LMFDB - Embedded newform 875.2.bb.a.143.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(82,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([27, 50]))

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

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

chi := DirichletCharacter("875.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			143.12
Character	$\chi$	$=$	875.143
Dual form			875.2.bb.a.257.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0406780 + 0.776182i) q^{2} +(0.872864 + 0.706831i) q^{3} +(1.38824 - 0.145910i) q^{4} +(-0.513123 + 0.706254i) q^{6} +(-1.24404 + 2.33503i) q^{7} +(0.412900 + 2.60695i) q^{8} +(-0.361454 - 1.70051i) q^{9} +(1.29854 + 0.276014i) q^{11} +(1.31488 + 0.853891i) q^{12} +(0.912442 + 1.79077i) q^{13} +(-1.86302 - 0.870614i) q^{14} +(0.724094 - 0.153911i) q^{16} +(0.868077 + 0.333224i) q^{17} +(1.30520 - 0.349728i) q^{18} +(-0.550884 + 5.24131i) q^{19} +(-2.73635 + 1.15884i) q^{21} +(-0.161415 + 1.01913i) q^{22} +(-1.14388 + 0.0599482i) q^{23} +(-1.48227 + 2.56736i) q^{24} +(-1.35285 + 0.781066i) q^{26} +(2.41619 - 4.74204i) q^{27} +(-1.38631 + 3.42310i) q^{28} +(4.04060 + 5.56140i) q^{29} +(-3.98545 - 8.95147i) q^{31} +(1.51519 + 5.65478i) q^{32} +(0.938356 + 1.15877i) q^{33} +(-0.223331 + 0.687341i) q^{34} +(-0.749906 - 2.30797i) q^{36} +(-4.17386 + 6.42719i) q^{37} +(-4.09062 - 0.214381i) q^{38} +(-0.469333 + 2.20804i) q^{39} +(-0.0622653 - 0.0202312i) q^{41} +(-1.01078 - 2.07676i) q^{42} +(3.34331 + 3.34331i) q^{43} +(1.84296 + 0.193703i) q^{44} +(-0.0930614 - 0.885420i) q^{46} +(-0.0668935 - 0.174263i) q^{47} +(0.740824 + 0.377469i) q^{48} +(-3.90475 - 5.80972i) q^{49} +(0.522180 + 0.904443i) q^{51} +(1.52798 + 2.35288i) q^{52} +(7.02928 - 8.68044i) q^{53} +(3.77898 + 1.68251i) q^{54} +(-6.60097 - 2.27900i) q^{56} +(-4.18557 + 4.18557i) q^{57} +(-4.15230 + 3.36247i) q^{58} +(3.22860 + 3.58572i) q^{59} +(-3.39928 - 3.06073i) q^{61} +(6.78585 - 3.45756i) q^{62} +(4.42040 + 1.27148i) q^{63} +(-2.91943 + 0.948580i) q^{64} +(-0.861248 + 0.775472i) q^{66} +(3.04412 - 7.93020i) q^{67} +(1.25372 + 0.335933i) q^{68} +(-1.04082 - 0.756203i) q^{69} +(8.72491 - 6.33902i) q^{71} +(4.28389 - 1.64443i) q^{72} +(1.38114 - 0.896926i) q^{73} +(-5.15845 - 2.97823i) q^{74} +7.35658i q^{76} +(-2.25993 + 2.68877i) q^{77} +(-1.73293 - 0.274469i) q^{78} +(4.24463 - 9.53360i) q^{79} +(0.696236 - 0.309984i) q^{81} +(0.0131703 - 0.0491522i) q^{82} +(-6.17863 + 0.978599i) q^{83} +(-3.62962 + 2.00801i) q^{84} +(-2.45902 + 2.73102i) q^{86} +(-0.404083 + 7.71037i) q^{87} +(-0.183385 + 3.49920i) q^{88} +(-10.5019 + 11.6635i) q^{89} +(-5.31661 - 0.0971966i) q^{91} +(-1.57923 + 0.250126i) q^{92} +(2.84842 - 10.6304i) q^{93} +(0.132539 - 0.0590102i) q^{94} +(-2.67442 + 6.00684i) q^{96} +(-17.1820 - 2.72136i) q^{97} +(4.35057 - 3.26713i) q^{98} -2.30795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.0406780	+	0.776182i	0.0287637	+	0.548844i	0.974566	+	0.224101i	$0.0719445\pi$
$2$	0.0406780	+	0.776182i	0.0287637	+	0.548844i	−0.945802	+	0.324743i	$0.894722\pi$
$3$	0.872864	+	0.706831i	0.503948	+	0.408089i	0.847297	−	0.531119i	$-0.178228\pi$
$3$	0.872864	+	0.706831i	0.503948	+	0.408089i	−0.343349	+	0.939208i	$0.611561\pi$
$4$	1.38824	−	0.145910i	0.694120	−	0.0729549i
$5$		0			0
$5$		0			0
$6$	−0.513123	+	0.706254i	−0.209482	+	0.288327i
$7$	−1.24404	+	2.33503i	−0.470201	+	0.882559i
$7$	−1.24404	+	2.33503i	−0.470201	+	0.882559i
$8$	0.412900	+	2.60695i	0.145982	+	0.921695i
$9$	−0.361454	−	1.70051i	−0.120485	−	0.566836i
$10$		0			0
$11$	1.29854	+	0.276014i	0.391525	+	0.0832213i	0.399468	−	0.916747i	$-0.369195\pi$
$11$	1.29854	+	0.276014i	0.391525	+	0.0832213i	−0.00794259	+	0.999968i	$0.502528\pi$
$12$	1.31488	+	0.853891i	0.379572	+	0.246497i
$13$	0.912442	+	1.79077i	0.253066	+	0.496670i	0.982233	−	0.187666i	$-0.0600923\pi$
$13$	0.912442	+	1.79077i	0.253066	+	0.496670i	−0.729167	+	0.684336i	$0.760092\pi$
$14$	−1.86302	−	0.870614i	−0.497912	−	0.232681i
$15$		0			0
$16$	0.724094	−	0.153911i	0.181023	−	0.0384777i
$17$	0.868077	+	0.333224i	0.210540	+	0.0808186i	0.461352	−	0.887217i	$-0.347364\pi$
$17$	0.868077	+	0.333224i	0.210540	+	0.0808186i	−0.250813	+	0.968036i	$0.580698\pi$
$18$	1.30520	−	0.349728i	0.307639	−	0.0824316i
$19$	−0.550884	+	5.24131i	−0.126382	+	1.20244i	0.729027	+	0.684485i	$0.239973\pi$
$19$	−0.550884	+	5.24131i	−0.126382	+	1.20244i	−0.855408	+	0.517954i	$0.826694\pi$
$20$		0			0
$21$	−2.73635	+	1.15884i	−0.597120	+	0.252880i
$22$	−0.161415	+	1.01913i	−0.0344138	+	0.217280i
$23$	−1.14388	+	0.0599482i	−0.238515	+	0.0125001i	−0.171219	−	0.985233i	$-0.554771\pi$
$23$	−1.14388	+	0.0599482i	−0.238515	+	0.0125001i	−0.0672962	+	0.997733i	$0.521437\pi$
$24$	−1.48227	+	2.56736i	−0.302566	+	0.524060i
$25$		0			0
$26$	−1.35285	+	0.781066i	−0.265315	+	0.153180i
$27$	2.41619	−	4.74204i	0.464996	−	0.912607i
$28$	−1.38631	+	3.42310i	−0.261989	+	0.646905i
$29$	4.04060	+	5.56140i	0.750320	+	1.03273i	0.997958	+	0.0638742i	$0.0203456\pi$
$29$	4.04060	+	5.56140i	0.750320	+	1.03273i	−0.247638	+	0.968853i	$0.579654\pi$
$30$		0			0
$31$	−3.98545	−	8.95147i	−0.715808	−	1.60773i	−0.791915	−	0.610631i	$-0.790916\pi$
$31$	−3.98545	−	8.95147i	−0.715808	−	1.60773i	0.0761073	−	0.997100i	$-0.475751\pi$
$32$	1.51519	+	5.65478i	0.267851	+	0.999634i
$33$	0.938356	+	1.15877i	0.163347	+	0.201716i
$34$	−0.223331	+	0.687341i	−0.0383009	+	0.117878i
$35$		0			0
$36$	−0.749906	−	2.30797i	−0.124984	−	0.384662i
$37$	−4.17386	+	6.42719i	−0.686179	+	1.05662i	0.308259	+	0.951302i	$0.400254\pi$
$37$	−4.17386	+	6.42719i	−0.686179	+	1.05662i	−0.994438	+	0.105321i	$0.966413\pi$
$38$	−4.09062	−	0.214381i	−0.663587	−	0.0347771i
$39$	−0.469333	+	2.20804i	−0.0751534	+	0.353569i
$40$		0			0
$41$	−0.0622653	−	0.0202312i	−0.00972421	−	0.00315959i	0.304151	−	0.952624i	$-0.401627\pi$
$41$	−0.0622653	−	0.0202312i	−0.00972421	−	0.00315959i	−0.313875	+	0.949464i	$0.601627\pi$
$42$	−1.01078	−	2.07676i	−0.155967	−	0.320452i
$43$	3.34331	+	3.34331i	0.509850	+	0.509850i	0.914480	−	0.404630i	$-0.132600\pi$
$43$	3.34331	+	3.34331i	0.509850	+	0.509850i	−0.404630	+	0.914480i	$0.632600\pi$
$44$	1.84296	+	0.193703i	0.277837	+	0.0292018i
$45$		0			0
$46$	−0.0930614	−	0.885420i	−0.0137212	−	0.130548i
$47$	−0.0668935	−	0.174263i	−0.00975741	−	0.0254189i	0.928615	−	0.371044i	$-0.121000\pi$
$47$	−0.0668935	−	0.174263i	−0.00975741	−	0.0254189i	−0.938373	+	0.345625i	$0.887667\pi$
$48$	0.740824	+	0.377469i	0.106929	+	0.0544829i
$49$	−3.90475	−	5.80972i	−0.557822	−	0.829961i
$50$		0			0
$51$	0.522180	+	0.904443i	0.0731199	+	0.126647i
$52$	1.52798	+	2.35288i	0.211892	+	0.326286i
$53$	7.02928	−	8.68044i	0.965546	−	1.19235i	−0.0157564	−	0.999876i	$-0.505016\pi$
$53$	7.02928	−	8.68044i	0.965546	−	1.19235i	0.981302	−	0.192474i	$-0.0616510\pi$
$54$	3.77898	+	1.68251i	0.514254	+	0.228960i
$55$		0			0
$56$	−6.60097	−	2.27900i	−0.882092	−	0.304544i
$57$	−4.18557	+	4.18557i	−0.554392	+	0.554392i
$58$	−4.15230	+	3.36247i	−0.545224	+	0.441514i
$59$	3.22860	+	3.58572i	0.420327	+	0.466821i	0.915702	−	0.401859i	$-0.131636\pi$
$59$	3.22860	+	3.58572i	0.420327	+	0.466821i	−0.495374	+	0.868680i	$0.664969\pi$
$60$		0			0
$61$	−3.39928	−	3.06073i	−0.435233	−	0.391886i	0.422182	−	0.906511i	$-0.361264\pi$
$61$	−3.39928	−	3.06073i	−0.435233	−	0.391886i	−0.857415	+	0.514625i	$0.827931\pi$
$62$	6.78585	−	3.45756i	0.861804	−	0.439111i
$63$	4.42040	+	1.27148i	0.556919	+	0.160192i
$64$	−2.91943	+	0.948580i	−0.364929	+	0.118573i
$65$		0			0
$66$	−0.861248	+	0.775472i	−0.106012	+	0.0954540i
$67$	3.04412	−	7.93020i	0.371899	−	0.968829i	−0.612120	−	0.790765i	$-0.709683\pi$
$67$	3.04412	−	7.93020i	0.371899	−	0.968829i	0.984019	−	0.178064i	$-0.0569835\pi$
$68$	1.25372	+	0.335933i	0.152036	+	0.0407379i
$69$	−1.04082	−	0.756203i	−0.125300	−	0.0910361i
$70$		0			0
$71$	8.72491	−	6.33902i	1.03546	−	0.752303i	0.0660625	−	0.997815i	$-0.478956\pi$
$71$	8.72491	−	6.33902i	1.03546	−	0.752303i	0.969393	+	0.245513i	$0.0789563\pi$
$72$	4.28389	−	1.64443i	0.504862	−	0.193798i
$73$	1.38114	−	0.896926i	0.161651	−	0.104977i	−0.461279	−	0.887255i	$-0.652609\pi$
$73$	1.38114	−	0.896926i	0.161651	−	0.104977i	0.622929	+	0.782278i	$0.285942\pi$
$74$	−5.15845	−	2.97823i	−0.599658	−	0.346213i
$75$		0			0
$76$			7.35658i			0.843857i
$77$	−2.25993	+	2.68877i	−0.257543	+	0.306414i
$78$	−1.73293	−	0.274469i	−0.196216	−	0.0310775i
$79$	4.24463	−	9.53360i	0.477558	−	1.07261i	−0.500775	−	0.865577i	$-0.666952\pi$
$79$	4.24463	−	9.53360i	0.477558	−	1.07261i	0.978333	−	0.207036i	$-0.0663817\pi$
$80$		0			0
$81$	0.696236	−	0.309984i	0.0773596	−	0.0344427i
$82$	0.0131703	−	0.0491522i	0.00145442	−	0.00542796i
$83$	−6.17863	+	0.978599i	−0.678193	+	0.107415i	−0.486022	−	0.873946i	$-0.661553\pi$
$83$	−6.17863	+	0.978599i	−0.678193	+	0.107415i	−0.192170	+	0.981362i	$0.561553\pi$
$84$	−3.62962	+	2.00801i	−0.396024	+	0.219092i
$85$		0			0
$86$	−2.45902	+	2.73102i	−0.265163	+	0.294493i
$87$	−0.404083	+	7.71037i	−0.0433223	+	0.826638i
$88$	−0.183385	+	3.49920i	−0.0195489	+	0.373016i
$89$	−10.5019	+	11.6635i	−1.11320	+	1.23633i	−0.144125	+	0.989559i	$0.546037\pi$
$89$	−10.5019	+	11.6635i	−1.11320	+	1.23633i	−0.969073	+	0.246773i	$0.920630\pi$
$90$		0			0
$91$	−5.31661	−	0.0971966i	−0.557332	−	0.0101890i
$92$	−1.57923	+	0.250126i	−0.164646	+	0.0260774i
$93$	2.84842	−	10.6304i	0.295367	−	1.10233i
$94$	0.132539	−	0.0590102i	0.0136704	−	0.00608644i
$95$		0			0
$96$	−2.67442	+	6.00684i	−0.272957	+	0.613071i
$97$	−17.1820	−	2.72136i	−1.74457	−	0.276312i	−0.798902	−	0.601461i	$-0.794586\pi$
$97$	−17.1820	−	2.72136i	−1.74457	−	0.276312i	−0.945663	+	0.325149i	$0.894586\pi$
$98$	4.35057	−	3.26713i	0.439474	−	0.330030i
$99$		−	2.30795i		−	0.231958i
$100$		0			0
$101$	−3.07011	−	1.77253i	−0.305487	−	0.176373i	0.339418	−	0.940636i	$-0.389770\pi$
$101$	−3.07011	−	1.77253i	−0.305487	−	0.176373i	−0.644905	+	0.764262i	$0.723103\pi$
$102$	−0.680771	+	0.442098i	−0.0674064	+	0.0437742i
$103$	5.94199	−	2.28092i	0.585482	−	0.224745i	−0.0475531	−	0.998869i	$-0.515142\pi$
$103$	5.94199	−	2.28092i	0.585482	−	0.224745i	0.633035	+	0.774123i	$0.281809\pi$
$104$	−4.29169	+	3.11810i	−0.420835	+	0.305755i
$105$		0			0
$106$	7.02354	+	5.10290i	0.682186	+	0.495637i
$107$	9.52075	+	2.55108i	0.920406	+	0.246622i	0.687759	−	0.725939i	$-0.258595\pi$
$107$	9.52075	+	2.55108i	0.920406	+	0.246622i	0.232647	+	0.972561i	$0.425261\pi$
$108$	2.66234	−	6.93564i	0.256184	−	0.667382i
$109$	8.04882	−	7.24719i	0.770937	−	0.694155i	−0.186609	−	0.982434i	$-0.559750\pi$
$109$	8.04882	−	7.24719i	0.770937	−	0.694155i	0.957546	+	0.288279i	$0.0930831\pi$
$110$		0			0
$111$	−8.18615	+	2.65984i	−0.776995	+	0.252461i
$112$	−0.541411	+	1.88225i	−0.0511586	+	0.177856i
$113$	−5.89008	+	3.00115i	−0.554092	+	0.282324i	−0.708533	−	0.705678i	$-0.750643\pi$
$113$	−5.89008	+	3.00115i	−0.554092	+	0.282324i	0.154440	+	0.988002i	$0.450643\pi$
$114$	−3.41903	−	3.07851i	−0.320221	−	0.288328i
$115$		0			0
$116$	6.42078	+	7.13100i	0.596154	+	0.662096i
$117$	2.71541	−	2.19890i	0.251040	−	0.203288i
$118$	−2.65184	+	2.65184i	−0.244122	+	0.244122i
$119$	−1.85801	+	1.61245i	−0.170323	+	0.147813i
$120$		0			0
$121$	−8.43897	−	3.75727i	−0.767179	−	0.341570i
$122$	2.23741	−	2.76297i	0.202565	−	0.250147i
$123$	−0.0400491	−	0.0616702i	−0.00361110	−	0.00556061i
$124$	−6.83886	−	11.8453i	−0.614148	−	1.06374i
$125$		0			0
$126$	−0.807091	+	3.48276i	−0.0719014	+	0.310269i
$127$	−16.4754	−	8.39463i	−1.46195	−	0.744903i	−0.471387	−	0.881927i	$-0.656246\pi$
$127$	−16.4754	−	8.39463i	−1.46195	−	0.744903i	−0.990568	+	0.137023i	$0.956246\pi$
$128$	3.34093	+	8.70343i	0.295299	+	0.769281i
$129$	0.555099	+	5.28141i	0.0488737	+	0.465003i
$130$		0			0
$131$	16.6657	+	1.75164i	1.45609	+	0.153041i	0.799255	−	0.600992i	$-0.205228\pi$
$131$	16.6657	+	1.75164i	1.45609	+	0.153041i	0.656836	+	0.754033i	$0.271894\pi$
$132$	1.47174	+	1.47174i	0.128098	+	0.128098i
$133$	−11.5533	−	7.80671i	−1.00180	−	0.676928i
$134$	6.27911	+	2.04021i	0.542433	+	0.176247i
$135$		0			0
$136$	−0.510268	+	2.40062i	−0.0437551	+	0.205852i
$137$	−3.29801	−	0.172842i	−0.281768	−	0.0147669i	−0.0890717	−	0.996025i	$-0.528390\pi$
$137$	−3.29801	−	0.172842i	−0.281768	−	0.0147669i	−0.192697	+	0.981258i	$0.561723\pi$
$138$	0.544613	−	0.838630i	0.0463605	−	0.0713889i
$139$	2.66592	+	8.20486i	0.226120	+	0.695927i	0.998176	+	0.0603721i	$0.0192287\pi$
$139$	2.66592	+	8.20486i	0.226120	+	0.695927i	−0.772055	+	0.635555i	$0.780771\pi$
$140$		0			0
$141$	0.0647859	−	0.199391i	0.00545596	−	0.0167917i
$142$	5.27514	+	6.51426i	0.442680	+	0.546665i
$143$	0.690568	+	2.57723i	0.0577482	+	0.215519i
$144$	−0.523454	−	1.17570i	−0.0436211	−	0.0979747i
$145$		0			0
$146$	0.752360	+	1.03553i	0.0622658	+	0.0857015i
$147$	0.698176	−	7.83110i	0.0575846	−	0.645898i
$148$	−4.85653	+	9.53148i	−0.399205	+	0.783483i
$149$	0.0342344	−	0.0197652i	0.00280459	−	0.00161923i	−0.498597	−	0.866834i	$-0.666151\pi$
$149$	0.0342344	−	0.0197652i	0.00280459	−	0.00161923i	0.501402	+	0.865215i	$0.332818\pi$
$150$		0			0
$151$	4.89690	−	8.48169i	0.398504	−	0.690230i	−0.595037	−	0.803698i	$-0.702863\pi$
$151$	4.89690	−	8.48169i	0.398504	−	0.690230i	0.993542	+	0.113468i	$0.0361960\pi$
$152$	−13.8913	+	0.728012i	−1.12673	+	0.0590496i
$153$	0.252879	−	1.59662i	0.0204441	−	0.129079i
$154$	−2.17890	−	1.64475i	−0.175581	−	0.132537i
$155$		0			0
$156$	−0.329372	+	3.13377i	−0.0263709	+	0.250902i
$157$	12.7152	−	3.40702i	1.01478	−	0.271910i	0.287156	−	0.957884i	$-0.407290\pi$
$157$	12.7152	−	3.40702i	1.01478	−	0.271910i	0.727626	+	0.685974i	$0.240624\pi$
$158$	7.57247	+	2.90680i	0.602434	+	0.231253i
$159$	12.2712	−	2.60832i	0.973170	−	0.206854i
$160$		0			0
$161$	1.28304	−	2.74557i	0.101118	−	0.216381i
$162$	0.268926	+	0.527797i	0.0211288	+	0.0414676i
$163$	−2.92862	−	1.90187i	−0.229387	−	0.148966i	0.424828	−	0.905274i	$-0.360334\pi$
$163$	−2.92862	−	1.90187i	−0.229387	−	0.148966i	−0.654216	+	0.756308i	$0.727001\pi$
$164$	−0.0893911	−	0.0190007i	−0.00698027	−	0.00148370i
$165$		0			0
$166$	−1.01091	−	4.75594i	−0.0784615	−	0.369132i
$167$	−2.99626	−	18.9176i	−0.231857	−	1.46389i	−0.779092	−	0.626910i	$-0.784319\pi$
$167$	−2.99626	−	18.9176i	−0.231857	−	1.46389i	0.547235	−	0.836979i	$-0.315681\pi$
$168$	−4.15088	−	6.65503i	−0.320247	−	0.513447i
$169$	5.26691	−	7.24928i	0.405147	−	0.557637i
$170$		0			0
$171$	9.11202	−	0.957712i	0.696813	−	0.0732380i
$172$	5.12914	+	4.15350i	0.391093	+	0.316701i
$173$	0.259502	+	4.95159i	0.0197296	+	0.376462i	0.990594	+	0.136833i	$0.0436925\pi$
$173$	0.259502	+	4.95159i	0.0197296	+	0.376462i	−0.970865	+	0.239629i	$0.922974\pi$
$174$	−6.00109			−0.454941
$175$		0			0
$176$	0.982748			0.0740774
$177$	0.283626	+	5.41192i	0.0213187	+	0.406785i
$178$	−9.48023	−	7.67694i	−0.710573	−	0.575411i
$179$	20.1419	−	2.11700i	1.50548	−	0.158232i	0.684424	−	0.729085i	$-0.260054\pi$
$179$	20.1419	−	2.11700i	1.50548	−	0.158232i	0.821052	+	0.570853i	$0.193387\pi$
$180$		0			0
$181$	2.67679	−	3.68429i	0.198965	−	0.273851i	−0.697863	−	0.716231i	$-0.745866\pi$
$181$	2.67679	−	3.68429i	0.198965	−	0.273851i	0.896828	+	0.442380i	$0.145866\pi$
$182$	−0.140827	−	4.13061i	−0.0104388	−	0.306181i
$183$	−0.803693	−	5.07431i	−0.0594107	−	0.375104i
$184$	−0.628589	−	2.95728i	−0.0463402	−	0.218014i
$185$		0			0
$186$	8.36704	+	1.77847i	0.613501	+	0.130404i
$187$	1.03526	+	0.672306i	0.0757058	+	0.0491639i
$188$	−0.118291	−	0.232159i	−0.00862725	−	0.0169319i
$189$	8.06700	+	11.5412i	0.586788	+	0.839495i
$190$		0			0
$191$	15.1405	−	3.21821i	1.09553	−	0.232861i	0.375510	−	0.926818i	$-0.377468\pi$
$191$	15.1405	−	3.21821i	1.09553	−	0.232861i	0.720016	+	0.693957i	$0.244134\pi$
$192$	−3.21875	−	1.23556i	−0.232293	−	0.0891690i
$193$	−7.57383	+	2.02940i	−0.545176	+	0.146080i	−0.520887	−	0.853625i	$-0.674399\pi$
$193$	−7.57383	+	2.02940i	−0.545176	+	0.146080i	−0.0242890	+	0.999705i	$0.507732\pi$
$194$	1.41334	−	13.4470i	0.101472	−	0.965442i
$195$		0			0
$196$	−6.26843	−	7.49555i	−0.447745	−	0.535396i
$197$	2.55912	−	16.1577i	0.182330	−	1.15119i	−0.711469	−	0.702718i	$-0.751970\pi$
$197$	2.55912	−	16.1577i	0.182330	−	1.15119i	0.893799	−	0.448469i	$-0.148030\pi$
$198$	1.79139	−	0.0938827i	0.127308	−	0.00667196i
$199$	13.6561	−	23.6530i	0.968053	−	1.67672i	0.266874	−	0.963731i	$-0.414009\pi$
$199$	13.6561	−	23.6530i	0.968053	−	1.67672i	0.701179	−	0.712985i	$-0.252657\pi$
$200$		0			0
$201$	8.26242	−	4.77031i	0.582786	−	0.336472i
$202$	1.25092	−	2.45507i	0.0880144	−	0.172738i
$203$	−18.0127	+	2.51634i	−1.26424	+	0.176613i
$204$	0.856878	+	1.17939i	0.0599935	+	0.0825739i
$205$		0			0
$206$	2.01212	+	4.51928i	0.140191	+	0.314873i
$207$	0.515402	+	1.92351i	0.0358229	+	0.133693i
$208$	0.936312	+	1.15625i	0.0649216	+	0.0801715i
$209$	−2.16202	+	6.65402i	−0.149550	+	0.460268i
$210$		0			0
$211$	4.53761	+	13.9653i	0.312382	+	0.961413i	0.976819	+	0.214068i	$0.0686715\pi$
$211$	4.53761	+	13.9653i	0.312382	+	0.961413i	−0.664437	+	0.747345i	$0.731328\pi$
$212$	8.49176	−	13.0762i	0.583216	−	0.898075i
$213$	12.0963	+	0.633938i	0.828823	+	0.0434367i
$214$	−1.59282	+	7.49361i	−0.108883	+	0.512253i
$215$		0			0
$216$	13.3599	+	4.34090i	0.909027	+	0.295361i
$217$	25.8600	+	1.82978i	1.75549	+	0.124214i
$218$	5.95255	+	5.95255i	0.403158	+	0.403158i
$219$	1.83953	+	0.193342i	0.124304	+	0.0130648i
$220$		0			0
$221$	0.195344	+	1.85857i	0.0131402	+	0.125021i
$222$	−2.39752	−	6.24575i	−0.160911	−	0.419187i
$223$	−19.2642	−	9.81559i	−1.29003	−	0.657301i	−0.331809	−	0.943346i	$-0.607659\pi$
$223$	−19.2642	−	9.81559i	−1.29003	−	0.657301i	−0.958216	+	0.286046i	$0.907659\pi$
$224$	−15.0891	−	3.49672i	−1.00818	−	0.233634i
$225$		0			0
$226$	−2.56903	−	4.44970i	−0.170890	−	0.295989i
$227$	−5.12019	−	7.88440i	−0.339839	−	0.523306i	0.626891	−	0.779107i	$-0.284327\pi$
$227$	−5.12019	−	7.88440i	−0.339839	−	0.523306i	−0.966729	+	0.255801i	$0.917661\pi$
$228$	−5.19986	+	6.42129i	−0.344369	+	0.425260i
$229$	2.84380	+	1.26614i	0.187923	+	0.0836689i	0.498541	−	0.866866i	$-0.333869\pi$
$229$	2.84380	+	1.26614i	0.187923	+	0.0836689i	−0.310618	+	0.950535i	$0.600536\pi$
$230$		0			0
$231$	−3.87312	+	0.749537i	−0.254833	+	0.0493159i
$232$	−12.8299	+	12.8299i	−0.842326	+	0.842326i
$233$	22.6587	−	18.3487i	1.48442	−	1.20206i	0.555644	−	0.831420i	$-0.312472\pi$
$233$	22.6587	−	18.3487i	1.48442	−	1.20206i	0.928777	−	0.370640i	$-0.120862\pi$
$234$	1.81720	+	2.01821i	0.118794	+	0.131934i
$235$		0			0
$236$	5.00526	+	4.50675i	0.325814	+	0.293365i
$237$	10.4436	−	5.32129i	0.678386	−	0.345655i
$238$	−1.32713	−	1.37656i	−0.0860252	−	0.0892292i
$239$	−3.05660	+	0.993150i	−0.197715	+	0.0642416i	−0.406201	−	0.913784i	$-0.633147\pi$
$239$	−3.05660	+	0.993150i	−0.197715	+	0.0642416i	0.208485	+	0.978025i	$0.433147\pi$
$240$		0			0
$241$	−19.9300	+	17.9451i	−1.28381	+	1.15594i	−0.304733	+	0.952438i	$0.598567\pi$
$241$	−19.9300	+	17.9451i	−1.28381	+	1.15594i	−0.979074	+	0.203506i	$0.934766\pi$
$242$	2.57305	−	6.70302i	0.165402	−	0.430886i
$243$	−14.5955	−	3.91085i	−0.936301	−	0.250881i
$244$	−5.16561	−	3.75303i	−0.330694	−	0.240263i
$245$		0			0
$246$	0.0462382	−	0.0335940i	0.00294804	−	0.00214188i
$247$	−9.88862	+	3.79589i	−0.629198	+	0.241527i
$248$	21.6904	−	14.0859i	1.37734	−	0.894457i
$249$	−6.08480	−	3.51306i	−0.385609	−	0.222631i
$250$		0			0
$251$			13.7541i			0.868150i	0.900877	+	0.434075i	$0.142925\pi$
$251$			13.7541i			0.868150i	−0.900877	+	0.434075i	$0.857075\pi$
$252$	6.32210	+	1.12014i	0.398255	+	0.0705625i
$253$	−1.50192	−	0.237881i	−0.0944250	−	0.0149555i
$254$	5.84558	−	13.1294i	0.366784	−	0.823811i
$255$		0			0
$256$	−12.2281	+	5.44431i	−0.764257	+	0.340269i
$257$	−2.39177	+	8.92621i	−0.149195	+	0.556802i	0.850338	+	0.526237i	$0.176397\pi$
$257$	−2.39177	+	8.92621i	−0.149195	+	0.556802i	−0.999533	+	0.0305651i	$0.990269\pi$
$258$	−4.07676	+	0.645695i	−0.253808	+	0.0401992i
$259$	−9.81526	−	17.7418i	−0.609890	−	1.10242i
$260$		0			0
$261$	7.99672	−	8.88126i	0.494985	−	0.549736i
$262$	−0.681663	+	13.0069i	−0.0421133	+	0.803569i
$263$	0.439194	−	8.38032i	0.0270819	−	0.516752i	−0.951085	−	0.308930i	$-0.900029\pi$
$263$	0.439194	−	8.38032i	0.0270819	−	0.516752i	0.978167	−	0.207822i	$-0.0666376\pi$
$264$	−2.63341	+	2.92470i	−0.162075	+	0.180003i
$265$		0			0
$266$	5.58947	−	9.28504i	0.342712	−	0.569303i
$267$	−17.4109	+	2.75761i	−1.06553	+	0.168763i
$268$	3.06887	−	11.4532i	0.187461	−	0.699615i
$269$	−4.02317	+	1.79123i	−0.245297	+	0.109213i	−0.525703	−	0.850668i	$-0.676198\pi$
$269$	−4.02317	+	1.79123i	−0.245297	+	0.109213i	0.280406	+	0.959882i	$0.409531\pi$
$270$		0			0
$271$	−1.39604	+	3.13556i	−0.0848035	+	0.190472i	−0.950970	−	0.309285i	$-0.899910\pi$
$271$	−1.39604	+	3.13556i	−0.0848035	+	0.190472i	0.866166	+	0.499756i	$0.166577\pi$
$272$	0.679856	+	0.107679i	0.0412223	+	0.00652898i
$273$	−4.57197	−	3.84278i	−0.276708	−	0.232576i
$274$		−	2.56689i		−	0.155072i
$275$		0			0
$276$	−1.55525	−	0.897924i	−0.0936150	−	0.0540487i
$277$	−6.45697	+	4.19321i	−0.387962	+	0.251945i	−0.723851	−	0.689956i	$-0.757630\pi$
$277$	−6.45697	+	4.19321i	−0.387962	+	0.251945i	0.335889	+	0.941901i	$0.390963\pi$
$278$	−6.26003	+	2.40300i	−0.375451	+	0.144122i
$279$	−13.7815	+	10.0128i	−0.825076	+	0.599453i
$280$		0			0
$281$	19.6291	+	14.2614i	1.17097	+	0.850761i	0.991125	−	0.132934i	$-0.0424398\pi$
$281$	19.6291	+	14.2614i	1.17097	+	0.850761i	0.179847	+	0.983695i	$0.442440\pi$
$282$	0.157399	+	0.0421749i	0.00937296	+	0.00251148i
$283$	−2.59792	+	6.76781i	−0.154430	+	0.402304i	−0.988868	−	0.148798i	$-0.952459\pi$
$283$	−2.59792	+	6.76781i	−0.154430	+	0.402304i	0.834437	+	0.551103i	$0.185793\pi$
$284$	11.1873	−	10.0731i	0.663846	−	0.597730i
$285$		0			0
$286$	−1.97231	+	0.640843i	−0.116625	+	0.0378939i
$287$	0.124701	−	0.120223i	0.00736086	−	0.00709655i
$288$	9.06833	−	4.62055i	0.534357	−	0.272268i
$289$	−11.9909	−	10.7967i	−0.705350	−	0.635100i
$290$		0			0
$291$	−13.0740	−	14.5201i	−0.766410	−	0.851185i
$292$	1.78649	−	1.44667i	0.104546	−	0.0846599i
$293$	−22.0206	+	22.0206i	−1.28645	+	1.28645i	−0.349529	+	0.936925i	$0.613658\pi$
$293$	−22.0206	+	22.0206i	−1.28645	+	1.28645i	−0.936925	+	0.349529i	$0.886342\pi$
$294$	6.10676	+	0.223359i	0.356154	+	0.0130265i
$295$		0			0
$296$	−18.4787	−	8.22726i	−1.07405	−	0.478200i
$297$	4.44640	−	5.49084i	0.258006	−	0.318611i
$298$	0.0167340	+	0.0257681i	0.000969375	+	0.00149271i
$299$	−1.15108	−	1.99372i	−0.0665684	−	0.115300i
$300$		0			0
$301$	−11.9659	+	3.64755i	−0.689705	+	0.210241i
$302$	6.78253	+	3.45587i	0.390291	+	0.198863i
$303$	−1.42691	−	3.71722i	−0.0819738	−	0.213549i
$304$	0.407803	+	3.87999i	0.0233891	+	0.222533i
$305$		0			0
$306$	1.24955	+	0.131333i	0.0714322	+	0.00750783i
$307$	−2.33566	−	2.33566i	−0.133303	−	0.133303i	0.637307	−	0.770610i	$-0.280048\pi$
$307$	−2.33566	−	2.33566i	−0.133303	−	0.133303i	−0.770610	+	0.637307i	$0.780048\pi$
$308$	−2.74501	+	4.06240i	−0.156412	+	0.231477i
$309$	6.79877	+	2.20905i	0.386768	+	0.125669i
$310$		0			0
$311$	1.28441	−	6.04267i	0.0728321	−	0.342648i	−0.926611	−	0.376022i	$-0.877292\pi$
$311$	1.28441	−	6.04267i	0.0728321	−	0.342648i	0.999443	+	0.0333736i	$0.0106251\pi$
$312$	−5.95003	−	0.311828i	−0.336854	−	0.0176538i
$313$	6.10018	−	9.39345i	0.344802	−	0.530949i	−0.623144	−	0.782107i	$-0.714145\pi$
$313$	6.10018	−	9.39345i	0.344802	−	0.530949i	0.967946	+	0.251158i	$0.0808115\pi$
$314$	3.16170	+	9.73071i	0.178425	+	0.549136i
$315$		0			0
$316$	4.50152	−	13.8542i	0.253230	−	0.779362i
$317$	5.65947	+	6.98886i	0.317867	+	0.392534i	0.910888	−	0.412654i	$-0.135398\pi$
$317$	5.65947	+	6.98886i	0.317867	+	0.392534i	−0.593021	+	0.805187i	$0.702065\pi$
$318$	2.52370	+	9.41859i	0.141522	+	0.528168i
$319$	3.71186	+	8.33698i	0.207824	+	0.466781i
$320$		0			0
$321$	6.50714	+	8.95630i	0.363193	+	0.499892i
$322$	2.18326	+	0.884192i	0.121668	+	0.0492741i
$323$	−2.22474	+	4.36630i	−0.123788	+	0.242947i
$324$	0.921313	−	0.531920i	0.0511840	−	0.0295511i
$325$		0			0
$326$	1.35707	−	2.35051i	0.0751610	−	0.130183i
$327$	12.1481	−	0.636653i	0.671790	−	0.0352070i
$328$	0.0270324	−	0.170676i	0.00149262	−	0.00942401i
$329$	0.490129	+	0.0605914i	0.0270217	+	0.00334051i
$330$		0			0
$331$	0.755353	−	7.18671i	0.0415180	−	0.395017i	−0.953953	−	0.299955i	$-0.903028\pi$
$331$	0.755353	−	7.18671i	0.0415180	−	0.395017i	0.995471	−	0.0950622i	$-0.0303050\pi$
$332$	−8.43463	+	2.26005i	−0.462910	+	0.124036i
$333$	12.4381	+	4.77456i	0.681606	+	0.261644i
$334$	14.5616	−	3.09517i	0.796777	−	0.169360i
$335$		0			0
$336$	−1.80301	+	1.26026i	−0.0983624	+	0.0687531i
$337$	4.60585	+	9.03950i	0.250897	+	0.492413i	0.981763	−	0.190108i	$-0.0608838\pi$
$337$	4.60585	+	9.03950i	0.250897	+	0.492413i	−0.730866	+	0.682521i	$0.760884\pi$
$338$	5.84101	+	3.79320i	0.317709	+	0.206323i
$339$	−7.26254	−	1.54370i	−0.394447	−	0.0838423i
$340$		0			0
$341$	−2.70455	−	12.7239i	−0.146459	−	0.689038i
$342$	1.11402	+	7.03363i	0.0602392	+	0.380335i
$343$	18.4235	−	1.89023i	0.994778	−	0.102063i
$344$	−7.33539	+	10.0963i	−0.395498	+	0.544356i
$345$		0			0
$346$	−3.83278	+	0.402841i	−0.206051	+	0.0216569i
$347$	−6.22958	−	5.04462i	−0.334422	−	0.270809i	0.447370	−	0.894349i	$-0.352361\pi$
$347$	−6.22958	−	5.04462i	−0.334422	−	0.270809i	−0.781792	+	0.623540i	$0.785694\pi$
$348$	0.564054	+	10.7628i	0.0302365	+	0.576946i
$349$	−8.82065			−0.472158			−0.236079	−	0.971734i	$-0.575862\pi$
$349$	−8.82065			−0.472158			−0.236079	+	0.971734i	$0.575862\pi$
$350$		0			0
$351$	10.6965			0.570939
$352$	0.406747	+	7.76119i	0.0216797	+	0.413673i
$353$	13.0839	+	10.5951i	0.696387	+	0.563923i	0.910814	−	0.412817i	$-0.135455\pi$
$353$	13.0839	+	10.5951i	0.696387	+	0.563923i	−0.214427	+	0.976740i	$0.568789\pi$
$354$	−4.18910	+	0.440292i	−0.222648	+	0.0234012i
$355$		0			0
$356$	−12.8773	+	17.7241i	−0.682497	+	0.939376i
$357$	−2.76151	+	0.0941494i	−0.146155	+	0.00498292i
$358$	2.46251	+	15.5477i	0.130148	+	0.821720i
$359$	2.87394	+	13.5208i	0.151681	+	0.713602i	0.986590	+	0.163215i	$0.0521865\pi$
$359$	2.87394	+	13.5208i	0.151681	+	0.713602i	−0.834910	+	0.550387i	$0.814480\pi$
$360$		0			0
$361$	−8.58309	−	1.82439i	−0.451742	−	0.0960206i
$362$	2.96857	+	1.92781i	0.156024	+	0.101323i
$363$	−4.71031	−	9.24451i	−0.247227	−	0.485211i
$364$	−7.39491	+	0.640814i	−0.387599	+	0.0335878i
$365$		0			0
$366$	3.90590	−	0.830225i	0.204165	−	0.0433966i
$367$	−0.970143	−	0.372403i	−0.0506410	−	0.0194393i	0.332916	−	0.942957i	$-0.391968\pi$
$367$	−0.970143	−	0.372403i	−0.0506410	−	0.0194393i	−0.383557	+	0.923517i	$0.625301\pi$
$368$	−0.819049	+	0.219464i	−0.0426959	+	0.0114403i
$369$	−0.0118973	+	0.113195i	−0.000619350	+	0.00589272i
$370$		0			0
$371$	11.5244	+	27.2124i	0.598319	+	1.41280i
$372$	2.40320	−	15.1732i	0.124600	−	0.786695i
$373$	−21.9752	+	1.15167i	−1.13783	+	0.0596314i	−0.611930	−	0.790912i	$-0.709606\pi$
$373$	−21.9752	+	1.15167i	−1.13783	+	0.0596314i	−0.525904	+	0.850544i	$0.676273\pi$
$374$	−0.479720	+	0.830899i	−0.0248057	+	0.0429648i
$375$		0			0
$376$	0.426675	−	0.246341i	0.0220041	−	0.0127041i
$377$	−6.27237	+	12.3102i	−0.323044	+	0.634009i
$378$	−8.62989	+	6.73093i	−0.443874	+	0.346202i
$379$	17.8299	+	24.5408i	0.915862	+	1.26058i	0.965125	+	0.261790i	$0.0843129\pi$
$379$	17.8299	+	24.5408i	0.915862	+	1.26058i	−0.0492625	+	0.998786i	$0.515687\pi$
$380$		0			0
$381$	−8.44719	−	18.9727i	−0.432762	−	0.972000i
$382$	3.11380	+	11.6209i	0.159316	+	0.594575i
$383$	13.4576	+	16.6188i	0.687652	+	0.849179i	0.994733	−	0.102504i	$-0.0326855\pi$
$383$	13.4576	+	16.6188i	0.687652	+	0.849179i	−0.307081	+	0.951683i	$0.599352\pi$
$384$	−3.23567	+	9.95838i	−0.165120	+	0.508186i
$385$		0			0
$386$	−1.88327	−	5.79612i	−0.0958562	−	0.295015i
$387$	4.47688	−	6.89379i	0.227572	−	0.350431i
$388$	−24.2498	−	1.27088i	−1.23110	−	0.0645190i
$389$	−4.37542	+	20.5847i	−0.221842	+	1.04369i	0.716395	+	0.697695i	$0.245791\pi$
$389$	−4.37542	+	20.5847i	−0.221842	+	1.04369i	−0.938238	+	0.345992i	$0.887543\pi$
$390$		0			0
$391$	−1.01295	−	0.329128i	−0.0512271	−	0.0166447i
$392$	13.5334	−	12.5783i	0.683539	−	0.635301i
$393$	13.3088	+	13.3088i	0.671340	+	0.671340i
$394$	12.6454	+	1.32909i	0.637066	+	0.0669583i
$395$		0			0
$396$	−0.336752	−	3.20399i	−0.0169224	−	0.161006i
$397$	1.83661	+	4.78454i	0.0921770	+	0.240129i	0.971916	−	0.235327i	$-0.0756162\pi$
$397$	1.83661	+	4.78454i	0.0921770	+	0.240129i	−0.879739	+	0.475457i	$0.842283\pi$
$398$	18.9145	+	9.63744i	0.948100	+	0.483081i
$399$	−4.56645	−	14.9804i	−0.228608	−	0.749960i
$400$		0			0
$401$	−17.1661	−	29.7326i	−0.857235	−	1.48477i	−0.874556	−	0.484924i	$-0.838847\pi$
$401$	−17.1661	−	29.7326i	−0.857235	−	1.48477i	0.0173216	−	0.999850i	$-0.494486\pi$
$402$	4.03873	+	6.21910i	0.201433	+	0.310180i
$403$	12.3935	−	15.3047i	0.617364	−	0.762382i
$404$	−4.52068	−	2.01273i	−0.224912	−	0.100137i
$405$		0			0
$406$	−2.68586	−	13.8788i	−0.133297	−	0.688792i
$407$	−7.19393	+	7.19393i	−0.356590	+	0.356590i
$408$	−2.14223	+	1.73474i	−0.106056	+	0.0858825i
$409$	−17.5576	−	19.4997i	−0.868168	−	0.964198i	0.131464	−	0.991321i	$-0.458032\pi$
$409$	−17.5576	−	19.4997i	−0.868168	−	0.964198i	−0.999632	+	0.0271225i	$0.991366\pi$
$410$		0			0
$411$	−2.75655	−	2.48201i	−0.135970	−	0.122428i
$412$	7.91610	−	4.03345i	0.389998	−	0.198714i
$413$	−12.3893	+	3.07812i	−0.609635	+	0.151464i
$414$	−1.47203	+	0.478291i	−0.0723462	+	0.0235067i
$415$		0			0
$416$	−8.74388	+	7.87302i	−0.428704	+	0.386007i
$417$	−3.47247	+	9.04608i	−0.170047	+	0.442989i
$418$	−5.25268	−	1.40745i	−0.256917	−	0.0688407i
$419$	−20.8379	−	15.1396i	−1.01800	−	0.739617i	−0.0521248	−	0.998641i	$-0.516599\pi$
$419$	−20.8379	−	15.1396i	−1.01800	−	0.739617i	−0.965871	+	0.259023i	$0.916599\pi$
$420$		0			0
$421$	−9.53283	+	6.92601i	−0.464602	+	0.337553i	−0.795334	−	0.606172i	$-0.792704\pi$
$421$	−9.53283	+	6.92601i	−0.464602	+	0.337553i	0.330732	+	0.943725i	$0.392704\pi$
$422$	−10.6551	+	4.09009i	−0.518680	+	0.199103i
$423$	−0.272158	+	0.176741i	−0.0132328	+	0.00859345i
$424$	25.5318	+	14.7408i	1.23994	+	0.715877i
$425$		0			0
$426$			9.41470i			0.456144i
$427$	11.3757	−	4.12978i	0.550510	−	0.199854i
$428$	13.5893	+	2.15233i	0.656864	+	0.104037i
$429$	−1.21890	+	2.73769i	−0.0588489	+	0.132177i
$430$		0			0
$431$	−14.2385	+	6.33937i	−0.685842	+	0.305357i	−0.719914	−	0.694063i	$-0.755819\pi$
$431$	−14.2385	+	6.33937i	−0.685842	+	0.305357i	0.0340723	+	0.999419i	$0.489152\pi$
$432$	1.01970	−	3.80556i	0.0490602	−	0.183095i
$433$	0.766591	−	0.121416i	0.0368400	−	0.00583489i	−0.137987	−	0.990434i	$-0.544063\pi$
$433$	0.766591	−	0.121416i	0.0368400	−	0.00583489i	0.174827	+	0.984599i	$0.444063\pi$
$434$	−0.368312	+	20.1465i	−0.0176796	+	0.967063i
$435$		0			0
$436$	10.1163	−	11.2352i	0.484481	−	0.538070i
$437$	0.315938	−	6.02845i	0.0151134	−	0.288380i
$438$	−0.0752404	+	1.43567i	−0.00359512	+	0.0685991i
$439$	−7.06803	+	7.84984i	−0.337339	+	0.374653i	−0.887817	−	0.460197i	$-0.847779\pi$
$439$	−7.06803	+	7.84984i	−0.337339	+	0.374653i	0.550478	+	0.834850i	$0.314445\pi$
$440$		0			0
$441$	−8.46810	+	8.74002i	−0.403243	+	0.416191i
$442$	−1.43464	+	0.227225i	−0.0682391	+	0.0108080i
$443$	7.03490	−	26.2546i	0.334238	−	1.24739i	−0.570455	−	0.821329i	$-0.693233\pi$
$443$	7.03490	−	26.2546i	0.334238	−	1.24739i	0.904693	−	0.426064i	$-0.140100\pi$
$444$	−10.9762	+	4.88694i	−0.520909	+	0.231924i
$445$		0			0
$446$	6.83506	−	15.3518i	0.323650	−	0.726929i
$447$	0.0438526	+	0.00694557i	0.00207416	+	0.000328514i
$448$	1.41691	−	7.99703i	0.0669426	−	0.377824i
$449$			39.0168i			1.84131i	0.390372	+	0.920657i	$0.372346\pi$
$449$			39.0168i			1.84131i	−0.390372	+	0.920657i	$0.627654\pi$
$450$		0			0
$451$	−0.0752701	−	0.0434572i	−0.00354433	−	0.00204632i
$452$	−7.73894	+	5.02573i	−0.364009	+	0.236390i
$453$	10.2694	−	3.94207i	0.482501	−	0.185215i
$454$	5.91145	−	4.29492i	0.277438	−	0.201571i
$455$		0			0
$456$	−12.6398	−	9.18334i	−0.591912	−	0.430049i
$457$	−22.2310	−	5.95677i	−1.03992	−	0.278646i	−0.301840	−	0.953359i	$-0.597601\pi$
$457$	−22.2310	−	5.95677i	−1.03992	−	0.278646i	−0.738080	+	0.674713i	$0.764268\pi$
$458$	−0.867075	+	2.25881i	−0.0405158	+	0.105547i
$459$	3.67760	−	3.31133i	0.171656	−	0.154560i
$460$		0			0
$461$	−23.0880	+	7.50175i	−1.07532	+	0.349391i	−0.792556	−	0.609799i	$-0.791250\pi$
$461$	−23.0880	+	7.50175i	−1.07532	+	0.349391i	−0.282760	+	0.959191i	$0.591250\pi$
$462$	−0.739328	−	2.97576i	−0.0343967	−	0.138445i
$463$	5.49284	−	2.79874i	0.255274	−	0.130069i	−0.321671	−	0.946851i	$-0.604245\pi$
$463$	5.49284	−	2.79874i	0.255274	−	0.130069i	0.576945	+	0.816783i	$0.304245\pi$
$464$	3.78173	+	3.40509i	0.175563	+	0.158077i
$465$		0			0
$466$	15.1636	+	16.8409i	0.702441	+	0.780140i
$467$	−22.7963	+	18.4601i	−1.05489	+	0.854231i	−0.989630	−	0.143637i	$-0.954120\pi$
$467$	−22.7963	+	18.4601i	−1.05489	+	0.854231i	−0.0652571	+	0.997868i	$0.520787\pi$
$468$	3.44880	−	3.44880i	0.159421	−	0.159421i
$469$	14.7303	+	16.9736i	0.680182	+	0.783767i
$470$		0			0
$471$	13.5068	+	6.01362i	0.622361	+	0.277093i
$472$	−8.01470	+	9.89733i	−0.368906	+	0.455561i
$473$	3.41863	+	5.26423i	0.157189	+	0.242050i
$474$	4.55512	+	7.88970i	0.209224	+	0.362386i
$475$		0			0
$476$	−2.34409	+	2.50956i	−0.107441	+	0.115026i
$477$	−17.3019	−	8.81577i	−0.792200	−	0.403646i
$478$	−0.895202	−	2.33208i	−0.0409456	−	0.106667i
$479$	−0.950688	−	9.04519i	−0.0434380	−	0.413285i	−0.994536	−	0.104395i	$-0.966709\pi$
$479$	−0.950688	−	9.04519i	−0.0434380	−	0.413285i	0.951098	−	0.308890i	$-0.0999574\pi$
$480$		0			0
$481$	−15.3180	−	1.60999i	−0.698441	−	0.0734091i
$482$	−14.7394	−	14.7394i	−0.671360	−	0.671360i
$483$	3.06058	−	1.48961i	0.139261	−	0.0677798i
$484$	−12.2635	−	3.98466i	−0.557433	−	0.181121i
$485$		0			0
$486$	2.44182	−	11.4878i	0.110763	−	0.521099i
$487$	−0.530438	−	0.0277991i	−0.0240364	−	0.00125970i	0.0403139	−	0.999187i	$-0.487164\pi$
$487$	−0.530438	−	0.0277991i	−0.0240364	−	0.00125970i	−0.0643504	+	0.997927i	$0.520498\pi$
$488$	6.57559	−	10.1255i	0.297663	−	0.458361i
$489$	−1.21199	−	3.73011i	−0.0548080	−	0.168682i
$490$		0			0
$491$	1.98288	−	6.10267i	0.0894861	−	0.275410i	−0.896291	−	0.443466i	$-0.853749\pi$
$491$	1.98288	−	6.10267i	0.0894861	−	0.275410i	0.985777	+	0.168056i	$0.0537489\pi$
$492$	−0.0645960	−	0.0797694i	−0.00291221	−	0.00359628i
$493$	1.65436	+	6.17415i	0.0745086	+	0.278070i
$494$	−3.34855	−	7.52097i	−0.150658	−	0.338384i
$495$		0			0
$496$	−4.26357	−	5.86830i	−0.191440	−	0.263494i
$497$	3.94772	+	28.2589i	0.177079	+	1.26758i
$498$	2.47926	−	4.86582i	0.111098	−	0.218043i
$499$	−5.43364	+	3.13711i	−0.243243	+	0.140437i	−0.616666	−	0.787225i	$-0.711517\pi$
$499$	−5.43364	+	3.13711i	−0.243243	+	0.140437i	0.373423	+	0.927661i	$0.378184\pi$
$500$		0			0
$501$	10.7562	−	18.6303i	0.480553	−	0.832343i
$502$	−10.6757	+	0.559489i	−0.476479	+	0.0249712i
$503$	−0.780151	+	4.92568i	−0.0347852	+	0.219625i	−0.998957	−	0.0456521i	$-0.985463\pi$
$503$	−0.780151	+	4.92568i	−0.0347852	+	0.219625i	0.964172	+	0.265277i	$0.0854634\pi$
$504$	−1.48951	+	12.0488i	−0.0663480	+	0.536695i
$505$		0			0
$506$	0.123544	−	1.17544i	0.00549220	−	0.0522548i
$507$	9.72131	−	2.60482i	0.431739	−	0.115684i
$508$	−24.0966	−	9.24984i	−1.06912	−	0.410395i
$509$	22.1320	−	4.70429i	0.980982	−	0.208514i	0.310609	−	0.950538i	$-0.399467\pi$
$509$	22.1320	−	4.70429i	0.980982	−	0.208514i	0.670374	+	0.742024i	$0.266134\pi$
$510$		0			0
$511$	0.376159	+	4.34082i	0.0166403	+	0.192027i
$512$	3.74158	+	7.34327i	0.165356	+	0.324530i
$513$	23.5235	+	15.2763i	1.03859	+	0.674467i
$514$	−7.02566	−	1.49335i	−0.309889	−	0.0658688i
$515$		0			0
$516$	1.54122	+	7.25087i	0.0678484	+	0.319202i
$517$	−0.0387649	−	0.244752i	−0.00170488	−	0.0107642i
$518$	13.3716	−	8.34013i	0.587513	−	0.366444i
$519$	−3.27343	+	4.50548i	−0.143687	+	0.197769i
$520$		0			0
$521$	30.6917	−	3.22582i	1.34463	−	0.141326i	0.595287	−	0.803513i	$-0.297038\pi$
$521$	30.6917	−	3.22582i	1.34463	−	0.141326i	0.749339	+	0.662187i	$0.230372\pi$
$522$	7.21877	+	5.84564i	0.315957	+	0.255857i
$523$	1.60327	+	30.5923i	0.0701062	+	1.33771i	0.776603	+	0.629990i	$0.216941\pi$
$523$	1.60327	+	30.5923i	0.0701062	+	1.33771i	−0.706497	+	0.707716i	$0.749726\pi$
$524$	23.3916			1.02187
$525$		0			0
$526$	6.52252			0.284395
$527$	−0.476838	−	9.09861i	−0.0207714	−	0.396342i
$528$	0.857805	+	0.694637i	0.0373312	+	0.0302302i
$529$	−21.5691	+	2.26701i	−0.937789	+	0.0985656i
$530$		0			0
$531$	4.93056	−	6.78633i	0.213968	−	0.294502i
$532$	−17.1778	−	9.15184i	−0.744754	−	0.396783i
$533$	−0.0205840	−	0.129963i	−0.000891594	−	0.00562930i
$534$	−2.84865	−	13.4018i	−0.123273	−	0.579954i
$535$		0			0
$536$	21.9306	+	4.66148i	0.947256	+	0.201345i
$537$	19.0775	+	12.3891i	0.823254	+	0.534628i
$538$	−1.55398	−	3.04985i	−0.0669966	−	0.131488i
$539$	−3.46693	−	8.62194i	−0.149331	−	0.371373i
$540$		0			0
$541$	−38.7310	+	8.23253i	−1.66518	+	0.353944i	−0.941712	−	0.336419i	$-0.890784\pi$
$541$	−38.7310	+	8.23253i	−1.66518	+	0.353944i	−0.723463	+	0.690363i	$0.757451\pi$
$542$	−2.49056	−	0.956035i	−0.106979	−	0.0410652i
$543$	4.94065	−	1.32384i	0.212023	−	0.0568115i
$544$	−0.569001	+	5.41369i	−0.0243957	+	0.232110i
$545$		0			0
$546$	2.79672	−	3.70500i	0.119689	−	0.158559i
$547$	−5.86395	+	37.0235i	−0.250724	+	1.58301i	0.465440	+	0.885079i	$0.345896\pi$
$547$	−5.86395	+	37.0235i	−0.250724	+	1.58301i	−0.716164	+	0.697932i	$0.754104\pi$
$548$	−4.60365	+	0.241267i	−0.196658	+	0.0103064i
$549$	−3.97611	+	6.88682i	−0.169696	+	0.293922i
$550$		0			0
$551$	−31.3750	+	18.1143i	−1.33662	+	0.771697i
$552$	1.54162	−	3.02561i	0.0656159	−	0.128778i
$553$	16.9808	+	21.7715i	0.722097	+	0.925817i
$554$	−3.51735	−	4.84122i	−0.149438	−	0.205684i
$555$		0			0
$556$	4.89811	+	11.0013i	0.207726	+	0.466560i
$557$	1.55832	+	5.81572i	0.0660280	+	0.246420i	0.991050	−	0.133495i	$-0.0426200\pi$
$557$	1.55832	+	5.81572i	0.0660280	+	0.246420i	−0.925021	+	0.379915i	$0.875953\pi$
$558$	−8.33239	−	10.2896i	−0.352738	−	0.435595i
$559$	−2.93652	+	9.03767i	−0.124201	+	0.382253i
$560$		0			0
$561$	0.428435	+	1.31859i	0.0180885	+	0.0556708i
$562$	−10.2709	+	15.8159i	−0.433253	+	0.667152i
$563$	−30.1805	−	1.58169i	−1.27196	−	0.0666604i	−0.595628	−	0.803260i	$-0.703097\pi$
$563$	−30.1805	−	1.58169i	−1.27196	−	0.0666604i	−0.676329	+	0.736600i	$0.736430\pi$
$564$	0.0608453	−	0.286255i	0.00256205	−	0.0120535i
$565$		0			0
$566$	−5.35873	−	1.74116i	−0.225244	−	0.0731863i
$567$	−0.142319	+	2.01137i	−0.00597682	+	0.0844694i
$568$	20.1280	+	20.1280i	0.844552	+	0.844552i
$569$	4.95634	+	0.520932i	0.207781	+	0.0218386i	0.207847	−	0.978161i	$-0.433354\pi$
$569$	4.95634	+	0.520932i	0.207781	+	0.0218386i	−6.62580e−5		1.00000i	$0.500021\pi$
$570$		0			0
$571$	0.255295	+	2.42897i	0.0106837	+	0.101649i	0.998564	−	0.0535674i	$-0.0170592\pi$
$571$	0.255295	+	2.42897i	0.0106837	+	0.101649i	−0.987880	+	0.155216i	$0.950393\pi$
$572$	1.33472	+	3.47706i	0.0558073	+	0.145383i
$573$	15.4903	+	7.89270i	0.647117	+	0.329722i
$574$	0.0983877	+	0.0919002i	0.00410662	+	0.00383584i
$575$		0			0
$576$	2.66831	+	4.62165i	0.111180	+	0.192569i
$577$	13.2368	+	20.3829i	0.551057	+	0.848553i	0.998963	−	0.0455274i	$-0.0144968\pi$
$577$	13.2368	+	20.3829i	0.551057	+	0.848553i	−0.447906	+	0.894081i	$0.647830\pi$
$578$	7.89244	−	9.74635i	0.328282	−	0.405395i
$579$	−8.04537	−	3.58203i	−0.334354	−	0.148864i
$580$		0			0
$581$	5.40137	−	15.6447i	0.224087	−	0.649052i
$582$	10.7384	−	10.7384i	0.445123	−	0.445123i
$583$	11.5237	−	9.33174i	0.477264	−	0.386481i
$584$	2.90851	+	3.23023i	0.120355	+	0.133668i
$585$		0			0
$586$	−17.9877	−	16.1962i	−0.743066	−	0.669060i
$587$	8.03430	−	4.09368i	0.331611	−	0.168964i	−0.280255	−	0.959926i	$-0.590419\pi$
$587$	8.03430	−	4.09368i	0.331611	−	0.168964i	0.611866	+	0.790961i	$0.290419\pi$
$588$	−0.173399	−	10.9733i	−0.00715085	−	0.452532i
$589$	49.1130	−	15.9578i	2.02366	−	0.657528i
$590$		0			0
$591$	13.6545	−	12.2946i	0.561671	−	0.505731i
$592$	−2.03306	+	5.29629i	−0.0835581	+	0.217676i
$593$	−24.7752	−	6.63849i	−1.01740	−	0.272610i	−0.288679	−	0.957426i	$-0.593216\pi$
$593$	−24.7752	−	6.63849i	−1.01740	−	0.272610i	−0.728716	+	0.684816i	$0.759883\pi$
$594$	4.44277	+	3.22786i	0.182289	+	0.132441i
$595$		0			0
$596$	0.0446416	−	0.0324340i	0.00182859	−	0.00132855i
$597$	28.6386	−	10.9933i	1.17210	−	0.449926i
$598$	1.50067	−	0.974545i	0.0613669	−	0.0398521i
$599$	−23.1803	−	13.3832i	−0.947123	−	0.546822i	−0.0549370	−	0.998490i	$-0.517496\pi$
$599$	−23.1803	−	13.3832i	−0.947123	−	0.546822i	−0.892186	+	0.451668i	$0.850829\pi$
$600$		0			0
$601$		−	3.83116i		−	0.156276i	−0.996943	−	0.0781382i	$-0.975102\pi$
$601$		−	3.83116i		−	0.156276i	0.996943	−	0.0781382i	$-0.0248975\pi$
$602$	−3.31791	−	9.13938i	−0.135228	−	0.372493i
$603$	−14.5857	−	2.31015i	−0.593975	−	0.0940764i
$604$	5.56051	−	12.4891i	0.226254	−	0.508175i
$605$		0			0
$606$	2.82720	−	1.25875i	0.114847	−	0.0511332i
$607$	8.71399	−	32.5210i	0.353690	−	1.31999i	−0.528435	−	0.848974i	$-0.677221\pi$
$607$	8.71399	−	32.5210i	0.353690	−	1.31999i	0.882125	−	0.471015i	$-0.156112\pi$
$608$	−30.4732	+	4.82648i	−1.23585	+	0.195740i
$609$	−17.5013	−	10.5355i	−0.709187	−	0.426921i
$610$		0			0
$611$	0.251029	−	0.278796i	0.0101555	−	0.0112789i
$612$	0.118095	−	2.25339i	0.00477370	−	0.0910877i
$613$	−2.32439	+	44.3520i	−0.0938813	+	1.79136i	0.394666	+	0.918825i	$0.370860\pi$
$613$	−2.32439	+	44.3520i	−0.0938813	+	1.79136i	−0.488547	+	0.872537i	$0.662473\pi$
$614$	1.71789	−	1.90791i	0.0693284	−	0.0769970i
$615$		0			0
$616$	−7.94261	−	4.78134i	−0.320017	−	0.192646i
$617$	34.5246	−	5.46815i	1.38991	−	0.220140i	0.583794	−	0.811902i	$-0.301568\pi$
$617$	34.5246	−	5.46815i	1.38991	−	0.220140i	0.806112	+	0.591762i	$0.201568\pi$
$618$	−1.43807	+	5.36695i	−0.0578476	+	0.215890i
$619$	−12.2138	+	5.43792i	−0.490913	+	0.218568i	−0.637237	−	0.770668i	$-0.719923\pi$
$619$	−12.2138	+	5.43792i	−0.490913	+	0.218568i	0.146324	+	0.989237i	$0.453256\pi$
$620$		0			0
$621$	−2.47955	+	5.56917i	−0.0995011	+	0.223483i
$622$	4.74246	+	0.751132i	0.190155	+	0.0301176i
$623$	−14.1700	−	39.0321i	−0.567709	−	1.56379i
$624$			1.67106i			0.0668960i
$625$		0			0
$626$	7.53917	+	4.35274i	0.301326	+	0.173971i
$627$	−6.59042	+	4.27987i	−0.263196	+	0.170921i
$628$	17.1546	−	6.58503i	0.684543	−	0.262771i
$629$	−5.76493	+	4.18846i	−0.229863	+	0.167005i
$630$		0			0
$631$	11.1996	+	8.13699i	0.445849	+	0.323928i	0.787955	−	0.615733i	$-0.211140\pi$
$631$	11.1996	+	8.13699i	0.445849	+	0.323928i	−0.342106	+	0.939662i	$0.611140\pi$
$632$	26.6062	+	7.12911i	1.05834	+	0.283581i
$633$	−5.91041	+	15.3972i	−0.234918	+	0.611982i
$634$	−5.19442	+	4.67707i	−0.206297	+	0.185750i
$635$		0			0
$636$	16.6548	−	5.41147i	0.660405	−	0.214579i
$637$	6.84101	−	12.2935i	0.271051	−	0.487088i
$638$	−6.32003	+	3.22021i	−0.250212	+	0.127489i
$639$	−13.9332	−	12.5455i	−0.551189	−	0.496293i
$640$		0			0
$641$	−1.56927	−	1.74285i	−0.0619824	−	0.0688384i	0.711356	−	0.702832i	$-0.248081\pi$
$641$	−1.56927	−	1.74285i	−0.0619824	−	0.0688384i	−0.773339	+	0.633993i	$0.781415\pi$
$642$	−6.68703	+	5.41505i	−0.263916	+	0.213715i
$643$	−16.5284	+	16.5284i	−0.651816	+	0.651816i	−0.953430	−	0.301614i	$-0.902475\pi$
$643$	−16.5284	+	16.5284i	−0.651816	+	0.651816i	0.301614	+	0.953430i	$0.402475\pi$
$644$	1.38057	−	3.99872i	0.0544020	−	0.157572i
$645$		0			0
$646$	−3.47954	−	1.54919i	−0.136901	−	0.0609521i
$647$	7.37948	−	9.11290i	0.290117	−	0.358265i	−0.611161	−	0.791507i	$-0.709297\pi$
$647$	7.37948	−	9.11290i	0.290117	−	0.358265i	0.901278	+	0.433242i	$0.142630\pi$
$648$	1.09559	+	1.68706i	0.0430388	+	0.0662739i
$649$	3.20276	+	5.54735i	0.125719	+	0.217752i
$650$		0			0
$651$	21.2789	+	19.8758i	0.833986	+	0.778994i
$652$	−4.34313	−	2.21293i	−0.170090	−	0.0866652i
$653$	7.45920	+	19.4319i	0.291901	+	0.760429i	0.998599	+	0.0529133i	$0.0168507\pi$
$653$	7.45920	+	19.4319i	0.291901	+	0.760429i	−0.706698	+	0.707515i	$0.749816\pi$
$654$	0.988318	+	9.40322i	0.0386463	+	0.367695i
$655$		0			0
$656$	−0.0481998	−	0.00506600i	−0.00188188	−	0.000197794i
$657$	−2.02445	−	2.02445i	−0.0789813	−	0.0789813i
$658$	−0.0270925	+	0.382894i	−0.00105618	+	0.0149268i
$659$	−30.5370	−	9.92209i	−1.18955	−	0.386510i	−0.353646	−	0.935379i	$-0.615058\pi$
$659$	−30.5370	−	9.92209i	−1.18955	−	0.386510i	−0.835908	+	0.548870i	$0.815058\pi$
$660$		0			0
$661$	2.10304	−	9.89402i	0.0817988	−	0.384833i	−0.918136	−	0.396266i	$-0.870306\pi$
$661$	2.10304	−	9.89402i	0.0817988	−	0.384833i	0.999935	+	0.0114328i	$0.00363925\pi$
$662$	5.60892	+	0.293951i	0.217997	+	0.0114247i
$663$	−1.14319	+	1.76035i	−0.0443977	+	0.0683665i
$664$	−5.10231	−	15.7033i	−0.198008	−	0.609406i
$665$		0			0
$666$	−3.19997	+	9.84849i	−0.123996	+	0.381621i
$667$	−4.95535	−	6.11935i	−0.191872	−	0.236942i
$668$	−6.91979	−	25.8250i	−0.267735	−	0.999199i
$669$	−9.87704	−	22.1842i	−0.381868	−	0.857691i
$670$		0			0
$671$	−3.56931	−	4.91273i	−0.137792	−	0.189654i
$672$	−10.6991	−	13.7176i	−0.412727	−	0.529167i
$673$	5.12781	−	10.0639i	0.197663	−	0.387935i	−0.770806	−	0.637070i	$-0.780146\pi$
$673$	5.12781	−	10.0639i	0.197663	−	0.387935i	0.968469	+	0.249135i	$0.0801463\pi$
$674$	−6.82894	+	3.94269i	−0.263041	+	0.151867i
$675$		0			0
$676$	6.25399	−	10.8322i	0.240538	−	0.416624i
$677$	24.4201	−	1.27981i	0.938542	−	0.0491869i	0.423074	−	0.906095i	$-0.360951\pi$
$677$	24.4201	−	1.27981i	0.938542	−	0.0491869i	0.515469	+	0.856908i	$0.327618\pi$
$678$	0.902768	−	5.69985i	0.0346706	−	0.218901i
$679$	27.7294	−	36.7350i	1.06416	−	1.40976i
$680$		0			0
$681$	1.10371	−	10.5011i	0.0422943	−	0.402404i
$682$	9.76605	−	2.61681i	0.373961	−	0.100203i
$683$	15.3920	+	5.90842i	0.588957	+	0.226079i	0.634552	−	0.772881i	$-0.281185\pi$
$683$	15.3920	+	5.90842i	0.588957	+	0.226079i	−0.0455944	+	0.998960i	$0.514518\pi$
$684$	12.5099	−	2.65907i	0.478329	−	0.101672i
$685$		0			0
$686$	2.21659	+	14.2231i	0.0846299	+	0.543042i
$687$	1.58730	+	3.11525i	0.0605593	+	0.118854i
$688$	2.93544	+	1.90630i	0.111913	+	0.0726770i
$689$	21.9585	+	4.66741i	0.836550	+	0.177814i
$690$		0			0
$691$	5.84621	+	27.5043i	0.222400	+	1.04631i	0.937687	+	0.347480i	$0.112963\pi$
$691$	5.84621	+	27.5043i	0.222400	+	1.04631i	−0.715287	+	0.698831i	$0.753704\pi$
$692$	1.08274	+	6.83613i	0.0411594	+	0.259870i
$693$	5.38914	+	2.87117i	0.204716	+	0.109067i
$694$	3.66214	−	5.04050i	0.139013	−	0.191335i
$695$		0			0
$696$	−20.2674	+	2.13019i	−0.768233	+	0.0807445i
$697$	−0.0473096	−	0.0383106i	−0.00179198	−	0.00145112i
$698$	−0.358806	−	6.84643i	−0.0135810	−	0.259141i
$699$	32.7474			1.23862
$700$		0			0
$701$	−35.1051			−1.32590			−0.662951	−	0.748663i	$-0.730696\pi$
$701$	−35.1051			−1.32590			−0.662951	+	0.748663i	$0.730696\pi$
$702$	0.435113	+	8.30246i	0.0164223	+	0.313356i
$703$	−31.3876	−	25.4172i	−1.18381	−	0.958627i
$704$	−4.05282	+	0.425969i	−0.152747	+	0.0160543i
$705$		0			0
$706$	−7.69154	+	10.5865i	−0.289475	+	0.398428i
$707$	7.95823	−	4.96372i	0.299300	−	0.186680i
$708$	1.18339	+	7.47165i	0.0444746	+	0.280802i
$709$	10.9224	+	51.3859i	0.410200	+	1.92984i	0.365421	+	0.930842i	$0.380925\pi$
$709$	10.9224	+	51.3859i	0.410200	+	1.92984i	0.0447789	+	0.998997i	$0.485742\pi$
$710$		0			0
$711$	−17.7462	−	3.77207i	−0.665534	−	0.141464i
$712$	−34.7425	−	22.5620i	−1.30203	−	0.845548i
$713$	5.09550	+	10.0005i	0.190828	+	0.374521i
$714$	−0.185410	−	2.13961i	−0.00693879	−	0.0800728i
$715$		0			0
$716$	27.6529	−	5.87780i	1.03344	−	0.219664i
$717$	−3.36999	−	1.29362i	−0.125854	−	0.0483110i
$718$	−10.3777	+	2.78070i	−0.387293	+	0.103775i
$719$	0.289532	−	2.75471i	0.0107977	−	0.102733i	−0.987796	−	0.155756i	$-0.950219\pi$
$719$	0.289532	−	2.75471i	0.0107977	−	0.102733i	0.998593	+	0.0530223i	$0.0168854\pi$
$720$		0			0
$721$	−2.06603	+	16.7123i	−0.0769430	+	0.622398i
$722$	1.06692	−	6.73625i	0.0397066	−	0.250697i
$723$	−30.0803	+	1.57644i	−1.11870	+	0.0586286i
$724$	3.17846	−	5.50525i	0.118126	−	0.204601i
$725$		0			0
$726$	6.98382	−	4.03211i	0.259194	−	0.149646i
$727$	−2.70831	+	5.31536i	−0.100446	+	0.197136i	−0.935761	−	0.352636i	$-0.885285\pi$
$727$	−2.70831	+	5.31536i	−0.100446	+	0.197136i	0.835315	+	0.549772i	$0.185285\pi$
$728$	−1.94184	−	13.9003i	−0.0719695	−	0.515178i
$729$	−11.3195	−	15.5799i	−0.419239	−	0.577033i
$730$		0			0
$731$	1.78818	+	4.01632i	0.0661383	+	0.148549i
$732$	−1.85611	−	6.92710i	−0.0686038	−	0.256033i
$733$	−18.9592	−	23.4127i	−0.700275	−	0.864768i	0.295618	−	0.955306i	$-0.404475\pi$
$733$	−18.9592	−	23.4127i	−0.700275	−	0.864768i	−0.995893	+	0.0905384i	$0.971141\pi$
$734$	0.249589	−	0.768156i	0.00921250	−	0.0283532i
$735$		0			0
$736$	−2.07219	−	6.37755i	−0.0763820	−	0.235080i
$737$	6.14177	−	9.45749i	0.226235	−	0.348371i
$738$	−0.0883442	−	0.00462993i	−0.00325200	−	0.000170430i
$739$	9.39272	−	44.1893i	0.345517	−	1.62553i	−0.371472	−	0.928444i	$-0.621147\pi$
$739$	9.39272	−	44.1893i	0.345517	−	1.62553i	0.716989	−	0.697084i	$-0.245520\pi$
$740$		0			0
$741$	−11.3145	−	3.67629i	−0.415648	−	0.135052i
$742$	−20.6530	+	10.0520i	−0.758194	+	0.369021i
$743$	−23.4363	−	23.4363i	−0.859793	−	0.859793i	0.131520	−	0.991313i	$-0.458014\pi$
$743$	−23.4363	−	23.4363i	−0.859793	−	0.859793i	−0.991313	+	0.131520i	$0.958014\pi$
$744$	28.8891	+	3.03637i	1.05913	+	0.111319i
$745$		0			0
$746$	−1.78782	−	17.0099i	−0.0654566	−	0.622778i
$747$	3.89741	+	10.1531i	0.142599	+	0.371482i
$748$	1.53529	+	0.782267i	0.0561356	+	0.0286025i
$749$	−17.8010	+	19.0576i	−0.650434	+	0.696351i
$750$		0			0
$751$	19.3994	+	33.6008i	0.707894	+	1.22611i	0.965637	+	0.259895i	$0.0836881\pi$
$751$	19.3994	+	33.6008i	0.707894	+	1.22611i	−0.257742	+	0.966214i	$0.582979\pi$
$752$	−0.0752582	−	0.115887i	−0.00274438	−	0.00422598i
$753$	−9.72182	+	12.0054i	−0.354283	+	0.437503i
$754$	−9.81013	−	4.36775i	−0.357264	−	0.159064i
$755$		0			0
$756$	12.8829	+	14.8448i	0.468546	+	0.539901i
$757$	−2.63808	+	2.63808i	−0.0958825	+	0.0958825i	−0.753421	−	0.657538i	$-0.771598\pi$
$757$	−2.63808	+	2.63808i	−0.0958825	+	0.0958825i	0.657538	+	0.753421i	$0.271598\pi$
$758$	−18.3229	+	14.8376i	−0.665516	+	0.538924i
$759$	−1.14283	−	1.26924i	−0.0414821	−	0.0460706i
$760$		0			0
$761$	29.5054	+	26.5668i	1.06957	+	0.963044i	0.999405	−	0.0344912i	$-0.0109811\pi$
$761$	29.5054	+	26.5668i	1.06957	+	0.963044i	0.0701640	+	0.997535i	$0.477648\pi$
$762$	14.3827	−	7.32833i	0.521029	−	0.265477i
$763$	6.90941	+	27.8100i	0.250138	+	1.00679i
$764$	20.5490	−	6.67679i	0.743438	−	0.241558i
$765$		0			0
$766$	−12.3518	+	11.1216i	−0.446287	+	0.401839i
$767$	−3.47528	+	9.05342i	−0.125485	+	0.326900i
$768$	−14.5217	−	3.89107i	−0.524006	−	0.140407i
$769$	0.563611	+	0.409487i	0.0203243	+	0.0147665i	0.597901	−	0.801570i	$-0.296002\pi$
$769$	0.563611	+	0.409487i	0.0203243	+	0.0147665i	−0.577577	+	0.816336i	$0.696002\pi$
$770$		0			0
$771$	−8.39701	+	6.10079i	−0.302411	+	0.219714i
$772$	−10.2182	+	3.92239i	−0.367760	+	0.141170i
$773$	27.4809	−	17.8463i	0.988421	−	0.641888i	0.0541802	−	0.998531i	$-0.482745\pi$
$773$	27.4809	−	17.8463i	0.988421	−	0.641888i	0.934241	+	0.356643i	$0.116079\pi$
$774$	5.53295	+	3.19445i	0.198878	+	0.114822i
$775$		0			0
$776$		−	45.9162i		−	1.64829i
$777$	3.97304	−	22.4239i	0.142532	−	0.804452i
$778$	−16.1555	−	2.55878i	−0.579202	−	0.0917365i
$779$	0.140339	−	0.315207i	0.00502817	−	0.0112935i
$780$		0			0
$781$	13.0793	−	5.82329i	0.468015	−	0.208374i
$782$	0.214258	−	0.799623i	0.00766186	−	0.0285945i
$783$	36.1353	−	5.72327i	1.29137	−	0.204533i
$784$	−3.72159	−	3.60580i	−0.132914	−	0.128779i
$785$		0			0
$786$	−9.78868	+	10.8714i	−0.349151	+	0.387771i
$787$	1.39588	−	26.6351i	0.0497579	−	0.949438i	−0.853701	−	0.520763i	$-0.825647\pi$
$787$	1.39588	−	26.6351i	0.0497579	−	0.949438i	0.903459	−	0.428674i	$-0.141019\pi$
$788$	1.19511	−	22.8041i	0.0425741	−	0.812363i
$789$	6.30682	−	7.00444i	0.224529	−	0.249365i
$790$		0			0
$791$	0.319693	−	17.4871i	0.0113670	−	0.621768i
$792$	6.01670	−	0.952952i	0.213794	−	0.0338617i
$793$	2.37940	−	8.88006i	0.0844951	−	0.315340i
$794$	−3.63897	+	1.62017i	−0.129142	+	0.0574978i
$795$		0			0
$796$	15.5067	−	34.8286i	0.549620	−	1.23447i
$797$	−16.3812	−	2.59453i	−0.580252	−	0.0919030i	−0.140593	−	0.990067i	$-0.544901\pi$
$797$	−16.3812	−	2.59453i	−0.580252	−	0.0919030i	−0.439660	+	0.898165i	$0.644901\pi$
$798$	11.4418	−	4.15377i	0.405035	−	0.147042i
$799$		−	0.173565i		−	0.00614027i
$800$		0			0
$801$	23.6299	+	13.6427i	0.834921	+	0.482042i
$802$	22.3796	−	14.5335i	0.790252	−	0.513196i
$803$	2.04104	−	0.783481i	0.0720267	−	0.0276484i
$804$	10.7742	−	7.82790i	0.379976	−	0.276069i
$805$		0			0
$806$	12.3834	+	8.99706i	0.436186	+	0.316908i
$807$	−4.77777	−	1.28020i	−0.168186	−	0.0450652i
$808$	3.35324	−	8.73549i	0.117967	−	0.307314i
$809$	−32.1490	+	28.9471i	−1.13030	+	1.01773i	−0.130645	+	0.991429i	$0.541705\pi$
$809$	−32.1490	+	28.9471i	−1.13030	+	1.01773i	−0.999654	+	0.0262968i	$0.991628\pi$
$810$		0			0
$811$	24.7816	−	8.05202i	0.870198	−	0.282745i	0.160317	−	0.987066i	$-0.448748\pi$
$811$	24.7816	−	8.05202i	0.870198	−	0.282745i	0.709881	+	0.704321i	$0.248748\pi$
$812$	−24.6388	+	6.12152i	−0.864652	+	0.214823i
$813$	−3.43487	+	1.75015i	−0.120466	+	0.0613805i
$814$	−5.87644	−	5.29117i	−0.205969	−	0.185455i
$815$		0			0
$816$	0.517311	+	0.574532i	0.0181095	+	0.0201127i
$817$	−19.3651	+	15.6816i	−0.677500	+	0.548629i
$818$	14.4211	−	14.4211i	0.504223	−	0.504223i
$819$	1.75643	+	9.07607i	0.0613745	+	0.317144i
$820$		0			0
$821$	24.2885	+	10.8140i	0.847676	+	0.377410i	0.784151	−	0.620571i	$-0.213099\pi$
$821$	24.2885	+	10.8140i	0.847676	+	0.377410i	0.0635253	+	0.997980i	$0.479766\pi$
$822$	1.81436	−	2.24055i	0.0632830	−	0.0781480i
$823$	−1.32048	−	2.03336i	−0.0460290	−	0.0708785i	0.814907	−	0.579592i	$-0.196788\pi$
$823$	−1.32048	−	2.03336i	−0.0460290	−	0.0708785i	−0.860936	+	0.508713i	$0.830121\pi$
$824$	8.39968	+	14.5487i	0.292617	+	0.506827i
$825$		0			0
$826$	−2.89315	−	9.49111i	−0.100666	−	0.330238i
$827$	5.66953	+	2.88877i	0.197149	+	0.100452i	0.549778	−	0.835311i	$-0.314712\pi$
$827$	5.66953	+	2.88877i	0.197149	+	0.100452i	−0.352629	+	0.935763i	$0.614712\pi$
$828$	0.996160	+	2.59509i	0.0346190	+	0.0901855i
$829$	1.85268	+	17.6271i	0.0643462	+	0.612213i	0.978414	+	0.206653i	$0.0662570\pi$
$829$	1.85268	+	17.6271i	0.0643462	+	0.612213i	−0.914068	+	0.405561i	$0.867076\pi$
$830$		0			0
$831$	−8.59994	−	0.903890i	−0.298329	−	0.0313556i
$832$	−4.36250	−	4.36250i	−0.151242	−	0.151242i
$833$	−1.45369	−	6.34445i	−0.0503674	−	0.219822i
$834$	−7.16266	−	2.32729i	−0.248023	−	0.0805875i
$835$		0			0
$836$	−2.03052	+	9.55283i	−0.0702269	+	0.330391i
$837$	−52.0778	−	2.72928i	−1.80007	−	0.0943379i
$838$	10.9034	−	16.7898i	0.376653	−	0.579995i
$839$	−7.84911	−	24.1571i	−0.270981	−	0.833995i	−0.990255	−	0.139268i	$-0.955525\pi$
$839$	−7.84911	−	24.1571i	−0.270981	−	0.833995i	0.719273	−	0.694727i	$-0.244475\pi$
$840$		0			0
$841$	−5.64130	+	17.3621i	−0.194528	+	0.598695i
$842$	−5.76362	−	7.11748i	−0.198627	−	0.245284i
$843$	7.05313	+	26.3226i	0.242923	+	0.906600i
$844$	8.33697	+	18.7251i	0.286970	+	0.644546i
$845$		0			0
$846$	−0.148254	−	0.204054i	−0.00509708	−	0.00701553i
$847$	19.2717	−	15.0311i	0.662184	−	0.516474i
$848$	3.75384	−	7.36733i	0.128908	−	0.252995i
$849$	−7.05132	+	4.07108i	−0.242001	+	0.139719i
$850$		0			0
$851$	4.38910	−	7.60214i	0.150456	−	0.260598i
$852$	16.8850	−	0.884906i	0.578471	−	0.0303164i
$853$	3.15894	−	19.9447i	0.108160	−	0.682895i	−0.872711	−	0.488237i	$-0.837640\pi$
$853$	3.15894	−	19.9447i	0.108160	−	0.682895i	0.980871	−	0.194658i	$-0.0623597\pi$
$854$	3.66821	+	8.66164i	0.125523	+	0.296395i
$855$		0			0
$856$	−2.71941	+	25.8734i	−0.0929475	+	0.884336i
$857$	−3.59245	+	0.962594i	−0.122716	+	0.0328816i	−0.319654	−	0.947534i	$-0.603567\pi$
$857$	−3.59245	+	0.962594i	−0.122716	+	0.0328816i	0.196938	+	0.980416i	$0.436900\pi$
$858$	−2.17453	−	0.834723i	−0.0742372	−	0.0284970i
$859$	−21.6111	+	4.59358i	−0.737361	+	0.156731i	−0.561258	−	0.827641i	$-0.689682\pi$
$859$	−21.6111	+	4.59358i	−0.737361	+	0.156731i	−0.176103	+	0.984372i	$0.556349\pi$
$860$		0			0
$861$	0.193824	−	0.0167960i	0.00660552	−	0.000572408i
$862$	−5.49970	−	10.7938i	−0.187320	−	0.367637i
$863$	33.0348	+	21.4531i	1.12452	+	0.730270i	0.966373	−	0.257146i	$-0.0827820\pi$
$863$	33.0348	+	21.4531i	1.12452	+	0.730270i	0.158145	+	0.987416i	$0.449449\pi$
$864$	30.4762	+	6.47792i	1.03682	+	0.220383i
$865$		0			0
$866$	0.125424	+	0.590076i	0.00426210	+	0.0200516i
$867$	−2.83502	−	17.8996i	−0.0962823	−	0.607903i
$868$	36.1669	−	1.23305i	1.22758	−	0.0418525i
$869$	8.14324	−	11.2082i	0.276240	−	0.380212i
$870$		0			0
$871$	16.9787	−	1.78454i	0.575303	−	0.0604667i
$872$	22.2164	+	17.9905i	0.752343	+	0.609235i
$873$	1.58281	+	30.2017i	0.0535699	+	1.02217i
$874$	4.69203			0.158710
$875$		0			0
$876$	2.58191			0.0872347
$877$	1.17820	+	22.4814i	0.0397851	+	0.759145i	0.943573	+	0.331164i	$0.107441\pi$
$877$	1.17820	+	22.4814i	0.0397851	+	0.759145i	−0.903788	+	0.427980i	$0.859225\pi$
$878$	−6.38042	−	5.16677i	−0.215329	−	0.174370i
$879$	−34.7858	+	3.65613i	−1.17329	+	0.123318i
$880$		0			0
$881$	1.48864	−	2.04893i	0.0501535	−	0.0690304i	−0.783204	−	0.621765i	$-0.786416\pi$
$881$	1.48864	−	2.04893i	0.0501535	−	0.0690304i	0.833357	+	0.552735i	$0.186416\pi$
$882$	−7.12831	−	6.21726i	−0.240023	−	0.209346i
$883$	−6.64738	−	41.9699i	−0.223702	−	1.41240i	−0.802366	−	0.596833i	$-0.796426\pi$
$883$	−6.64738	−	41.9699i	−0.223702	−	1.41240i	0.578664	−	0.815566i	$-0.303574\pi$
$884$	0.542368	+	2.55164i	0.0182418	+	0.0858209i
$885$		0			0
$886$	20.6645	+	4.39238i	0.694238	+	0.147565i
$887$	−26.6711	−	17.3204i	−0.895528	−	0.581563i	0.0127551	−	0.999919i	$-0.495940\pi$
$887$	−26.6711	−	17.3204i	−0.895528	−	0.581563i	−0.908283	+	0.418356i	$0.862606\pi$
$888$	−10.3141	−	20.2426i	−0.346120	−	0.679298i
$889$	40.0977	−	28.0274i	1.34483	−	0.940008i
$890$		0			0
$891$	0.989652	−	0.210357i	0.0331546	−	0.00704723i
$892$	−28.1755	−	10.8156i	−0.943385	−	0.362132i
$893$	0.950220	−	0.254611i	0.0317979	−	0.00852022i
$894$	−0.00360720	+	0.0343202i	−0.000120643	+	0.00114784i
$895$		0			0
$896$	−24.4790	−	3.02618i	−0.817787	−	0.101098i
$897$	0.404492	−	2.55386i	0.0135056	−	0.0852710i
$898$	−30.2841	+	1.58712i	−1.01059	+	0.0529630i
$899$	33.6791	−	58.3340i	1.12326	−	1.94555i
$900$		0			0
$901$	8.99448	−	5.19297i	0.299650	−	0.173003i
$902$	0.0306689	−	0.0601911i	0.00102116	−	0.00200414i
$903$	−13.0228	−	5.27409i	−0.433373	−	0.175511i
$904$	−10.2558	−	14.1160i	−0.341104	−	0.469490i
$905$		0			0
$906$	3.47751	+	7.81061i	0.115532	+	0.259490i
$907$	−5.62950	−	21.0096i	−0.186924	−	0.697611i	−0.994210	−	0.107451i	$-0.965731\pi$
$907$	−5.62950	−	21.0096i	−0.186924	−	0.697611i	0.807286	−	0.590160i	$-0.200936\pi$
$908$	−8.25846	−	10.1983i	−0.274067	−	0.338444i
$909$	−1.90450	+	5.86143i	−0.0631681	+	0.194411i
$910$		0			0
$911$	1.19819	+	3.68765i	0.0396978	+	0.122177i	0.968941	−	0.247290i	$-0.0795401\pi$
$911$	1.19819	+	3.68765i	0.0396978	+	0.122177i	−0.929244	+	0.369468i	$0.879540\pi$
$912$	−2.38654	+	3.67495i	−0.0790263	+	0.121690i
$913$	−8.29332	−	0.434634i	−0.274469	−	0.0143843i
$914$	3.71923	−	17.4976i	0.123021	−	0.578769i
$915$		0			0
$916$	4.13261	+	1.34277i	0.136545	+	0.0443663i
$917$	−24.8229	+	36.7359i	−0.819724	+	1.21313i
$918$	2.71979	+	2.71979i	0.0897665	+	0.0897665i
$919$	7.89240	+	0.829525i	0.260346	+	0.0273635i	0.233802	−	0.972284i	$-0.424883\pi$
$919$	7.89240	+	0.829525i	0.260346	+	0.0273635i	0.0265440	+	0.999648i	$0.491550\pi$
$920$		0			0
$921$	−0.387796	−	3.68963i	−0.0127783	−	0.121578i
$922$	−6.76190	−	17.6154i	−0.222691	−	0.580131i
$923$	19.3127	+	9.84030i	0.635684	+	0.323897i
$924$	−5.26745	+	1.60566i	−0.173286	+	0.0528224i
$925$		0			0
$926$	2.39577	+	4.14960i	0.0787299	+	0.136364i
$927$	−6.02647	−	9.27996i	−0.197935	−	0.304794i
$928$	−25.3262	+	31.2753i	−0.831375	+	1.02666i
$929$	−44.5122	−	19.8181i	−1.46040	−	0.650211i	−0.485779	−	0.874082i	$-0.661464\pi$
$929$	−44.5122	−	19.8181i	−1.46040	−	0.650211i	−0.974619	+	0.223870i	$0.928131\pi$
$930$		0			0
$931$	32.6017	−	17.2656i	1.06848	−	0.565856i
$932$	28.7785	−	28.7785i	0.942670	−	0.942670i
$933$	5.39226	−	4.36656i	0.176535	−	0.142955i
$934$	−15.2557	−	16.9432i	−0.499182	−	0.554398i
$935$		0			0
$936$	6.85360	+	6.17101i	0.224017	+	0.201706i
$937$	−36.8319	+	18.7668i	−1.20325	+	0.613085i	−0.936495	−	0.350680i	$-0.885950\pi$
$937$	−36.8319	+	18.7668i	−1.20325	+	0.613085i	−0.266752	+	0.963765i	$0.585950\pi$
$938$	−12.5754	+	12.1238i	−0.410601	+	0.395858i
$939$	11.9642	−	3.88740i	0.390437	−	0.126861i
$940$		0			0
$941$	33.6343	−	30.2845i	1.09645	−	0.987246i	0.0964808	−	0.995335i	$-0.469241\pi$
$941$	33.6343	−	30.2845i	1.09645	−	0.987246i	0.999967	+	0.00808856i	$0.00257470\pi$
$942$	−4.11824	+	10.7284i	−0.134179	+	0.349549i
$943$	0.0724368	+	0.0194094i	0.00235887	+	0.000632057i
$944$	2.88969	+	2.09948i	0.0940513	+	0.0683323i
$945$		0			0
$946$	−3.94694	+	2.86762i	−0.128326	+	0.0932344i
$947$	−7.46435	+	2.86529i	−0.242559	+	0.0931095i	−0.476611	−	0.879115i	$-0.658135\pi$
$947$	−7.46435	+	2.86529i	−0.242559	+	0.0931095i	0.234052	+	0.972224i	$0.424801\pi$
$948$	13.7218	−	8.91106i	0.445664	−	0.289418i
$949$	2.86640	+	1.65492i	0.0930472	+	0.0537208i
$950$		0			0
$951$			10.1006i			0.327535i
$952$	−4.97074	−	4.17795i	−0.161102	−	0.135408i
$953$	−1.51399	−	0.239793i	−0.0490430	−	0.00776765i	0.131865	−	0.991268i	$-0.457904\pi$
$953$	−1.51399	−	0.239793i	−0.0490430	−	0.00776765i	−0.180908	+	0.983500i	$0.557904\pi$
$954$	6.13884	−	13.7881i	0.198752	−	0.446405i
$955$		0			0
$956$	−4.09839	+	1.82472i	−0.132551	+	0.0590156i
$957$	−2.65289	+	9.90071i	−0.0857556	+	0.320044i
$958$	6.98204	−	1.10585i	0.225580	−	0.0357283i
$959$	4.50644	−	7.48595i	0.145520	−	0.241734i
$960$		0			0
$961$	−43.5019	+	48.3137i	−1.40329	+	1.55851i
$962$	0.626538	−	11.9551i	0.0202004	−	0.385447i
$963$	0.896813	−	17.1122i	0.0288994	−	0.551433i
$964$	−25.0493	+	27.8201i	−0.806783	+	0.896024i
$965$		0			0
$966$	1.28071	+	2.31497i	0.0412062	+	0.0744830i
$967$	19.6701	−	3.11543i	0.632547	−	0.100186i	0.168076	−	0.985774i	$-0.446245\pi$
$967$	19.6701	−	3.11543i	0.632547	−	0.100186i	0.464471	+	0.885588i	$0.346245\pi$
$968$	6.31056	−	23.5513i	0.202829	−	0.756969i
$969$	−5.02813	+	2.23867i	−0.161527	+	0.0719163i
$970$		0			0
$971$	−12.0980	+	27.1725i	−0.388242	+	0.872007i	0.608665	+	0.793427i	$0.291705\pi$
$971$	−12.0980	+	27.1725i	−0.388242	+	0.872007i	−0.996908	+	0.0785798i	$0.974961\pi$
$972$	−20.8327	−	3.29957i	−0.668208	−	0.105834i
$973$	−22.4751	−	3.98212i	−0.720519	−	0.127661i
$974$		−	0.412847i		−	0.0132285i
$975$		0			0
$976$	−2.93248	−	1.69307i	−0.0938663	−	0.0541938i
$977$	26.8835	−	17.4584i	0.860080	−	0.558542i	−0.0375488	−	0.999295i	$-0.511955\pi$
$977$	26.8835	−	17.4584i	0.860080	−	0.558542i	0.897629	+	0.440752i	$0.145288\pi$
$978$	2.84595	−	1.09246i	0.0910033	−	0.0349329i
$979$	−16.8565	+	12.2469i	−0.538735	+	0.391414i
$980$		0			0
$981$	−15.2332	−	11.0676i	−0.486358	−	0.353360i
$982$	4.81745	+	1.29083i	0.153731	+	0.0411921i
$983$	−13.8198	+	36.0017i	−0.440782	+	1.14828i	0.515774	+	0.856725i	$0.327504\pi$
$983$	−13.8198	+	36.0017i	−0.440782	+	1.14828i	−0.956555	+	0.291550i	$0.905829\pi$
$984$	0.144235	−	0.129870i	0.00459803	−	0.00414009i
$985$		0			0
$986$	−4.72497	+	1.53524i	−0.150474	+	0.0488919i
$987$	0.384988	+	0.399326i	0.0122543	+	0.0127107i
$988$	−13.1739	+	6.71245i	−0.419118	+	0.213551i
$989$	−4.02477	−	3.62392i	−0.127980	−	0.115234i
$990$		0			0
$991$	3.12017	+	3.46530i	0.0991154	+	0.110079i	0.790662	−	0.612253i	$-0.209737\pi$
$991$	3.12017	+	3.46530i	0.0991154	+	0.110079i	−0.691546	+	0.722332i	$0.743070\pi$
$992$	44.5799	−	36.1001i	1.41541	−	1.14618i
$993$	5.73911	−	5.73911i	0.182125	−	0.182125i
$994$	−21.7735	+	4.21366i	−0.690613	+	0.133649i
$995$		0			0
$996$	−8.95976	−	3.98914i	−0.283901	−	0.126401i
$997$	10.2537	−	12.6622i	0.324737	−	0.401017i	−0.588466	−	0.808522i	$-0.700268\pi$
$997$	10.2537	−	12.6622i	0.324737	−	0.401017i	0.913203	+	0.407505i	$0.133601\pi$
$998$	−2.65600	−	4.08988i	−0.0840743	−	0.129463i
$999$	20.3931	+	35.3220i	0.645210	+	1.11754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.143.12		288
5.2	odd	4		875.2.bb.c.857.7		288
5.3	odd	4		175.2.x.a.17.12	yes	288
5.4	even	2		875.2.bb.b.143.7		288
7.5	odd	6	inner	875.2.bb.a.768.12		288
25.3	odd	20		875.2.bb.b.507.7		288
25.4	even	10		175.2.x.a.3.7	✓	288
25.21	even	5		875.2.bb.c.493.12		288
25.22	odd	20	inner	875.2.bb.a.507.12		288
35.12	even	12		875.2.bb.c.607.12		288
35.19	odd	6		875.2.bb.b.768.7		288
35.33	even	12		175.2.x.a.117.7	yes	288
175.47	even	60	inner	875.2.bb.a.257.12		288
175.54	odd	30		175.2.x.a.103.12	yes	288
175.96	odd	30		875.2.bb.c.243.7		288
175.103	even	60		875.2.bb.b.257.7		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.7	✓	288	25.4	even	10
175.2.x.a.17.12	yes	288	5.3	odd	4
175.2.x.a.103.12	yes	288	175.54	odd	30
175.2.x.a.117.7	yes	288	35.33	even	12
875.2.bb.a.143.12		288	1.1	even	1	trivial
875.2.bb.a.257.12		288	175.47	even	60	inner
875.2.bb.a.507.12		288	25.22	odd	20	inner
875.2.bb.a.768.12		288	7.5	odd	6	inner
875.2.bb.b.143.7		288	5.4	even	2
875.2.bb.b.257.7		288	175.103	even	60
875.2.bb.b.507.7		288	25.3	odd	20
875.2.bb.b.768.7		288	35.19	odd	6
875.2.bb.c.243.7		288	175.96	odd	30
875.2.bb.c.493.12		288	25.21	even	5
875.2.bb.c.607.12		288	35.12	even	12
875.2.bb.c.857.7		288	5.2	odd	4

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0406780 + 0.776182i) q^{2} +(0.872864 + 0.706831i) q^{3} +(1.38824 - 0.145910i) q^{4} +(-0.513123 + 0.706254i) q^{6} +(-1.24404 + 2.33503i) q^{7} +(0.412900 + 2.60695i) q^{8} +(-0.361454 - 1.70051i) q^{9} +(1.29854 + 0.276014i) q^{11} +(1.31488 + 0.853891i) q^{12} +(0.912442 + 1.79077i) q^{13} +(-1.86302 - 0.870614i) q^{14} +(0.724094 - 0.153911i) q^{16} +(0.868077 + 0.333224i) q^{17} +(1.30520 - 0.349728i) q^{18} +(-0.550884 + 5.24131i) q^{19} +(-2.73635 + 1.15884i) q^{21} +(-0.161415 + 1.01913i) q^{22} +(-1.14388 + 0.0599482i) q^{23} +(-1.48227 + 2.56736i) q^{24} +(-1.35285 + 0.781066i) q^{26} +(2.41619 - 4.74204i) q^{27} +(-1.38631 + 3.42310i) q^{28} +(4.04060 + 5.56140i) q^{29} +(-3.98545 - 8.95147i) q^{31} +(1.51519 + 5.65478i) q^{32} +(0.938356 + 1.15877i) q^{33} +(-0.223331 + 0.687341i) q^{34} +(-0.749906 - 2.30797i) q^{36} +(-4.17386 + 6.42719i) q^{37} +(-4.09062 - 0.214381i) q^{38} +(-0.469333 + 2.20804i) q^{39} +(-0.0622653 - 0.0202312i) q^{41} +(-1.01078 - 2.07676i) q^{42} +(3.34331 + 3.34331i) q^{43} +(1.84296 + 0.193703i) q^{44} +(-0.0930614 - 0.885420i) q^{46} +(-0.0668935 - 0.174263i) q^{47} +(0.740824 + 0.377469i) q^{48} +(-3.90475 - 5.80972i) q^{49} +(0.522180 + 0.904443i) q^{51} +(1.52798 + 2.35288i) q^{52} +(7.02928 - 8.68044i) q^{53} +(3.77898 + 1.68251i) q^{54} +(-6.60097 - 2.27900i) q^{56} +(-4.18557 + 4.18557i) q^{57} +(-4.15230 + 3.36247i) q^{58} +(3.22860 + 3.58572i) q^{59} +(-3.39928 - 3.06073i) q^{61} +(6.78585 - 3.45756i) q^{62} +(4.42040 + 1.27148i) q^{63} +(-2.91943 + 0.948580i) q^{64} +(-0.861248 + 0.775472i) q^{66} +(3.04412 - 7.93020i) q^{67} +(1.25372 + 0.335933i) q^{68} +(-1.04082 - 0.756203i) q^{69} +(8.72491 - 6.33902i) q^{71} +(4.28389 - 1.64443i) q^{72} +(1.38114 - 0.896926i) q^{73} +(-5.15845 - 2.97823i) q^{74} +7.35658i q^{76} +(-2.25993 + 2.68877i) q^{77} +(-1.73293 - 0.274469i) q^{78} +(4.24463 - 9.53360i) q^{79} +(0.696236 - 0.309984i) q^{81} +(0.0131703 - 0.0491522i) q^{82} +(-6.17863 + 0.978599i) q^{83} +(-3.62962 + 2.00801i) q^{84} +(-2.45902 + 2.73102i) q^{86} +(-0.404083 + 7.71037i) q^{87} +(-0.183385 + 3.49920i) q^{88} +(-10.5019 + 11.6635i) q^{89} +(-5.31661 - 0.0971966i) q^{91} +(-1.57923 + 0.250126i) q^{92} +(2.84842 - 10.6304i) q^{93} +(0.132539 - 0.0590102i) q^{94} +(-2.67442 + 6.00684i) q^{96} +(-17.1820 - 2.72136i) q^{97} +(4.35057 - 3.26713i) q^{98} -2.30795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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