LMFDB - Embedded newform 475.2.bb.b.393.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(32,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			393.4
Character	$\chi$	$=$	475.393
Dual form			475.2.bb.b.307.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.297624 + 0.0260387i) q^{2} +(-1.75625 + 0.818952i) q^{3} +(-1.88171 - 0.331797i) q^{4} +(-0.544026 + 0.198009i) q^{6} +(-0.0866366 - 0.323332i) q^{7} +(-1.12856 - 0.302398i) q^{8} +(0.485360 - 0.578430i) q^{9} +(0.885063 + 1.53297i) q^{11} +(3.57648 - 0.958315i) q^{12} +(0.968521 - 2.07700i) q^{13} +(-0.0173660 - 0.0984873i) q^{14} +(3.26301 + 1.18764i) q^{16} +(0.238918 - 2.73085i) q^{17} +(0.159516 - 0.159516i) q^{18} +(-0.174252 - 4.35541i) q^{19} +(0.416949 + 0.496900i) q^{21} +(0.223499 + 0.479296i) q^{22} +(7.04590 - 4.93359i) q^{23} +(2.22969 - 0.393154i) q^{24} +(0.342337 - 0.592946i) q^{26} +(1.12592 - 4.20197i) q^{27} +(0.0557446 + 0.637164i) q^{28} +(4.70481 + 3.94780i) q^{29} +(-1.80927 - 1.04458i) q^{31} +(3.05804 + 1.42599i) q^{32} +(-2.80982 - 1.96746i) q^{33} +(0.142216 - 0.806545i) q^{34} +(-1.10523 + 0.927398i) q^{36} +(4.27833 + 4.27833i) q^{37} +(0.0615479 - 1.30081i) q^{38} +4.44090i q^{39} +(2.08289 - 5.72270i) q^{41} +(0.111155 + 0.158746i) q^{42} +(-3.06524 + 4.37761i) q^{43} +(-1.15680 - 3.17828i) q^{44} +(2.22549 - 1.28489i) q^{46} +(-5.75408 + 0.503417i) q^{47} +(-6.70326 + 0.586460i) q^{48} +(5.96514 - 3.44398i) q^{49} +(1.81683 + 4.99171i) q^{51} +(-2.51162 + 3.58697i) q^{52} +(-1.22167 - 1.74473i) q^{53} +(0.444513 - 1.22129i) q^{54} +0.391100i q^{56} +(3.87290 + 7.50648i) q^{57} +(1.29747 + 1.29747i) q^{58} +(-1.26888 + 1.06472i) q^{59} +(1.59718 - 9.05803i) q^{61} +(-0.511282 - 0.358003i) q^{62} +(-0.229075 - 0.106819i) q^{63} +(-5.14139 - 2.96838i) q^{64} +(-0.785040 - 0.658727i) q^{66} +(-0.957732 - 10.9469i) q^{67} +(-1.35566 + 5.05941i) q^{68} +(-8.33397 + 14.4349i) q^{69} +(-15.3710 + 2.71031i) q^{71} +(-0.722676 + 0.506024i) q^{72} +(2.33808 + 5.01402i) q^{73} +(1.16193 + 1.38473i) q^{74} +(-1.11722 + 8.25346i) q^{76} +(0.418981 - 0.418981i) q^{77} +(-0.115635 + 1.32172i) q^{78} +(-14.0660 - 5.11962i) q^{79} +(1.85719 + 10.5326i) q^{81} +(0.768931 - 1.64898i) q^{82} +(3.20933 - 0.859936i) q^{83} +(-0.619708 - 1.07337i) q^{84} +(-1.02628 + 1.22307i) q^{86} +(-11.4959 - 3.08031i) q^{87} +(-0.535283 - 1.99770i) q^{88} +(9.75391 - 3.55013i) q^{89} +(-0.755470 - 0.133210i) q^{91} +(-14.8953 + 6.94580i) q^{92} +(4.03298 + 0.352840i) q^{93} -1.72566 q^{94} -6.53849 q^{96} +(-5.97565 - 0.522802i) q^{97} +(1.86504 - 0.869685i) q^{98} +(1.31629 + 0.232098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	0.297624	+	0.0260387i	0.210452	+	0.0184122i	0.191894	−	0.981416i	$-0.438537\pi$
$2$	0.297624	+	0.0260387i	0.210452	+	0.0184122i	0.0185578	+	0.999828i	$0.494093\pi$
$3$	−1.75625	+	0.818952i	−1.01397	+	0.472822i	−0.857293	−	0.514828i	$-0.827856\pi$
$3$	−1.75625	+	0.818952i	−1.01397	+	0.472822i	−0.156676	+	0.987650i	$0.550078\pi$
$4$	−1.88171	−	0.331797i	−0.940857	−	0.165898i
$5$		0			0
$5$		0			0
$6$	−0.544026	+	0.198009i	−0.222098	+	0.0808369i
$7$	−0.0866366	−	0.323332i	−0.0327456	−	0.122208i	0.947618	−	0.319405i	$-0.103483\pi$
$7$	−0.0866366	−	0.323332i	−0.0327456	−	0.122208i	−0.980364	+	0.197197i	$0.936816\pi$
$8$	−1.12856	−	0.302398i	−0.399008	−	0.106914i
$9$	0.485360	−	0.578430i	0.161787	−	0.192810i
$10$		0			0
$11$	0.885063	+	1.53297i	0.266856	+	0.462209i	0.968048	−	0.250764i	$-0.0806817\pi$
$11$	0.885063	+	1.53297i	0.266856	+	0.462209i	−0.701192	+	0.712973i	$0.747348\pi$
$12$	3.57648	−	0.958315i	1.03244	−	0.276642i
$13$	0.968521	−	2.07700i	0.268619	−	0.576056i	−0.725012	−	0.688736i	$-0.758166\pi$
$13$	0.968521	−	2.07700i	0.268619	−	0.576056i	0.993631	+	0.112680i	$0.0359436\pi$
$14$	−0.0173660	−	0.0984873i	−0.00464125	−	0.0263218i
$15$		0			0
$16$	3.26301	+	1.18764i	0.815752	+	0.296909i
$17$	0.238918	−	2.73085i	0.0579462	−	0.662328i	−0.910566	−	0.413363i	$-0.864354\pi$
$17$	0.238918	−	2.73085i	0.0579462	−	0.662328i	0.968512	−	0.248965i	$-0.0800905\pi$
$18$	0.159516	−	0.159516i	0.0375984	−	0.0375984i
$19$	−0.174252	−	4.35541i	−0.0399761	−	0.999201i
$19$	−0.174252	−	4.35541i	−0.0399761	−	0.999201i
$20$		0			0
$21$	0.416949	+	0.496900i	0.0909857	+	0.108432i
$22$	0.223499	+	0.479296i	0.0476502	+	0.102186i
$23$	7.04590	−	4.93359i	1.46917	−	1.02872i	0.480772	−	0.876845i	$-0.340356\pi$
$23$	7.04590	−	4.93359i	1.46917	−	1.02872i	0.988399	−	0.151879i	$-0.0485325\pi$
$24$	2.22969	−	0.393154i	0.455133	−	0.0802523i
$25$		0			0
$26$	0.342337	−	0.592946i	0.0671379	−	0.116286i
$27$	1.12592	−	4.20197i	0.216683	−	0.808670i
$28$	0.0557446	+	0.637164i	0.0105347	+	0.120413i
$29$	4.70481	+	3.94780i	0.873661	+	0.733089i	0.964866	−	0.262744i	$-0.0846273\pi$
$29$	4.70481	+	3.94780i	0.873661	+	0.733089i	−0.0912048	+	0.995832i	$0.529072\pi$
$30$		0			0
$31$	−1.80927	−	1.04458i	−0.324954	−	0.187612i	0.328645	−	0.944454i	$-0.393408\pi$
$31$	−1.80927	−	1.04458i	−0.324954	−	0.187612i	−0.653599	+	0.756841i	$0.726742\pi$
$32$	3.05804	+	1.42599i	0.540590	+	0.252081i
$33$	−2.80982	−	1.96746i	−0.489127	−	0.342490i
$34$	0.142216	−	0.806545i	0.0243898	−	0.138321i
$35$		0			0
$36$	−1.10523	+	0.927398i	−0.184205	+	0.154566i
$37$	4.27833	+	4.27833i	0.703353	+	0.703353i	0.965129	−	0.261776i	$-0.0843082\pi$
$37$	4.27833	+	4.27833i	0.703353	+	0.703353i	−0.261776	+	0.965129i	$0.584308\pi$
$38$	0.0615479	−	1.30081i	0.00998439	−	0.211020i
$39$			4.44090i			0.711113i
$40$		0			0
$41$	2.08289	−	5.72270i	0.325293	−	0.893736i	−0.663992	−	0.747740i	$-0.731139\pi$
$41$	2.08289	−	5.72270i	0.325293	−	0.893736i	0.989285	−	0.145996i	$-0.0466387\pi$
$42$	0.111155	+	0.158746i	0.0171516	+	0.0244951i
$43$	−3.06524	+	4.37761i	−0.467444	+	0.667580i	−0.981783	−	0.190008i	$-0.939149\pi$
$43$	−3.06524	+	4.37761i	−0.467444	+	0.667580i	0.514338	+	0.857587i	$0.328038\pi$
$44$	−1.15680	−	3.17828i	−0.174394	−	0.479144i
$45$		0			0
$46$	2.22549	−	1.28489i	0.328131	−	0.189446i
$47$	−5.75408	+	0.503417i	−0.839319	+	0.0734309i	−0.498704	−	0.866772i	$-0.666191\pi$
$47$	−5.75408	+	0.503417i	−0.839319	+	0.0734309i	−0.340615	+	0.940203i	$0.610635\pi$
$48$	−6.70326	+	0.586460i	−0.967533	+	0.0846482i
$49$	5.96514	−	3.44398i	0.852163	−	0.491996i
$50$		0			0
$51$	1.81683	+	4.99171i	0.254408	+	0.698979i
$52$	−2.51162	+	3.58697i	−0.348299	+	0.497423i
$53$	−1.22167	−	1.74473i	−0.167809	−	0.239656i	0.726436	−	0.687235i	$-0.241176\pi$
$53$	−1.22167	−	1.74473i	−0.167809	−	0.239656i	−0.894245	+	0.447578i	$0.852287\pi$
$54$	0.444513	−	1.22129i	0.0604906	−	0.166197i
$55$		0			0
$56$			0.391100i			0.0522629i
$57$	3.87290	+	7.50648i	0.512979	+	0.994258i
$58$	1.29747	+	1.29747i	0.170366	+	0.170366i
$59$	−1.26888	+	1.06472i	−0.165194	+	0.138614i	−0.721637	−	0.692271i	$-0.756610\pi$
$59$	−1.26888	+	1.06472i	−0.165194	+	0.138614i	0.556443	+	0.830886i	$0.312166\pi$
$60$		0			0
$61$	1.59718	−	9.05803i	0.204497	−	1.15976i	−0.693731	−	0.720234i	$-0.744035\pi$
$61$	1.59718	−	9.05803i	0.204497	−	1.15976i	0.898229	−	0.439528i	$-0.144854\pi$
$62$	−0.511282	−	0.358003i	−0.0649329	−	0.0454665i
$63$	−0.229075	−	0.106819i	−0.0288607	−	0.0134580i
$64$	−5.14139	−	2.96838i	−0.642674	−	0.371048i
$65$		0			0
$66$	−0.785040	−	0.658727i	−0.0966317	−	0.0810836i
$67$	−0.957732	−	10.9469i	−0.117006	−	1.33738i	−0.796918	−	0.604087i	$-0.793538\pi$
$67$	−0.957732	−	10.9469i	−0.117006	−	1.33738i	0.679913	−	0.733293i	$-0.262018\pi$
$68$	−1.35566	+	5.05941i	−0.164398	+	0.613543i
$69$	−8.33397	+	14.4349i	−1.00329	+	1.73775i
$70$		0			0
$71$	−15.3710	+	2.71031i	−1.82420	+	0.321655i	−0.977583	−	0.210553i	$-0.932474\pi$
$71$	−15.3710	+	2.71031i	−1.82420	+	0.321655i	−0.846614	+	0.532208i	$0.821363\pi$
$72$	−0.722676	+	0.506024i	−0.0851682	+	0.0596354i
$73$	2.33808	+	5.01402i	0.273651	+	0.586846i	0.994320	−	0.106433i	$-0.0339430\pi$
$73$	2.33808	+	5.01402i	0.273651	+	0.586846i	−0.720669	+	0.693279i	$0.756165\pi$
$74$	1.16193	+	1.38473i	0.135072	+	0.160972i
$75$		0			0
$76$	−1.11722	+	8.25346i	−0.128154	+	0.946737i
$77$	0.418981	−	0.418981i	0.0477473	−	0.0477473i
$78$	−0.115635	+	1.32172i	−0.0130931	+	0.149655i
$79$	−14.0660	−	5.11962i	−1.58255	−	0.576002i	−0.606796	−	0.794857i	$-0.707546\pi$
$79$	−14.0660	−	5.11962i	−1.58255	−	0.576002i	−0.975757	+	0.218855i	$0.929768\pi$
$80$		0			0
$81$	1.85719	+	10.5326i	0.206354	+	1.17029i
$82$	0.768931	−	1.64898i	0.0849142	−	0.182099i
$83$	3.20933	−	0.859936i	0.352269	−	0.0943903i	−0.0783450	−	0.996926i	$-0.524964\pi$
$83$	3.20933	−	0.859936i	0.352269	−	0.0943903i	0.430614	+	0.902536i	$0.358297\pi$
$84$	−0.619708	−	1.07337i	−0.0676157	−	0.117114i
$85$		0			0
$86$	−1.02628	+	1.22307i	−0.110666	+	0.131887i
$87$	−11.4959	−	3.08031i	−1.23249	−	0.330244i
$88$	−0.535283	−	1.99770i	−0.0570613	−	0.212956i
$89$	9.75391	−	3.55013i	1.03391	−	0.376313i	0.231343	−	0.972872i	$-0.425688\pi$
$89$	9.75391	−	3.55013i	1.03391	−	0.376313i	0.802569	+	0.596559i	$0.203466\pi$
$90$		0			0
$91$	−0.755470	−	0.133210i	−0.0791948	−	0.0139642i
$92$	−14.8953	+	6.94580i	−1.55294	+	0.724150i
$93$	4.03298	+	0.352840i	0.418201	+	0.0365878i
$94$	−1.72566			−0.177988
$95$		0			0
$96$	−6.53849			−0.667332
$97$	−5.97565	−	0.522802i	−0.606736	−	0.0530825i	−0.220352	−	0.975420i	$-0.570720\pi$
$97$	−5.97565	−	0.522802i	−0.606736	−	0.0530825i	−0.386384	+	0.922338i	$0.626276\pi$
$98$	1.86504	−	0.869685i	0.188398	−	0.0878514i
$99$	1.31629	+	0.232098i	0.132292	+	0.0233267i
$100$		0			0
$101$	10.0826	−	3.66976i	1.00326	−	0.365155i	0.212416	−	0.977179i	$-0.431867\pi$
$101$	10.0826	−	3.66976i	1.00326	−	0.365155i	0.790839	+	0.612024i	$0.209645\pi$
$102$	0.410756	+	1.53296i	0.0406709	+	0.151786i
$103$	10.3664	+	2.77767i	1.02143	+	0.273692i	0.730398	−	0.683021i	$-0.239334\pi$
$103$	10.3664	+	2.77767i	1.02143	+	0.273692i	0.291033	+	0.956713i	$0.406001\pi$
$104$	−1.72112	+	2.05115i	−0.168770	+	0.201132i
$105$		0			0
$106$	−0.318168	−	0.551083i	−0.0309032	−	0.0535259i
$107$	2.12744	−	0.570046i	0.205668	−	0.0551085i	−0.154514	−	0.987991i	$-0.549381\pi$
$107$	2.12744	−	0.570046i	0.205668	−	0.0551085i	0.360182	+	0.932882i	$0.382715\pi$
$108$	−3.51285	+	7.53334i	−0.338024	+	0.724896i
$109$	1.51271	+	8.57902i	0.144892	+	0.821721i	0.967454	+	0.253046i	$0.0814325\pi$
$109$	1.51271	+	8.57902i	0.144892	+	0.821721i	−0.822563	+	0.568675i	$0.807456\pi$
$110$		0			0
$111$	−11.0175	−	4.01006i	−1.04574	−	0.380618i
$112$	0.101306	−	1.15793i	0.00957247	−	0.109414i
$113$	8.30039	−	8.30039i	0.780835	−	0.780835i	−0.199137	−	0.979972i	$-0.563814\pi$
$113$	8.30039	−	8.30039i	0.780835	−	0.780835i	0.979972	+	0.199137i	$0.0638138\pi$
$114$	0.957209	+	2.33495i	0.0896509	+	0.218688i
$115$		0			0
$116$	−7.54323	−	8.98967i	−0.700372	−	0.834670i
$117$	−0.731317	−	1.56831i	−0.0676103	−	0.144991i
$118$	−0.405372	+	0.283845i	−0.0373176	+	0.0261300i
$119$	−0.903671	+	0.159342i	−0.0828394	+	0.0146068i
$120$		0			0
$121$	3.93333	−	6.81272i	0.357575	−	0.619338i
$122$	0.711217	−	2.65430i	0.0643906	−	0.240309i
$123$	1.02854	+	11.7563i	0.0927404	+	1.06003i
$124$	3.05794	+	2.56591i	0.274611	+	0.230426i
$125$		0			0
$126$	−0.0653967	−	0.0377568i	−0.00582600	−	0.00336364i
$127$	6.06809	+	2.82960i	0.538456	+	0.251086i	0.672769	−	0.739853i	$-0.265105\pi$
$127$	6.06809	+	2.82960i	0.538456	+	0.251086i	−0.134313	+	0.990939i	$0.542883\pi$
$128$	−6.98083	−	4.88803i	−0.617024	−	0.432045i
$129$	1.79826	−	10.1985i	0.158328	−	0.897924i
$130$		0			0
$131$	5.62950	−	4.72371i	0.491851	−	0.412712i	−0.362838	−	0.931852i	$-0.618192\pi$
$131$	5.62950	−	4.72371i	0.491851	−	0.412712i	0.854689	+	0.519140i	$0.173748\pi$
$132$	4.63448	+	4.63448i	0.403380	+	0.403380i
$133$	−1.39315	+	0.433679i	−0.120801	+	0.0376048i
$134$		−	3.28301i		−	0.283609i
$135$		0			0
$136$	−1.09544	+	3.00969i	−0.0939331	+	0.258079i
$137$	−3.01799	−	4.31014i	−0.257845	−	0.368240i	0.669269	−	0.743020i	$-0.266607\pi$
$137$	−3.01799	−	4.31014i	−0.257845	−	0.368240i	−0.927114	+	0.374780i	$0.877718\pi$
$138$	−2.85625	+	4.07915i	−0.243140	+	0.347240i
$139$	6.35505	+	17.4603i	0.539028	+	1.48097i	0.848052	+	0.529913i	$0.177775\pi$
$139$	6.35505	+	17.4603i	0.539028	+	1.48097i	−0.309024	+	0.951054i	$0.600002\pi$
$140$		0			0
$141$	9.69332	−	5.59644i	0.816324	−	0.471305i
$142$	−4.64534	+	0.406414i	−0.389828	+	0.0341055i
$143$	4.04119	−	0.353558i	0.337941	−	0.0295660i
$144$	2.27070	−	1.31099i	0.189225	−	0.109249i
$145$		0			0
$146$	0.565308	+	1.55317i	0.0467853	+	0.128541i
$147$	−7.65581	+	10.9336i	−0.631441	+	0.901791i
$148$	−6.63105	−	9.47012i	−0.545069	−	0.778439i
$149$	6.71169	−	18.4402i	0.549843	−	1.51068i	−0.284080	−	0.958800i	$-0.591688\pi$
$149$	6.71169	−	18.4402i	0.549843	−	1.51068i	0.833923	−	0.551880i	$-0.186090\pi$
$150$		0			0
$151$		−	1.28151i		−	0.104288i	−0.998640	−	0.0521440i	$-0.983395\pi$
$151$		−	1.28151i		−	0.104288i	0.998640	−	0.0521440i	$-0.0166055\pi$
$152$	−1.12041	+	4.96806i	−0.0908776	+	0.402963i
$153$	−1.46364	−	1.46364i	−0.118329	−	0.118329i
$154$	0.135608	−	0.113789i	0.0109276	−	0.00916938i
$155$		0			0
$156$	1.47348	−	8.35649i	0.117972	−	0.669055i
$157$	13.3302	+	9.33390i	1.06387	+	0.744926i	0.968122	−	0.250480i	$-0.0805883\pi$
$157$	13.3302	+	9.33390i	1.06387	+	0.744926i	0.0957434	+	0.995406i	$0.469477\pi$
$158$	−4.05308	−	1.88998i	−0.322446	−	0.150359i
$159$	3.57440	+	2.06368i	0.283468	+	0.163661i
$160$		0			0
$161$	−2.20562	−	1.85074i	−0.173827	−	0.145858i
$162$	0.278487	+	3.18312i	0.0218800	+	0.250089i
$163$	−2.63825	+	9.84609i	−0.206644	+	0.771205i	0.782298	+	0.622904i	$0.214047\pi$
$163$	−2.63825	+	9.84609i	−0.206644	+	0.771205i	−0.988942	+	0.148301i	$0.952619\pi$
$164$	−5.81818	+	10.0774i	−0.454324	+	0.786912i
$165$		0			0
$166$	0.977564	−	0.172371i	0.0758737	−	0.0133786i
$167$	−2.13302	+	1.49356i	−0.165058	+	0.115575i	−0.653187	−	0.757197i	$-0.726568\pi$
$167$	−2.13302	+	1.49356i	−0.165058	+	0.115575i	0.488129	+	0.872772i	$0.337680\pi$
$168$	−0.320292	−	0.686868i	−0.0247111	−	0.0529930i
$169$	4.98034	+	5.93534i	0.383103	+	0.456565i
$170$		0			0
$171$	−2.60388	−	2.01315i	−0.199123	−	0.153950i
$172$	7.22038	−	7.22038i	0.550549	−	0.550549i
$173$	1.59591	−	18.2413i	0.121335	−	1.38686i	−0.654565	−	0.756006i	$-0.727148\pi$
$173$	1.59591	−	18.2413i	0.121335	−	1.38686i	0.775900	−	0.630856i	$-0.217296\pi$
$174$	−3.34124	−	1.21611i	−0.253299	−	0.0921931i
$175$		0			0
$176$	1.06735	+	6.05324i	0.0804545	+	0.456280i
$177$	1.35651	−	2.90905i	0.101962	−	0.218658i
$178$	2.99544	−	0.802625i	0.224518	−	0.0601593i
$179$	−3.88436	−	6.72790i	−0.290331	−	0.502867i	0.683557	−	0.729897i	$-0.260432\pi$
$179$	−3.88436	−	6.72790i	−0.290331	−	0.502867i	−0.973888	+	0.227030i	$0.927099\pi$
$180$		0			0
$181$	−12.3085	+	14.6688i	−0.914887	+	1.09032i	0.0807244	+	0.996736i	$0.474277\pi$
$181$	−12.3085	+	14.6688i	−0.914887	+	1.09032i	−0.995611	+	0.0935835i	$0.970168\pi$
$182$	−0.221377	−	0.0593179i	−0.0164096	−	0.00439693i
$183$	4.61305	+	17.2162i	0.341007	+	1.27265i
$184$	−9.44366	+	3.43721i	−0.696196	+	0.253395i
$185$		0			0
$186$	1.19112	+	0.210027i	0.0873375	+	0.0154000i
$187$	4.39778	−	2.05072i	0.321597	−	0.149963i
$188$	10.9946	+	0.961900i	0.801861	+	0.0701538i
$189$	−1.45618			−0.105921
$190$		0			0
$191$	15.8411			1.14622			0.573110	−	0.819478i	$-0.305737\pi$
$191$	15.8411			1.14622			0.573110	+	0.819478i	$0.305737\pi$
$192$	11.4605	+	1.00267i	0.827092	+	0.0723611i
$193$	−24.5928	+	11.4678i	−1.77023	+	0.825470i	−0.794252	+	0.607589i	$0.792137\pi$
$193$	−24.5928	+	11.4678i	−1.77023	+	0.825470i	−0.975975	+	0.217882i	$0.930085\pi$
$194$	−1.76488	−	0.311197i	−0.126711	−	0.0223426i
$195$		0			0
$196$	−12.3674	+	4.50136i	−0.883385	+	0.321526i
$197$	−3.74333	−	13.9703i	−0.266701	−	0.995343i	−0.961201	−	0.275850i	$-0.911041\pi$
$197$	−3.74333	−	13.9703i	−0.266701	−	0.995343i	0.694499	−	0.719493i	$-0.255626\pi$
$198$	0.385716	+	0.103352i	0.0274117	+	0.00734494i
$199$	2.04942	−	2.44240i	0.145279	−	0.173137i	−0.688498	−	0.725239i	$-0.741729\pi$
$199$	2.04942	−	2.44240i	0.145279	−	0.173137i	0.833777	+	0.552101i	$0.186174\pi$
$200$		0			0
$201$	10.6470	+	18.4412i	0.750983	+	1.30074i
$202$	3.09638	−	0.829671i	0.217860	−	0.0583755i
$203$	0.868843	−	1.86324i	0.0609808	−	0.130774i
$204$	−1.76253	−	9.99579i	−0.123402	−	0.699845i
$205$		0			0
$206$	3.01296	+	1.09663i	0.209923	+	0.0764057i
$207$	0.566063	−	6.47013i	0.0393441	−	0.449705i
$208$	5.62701	−	5.62701i	0.390163	−	0.390163i
$209$	6.52251	−	4.12194i	0.451172	−	0.285120i
$210$		0			0
$211$	0.360006	+	0.429039i	0.0247838	+	0.0295362i	0.778294	−	0.627900i	$-0.216085\pi$
$211$	0.360006	+	0.429039i	0.0247838	+	0.0295362i	−0.753510	+	0.657436i	$0.771641\pi$
$212$	1.71994	+	3.68842i	0.118126	+	0.253322i
$213$	24.7756	−	17.3480i	1.69759	−	1.18867i
$214$	0.648021	−	0.114264i	0.0442978	−	0.00781090i
$215$		0			0
$216$	−2.54134	+	4.40173i	−0.172916	+	0.299499i
$217$	−0.180998	+	0.675493i	−0.0122869	+	0.0458555i
$218$	0.226833	+	2.59271i	0.0153630	+	0.175600i
$219$	−8.21248	−	6.89109i	−0.554948	−	0.465656i
$220$		0			0
$221$	−5.44058	−	3.14112i	−0.365973	−	0.211294i
$222$	−3.17467	−	1.48037i	−0.213070	−	0.0993560i
$223$	−18.4399	−	12.9118i	−1.23483	−	0.864635i	−0.240463	−	0.970658i	$-0.577299\pi$
$223$	−18.4399	−	12.9118i	−1.23483	−	0.864635i	−0.994364	+	0.106023i	$0.966188\pi$
$224$	0.196130	−	1.11231i	0.0131045	−	0.0743191i
$225$		0			0
$226$	2.68653	−	2.25426i	0.178705	−	0.149951i
$227$	−11.5076	−	11.5076i	−0.763785	−	0.763785i	0.213220	−	0.977004i	$-0.431605\pi$
$227$	−11.5076	−	11.5076i	−0.763785	−	0.763785i	−0.977004	+	0.213220i	$0.931605\pi$
$228$	−4.79707	−	15.4101i	−0.317694	−	1.02056i
$229$		−	11.5082i		−	0.760486i	−0.924887	−	0.380243i	$-0.875840\pi$
$229$		−	11.5082i		−	0.760486i	0.924887	−	0.380243i	$-0.124160\pi$
$230$		0			0
$231$	−0.392709	+	1.07896i	−0.0258384	+	0.0709903i
$232$	−4.11587	−	5.87808i	−0.270220	−	0.385915i
$233$	−10.0958	+	14.4183i	−0.661398	+	0.944574i	0.338596	+	0.940932i	$0.390048\pi$
$233$	−10.0958	+	14.4183i	−0.661398	+	0.944574i	−0.999993	+	0.00364164i	$0.998841\pi$
$234$	−0.176820	−	0.485810i	−0.0115591	−	0.0317584i
$235$		0			0
$236$	2.74094	−	1.58248i	0.178420	−	0.103011i
$237$	28.8962	−	2.52809i	1.87701	−	0.164217i
$238$	−0.273103	+	0.0238934i	−0.0177026	+	0.00154878i
$239$	−2.74935	+	1.58734i	−0.177841	+	0.102676i	−0.586278	−	0.810110i	$-0.699407\pi$
$239$	−2.74935	+	1.58734i	−0.177841	+	0.102676i	0.408437	+	0.912786i	$0.366074\pi$
$240$		0			0
$241$	2.63620	+	7.24289i	0.169812	+	0.466555i	0.995183	−	0.0980359i	$-0.0312560\pi$
$241$	2.63620	+	7.24289i	0.169812	+	0.466555i	−0.825371	+	0.564591i	$0.809034\pi$
$242$	1.34805	−	1.92521i	0.0866557	−	0.123757i
$243$	−4.40186	−	6.28651i	−0.282379	−	0.403280i
$244$	−6.01085	+	16.5147i	−0.384805	+	1.05724i
$245$		0			0
$246$			3.52573i			0.224792i
$247$	−9.21496	−	3.85639i	−0.586334	−	0.245376i
$248$	1.72600	+	1.72600i	0.109601	+	0.109601i
$249$	−4.93212	+	4.13854i	−0.312561	+	0.262270i
$250$		0			0
$251$	−0.155567	+	0.882266i	−0.00981932	+	0.0556881i	−0.989324	−	0.145735i	$-0.953445\pi$
$251$	−0.155567	+	0.882266i	−0.00981932	+	0.0556881i	0.979504	+	0.201423i	$0.0645565\pi$
$252$	0.395611	+	0.277010i	0.0249211	+	0.0174500i
$253$	13.7991	+	6.43464i	0.867544	+	0.404542i
$254$	1.73233	+	1.00016i	0.108696	+	0.0627557i
$255$		0			0
$256$	7.14527	+	5.99559i	0.446579	+	0.374725i
$257$	0.187810	+	2.14668i	0.0117153	+	0.133906i	0.999800	−	0.0200056i	$-0.00636840\pi$
$257$	0.187810	+	2.14668i	0.0117153	+	0.133906i	−0.988085	+	0.153912i	$0.950813\pi$
$258$	0.800760	−	2.98848i	0.0498532	−	0.186055i
$259$	1.01266	−	1.75398i	0.0629237	−	0.108987i
$260$		0			0
$261$	4.56705	−	0.805295i	0.282693	−	0.0498465i
$262$	1.79847	−	1.25930i	0.111110	−	0.0778000i
$263$	−12.4532	−	26.7060i	−0.767899	−	1.64676i	−0.762679	−	0.646778i	$-0.776116\pi$
$263$	−12.4532	−	26.7060i	−0.767899	−	1.64676i	−0.00522005	−	0.999986i	$-0.501662\pi$
$264$	2.57611	+	3.07009i	0.158549	+	0.188951i
$265$		0			0
$266$	−0.425927	+	0.0927976i	−0.0261153	+	0.00568978i
$267$	−14.2229	+	14.2229i	−0.870427	+	0.870427i
$268$	−1.82998	+	20.9168i	−0.111784	+	1.27769i
$269$	5.89502	+	2.14561i	0.359426	+	0.130820i	0.515420	−	0.856938i	$-0.327636\pi$
$269$	5.89502	+	2.14561i	0.359426	+	0.130820i	−0.155994	+	0.987758i	$0.549858\pi$
$270$		0			0
$271$	−1.04597	−	5.93198i	−0.0635381	−	0.360342i	−0.999955	−	0.00945382i	$-0.996991\pi$
$271$	−1.04597	−	5.93198i	−0.0635381	−	0.360342i	0.936417	−	0.350889i	$-0.114120\pi$
$272$	4.02285	−	8.62703i	0.243921	−	0.523091i
$273$	1.43588	−	0.384744i	0.0869037	−	0.0232858i
$274$	−0.785996	−	1.36139i	−0.0474838	−	0.0822443i
$275$		0			0
$276$	20.4716	−	24.3971i	1.23224	−	1.46853i
$277$	21.8337	+	5.85032i	1.31186	+	0.351512i	0.845922	−	0.533306i	$-0.179051\pi$
$277$	21.8337	+	5.85032i	1.31186	+	0.351512i	0.465937	+	0.884818i	$0.345717\pi$
$278$	1.43677	+	5.36209i	0.0861716	+	0.321597i
$279$	−1.48236	+	0.539536i	−0.0887468	+	0.0323012i
$280$		0			0
$281$	−11.8624	−	2.09165i	−0.707649	−	0.124778i	−0.191771	−	0.981440i	$-0.561423\pi$
$281$	−11.8624	−	2.09165i	−0.707649	−	0.124778i	−0.515878	+	0.856662i	$0.672534\pi$
$282$	3.03069	−	1.41323i	0.180475	−	0.0841568i
$283$	11.6168	+	1.01634i	0.690549	+	0.0604152i	0.427028	−	0.904238i	$-0.359561\pi$
$283$	11.6168	+	1.01634i	0.690549	+	0.0604152i	0.263521	+	0.964654i	$0.415116\pi$
$284$	29.8230			1.76967
$285$		0			0
$286$	1.21196			0.0716647
$287$	−2.03079	−	0.177671i	−0.119874	−	0.0104876i
$288$	2.30909	−	1.07674i	0.136064	−	0.0634478i
$289$	9.34127	+	1.64712i	0.549487	+	0.0968893i
$290$		0			0
$291$	10.9229	−	3.97560i	0.640310	−	0.233054i
$292$	−2.73595	−	10.2107i	−0.160109	−	0.597537i
$293$	−12.1638	−	3.25928i	−0.710616	−	0.190409i	−0.114635	−	0.993408i	$-0.536570\pi$
$293$	−12.1638	−	3.25928i	−0.710616	−	0.190409i	−0.595981	+	0.802999i	$0.703237\pi$
$294$	−2.56325	+	3.05476i	−0.149492	+	0.178157i
$295$		0			0
$296$	−3.53461	−	6.12213i	−0.205445	−	0.355841i
$297$	7.43802	−	1.99301i	0.431598	−	0.115646i
$298$	2.47772	−	5.31348i	0.143530	−	0.307802i
$299$	−3.42297	−	19.4126i	−0.197955	−	1.12266i
$300$		0			0
$301$	1.68098	+	0.611828i	0.0968903	+	0.0352652i
$302$	0.0333690	−	0.381409i	0.00192017	−	0.0219476i
$303$	−14.7022	+	14.7022i	−0.844617	+	0.844617i
$304$	4.60407	−	14.4187i	0.264061	−	0.826969i
$305$		0			0
$306$	−0.397504	−	0.473727i	−0.0227238	−	0.0270812i
$307$	6.97832	+	14.9650i	0.398273	+	0.854100i	0.998525	+	0.0542891i	$0.0172893\pi$
$307$	6.97832	+	14.9650i	0.398273	+	0.854100i	−0.600252	+	0.799811i	$0.704933\pi$
$308$	−0.927419	+	0.649385i	−0.0528446	+	0.0370022i
$309$	−20.4807	+	3.61131i	−1.16511	+	0.205440i
$310$		0			0
$311$	2.66572	−	4.61716i	0.151159	−	0.261815i	−0.780495	−	0.625162i	$-0.785033\pi$
$311$	2.66572	−	4.61716i	0.151159	−	0.261815i	0.931654	+	0.363347i	$0.118366\pi$
$312$	1.34292	−	5.01184i	0.0760278	−	0.283740i
$313$	−1.71309	−	19.5807i	−0.0968296	−	1.10677i	−0.876769	−	0.480912i	$-0.840306\pi$
$313$	−1.71309	−	19.5807i	−0.0968296	−	1.10677i	0.779939	−	0.625855i	$-0.215250\pi$
$314$	3.72434	+	3.12509i	0.210177	+	0.176359i
$315$		0			0
$316$	24.7696	+	14.3007i	1.39340	+	0.804479i
$317$	16.5516	+	7.71815i	0.929632	+	0.433495i	0.827620	−	0.561289i	$-0.189694\pi$
$317$	16.5516	+	7.71815i	0.929632	+	0.433495i	0.102012	+	0.994783i	$0.467472\pi$
$318$	1.01009	+	0.707274i	0.0566431	+	0.0396619i
$319$	−1.88783	+	10.7064i	−0.105698	+	0.599443i
$320$		0			0
$321$	−3.26947	+	2.74342i	−0.182484	+	0.153122i
$322$	−0.608255	−	0.608255i	−0.0338967	−	0.0338967i
$323$	−11.9356	−	0.564733i	−0.664115	−	0.0314226i
$324$		−	20.4356i		−	1.13531i
$325$		0			0
$326$	−1.04159	+	2.86174i	−0.0576881	+	0.158497i
$327$	−9.68250	−	13.8280i	−0.535443	−	0.764692i
$328$	−4.08121	+	5.82858i	−0.225347	+	0.321829i
$329$	0.661285	+	1.81687i	0.0364578	+	0.100167i
$330$		0			0
$331$	−10.5135	+	6.06999i	−0.577875	+	0.333637i	−0.760289	−	0.649585i	$-0.774942\pi$
$331$	−10.5135	+	6.06999i	−0.577875	+	0.333637i	0.182413	+	0.983222i	$0.441609\pi$
$332$	−6.32436	+	0.553310i	−0.347094	+	0.0303668i
$333$	4.55124	−	0.398182i	0.249406	−	0.0218202i
$334$	−0.673729	+	0.388978i	−0.0368648	+	0.0212839i
$335$		0			0
$336$	0.770369	+	2.11657i	0.0420271	+	0.115468i
$337$	−11.9360	+	17.0464i	−0.650195	+	0.928575i	−0.999966	−	0.00826058i	$-0.997371\pi$
$337$	−11.9360	+	17.0464i	−0.650195	+	0.928575i	0.349771	+	0.936835i	$0.386259\pi$
$338$	1.32772	+	1.89618i	0.0722185	+	0.103139i
$339$	−7.77992	+	21.3752i	−0.422547	+	1.16094i
$340$		0			0
$341$		−	3.69808i		−	0.200262i
$342$	−0.722556	−	0.666964i	−0.0390713	−	0.0360653i
$343$	−3.28722	−	3.28722i	−0.177493	−	0.177493i
$344$	4.78310	−	4.01350i	0.257888	−	0.216393i
$345$		0			0
$346$	0.949961	−	5.38750i	0.0510702	−	0.289634i
$347$	7.40032	+	5.18176i	0.397270	+	0.278171i	0.755093	−	0.655618i	$-0.227592\pi$
$347$	7.40032	+	5.18176i	0.397270	+	0.278171i	−0.357823	+	0.933790i	$0.616481\pi$
$348$	20.6099	+	9.61055i	1.10481	+	0.515180i
$349$	1.17548	+	0.678665i	0.0629221	+	0.0363281i	0.531131	−	0.847290i	$-0.321767\pi$
$349$	1.17548	+	0.678665i	0.0629221	+	0.0363281i	−0.468209	+	0.883618i	$0.655101\pi$
$350$		0			0
$351$	−7.63703	−	6.40823i	−0.407634	−	0.342046i
$352$	0.520556	+	5.94999i	0.0277457	+	0.317135i
$353$	6.50831	−	24.2894i	0.346403	−	1.29279i	−0.544563	−	0.838720i	$-0.683304\pi$
$353$	6.50831	−	24.2894i	0.346403	−	1.29279i	0.890965	−	0.454072i	$-0.150029\pi$
$354$	0.479479	−	0.830482i	0.0254840	−	0.0441396i
$355$		0			0
$356$	−19.5320	+	3.44402i	−1.03519	+	0.182533i
$357$	1.45658	−	1.01991i	0.0770902	−	0.0539791i
$358$	−0.980892	−	2.10353i	−0.0518417	−	0.111175i
$359$	1.32860	+	1.58336i	0.0701208	+	0.0835667i	0.799964	−	0.600047i	$-0.204852\pi$
$359$	1.32860	+	1.58336i	0.0701208	+	0.0835667i	−0.729844	+	0.683614i	$0.760407\pi$
$360$		0			0
$361$	−18.9393	+	1.51788i	−0.996804	+	0.0798883i
$362$	−4.04527	+	4.04527i	−0.212615	+	0.212615i
$363$	−1.32861	+	15.1860i	−0.0697337	+	0.797060i
$364$	1.37738	+	0.501325i	0.0721943	+	0.0262766i
$365$		0			0
$366$	0.924669	+	5.24406i	0.0483332	+	0.274111i
$367$	−2.99889	+	6.43114i	−0.156541	+	0.335703i	−0.968899	−	0.247456i	$-0.920406\pi$
$367$	−2.99889	+	6.43114i	−0.156541	+	0.335703i	0.812358	+	0.583158i	$0.198183\pi$
$368$	28.8501	−	7.73037i	1.50392	−	0.402973i
$369$	−2.29923	−	3.98238i	−0.119693	−	0.207314i
$370$		0			0
$371$	−0.458284	+	0.546162i	−0.0237929	+	0.0283553i
$372$	−7.47185	−	2.00208i	−0.387397	−	0.103803i
$373$	6.17989	+	23.0637i	0.319983	+	1.19419i	0.919260	+	0.393650i	$0.128788\pi$
$373$	6.17989	+	23.0637i	0.319983	+	1.19419i	−0.599277	+	0.800541i	$0.704545\pi$
$374$	1.36228	−	0.495830i	0.0704419	−	0.0256388i
$375$		0			0
$376$	6.64609	+	1.17188i	0.342746	+	0.0604353i
$377$	12.7563	−	5.94835i	0.656982	−	0.306356i
$378$	−0.433394	−	0.0379170i	−0.0222914	−	0.00195024i
$379$	16.2074			0.832518			0.416259	−	0.909246i	$-0.363341\pi$
$379$	16.2074			0.832518			0.416259	+	0.909246i	$0.363341\pi$
$380$		0			0
$381$	−12.9744			−0.664697
$382$	4.71468	+	0.412481i	0.241224	+	0.0211044i
$383$	−5.70067	+	2.65826i	−0.291290	+	0.135831i	−0.562771	−	0.826613i	$-0.690265\pi$
$383$	−5.70067	+	2.65826i	−0.291290	+	0.135831i	0.271480	+	0.962444i	$0.412487\pi$
$384$	16.2631	+	2.86763i	0.829924	+	0.146338i
$385$		0			0
$386$	−7.61801	+	2.77273i	−0.387746	+	0.141128i
$387$	1.04440	+	3.89774i	0.0530897	+	0.198133i
$388$	11.0710	+	2.96647i	0.562045	+	0.150600i
$389$	−13.5012	+	16.0901i	−0.684537	+	0.815799i	−0.990683	−	0.136185i	$-0.956516\pi$
$389$	−13.5012	+	16.0901i	−0.684537	+	0.815799i	0.306147	+	0.951984i	$0.400960\pi$
$390$		0			0
$391$	−11.7895	−	20.4200i	−0.596221	−	1.03268i
$392$	−7.77350	+	2.08290i	−0.392621	+	0.105202i
$393$	−6.01830	+	12.9063i	−0.303583	+	0.651036i
$394$	−0.750336	−	4.25537i	−0.0378014	−	0.214382i
$395$		0			0
$396$	−2.39988	−	0.873483i	−0.120598	−	0.0438942i
$397$	−0.242726	+	2.77437i	−0.0121821	+	0.139242i	−0.999850	−	0.0173218i	$-0.994486\pi$
$397$	−0.242726	+	2.77437i	−0.0121821	+	0.139242i	0.987668	+	0.156563i	$0.0500416\pi$
$398$	0.673552	−	0.673552i	0.0337621	−	0.0337621i
$399$	2.09155	−	1.90257i	0.104709	−	0.0952476i
$400$		0			0
$401$	14.4597	+	17.2324i	0.722083	+	0.860545i	0.994831	−	0.101541i	$-0.0323772\pi$
$401$	14.4597	+	17.2324i	0.722083	+	0.860545i	−0.272749	+	0.962085i	$0.587933\pi$
$402$	2.68862	+	5.76577i	0.134096	+	0.287570i
$403$	−3.92191	+	2.74615i	−0.195364	+	0.136795i
$404$	−20.1902	+	3.56007i	−1.00450	+	0.177120i
$405$		0			0
$406$	0.307105	−	0.531921i	0.0152414	−	0.0263988i
$407$	−2.77197	+	10.3452i	−0.137402	+	0.512790i
$408$	−0.540932	−	6.18288i	−0.0267801	−	0.306098i
$409$	−18.6505	−	15.6496i	−0.922209	−	0.773825i	0.0521935	−	0.998637i	$-0.483379\pi$
$409$	−18.6505	−	15.6496i	−0.922209	−	0.773825i	−0.974402	+	0.224812i	$0.927823\pi$
$410$		0			0
$411$	8.83014	+	5.09808i	0.435559	+	0.251470i
$412$	−18.5850	−	8.66631i	−0.915616	−	0.426959i
$413$	0.454188	+	0.318026i	0.0223491	+	0.0156490i
$414$	0.336948	−	1.91092i	0.0165601	−	0.0939168i
$415$		0			0
$416$	5.92355	−	4.97045i	0.290426	−	0.243696i
$417$	−25.4602	−	25.4602i	−1.24679	−	1.24679i
$418$	2.04859	−	1.05695i	0.100200	−	0.0516971i
$419$			3.10801i			0.151836i	0.997114	+	0.0759182i	$0.0241888\pi$
$419$			3.10801i			0.151836i	−0.997114	+	0.0759182i	$0.975811\pi$
$420$		0			0
$421$	−7.35818	+	20.2164i	−0.358616	+	0.985289i	0.620894	+	0.783894i	$0.286770\pi$
$421$	−7.35818	+	20.2164i	−0.358616	+	0.985289i	−0.979510	+	0.201395i	$0.935453\pi$
$422$	0.0959748	+	0.137066i	0.00467198	+	0.00667228i
$423$	−2.50161	+	3.57267i	−0.121632	+	0.173709i
$424$	0.851132	+	2.33847i	0.0413346	+	0.113566i
$425$		0			0
$426$	7.82552	−	4.51807i	0.379148	−	0.218901i
$427$	−3.06713	+	0.268339i	−0.148429	+	0.0129858i
$428$	−4.19238	+	0.366785i	−0.202646	+	0.0177292i
$429$	−6.80778	+	3.93047i	−0.328683	+	0.189765i
$430$		0			0
$431$	−6.33738	−	17.4118i	−0.305261	−	0.838698i	−0.993564	−	0.113274i	$-0.963866\pi$
$431$	−6.33738	−	17.4118i	−0.305261	−	0.838698i	0.688303	−	0.725424i	$-0.258356\pi$
$432$	8.66429	−	12.3739i	0.416861	−	0.595339i
$433$	5.25844	+	7.50983i	0.252704	+	0.360899i	0.925382	−	0.379037i	$-0.123745\pi$
$433$	5.25844	+	7.50983i	0.252704	+	0.360899i	−0.672677	+	0.739936i	$0.734856\pi$
$434$	−0.0714583	+	0.196330i	−0.00343011	+	0.00942414i
$435$		0			0
$436$		−	16.6452i		−	0.797159i
$437$	−22.7156	−	29.8281i	−1.08663	−	1.42687i
$438$	−2.26479	−	2.26479i	−0.108216	−	0.108216i
$439$	−13.5592	+	11.3775i	−0.647147	+	0.543021i	−0.906204	−	0.422841i	$-0.861033\pi$
$439$	−13.5592	+	11.3775i	−0.647147	+	0.543021i	0.259057	+	0.965862i	$0.416588\pi$
$440$		0			0
$441$	0.903144	−	5.12198i	0.0430068	−	0.243904i
$442$	−1.53745	−	1.07654i	−0.0731293	−	0.0512057i
$443$	4.31463	+	2.01194i	0.204994	+	0.0955903i	0.522404	−	0.852698i	$-0.325035\pi$
$443$	4.31463	+	2.01194i	0.204994	+	0.0955903i	−0.317410	+	0.948288i	$0.602813\pi$
$444$	19.4013	+	11.2014i	0.920747	+	0.531593i
$445$		0			0
$446$	−5.15195	−	4.32300i	−0.243952	−	0.204700i
$447$	3.31426	+	37.8821i	0.156759	+	1.79176i
$448$	−0.514341	+	1.91955i	−0.0243003	+	0.0906901i
$449$	1.65599	−	2.86825i	0.0781508	−	0.135361i	−0.824301	−	0.566151i	$-0.808432\pi$
$449$	1.65599	−	2.86825i	0.0781508	−	0.135361i	0.902452	+	0.430790i	$0.141765\pi$
$450$		0			0
$451$	10.6162	−	1.87193i	0.499899	−	0.0881458i
$452$	−18.3730	+	12.8649i	−0.864193	+	0.605115i
$453$	1.04950	+	2.25065i	0.0493097	+	0.105745i
$454$	−3.12529	−	3.72457i	−0.146677	−	0.174803i
$455$		0			0
$456$	−2.10088	−	9.64271i	−0.0983826	−	0.451561i
$457$	−20.2603	+	20.2603i	−0.947736	+	0.947736i	−0.998700	−	0.0509647i	$-0.983770\pi$
$457$	−20.2603	+	20.2603i	−0.947736	+	0.947736i	0.0509647	+	0.998700i	$0.483770\pi$
$458$	0.299660	−	3.42513i	0.0140022	−	0.160046i
$459$	−11.2060	−	4.07864i	−0.523049	−	0.190374i
$460$		0			0
$461$	2.78058	+	15.7694i	0.129504	+	0.734455i	0.978530	+	0.206104i	$0.0660785\pi$
$461$	2.78058	+	15.7694i	0.129504	+	0.734455i	−0.849026	+	0.528351i	$0.822810\pi$
$462$	−0.144974	+	0.310898i	−0.00674481	+	0.0144643i
$463$	−27.3267	+	7.32218i	−1.26998	+	0.340291i	−0.830024	−	0.557728i	$-0.811673\pi$
$463$	−27.3267	+	7.32218i	−1.26998	+	0.340291i	−0.439958	+	0.898018i	$0.645007\pi$
$464$	10.6633	+	18.4693i	0.495029	+	0.857416i
$465$		0			0
$466$	−3.38018	+	4.02835i	−0.156584	+	0.186610i
$467$	1.48896	+	0.398965i	0.0689007	+	0.0184619i	0.293105	−	0.956080i	$-0.405312\pi$
$467$	1.48896	+	0.398965i	0.0689007	+	0.0184619i	−0.224204	+	0.974542i	$0.571978\pi$
$468$	0.855767	+	3.19377i	0.0395579	+	0.147632i
$469$	−3.45652	+	1.25807i	−0.159607	+	0.0580923i
$470$		0			0
$471$	−31.0551	−	5.47586i	−1.43094	−	0.252314i
$472$	1.75398	−	0.817894i	0.0807335	−	0.0376466i
$473$	−9.42369	−	0.824466i	−0.433302	−	0.0379090i
$474$	8.66602			0.398044
$475$		0			0
$476$	1.75332			0.0803632
$477$	−1.60215	−	0.140170i	−0.0733575	−	0.00641795i
$478$	−0.859605	+	0.400840i	−0.0393174	+	0.0183340i
$479$	16.5181	+	2.91258i	0.754730	+	0.133079i	0.537759	−	0.843099i	$-0.319271\pi$
$479$	16.5181	+	2.91258i	0.754730	+	0.133079i	0.216971	+	0.976178i	$0.430382\pi$
$480$		0			0
$481$	13.0297	−	4.74243i	0.594105	−	0.216236i
$482$	0.595999	+	2.22430i	0.0271470	+	0.101314i
$483$	5.38928	+	1.44405i	0.245221	+	0.0657067i
$484$	−9.66184	+	11.5145i	−0.439174	+	0.523388i
$485$		0			0
$486$	−1.14641	−	1.98563i	−0.0520020	−	0.0900702i
$487$	−3.88785	+	1.04175i	−0.176175	+	0.0472060i	−0.345828	−	0.938298i	$-0.612402\pi$
$487$	−3.88785	+	1.04175i	−0.176175	+	0.0472060i	0.169653	+	0.985504i	$0.445735\pi$
$488$	−4.54165	+	9.73959i	−0.205591	+	0.440891i
$489$	−3.43005	−	19.4528i	−0.155112	−	0.879685i
$490$		0			0
$491$	−10.9927	−	4.00100i	−0.496091	−	0.180563i	0.0818437	−	0.996645i	$-0.473919\pi$
$491$	−10.9927	−	4.00100i	−0.496091	−	0.180563i	−0.577935	+	0.816083i	$0.696141\pi$
$492$	1.96528	−	22.4632i	0.0886015	−	1.01272i
$493$	11.9049	−	11.9049i	0.536171	−	0.536171i
$494$	−2.64218	−	1.38770i	−0.118877	−	0.0624355i
$495$		0			0
$496$	−4.66307	−	5.55723i	−0.209378	−	0.249527i
$497$	2.20802	+	4.73511i	0.0990432	+	0.212399i
$498$	−1.57568	+	1.10330i	−0.0706079	+	0.0494402i
$499$	−25.5639	+	4.50760i	−1.14440	+	0.201788i	−0.713527	−	0.700627i	$-0.752904\pi$
$499$	−25.5639	+	4.50760i	−1.14440	+	0.201788i	−0.430868	+	0.902415i	$0.641792\pi$
$500$		0			0
$501$	2.52296	−	4.36990i	0.112718	−	0.195233i
$502$	−0.0692736	+	0.258533i	−0.00309183	+	0.0115389i
$503$	2.84355	+	32.5020i	0.126788	+	1.44919i	0.747035	+	0.664784i	$0.231477\pi$
$503$	2.84355	+	32.5020i	0.126788	+	1.44919i	−0.620248	+	0.784406i	$0.712968\pi$
$504$	0.226224	+	0.189824i	0.0100768	+	0.00845545i
$505$		0			0
$506$	3.93940	+	2.27441i	0.175128	+	0.101110i
$507$	−13.6075	−	6.34527i	−0.604329	−	0.281803i
$508$	−10.4796	−	7.33786i	−0.464955	−	0.325565i
$509$	−1.27621	+	7.23775i	−0.0565671	+	0.320808i	−0.999940	−	0.0109254i	$-0.996522\pi$
$509$	−1.27621	+	7.23775i	−0.0565671	+	0.320808i	0.943373	+	0.331733i	$0.107633\pi$
$510$		0			0
$511$	1.41863	−	1.19037i	0.0627565	−	0.0526590i
$512$	14.0224	+	14.0224i	0.619710	+	0.619710i
$513$	−18.4975	−	4.17163i	−0.816686	−	0.184182i
$514$			0.643793i			0.0283965i
$515$		0			0
$516$	−6.76763	+	18.5939i	−0.297928	+	0.818551i
$517$	−5.86445	−	8.37530i	−0.257918	−	0.368345i
$518$	0.347063	−	0.495658i	0.0152491	−	0.0217780i
$519$	12.1360	+	33.3433i	0.532709	+	1.46361i
$520$		0			0
$521$	−25.6025	+	14.7816i	−1.12166	+	0.647593i	−0.941825	−	0.336103i	$-0.890891\pi$
$521$	−25.6025	+	14.7816i	−1.12166	+	0.647593i	−0.179839	+	0.983696i	$0.557558\pi$
$522$	1.38023	−	0.120755i	0.0604112	−	0.00528529i
$523$	36.7539	−	3.21555i	1.60714	−	0.140606i	0.752055	−	0.659100i	$-0.229063\pi$
$523$	36.7539	−	3.21555i	1.60714	−	0.140606i	0.855082	+	0.518494i	$0.173507\pi$
$524$	−12.1604	+	7.02082i	−0.531230	+	0.306706i
$525$		0			0
$526$	−3.01099	−	8.27262i	−0.131285	−	0.360703i
$527$	−3.28486	+	4.69127i	−0.143091	+	0.204355i
$528$	−6.83184	−	9.75687i	−0.297318	−	0.424613i
$529$	17.4379	−	47.9102i	0.758169	−	2.08305i
$530$		0			0
$531$			1.25073i			0.0542770i
$532$	2.76540	−	0.353818i	0.119895	−	0.0153400i
$533$	−9.86873	−	9.86873i	−0.427462	−	0.427462i
$534$	−4.60342	+	3.86273i	−0.199209	+	0.167157i
$535$		0			0
$536$	−2.22947	+	12.6439i	−0.0962983	+	0.546135i
$537$	12.3317	+	8.63476i	0.532153	+	0.372618i
$538$	1.69863	+	0.792084i	0.0732332	+	0.0341492i
$539$	10.5590	+	6.09627i	0.454810	+	0.262585i
$540$		0			0
$541$	30.1856	+	25.3287i	1.29778	+	1.08897i	0.990524	+	0.137341i	$0.0438556\pi$
$541$	30.1856	+	25.3287i	1.29778	+	1.08897i	0.307257	+	0.951627i	$0.400589\pi$
$542$	−0.156844	−	1.79274i	−0.00673703	−	0.0770046i
$543$	9.60385	−	35.8421i	0.412141	−	1.53813i
$544$	4.62478	−	8.01036i	0.198286	−	0.343441i
$545$		0			0
$546$	0.437372	−	0.0771204i	0.0187178	−	0.00330045i
$547$	−3.33017	+	2.33181i	−0.142388	+	0.0997010i	−0.642600	−	0.766202i	$-0.722144\pi$
$547$	−3.33017	+	2.33181i	−0.142388	+	0.0997010i	0.500212	+	0.865903i	$0.333255\pi$
$548$	4.24891	+	9.11181i	0.181504	+	0.389237i
$549$	−4.46423	−	5.32026i	−0.190529	−	0.227063i
$550$		0			0
$551$	16.3745	−	21.1793i	0.697577	−	0.902269i
$552$	13.7705	−	13.7705i	0.586111	−	0.586111i
$553$	−0.436704	+	4.99155i	−0.0185705	+	0.212262i
$554$	6.34589	+	2.30972i	0.269611	+	0.0981304i
$555$		0			0
$556$	−6.16509	−	34.9640i	−0.261458	−	1.48280i
$557$	−0.133737	+	0.286800i	−0.00566663	+	0.0121521i	−0.909121	−	0.416533i	$-0.863245\pi$
$557$	−0.133737	+	0.286800i	−0.00566663	+	0.0121521i	0.903454	+	0.428685i	$0.141023\pi$
$558$	−0.455236	+	0.121980i	−0.0192717	+	0.00516383i
$559$	6.12355	+	10.6063i	0.258999	+	0.448599i
$560$		0			0
$561$	−6.04415	+	7.20314i	−0.255184	+	0.304117i
$562$	−3.47606	−	0.931407i	−0.146629	−	0.0392890i
$563$	12.0964	+	45.1444i	0.509803	+	1.90261i	0.422330	+	0.906442i	$0.361212\pi$
$563$	12.0964	+	45.1444i	0.509803	+	1.90261i	0.0874723	+	0.996167i	$0.472121\pi$
$564$	−20.0969	+	7.31468i	−0.846233	+	0.308004i
$565$		0			0
$566$	3.43098	+	0.604975i	0.144215	+	0.0254290i
$567$	3.24463	−	1.51300i	0.136262	−	0.0635399i
$568$	18.1667	+	1.58938i	0.762258	+	0.0666889i
$569$	−25.5911			−1.07283			−0.536417	−	0.843953i	$-0.680223\pi$
$569$	−25.5911			−1.07283			−0.536417	+	0.843953i	$0.680223\pi$
$570$		0			0
$571$	−2.95798			−0.123788			−0.0618938	−	0.998083i	$-0.519714\pi$
$571$	−2.95798			−0.123788			−0.0618938	+	0.998083i	$0.519714\pi$
$572$	−7.72167	−	0.675558i	−0.322859	−	0.0282465i
$573$	−27.8208	+	12.9731i	−1.16223	+	0.541958i
$574$	−0.599785	−	0.105758i	−0.0250345	−	0.00441426i
$575$		0			0
$576$	−4.21243	+	1.53320i	−0.175518	+	0.0638833i
$577$	1.90612	+	7.11374i	0.0793528	+	0.296149i	0.994185	−	0.107685i	$-0.0343439\pi$
$577$	1.90612	+	7.11374i	0.0793528	+	0.296149i	−0.914832	+	0.403834i	$0.867677\pi$
$578$	2.73730	+	0.733456i	0.113857	+	0.0305078i
$579$	33.7994	−	40.2806i	1.40466	−	1.67400i
$580$		0			0
$581$	−0.556090	−	0.963176i	−0.0230705	−	0.0399593i
$582$	3.35443	−	0.898816i	0.139046	−	0.0372571i
$583$	1.59336	−	3.41698i	0.0659904	−	0.141517i
$584$	−1.12244	−	6.36567i	−0.0464469	−	0.263413i
$585$		0			0
$586$	−3.53536	−	1.28677i	−0.146045	−	0.0531559i
$587$	−0.255196	+	2.91690i	−0.0105331	+	0.120394i	−0.999641	−	0.0267997i	$-0.991468\pi$
$587$	−0.255196	+	2.91690i	−0.0105331	+	0.120394i	0.989108	+	0.147193i	$0.0470239\pi$
$588$	18.0338	−	18.0338i	0.743701	−	0.743701i
$589$	−4.23432	+	8.06213i	−0.174472	+	0.332194i
$590$		0			0
$591$	18.0152	+	21.4697i	0.741047	+	0.883146i
$592$	8.87911	+	19.0413i	0.364929	+	0.782593i
$593$	−2.83613	+	1.98588i	−0.116466	+	0.0815502i	−0.630358	−	0.776304i	$-0.717092\pi$
$593$	−2.83613	+	1.98588i	−0.116466	+	0.0815502i	0.513892	+	0.857855i	$0.328203\pi$
$594$	2.26563	−	0.399491i	0.0929599	−	0.0163913i
$595$		0			0
$596$	−18.7479	+	32.4723i	−0.767943	+	1.33012i
$597$	−1.59908	+	5.96783i	−0.0654458	+	0.244247i
$598$	−0.513277	−	5.86679i	−0.0209895	−	0.239911i
$599$	−12.9017	−	10.8258i	−0.527151	−	0.442332i	0.339965	−	0.940438i	$-0.389585\pi$
$599$	−12.9017	−	10.8258i	−0.527151	−	0.442332i	−0.867116	+	0.498106i	$0.834029\pi$
$600$		0			0
$601$	3.51772	+	2.03096i	0.143491	+	0.0828445i	0.570027	−	0.821626i	$-0.306933\pi$
$601$	3.51772	+	2.03096i	0.143491	+	0.0828445i	−0.426536	+	0.904471i	$0.640266\pi$
$602$	0.484370	+	0.225865i	0.0197414	+	0.00920559i
$603$	−6.79688	−	4.75922i	−0.276790	−	0.193811i
$604$	−0.425202	+	2.41144i	−0.0173012	+	0.0981201i
$605$		0			0
$606$	−4.75854	+	3.99289i	−0.193303	+	0.162200i
$607$	−24.9122	−	24.9122i	−1.01116	−	1.01116i	−0.999937	−	0.0112183i	$-0.996429\pi$
$607$	−24.9122	−	24.9122i	−1.01116	−	1.01116i	−0.0112183	−	0.999937i	$-0.503571\pi$
$608$	5.67790	−	13.5675i	0.230269	−	0.550236i
$609$			3.98385i			0.161434i
$610$		0			0
$611$	−4.52735	+	12.4388i	−0.183157	+	0.503220i
$612$	2.26853	+	3.23979i	0.0916997	+	0.130961i
$613$	−5.19022	+	7.41240i	−0.209631	+	0.299384i	−0.910174	−	0.414226i	$-0.864052\pi$
$613$	−5.19022	+	7.41240i	−0.209631	+	0.299384i	0.700543	+	0.713610i	$0.252941\pi$
$614$	1.68724	+	4.63566i	0.0680916	+	0.187080i
$615$		0			0
$616$	−0.599546	+	0.346148i	−0.0241564	+	0.0139467i
$617$	42.1238	−	3.68535i	1.69584	−	0.148367i	0.802171	−	0.597094i	$-0.203678\pi$
$617$	42.1238	−	3.68535i	1.69584	−	0.148367i	0.893669	+	0.448727i	$0.148122\pi$
$618$	−6.18959	+	0.541519i	−0.248982	+	0.0217831i
$619$	15.6339	−	9.02621i	0.628378	−	0.362794i	−0.151746	−	0.988420i	$-0.548489\pi$
$619$	15.6339	−	9.02621i	0.628378	−	0.362794i	0.780124	+	0.625625i	$0.215156\pi$
$620$		0			0
$621$	−12.7977	−	35.1615i	−0.513555	−	1.41098i
$622$	0.913606	−	1.30476i	0.0366323	−	0.0523163i
$623$	−1.99292	−	2.84618i	−0.0798446	−	0.114030i
$624$	−5.27417	+	14.4907i	−0.211136	+	0.580091i
$625$		0			0
$626$		−	5.87229i		−	0.234704i
$627$	−8.07948	+	12.5808i	−0.322663	+	0.502427i
$628$	−21.9866	−	21.9866i	−0.877363	−	0.877363i
$629$	12.7056	−	10.6613i	0.506607	−	0.425094i
$630$		0			0
$631$	−2.44081	+	13.8425i	−0.0971672	+	0.551062i	0.896895	+	0.442244i	$0.145818\pi$
$631$	−2.44081	+	13.8425i	−0.0971672	+	0.551062i	−0.994062	+	0.108818i	$0.965293\pi$
$632$	14.3263	+	10.0314i	0.569869	+	0.399026i
$633$	−0.983622	−	0.458670i	−0.0390954	−	0.0182305i
$634$	4.72519	+	2.72809i	0.187661	+	0.108346i
$635$		0			0
$636$	−6.04127	−	5.06923i	−0.239552	−	0.201008i
$637$	−1.37577	−	15.7252i	−0.0545101	−	0.623053i
$638$	−0.840643	+	3.13732i	−0.0332814	+	0.124208i
$639$	−5.89272	+	10.2065i	−0.233112	+	0.403763i
$640$		0			0
$641$	23.1158	−	4.07593i	0.913018	−	0.160990i	0.302645	−	0.953103i	$-0.402130\pi$
$641$	23.1158	−	4.07593i	0.913018	−	0.160990i	0.610374	+	0.792114i	$0.291019\pi$
$642$	−1.04451	+	0.731373i	−0.0412235	+	0.0288650i
$643$	−4.67679	−	10.0294i	−0.184435	−	0.395521i	0.792251	−	0.610195i	$-0.208909\pi$
$643$	−4.67679	−	10.0294i	−0.184435	−	0.395521i	−0.976686	+	0.214674i	$0.931131\pi$
$644$	3.53628	+	4.21437i	0.139349	+	0.166070i
$645$		0			0
$646$	−3.53762	−	0.478866i	−0.139186	−	0.0188407i
$647$	10.3878	−	10.3878i	0.408386	−	0.408386i	−0.472790	−	0.881175i	$-0.656753\pi$
$647$	10.3878	−	10.3878i	0.408386	−	0.408386i	0.881175	+	0.472790i	$0.156753\pi$
$648$	1.08909	−	12.4484i	0.0427835	−	0.489018i
$649$	−2.75522	−	1.00282i	−0.108152	−	0.0393640i
$650$		0			0
$651$	−0.235319	−	1.33456i	−0.00922289	−	0.0523056i
$652$	8.23134	−	17.6522i	0.322364	−	0.691312i
$653$	19.7746	−	5.29859i	0.773841	−	0.207350i	0.149773	−	0.988720i	$-0.452146\pi$
$653$	19.7746	−	5.29859i	0.773841	−	0.207350i	0.624067	+	0.781370i	$0.285479\pi$
$654$	−2.52168	−	4.36767i	−0.0986054	−	0.170790i
$655$		0			0
$656$	13.5930	−	16.1995i	0.530717	−	0.632484i
$657$	4.03507	+	1.08119i	0.157423	+	0.0421813i
$658$	0.149505	+	0.557961i	0.00582832	+	0.0217516i
$659$	1.78757	−	0.650624i	0.0696340	−	0.0253447i	−0.306968	−	0.951720i	$-0.599315\pi$
$659$	1.78757	−	0.650624i	0.0696340	−	0.0253447i	0.376602	+	0.926375i	$0.377092\pi$
$660$		0			0
$661$	14.1497	+	2.49497i	0.550360	+	0.0970433i	0.441911	−	0.897059i	$-0.354301\pi$
$661$	14.1497	+	2.49497i	0.550360	+	0.0970433i	0.108448	+	0.994102i	$0.465412\pi$
$662$	−3.28713	+	1.53281i	−0.127758	+	0.0595745i
$663$	12.1274	+	1.06101i	0.470990	+	0.0412063i
$664$	−3.88198			−0.150650
$665$		0			0
$666$	1.36493			0.0528898
$667$	52.6264	+	4.60422i	2.03770	+	0.178276i
$668$	4.50930	−	2.10272i	0.174470	−	0.0813566i
$669$	42.9591	+	7.57485i	1.66090	+	0.292861i
$670$		0			0
$671$	15.2993	−	5.56850i	0.590624	−	0.214969i
$672$	0.566473	+	2.11410i	0.0218522	+	0.0815534i
$673$	−13.2264	−	3.54401i	−0.509842	−	0.136612i	−0.00527799	−	0.999986i	$-0.501680\pi$
$673$	−13.2264	−	3.54401i	−0.509842	−	0.136612i	−0.504564	+	0.863374i	$0.668347\pi$
$674$	−3.99630	+	4.76261i	−0.153932	+	0.183449i
$675$		0			0
$676$	−7.40225	−	12.8211i	−0.284702	−	0.493118i
$677$	30.7746	−	8.24603i	1.18276	−	0.316921i	0.386742	−	0.922188i	$-0.373600\pi$
$677$	30.7746	−	8.24603i	1.18276	−	0.316921i	0.796023	+	0.605267i	$0.206934\pi$
$678$	−2.87207	+	6.15918i	−0.110301	+	0.236542i
$679$	0.348672	+	1.97741i	0.0133808	+	0.0758862i
$680$		0			0
$681$	29.6343	+	10.7860i	1.13559	+	0.413320i
$682$	0.0962933	−	1.10064i	0.00368726	−	0.0421456i
$683$	1.98056	−	1.98056i	0.0757839	−	0.0757839i	−0.668199	−	0.743983i	$-0.732934\pi$
$683$	1.98056	−	1.98056i	0.0757839	−	0.0757839i	0.743983	+	0.668199i	$0.232934\pi$
$684$	4.23179	+	4.65213i	0.161807	+	0.177879i
$685$		0			0
$686$	−0.892759	−	1.06395i	−0.0340857	−	0.0406218i
$687$	9.42469	+	20.2113i	0.359574	+	0.771110i
$688$	−15.2009	+	10.6438i	−0.579529	+	0.405791i
$689$	−4.80701	+	0.847605i	−0.183132	+	0.0322912i
$690$		0			0
$691$	9.82610	−	17.0193i	0.373802	−	0.647445i	−0.616345	−	0.787476i	$-0.711387\pi$
$691$	9.82610	−	17.0193i	0.373802	−	0.647445i	0.990147	+	0.140032i	$0.0447205\pi$
$692$	−9.05546	+	33.7954i	−0.344237	+	1.28471i
$693$	−0.0389944	−	0.445708i	−0.00148127	−	0.0169310i
$694$	2.06759	+	1.73491i	0.0784845	+	0.0658563i
$695$		0			0
$696$	12.0424	+	6.95265i	0.456464	+	0.263540i
$697$	−15.1302	−	7.05533i	−0.573097	−	0.267240i
$698$	0.332180	+	0.232595i	0.0125732	+	0.00880385i
$699$	5.92283	−	33.5900i	0.224022	−	1.27049i
$700$		0			0
$701$	25.1461	−	21.1001i	0.949755	−	0.796939i	−0.0295010	−	0.999565i	$-0.509392\pi$
$701$	25.1461	−	21.1001i	0.949755	−	0.796939i	0.979256	+	0.202625i	$0.0649474\pi$
$702$	−2.10610	−	2.10610i	−0.0794896	−	0.0794896i
$703$	17.8884	−	19.3794i	0.674673	−	0.730908i
$704$		−	10.5088i		−	0.396066i
$705$		0			0
$706$	2.56949	−	7.05962i	0.0967042	−	0.265692i
$707$	−2.06007	−	2.94209i	−0.0774770	−	0.110649i
$708$	−3.51779	+	5.02392i	−0.132206	+	0.188810i
$709$	−6.40035	−	17.5848i	−0.240370	−	0.660412i	−0.999950	−	0.00999760i	$-0.996818\pi$
$709$	−6.40035	−	17.5848i	−0.240370	−	0.660412i	0.759580	−	0.650414i	$-0.225405\pi$
$710$		0			0
$711$	−9.78844	+	5.65136i	−0.367095	+	0.211943i
$712$	−12.0815	+	1.05699i	−0.452772	+	0.0396125i
$713$	−17.9015	+	1.56617i	−0.670415	+	0.0586537i
$714$	0.460069	−	0.265621i	0.0172176	−	0.00994061i
$715$		0			0
$716$	5.07695	+	13.9488i	0.189735	+	0.521291i
$717$	3.52859	−	5.03934i	0.131778	−	0.188198i
$718$	0.354194	+	0.505842i	0.0132184	+	0.0188778i
$719$	2.67044	−	7.33697i	0.0995905	−	0.273623i	−0.879885	−	0.475187i	$-0.842380\pi$
$719$	2.67044	−	7.33697i	0.0995905	−	0.273623i	0.979475	+	0.201564i	$0.0646026\pi$
$720$		0			0
$721$		−	3.59244i		−	0.133789i
$722$	−5.67630	−	0.0413976i	−0.211250	−	0.00154066i
$723$	−10.5614	−	10.5614i	−0.392782	−	0.392782i
$724$	28.0282	−	23.5185i	1.04166	−	0.874057i
$725$		0			0
$726$	−0.790850	+	4.48513i	−0.0293512	+	0.166459i
$727$	−24.5663	−	17.2015i	−0.911115	−	0.637970i	0.0211378	−	0.999777i	$-0.493271\pi$
$727$	−24.5663	−	17.2015i	−0.911115	−	0.637970i	−0.932253	+	0.361807i	$0.882160\pi$
$728$	0.812315	+	0.378788i	0.0301064	+	0.0140388i
$729$	−14.9076	−	8.60690i	−0.552133	−	0.318774i
$730$		0			0
$731$	11.2223	+	9.41660i	0.415070	+	0.348285i
$732$	−2.96818	−	33.9265i	−0.109707	−	1.25396i
$733$	4.87884	−	18.2081i	0.180204	−	0.672531i	−0.815402	−	0.578895i	$-0.803484\pi$
$733$	4.87884	−	18.2081i	0.180204	−	0.672531i	0.995606	−	0.0936365i	$-0.0298491\pi$
$734$	−1.06000	+	1.83597i	−0.0391253	+	0.0677670i
$735$		0			0
$736$	28.5819	−	5.03976i	1.05354	−	0.185768i
$737$	15.9337	−	11.1569i	0.586926	−	0.410970i
$738$	−0.580609	−	1.24512i	−0.0213725	−	0.0458335i
$739$	19.7272	+	23.5100i	0.725678	+	0.864829i	0.995169	−	0.0981738i	$-0.0313001\pi$
$739$	19.7272	+	23.5100i	0.725678	+	0.864829i	−0.269492	+	0.963003i	$0.586856\pi$
$740$		0			0
$741$	19.3419	−	0.773834i	0.710544	−	0.0284275i
$742$	−0.150618	+	0.150618i	−0.00552935	+	0.00552935i
$743$	−1.19259	+	13.6313i	−0.0437517	+	0.500084i	0.942428	+	0.334408i	$0.108536\pi$
$743$	−1.19259	+	13.6313i	−0.0437517	+	0.500084i	−0.986180	+	0.165676i	$0.947019\pi$
$744$	−4.44479	−	1.61777i	−0.162954	−	0.0593103i
$745$		0			0
$746$	1.23874	+	7.02522i	0.0453533	+	0.257212i
$747$	1.06027	−	2.27375i	0.0387931	−	0.0831921i
$748$	−8.95578	+	2.39969i	−0.327456	+	0.0877415i
$749$	−0.368629	−	0.638484i	−0.0134694	−	0.0233297i
$750$		0			0
$751$	−14.7692	+	17.6012i	−0.538934	+	0.642277i	−0.964948	−	0.262440i	$-0.915473\pi$
$751$	−14.7692	+	17.6012i	−0.538934	+	0.642277i	0.426014	+	0.904717i	$0.359917\pi$
$752$	−19.3735	−	5.19111i	−0.706478	−	0.189300i
$753$	−0.449318	−	1.67688i	−0.0163741	−	0.0611088i
$754$	3.95146	−	1.43822i	0.143904	−	0.0523767i
$755$		0			0
$756$	2.74011	+	0.483156i	0.0996569	+	0.0175722i
$757$	2.99560	−	1.39687i	0.108877	−	0.0507702i	−0.367417	−	0.930056i	$-0.619758\pi$
$757$	2.99560	−	1.39687i	0.108877	−	0.0507702i	0.476294	+	0.879286i	$0.341980\pi$
$758$	4.82371	+	0.422020i	0.175205	+	0.0153284i
$759$	−29.5043			−1.07094
$760$		0			0
$761$	−39.1861			−1.42050			−0.710248	−	0.703952i	$-0.751417\pi$
$761$	−39.1861			−1.42050			−0.710248	+	0.703952i	$0.751417\pi$
$762$	−3.86148	−	0.337836i	−0.139887	−	0.0122385i
$763$	2.64282	−	1.23237i	0.0956764	−	0.0446146i
$764$	−29.8084	−	5.25602i	−1.07843	−	0.190156i
$765$		0			0
$766$	−1.76587	+	0.642725i	−0.0638036	+	0.0232226i
$767$	0.982478	+	3.66666i	0.0354752	+	0.132395i
$768$	−17.4590	−	4.67811i	−0.629996	−	0.168807i
$769$	−22.2353	+	26.4990i	−0.801825	+	0.955578i	−0.999696	−	0.0246499i	$-0.992153\pi$
$769$	−22.2353	+	26.4990i	−0.801825	+	0.955578i	0.197871	+	0.980228i	$0.436597\pi$
$770$		0			0
$771$	−2.08787	−	3.61629i	−0.0751927	−	0.130238i
$772$	50.0815	−	13.4193i	1.80247	−	0.482972i
$773$	7.07654	−	15.1757i	0.254526	−	0.545832i	−0.736977	−	0.675918i	$-0.763748\pi$
$773$	7.07654	−	15.1757i	0.254526	−	0.545832i	0.991503	+	0.130086i	$0.0415253\pi$
$774$	0.209345	+	1.18726i	0.00752476	+	0.0426751i
$775$		0			0
$776$	6.58582	+	2.39704i	0.236417	+	0.0860488i
$777$	−0.342058	+	3.90974i	−0.0122713	+	0.140261i
$778$	−4.43724	+	4.43724i	−0.159083	+	0.159083i
$779$	−25.2877	−	8.07467i	−0.906026	−	0.289305i
$780$		0			0
$781$	−17.7591	−	21.1645i	−0.635470	−	0.757324i
$782$	−2.97713	−	6.38447i	−0.106462	−	0.228308i
$783$	21.8858	−	15.3246i	0.782134	−	0.547656i
$784$	23.5545	−	4.15329i	0.841232	−	0.148332i
$785$		0			0
$786$	−2.12725	+	3.68451i	−0.0758766	+	0.131422i
$787$	11.9180	−	44.4784i	0.424830	−	1.58549i	−0.339465	−	0.940619i	$-0.610246\pi$
$787$	11.9180	−	44.4784i	0.424830	−	1.58549i	0.764295	−	0.644867i	$-0.223087\pi$
$788$	2.40858	+	27.5301i	0.0858019	+	0.980721i
$789$	43.7419	+	36.7038i	1.55725	+	1.30669i
$790$		0			0
$791$	−3.40290	−	1.96467i	−0.120993	−	0.0698555i
$792$	−1.41533	−	0.659982i	−0.0502917	−	0.0234514i
$793$	−17.2666	−	12.0902i	−0.613156	−	0.429336i
$794$	−0.144482	+	0.819399i	−0.00512748	+	0.0290794i
$795$		0			0
$796$	−4.66680	+	3.91591i	−0.165410	+	0.138796i
$797$	14.9095	+	14.9095i	0.528121	+	0.528121i	0.920012	−	0.391891i	$-0.128179\pi$
$797$	14.9095	+	14.9095i	0.528121	+	0.528121i	−0.391891	+	0.920012i	$0.628179\pi$
$798$	0.672036	−	0.511789i	0.0237898	−	0.0181171i
$799$			15.8338i			0.560160i
$800$		0			0
$801$	2.68066	−	7.36505i	0.0947164	−	0.260231i
$802$	3.85484	+	5.50528i	0.136119	+	0.194398i
$803$	−5.61702	+	8.02193i	−0.198220	+	0.283088i
$804$	−13.9159	−	38.2337i	−0.490777	−	1.34840i
$805$		0			0
$806$	−1.23876	+	0.715198i	−0.0436335	+	0.0251918i
$807$	−12.1103	+	1.05951i	−0.426302	+	0.0372966i
$808$	−12.4886	+	1.09261i	−0.439347	+	0.0384379i
$809$	−0.0883067	+	0.0509839i	−0.00310470	+	0.00179250i	−0.501552	−	0.865128i	$-0.667237\pi$
$809$	−0.0883067	+	0.0509839i	−0.00310470	+	0.00179250i	0.498447	+	0.866920i	$0.333904\pi$
$810$		0			0
$811$	13.8775	+	38.1282i	0.487306	+	1.33886i	0.903111	+	0.429407i	$0.141278\pi$
$811$	13.8775	+	38.1282i	0.487306	+	1.33886i	−0.415805	+	0.909454i	$0.636500\pi$
$812$	−2.25313	+	3.21780i	−0.0790694	+	0.112923i
$813$	6.69499	+	9.56143i	0.234803	+	0.335334i
$814$	−1.09438	+	3.00679i	−0.0383580	+	0.105388i
$815$		0			0
$816$			18.4457i			0.645730i
$817$	19.6004	+	12.5876i	0.685733	+	0.440383i
$818$	−5.14334	−	5.14334i	−0.179833	−	0.179833i
$819$	−0.443728	+	0.372332i	−0.0155051	+	0.0130103i
$820$		0			0
$821$	−1.91779	+	10.8763i	−0.0669314	+	0.379587i	0.932880	+	0.360186i	$0.117287\pi$
$821$	−1.91779	+	10.8763i	−0.0669314	+	0.379587i	−0.999812	+	0.0194006i	$0.993824\pi$
$822$	2.49531	+	1.74724i	0.0870340	+	0.0609419i
$823$	41.8739	+	19.5261i	1.45963	+	0.680638i	0.980394	−	0.197047i	$-0.0631353\pi$
$823$	41.8739	+	19.5261i	1.45963	+	0.680638i	0.479238	+	0.877685i	$0.340913\pi$
$824$	−10.8592	−	6.26956i	−0.378298	−	0.218410i
$825$		0			0
$826$	0.126896	+	0.106479i	0.00441528	+	0.00370486i
$827$	−1.94055	−	22.1806i	−0.0674796	−	0.771295i	−0.952260	−	0.305287i	$-0.901247\pi$
$827$	−1.94055	−	22.1806i	−0.0674796	−	0.771295i	0.884781	−	0.466008i	$-0.154308\pi$
$828$	−3.21194	+	11.9871i	−0.111622	+	0.416581i
$829$	−13.8403	+	23.9721i	−0.480694	+	0.832587i	−0.999755	−	0.0221506i	$-0.992949\pi$
$829$	−13.8403	+	23.9721i	−0.480694	+	0.832587i	0.519060	+	0.854738i	$0.326282\pi$
$830$		0			0
$831$	−43.1365	+	7.60613i	−1.49639	+	0.263854i
$832$	−11.1449	+	7.80373i	−0.386379	+	0.270545i
$833$	−7.97980	−	17.1127i	−0.276484	−	0.592921i
$834$	−6.91462	−	8.24052i	−0.239434	−	0.285346i
$835$		0			0
$836$	−13.6411	+	5.59216i	−0.471789	+	0.193409i
$837$	−6.42639	+	6.42639i	−0.222128	+	0.222128i
$838$	−0.0809287	+	0.925019i	−0.00279564	+	0.0319543i
$839$	−35.1412	−	12.7903i	−1.21321	−	0.441572i	−0.345393	−	0.938458i	$-0.612254\pi$
$839$	−35.1412	−	12.7903i	−1.21321	−	0.441572i	−0.867815	+	0.496887i	$0.834476\pi$
$840$		0			0
$841$	1.51428	+	8.58788i	0.0522164	+	0.296134i
$842$	−2.71638	+	5.82530i	−0.0936127	+	0.200753i
$843$	22.5462	−	6.04123i	0.776532	−	0.208071i
$844$	−0.535075	−	0.926777i	−0.0184180	−	0.0319010i
$845$		0			0
$846$	−0.837567	+	0.998173i	−0.0287961	+	0.0343179i
$847$	−2.54354	−	0.681540i	−0.0873972	−	0.0234180i
$848$	−1.91422	−	7.14395i	−0.0657344	−	0.245324i
$849$	−21.2344	+	7.72868i	−0.728762	+	0.265248i
$850$		0			0
$851$	51.2522	+	9.03714i	1.75690	+	0.309789i
$852$	−52.3766	+	24.4236i	−1.79439	+	0.836739i
$853$	18.2820	+	1.59947i	0.625964	+	0.0547648i	0.395725	−	0.918369i	$-0.370493\pi$
$853$	18.2820	+	1.59947i	0.625964	+	0.0547648i	0.230240	+	0.973134i	$0.426049\pi$
$854$	−0.919837			−0.0314762
$855$		0			0
$856$	−2.57334			−0.0879549
$857$	−48.7757	−	4.26732i	−1.66615	−	0.145769i	−0.785283	−	0.619138i	$-0.787482\pi$
$857$	−48.7757	−	4.26732i	−1.66615	−	0.145769i	−0.880864	+	0.473369i	$0.843038\pi$
$858$	−2.12850	+	0.992537i	−0.0726659	+	0.0338846i
$859$	2.01743	+	0.355727i	0.0688338	+	0.0121373i	0.207959	−	0.978138i	$-0.433318\pi$
$859$	2.01743	+	0.355727i	0.0688338	+	0.0121373i	−0.139125	+	0.990275i	$0.544429\pi$
$860$		0			0
$861$	3.71207	−	1.35108i	0.126507	−	0.0460448i
$862$	−1.43278	−	5.34719i	−0.0488005	−	0.182126i
$863$	−33.3761	−	8.94309i	−1.13613	−	0.304426i	−0.358738	−	0.933438i	$-0.616793\pi$
$863$	−33.3761	−	8.94309i	−1.13613	−	0.304426i	−0.777396	+	0.629012i	$0.783460\pi$
$864$	9.43506	−	11.2443i	0.320987	−	0.382538i
$865$		0			0
$866$	1.36949	+	2.37203i	0.0465372	+	0.0806048i
$867$	−17.7545	+	4.75730i	−0.602974	+	0.161566i
$868$	0.564713	−	1.21103i	0.0191676	−	0.0411051i
$869$	−4.60109	−	26.0941i	−0.156081	−	0.885181i
$870$		0			0
$871$	−23.6644	−	8.61312i	−0.801836	−	0.291844i
$872$	0.887084	−	10.1394i	0.0300405	−	0.343364i
$873$	−3.20275	+	3.20275i	−0.108397	+	0.108397i
$874$	−5.98402	−	9.46905i	−0.202412	−	0.320295i
$875$		0			0
$876$	13.1671	+	15.6919i	0.444875	+	0.530181i
$877$	−17.7162	−	37.9925i	−0.598234	−	1.28292i	−0.939371	−	0.342903i	$-0.888590\pi$
$877$	−17.7162	−	37.9925i	−0.598234	−	1.28292i	0.341137	−	0.940014i	$-0.389188\pi$
$878$	−4.33181	+	3.03316i	−0.146191	+	0.102364i
$879$	24.0318	−	4.23745i	0.810572	−	0.142926i
$880$		0			0
$881$	2.70678	−	4.68828i	0.0911936	−	0.157952i	−0.816820	−	0.576893i	$-0.804265\pi$
$881$	2.70678	−	4.68828i	0.0911936	−	0.157952i	0.908014	+	0.418941i	$0.137598\pi$
$882$	0.402167	−	1.50091i	0.0135417	−	0.0505382i
$883$	−2.66819	−	30.4975i	−0.0897917	−	1.02632i	−0.898751	−	0.438459i	$-0.855524\pi$
$883$	−2.66819	−	30.4975i	−0.0897917	−	1.02632i	0.808959	−	0.587864i	$-0.200031\pi$
$884$	9.19539	+	7.71585i	0.309275	+	0.259512i
$885$		0			0
$886$	1.23175	+	0.711150i	0.0413814	+	0.0238916i
$887$	33.6111	+	15.6731i	1.12855	+	0.526252i	0.894988	−	0.446090i	$-0.147184\pi$
$887$	33.6111	+	15.6731i	1.12855	+	0.526252i	0.233562	+	0.972342i	$0.424962\pi$
$888$	11.2214	+	7.85729i	0.376565	+	0.263673i
$889$	0.389181	−	2.20715i	0.0130527	−	0.0740256i
$890$		0			0
$891$	−14.5025	+	12.1690i	−0.485852	+	0.407678i
$892$	30.4145	+	30.4145i	1.01835	+	1.01835i
$893$	3.19525	+	24.9737i	0.106925	+	0.835713i
$894$			11.3609i			0.379966i
$895$		0			0
$896$	−0.975662	+	2.68061i	−0.0325946	+	0.0895529i
$897$	21.9096	+	31.2901i	0.731539	+	1.04475i
$898$	0.567547	−	0.810541i	0.0189393	−	0.0270481i
$899$	−4.38846	−	12.0572i	−0.146363	−	0.402130i
$900$		0			0
$901$	−5.05646	+	2.91935i	−0.168455	+	0.0972577i
$902$	3.20839	−	0.280698i	0.106828	−	0.00934622i
$903$	−3.45328	+	0.302123i	−0.114918	+	0.0100540i
$904$	−11.8776	+	6.85751i	−0.395041	+	0.228077i
$905$		0			0
$906$	0.253751	+	0.697176i	0.00843032	+	0.0231621i
$907$	0.162899	−	0.232644i	0.00540896	−	0.00772480i	−0.816438	−	0.577432i	$-0.804055\pi$
$907$	0.162899	−	0.232644i	0.00540896	−	0.00772480i	0.821847	+	0.569708i	$0.192944\pi$
$908$	17.8358	+	25.4721i	0.591901	+	0.845323i
$909$	2.77099	−	7.61323i	0.0919079	−	0.252515i
$910$		0			0
$911$		−	35.0022i		−	1.15968i	−0.814732	−	0.579838i	$-0.803116\pi$
$911$		−	35.0022i		−	1.15968i	0.814732	−	0.579838i	$-0.196884\pi$
$912$	3.72233	+	29.0933i	0.123259	+	0.963375i
$913$	4.15872	+	4.15872i	0.137633	+	0.137633i
$914$	−6.55749	+	5.50239i	−0.216903	+	0.182003i
$915$		0			0
$916$	−3.81840	+	21.6552i	−0.126163	+	0.715508i
$917$	−2.01505	−	1.41095i	−0.0665427	−	0.0465937i
$918$	−3.22896	−	1.50569i	−0.106572	−	0.0496951i
$919$	10.2856	+	5.93841i	0.339291	+	0.195890i	0.659959	−	0.751302i	$-0.270574\pi$
$919$	10.2856	+	5.93841i	0.339291	+	0.195890i	−0.320667	+	0.947192i	$0.603907\pi$
$920$		0			0
$921$	−24.5113	−	20.5674i	−0.807675	−	0.677719i
$922$	0.416950	+	4.76576i	0.0137315	+	0.156952i
$923$	−9.25777	+	34.5505i	−0.304723	+	1.13724i
$924$	1.09696	−	1.89999i	0.0360874	−	0.0625052i
$925$		0			0
$926$	−8.32375	+	1.46770i	−0.273535	+	0.0482317i
$927$	6.63812	−	4.64806i	0.218025	−	0.152662i
$928$	8.75798	+	18.7815i	0.287495	+	0.616534i
$929$	34.7475	+	41.4104i	1.14003	+	1.35863i	0.924067	+	0.382230i	$0.124844\pi$
$929$	34.7475	+	41.4104i	1.14003	+	1.35863i	0.215960	+	0.976402i	$0.430712\pi$
$930$		0			0
$931$	−16.0394	−	25.3805i	−0.525669	−	0.831814i
$932$	23.7813	−	23.7813i	0.778984	−	0.778984i
$933$	−0.900430	+	10.2920i	−0.0294788	+	0.336944i
$934$	0.432760	+	0.157512i	0.0141604	+	0.00515395i
$935$		0			0
$936$	0.351083	+	1.99109i	0.0114755	+	0.0650809i
$937$	−7.52427	+	16.1359i	−0.245807	+	0.527135i	−0.990040	−	0.140785i	$-0.955037\pi$
$937$	−7.52427	+	16.1359i	−0.245807	+	0.527135i	0.744233	+	0.667920i	$0.232815\pi$
$938$	−1.06150	+	0.284428i	−0.0346592	+	0.00928692i
$939$	19.0443	+	32.9856i	0.621486	+	1.07645i
$940$		0			0
$941$	20.1771	−	24.0461i	0.657754	−	0.783881i	−0.329307	−	0.944223i	$-0.606815\pi$
$941$	20.1771	−	24.0461i	0.657754	−	0.783881i	0.987062	+	0.160342i	$0.0512596\pi$
$942$	−9.10016	−	2.43838i	−0.296499	−	0.0794468i
$943$	−13.5576	−	50.5977i	−0.441497	−	1.64769i
$944$	−5.40486	+	1.96721i	−0.175913	+	0.0640271i
$945$		0			0
$946$	−2.78325	−	0.490762i	−0.0904912	−	0.0159560i
$947$	22.7589	−	10.6127i	0.739565	−	0.344865i	−0.0160582	−	0.999871i	$-0.505112\pi$
$947$	22.7589	−	10.6127i	0.739565	−	0.344865i	0.755624	+	0.655006i	$0.227334\pi$
$948$	−55.2131	−	4.83052i	−1.79324	−	0.156888i
$949$	12.6786			0.411564
$950$		0			0
$951$	−35.3895			−1.14758
$952$	1.06804	+	0.0934410i	0.0346152	+	0.00302844i
$953$	−1.38466	+	0.645677i	−0.0448535	+	0.0209155i	−0.444916	−	0.895572i	$-0.646766\pi$
$953$	−1.38466	+	0.645677i	−0.0448535	+	0.0209155i	0.400062	+	0.916488i	$0.368989\pi$
$954$	−0.473189	−	0.0834359i	−0.0153200	−	0.00270134i
$955$		0			0
$956$	5.70017	−	2.07469i	0.184357	−	0.0671003i
$957$	−5.45253	−	20.3491i	−0.176255	−	0.657794i
$958$	4.84033	+	1.29696i	0.156384	+	0.0419030i
$959$	−1.13214	+	1.34923i	−0.0365587	+	0.0435689i
$960$		0			0
$961$	−13.3177	−	23.0669i	−0.429603	−	0.744095i
$962$	4.00145	−	1.07218i	0.129012	−	0.0345686i
$963$	0.702844	−	1.50725i	0.0226488	−	0.0485706i
$964$	−2.55740	−	14.5037i	−0.0823682	−	0.467133i
$965$		0			0
$966$	1.56638	+	0.570115i	0.0503974	+	0.0183431i
$967$	−1.75903	+	20.1058i	−0.0565665	+	0.646558i	0.913998	+	0.405718i	$0.132978\pi$
$967$	−1.75903	+	20.1058i	−0.0565665	+	0.646558i	−0.970565	+	0.240840i	$0.922577\pi$
$968$	−6.49917	+	6.49917i	−0.208891	+	0.208891i
$969$	21.4244	−	8.78288i	0.688250	−	0.282147i
$970$		0			0
$971$	−1.63397	−	1.94730i	−0.0524367	−	0.0624917i	0.739189	−	0.673499i	$-0.235209\pi$
$971$	−1.63397	−	1.94730i	−0.0524367	−	0.0624917i	−0.791625	+	0.611007i	$0.790765\pi$
$972$	6.19720	+	13.2899i	0.198775	+	0.426275i
$973$	5.09491	−	3.56750i	0.163335	−	0.114369i
$974$	−1.18424	+	0.208814i	−0.0379456	+	0.00669083i
$975$		0			0
$976$	15.9692	−	27.6595i	0.511163	−	0.885361i
$977$	−15.0379	+	56.1223i	−0.481106	+	1.79551i	0.115882	+	0.993263i	$0.463030\pi$
$977$	−15.0379	+	56.1223i	−0.481106	+	1.79551i	−0.596989	+	0.802250i	$0.703636\pi$
$978$	−0.514339	−	5.87892i	−0.0164468	−	0.187987i
$979$	14.0751	+	11.8104i	0.449842	+	0.377462i
$980$		0			0
$981$	5.69657	+	3.28892i	0.181877	+	0.105007i
$982$	−3.16750	−	1.47703i	−0.101079	−	0.0471338i
$983$	26.9174	+	18.8478i	0.858531	+	0.601150i	0.917778	−	0.397093i	$-0.129981\pi$
$983$	26.9174	+	18.8478i	0.858531	+	0.601150i	−0.0592470	+	0.998243i	$0.518870\pi$
$984$	2.39430	−	13.5787i	0.0763275	−	0.432875i
$985$		0			0
$986$	3.85318	−	3.23320i	0.122710	−	0.102966i
$987$	−2.64930	−	2.64930i	−0.0843283	−	0.0843283i
$988$	16.0604	+	10.3141i	0.510949	+	0.328136i
$989$			45.9668i			1.46166i
$990$		0			0
$991$	6.36348	−	17.4835i	0.202143	−	0.555383i	−0.796653	−	0.604436i	$-0.793398\pi$
$991$	6.36348	−	17.4835i	0.202143	−	0.555383i	0.998796	+	0.0490538i	$0.0156206\pi$
$992$	−4.04326	−	5.77437i	−0.128373	−	0.183336i
$993$	13.4933	−	19.2705i	0.428198	−	0.611530i
$994$	0.533863	+	1.46678i	0.0169331	+	0.0465233i
$995$		0			0
$996$	10.6540	−	6.15109i	0.337585	−	0.194905i
$997$	−51.6752	+	4.52099i	−1.63657	+	0.143181i	−0.867993	−	0.496577i	$-0.834590\pi$
$997$	−51.6752	+	4.52099i	−1.63657	+	0.143181i	−0.768577	+	0.639758i	$0.779035\pi$
$998$	−7.72579	+	0.675919i	−0.244555	+	0.0213958i
$999$	22.7945	−	13.1604i	0.721185	−	0.416376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.bb.b.393.4		96
5.2	odd	4	inner	475.2.bb.b.32.5		96
5.3	odd	4		95.2.r.a.32.4	yes	96
5.4	even	2		95.2.r.a.13.5	yes	96
15.8	even	4		855.2.dl.a.127.5		96
15.14	odd	2		855.2.dl.a.298.4		96
19.3	odd	18	inner	475.2.bb.b.193.5		96
95.3	even	36		95.2.r.a.22.5	yes	96
95.22	even	36	inner	475.2.bb.b.307.4		96
95.79	odd	18		95.2.r.a.3.4	✓	96
285.98	odd	36		855.2.dl.a.307.4		96
285.269	even	18		855.2.dl.a.478.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.3.4	✓	96	95.79	odd	18
95.2.r.a.13.5	yes	96	5.4	even	2
95.2.r.a.22.5	yes	96	95.3	even	36
95.2.r.a.32.4	yes	96	5.3	odd	4
475.2.bb.b.32.5		96	5.2	odd	4	inner
475.2.bb.b.193.5		96	19.3	odd	18	inner
475.2.bb.b.307.4		96	95.22	even	36	inner
475.2.bb.b.393.4		96	1.1	even	1	trivial
855.2.dl.a.127.5		96	15.8	even	4
855.2.dl.a.298.4		96	15.14	odd	2
855.2.dl.a.307.4		96	285.98	odd	36
855.2.dl.a.478.5		96	285.269	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.297624 + 0.0260387i) q^{2} +(-1.75625 + 0.818952i) q^{3} +(-1.88171 - 0.331797i) q^{4} +(-0.544026 + 0.198009i) q^{6} +(-0.0866366 - 0.323332i) q^{7} +(-1.12856 - 0.302398i) q^{8} +(0.485360 - 0.578430i) q^{9} +(0.885063 + 1.53297i) q^{11} +(3.57648 - 0.958315i) q^{12} +(0.968521 - 2.07700i) q^{13} +(-0.0173660 - 0.0984873i) q^{14} +(3.26301 + 1.18764i) q^{16} +(0.238918 - 2.73085i) q^{17} +(0.159516 - 0.159516i) q^{18} +(-0.174252 - 4.35541i) q^{19} +(0.416949 + 0.496900i) q^{21} +(0.223499 + 0.479296i) q^{22} +(7.04590 - 4.93359i) q^{23} +(2.22969 - 0.393154i) q^{24} +(0.342337 - 0.592946i) q^{26} +(1.12592 - 4.20197i) q^{27} +(0.0557446 + 0.637164i) q^{28} +(4.70481 + 3.94780i) q^{29} +(-1.80927 - 1.04458i) q^{31} +(3.05804 + 1.42599i) q^{32} +(-2.80982 - 1.96746i) q^{33} +(0.142216 - 0.806545i) q^{34} +(-1.10523 + 0.927398i) q^{36} +(4.27833 + 4.27833i) q^{37} +(0.0615479 - 1.30081i) q^{38} +4.44090i q^{39} +(2.08289 - 5.72270i) q^{41} +(0.111155 + 0.158746i) q^{42} +(-3.06524 + 4.37761i) q^{43} +(-1.15680 - 3.17828i) q^{44} +(2.22549 - 1.28489i) q^{46} +(-5.75408 + 0.503417i) q^{47} +(-6.70326 + 0.586460i) q^{48} +(5.96514 - 3.44398i) q^{49} +(1.81683 + 4.99171i) q^{51} +(-2.51162 + 3.58697i) q^{52} +(-1.22167 - 1.74473i) q^{53} +(0.444513 - 1.22129i) q^{54} +0.391100i q^{56} +(3.87290 + 7.50648i) q^{57} +(1.29747 + 1.29747i) q^{58} +(-1.26888 + 1.06472i) q^{59} +(1.59718 - 9.05803i) q^{61} +(-0.511282 - 0.358003i) q^{62} +(-0.229075 - 0.106819i) q^{63} +(-5.14139 - 2.96838i) q^{64} +(-0.785040 - 0.658727i) q^{66} +(-0.957732 - 10.9469i) q^{67} +(-1.35566 + 5.05941i) q^{68} +(-8.33397 + 14.4349i) q^{69} +(-15.3710 + 2.71031i) q^{71} +(-0.722676 + 0.506024i) q^{72} +(2.33808 + 5.01402i) q^{73} +(1.16193 + 1.38473i) q^{74} +(-1.11722 + 8.25346i) q^{76} +(0.418981 - 0.418981i) q^{77} +(-0.115635 + 1.32172i) q^{78} +(-14.0660 - 5.11962i) q^{79} +(1.85719 + 10.5326i) q^{81} +(0.768931 - 1.64898i) q^{82} +(3.20933 - 0.859936i) q^{83} +(-0.619708 - 1.07337i) q^{84} +(-1.02628 + 1.22307i) q^{86} +(-11.4959 - 3.08031i) q^{87} +(-0.535283 - 1.99770i) q^{88} +(9.75391 - 3.55013i) q^{89} +(-0.755470 - 0.133210i) q^{91} +(-14.8953 + 6.94580i) q^{92} +(4.03298 + 0.352840i) q^{93} -1.72566 q^{94} -6.53849 q^{96} +(-5.97565 - 0.522802i) q^{97} +(1.86504 - 0.869685i) q^{98} +(1.31629 + 0.232098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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