−	30.3072i	0.589518	−	1.02107i	−0.404778	−	0.914415i	$-0.632651\pi$
$881$	17.4979	−	30.3072i	0.589518	−	1.02107i	0.994296	−	0.106660i	$-0.0340156\pi$
$882$		0			0
$883$	−22.3562			−0.752346			−0.376173	−	0.926549i	$-0.622760\pi$
$883$	−22.3562			−0.752346			−0.376173	+	0.926549i	$0.622760\pi$
$884$	3.01945	−	2.28297i	0.101555	−	0.0767847i
$885$		0			0
$886$	37.6436	+	65.2006i	1.26466	+	2.19046i
$887$	−6.93763	−	12.0163i	−0.232943	−	0.403469i	0.725730	−	0.687980i	$-0.241502\pi$
$887$	−6.93763	−	12.0163i	−0.232943	−	0.403469i	−0.958673	+	0.284511i	$0.908169\pi$
$888$		0			0
$889$	9.64712	+	16.7093i	0.323554	+	0.560412i
$890$	3.03754	+	5.26117i	0.101819	+	0.176355i
$891$		0			0
$892$	26.4127			0.884363
$893$	5.12829	−	8.88246i	0.171612	−	0.297240i
$894$		0			0
$895$	3.00920	+	5.21208i	0.100586	+	0.174221i
$896$	−8.40707	+	14.5615i	−0.280861	+	0.486465i
$897$		0			0
$898$	−5.80953	−	10.0624i	−0.193866	−	0.335787i
$899$	10.7934	−	18.6947i	0.359981	−	0.623505i
$900$		0			0
$901$	0.258185	+	0.447190i	0.00860141	+	0.0148981i
$902$	57.9259	+	100.331i	1.92872	+	3.34064i
$903$		0			0
$904$	108.886			3.62149
$905$	5.74163	−	9.94479i	0.190858	−	0.330576i
$906$		0			0
$907$	−47.0793			−1.56324			−0.781621	−	0.623754i	$-0.785607\pi$
$907$	−47.0793			−1.56324			−0.781621	+	0.623754i	$0.785607\pi$
$908$	−14.0833	+	24.3930i	−0.467371	+	0.809509i
$909$		0			0
$910$	−7.67132	+	5.80020i	−0.254302	+	0.192275i
$911$	−18.3507	−	31.7844i	−0.607987	−	1.05306i	−0.991572	−	0.129558i	$-0.958644\pi$
$911$	−18.3507	−	31.7844i	−0.607987	−	1.05306i	0.383585	−	0.923505i	$-0.374689\pi$
$912$		0			0
$913$	6.31851	+	10.9440i	0.209112	+	0.362193i
$914$	−36.0107			−1.19113
$915$		0			0
$916$	57.8618	−	100.220i	1.91181	−	3.31135i
$917$	−15.2447	−	26.4045i	−0.503423	−	0.871955i
$918$		0			0
$919$	−3.87476	−	6.71128i	−0.127817	−	0.221385i	0.795014	−	0.606591i	$-0.207464\pi$
$919$	−3.87476	−	6.71128i	−0.127817	−	0.221385i	−0.922830	+	0.385206i	$0.874130\pi$
$920$	16.8649			0.556019
$921$		0			0
$922$	2.66412	−	4.61439i	0.0877381	−	0.151967i
$923$	4.52723	−	3.42299i	0.149015	−	0.112669i
$924$		0			0
$925$	−43.1632			−1.41920
$926$	−55.1048	+	95.4443i	−1.81085	+	3.13649i
$927$		0			0
$928$	96.8515			3.17931
$929$	−9.51347	+	16.4778i	−0.312127	+	0.540619i	−0.978823	−	0.204711i	$-0.934375\pi$
$929$	−9.51347	+	16.4778i	−0.312127	+	0.540619i	0.666696	+	0.745330i	$0.267708\pi$
$930$		0			0
$931$	8.26356	−	14.3129i	0.270827	−	0.469086i
$932$	−77.9218			−2.55241
$933$		0			0
$934$	66.5835			2.17868
$935$	0.682990			0.0223362
$936$		0			0
$937$	−19.2901			−0.630179			−0.315090	−	0.949062i	$-0.602035\pi$
$937$	−19.2901			−0.630179			−0.315090	+	0.949062i	$0.602035\pi$
$938$	20.3473			0.664364
$939$		0			0
$940$	−9.37103			−0.305649
$941$	−19.9180	+	34.4989i	−0.649307	+	1.12463i	0.333981	+	0.942580i	$0.391608\pi$
$941$	−19.9180	+	34.4989i	−0.649307	+	1.12463i	−0.983289	+	0.182053i	$0.941726\pi$
$942$		0			0
$943$	−13.7754	+	23.8597i	−0.448589	+	0.776978i
$944$	34.1668			1.11203
$945$		0			0
$946$	40.3931	−	69.9629i	1.31329	−	2.27469i
$947$	16.2284			0.527351			0.263675	−	0.964611i	$-0.415065\pi$
$947$	16.2284			0.527351			0.263675	+	0.964611i	$0.415065\pi$
$948$		0			0
$949$	−1.35255	−	10.8705i	−0.0439055	−	0.352870i
$950$	21.8322	−	37.8144i	0.708329	−	1.22686i
$951$		0			0
$952$	−2.60913			−0.0845625
$953$	−4.95942	−	8.58997i	−0.160651	−	0.278256i	0.774451	−	0.632634i	$-0.218026\pi$
$953$	−4.95942	−	8.58997i	−0.160651	−	0.278256i	−0.935102	+	0.354377i	$0.884693\pi$
$954$		0			0
$955$	0.176350	+	0.305448i	0.00570656	+	0.00988405i
$956$	30.1891	−	52.2890i	0.976384	−	1.69115i
$957$		0			0
$958$	16.2358			0.524555
$959$	10.9875	+	19.0309i	0.354805	+	0.614540i
$960$		0			0
$961$	10.5057	+	18.1964i	0.338894	+	0.586981i
$962$	83.1567	+	35.1395i	2.68108	+	1.13294i
$963$		0			0
$964$	45.0635	−	78.0523i	1.45140	−	2.51389i
$965$	−16.0251			−0.515865
$966$		0			0
$967$	17.1795	−	29.7558i	0.552456	−	0.956882i	−0.445640	−	0.895212i	$-0.647024\pi$
$967$	17.1795	−	29.7558i	0.552456	−	0.956882i	0.998097	−	0.0616702i	$-0.0196427\pi$
$968$	119.369			3.83666
$969$		0			0
$970$	8.08733	+	14.0077i	0.259669	+	0.449759i
$971$	−28.7211	−	49.7464i	−0.921705	−	1.59644i	−0.796777	−	0.604273i	$-0.793463\pi$
$971$	−28.7211	−	49.7464i	−0.921705	−	1.59644i	−0.124928	−	0.992166i	$-0.539870\pi$
$972$		0			0
$973$	−2.70399	+	4.68344i	−0.0866859	+	0.150144i
$974$	−14.7446	−	25.5383i	−0.472446	−	0.818300i
$975$		0			0
$976$	−46.0558	+	79.7711i	−1.47421	+	2.55341i
$977$	−8.57672	−	14.8553i	−0.274394	−	0.475264i	0.695588	−	0.718441i	$-0.255144\pi$
$977$	−8.57672	−	14.8553i	−0.274394	−	0.475264i	−0.969982	+	0.243177i	$0.921810\pi$
$978$		0			0
$979$	−8.93727	+	15.4798i	−0.285636	+	0.494737i
$980$	−15.1002			−0.482358
$981$		0			0
$982$	3.02438	+	5.23839i	0.0965119	+	0.167164i
$983$	30.5798	+	52.9658i	0.975346	+	1.68935i	0.678790	+	0.734333i	$0.262505\pi$
$983$	30.5798	+	52.9658i	0.975346	+	1.68935i	0.296556	+	0.955016i	$0.404162\pi$
$984$		0			0
$985$	−5.84715	−	10.1276i	−0.186306	−	0.322691i
$986$	1.88376	+	3.26276i	0.0599910	+	0.103907i
$987$		0			0
$988$	−52.1976	+	39.4660i	−1.66063	+	1.25558i
$989$	19.2118			0.610900
$990$		0			0
$991$	11.0154	−	19.0792i	0.349915	−	0.606071i	−0.636319	−	0.771426i	$-0.719544\pi$
$991$	11.0154	−	19.0792i	0.349915	−	0.606071i	0.986234	+	0.165355i	$0.0528770\pi$
$992$	22.4074	−	38.8107i	0.711436	−	1.23224i
$993$		0			0
$994$	−6.47237			−0.205291
$995$	11.1462			0.353359
$996$		0			0
$997$	−16.4450	+	28.4835i	−0.520818	+	0.902083i	0.478889	+	0.877875i	$0.341040\pi$
$997$	−16.4450	+	28.4835i	−0.520818	+	0.902083i	−0.999707	+	0.0242074i	$0.992294\pi$
$998$	−15.0788	+	26.1173i	−0.477311	+	0.826727i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.h.a.334.12		24
3.2	odd	2		117.2.h.a.22.1	yes	24
9.2	odd	6		117.2.f.a.61.12	✓	24
9.7	even	3		351.2.f.a.100.1		24
13.3	even	3		351.2.f.a.172.1		24
39.29	odd	6		117.2.f.a.94.12	yes	24
117.16	even	3	inner	351.2.h.a.289.12		24
117.29	odd	6		117.2.h.a.16.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.12	✓	24	9.2	odd	6
117.2.f.a.94.12	yes	24	39.29	odd	6
117.2.h.a.16.1	yes	24	117.29	odd	6
117.2.h.a.22.1	yes	24	3.2	odd	2
351.2.f.a.100.1		24	9.7	even	3
351.2.f.a.172.1		24	13.3	even	3
351.2.h.a.289.12		24	117.16	even	3	inner
351.2.h.a.334.12		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.65628 q^{2} +5.05585 q^{4} +(-0.324360 + 0.561808i) q^{5} +(-0.773958 + 1.34053i) q^{7} +8.11720 q^{8} +(-0.861592 + 1.49232i) q^{10} -5.07008 q^{11} +(-0.445184 - 3.57796i) q^{13} +(-2.05585 + 3.56084i) q^{14} +11.4499 q^{16} +(0.103828 + 0.179835i) q^{17} +(-1.79488 - 3.10883i) q^{19} +(-1.63991 + 2.84041i) q^{20} -13.4676 q^{22} +(-1.60137 - 2.77365i) q^{23} +(2.28958 + 3.96567i) q^{25} +(-1.18254 - 9.50408i) q^{26} +(-3.91301 + 6.77754i) q^{28} +6.83026 q^{29} +(1.58024 - 2.73705i) q^{31} +14.1798 q^{32} +(0.275796 + 0.477692i) q^{34} +(-0.502082 - 0.869631i) q^{35} +(-4.71300 + 8.16316i) q^{37} +(-4.76772 - 8.25793i) q^{38} +(-2.63289 + 4.56031i) q^{40} +(-4.30114 - 7.44979i) q^{41} +(-2.99929 + 5.19492i) q^{43} -25.6335 q^{44} +(-4.25368 - 7.36759i) q^{46} +(1.42859 + 2.47438i) q^{47} +(2.30198 + 3.98714i) q^{49} +(6.08178 + 10.5340i) q^{50} +(-2.25078 - 18.0896i) q^{52} +2.48667 q^{53} +(1.64453 - 2.84841i) q^{55} +(-6.28237 + 10.8814i) q^{56} +18.1431 q^{58} +2.98403 q^{59} +(-4.02238 + 6.96697i) q^{61} +(4.19756 - 7.27038i) q^{62} +14.7657 q^{64} +(2.15453 + 0.910439i) q^{65} +(-2.47432 - 4.28565i) q^{67} +(0.524937 + 0.909217i) q^{68} +(-1.33367 - 2.30999i) q^{70} +(0.787066 + 1.36324i) q^{71} +3.03817 q^{73} +(-12.5191 + 21.6837i) q^{74} +(-9.07465 - 15.7178i) q^{76} +(3.92403 - 6.79661i) q^{77} +(3.23418 + 5.60177i) q^{79} +(-3.71389 + 6.43264i) q^{80} +(-11.4251 - 19.7888i) q^{82} +(-1.24623 - 2.15854i) q^{83} -0.134710 q^{85} +(-7.96696 + 13.7992i) q^{86} -41.1548 q^{88} +(1.76275 - 3.05317i) q^{89} +(5.14094 + 2.17241i) q^{91} +(-8.09626 - 14.0231i) q^{92} +(3.79473 + 6.57267i) q^{94} +2.32875 q^{95} +(4.69325 - 8.12894i) q^{97} +(6.11471 + 10.5910i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 18 q^{4} + 2 q^{5} + 3 q^{7} + 18 q^{8} - 6 q^{11} - 2 q^{14} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 11 q^{20} - 18 q^{22} - 17 q^{23} - 6 q^{25} + 12 q^{26} + 24 q^{29} - 6 q^{31} + 38 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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