LMFDB - Embedded newform 961.2.d.s.388.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,8,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			388.6
Character	$\chi$	$=$	961.388
Dual form			961.2.d.s.374.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.100459 + 0.0729880i) q^{2} +(1.19674 + 0.869483i) q^{3} +(-0.613269 + 1.88745i) q^{4} -1.22944 q^{5} -0.183686 q^{6} +(0.824157 - 2.53649i) q^{7} +(-0.152897 - 0.470567i) q^{8} +(-0.250863 - 0.772076i) q^{9} +(0.123509 - 0.0897347i) q^{10} +(1.74036 - 5.35627i) q^{11} +(-2.37503 + 1.72556i) q^{12} +(-0.0108937 - 0.00791476i) q^{13} +(0.102339 + 0.314968i) q^{14} +(-1.47133 - 1.06898i) q^{15} +(-3.16141 - 2.29690i) q^{16} +(-1.09542 - 3.37135i) q^{17} +(0.0815539 + 0.0592523i) q^{18} +(4.82486 - 3.50546i) q^{19} +(0.753981 - 2.32051i) q^{20} +(3.19174 - 2.31894i) q^{21} +(0.216108 + 0.665113i) q^{22} +(1.26378 + 3.88953i) q^{23} +(0.226173 - 0.696088i) q^{24} -3.48847 q^{25} +0.00167206 q^{26} +(1.74243 - 5.36266i) q^{27} +(4.28207 + 3.11111i) q^{28} +(-2.39871 + 1.74276i) q^{29} +0.225832 q^{30} +1.47481 q^{32} +(6.73995 - 4.89686i) q^{33} +(0.356114 + 0.258732i) q^{34} +(-1.01326 + 3.11848i) q^{35} +1.61110 q^{36} -10.6352 q^{37} +(-0.228845 + 0.704314i) q^{38} +(-0.00615523 - 0.0189438i) q^{39} +(0.187978 + 0.578537i) q^{40} +(5.78021 - 4.19957i) q^{41} +(-0.151386 + 0.465918i) q^{42} +(-2.56914 + 1.86659i) q^{43} +(9.04238 + 6.56967i) q^{44} +(0.308422 + 0.949225i) q^{45} +(-0.410848 - 0.298498i) q^{46} +(7.93669 + 5.76634i) q^{47} +(-1.78628 - 5.49759i) q^{48} +(-0.0914452 - 0.0664388i) q^{49} +(0.350449 - 0.254616i) q^{50} +(1.62040 - 4.98709i) q^{51} +(0.0216195 - 0.0157075i) q^{52} +(-2.44379 - 7.52122i) q^{53} +(0.216366 + 0.665906i) q^{54} +(-2.13968 + 6.58524i) q^{55} -1.31960 q^{56} +8.82205 q^{57} +(0.113772 - 0.350154i) q^{58} +(8.40644 + 6.10763i) q^{59} +(2.91997 - 2.12148i) q^{60} -3.70951 q^{61} -2.16512 q^{63} +(6.17467 - 4.48616i) q^{64} +(0.0133932 + 0.00973076i) q^{65} +(-0.319679 + 0.983871i) q^{66} +3.56973 q^{67} +7.03504 q^{68} +(-1.86946 + 5.75360i) q^{69} +(-0.125821 - 0.387236i) q^{70} +(1.16243 + 3.57758i) q^{71} +(-0.324958 + 0.236096i) q^{72} +(1.09707 - 3.37645i) q^{73} +(1.06841 - 0.776245i) q^{74} +(-4.17479 - 3.03316i) q^{75} +(3.65745 + 11.2565i) q^{76} +(-12.1518 - 8.82882i) q^{77} +(0.00200102 + 0.00145383i) q^{78} +(1.00736 + 3.10032i) q^{79} +(3.88678 + 2.82391i) q^{80} +(4.77768 - 3.47119i) q^{81} +(-0.274158 + 0.843772i) q^{82} +(1.67486 - 1.21685i) q^{83} +(2.41947 + 7.44638i) q^{84} +(1.34676 + 4.14489i) q^{85} +(0.121855 - 0.375033i) q^{86} -4.38594 q^{87} -2.78658 q^{88} +(-2.72068 + 8.37339i) q^{89} +(-0.100266 - 0.0728475i) q^{90} +(-0.0290539 + 0.0211089i) q^{91} -8.11632 q^{92} -1.21819 q^{94} +(-5.93190 + 4.30977i) q^{95} +(1.76496 + 1.28232i) q^{96} +(1.04679 - 3.22170i) q^{97} +0.0140358 q^{98} -4.57204 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{2} - 8 q^{4} - 64 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} + 8 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 32 q^{32} + 32 q^{33} + 16 q^{35} - 160 q^{36} + 24 q^{38} + 32 q^{39} + 32 q^{41}+ \cdots + 64 q^{98}+O(q^{100}) $ 64 * q + 8 * q^2 - 8 * q^4 - 64 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 + 8 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 32 * q^32 + 32 * q^33 + 16 * q^35 - 160 * q^36 + 24 * q^38 + 32 * q^39 + 32 * q^41 + 16 * q^45 + 32 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 192 * q^56 + 64 * q^59 - 64 * q^63 + 16 * q^64 + 64 * q^67 + 32 * q^69 - 88 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 - 32 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 - 128 * q^87 - 40 * q^90 - 128 * q^94 + 48 * q^95 + 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.100459	+	0.0729880i	−0.0710355	+	0.0516103i	−0.622736	−	0.782432i	$-0.713979\pi$
$2$	−0.100459	+	0.0729880i	−0.0710355	+	0.0516103i	0.551701	+	0.834042i	$0.313979\pi$
$3$	1.19674	+	0.869483i	0.690939	+	0.501996i	0.876969	−	0.480548i	$-0.159562\pi$
$3$	1.19674	+	0.869483i	0.690939	+	0.501996i	−0.186030	+	0.982544i	$0.559562\pi$
$4$	−0.613269	+	1.88745i	−0.306635	+	0.943724i
$5$	−1.22944			−0.549824			−0.274912	−	0.961469i	$-0.588649\pi$
$5$	−1.22944			−0.549824			−0.274912	+	0.961469i	$0.588649\pi$
$6$	−0.183686			−0.0749894
$7$	0.824157	−	2.53649i	0.311502	−	0.958704i	−0.665669	−	0.746248i	$-0.731854\pi$
$7$	0.824157	−	2.53649i	0.311502	−	0.958704i	0.977170	−	0.212457i	$-0.0681465\pi$
$8$	−0.152897	−	0.470567i	−0.0540571	−	0.166371i
$9$	−0.250863	−	0.772076i	−0.0836209	−	0.257359i
$10$	0.123509	−	0.0897347i	0.0390571	−	0.0283766i
$11$	1.74036	−	5.35627i	0.524738	−	1.61498i	−0.240096	−	0.970749i	$-0.577179\pi$
$11$	1.74036	−	5.35627i	0.524738	−	1.61498i	0.764833	−	0.644228i	$-0.222821\pi$
$12$	−2.37503	+	1.72556i	−0.685612	+	0.498126i
$13$	−0.0108937	−	0.00791476i	−0.00302138	−	0.00219516i	0.586274	−	0.810113i	$-0.300594\pi$
$13$	−0.0108937	−	0.00791476i	−0.00302138	−	0.00219516i	−0.589295	+	0.807918i	$0.700594\pi$
$14$	0.102339	+	0.314968i	0.0273513	+	0.0841788i
$15$	−1.47133	−	1.06898i	−0.379895	−	0.276010i
$16$	−3.16141	−	2.29690i	−0.790353	−	0.574225i
$17$	−1.09542	−	3.37135i	−0.265678	−	0.817673i	−0.991536	−	0.129829i	$-0.958557\pi$
$17$	−1.09542	−	3.37135i	−0.265678	−	0.817673i	0.725858	−	0.687844i	$-0.241443\pi$
$18$	0.0815539	+	0.0592523i	0.0192224	+	0.0139659i
$19$	4.82486	−	3.50546i	1.10690	−	0.804209i	0.124726	−	0.992191i	$-0.460195\pi$
$19$	4.82486	−	3.50546i	1.10690	−	0.804209i	0.982172	+	0.187983i	$0.0601949\pi$
$20$	0.753981	−	2.32051i	0.168595	−	0.518883i
$21$	3.19174	−	2.31894i	0.696495	−	0.506033i
$22$	0.216108	+	0.665113i	0.0460745	+	0.141803i
$23$	1.26378	+	3.88953i	0.263517	+	0.811022i	0.992031	+	0.125992i	$0.0402113\pi$
$23$	1.26378	+	3.88953i	0.263517	+	0.811022i	−0.728514	+	0.685031i	$0.759789\pi$
$24$	0.226173	−	0.696088i	0.0461673	−	0.142088i
$25$	−3.48847			−0.697693
$26$	0.00167206			0.000327918
$27$	1.74243	−	5.36266i	0.335331	−	1.03204i
$28$	4.28207	+	3.11111i	0.809235	+	0.587944i
$29$	−2.39871	+	1.74276i	−0.445429	+	0.323623i	−0.787788	−	0.615946i	$-0.788774\pi$
$29$	−2.39871	+	1.74276i	−0.445429	+	0.323623i	0.342359	+	0.939569i	$0.388774\pi$
$30$	0.225832			0.0412310
$31$		0			0
$31$		0			0
$32$	1.47481			0.260712
$33$	6.73995	−	4.89686i	1.17327	−	0.852434i
$34$	0.356114	+	0.258732i	0.0610730	+	0.0443721i
$35$	−1.01326	+	3.11848i	−0.171271	+	0.527119i
$36$	1.61110			0.268517
$37$	−10.6352			−1.74842			−0.874211	−	0.485546i	$-0.838621\pi$
$37$	−10.6352			−1.74842			−0.874211	+	0.485546i	$0.838621\pi$
$38$	−0.228845	+	0.704314i	−0.0371236	+	0.114255i
$39$	−0.00615523	−	0.0189438i	−0.000985625	−	0.00303344i
$40$	0.187978	+	0.578537i	0.0297219	+	0.0914747i
$41$	5.78021	−	4.19957i	0.902717	−	0.655862i	−0.0364457	−	0.999336i	$-0.511604\pi$
$41$	5.78021	−	4.19957i	0.902717	−	0.655862i	0.939162	+	0.343474i	$0.111604\pi$
$42$	−0.151386	+	0.465918i	−0.0233593	+	0.0718927i
$43$	−2.56914	+	1.86659i	−0.391790	+	0.284652i	−0.766189	−	0.642616i	$-0.777849\pi$
$43$	−2.56914	+	1.86659i	−0.391790	+	0.284652i	0.374399	+	0.927268i	$0.377849\pi$
$44$	9.04238	+	6.56967i	1.36319	+	0.990416i
$45$	0.308422	+	0.949225i	0.0459768	+	0.141502i
$46$	−0.410848	−	0.298498i	−0.0605762	−	0.0440112i
$47$	7.93669	+	5.76634i	1.15768	+	0.841107i	0.989484	−	0.144645i	$-0.0462041\pi$
$47$	7.93669	+	5.76634i	1.15768	+	0.841107i	0.168201	+	0.985753i	$0.446204\pi$
$48$	−1.78628	−	5.49759i	−0.257827	−	0.793509i
$49$	−0.0914452	−	0.0664388i	−0.0130636	−	0.00949126i
$50$	0.350449	−	0.254616i	0.0495610	−	0.0360082i
$51$	1.62040	−	4.98709i	0.226902	−	0.698332i
$52$	0.0216195	−	0.0157075i	0.00299808	−	0.00217824i
$53$	−2.44379	−	7.52122i	−0.335681	−	1.03312i	−0.966386	−	0.257097i	$-0.917234\pi$
$53$	−2.44379	−	7.52122i	−0.335681	−	1.03312i	0.630705	−	0.776023i	$-0.282766\pi$
$54$	0.216366	+	0.665906i	0.0294437	+	0.0906183i
$55$	−2.13968	+	6.58524i	−0.288514	+	0.887954i
$56$	−1.31960			−0.176339
$57$	8.82205			1.16851
$58$	0.113772	−	0.350154i	0.0149390	−	0.0459775i
$59$	8.40644	+	6.10763i	1.09442	+	0.795146i	0.980141	−	0.198302i	$-0.0635426\pi$
$59$	8.40644	+	6.10763i	1.09442	+	0.795146i	0.114284	+	0.993448i	$0.463543\pi$
$60$	2.91997	−	2.12148i	0.376966	−	0.273882i
$61$	−3.70951			−0.474954			−0.237477	−	0.971393i	$-0.576320\pi$
$61$	−3.70951			−0.474954			−0.237477	+	0.971393i	$0.576320\pi$
$62$		0			0
$63$	−2.16512			−0.272779
$64$	6.17467	−	4.48616i	0.771834	−	0.560770i
$65$	0.0133932	+	0.00973076i	0.00166123	+	0.00120695i
$66$	−0.319679	+	0.983871i	−0.0393498	+	0.121106i
$67$	3.56973			0.436112			0.218056	−	0.975936i	$-0.430028\pi$
$67$	3.56973			0.436112			0.218056	+	0.975936i	$0.430028\pi$
$68$	7.03504			0.853124
$69$	−1.86946	+	5.75360i	−0.225056	+	0.692652i
$70$	−0.125821	−	0.387236i	−0.0150384	−	0.0462835i
$71$	1.16243	+	3.57758i	0.137955	+	0.424580i	0.996038	−	0.0889300i	$-0.0283447\pi$
$71$	1.16243	+	3.57758i	0.137955	+	0.424580i	−0.858083	+	0.513510i	$0.828345\pi$
$72$	−0.324958	+	0.236096i	−0.0382967	+	0.0278242i
$73$	1.09707	−	3.37645i	0.128403	−	0.395183i	−0.866103	−	0.499866i	$-0.833383\pi$
$73$	1.09707	−	3.37645i	0.128403	−	0.395183i	0.994506	+	0.104683i	$0.0333827\pi$
$74$	1.06841	−	0.776245i	0.124200	−	0.0902367i
$75$	−4.17479	−	3.03316i	−0.482063	−	0.350239i
$76$	3.65745	+	11.2565i	0.419538	+	1.29120i
$77$	−12.1518	−	8.82882i	−1.38483	−	1.00614i
$78$	0.00200102	+	0.00145383i	0.000226571	+	0.000164614i
$79$	1.00736	+	3.10032i	0.113336	+	0.348814i	0.991596	−	0.129370i	$-0.0412954\pi$
$79$	1.00736	+	3.10032i	0.113336	+	0.348814i	−0.878260	+	0.478183i	$0.841295\pi$
$80$	3.88678	+	2.82391i	0.434556	+	0.315723i
$81$	4.77768	−	3.47119i	0.530853	−	0.385688i
$82$	−0.274158	+	0.843772i	−0.0302757	+	0.0931790i
$83$	1.67486	−	1.21685i	0.183839	−	0.133567i	−0.492059	−	0.870562i	$-0.663756\pi$
$83$	1.67486	−	1.21685i	0.183839	−	0.133567i	0.675899	+	0.736995i	$0.263756\pi$
$84$	2.41947	+	7.44638i	0.263986	+	0.812466i
$85$	1.34676	+	4.14489i	0.146076	+	0.449577i
$86$	0.121855	−	0.375033i	0.0131400	−	0.0404408i
$87$	−4.38594			−0.470222
$88$	−2.78658			−0.297051
$89$	−2.72068	+	8.37339i	−0.288392	+	0.887578i	0.696970	+	0.717100i	$0.254531\pi$
$89$	−2.72068	+	8.37339i	−0.288392	+	0.887578i	−0.985362	+	0.170478i	$0.945469\pi$
$90$	−0.100266	−	0.0728475i	−0.0105690	−	0.00767880i
$91$	−0.0290539	+	0.0211089i	−0.00304567	+	0.00221281i
$92$	−8.11632			−0.846185
$93$		0			0
$94$	−1.21819			−0.125647
$95$	−5.93190	+	4.30977i	−0.608600	+	0.442174i
$96$	1.76496	+	1.28232i	0.180136	+	0.130876i
$97$	1.04679	−	3.22170i	0.106286	−	0.327114i	−0.883744	−	0.467970i	$-0.844986\pi$
$97$	1.04679	−	3.22170i	0.106286	−	0.327114i	0.990030	+	0.140856i	$0.0449855\pi$
$98$	0.0140358			0.00141783
$99$	−4.57204			−0.459508
$100$	2.13937	−	6.58430i	0.213937	−	0.658430i
$101$	−2.67867	−	8.24411i	−0.266538	−	0.820319i	−0.991335	−	0.131357i	$-0.958067\pi$
$101$	−2.67867	−	8.24411i	−0.266538	−	0.820319i	0.724797	−	0.688962i	$-0.241933\pi$
$102$	0.201213	+	0.619270i	0.0199230	+	0.0613168i
$103$	−2.16894	+	1.57583i	−0.213712	+	0.155271i	−0.689492	−	0.724294i	$-0.742166\pi$
$103$	−2.16894	+	1.57583i	−0.213712	+	0.155271i	0.475779	+	0.879565i	$0.342166\pi$
$104$	−0.00205881	+	0.00633638i	−0.000201883	+	0.000621333i
$105$	−3.92407	+	2.85100i	−0.382950	+	0.278229i
$106$	0.794461	+	0.577210i	0.0771649	+	0.0560636i
$107$	−2.46463	−	7.58534i	−0.238264	−	0.733302i	−0.996672	−	0.0815214i	$-0.974022\pi$
$107$	−2.46463	−	7.58534i	−0.238264	−	0.733302i	0.758407	−	0.651781i	$-0.225978\pi$
$108$	9.05316	+	6.57751i	0.871141	+	0.632921i
$109$	−5.09596	−	3.70243i	−0.488105	−	0.354629i	0.316350	−	0.948642i	$-0.397542\pi$
$109$	−5.09596	−	3.70243i	−0.488105	−	0.354629i	−0.804455	+	0.594014i	$0.797542\pi$
$110$	−0.265693	−	0.817720i	−0.0253329	−	0.0779666i
$111$	−12.7276	−	9.24716i	−1.20805	−	0.877702i
$112$	−8.43157	+	6.12590i	−0.796709	+	0.578843i
$113$	−0.848955	+	2.61281i	−0.0798629	+	0.245793i	−0.983014	−	0.183530i	$-0.941248\pi$
$113$	−0.848955	+	2.61281i	−0.0798629	+	0.245793i	0.903151	+	0.429323i	$0.141248\pi$
$114$	−0.886258	+	0.643904i	−0.0830056	+	0.0603071i
$115$	−1.55375	−	4.78196i	−0.144888	−	0.445920i
$116$	−1.81832	−	5.59622i	−0.168827	−	0.519596i
$117$	−0.00337797	+	0.0103963i	−0.000312293	+	0.000961139i
$118$	−1.29029			−0.118781
$119$	−9.45421			−0.866666
$120$	−0.278067	+	0.855802i	−0.0253839	+	0.0781237i
$121$	−16.7616	−	12.1780i	−1.52378	−	1.10709i
$122$	0.372655	−	0.270750i	0.0337386	−	0.0245125i
$123$	10.5689			0.952962
$124$		0			0
$125$	10.4361			0.933433
$126$	0.217506	−	0.158028i	0.0193770	−	0.0140782i
$127$	1.40392	+	1.02001i	0.124577	+	0.0905108i	0.648329	−	0.761360i	$-0.275468\pi$
$127$	1.40392	+	1.02001i	0.124577	+	0.0905108i	−0.523752	+	0.851871i	$0.675468\pi$
$128$	−1.20435	+	3.70660i	−0.106450	+	0.327621i
$129$	−4.69756			−0.413597
$130$	−0.00205571			−0.000180297
$131$	2.18456	−	6.72339i	0.190866	−	0.587426i	−0.809134	−	0.587624i	$-0.800063\pi$
$131$	2.18456	−	6.72339i	0.190866	−	0.587426i	1.00000		0.000198766i	$6.32693e-5\pi$
$132$	5.10917	+	15.7244i	0.444696	+	1.36863i
$133$	−4.91515	−	15.1273i	−0.426197	−	1.31170i
$134$	−0.358613	+	0.260547i	−0.0309794	+	0.0225079i
$135$	−2.14223	+	6.59309i	−0.184373	+	0.567443i
$136$	−1.41896	+	1.03094i	−0.121675	+	0.0884021i
$137$	−7.71567	−	5.60576i	−0.659194	−	0.478933i	0.207196	−	0.978299i	$-0.433566\pi$
$137$	−7.71567	−	5.60576i	−0.659194	−	0.478933i	−0.866391	+	0.499367i	$0.833566\pi$
$138$	−0.232139	−	0.714451i	−0.0197610	−	0.0608181i
$139$	10.7991	+	7.84598i	0.915965	+	0.665488i	0.942516	−	0.334160i	$-0.108453\pi$
$139$	10.7991	+	7.84598i	0.915965	+	0.665488i	−0.0265514	+	0.999647i	$0.508453\pi$
$140$	−5.26457	−	3.82493i	−0.444937	−	0.323266i
$141$	4.48442	+	13.8016i	0.377657	+	1.16231i
$142$	−0.377897	−	0.274558i	−0.0317124	−	0.0230404i
$143$	−0.0613526	+	0.0445753i	−0.00513056	+	0.00372757i
$144$	−0.980302	+	3.01706i	−0.0816918	+	0.251422i
$145$	2.94908	−	2.14263i	0.244908	−	0.177936i
$146$	0.136229	+	0.419269i	0.0112744	+	0.0346990i
$147$	−0.0516688	−	0.159020i	−0.00426157	−	0.0131158i
$148$	6.52226	−	20.0735i	0.536127	−	1.65003i
$149$	18.1985			1.49088			0.745440	−	0.666573i	$-0.232239\pi$
$149$	18.1985			1.49088			0.745440	+	0.666573i	$0.232239\pi$
$150$	0.640781			0.0523196
$151$	2.03815	−	6.27280i	0.165863	−	0.510473i	−0.833236	−	0.552917i	$-0.813515\pi$
$151$	2.03815	−	6.27280i	0.165863	−	0.510473i	0.999099	+	0.0424444i	$0.0135145\pi$
$152$	−2.38726	−	1.73445i	−0.193632	−	0.140682i
$153$	−2.32814	+	1.69149i	−0.188219	+	0.136749i
$154$	1.86516			0.150299
$155$		0			0
$156$	0.0395303			0.00316496
$157$	−12.7219	+	9.24301i	−1.01532	+	0.737672i	−0.965318	−	0.261077i	$-0.915922\pi$
$157$	−12.7219	+	9.24301i	−1.01532	+	0.737672i	−0.0500010	+	0.998749i	$0.515922\pi$
$158$	−0.327485	−	0.237932i	−0.0260533	−	0.0189288i
$159$	3.61499	−	11.1258i	0.286687	−	0.882333i
$160$	−1.81319			−0.143346
$161$	10.9073			0.859617
$162$	−0.226608	+	0.697427i	−0.0178040	+	0.0547950i
$163$	−2.22380	−	6.84415i	−0.174181	−	0.536075i	0.825414	−	0.564528i	$-0.190942\pi$
$163$	−2.22380	−	6.84415i	−0.174181	−	0.536075i	−0.999595	+	0.0284531i	$0.990942\pi$
$164$	4.38164	+	13.4853i	0.342149	+	1.05303i
$165$	−8.28640	+	6.02042i	−0.645095	+	0.468689i
$166$	−0.0794393	+	0.244489i	−0.00616568	+	0.0189760i
$167$	16.5608	−	12.0321i	1.28151	−	0.931073i	0.281914	−	0.959440i	$-0.409031\pi$
$167$	16.5608	−	12.0321i	1.28151	−	0.931073i	0.999598	+	0.0283669i	$0.00903067\pi$
$168$	−1.57922	−	1.14737i	−0.121840	−	0.0885217i
$169$	−4.01716	−	12.3636i	−0.309013	−	0.951043i
$170$	−0.437822	−	0.318096i	−0.0335794	−	0.0243969i
$171$	−3.91686	−	2.84577i	−0.299530	−	0.217621i
$172$	−1.94751	−	5.99383i	−0.148497	−	0.457026i
$173$	17.0439	+	12.3831i	1.29582	+	0.941471i	0.999906	−	0.0137429i	$-0.00437462\pi$
$173$	17.0439	+	12.3831i	1.29582	+	0.941471i	0.295918	+	0.955213i	$0.404375\pi$
$174$	0.440609	−	0.320121i	0.0334025	−	0.0242683i
$175$	−2.87504	+	8.84847i	−0.217333	+	0.668881i
$176$	−17.8048	+	12.9360i	−1.34209	+	0.975085i
$177$	4.74984	+	14.6185i	0.357020	+	1.09879i
$178$	−0.337840	−	1.03976i	−0.0253221	−	0.0779336i
$179$	−3.23816	+	9.96604i	−0.242032	+	0.744897i	0.754079	+	0.656784i	$0.228084\pi$
$179$	−3.23816	+	9.96604i	−0.242032	+	0.744897i	−0.996111	+	0.0881128i	$0.971916\pi$
$180$	−1.98076			−0.147637
$181$	−9.53710			−0.708887			−0.354443	−	0.935077i	$-0.615330\pi$
$181$	−9.53710			−0.708887			−0.354443	+	0.935077i	$0.615330\pi$
$182$	0.00137804	−	0.00424117i	0.000102147	−	0.000314376i
$183$	−4.43932	−	3.22536i	−0.328164	−	0.238425i
$184$	1.63706	−	1.18939i	0.120685	−	0.0876831i
$185$	13.0754			0.961325
$186$		0			0
$187$	−19.9643			−1.45994
$188$	−15.7510	+	11.4438i	−1.14876	+	0.834623i
$189$	−12.1663	−	8.83934i	−0.884969	−	0.642967i
$190$	0.281353	−	0.865915i	0.0204115	−	0.0628201i
$191$	−10.0046			−0.723905			−0.361952	−	0.932197i	$-0.617890\pi$
$191$	−10.0046			−0.723905			−0.361952	+	0.932197i	$0.617890\pi$
$192$	11.2901			0.814794
$193$	−6.39064	+	19.6684i	−0.460009	+	1.41576i	0.405144	+	0.914253i	$0.367221\pi$
$193$	−6.39064	+	19.6684i	−0.460009	+	1.41576i	−0.865153	+	0.501508i	$0.832779\pi$
$194$	0.129985	+	0.400053i	0.00933239	+	0.0287221i
$195$	0.00756751	+	0.0232904i	0.000541921	+	0.00166786i
$196$	0.181480	−	0.131853i	0.0129629	−	0.00941809i
$197$	−0.232778	+	0.716417i	−0.0165847	+	0.0510426i	−0.959006	−	0.283384i	$-0.908543\pi$
$197$	−0.232778	+	0.716417i	−0.0165847	+	0.0510426i	0.942422	+	0.334427i	$0.108543\pi$
$198$	0.459305	−	0.333704i	0.0326414	−	0.0237153i
$199$	−8.00169	−	5.81357i	−0.567225	−	0.412113i	0.266871	−	0.963732i	$-0.414010\pi$
$199$	−8.00169	−	5.81357i	−0.567225	−	0.412113i	−0.834096	+	0.551619i	$0.814010\pi$
$200$	0.533375	+	1.64156i	0.0377153	+	0.116076i
$201$	4.27204	+	3.10382i	0.301327	+	0.218927i
$202$	0.870819	+	0.632687i	0.0612706	+	0.0445157i
$203$	2.44360	+	7.52062i	0.171507	+	0.527844i
$204$	8.41913	+	6.11685i	0.589457	+	0.428265i
$205$	−7.10644	+	5.16313i	−0.496336	+	0.360609i
$206$	0.102874	−	0.316614i	0.00716757	−	0.0220595i
$207$	2.68598	−	1.95148i	0.186688	−	0.135637i
$208$	0.0162602	+	0.0500437i	0.00112744	+	0.00346990i
$209$	−10.3792	−	31.9440i	−0.717947	−	2.20961i
$210$	0.186121	−	0.572820i	0.0128435	−	0.0395283i
$211$	14.0629			0.968128			0.484064	−	0.875033i	$-0.339160\pi$
$211$	14.0629			0.968128			0.484064	+	0.875033i	$0.339160\pi$
$212$	15.6946			1.07791
$213$	−1.71952	+	5.29215i	−0.117820	+	0.362612i
$214$	0.801234	+	0.582130i	0.0547712	+	0.0397936i
$215$	3.15861	−	2.29487i	0.215416	−	0.156509i
$216$	−2.78990			−0.189829
$217$		0			0
$218$	0.782170			0.0529753
$219$	4.24868	−	3.08684i	0.287099	−	0.208590i
$220$	−11.1171	−	8.07705i	−0.749515	−	0.544555i
$221$	−0.0147502	+	0.0453966i	−0.000992209	+	0.00305371i
$222$	1.95354			0.131113
$223$	9.89557			0.662656			0.331328	−	0.943516i	$-0.392503\pi$
$223$	9.89557			0.662656			0.331328	+	0.943516i	$0.392503\pi$
$224$	1.21547	−	3.74084i	0.0812122	−	0.249945i
$225$	0.875126	+	2.69336i	0.0583418	+	0.179557i
$226$	−0.105419	−	0.324445i	−0.00701234	−	0.0215818i
$227$	−7.60846	+	5.52787i	−0.504991	+	0.366898i	−0.810920	−	0.585157i	$-0.801033\pi$
$227$	−7.60846	+	5.52787i	−0.504991	+	0.366898i	0.305929	+	0.952054i	$0.401033\pi$
$228$	−5.41029	+	16.6512i	−0.358305	+	1.10275i
$229$	11.9367	−	8.67254i	0.788801	−	0.573097i	−0.118807	−	0.992917i	$-0.537907\pi$
$229$	11.9367	−	8.67254i	0.788801	−	0.573097i	0.907607	+	0.419820i	$0.137907\pi$
$230$	0.505115	+	0.366987i	0.0333063	+	0.0241984i
$231$	−6.86608	−	21.1316i	−0.451755	−	1.39036i
$232$	1.18684	+	0.862292i	0.0779200	+	0.0566122i
$233$	23.1265	+	16.8024i	1.51507	+	1.10076i	0.963864	+	0.266393i	$0.0858320\pi$
$233$	23.1265	+	16.8024i	1.51507	+	1.10076i	0.551206	+	0.834369i	$0.314168\pi$
$234$	−0.000419458	−	0.00129096i	−2.74208e−5	−	8.43926e-5i
$235$	−9.75772	−	7.08940i	−0.636523	−	0.462461i
$236$	−16.6833	+	12.1211i	−1.08599	+	0.789016i
$237$	−1.49014	+	4.58617i	−0.0967947	+	0.297904i
$238$	0.949764	−	0.690044i	0.0615641	−	0.0447289i
$239$	−2.78386	−	8.56784i	−0.180073	−	0.554208i	0.819756	−	0.572713i	$-0.194109\pi$
$239$	−2.78386	−	8.56784i	−0.180073	−	0.554208i	−0.999829	+	0.0185055i	$0.994109\pi$
$240$	2.19613	+	6.75899i	0.141759	+	0.436291i
$241$	0.243556	−	0.749587i	0.0156888	−	0.0482851i	−0.942906	−	0.333060i	$-0.891919\pi$
$241$	0.243556	−	0.749587i	0.0156888	−	0.0482851i	0.958594	+	0.284775i	$0.0919188\pi$
$242$	2.57271			0.165380
$243$	−8.18011			−0.524754
$244$	2.27493	−	7.00150i	0.145637	−	0.448225i
$245$	0.112427	+	0.0816829i	0.00718269	+	0.00521853i
$246$	−1.06174	+	0.771400i	−0.0676942	+	0.0491827i
$247$	−0.0803056			−0.00510972
$248$		0			0
$249$	3.06241			0.194072
$250$	−1.04840	+	0.761710i	−0.0663069	+	0.0481748i
$251$	15.9957	+	11.6216i	1.00964	+	0.733547i	0.964134	−	0.265417i	$-0.0855096\pi$
$251$	15.9957	+	11.6216i	1.00964	+	0.733547i	0.0455071	+	0.998964i	$0.485510\pi$
$252$	1.32780	−	4.08655i	0.0836435	−	0.257428i
$253$	23.0328			1.44806
$254$	−0.215485			−0.0135207
$255$	−1.99220	+	6.13135i	−0.124756	+	0.383960i
$256$	4.56748	+	14.0572i	0.285467	+	0.878578i
$257$	−2.78876	−	8.58292i	−0.173958	−	0.535388i	0.825626	−	0.564217i	$-0.190822\pi$
$257$	−2.78876	−	8.58292i	−0.173958	−	0.535388i	−0.999584	+	0.0288295i	$0.990822\pi$
$258$	0.471914	−	0.342866i	0.0293801	−	0.0213459i
$259$	−8.76510	+	26.9762i	−0.544637	+	1.67622i
$260$	−0.0265800	+	0.0193115i	−0.00164842	+	0.00119765i
$261$	1.94729	+	1.41479i	0.120535	+	0.0875734i
$262$	0.271267	+	0.834875i	0.0167590	+	0.0515788i
$263$	2.53060	+	1.83859i	0.156044	+	0.113372i	0.663067	−	0.748560i	$-0.269254\pi$
$263$	2.53060	+	1.83859i	0.156044	+	0.113372i	−0.507024	+	0.861932i	$0.669254\pi$
$264$	−3.33482	−	2.42289i	−0.205244	−	0.149118i
$265$	3.00451	+	9.24693i	0.184566	+	0.568034i
$266$	1.59788	+	1.16093i	0.0979725	+	0.0711812i
$267$	−10.5365	+	7.65520i	−0.644822	+	0.468491i
$268$	−2.18920	+	6.73768i	−0.133727	+	0.411569i
$269$	−11.3081	+	8.21584i	−0.689469	+	0.500929i	−0.876486	−	0.481428i	$-0.840118\pi$
$269$	−11.3081	+	8.21584i	−0.689469	+	0.500929i	0.187016	+	0.982357i	$0.440118\pi$
$270$	−0.266010	−	0.818695i	−0.0161889	−	0.0498242i
$271$	4.34439	+	13.3707i	0.263903	+	0.812209i	0.991944	+	0.126676i	$0.0404309\pi$
$271$	4.34439	+	13.3707i	0.263903	+	0.812209i	−0.728041	+	0.685533i	$0.759569\pi$
$272$	−4.28059	+	13.1743i	−0.259549	+	0.798810i
$273$	−0.0531238			−0.00321520
$274$	1.18427			0.0715441
$275$	−6.07118	+	18.6852i	−0.366106	+	1.12676i
$276$	−9.71314	−	7.05701i	−0.584662	−	0.424782i
$277$	−17.8160	+	12.9441i	−1.07046	+	0.777735i	−0.975995	−	0.217793i	$-0.930114\pi$
$277$	−17.8160	+	12.9441i	−1.07046	+	0.777735i	−0.0944658	+	0.995528i	$0.530114\pi$
$278$	−1.65753			−0.0994121
$279$		0			0
$280$	1.62238			0.0969556
$281$	−1.88198	+	1.36734i	−0.112269	+	0.0815684i	−0.642503	−	0.766283i	$-0.722104\pi$
$281$	−1.88198	+	1.36734i	−0.112269	+	0.0815684i	0.530234	+	0.847851i	$0.322104\pi$
$282$	−1.45786	−	1.05919i	−0.0868141	−	0.0630741i
$283$	4.30444	−	13.2477i	0.255873	−	0.787495i	−0.737784	−	0.675037i	$-0.764128\pi$
$283$	4.30444	−	13.2477i	0.255873	−	0.787495i	0.993657	−	0.112458i	$-0.0358723\pi$
$284$	−7.46537			−0.442988
$285$	−10.8462			−0.642475
$286$	0.00290998	−	0.00895601i	0.000172071	−	0.000529580i
$287$	−5.88838	−	18.1226i	−0.347580	−	1.06974i
$288$	−0.369974	−	1.13866i	−0.0218010	−	0.0670964i
$289$	3.58721	−	2.60626i	0.211012	−	0.153309i
$290$	−0.139876	+	0.430495i	−0.00821382	+	0.0252795i
$291$	4.05395	−	2.94537i	0.237647	−	0.172661i
$292$	5.70007	+	4.14134i	0.333571	+	0.242354i
$293$	7.99130	+	24.5947i	0.466857	+	1.43684i	0.856633	+	0.515927i	$0.172552\pi$
$293$	7.99130	+	24.5947i	0.466857	+	1.43684i	−0.389776	+	0.920910i	$0.627448\pi$
$294$	0.0167972	+	0.0122039i	0.000979632	+	0.000711744i
$295$	−10.3353	−	7.50900i	−0.601742	−	0.437191i
$296$	1.62609	+	5.00460i	0.0945147	+	0.290886i
$297$	−25.6914	−	18.6659i	−1.49077	−	1.08311i
$298$	−1.82821	+	1.32827i	−0.105905	+	0.0769448i
$299$	0.0170173	−	0.0523740i	0.000984139	−	0.00302887i
$300$	8.28521	−	6.01956i	0.478347	−	0.347539i
$301$	2.61722	+	8.05496i	0.150854	+	0.464280i
$302$	0.253087	+	0.778922i	0.0145635	+	0.0448219i
$303$	3.96244	−	12.1951i	0.227636	−	0.700591i
$304$	−23.3051			−1.33664
$305$	4.56064			0.261141
$306$	0.110425	−	0.339853i	0.00631257	−	0.0194281i
$307$	0.530442	+	0.385389i	0.0302739	+	0.0219953i	0.602819	−	0.797878i	$-0.294044\pi$
$307$	0.530442	+	0.385389i	0.0302739	+	0.0219953i	−0.572545	+	0.819873i	$0.694044\pi$
$308$	24.1163	−	17.5215i	1.37415	−	0.998380i
$309$	−3.96582			−0.225608
$310$		0			0
$311$	−22.0394			−1.24974			−0.624869	−	0.780730i	$-0.714848\pi$
$311$	−22.0394			−1.24974			−0.624869	+	0.780730i	$0.714848\pi$
$312$	−0.00797324	+	0.00579290i	−0.000451396	+	0.000327958i
$313$	−7.69647	−	5.59181i	−0.435030	−	0.316068i	0.348627	−	0.937262i	$-0.386648\pi$
$313$	−7.69647	−	5.59181i	−0.435030	−	0.316068i	−0.783657	+	0.621194i	$0.786648\pi$
$314$	0.603407	−	1.85709i	0.0340522	−	0.104802i
$315$	2.66189			0.149981
$316$	−6.46948			−0.363937
$317$	−0.647400	+	1.99249i	−0.0363616	+	0.111910i	−0.967590	−	0.252527i	$-0.918738\pi$
$317$	−0.647400	+	1.99249i	−0.0363616	+	0.111910i	0.931228	+	0.364436i	$0.118738\pi$
$318$	0.448890	+	1.38154i	0.0251725	+	0.0774730i
$319$	5.16011	+	15.8812i	0.288911	+	0.889175i
$320$	−7.59141	+	5.51549i	−0.424373	+	0.308325i
$321$	3.64581	−	11.2206i	0.203489	−	0.626275i
$322$	−1.09574	+	0.796103i	−0.0610633	+	0.0443651i
$323$	−17.1034	−	12.4263i	−0.951659	−	0.691420i
$324$	3.62168	+	11.1464i	0.201205	+	0.619244i
$325$	0.0380024	+	0.0276104i	0.00210799	+	0.00153155i
$326$	0.722942	+	0.525248i	0.0400401	+	0.0290908i
$327$	−2.87934	−	8.86171i	−0.159228	−	0.490054i
$328$	−2.85995	−	2.07788i	−0.157914	−	0.114732i
$329$	21.1674	−	15.3790i	1.16699	−	0.847871i
$330$	0.393028	−	1.20962i	0.0216355	−	0.0665871i
$331$	−2.02852	+	1.47381i	−0.111498	+	0.0810078i	−0.642137	−	0.766590i	$-0.721952\pi$
$331$	−2.02852	+	1.47381i	−0.111498	+	0.0810078i	0.530639	+	0.847598i	$0.321952\pi$
$332$	1.26961	+	3.90747i	0.0696790	+	0.214450i
$333$	2.66799	+	8.21122i	0.146205	+	0.449972i
$334$	−0.785486	+	2.41748i	−0.0429799	+	0.132278i
$335$	−4.38878			−0.239785
$336$	−15.4168			−0.841054
$337$	−8.40949	+	25.8818i	−0.458094	+	1.40987i	0.409370	+	0.912369i	$0.365749\pi$
$337$	−8.40949	+	25.8818i	−0.458094	+	1.40987i	−0.867464	+	0.497500i	$0.834251\pi$
$338$	1.30595	+	0.948831i	0.0710345	+	0.0516096i
$339$	−3.28778	+	2.38871i	−0.178568	+	0.129737i
$340$	−8.64920			−0.469069
$341$		0			0
$342$	0.601193			0.0325088
$343$	14.8598	−	10.7963i	0.802354	−	0.582944i
$344$	1.27117	+	0.923557i	0.0685368	+	0.0497949i
$345$	2.29839	−	7.07373i	0.123741	−	0.380837i
$346$	−2.61604			−0.140639
$347$	24.3284			1.30602			0.653010	−	0.757350i	$-0.273506\pi$
$347$	24.3284			1.30602			0.653010	+	0.757350i	$0.273506\pi$
$348$	2.68976	−	8.27823i	0.144186	−	0.443760i
$349$	3.75938	+	11.5702i	0.201235	+	0.619338i	0.999847	+	0.0174918i	$0.00556808\pi$
$349$	3.75938	+	11.5702i	0.201235	+	0.619338i	−0.798612	+	0.601846i	$0.794432\pi$
$350$	−0.357007	−	1.09876i	−0.0190828	−	0.0587310i
$351$	−0.0614257	+	0.0446284i	−0.00327866	+	0.00238209i
$352$	2.56669	−	7.89947i	0.136805	−	0.421043i
$353$	−22.6650	+	16.4671i	−1.20633	+	0.876453i	−0.994893	−	0.100938i	$-0.967816\pi$
$353$	−22.6650	+	16.4671i	−1.20633	+	0.876453i	−0.211441	+	0.977391i	$0.567816\pi$
$354$	−1.54414	−	1.12189i	−0.0820703	−	0.0596275i
$355$	−1.42914	−	4.39844i	−0.0758508	−	0.233445i
$356$	−14.1358	−	10.2703i	−0.749198	−	0.544324i
$357$	−11.3142	−	8.22028i	−0.598813	−	0.435063i
$358$	−0.402098	−	1.23753i	−0.0212515	−	0.0654054i
$359$	19.6888	+	14.3047i	1.03913	+	0.754974i	0.970116	−	0.242641i	$-0.0780138\pi$
$359$	19.6888	+	14.3047i	1.03913	+	0.754974i	0.0690167	+	0.997616i	$0.478014\pi$
$360$	0.399518	−	0.290267i	0.0210564	−	0.0152984i
$361$	5.11965	−	15.7567i	0.269455	−	0.829298i
$362$	0.958091	−	0.696094i	0.0503561	−	0.0365859i
$363$	−9.47073	−	29.1479i	−0.497085	−	1.52987i
$364$	−0.0220241	−	0.0677831i	−0.00115437	−	0.00355280i
$365$	−1.34879	+	4.15115i	−0.0705990	+	0.217281i
$366$	0.681384			0.0356165
$367$	−1.68920			−0.0881753			−0.0440876	−	0.999028i	$-0.514038\pi$
$367$	−1.68920			−0.0881753			−0.0440876	+	0.999028i	$0.514038\pi$
$368$	4.93852	−	15.1992i	0.257438	−	0.792312i
$369$	−4.69242	−	3.40925i	−0.244278	−	0.177478i
$370$	−1.31355	+	0.954350i	−0.0682882	+	0.0496143i
$371$	−21.0916			−1.09502
$372$		0			0
$373$	24.2842			1.25739			0.628695	−	0.777652i	$-0.283589\pi$
$373$	24.2842			1.25739			0.628695	+	0.777652i	$0.283589\pi$
$374$	2.00560	−	1.45716i	0.103707	−	0.0753477i
$375$	12.4893	+	9.07402i	0.644945	+	0.468580i
$376$	1.49996	−	4.61640i	0.0773545	−	0.238073i
$377$	0.0399245			0.00205621
$378$	1.86739			0.0960480
$379$	4.12369	−	12.6914i	0.211820	−	0.651914i	−0.787545	−	0.616258i	$-0.788648\pi$
$379$	4.12369	−	12.6914i	0.211820	−	0.651914i	0.999364	−	0.0356559i	$-0.0113520\pi$
$380$	−4.49663	−	13.8392i	−0.230672	−	0.709936i
$381$	0.793247	+	2.44136i	0.0406393	+	0.125075i
$382$	1.00505	−	0.730213i	0.0514229	−	0.0373609i
$383$	7.73918	−	23.8187i	0.395453	−	1.21708i	−0.533154	−	0.846018i	$-0.678994\pi$
$383$	7.73918	−	23.8187i	0.395453	−	1.21708i	0.928608	−	0.371063i	$-0.121006\pi$
$384$	−4.66412	+	3.38869i	−0.238015	+	0.172928i
$385$	14.9400	+	10.8545i	0.761413	+	0.553199i
$386$	−0.793556	−	2.44231i	−0.0403909	−	0.124311i
$387$	2.08565	+	1.51531i	0.106020	+	0.0770277i
$388$	5.43882	+	3.95154i	0.276114	+	0.200609i
$389$	6.77878	+	20.8630i	0.343698	+	1.05779i	0.962277	+	0.272071i	$0.0877086\pi$
$389$	6.77878	+	20.8630i	0.343698	+	1.05779i	−0.618579	+	0.785722i	$0.712291\pi$
$390$	−0.00246015	−	0.00178740i	−0.000124574	−	9.05086e-5i
$391$	11.7286	−	8.52132i	0.593141	−	0.430942i
$392$	−0.0172823	+	0.0531894i	−0.000872887	+	0.00268647i
$393$	8.46024	−	6.14672i	0.426762	−	0.310061i
$394$	−0.0289051	−	0.0889608i	−0.00145622	−	0.00448178i
$395$	−1.23849	−	3.81168i	−0.0623152	−	0.191786i
$396$	2.80389	−	8.62950i	0.140901	−	0.433649i
$397$	2.21630			0.111233			0.0556165	−	0.998452i	$-0.482288\pi$
$397$	2.21630			0.111233			0.0556165	+	0.998452i	$0.482288\pi$
$398$	1.22817			0.0615624
$399$	7.27075	−	22.3771i	0.363993	−	1.12025i
$400$	11.0285	+	8.01266i	0.551424	+	0.400633i
$401$	21.5761	−	15.6760i	1.07746	−	0.782821i	0.100222	−	0.994965i	$-0.468045\pi$
$401$	21.5761	−	15.6760i	1.07746	−	0.782821i	0.977238	+	0.212144i	$0.0680447\pi$
$402$	−0.655708			−0.0327038
$403$		0			0
$404$	17.2031			0.855885
$405$	−5.87389	+	4.26763i	−0.291876	+	0.212060i
$406$	−0.794398	−	0.577164i	−0.0394253	−	0.0286442i
$407$	−18.5091	+	56.9652i	−0.917464	+	2.82366i
$408$	−2.59451			−0.128448
$409$	−37.8777			−1.87293			−0.936465	−	0.350760i	$-0.885923\pi$
$409$	−37.8777			−1.87293			−0.936465	+	0.350760i	$0.885923\pi$
$410$	0.337062	−	1.03737i	0.0166463	−	0.0512321i
$411$	−4.35954	−	13.4173i	−0.215040	−	0.661827i
$412$	−1.64415	−	5.06017i	−0.0810015	−	0.249297i
$413$	22.4202	−	16.2892i	1.10323	−	0.801540i
$414$	−0.127397	+	0.392088i	−0.00626123	+	0.0192701i
$415$	−2.05914	+	1.49606i	−0.101079	+	0.0734385i
$416$	−0.0160662	−	0.0116727i	−0.000787708	−	0.000572304i
$417$	6.10174	+	18.7792i	0.298803	+	0.919622i
$418$	3.37422	+	2.45152i	0.165039	+	0.119908i
$419$	7.41627	+	5.38824i	0.362309	+	0.263233i	0.754014	−	0.656858i	$-0.228115\pi$
$419$	7.41627	+	5.38824i	0.362309	+	0.263233i	−0.391706	+	0.920091i	$0.628115\pi$
$420$	−2.97461	−	9.15491i	−0.145146	−	0.446714i
$421$	2.64394	+	1.92093i	0.128858	+	0.0936205i	0.650347	−	0.759637i	$-0.274623\pi$
$421$	2.64394	+	1.92093i	0.128858	+	0.0936205i	−0.521490	+	0.853258i	$0.674623\pi$
$422$	−1.41275	+	1.02642i	−0.0687715	+	0.0499654i
$423$	2.46104	−	7.57429i	0.119660	−	0.368275i
$424$	−3.16559	+	2.29994i	−0.153735	+	0.111695i
$425$	3.82133	+	11.7609i	0.185362	+	0.570485i
$426$	−0.213521	−	0.657150i	−0.0103451	−	0.0318390i
$427$	−3.05722	+	9.40914i	−0.147949	+	0.455340i
$428$	15.8284			0.765095
$429$	−0.112181			−0.00541613
$430$	−0.149815	+	0.461082i	−0.00722470	+	0.0222353i
$431$	18.9881	+	13.7957i	0.914624	+	0.664513i	0.942180	−	0.335107i	$-0.108772\pi$
$431$	18.9881	+	13.7957i	0.914624	+	0.664513i	−0.0275558	+	0.999620i	$0.508772\pi$
$432$	−17.8260	+	12.9514i	−0.857656	+	0.623124i
$433$	27.3421			1.31398			0.656990	−	0.753900i	$-0.271829\pi$
$433$	27.3421			1.31398			0.656990	+	0.753900i	$0.271829\pi$
$434$		0			0
$435$	5.39227			0.258540
$436$	10.1133	−	7.34778i	0.484341	−	0.351895i
$437$	19.7322	+	14.3363i	0.943918	+	0.685797i
$438$	−0.201517	+	0.620205i	−0.00962885	+	0.0296345i
$439$	−33.0439			−1.57710			−0.788551	−	0.614970i	$-0.789168\pi$
$439$	−33.0439			−1.57710			−0.788551	+	0.614970i	$0.789168\pi$
$440$	3.42595			0.163326
$441$	−0.0283557	+	0.0872697i	−0.00135027	+	0.00415570i
$442$	−0.00183161	−	0.00563711i	−8.71207e−5	−	0.000268130i
$443$	−4.11812	−	12.6743i	−0.195658	−	0.602173i	−0.999968	−	0.00796343i	$-0.997465\pi$
$443$	−4.11812	−	12.6743i	−0.195658	−	0.602173i	0.804311	−	0.594209i	$-0.202535\pi$
$444$	25.2590	−	18.3517i	1.19874	−	0.870935i
$445$	3.34493	−	10.2946i	0.158565	−	0.488012i
$446$	−0.994103	+	0.722258i	−0.0470721	+	0.0341999i
$447$	21.7789	+	15.8233i	1.03011	+	0.748416i
$448$	−6.29022	−	19.3593i	−0.297185	−	0.914641i
$449$	−9.13730	−	6.63863i	−0.431216	−	0.313297i	0.350919	−	0.936406i	$-0.385869\pi$
$449$	−9.13730	−	6.63863i	−0.431216	−	0.313297i	−0.782135	+	0.623109i	$0.785869\pi$
$450$	−0.284498	−	0.206700i	−0.0134114	−	0.00974392i
$451$	−12.4344	−	38.2691i	−0.585513	−	1.80202i
$452$	−4.41091	−	3.20472i	−0.207472	−	0.150737i
$453$	7.89323	−	5.73477i	0.370857	−	0.269443i
$454$	0.360873	−	1.11065i	0.0169366	−	0.0521255i
$455$	0.0357201	−	0.0259522i	0.00167459	−	0.00121666i
$456$	−1.34886	−	4.15137i	−0.0631662	−	0.194406i
$457$	1.40624	+	4.32796i	0.0657811	+	0.202453i	0.978545	−	0.206035i	$-0.0660561\pi$
$457$	1.40624	+	4.32796i	0.0657811	+	0.202453i	−0.912764	+	0.408488i	$0.866056\pi$
$458$	−0.566165	+	1.74248i	−0.0264551	+	0.0814205i
$459$	−19.9881			−0.932965
$460$	9.97857			0.465253
$461$	8.89850	−	27.3868i	0.414444	−	1.27553i	−0.498302	−	0.867003i	$-0.666043\pi$
$461$	8.89850	−	27.3868i	0.414444	−	1.27553i	0.912747	−	0.408526i	$-0.133957\pi$
$462$	2.23212	+	1.62173i	0.103847	+	0.0754496i
$463$	−9.74989	+	7.08371i	−0.453116	+	0.329208i	−0.790825	−	0.612043i	$-0.790348\pi$
$463$	−9.74989	+	7.08371i	−0.453116	+	0.329208i	0.337709	+	0.941251i	$0.390348\pi$
$464$	11.5863			0.537879
$465$		0			0
$466$	−3.54965			−0.164435
$467$	15.4765	−	11.2443i	0.716166	−	0.520325i	−0.168991	−	0.985618i	$-0.554051\pi$
$467$	15.4765	−	11.2443i	0.716166	−	0.520325i	0.885157	+	0.465292i	$0.154051\pi$
$468$	−0.0175509	−	0.0127515i	−0.000811291	−	0.000589437i
$469$	2.94202	−	9.05459i	0.135850	−	0.418102i
$470$	1.49770			0.0690836
$471$	−23.2615			−1.07183
$472$	1.58874	−	4.88963i	0.0731276	−	0.225064i
$473$	5.52673	+	17.0095i	0.254119	+	0.782099i
$474$	−0.185037	−	0.569486i	−0.00849903	−	0.0261573i
$475$	−16.8313	+	12.2287i	−0.772275	+	0.561091i
$476$	5.79798	−	17.8443i	0.265750	−	0.817894i
$477$	−5.19390	+	3.77359i	−0.237812	+	0.172781i
$478$	0.905015	+	0.657532i	0.0413944	+	0.0300748i
$479$	−3.79815	−	11.6895i	−0.173542	−	0.534107i	0.826022	−	0.563638i	$-0.190599\pi$
$479$	−3.79815	−	11.6895i	−0.173542	−	0.534107i	−0.999564	+	0.0295311i	$0.990599\pi$
$480$	−2.16992	−	1.57654i	−0.0990431	−	0.0719590i
$481$	0.115857	+	0.0841754i	0.00528264	+	0.00383807i
$482$	0.0302434	+	0.0930797i	0.00137755	+	0.00423966i
$483$	13.0532	+	9.48373i	0.593943	+	0.431525i
$484$	33.2648	−	24.1683i	1.51204	−	1.09856i
$485$	−1.28697	+	3.96090i	−0.0584385	+	0.179855i
$486$	0.821769	−	0.597050i	0.0372762	−	0.0270827i
$487$	4.67441	+	14.3864i	0.211818	+	0.651908i	0.999364	+	0.0356526i	$0.0113510\pi$
$487$	4.67441	+	14.3864i	0.211818	+	0.651908i	−0.787547	+	0.616255i	$0.788649\pi$
$488$	0.567171	+	1.74557i	0.0256746	+	0.0790184i
$489$	3.28956	−	10.1242i	0.148759	−	0.457834i
$490$	−0.0172562			−0.000779556
$491$	30.5340			1.37798			0.688990	−	0.724771i	$-0.258054\pi$
$491$	30.5340			1.37798			0.688990	+	0.724771i	$0.258054\pi$
$492$	−6.48156	+	19.9482i	−0.292211	+	0.899334i
$493$	8.50307	+	6.17784i	0.382959	+	0.278236i
$494$	0.00806745	−	0.00586135i	0.000362972	−	0.000263714i
$495$	5.62108			0.252649
$496$		0			0
$497$	10.0325			0.450020
$498$	−0.307647	+	0.223519i	−0.0137860	+	0.0100161i
$499$	−23.3217	−	16.9442i	−1.04402	−	0.758526i	−0.0729546	−	0.997335i	$-0.523243\pi$
$499$	−23.3217	−	16.9442i	−1.04402	−	0.758526i	−0.971066	+	0.238810i	$0.923243\pi$
$500$	−6.40014	+	19.6976i	−0.286223	+	0.880903i
$501$	30.2807			1.35284
$502$	−2.45516			−0.109579
$503$	−0.963471	+	2.96526i	−0.0429590	+	0.132214i	−0.970236	−	0.242162i	$-0.922143\pi$
$503$	−0.963471	+	2.96526i	−0.0429590	+	0.132214i	0.927277	+	0.374377i	$0.122143\pi$
$504$	0.331039	+	1.01883i	0.0147457	+	0.0453825i
$505$	3.29328	+	10.1357i	0.146549	+	0.451032i
$506$	−2.31386	+	1.68112i	−0.102864	+	0.0747349i
$507$	5.94241	−	18.2888i	0.263911	−	0.812236i
$508$	−2.78619	+	2.02428i	−0.123617	+	0.0898130i
$509$	10.7565	+	7.81503i	0.476772	+	0.346395i	0.800075	−	0.599900i	$-0.204793\pi$
$509$	10.7565	+	7.81503i	0.476772	+	0.346395i	−0.323302	+	0.946296i	$0.604793\pi$
$510$	−0.247380	−	0.761358i	−0.0109542	−	0.0337135i
$511$	−7.66017	−	5.56544i	−0.338866	−	0.246201i
$512$	−7.79091	−	5.66043i	−0.344313	−	0.250158i
$513$	−10.3916	−	31.9821i	−0.458801	−	1.41204i
$514$	0.906608	+	0.658689i	0.0399887	+	0.0290535i
$515$	2.66659	−	1.93739i	0.117504	−	0.0853718i
$516$	2.88087	−	8.86640i	0.126823	−	0.390322i
$517$	44.6988	−	32.4756i	1.96585	−	1.42827i
$518$	−1.08840	−	3.34976i	−0.0478217	−	0.147180i
$519$	9.63022	+	29.6388i	0.422720	+	1.30100i
$520$	0.00253120	−	0.00779022i	0.000111000	−	0.000341624i
$521$	8.44298			0.369894			0.184947	−	0.982749i	$-0.440789\pi$
$521$	8.44298			0.369894			0.184947	+	0.982749i	$0.440789\pi$
$522$	−0.298887			−0.0130819
$523$	12.2569	−	37.7229i	0.535958	−	1.64951i	−0.205613	−	0.978633i	$-0.565919\pi$
$523$	12.2569	−	37.7229i	0.535958	−	1.64951i	0.741570	−	0.670875i	$-0.234081\pi$
$524$	11.3503	+	8.24650i	0.495842	+	0.360250i
$525$	−11.1343	+	8.08953i	−0.485940	+	0.353056i
$526$	−0.388418			−0.0169358
$527$		0			0
$528$	−32.5554			−1.41679
$529$	5.07612	−	3.68802i	0.220701	−	0.160349i
$530$	−0.976746	−	0.709648i	−0.0424271	−	0.0308251i
$531$	2.60670	−	8.02259i	0.113121	−	0.348151i
$532$	31.5662			1.36857
$533$	−0.0962066			−0.00416717
$534$	0.499750	−	1.53807i	0.0216263	−	0.0665589i
$535$	3.03012	+	9.32576i	0.131004	+	0.403188i
$536$	−0.545799	−	1.67980i	−0.0235749	−	0.0725562i
$537$	−12.5405	+	9.11124i	−0.541164	+	0.393179i
$538$	0.536350	−	1.65072i	0.0231237	−	0.0711674i
$539$	−0.515012	+	0.374178i	−0.0221831	+	0.0161170i
$540$	−11.1304	−	8.08668i	−0.478974	−	0.347995i
$541$	6.74558	+	20.7608i	0.290015	+	0.892575i	0.984850	+	0.173406i	$0.0554773\pi$
$541$	6.74558	+	20.7608i	0.290015	+	0.892575i	−0.694835	+	0.719169i	$0.744523\pi$
$542$	−1.41233	−	1.02612i	−0.0606649	−	0.0440756i
$543$	−11.4134	−	8.29235i	−0.489797	−	0.355859i
$544$	−1.61553	−	4.97210i	−0.0692654	−	0.213177i
$545$	6.26520	+	4.55194i	0.268372	+	0.194984i
$546$	0.00533678	−	0.00387740i	0.000228393	−	0.000165937i
$547$	8.44857	−	26.0020i	0.361235	−	1.11177i	−0.591071	−	0.806620i	$-0.701295\pi$
$547$	8.44857	−	26.0020i	0.361235	−	1.11177i	0.952305	−	0.305146i	$-0.0987054\pi$
$548$	15.3124	−	11.1251i	0.654112	−	0.475240i
$549$	0.930578	+	2.86402i	0.0397161	+	0.122234i
$550$	−0.753887	−	2.32022i	−0.0321458	−	0.0989347i
$551$	−5.46423	+	16.8172i	−0.232784	+	0.716436i
$552$	2.99329			0.127403
$553$	8.69417			0.369714
$554$	0.845023	−	2.60071i	0.0359016	−	0.110494i
$555$	15.6479	+	11.3689i	0.664217	+	0.482582i
$556$	−21.4316	+	15.5710i	−0.908903	+	0.660357i
$557$	−27.9171			−1.18289			−0.591443	−	0.806347i	$-0.701441\pi$
$557$	−27.9171			−1.18289			−0.591443	+	0.806347i	$0.701441\pi$
$558$		0			0
$559$	0.0427611			0.00180860
$560$	10.3662	−	7.53145i	0.438050	−	0.318262i
$561$	−23.8921	−	17.3586i	−1.00873	−	0.732882i
$562$	0.0892630	−	0.274723i	0.00376533	−	0.0115885i
$563$	−25.7662			−1.08591			−0.542957	−	0.839760i	$-0.682695\pi$
$563$	−25.7662			−1.08591			−0.542957	+	0.839760i	$0.682695\pi$
$564$	−28.8000			−1.21270
$565$	1.04374	−	3.21231i	0.0439106	−	0.135143i
$566$	0.534503	+	1.64503i	0.0224668	+	0.0691458i
$567$	−4.86709	−	14.9794i	−0.204399	−	0.629074i
$568$	1.50576	−	1.09400i	0.0631803	−	0.0459032i
$569$	5.01022	−	15.4199i	0.210039	−	0.646434i	−0.789429	−	0.613841i	$-0.789623\pi$
$569$	5.01022	−	15.4199i	0.210039	−	0.646434i	0.999469	−	0.0325931i	$-0.0103765\pi$
$570$	1.08960	−	0.791644i	0.0456385	−	0.0331583i
$571$	7.58814	+	5.51310i	0.317554	+	0.230716i	0.735131	−	0.677925i	$-0.237121\pi$
$571$	7.58814	+	5.51310i	0.317554	+	0.230716i	−0.417577	+	0.908641i	$0.637121\pi$
$572$	−0.0465079	−	0.143137i	−0.00194459	−	0.00598484i
$573$	−11.9729	−	8.69880i	−0.500174	−	0.363398i
$574$	1.91427	+	1.39080i	0.0799002	+	0.0580509i
$575$	−4.40867	−	13.5685i	−0.183854	−	0.565845i
$576$	−5.01265	−	3.64191i	−0.208861	−	0.151746i
$577$	−25.6267	+	18.6189i	−1.06685	+	0.775115i	−0.975344	−	0.220689i	$-0.929169\pi$
$577$	−25.6267	+	18.6189i	−1.06685	+	0.775115i	−0.0915103	+	0.995804i	$0.529169\pi$
$578$	−0.170143	+	0.523646i	−0.00707702	+	0.0217808i
$579$	−24.7493	+	17.9814i	−1.02854	+	0.747282i
$580$	2.23553	+	6.88025i	0.0928253	+	0.285687i
$581$	−1.70620	−	5.25114i	−0.0707851	−	0.217854i
$582$	−0.192281	+	0.591780i	−0.00797030	+	0.0245301i
$583$	−44.5388			−1.84461
$584$	−1.75658			−0.0726880
$585$	0.00415302	−	0.0127817i	0.000171706	−	0.000528458i
$586$	−2.59792	−	1.88750i	−0.107319	−	0.0779718i
$587$	0.151126	−	0.109799i	0.00623763	−	0.00453190i	−0.584662	−	0.811277i	$-0.698773\pi$
$587$	0.151126	−	0.109799i	0.00623763	−	0.00453190i	0.590900	+	0.806745i	$0.298773\pi$
$588$	0.331829			0.0136844
$589$		0			0
$590$	1.58634			0.0653086
$591$	−0.901487	+	0.654969i	−0.0370822	+	0.0269418i
$592$	33.6224	+	24.4281i	1.38187	+	1.00399i
$593$	−4.16147	+	12.8077i	−0.170891	+	0.525949i	−0.999422	−	0.0339946i	$-0.989177\pi$
$593$	−4.16147	+	12.8077i	−0.170891	+	0.525949i	0.828531	+	0.559943i	$0.189177\pi$
$594$	3.94333			0.161797
$595$	11.6234			0.476514
$596$	−11.1606	+	34.3487i	−0.457155	+	1.40698i
$597$	−4.52115	−	13.9147i	−0.185038	−	0.569489i
$598$	0.00211312	+	0.00650352i	8.64120e−5	+	0.000265949i
$599$	14.9599	−	10.8690i	0.611245	−	0.444095i	−0.238608	−	0.971116i	$-0.576691\pi$
$599$	14.9599	−	10.8690i	0.611245	−	0.444095i	0.849852	+	0.527021i	$0.176691\pi$
$600$	−0.788996	+	2.42828i	−0.0322106	+	0.0991341i
$601$	−14.4495	+	10.4982i	−0.589408	+	0.428230i	−0.842103	−	0.539316i	$-0.818683\pi$
$601$	−14.4495	+	10.4982i	−0.589408	+	0.428230i	0.252696	+	0.967546i	$0.418683\pi$
$602$	−0.850839	−	0.618171i	−0.0346776	−	0.0251948i
$603$	−0.895512	−	2.75610i	−0.0364681	−	0.112237i
$604$	10.5896	+	7.69382i	0.430886	+	0.313057i
$605$	20.6075	+	14.9722i	0.837814	+	0.608708i
$606$	0.492034	+	1.51432i	0.0199875	+	0.0615152i
$607$	−23.4295	−	17.0225i	−0.950974	−	0.690923i	6.33966e−5	−	1.00000i	$-0.499980\pi$
$607$	−23.4295	−	17.0225i	−0.950974	−	0.690923i	−0.951037	+	0.309077i	$0.899980\pi$
$608$	7.11574	−	5.16989i	0.288581	−	0.209667i
$609$	−3.61470	+	11.1249i	−0.146475	+	0.450804i
$610$	−0.458159	+	0.332872i	−0.0185503	+	0.0134776i
$611$	−0.0408209	−	0.125634i	−0.00165144	−	0.00508261i
$612$	−1.76483	−	5.43159i	−0.0713391	−	0.219559i
$613$	6.37948	−	19.6340i	0.257665	−	0.793011i	−0.735628	−	0.677386i	$-0.763113\pi$
$613$	6.37948	−	19.6340i	0.257665	−	0.793011i	0.993293	−	0.115625i	$-0.0368871\pi$
$614$	−0.0814167			−0.00328571
$615$	−12.9938			−0.523962
$616$	−2.29658	+	7.06815i	−0.0925319	+	0.284784i
$617$	−0.564340	−	0.410017i	−0.0227195	−	0.0165067i	0.576368	−	0.817191i	$-0.304470\pi$
$617$	−0.564340	−	0.410017i	−0.0227195	−	0.0165067i	−0.599087	+	0.800684i	$0.704470\pi$
$618$	0.398404	−	0.289457i	0.0160262	−	0.0116437i
$619$	2.41091			0.0969026			0.0484513	−	0.998826i	$-0.484571\pi$
$619$	2.41091			0.0969026			0.0484513	+	0.998826i	$0.484571\pi$
$620$		0			0
$621$	23.0603			0.925376
$622$	2.21406	−	1.60861i	0.0887758	−	0.0644994i
$623$	18.9968	+	13.8020i	0.761090	+	0.552965i
$624$	−0.0240529	+	0.0740272i	−0.000962887	+	0.00296346i
$625$	4.61172			0.184469
$626$	1.18132			0.0472150
$627$	15.3535	−	47.2533i	0.613161	−	1.88712i
$628$	−9.64375	−	29.6804i	−0.384827	−	1.18438i
$629$	11.6500	+	35.8552i	0.464518	+	1.42964i
$630$	−0.267412	+	0.194286i	−0.0106540	+	0.00774055i
$631$	−11.2524	+	34.6314i	−0.447951	+	1.37865i	0.431263	+	0.902226i	$0.358068\pi$
$631$	−11.2524	+	34.6314i	−0.447951	+	1.37865i	−0.879214	+	0.476426i	$0.841932\pi$
$632$	1.30489	−	0.948058i	0.0519058	−	0.0377117i
$633$	16.8296	+	12.2274i	0.668917	+	0.485997i
$634$	−0.0803907	−	0.247417i	−0.00319272	−	0.00982619i
$635$	−1.72604	−	1.25404i	−0.0684957	−	0.0497651i
$636$	18.7824	+	13.6462i	0.744771	+	0.541108i
$637$	0.000470332		0.00144753i	1.86352e−5		5.73534e-5i
$638$	−1.67752	−	1.21879i	−0.0664135	−	0.0482523i
$639$	2.47055	−	1.79496i	0.0977336	−	0.0710076i
$640$	1.48068	−	4.55707i	0.0585290	−	0.180134i
$641$	1.73915	−	1.26357i	0.0686924	−	0.0499079i	−0.552909	−	0.833242i	$-0.686482\pi$
$641$	1.73915	−	1.26357i	0.0686924	−	0.0499079i	0.621602	+	0.783334i	$0.286482\pi$
$642$	0.452717	+	1.39332i	0.0178673	+	0.0549899i
$643$	5.48360	+	16.8768i	0.216252	+	0.665555i	0.999062	+	0.0432947i	$0.0137854\pi$
$643$	5.48360	+	16.8768i	0.216252	+	0.665555i	−0.782810	+	0.622260i	$0.786215\pi$
$644$	−6.68912	+	20.5870i	−0.263588	+	0.811241i
$645$	5.77539			0.227406
$646$	2.62517			0.103286
$647$	−12.4133	+	38.2042i	−0.488018	+	1.50196i	0.339545	+	0.940590i	$0.389727\pi$
$647$	−12.4133	+	38.2042i	−0.488018	+	1.50196i	−0.827562	+	0.561374i	$0.810273\pi$
$648$	−2.36392	−	1.71749i	−0.0928635	−	0.0674693i
$649$	47.3444	−	34.3977i	1.85843	−	1.35023i
$650$	−0.00583292			−0.000228786
$651$		0			0
$652$	14.2818			0.559317
$653$	1.95480	−	1.42024i	0.0764971	−	0.0555784i	−0.548879	−	0.835902i	$-0.684945\pi$
$653$	1.95480	−	1.42024i	0.0764971	−	0.0555784i	0.625377	+	0.780323i	$0.284945\pi$
$654$	0.936056	+	0.680084i	0.0366027	+	0.0265934i
$655$	−2.68580	+	8.26604i	−0.104943	+	0.322981i
$656$	−27.9196			−1.09008
$657$	−2.88209			−0.112441
$658$	−1.00398	+	3.08993i	−0.0391391	+	0.120458i
$659$	8.14816	+	25.0775i	0.317407	+	0.976879i	0.974752	+	0.223289i	$0.0716795\pi$
$659$	8.14816	+	25.0775i	0.317407	+	0.976879i	−0.657345	+	0.753590i	$0.728321\pi$
$660$	−6.28144	−	19.3323i	−0.244505	−	0.752508i
$661$	30.5920	−	22.2264i	1.18989	−	0.864505i	0.196637	−	0.980476i	$-0.436998\pi$
$661$	30.5920	−	22.2264i	1.18989	−	0.864505i	0.993253	+	0.115971i	$0.0369981\pi$
$662$	0.0962138	−	0.296116i	0.00373945	−	0.0115089i
$663$	−0.0571238	+	0.0415029i	−0.00221851	+	0.00161184i
$664$	−0.828692	−	0.602080i	−0.0321595	−	0.0233652i
$665$	6.04290	+	18.5981i	0.234334	+	0.721205i
$666$	−0.867345	−	0.630163i	−0.0336089	−	0.0244183i
$667$	−9.80998	−	7.12737i	−0.379844	−	0.275973i
$668$	12.5538	+	38.6365i	0.485720	+	1.49489i
$669$	11.8424	+	8.60403i	0.457855	+	0.332651i
$670$	0.440895	−	0.320329i	0.0170332	−	0.0123754i
$671$	−6.45587	+	19.8691i	−0.249226	+	0.767040i
$672$	4.70720	−	3.41998i	0.181584	−	0.131929i
$673$	−7.99715	−	24.6127i	−0.308268	−	0.948750i	−0.978438	−	0.206543i	$-0.933779\pi$
$673$	−7.99715	−	24.6127i	−0.308268	−	0.948750i	0.670170	−	0.742208i	$-0.266221\pi$
$674$	−1.04425	−	3.21386i	−0.0402228	−	0.123793i
$675$	−6.07842	+	18.7074i	−0.233958	+	0.720050i
$676$	25.7992			0.992276
$677$	19.9464			0.766602			0.383301	−	0.923623i	$-0.374787\pi$
$677$	19.9464			0.766602			0.383301	+	0.923623i	$0.374787\pi$
$678$	0.155941	−	0.479937i	0.00598887	−	0.0184319i
$679$	−7.30909	−	5.31037i	−0.280497	−	0.203793i
$680$	1.74454	−	1.26748i	0.0668999	−	0.0486057i
$681$	−13.9117			−0.533099
$682$		0			0
$683$	−10.3960			−0.397793			−0.198897	−	0.980020i	$-0.563736\pi$
$683$	−10.3960			−0.397793			−0.198897	+	0.980020i	$0.563736\pi$
$684$	7.77333	−	5.64766i	0.297221	−	0.215944i
$685$	9.48599	+	6.89198i	0.362441	+	0.263329i
$686$	−0.704808	+	2.16918i	−0.0269097	+	0.0828195i
$687$	21.8258			0.832706
$688$	12.4095			0.473107
$689$	−0.0329066	+	0.101276i	−0.00125364	+	0.00385832i
$690$	0.285402	+	0.878378i	0.0108651	+	0.0334393i
$691$	−4.15638	−	12.7920i	−0.158116	−	0.486632i	0.840347	−	0.542049i	$-0.182351\pi$
$691$	−4.15638	−	12.7920i	−0.158116	−	0.486632i	−0.998463	+	0.0554169i	$0.982351\pi$
$692$	−33.8250	+	24.5753i	−1.28583	+	0.934212i
$693$	−3.76808	+	11.5970i	−0.143138	+	0.440532i
$694$	−2.44402	+	1.77568i	−0.0927738	+	0.0674041i
$695$	−13.2769	−	9.64620i	−0.503620	−	0.365901i
$696$	0.670595	+	2.06388i	0.0254189	+	0.0782312i
$697$	−20.4900	−	14.8868i	−0.776113	−	0.563879i
$698$	−1.22215	−	0.887945i	−0.0462591	−	0.0336092i
$699$	13.0671	+	40.2163i	0.494242	+	1.52112i
$700$	−14.9379	−	10.8530i	−0.564598	−	0.410204i
$701$	1.23221	−	0.895251i	0.0465398	−	0.0338132i	−0.564272	−	0.825589i	$-0.690843\pi$
$701$	1.23221	−	0.895251i	0.0465398	−	0.0338132i	0.610812	+	0.791776i	$0.290843\pi$
$702$	0.00291345	−	0.00896669i	0.000109961	−	0.000338426i
$703$	−51.3135	+	37.2814i	−1.93533	+	1.40610i
$704$	−13.2830	−	40.8807i	−0.500620	−	1.54075i
$705$	−5.51335	−	16.9683i	−0.207645	−	0.639065i
$706$	1.07501	−	3.30854i	0.0404585	−	0.124519i
$707$	−23.1188			−0.869471
$708$	−30.5046			−1.14643
$709$	−0.477453	+	1.46945i	−0.0179311	+	0.0551863i	−0.959622	−	0.281294i	$-0.909236\pi$
$709$	−0.477453	+	1.46945i	−0.0179311	+	0.0551863i	0.941691	+	0.336480i	$0.109236\pi$
$710$	0.464603	+	0.337554i	0.0174363	+	0.0126682i
$711$	2.14098	−	1.55551i	0.0802930	−	0.0583363i
$712$	4.35623			0.163257
$713$		0			0
$714$	1.73660			0.0649908
$715$	0.0754297	−	0.0548029i	0.00282091	−	0.00204951i
$716$	−16.8245	−	12.2237i	−0.628762	−	0.456822i
$717$	4.11804	−	12.6740i	0.153791	−	0.473320i
$718$	−3.02199			−0.112780
$719$	36.4715			1.36016			0.680079	−	0.733139i	$-0.261946\pi$
$719$	36.4715			1.36016			0.680079	+	0.733139i	$0.261946\pi$
$720$	1.20523	−	3.70931i	0.0449162	−	0.138238i
$721$	2.20953	+	6.80024i	0.0822872	+	0.253254i
$722$	0.635730	+	1.95658i	0.0236594	+	0.0728163i
$723$	0.943227	−	0.685294i	0.0350790	−	0.0254864i
$724$	5.84881	−	18.0008i	0.217369	−	0.668994i
$725$	8.36782	−	6.07957i	0.310773	−	0.225790i
$726$	3.07887	+	2.23693i	0.114268	+	0.0830203i
$727$	3.49967	+	10.7709i	0.129795	+	0.399469i	0.994744	−	0.102391i	$-0.0326492\pi$
$727$	3.49967	+	10.7709i	0.129795	+	0.399469i	−0.864949	+	0.501860i	$0.832649\pi$
$728$	0.0143754	+	0.0104443i	0.000532787	+	0.000387093i
$729$	−24.1225	−	17.5260i	−0.893426	−	0.649112i
$730$	−0.167486	−	0.515468i	−0.00619893	−	0.0190783i
$731$	9.10721	+	6.61677i	0.336842	+	0.244730i
$732$	8.81019	−	6.40098i	0.325634	−	0.236587i
$733$	0.563521	−	1.73434i	0.0208141	−	0.0640593i	−0.940110	−	0.340871i	$-0.889278\pi$
$733$	0.563521	−	1.73434i	0.0208141	−	0.0640593i	0.960924	+	0.276812i	$0.0892779\pi$
$734$	0.169696	−	0.123291i	0.00626358	−	0.00455076i
$735$	0.0635239	+	0.195507i	0.00234312	+	0.00721137i
$736$	1.86384	+	5.73630i	0.0687020	+	0.211443i
$737$	6.21261	−	19.1204i	0.228844	−	0.704311i
$738$	0.720232			0.0265121
$739$	−35.2840			−1.29794			−0.648971	−	0.760813i	$-0.724800\pi$
$739$	−35.2840			−1.29794			−0.648971	+	0.760813i	$0.724800\pi$
$740$	−8.01876	+	24.6792i	−0.294776	+	0.907226i
$741$	−0.0961050	−	0.0698244i	−0.00353051	−	0.00256506i
$742$	2.11885	−	1.53943i	0.0777854	−	0.0565144i
$743$	−26.9859			−0.990018			−0.495009	−	0.868888i	$-0.664835\pi$
$743$	−26.9859			−0.990018			−0.495009	+	0.868888i	$0.664835\pi$
$744$		0			0
$745$	−22.3741			−0.819722
$746$	−2.43958	+	1.77246i	−0.0893194	+	0.0648943i
$747$	−1.35966	−	0.987854i	−0.0497475	−	0.0361437i
$748$	12.2435	−	37.6816i	0.447667	−	1.37778i
$749$	−21.2714			−0.777240
$750$	−1.91696			−0.0699976
$751$	−6.53898	+	20.1249i	−0.238611	+	0.734369i	0.758011	+	0.652242i	$0.226171\pi$
$751$	−6.53898	+	20.1249i	−0.238611	+	0.734369i	−0.996622	+	0.0821269i	$0.973829\pi$
$752$	−11.8464	−	36.4596i	−0.431995	−	1.32954i
$753$	9.03797	+	27.8160i	0.329362	+	1.01367i
$754$	−0.00401079	+	0.00291401i	−0.000146064	+	0.000106122i
$755$	−2.50580	+	7.71206i	−0.0911954	+	0.280670i
$756$	24.1450	−	17.5424i	0.878146	−	0.638010i
$757$	−43.3778	−	31.5158i	−1.57659	−	1.14546i	−0.920472	−	0.390808i	$-0.872196\pi$
$757$	−43.3778	−	31.5158i	−1.57659	−	1.14546i	−0.656122	−	0.754655i	$-0.727804\pi$
$758$	0.512057	+	1.57595i	0.0185988	+	0.0572411i
$759$	27.5643	+	20.0266i	1.00052	+	0.726921i
$760$	2.93501	+	2.13241i	0.106464	+	0.0773505i
$761$	−2.54871	−	7.84411i	−0.0923906	−	0.284349i	0.894174	−	0.447719i	$-0.147764\pi$
$761$	−2.54871	−	7.84411i	−0.0923906	−	0.284349i	−0.986565	+	0.163370i	$0.947764\pi$
$762$	−0.257880	−	0.187360i	−0.00934199	−	0.00678735i
$763$	−13.5911	+	9.87449i	−0.492030	+	0.357480i
$764$	6.13549	−	18.8831i	0.221974	−	0.683166i
$765$	2.86232	−	2.07960i	0.103488	−	0.0751881i
$766$	0.961009	+	2.95768i	0.0347227	+	0.106865i
$767$	−0.0432370	−	0.133070i	−0.00156120	−	0.00480487i
$768$	−6.75646	+	20.7942i	−0.243803	+	0.750347i
$769$	26.3326			0.949577			0.474788	−	0.880100i	$-0.342525\pi$
$769$	26.3326			0.949577			0.474788	+	0.880100i	$0.342525\pi$
$770$	−2.29311			−0.0826381
$771$	4.12528	−	12.6963i	0.148568	−	0.457247i
$772$	−33.2039	−	24.1240i	−1.19503	−	0.868243i
$773$	9.58201	−	6.96174i	0.344641	−	0.250396i	−0.401976	−	0.915650i	$-0.631677\pi$
$773$	9.58201	−	6.96174i	0.344641	−	0.250396i	0.746617	+	0.665254i	$0.231677\pi$
$774$	−0.320123			−0.0115066
$775$		0			0
$776$	−1.67608			−0.0601677
$777$	−33.9449	+	24.6624i	−1.21777	+	0.884760i
$778$	−2.20374	−	1.60111i	−0.0790078	−	0.0574026i
$779$	13.1672	−	40.5246i	0.471766	−	1.45194i
$780$	−0.0486004			−0.00174017
$781$	21.1855			0.758078
$782$	−0.556293	+	1.71209i	−0.0198930	+	0.0612244i
$783$	5.16626	+	15.9001i	0.184627	+	0.568224i
$784$	0.136493	+	0.420081i	0.00487474	+	0.0150029i
$785$	15.6409	−	11.3638i	0.558247	−	0.405590i
$786$	−0.401273	+	1.23499i	−0.0143129	+	0.0440507i
$787$	−31.4520	+	22.8512i	−1.12114	+	0.814557i	−0.984382	−	0.176047i	$-0.943669\pi$
$787$	−31.4520	+	22.8512i	−1.12114	+	0.814557i	−0.136760	+	0.990604i	$0.543669\pi$
$788$	−1.20944	−	0.878713i	−0.0430847	−	0.0313028i
$789$	1.42985	+	4.40064i	0.0509041	+	0.156667i
$790$	0.402625	+	0.292524i	0.0143247	+	0.0104075i
$791$	5.92771	+	4.30674i	0.210765	+	0.153130i
$792$	0.699050	+	2.15145i	0.0248397	+	0.0764486i
$793$	0.0404104	+	0.0293599i	0.00143501	+	0.00104260i
$794$	−0.222648	+	0.161763i	−0.00790149	+	0.00574077i
$795$	−4.44443	+	13.6786i	−0.157628	+	0.485128i
$796$	15.8800	−	11.5375i	0.562851	−	0.408936i
$797$	16.0894	+	49.5180i	0.569915	+	1.75402i	0.652877	+	0.757464i	$0.273562\pi$
$797$	16.0894	+	49.5180i	0.569915	+	1.75402i	−0.0829623	+	0.996553i	$0.526438\pi$
$798$	0.902843	+	2.77866i	0.0319603	+	0.0983636i
$799$	10.7464	−	33.0739i	0.380179	−	1.17007i
$800$	−5.14482			−0.181897
$801$	7.14742			0.252542
$802$	−1.02337	+	3.14960i	−0.0361363	+	0.111216i
$803$	−16.1759	−	11.7525i	−0.570834	−	0.414735i
$804$	−8.47821	+	6.15978i	−0.299003	+	0.217239i
$805$	−13.4099			−0.472638
$806$		0			0
$807$	−20.6764			−0.727845
$808$	−3.46985	+	2.52099i	−0.122069	+	0.0886882i
$809$	−25.2480	−	18.3437i	−0.887672	−	0.644932i	0.0475976	−	0.998867i	$-0.484843\pi$
$809$	−25.2480	−	18.3437i	−0.887672	−	0.644932i	−0.935270	+	0.353935i	$0.884843\pi$
$810$	0.278602	−	0.857448i	0.00978907	−	0.0301276i
$811$	16.4241			0.576729			0.288364	−	0.957521i	$-0.406889\pi$
$811$	16.4241			0.576729			0.288364	+	0.957521i	$0.406889\pi$
$812$	−15.6934			−0.550729
$813$	−6.42645	+	19.7786i	−0.225386	+	0.693665i
$814$	−2.29836	−	7.07364i	−0.0805576	−	0.247931i
$815$	2.73404	+	8.41450i	0.0957692	+	0.294747i
$816$	−16.5776	+	12.0443i	−0.580332	+	0.421636i
$817$	−5.85247	+	18.0120i	−0.204752	+	0.630161i
$818$	3.80517	−	2.76462i	0.133045	−	0.0966625i
$819$	0.0235862	+	0.0171364i	0.000824169	+	0.000598794i
$820$	−5.38699	−	16.5794i	−0.188122	−	0.578979i
$821$	32.5771	+	23.6686i	1.13695	+	0.826041i	0.986691	−	0.162606i	$-0.0519900\pi$
$821$	32.5771	+	23.6686i	1.13695	+	0.826041i	0.150257	+	0.988647i	$0.451990\pi$
$822$	1.41726	+	1.02970i	0.0494326	+	0.0359149i
$823$	7.20026	+	22.1601i	0.250985	+	0.772453i	0.994594	+	0.103838i	$0.0331124\pi$
$823$	7.20026	+	22.1601i	0.250985	+	0.772453i	−0.743609	+	0.668615i	$0.766888\pi$
$824$	1.07316	+	0.779695i	0.0373852	+	0.0271620i
$825$	−23.5121	+	17.0825i	−0.818586	+	0.594737i
$826$	−1.06340	+	3.27281i	−0.0370004	+	0.113876i
$827$	−19.5271	+	14.1873i	−0.679024	+	0.493339i	−0.873034	−	0.487660i	$-0.837851\pi$
$827$	−19.5271	+	14.1873i	−0.679024	+	0.493339i	0.194010	+	0.981000i	$0.437851\pi$
$828$	2.03608	+	6.26642i	0.0707588	+	0.217773i
$829$	−7.02067	−	21.6074i	−0.243838	−	0.750456i	−0.995825	−	0.0912787i	$-0.970905\pi$
$829$	−7.02067	−	21.6074i	−0.243838	−	0.750456i	0.751987	−	0.659177i	$-0.229095\pi$
$830$	0.0976662	−	0.300586i	0.00339004	−	0.0104335i
$831$	−32.5758			−1.13004
$832$	−0.102772			−0.00356298
$833$	−0.123818	+	0.381073i	−0.00429004	+	0.0132034i
$834$	−1.98364	−	1.44120i	−0.0686877	−	0.0499045i
$835$	−20.3606	+	14.7928i	−0.704606	+	0.511927i
$836$	66.6580			2.30541
$837$		0			0
$838$	−1.13831			−0.0393223
$839$	4.86591	−	3.53529i	0.167990	−	0.122052i	−0.500614	−	0.865671i	$-0.666892\pi$
$839$	4.86591	−	3.53529i	0.167990	−	0.122052i	0.668604	+	0.743619i	$0.266892\pi$
$840$	1.94157	+	1.41063i	0.0669904	+	0.0486714i
$841$	−6.24491	+	19.2199i	−0.215342	+	0.662754i
$842$	−0.405813			−0.0139852
$843$	−3.44111			−0.118518
$844$	−8.62432	+	26.5429i	−0.296861	+	0.913646i
$845$	4.93888	+	15.2003i	0.169903	+	0.522907i
$846$	0.305598	+	0.940535i	0.0105067	+	0.0323363i
$847$	−44.7037	+	32.4792i	−1.53604	+	1.11600i
$848$	−9.54966	+	29.3908i	−0.327937	+	1.00929i
$849$	16.6700	−	12.1114i	0.572112	−	0.415664i
$850$	−1.24229	−	0.902576i	−0.0426102	−	0.0309581i
$851$	−13.4406	−	41.3660i	−0.460739	−	1.41801i
$852$	−8.93412	−	6.49102i	−0.306078	−	0.222379i
$853$	−8.74856	−	6.35620i	−0.299545	−	0.217632i	0.427852	−	0.903849i	$-0.359270\pi$
$853$	−8.74856	−	6.35620i	−0.299545	−	0.217632i	−0.727397	+	0.686216i	$0.759270\pi$
$854$	−0.379629	−	1.16838i	−0.0129906	−	0.0399810i
$855$	4.81557	+	3.49871i	0.164689	+	0.119654i
$856$	−3.19258	+	2.31955i	−0.109120	+	0.0792804i
$857$	−10.5325	+	32.4158i	−0.359785	+	1.10730i	0.593398	+	0.804909i	$0.297786\pi$
$857$	−10.5325	+	32.4158i	−0.359785	+	1.10730i	−0.953183	+	0.302394i	$0.902214\pi$
$858$	0.0112696	−	0.00818785i	0.000384738	−	0.000279528i
$859$	−2.32317	−	7.14998i	−0.0792655	−	0.243954i	0.903569	−	0.428442i	$-0.140937\pi$
$859$	−2.32317	−	7.14998i	−0.0792655	−	0.243954i	−0.982835	+	0.184488i	$0.940937\pi$
$860$	2.39436	+	7.36909i	0.0816471	+	0.251284i
$861$	8.71040	−	26.8079i	0.296850	−	0.913609i
$862$	−2.91445			−0.0992666
$863$	−22.2748			−0.758243			−0.379121	−	0.925347i	$-0.623774\pi$
$863$	−22.2748			−0.758243			−0.379121	+	0.925347i	$0.623774\pi$
$864$	2.56975	−	7.90889i	0.0874248	−	0.269066i
$865$	−20.9545	−	15.2244i	−0.712475	−	0.517644i
$866$	−2.74677	+	1.99565i	−0.0933392	+	0.0678149i
$867$	6.55906			0.222757
$868$		0			0
$869$	18.3594			0.622798
$870$	−0.541704	+	0.393571i	−0.0183655	+	0.0133433i
$871$	−0.0388877	−	0.0282535i	−0.00131766	−	0.000957335i
$872$	−0.963089	+	2.96408i	−0.0326143	+	0.100377i
$873$	−2.75000			−0.0930734
$874$	−3.02866			−0.102446
$875$	8.60098	−	26.4711i	0.290766	−	0.894886i
$876$	3.22068	+	9.91223i	0.108817	+	0.334903i
$877$	−8.39459	−	25.8359i	−0.283465	−	0.872416i	−0.986854	−	0.161611i	$-0.948331\pi$
$877$	−8.39459	−	25.8359i	−0.283465	−	0.872416i	0.703389	−	0.710805i	$-0.251669\pi$
$878$	3.31957	−	2.41181i	0.112030	−	0.0813947i
$879$	−11.8212	+	36.3818i	−0.398718	+	1.22713i
$880$	21.8900	−	15.9041i	0.737913	−	0.536125i
$881$	18.4210	+	13.3836i	0.620618	+	0.450905i	0.853137	−	0.521686i	$-0.174697\pi$
$881$	18.4210	+	13.3836i	0.620618	+	0.450905i	−0.232519	+	0.972592i	$0.574697\pi$
$882$	−0.00352105	−	0.0108367i	−0.000118560	−	0.000364890i
$883$	16.6118	+	12.0692i	0.559031	+	0.406160i	0.831104	−	0.556117i	$-0.187709\pi$
$883$	16.6118	+	12.0692i	0.559031	+	0.406160i	−0.272073	+	0.962277i	$0.587709\pi$
$884$	−0.0766379	−	0.0556807i	−0.00257761	−	0.00187274i
$885$	−5.83967	−	17.9727i	−0.196298	−	0.604144i
$886$	1.33877	+	0.972676i	0.0449770	+	0.0326777i
$887$	−43.4506	+	31.5687i	−1.45893	+	1.05997i	−0.475287	+	0.879831i	$0.657656\pi$
$887$	−43.4506	+	31.5687i	−1.45893	+	1.05997i	−0.983641	+	0.180142i	$0.942344\pi$
$888$	−2.40540	+	7.40307i	−0.0807200	+	0.248431i
$889$	3.74428	−	2.72038i	0.125579	−	0.0912387i
$890$	0.415355	+	1.27833i	0.0139227	+	0.0428498i
$891$	−10.2778	−	31.6317i	−0.344318	−	1.05970i
$892$	−6.06865	+	18.6774i	−0.203193	+	0.625365i
$893$	58.5071			1.95787
$894$	−3.34281			−0.111800
$895$	3.98114	−	12.2527i	0.133075	−	0.409562i
$896$	8.40921	+	6.10965i	0.280932	+	0.204109i
$897$	0.0659037	−	0.0478818i	0.00220046	−	0.00159873i
$898$	1.40247			0.0468010
$899$		0			0
$900$	−5.62027			−0.187342
$901$	−22.6797	+	16.4778i	−0.755571	+	0.548955i
$902$	4.04234	+	2.93693i	0.134595	+	0.0977891i
$903$	−3.87152	+	11.9153i	−0.128836	+	0.396517i
$904$	1.35931			0.0452099
$905$	11.7253			0.389763
$906$	−0.374380	+	1.15222i	−0.0124379	+	0.0382801i
$907$	16.4857	+	50.7377i	0.547398	+	1.68472i	0.715219	+	0.698901i	$0.246327\pi$
$907$	16.4857	+	50.7377i	0.547398	+	1.68472i	−0.167821	+	0.985818i	$0.553673\pi$
$908$	−5.76754	−	17.7506i	−0.191402	−	0.589076i
$909$	−5.69310	+	4.13628i	−0.188828	+	0.137192i
$910$	−0.00169422	+	0.00521428i	−5.61630e−5	+	0.000172852i
$911$	36.0388	−	26.1837i	1.19402	−	0.867506i	0.200336	−	0.979727i	$-0.435797\pi$
$911$	36.0388	−	26.1837i	1.19402	−	0.867506i	0.993683	+	0.112221i	$0.0357966\pi$
$912$	−27.8901	−	20.2634i	−0.923535	−	0.670987i
$913$	−3.60296	−	11.0888i	−0.119240	−	0.366984i
$914$	−0.457159	−	0.332145i	−0.0151215	−	0.0109864i
$915$	5.45790	+	3.96540i	0.180433	+	0.131092i
$916$	9.04854	+	27.8485i	0.298972	+	0.920142i
$917$	−15.2534	−	11.0823i	−0.503712	−	0.365968i
$918$	2.00799	−	1.45889i	0.0662737	−	0.0481506i
$919$	−3.60281	+	11.0883i	−0.118846	+	0.365770i	−0.992730	−	0.120365i	$-0.961594\pi$
$919$	−3.60281	+	11.0883i	−0.118846	+	0.365770i	0.873884	+	0.486135i	$0.161594\pi$
$920$	−2.01267	+	1.46229i	−0.0663558	+	0.0482103i
$921$	0.299713	+	0.922421i	0.00987587	+	0.0303948i
$922$	1.10497	+	3.40074i	0.0363902	+	0.111997i
$923$	0.0156525	−	0.0481735i	0.000515209	−	0.00158565i
$924$	44.0956			1.45064
$925$	37.1007			1.21986
$926$	0.462442	−	1.42325i	0.0151968	−	0.0467709i
$927$	1.76077	+	1.27927i	0.0578312	+	0.0420168i
$928$	−3.53764	+	2.57024i	−0.116129	+	0.0843723i
$929$	16.1137			0.528675			0.264337	−	0.964430i	$-0.414847\pi$
$929$	16.1137			0.528675			0.264337	+	0.964430i	$0.414847\pi$
$930$		0			0
$931$	−0.674109			−0.0220930
$932$	−45.8965	+	33.3457i	−1.50339	+	1.09228i
$933$	−26.3754	−	19.1629i	−0.863493	−	0.627364i
$934$	−0.734057	+	2.25920i	−0.0240191	+	0.0739232i
$935$	24.5450			0.802708
$936$	0.00540865			0.000176787
$937$	13.9949	−	43.0718i	0.457193	−	1.40710i	−0.411348	−	0.911478i	$-0.634942\pi$
$937$	13.9949	−	43.0718i	0.457193	−	1.40710i	0.868541	−	0.495617i	$-0.165058\pi$
$938$	0.365324	+	1.12435i	0.0119282	+	0.0367114i
$939$	−4.34869	−	13.3839i	−0.141914	−	0.436767i
$940$	19.3650	−	14.0695i	0.631616	−	0.458896i
$941$	−7.57364	+	23.3093i	−0.246893	+	0.759860i	0.748426	+	0.663219i	$0.230810\pi$
$941$	−7.57364	+	23.3093i	−0.246893	+	0.759860i	−0.995319	+	0.0966415i	$0.969190\pi$
$942$	2.33683	−	1.69781i	0.0761382	−	0.0553176i
$943$	23.6393	+	17.1749i	0.769800	+	0.559293i
$944$	−12.5476	−	38.6175i	−0.408389	−	1.25689i
$945$	14.9578	+	10.8675i	0.486577	+	0.353519i
$946$	−1.79670	−	1.30538i	−0.0584159	−	0.0424416i
$947$	−13.8297	−	42.5633i	−0.449404	−	1.38312i	−0.877581	−	0.479428i	$-0.840844\pi$
$947$	−13.8297	−	42.5633i	−0.449404	−	1.38312i	0.428178	−	0.903695i	$-0.359156\pi$
$948$	−7.74230	−	5.62511i	−0.251458	−	0.182695i
$949$	−0.0386750	+	0.0280990i	−0.00125544	+	0.000912133i
$950$	0.798319	−	2.45697i	0.0259009	−	0.0797148i
$951$	−2.50721	+	1.82159i	−0.0813018	+	0.0590692i
$952$	1.44552	+	4.44884i	0.0468495	+	0.144188i
$953$	−9.52117	−	29.3032i	−0.308421	−	0.949222i	−0.978378	−	0.206823i	$-0.933688\pi$
$953$	−9.52117	−	29.3032i	−0.308421	−	0.949222i	0.669957	−	0.742400i	$-0.266312\pi$
$954$	0.246349	−	0.758185i	0.00797585	−	0.0245472i
$955$	12.3001			0.398020
$956$	17.8786			0.578236
$957$	−7.63311	+	23.4923i	−0.246743	+	0.759398i
$958$	1.23475	+	0.897100i	0.0398931	+	0.0289840i
$959$	−20.5779	+	14.9507i	−0.664495	+	0.482784i
$960$	−13.8806			−0.447994
$961$		0			0
$962$	−0.0177828			−0.000573339
$963$	−5.23818	+	3.80576i	−0.168798	+	0.122639i
$964$	1.26544	+	0.919397i	0.0407571	+	0.0296118i
$965$	7.85694	−	24.1812i	0.252924	−	0.778420i
$966$	−2.00352			−0.0644622
$967$	44.5447			1.43246			0.716230	−	0.697864i	$-0.245866\pi$
$967$	44.5447			1.43246			0.716230	+	0.697864i	$0.245866\pi$
$968$	−3.16779	+	9.74946i	−0.101817	+	0.313359i
$969$	−9.66384	−	29.7422i	−0.310447	−	0.955459i
$970$	−0.159810	−	0.491843i	−0.00513118	−	0.0157921i
$971$	−5.14318	+	3.73674i	−0.165053	+	0.119918i	−0.667245	−	0.744838i	$-0.732527\pi$
$971$	−5.14318	+	3.73674i	−0.165053	+	0.119918i	0.502193	+	0.864756i	$0.332527\pi$
$972$	5.01661	−	15.4395i	0.160908	−	0.495223i
$973$	28.8014	−	20.9254i	0.923331	−	0.670839i
$974$	−1.51962	−	1.10407i	−0.0486918	−	0.0353766i
$975$	0.0214723	+	0.0660849i	0.000687664	+	0.00211641i
$976$	11.7273	+	8.52037i	0.375381	+	0.272730i
$977$	10.8675	+	7.89569i	0.347682	+	0.252605i	0.747896	−	0.663816i	$-0.231064\pi$
$977$	10.8675	+	7.89569i	0.347682	+	0.252605i	−0.400214	+	0.916422i	$0.631064\pi$
$978$	0.408480	+	1.25717i	0.0130618	+	0.0401999i
$979$	40.1152	+	29.1454i	1.28209	+	0.931492i
$980$	−0.223120	+	0.162106i	−0.00712731	+	0.00517829i
$981$	−1.58017	+	4.86327i	−0.0504511	+	0.155272i
$982$	−3.06743	+	2.22862i	−0.0978855	+	0.0711180i
$983$	13.0336	+	40.1133i	0.415708	+	1.27942i	0.911616	+	0.411042i	$0.134835\pi$
$983$	13.0336	+	40.1133i	0.415708	+	1.27942i	−0.495909	+	0.868375i	$0.665165\pi$
$984$	−1.61594	−	4.97336i	−0.0515144	−	0.158545i
$985$	0.286188	−	0.880795i	0.00911870	−	0.0280645i
$986$	−1.30512			−0.0415635
$987$	38.7036			1.23195
$988$	0.0492490	−	0.151573i	0.00156682	−	0.00482217i
$989$	−10.5070	−	7.63377i	−0.334102	−	0.242740i
$990$	−0.564690	+	0.410271i	−0.0179470	+	0.0130393i
$991$	40.1209			1.27448			0.637241	−	0.770665i	$-0.280076\pi$
$991$	40.1209			1.27448			0.637241	+	0.770665i	$0.280076\pi$
$992$		0			0
$993$	−3.70907			−0.117704
$994$	−1.00786	+	0.732254i	−0.0319674	+	0.0232257i
$995$	9.83763	+	7.14746i	0.311874	+	0.226590i
$996$	−1.87808	+	5.78013i	−0.0595092	+	0.183150i
$997$	−40.6053			−1.28598			−0.642991	−	0.765874i	$-0.722307\pi$
$997$	−40.6053			−1.28598			−0.642991	+	0.765874i	$0.722307\pi$
$998$	3.57960			0.113310
$999$	−18.5312	+	57.0331i	−0.586301	+	1.80445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.s.388.6		64
31.2	even	5	inner	961.2.d.s.374.6		64
31.3	odd	30		961.2.g.w.547.12		128
31.4	even	5	inner	961.2.d.s.628.11		64
31.5	even	3		961.2.g.w.338.6		128
31.6	odd	6		961.2.g.w.235.6		128
31.7	even	15		961.2.g.w.846.12		128
31.8	even	5		961.2.a.l.1.11	✓	16
31.9	even	15		961.2.c.l.521.12		32
31.10	even	15		961.2.g.w.732.5		128
31.11	odd	30		961.2.g.w.448.12		128
31.12	odd	30		961.2.g.w.816.5		128
31.13	odd	30		961.2.g.w.844.11		128
31.14	even	15		961.2.c.l.439.12		32
31.15	odd	10	inner	961.2.d.s.531.12		64
31.16	even	5	inner	961.2.d.s.531.11		64
31.17	odd	30		961.2.c.l.439.11		32
31.18	even	15		961.2.g.w.844.12		128
31.19	even	15		961.2.g.w.816.6		128
31.20	even	15		961.2.g.w.448.11		128
31.21	odd	30		961.2.g.w.732.6		128
31.22	odd	30		961.2.c.l.521.11		32
31.23	odd	10		961.2.a.l.1.12	yes	16
31.24	odd	30		961.2.g.w.846.11		128
31.25	even	3		961.2.g.w.235.5		128
31.26	odd	6		961.2.g.w.338.5		128
31.27	odd	10	inner	961.2.d.s.628.12		64
31.28	even	15		961.2.g.w.547.11		128
31.29	odd	10	inner	961.2.d.s.374.5		64
31.30	odd	2	inner	961.2.d.s.388.5		64
93.8	odd	10		8649.2.a.bs.1.5		16
93.23	even	10		8649.2.a.bs.1.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.11	✓	16	31.8	even	5
961.2.a.l.1.12	yes	16	31.23	odd	10
961.2.c.l.439.11		32	31.17	odd	30
961.2.c.l.439.12		32	31.14	even	15
961.2.c.l.521.11		32	31.22	odd	30
961.2.c.l.521.12		32	31.9	even	15
961.2.d.s.374.5		64	31.29	odd	10	inner
961.2.d.s.374.6		64	31.2	even	5	inner
961.2.d.s.388.5		64	31.30	odd	2	inner
961.2.d.s.388.6		64	1.1	even	1	trivial
961.2.d.s.531.11		64	31.16	even	5	inner
961.2.d.s.531.12		64	31.15	odd	10	inner
961.2.d.s.628.11		64	31.4	even	5	inner
961.2.d.s.628.12		64	31.27	odd	10	inner
961.2.g.w.235.5		128	31.25	even	3
961.2.g.w.235.6		128	31.6	odd	6
961.2.g.w.338.5		128	31.26	odd	6
961.2.g.w.338.6		128	31.5	even	3
961.2.g.w.448.11		128	31.20	even	15
961.2.g.w.448.12		128	31.11	odd	30
961.2.g.w.547.11		128	31.28	even	15
961.2.g.w.547.12		128	31.3	odd	30
961.2.g.w.732.5		128	31.10	even	15
961.2.g.w.732.6		128	31.21	odd	30
961.2.g.w.816.5		128	31.12	odd	30
961.2.g.w.816.6		128	31.19	even	15
961.2.g.w.844.11		128	31.13	odd	30
961.2.g.w.844.12		128	31.18	even	15
961.2.g.w.846.11		128	31.24	odd	30
961.2.g.w.846.12		128	31.7	even	15
8649.2.a.bs.1.5		16	93.8	odd	10
8649.2.a.bs.1.6		16	93.23	even	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.100459 + 0.0729880i) q^{2} +(1.19674 + 0.869483i) q^{3} +(-0.613269 + 1.88745i) q^{4} -1.22944 q^{5} -0.183686 q^{6} +(0.824157 - 2.53649i) q^{7} +(-0.152897 - 0.470567i) q^{8} +(-0.250863 - 0.772076i) q^{9} +(0.123509 - 0.0897347i) q^{10} +(1.74036 - 5.35627i) q^{11} +(-2.37503 + 1.72556i) q^{12} +(-0.0108937 - 0.00791476i) q^{13} +(0.102339 + 0.314968i) q^{14} +(-1.47133 - 1.06898i) q^{15} +(-3.16141 - 2.29690i) q^{16} +(-1.09542 - 3.37135i) q^{17} +(0.0815539 + 0.0592523i) q^{18} +(4.82486 - 3.50546i) q^{19} +(0.753981 - 2.32051i) q^{20} +(3.19174 - 2.31894i) q^{21} +(0.216108 + 0.665113i) q^{22} +(1.26378 + 3.88953i) q^{23} +(0.226173 - 0.696088i) q^{24} -3.48847 q^{25} +0.00167206 q^{26} +(1.74243 - 5.36266i) q^{27} +(4.28207 + 3.11111i) q^{28} +(-2.39871 + 1.74276i) q^{29} +0.225832 q^{30} +1.47481 q^{32} +(6.73995 - 4.89686i) q^{33} +(0.356114 + 0.258732i) q^{34} +(-1.01326 + 3.11848i) q^{35} +1.61110 q^{36} -10.6352 q^{37} +(-0.228845 + 0.704314i) q^{38} +(-0.00615523 - 0.0189438i) q^{39} +(0.187978 + 0.578537i) q^{40} +(5.78021 - 4.19957i) q^{41} +(-0.151386 + 0.465918i) q^{42} +(-2.56914 + 1.86659i) q^{43} +(9.04238 + 6.56967i) q^{44} +(0.308422 + 0.949225i) q^{45} +(-0.410848 - 0.298498i) q^{46} +(7.93669 + 5.76634i) q^{47} +(-1.78628 - 5.49759i) q^{48} +(-0.0914452 - 0.0664388i) q^{49} +(0.350449 - 0.254616i) q^{50} +(1.62040 - 4.98709i) q^{51} +(0.0216195 - 0.0157075i) q^{52} +(-2.44379 - 7.52122i) q^{53} +(0.216366 + 0.665906i) q^{54} +(-2.13968 + 6.58524i) q^{55} -1.31960 q^{56} +8.82205 q^{57} +(0.113772 - 0.350154i) q^{58} +(8.40644 + 6.10763i) q^{59} +(2.91997 - 2.12148i) q^{60} -3.70951 q^{61} -2.16512 q^{63} +(6.17467 - 4.48616i) q^{64} +(0.0133932 + 0.00973076i) q^{65} +(-0.319679 + 0.983871i) q^{66} +3.56973 q^{67} +7.03504 q^{68} +(-1.86946 + 5.75360i) q^{69} +(-0.125821 - 0.387236i) q^{70} +(1.16243 + 3.57758i) q^{71} +(-0.324958 + 0.236096i) q^{72} +(1.09707 - 3.37645i) q^{73} +(1.06841 - 0.776245i) q^{74} +(-4.17479 - 3.03316i) q^{75} +(3.65745 + 11.2565i) q^{76} +(-12.1518 - 8.82882i) q^{77} +(0.00200102 + 0.00145383i) q^{78} +(1.00736 + 3.10032i) q^{79} +(3.88678 + 2.82391i) q^{80} +(4.77768 - 3.47119i) q^{81} +(-0.274158 + 0.843772i) q^{82} +(1.67486 - 1.21685i) q^{83} +(2.41947 + 7.44638i) q^{84} +(1.34676 + 4.14489i) q^{85} +(0.121855 - 0.375033i) q^{86} -4.38594 q^{87} -2.78658 q^{88} +(-2.72068 + 8.37339i) q^{89} +(-0.100266 - 0.0728475i) q^{90} +(-0.0290539 + 0.0211089i) q^{91} -8.11632 q^{92} -1.21819 q^{94} +(-5.93190 + 4.30977i) q^{95} +(1.76496 + 1.28232i) q^{96} +(1.04679 - 3.22170i) q^{97} +0.0140358 q^{98} -4.57204 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{2} - 8 q^{4} - 64 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} + 8 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 32 q^{32} + 32 q^{33} + 16 q^{35} - 160 q^{36} + 24 q^{38} + 32 q^{39} + 32 q^{41}+ \cdots + 64 q^{98}+O(q^{100}) \) 64 * q + 8 * q^2 - 8 * q^4 - 64 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 + 8 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 32 * q^32 + 32 * q^33 + 16 * q^35 - 160 * q^36 + 24 * q^38 + 32 * q^39 + 32 * q^41 + 16 * q^45 + 32 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 192 * q^56 + 64 * q^59 - 64 * q^63 + 16 * q^64 + 64 * q^67 + 32 * q^69 - 88 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 - 32 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 - 128 * q^87 - 40 * q^90 - 128 * q^94 + 48 * q^95 + 64 * q^98

Introduction

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