LMFDB - Embedded newform 483.2.u.a.113.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(113,483)] 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("483.113"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.8
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18675 + 1.84662i) q^{2} +(-1.11165 + 1.32824i) q^{3} +(-1.17080 - 2.56370i) q^{4} +(-0.291860 - 0.0856978i) q^{5} +(-1.13351 - 3.62910i) q^{6} +(0.755750 + 0.654861i) q^{7} +(1.77815 + 0.255660i) q^{8} +(-0.528462 - 2.95309i) q^{9} +(0.504617 - 0.437253i) q^{10} +(-0.836482 + 0.537574i) q^{11} +(4.70674 + 1.29483i) q^{12} +(-3.61173 - 4.16816i) q^{13} +(-2.10617 + 0.618426i) q^{14} +(0.438274 - 0.292395i) q^{15} +(1.10898 - 1.27983i) q^{16} +(1.15831 - 2.53635i) q^{17} +(6.08039 + 2.52871i) q^{18} +(5.06517 - 2.31318i) q^{19} +(0.122007 + 0.848576i) q^{20} +(-1.70994 + 0.275843i) q^{21} -2.18263i q^{22} +(-2.57734 - 4.04442i) q^{23} +(-2.31626 + 2.07762i) q^{24} +(-4.12843 - 2.65318i) q^{25} +(11.9833 - 1.72293i) q^{26} +(4.50989 + 2.58088i) q^{27} +(0.794033 - 2.70423i) q^{28} +(5.53304 + 2.52686i) q^{29} +(0.0198205 + 1.15633i) q^{30} +(-1.34033 + 9.32221i) q^{31} +(2.05951 + 7.01403i) q^{32} +(0.215847 - 1.70865i) q^{33} +(3.30906 + 5.14899i) q^{34} +(-0.164453 - 0.255894i) q^{35} +(-6.95210 + 4.81230i) q^{36} +(-1.36957 - 4.66434i) q^{37} +(-1.73952 + 12.0986i) q^{38} +(9.55132 - 0.163718i) q^{39} +(-0.497062 - 0.227001i) q^{40} +(1.83160 - 6.23784i) q^{41} +(1.51990 - 3.48498i) q^{42} +(-12.2999 + 1.76845i) q^{43} +(2.35753 + 1.51510i) q^{44} +(-0.0988362 + 0.907176i) q^{45} +(10.5272 + 0.0403465i) q^{46} -3.18603i q^{47} +(0.467126 + 2.89571i) q^{48} +(0.142315 + 0.989821i) q^{49} +(9.79884 - 4.47498i) q^{50} +(2.08126 + 4.35807i) q^{51} +(-6.45729 + 14.1395i) q^{52} +(-3.64745 + 4.20938i) q^{53} +(-10.1180 + 5.26519i) q^{54} +(0.290205 - 0.0852117i) q^{55} +(1.17642 + 1.35766i) q^{56} +(-2.55823 + 9.29923i) q^{57} +(-11.2325 + 7.21869i) q^{58} +(1.80151 - 1.56102i) q^{59} +(-1.26274 - 0.781266i) q^{60} +(2.63302 + 0.378571i) q^{61} +(-15.6240 - 13.5382i) q^{62} +(1.53448 - 2.57786i) q^{63} +(-12.1467 - 3.56659i) q^{64} +(0.696918 + 1.52604i) q^{65} +(2.89907 + 2.42633i) q^{66} +(4.46363 - 6.94555i) q^{67} -7.85861 q^{68} +(8.23708 + 1.07265i) q^{69} +0.667704 q^{70} +(2.99309 - 4.65734i) q^{71} +(-0.184701 - 5.38615i) q^{72} +(0.474011 + 1.03794i) q^{73} +(10.2386 + 3.00633i) q^{74} +(8.11344 - 2.53415i) q^{75} +(-11.8606 - 10.2773i) q^{76} +(-0.984207 - 0.141508i) q^{77} +(-11.0327 + 17.8320i) q^{78} +(9.44337 - 8.18272i) q^{79} +(-0.433344 + 0.278493i) q^{80} +(-8.44146 + 3.12119i) q^{81} +(9.34528 + 10.7850i) q^{82} +(9.84079 - 2.88952i) q^{83} +(2.70918 + 4.06083i) q^{84} +(-0.555426 + 0.640995i) q^{85} +(11.3312 - 24.8119i) q^{86} +(-9.50709 + 4.54025i) q^{87} +(-1.62483 + 0.742034i) q^{88} +(-1.95139 - 13.5722i) q^{89} +(-1.55792 - 1.25911i) q^{90} -5.51527i q^{91} +(-7.35111 + 11.3427i) q^{92} +(-10.8922 - 12.1433i) q^{93} +(5.88340 + 3.78103i) q^{94} +(-1.67655 + 0.241052i) q^{95} +(-11.6058 - 5.06163i) q^{96} +(1.90569 - 6.49020i) q^{97} +(-1.99672 - 0.911871i) q^{98} +(2.02955 + 2.18612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−1.18675	+	1.84662i	−0.839160	+	1.30576i	0.110944	+	0.993827i	$0.464613\pi$
$2$	−1.18675	+	1.84662i	−0.839160	+	1.30576i	−0.950104	+	0.311932i	$0.899024\pi$
$3$	−1.11165	+	1.32824i	−0.641812	+	0.766862i
$3$	−1.11165	+	1.32824i	−0.641812	+	0.766862i
$4$	−1.17080	−	2.56370i	−0.585401	−	1.28185i
$5$	−0.291860	−	0.0856978i	−0.130524	−	0.0383252i	0.215818	−	0.976434i	$-0.430758\pi$
$5$	−0.291860	−	0.0856978i	−0.130524	−	0.0383252i	−0.346342	+	0.938108i	$0.612576\pi$
$6$	−1.13351	−	3.62910i	−0.462753	−	1.48157i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$8$	1.77815	+	0.255660i	0.628672	+	0.0903894i
$9$	−0.528462	−	2.95309i	−0.176154	−	0.984363i
$10$	0.504617	−	0.437253i	0.159574	−	0.138271i
$11$	−0.836482	+	0.537574i	−0.252209	+	0.162085i	−0.660637	−	0.750706i	$-0.729714\pi$
$11$	−0.836482	+	0.537574i	−0.252209	+	0.162085i	0.408428	+	0.912791i	$0.366077\pi$
$12$	4.70674	+	1.29483i	1.35872	+	0.373785i
$13$	−3.61173	−	4.16816i	−1.00171	−	1.15604i	−0.987735	−	0.156138i	$-0.950096\pi$
$13$	−3.61173	−	4.16816i	−1.00171	−	1.15604i	−0.0139794	−	0.999902i	$-0.504450\pi$
$14$	−2.10617	+	0.618426i	−0.562897	+	0.165281i
$15$	0.438274	−	0.292395i	0.113162	−	0.0754961i
$16$	1.10898	−	1.27983i	0.277244	−	0.319956i
$17$	1.15831	−	2.53635i	0.280933	−	0.615156i	−0.715586	−	0.698524i	$-0.753840\pi$
$17$	1.15831	−	2.53635i	0.280933	−	0.615156i	0.996519	+	0.0833679i	$0.0265677\pi$
$18$	6.08039	+	2.52871i	1.43316	+	0.596023i
$19$	5.06517	−	2.31318i	1.16203	−	0.530681i	0.261383	−	0.965235i	$-0.415821\pi$
$19$	5.06517	−	2.31318i	1.16203	−	0.530681i	0.900646	+	0.434554i	$0.143094\pi$
$20$	0.122007	+	0.848576i	0.0272816	+	0.189747i
$21$	−1.70994	+	0.275843i	−0.373141	+	0.0601938i
$22$		−	2.18263i		−	0.465339i
$23$	−2.57734	−	4.04442i	−0.537413	−	0.843319i
$23$	−2.57734	−	4.04442i	−0.537413	−	0.843319i
$24$	−2.31626	+	2.07762i	−0.472805	+	0.424091i
$25$	−4.12843	−	2.65318i	−0.825686	−	0.530636i
$26$	11.9833	−	1.72293i	2.35011	−	0.337895i
$27$	4.50989	+	2.58088i	0.867928	+	0.496690i
$28$	0.794033	−	2.70423i	0.150058	−	0.511051i
$29$	5.53304	+	2.52686i	1.02746	+	0.469225i	0.856552	−	0.516062i	$-0.172602\pi$
$29$	5.53304	+	2.52686i	1.02746	+	0.469225i	0.170909	+	0.985287i	$0.445330\pi$
$30$	0.0198205	+	1.15633i	0.00361871	+	0.211115i
$31$	−1.34033	+	9.32221i	−0.240731	+	1.67432i	0.407754	+	0.913092i	$0.366312\pi$
$31$	−1.34033	+	9.32221i	−0.240731	+	1.67432i	−0.648485	+	0.761227i	$0.724597\pi$
$32$	2.05951	+	7.01403i	0.364073	+	1.23992i
$33$	0.215847	−	1.70865i	0.0375741	−	0.297437i
$34$	3.30906	+	5.14899i	0.567498	+	0.883045i
$35$	−0.164453	−	0.255894i	−0.0277976	−	0.0432539i
$36$	−6.95210	+	4.81230i	−1.15868	+	0.802050i
$37$	−1.36957	−	4.66434i	−0.225157	−	0.766813i	−0.992139	−	0.125144i	$-0.960061\pi$
$37$	−1.36957	−	4.66434i	−0.225157	−	0.766813i	0.766982	−	0.641669i	$-0.221758\pi$
$38$	−1.73952	+	12.0986i	−0.282187	+	1.96266i
$39$	9.55132	−	0.163718i	1.52944	−	0.0262159i
$40$	−0.497062	−	0.227001i	−0.0785924	−	0.0358919i
$41$	1.83160	−	6.23784i	0.286047	−	0.974187i	−0.683636	−	0.729823i	$-0.739603\pi$
$41$	1.83160	−	6.23784i	0.286047	−	0.974187i	0.969683	−	0.244364i	$-0.0785793\pi$
$42$	1.51990	−	3.48498i	0.234526	−	0.537744i
$43$	−12.2999	+	1.76845i	−1.87571	+	0.269687i	−0.983362	−	0.181657i	$-0.941854\pi$
$43$	−12.2999	+	1.76845i	−1.87571	+	0.269687i	−0.892350	+	0.451344i	$0.850945\pi$
$44$	2.35753	+	1.51510i	0.355412	+	0.228409i
$45$	−0.0988362	+	0.907176i	−0.0147336	+	0.135234i
$46$	10.5272	+	0.0403465i	1.55215	+	0.00594876i
$47$		−	3.18603i		−	0.464731i	−0.972629	−	0.232365i	$-0.925354\pi$
$47$		−	3.18603i		−	0.464731i	0.972629	−	0.232365i	$-0.0746465\pi$
$48$	0.467126	+	2.89571i	0.0674239	+	0.417960i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	9.79884	−	4.47498i	1.38577	−	0.632858i
$51$	2.08126	+	4.35807i	0.291434	+	0.610251i
$52$	−6.45729	+	14.1395i	−0.895465	+	1.96079i
$53$	−3.64745	+	4.20938i	−0.501015	+	0.578203i	−0.948775	−	0.315951i	$-0.897676\pi$
$53$	−3.64745	+	4.20938i	−0.501015	+	0.578203i	0.447760	+	0.894154i	$0.352222\pi$
$54$	−10.1180	+	5.26519i	−1.37689	+	0.716502i
$55$	0.290205	−	0.0852117i	0.0391312	−	0.0114899i
$56$	1.17642	+	1.35766i	0.157205	+	0.181425i
$57$	−2.55823	+	9.29923i	−0.338846	+	1.23171i
$58$	−11.2325	+	7.21869i	−1.47490	+	0.947860i
$59$	1.80151	−	1.56102i	0.234537	−	0.203227i	−0.529661	−	0.848210i	$-0.677681\pi$
$59$	1.80151	−	1.56102i	0.234537	−	0.203227i	0.764198	+	0.644982i	$0.223135\pi$
$60$	−1.26274	−	0.781266i	−0.163020	−	0.100861i
$61$	2.63302	+	0.378571i	0.337123	+	0.0484710i	0.308798	−	0.951128i	$-0.400073\pi$
$61$	2.63302	+	0.378571i	0.337123	+	0.0484710i	0.0283257	+	0.999599i	$0.490982\pi$
$62$	−15.6240	−	13.5382i	−1.98425	−	1.71936i
$63$	1.53448	−	2.57786i	0.193326	−	0.324780i
$64$	−12.1467	−	3.56659i	−1.51833	−	0.445823i
$65$	0.696918	+	1.52604i	0.0864420	+	0.189282i
$66$	2.89907	+	2.42633i	0.356851	+	0.298660i
$67$	4.46363	−	6.94555i	0.545320	−	0.848534i	−0.453773	−	0.891117i	$-0.649922\pi$
$67$	4.46363	−	6.94555i	0.545320	−	0.848534i	0.999093	+	0.0425833i	$0.0135588\pi$
$68$	−7.85861			−0.952996
$69$	8.23708	+	1.07265i	0.991627	+	0.129131i
$70$	0.667704			0.0798058
$71$	2.99309	−	4.65734i	0.355214	−	0.552725i	−0.616956	−	0.786997i	$-0.711635\pi$
$71$	2.99309	−	4.65734i	0.355214	−	0.552725i	0.972171	+	0.234273i	$0.0752709\pi$
$72$	−0.184701	−	5.38615i	−0.0217672	−	0.634764i
$73$	0.474011	+	1.03794i	0.0554788	+	0.121482i	0.935341	−	0.353747i	$-0.115093\pi$
$73$	0.474011	+	1.03794i	0.0554788	+	0.121482i	−0.879862	+	0.475229i	$0.842365\pi$
$74$	10.2386	+	3.00633i	1.19021	+	0.349479i
$75$	8.11344	−	2.53415i	0.936860	−	0.292618i
$76$	−11.8606	−	10.2773i	−1.36051	−	1.17889i
$77$	−0.984207	−	0.141508i	−0.112161	−	0.0161263i
$78$	−11.0327	+	17.8320i	−1.24921	+	2.01907i
$79$	9.44337	−	8.18272i	1.06246	−	0.920628i	0.0654482	−	0.997856i	$-0.479152\pi$
$79$	9.44337	−	8.18272i	1.06246	−	0.920628i	0.997013	+	0.0772276i	$0.0246068\pi$
$80$	−0.433344	+	0.278493i	−0.0484493	+	0.0311365i
$81$	−8.44146	+	3.12119i	−0.937939	+	0.346799i
$82$	9.34528	+	10.7850i	1.03201	+	1.19101i
$83$	9.84079	−	2.88952i	1.08017	−	0.317166i	0.307221	−	0.951638i	$-0.400601\pi$
$83$	9.84079	−	2.88952i	1.08017	−	0.317166i	0.772945	+	0.634472i	$0.218783\pi$
$84$	2.70918	+	4.06083i	0.295596	+	0.443072i
$85$	−0.555426	+	0.640995i	−0.0602444	+	0.0695257i
$86$	11.3312	−	24.8119i	1.22188	−	2.67554i
$87$	−9.50709	+	4.54025i	−1.01927	+	0.486765i
$88$	−1.62483	+	0.742034i	−0.173207	+	0.0791011i
$89$	−1.95139	−	13.5722i	−0.206847	−	1.43865i	−0.783363	−	0.621564i	$-0.786498\pi$
$89$	−1.95139	−	13.5722i	−0.206847	−	1.43865i	0.576517	−	0.817085i	$-0.304412\pi$
$90$	−1.55792	−	1.25911i	−0.164219	−	0.132721i
$91$		−	5.51527i		−	0.578157i
$92$	−7.35111	+	11.3427i	−0.766407	+	1.18256i
$93$	−10.8922	−	12.1433i	−1.12947	−	1.25921i
$94$	5.88340	+	3.78103i	0.606826	+	0.389983i
$95$	−1.67655	+	0.241052i	−0.172011	+	0.0247314i
$96$	−11.6058	−	5.06163i	−1.18451	−	0.516601i
$97$	1.90569	−	6.49020i	0.193494	−	0.658980i	−0.804399	−	0.594090i	$-0.797512\pi$
$97$	1.90569	−	6.49020i	0.193494	−	0.658980i	0.997892	−	0.0648896i	$-0.0206695\pi$
$98$	−1.99672	−	0.911871i	−0.201699	−	0.0921128i
$99$	2.02955	+	2.18612i	0.203978	+	0.219713i
$100$	−1.96838	+	13.6904i	−0.196838	+	1.36904i
$101$	1.85724	+	6.32518i	0.184802	+	0.629379i	0.998821	+	0.0485404i	$0.0154570\pi$
$101$	1.85724	+	6.32518i	0.184802	+	0.629379i	−0.814019	+	0.580838i	$0.802725\pi$
$102$	−10.5176	−	1.32865i	−1.04140	−	0.131556i
$103$	−2.26510	−	3.52456i	−0.223187	−	0.347285i	0.711544	−	0.702641i	$-0.247996\pi$
$103$	−2.26510	−	3.52456i	−0.223187	−	0.347285i	−0.934731	+	0.355356i	$0.884360\pi$
$104$	−5.35658	−	8.33500i	−0.525256	−	0.817314i
$105$	0.522703	+	0.0660311i	0.0510106	+	0.00644397i
$106$	−3.44452	−	11.7309i	−0.334561	−	1.13941i
$107$	−0.145184	+	1.00978i	−0.0140355	+	0.0976190i	−0.995635	−	0.0933322i	$-0.970248\pi$
$107$	−0.145184	+	1.00978i	−0.0140355	+	0.0976190i	0.981600	+	0.190951i	$0.0611572\pi$
$108$	1.33641	−	14.5837i	0.128596	−	1.40332i
$109$	−10.6189	−	4.84948i	−1.01710	−	0.464496i	−0.164124	−	0.986440i	$-0.552480\pi$
$109$	−10.6189	−	4.84948i	−1.01710	−	0.464496i	−0.852980	+	0.521944i	$0.825207\pi$
$110$	−0.187047	+	0.637023i	−0.0178342	+	0.0607378i
$111$	7.71787	+	3.36599i	0.732548	+	0.319486i
$112$	1.67622	−	0.241003i	0.158387	−	0.0227727i
$113$	−11.8265	−	7.60041i	−1.11254	−	0.714986i	−0.150695	−	0.988580i	$-0.548151\pi$
$113$	−11.8265	−	7.60041i	−1.11254	−	0.714986i	−0.961845	+	0.273594i	$0.911788\pi$
$114$	−14.1362	−	15.7600i	−1.32397	−	1.47606i
$115$	0.405625	+	1.40128i	0.0378247	+	0.130670i
$116$		−	17.1435i		−	1.59173i
$117$	−10.4003	+	12.8685i	−0.961507	+	1.18969i
$118$	0.744664	+	5.17925i	0.0685519	+	0.476789i
$119$	2.53635	−	1.15831i	0.232507	−	0.106183i
$120$	0.854072	−	0.407874i	0.0779657	−	0.0372336i
$121$	−4.15885	+	9.10661i	−0.378077	+	0.827874i
$122$	−3.82382	+	4.41292i	−0.346192	+	0.399527i
$123$	6.24928	+	9.36711i	0.563478	+	0.844604i
$124$	25.4686	−	7.47826i	2.28715	−	0.671568i
$125$	1.97353	+	2.27758i	0.176518	+	0.203713i
$126$	2.93930	+	5.89288i	0.261853	+	0.524980i
$127$	12.6680	−	8.14122i	1.12410	−	0.722416i	0.159781	−	0.987152i	$-0.448921\pi$
$127$	12.6680	−	8.14122i	1.12410	−	0.722416i	0.964321	+	0.264736i	$0.0852848\pi$
$128$	9.95195	−	8.62341i	0.879636	−	0.762209i
$129$	11.3242	−	18.3031i	0.997043	−	1.61150i
$130$	−3.64508	−	0.524084i	−0.319695	−	0.0459652i
$131$	−13.4681	−	11.6702i	−1.17672	−	1.01963i	−0.999370	−	0.0354827i	$-0.988703\pi$
$131$	−13.4681	−	11.6702i	−1.17672	−	1.01963i	−0.177347	−	0.984148i	$-0.556751\pi$
$132$	−4.63317	+	1.44712i	−0.403266	+	0.125956i
$133$	5.34281	+	1.56879i	0.463280	+	0.136031i
$134$	7.52858	+	16.4853i	0.650370	+	1.42411i
$135$	−1.09508	−	1.13974i	−0.0942494	−	0.0980934i
$136$	2.70810	−	4.21389i	0.232218	−	0.361338i
$137$	−16.3918			−1.40045			−0.700224	−	0.713923i	$-0.746917\pi$
$137$	−16.3918			−1.40045			−0.700224	+	0.713923i	$0.746917\pi$
$138$	−11.7561	+	13.9378i	−1.00075	+	1.18646i
$139$	4.87172			0.413214			0.206607	−	0.978424i	$-0.433758\pi$
$139$	4.87172			0.413214			0.206607	+	0.978424i	$0.433758\pi$
$140$	−0.463493	+	0.721209i	−0.0391723	+	0.0609532i
$141$	4.23183	+	3.54176i	0.356384	+	0.298270i
$142$	5.04829	+	11.0542i	0.423643	+	0.927649i
$143$	5.26185	+	1.54502i	0.440018	+	0.129201i
$144$	−4.36549	−	2.59856i	−0.363791	−	0.216547i
$145$	−1.39833	−	1.21166i	−0.116125	−	0.100623i
$146$	−2.47922	−	0.356458i	−0.205181	−	0.0295006i
$147$	−1.47293	−	0.911308i	−0.121485	−	0.0751634i
$148$	−10.3545	+	8.97219i	−0.851132	+	0.737510i
$149$	−5.14491	+	3.30643i	−0.421488	+	0.270874i	−0.734146	−	0.678992i	$-0.762417\pi$
$149$	−5.14491	+	3.30643i	−0.421488	+	0.270874i	0.312658	+	0.949866i	$0.398781\pi$
$150$	−4.94903	+	17.9899i	−0.404087	+	1.46887i
$151$	−8.33269	−	9.61644i	−0.678105	−	0.782575i	0.307517	−	0.951543i	$-0.400502\pi$
$151$	−8.33269	−	9.61644i	−0.678105	−	0.782575i	−0.985622	+	0.168968i	$0.945957\pi$
$152$	9.59803	−	2.81824i	0.778503	−	0.228589i
$153$	−8.10220	−	2.08024i	−0.655024	−	0.168177i
$154$	1.42932	−	1.64952i	0.115178	−	0.132922i
$155$	1.19008	−	2.60592i	0.0955897	−	0.209312i
$156$	−11.6024	−	24.2950i	−0.928938	−	1.94516i
$157$	3.64802	−	1.66599i	0.291143	−	0.132961i	−0.264489	−	0.964389i	$-0.585203\pi$
$157$	3.64802	−	1.66599i	0.291143	−	0.132961i	0.555633	+	0.831428i	$0.312476\pi$
$158$	3.90346	+	27.1492i	0.310543	+	2.15987i
$159$	−1.53639	−	9.52406i	−0.121844	−	0.755307i
$160$		−	2.22361i		−	0.175792i
$161$	0.700706	−	4.74437i	0.0552234	−	0.373908i
$162$	4.25425	−	19.2923i	0.334246	−	1.51574i
$163$	−8.64253	−	5.55422i	−0.676935	−	0.435040i	0.156485	−	0.987680i	$-0.449984\pi$
$163$	−8.64253	−	5.55422i	−0.676935	−	0.435040i	−0.833420	+	0.552641i	$0.813620\pi$
$164$	−18.1364	+	2.60762i	−1.41621	+	0.203621i
$165$	−0.209424	+	0.480188i	−0.0163037	+	0.0373826i
$166$	−6.34273	+	21.6014i	−0.492291	+	1.67659i
$167$	−7.63369	−	3.48619i	−0.590712	−	0.269769i	0.0975506	−	0.995231i	$-0.468899\pi$
$167$	−7.63369	−	3.48619i	−0.590712	−	0.269769i	−0.688263	+	0.725461i	$0.741626\pi$
$168$	−3.11106	+	0.0533264i	−0.240024	+	0.00411422i
$169$	−2.47887	+	17.2409i	−0.190682	+	1.32622i
$170$	−0.524524	−	1.78636i	−0.0402291	−	0.137008i
$171$	−9.50779	−	13.7355i	−0.727079	−	1.05038i
$172$	18.9345	+	29.4626i	1.44374	+	2.24651i
$173$	8.53659	+	13.2832i	0.649025	+	1.00990i	0.997366	+	0.0725343i	$0.0231087\pi$
$173$	8.53659	+	13.2832i	0.649025	+	1.00990i	−0.348341	+	0.937368i	$0.613255\pi$
$174$	2.89844	−	22.9442i	0.219731	−	1.73939i
$175$	−1.38260	−	4.70869i	−0.104514	−	0.355943i
$176$	−0.239636	+	1.66671i	−0.0180633	+	0.125633i
$177$	0.0707603	+	4.12816i	0.00531867	+	0.310291i
$178$	27.3785	+	12.5033i	2.05211	+	0.937166i
$179$	−3.14576	+	10.7135i	−0.235125	+	0.800763i	0.754401	+	0.656413i	$0.227927\pi$
$179$	−3.14576	+	10.7135i	−0.235125	+	0.800763i	−0.989527	+	0.144350i	$0.953891\pi$
$180$	2.44144	−	0.808737i	0.181974	−	0.0602797i
$181$	3.65483	−	0.525486i	0.271662	−	0.0390590i	−0.00513766	−	0.999987i	$-0.501635\pi$
$181$	3.65483	−	0.525486i	0.271662	−	0.0390590i	0.276799	+	0.960928i	$0.410726\pi$
$182$	10.1846	+	6.54526i	0.754934	+	0.485167i
$183$	−3.42983	+	3.07645i	−0.253541	+	0.227418i
$184$	−3.54891	−	7.85051i	−0.261629	−	0.578748i
$185$			1.47870i			0.108716i
$186$	35.3505	−	5.70262i	2.59202	−	0.418137i
$187$	0.394570	+	2.74430i	0.0288538	+	0.200683i
$188$	−8.16803	+	3.73021i	−0.595715	+	0.272054i
$189$	1.71823	+	4.90384i	0.124983	+	0.356702i
$190$	1.54452	−	3.38203i	0.112051	−	0.245358i
$191$	−2.86357	+	3.30474i	−0.207201	+	0.239123i	−0.849833	−	0.527053i	$-0.823297\pi$
$191$	−2.86357	+	3.30474i	−0.207201	+	0.239123i	0.642632	+	0.766175i	$0.277843\pi$
$192$	18.2402	−	12.1689i	1.31637	−	0.878218i
$193$	−8.95887	+	2.63056i	−0.644873	+	0.189352i	−0.587785	−	0.809017i	$-0.700000\pi$
$193$	−8.95887	+	2.63056i	−0.644873	+	0.189352i	−0.0570884	+	0.998369i	$0.518182\pi$
$194$	9.72335	+	11.2213i	0.698096	+	0.805646i
$195$	−2.80168	−	0.770745i	−0.200632	−	0.0551942i
$196$	2.37098	−	1.52374i	0.169356	−	0.108838i
$197$	8.20311	−	7.10804i	0.584448	−	0.506427i	−0.311701	−	0.950180i	$-0.600899\pi$
$197$	8.20311	−	7.10804i	0.584448	−	0.506427i	0.896149	+	0.443753i	$0.146353\pi$
$198$	−6.44551	+	1.15344i	−0.458062	+	0.0819714i
$199$	19.3933	+	2.78833i	1.37475	+	0.197659i	0.789778	−	0.613393i	$-0.210196\pi$
$199$	19.3933	+	2.78833i	1.37475	+	0.197659i	0.584974	+	0.811052i	$0.301105\pi$
$200$	−6.66267	−	5.77323i	−0.471122	−	0.408229i
$201$	4.26338	+	13.6498i	0.300715	+	0.962784i
$202$	−13.8843	−	4.07680i	−0.976895	−	0.286842i
$203$	2.52686	+	5.53304i	0.177351	+	0.388343i
$204$	8.73603	−	10.4381i	0.611645	−	0.730816i
$205$	−1.06914	+	1.66361i	−0.0746719	+	0.116192i
$206$	9.19664			0.640761
$207$	−10.5815	+	9.74844i	−0.735465	+	0.677563i
$208$	−9.33985			−0.647602
$209$	−2.99341	+	4.65784i	−0.207059	+	0.322190i
$210$	−0.742254	+	0.886873i	−0.0512204	+	0.0612001i
$211$	−5.26353	−	11.5255i	−0.362357	−	0.793450i	−0.999738	−	0.0229016i	$-0.992710\pi$
$211$	−5.26353	−	11.5255i	−0.362357	−	0.793450i	0.637381	−	0.770549i	$-0.280018\pi$
$212$	15.0620	+	4.42261i	1.03446	+	0.303746i
$213$	2.85881	+	9.15289i	0.195882	+	0.627146i
$214$	−1.69238	−	1.46646i	−0.115689	−	0.100245i
$215$	3.74139	+	0.537931i	0.255161	+	0.0366866i
$216$	7.35944	+	5.74219i	0.500746	+	0.390707i
$217$	−7.11771	+	6.16753i	−0.483181	+	0.418679i
$218$	21.5571	−	13.8539i	1.46003	−	0.938306i
$219$	−1.90557	−	0.524225i	−0.128767	−	0.0354238i
$220$	−0.558229	−	0.644231i	−0.0376358	−	0.0434340i
$221$	−14.7555	+	4.33259i	−0.992560	+	0.291442i
$222$	−15.3749	+	10.2574i	−1.03190	+	0.688431i
$223$	6.31358	−	7.28626i	0.422789	−	0.487924i	−0.503896	−	0.863765i	$-0.668100\pi$
$223$	6.31358	−	7.28626i	0.422789	−	0.487924i	0.926684	+	0.375840i	$0.122646\pi$
$224$	−3.03674	+	6.64954i	−0.202901	+	0.444291i
$225$	−5.65336	+	13.5937i	−0.376890	+	0.906248i
$226$	28.0702	−	12.8192i	1.86720	−	0.852721i
$227$	2.51136	+	17.4669i	0.166685	+	1.15932i	0.885677	+	0.464301i	$0.153695\pi$
$227$	2.51136	+	17.4669i	0.166685	+	1.15932i	−0.718992	+	0.695018i	$0.755396\pi$
$228$	26.8356	−	4.32903i	1.77723	−	0.286697i
$229$		−	5.58011i		−	0.368744i	−0.982857	−	0.184372i	$-0.940975\pi$
$229$		−	5.58011i		−	0.368744i	0.982857	−	0.184372i	$-0.0590251\pi$
$230$	−3.06900	−	0.913931i	−0.202364	−	0.0602628i
$231$	1.28205	−	1.14996i	0.0843528	−	0.0756618i
$232$	9.19258	+	5.90771i	0.603522	+	0.387860i
$233$	−7.60877	+	1.09398i	−0.498467	+	0.0716687i	−0.386963	−	0.922095i	$-0.626476\pi$
$233$	−7.60877	+	1.09398i	−0.498467	+	0.0716687i	−0.111504	+	0.993764i	$0.535567\pi$
$234$	−11.4207	−	34.4771i	−0.746592	−	2.25384i
$235$	−0.273036	+	0.929875i	−0.0178109	+	0.0606584i
$236$	−6.11120	−	2.79089i	−0.397805	−	0.181671i
$237$	0.370919	+	21.6394i	0.0240938	+	1.40563i
$238$	−0.871055	+	6.05832i	−0.0564621	+	0.392703i
$239$	5.15821	+	17.5673i	0.333657	+	1.13633i	0.940013	+	0.341138i	$0.110812\pi$
$239$	5.15821	+	17.5673i	0.333657	+	1.13633i	−0.606356	+	0.795193i	$0.707369\pi$
$240$	0.111820	−	0.885173i	0.00721798	−	0.0571377i
$241$	−5.28398	−	8.22203i	−0.340371	−	0.529628i	0.628301	−	0.777970i	$-0.283751\pi$
$241$	−5.28398	−	8.22203i	−0.340371	−	0.529628i	−0.968672	+	0.248343i	$0.920114\pi$
$242$	−11.8809	−	18.4871i	−0.763736	−	1.18840i
$243$	5.23825	−	14.6820i	0.336034	−	0.941850i
$244$	−2.11220	−	7.19350i	−0.135220	−	0.460517i
$245$	0.0432895	−	0.301085i	0.00276567	−	0.0192356i
$246$	−24.7138	+	0.423618i	−1.57570	+	0.0270089i
$247$	−27.9358	−	12.7578i	−1.77751	−	0.811762i
$248$	−4.76663	+	16.2336i	−0.302681	+	1.03084i
$249$	−7.10154	+	16.2831i	−0.450042	+	1.03190i
$250$	−6.54792	+	0.941449i	−0.414127	+	0.0595425i
$251$	23.5175	+	15.1138i	1.48441	+	0.953974i	0.996717	+	0.0809602i	$0.0257987\pi$
$251$	23.5175	+	15.1138i	1.48441	+	0.953974i	0.487695	+	0.873014i	$0.337838\pi$
$252$	−8.40544	−	0.915766i	−0.529493	−	0.0576878i
$253$	4.33007	+	1.99757i	0.272229	+	0.125586i
$254$			33.0546i			2.07403i
$255$	−0.233958	−	1.45030i	−0.0146510	−	0.0908215i
$256$	0.510426	+	3.55009i	0.0319016	+	0.221881i
$257$	26.7259	−	12.2053i	1.66712	−	0.761347i	0.667255	−	0.744830i	$-0.267469\pi$
$257$	26.7259	−	12.2053i	1.66712	−	0.761347i	0.999864	−	0.0165176i	$-0.00525796\pi$
$258$	20.3599	+	42.6328i	1.26755	+	2.65420i
$259$	2.01944	−	4.42195i	0.125482	−	0.274767i
$260$	3.09635	−	3.57338i	0.192027	−	0.221611i
$261$	4.53802	−	17.6749i	0.280897	−	1.09405i
$262$	37.5338	−	11.0209i	2.31885	−	0.680875i
$263$	−2.30338	−	2.65825i	−0.142033	−	0.163915i	0.680276	−	0.732956i	$-0.261860\pi$
$263$	−2.30338	−	2.65825i	−0.142033	−	0.163915i	−0.822309	+	0.569041i	$0.807314\pi$
$264$	0.820641	−	2.98305i	0.0505069	−	0.183594i
$265$	1.42528	−	0.915971i	0.0875541	−	0.0562676i
$266$	−9.23755	+	8.00439i	−0.566391	+	0.490780i
$267$	20.1964	+	12.4956i	1.23600	+	0.764720i
$268$	−23.0323	−	3.31155i	−1.40692	−	0.202285i
$269$	1.52636	+	1.32260i	0.0930638	+	0.0806402i	0.700150	−	0.713996i	$-0.253116\pi$
$269$	1.52636	+	1.32260i	0.0930638	+	0.0806402i	−0.607086	+	0.794636i	$0.707662\pi$
$270$	3.40426	−	0.669607i	0.207177	−	0.0407510i
$271$	−10.9492	−	3.21496i	−0.665114	−	0.195295i	−0.0682877	−	0.997666i	$-0.521754\pi$
$271$	−10.9492	−	3.21496i	−0.665114	−	0.195295i	−0.596826	+	0.802371i	$0.703572\pi$
$272$	−1.96155	−	4.29520i	−0.118936	−	0.260434i
$273$	7.32562	+	6.13106i	0.443367	+	0.371068i
$274$	19.4530	−	30.2695i	1.17520	−	1.82865i
$275$	4.87964			0.294253
$276$	−6.89404	−	22.3732i	−0.414973	−	1.34671i
$277$	−1.88598			−0.113317			−0.0566587	−	0.998394i	$-0.518045\pi$
$277$	−1.88598			−0.113317			−0.0566587	+	0.998394i	$0.518045\pi$
$278$	−5.78153	+	8.99623i	−0.346753	+	0.539558i
$279$	28.2376	−	0.968321i	1.69054	−	0.0579719i
$280$	−0.227001	−	0.497062i	−0.0135659	−	0.0297051i
$281$	−31.8722	−	9.35852i	−1.90134	−	0.558282i	−0.988791	−	0.149304i	$-0.952297\pi$
$281$	−31.8722	−	9.35852i	−1.90134	−	0.558282i	−0.912544	−	0.408978i	$-0.865885\pi$
$282$	−11.5624	+	3.61140i	−0.688532	+	0.215056i
$283$	17.7671	+	15.3953i	1.05615	+	0.915157i	0.996544	−	0.0830653i	$-0.0264710\pi$
$283$	17.7671	+	15.3953i	1.05615	+	0.915157i	0.0596032	+	0.998222i	$0.481016\pi$
$284$	−15.4443	−	2.22056i	−0.916453	−	0.131766i
$285$	1.54357	−	2.49484i	0.0914331	−	0.147781i
$286$	−9.09757	+	7.88309i	−0.537951	+	0.466137i
$287$	5.46914	−	3.51481i	0.322833	−	0.207472i
$288$	19.6247	−	9.78855i	1.15640	−	0.576796i
$289$	6.04123	+	6.97195i	0.355366	+	0.410115i
$290$	3.89694	−	1.14424i	0.228836	−	0.0671924i
$291$	6.50209	+	9.74606i	0.381160	+	0.571324i
$292$	2.10599	−	2.43045i	0.123244	−	0.142231i
$293$	1.32621	−	2.90400i	0.0774781	−	0.169653i	−0.866929	−	0.498431i	$-0.833910\pi$
$293$	1.32621	−	2.90400i	0.0774781	−	0.169653i	0.944407	+	0.328778i	$0.106637\pi$
$294$	3.43084	−	1.63845i	0.200091	−	0.0955561i
$295$	−0.659565	+	0.301213i	−0.0384014	+	0.0175373i
$296$	−1.24283	−	8.64405i	−0.0722379	−	0.502425i
$297$	−5.15985	+	0.265542i	−0.299405	+	0.0154083i
$298$		−	13.4246i		−	0.777668i
$299$	−7.54912	+	25.3501i	−0.436577	+	1.46604i
$300$	−15.9960	−	17.8334i	−0.923531	−	1.02961i
$301$	−10.4537	−	6.71819i	−0.602542	−	0.387230i
$302$	27.6468	−	3.97500i	1.59089	−	0.228736i
$303$	−10.4660	−	4.56453i	−0.601255	−	0.262225i
$304$	2.65667	−	9.04780i	0.152371	−	0.518927i
$305$	−0.736030	−	0.336134i	−0.0421449	−	0.0192470i
$306$	13.4567	−	12.4930i	0.769269	−	0.714176i
$307$	−2.76101	+	19.2032i	−0.157579	+	1.09599i	0.745498	+	0.666507i	$0.232211\pi$
$307$	−2.76101	+	19.2032i	−0.157579	+	1.09599i	−0.903077	+	0.429478i	$0.858698\pi$
$308$	0.789529	+	2.68889i	0.0449876	+	0.153214i
$309$	7.19948	+	0.909482i	0.409564	+	0.0517386i
$310$	3.39981	+	5.29021i	0.193096	+	0.300464i
$311$	−13.9872	−	21.7645i	−0.793143	−	1.23415i	−0.968344	−	0.249621i	$-0.919694\pi$
$311$	−13.9872	−	21.7645i	−0.793143	−	1.23415i	0.175201	−	0.984533i	$-0.443943\pi$
$312$	17.0256	+	2.15077i	0.963883	+	0.121764i
$313$	4.20409	+	14.3178i	0.237629	+	0.809290i	0.988808	+	0.149192i	$0.0476672\pi$
$313$	4.20409	+	14.3178i	0.237629	+	0.809290i	−0.751179	+	0.660098i	$0.770515\pi$
$314$	−1.25283	+	8.71363i	−0.0707013	+	0.491738i
$315$	−0.668769	+	0.620874i	−0.0376809	+	0.0349823i
$316$	−32.0344	−	14.6296i	−1.80207	−	0.822979i
$317$	4.07696	−	13.8848i	0.228985	−	0.779851i	−0.762197	−	0.647345i	$-0.775879\pi$
$317$	4.07696	−	13.8848i	0.228985	−	0.779851i	0.991182	−	0.132506i	$-0.0423024\pi$
$318$	19.4106	+	8.46556i	1.08850	+	0.474725i
$319$	−5.98666	+	0.860752i	−0.335189	+	0.0481929i
$320$	3.23948	+	2.08189i	0.181092	+	0.116381i
$321$	−1.17984	−	1.31536i	−0.0658522	−	0.0734164i
$322$	7.92949	+	6.92432i	0.441893	+	0.385878i
$323$		−	15.5265i		−	0.863915i
$324$	17.8851	+	17.9871i	0.993615	+	0.999281i
$325$	3.85190	+	26.7905i	0.213665	+	1.48607i
$326$	20.5131	−	9.36801i	1.13611	−	0.518846i
$327$	18.2458	−	8.71353i	1.00899	−	0.481859i
$328$	4.85162	−	10.6236i	0.267886	−	0.586588i
$329$	2.08641	−	2.40784i	0.115027	−	0.132749i
$330$	−0.638191	−	0.956592i	−0.0351313	−	0.0526586i
$331$	4.89393	−	1.43699i	0.268995	−	0.0789840i	−0.144454	−	0.989512i	$-0.546142\pi$
$331$	4.89393	−	1.43699i	0.268995	−	0.0789840i	0.413448	+	0.910528i	$0.364324\pi$
$332$	−18.9295	−	21.8458i	−1.03889	−	1.19894i
$333$	−13.0504	+	6.50940i	−0.715160	+	0.356713i
$334$	15.4970	−	9.95929i	0.847956	−	0.544948i
$335$	−1.89797	+	1.64460i	−0.103697	+	0.0898543i
$336$	−1.54326	+	2.49433i	−0.0841915	+	0.136077i
$337$	−2.62857	−	0.377932i	−0.143187	−	0.0205872i	0.0703484	−	0.997522i	$-0.477589\pi$
$337$	−2.62857	−	0.377932i	−0.143187	−	0.0205872i	−0.213536	+	0.976935i	$0.568498\pi$
$338$	−28.8956	−	25.0382i	−1.57172	−	1.36190i
$339$	23.2421	−	7.25942i	1.26234	−	0.394278i
$340$	2.29361	+	0.673465i	0.124389	+	0.0365238i
$341$	−3.89022	−	8.51839i	−0.210667	−	0.461297i
$342$	36.6476	−	1.25671i	1.98167	−	0.0679553i
$343$	−0.540641	+	0.841254i	−0.0291919	+	0.0454234i
$344$	−22.3232			−1.20358
$345$	−2.31215	−	1.01896i	−0.124482	−	0.0548591i
$346$	−34.6598			−1.86332
$347$	−12.5713	+	19.5614i	−0.674865	+	1.05011i	0.319853	+	0.947467i	$0.396366\pi$
$347$	−12.5713	+	19.5614i	−0.674865	+	1.05011i	−0.994718	+	0.102643i	$0.967270\pi$
$348$	22.7708	+	19.0576i	1.22064	+	1.02159i
$349$	−1.56172	−	3.41968i	−0.0835967	−	0.183051i	0.863217	−	0.504832i	$-0.168446\pi$
$349$	−1.56172	−	3.41968i	−0.0835967	−	0.183051i	−0.946814	+	0.321781i	$0.895718\pi$
$350$	10.3360	+	3.03491i	0.552480	+	0.162223i
$351$	−5.53099	−	28.1194i	−0.295222	−	1.50090i
$352$	−5.49330	−	4.75997i	−0.292794	−	0.253708i
$353$	−20.5854	−	2.95974i	−1.09565	−	0.157531i	−0.429296	−	0.903164i	$-0.641238\pi$
$353$	−20.5854	−	2.95974i	−1.09565	−	0.157531i	−0.666357	+	0.745633i	$0.732147\pi$
$354$	−7.70712	−	4.76843i	−0.409629	−	0.253439i
$355$	−1.27269	+	1.10279i	−0.0675472	+	0.0585300i
$356$	−32.5103	+	20.8931i	−1.72304	+	1.10733i
$357$	−1.28102	+	4.65654i	−0.0677987	+	0.246450i
$358$	−16.0505	−	18.5233i	−0.848296	−	0.978985i
$359$	2.89568	−	0.850248i	0.152828	−	0.0448744i	−0.204424	−	0.978883i	$-0.565532\pi$
$359$	2.89568	−	0.850248i	0.152828	−	0.0448744i	0.357252	+	0.934008i	$0.383714\pi$
$360$	−0.407674	+	1.58783i	−0.0214863	+	0.0836859i
$361$	7.86274	−	9.07409i	0.413828	−	0.477584i
$362$	−3.36701	+	7.37272i	−0.176966	+	0.387501i
$363$	−7.47261	−	15.6473i	−0.392210	−	0.821272i
$364$	−14.1395	+	6.45729i	−0.741111	+	0.338454i
$365$	−0.0493957	−	0.343555i	−0.00258549	−	0.0179825i
$366$	−1.61068	−	9.98459i	−0.0841917	−	0.521903i
$367$		−	11.3218i		−	0.590991i	−0.955344	−	0.295496i	$-0.904515\pi$
$367$		−	11.3218i		−	0.590991i	0.955344	−	0.295496i	$-0.0954847\pi$
$368$	−8.03436	−	1.18661i	−0.418820	−	0.0618565i
$369$	−19.3888	−	2.11240i	−1.00934	−	0.109967i
$370$	−2.73061	−	1.75485i	−0.141957	−	0.0912305i
$371$	−5.51311	+	0.792666i	−0.286227	+	0.0411532i
$372$	−18.3793	+	42.1417i	−0.952921	+	2.18495i
$373$	−3.89547	+	13.2667i	−0.201700	+	0.686926i	0.795063	+	0.606527i	$0.207438\pi$
$373$	−3.89547	+	13.2667i	−0.201700	+	0.686926i	−0.996763	+	0.0803993i	$0.974380\pi$
$374$	−5.53593	−	2.52818i	−0.286256	−	0.130729i
$375$	−5.21906	+	0.0894594i	−0.269511	+	0.00461966i
$376$	0.814540	−	5.66525i	0.0420067	−	0.292163i
$377$	−9.45153	−	32.1889i	−0.486778	−	1.65782i
$378$	−11.0947	−	2.64673i	−0.570648	−	0.136133i
$379$	19.4348	+	30.2411i	0.998296	+	1.55338i	0.822352	+	0.568979i	$0.192661\pi$
$379$	19.4348	+	30.2411i	0.998296	+	1.55338i	0.175944	+	0.984400i	$0.443702\pi$
$380$	2.58090	+	4.01596i	0.132397	+	0.206014i
$381$	−3.26886	+	25.8764i	−0.167469	+	1.32569i
$382$	−2.70425	−	9.20984i	−0.138362	−	0.471217i
$383$	−5.26688	+	36.6319i	−0.269125	+	1.87181i	0.187669	+	0.982232i	$0.439907\pi$
$383$	−5.26688	+	36.6319i	−0.269125	+	1.87181i	−0.456794	+	0.889573i	$0.651002\pi$
$384$	0.390895	+	22.8048i	0.0199478	+	1.16375i
$385$	0.275124	+	0.125645i	0.0140216	+	0.00640345i
$386$	5.77430	−	19.6655i	0.293904	−	1.00095i
$387$	11.7224	+	35.3880i	0.595884	+	1.79887i
$388$	−18.8701	+	2.71311i	−0.957984	+	0.137737i
$389$	−2.37354	−	1.52538i	−0.120343	−	0.0773398i	0.479085	−	0.877769i	$-0.340969\pi$
$389$	−2.37354	−	1.52538i	−0.120343	−	0.0773398i	−0.599428	+	0.800429i	$0.704605\pi$
$390$	4.74817	−	4.25896i	0.240433	−	0.215661i
$391$	−13.2434	+	1.85234i	−0.669750	+	0.0936770i
$392$			1.79644i			0.0907338i
$393$	30.4728	−	4.91577i	1.53715	−	0.247968i
$394$	3.39080	+	23.5835i	0.170826	+	1.18812i
$395$	−3.45738	+	1.57893i	−0.173960	+	0.0794448i
$396$	3.22834	−	7.76268i	0.162230	−	0.390089i
$397$	−1.87151	+	4.09803i	−0.0939284	+	0.205674i	−0.950764	−	0.309915i	$-0.899700\pi$
$397$	−1.87151	+	4.09803i	−0.0939284	+	0.205674i	0.856836	+	0.515589i	$0.172427\pi$
$398$	−28.1640	+	32.5030i	−1.41173	+	1.62923i
$399$	−8.02308	+	5.35261i	−0.401656	+	0.267965i
$400$	−7.97394	+	2.34136i	−0.398697	+	0.117068i
$401$	11.7198	+	13.5254i	0.585261	+	0.675427i	0.968727	−	0.248128i	$-0.0798153\pi$
$401$	11.7198	+	13.5254i	0.585261	+	0.675427i	−0.383466	+	0.923555i	$0.625270\pi$
$402$	−30.2656	−	8.32610i	−1.50951	−	0.415268i
$403$	43.6974	−	28.0826i	2.17672	−	1.39890i
$404$	14.0414	−	12.1669i	0.698585	−	0.605328i
$405$	2.73120	−	0.187537i	0.135714	−	0.00931877i
$406$	−13.2162	−	1.90020i	−0.655908	−	0.0943054i
$407$	3.65305	+	3.16539i	0.181075	+	0.156903i
$408$	2.58661	+	8.28140i	0.128056	+	0.409990i
$409$	−23.4051	−	6.87234i	−1.15731	−	0.339816i	−0.353921	−	0.935276i	$-0.615152\pi$
$409$	−23.4051	−	6.87234i	−1.15731	−	0.339816i	−0.803385	+	0.595460i	$0.796970\pi$
$410$	−1.80326	−	3.94859i	−0.0890567	−	0.195007i
$411$	18.2220	−	21.7723i	0.898825	−	1.07395i
$412$	−6.38394	+	9.93360i	−0.314514	+	0.489393i
$413$	2.38374			0.117296
$414$	−5.44407	−	31.1090i	−0.267561	−	1.52892i
$415$	−3.11976			−0.153143
$416$	21.7972	−	33.9172i	1.06870	−	1.66293i
$417$	−5.41566	+	6.47084i	−0.265206	+	0.316878i
$418$	−5.04883	−	11.0554i	−0.246946	−	0.540737i
$419$	−25.1041	−	7.37123i	−1.22642	−	0.360108i	−0.396520	−	0.918026i	$-0.629782\pi$
$419$	−25.1041	−	7.37123i	−1.22642	−	0.360108i	−0.829896	+	0.557918i	$0.811600\pi$
$420$	−0.442699	−	1.41736i	−0.0216015	−	0.0691603i
$421$	12.4198	+	10.7618i	0.605304	+	0.524499i	0.902708	−	0.430253i	$-0.141576\pi$
$421$	12.4198	+	10.7618i	0.605304	+	0.524499i	−0.297405	+	0.954751i	$0.596121\pi$
$422$	27.5298	+	3.95819i	1.34013	+	0.192682i
$423$	−9.40864	+	1.68370i	−0.457463	+	0.0818642i
$424$	−7.56189	+	6.55241i	−0.367238	+	0.318213i
$425$	−11.5114	+	7.39794i	−0.558386	+	0.358853i
$426$	−20.2946	−	5.58307i	−0.983278	−	0.270501i
$427$	1.74199	+	2.01037i	0.0843009	+	0.0972884i
$428$	2.75875	−	0.810043i	0.133349	−	0.0391549i
$429$	−7.90150	+	5.27149i	−0.381488	+	0.254510i
$430$	−5.43346	+	6.27054i	−0.262025	+	0.302392i
$431$	12.0541	−	26.3947i	0.580624	−	1.27139i	−0.360320	−	0.932829i	$-0.617332\pi$
$431$	12.0541	−	26.3947i	0.580624	−	1.27139i	0.940944	−	0.338561i	$-0.109940\pi$
$432$	8.30443	−	2.90974i	0.399547	−	0.139995i
$433$	−2.71484	+	1.23982i	−0.130467	+	0.0595822i	−0.479579	−	0.877499i	$-0.659211\pi$
$433$	−2.71484	+	1.23982i	−0.130467	+	0.0595822i	0.349112	+	0.937081i	$0.386483\pi$
$434$	−2.94214	−	20.4630i	−0.141227	−	0.982257i
$435$	3.16383	−	0.510379i	0.151694	−	0.0244708i
$436$			32.9014i			1.57569i
$437$	−22.4101	−	14.5238i	−1.07202	−	0.694767i
$438$	3.22949	−	2.89675i	0.154311	−	0.138412i
$439$	−8.91671	−	5.73042i	−0.425571	−	0.273498i	0.310275	−	0.950647i	$-0.399579\pi$
$439$	−8.91671	−	5.73042i	−0.425571	−	0.273498i	−0.735846	+	0.677149i	$0.763215\pi$
$440$	0.537813	−	0.0773259i	0.0256392	−	0.00368637i
$441$	2.84782	−	0.943352i	0.135611	−	0.0449215i
$442$	9.51041	−	32.3895i	0.452364	−	1.54061i
$443$	17.8836	+	8.16715i	0.849674	+	0.388033i	0.792161	−	0.610312i	$-0.208956\pi$
$443$	17.8836	+	8.16715i	0.849674	+	0.388033i	0.0575126	+	0.998345i	$0.481683\pi$
$444$	−0.406706	−	23.7272i	−0.0193014	−	1.12604i
$445$	−0.593575	+	4.12841i	−0.0281382	+	0.195705i
$446$	5.96232	+	20.3058i	0.282324	+	0.961507i
$447$	1.32760	−	10.5093i	0.0627933	−	0.497073i
$448$	−6.84423	−	10.6498i	−0.323359	−	0.503157i
$449$	−16.0256	−	24.9363i	−0.756295	−	1.17682i	−0.979382	−	0.202019i	$-0.935250\pi$
$449$	−16.0256	−	24.9363i	−0.756295	−	1.17682i	0.223087	−	0.974799i	$-0.428387\pi$
$450$	−18.3933	−	26.5720i	−0.867070	−	1.25262i
$451$	1.82121	+	6.20246i	0.0857573	+	0.292062i
$452$	−5.63871	+	39.2181i	−0.265223	+	1.84466i
$453$	22.0360	−	0.377717i	1.03534	−	0.0177467i
$454$	−35.2351	−	16.0913i	−1.65367	−	0.755204i
$455$	−0.472646	+	1.60969i	−0.0221580	+	0.0754632i
$456$	−6.92636	+	15.8814i	−0.324356	+	0.743715i
$457$	18.3838	−	2.64320i	0.859960	−	0.123644i	0.301794	−	0.953373i	$-0.402414\pi$
$457$	18.3838	−	2.64320i	0.859960	−	0.123644i	0.558166	+	0.829730i	$0.311505\pi$
$458$	10.3044	+	6.62220i	0.481491	+	0.309435i
$459$	11.7699	−	8.44920i	0.549371	−	0.394375i
$460$	3.11754	−	2.68052i	0.145356	−	0.124980i
$461$		−	0.492022i		−	0.0229158i	−0.999934	−	0.0114579i	$-0.996353\pi$
$461$		−	0.492022i		−	0.0229158i	0.999934	−	0.0114579i	$-0.00364724\pi$
$462$	0.602064	+	3.73218i	0.0280105	+	0.173637i
$463$	−0.594050	−	4.13171i	−0.0276078	−	0.192017i	0.971350	−	0.237652i	$-0.0763778\pi$
$463$	−0.594050	−	4.13171i	−0.0276078	−	0.192017i	−0.998958	+	0.0456355i	$0.985469\pi$
$464$	9.36994	−	4.27911i	0.434989	−	0.198653i
$465$	2.13834	+	4.47759i	0.0991630	+	0.207643i
$466$	7.00956	−	15.3488i	0.324712	−	0.711019i
$467$	−11.5975	+	13.3842i	−0.536666	+	0.619346i	−0.957724	−	0.287688i	$-0.907113\pi$
$467$	−11.5975	+	13.3842i	−0.536666	+	0.619346i	0.421058	+	0.907034i	$0.361659\pi$
$468$	45.1676	+	11.5968i	2.08787	+	0.536060i
$469$	7.92176	−	2.32604i	0.365793	−	0.107406i
$470$	−1.39310	−	1.60773i	−0.0642590	−	0.0741588i
$471$	−1.84248	+	6.69746i	−0.0848969	+	0.308603i
$472$	3.60245	−	2.31516i	0.165816	−	0.106564i
$473$	9.33794	−	8.09137i	0.429359	−	0.372042i
$474$	−40.4000	−	24.9957i	−1.85563	−	1.14809i
$475$	−27.0485	−	3.88898i	−1.24107	−	0.178439i
$476$	−5.93914	−	5.14629i	−0.272220	−	0.235880i
$477$	14.3582	+	8.54673i	0.657417	+	0.391328i
$478$	−38.5616	−	11.3227i	−1.76377	−	0.517889i
$479$	−1.21588	−	2.66240i	−0.0555549	−	0.121648i	0.879819	−	0.475309i	$-0.157664\pi$
$479$	−1.21588	−	2.66240i	−0.0555549	−	0.121648i	−0.935374	+	0.353661i	$0.884937\pi$
$480$	2.95350	+	2.47188i	0.134808	+	0.112825i
$481$	−14.4952	+	22.5550i	−0.660924	+	1.02842i
$482$	21.4538			0.977192
$483$	5.52273	+	6.20479i	0.251293	+	0.282328i
$484$	28.2158			1.28254
$485$	−1.11239	+	1.73091i	−0.0505111	+	0.0785968i
$486$	20.8956	+	27.0969i	0.947842	+	1.22914i
$487$	−11.3825	−	24.9242i	−0.515791	−	1.12943i	−0.971008	−	0.239045i	$-0.923166\pi$
$487$	−11.3825	−	24.9242i	−0.515791	−	1.12943i	0.455217	−	0.890380i	$-0.349562\pi$
$488$	4.58512	+	1.34631i	0.207559	+	0.0609448i
$489$	16.9848	−	5.30503i	0.768081	−	0.239902i
$490$	0.504617	+	0.437253i	0.0227963	+	0.0197531i
$491$	−9.37830	−	1.34840i	−0.423237	−	0.0608523i	−0.0725941	−	0.997362i	$-0.523128\pi$
$491$	−9.37830	−	1.34840i	−0.423237	−	0.0608523i	−0.350643	+	0.936509i	$0.614037\pi$
$492$	16.6978	−	26.9883i	0.752794	−	1.21673i
$493$	12.8180	−	11.1069i	0.577294	−	0.500228i
$494$	56.7117	−	36.4464i	2.55158	−	1.63980i
$495$	−0.405000	−	0.811968i	−0.0182034	−	0.0364953i
$496$	10.4444	+	12.0535i	0.468968	+	0.541218i
$497$	5.31194	−	1.55973i	0.238273	−	0.0699632i
$498$	−21.6410	−	32.4379i	−0.969754	−	1.45358i
$499$	2.07867	−	2.39892i	0.0930542	−	0.107390i	−0.707313	−	0.706901i	$-0.750093\pi$
$499$	2.07867	−	2.39892i	0.0930542	−	0.107390i	0.800367	+	0.599511i	$0.204638\pi$
$500$	3.52841	−	7.72614i	0.157795	−	0.345524i
$501$	13.1165	−	6.26397i	0.586002	−	0.279854i
$502$	−55.8189	+	25.4916i	−2.49132	+	1.13775i
$503$	−3.34169	−	23.2420i	−0.148999	−	1.03631i	−0.917863	−	0.396897i	$-0.870087\pi$
$503$	−3.34169	−	23.2420i	−0.148999	−	1.03631i	0.768864	−	0.639412i	$-0.220822\pi$
$504$	3.38759	−	4.19153i	0.150895	−	0.186706i
$505$		−	2.00523i		−	0.0892314i
$506$	−8.82748	+	5.62539i	−0.392429	+	0.250079i
$507$	−20.1445	−	22.4584i	−0.894648	−	0.997413i
$508$	−35.7033	−	22.9451i	−1.58408	−	1.01803i
$509$	−12.3677	+	1.77820i	−0.548187	+	0.0788174i	−0.410843	−	0.911706i	$-0.634766\pi$
$509$	−12.3677	+	1.77820i	−0.548187	+	0.0788174i	−0.137344	+	0.990523i	$0.543857\pi$
$510$	2.95581	+	1.28912i	0.130886	+	0.0570831i
$511$	−0.321472	+	1.09483i	−0.0142211	+	0.0484326i
$512$	16.7952	+	7.67012i	0.742251	+	0.338974i
$513$	28.8134	+	2.64038i	1.27214	+	0.116576i
$514$	−9.17843	+	63.8374i	−0.404843	+	2.81575i
$515$	0.359044	+	1.22279i	0.0158214	+	0.0538827i
$516$	−60.1821	−	7.60257i	−2.64937	−	0.334685i
$517$	1.71273	+	2.66506i	0.0753258	+	0.117209i
$518$	5.76910	+	8.97690i	0.253480	+	0.394422i
$519$	−27.1330	−	3.42761i	−1.19101	−	0.150455i
$520$	0.849080	+	2.89170i	0.0372346	+	0.126809i
$521$	−3.11844	+	21.6892i	−0.136621	+	0.950223i	0.800030	+	0.599960i	$0.204817\pi$
$521$	−3.11844	+	21.6892i	−0.136621	+	0.950223i	−0.936651	+	0.350263i	$0.886092\pi$
$522$	27.2534	+	29.3557i	1.19285	+	1.28487i
$523$	−13.4719	−	6.15241i	−0.589085	−	0.269026i	0.0984917	−	0.995138i	$-0.468598\pi$
$523$	−13.4719	−	6.15241i	−0.589085	−	0.269026i	−0.687577	+	0.726112i	$0.741325\pi$
$524$	−14.1504	+	48.1918i	−0.618162	+	2.10527i
$525$	7.79125	+	3.39799i	0.340038	+	0.148301i
$526$	7.64232	−	1.09880i	0.333221	−	0.0479100i
$527$	22.0919	+	14.1976i	0.962339	+	0.618458i
$528$	−1.94740	−	2.17109i	−0.0847498	−	0.0944847i
$529$	−9.71463	+	20.8477i	−0.422375	+	0.906421i
$530$			3.71898i			0.161542i
$531$	−5.56186	−	4.49508i	−0.241364	−	0.195070i
$532$	−2.23347	−	15.5341i	−0.0968331	−	0.673489i
$533$	−32.6156	+	14.8950i	−1.41274	+	0.645175i
$534$	−47.0429	+	22.4660i	−2.03574	+	0.972198i
$535$	0.128909	−	0.282272i	0.00557324	−	0.0122037i
$536$	9.71272	−	11.2091i	0.419526	−	0.484158i
$537$	−10.7331	−	16.0880i	−0.463168	−	0.694248i
$538$	−4.25375	+	1.24901i	−0.183392	+	0.0538488i
$539$	−0.651146	−	0.751463i	−0.0280469	−	0.0323678i
$540$	−1.63983	+	4.14187i	−0.0705672	+	0.178238i
$541$	15.3475	−	9.86321i	0.659838	−	0.424052i	−0.167411	−	0.985887i	$-0.553541\pi$
$541$	15.3475	−	9.86321i	0.659838	−	0.424052i	0.827249	+	0.561835i	$0.189904\pi$
$542$	18.9307	−	16.4036i	0.813145	−	0.704594i
$543$	−3.36493	+	5.43867i	−0.144403	+	0.233396i
$544$	20.1756	+	2.90082i	0.865023	+	0.124372i
$545$	2.68363	+	2.32538i	0.114954	+	0.0996084i
$546$	−20.0154	+	6.25161i	−0.856582	+	0.267544i
$547$	5.75381	+	1.68947i	0.246015	+	0.0722365i	0.402415	−	0.915457i	$-0.368171\pi$
$547$	5.75381	+	1.68947i	0.246015	+	0.0722365i	−0.156400	+	0.987694i	$0.549989\pi$
$548$	19.1916	+	42.0237i	0.819824	+	1.79516i
$549$	−0.273498	−	7.97559i	−0.0116726	−	0.340390i
$550$	−5.79092	+	9.01085i	−0.246926	+	0.384224i
$551$	33.8709			1.44295
$552$	14.3725	+	4.01322i	0.611736	+	0.170814i
$553$	12.4954			0.531357
$554$	2.23819	−	3.48269i	0.0950914	−	0.147965i
$555$	−1.96408	−	1.64380i	−0.0833705	−	0.0697755i
$556$	−5.70382	−	12.4896i	−0.241896	−	0.529678i
$557$	0.0511684	+	0.0150244i	0.00216807	+	0.000636604i	0.282816	−	0.959174i	$-0.408731\pi$
$557$	0.0511684	+	0.0150244i	0.00216807	+	0.000636604i	−0.280648	+	0.959811i	$0.590549\pi$
$558$	−31.7229	+	53.2934i	−1.34294	+	2.25609i
$559$	51.7950	+	44.8807i	2.19070	+	1.89825i
$560$	−0.509874	−	0.0733087i	−0.0215461	−	0.00309786i
$561$	−4.08372	−	2.52661i	−0.172415	−	0.106674i
$562$	55.1060	−	47.7496i	2.32451	−	2.01420i
$563$	34.9598	−	22.4673i	1.47338	−	0.946884i	0.475644	−	0.879638i	$-0.342215\pi$
$563$	34.9598	−	22.4673i	1.47338	−	0.946884i	0.997736	−	0.0672467i	$-0.0214215\pi$
$564$	4.12537	−	14.9958i	0.173709	−	0.631438i
$565$	2.80033	+	3.23176i	0.117811	+	0.135961i
$566$	−49.5145	+	14.5388i	−2.08125	+	0.611110i
$567$	−8.42357	−	3.16914i	−0.353757	−	0.133091i
$568$	6.51287	−	7.51625i	0.273274	−	0.315375i
$569$	−1.71560	+	3.75663i	−0.0719215	+	0.157486i	−0.942178	−	0.335112i	$-0.891226\pi$
$569$	−1.71560	+	3.75663i	−0.0719215	+	0.157486i	0.870257	+	0.492599i	$0.163953\pi$
$570$	2.77519	+	5.81114i	0.116240	+	0.243402i
$571$	−24.5419	+	11.2079i	−1.02705	+	0.469037i	−0.856409	−	0.516297i	$-0.827310\pi$
$571$	−24.5419	+	11.2079i	−1.02705	+	0.469037i	−0.170637	+	0.985334i	$0.554583\pi$
$572$	−2.19962	−	15.2987i	−0.0919708	−	0.639671i
$573$	−1.20620	−	7.47724i	−0.0503899	−	0.312366i
$574$			14.2706i			0.595645i
$575$	−0.0902013	+	23.5352i	−0.00376165	+	0.981488i
$576$	−4.11338	+	37.7550i	−0.171391	+	1.57313i
$577$	31.4557	+	20.2154i	1.30952	+	0.841576i	0.994214	−	0.107415i	$-0.0342572\pi$
$577$	31.4557	+	20.2154i	1.30952	+	0.841576i	0.315304	+	0.948991i	$0.397894\pi$
$578$	−20.0440	+	2.88189i	−0.833720	+	0.119871i
$579$	6.46511	−	14.8238i	0.268681	−	0.616057i
$580$	−1.46916	+	5.00350i	−0.0610036	+	0.207759i
$581$	9.32940	+	4.26060i	0.387049	+	0.176759i
$582$	−25.7137	+	0.440755i	−1.06587	+	0.0182699i
$583$	0.788170	−	5.48184i	0.0326427	−	0.227035i
$584$	0.577505	+	1.96680i	0.0238973	+	0.0813868i
$585$	4.13823	−	2.86451i	0.171095	−	0.118433i
$586$	3.78870	+	5.89533i	0.156510	+	0.243534i
$587$	−10.0966	−	15.7106i	−0.416730	−	0.648444i	0.567900	−	0.823097i	$-0.307756\pi$
$587$	−10.0966	−	15.7106i	−0.416730	−	0.648444i	−0.984630	+	0.174653i	$0.944120\pi$
$588$	−0.611811	+	4.84311i	−0.0252306	+	0.199726i
$589$	14.7750	+	50.3190i	0.608793	+	2.07336i
$590$	0.226513	−	1.57543i	0.00932539	−	0.0648595i
$591$	0.322204	+	18.7974i	0.0132537	+	0.773221i
$592$	−7.48837	−	3.41982i	−0.307770	−	0.140554i
$593$	−8.14919	+	27.7536i	−0.334647	+	1.13970i	0.604619	+	0.796515i	$0.293325\pi$
$593$	−8.14919	+	27.7536i	−0.334647	+	1.13970i	−0.939266	+	0.343189i	$0.888493\pi$
$594$	5.63311	−	9.84343i	0.231129	−	0.403881i
$595$	−0.839525	+	0.120706i	−0.0344172	+	0.00494844i
$596$	14.5004	+	9.31883i	0.593959	+	0.381714i
$597$	−25.2621	+	22.6593i	−1.03391	+	0.927385i
$598$	−37.8532	−	44.0247i	−1.54793	−	1.80030i
$599$			12.4688i			0.509459i	0.967012	+	0.254730i	$0.0819865\pi$
$599$			12.4688i			0.509459i	−0.967012	+	0.254730i	$0.918013\pi$
$600$	15.0748	−	2.43182i	0.615427	−	0.0992787i
$601$	−5.74996	−	39.9918i	−0.234546	−	1.63130i	−0.678041	−	0.735024i	$-0.737171\pi$
$601$	−5.74996	−	39.9918i	−0.234546	−	1.63130i	0.443495	−	0.896277i	$-0.353738\pi$
$602$	24.8119	−	11.3312i	1.01126	−	0.461826i
$603$	−22.8697	−	9.51104i	−0.931325	−	0.387319i
$604$	−14.8977	+	32.6215i	−0.606180	+	1.32735i
$605$	1.99422	−	2.30145i	0.0810765	−	0.0935672i
$606$	20.8495	−	13.9097i	0.846952	−	0.565045i
$607$	33.3128	−	9.78152i	1.35212	−	0.397020i	0.476145	−	0.879367i	$-0.342034\pi$
$607$	33.3128	−	9.78152i	1.35212	−	0.397020i	0.875980	+	0.482347i	$0.160216\pi$
$608$	26.6565	+	30.7632i	1.08106	+	1.24761i
$609$	−10.1582	−	2.79453i	−0.411631	−	0.113240i
$610$	1.49420	−	0.960262i	0.0604982	−	0.0388799i
$611$	−13.2799	+	11.5071i	−0.537247	+	0.465528i
$612$	4.15298	+	23.2072i	0.167874	+	0.938094i
$613$	3.27543	+	0.470936i	0.132294	+	0.0190209i	0.208143	−	0.978098i	$-0.433258\pi$
$613$	3.27543	+	0.470936i	0.132294	+	0.0190209i	−0.0758499	+	0.997119i	$0.524167\pi$
$614$	−32.1844	−	27.8880i	−1.29886	−	1.12547i
$615$	−1.02117	−	3.26943i	−0.0411777	−	0.131836i
$616$	−1.71389	−	0.503244i	−0.0690547	−	0.0202763i
$617$	15.1365	+	33.1443i	0.609373	+	1.33434i	0.923002	+	0.384795i	$0.125728\pi$
$617$	15.1365	+	33.1443i	0.609373	+	1.33434i	−0.313630	+	0.949545i	$0.601545\pi$
$618$	−10.2235	+	12.2154i	−0.411248	+	0.491375i
$619$	−16.3172	+	25.3900i	−0.655843	+	1.02051i	0.340918	+	0.940093i	$0.389262\pi$
$619$	−16.3172	+	25.3900i	−0.655843	+	1.02051i	−0.996761	+	0.0804188i	$0.974374\pi$
$620$	−8.07414			−0.324265
$621$	−1.18537	−	24.8917i	−0.0475671	−	0.998868i
$622$	56.7902			2.27708
$623$	7.41314	−	11.5351i	0.297001	−	0.462143i
$624$	10.3827	−	12.4056i	0.415639	−	0.496621i
$625$	9.81238	+	21.4861i	0.392495	+	0.859445i
$626$	−31.4288	−	9.22832i	−1.25615	−	0.368838i
$627$	−2.85912	−	9.15388i	−0.114182	−	0.365571i
$628$	−8.54221	−	7.40187i	−0.340871	−	0.295367i
$629$	−13.4168	−	1.92905i	−0.534964	−	0.0769161i
$630$	−0.352856	−	1.97179i	−0.0140581	−	0.0785579i
$631$	−5.95338	+	5.15863i	−0.237000	+	0.205362i	−0.765261	−	0.643720i	$-0.777390\pi$
$631$	−5.95338	+	5.15863i	−0.237000	+	0.205362i	0.528260	+	0.849082i	$0.322844\pi$
$632$	18.8837	−	12.1358i	0.751155	−	0.482738i
$633$	21.1599	+	5.82112i	0.841032	+	0.231369i
$634$	20.8017	+	24.0065i	0.826142	+	0.953418i
$635$	−4.39496	+	1.29048i	−0.174409	+	0.0512110i
$636$	−22.6180	+	15.0896i	−0.896863	+	0.598343i
$637$	3.61173	−	4.16816i	0.143102	−	0.165149i
$638$	5.51520	−	12.0766i	0.218349	−	0.478117i
$639$	−15.3353	−	6.37763i	−0.606654	−	0.252295i
$640$	−3.64358	+	1.66397i	−0.144025	+	0.0657741i
$641$	−6.71314	−	46.6909i	−0.265153	−	1.84418i	−0.492431	−	0.870351i	$-0.663892\pi$
$641$	−6.71314	−	46.6909i	−0.265153	−	1.84418i	0.227278	−	0.973830i	$-0.427017\pi$
$642$	3.82915	−	0.617707i	0.151125	−	0.0243789i
$643$			22.2960i			0.879269i	0.898177	+	0.439634i	$0.144892\pi$
$643$			22.2960i			0.879269i	−0.898177	+	0.439634i	$0.855108\pi$
$644$	−12.9835	+	3.75831i	−0.511622	+	0.148098i
$645$	−4.87363	+	4.37149i	−0.191899	+	0.172127i
$646$	28.6715	+	18.4260i	1.12806	+	0.724963i
$647$	15.4736	−	2.22477i	0.608332	−	0.0874649i	0.168737	−	0.985661i	$-0.446031\pi$
$647$	15.4736	−	2.22477i	0.608332	−	0.0874649i	0.439595	+	0.898196i	$0.355122\pi$
$648$	−15.8082	+	3.39181i	−0.621003	+	0.133243i
$649$	−0.667769	+	2.27421i	−0.0262122	+	0.0892706i
$650$	−54.0433	−	24.6807i	−2.11975	−	0.968058i
$651$	−0.279571	−	16.3102i	−0.0109573	−	0.639247i
$652$	−4.12065	+	28.6597i	−0.161377	+	1.12240i
$653$	−8.81046	−	30.0057i	−0.344780	−	1.17421i	−0.931292	−	0.364272i	$-0.881318\pi$
$653$	−8.81046	−	30.0057i	−0.344780	−	1.17421i	0.586513	−	0.809940i	$-0.300500\pi$
$654$	−5.56262	+	44.0338i	−0.217516	+	1.72186i
$655$	2.93070	+	4.56026i	0.114512	+	0.178184i
$656$	−5.95216	−	9.26174i	−0.232393	−	0.361610i
$657$	2.81463	−	1.94831i	0.109809	−	0.0760108i
$658$	1.97033	+	6.71032i	0.0768114	+	0.261595i
$659$	3.46332	−	24.0879i	0.134912	−	0.938333i	−0.804111	−	0.594479i	$-0.797358\pi$
$659$	3.46332	−	24.0879i	0.134912	−	0.938333i	0.939023	−	0.343854i	$-0.111733\pi$
$660$	1.47625	−	0.0253043i	0.0574630	−	0.000984968i
$661$	19.9117	+	9.09337i	0.774476	+	0.353691i	0.763131	−	0.646244i	$-0.223661\pi$
$661$	19.9117	+	9.09337i	0.774476	+	0.353691i	0.0113453	+	0.999936i	$0.496389\pi$
$662$	−3.15431	+	10.7426i	−0.122596	+	0.417523i
$663$	10.6482	−	24.4152i	0.413541	−	0.948207i
$664$	18.2372	−	2.62211i	0.707739	−	0.101757i
$665$	−1.42491	−	0.915734i	−0.0552557	−	0.0355107i
$666$	3.46723	−	31.8243i	0.134352	−	1.23317i
$667$	−4.04087	−	28.8905i	−0.156463	−	1.11864i
$668$			23.6521i			0.915128i
$669$	2.65943	+	16.4858i	0.102819	+	0.637376i
$670$	−0.784537	−	5.45658i	−0.0303093	−	0.210806i
$671$	−2.40598	+	1.09878i	−0.0928819	+	0.0424178i
$672$	−5.45641	−	11.4255i	−0.210486	−	0.440749i
$673$	7.66072	−	16.7746i	0.295299	−	0.646614i	−0.702587	−	0.711597i	$-0.747972\pi$
$673$	7.66072	−	16.7746i	0.295299	−	0.646614i	0.997886	+	0.0649830i	$0.0206993\pi$
$674$	3.81736	−	4.40547i	0.147039	−	0.169692i
$675$	−11.7712	−	22.6205i	−0.453074	−	0.870664i
$676$	47.1028	−	13.8306i	1.81164	−	0.531947i
$677$	−11.6507	−	13.4456i	−0.447771	−	0.516755i	0.486325	−	0.873778i	$-0.338337\pi$
$677$	−11.6507	−	13.4456i	−0.447771	−	0.516755i	−0.934096	+	0.357023i	$0.883792\pi$
$678$	−14.1772	+	51.5345i	−0.544472	+	1.97917i
$679$	5.69040	−	3.65700i	0.218378	−	0.140343i
$680$	−1.15151	+	0.997787i	−0.0441583	+	0.0382634i
$681$	−25.9921	−	16.0814i	−0.996018	−	0.616241i
$682$	20.3470	+	2.92545i	0.779126	+	0.112021i
$683$	28.3187	+	24.5383i	1.08359	+	0.938932i	0.998350	−	0.0574291i	$-0.0182903\pi$
$683$	28.3187	+	24.5383i	1.08359	+	0.938932i	0.0852354	+	0.996361i	$0.472836\pi$
$684$	−24.0818	+	40.4566i	−0.920792	+	1.54690i
$685$	4.78412	+	1.40474i	0.182792	+	0.0536725i
$686$	−0.911871	−	1.99672i	−0.0348154	−	0.0762351i
$687$	7.41174	+	6.20314i	0.282776	+	0.236664i
$688$	−11.3769	+	17.7029i	−0.433742	+	0.674915i
$689$	30.7190			1.17030
$690$	4.62558	−	3.06041i	0.176093	−	0.116508i
$691$	−28.2748			−1.07562			−0.537811	−	0.843065i	$-0.680749\pi$
$691$	−28.2748			−1.07562			−0.537811	+	0.843065i	$0.680749\pi$
$692$	24.0594	−	37.4372i	0.914603	−	1.42315i
$693$	0.102232	+	2.98123i	0.00388347	+	0.113248i
$694$	−21.2034	−	46.4290i	−0.804871	−	1.76242i
$695$	−1.42186	−	0.417496i	−0.0539342	−	0.0158365i
$696$	−18.0658	+	5.64267i	−0.684783	+	0.213885i
$697$	−13.6998	−	11.8710i	−0.518917	−	0.449645i
$698$	8.16822	+	1.17441i	0.309172	+	0.0444522i
$699$	7.00523	−	11.3224i	0.264962	−	0.428253i
$700$	−10.4529	+	9.05750i	−0.395083	+	0.342341i
$701$	37.8039	−	24.2951i	1.42783	−	0.917612i	0.427927	−	0.903813i	$-0.359244\pi$
$701$	37.8039	−	24.2951i	1.42783	−	0.917612i	0.999905	−	0.0137990i	$-0.00439248\pi$
$702$	58.4898	+	23.1571i	2.20755	+	0.874008i
$703$	−17.7266	−	20.4576i	−0.668571	−	0.771572i
$704$	12.0778	−	3.54636i	0.455199	−	0.133658i
$705$	−0.931580	−	1.39636i	−0.0350853	−	0.0525898i
$706$	29.8953	−	34.5011i	1.12513	−	1.29846i
$707$	−2.73850	+	5.99648i	−0.102992	+	0.225521i
$708$	10.5005	−	5.01466i	0.394633	−	0.188463i
$709$	38.9917	−	17.8069i	1.46437	−	0.668753i	0.485684	−	0.874135i	$-0.338571\pi$
$709$	38.9917	−	17.8069i	1.46437	−	0.668753i	0.978682	+	0.205381i	$0.0658434\pi$
$710$	−0.526072	−	3.65891i	−0.0197431	−	0.137316i
$711$	−29.1548	−	23.5628i	−1.09339	−	0.883675i
$712$		−	24.6323i		−	0.923135i
$713$	41.1574	−	18.6057i	1.54136	−	0.696787i
$714$	−7.07861	−	7.89171i	−0.264911	−	0.295340i
$715$	−1.40332	−	0.901858i	−0.0524811	−	0.0337276i
$716$	31.1492	−	4.47858i	1.16410	−	0.167372i
$717$	−29.0677	−	12.6773i	−1.08555	−	0.473443i
$718$	−1.86637	+	6.35626i	−0.0696521	+	0.237213i
$719$	36.2717	+	16.5647i	1.35271	+	0.617760i	0.954135	−	0.299378i	$-0.0967792\pi$
$719$	36.2717	+	16.5647i	1.35271	+	0.617760i	0.398570	+	0.917138i	$0.369506\pi$
$720$	1.05142	+	1.13253i	0.0391841	+	0.0422069i
$721$	0.596250	−	4.14701i	0.0222055	−	0.154443i
$722$	7.42528	+	25.2882i	0.276340	+	0.941129i
$723$	16.7948	+	2.12162i	0.624605	+	0.0789039i
$724$	−5.62627	−	8.75465i	−0.209099	−	0.325364i
$725$	−16.1386	−	25.1121i	−0.599371	−	0.932640i
$726$	37.7628	+	4.77043i	1.40151	+	0.177047i
$727$	−9.14334	−	31.1394i	−0.339108	−	1.15490i	−0.935831	−	0.352448i	$-0.885349\pi$
$727$	−9.14334	−	31.1394i	−0.339108	−	1.15490i	0.596723	−	0.802447i	$-0.296469\pi$
$728$	1.41003	−	9.80699i	0.0522593	−	0.363471i
$729$	13.6781	+	23.2789i	0.506598	+	0.862182i
$730$	0.693036	+	0.316499i	0.0256504	+	0.0117142i
$731$	−9.76169	+	33.2453i	−0.361049	+	1.22962i
$732$	11.9027	+	5.19114i	0.439938	+	0.191870i
$733$	0.556176	−	0.0799661i	0.0205428	−	0.00295362i	−0.132036	−	0.991245i	$-0.542151\pi$
$733$	0.556176	−	0.0799661i	0.0205428	−	0.00295362i	0.152579	+	0.988291i	$0.451242\pi$
$734$	20.9070	+	13.4361i	0.771692	+	0.495936i
$735$	0.351792	+	0.392201i	0.0129760	+	0.0144665i
$736$	23.0596	−	26.4071i	0.849989	−	0.973377i
$737$			8.20936i			0.302396i
$738$	26.9105	−	33.2969i	0.990590	−	1.22568i
$739$	3.32078	+	23.0965i	0.122157	+	0.849619i	0.955105	+	0.296268i	$0.0957422\pi$
$739$	3.32078	+	23.0965i	0.122157	+	0.849619i	−0.832948	+	0.553351i	$0.813349\pi$
$740$	3.79095	−	1.73127i	0.139358	−	0.0636427i
$741$	48.0003	−	22.9232i	1.76334	−	0.842106i
$742$	5.07894	−	11.1213i	0.186454	−	0.408277i
$743$	−25.2661	+	29.1586i	−0.926922	+	1.06973i	0.0704672	+	0.997514i	$0.477551\pi$
$743$	−25.2661	+	29.1586i	−0.926922	+	1.06973i	−0.997389	+	0.0722111i	$0.976994\pi$
$744$	−16.2634	−	24.3774i	−0.596246	−	0.893719i
$745$	1.78495	−	0.524108i	0.0653954	−	0.0192018i
$746$	−19.8757	−	22.9378i	−0.727701	−	0.839812i
$747$	−13.7335	−	27.5337i	−0.502482	−	1.00741i
$748$	6.57358	−	4.22459i	0.240354	−	0.154466i
$749$	−0.770988	+	0.668065i	−0.0281713	+	0.0244106i
$750$	6.02853	−	9.74380i	0.220131	−	0.355793i
$751$	26.4389	+	3.80135i	0.964771	+	0.138713i	0.606656	−	0.794964i	$-0.292511\pi$
$751$	26.4389	+	3.80135i	0.964771	+	0.138713i	0.358115	+	0.933678i	$0.383420\pi$
$752$	−4.07757	−	3.53323i	−0.148694	−	0.128844i
$753$	−46.2181	+	14.4357i	−1.68428	+	0.526067i
$754$	70.6574	+	20.7469i	2.57319	+	0.755557i
$755$	1.60787	+	3.52075i	0.0585164	+	0.128133i
$756$	10.5603	−	10.1465i	0.384073	−	0.369023i
$757$	−11.0570	+	17.2051i	−0.401875	+	0.625330i	−0.981929	−	0.189248i	$-0.939395\pi$
$757$	−11.0570	+	17.2051i	−0.401875	+	0.625330i	0.580054	+	0.814578i	$0.303031\pi$
$758$	−78.9080			−2.86607
$759$	−7.46679	+	3.53079i	−0.271027	+	0.128160i
$760$	−3.04280			−0.110374
$761$	28.3293	−	44.0812i	1.02694	−	1.59794i	0.250119	−	0.968215i	$-0.419530\pi$
$761$	28.3293	−	44.0812i	1.02694	−	1.59794i	0.776816	−	0.629727i	$-0.216833\pi$
$762$	−43.9045	−	36.7452i	−1.59049	−	1.33114i
$763$	−4.84948	−	10.6189i	−0.175563	−	0.384429i
$764$	11.8250	+	3.47214i	0.427815	+	0.125618i
$765$	2.18644	+	1.30148i	0.0790508	+	0.0470551i
$766$	−61.3949	−	53.1990i	−2.21829	−	1.92216i
$767$	−13.0132	−	1.87101i	−0.469878	−	0.0675583i
$768$	−5.28280	−	3.26849i	−0.190627	−	0.117942i
$769$	−6.16073	+	5.33830i	−0.222162	+	0.192504i	−0.758829	−	0.651290i	$-0.774228\pi$
$769$	−6.16073	+	5.33830i	−0.222162	+	0.192504i	0.536668	+	0.843794i	$0.319683\pi$
$770$	−0.558522	+	0.358940i	−0.0201277	+	0.0129353i
$771$	−13.4983	+	49.0666i	−0.486129	+	1.76709i
$772$	17.2330	+	19.8880i	0.620230	+	0.715784i
$773$	4.10100	−	1.20416i	0.147503	−	0.0433107i	−0.207148	−	0.978310i	$-0.566418\pi$
$773$	4.10100	−	1.20416i	0.147503	−	0.0433107i	0.354650	+	0.934999i	$0.384600\pi$
$774$	−79.2599	−	20.3499i	−2.84894	−	0.731463i
$775$	30.2670	−	34.9300i	1.08722	−	1.25472i
$776$	5.04790	−	11.0533i	0.181209	−	0.396792i
$777$	3.62852	+	7.59798i	0.130172	+	0.272576i
$778$	5.63359	−	2.57278i	0.201974	−	0.0922385i
$779$	−5.15194	−	35.8325i	−0.184587	−	1.28383i
$780$	1.30425	+	8.08505i	0.0466998	+	0.289491i
$781$			5.50479i			0.196977i
$782$	12.2961	−	26.6539i	0.439708	−	0.953142i
$783$	18.4319	+	25.6759i	0.658702	+	0.917583i
$784$	1.42462	+	0.915549i	0.0508794	+	0.0326982i
$785$	−1.20748	+	0.173610i	−0.0430969	+	0.00619639i
$786$	−27.0860	+	62.1055i	−0.966127	+	2.21523i
$787$	5.69068	−	19.3807i	0.202851	−	0.690847i	−0.793733	−	0.608266i	$-0.791866\pi$
$787$	5.69068	−	19.3807i	0.202851	−	0.690847i	0.996584	−	0.0825810i	$-0.0263163\pi$
$788$	−27.8271	−	12.7082i	−0.991299	−	0.452711i
$789$	6.09136	−	0.104411i	0.216858	−	0.00371714i
$790$	1.18736	−	8.25828i	0.0422444	−	0.293816i
$791$	−3.96064	−	13.4887i	−0.140824	−	0.479603i
$792$	3.04995	+	4.40613i	0.108375	+	0.156565i
$793$	−7.93182	−	12.3421i	−0.281667	−	0.438282i
$794$	−5.34650	−	8.31932i	−0.189740	−	0.295242i
$795$	−0.367780	+	2.91136i	−0.0130438	+	0.103255i
$796$	−15.5572	−	52.9831i	−0.551412	−	1.87794i
$797$	−7.56005	+	52.5813i	−0.267791	+	1.86252i	0.201510	+	0.979486i	$0.435415\pi$
$797$	−7.56005	+	52.5813i	−0.267791	+	1.86252i	−0.469301	+	0.883039i	$0.655494\pi$
$798$	−0.362835	−	21.1678i	−0.0128442	−	0.749332i
$799$	−8.08091	−	3.69043i	−0.285882	−	0.130558i
$800$	10.1070	−	34.4212i	0.357335	−	1.21697i
$801$	−39.0486	+	12.9350i	−1.37972	+	0.457036i
$802$	−38.8849	+	5.59080i	−1.37307	+	0.197418i
$803$	−0.954472	−	0.613402i	−0.0336826	−	0.0216465i
$804$	30.0025	−	26.9113i	1.05811	−	0.949087i
$805$	−0.611090	+	1.32464i	−0.0215381	+	0.0466875i
$806$			114.020i			4.01617i
$807$	−3.45351	+	0.557109i	−0.121569	+	0.0196112i
$808$	1.68536	+	11.7220i	0.0592908	+	0.412377i
$809$	−27.6915	+	12.6463i	−0.973581	+	0.444620i	−0.837715	−	0.546108i	$-0.816109\pi$
$809$	−27.6915	+	12.6463i	−0.973581	+	0.444620i	−0.135866	+	0.990727i	$0.543382\pi$
$810$	−2.89495	+	5.26606i	−0.101718	+	0.185030i
$811$	−0.815746	+	1.78623i	−0.0286447	+	0.0627231i	−0.923414	−	0.383806i	$-0.874613\pi$
$811$	−0.815746	+	1.78623i	−0.0286447	+	0.0627231i	0.894769	+	0.446530i	$0.147340\pi$
$812$	11.2266	−	12.9562i	0.393977	−	0.454673i
$813$	16.4419	−	10.9692i	0.576642	−	0.384708i
$814$	−10.1805	+	2.98928i	−0.356828	+	0.104774i
$815$	2.04642	+	2.36170i	0.0716831	+	0.0827267i
$816$	7.88563	+	2.16934i	0.276052	+	0.0759422i
$817$	−58.2101	+	37.4094i	−2.03651	+	1.30879i
$818$	40.4666	−	35.0645i	1.41488	−	1.22600i
$819$	−16.2871	+	2.91461i	−0.569116	+	0.101845i
$820$	5.51675	+	0.793189i	0.192653	+	0.0276994i
$821$	19.5198	+	16.9140i	0.681246	+	0.590303i	0.925198	−	0.379484i	$-0.123899\pi$
$821$	19.5198	+	16.9140i	0.681246	+	0.590303i	−0.243952	+	0.969787i	$0.578444\pi$
$822$	18.5803	+	59.4875i	0.648062	+	2.07487i
$823$	48.6690	+	14.2905i	1.69650	+	0.498136i	0.979923	−	0.199376i	$-0.0638914\pi$
$823$	48.6690	+	14.2905i	1.69650	+	0.498136i	0.716573	+	0.697512i	$0.245710\pi$
$824$	−3.12660	−	6.84630i	−0.108920	−	0.238502i
$825$	−5.42446	+	6.48135i	−0.188855	+	0.225652i
$826$	−2.82891	+	4.40187i	−0.0984304	+	0.153161i
$827$	−4.38316			−0.152418			−0.0762088	−	0.997092i	$-0.524282\pi$
$827$	−4.38316			−0.152418			−0.0762088	+	0.997092i	$0.524282\pi$
$828$	37.3809	+	15.7143i	1.29908	+	0.546109i
$829$	2.84164			0.0986941			0.0493470	−	0.998782i	$-0.484286\pi$
$829$	2.84164			0.0986941			0.0493470	+	0.998782i	$0.484286\pi$
$830$	3.70238	−	5.76101i	0.128511	−	0.199968i
$831$	2.09655	−	2.50504i	0.0727285	−	0.0868988i
$832$	29.0044	+	63.5109i	1.00555	+	2.20184i
$833$	2.67538	+	0.785564i	0.0926965	+	0.0272182i
$834$	−5.52214	−	17.6799i	−0.191216	−	0.612206i
$835$	1.92921	+	1.67167i	0.0667630	+	0.0578505i
$836$	15.4460	+	2.22080i	0.534211	+	0.0768079i
$837$	−30.1042	+	38.5829i	−1.04055	+	1.33362i
$838$	43.4042	−	37.6100i	1.49937	−	1.29922i
$839$	9.56149	−	6.14479i	0.330099	−	0.212142i	−0.365084	−	0.930975i	$-0.618960\pi$
$839$	9.56149	−	6.14479i	0.330099	−	0.212142i	0.695183	+	0.718833i	$0.255323\pi$
$840$	0.912565	+	0.251048i	0.0314865	+	0.00866196i
$841$	5.23860	+	6.04566i	0.180641	+	0.208471i
$842$	−34.6122	+	10.1631i	−1.19282	+	0.350242i
$843$	47.8612	−	31.9306i	1.64843	−	1.09975i
$844$	−23.3854	+	26.9882i	−0.804960	+	0.928973i
$845$	2.20099	−	4.81950i	0.0757164	−	0.165796i
$846$	8.05656	−	19.3723i	0.276990	−	0.666034i
$847$	−9.10661	+	4.15885i	−0.312907	+	0.142900i
$848$	1.34234	+	9.33619i	0.0460962	+	0.320606i
$849$	−40.1996	+	6.48487i	−1.37965	+	0.222560i
$850$		−	30.0368i		−	1.03025i
$851$	−15.3347	+	17.5607i	−0.525666	+	0.601974i
$852$	20.1182	−	18.0454i	0.689237	−	0.618224i
$853$	−26.1338	−	16.7952i	−0.894805	−	0.575057i	0.0104401	−	0.999946i	$-0.496677\pi$
$853$	−26.1338	−	16.7952i	−0.894805	−	0.575057i	−0.905245	+	0.424889i	$0.860313\pi$
$854$	−5.77969	+	0.830995i	−0.197777	+	0.0284361i
$855$	1.59784	+	4.82362i	0.0546451	+	0.164964i
$856$	−0.516320	+	1.75842i	−0.0176474	+	0.0601017i
$857$	−3.26115	−	1.48932i	−0.111399	−	0.0508742i	0.358936	−	0.933362i	$-0.383140\pi$
$857$	−3.26115	−	1.48932i	−0.111399	−	0.0508742i	−0.470335	+	0.882488i	$0.655867\pi$
$858$	−0.357337	−	20.8470i	−0.0121993	−	0.711706i
$859$	−5.46638	+	38.0195i	−0.186510	+	1.29721i	0.654448	+	0.756107i	$0.272901\pi$
$859$	−5.46638	+	38.0195i	−0.186510	+	1.29721i	−0.840958	+	0.541101i	$0.818008\pi$
$860$	−3.00134	−	10.2216i	−0.102345	−	0.348554i
$861$	−1.41126	+	11.1716i	−0.0480957	+	0.380727i
$862$	34.4359	+	53.5833i	1.17289	+	1.82506i
$863$	−4.38038	−	6.81600i	−0.149110	−	0.232019i	0.758661	−	0.651485i	$-0.225854\pi$
$863$	−4.38038	−	6.81600i	−0.149110	−	0.232019i	−0.907771	+	0.419466i	$0.862217\pi$
$864$	−8.81422	+	36.9478i	−0.299866	+	1.25699i
$865$	−1.35315	−	4.60840i	−0.0460084	−	0.156690i
$866$	0.932351	−	6.48464i	0.0316826	−	0.220357i
$867$	−15.9762	+	0.273846i	−0.542580	+	0.00930031i
$868$	24.1451	+	11.0267i	0.819539	+	0.374271i
$869$	−3.50038	+	11.9212i	−0.118742	+	0.404399i
$870$	−2.81220	+	6.44809i	−0.0953426	+	0.218611i
$871$	−45.0716	+	6.48032i	−1.52719	+	0.219577i
$872$	−17.6422	−	11.3379i	−0.597439	−	0.383951i
$873$	−20.1732	−	2.19786i	−0.682760	−	0.0743861i
$874$	53.4152	−	24.1469i	1.80680	−	0.816782i
$875$			3.01367i			0.101881i
$876$	0.887094	+	5.49908i	0.0299721	+	0.185797i
$877$	0.0415088	+	0.288700i	0.00140165	+	0.00974871i	0.990510	−	0.137439i	$-0.0438870\pi$
$877$	0.0415088	+	0.288700i	0.00140165	+	0.00974871i	−0.989109	+	0.147187i	$0.952978\pi$
$878$	21.1638	−	9.66520i	0.714245	−	0.326185i
$879$	2.38293	+	4.98976i	0.0803743	+	0.168301i
$880$	0.212773	−	0.465909i	0.00717259	−	0.0157058i
$881$	7.06085	−	8.14866i	0.237886	−	0.274535i	−0.624236	−	0.781236i	$-0.714590\pi$
$881$	7.06085	−	8.14866i	0.237886	−	0.274535i	0.862122	+	0.506701i	$0.169135\pi$
$882$	−1.63764	+	6.37837i	−0.0551423	+	0.214771i
$883$	−47.3743	+	13.9103i	−1.59427	+	0.468120i	−0.953945	−	0.299982i	$-0.903019\pi$
$883$	−47.3743	+	13.9103i	−1.59427	+	0.468120i	−0.640327	+	0.768103i	$0.721201\pi$
$884$	28.3832	+	32.7560i	0.954630	+	1.10170i
$885$	0.333122	−	1.21091i	0.0111978	−	0.0407042i
$886$	−36.3050	+	23.3318i	−1.21969	+	0.783847i
$887$	−3.76898	+	3.26584i	−0.126550	+	0.109656i	−0.715836	−	0.698268i	$-0.753954\pi$
$887$	−3.76898	+	3.26584i	−0.126550	+	0.109656i	0.589287	+	0.807924i	$0.299409\pi$
$888$	12.8630	+	7.95840i	0.431654	+	0.267066i
$889$	14.9052	+	2.14304i	0.499904	+	0.0718753i
$890$	−6.91918	−	5.99550i	−0.231931	−	0.200970i
$891$	5.38325	−	7.14873i	0.180346	−	0.239491i
$892$	−26.0717	−	7.65536i	−0.872947	−	0.256320i
$893$	−7.36988	−	16.1378i	−0.246624	−	0.540031i
$894$	17.8312	+	14.9235i	0.596364	+	0.499117i
$895$	1.83624	−	2.85725i	0.0613789	−	0.0955074i
$896$	13.1683			0.439922
$897$	−25.2792	−	38.2076i	−0.844047	−	1.27571i
$898$	65.0664			2.17129
$899$	−30.9720	+	48.1934i	−1.03297	+	1.60734i
$900$	41.4692	−	1.42206i	1.38231	−	0.0474019i
$901$	6.45159	+	14.1270i	0.214933	+	0.470639i
$902$	−13.6149	−	3.99770i	−0.453327	−	0.133109i
$903$	20.5443	−	6.41679i	0.683671	−	0.213537i
$904$	−19.0861	−	16.5382i	−0.634796	−	0.550054i
$905$	−1.11173	−	0.159843i	−0.0369552	−	0.00531336i
$906$	−25.4538	+	41.1405i	−0.845645	+	1.36680i
$907$	−5.79437	+	5.02085i	−0.192399	+	0.166714i	−0.745733	−	0.666245i	$-0.767901\pi$
$907$	−5.79437	+	5.02085i	−0.192399	+	0.166714i	0.553334	+	0.832959i	$0.313355\pi$
$908$	41.8396	−	26.8887i	1.38850	−	0.892332i
$909$	17.6973	−	8.82721i	0.586983	−	0.292780i
$910$	−2.41157	−	2.78310i	−0.0799427	−	0.0922588i
$911$	32.9636	−	9.67899i	1.09213	−	0.320679i	0.314411	−	0.949287i	$-0.398193\pi$
$911$	32.9636	−	9.67899i	1.09213	−	0.320679i	0.777723	+	0.628608i	$0.216375\pi$
$912$	9.06438	+	13.5867i	0.300152	+	0.449901i
$913$	−6.67831	+	7.70718i	−0.221020	+	0.255071i
$914$	−16.9361	+	37.0848i	−0.560195	+	1.22666i
$915$	1.26468	−	0.603964i	0.0418089	−	0.0199664i
$916$	−14.3057	+	6.53320i	−0.472674	+	0.215863i
$917$	−2.53618	−	17.6395i	−0.0837520	−	0.582508i
$918$	1.63455	+	31.7616i	0.0539482	+	1.04829i
$919$		−	2.13583i		−	0.0704545i	−0.999379	−	0.0352273i	$-0.988784\pi$
$919$		−	2.13583i		−	0.0704545i	0.999379	−	0.0352273i	$-0.0112155\pi$
$920$	0.363013	+	2.59538i	0.0119682	+	0.0855673i
$921$	−22.4373	−	25.0146i	−0.739333	−	0.824258i
$922$	0.908579	+	0.583908i	0.0299224	+	0.0192300i
$923$	−30.2228	+	4.34538i	−0.994795	+	0.143030i
$924$	−4.44918	−	1.94042i	−0.146367	−	0.0638351i
$925$	−6.72115	+	22.8901i	−0.220990	+	0.752623i
$926$	8.33469	+	3.80632i	0.273895	+	0.125084i
$927$	−9.21132	+	8.55163i	−0.302540	+	0.280873i
$928$	−6.32812	+	44.0130i	−0.207731	+	1.44480i
$929$	−16.6239	−	56.6158i	−0.545412	−	1.85750i	−0.513635	−	0.858009i	$-0.671701\pi$
$929$	−16.6239	−	56.6158i	−0.545412	−	1.85750i	−0.0317772	−	0.999495i	$-0.510117\pi$
$930$	−10.8061	−	1.36509i	−0.354346	−	0.0447631i
$931$	3.01049	+	4.68441i	0.0986648	+	0.153525i
$932$	11.7130	+	18.2258i	0.383672	+	0.597005i
$933$	44.4575	+	5.61615i	1.45547	+	0.183864i
$934$	−10.9522	−	37.2998i	−0.358367	−	1.22049i
$935$	0.120021	−	0.834764i	0.00392510	−	0.0272997i
$936$	−21.7832	+	20.2232i	−0.712008	+	0.661016i
$937$	−17.2621	−	7.88333i	−0.563928	−	0.257537i	0.112990	−	0.993596i	$-0.463957\pi$
$937$	−17.2621	−	7.88333i	−0.563928	−	0.257537i	−0.676917	+	0.736059i	$0.736685\pi$
$938$	−5.10585	+	17.3889i	−0.166712	+	0.567768i
$939$	−23.6910	−	10.3324i	−0.773127	−	0.337184i
$940$	2.70359	−	0.388718i	0.0881814	−	0.0126786i
$941$	15.7294	+	10.1087i	0.512765	+	0.329534i	0.771304	−	0.636467i	$-0.219605\pi$
$941$	15.7294	+	10.1087i	0.512765	+	0.329534i	−0.258539	+	0.966001i	$0.583241\pi$
$942$	−10.1811	−	11.3506i	−0.331718	−	0.369822i
$943$	−29.9491	+	8.66930i	−0.975276	+	0.282311i
$944$		−	4.03675i		−	0.131385i
$945$	−0.0812336	−	1.57848i	−0.00264253	−	0.0513481i
$946$	3.85989	+	26.8461i	0.125496	+	0.872842i
$947$	8.66709	−	3.95813i	0.281643	−	0.128622i	−0.269585	−	0.962976i	$-0.586887\pi$
$947$	8.66709	−	3.95813i	0.281643	−	0.128622i	0.551228	+	0.834355i	$0.314159\pi$
$948$	55.0427	−	26.2864i	1.78770	−	0.853743i
$949$	2.61430	−	5.72452i	0.0848638	−	0.185826i
$950$	39.2813	−	45.3331i	1.27445	−	1.47080i
$951$	13.9103	+	20.8503i	0.451072	+	0.676117i
$952$	4.80616	−	1.41122i	0.155769	−	0.0457378i
$953$	21.4655	+	24.7725i	0.695335	+	0.802459i	0.988114	−	0.153721i	$-0.0491257\pi$
$953$	21.4655	+	24.7725i	0.695335	+	0.802459i	−0.292780	+	0.956180i	$0.594580\pi$
$954$	−32.8222	+	16.3713i	−1.06266	+	0.530041i
$955$	1.11897	−	0.719119i	0.0362091	−	0.0232702i
$956$	38.9979	−	33.7919i	1.26128	−	1.09291i
$957$	5.51179	−	8.90860i	0.178171	−	0.287974i
$958$	6.35940	+	0.914344i	0.205463	+	0.0295411i
$959$	−12.3881	−	10.7344i	−0.400033	−	0.346631i
$960$	−6.36642	+	1.98849i	−0.205475	+	0.0641781i
$961$	−55.3629	−	16.2560i	−1.78590	−	0.524388i
$962$	−24.4483	−	53.5343i	−0.788244	−	1.72601i
$963$	3.05869	−	0.104888i	0.0985650	−	0.00337998i
$964$	−14.8923	+	23.1729i	−0.479649	+	0.746349i
$965$	2.84017			0.0914282
$966$	−18.0120	+	2.83485i	−0.579527	+	0.0912099i
$967$	−52.5996			−1.69149			−0.845744	−	0.533589i	$-0.820843\pi$
$967$	−52.5996			−1.69149			−0.845744	+	0.533589i	$0.820843\pi$
$968$	−9.72326	+	15.1297i	−0.312517	+	0.486287i
$969$	20.6229	+	17.2600i	0.662503	+	0.554471i
$970$	−1.87621	−	4.10833i	−0.0602415	−	0.131911i
$971$	8.52052	+	2.50185i	0.273436	+	0.0802882i	0.415576	−	0.909558i	$-0.363580\pi$
$971$	8.52052	+	2.50185i	0.273436	+	0.0802882i	−0.142140	+	0.989847i	$0.545398\pi$
$972$	−43.7732	+	3.76040i	−1.40402	+	0.120615i
$973$	3.68180	+	3.19030i	0.118033	+	0.102276i
$974$	59.5339	+	8.55968i	1.90759	+	0.274270i
$975$	−39.8663	−	24.6655i	−1.27674	−	0.789928i
$976$	3.40446	−	2.94998i	0.108974	−	0.0944265i
$977$	−6.77879	+	4.35647i	−0.216873	+	0.139376i	−0.644567	−	0.764548i	$-0.722962\pi$
$977$	−6.77879	+	4.35647i	−0.216873	+	0.139376i	0.427694	+	0.903923i	$0.359326\pi$
$978$	−10.3604	+	37.6603i	−0.331289	+	1.20424i
$979$	8.92836	+	10.3039i	0.285352	+	0.329313i
$980$	−0.822576	+	0.241530i	−0.0262762	+	0.00771539i
$981$	−8.70926	+	33.9212i	−0.278065	+	1.08302i
$982$	13.6197	−	15.7180i	0.434622	−	0.501580i
$983$	−8.92166	+	19.5357i	−0.284557	+	0.623093i	−0.996895	−	0.0787440i	$-0.974909\pi$
$983$	−8.92166	+	19.5357i	−0.284557	+	0.623093i	0.712338	+	0.701837i	$0.247636\pi$
$984$	8.71738	+	18.2538i	0.277900	+	0.581911i
$985$	−3.00330	+	1.37156i	−0.0956932	+	0.0437016i
$986$	5.29839	+	36.8511i	0.168735	+	1.17358i
$987$	0.878844	+	5.44794i	0.0279739	+	0.173410i
$988$			86.5558i			2.75371i
$989$	38.8533	+	45.1879i	1.23546	+	1.43689i
$990$	1.98003	+	0.215723i	0.0629296	+	0.00685613i
$991$	3.50611	+	2.25324i	0.111375	+	0.0715766i	0.595143	−	0.803620i	$-0.297096\pi$
$991$	3.50611	+	2.25324i	0.111375	+	0.0715766i	−0.483767	+	0.875197i	$0.660732\pi$
$992$	−68.1467	+	9.79802i	−2.16366	+	0.311087i
$993$	−3.53168	+	8.09776i	−0.112074	+	0.256975i
$994$	−3.42373	+	11.6601i	−0.108594	+	0.369837i
$995$	−5.42116	−	2.47576i	−0.171862	−	0.0784869i
$996$	50.0595	−	0.858064i	1.58620	−	0.0271888i
$997$	7.03809	−	48.9510i	0.222899	−	1.55029i	−0.504095	−	0.863648i	$-0.668174\pi$
$997$	7.03809	−	48.9510i	0.222899	−	1.55029i	0.726993	−	0.686645i	$-0.240917\pi$
$998$	1.96302	+	6.68544i	0.0621384	+	0.211624i
$999$	5.86147	−	24.5703i	0.185449	−	0.777371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.8	✓	480
3.2	odd	2	inner	483.2.u.a.113.41	yes	480
23.11	odd	22	inner	483.2.u.a.218.41	yes	480
69.11	even	22	inner	483.2.u.a.218.8	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.8	✓	480	1.1	even	1	trivial
483.2.u.a.113.41	yes	480	3.2	odd	2	inner
483.2.u.a.218.8	yes	480	69.11	even	22	inner
483.2.u.a.218.41	yes	480	23.11	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18675 + 1.84662i) q^{2} +(-1.11165 + 1.32824i) q^{3} +(-1.17080 - 2.56370i) q^{4} +(-0.291860 - 0.0856978i) q^{5} +(-1.13351 - 3.62910i) q^{6} +(0.755750 + 0.654861i) q^{7} +(1.77815 + 0.255660i) q^{8} +(-0.528462 - 2.95309i) q^{9} +(0.504617 - 0.437253i) q^{10} +(-0.836482 + 0.537574i) q^{11} +(4.70674 + 1.29483i) q^{12} +(-3.61173 - 4.16816i) q^{13} +(-2.10617 + 0.618426i) q^{14} +(0.438274 - 0.292395i) q^{15} +(1.10898 - 1.27983i) q^{16} +(1.15831 - 2.53635i) q^{17} +(6.08039 + 2.52871i) q^{18} +(5.06517 - 2.31318i) q^{19} +(0.122007 + 0.848576i) q^{20} +(-1.70994 + 0.275843i) q^{21} -2.18263i q^{22} +(-2.57734 - 4.04442i) q^{23} +(-2.31626 + 2.07762i) q^{24} +(-4.12843 - 2.65318i) q^{25} +(11.9833 - 1.72293i) q^{26} +(4.50989 + 2.58088i) q^{27} +(0.794033 - 2.70423i) q^{28} +(5.53304 + 2.52686i) q^{29} +(0.0198205 + 1.15633i) q^{30} +(-1.34033 + 9.32221i) q^{31} +(2.05951 + 7.01403i) q^{32} +(0.215847 - 1.70865i) q^{33} +(3.30906 + 5.14899i) q^{34} +(-0.164453 - 0.255894i) q^{35} +(-6.95210 + 4.81230i) q^{36} +(-1.36957 - 4.66434i) q^{37} +(-1.73952 + 12.0986i) q^{38} +(9.55132 - 0.163718i) q^{39} +(-0.497062 - 0.227001i) q^{40} +(1.83160 - 6.23784i) q^{41} +(1.51990 - 3.48498i) q^{42} +(-12.2999 + 1.76845i) q^{43} +(2.35753 + 1.51510i) q^{44} +(-0.0988362 + 0.907176i) q^{45} +(10.5272 + 0.0403465i) q^{46} -3.18603i q^{47} +(0.467126 + 2.89571i) q^{48} +(0.142315 + 0.989821i) q^{49} +(9.79884 - 4.47498i) q^{50} +(2.08126 + 4.35807i) q^{51} +(-6.45729 + 14.1395i) q^{52} +(-3.64745 + 4.20938i) q^{53} +(-10.1180 + 5.26519i) q^{54} +(0.290205 - 0.0852117i) q^{55} +(1.17642 + 1.35766i) q^{56} +(-2.55823 + 9.29923i) q^{57} +(-11.2325 + 7.21869i) q^{58} +(1.80151 - 1.56102i) q^{59} +(-1.26274 - 0.781266i) q^{60} +(2.63302 + 0.378571i) q^{61} +(-15.6240 - 13.5382i) q^{62} +(1.53448 - 2.57786i) q^{63} +(-12.1467 - 3.56659i) q^{64} +(0.696918 + 1.52604i) q^{65} +(2.89907 + 2.42633i) q^{66} +(4.46363 - 6.94555i) q^{67} -7.85861 q^{68} +(8.23708 + 1.07265i) q^{69} +0.667704 q^{70} +(2.99309 - 4.65734i) q^{71} +(-0.184701 - 5.38615i) q^{72} +(0.474011 + 1.03794i) q^{73} +(10.2386 + 3.00633i) q^{74} +(8.11344 - 2.53415i) q^{75} +(-11.8606 - 10.2773i) q^{76} +(-0.984207 - 0.141508i) q^{77} +(-11.0327 + 17.8320i) q^{78} +(9.44337 - 8.18272i) q^{79} +(-0.433344 + 0.278493i) q^{80} +(-8.44146 + 3.12119i) q^{81} +(9.34528 + 10.7850i) q^{82} +(9.84079 - 2.88952i) q^{83} +(2.70918 + 4.06083i) q^{84} +(-0.555426 + 0.640995i) q^{85} +(11.3312 - 24.8119i) q^{86} +(-9.50709 + 4.54025i) q^{87} +(-1.62483 + 0.742034i) q^{88} +(-1.95139 - 13.5722i) q^{89} +(-1.55792 - 1.25911i) q^{90} -5.51527i q^{91} +(-7.35111 + 11.3427i) q^{92} +(-10.8922 - 12.1433i) q^{93} +(5.88340 + 3.78103i) q^{94} +(-1.67655 + 0.241052i) q^{95} +(-11.6058 - 5.06163i) q^{96} +(1.90569 - 6.49020i) q^{97} +(-1.99672 - 0.911871i) q^{98} +(2.02955 + 2.18612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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