LMFDB - Embedded newform 875.2.bb.c.607.12

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			607.12
Character	$\chi$	$=$	875.607
Dual form			875.2.bb.c.493.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.423319 + 0.651855i) q^{2} +(-0.402507 - 1.04857i) q^{3} +(0.567758 - 1.27521i) q^{4} +(0.513123 - 0.706254i) q^{6} +(-1.24404 - 2.33503i) q^{7} +(2.60695 - 0.412900i) q^{8} +(1.29196 - 1.16328i) q^{9} +(-0.888306 + 0.986564i) q^{11} +(-1.56566 - 0.0820529i) q^{12} +(-1.79077 + 0.912442i) q^{13} +(0.995478 - 1.79939i) q^{14} +(-0.495338 - 0.550128i) q^{16} +(0.585165 + 0.722619i) q^{17} +(1.30520 + 0.349728i) q^{18} +(4.81455 - 2.14358i) q^{19} +(-1.94770 + 2.24432i) q^{21} +(-1.01913 - 0.161415i) q^{22} +(0.960654 - 0.623856i) q^{23} +(-1.48227 - 2.56736i) q^{24} +(-1.35285 - 0.781066i) q^{26} +(-4.74204 - 2.41619i) q^{27} +(-3.68396 + 0.260667i) q^{28} +(-4.04060 - 5.56140i) q^{29} +(-9.74492 - 1.02423i) q^{31} +(1.51519 - 5.65478i) q^{32} +(1.39203 + 0.534349i) q^{33} +(-0.223331 + 0.687341i) q^{34} +(-0.749906 - 2.30797i) q^{36} +(-0.401079 + 7.65304i) q^{37} +(3.43539 + 2.23097i) q^{38} +(1.67755 + 1.51047i) q^{39} +(0.0622653 + 0.0202312i) q^{41} +(-2.28747 - 0.319555i) q^{42} +(3.34331 - 3.34331i) q^{43} +(0.753729 + 1.69290i) q^{44} +(0.813327 + 0.362116i) q^{46} +(0.145063 + 0.117470i) q^{47} +(-0.377469 + 0.740824i) q^{48} +(-3.90475 + 5.80972i) q^{49} +(0.522180 - 0.904443i) q^{51} +(0.146828 + 2.80164i) q^{52} +(10.4278 - 4.00284i) q^{53} +(-0.432393 - 4.11394i) q^{54} +(-4.20727 - 5.57365i) q^{56} +(-4.18557 - 4.18557i) q^{57} +(1.91476 - 4.98813i) q^{58} +(-4.71962 + 1.00319i) q^{59} +(0.951026 - 4.47423i) q^{61} +(-3.45756 - 6.78585i) q^{62} +(-4.32354 - 1.56960i) q^{63} +(2.91943 - 0.948580i) q^{64} +(0.240954 + 1.13360i) q^{66} +(-6.60139 + 5.34570i) q^{67} +(1.25372 - 0.335933i) q^{68} +(-1.04082 - 0.756203i) q^{69} +(8.72491 - 6.33902i) q^{71} +(2.88774 - 3.56607i) q^{72} +(-1.64457 + 0.0861882i) q^{73} +(-5.15845 + 2.97823i) q^{74} -7.35658i q^{76} +(3.40874 + 0.846904i) q^{77} +(-0.274469 + 1.73293i) q^{78} +(10.3787 - 1.09084i) q^{79} +(-0.0796638 + 0.757950i) q^{81} +(0.0131703 + 0.0491522i) q^{82} +(-0.978599 - 6.17863i) q^{83} +(1.75614 + 3.75795i) q^{84} +(3.59464 + 0.764065i) q^{86} +(-4.20513 + 6.47533i) q^{87} +(-1.90842 + 2.93870i) q^{88} +(15.3519 + 3.26314i) q^{89} +(4.35836 + 3.04639i) q^{91} +(-0.250126 - 1.57923i) q^{92} +(2.84842 + 10.6304i) q^{93} +(-0.0151652 + 0.144287i) q^{94} +(-6.53929 + 0.687307i) q^{96} +(-2.72136 + 17.1820i) q^{97} +(-5.44005 - 0.0859631i) q^{98} +2.30795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.423319	+	0.651855i	0.299332	+	0.460931i	0.956049	−	0.293206i	$-0.0947222\pi$
$2$	0.423319	+	0.651855i	0.299332	+	0.460931i	−0.656717	+	0.754137i	$0.728056\pi$
$3$	−0.402507	−	1.04857i	−0.232387	−	0.605390i	0.766953	−	0.641703i	$-0.221772\pi$
$3$	−0.402507	−	1.04857i	−0.232387	−	0.605390i	−0.999340	+	0.0363135i	$0.988439\pi$
$4$	0.567758	−	1.27521i	0.283879	−	0.637603i
$5$		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
$8$	2.60695	−	0.412900i	0.921695	−	0.145982i
$9$	1.29196	−	1.16328i	0.430652	−	0.387761i
$10$		0			0
$11$	−0.888306	+	0.986564i	−0.267834	+	0.297460i	−0.862027	−	0.506863i	$-0.830805\pi$
$11$	−0.888306	+	0.986564i	−0.267834	+	0.297460i	0.594192	+	0.804323i	$0.297472\pi$
$12$	−1.56566	−	0.0820529i	−0.451968	−	0.0236866i
$13$	−1.79077	+	0.912442i	−0.496670	+	0.253066i	−0.684336	−	0.729167i	$-0.739908\pi$
$13$	−1.79077	+	0.912442i	−0.496670	+	0.253066i	0.187666	+	0.982233i	$0.439908\pi$
$14$	0.995478	−	1.79939i	0.266053	−	0.480908i
$15$		0			0
$16$	−0.495338	−	0.550128i	−0.123834	−	0.137532i
$17$	0.585165	+	0.722619i	0.141923	+	0.175261i	0.843151	−	0.537676i	$-0.180698\pi$
$17$	0.585165	+	0.722619i	0.141923	+	0.175261i	−0.701228	+	0.712937i	$0.747364\pi$
$18$	1.30520	+	0.349728i	0.307639	+	0.0824316i
$19$	4.81455	−	2.14358i	1.10453	−	0.491770i	0.228268	−	0.973598i	$-0.426694\pi$
$19$	4.81455	−	2.14358i	1.10453	−	0.491770i	0.876266	+	0.481828i	$0.160027\pi$
$20$		0			0
$21$	−1.94770	+	2.24432i	−0.425023	+	0.489750i
$22$	−1.01913	−	0.161415i	−0.217280	−	0.0344138i
$23$	0.960654	−	0.623856i	0.200310	−	0.130083i	−0.440586	−	0.897710i	$-0.645229\pi$
$23$	0.960654	−	0.623856i	0.200310	−	0.130083i	0.640897	+	0.767627i	$0.278563\pi$
$24$	−1.48227	−	2.56736i	−0.302566	−	0.524060i
$25$		0			0
$26$	−1.35285	−	0.781066i	−0.265315	−	0.153180i
$27$	−4.74204	−	2.41619i	−0.912607	−	0.464996i
$28$	−3.68396	+	0.260667i	−0.696202	+	0.0492614i
$29$	−4.04060	−	5.56140i	−0.750320	−	1.03273i	−0.997958	−	0.0638742i	$-0.979654\pi$
$29$	−4.04060	−	5.56140i	−0.750320	−	1.03273i	0.247638	−	0.968853i	$-0.420346\pi$
$30$		0			0
$31$	−9.74492	−	1.02423i	−1.75024	−	0.183958i	−0.825460	−	0.564461i	$-0.809084\pi$
$31$	−9.74492	−	1.02423i	−1.75024	−	0.183958i	−0.924780	+	0.380503i	$0.875751\pi$
$32$	1.51519	−	5.65478i	0.267851	−	0.999634i
$33$	1.39203	+	0.534349i	0.242321	+	0.0930182i
$34$	−0.223331	+	0.687341i	−0.0383009	+	0.117878i
$35$		0			0
$36$	−0.749906	−	2.30797i	−0.124984	−	0.384662i
$37$	−0.401079	+	7.65304i	−0.0659369	+	1.25815i	0.742612	+	0.669722i	$0.233587\pi$
$37$	−0.401079	+	7.65304i	−0.0659369	+	1.25815i	−0.808549	+	0.588430i	$0.799746\pi$
$38$	3.43539	+	2.23097i	0.557295	+	0.361911i
$39$	1.67755	+	1.51047i	0.268623	+	0.241869i
$40$		0			0
$41$	0.0622653	+	0.0202312i	0.00972421	+	0.00315959i	0.313875	−	0.949464i	$-0.398373\pi$
$41$	0.0622653	+	0.0202312i	0.00972421	+	0.00315959i	−0.304151	+	0.952624i	$0.598373\pi$
$42$	−2.28747	−	0.319555i	−0.352964	−	0.0493085i
$43$	3.34331	−	3.34331i	0.509850	−	0.509850i	−0.404630	−	0.914480i	$-0.632600\pi$
$43$	3.34331	−	3.34331i	0.509850	−	0.509850i	0.914480	+	0.404630i	$0.132600\pi$
$44$	0.753729	+	1.69290i	0.113629	+	0.255215i
$45$		0			0
$46$	0.813327	+	0.362116i	0.119919	+	0.0533912i
$47$	0.145063	+	0.117470i	0.0211596	+	0.0171347i	0.639842	−	0.768507i	$-0.279000\pi$
$47$	0.145063	+	0.117470i	0.0211596	+	0.0171347i	−0.618682	+	0.785641i	$0.712333\pi$
$48$	−0.377469	+	0.740824i	−0.0544829	+	0.106929i
$49$	−3.90475	+	5.80972i	−0.557822	+	0.829961i
$50$		0			0
$51$	0.522180	−	0.904443i	0.0731199	−	0.126647i
$52$	0.146828	+	2.80164i	0.0203614	+	0.388518i
$53$	10.4278	−	4.00284i	1.43236	−	0.549832i	0.486292	−	0.873796i	$-0.338349\pi$
$53$	10.4278	−	4.00284i	1.43236	−	0.549832i	0.946069	+	0.323964i	$0.105016\pi$
$54$	−0.432393	−	4.11394i	−0.0588412	−	0.559837i
$55$		0			0
$56$	−4.20727	−	5.57365i	−0.562220	−	0.744810i
$57$	−4.18557	−	4.18557i	−0.554392	−	0.554392i
$58$	1.91476	−	4.98813i	0.251421	−	0.654974i
$59$	−4.71962	+	1.00319i	−0.614442	+	0.130604i	−0.504612	−	0.863347i	$-0.668364\pi$
$59$	−4.71962	+	1.00319i	−0.614442	+	0.130604i	−0.109831	+	0.993950i	$0.535031\pi$
$60$		0			0
$61$	0.951026	−	4.47423i	0.121766	−	0.572866i	−0.874386	−	0.485231i	$-0.838736\pi$
$61$	0.951026	−	4.47423i	0.121766	−	0.572866i	0.996153	−	0.0876354i	$-0.0279310\pi$
$62$	−3.45756	−	6.78585i	−0.439111	−	0.861804i
$63$	−4.32354	−	1.56960i	−0.544715	−	0.197750i
$64$	2.91943	−	0.948580i	0.364929	−	0.118573i
$65$		0			0
$66$	0.240954	+	1.13360i	0.0296594	+	0.139536i
$67$	−6.60139	+	5.34570i	−0.806488	+	0.653081i	−0.941217	−	0.337801i	$-0.890317\pi$
$67$	−6.60139	+	5.34570i	−0.806488	+	0.653081i	0.134730	+	0.990882i	$0.456983\pi$
$68$	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	$0.0789563\pi$
$72$	2.88774	−	3.56607i	0.340324	−	0.420265i
$73$	−1.64457	+	0.0861882i	−0.192482	+	0.0100876i	−0.148333	−	0.988937i	$-0.547391\pi$
$73$	−1.64457	+	0.0861882i	−0.192482	+	0.0100876i	−0.0441488	+	0.999025i	$0.514058\pi$
$74$	−5.15845	+	2.97823i	−0.599658	+	0.346213i
$75$		0			0
$76$		−	7.35658i		−	0.843857i
$77$	3.40874	+	0.846904i	0.388462	+	0.0965136i
$78$	−0.274469	+	1.73293i	−0.0310775	+	0.196216i
$79$	10.3787	−	1.09084i	1.16769	−	0.122729i	0.499224	−	0.866473i	$-0.333618\pi$
$79$	10.3787	−	1.09084i	1.16769	−	0.122729i	0.668465	+	0.743744i	$0.266952\pi$
$80$		0			0
$81$	−0.0796638	+	0.757950i	−0.00885153	+	0.0842167i
$82$	0.0131703	+	0.0491522i	0.00145442	+	0.00542796i
$83$	−0.978599	−	6.17863i	−0.107415	−	0.678193i	−0.981362	−	0.192170i	$-0.938447\pi$
$83$	−0.978599	−	6.17863i	−0.107415	−	0.678193i	0.873946	−	0.486022i	$-0.161553\pi$
$84$	1.75614	+	3.75795i	0.191611	+	0.410026i
$85$		0			0
$86$	3.59464	+	0.764065i	0.387620	+	0.0823912i
$87$	−4.20513	+	6.47533i	−0.450837	+	0.694228i
$88$	−1.90842	+	2.93870i	−0.203438	+	0.313267i
$89$	15.3519	+	3.26314i	1.62729	+	0.345892i	0.929046	−	0.369964i	$-0.120630\pi$
$89$	15.3519	+	3.26314i	1.62729	+	0.345892i	0.698248	+	0.715856i	$0.253963\pi$
$90$		0			0
$91$	4.35836	+	3.04639i	0.456880	+	0.319349i
$92$	−0.250126	−	1.57923i	−0.0260774	−	0.164646i
$93$	2.84842	+	10.6304i	0.295367	+	1.10233i
$94$	−0.0151652	+	0.144287i	−0.00156417	+	0.0148821i
$95$		0			0
$96$	−6.53929	+	0.687307i	−0.667413	+	0.0701479i
$97$	−2.72136	+	17.1820i	−0.276312	+	1.74457i	0.325149	+	0.945663i	$0.394586\pi$
$97$	−2.72136	+	17.1820i	−0.276312	+	1.74457i	−0.601461	+	0.798902i	$0.705414\pi$
$98$	−5.44005	−	0.0859631i	−0.549528	−	0.00868358i
$99$			2.30795i			0.231958i
$100$		0			0
$101$	−3.07011	+	1.77253i	−0.305487	+	0.176373i	−0.644905	−	0.764262i	$-0.723103\pi$
$101$	−3.07011	+	1.77253i	−0.305487	+	0.176373i	0.339418	+	0.940636i	$0.389770\pi$
$102$	0.810614	−	0.0424825i	0.0802628	−	0.00420639i
$103$	4.00546	−	4.94633i	0.394669	−	0.487376i	−0.540617	−	0.841269i	$-0.681809\pi$
$103$	4.00546	−	4.94633i	0.394669	−	0.487376i	0.935286	+	0.353893i	$0.115142\pi$
$104$	−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	0.232647	−	0.972561i	$-0.425261\pi$
$107$	9.52075	−	2.55108i	0.920406	−	0.246622i	0.687759	+	0.725939i	$0.258595\pi$
$108$	−5.77347	+	4.67527i	−0.555553	+	0.449878i
$109$	−2.25184	−	10.5941i	−0.215687	−	1.01473i	−0.944118	−	0.329609i	$-0.893083\pi$
$109$	−2.25184	−	10.5941i	−0.215687	−	1.01473i	0.728430	−	0.685120i	$-0.240250\pi$
$110$		0			0
$111$	8.18615	−	2.65984i	0.776995	−	0.252461i
$112$	−0.668350	+	1.84101i	−0.0631531	+	0.173959i
$113$	3.00115	+	5.89008i	0.282324	+	0.554092i	0.988002	−	0.154440i	$-0.0493575\pi$
$113$	3.00115	+	5.89008i	0.282324	+	0.554092i	−0.705678	+	0.708533i	$0.749357\pi$
$114$	0.956551	−	4.50022i	0.0895892	−	0.421484i
$115$		0			0
$116$	−9.38601	+	1.99506i	−0.871470	+	0.185237i
$117$	−1.25217	+	3.26200i	−0.115763	+	0.301572i
$118$	−2.65184	−	2.65184i	−0.244122	−	0.244122i
$119$	0.959372	−	2.26534i	0.0879455	−	0.207664i
$120$		0			0
$121$	0.965593	+	9.18700i	0.0877811	+	0.835182i
$122$	3.31913	−	1.27410i	0.300500	−	0.115351i
$123$	−0.00384843	−	0.0734325i	−0.000347002	−	0.00662118i
$124$	−6.83886	+	11.8453i	−0.614148	+	1.06374i
$125$		0			0
$126$	−0.807091	−	3.48276i	−0.0719014	−	0.310269i
$127$	8.39463	−	16.4754i	0.744903	−	1.46195i	−0.137023	−	0.990568i	$-0.543754\pi$
$127$	8.39463	−	16.4754i	0.744903	−	1.46195i	0.881927	−	0.471387i	$-0.156246\pi$
$128$	−7.24505	−	5.86692i	−0.640378	−	0.518568i
$129$	−4.85139	−	2.15998i	−0.427141	−	0.190175i
$130$		0			0
$131$	6.81590	+	15.3088i	0.595508	+	1.33753i	0.920102	+	0.391679i	$0.128106\pi$
$131$	6.81590	+	15.3088i	0.595508	+	1.33753i	−0.324594	+	0.945853i	$0.605228\pi$
$132$	1.47174	−	1.47174i	0.128098	−	0.128098i
$133$	−10.9948	−	8.57545i	−0.953370	−	0.743586i
$134$	−6.27911	−	2.04021i	−0.542433	−	0.176247i
$135$		0			0
$136$	1.82386	+	1.64221i	0.156395	+	0.140819i
$137$	2.76974	+	1.79869i	0.236635	+	0.153673i	0.657509	−	0.753446i	$-0.271610\pi$
$137$	2.76974	+	1.79869i	0.236635	+	0.153673i	−0.420874	+	0.907119i	$0.638277\pi$
$138$	0.0523334	−	0.998581i	0.00445492	−	0.0850048i
$139$	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
$142$	7.82554	+	3.00394i	0.656705	+	0.252085i
$143$	0.690568	−	2.57723i	0.0577482	−	0.215519i
$144$	−1.27991	−	0.134524i	−0.106659	−	0.0112103i
$145$		0			0
$146$	−0.752360	−	1.03553i	−0.0622658	−	0.0857015i
$147$	7.66357	+	1.75594i	0.632080	+	0.144827i
$148$	9.53148	+	4.85653i	0.783483	+	0.399205i
$149$	0.0342344	+	0.0197652i	0.00280459	+	0.00161923i	0.501402	−	0.865215i	$-0.332818\pi$
$149$	0.0342344	+	0.0197652i	0.00280459	+	0.00161923i	−0.498597	+	0.866834i	$0.666151\pi$
$150$		0			0
$151$	4.89690	+	8.48169i	0.398504	+	0.690230i	0.993542	−	0.113468i	$-0.0361960\pi$
$151$	4.89690	+	8.48169i	0.398504	+	0.690230i	−0.595037	+	0.803698i	$0.702863\pi$
$152$	11.6662	−	7.57612i	0.946254	−	0.614505i
$153$	1.59662	+	0.252879i	0.129079	+	0.0204441i
$154$	0.890929	+	2.58052i	0.0717931	+	0.207944i
$155$		0			0
$156$	2.87861	−	1.28164i	0.230473	−	0.102613i
$157$	12.7152	+	3.40702i	1.01478	+	0.271910i	0.727626	−	0.685974i	$-0.240624\pi$
$157$	12.7152	+	3.40702i	1.01478	+	0.271910i	0.287156	+	0.957884i	$0.407290\pi$
$158$	5.10455	+	6.30360i	0.406096	+	0.501487i
$159$	−8.39448	−	9.32301i	−0.665725	−	0.739363i
$160$		0			0
$161$	−2.65181	−	1.46706i	−0.208992	−	0.115621i
$162$	−0.527797	+	0.268926i	−0.0414676	+	0.0211288i
$163$	3.48720	+	0.182756i	0.273138	+	0.0143146i	0.188413	−	0.982090i	$-0.439666\pi$
$163$	3.48720	+	0.182756i	0.273138	+	0.0143146i	0.0847249	+	0.996404i	$0.472999\pi$
$164$	0.0611506	−	0.0679147i	0.00477506	−	0.00530324i
$165$		0			0
$166$	3.61331	−	3.25344i	0.280447	−	0.252516i
$167$	−18.9176	+	2.99626i	−1.46389	+	0.231857i	−0.836979	−	0.547235i	$-0.815681\pi$
$167$	−18.9176	+	2.99626i	−1.46389	+	0.231857i	−0.626910	+	0.779092i	$0.715681\pi$
$168$	−4.15088	+	6.65503i	−0.320247	+	0.513447i
$169$	−5.26691	+	7.24928i	−0.405147	+	0.557637i
$170$		0			0
$171$	3.72661	−	8.37009i	0.284981	−	0.640077i
$172$	−2.36522	−	6.16160i	−0.180346	−	0.469818i
$173$	2.70053	+	4.15845i	0.205317	+	0.316161i	0.926296	−	0.376796i	$-0.122974\pi$
$173$	2.70053	+	4.15845i	0.205317	+	0.316161i	−0.720979	+	0.692957i	$0.756308\pi$
$174$	−6.00109			−0.454941
$175$		0			0
$176$	0.982748			0.0740774
$177$	2.95159	+	4.54504i	0.221855	+	0.341626i
$178$	4.37165	+	11.3885i	0.327669	+	0.853607i
$179$	8.23757	−	18.5019i	0.615705	−	1.38290i	−0.289194	−	0.957270i	$-0.593387\pi$
$179$	8.23757	−	18.5019i	0.615705	−	1.38290i	0.904899	−	0.425626i	$-0.139946\pi$
$180$		0			0
$181$	−2.67679	+	3.68429i	−0.198965	+	0.273851i	−0.896828	−	0.442380i	$-0.854134\pi$
$181$	−2.67679	+	3.68429i	−0.198965	+	0.273851i	0.697863	+	0.716231i	$0.254134\pi$
$182$	−0.140827	+	4.13061i	−0.0104388	+	0.306181i
$183$	−5.07431	+	0.803693i	−0.375104	+	0.0594107i
$184$	2.24679	−	2.02301i	0.165635	−	0.149139i
$185$		0			0
$186$	−5.72372	+	6.35683i	−0.419683	+	0.466105i
$187$	−1.23272	−	0.0646039i	−0.0901451	−	0.00472430i
$188$	0.232159	−	0.118291i	0.0169319	−	0.00862725i
$189$	0.257382	+	14.0787i	0.0187218	+	1.02407i
$190$		0			0
$191$	−10.3573	−	11.5029i	−0.749427	−	0.832323i	0.240976	−	0.970531i	$-0.422532\pi$
$191$	−10.3573	−	11.5029i	−0.749427	−	0.832323i	−0.990403	+	0.138208i	$0.955866\pi$
$192$	−2.16974	−	2.67940i	−0.156587	−	0.193369i
$193$	−7.57383	−	2.02940i	−0.545176	−	0.146080i	−0.0242890	−	0.999705i	$-0.507732\pi$
$193$	−7.57383	−	2.02940i	−0.545176	−	0.146080i	−0.520887	+	0.853625i	$0.674399\pi$
$194$	−12.3522	+	5.49953i	−0.886833	+	0.394843i
$195$		0			0
$196$	5.19164	+	8.27788i	0.370831	+	0.591277i
$197$	16.1577	+	2.55912i	1.15119	+	0.182330i	0.702718	−	0.711469i	$-0.251970\pi$
$197$	16.1577	+	2.55912i	1.15119	+	0.182330i	0.448469	+	0.893799i	$0.351970\pi$
$198$	−1.50445	+	0.976999i	−0.106916	+	0.0694323i
$199$	13.6561	+	23.6530i	0.968053	+	1.67672i	0.701179	+	0.712985i	$0.252657\pi$
$199$	13.6561	+	23.6530i	0.968053	+	1.67672i	0.266874	+	0.963731i	$0.414009\pi$
$200$		0			0
$201$	8.26242	+	4.77031i	0.582786	+	0.336472i
$202$	−2.45507	−	1.25092i	−0.172738	−	0.0880144i
$203$	−7.95942	+	16.3535i	−0.558641	+	1.14779i
$204$	−0.856878	−	1.17939i	−0.0599935	−	0.0825739i
$205$		0			0
$206$	4.91987	+	0.517100i	0.342784	+	0.0360280i
$207$	0.515402	−	1.92351i	0.0358229	−	0.133693i
$208$	1.38899	+	0.533185i	0.0963095	+	0.0369697i
$209$	−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	$0.731328\pi$
$212$	0.815998	−	15.5702i	0.0560430	−	1.06936i
$213$	−10.1587	−	6.59714i	−0.696063	−	0.452029i
$214$	5.69325	+	5.12622i	0.389182	+	0.350421i
$215$		0			0
$216$	−13.3599	−	4.34090i	−0.909027	−	0.295361i
$217$	9.73141	+	24.0289i	0.660611	+	1.63119i
$218$	5.95255	−	5.95255i	0.403158	−	0.403158i
$219$	0.752324	+	1.68975i	0.0508373	+	0.114183i
$220$		0			0
$221$	−1.70724	−	0.760113i	−0.114842	−	0.0511307i
$222$	5.19919	+	4.21022i	0.348947	+	0.282571i
$223$	9.81559	−	19.2642i	0.657301	−	1.29003i	−0.286046	−	0.958216i	$-0.592341\pi$
$223$	9.81559	−	19.2642i	0.657301	−	1.29003i	0.943346	−	0.331809i	$-0.107659\pi$
$224$	−15.0891	+	3.49672i	−1.00818	+	0.233634i
$225$		0			0
$226$	−2.56903	+	4.44970i	−0.170890	+	0.295989i
$227$	−0.492014	−	9.38818i	−0.0326561	−	0.623116i	−0.965113	−	0.261834i	$-0.915673\pi$
$227$	−0.492014	−	9.38818i	−0.0326561	−	0.623116i	0.932457	−	0.361281i	$-0.117661\pi$
$228$	−7.71385	+	2.96107i	−0.510862	+	0.196102i
$229$	−0.325389	−	3.09587i	−0.0215023	−	0.204581i	0.978496	−	0.206265i	$-0.0661307\pi$
$229$	−0.325389	−	3.09587i	−0.0215023	−	0.204581i	−0.999999	+	0.00168368i	$0.999464\pi$
$230$		0			0
$231$	−0.484007	−	3.91517i	−0.0318454	−	0.257600i
$232$	−12.8299	−	12.8299i	−0.842326	−	0.842326i
$233$	−10.4487	+	27.2198i	−0.684516	+	1.78323i	−0.0654920	+	0.997853i	$0.520862\pi$
$233$	−10.4487	+	27.2198i	−0.684516	+	1.78323i	−0.619024	+	0.785372i	$0.712472\pi$
$234$	−2.65642	+	0.564639i	−0.173656	+	0.0369116i
$235$		0			0
$236$	−1.40033	+	6.58805i	−0.0911540	+	0.428846i
$237$	−5.32129	−	10.4436i	−0.345655	−	0.678386i
$238$	1.88279	−	0.333592i	0.122043	−	0.0216236i
$239$	3.05660	−	0.993150i	0.197715	−	0.0642416i	−0.208485	−	0.978025i	$-0.566853\pi$
$239$	3.05660	−	0.993150i	0.197715	−	0.0642416i	0.406201	+	0.913784i	$0.366853\pi$
$240$		0			0
$241$	5.57588	+	26.2325i	0.359174	+	1.68978i	0.672469	+	0.740125i	$0.265234\pi$
$241$	5.57588	+	26.2325i	0.359174	+	1.68978i	−0.313295	+	0.949656i	$0.601433\pi$
$242$	−5.57983	+	4.51846i	−0.358685	+	0.290458i
$243$	−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
$247$	−6.66586	+	8.23165i	−0.424138	+	0.523767i
$248$	−25.8274	+	1.35356i	−1.64004	+	0.0859510i
$249$	−6.08480	+	3.51306i	−0.385609	+	0.222631i
$250$		0			0
$251$		−	13.7541i		−	0.868150i	−0.900877	−	0.434075i	$-0.857075\pi$
$251$		−	13.7541i		−	0.868150i	0.900877	−	0.434075i	$-0.142925\pi$
$252$	−4.45628	+	4.62225i	−0.280719	+	0.291175i
$253$	−0.237881	+	1.50192i	−0.0149555	+	0.0944250i
$254$	14.2932	−	1.50227i	0.896833	−	0.0942610i
$255$		0			0
$256$	1.39915	−	13.3120i	0.0874468	−	0.832000i
$257$	−2.39177	−	8.92621i	−0.149195	−	0.556802i	−0.999533	−	0.0305651i	$-0.990269\pi$
$257$	−2.39177	−	8.92621i	−0.149195	−	0.556802i	0.850338	−	0.526237i	$-0.176397\pi$
$258$	−0.645695	−	4.07676i	−0.0401992	−	0.253808i
$259$	18.3691	−	8.58412i	1.14140	−	0.533391i
$260$		0			0
$261$	−11.6898	−	2.48474i	−0.723578	−	0.153801i
$262$	−7.09379	+	10.9235i	−0.438256	+	0.674854i
$263$	4.57051	−	7.03797i	0.281830	−	0.433980i	−0.669198	−	0.743084i	$-0.733362\pi$
$263$	4.57051	−	7.03797i	0.281830	−	0.433980i	0.951028	+	0.309104i	$0.100029\pi$
$264$	3.84957	+	0.818252i	0.236925	+	0.0503599i
$265$		0			0
$266$	0.935639	−	10.7972i	0.0573677	−	0.662017i
$267$	−2.75761	−	17.4109i	−0.168763	−	1.06553i
$268$	3.06887	+	11.4532i	0.187461	+	0.699615i
$269$	0.460334	−	4.37978i	0.0280670	−	0.267040i	−0.971485	−	0.237102i	$-0.923802\pi$
$269$	0.460334	−	4.37978i	0.0280670	−	0.267040i	0.999552	−	0.0299378i	$-0.00953093\pi$
$270$		0			0
$271$	−3.41350	+	0.358773i	−0.207355	+	0.0217939i	−0.207636	−	0.978206i	$-0.566577\pi$
$271$	−3.41350	+	0.358773i	−0.207355	+	0.0217939i	0.000281350		1.00000i	$0.499910\pi$
$272$	0.107679	−	0.679856i	0.00652898	−	0.0412223i
$273$	1.44007	−	5.79622i	0.0871572	−	0.350803i
$274$			2.56689i			0.155072i
$275$		0			0
$276$	−1.55525	+	0.897924i	−0.0936150	+	0.0540487i
$277$	7.68850	−	0.402937i	0.461957	−	0.0242102i	0.180062	−	0.983655i	$-0.442370\pi$
$277$	7.68850	−	0.402937i	0.461957	−	0.0242102i	0.281895	+	0.959445i	$0.409037\pi$
$278$	−4.21984	+	5.21107i	−0.253089	+	0.312539i
$279$	−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
$283$	5.63377	−	4.56213i	0.334893	−	0.271191i	−0.447093	−	0.894488i	$-0.647541\pi$
$283$	5.63377	−	4.56213i	0.334893	−	0.271191i	0.781985	+	0.623297i	$0.214207\pi$
$284$	−3.12991	−	14.7251i	−0.185726	−	0.873772i
$285$		0			0
$286$	1.97231	−	0.640843i	0.116625	−	0.0378939i
$287$	−0.0302197	−	0.170560i	−0.00178381	−	0.0100678i
$288$	−4.62055	−	9.06833i	−0.272268	−	0.534357i
$289$	3.35474	−	15.7828i	0.197338	−	0.928400i
$290$		0			0
$291$	19.1118	−	4.06234i	1.12035	−	0.238138i
$292$	−0.823809	+	2.14610i	−0.0482098	+	0.125591i
$293$	−22.0206	−	22.0206i	−1.28645	−	1.28645i	−0.936925	−	0.349529i	$-0.886342\pi$
$293$	−22.0206	−	22.0206i	−1.28645	−	1.28645i	−0.349529	−	0.936925i	$-0.613658\pi$
$294$	2.09952	+	5.73885i	0.122446	+	0.334697i
$295$		0			0
$296$	2.11435	+	20.1167i	0.122894	+	1.16926i
$297$	6.59611	−	2.53201i	0.382745	−	0.146922i
$298$	0.00160802	+	0.0306828i	9.31501e−5	+	0.00177741i
$299$	−1.15108	+	1.99372i	−0.0665684	+	0.115300i
$300$		0			0
$301$	−11.9659	−	3.64755i	−0.689705	−	0.210241i
$302$	−3.45587	+	6.78253i	−0.198863	+	0.390291i
$303$	3.09435	+	2.50576i	0.177766	+	0.143952i
$304$	−3.56407	−	1.58683i	−0.204414	−	0.0910108i
$305$		0			0
$306$	0.511039	+	1.14781i	0.0292141	+	0.0656160i
$307$	−2.33566	+	2.33566i	−0.133303	+	0.133303i	−0.770610	−	0.637307i	$-0.780048\pi$
$307$	−2.33566	+	2.33566i	−0.133303	+	0.133303i	0.637307	+	0.770610i	$0.280048\pi$
$308$	3.01532	−	3.86601i	0.171814	−	0.220286i
$309$	−6.79877	−	2.20905i	−0.386768	−	0.125669i
$310$		0			0
$311$	−4.59090	−	4.13366i	−0.260326	−	0.234399i	0.528624	−	0.848856i	$-0.322708\pi$
$311$	−4.59090	−	4.13366i	−0.260326	−	0.234399i	−0.788950	+	0.614458i	$0.789375\pi$
$312$	4.99696	+	3.24507i	0.282897	+	0.183716i
$313$	0.586184	−	11.1851i	0.0331331	−	0.632216i	−0.930712	−	0.365753i	$-0.880811\pi$
$313$	0.586184	−	11.1851i	0.0331331	−	0.632216i	0.963845	−	0.266463i	$-0.0858552\pi$
$314$	3.16170	+	9.73071i	0.178425	+	0.549136i
$315$		0			0
$316$	4.50152	−	13.8542i	0.253230	−	0.779362i
$317$	8.39567	+	3.22280i	0.471548	+	0.181010i	0.582525	−	0.812813i	$-0.302065\pi$
$317$	8.39567	+	3.22280i	0.471548	+	0.181010i	−0.110977	+	0.993823i	$0.535398\pi$
$318$	2.52370	−	9.41859i	0.141522	−	0.528168i
$319$	9.07597	+	0.953923i	0.508157	+	0.0534094i
$320$		0			0
$321$	−6.50714	−	8.95630i	−0.363193	−	0.499892i
$322$	−0.166253	−	2.34963i	−0.00926494	−	0.130940i
$323$	4.36630	+	2.22474i	0.242947	+	0.123788i
$324$	0.921313	+	0.531920i	0.0511840	+	0.0295511i
$325$		0			0
$326$	1.35707	+	2.35051i	0.0751610	+	0.130183i
$327$	−10.2022	+	6.62539i	−0.564183	+	0.366385i
$328$	0.170676	+	0.0270324i	0.00942401	+	0.00149262i
$329$	0.0938322	−	0.484864i	0.00517314	−	0.0267314i
$330$		0			0
$331$	−6.60155	+	2.93920i	−0.362854	+	0.161553i	−0.580062	−	0.814572i	$-0.696972\pi$
$331$	−6.60155	+	2.93920i	−0.362854	+	0.161553i	0.217208	+	0.976125i	$0.430305\pi$
$332$	−8.43463	−	2.26005i	−0.462910	−	0.124036i
$333$	8.38447	+	10.3540i	0.459466	+	0.567394i
$334$	−9.96132	−	11.0632i	−0.545059	−	0.605349i
$335$		0			0
$336$	2.19943	−	0.0402094i	0.119989	−	0.00219360i
$337$	−9.03950	+	4.60585i	−0.492413	+	0.250897i	−0.682521	−	0.730866i	$-0.739116\pi$
$337$	−9.03950	+	4.60585i	−0.492413	+	0.250897i	0.190108	+	0.981763i	$0.439116\pi$
$338$	−6.95506	−	0.364499i	−0.378305	−	0.0198261i
$339$	4.96815	−	5.51769i	0.269833	−	0.299680i
$340$		0			0
$341$	9.66695	−	8.70416i	0.523494	−	0.471356i
$342$	7.03363	−	1.11402i	0.380335	−	0.0602392i
$343$	18.4235	+	1.89023i	0.994778	+	0.102063i
$344$	7.33539	−	10.0963i	0.395498	−	0.544356i
$345$		0			0
$346$	−1.56752	+	3.52070i	−0.0842703	+	0.189274i
$347$	2.87267	+	7.48356i	0.154213	+	0.401738i	0.988821	−	0.149105i	$-0.0476393\pi$
$347$	2.87267	+	7.48356i	0.154213	+	0.401738i	−0.834608	+	0.550844i	$0.814306\pi$
$348$	5.86988	+	9.03883i	0.314659	+	0.484532i
$349$	−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
$352$	4.23285	+	6.51801i	0.225612	+	0.347411i
$353$	−6.03343	−	15.7176i	−0.321127	−	0.836565i	−0.995197	−	0.0978967i	$-0.968789\pi$
$353$	−6.03343	−	15.7176i	−0.321127	−	0.836565i	0.674070	−	0.738668i	$-0.264545\pi$
$354$	−1.71324	+	3.84801i	−0.0910579	+	0.204519i
$355$		0			0
$356$	12.8773	−	17.7241i	0.682497	−	0.939376i
$357$	−2.76151	−	0.0941494i	−0.146155	−	0.00498292i
$358$	15.5477	−	2.46251i	0.821720	−	0.130148i
$359$	−10.2724	+	9.24932i	−0.542157	+	0.488161i	−0.894104	−	0.447859i	$-0.852187\pi$
$359$	−10.2724	+	9.24932i	−0.542157	+	0.488161i	0.351947	+	0.936020i	$0.385520\pi$
$360$		0			0
$361$	5.87151	−	6.52098i	0.309027	−	0.343209i
$362$	−3.53476	−	0.185249i	−0.185783	−	0.00973647i
$363$	9.24451	−	4.71031i	0.485211	−	0.247227i
$364$	6.35927	−	3.82819i	0.333316	−	0.200652i
$365$		0			0
$366$	−2.67195	−	2.96750i	−0.139665	−	0.155114i
$367$	−0.653967	−	0.807582i	−0.0341368	−	0.0421554i	0.759792	−	0.650167i	$-0.225301\pi$
$367$	−0.653967	−	0.807582i	−0.0341368	−	0.0421554i	−0.793928	+	0.608011i	$0.791968\pi$
$368$	−0.819049	−	0.219464i	−0.0426959	−	0.0114403i
$369$	0.103979	−	0.0462943i	0.00541292	−	0.00240999i
$370$		0			0
$371$	−22.3192	−	19.3695i	−1.15876	−	1.00561i
$372$	15.1732	+	2.40320i	0.786695	+	0.124600i
$373$	18.4553	−	11.9850i	0.955577	−	0.620559i	0.0301748	−	0.999545i	$-0.490394\pi$
$373$	18.4553	−	11.9850i	0.955577	−	0.620559i	0.925403	+	0.378985i	$0.123727\pi$
$374$	−0.479720	−	0.830899i	−0.0248057	−	0.0429648i
$375$		0			0
$376$	0.426675	+	0.246341i	0.0220041	+	0.0127041i
$377$	12.3102	+	6.27237i	0.634009	+	0.323044i
$378$	−9.06828	+	6.12754i	−0.466422	+	0.315167i
$379$	−17.8299	−	24.5408i	−0.915862	−	1.26058i	−0.965125	−	0.261790i	$-0.915687\pi$
$379$	−17.8299	−	24.5408i	−0.915862	−	1.26058i	0.0492625	−	0.998786i	$-0.484313\pi$
$380$		0			0
$381$	−20.6544	−	2.17087i	−1.05816	−	0.111217i
$382$	3.11380	−	11.6209i	0.159316	−	0.594575i
$383$	19.9640	+	7.66347i	1.02011	+	0.391585i	0.810212	−	0.586137i	$-0.199352\pi$
$383$	19.9640	+	7.66347i	1.02011	+	0.391585i	0.209902	+	0.977722i	$0.432685\pi$
$384$	−3.23567	+	9.95838i	−0.165120	+	0.508186i
$385$		0			0
$386$	−1.88327	−	5.79612i	−0.0958562	−	0.295015i
$387$	0.430196	−	8.20863i	0.0218681	−	0.417268i
$388$	20.3655	+	13.2255i	1.03390	+	0.671423i
$389$	15.6392	+	14.0816i	0.792938	+	0.713964i	0.962419	−	0.271569i	$-0.0875426\pi$
$389$	15.6392	+	14.0816i	0.792938	+	0.713964i	−0.169481	+	0.985533i	$0.554209\pi$
$390$		0			0
$391$	1.01295	+	0.329128i	0.0512271	+	0.0166447i
$392$	−7.78066	+	16.7579i	−0.392982	+	0.846403i
$393$	13.3088	−	13.3088i	0.671340	−	0.671340i
$394$	5.17168	+	11.6158i	0.260545	+	0.585195i
$395$		0			0
$396$	2.94311	+	1.31036i	0.147897	+	0.0658479i
$397$	−3.98282	−	3.22523i	−0.199892	−	0.161869i	0.524148	−	0.851627i	$-0.324384\pi$
$397$	−3.98282	−	3.22523i	−0.199892	−	0.161869i	−0.724040	+	0.689758i	$0.757717\pi$
$398$	−9.63744	+	18.9145i	−0.483081	+	0.948100i
$399$	−4.56645	+	14.9804i	−0.228608	+	0.749960i
$400$		0			0
$401$	−17.1661	+	29.7326i	−0.857235	+	1.48477i	0.0173216	+	0.999850i	$0.494486\pi$
$401$	−17.1661	+	29.7326i	−0.857235	+	1.48477i	−0.874556	+	0.484924i	$0.838847\pi$
$402$	0.388093	+	7.40526i	0.0193563	+	0.369341i
$403$	18.3854	−	7.05751i	0.915844	−	0.351560i
$404$	0.517259	+	4.92139i	0.0257346	+	0.244848i
$405$		0			0
$406$	−14.0295	+	1.73437i	−0.696272	+	0.0860755i
$407$	−7.19393	−	7.19393i	−0.356590	−	0.356590i
$408$	0.987852	−	2.57344i	0.0489060	−	0.127404i
$409$	25.6660	−	5.45549i	1.26910	−	0.269756i	0.476327	−	0.879268i	$-0.341968\pi$
$409$	25.6660	−	5.45549i	1.26910	−	0.269756i	0.792777	+	0.609512i	$0.208634\pi$
$410$		0			0
$411$	0.771207	−	3.62824i	0.0380408	−	0.178968i
$412$	−4.03345	−	7.91610i	−0.198714	−	0.389998i
$413$	8.21385	+	9.77247i	0.404177	+	0.480872i
$414$	1.47203	−	0.478291i	0.0723462	−	0.0235067i
$415$		0			0
$416$	2.44630	+	11.5089i	0.119940	+	0.564272i
$417$	7.53028	−	6.09790i	0.368760	−	0.298616i
$418$	−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	$0.392704\pi$
$422$	−7.18251	+	8.86966i	−0.349639	+	0.431768i
$423$	0.324066	−	0.0169836i	0.0157566	−	0.000825770i
$424$	25.5318	−	14.7408i	1.23994	−	0.715877i
$425$		0			0
$426$		−	9.41470i		−	0.456144i
$427$	−11.6306	+	3.34542i	−0.562843	+	0.161896i
$428$	2.15233	−	13.5893i	0.104037	−	0.656864i
$429$	−2.98036	+	0.313248i	−0.143893	+	0.0151238i
$430$		0			0
$431$	1.62917	−	15.5005i	0.0784745	−	0.746635i	−0.882559	−	0.470202i	$-0.844181\pi$
$431$	1.62917	−	15.5005i	0.0784745	−	0.746635i	0.961033	−	0.276433i	$-0.0891523\pi$
$432$	1.01970	+	3.80556i	0.0490602	+	0.183095i
$433$	0.121416	+	0.766591i	0.00583489	+	0.0368400i	0.990434	−	0.137987i	$-0.0440633\pi$
$433$	0.121416	+	0.766591i	0.00583489	+	0.0368400i	−0.984599	+	0.174827i	$0.944063\pi$
$434$	−11.5439	+	16.5154i	−0.554123	+	0.792763i
$435$		0			0
$436$	−14.7881	−	3.14331i	−0.708223	−	0.150537i
$437$	3.28784	−	5.06282i	0.157279	−	0.242188i
$438$	−0.782996	+	1.20571i	−0.0374130	+	0.0576110i
$439$	10.3322	+	2.19617i	0.493128	+	0.104818i	0.447762	−	0.894153i	$-0.352221\pi$
$439$	10.3322	+	2.19617i	0.493128	+	0.104818i	0.0453661	+	0.998970i	$0.485555\pi$
$440$		0			0
$441$	1.71358	+	12.0482i	0.0815991	+	0.573726i
$442$	−0.227225	−	1.43464i	−0.0108080	−	0.0682391i
$443$	7.03490	+	26.2546i	0.334238	+	1.24739i	0.904693	+	0.426064i	$0.140100\pi$
$443$	7.03490	+	26.2546i	0.334238	+	1.24739i	−0.570455	+	0.821329i	$0.693233\pi$
$444$	1.25591	−	11.9492i	0.0596028	−	0.567083i
$445$		0			0
$446$	16.7126	−	1.75656i	0.791364	−	0.0831757i
$447$	0.00694557	−	0.0438526i	0.000328514	−	0.00207416i
$448$	−5.84684	−	5.63690i	−0.276237	−	0.266318i
$449$		−	39.0168i		−	1.84131i	−0.390372	−	0.920657i	$-0.627654\pi$
$449$		−	39.0168i		−	1.84131i	0.390372	−	0.920657i	$-0.372346\pi$
$450$		0			0
$451$	−0.0752701	+	0.0434572i	−0.00354433	+	0.00204632i
$452$	9.21499	−	0.482937i	0.433437	−	0.0227154i
$453$	6.92257	−	8.54866i	0.325251	−	0.401651i
$454$	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	−0.738080	−	0.674713i	$-0.764268\pi$
$457$	−22.2310	+	5.95677i	−1.03992	+	0.278646i	−0.301840	+	0.953359i	$0.597601\pi$
$458$	1.88031	−	1.52265i	0.0878613	−	0.0711487i
$459$	−1.02889	−	4.84056i	−0.0480246	−	0.225938i
$460$		0			0
$461$	23.0880	−	7.50175i	1.07532	−	0.349391i	0.282760	−	0.959191i	$-0.408750\pi$
$461$	23.0880	−	7.50175i	1.07532	−	0.349391i	0.792556	+	0.609799i	$0.208750\pi$
$462$	2.34724	−	1.97287i	0.109203	−	0.0917863i
$463$	−2.79874	−	5.49284i	−0.130069	−	0.255274i	0.816783	−	0.576945i	$-0.195755\pi$
$463$	−2.79874	−	5.49284i	−0.130069	−	0.255274i	−0.946851	+	0.321671i	$0.895755\pi$
$464$	−1.05803	+	4.97762i	−0.0491176	+	0.231080i
$465$		0			0
$466$	−22.1665	+	4.71162i	−1.02684	+	0.218262i
$467$	10.5121	−	27.3851i	0.486444	−	1.26723i	−0.442420	−	0.896808i	$-0.645880\pi$
$467$	10.5121	−	27.3851i	0.486444	−	1.26723i	0.928864	−	0.370422i	$-0.120787\pi$
$468$	3.44880	+	3.44880i	0.159421	+	0.159421i
$469$	20.6947	+	8.76422i	0.955594	+	0.404694i
$470$		0			0
$471$	−1.54546	−	14.7041i	−0.0712109	−	0.677527i
$472$	−11.8896	+	4.56399i	−0.547263	+	0.210075i
$473$	0.328506	+	6.26828i	0.0151047	+	0.288216i
$474$	4.55512	−	7.88970i	0.209224	−	0.362386i
$475$		0			0
$476$	−2.34409	−	2.50956i	−0.107441	−	0.115026i
$477$	8.81577	−	17.3019i	0.403646	−	0.792200i
$478$	1.94131	+	1.57204i	0.0887934	+	0.0719035i
$479$	8.30871	+	3.69927i	0.379635	+	0.169024i	0.587677	−	0.809096i	$-0.300043\pi$
$479$	8.30871	+	3.69927i	0.379635	+	0.169024i	−0.208043	+	0.978120i	$0.566709\pi$
$480$		0			0
$481$	−6.26471	−	14.0708i	−0.285646	−	0.641572i
$482$	−14.7394	+	14.7394i	−0.671360	+	0.671360i
$483$	−0.470937	+	3.37110i	−0.0214284	+	0.153390i
$484$	12.2635	+	3.98466i	0.557433	+	0.181121i
$485$		0			0
$486$	−8.72786	−	7.85860i	−0.395904	−	0.356473i
$487$	0.445473	+	0.289294i	0.0201863	+	0.0131091i	0.554693	−	0.832055i	$-0.312836\pi$
$487$	0.445473	+	0.289294i	0.0201863	+	0.0131091i	−0.534506	+	0.845164i	$0.679502\pi$
$488$	0.631868	−	12.0568i	0.0286033	−	0.545784i
$489$	−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	$0.0537489\pi$
$492$	−0.0958265	−	0.0367843i	−0.00432019	−	0.00165837i
$493$	1.65436	−	6.17415i	0.0745086	−	0.278070i
$494$	−8.18762	−	0.860554i	−0.368379	−	0.0387181i
$495$		0			0
$496$	4.26357	+	5.86830i	0.191440	+	0.263494i
$497$	−25.6559	−	12.4870i	−1.15082	−	0.560118i
$498$	−4.86582	−	2.47926i	−0.218043	−	0.111098i
$499$	−5.43364	−	3.13711i	−0.243243	−	0.140437i	0.373423	−	0.927661i	$-0.378184\pi$
$499$	−5.43364	−	3.13711i	−0.243243	−	0.140437i	−0.616666	+	0.787225i	$0.711517\pi$
$500$		0			0
$501$	10.7562	+	18.6303i	0.480553	+	0.832343i
$502$	8.96567	−	5.82237i	0.400157	−	0.259865i
$503$	−4.92568	−	0.780151i	−0.219625	−	0.0347852i	0.0456521	−	0.998957i	$-0.485463\pi$
$503$	−4.92568	−	0.780151i	−0.219625	−	0.0347852i	−0.265277	+	0.964172i	$0.585463\pi$
$504$	−11.9193	−	2.30666i	−0.530929	−	0.102747i
$505$		0			0
$506$	−1.07973	+	0.480729i	−0.0480001	+	0.0213710i
$507$	9.72131	+	2.60482i	0.431739	+	0.115684i
$508$	−16.2434	−	20.0589i	−0.720684	−	0.889971i
$509$	−15.1400	−	16.8147i	−0.671070	−	0.745298i	0.307425	−	0.951572i	$-0.400533\pi$
$509$	−15.1400	−	16.8147i	−0.671070	−	0.745298i	−0.978494	+	0.206274i	$0.933866\pi$
$510$		0			0
$511$	2.24715	+	3.73290i	0.0994082	+	0.165134i
$512$	−7.34327	+	3.74158i	−0.324530	+	0.165356i
$513$	−28.0101	−	1.46795i	−1.23668	−	0.0648115i
$514$	4.80611	−	5.33772i	0.211988	−	0.235437i
$515$		0			0
$516$	−5.50883	+	4.96017i	−0.242513	+	0.218359i
$517$	−0.244752	+	0.0387649i	−0.0107642	+	0.00170488i
$518$	13.3716	+	8.34013i	0.587513	+	0.366444i
$519$	3.27343	−	4.50548i	0.143687	−	0.197769i
$520$		0			0
$521$	12.5522	−	28.1927i	0.549921	−	1.23514i	−0.398219	−	0.917290i	$-0.630372\pi$
$521$	12.5522	−	28.1927i	0.549921	−	1.23514i	0.948140	−	0.317853i	$-0.102962\pi$
$522$	−3.32882	−	8.67186i	−0.145698	−	0.379557i
$523$	16.6846	+	25.6920i	0.729567	+	1.12343i	0.987553	+	0.157286i	$0.0502743\pi$
$523$	16.6846	+	25.6920i	0.729567	+	1.12343i	−0.257987	+	0.966149i	$0.583059\pi$
$524$	23.3916			1.02187
$525$		0			0
$526$	6.52252			0.284395
$527$	−4.96226	−	7.64121i	−0.216159	−	0.332856i
$528$	−0.395563	−	1.03048i	−0.0172147	−	0.0448457i
$529$	−8.82128	+	19.8129i	−0.383534	+	0.861432i
$530$		0			0
$531$	−4.93056	+	6.78633i	−0.213968	+	0.294502i
$532$	−17.1778	+	9.15184i	−0.744754	+	0.396783i
$533$	−0.129963	+	0.0205840i	−0.00562930	+	0.000891594i
$534$	10.1820	−	9.16792i	0.440619	−	0.396735i
$535$		0			0
$536$	−15.0022	+	16.6617i	−0.647998	+	0.719675i
$537$	−22.7161	−	1.19050i	−0.980273	−	0.0513739i
$538$	3.04985	−	1.55398i	0.131488	−	0.0669966i
$539$	−2.26305	−	9.01310i	−0.0974764	−	0.388222i
$540$		0			0
$541$	26.4951	+	29.4258i	1.13911	+	1.26511i	0.959603	+	0.281356i	$0.0907841\pi$
$541$	26.4951	+	29.4258i	1.13911	+	1.26511i	0.179509	+	0.983756i	$0.442549\pi$
$542$	−1.67887	−	2.07323i	−0.0721135	−	0.0890528i
$543$	4.94065	+	1.32384i	0.212023	+	0.0568115i
$544$	4.97289	−	2.21407i	0.213211	−	0.0949276i
$545$		0			0
$546$	4.38790	−	1.51493i	0.187785	−	0.0648331i
$547$	−37.0235	−	5.86395i	−1.58301	−	0.250724i	−0.697932	−	0.716164i	$-0.745896\pi$
$547$	−37.0235	−	5.86395i	−1.58301	−	0.250724i	−0.885079	+	0.465440i	$0.845896\pi$
$548$	3.86625	−	2.51077i	0.165158	−	0.107255i
$549$	−3.97611	−	6.88682i	−0.169696	−	0.293922i
$550$		0			0
$551$	−31.3750	−	18.1143i	−1.33662	−	0.771697i
$552$	−3.02561	−	1.54162i	−0.128778	−	0.0656159i
$553$	−15.4586	−	22.8774i	−0.657365	−	0.972848i
$554$	3.51735	+	4.84122i	0.149438	+	0.205684i
$555$		0			0
$556$	11.9765	+	1.25878i	0.507916	+	0.0533841i
$557$	1.55832	−	5.81572i	0.0660280	−	0.246420i	−0.925021	−	0.379915i	$-0.875953\pi$
$557$	1.55832	−	5.81572i	0.0660280	−	0.246420i	0.991050	+	0.133495i	$0.0426200\pi$
$558$	−12.3609	−	4.74490i	−0.523278	−	0.200868i
$559$	−2.93652	+	9.03767i	−0.124201	+	0.382253i
$560$		0			0
$561$	0.428435	+	1.31859i	0.0180885	+	0.0556708i
$562$	−0.986964	+	18.8324i	−0.0416326	+	0.794397i
$563$	25.3462	+	16.4600i	1.06822	+	0.693708i	0.954018	−	0.299750i	$-0.0969033\pi$
$563$	25.3462	+	16.4600i	1.06822	+	0.693708i	0.114199	+	0.993458i	$0.463570\pi$
$564$	−0.217481	−	0.195821i	−0.00915761	−	0.00824555i
$565$		0			0
$566$	5.35873	+	1.74116i	0.225244	+	0.0731863i
$567$	1.86894	−	0.756899i	0.0784882	−	0.0317868i
$568$	20.1280	−	20.1280i	0.844552	−	0.844552i
$569$	2.02703	+	4.55278i	0.0849775	+	0.190863i	0.951036	−	0.309080i	$-0.100021\pi$
$569$	2.02703	+	4.55278i	0.0849775	+	0.190863i	−0.866059	+	0.499943i	$0.833354\pi$
$570$		0			0
$571$	−2.23119	−	0.993391i	−0.0933725	−	0.0415721i	0.359519	−	0.933138i	$-0.382941\pi$
$571$	−2.23119	−	0.993391i	−0.0933725	−	0.0415721i	−0.452891	+	0.891566i	$0.649607\pi$
$572$	−2.89443	−	2.34386i	−0.121022	−	0.0980018i
$573$	−7.89270	+	15.4903i	−0.329722	+	0.647117i
$574$	0.0983877	−	0.0919002i	0.00410662	−	0.00383584i
$575$		0			0
$576$	2.66831	−	4.62165i	0.111180	−	0.192569i
$577$	1.27197	+	24.2706i	0.0529527	+	1.01040i	0.887891	+	0.460054i	$0.152170\pi$
$577$	1.27197	+	24.2706i	0.0529527	+	1.01040i	−0.834938	+	0.550343i	$0.814497\pi$
$578$	11.7082	−	4.49437i	0.486998	−	0.186941i
$579$	0.920556	+	8.75851i	0.0382570	+	0.363991i
$580$		0			0
$581$	−13.2099	+	9.97149i	−0.548038	+	0.413687i
$582$	10.7384	+	10.7384i	0.445123	+	0.445123i
$583$	−5.31398	+	13.8434i	−0.220083	+	0.573335i
$584$	−4.25172	+	0.903731i	−0.175937	+	0.0373966i
$585$		0			0
$586$	5.03247	−	23.6759i	0.207890	−	0.978044i
$587$	−4.09368	−	8.03430i	−0.168964	−	0.331611i	0.790961	−	0.611866i	$-0.209581\pi$
$587$	−4.09368	−	8.03430i	−0.168964	−	0.331611i	−0.959926	+	0.280255i	$0.909581\pi$
$588$	6.59023	−	8.77567i	0.271777	−	0.361903i
$589$	−49.1130	+	15.9578i	−2.02366	+	0.657528i
$590$		0			0
$591$	−3.82016	−	17.9724i	−0.157140	−	0.739287i
$592$	4.40882	−	3.57019i	0.181202	−	0.146734i
$593$	−24.7752	+	6.63849i	−1.01740	+	0.272610i	−0.728716	−	0.684816i	$-0.759883\pi$
$593$	−24.7752	+	6.63849i	−1.01740	+	0.272610i	−0.288679	+	0.957426i	$0.593216\pi$
$594$	4.44277	+	3.22786i	0.182289	+	0.132441i
$595$		0			0
$596$	0.0446416	−	0.0324340i	0.00182859	−	0.00132855i
$597$	19.3051	−	23.8398i	0.790104	−	0.975697i
$598$	−1.78689	+	0.0936469i	−0.0730714	+	0.00382951i
$599$	−23.1803	+	13.3832i	−0.947123	+	0.546822i	−0.892186	−	0.451668i	$-0.850829\pi$
$599$	−23.1803	+	13.3832i	−0.947123	+	0.546822i	−0.0549370	+	0.998490i	$0.517496\pi$
$600$		0			0
$601$			3.83116i			0.156276i	0.996943	+	0.0781382i	$0.0248975\pi$
$601$			3.83116i			0.156276i	−0.996943	+	0.0781382i	$0.975102\pi$
$602$	−2.68775	−	9.34413i	−0.109544	−	0.380838i
$603$	−2.31015	+	14.5857i	−0.0940764	+	0.593975i
$604$	13.5961	−	1.42901i	0.553219	−	0.0581457i
$605$		0			0
$606$	−0.323490	+	3.07780i	−0.0131409	+	0.125027i
$607$	8.71399	+	32.5210i	0.353690	+	1.31999i	0.882125	+	0.471015i	$0.156112\pi$
$607$	8.71399	+	32.5210i	0.353690	+	1.31999i	−0.528435	+	0.848974i	$0.677221\pi$
$608$	−4.82648	−	30.4732i	−0.195740	−	1.23585i
$609$	20.3514	+	1.76358i	0.824682	+	0.0714637i
$610$		0			0
$611$	−0.366959	−	0.0779995i	−0.0148456	−	0.00315552i
$612$	1.22897	−	1.89244i	0.0496780	−	0.0764974i
$613$	−24.1890	+	37.2478i	−0.976985	+	1.50442i	−0.117622	+	0.993058i	$0.537527\pi$
$613$	−24.1890	+	37.2478i	−0.976985	+	1.50442i	−0.859363	+	0.511366i	$0.829140\pi$
$614$	−2.51124	−	0.533781i	−0.101346	−	0.0215417i
$615$		0			0
$616$	9.23610	+	0.800364i	0.372133	+	0.0322476i
$617$	5.46815	+	34.5246i	0.220140	+	1.38991i	0.811902	+	0.583794i	$0.198432\pi$
$617$	5.46815	+	34.5246i	0.220140	+	1.38991i	−0.591762	+	0.806112i	$0.701568\pi$
$618$	−1.43807	−	5.36695i	−0.0578476	−	0.215890i
$619$	1.39751	−	13.2964i	0.0561706	−	0.534427i	−0.929866	−	0.367898i	$-0.880077\pi$
$619$	1.39751	−	13.2964i	0.0561706	−	0.534427i	0.986037	−	0.166529i	$-0.0532559\pi$
$620$		0			0
$621$	−6.06282	+	0.637228i	−0.243293	+	0.0255711i
$622$	0.751132	−	4.74246i	0.0301176	−	0.190155i
$623$	−11.4787	−	39.9066i	−0.459885	−	1.59882i
$624$		−	1.67106i		−	0.0668960i
$625$		0			0
$626$	7.53917	−	4.35274i	0.301326	−	0.173971i
$627$	7.84740	−	0.411265i	0.313395	−	0.0164243i
$628$	11.5638	−	14.2801i	0.461446	−	0.569838i
$629$	−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
$633$	12.8171	−	10.3791i	0.509436	−	0.412533i
$634$	1.45326	+	6.83703i	0.0577162	+	0.271533i
$635$		0			0
$636$	−16.6548	+	5.41147i	−0.660405	+	0.214579i
$637$	1.69147	−	13.9667i	0.0670186	−	0.553382i
$638$	3.22021	+	6.32003i	0.127489	+	0.250212i
$639$	3.89813	−	18.3393i	0.154208	−	0.725490i
$640$		0			0
$641$	2.29399	−	0.487602i	0.0906070	−	0.0192591i	−0.162385	−	0.986727i	$-0.551919\pi$
$641$	2.29399	−	0.487602i	0.0906070	−	0.0192591i	0.252992	+	0.967468i	$0.418585\pi$
$642$	3.08361	−	8.03308i	0.121700	−	0.317041i
$643$	−16.5284	−	16.5284i	−0.651816	−	0.651816i	0.301614	−	0.953430i	$-0.402475\pi$
$643$	−16.5284	−	16.5284i	−0.651816	−	0.651816i	−0.953430	+	0.301614i	$0.902475\pi$
$644$	−3.37639	+	2.54867i	−0.133048	+	0.100432i
$645$		0			0
$646$	0.398131	+	3.78797i	0.0156643	+	0.149036i
$647$	10.9473	−	4.20226i	0.430381	−	0.165208i	−0.133527	−	0.991045i	$-0.542630\pi$
$647$	10.9473	−	4.20226i	0.430381	−	0.165208i	0.563909	+	0.825837i	$0.309297\pi$
$648$	0.105278	+	2.00883i	0.00413572	+	0.0789143i
$649$	3.20276	−	5.54735i	0.125719	−	0.217752i
$650$		0			0
$651$	21.2789	−	19.8758i	0.833986	−	0.778994i
$652$	2.21293	−	4.34313i	0.0866652	−	0.170090i
$653$	−16.1758	−	13.0989i	−0.633008	−	0.512600i	0.258261	−	0.966075i	$-0.416851\pi$
$653$	−16.1758	−	13.0989i	−0.633008	−	0.512600i	−0.891269	+	0.453475i	$0.850184\pi$
$654$	−8.63758	−	3.84570i	−0.337756	−	0.150379i
$655$		0			0
$656$	−0.0197126	−	0.0442752i	−0.000769648	−	0.00172866i
$657$	−2.02445	+	2.02445i	−0.0789813	+	0.0789813i
$658$	0.355782	−	0.144087i	0.0138698	−	0.00561711i
$659$	30.5370	+	9.92209i	1.18955	+	0.386510i	0.835908	−	0.548870i	$-0.184942\pi$
$659$	30.5370	+	9.92209i	1.18955	+	0.386510i	0.353646	+	0.935379i	$0.384942\pi$
$660$		0			0
$661$	−7.51696	−	6.76830i	−0.292376	−	0.263256i	0.509868	−	0.860252i	$-0.329694\pi$
$661$	−7.51696	−	6.76830i	−0.292376	−	0.263256i	−0.802244	+	0.596996i	$0.796361\pi$
$662$	−4.71049	−	3.05903i	−0.183079	−	0.118893i
$663$	−0.109852	+	2.09611i	−0.00426631	+	0.0814060i
$664$	−5.10231	−	15.7033i	−0.198008	−	0.609406i
$665$		0			0
$666$	−3.19997	+	9.84849i	−0.123996	+	0.381621i
$667$	−7.35113	−	2.82183i	−0.284637	−	0.109262i
$668$	−6.91979	+	25.8250i	−0.267735	+	0.999199i
$669$	−24.1506	−	2.53833i	−0.933716	−	0.0981375i
$670$		0			0
$671$	3.56931	+	4.91273i	0.137792	+	0.189654i
$672$	9.73998	+	14.4144i	0.375728	+	0.556048i
$673$	−10.0639	−	5.12781i	−0.387935	−	0.197663i	0.249135	−	0.968469i	$-0.419854\pi$
$673$	−10.0639	−	5.12781i	−0.387935	−	0.197663i	−0.637070	+	0.770806i	$0.719854\pi$
$674$	−6.82894	−	3.94269i	−0.263041	−	0.151867i
$675$		0			0
$676$	6.25399	+	10.8322i	0.240538	+	0.416624i
$677$	−20.5086	+	13.3184i	−0.788208	+	0.511868i	−0.874863	−	0.484370i	$-0.839049\pi$
$677$	−20.5086	+	13.3184i	−0.788208	+	0.511868i	0.0866551	+	0.996238i	$0.472382\pi$
$678$	5.69985	+	0.902768i	0.218901	+	0.0346706i
$679$	43.5059	−	15.0205i	1.66960	−	0.576435i
$680$		0			0
$681$	−9.64609	+	4.29471i	−0.369639	+	0.164574i
$682$	9.76605	+	2.61681i	0.373961	+	0.100203i
$683$	10.3756	+	12.8128i	0.397012	+	0.490269i	0.935978	−	0.352058i	$-0.114518\pi$
$683$	10.3756	+	12.8128i	0.397012	+	0.490269i	−0.538966	+	0.842328i	$0.681185\pi$
$684$	−8.55778	−	9.50438i	−0.327215	−	0.363409i
$685$		0			0
$686$	6.56689	+	12.8096i	0.250725	+	0.489074i
$687$	−3.11525	+	1.58730i	−0.118854	+	0.0605593i
$688$	−3.49532	−	0.183182i	−0.133258	−	0.00698375i
$689$	−15.0213	+	16.6829i	−0.572267	+	0.635567i
$690$		0			0
$691$	−20.8963	+	18.8151i	−0.794932	+	0.715760i	−0.962849	−	0.270041i	$-0.912963\pi$
$691$	−20.8963	+	18.8151i	−0.794932	+	0.715760i	0.167917	+	0.985801i	$0.446296\pi$
$692$	6.83613	−	1.08274i	0.259870	−	0.0411594i
$693$	5.38914	−	2.87117i	0.204716	−	0.109067i
$694$	−3.66214	+	5.04050i	−0.139013	+	0.191335i
$695$		0			0
$696$	−8.28889	+	18.6172i	−0.314190	+	0.705681i
$697$	0.0218160	+	0.0568327i	0.000826341	+	0.00215269i
$698$	−3.73395	−	5.74978i	−0.141332	−	0.217632i
$699$	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	$0.730696\pi$
$702$	4.52805	+	6.97258i	0.170900	+	0.263163i
$703$	14.4739	+	37.7057i	0.545892	+	1.42210i
$704$	−1.65751	+	3.72283i	−0.0624698	+	0.140310i
$705$		0			0
$706$	7.69154	−	10.5865i	0.289475	−	0.398428i
$707$	7.95823	+	4.96372i	0.299300	+	0.186680i
$708$	7.47165	−	1.18339i	0.280802	−	0.0444746i
$709$	−39.0403	+	35.1521i	−1.46619	+	1.32016i	−0.623423	+	0.781885i	$0.714258\pi$
$709$	−39.0403	+	35.1521i	−1.46619	+	1.32016i	−0.842767	+	0.538278i	$0.819075\pi$
$710$		0			0
$711$	12.1398	−	13.4826i	0.455278	−	0.505638i
$712$	41.3689	+	2.16805i	1.55036	+	0.0812511i
$713$	−10.0005	+	5.09550i	−0.374521	+	0.190828i
$714$	−1.10763	−	1.83996i	−0.0414520	−	0.0688588i
$715$		0			0
$716$	−18.9168	−	21.0092i	−0.706953	−	0.785151i
$717$	−2.27169	−	2.80530i	−0.0848377	−	0.104766i
$718$	−10.3777	−	2.78070i	−0.387293	−	0.103775i
$719$	−2.53041	+	1.12661i	−0.0943685	+	0.0420156i	−0.453378	−	0.891318i	$-0.649781\pi$
$719$	−2.53041	+	1.12661i	−0.0943685	+	0.0420156i	0.359009	+	0.933334i	$0.383115\pi$
$720$		0			0
$721$	−16.5328	−	3.19947i	−0.615712	−	0.119154i
$722$	6.73625	+	1.06692i	0.250697	+	0.0397066i
$723$	25.2621	−	16.4054i	0.939508	−	0.610124i
$724$	3.17846	+	5.50525i	0.118126	+	0.204601i
$725$		0			0
$726$	6.98382	+	4.03211i	0.259194	+	0.149646i
$727$	5.31536	+	2.70831i	0.197136	+	0.100446i	0.549772	−	0.835315i	$-0.314715\pi$
$727$	5.31536	+	2.70831i	0.197136	+	0.100446i	−0.352636	+	0.935761i	$0.614715\pi$
$728$	12.6199	+	6.14222i	0.467724	+	0.227646i
$729$	11.3195	+	15.5799i	0.419239	+	0.577033i
$730$		0			0
$731$	4.37233	+	0.459550i	0.161716	+	0.0169971i
$732$	−1.85611	+	6.92710i	−0.0686038	+	0.256033i
$733$	−28.1255	−	10.7964i	−1.03884	−	0.398773i	−0.221641	−	0.975128i	$-0.571141\pi$
$733$	−28.1255	−	10.7964i	−1.03884	−	0.398773i	−0.817199	+	0.576355i	$0.804475\pi$
$734$	0.249589	−	0.768156i	0.00921250	−	0.0283532i
$735$		0			0
$736$	−2.07219	−	6.37755i	−0.0763820	−	0.235080i
$737$	0.590180	−	11.2613i	0.0217396	−	0.414816i
$738$	0.0741934	+	0.0481817i	0.00273110	+	0.00177359i
$739$	−33.5727	−	30.2290i	−1.23499	−	1.11199i	−0.989792	−	0.142517i	$-0.954480\pi$
$739$	−33.5727	−	30.2290i	−1.23499	−	1.11199i	−0.245198	−	0.969473i	$-0.578853\pi$
$740$		0			0
$741$	11.3145	+	3.67629i	0.415648	+	0.135052i
$742$	3.17791	−	22.7484i	0.116665	−	0.835119i
$743$	−23.4363	+	23.4363i	−0.859793	+	0.859793i	−0.991313	−	0.131520i	$-0.958014\pi$
$743$	−23.4363	+	23.4363i	−0.859793	+	0.859793i	0.131520	+	0.991313i	$0.458014\pi$
$744$	11.8150	+	26.5369i	0.433159	+	0.972891i
$745$		0			0
$746$	15.6249	+	6.95667i	0.572070	+	0.254702i
$747$	−8.45180	−	6.84413i	−0.309235	−	0.250414i
$748$	−0.782267	+	1.53529i	−0.0286025	+	0.0561356i
$749$	−17.8010	−	19.0576i	−0.650434	−	0.696351i
$750$		0			0
$751$	19.3994	−	33.6008i	0.707894	−	1.22611i	−0.257742	−	0.966214i	$-0.582979\pi$
$751$	19.3994	−	33.6008i	0.707894	−	1.22611i	0.965637	−	0.259895i	$-0.0836881\pi$
$752$	−0.00723178	−	0.137991i	−0.000263716	−	0.00503200i
$753$	−14.4221	+	5.53611i	−0.525569	+	0.201747i
$754$	1.12248	+	10.6797i	0.0408784	+	0.388932i
$755$		0			0
$756$	18.0993	+	7.66505i	0.658265	+	0.278775i
$757$	−2.63808	−	2.63808i	−0.0958825	−	0.0958825i	0.657538	−	0.753421i	$-0.271598\pi$
$757$	−2.63808	−	2.63808i	−0.0958825	−	0.0958825i	−0.753421	+	0.657538i	$0.771598\pi$
$758$	8.44928	−	22.0111i	0.306892	−	0.799480i
$759$	1.67061	−	0.355100i	0.0606394	−	0.0128893i
$760$		0			0
$761$	−8.25480	+	38.8358i	−0.299236	+	1.40780i	0.529573	+	0.848265i	$0.322352\pi$
$761$	−8.25480	+	38.8358i	−0.299236	+	1.40780i	−0.828809	+	0.559532i	$0.810981\pi$
$762$	−7.32833	−	14.3827i	−0.265477	−	0.521029i
$763$	−21.9362	+	18.4375i	−0.794142	+	0.667483i
$764$	−20.5490	+	6.67679i	−0.743438	+	0.241558i
$765$		0			0
$766$	3.45569	+	16.2577i	0.124859	+	0.587416i
$767$	7.53640	−	6.10285i	0.272124	−	0.220361i
$768$	−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
$772$	−6.88801	+	8.50598i	−0.247905	+	0.306137i
$773$	−32.7224	+	1.71491i	−1.17694	+	0.0616809i	−0.630755	−	0.775982i	$-0.717255\pi$
$773$	−32.7224	+	1.71491i	−1.17694	+	0.0616809i	−0.546187	+	0.837663i	$0.683921\pi$
$774$	5.53295	−	3.19445i	0.198878	−	0.114822i
$775$		0			0
$776$			45.9162i			1.64829i
$777$	−16.3947	−	15.8060i	−0.588156	−	0.567037i
$778$	−2.55878	+	16.1555i	−0.0917365	+	0.579202i
$779$	0.343147	−	0.0360662i	0.0122945	−	0.00129221i
$780$		0			0
$781$	−1.49654	+	14.2387i	−0.0535505	+	0.509499i
$782$	0.214258	+	0.799623i	0.00766186	+	0.0285945i
$783$	5.72327	+	36.1353i	0.204533	+	1.29137i
$784$	5.13027	−	0.729660i	0.183224	−	0.0260593i
$785$		0			0
$786$	14.3093	+	3.04153i	0.510395	+	0.108488i
$787$	14.5264	−	22.3687i	0.517810	−	0.797358i	−0.478945	−	0.877845i	$-0.658981\pi$
$787$	14.5264	−	22.3687i	0.517810	−	0.797358i	0.996756	+	0.0804867i	$0.0256474\pi$
$788$	12.4371	−	19.1514i	0.443052	−	0.682240i
$789$	−9.21943	−	1.95965i	−0.328221	−	0.0697654i
$790$		0			0
$791$	10.0200	−	14.3352i	0.356270	−	0.509702i
$792$	0.952952	+	6.01670i	0.0338617	+	0.213794i
$793$	2.37940	+	8.88006i	0.0844951	+	0.315340i
$794$	0.416373	−	3.96152i	0.0147765	−	0.140589i
$795$		0			0
$796$	37.9158	−	3.98511i	1.34389	−	0.141248i
$797$	−2.59453	+	16.3812i	−0.0919030	+	0.580252i	0.898165	+	0.439660i	$0.144901\pi$
$797$	−2.59453	+	16.3812i	−0.0919030	+	0.580252i	−0.990067	+	0.140593i	$0.955099\pi$
$798$	−11.6981	+	3.36485i	−0.414109	+	0.119114i
$799$			0.173565i			0.00614027i
$800$		0			0
$801$	23.6299	−	13.6427i	0.834921	−	0.482042i
$802$	−26.6481	+	1.39657i	−0.940976	+	0.0493145i
$803$	1.37585	−	1.69903i	0.0485527	−	0.0599576i
$804$	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
$808$	−7.27174	+	5.88854i	−0.255819	+	0.207158i
$809$	8.99442	+	42.3154i	0.316227	+	1.48773i	0.793280	+	0.608857i	$0.208372\pi$
$809$	8.99442	+	42.3154i	0.316227	+	1.48773i	−0.477053	+	0.878874i	$0.658295\pi$
$810$		0			0
$811$	−24.7816	+	8.05202i	−0.870198	+	0.282745i	−0.709881	−	0.704321i	$-0.751252\pi$
$811$	−24.7816	+	8.05202i	−0.870198	+	0.282745i	−0.160317	+	0.987066i	$0.551252\pi$
$812$	16.3351	+	19.4347i	0.573248	+	0.682025i
$813$	1.75015	+	3.43487i	0.0613805	+	0.120466i
$814$	1.64407	−	7.73473i	0.0576245	−	0.271102i
$815$		0			0
$816$	−0.756215	+	0.160738i	−0.0264728	+	0.00562697i
$817$	8.92991	−	23.2632i	0.312418	−	0.813876i
$818$	14.4211	+	14.4211i	0.504223	+	0.504223i
$819$	9.17462	−	1.13420i	0.320587	−	0.0396321i
$820$		0			0
$821$	−2.77911	−	26.4415i	−0.0969916	−	0.922814i	−0.929505	−	0.368809i	$-0.879766\pi$
$821$	−2.77911	−	26.4415i	−0.0969916	−	0.922814i	0.832514	−	0.554005i	$-0.186901\pi$
$822$	2.69155	−	1.03319i	0.0938787	−	0.0360367i
$823$	−0.126889	−	2.42118i	−0.00442306	−	0.0843971i	0.995526	−	0.0944878i	$-0.0301213\pi$
$823$	−0.126889	−	2.42118i	−0.00442306	−	0.0843971i	−0.999949	+	0.0100907i	$0.996788\pi$
$824$	8.39968	−	14.5487i	0.292617	−	0.506827i
$825$		0			0
$826$	−2.89315	+	9.49111i	−0.100666	+	0.330238i
$827$	−2.88877	+	5.66953i	−0.100452	+	0.197149i	−0.935763	−	0.352629i	$-0.885288\pi$
$827$	−2.88877	+	5.66953i	−0.100452	+	0.197149i	0.835311	+	0.549778i	$0.185288\pi$
$828$	−2.16024	−	1.74933i	−0.0750736	−	0.0607934i
$829$	−16.1918	−	7.20907i	−0.562365	−	0.250381i	0.105808	−	0.994387i	$-0.466257\pi$
$829$	−16.1918	−	7.20907i	−0.562365	−	0.250381i	−0.668174	+	0.744005i	$0.732924\pi$
$830$		0			0
$831$	−3.51718	−	7.89971i	−0.122010	−	0.274038i
$832$	−4.36250	+	4.36250i	−0.151242	+	0.151242i
$833$	−6.48314	+	0.578000i	−0.224628	+	0.0200265i
$834$	7.16266	+	2.32729i	0.248023	+	0.0805875i
$835$		0			0
$836$	7.25773	+	6.53489i	0.251014	+	0.226014i
$837$	43.7361	+	28.4026i	1.51174	+	0.981736i
$838$	1.04774	−	19.9921i	0.0361937	−	0.690617i
$839$	−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
$842$	−8.55018	−	3.28211i	−0.294659	−	0.113109i
$843$	7.05313	−	26.3226i	0.242923	−	0.906600i
$844$	20.3849	+	2.14254i	0.701678	+	0.0737493i
$845$		0			0
$846$	0.148254	+	0.204054i	0.00509708	+	0.00701553i
$847$	20.2507	−	13.6836i	0.695823	−	0.470175i
$848$	−7.36733	−	3.75384i	−0.252995	−	0.128908i
$849$	−7.05132	−	4.07108i	−0.242001	−	0.139719i
$850$		0			0
$851$	4.38910	+	7.60214i	0.150456	+	0.260598i
$852$	−14.1804	+	9.20886i	−0.485812	+	0.315490i
$853$	19.9447	+	3.15894i	0.682895	+	0.108160i	0.488237	−	0.872711i	$-0.337640\pi$
$853$	19.9447	+	3.15894i	0.682895	+	0.108160i	0.194658	+	0.980871i	$0.437640\pi$
$854$	−7.10417	−	6.16527i	−0.243100	−	0.210971i
$855$		0			0
$856$	23.7668	−	10.5816i	0.812331	−	0.361673i
$857$	−3.59245	−	0.962594i	−0.122716	−	0.0328816i	0.196938	−	0.980416i	$-0.436900\pi$
$857$	−3.59245	−	0.962594i	−0.122716	−	0.0328816i	−0.319654	+	0.947534i	$0.603567\pi$
$858$	−1.46584	−	1.81016i	−0.0500428	−	0.0617977i
$859$	14.7837	+	16.4190i	0.504413	+	0.560208i	0.940542	−	0.339677i	$-0.110318\pi$
$859$	14.7837	+	16.4190i	0.504413	+	0.560208i	−0.436129	+	0.899884i	$0.643651\pi$
$860$		0			0
$861$	−0.166680	+	0.100339i	−0.00568043	+	0.00341954i
$862$	10.7938	−	5.49970i	0.367637	−	0.187320i
$863$	−39.3355	−	2.06149i	−1.33900	−	0.0701738i	−0.630666	−	0.776055i	$-0.717218\pi$
$863$	−39.3355	−	2.06149i	−1.33900	−	0.0701738i	−0.708331	+	0.705881i	$0.750551\pi$
$864$	−20.8482	+	23.1542i	−0.709269	+	0.787723i
$865$		0			0
$866$	−0.448308	+	0.403659i	−0.0152341	+	0.0137169i
$867$	−17.8996	+	2.83502i	−0.607903	+	0.0962823i
$868$	36.1669	+	1.23305i	1.22758	+	0.0418525i
$869$	−8.14324	+	11.2082i	−0.276240	+	0.380212i
$870$		0			0
$871$	6.94391	−	15.5963i	0.235286	−	0.528460i
$872$	−10.2447	−	26.6884i	−0.346930	−	0.903785i
$873$	16.4716	+	25.3641i	0.557480	+	0.858444i
$874$	4.69203			0.158710
$875$		0			0
$876$	2.58191			0.0872347
$877$	12.2611	+	18.8804i	0.414027	+	0.637546i	0.982740	−	0.184990i	$-0.0592253\pi$
$877$	12.2611	+	18.8804i	0.414027	+	0.637546i	−0.568713	+	0.822536i	$0.692559\pi$
$878$	2.94223	+	7.66476i	0.0992953	+	0.258673i
$879$	−14.2266	+	31.9534i	−0.479851	+	1.07776i
$880$		0			0
$881$	−1.48864	+	2.04893i	−0.0501535	+	0.0690304i	−0.833357	−	0.552735i	$-0.813584\pi$
$881$	−1.48864	+	2.04893i	−0.0501535	+	0.0690304i	0.783204	+	0.621765i	$0.213584\pi$
$882$	−7.12831	+	6.21726i	−0.240023	+	0.209346i
$883$	−41.9699	+	6.64738i	−1.41240	+	0.223702i	−0.815566	−	0.578664i	$-0.803574\pi$
$883$	−41.9699	+	6.64738i	−1.41240	+	0.223702i	−0.596833	+	0.802366i	$0.703574\pi$
$884$	−1.93860	+	1.74552i	−0.0652022	+	0.0587083i
$885$		0			0
$886$	−14.1362	+	15.6998i	−0.474914	+	0.527445i
$887$	31.7581	+	1.66437i	1.06633	+	0.0558841i	0.577418	−	0.816448i	$-0.304060\pi$
$887$	31.7581	+	1.66437i	1.06633	+	0.0558841i	0.488913	+	0.872333i	$0.337394\pi$
$888$	20.2426	−	10.3141i	0.679298	−	0.346120i
$889$	−48.9138	+	0.894227i	−1.64052	+	0.0299914i
$890$		0			0
$891$	−0.677001	−	0.751885i	−0.0226804	−	0.0251891i
$892$	−18.9929	−	23.4543i	−0.635930	−	0.785308i
$893$	0.950220	+	0.254611i	0.0317979	+	0.00852022i
$894$	0.0315257	−	0.0140362i	0.00105438	−	0.000469440i
$895$		0			0
$896$	−4.68636	+	24.2161i	−0.156560	+	0.809002i
$897$	2.55386	+	0.404492i	0.0852710	+	0.0135056i
$898$	25.4333	−	16.5165i	0.848719	−	0.551164i
$899$	33.6791	+	58.3340i	1.12326	+	1.94555i
$900$		0			0
$901$	8.99448	+	5.19297i	0.299650	+	0.173003i
$902$	−0.0601911	−	0.0306689i	−0.00200414	−	0.00102116i
$903$	0.991680	+	14.0152i	0.0330010	+	0.466398i
$904$	10.2558	+	14.1160i	0.341104	+	0.469490i
$905$		0			0
$906$	8.50294	+	0.893695i	0.282491	+	0.0296910i
$907$	−5.62950	+	21.0096i	−0.186924	+	0.697611i	0.807286	+	0.590160i	$0.200936\pi$
$907$	−5.62950	+	21.0096i	−0.186924	+	0.697611i	−0.994210	+	0.107451i	$0.965731\pi$
$908$	−12.2512	−	4.70280i	−0.406571	−	0.156068i
$909$	−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	$0.879540\pi$
$912$	−0.229330	+	4.37587i	−0.00759387	+	0.144900i
$913$	6.96491	+	4.52306i	0.230505	+	0.149692i
$914$	−13.2937	−	11.9697i	−0.439718	−	0.395924i
$915$		0			0
$916$	−4.13261	−	1.34277i	−0.136545	−	0.0443663i
$917$	27.2672	−	34.9600i	0.900444	−	1.15448i
$918$	2.71979	−	2.71979i	0.0897665	−	0.0897665i
$919$	3.22781	+	7.24979i	0.106476	+	0.239148i	0.958924	−	0.283663i	$-0.0915498\pi$
$919$	3.22781	+	7.24979i	0.106476	+	0.239148i	−0.852448	+	0.522812i	$0.824883\pi$
$920$		0			0
$921$	3.38921	+	1.50898i	0.111678	+	0.0497224i
$922$	14.6637	+	11.8744i	0.482922	+	0.391062i
$923$	−9.84030	+	19.3127i	−0.323897	+	0.635684i
$924$	−5.26745	−	1.60566i	−0.173286	−	0.0528224i
$925$		0			0
$926$	2.39577	−	4.14960i	0.0787299	−	0.136364i
$927$	−0.579102	−	11.0499i	−0.0190202	−	0.362927i
$928$	−37.5708	+	14.4221i	−1.23332	+	0.473428i
$929$	5.09312	+	48.4578i	0.167100	+	1.58985i	0.681187	+	0.732109i	$0.261464\pi$
$929$	5.09312	+	48.4578i	0.167100	+	1.58985i	−0.514087	+	0.857738i	$0.671869\pi$
$930$		0			0
$931$	−6.34605	+	36.3414i	−0.207983	+	1.19104i
$932$	28.7785	+	28.7785i	0.942670	+	0.942670i
$933$	−2.48655	+	6.47768i	−0.0814060	+	0.212070i
$934$	22.3011	−	4.74024i	0.729713	−	0.155105i
$935$		0			0
$936$	−1.91745	+	9.02090i	−0.0626738	+	0.294857i
$937$	18.7668	+	36.8319i	0.613085	+	1.20325i	0.963765	+	0.266752i	$0.0859503\pi$
$937$	18.7668	+	36.8319i	0.613085	+	1.20325i	−0.350680	+	0.936495i	$0.614050\pi$
$938$	3.04749	+	17.2000i	0.0995039	+	0.561601i
$939$	−11.9642	+	3.88740i	−0.390437	+	0.126861i
$940$		0			0
$941$	−9.40997	−	44.2704i	−0.306756	−	1.44318i	−0.813745	−	0.581222i	$-0.802575\pi$
$941$	−9.40997	−	44.2704i	−0.306756	−	1.44318i	0.506989	−	0.861953i	$-0.330759\pi$
$942$	8.93068	−	7.23192i	0.290977	−	0.235629i
$943$	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
$947$	−5.03167	+	6.21359i	−0.163507	+	0.201915i	−0.852314	−	0.523030i	$-0.824801\pi$
$947$	−5.03167	+	6.21359i	−0.163507	+	0.201915i	0.688807	+	0.724945i	$0.258135\pi$
$948$	−16.3390	+	0.856289i	−0.530665	+	0.0278110i
$949$	2.86640	−	1.65492i	0.0930472	−	0.0537208i
$950$		0			0
$951$		−	10.1006i		−	0.327535i
$952$	1.56567	−	6.30176i	0.0507438	−	0.204241i
$953$	−0.239793	+	1.51399i	−0.00776765	+	0.0490430i	−0.991268	−	0.131865i	$-0.957904\pi$
$953$	−0.239793	+	1.51399i	−0.00776765	+	0.0490430i	0.983500	+	0.180908i	$0.0579035\pi$
$954$	15.0102	−	1.57764i	0.485974	−	0.0510779i
$955$		0			0
$956$	0.468940	−	4.46167i	0.0151666	−	0.144301i
$957$	−2.65289	−	9.90071i	−0.0857556	−	0.320044i
$958$	1.10585	+	6.98204i	0.0357283	+	0.225580i
$959$	0.754348	−	8.70508i	0.0243592	−	0.281102i
$960$		0			0
$961$	63.5919	+	13.5169i	2.05135	+	0.436028i
$962$	6.52013	−	10.0401i	0.210217	−	0.323706i
$963$	9.33277	−	14.3712i	0.300744	−	0.463106i
$964$	36.6175	+	7.78329i	1.17937	+	0.250683i
$965$		0			0
$966$	−2.39682	+	1.12007i	−0.0771165	+	0.0360376i
$967$	3.11543	+	19.6701i	0.100186	+	0.632547i	0.985774	+	0.168076i	$0.0537555\pi$
$967$	3.11543	+	19.6701i	0.100186	+	0.632547i	−0.885588	+	0.464471i	$0.846245\pi$
$968$	6.31056	+	23.5513i	0.202829	+	0.756969i
$969$	0.575322	−	5.47382i	0.0184820	−	0.175844i
$970$		0			0
$971$	−29.5811	+	3.10909i	−0.949301	+	0.0997756i	−0.566506	−	0.824058i	$-0.691705\pi$
$971$	−29.5811	+	3.10909i	−0.949301	+	0.0997756i	−0.382795	+	0.923833i	$0.625039\pi$
$972$	−3.29957	+	20.8327i	−0.105834	+	0.668208i
$973$	15.8421	−	16.4321i	0.507875	−	0.526791i
$974$			0.412847i			0.0132285i
$975$		0			0
$976$	−2.93248	+	1.69307i	−0.0938663	+	0.0541938i
$977$	−32.0110	+	1.67762i	−1.02412	+	0.0536720i	−0.556993	−	0.830517i	$-0.688045\pi$
$977$	−32.0110	+	1.67762i	−1.02412	+	0.0536720i	−0.467129	+	0.884189i	$0.654712\pi$
$978$	1.91843	−	2.36907i	0.0613448	−	0.0757545i
$979$	−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
$983$	29.9691	−	24.2685i	0.955866	−	0.774045i	−0.0183109	−	0.999832i	$-0.505829\pi$
$983$	29.9691	−	24.2685i	0.955866	−	0.774045i	0.974177	+	0.225788i	$0.0724955\pi$
$984$	−0.0403529	−	0.189846i	−0.00128640	−	0.00605206i
$985$		0			0
$986$	4.72497	−	1.53524i	0.150474	−	0.0488919i
$987$	−0.546180	+	0.0967716i	−0.0173851	+	0.00308027i
$988$	6.71245	+	13.1739i	0.213551	+	0.419118i
$989$	1.12602	−	5.29751i	0.0358054	−	0.168451i
$990$		0			0
$991$	−4.56112	+	0.969496i	−0.144889	+	0.0307971i	−0.279785	−	0.960063i	$-0.590263\pi$
$991$	−4.56112	+	0.969496i	−0.144889	+	0.0307971i	0.134896	+	0.990860i	$0.456930\pi$
$992$	−20.5573	+	53.5535i	−0.652694	+	1.70033i
$993$	5.73911	+	5.73911i	0.182125	+	0.182125i
$994$	−2.72094	−	22.0099i	−0.0863030	−	0.698112i
$995$		0			0
$996$	1.02518	+	9.75395i	0.0324841	+	0.309066i
$997$	15.2110	−	5.83897i	0.481739	−	0.184922i	−0.105365	−	0.994434i	$-0.533601\pi$
$997$	15.2110	−	5.83897i	0.481739	−	0.184922i	0.587104	+	0.809511i	$0.300268\pi$
$998$	−0.255223	−	4.86995i	−0.00807894	−	0.154155i
$999$	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.c.607.12		288
5.2	odd	4		875.2.bb.b.768.7		288
5.3	odd	4		875.2.bb.a.768.12		288
5.4	even	2		175.2.x.a.117.7	yes	288
7.3	odd	6	inner	875.2.bb.c.857.7		288
25.3	odd	20	inner	875.2.bb.c.243.7		288
25.4	even	10		875.2.bb.b.257.7		288
25.21	even	5		875.2.bb.a.257.12		288
25.22	odd	20		175.2.x.a.103.12	yes	288
35.3	even	12		875.2.bb.a.143.12		288
35.17	even	12		875.2.bb.b.143.7		288
35.24	odd	6		175.2.x.a.17.12	yes	288
175.3	even	60	inner	875.2.bb.c.493.12		288
175.122	even	60		175.2.x.a.3.7	✓	288
175.129	odd	30		875.2.bb.b.507.7		288
175.171	odd	30		875.2.bb.a.507.12		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.7	✓	288	175.122	even	60
175.2.x.a.17.12	yes	288	35.24	odd	6
175.2.x.a.103.12	yes	288	25.22	odd	20
175.2.x.a.117.7	yes	288	5.4	even	2
875.2.bb.a.143.12		288	35.3	even	12
875.2.bb.a.257.12		288	25.21	even	5
875.2.bb.a.507.12		288	175.171	odd	30
875.2.bb.a.768.12		288	5.3	odd	4
875.2.bb.b.143.7		288	35.17	even	12
875.2.bb.b.257.7		288	25.4	even	10
875.2.bb.b.507.7		288	175.129	odd	30
875.2.bb.b.768.7		288	5.2	odd	4
875.2.bb.c.243.7		288	25.3	odd	20	inner
875.2.bb.c.493.12		288	175.3	even	60	inner
875.2.bb.c.607.12		288	1.1	even	1	trivial
875.2.bb.c.857.7		288	7.3	odd	6	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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.423319 + 0.651855i) q^{2} +(-0.402507 - 1.04857i) q^{3} +(0.567758 - 1.27521i) q^{4} +(0.513123 - 0.706254i) q^{6} +(-1.24404 - 2.33503i) q^{7} +(2.60695 - 0.412900i) q^{8} +(1.29196 - 1.16328i) q^{9} +(-0.888306 + 0.986564i) q^{11} +(-1.56566 - 0.0820529i) q^{12} +(-1.79077 + 0.912442i) q^{13} +(0.995478 - 1.79939i) q^{14} +(-0.495338 - 0.550128i) q^{16} +(0.585165 + 0.722619i) q^{17} +(1.30520 + 0.349728i) q^{18} +(4.81455 - 2.14358i) q^{19} +(-1.94770 + 2.24432i) q^{21} +(-1.01913 - 0.161415i) q^{22} +(0.960654 - 0.623856i) q^{23} +(-1.48227 - 2.56736i) q^{24} +(-1.35285 - 0.781066i) q^{26} +(-4.74204 - 2.41619i) q^{27} +(-3.68396 + 0.260667i) q^{28} +(-4.04060 - 5.56140i) q^{29} +(-9.74492 - 1.02423i) q^{31} +(1.51519 - 5.65478i) q^{32} +(1.39203 + 0.534349i) q^{33} +(-0.223331 + 0.687341i) q^{34} +(-0.749906 - 2.30797i) q^{36} +(-0.401079 + 7.65304i) q^{37} +(3.43539 + 2.23097i) q^{38} +(1.67755 + 1.51047i) q^{39} +(0.0622653 + 0.0202312i) q^{41} +(-2.28747 - 0.319555i) q^{42} +(3.34331 - 3.34331i) q^{43} +(0.753729 + 1.69290i) q^{44} +(0.813327 + 0.362116i) q^{46} +(0.145063 + 0.117470i) q^{47} +(-0.377469 + 0.740824i) q^{48} +(-3.90475 + 5.80972i) q^{49} +(0.522180 - 0.904443i) q^{51} +(0.146828 + 2.80164i) q^{52} +(10.4278 - 4.00284i) q^{53} +(-0.432393 - 4.11394i) q^{54} +(-4.20727 - 5.57365i) q^{56} +(-4.18557 - 4.18557i) q^{57} +(1.91476 - 4.98813i) q^{58} +(-4.71962 + 1.00319i) q^{59} +(0.951026 - 4.47423i) q^{61} +(-3.45756 - 6.78585i) q^{62} +(-4.32354 - 1.56960i) q^{63} +(2.91943 - 0.948580i) q^{64} +(0.240954 + 1.13360i) q^{66} +(-6.60139 + 5.34570i) q^{67} +(1.25372 - 0.335933i) q^{68} +(-1.04082 - 0.756203i) q^{69} +(8.72491 - 6.33902i) q^{71} +(2.88774 - 3.56607i) q^{72} +(-1.64457 + 0.0861882i) q^{73} +(-5.15845 + 2.97823i) q^{74} -7.35658i q^{76} +(3.40874 + 0.846904i) q^{77} +(-0.274469 + 1.73293i) q^{78} +(10.3787 - 1.09084i) q^{79} +(-0.0796638 + 0.757950i) q^{81} +(0.0131703 + 0.0491522i) q^{82} +(-0.978599 - 6.17863i) q^{83} +(1.75614 + 3.75795i) q^{84} +(3.59464 + 0.764065i) q^{86} +(-4.20513 + 6.47533i) q^{87} +(-1.90842 + 2.93870i) q^{88} +(15.3519 + 3.26314i) q^{89} +(4.35836 + 3.04639i) q^{91} +(-0.250126 - 1.57923i) q^{92} +(2.84842 + 10.6304i) q^{93} +(-0.0151652 + 0.144287i) q^{94} +(-6.53929 + 0.687307i) q^{96} +(-2.72136 + 17.1820i) q^{97} +(-5.44005 - 0.0859631i) q^{98} +2.30795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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