LMFDB - Embedded newform 950.2.bb.e.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.e.507.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(-0.507694 + 1.08875i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(1.12886 + 0.410871i) q^{6} +(-2.08332 - 0.558224i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.00073 + 1.19263i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.507694 + 1.08875i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(1.12886 + 0.410871i) q^{6} +(-2.08332 - 0.558224i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.00073 + 1.19263i) q^{9} +(1.76610 - 3.05898i) q^{11} +(0.310921 - 1.16037i) q^{12} +(-3.57802 + 1.66846i) q^{13} +(-0.374526 + 2.12404i) q^{14} +(0.939693 - 0.342020i) q^{16} +(3.38928 - 0.296524i) q^{17} +(1.10087 - 1.10087i) q^{18} +(-3.61257 + 2.43913i) q^{19} +(1.66546 - 1.98481i) q^{21} +(-3.20126 - 1.49277i) q^{22} +(0.575024 - 0.821220i) q^{23} +(-1.18306 - 0.208605i) q^{24} +(1.97396 + 3.41899i) q^{26} +(-5.28766 + 1.41682i) q^{27} +(2.14860 + 0.187978i) q^{28} +(-3.70708 + 3.11061i) q^{29} +(-7.58434 + 4.37882i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(2.43384 + 3.47588i) q^{33} +(-0.590790 - 3.35054i) q^{34} +(-1.19263 - 1.00073i) q^{36} +(-5.28519 - 5.28519i) q^{37} +(2.74471 + 3.38623i) q^{38} -4.74265i q^{39} +(1.31823 + 3.62180i) q^{41} +(-2.12242 - 1.48613i) q^{42} +(0.100570 - 0.0704198i) q^{43} +(-1.20809 + 3.31919i) q^{44} +(-0.868212 - 0.501262i) q^{46} +(-0.833128 + 9.52270i) q^{47} +(-0.104701 + 1.19674i) q^{48} +(-2.03357 - 1.17408i) q^{49} +(-1.39788 + 3.84064i) q^{51} +(3.23394 - 2.26443i) q^{52} +(-6.70791 - 4.69693i) q^{53} +(1.87228 + 5.14406i) q^{54} -2.15681i q^{56} +(-0.821538 - 5.17153i) q^{57} +(3.42187 + 3.42187i) q^{58} +(-8.23251 - 6.90789i) q^{59} +(2.05490 + 11.6539i) q^{61} +(5.02318 + 7.17384i) q^{62} +(-1.41909 - 3.04325i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(3.25053 - 2.72752i) q^{66} +(-0.747124 - 0.0653649i) q^{67} +(-3.28630 + 0.880561i) q^{68} +(0.602170 + 1.04299i) q^{69} +(-6.22740 - 1.09806i) q^{71} +(-0.892979 + 1.27531i) q^{72} +(-4.25102 - 1.98228i) q^{73} +(-4.80444 + 5.72571i) q^{74} +(3.13413 - 3.02939i) q^{76} +(-5.38695 + 5.38695i) q^{77} +(-4.72461 + 0.413350i) q^{78} +(1.08296 - 0.394167i) q^{79} +(0.330903 - 1.87665i) q^{81} +(3.49313 - 1.62887i) q^{82} +(-1.53842 + 5.74146i) q^{83} +(-1.29550 + 2.24386i) q^{84} +(-0.0789171 - 0.0940498i) q^{86} +(-1.50463 - 5.61534i) q^{87} +(3.41185 + 0.914202i) q^{88} +(12.1347 + 4.41667i) q^{89} +(8.38554 - 1.47860i) q^{91} +(-0.423685 + 0.908596i) q^{92} +(-0.916932 - 10.4806i) q^{93} +9.55907 q^{94} +1.20131 q^{96} +(1.13186 + 12.9372i) q^{97} +(-0.992379 + 2.12816i) q^{98} +(5.41561 - 0.954918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	−0.507694	+	1.08875i	−0.293117	+	0.628592i	−0.996624	−	0.0820960i	$-0.973839\pi$
$3$	−0.507694	+	1.08875i	−0.293117	+	0.628592i	0.703507	+	0.710688i	$0.251616\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	1.12886	+	0.410871i	0.460855	+	0.167737i
$7$	−2.08332	−	0.558224i	−0.787421	−	0.210989i	−0.157367	−	0.987540i	$-0.550300\pi$
$7$	−2.08332	−	0.558224i	−0.787421	−	0.210989i	−0.630054	+	0.776552i	$0.716967\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	1.00073	+	1.19263i	0.333577	+	0.397542i
$10$		0			0
$11$	1.76610	−	3.05898i	0.532500	−	0.922317i	−0.466780	−	0.884374i	$-0.654586\pi$
$11$	1.76610	−	3.05898i	0.532500	−	0.922317i	0.999280	−	0.0379435i	$-0.0120807\pi$
$12$	0.310921	−	1.16037i	0.0897552	−	0.334971i
$13$	−3.57802	+	1.66846i	−0.992365	+	0.462747i	−0.849838	−	0.527043i	$-0.823301\pi$
$13$	−3.57802	+	1.66846i	−0.992365	+	0.462747i	−0.142527	+	0.989791i	$0.545523\pi$
$14$	−0.374526	+	2.12404i	−0.100096	+	0.567675i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	3.38928	−	0.296524i	0.822021	−	0.0719175i	0.331619	−	0.943414i	$-0.392405\pi$
$17$	3.38928	−	0.296524i	0.822021	−	0.0719175i	0.490403	+	0.871496i	$0.336850\pi$
$18$	1.10087	−	1.10087i	0.259477	−	0.259477i
$19$	−3.61257	+	2.43913i	−0.828779	+	0.559576i
$19$	−3.61257	+	2.43913i	−0.828779	+	0.559576i
$20$		0			0
$21$	1.66546	−	1.98481i	0.363433	−	0.433122i
$22$	−3.20126	−	1.49277i	−0.682512	−	0.318261i
$23$	0.575024	−	0.821220i	0.119901	−	0.171236i	−0.754715	−	0.656053i	$-0.772225\pi$
$23$	0.575024	−	0.821220i	0.119901	−	0.171236i	0.874616	+	0.484817i	$0.161114\pi$
$24$	−1.18306	−	0.208605i	−0.241490	−	0.0425813i
$25$		0			0
$26$	1.97396	+	3.41899i	0.387125	+	0.670520i
$27$	−5.28766	+	1.41682i	−1.01761	+	0.272668i
$28$	2.14860	+	0.187978i	0.406048	+	0.0355246i
$29$	−3.70708	+	3.11061i	−0.688388	+	0.577626i	−0.918444	−	0.395551i	$-0.870554\pi$
$29$	−3.70708	+	3.11061i	−0.688388	+	0.577626i	0.230056	+	0.973177i	$0.426109\pi$
$30$		0			0
$31$	−7.58434	+	4.37882i	−1.36219	+	0.786460i	−0.989915	−	0.141664i	$-0.954755\pi$
$31$	−7.58434	+	4.37882i	−1.36219	+	0.786460i	−0.372273	+	0.928123i	$0.621422\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	2.43384	+	3.47588i	0.423676	+	0.605073i
$34$	−0.590790	−	3.35054i	−0.101320	−	0.574613i
$35$		0			0
$36$	−1.19263	−	1.00073i	−0.198771	−	0.166789i
$37$	−5.28519	−	5.28519i	−0.868880	−	0.868880i	0.123468	−	0.992349i	$-0.460598\pi$
$37$	−5.28519	−	5.28519i	−0.868880	−	0.868880i	−0.992349	+	0.123468i	$0.960598\pi$
$38$	2.74471	+	3.38623i	0.445250	+	0.549320i
$39$		−	4.74265i		−	0.759432i
$40$		0			0
$41$	1.31823	+	3.62180i	0.205873	+	0.565630i	0.999060	−	0.0433472i	$-0.0138022\pi$
$41$	1.31823	+	3.62180i	0.205873	+	0.565630i	−0.793187	+	0.608978i	$0.791580\pi$
$42$	−2.12242	−	1.48613i	−0.327496	−	0.229315i
$43$	0.100570	−	0.0704198i	0.0153368	−	0.0107389i	−0.565883	−	0.824486i	$-0.691465\pi$
$43$	0.100570	−	0.0704198i	0.0153368	−	0.0107389i	0.581220	+	0.813747i	$0.302576\pi$
$44$	−1.20809	+	3.31919i	−0.182126	+	0.500386i
$45$		0			0
$46$	−0.868212	−	0.501262i	−0.128011	−	0.0739071i
$47$	−0.833128	+	9.52270i	−0.121524	+	1.38903i	0.653418	+	0.756997i	$0.273334\pi$
$47$	−0.833128	+	9.52270i	−0.121524	+	1.38903i	−0.774943	+	0.632031i	$0.782221\pi$
$48$	−0.104701	+	1.19674i	−0.0151123	+	0.172734i
$49$	−2.03357	−	1.17408i	−0.290511	−	0.167726i
$50$		0			0
$51$	−1.39788	+	3.84064i	−0.195742	+	0.537796i
$52$	3.23394	−	2.26443i	0.448467	−	0.314020i
$53$	−6.70791	−	4.69693i	−0.921402	−	0.645172i	0.0135650	−	0.999908i	$-0.495682\pi$
$53$	−6.70791	−	4.69693i	−0.921402	−	0.645172i	−0.934967	+	0.354736i	$0.884571\pi$
$54$	1.87228	+	5.14406i	0.254785	+	0.700017i
$55$		0			0
$56$		−	2.15681i		−	0.288216i
$57$	−0.821538	−	5.17153i	−0.108815	−	0.684986i
$58$	3.42187	+	3.42187i	0.449313	+	0.449313i
$59$	−8.23251	−	6.90789i	−1.07178	−	0.899331i	−0.0765686	−	0.997064i	$-0.524396\pi$
$59$	−8.23251	−	6.90789i	−1.07178	−	0.899331i	−0.995213	+	0.0977330i	$0.968841\pi$
$60$		0			0
$61$	2.05490	+	11.6539i	0.263103	+	1.49213i	0.774383	+	0.632717i	$0.218060\pi$
$61$	2.05490	+	11.6539i	0.263103	+	1.49213i	−0.511280	+	0.859414i	$0.670829\pi$
$62$	5.02318	+	7.17384i	0.637944	+	0.911079i
$63$	−1.41909	−	3.04325i	−0.178789	−	0.383414i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	3.25053	−	2.72752i	0.400112	−	0.335734i
$67$	−0.747124	−	0.0653649i	−0.0912758	−	0.00798560i	0.0414263	−	0.999142i	$-0.486810\pi$
$67$	−0.747124	−	0.0653649i	−0.0912758	−	0.00798560i	−0.132702	+	0.991156i	$0.542365\pi$
$68$	−3.28630	+	0.880561i	−0.398522	+	0.106784i
$69$	0.602170	+	1.04299i	0.0724927	+	0.125561i
$70$		0			0
$71$	−6.22740	−	1.09806i	−0.739056	−	0.130316i	−0.208568	−	0.978008i	$-0.566880\pi$
$71$	−6.22740	−	1.09806i	−0.739056	−	0.130316i	−0.530488	+	0.847692i	$0.677991\pi$
$72$	−0.892979	+	1.27531i	−0.105239	+	0.150296i
$73$	−4.25102	−	1.98228i	−0.497544	−	0.232008i	0.157614	−	0.987501i	$-0.449620\pi$
$73$	−4.25102	−	1.98228i	−0.497544	−	0.232008i	−0.655157	+	0.755492i	$0.727398\pi$
$74$	−4.80444	+	5.72571i	−0.558505	+	0.665601i
$75$		0			0
$76$	3.13413	−	3.02939i	0.359509	−	0.347495i
$77$	−5.38695	+	5.38695i	−0.613900	+	0.613900i
$78$	−4.72461	+	0.413350i	−0.534956	+	0.0468026i
$79$	1.08296	−	0.394167i	0.121843	−	0.0443472i	−0.280379	−	0.959889i	$-0.590460\pi$
$79$	1.08296	−	0.394167i	0.121843	−	0.0443472i	0.402222	+	0.915542i	$0.368238\pi$
$80$		0			0
$81$	0.330903	−	1.87665i	0.0367670	−	0.208516i
$82$	3.49313	−	1.62887i	0.385751	−	0.179879i
$83$	−1.53842	+	5.74146i	−0.168864	+	0.630207i	0.828652	+	0.559764i	$0.189108\pi$
$83$	−1.53842	+	5.74146i	−0.168864	+	0.630207i	−0.997516	+	0.0704436i	$0.977559\pi$
$84$	−1.29550	+	2.24386i	−0.141350	+	0.244826i
$85$		0			0
$86$	−0.0789171	−	0.0940498i	−0.00850985	−	0.0101416i
$87$	−1.50463	−	5.61534i	−0.161313	−	0.602028i
$88$	3.41185	+	0.914202i	0.363704	+	0.0974543i
$89$	12.1347	+	4.41667i	1.28628	+	0.468166i	0.892503	−	0.451042i	$-0.148947\pi$
$89$	12.1347	+	4.41667i	1.28628	+	0.468166i	0.393773	+	0.919208i	$0.371170\pi$
$90$		0			0
$91$	8.38554	−	1.47860i	0.879043	−	0.154999i
$92$	−0.423685	+	0.908596i	−0.0441722	+	0.0947277i
$93$	−0.916932	−	10.4806i	−0.0950815	−	1.08679i
$94$	9.55907			0.985943
$95$		0			0
$96$	1.20131			0.122608
$97$	1.13186	+	12.9372i	0.114923	+	1.31358i	0.806483	+	0.591258i	$0.201368\pi$
$97$	1.13186	+	12.9372i	0.114923	+	1.31358i	−0.691560	+	0.722319i	$0.743076\pi$
$98$	−0.992379	+	2.12816i	−0.100245	+	0.214977i
$99$	5.41561	−	0.954918i	0.544289	−	0.0959729i
$100$		0			0
$101$	2.42134	+	0.881297i	0.240933	+	0.0876923i	0.459664	−	0.888093i	$-0.347970\pi$
$101$	2.42134	+	0.881297i	0.240933	+	0.0876923i	−0.218732	+	0.975785i	$0.570192\pi$
$102$	3.94785	+	1.05782i	0.390896	+	0.104740i
$103$	−1.24827	−	4.65860i	−0.122995	−	0.459025i	0.876765	−	0.480919i	$-0.159697\pi$
$103$	−1.24827	−	4.65860i	−0.122995	−	0.459025i	−0.999760	+	0.0218940i	$0.993030\pi$
$104$	−2.53767	−	3.02428i	−0.248839	−	0.296555i
$105$		0			0
$106$	−4.09442	+	7.09174i	−0.397685	+	0.688811i
$107$	0.0938049	−	0.350085i	0.00906846	−	0.0338440i	−0.961243	−	0.275701i	$-0.911090\pi$
$107$	0.0938049	−	0.350085i	0.00906846	−	0.0338440i	0.970312	+	0.241857i	$0.0777566\pi$
$108$	4.96130	−	2.31349i	0.477401	−	0.222616i
$109$	−1.81325	+	10.2834i	−0.173678	+	0.984975i	0.765981	+	0.642863i	$0.222253\pi$
$109$	−1.81325	+	10.2834i	−0.173678	+	0.984975i	−0.939659	+	0.342112i	$0.888858\pi$
$110$		0			0
$111$	8.43753	−	3.07101i	0.800855	−	0.291487i
$112$	−2.14860	+	0.187978i	−0.203024	+	0.0177623i
$113$	8.22686	−	8.22686i	0.773918	−	0.773918i	−0.204871	−	0.978789i	$-0.565677\pi$
$113$	8.22686	−	8.22686i	0.773918	−	0.773918i	0.978789	+	0.204871i	$0.0656775\pi$
$114$	−5.08025	+	1.26914i	−0.475809	+	0.118866i
$115$		0			0
$116$	3.11061	−	3.70708i	0.288813	−	0.344194i
$117$	−5.57049	−	2.59756i	−0.514992	−	0.240145i
$118$	−6.16410	+	8.80324i	−0.567451	+	0.810404i
$119$	−7.22648	−	1.27422i	−0.662450	−	0.116808i
$120$		0			0
$121$	−0.738236	−	1.27866i	−0.0671124	−	0.116242i
$122$	11.4305	−	3.06279i	1.03487	−	0.277292i
$123$	−4.61251	−	0.403542i	−0.415896	−	0.0363862i
$124$	6.70874	−	5.62931i	0.602463	−	0.505527i
$125$		0			0
$126$	−2.90799	+	1.67893i	−0.259064	+	0.149571i
$127$	−5.90028	−	12.6532i	−0.523565	−	1.12279i	−0.973281	−	0.229618i	$-0.926252\pi$
$127$	−5.90028	−	12.6532i	−0.523565	−	1.12279i	0.449716	−	0.893172i	$-0.351525\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	0.0256111	+	0.145248i	0.00225493	+	0.0127883i
$130$		0			0
$131$	−13.6094	−	11.4197i	−1.18906	−	0.997741i	−0.999875	−	0.0158000i	$-0.994970\pi$
$131$	−13.6094	−	11.4197i	−1.18906	−	0.997741i	−0.189186	−	0.981941i	$-0.560585\pi$
$132$	−3.00044	−	3.00044i	−0.261155	−	0.261155i
$133$	8.88771	−	3.06487i	0.770662	−	0.265758i
$134$			0.749978i			0.0647883i
$135$		0			0
$136$	1.16363	+	3.19705i	0.0997805	+	0.274145i
$137$	14.9927	+	10.4980i	1.28091	+	0.896905i	0.998060	−	0.0622587i	$-0.0198304\pi$
$137$	14.9927	+	10.4980i	1.28091	+	0.896905i	0.282853	+	0.959163i	$0.408719\pi$
$138$	0.986537	−	0.690781i	0.0839796	−	0.0588032i
$139$	7.78892	−	21.3999i	0.660647	−	1.81511i	0.0866781	−	0.996236i	$-0.472375\pi$
$139$	7.78892	−	21.3999i	0.660647	−	1.81511i	0.573969	−	0.818877i	$-0.305403\pi$
$140$		0			0
$141$	−9.94490	−	5.74169i	−0.837512	−	0.483538i
$142$	−0.551126	+	6.29940i	−0.0462495	+	0.528634i
$143$	−1.21537	+	13.8918i	−0.101635	+	1.16169i
$144$	1.34828	+	0.778431i	0.112357	+	0.0648692i
$145$		0			0
$146$	−1.60424	+	4.40761i	−0.132768	+	0.364776i
$147$	2.31072	−	1.61799i	0.190585	−	0.133449i
$148$	6.12266	+	4.28713i	0.503280	+	0.352400i
$149$	−2.95717	−	8.12476i	−0.242261	−	0.665606i	−0.999916	−	0.0129513i	$-0.995877\pi$
$149$	−2.95717	−	8.12476i	−0.242261	−	0.665606i	0.757655	−	0.652655i	$-0.226345\pi$
$150$		0			0
$151$		−	2.46429i		−	0.200541i	−0.994960	−	0.100270i	$-0.968029\pi$
$151$		−	2.46429i		−	0.200541i	0.994960	−	0.100270i	$-0.0319708\pi$
$152$	−3.29102	−	2.85818i	−0.266937	−	0.231829i
$153$	3.74540	+	3.74540i	0.302798	+	0.302798i
$154$	5.83595	+	4.89695i	0.470275	+	0.394607i
$155$		0			0
$156$	0.823553	+	4.67060i	0.0659370	+	0.373947i
$157$	13.2975	+	18.9908i	1.06125	+	1.51563i	0.841637	+	0.540043i	$0.181592\pi$
$157$	13.2975	+	18.9908i	1.06125	+	1.51563i	0.219618	+	0.975586i	$0.429519\pi$
$158$	−0.487053	−	1.04449i	−0.0387479	−	0.0830951i
$159$	8.51936	−	4.91866i	0.675629	−	0.390075i
$160$		0			0
$161$	−1.65638	+	1.38987i	−0.130541	+	0.109537i
$162$	−1.89835	−	0.166084i	−0.149148	−	0.0130488i
$163$	11.5157	−	3.08563i	0.901981	−	0.241685i	0.222114	−	0.975021i	$-0.428704\pi$
$163$	11.5157	−	3.08563i	0.901981	−	0.241685i	0.679867	+	0.733335i	$0.262037\pi$
$164$	−1.92712	−	3.33787i	−0.150483	−	0.260644i
$165$		0			0
$166$	5.85370	+	1.03216i	0.454335	+	0.0801115i
$167$	−0.132096	+	0.188653i	−0.0102219	+	0.0145984i	−0.824230	−	0.566254i	$-0.808392\pi$
$167$	−0.132096	+	0.188653i	−0.0102219	+	0.0145984i	0.814009	+	0.580853i	$0.197281\pi$
$168$	2.34824	+	1.09500i	0.181170	+	0.0844811i
$169$	1.66226	−	1.98100i	0.127866	−	0.152385i
$170$		0			0
$171$	−6.52418	−	1.86752i	−0.498916	−	0.142813i
$172$	−0.0868138	+	0.0868138i	−0.00661949	+	0.00661949i
$173$	11.4785	−	1.00424i	0.872694	−	0.0763508i	0.357997	−	0.933723i	$-0.383460\pi$
$173$	11.4785	−	1.00424i	0.872694	−	0.0763508i	0.514697	+	0.857372i	$0.327904\pi$
$174$	−5.46284	+	1.98831i	−0.414137	+	0.150733i
$175$		0			0
$176$	0.613361	−	3.47854i	0.0462338	−	0.262205i
$177$	11.7006	−	5.45608i	0.879470	−	0.410104i
$178$	3.34225	−	12.4735i	0.250513	−	0.934926i
$179$	−7.38913	+	12.7984i	−0.552290	+	0.956594i	0.445819	+	0.895123i	$0.352912\pi$
$179$	−7.38913	+	12.7984i	−0.552290	+	0.956594i	−0.998109	+	0.0614707i	$0.980421\pi$
$180$		0			0
$181$	9.19041	+	10.9527i	0.683118	+	0.814108i	0.990505	−	0.137477i	$-0.0438992\pi$
$181$	9.19041	+	10.9527i	0.683118	+	0.814108i	−0.307387	+	0.951584i	$0.599455\pi$
$182$	−2.20382	−	8.22476i	−0.163358	−	0.609660i
$183$	−13.7315	−	3.67935i	−1.01506	−	0.271985i
$184$	0.942065	+	0.342884i	0.0694499	+	0.0252777i
$185$		0			0
$186$	−10.3608	+	1.82689i	−0.759690	+	0.133954i
$187$	5.07876	−	10.8914i	0.371395	−	0.796460i
$188$	−0.833128	−	9.52270i	−0.0607621	−	0.694514i
$189$	11.8068			0.858818
$190$		0			0
$191$	−2.60656			−0.188604			−0.0943020	−	0.995544i	$-0.530062\pi$
$191$	−2.60656			−0.188604			−0.0943020	+	0.995544i	$0.530062\pi$
$192$	−0.104701	−	1.19674i	−0.00755613	−	0.0863670i
$193$	−3.45713	+	7.41384i	−0.248850	+	0.533660i	−0.990563	−	0.137057i	$-0.956236\pi$
$193$	−3.45713	+	7.41384i	−0.248850	+	0.533660i	0.741714	+	0.670717i	$0.234013\pi$
$194$	12.7894	−	2.25511i	0.918222	−	0.161907i
$195$		0			0
$196$	2.20656	+	0.803121i	0.157611	+	0.0573658i
$197$	−14.7383	−	3.94910i	−1.05006	−	0.281362i	−0.307782	−	0.951457i	$-0.599587\pi$
$197$	−14.7383	−	3.94910i	−1.05006	−	0.281362i	−0.742275	+	0.670095i	$0.766253\pi$
$198$	−1.42329	−	5.31178i	−0.101149	−	0.377491i
$199$	−4.22800	−	5.03873i	−0.299715	−	0.357186i	0.595078	−	0.803668i	$-0.297121\pi$
$199$	−4.22800	−	5.03873i	−0.299715	−	0.357186i	−0.894793	+	0.446482i	$0.852677\pi$
$200$		0			0
$201$	0.450477	−	0.780249i	0.0317742	−	0.0550345i
$202$	0.666909	−	2.48894i	0.0469236	−	0.175121i
$203$	9.45946	−	4.41102i	0.663924	−	0.309593i
$204$	0.709721	−	4.02503i	0.0496904	−	0.281808i
$205$		0			0
$206$	−4.53208	+	1.64954i	−0.315765	+	0.114929i
$207$	1.55485	−	0.136032i	0.108070	−	0.00945488i
$208$	−2.79160	+	2.79160i	−0.193562	+	0.193562i
$209$	1.08110	+	15.3585i	0.0747812	+	1.06237i
$210$		0			0
$211$	17.7136	−	21.1103i	1.21946	−	1.45329i	0.367224	−	0.930133i	$-0.380308\pi$
$211$	17.7136	−	21.1103i	1.21946	−	1.45329i	0.852234	−	0.523160i	$-0.175247\pi$
$212$	7.42161	+	3.46075i	0.509718	+	0.237686i
$213$	4.35713	−	6.22263i	0.298546	−	0.426367i
$214$	−0.356928	−	0.0629360i	−0.0243991	−	0.00430222i
$215$		0			0
$216$	−2.73709	−	4.74079i	−0.186236	−	0.322570i
$217$	18.2450	−	4.88872i	1.23855	−	0.331868i
$218$	10.4023	+	0.910087i	0.704536	+	0.0616389i
$219$	4.31643	−	3.62192i	0.291678	−	0.244746i
$220$		0			0
$221$	−11.6322	+	6.71585i	−0.782466	+	0.451757i
$222$	−3.79470	−	8.13777i	−0.254684	−	0.546171i
$223$	−6.25856	−	8.93815i	−0.419104	−	0.598543i	0.552975	−	0.833198i	$-0.313493\pi$
$223$	−6.25856	−	8.93815i	−0.419104	−	0.598543i	−0.972079	+	0.234656i	$0.924604\pi$
$224$	0.374526	+	2.12404i	0.0250241	+	0.141919i
$225$		0			0
$226$	−8.91257	−	7.47854i	−0.592856	−	0.497465i
$227$	4.16431	+	4.16431i	0.276395	+	0.276395i	0.831668	−	0.555273i	$-0.187386\pi$
$227$	4.16431	+	4.16431i	0.276395	+	0.276395i	−0.555273	+	0.831668i	$0.687386\pi$
$228$	1.70708	+	4.95030i	0.113054	+	0.327842i
$229$		−	25.8072i		−	1.70539i	−0.522411	−	0.852694i	$-0.674967\pi$
$229$		−	25.8072i		−	1.70539i	0.522411	−	0.852694i	$-0.325033\pi$
$230$		0			0
$231$	−3.13014	−	8.59999i	−0.205948	−	0.565837i
$232$	−3.96408	−	2.77568i	−0.260255	−	0.182232i
$233$	−21.7082	+	15.2002i	−1.42215	+	0.995799i	−0.426319	+	0.904573i	$0.640190\pi$
$233$	−21.7082	+	15.2002i	−1.42215	+	0.995799i	−0.995830	+	0.0912262i	$0.970921\pi$
$234$	−2.10218	+	5.77568i	−0.137424	+	0.377568i
$235$		0			0
$236$	9.30698	+	5.37339i	0.605833	+	0.349778i
$237$	−0.120664	+	1.37920i	−0.00783798	+	0.0895885i
$238$	−0.639545	+	7.31004i	−0.0414556	+	0.473839i
$239$	6.79736	+	3.92446i	0.439685	+	0.253852i	0.703464	−	0.710731i	$-0.251636\pi$
$239$	6.79736	+	3.92446i	0.439685	+	0.253852i	−0.263779	+	0.964583i	$0.584969\pi$
$240$		0			0
$241$	7.15466	−	19.6573i	0.460872	−	1.26624i	−0.463958	−	0.885857i	$-0.653571\pi$
$241$	7.15466	−	19.6573i	0.460872	−	1.26624i	0.924831	−	0.380379i	$-0.124207\pi$
$242$	−1.20946	+	0.846870i	−0.0777468	+	0.0544389i
$243$	−11.5774	−	8.10656i	−0.742689	−	0.520036i
$244$	−4.04736	−	11.1200i	−0.259106	−	0.711887i
$245$		0			0
$246$			4.63013i			0.295206i
$247$	8.85625	−	14.7547i	0.563509	−	0.938819i
$248$	−6.19259	−	6.19259i	−0.393230	−	0.393230i
$249$	−5.46999	−	4.58987i	−0.346647	−	0.290871i
$250$		0			0
$251$	−1.80490	−	10.2361i	−0.113924	−	0.646095i	−0.987277	−	0.159008i	$-0.949170\pi$
$251$	−1.80490	−	10.2361i	−0.113924	−	0.646095i	0.873353	−	0.487087i	$-0.161941\pi$
$252$	1.92599	+	2.75059i	0.121326	+	0.173271i
$253$	−1.49654	−	3.20935i	−0.0940869	−	0.201770i
$254$	−12.0908	+	6.98063i	−0.758644	+	0.438003i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−16.3993	−	1.43475i	−1.02296	−	0.0894974i	−0.436689	−	0.899613i	$-0.643849\pi$
$257$	−16.3993	−	1.43475i	−1.02296	−	0.0894974i	−0.586271	+	0.810115i	$0.699405\pi$
$258$	0.142463	−	0.0381728i	0.00886935	−	0.00237653i
$259$	8.06042	+	13.9611i	0.500850	+	0.867498i
$260$		0			0
$261$	−7.41959	−	1.30827i	−0.459261	−	0.0809801i
$262$	−10.1901	+	14.5529i	−0.629545	+	0.899083i
$263$	−2.02923	−	0.946243i	−0.125127	−	0.0583479i	0.359046	−	0.933320i	$-0.383102\pi$
$263$	−2.02923	−	0.946243i	−0.125127	−	0.0583479i	−0.484174	+	0.874972i	$0.660880\pi$
$264$	−2.72752	+	3.25053i	−0.167867	+	0.200056i
$265$		0			0
$266$	−3.82783	−	8.58677i	−0.234699	−	0.526488i
$267$	−10.9694	+	10.9694i	−0.671315	+	0.671315i
$268$	0.747124	−	0.0653649i	0.0456379	−	0.00399280i
$269$	8.00877	−	2.91495i	0.488303	−	0.177728i	−0.0861226	−	0.996285i	$-0.527448\pi$
$269$	8.00877	−	2.91495i	0.488303	−	0.177728i	0.574426	+	0.818557i	$0.305225\pi$
$270$		0			0
$271$	−3.74161	+	21.2197i	−0.227287	+	1.28901i	0.630978	+	0.775800i	$0.282654\pi$
$271$	−3.74161	+	21.2197i	−0.227287	+	1.28901i	−0.858265	+	0.513207i	$0.828457\pi$
$272$	3.08346	−	1.43784i	0.186963	−	0.0871820i
$273$	−2.64746	+	9.88046i	−0.160232	+	0.597993i
$274$	9.15135	−	15.8506i	0.552853	−	0.957570i
$275$		0			0
$276$	−0.774135	−	0.922578i	−0.0465974	−	0.0555327i
$277$	0.473538	+	1.76727i	0.0284521	+	0.106185i	0.978692	−	0.205335i	$-0.0658285\pi$
$277$	0.473538	+	1.76727i	0.0284521	+	0.106185i	−0.950240	+	0.311520i	$0.899162\pi$
$278$	−21.9973	−	5.89416i	−1.31931	−	0.353508i
$279$	−12.8122	−	4.66325i	−0.767045	−	0.279182i
$280$		0			0
$281$	−6.29502	+	1.10998i	−0.375529	+	0.0662160i	−0.358227	−	0.933634i	$-0.616619\pi$
$281$	−6.29502	+	1.10998i	−0.375529	+	0.0662160i	−0.0173020	+	0.999850i	$0.505508\pi$
$282$	−4.85309	+	10.4075i	−0.288997	+	0.619756i
$283$	1.42999	+	16.3449i	0.0850041	+	0.971602i	0.912216	+	0.409711i	$0.134370\pi$
$283$	1.42999	+	16.3449i	0.0850041	+	0.971602i	−0.827211	+	0.561891i	$0.810074\pi$
$284$	6.32347			0.375229
$285$		0			0
$286$	13.9448			0.824575
$287$	−0.724514	−	8.28123i	−0.0427667	−	0.488826i
$288$	0.657958	−	1.41100i	0.0387706	−	0.0831437i
$289$	−5.34244	+	0.942016i	−0.314261	+	0.0554127i
$290$		0			0
$291$	−14.6601	−	5.33584i	−0.859391	−	0.312793i
$292$	4.53065	+	1.21398i	0.265136	+	0.0710431i
$293$	−4.66762	−	17.4198i	−0.272685	−	1.01767i	−0.957377	−	0.288842i	$-0.906730\pi$
$293$	−4.66762	−	17.4198i	−0.272685	−	1.01767i	0.684692	−	0.728833i	$-0.259937\pi$
$294$	−1.81322	−	2.16091i	−0.105749	−	0.126027i
$295$		0			0
$296$	3.73719	−	6.47301i	0.217220	−	0.376236i
$297$	−5.00451	+	18.6771i	−0.290391	+	1.08376i
$298$	−7.83611	+	3.65404i	−0.453934	+	0.211673i
$299$	−0.687278	+	3.89775i	−0.0397463	+	0.225413i
$300$		0			0
$301$	−0.248829	+	0.0905665i	−0.0143423	+	0.00522016i
$302$	−2.45491	+	0.214777i	−0.141264	+	0.0123590i
$303$	−2.18882	+	2.18882i	−0.125744	+	0.125744i
$304$	−2.56047	+	3.52761i	−0.146853	+	0.202322i
$305$		0			0
$306$	3.40472	−	4.05758i	0.194635	−	0.231956i
$307$	−13.2982	−	6.20104i	−0.758967	−	0.353912i	0.00430411	−	0.999991i	$-0.498630\pi$
$307$	−13.2982	−	6.20104i	−0.758967	−	0.353912i	−0.763271	+	0.646079i	$0.776408\pi$
$308$	4.36968	−	6.24054i	0.248985	−	0.355588i
$309$	5.70580	+	1.00609i	0.324592	+	0.0572343i
$310$		0			0
$311$	6.35047	+	10.9993i	0.360102	+	0.623715i	0.987977	−	0.154599i	$-0.0494085\pi$
$311$	6.35047	+	10.9993i	0.360102	+	0.623715i	−0.627875	+	0.778314i	$0.716075\pi$
$312$	4.58105	−	1.22749i	0.259351	−	0.0694929i
$313$	8.31177	+	0.727186i	0.469809	+	0.0411030i	0.319603	−	0.947552i	$-0.396451\pi$
$313$	8.31177	+	0.727186i	0.469809	+	0.0411030i	0.150207	+	0.988655i	$0.452006\pi$
$314$	17.7596	−	14.9020i	1.00223	−	0.840971i
$315$		0			0
$316$	−0.998065	+	0.576233i	−0.0561455	+	0.0324156i
$317$	5.95650	+	12.7738i	0.334550	+	0.717445i	0.999568	−	0.0293820i	$-0.00935394\pi$
$317$	5.95650	+	12.7738i	0.334550	+	0.717445i	−0.665018	+	0.746827i	$0.731576\pi$
$318$	−5.64245	−	8.05825i	−0.316413	−	0.451884i
$319$	2.96821	+	16.8336i	0.166188	+	0.942498i
$320$		0			0
$321$	0.333532	+	0.279866i	0.0186159	+	0.0156206i
$322$	1.52895	+	1.52895i	0.0852048	+	0.0852048i
$323$	−11.5207	+	9.33812i	−0.641031	+	0.519587i
$324$			1.90560i			0.105866i
$325$		0			0
$326$	−4.07755	−	11.2030i	−0.225835	−	0.620476i
$327$	−10.2756	−	7.19502i	−0.568240	−	0.397886i
$328$	−3.15721	+	2.21070i	−0.174328	+	0.122066i
$329$	7.05147	−	19.3737i	0.388760	−	1.06811i
$330$		0			0
$331$	10.9280	+	6.30928i	0.600656	+	0.346789i	0.769300	−	0.638888i	$-0.220605\pi$
$331$	10.9280	+	6.30928i	0.600656	+	0.346789i	−0.168643	+	0.985677i	$0.553939\pi$
$332$	0.518054	−	5.92138i	0.0284319	−	0.324978i
$333$	1.01420	−	11.5923i	0.0555776	−	0.635255i
$334$	0.199448	+	0.115151i	0.0109133	+	0.00630080i
$335$		0			0
$336$	0.886171	−	2.43474i	0.0483446	−	0.132826i
$337$	22.8224	−	15.9804i	1.24321	−	0.870508i	0.248051	−	0.968747i	$-0.420210\pi$
$337$	22.8224	−	15.9804i	1.24321	−	0.870508i	0.995163	+	0.0982389i	$0.0313209\pi$
$338$	−2.11834	−	1.48327i	−0.115222	−	0.0806795i
$339$	4.78030	+	13.1338i	0.259630	+	0.713328i
$340$		0			0
$341$			30.9338i			1.67516i
$342$	−1.29179	+	6.66212i	−0.0698521	+	0.360246i
$343$	14.2568	+	14.2568i	0.769797	+	0.769797i
$344$	0.0940498	+	0.0789171i	0.00507082	+	0.00425493i
$345$		0			0
$346$	−2.00083	−	11.3473i	−0.107566	−	0.610034i
$347$	6.56890	+	9.38136i	0.352637	+	0.503618i	0.955807	−	0.293995i	$-0.0949849\pi$
$347$	6.56890	+	9.38136i	0.352637	+	0.503618i	−0.603170	+	0.797613i	$0.706096\pi$
$348$	2.45686	+	5.26876i	0.131702	+	0.282435i
$349$	4.80278	−	2.77289i	0.257087	−	0.148429i	−0.365918	−	0.930647i	$-0.619245\pi$
$349$	4.80278	−	2.77289i	0.257087	−	0.148429i	0.623005	+	0.782218i	$0.285912\pi$
$350$		0			0
$351$	16.5555	−	13.8917i	0.883665	−	0.741483i
$352$	−3.51876	−	0.307852i	−0.187551	−	0.0164086i
$353$	21.4063	−	5.73581i	1.13934	−	0.305286i	0.360657	−	0.932698i	$-0.382552\pi$
$353$	21.4063	−	5.73581i	1.13934	−	0.305286i	0.778687	+	0.627412i	$0.215886\pi$
$354$	−6.45509	−	11.1805i	−0.343084	−	0.594239i
$355$		0			0
$356$	−12.7173	−	2.24240i	−0.674015	−	0.118847i
$357$	5.05616	−	7.22094i	0.267600	−	0.382173i
$358$	13.3937	+	6.24556i	0.707877	+	0.330088i
$359$	−6.30092	+	7.50914i	−0.332550	+	0.396317i	−0.906246	−	0.422751i	$-0.861065\pi$
$359$	−6.30092	+	7.50914i	−0.332550	+	0.396317i	0.573696	+	0.819068i	$0.305509\pi$
$360$		0			0
$361$	7.10125	−	17.6231i	0.373750	−	0.927529i
$362$	10.1100	−	10.1100i	0.531371	−	0.531371i
$363$	1.76695	−	0.154588i	0.0927407	−	0.00811376i
$364$	−8.00139	+	2.91227i	−0.419387	+	0.152644i
$365$		0			0
$366$	−2.46857	+	13.9999i	−0.129034	+	0.731788i
$367$	9.61824	−	4.48506i	0.502068	−	0.234118i	−0.155049	−	0.987907i	$-0.549554\pi$
$367$	9.61824	−	4.48506i	0.502068	−	0.234118i	0.657117	+	0.753789i	$0.271776\pi$
$368$	0.259472	−	0.968364i	0.0135259	−	0.0504795i
$369$	−3.00026	+	5.19660i	−0.156187	+	0.270524i
$370$		0			0
$371$	11.3528	+	13.5297i	0.589407	+	0.702427i
$372$	2.72294	+	10.1621i	0.141178	+	0.526882i
$373$	−5.27496	−	1.41342i	−0.273127	−	0.0731842i	0.119656	−	0.992815i	$-0.461821\pi$
$373$	−5.27496	−	1.41342i	−0.273127	−	0.0731842i	−0.392783	+	0.919631i	$0.628488\pi$
$374$	−11.2926	−	4.11018i	−0.583928	−	0.212532i
$375$		0			0
$376$	−9.41385	+	1.65992i	−0.485482	+	0.0856036i
$377$	8.07410	−	17.3150i	0.415837	−	0.891766i
$378$	−1.02903	−	11.7619i	−0.0529276	−	0.604965i
$379$	−11.4538			−0.588342			−0.294171	−	0.955753i	$-0.595044\pi$
$379$	−11.4538			−0.588342			−0.294171	+	0.955753i	$0.595044\pi$
$380$		0			0
$381$	16.7718			0.859243
$382$	0.227177	+	2.59664i	0.0116234	+	0.132856i
$383$	−12.4321	+	26.6607i	−0.635251	+	1.36230i	0.280227	+	0.959934i	$0.409590\pi$
$383$	−12.4321	+	26.6607i	−0.635251	+	1.36230i	−0.915479	+	0.402367i	$0.868188\pi$
$384$	−1.18306	+	0.208605i	−0.0603726	+	0.0106453i
$385$		0			0
$386$	7.68693	+	2.79781i	0.391255	+	0.142405i
$387$	0.184628	+	0.0494709i	0.00938517	+	0.00251475i
$388$	−3.36119	−	12.5441i	−0.170639	−	0.636832i
$389$	−4.90364	−	5.84393i	−0.248624	−	0.296299i	0.627270	−	0.778802i	$-0.284172\pi$
$389$	−4.90364	−	5.84393i	−0.248624	−	0.296299i	−0.875894	+	0.482503i	$0.839728\pi$
$390$		0			0
$391$	1.70541	−	2.95385i	0.0862462	−	0.149383i
$392$	0.607751	−	2.26816i	0.0306960	−	0.114559i
$393$	19.3426	−	9.01962i	0.975707	−	0.454980i
$394$	−2.64955	+	15.0264i	−0.133483	+	0.757017i
$395$		0			0
$396$	−5.16752	+	1.88082i	−0.259677	+	0.0945148i
$397$	−29.0956	+	2.54553i	−1.46026	+	0.127757i	−0.789425	−	0.613847i	$-0.789621\pi$
$397$	−29.0956	+	2.54553i	−1.46026	+	0.127757i	−0.670839	+	0.741603i	$0.734066\pi$
$398$	−4.65106	+	4.65106i	−0.233137	+	0.233137i
$399$	−1.17534	+	11.2325i	−0.0588408	+	0.562331i
$400$		0			0
$401$	−14.0943	+	16.7969i	−0.703835	+	0.838798i	−0.992955	−	0.118495i	$-0.962193\pi$
$401$	−14.0943	+	16.7969i	−0.703835	+	0.838798i	0.289120	+	0.957293i	$0.406637\pi$
$402$	−0.816542	−	0.380760i	−0.0407254	−	0.0189906i
$403$	19.8311	−	28.3217i	0.987856	−	1.41080i
$404$	−2.53759	−	0.447446i	−0.126250	−	0.0222613i
$405$		0			0
$406$	−5.21868	−	9.03901i	−0.258999	−	0.448599i
$407$	−25.5015	+	6.83310i	−1.26406	+	0.338704i
$408$	−4.07157	−	0.356216i	−0.201573	−	0.0176353i
$409$	−2.64453	+	2.21903i	−0.130764	+	0.109724i	−0.705824	−	0.708387i	$-0.749423\pi$
$409$	−2.64453	+	2.21903i	−0.130764	+	0.109724i	0.575060	+	0.818111i	$0.304979\pi$
$410$		0			0
$411$	−19.0414	+	10.9936i	−0.939245	+	0.542273i
$412$	2.03826	+	4.37106i	0.100418	+	0.215347i
$413$	13.2948	+	18.9869i	0.654194	+	0.934286i
$414$	−0.271029	−	1.53708i	−0.0133203	−	0.0755434i
$415$		0			0
$416$	3.02428	+	2.53767i	0.148277	+	0.124419i
$417$	19.3448	+	19.3448i	0.947319	+	0.947319i
$418$	15.2059	−	2.41557i	0.743743	−	0.118149i
$419$			34.7913i			1.69967i	0.527052	+	0.849833i	$0.323297\pi$
$419$			34.7913i			1.69967i	−0.527052	+	0.849833i	$0.676703\pi$
$420$		0			0
$421$	5.19898	+	14.2841i	0.253383	+	0.696163i	0.999538	+	0.0303914i	$0.00967538\pi$
$421$	5.19898	+	14.2841i	0.253383	+	0.696163i	−0.746155	+	0.665772i	$0.768102\pi$
$422$	−22.5738	−	15.8064i	−1.09888	−	0.769441i
$423$	−12.1907	+	8.53605i	−0.592734	+	0.415037i
$424$	2.80075	−	7.69499i	0.136016	−	0.373702i
$425$		0			0
$426$	−6.57870	−	3.79821i	−0.318739	−	0.184024i
$427$	2.22448	−	25.4259i	0.107650	−	1.23045i
$428$	−0.0315882	+	0.361055i	−0.00152687	+	0.0174523i
$429$	−14.5077	−	8.37601i	−0.700437	−	0.404398i
$430$		0			0
$431$	−0.796607	+	2.18866i	−0.0383712	+	0.105424i	−0.957399	−	0.288770i	$-0.906754\pi$
$431$	−0.796607	+	2.18866i	−0.0383712	+	0.105424i	0.919027	+	0.394194i	$0.128976\pi$
$432$	−4.48419	+	3.13987i	−0.215746	+	0.151067i
$433$	26.0736	+	18.2569i	1.25302	+	0.877371i	0.996028	−	0.0890434i	$-0.0283810\pi$
$433$	26.0736	+	18.2569i	1.25302	+	0.877371i	0.256988	+	0.966415i	$0.417270\pi$
$434$	−6.46027	−	17.7495i	−0.310103	−	0.852001i
$435$		0			0
$436$		−	10.4421i		−	0.500085i
$437$	−0.0742477	+	4.36927i	−0.00355175	+	0.209011i
$438$	−3.98434	−	3.98434i	−0.190379	−	0.190379i
$439$	−13.9221	−	11.6820i	−0.664466	−	0.557553i	0.246956	−	0.969027i	$-0.420570\pi$
$439$	−13.9221	−	11.6820i	−0.664466	−	0.557553i	−0.911422	+	0.411474i	$0.865014\pi$
$440$		0			0
$441$	−0.634818	−	3.60023i	−0.0302294	−	0.171440i
$442$	7.70410	+	11.0026i	0.366447	+	0.523340i
$443$	0.224808	+	0.482102i	0.0106809	+	0.0229054i	0.911576	−	0.411132i	$-0.134866\pi$
$443$	0.224808	+	0.482102i	0.0106809	+	0.0229054i	−0.900895	+	0.434037i	$0.857089\pi$
$444$	−7.77607	+	4.48952i	−0.369036	+	0.213063i
$445$		0			0
$446$	−8.35867	+	7.01375i	−0.395794	+	0.332111i
$447$	10.3472	+	0.905263i	0.489406	+	0.0428175i
$448$	2.08332	−	0.558224i	0.0984276	−	0.0263736i
$449$	−2.97196	−	5.14759i	−0.140256	−	0.242930i	0.787337	−	0.616523i	$-0.211459\pi$
$449$	−2.97196	−	5.14759i	−0.140256	−	0.242930i	−0.927593	+	0.373593i	$0.878126\pi$
$450$		0			0
$451$	13.4071	+	2.36404i	0.631318	+	0.111318i
$452$	−6.67330	+	9.53046i	−0.313885	+	0.448275i
$453$	2.68300	+	1.25111i	0.126059	+	0.0587821i
$454$	3.78552	−	4.51141i	0.177663	−	0.211731i
$455$		0			0
$456$	4.78268	−	2.13203i	0.223970	−	0.0998417i
$457$	−7.40151	+	7.40151i	−0.346228	+	0.346228i	−0.858703	−	0.512474i	$-0.828729\pi$
$457$	−7.40151	+	7.40151i	−0.346228	+	0.346228i	0.512474	+	0.858703i	$0.328729\pi$
$458$	−25.7090	+	2.24924i	−1.20130	+	0.105100i
$459$	−17.5012	+	6.36993i	−0.816888	+	0.297323i
$460$		0			0
$461$	−7.09872	+	40.2589i	−0.330620	+	1.87504i	0.136188	+	0.990683i	$0.456515\pi$
$461$	−7.09872	+	40.2589i	−0.330620	+	1.87504i	−0.466808	+	0.884359i	$0.654596\pi$
$462$	−8.29445	+	3.86777i	−0.385893	+	0.179945i
$463$	−2.96635	+	11.0706i	−0.137858	+	0.514493i	0.862112	+	0.506718i	$0.169141\pi$
$463$	−2.96635	+	11.0706i	−0.137858	+	0.514493i	−0.999970	+	0.00777472i	$0.997525\pi$
$464$	−2.41963	+	4.19092i	−0.112328	+	0.194558i
$465$		0			0
$466$	17.0344	+	20.3008i	0.789102	+	0.940415i
$467$	−5.60446	−	20.9161i	−0.259343	−	0.967883i	−0.965622	−	0.259949i	$-0.916294\pi$
$467$	−5.60446	−	20.9161i	−0.259343	−	0.967883i	0.706279	−	0.707934i	$-0.250372\pi$
$468$	5.93692	+	1.59079i	0.274434	+	0.0735344i
$469$	1.52001	+	0.553238i	0.0701875	+	0.0255462i
$470$		0			0
$471$	−27.4273	+	4.83618i	−1.26379	+	0.222839i
$472$	4.54178	−	9.73989i	0.209053	−	0.448315i
$473$	−0.0377960	−	0.432010i	−0.00173786	−	0.0198638i
$474$	1.38447			0.0635906
$475$		0			0
$476$	7.33796			0.336335
$477$	−1.11114	−	12.7004i	−0.0508756	−	0.581510i
$478$	3.31710	−	7.11353i	0.151720	−	0.325366i
$479$	23.7956	−	4.19581i	1.08725	−	0.191711i	0.398830	−	0.917025i	$-0.369416\pi$
$479$	23.7956	−	4.19581i	1.08725	−	0.191711i	0.688419	+	0.725314i	$0.258305\pi$
$480$		0			0
$481$	27.7287	+	10.0924i	1.26432	+	0.460174i
$482$	−20.2060	−	5.41419i	−0.920360	−	0.246610i
$483$	−0.672291	−	2.50902i	−0.0305903	−	0.114165i
$484$	0.949058	+	1.13104i	0.0431390	+	0.0514111i
$485$		0			0
$486$	−7.06668	+	12.2399i	−0.320551	+	0.555211i
$487$	−8.76100	+	32.6965i	−0.396999	+	1.48162i	0.421351	+	0.906898i	$0.361556\pi$
$487$	−8.76100	+	32.6965i	−0.396999	+	1.48162i	−0.818349	+	0.574721i	$0.805111\pi$
$488$	−10.7250	+	5.00114i	−0.485497	+	0.226391i
$489$	−2.48698	+	14.1044i	−0.112465	+	0.637821i
$490$		0			0
$491$	32.3953	−	11.7909i	1.46198	−	0.532118i	0.516071	−	0.856546i	$-0.327394\pi$
$491$	32.3953	−	11.7909i	1.46198	−	0.532118i	0.945910	+	0.324428i	$0.105172\pi$
$492$	4.61251	−	0.403542i	0.207948	−	0.0181931i
$493$	−11.6420	+	11.6420i	−0.524328	+	0.524328i
$494$	−15.4704	−	7.53659i	−0.696047	−	0.339087i
$495$		0			0
$496$	−5.62931	+	6.70874i	−0.252763	+	0.301232i
$497$	12.3607	+	5.76389i	0.554453	+	0.258546i
$498$	−4.09566	+	5.84921i	−0.183531	+	0.262109i
$499$	10.3228	+	1.82019i	0.462111	+	0.0814827i	0.399857	−	0.916578i	$-0.369060\pi$
$499$	10.3228	+	1.82019i	0.462111	+	0.0814827i	0.0622545	+	0.998060i	$0.480171\pi$
$500$		0			0
$501$	−0.138332	−	0.239598i	−0.00618023	−	0.0107045i
$502$	−10.0398	+	2.69016i	−0.448099	+	0.120068i
$503$	37.4446	+	3.27598i	1.66957	+	0.146069i	0.882349	−	0.470596i	$-0.155961\pi$
$503$	37.4446	+	3.27598i	1.66957	+	0.146069i	0.787226	+	0.616665i	$0.211517\pi$
$504$	2.57227	−	2.15839i	0.114578	−	0.0961422i
$505$		0			0
$506$	−3.06670	+	1.77056i	−0.136332	+	0.0787110i
$507$	1.31290	+	2.81553i	0.0583080	+	0.125042i
$508$	8.00785	+	11.4364i	0.355291	+	0.507408i
$509$	5.93123	+	33.6377i	0.262897	+	1.49096i	0.774957	+	0.632014i	$0.217772\pi$
$509$	5.93123	+	33.6377i	0.262897	+	1.49096i	−0.512059	+	0.858950i	$0.671117\pi$
$510$		0			0
$511$	7.74967	+	6.50274i	0.342825	+	0.287664i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	15.6462	−	18.0157i	0.690796	−	0.795412i
$514$			16.4619i			0.726105i
$515$		0			0
$516$	−0.0504440	−	0.138594i	−0.00222067	−	0.00610125i
$517$	27.6583	+	19.3666i	1.21641	+	0.851741i
$518$	13.2054	−	9.24653i	0.580213	−	0.406269i
$519$	−4.73420	+	13.0071i	−0.207808	+	0.570949i
$520$		0			0
$521$	−33.3527	−	19.2562i	−1.46121	−	0.843630i	−0.462142	−	0.886806i	$-0.652919\pi$
$521$	−33.3527	−	19.2562i	−1.46121	−	0.843630i	−0.999067	+	0.0431760i	$0.986252\pi$
$522$	−0.656636	+	7.50538i	−0.0287402	+	0.328502i
$523$	−2.44469	+	27.9429i	−0.106899	+	1.22186i	0.733424	+	0.679772i	$0.237921\pi$
$523$	−2.44469	+	27.9429i	−0.106899	+	1.22186i	−0.840322	+	0.542087i	$0.817634\pi$
$524$	15.3857	+	8.88293i	0.672127	+	0.388052i
$525$		0			0
$526$	−0.765784	+	2.10397i	−0.0333898	+	0.0917376i
$527$	−24.4070	+	17.0900i	−1.06319	+	0.744452i
$528$	3.47588	+	2.43384i	0.151268	+	0.105919i
$529$	7.52271	+	20.6685i	0.327075	+	0.898630i
$530$		0			0
$531$		−	16.7312i		−	0.726074i
$532$	−8.22047	+	4.56165i	−0.356403	+	0.197772i
$533$	−10.7595	−	10.7595i	−0.466045	−	0.466045i
$534$	11.8837	+	9.97160i	0.514257	+	0.431513i
$535$		0			0
$536$	−0.130232	−	0.738584i	−0.00562518	−	0.0319020i
$537$	−10.1828	−	14.5426i	−0.439422	−	0.627559i
$538$	−3.60187	−	7.72424i	−0.155288	−	0.333015i
$539$	−7.18300	+	4.14711i	−0.309394	+	0.178629i
$540$		0			0
$541$	27.5945	−	23.1545i	1.18638	−	0.995492i	0.186466	−	0.982461i	$-0.440297\pi$
$541$	27.5945	−	23.1545i	1.18638	−	0.995492i	0.999915	−	0.0130303i	$-0.00414778\pi$
$542$	21.4651	+	1.87795i	0.922005	+	0.0806649i
$543$	−16.5907	+	4.44547i	−0.711976	+	0.190773i
$544$	−1.70111	−	2.94641i	−0.0729346	−	0.126326i
$545$		0			0
$546$	10.0736	+	1.77625i	0.431110	+	0.0760164i
$547$	16.3933	−	23.4121i	0.700929	−	1.00103i	−0.297991	−	0.954569i	$-0.596317\pi$
$547$	16.3933	−	23.4121i	0.700929	−	1.00103i	0.998920	−	0.0464615i	$-0.0147945\pi$
$548$	−16.5879	−	7.73506i	−0.708599	−	0.330425i
$549$	−11.8424	+	14.1132i	−0.505419	+	0.602335i
$550$		0			0
$551$	5.80488	−	20.2794i	0.247296	−	0.863930i
$552$	−0.851597	+	0.851597i	−0.0362464	+	0.0362464i
$553$	−2.47619	+	0.216639i	−0.105298	+	0.00921242i
$554$	1.71927	−	0.625763i	0.0730448	−	0.0265861i
$555$		0			0
$556$	−3.95454	+	22.4273i	−0.167710	+	0.951129i
$557$	−6.46151	+	3.01305i	−0.273783	+	0.127667i	−0.554661	−	0.832076i	$-0.687152\pi$
$557$	−6.46151	+	3.01305i	−0.273783	+	0.127667i	0.280878	+	0.959743i	$0.409374\pi$
$558$	−3.52885	+	13.1699i	−0.149388	+	0.557525i
$559$	−0.242349	+	0.419761i	−0.0102503	+	0.0177540i
$560$		0			0
$561$	9.27963	+	11.0590i	0.391786	+	0.466913i
$562$	1.65441	+	6.17433i	0.0697869	+	0.260448i
$563$	−21.9586	−	5.88380i	−0.925446	−	0.247972i	−0.235534	−	0.971866i	$-0.575684\pi$
$563$	−21.9586	−	5.88380i	−0.925446	−	0.247972i	−0.689912	+	0.723894i	$0.742351\pi$
$564$	10.7908	+	3.92755i	0.454377	+	0.165380i
$565$		0			0
$566$	16.1580	−	2.84910i	0.679173	−	0.119757i
$567$	−1.73697	+	3.72494i	−0.0729457	+	0.156433i
$568$	−0.551126	−	6.29940i	−0.0231247	−	0.264317i
$569$	4.58816			0.192346			0.0961728	−	0.995365i	$-0.469340\pi$
$569$	4.58816			0.192346			0.0961728	+	0.995365i	$0.469340\pi$
$570$		0			0
$571$	−40.9745			−1.71473			−0.857365	−	0.514710i	$-0.827900\pi$
$571$	−40.9745			−1.71473			−0.857365	+	0.514710i	$0.827900\pi$
$572$	−1.21537	−	13.8918i	−0.0508173	−	0.580844i
$573$	1.32334	−	2.83790i	0.0552831	−	0.118555i
$574$	−8.18658	+	1.44351i	−0.341701	+	0.0602511i
$575$		0			0
$576$	−1.46297	−	0.532478i	−0.0609571	−	0.0221866i
$577$	−0.199630	−	0.0534908i	−0.00831072	−	0.00222685i	0.254661	−	0.967030i	$-0.418036\pi$
$577$	−0.199630	−	0.0534908i	−0.00831072	−	0.00222685i	−0.262972	+	0.964803i	$0.584703\pi$
$578$	1.40406	+	5.24001i	0.0584010	+	0.217956i
$579$	−6.31668	−	7.52792i	−0.262512	−	0.312850i
$580$		0			0
$581$	6.41004	−	11.1025i	0.265933	−	0.460610i
$582$	−4.03782	+	15.0694i	−0.167373	+	0.624645i
$583$	−26.2146	+	12.2241i	−1.08570	+	0.506270i
$584$	0.814493	−	4.61922i	0.0337040	−	0.191145i
$585$		0			0
$586$	−16.9467	+	6.16809i	−0.700061	+	0.254802i
$587$	−21.8454	+	1.91122i	−0.901656	+	0.0788846i	−0.528548	−	0.848903i	$-0.677263\pi$
$587$	−21.8454	+	1.91122i	−0.901656	+	0.0788846i	−0.373108	+	0.927788i	$0.621708\pi$
$588$	−1.99466	+	1.99466i	−0.0822583	+	0.0822583i
$589$	16.7184	−	34.3180i	0.688870	−	1.41405i
$590$		0			0
$591$	11.7821	−	14.0414i	0.484652	−	0.577586i
$592$	−6.77410	−	3.15881i	−0.278414	−	0.129826i
$593$	−1.47471	+	2.10610i	−0.0605591	+	0.0864873i	−0.848289	−	0.529533i	$-0.822367\pi$
$593$	−1.47471	+	2.10610i	−0.0605591	+	0.0864873i	0.787730	+	0.616020i	$0.211256\pi$
$594$	19.0422	+	3.35765i	0.781311	+	0.137766i
$595$		0			0
$596$	4.32309	+	7.48782i	0.177081	+	0.306713i
$597$	7.63246	−	2.04511i	0.312376	−	0.0837009i
$598$	3.94282	+	0.344952i	0.161234	+	0.0141061i
$599$	−19.7650	+	16.5848i	−0.807577	+	0.677637i	−0.950028	−	0.312164i	$-0.898946\pi$
$599$	−19.7650	+	16.5848i	−0.807577	+	0.677637i	0.142451	+	0.989802i	$0.454502\pi$
$600$		0			0
$601$	13.2906	−	7.67333i	0.542134	−	0.313001i	−0.203809	−	0.979011i	$-0.565332\pi$
$601$	13.2906	−	7.67333i	0.542134	−	0.313001i	0.745944	+	0.666009i	$0.231999\pi$
$602$	0.111909	+	0.239989i	0.00456106	+	0.00978122i
$603$	−0.669715	−	0.956452i	−0.0272729	−	0.0389497i
$604$	0.427919	+	2.42685i	0.0174118	+	0.0987472i
$605$		0			0
$606$	2.37126	+	1.98972i	0.0963257	+	0.0808269i
$607$	−13.8416	−	13.8416i	−0.561815	−	0.561815i	0.368008	−	0.929823i	$-0.380040\pi$
$607$	−13.8416	−	13.8416i	−0.561815	−	0.561815i	−0.929823	+	0.368008i	$0.880040\pi$
$608$	3.73734	+	2.24327i	0.151569	+	0.0909767i
$609$			12.5385i			0.508084i
$610$		0			0
$611$	−12.9073	−	35.4625i	−0.522173	−	1.43466i
$612$	−4.33888	−	3.03812i	−0.175389	−	0.122809i
$613$	−31.2629	+	21.8905i	−1.26270	+	0.884150i	−0.996807	−	0.0798528i	$-0.974555\pi$
$613$	−31.2629	+	21.8905i	−1.26270	+	0.884150i	−0.265891	+	0.964003i	$0.585666\pi$
$614$	−5.01843	+	13.7880i	−0.202527	+	0.556439i
$615$		0			0
$616$	−6.59764	−	3.80915i	−0.265826	−	0.153475i
$617$	2.29208	−	26.1986i	0.0922757	−	1.05472i	−0.799023	−	0.601300i	$-0.794650\pi$
$617$	2.29208	−	26.1986i	0.0922757	−	1.05472i	0.891299	−	0.453416i	$-0.149795\pi$
$618$	0.504965	−	5.77178i	0.0203127	−	0.232175i
$619$	−30.2684	−	17.4755i	−1.21659	−	0.702399i	−0.252404	−	0.967622i	$-0.581221\pi$
$619$	−30.2684	−	17.4755i	−1.21659	−	0.702399i	−0.964187	+	0.265223i	$0.914555\pi$
$620$		0			0
$621$	−1.87701	+	5.15704i	−0.0753218	+	0.206945i
$622$	10.4040	−	7.28496i	0.417163	−	0.292100i
$623$	−22.8150	−	15.9752i	−0.914062	−	0.640033i
$624$	−1.62208	−	4.45664i	−0.0649353	−	0.178408i
$625$		0			0
$626$		−	8.34352i		−	0.333474i
$627$	−17.2705	−	6.62038i	−0.689718	−	0.264393i
$628$	−16.3932	−	16.3932i	−0.654159	−	0.654159i
$629$	−19.4802	−	16.3458i	−0.776726	−	0.651750i
$630$		0			0
$631$	3.85637	+	21.8706i	0.153520	+	0.870654i	0.960127	+	0.279566i	$0.0901904\pi$
$631$	3.85637	+	21.8706i	0.153520	+	0.870654i	−0.806607	+	0.591088i	$0.798698\pi$
$632$	0.661027	+	0.944045i	0.0262943	+	0.0375521i
$633$	13.9908	+	30.0034i	0.556085	+	1.19253i
$634$	12.2060	−	7.04714i	0.484762	−	0.279878i
$635$		0			0
$636$	−7.53582	+	6.32330i	−0.298815	+	0.250735i
$637$	9.23509	+	0.807965i	0.365907	+	0.0320128i
$638$	16.5108	−	4.42406i	0.653669	−	0.175150i
$639$	−4.92238	−	8.52581i	−0.194726	−	0.337276i
$640$		0			0
$641$	−9.20504	−	1.62310i	−0.363577	−	0.0641085i	−0.0111245	−	0.999938i	$-0.503541\pi$
$641$	−9.20504	−	1.62310i	−0.363577	−	0.0641085i	−0.352453	+	0.935830i	$0.614652\pi$
$642$	0.249732	−	0.356655i	0.00985614	−	0.0140760i
$643$	−0.535745	−	0.249822i	−0.0211277	−	0.00985202i	0.412026	−	0.911172i	$-0.364821\pi$
$643$	−0.535745	−	0.249822i	−0.0211277	−	0.00985202i	−0.433153	+	0.901320i	$0.642599\pi$
$644$	1.38987	−	1.65638i	0.0547686	−	0.0652707i
$645$		0			0
$646$	10.3067	+	10.6630i	0.405511	+	0.419531i
$647$	10.3352	−	10.3352i	0.406318	−	0.406318i	−0.474135	−	0.880452i	$-0.657239\pi$
$647$	10.3352	−	10.3352i	0.406318	−	0.406318i	0.880452	+	0.474135i	$0.157239\pi$
$648$	1.89835	−	0.166084i	0.0745741	−	0.00652438i
$649$	−35.6706	+	12.9830i	−1.40019	+	0.509628i
$650$		0			0
$651$	−3.94025	+	22.3463i	−0.154430	+	0.875819i
$652$	−10.8050	+	5.03844i	−0.423155	+	0.197320i
$653$	9.28936	−	34.6684i	0.363521	−	1.35668i	−0.505895	−	0.862595i	$-0.668838\pi$
$653$	9.28936	−	34.6684i	0.363521	−	1.35668i	0.869415	−	0.494082i	$-0.164496\pi$
$654$	−6.27207	+	10.8635i	−0.245257	+	0.424798i
$655$		0			0
$656$	2.47746	+	2.95252i	0.0967285	+	0.115277i
$657$	−1.89001	−	7.05360i	−0.0737362	−	0.275187i
$658$	−19.9146	−	5.33610i	−0.776352	−	0.208023i
$659$	−15.3519	−	5.58765i	−0.598027	−	0.217664i	0.0252293	−	0.999682i	$-0.491968\pi$
$659$	−15.3519	−	5.58765i	−0.598027	−	0.217664i	−0.623256	+	0.782018i	$0.714191\pi$
$660$		0			0
$661$	12.6122	−	2.22386i	0.490556	−	0.0864983i	0.0771019	−	0.997023i	$-0.475433\pi$
$661$	12.6122	−	2.22386i	0.490556	−	0.0864983i	0.413454	+	0.910525i	$0.364322\pi$
$662$	5.33283	−	11.4363i	0.207266	−	0.444484i
$663$	−1.40631	−	16.0742i	−0.0546165	−	0.624270i
$664$	−5.94400			−0.230672
$665$		0			0
$666$	−11.6366			−0.450909
$667$	0.422834	+	4.83301i	0.0163722	+	0.187135i
$668$	0.0973302	−	0.208725i	0.00376582	−	0.00807582i
$669$	12.9089	−	2.27618i	0.499086	−	0.0880023i
$670$		0			0
$671$	39.2783	+	14.2961i	1.51632	+	0.551895i
$672$	−2.50271	−	0.670598i	−0.0965440	−	0.0258689i
$673$	1.77540	+	6.62590i	0.0684368	+	0.255410i	0.991665	−	0.128842i	$-0.0411261\pi$
$673$	1.77540	+	6.62590i	0.0684368	+	0.255410i	−0.923228	+	0.384252i	$0.874459\pi$
$674$	−17.9087	−	21.3427i	−0.689817	−	0.822092i
$675$		0			0
$676$	−1.29301	+	2.23955i	−0.0497310	+	0.0861366i
$677$	−4.20588	+	15.6966i	−0.161645	+	0.603268i	0.836799	+	0.547510i	$0.184424\pi$
$677$	−4.20588	+	15.6966i	−0.161645	+	0.603268i	−0.998444	+	0.0557580i	$0.982242\pi$
$678$	12.6671	−	5.90679i	0.486479	−	0.226849i
$679$	4.86384	−	27.5842i	0.186657	−	1.05859i
$680$		0			0
$681$	−6.64811	+	2.41971i	−0.254756	+	0.0927236i
$682$	30.8161	−	2.69606i	1.18001	−	0.103237i
$683$	18.3995	−	18.3995i	0.704037	−	0.704037i	−0.261237	−	0.965275i	$-0.584131\pi$
$683$	18.3995	−	18.3995i	0.704037	−	0.704037i	0.965275	+	0.261237i	$0.0841305\pi$
$684$	6.74935	+	0.706235i	0.258068	+	0.0270036i
$685$		0			0
$686$	12.9600	−	15.4452i	0.494816	−	0.589699i
$687$	28.0977	+	13.1022i	1.07199	+	0.499879i
$688$	0.0704198	−	0.100570i	0.00268473	−	0.00383419i
$689$	31.8377	+	5.61384i	1.21292	+	0.213870i
$690$		0			0
$691$	−3.44201	−	5.96174i	−0.130940	−	0.226795i	0.793099	−	0.609093i	$-0.208466\pi$
$691$	−3.44201	−	5.96174i	−0.130940	−	0.226795i	−0.924039	+	0.382297i	$0.875133\pi$
$692$	−11.1297	+	2.98220i	−0.423089	+	0.113366i
$693$	−11.8155	−	1.03372i	−0.448834	−	0.0392679i
$694$	8.77314	−	7.36154i	0.333024	−	0.279440i
$695$		0			0
$696$	5.03458	−	2.90671i	0.190835	−	0.110179i
$697$	5.54179	+	11.8844i	0.209910	+	0.450154i
$698$	−3.18093	−	4.54284i	−0.120400	−	0.171949i
$699$	−5.52819	−	31.3519i	−0.209095	−	1.18584i
$700$		0			0
$701$	−26.9148	−	22.5842i	−1.01656	−	0.852995i	−0.0273682	−	0.999625i	$-0.508713\pi$
$701$	−26.9148	−	22.5842i	−1.01656	−	0.852995i	−0.989191	+	0.146631i	$0.953157\pi$
$702$	−15.2817	−	15.2817i	−0.576771	−	0.576771i
$703$	31.9844	+	6.20181i	1.20631	+	0.233906i
$704$			3.53221i			0.133125i
$705$		0			0
$706$	−7.57967	−	20.8250i	−0.285265	−	0.783758i
$707$	−4.55247	−	3.18767i	−0.171213	−	0.119885i
$708$	−10.5754	+	7.40497i	−0.397448	+	0.278296i
$709$	14.4966	−	39.8290i	0.544430	−	1.49581i	−0.296698	−	0.954971i	$-0.595885\pi$
$709$	14.4966	−	39.8290i	0.544430	−	1.49581i	0.841127	−	0.540837i	$-0.181892\pi$
$710$		0			0
$711$	1.55385	+	0.897115i	0.0582739	+	0.0336444i
$712$	−1.12548	+	12.8643i	−0.0421793	+	0.482111i
$713$	−0.765206	+	8.74634i	−0.0286572	+	0.327553i
$714$	−7.63414	−	4.40757i	−0.285700	−	0.164949i
$715$		0			0
$716$	5.05446	−	13.8870i	0.188894	−	0.518983i
$717$	−7.72375	+	5.40823i	−0.288449	+	0.201974i
$718$	8.02973	+	5.62248i	0.299667	+	0.209829i
$719$	5.51209	+	15.1443i	0.205566	+	0.564788i	0.999040	−	0.0438165i	$-0.0139517\pi$
$719$	5.51209	+	15.1443i	0.205566	+	0.564788i	−0.793473	+	0.608605i	$0.791729\pi$
$720$		0			0
$721$			10.4022i			0.387397i
$722$	−18.1749	−	5.53828i	−0.676400	−	0.206113i
$723$	17.7696	+	17.7696i	0.660857	+	0.660857i
$724$	−10.9527	−	9.19041i	−0.407054	−	0.341559i
$725$		0			0
$726$	−0.307999	−	1.74675i	−0.0114309	−	0.0648280i
$727$	−22.4960	−	32.1276i	−0.834331	−	1.19155i	−0.979361	−	0.202121i	$-0.935217\pi$
$727$	−22.4960	−	32.1276i	−0.834331	−	1.19155i	0.145029	−	0.989427i	$-0.453672\pi$
$728$	3.59855	+	7.71712i	0.133371	+	0.286015i
$729$	19.6547	−	11.3476i	0.727952	−	0.420283i
$730$		0			0
$731$	0.319979	−	0.268494i	0.0118348	−	0.00993061i
$732$	14.1618	+	1.23900i	0.523435	+	0.0457947i
$733$	−29.0419	+	7.78176i	−1.07269	+	0.287426i	−0.751597	−	0.659623i	$-0.770716\pi$
$733$	−29.0419	+	7.78176i	−1.07269	+	0.287426i	−0.321091	+	0.947048i	$0.604049\pi$
$734$	−5.30628	−	9.19074i	−0.195858	−	0.339237i
$735$		0			0
$736$	−0.987294	−	0.174087i	−0.0363921	−	0.00641692i
$737$	−1.51945	+	2.17000i	−0.0559696	+	0.0799329i
$738$	5.43832	+	2.53593i	0.200187	+	0.0933488i
$739$	12.4199	−	14.8015i	0.456875	−	0.544483i	−0.487599	−	0.873068i	$-0.662127\pi$
$739$	12.4199	−	14.8015i	0.456875	−	0.544483i	0.944474	+	0.328585i	$0.106572\pi$
$740$		0			0
$741$	11.5680	+	17.1331i	0.424960	+	0.629402i
$742$	12.4888	−	12.4888i	0.458477	−	0.458477i
$743$	14.3798	−	1.25807i	0.527544	−	0.0461541i	0.179727	−	0.983717i	$-0.442479\pi$
$743$	14.3798	−	1.25807i	0.527544	−	0.0461541i	0.347817	+	0.937562i	$0.386923\pi$
$744$	9.88615	−	3.59826i	0.362444	−	0.131919i
$745$		0			0
$746$	−0.948300	+	5.37808i	−0.0347197	+	0.196905i
$747$	−8.38696	+	3.91090i	−0.306863	+	0.143092i
$748$	−3.11032	+	11.6079i	−0.113725	+	0.424426i
$749$	−0.390851	+	0.676974i	−0.0142814	+	0.0247361i
$750$		0			0
$751$	−17.8509	−	21.2739i	−0.651389	−	0.776295i	0.334734	−	0.942313i	$-0.391354\pi$
$751$	−17.8509	−	21.2739i	−0.651389	−	0.776295i	−0.986123	+	0.166018i	$0.946909\pi$
$752$	2.47407	+	9.23336i	0.0902201	+	0.336706i
$753$	12.0609	+	3.23171i	0.439524	+	0.117770i
$754$	−17.9528	−	6.53428i	−0.653802	−	0.237964i
$755$		0			0
$756$	−11.6274	+	2.05023i	−0.422885	+	0.0745661i
$757$	1.76675	−	3.78881i	0.0642137	−	0.137707i	−0.871582	−	0.490250i	$-0.836905\pi$
$757$	1.76675	−	3.78881i	0.0642137	−	0.137707i	0.935795	+	0.352544i	$0.114683\pi$
$758$	0.998265	+	11.4102i	0.0362586	+	0.414438i
$759$	4.25397			0.154410
$760$		0			0
$761$	−26.4282			−0.958021			−0.479011	−	0.877809i	$-0.659004\pi$
$761$	−26.4282			−0.958021			−0.479011	+	0.877809i	$0.659004\pi$
$762$	−1.46175	−	16.7079i	−0.0529538	−	0.605264i
$763$	9.51803	−	20.4115i	0.344576	−	0.738945i
$764$	2.56696	−	0.452624i	0.0928694	−	0.0163754i
$765$		0			0
$766$	27.6428	+	10.0612i	0.998776	+	0.363525i
$767$	40.9817	+	10.9810i	1.47976	+	0.396501i
$768$	0.310921	+	1.16037i	0.0112194	+	0.0418714i
$769$	13.2306	+	15.7676i	0.477108	+	0.568595i	0.949890	−	0.312584i	$-0.101195\pi$
$769$	13.2306	+	15.7676i	0.477108	+	0.568595i	−0.472782	+	0.881179i	$0.656750\pi$
$770$		0			0
$771$	9.88792	−	17.1264i	0.356105	−	0.616791i
$772$	2.11721	−	7.90153i	0.0762000	−	0.284382i
$773$	12.9076	−	6.01894i	0.464256	−	0.216486i	−0.176393	−	0.984320i	$-0.556443\pi$
$773$	12.9076	−	6.01894i	0.464256	−	0.216486i	0.640649	+	0.767834i	$0.278665\pi$
$774$	0.0331913	−	0.188237i	0.00119304	−	0.00676604i
$775$		0			0
$776$	−12.2035	+	4.44170i	−0.438079	+	0.159448i
$777$	−19.2924	+	1.68786i	−0.692110	+	0.0605518i
$778$	−5.39431	+	5.39431i	−0.193395	+	0.193395i
$779$	−13.5962	−	9.86866i	−0.487136	−	0.353581i
$780$		0			0
$781$	−14.3572	+	17.1102i	−0.513740	+	0.612251i
$782$	−3.09125	−	1.44147i	−0.110543	−	0.0515470i
$783$	15.1946	−	21.7002i	0.543011	−	0.775500i
$784$	−2.31249	−	0.407755i	−0.0825891	−	0.0145627i
$785$		0			0
$786$	−10.6711	−	18.4829i	−0.380626	−	0.659264i
$787$	−43.5400	+	11.6665i	−1.55203	+	0.415866i	−0.930130	−	0.367230i	$-0.880306\pi$
$787$	−43.5400	+	11.6665i	−1.55203	+	0.415866i	−0.621902	+	0.783095i	$0.713640\pi$
$788$	15.2001	+	1.32984i	0.541481	+	0.0473735i
$789$	2.06045	−	1.72892i	0.0733540	−	0.0615514i
$790$		0			0
$791$	−21.7316	+	12.5467i	−0.772687	+	0.446111i
$792$	2.32404	+	4.98393i	0.0825813	+	0.177096i
$793$	−26.7966	−	38.2695i	−0.951574	−	1.35899i
$794$	5.07169	+	28.7630i	0.179988	+	1.02076i
$795$		0			0
$796$	5.03873	+	4.22800i	0.178593	+	0.149857i
$797$	18.2232	+	18.2232i	0.645499	+	0.645499i	0.951902	−	0.306403i	$-0.0991256\pi$
$797$	18.2232	+	18.2232i	0.645499	+	0.645499i	−0.306403	+	0.951902i	$0.599126\pi$
$798$	11.2922	+	0.191891i	0.399741	+	0.00679286i
$799$			32.5221i			1.15055i
$800$		0			0
$801$	6.87614	+	18.8920i	0.242957	+	0.667518i
$802$	17.9614	+	12.5767i	0.634239	+	0.444099i
$803$	−13.5715	+	9.50286i	−0.478927	+	0.335349i
$804$	−0.308144	+	0.846620i	−0.0108674	+	0.0298580i
$805$		0			0
$806$	−29.9423	−	17.2872i	−1.05467	−	0.608916i
$807$	−0.892339	+	10.1995i	−0.0314118	+	0.359039i
$808$	−0.224578	+	2.56693i	−0.00790062	+	0.0903044i
$809$	−2.35349	−	1.35879i	−0.0827443	−	0.0477724i	0.458057	−	0.888923i	$-0.348546\pi$
$809$	−2.35349	−	1.35879i	−0.0827443	−	0.0477724i	−0.540801	+	0.841150i	$0.681879\pi$
$810$		0			0
$811$	−0.0970403	+	0.266616i	−0.00340755	+	0.00936216i	−0.941385	−	0.337335i	$-0.890475\pi$
$811$	−0.0970403	+	0.266616i	−0.00340755	+	0.00936216i	0.937977	+	0.346697i	$0.112697\pi$
$812$	−8.54978	+	5.98662i	−0.300038	+	0.210089i
$813$	−21.2035	−	14.8468i	−0.743638	−	0.520701i
$814$	9.02970	+	24.8089i	0.316491	+	0.869551i
$815$		0			0
$816$			4.08712i			0.143078i
$817$	−0.191552	+	0.499700i	−0.00670156	+	0.0174823i
$818$	2.44107	+	2.44107i	0.0853500	+	0.0853500i
$819$	10.1551	+	8.52113i	0.354847	+	0.297752i
$820$		0			0
$821$	−6.51113	−	36.9264i	−0.227240	−	1.28874i	−0.858356	−	0.513054i	$-0.828514\pi$
$821$	−6.51113	−	36.9264i	−0.227240	−	1.28874i	0.631116	−	0.775688i	$-0.282597\pi$
$822$	12.6113	+	18.0108i	0.439870	+	0.628200i
$823$	17.8612	+	38.3034i	0.622601	+	1.33517i	0.924263	+	0.381757i	$0.124681\pi$
$823$	17.8612	+	38.3034i	0.622601	+	1.33517i	−0.301662	+	0.953415i	$0.597541\pi$
$824$	4.17678	−	2.41147i	0.145505	−	0.0840075i
$825$		0			0
$826$	17.7560	−	14.8990i	0.617809	−	0.518403i
$827$	4.11997	+	0.360451i	0.143265	+	0.0125341i	0.158563	−	0.987349i	$-0.449314\pi$
$827$	4.11997	+	0.360451i	0.143265	+	0.0125341i	−0.0152974	+	0.999883i	$0.504870\pi$
$828$	−1.50761	+	0.403963i	−0.0523930	+	0.0140387i
$829$	2.30721	+	3.99620i	0.0801326	+	0.138794i	0.903307	−	0.428995i	$-0.141132\pi$
$829$	2.30721	+	3.99620i	0.0801326	+	0.138794i	−0.823174	+	0.567789i	$0.807799\pi$
$830$		0			0
$831$	−2.16453	−	0.381665i	−0.0750867	−	0.0132398i
$832$	2.26443	−	3.23394i	0.0785050	−	0.112117i
$833$	−7.24049	−	3.37630i	−0.250868	−	0.116982i
$834$	17.5852	−	20.9572i	0.608925	−	0.725689i
$835$		0			0
$836$	−3.73165	−	14.9375i	−0.129062	−	0.516623i
$837$	33.8994	−	33.8994i	1.17173	−	1.17173i
$838$	34.6589	−	3.03226i	1.19727	−	0.104748i
$839$	15.3550	−	5.58878i	0.530115	−	0.192946i	−0.0630746	−	0.998009i	$-0.520091\pi$
$839$	15.3550	−	5.58878i	0.530115	−	0.192946i	0.593190	+	0.805063i	$0.297868\pi$
$840$		0			0
$841$	−0.969238	+	5.49682i	−0.0334220	+	0.189546i
$842$	13.7766	−	6.42413i	0.474773	−	0.221390i
$843$	1.98745	−	7.41726i	0.0684514	−	0.255464i
$844$	−13.7788	+	23.8655i	−0.474285	+	0.821486i
$845$		0			0
$846$	9.56607	+	11.4004i	0.328888	+	0.391954i
$847$	0.824202	+	3.07596i	0.0283199	+	0.105691i
$848$	−7.90981	−	2.11943i	−0.271624	−	0.0727815i
$849$	−18.5215	−	6.74129i	−0.635657	−	0.231360i
$850$		0			0
$851$	−7.37942	+	1.30119i	−0.252963	+	0.0446042i
$852$	−3.21039	+	6.88470i	−0.109986	+	0.235866i
$853$	−3.83805	−	43.8691i	−0.131412	−	1.50205i	−0.720202	−	0.693764i	$-0.755951\pi$
$853$	−3.83805	−	43.8691i	−0.131412	−	1.50205i	0.588790	−	0.808286i	$-0.299605\pi$
$854$	−25.5230			−0.873380
$855$		0			0
$856$	0.362434			0.0123877
$857$	−4.14265	−	47.3507i	−0.141510	−	1.61747i	−0.652436	−	0.757844i	$-0.726253\pi$
$857$	−4.14265	−	47.3507i	−0.141510	−	1.61747i	0.510926	−	0.859625i	$-0.329303\pi$
$858$	−7.07971	+	15.1825i	−0.241697	+	0.518322i
$859$	2.93530	−	0.517573i	0.100151	−	0.0176594i	−0.123348	−	0.992363i	$-0.539363\pi$
$859$	2.93530	−	0.517573i	0.100151	−	0.0176594i	0.223499	+	0.974704i	$0.428252\pi$
$860$		0			0
$861$	9.38406	+	3.41552i	0.319808	+	0.116401i
$862$	2.24976	+	0.602821i	0.0766271	+	0.0205322i
$863$	−5.42244	−	20.2368i	−0.184582	−	0.688869i	−0.994720	−	0.102630i	$-0.967274\pi$
$863$	−5.42244	−	20.2368i	−0.184582	−	0.688869i	0.810138	−	0.586240i	$-0.199392\pi$
$864$	3.51874	+	4.19347i	0.119710	+	0.142665i
$865$		0			0
$866$	15.9150	−	27.5655i	0.540813	−	0.936715i
$867$	1.68670	−	6.29486i	0.0572834	−	0.213784i
$868$	−17.1189	+	7.98266i	−0.581052	+	0.270949i
$869$	0.706878	−	4.00890i	0.0239792	−	0.135993i
$870$		0			0
$871$	2.78229	−	1.01267i	0.0942742	−	0.0343130i
$872$	−10.4023	+	0.910087i	−0.352268	+	0.0308194i
$873$	−14.2966	+	14.2966i	−0.483866	+	0.483866i
$874$	4.35912	−	0.306842i	0.147449	−	0.0103791i
$875$		0			0
$876$	−3.62192	+	4.31643i	−0.122373	+	0.145839i
$877$	−21.0116	−	9.79788i	−0.709512	−	0.330851i	0.0341404	−	0.999417i	$-0.489131\pi$
$877$	−21.0116	−	9.79788i	−0.709512	−	0.330851i	−0.743653	+	0.668566i	$0.766908\pi$
$878$	−10.4242	+	14.8873i	−0.351799	+	0.502422i
$879$	21.3356	+	3.76204i	0.719631	+	0.126890i
$880$		0			0
$881$	14.6312	+	25.3420i	0.492939	+	0.853795i	0.999967	−	0.00813455i	$-0.00258934\pi$
$881$	14.6312	+	25.3420i	0.492939	+	0.853795i	−0.507028	+	0.861929i	$0.669256\pi$
$882$	−3.53121	+	0.946184i	−0.118902	+	0.0318597i
$883$	−16.3195	−	1.42777i	−0.549193	−	0.0480482i	−0.190817	−	0.981626i	$-0.561114\pi$
$883$	−16.3195	−	1.42777i	−0.549193	−	0.0480482i	−0.358376	+	0.933577i	$0.616669\pi$
$884$	10.2893	−	8.63373i	0.346066	−	0.290384i
$885$		0			0
$886$	0.460674	−	0.265970i	0.0154767	−	0.00893545i
$887$	21.2430	+	45.5558i	0.713271	+	1.52962i	0.842910	+	0.538054i	$0.180840\pi$
$887$	21.2430	+	45.5558i	0.713271	+	1.52962i	−0.129639	+	0.991561i	$0.541382\pi$
$888$	5.15016	+	7.35520i	0.172828	+	0.246824i
$889$	5.22886	+	29.6543i	0.175370	+	0.994574i
$890$		0			0
$891$	−5.15621	−	4.32658i	−0.172740	−	0.144946i
$892$	7.71557	+	7.71557i	0.258336	+	0.258336i
$893$	−20.2174	−	36.4335i	−0.676550	−	1.21920i
$894$		−	10.3867i		−	0.347384i
$895$		0			0
$896$	−0.737673	−	2.02674i	−0.0246439	−	0.0677086i
$897$	−3.89476	−	2.72714i	−0.130042	−	0.0910566i
$898$	−4.86898	+	3.40929i	−0.162480	+	0.113770i
$899$	14.4950	−	39.8246i	0.483434	−	1.32823i
$900$		0			0
$901$	−24.1277	−	13.9301i	−0.803811	−	0.464080i
$902$	1.18654	−	13.5622i	0.0395073	−	0.451571i
$903$	0.0277246	−	0.316894i	0.000922618	−	0.0105456i
$904$	10.0758	+	5.81727i	0.335116	+	0.193479i
$905$		0			0
$906$	1.01251	−	2.78184i	0.0336382	−	0.0924203i
$907$	−4.62531	+	3.23868i	−0.153581	+	0.107539i	−0.647841	−	0.761775i	$-0.724328\pi$
$907$	−4.62531	+	3.23868i	−0.153581	+	0.107539i	0.494260	+	0.869314i	$0.335439\pi$
$908$	−4.82417	−	3.37792i	−0.160096	−	0.112100i
$909$	1.37206	+	3.76970i	0.0455083	+	0.125033i
$910$		0			0
$911$			38.3871i			1.27182i	0.771762	+	0.635911i	$0.219375\pi$
$911$			38.3871i			1.27182i	−0.771762	+	0.635911i	$0.780625\pi$
$912$	−2.54076	−	4.57866i	−0.0841330	−	0.151615i
$913$	14.8460	+	14.8460i	0.491331	+	0.491331i
$914$	8.01843	+	6.72826i	0.265226	+	0.222551i
$915$		0			0
$916$	4.48137	+	25.4151i	0.148069	+	0.839739i
$917$	21.9781	+	31.3879i	0.725779	+	1.03652i
$918$	7.87103	+	16.8795i	0.259783	+	0.557106i
$919$	42.9343	−	24.7881i	1.41627	−	0.817685i	0.420303	−	0.907384i	$-0.361924\pi$
$919$	42.9343	−	24.7881i	1.41627	−	0.817685i	0.995969	+	0.0896994i	$0.0285906\pi$
$920$		0			0
$921$	13.5028	−	11.3302i	0.444933	−	0.373343i
$922$	40.7244	+	3.56292i	1.34119	+	0.117338i
$923$	24.1138	−	6.46128i	0.793717	−	0.212676i
$924$	4.57596	+	7.92579i	0.150538	+	0.260739i
$925$		0			0
$926$	11.2870	+	1.99020i	0.370913	+	0.0654019i
$927$	4.30678	−	6.15072i	0.141453	−	0.202016i
$928$	4.38585	+	2.04516i	0.143973	+	0.0671356i
$929$	15.9108	−	18.9618i	0.522016	−	0.622115i	−0.439040	−	0.898468i	$-0.644681\pi$
$929$	15.9108	−	18.9618i	0.522016	−	0.622115i	0.961056	+	0.276353i	$0.0891258\pi$
$930$		0			0
$931$	10.2102	−	0.718702i	0.334625	−	0.0235545i
$932$	18.7389	−	18.7389i	0.613812	−	0.613812i
$933$	−15.1997	+	1.32980i	−0.497615	+	0.0435357i
$934$	−20.3481	+	7.40609i	−0.665809	+	0.242335i
$935$		0			0
$936$	1.06730	−	6.05298i	0.0348859	−	0.197848i
$937$	11.2534	−	5.24752i	0.367631	−	0.171429i	−0.230019	−	0.973186i	$-0.573879\pi$
$937$	11.2534	−	5.24752i	0.367631	−	0.171429i	0.597650	+	0.801757i	$0.296101\pi$
$938$	0.418656	−	1.56244i	0.0136696	−	0.0510156i
$939$	−5.01157	+	8.68029i	−0.163546	+	0.283271i
$940$		0			0
$941$	−28.4829	−	33.9446i	−0.928516	−	1.10656i	−0.994073	−	0.108714i	$-0.965327\pi$
$941$	−28.4829	−	33.9446i	−0.928516	−	1.10656i	0.0655567	−	0.997849i	$-0.479118\pi$
$942$	7.20823	+	26.9015i	0.234857	+	0.876497i
$943$	3.73231	+	1.00007i	0.121541	+	0.0325667i
$944$	−10.0987	−	3.67561i	−0.328684	−	0.119631i
$945$		0			0
$946$	−0.427072	+	0.0753043i	−0.0138853	+	0.00244835i
$947$	−19.5542	+	41.9342i	−0.635427	+	1.36268i	0.279924	+	0.960022i	$0.409691\pi$
$947$	−19.5542	+	41.9342i	−0.635427	+	1.36268i	−0.915352	+	0.402656i	$0.868087\pi$
$948$	−0.120664	−	1.37920i	−0.00391899	−	0.0447942i
$949$	18.5176			0.601107
$950$		0			0
$951$	−16.9315			−0.549043
$952$	−0.639545	−	7.31004i	−0.0207278	−	0.236920i
$953$	17.7200	−	38.0006i	0.574006	−	1.23096i	−0.378263	−	0.925698i	$-0.623478\pi$
$953$	17.7200	−	38.0006i	0.574006	−	1.23096i	0.952269	−	0.305261i	$-0.0987438\pi$
$954$	−12.5552	+	2.21382i	−0.406490	+	0.0716751i
$955$		0			0
$956$	−7.37557	−	2.68449i	−0.238543	−	0.0868225i
$957$	−19.8345	−	5.31465i	−0.641160	−	0.171798i
$958$	−6.25376	−	23.3394i	−0.202050	−	0.754061i
$959$	−25.3743	−	30.2400i	−0.819380	−	0.976499i
$960$		0			0
$961$	22.8482	−	39.5742i	0.737038	−	1.27659i
$962$	7.63729	−	28.5028i	0.246236	−	0.918966i
$963$	0.511393	−	0.238467i	0.0164794	−	0.00768448i
$964$	−3.63252	+	20.6010i	−0.116996	+	0.663514i
$965$		0			0
$966$	−2.44088	+	0.888408i	−0.0785341	+	0.0285841i
$967$	14.0574	−	1.22986i	0.452056	−	0.0395497i	0.141145	−	0.989989i	$-0.454922\pi$
$967$	14.0574	−	1.22986i	0.452056	−	0.0395497i	0.310911	+	0.950439i	$0.399366\pi$
$968$	1.04402	−	1.04402i	0.0335562	−	0.0335562i
$969$	−4.31790	−	17.2842i	−0.138711	−	0.555247i
$970$		0			0
$971$	1.63994	−	1.95441i	0.0526283	−	0.0627199i	−0.739088	−	0.673609i	$-0.764743\pi$
$971$	1.63994	−	1.95441i	0.0526283	−	0.0627199i	0.791716	+	0.610889i	$0.209188\pi$
$972$	12.8092	+	5.97302i	0.410855	+	0.191585i
$973$	−28.1727	+	40.2348i	−0.903176	+	1.28987i
$974$	33.3356	+	5.87797i	1.06814	+	0.188342i
$975$		0			0
$976$	5.91685	+	10.2483i	0.189394	+	0.328040i
$977$	−23.5989	+	6.32329i	−0.754994	+	0.202300i	−0.615732	−	0.787955i	$-0.711140\pi$
$977$	−23.5989	+	6.32329i	−0.754994	+	0.202300i	−0.139262	+	0.990256i	$0.544473\pi$
$978$	14.2674	+	1.24824i	0.456222	+	0.0399143i
$979$	34.9416	−	29.3195i	1.11674	−	0.937055i
$980$		0			0
$981$	−14.0789	+	8.12844i	−0.449504	+	0.259521i
$982$	−14.5695	−	31.2444i	−0.464932	−	0.997049i
$983$	22.8567	+	32.6427i	0.729015	+	1.04114i	0.996976	+	0.0777117i	$0.0247614\pi$
$983$	22.8567	+	32.6427i	0.729015	+	1.04114i	−0.267961	+	0.963430i	$0.586350\pi$
$984$	−0.804013	−	4.55978i	−0.0256310	−	0.145361i
$985$		0			0
$986$	12.6123	+	10.5830i	0.401659	+	0.337032i
$987$	17.5133	+	17.5133i	0.557453	+	0.557453i
$988$	−6.15957	+	16.0684i	−0.195962	+	0.511204i
$989$		−	0.123083i		−	0.00391382i
$990$		0			0
$991$	−1.57685	−	4.33235i	−0.0500901	−	0.137622i	0.912125	−	0.409913i	$-0.134441\pi$
$991$	−1.57685	−	4.33235i	−0.0500901	−	0.137622i	−0.962215	+	0.272291i	$0.912219\pi$
$992$	7.17384	+	5.02318i	0.227770	+	0.159486i
$993$	−12.4173	+	8.69470i	−0.394052	+	0.275918i
$994$	4.66465	−	12.8160i	0.147954	−	0.406499i
$995$		0			0
$996$	6.18391	+	3.57028i	0.195945	+	0.113129i
$997$	1.62090	−	18.5269i	0.0513343	−	0.586754i	−0.926348	−	0.376668i	$-0.877070\pi$
$997$	1.62090	−	18.5269i	0.0513343	−	0.586754i	0.977683	−	0.210086i	$-0.0673746\pi$
$998$	0.913569	−	10.4421i	0.0289185	−	0.330540i
$999$	35.4345	+	20.4581i	1.12110	+	0.647266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.193.2		120
5.2	odd	4	inner	950.2.bb.e.307.9		120
5.3	odd	4		190.2.r.a.117.2	yes	120
5.4	even	2		190.2.r.a.3.9	✓	120
19.13	odd	18	inner	950.2.bb.e.393.9		120
95.13	even	36		190.2.r.a.127.9	yes	120
95.32	even	36	inner	950.2.bb.e.507.2		120
95.89	odd	18		190.2.r.a.13.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.3.9	✓	120	5.4	even	2
190.2.r.a.13.2	yes	120	95.89	odd	18
190.2.r.a.117.2	yes	120	5.3	odd	4
190.2.r.a.127.9	yes	120	95.13	even	36
950.2.bb.e.193.2		120	1.1	even	1	trivial
950.2.bb.e.307.9		120	5.2	odd	4	inner
950.2.bb.e.393.9		120	19.13	odd	18	inner
950.2.bb.e.507.2		120	95.32	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.507694 + 1.08875i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(1.12886 + 0.410871i) q^{6} +(-2.08332 - 0.558224i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.00073 + 1.19263i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.507694 + 1.08875i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(1.12886 + 0.410871i) q^{6} +(-2.08332 - 0.558224i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.00073 + 1.19263i) q^{9} +(1.76610 - 3.05898i) q^{11} +(0.310921 - 1.16037i) q^{12} +(-3.57802 + 1.66846i) q^{13} +(-0.374526 + 2.12404i) q^{14} +(0.939693 - 0.342020i) q^{16} +(3.38928 - 0.296524i) q^{17} +(1.10087 - 1.10087i) q^{18} +(-3.61257 + 2.43913i) q^{19} +(1.66546 - 1.98481i) q^{21} +(-3.20126 - 1.49277i) q^{22} +(0.575024 - 0.821220i) q^{23} +(-1.18306 - 0.208605i) q^{24} +(1.97396 + 3.41899i) q^{26} +(-5.28766 + 1.41682i) q^{27} +(2.14860 + 0.187978i) q^{28} +(-3.70708 + 3.11061i) q^{29} +(-7.58434 + 4.37882i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(2.43384 + 3.47588i) q^{33} +(-0.590790 - 3.35054i) q^{34} +(-1.19263 - 1.00073i) q^{36} +(-5.28519 - 5.28519i) q^{37} +(2.74471 + 3.38623i) q^{38} -4.74265i q^{39} +(1.31823 + 3.62180i) q^{41} +(-2.12242 - 1.48613i) q^{42} +(0.100570 - 0.0704198i) q^{43} +(-1.20809 + 3.31919i) q^{44} +(-0.868212 - 0.501262i) q^{46} +(-0.833128 + 9.52270i) q^{47} +(-0.104701 + 1.19674i) q^{48} +(-2.03357 - 1.17408i) q^{49} +(-1.39788 + 3.84064i) q^{51} +(3.23394 - 2.26443i) q^{52} +(-6.70791 - 4.69693i) q^{53} +(1.87228 + 5.14406i) q^{54} -2.15681i q^{56} +(-0.821538 - 5.17153i) q^{57} +(3.42187 + 3.42187i) q^{58} +(-8.23251 - 6.90789i) q^{59} +(2.05490 + 11.6539i) q^{61} +(5.02318 + 7.17384i) q^{62} +(-1.41909 - 3.04325i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(3.25053 - 2.72752i) q^{66} +(-0.747124 - 0.0653649i) q^{67} +(-3.28630 + 0.880561i) q^{68} +(0.602170 + 1.04299i) q^{69} +(-6.22740 - 1.09806i) q^{71} +(-0.892979 + 1.27531i) q^{72} +(-4.25102 - 1.98228i) q^{73} +(-4.80444 + 5.72571i) q^{74} +(3.13413 - 3.02939i) q^{76} +(-5.38695 + 5.38695i) q^{77} +(-4.72461 + 0.413350i) q^{78} +(1.08296 - 0.394167i) q^{79} +(0.330903 - 1.87665i) q^{81} +(3.49313 - 1.62887i) q^{82} +(-1.53842 + 5.74146i) q^{83} +(-1.29550 + 2.24386i) q^{84} +(-0.0789171 - 0.0940498i) q^{86} +(-1.50463 - 5.61534i) q^{87} +(3.41185 + 0.914202i) q^{88} +(12.1347 + 4.41667i) q^{89} +(8.38554 - 1.47860i) q^{91} +(-0.423685 + 0.908596i) q^{92} +(-0.916932 - 10.4806i) q^{93} +9.55907 q^{94} +1.20131 q^{96} +(1.13186 + 12.9372i) q^{97} +(-0.992379 + 2.12816i) q^{98} +(5.41561 - 0.954918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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