LMFDB - Embedded newform 630.2.cd.a.23.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.18
Character	$\chi$	$=$	630.23
Dual form			630.2.cd.a.137.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.18452 + 1.26369i) q^{3} +1.00000i q^{4} +(0.379698 - 2.20359i) q^{5} +(0.0559834 - 1.73115i) q^{6} +(2.56402 - 0.652527i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.193831 + 2.99373i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.18452 + 1.26369i) q^{3} +1.00000i q^{4} +(0.379698 - 2.20359i) q^{5} +(0.0559834 - 1.73115i) q^{6} +(2.56402 - 0.652527i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.193831 + 2.99373i) q^{9} +(-1.82666 + 1.28969i) q^{10} +(-1.21248 - 0.700028i) q^{11} +(-1.26369 + 1.18452i) q^{12} +(3.21822 - 0.862319i) q^{13} +(-2.27444 - 1.35163i) q^{14} +(3.23442 - 2.13038i) q^{15} -1.00000 q^{16} +(0.694879 - 2.59332i) q^{17} +(2.25395 - 1.97983i) q^{18} +(0.845277 + 0.488021i) q^{19} +(2.20359 + 0.379698i) q^{20} +(3.86172 + 2.46720i) q^{21} +(0.362361 + 1.35235i) q^{22} +(-0.858823 - 0.230121i) q^{23} +(1.73115 + 0.0559834i) q^{24} +(-4.71166 - 1.67340i) q^{25} +(-2.88537 - 1.66587i) q^{26} +(-4.01275 + 3.30119i) q^{27} +(0.652527 + 2.56402i) q^{28} +(-1.59174 - 2.75698i) q^{29} +(-3.79349 - 0.780677i) q^{30} +6.25111 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.551591 - 2.36140i) q^{33} +(-2.32511 + 1.34240i) q^{34} +(-0.464351 - 5.89783i) q^{35} +(-2.99373 - 0.193831i) q^{36} +(1.56810 + 5.85224i) q^{37} +(-0.252618 - 0.942785i) q^{38} +(4.90174 + 3.04540i) q^{39} +(-1.28969 - 1.82666i) q^{40} +(-1.30462 - 0.753225i) q^{41} +(-0.986077 - 4.47523i) q^{42} +(0.951596 - 3.55140i) q^{43} +(0.700028 - 1.21248i) q^{44} +(6.52337 + 1.56384i) q^{45} +(0.444560 + 0.770000i) q^{46} +(4.45232 + 4.45232i) q^{47} +(-1.18452 - 1.26369i) q^{48} +(6.14842 - 3.34619i) q^{49} +(2.14837 + 4.51492i) q^{50} +(4.10026 - 2.19373i) q^{51} +(0.862319 + 3.21822i) q^{52} +(0.151267 + 0.0405318i) q^{53} +(5.17173 + 0.503149i) q^{54} +(-2.00296 + 2.40603i) q^{55} +(1.35163 - 2.27444i) q^{56} +(0.384539 + 1.64624i) q^{57} +(-0.823948 + 3.07501i) q^{58} +12.6063 q^{59} +(2.13038 + 3.23442i) q^{60} -1.57754 q^{61} +(-4.42020 - 4.42020i) q^{62} +(1.45650 + 7.80247i) q^{63} -1.00000i q^{64} +(-0.678250 - 7.41907i) q^{65} +(-1.27973 + 2.05980i) q^{66} +(-3.83290 + 3.83290i) q^{67} +(2.59332 + 0.694879i) q^{68} +(-0.726491 - 1.35787i) q^{69} +(-3.84205 + 4.49874i) q^{70} +4.15268i q^{71} +(1.97983 + 2.25395i) q^{72} +(-2.49135 + 9.29786i) q^{73} +(3.02934 - 5.24697i) q^{74} +(-3.46639 - 7.93626i) q^{75} +(-0.488021 + 0.845277i) q^{76} +(-3.56562 - 1.00371i) q^{77} +(-1.31263 - 5.61948i) q^{78} -3.87477i q^{79} +(-0.379698 + 2.20359i) q^{80} +(-8.92486 - 1.16056i) q^{81} +(0.389898 + 1.45512i) q^{82} +(-15.7031 - 4.20762i) q^{83} +(-2.46720 + 3.86172i) q^{84} +(-5.45079 - 2.51591i) q^{85} +(-3.18410 + 1.83834i) q^{86} +(1.59852 - 5.27717i) q^{87} +(-1.35235 + 0.362361i) q^{88} +(6.92869 - 12.0008i) q^{89} +(-3.50692 - 5.71852i) q^{90} +(7.68889 - 4.31098i) q^{91} +(0.230121 - 0.858823i) q^{92} +(7.40455 + 7.89947i) q^{93} -6.29653i q^{94} +(1.39635 - 1.67735i) q^{95} +(-0.0559834 + 1.73115i) q^{96} +(-12.3228 - 3.30188i) q^{97} +(-6.71370 - 1.98147i) q^{98} +(2.33071 - 3.49417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.18452	+	1.26369i	0.683882	+	0.729592i
$3$	1.18452	+	1.26369i	0.683882	+	0.729592i
$4$			1.00000i			0.500000i
$5$	0.379698	−	2.20359i	0.169806	−	0.985477i
$5$	0.379698	−	2.20359i	0.169806	−	0.985477i
$6$	0.0559834	−	1.73115i	0.0228551	−	0.706737i
$7$	2.56402	−	0.652527i	0.969109	−	0.246632i
$7$	2.56402	−	0.652527i	0.969109	−	0.246632i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.193831	+	2.99373i	−0.0646103	+	0.997911i
$10$	−1.82666	+	1.28969i	−0.577642	+	0.407836i
$11$	−1.21248	−	0.700028i	−0.365578	−	0.211066i	0.305947	−	0.952049i	$-0.401027\pi$
$11$	−1.21248	−	0.700028i	−0.365578	−	0.211066i	−0.671525	+	0.740982i	$0.734360\pi$
$12$	−1.26369	+	1.18452i	−0.364796	+	0.341941i
$13$	3.21822	−	0.862319i	0.892573	−	0.239164i	0.216749	−	0.976227i	$-0.430455\pi$
$13$	3.21822	−	0.862319i	0.892573	−	0.239164i	0.675824	+	0.737063i	$0.263788\pi$
$14$	−2.27444	−	1.35163i	−0.607871	−	0.361239i
$15$	3.23442	−	2.13038i	0.835124	−	0.550061i
$16$	−1.00000			−0.250000
$17$	0.694879	−	2.59332i	0.168533	−	0.628974i	−0.829030	−	0.559204i	$-0.811107\pi$
$17$	0.694879	−	2.59332i	0.168533	−	0.628974i	0.997563	−	0.0697697i	$-0.0222264\pi$
$18$	2.25395	−	1.97983i	0.531260	−	0.466650i
$19$	0.845277	+	0.488021i	0.193920	+	0.111960i	0.593816	−	0.804601i	$-0.297621\pi$
$19$	0.845277	+	0.488021i	0.193920	+	0.111960i	−0.399896	+	0.916560i	$0.630954\pi$
$20$	2.20359	+	0.379698i	0.492739	+	0.0849031i
$21$	3.86172	+	2.46720i	0.842697	+	0.538387i
$22$	0.362361	+	1.35235i	0.0772557	+	0.288322i
$23$	−0.858823	−	0.230121i	−0.179077	−	0.0479836i	0.168166	−	0.985759i	$-0.446215\pi$
$23$	−0.858823	−	0.230121i	−0.179077	−	0.0479836i	−0.347243	+	0.937775i	$0.612882\pi$
$24$	1.73115	+	0.0559834i	0.353369	+	0.0114276i
$25$	−4.71166	−	1.67340i	−0.942332	−	0.334680i
$26$	−2.88537	−	1.66587i	−0.565868	−	0.326704i
$27$	−4.01275	+	3.30119i	−0.772254	+	0.635314i
$28$	0.652527	+	2.56402i	0.123316	+	0.484555i
$29$	−1.59174	−	2.75698i	−0.295580	−	0.511959i	0.679540	−	0.733638i	$-0.262179\pi$
$29$	−1.59174	−	2.75698i	−0.295580	−	0.511959i	−0.975120	+	0.221680i	$0.928846\pi$
$30$	−3.79349	−	0.780677i	−0.692593	−	0.142532i
$31$	6.25111			1.12273			0.561366	−	0.827568i	$-0.310276\pi$
$31$	6.25111			1.12273			0.561366	+	0.827568i	$0.310276\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.551591	−	2.36140i	−0.0960197	−	0.411067i
$34$	−2.32511	+	1.34240i	−0.398753	+	0.230220i
$35$	−0.464351	−	5.89783i	−0.0784897	−	0.996915i
$36$	−2.99373	−	0.193831i	−0.498955	−	0.0323052i
$37$	1.56810	+	5.85224i	0.257794	+	0.962102i	0.966514	+	0.256612i	$0.0826063\pi$
$37$	1.56810	+	5.85224i	0.257794	+	0.962102i	−0.708720	+	0.705490i	$0.750727\pi$
$38$	−0.252618	−	0.942785i	−0.0409801	−	0.152940i
$39$	4.90174	+	3.04540i	0.784907	+	0.487654i
$40$	−1.28969	−	1.82666i	−0.203918	−	0.288821i
$41$	−1.30462	−	0.753225i	−0.203748	−	0.117634i	0.394655	−	0.918830i	$-0.370864\pi$
$41$	−1.30462	−	0.753225i	−0.203748	−	0.117634i	−0.598403	+	0.801196i	$0.704198\pi$
$42$	−0.986077	−	4.47523i	−0.152155	−	0.690542i
$43$	0.951596	−	3.55140i	0.145117	−	0.541584i	−0.854633	−	0.519232i	$-0.826218\pi$
$43$	0.951596	−	3.55140i	0.145117	−	0.541584i	0.999750	−	0.0223518i	$-0.00711540\pi$
$44$	0.700028	−	1.21248i	0.105533	−	0.182789i
$45$	6.52337	+	1.56384i	0.972447	+	0.233123i
$46$	0.444560	+	0.770000i	0.0655468	+	0.113530i
$47$	4.45232	+	4.45232i	0.649438	+	0.649438i	0.952857	−	0.303419i	$-0.0981283\pi$
$47$	4.45232	+	4.45232i	0.649438	+	0.649438i	−0.303419	+	0.952857i	$0.598128\pi$
$48$	−1.18452	−	1.26369i	−0.170971	−	0.182398i
$49$	6.14842	−	3.34619i	0.878345	−	0.478027i
$50$	2.14837	+	4.51492i	0.303826	+	0.638506i
$51$	4.10026	−	2.19373i	0.574151	−	0.307183i
$52$	0.862319	+	3.21822i	0.119582	+	0.446286i
$53$	0.151267	+	0.0405318i	0.0207781	+	0.00556747i	0.269193	−	0.963086i	$-0.413243\pi$
$53$	0.151267	+	0.0405318i	0.0207781	+	0.00556747i	−0.248415	+	0.968654i	$0.579910\pi$
$54$	5.17173	+	0.503149i	0.703784	+	0.0684699i
$55$	−2.00296	+	2.40603i	−0.270079	+	0.324428i
$56$	1.35163	−	2.27444i	0.180619	−	0.303935i
$57$	0.384539	+	1.64624i	0.0509334	+	0.218050i
$58$	−0.823948	+	3.07501i	−0.108190	+	0.403769i
$59$	12.6063			1.64120			0.820599	−	0.571505i	$-0.193640\pi$
$59$	12.6063			1.64120			0.820599	+	0.571505i	$0.193640\pi$
$60$	2.13038	+	3.23442i	0.275031	+	0.417562i
$61$	−1.57754			−0.201983			−0.100992	−	0.994887i	$-0.532202\pi$
$61$	−1.57754			−0.201983			−0.100992	+	0.994887i	$0.532202\pi$
$62$	−4.42020	−	4.42020i	−0.561366	−	0.561366i
$63$	1.45650	+	7.80247i	0.183502	+	0.983019i
$64$		−	1.00000i		−	0.125000i
$65$	−0.678250	−	7.41907i	−0.0841266	−	0.920222i
$66$	−1.27973	+	2.05980i	−0.157524	+	0.253544i
$67$	−3.83290	+	3.83290i	−0.468263	+	0.468263i	−0.901351	−	0.433088i	$-0.857424\pi$
$67$	−3.83290	+	3.83290i	−0.468263	+	0.468263i	0.433088	+	0.901351i	$0.357424\pi$
$68$	2.59332	+	0.694879i	0.314487	+	0.0842665i
$69$	−0.726491	−	1.35787i	−0.0874592	−	0.163468i
$70$	−3.84205	+	4.49874i	−0.459213	+	0.537702i
$71$			4.15268i			0.492833i	0.969164	+	0.246416i	$0.0792531\pi$
$71$			4.15268i			0.492833i	−0.969164	+	0.246416i	$0.920747\pi$
$72$	1.97983	+	2.25395i	0.233325	+	0.265630i
$73$	−2.49135	+	9.29786i	−0.291591	+	1.08823i	0.652296	+	0.757964i	$0.273806\pi$
$73$	−2.49135	+	9.29786i	−0.291591	+	1.08823i	−0.943887	+	0.330268i	$0.892861\pi$
$74$	3.02934	−	5.24697i	0.352154	−	0.609948i
$75$	−3.46639	−	7.93626i	−0.400264	−	0.916400i
$76$	−0.488021	+	0.845277i	−0.0559799	+	0.0969600i
$77$	−3.56562	−	1.00371i	−0.406341	−	0.114383i
$78$	−1.31263	−	5.61948i	−0.148626	−	0.636281i
$79$		−	3.87477i		−	0.435946i	−0.975955	−	0.217973i	$-0.930056\pi$
$79$		−	3.87477i		−	0.435946i	0.975955	−	0.217973i	$-0.0699444\pi$
$80$	−0.379698	+	2.20359i	−0.0424515	+	0.246369i
$81$	−8.92486	−	1.16056i	−0.991651	−	0.128951i
$82$	0.389898	+	1.45512i	0.0430570	+	0.160691i
$83$	−15.7031	−	4.20762i	−1.72363	−	0.461847i	−0.744934	−	0.667138i	$-0.767519\pi$
$83$	−15.7031	−	4.20762i	−1.72363	−	0.461847i	−0.978701	+	0.205292i	$0.934186\pi$
$84$	−2.46720	+	3.86172i	−0.269194	+	0.421349i
$85$	−5.45079	−	2.51591i	−0.591221	−	0.272889i
$86$	−3.18410	+	1.83834i	−0.343351	+	0.198234i
$87$	1.59852	−	5.27717i	0.171380	−	0.565772i
$88$	−1.35235	+	0.362361i	−0.144161	+	0.0386278i
$89$	6.92869	−	12.0008i	0.734440	−	1.27209i	−0.220529	−	0.975380i	$-0.570778\pi$
$89$	6.92869	−	12.0008i	0.734440	−	1.27209i	0.954969	−	0.296706i	$-0.0958883\pi$
$90$	−3.50692	−	5.71852i	−0.369662	−	0.602785i
$91$	7.68889	−	4.31098i	0.806015	−	0.451913i
$92$	0.230121	−	0.858823i	0.0239918	−	0.0895385i
$93$	7.40455	+	7.89947i	0.767816	+	0.819137i
$94$		−	6.29653i		−	0.649438i
$95$	1.39635	−	1.67735i	0.143263	−	0.172092i
$96$	−0.0559834	+	1.73115i	−0.00571378	+	0.176684i
$97$	−12.3228	−	3.30188i	−1.25119	−	0.335255i	−0.428394	−	0.903592i	$-0.640920\pi$
$97$	−12.3228	−	3.30188i	−1.25119	−	0.335255i	−0.822796	+	0.568337i	$0.807587\pi$
$98$	−6.71370	−	1.98147i	−0.678186	−	0.200159i
$99$	2.33071	−	3.49417i	0.234246	−	0.351177i
$100$	1.67340	−	4.71166i	0.167340	−	0.471166i
$101$	−13.1315	−	7.58149i	−1.30664	−	0.754386i	−0.325102	−	0.945679i	$-0.605399\pi$
$101$	−13.1315	−	7.58149i	−1.30664	−	0.754386i	−0.981533	+	0.191292i	$0.938732\pi$
$102$	−4.45052	−	1.34812i	−0.440667	−	0.133484i
$103$	−3.35821	+	12.5330i	−0.330895	+	1.23492i	0.577357	+	0.816492i	$0.304084\pi$
$103$	−3.35821	+	12.5330i	−0.330895	+	1.23492i	−0.908252	+	0.418424i	$0.862583\pi$
$104$	1.66587	−	2.88537i	0.163352	−	0.282934i
$105$	6.90300	−	7.57288i	0.673664	−	0.739038i
$106$	−0.0783014	−	0.135622i	−0.00760530	−	0.0131728i
$107$	15.7279	−	4.21428i	1.52047	−	0.407410i	0.600576	−	0.799568i	$-0.294938\pi$
$107$	15.7279	−	4.21428i	1.52047	−	0.407410i	0.919898	+	0.392158i	$0.128271\pi$
$108$	−3.30119	−	4.01275i	−0.317657	−	0.386127i
$109$	−17.8085	+	10.2817i	−1.70574	+	0.984810i	−0.766053	+	0.642777i	$0.777782\pi$
$109$	−17.8085	+	10.2817i	−1.70574	+	0.984810i	−0.939688	+	0.342033i	$0.888885\pi$
$110$	3.11762	−	0.285013i	0.297253	−	0.0271749i
$111$	−5.53798	+	8.91368i	−0.525641	+	0.846049i
$112$	−2.56402	+	0.652527i	−0.242277	+	0.0616580i
$113$	4.35225	+	16.2428i	0.409425	+	1.52800i	0.795745	+	0.605632i	$0.207079\pi$
$113$	4.35225	+	16.2428i	0.409425	+	1.52800i	−0.386320	+	0.922365i	$0.626254\pi$
$114$	0.892157	−	1.43598i	0.0835582	−	0.134492i
$115$	−0.833187	+	1.80512i	−0.0776951	+	0.168329i
$116$	2.75698	−	1.59174i	0.255979	−	0.147790i
$117$	1.95776	+	9.80162i	0.180995	+	0.906160i
$118$	−8.91398	−	8.91398i	−0.820599	−	0.820599i
$119$	0.0894708	−	7.10277i	0.00820177	−	0.651110i
$120$	0.780677	−	3.79349i	0.0712658	−	0.346296i
$121$	−4.51992	−	7.82873i	−0.410902	−	0.711703i
$122$	1.11549	+	1.11549i	0.100992	+	0.100992i
$123$	−0.593508	−	2.54085i	−0.0535148	−	0.229101i
$124$			6.25111i			0.561366i
$125$	−5.47650	+	9.74720i	−0.489833	+	0.871816i
$126$	4.48728	−	6.54709i	0.399758	−	0.583261i
$127$	8.08485	−	8.08485i	0.717415	−	0.717415i	−0.250660	−	0.968075i	$-0.580648\pi$
$127$	8.08485	−	8.08485i	0.717415	−	0.717415i	0.968075	+	0.250660i	$0.0806477\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	5.61506	−	3.00418i	0.494379	−	0.264503i
$130$	−4.76648	+	5.72567i	−0.418048	+	0.502174i
$131$	−17.1966	+	9.92846i	−1.50247	+	0.867454i	−0.502478	+	0.864590i	$0.667578\pi$
$131$	−17.1966	+	9.92846i	−1.50247	+	0.867454i	−0.999996	+	0.00286360i	$0.999088\pi$
$132$	2.36140	−	0.551591i	0.205534	−	0.0480098i
$133$	2.48576	+	0.699730i	0.215542	+	0.0606743i
$134$	5.42054			0.468263
$135$	5.75085	+	10.0959i	0.494954	+	0.868919i
$136$	−1.34240	−	2.32511i	−0.115110	−	0.199377i
$137$	−8.56175	+	2.29411i	−0.731479	+	0.195999i	−0.605288	−	0.796007i	$-0.706942\pi$
$137$	−8.56175	+	2.29411i	−0.731479	+	0.195999i	−0.126191	+	0.992006i	$0.540275\pi$
$138$	−0.446453	+	1.47387i	−0.0380046	+	0.125464i
$139$	11.4416	+	6.60583i	0.970466	+	0.560299i	0.899378	−	0.437171i	$-0.144020\pi$
$139$	11.4416	+	6.60583i	0.970466	+	0.560299i	0.0710880	+	0.997470i	$0.477353\pi$
$140$	5.89783	−	0.464351i	0.498457	−	0.0392449i
$141$	−0.352502	+	10.9002i	−0.0296860	+	0.917964i
$142$	2.93639	−	2.93639i	0.246416	−	0.246416i
$143$	−4.50569	−	1.20729i	−0.376784	−	0.100959i
$144$	0.193831	−	2.99373i	0.0161526	−	0.249478i
$145$	−6.67965	+	2.46074i	−0.554715	+	0.204353i
$146$	8.33623	−	4.81293i	0.689911	−	0.398321i
$147$	11.5115	+	3.80608i	0.949449	+	0.313920i
$148$	−5.85224	+	1.56810i	−0.481051	+	0.128897i
$149$	3.93967	+	6.82371i	0.322751	+	0.559020i	0.981055	−	0.193732i	$-0.0620592\pi$
$149$	3.93967	+	6.82371i	0.322751	+	0.559020i	−0.658304	+	0.752752i	$0.728726\pi$
$150$	−3.16068	+	8.06289i	−0.258068	+	0.658332i
$151$	5.83959	−	10.1145i	0.475219	−	0.823103i	−0.524378	−	0.851486i	$-0.675702\pi$
$151$	5.83959	−	10.1145i	0.475219	−	0.823103i	0.999597	+	0.0283820i	$0.00903549\pi$
$152$	0.942785	−	0.252618i	0.0764699	−	0.0204901i
$153$	7.62903	+	2.58295i	0.616770	+	0.208819i
$154$	1.81155	+	3.23101i	0.145979	+	0.260362i
$155$	2.37353	−	13.7749i	0.190647	−	1.10643i
$156$	−3.04540	+	4.90174i	−0.243827	+	0.392453i
$157$	−5.31581	+	5.31581i	−0.424248	+	0.424248i	−0.886663	−	0.462416i	$-0.846983\pi$
$157$	−5.31581	+	5.31581i	−0.424248	+	0.424248i	0.462416	+	0.886663i	$0.346983\pi$
$158$	−2.73988	+	2.73988i	−0.217973	+	0.217973i
$159$	0.127959	+	0.239165i	0.0101478	+	0.0189670i
$160$	1.82666	−	1.28969i	0.144410	−	0.101959i
$161$	−2.35220	−	0.0296298i	−0.185380	−	0.00233515i
$162$	5.49019	+	7.13147i	0.431350	+	0.560301i
$163$	−10.8476	+	2.90662i	−0.849653	+	0.227664i	−0.657269	−	0.753656i	$-0.728289\pi$
$163$	−10.8476	+	2.90662i	−0.849653	+	0.227664i	−0.192384	+	0.981320i	$0.561622\pi$
$164$	0.753225	−	1.30462i	0.0588170	−	0.101874i
$165$	−5.41301	+	0.318863i	−0.421402	+	0.0248235i
$166$	8.12850	+	14.0790i	0.630894	+	1.09274i
$167$	−24.8327	+	6.65391i	−1.92161	+	0.514895i	−0.934198	+	0.356754i	$0.883883\pi$
$167$	−24.8327	+	6.65391i	−1.92161	+	0.514895i	−0.987416	+	0.158141i	$0.949450\pi$
$168$	4.47523	−	0.986077i	0.345271	−	0.0760775i
$169$	−1.64500	+	0.949743i	−0.126539	+	0.0730572i
$170$	2.07527	+	5.63331i	0.159166	+	0.432055i
$171$	−1.62485	+	2.43594i	−0.124255	+	0.186281i
$172$	3.55140	+	0.951596i	0.270792	+	0.0725585i
$173$	−18.3604	+	18.3604i	−1.39592	+	1.39592i	−0.584589	+	0.811330i	$0.698744\pi$
$173$	−18.3604	+	18.3604i	−1.39592	+	1.39592i	−0.811330	+	0.584589i	$0.801256\pi$
$174$	−4.86185	+	2.60120i	−0.368576	+	0.197196i
$175$	−13.1727	−	1.21615i	−0.995765	−	0.0919324i
$176$	1.21248	+	0.700028i	0.0913945	+	0.0527666i
$177$	14.9324	+	15.9304i	1.12239	+	1.19741i
$178$	−13.3852	+	3.58655i	−1.00326	+	0.268824i
$179$	−1.40001	−	2.42489i	−0.104642	−	0.181245i	0.808950	−	0.587878i	$-0.200036\pi$
$179$	−1.40001	−	2.42489i	−0.104642	−	0.181245i	−0.913592	+	0.406632i	$0.866703\pi$
$180$	−1.56384	+	6.52337i	−0.116562	+	0.486224i
$181$	2.71266			0.201631			0.100815	−	0.994905i	$-0.467855\pi$
$181$	2.71266			0.201631			0.100815	+	0.994905i	$0.467855\pi$
$182$	−8.48519	−	2.38855i	−0.628964	−	0.177051i
$183$	−1.86863	−	1.99352i	−0.138133	−	0.147366i
$184$	−0.770000	+	0.444560i	−0.0567652	+	0.0327734i
$185$	13.4914	−	1.23338i	0.991905	−	0.0906798i
$186$	0.349958	−	10.8216i	0.0256602	−	0.793477i
$187$	−2.65793	+	2.65793i	−0.194367	+	0.194367i
$188$	−4.45232	+	4.45232i	−0.324719	+	0.324719i
$189$	−8.13466	+	11.0827i	−0.591709	+	0.806151i
$190$	−2.17343	+	0.198695i	−0.157677	+	0.0144149i
$191$		−	8.32800i		−	0.602593i	−0.953531	−	0.301296i	$-0.902581\pi$
$191$		−	8.32800i		−	0.602593i	0.953531	−	0.301296i	$-0.0974194\pi$
$192$	1.26369	−	1.18452i	0.0911991	−	0.0854853i
$193$	5.98669	+	5.98669i	0.430931	+	0.430931i	0.888945	−	0.458014i	$-0.151439\pi$
$193$	5.98669	+	5.98669i	0.430931	+	0.430931i	−0.458014	+	0.888945i	$0.651439\pi$
$194$	6.37875	+	11.0483i	0.457967	+	0.793223i
$195$	8.57201	−	9.64512i	0.613854	−	0.690701i
$196$	3.34619	+	6.14842i	0.239013	+	0.439173i
$197$	2.30556	+	2.30556i	0.164265	+	0.164265i	0.784453	−	0.620188i	$-0.212944\pi$
$197$	2.30556	+	2.30556i	0.164265	+	0.164265i	−0.620188	+	0.784453i	$0.712944\pi$
$198$	−4.11881	+	0.822685i	−0.292711	+	0.0584657i
$199$	−9.90016	+	5.71586i	−0.701803	+	0.405186i	−0.808019	−	0.589157i	$-0.799460\pi$
$199$	−9.90016	+	5.71586i	−0.701803	+	0.405186i	0.106215	+	0.994343i	$0.466127\pi$
$200$	−4.51492	+	2.14837i	−0.319253	+	0.151913i
$201$	−9.38374	−	0.303460i	−0.661878	−	0.0214044i
$202$	3.92447	+	14.6463i	0.276125	+	1.03051i
$203$	−5.88027	−	6.03031i	−0.412714	−	0.423245i
$204$	2.19373	+	4.10026i	0.153592	+	0.287076i
$205$	−2.15517	+	2.58886i	−0.150523	+	0.180814i
$206$	11.2368	−	6.48757i	0.782905	−	0.452011i
$207$	0.855387	−	2.52648i	0.0594535	−	0.175603i
$208$	−3.21822	+	0.862319i	−0.223143	+	0.0597910i
$209$	−0.683257	−	1.18344i	−0.0472619	−	0.0818600i
$210$	−10.2360	+	0.473679i	−0.706351	+	0.0326870i
$211$	5.02999	−	8.71220i	0.346279	−	0.599773i	−0.639306	−	0.768952i	$-0.720778\pi$
$211$	5.02999	−	8.71220i	0.346279	−	0.599773i	0.985585	+	0.169179i	$0.0541117\pi$
$212$	−0.0405318	+	0.151267i	−0.00278373	+	0.0103890i
$213$	−5.24771	+	4.91893i	−0.359567	+	0.337040i
$214$	−14.1012	−	8.14136i	−0.963941	−	0.556532i
$215$	−7.46454	−	3.44539i	−0.509077	−	0.234974i
$216$	−0.503149	+	5.17173i	−0.0342350	+	0.351892i
$217$	16.0280	−	4.07902i	1.08805	−	0.276902i
$218$	19.8628	+	5.32221i	1.34528	+	0.360466i
$219$	−14.7007	+	7.86519i	−0.993380	+	0.531480i
$220$	−2.40603	−	2.00296i	−0.162214	−	0.135039i
$221$		−	8.94509i		−	0.601712i
$222$	10.2189	−	2.38699i	0.685845	−	0.160204i
$223$	5.66397	−	21.1382i	0.379287	−	1.41552i	−0.467691	−	0.883892i	$-0.654914\pi$
$223$	5.66397	−	21.1382i	0.379287	−	1.41552i	0.846978	−	0.531627i	$-0.178419\pi$
$224$	2.27444	+	1.35163i	0.151968	+	0.0903096i
$225$	5.92298	−	13.7811i	0.394865	−	0.918739i
$226$	8.40791	−	14.5629i	0.559286	−	0.968711i
$227$	−4.39917	+	1.17875i	−0.291983	+	0.0782367i	−0.401837	−	0.915711i	$-0.631628\pi$
$227$	−4.39917	+	1.17875i	−0.291983	+	0.0782367i	0.109854	+	0.993948i	$0.464962\pi$
$228$	−1.64624	+	0.384539i	−0.109025	+	0.0254667i
$229$	10.7566	−	6.21035i	0.710819	−	0.410391i	−0.100545	−	0.994932i	$-0.532059\pi$
$229$	10.7566	−	6.21035i	0.710819	−	0.410391i	0.811364	+	0.584541i	$0.198725\pi$
$230$	1.86557	−	0.687262i	0.123012	−	0.0453167i
$231$	−2.95517	−	5.69476i	−0.194436	−	0.374688i
$232$	−3.07501	−	0.823948i	−0.201885	−	0.0540948i
$233$	0.782196	+	2.91920i	0.0512434	+	0.191243i	0.986803	−	0.161926i	$-0.0517707\pi$
$233$	0.782196	+	2.91920i	0.0512434	+	0.191243i	−0.935559	+	0.353169i	$0.885104\pi$
$234$	5.54645	−	8.31514i	0.362583	−	0.543578i
$235$	11.5017	−	8.12057i	0.750285	−	0.529728i
$236$			12.6063i			0.820599i
$237$	4.89651	−	4.58974i	0.318063	−	0.298135i
$238$	−5.08568	+	4.95915i	−0.329656	+	0.321454i
$239$	3.17214	−	5.49431i	0.205189	−	0.355397i	−0.745004	−	0.667060i	$-0.767553\pi$
$239$	3.17214	−	5.49431i	0.205189	−	0.355397i	0.950193	+	0.311663i	$0.100886\pi$
$240$	−3.23442	+	2.13038i	−0.208781	+	0.137515i
$241$	−2.93416	+	5.08212i	−0.189006	+	0.327368i	−0.944919	−	0.327304i	$-0.893860\pi$
$241$	−2.93416	+	5.08212i	−0.189006	+	0.327368i	0.755913	+	0.654672i	$0.227193\pi$
$242$	−2.33968	+	8.73182i	−0.150401	+	0.561302i
$243$	−9.10508	−	12.6530i	−0.584091	−	0.811688i
$244$		−	1.57754i		−	0.100992i
$245$	−5.03910	−	14.8192i	−0.321936	−	0.946761i
$246$	−1.37698	+	2.21633i	−0.0877930	+	0.141308i
$247$	3.14112	+	0.841659i	0.199864	+	0.0535535i
$248$	4.42020	−	4.42020i	0.280683	−	0.280683i
$249$	−13.2834	−	24.8278i	−0.841803	−	1.57340i
$250$	10.7648	−	3.01984i	0.680825	−	0.190991i
$251$			1.52378i			0.0961804i	0.998843	+	0.0480902i	$0.0153135\pi$
$251$			1.52378i			0.0961804i	−0.998843	+	0.0480902i	$0.984687\pi$
$252$	−7.80247	+	1.45650i	−0.491510	+	0.0917512i
$253$	0.880219	+	0.880219i	0.0553389	+	0.0553389i
$254$	−11.4337			−0.717415
$255$	−3.27723	−	9.86826i	−0.205228	−	0.617975i
$256$	1.00000			0.0625000
$257$	−5.29082	+	19.7456i	−0.330032	+	1.23170i	0.579123	+	0.815240i	$0.303395\pi$
$257$	−5.29082	+	19.7456i	−0.330032	+	1.23170i	−0.909155	+	0.416457i	$0.863271\pi$
$258$	−6.09473	−	1.84617i	−0.379441	−	0.114938i
$259$	7.83939	+	13.9820i	0.487116	+	0.868802i
$260$	7.41907	−	0.678250i	0.460111	−	0.0420633i
$261$	8.56220	−	4.23087i	0.529987	−	0.261884i
$262$	19.1803	+	5.13935i	1.18496	+	0.317510i
$263$	4.61056	+	17.2069i	0.284300	+	1.06102i	0.949350	+	0.314222i	$0.101744\pi$
$263$	4.61056	+	17.2069i	0.284300	+	1.06102i	−0.665050	+	0.746799i	$0.731590\pi$
$264$	−2.05980	−	1.27973i	−0.126772	−	0.0787619i
$265$	0.146751	−	0.317941i	0.00901486	−	0.0195309i
$266$	−1.26291	−	2.25248i	−0.0774341	−	0.138108i
$267$	23.3725	−	5.45950i	1.43038	−	0.334116i
$268$	−3.83290	−	3.83290i	−0.234131	−	0.234131i
$269$	5.71601	+	9.90043i	0.348512	+	0.603640i	0.985985	−	0.166832i	$-0.0533539\pi$
$269$	5.71601	+	9.90043i	0.348512	+	0.603640i	−0.637474	+	0.770472i	$0.720021\pi$
$270$	3.07243	−	11.2054i	0.186982	−	0.681937i
$271$	6.27563	−	10.8697i	0.381217	−	0.660288i	−0.610019	−	0.792387i	$-0.708838\pi$
$271$	6.27563	−	10.8697i	0.381217	−	0.660288i	0.991237	+	0.132099i	$0.0421716\pi$
$272$	−0.694879	+	2.59332i	−0.0421332	+	0.157243i
$273$	14.5554	+	4.60995i	0.880932	+	0.279007i
$274$	7.67625	+	4.43189i	0.463739	+	0.267740i
$275$	4.54139	+	5.32727i	0.273856	+	0.321246i
$276$	1.35787	−	0.726491i	0.0817342	−	0.0437296i
$277$	−3.67262	−	13.7064i	−0.220667	−	0.823539i	−0.984094	−	0.177646i	$-0.943152\pi$
$277$	−3.67262	−	13.7064i	−0.220667	−	0.823539i	0.763428	−	0.645893i	$-0.223515\pi$
$278$	−3.41943	−	12.7615i	−0.205084	−	0.765383i
$279$	−1.21166	+	18.7141i	−0.0725401	+	1.12039i
$280$	−4.49874	−	3.84205i	−0.268851	−	0.229606i
$281$	10.6559	−	6.15221i	0.635680	−	0.367010i	−0.147269	−	0.989097i	$-0.547048\pi$
$281$	10.6559	−	6.15221i	0.635680	−	0.367010i	0.782948	+	0.622087i	$0.213715\pi$
$282$	7.95687	−	7.45836i	0.473825	−	0.444139i
$283$	−18.8762	−	18.8762i	−1.12208	−	1.12208i	−0.991429	−	0.130647i	$-0.958295\pi$
$283$	−18.8762	−	18.8762i	−1.12208	−	1.12208i	−0.130647	−	0.991429i	$-0.541705\pi$
$284$	−4.15268			−0.246416
$285$	3.77365	−	0.222294i	0.223532	−	0.0131676i
$286$	2.33231	+	4.03969i	0.137913	+	0.238872i
$287$	−3.83658	−	1.07998i	−0.226466	−	0.0637494i
$288$	−2.25395	+	1.97983i	−0.132815	+	0.116663i
$289$	8.47996	+	4.89591i	0.498821	+	0.287994i
$290$	6.46323	+	2.98322i	0.379534	+	0.175181i
$291$	−10.4240	−	19.4834i	−0.611067	−	1.14213i
$292$	−9.29786	−	2.49135i	−0.544116	−	0.145795i
$293$	2.12748	+	7.93986i	0.124289	+	0.463851i	0.999813	−	0.0193219i	$-0.00615074\pi$
$293$	2.12748	+	7.93986i	0.124289	+	0.463851i	−0.875525	+	0.483173i	$0.839484\pi$
$294$	−5.44853	−	10.8311i	−0.317765	−	0.631685i
$295$	4.78658	−	27.7791i	0.278685	−	1.61736i
$296$	5.24697	+	3.02934i	0.304974	+	0.176077i
$297$	7.17632	−	1.19360i	0.416412	−	0.0692598i
$298$	2.03932	−	7.61086i	0.118135	−	0.440886i
$299$	−2.96232			−0.171315
$300$	7.93626	−	3.46639i	0.458200	−	0.200132i
$301$	0.122525	−	9.72682i	0.00706222	−	0.560645i
$302$	−11.2812	+	3.02279i	−0.649161	+	0.173942i
$303$	−5.97388	−	25.5746i	−0.343190	−	1.46922i
$304$	−0.845277	−	0.488021i	−0.0484800	−	0.0279899i
$305$	−0.598989	+	3.47626i	−0.0342980	+	0.199050i
$306$	−3.56812	−	7.22096i	−0.203976	−	0.412795i
$307$	16.8290	−	16.8290i	0.960480	−	0.960480i	−0.0387679	−	0.999248i	$-0.512343\pi$
$307$	16.8290	−	16.8290i	0.960480	−	0.960480i	0.999248	+	0.0387679i	$0.0123433\pi$
$308$	1.00371	−	3.56562i	0.0571916	−	0.203170i
$309$	−19.8157	+	10.6019i	−1.12728	+	0.603119i
$310$	−11.4187	+	8.06199i	−0.648537	+	0.457890i
$311$		−	5.16704i		−	0.292996i	−0.989211	−	0.146498i	$-0.953200\pi$
$311$		−	5.16704i		−	0.292996i	0.989211	−	0.146498i	$-0.0468002\pi$
$312$	5.61948	−	1.31263i	0.318140	−	0.0743132i
$313$	22.9654	+	22.9654i	1.29808	+	1.29808i	0.929658	+	0.368424i	$0.120103\pi$
$313$	22.9654	+	22.9654i	1.29808	+	1.29808i	0.368424	+	0.929658i	$0.379897\pi$
$314$	7.51769			0.424248
$315$	17.7465	−	0.246962i	0.999903	−	0.0139147i
$316$	3.87477			0.217973
$317$	−2.99584	−	2.99584i	−0.168263	−	0.168263i	0.617952	−	0.786216i	$-0.287962\pi$
$317$	−2.99584	−	2.99584i	−0.168263	−	0.168263i	−0.786216	+	0.617952i	$0.787962\pi$
$318$	0.0786349	−	0.259596i	0.00440962	−	0.0145574i
$319$			4.45707i			0.249548i
$320$	−2.20359	−	0.379698i	−0.123185	−	0.0212258i
$321$	23.9555	+	14.8833i	1.33707	+	0.830706i
$322$	1.64231	+	1.68421i	0.0915222	+	0.0938573i
$323$	1.85296	−	1.85296i	0.103102	−	0.103102i
$324$	1.16056	−	8.92486i	0.0644753	−	0.495826i
$325$	−16.6061	−	1.32242i	−0.921143	−	0.0733545i
$326$	9.72573	+	5.61515i	0.538659	+	0.310995i
$327$	−34.0874	−	10.3255i	−1.88504	−	0.571002i
$328$	−1.45512	+	0.389898i	−0.0803455	+	0.0215285i
$329$	14.3211	+	8.51059i	0.789548	+	0.469204i
$330$	4.05305	+	3.60211i	0.223113	+	0.198289i
$331$	−23.8031			−1.30834			−0.654169	−	0.756349i	$-0.726981\pi$
$331$	−23.8031			−1.30834			−0.654169	+	0.756349i	$0.726981\pi$
$332$	4.20762	−	15.7031i	0.230923	−	0.861817i
$333$	−17.8240	+	3.56013i	−0.976748	+	0.195094i
$334$	22.2644	+	12.8544i	1.21826	+	0.703360i
$335$	6.99081	+	9.90150i	0.381949	+	0.540977i
$336$	−3.86172	−	2.46720i	−0.210674	−	0.134597i
$337$	−8.77571	−	32.7514i	−0.478044	−	1.78408i	−0.609528	−	0.792765i	$-0.708641\pi$
$337$	−8.77571	−	32.7514i	−0.478044	−	1.78408i	0.131484	−	0.991318i	$-0.458026\pi$
$338$	1.83476	+	0.491623i	0.0997980	+	0.0267408i
$339$	−15.3706	+	24.7398i	−0.834816	+	1.34368i
$340$	2.51591	−	5.45079i	0.136444	−	0.295611i
$341$	−7.57937	−	4.37595i	−0.410446	−	0.236971i
$342$	2.87141	−	0.573531i	0.155268	−	0.0310130i
$343$	13.5812	−	12.5917i	0.733316	−	0.679888i
$344$	−1.83834	−	3.18410i	−0.0991168	−	0.171675i
$345$	−3.26804	+	1.08531i	−0.175946	+	0.0584311i
$346$	25.9656			1.39592
$347$	−10.9100	−	10.9100i	−0.585678	−	0.585678i	0.350780	−	0.936458i	$-0.385916\pi$
$347$	−10.9100	−	10.9100i	−0.585678	−	0.585678i	−0.936458	+	0.350780i	$0.885916\pi$
$348$	5.27717	+	1.59852i	0.282886	+	0.0856899i
$349$	10.9900	−	6.34509i	0.588282	−	0.339645i	−0.176136	−	0.984366i	$-0.556360\pi$
$349$	10.9900	−	6.34509i	0.588282	−	0.339645i	0.764418	+	0.644721i	$0.223026\pi$
$350$	8.45458	+	10.1745i	0.451916	+	0.543849i
$351$	−10.0672	+	14.0842i	−0.537348	+	0.751759i
$352$	−0.362361	−	1.35235i	−0.0193139	−	0.0720805i
$353$	6.16071	+	22.9921i	0.327902	+	1.22375i	0.911363	+	0.411605i	$0.135031\pi$
$353$	6.16071	+	22.9921i	0.327902	+	1.22375i	−0.583461	+	0.812141i	$0.698302\pi$
$354$	0.705743	−	21.8233i	0.0375098	−	1.15990i
$355$	9.15083	+	1.57677i	0.485676	+	0.0836860i
$356$	12.0008	+	6.92869i	0.636043	+	0.367220i
$357$	9.08169	−	8.30030i	0.480654	−	0.439298i
$358$	−0.724700	+	2.70462i	−0.0383016	+	0.142943i
$359$	7.75620	−	13.4341i	0.409356	−	0.709026i	−0.585461	−	0.810700i	$-0.699087\pi$
$359$	7.75620	−	13.4341i	0.409356	−	0.709026i	0.994818	+	0.101674i	$0.0324199\pi$
$360$	5.71852	−	3.50692i	0.301393	−	0.184831i
$361$	−9.02367	−	15.6295i	−0.474930	−	0.822603i
$362$	−1.91814	−	1.91814i	−0.100815	−	0.100815i
$363$	4.53917	−	14.9851i	0.238245	−	0.786512i
$364$	4.31098	+	7.68889i	0.225957	+	0.403007i
$365$	19.5427	+	9.02031i	1.02291	+	0.472145i
$366$	−0.0883161	+	2.73095i	−0.00461636	+	0.142749i
$367$	6.28673	+	23.4624i	0.328165	+	1.22473i	0.911092	+	0.412203i	$0.135241\pi$
$367$	6.28673	+	23.4624i	0.328165	+	1.22473i	−0.582927	+	0.812524i	$0.698093\pi$
$368$	0.858823	+	0.230121i	0.0447693	+	0.0119959i
$369$	2.50783	−	3.75970i	0.130552	−	0.195722i
$370$	−10.4120	−	8.66771i	−0.541292	−	0.450613i
$371$	0.414299	+	0.00521877i	0.0215093	+	0.000270945i
$372$	−7.89947	+	7.40455i	−0.409568	+	0.383908i
$373$	1.21066	−	4.51824i	0.0626856	−	0.233946i	−0.927474	−	0.373887i	$-0.878025\pi$
$373$	1.21066	−	4.51824i	0.0626856	−	0.233946i	0.990160	+	0.139941i	$0.0446914\pi$
$374$	3.75888			0.194367
$375$	−18.8045	+	4.62513i	−0.971059	+	0.238841i
$376$	6.29653			0.324719
$377$	−7.49998	−	7.49998i	−0.386268	−	0.386268i
$378$	13.5888	−	2.08461i	0.698930	−	0.107221i
$379$			11.4905i			0.590226i	0.955462	+	0.295113i	$0.0953573\pi$
$379$			11.4905i			0.590226i	−0.955462	+	0.295113i	$0.904643\pi$
$380$	1.67735	+	1.39635i	0.0860462	+	0.0716313i
$381$	19.7934	+	0.640098i	1.01405	+	0.0327932i
$382$	−5.88878	+	5.88878i	−0.301296	+	0.301296i
$383$	8.18813	+	2.19400i	0.418394	+	0.112108i	0.461873	−	0.886946i	$-0.347178\pi$
$383$	8.18813	+	2.19400i	0.418394	+	0.112108i	−0.0434793	+	0.999054i	$0.513844\pi$
$384$	−1.73115	−	0.0559834i	−0.0883422	−	0.00285689i
$385$	−3.56563	+	7.47608i	−0.181721	+	0.381017i
$386$		−	8.46646i		−	0.430931i
$387$	10.4475	+	3.53720i	0.531077	+	0.179806i
$388$	3.30188	−	12.3228i	0.167628	−	0.625595i
$389$	−15.1817	+	26.2955i	−0.769744	+	1.33324i	0.167958	+	0.985794i	$0.446283\pi$
$389$	−15.1817	+	26.2955i	−0.769744	+	1.33324i	−0.937702	+	0.347441i	$0.887051\pi$
$390$	−12.8815	+	0.758805i	−0.652278	+	0.0384236i
$391$	−1.19356	+	2.06730i	−0.0603608	+	0.104548i
$392$	1.98147	−	6.71370i	0.100080	−	0.339093i
$393$	−32.9162	−	9.97074i	−1.66040	−	0.502957i
$394$		−	3.26056i		−	0.164265i
$395$	−8.53842	−	1.47124i	−0.429615	−	0.0740262i
$396$	3.49417	+	2.33071i	0.175588	+	0.117123i
$397$	−1.06451	−	3.97279i	−0.0534260	−	0.199388i	0.934054	−	0.357131i	$-0.116245\pi$
$397$	−1.06451	−	3.97279i	−0.0534260	−	0.199388i	−0.987480	+	0.157743i	$0.949578\pi$
$398$	11.0422	+	2.95875i	0.553495	+	0.148309i
$399$	2.06018	+	3.97007i	0.103138	+	0.198752i
$400$	4.71166	+	1.67340i	0.235583	+	0.0836701i
$401$	−9.36334	+	5.40593i	−0.467583	+	0.269959i	−0.715227	−	0.698892i	$-0.753677\pi$
$401$	−9.36334	+	5.40593i	−0.467583	+	0.269959i	0.247644	+	0.968851i	$0.420344\pi$
$402$	6.42073	+	6.84988i	0.320237	+	0.341641i
$403$	20.1174	−	5.39045i	1.00212	−	0.268517i
$404$	7.58149	−	13.1315i	0.377193	−	0.653318i
$405$	−5.94615	+	19.2261i	−0.295466	+	0.955353i
$406$	−0.106089	+	8.42205i	−0.00526512	+	0.417979i
$407$	2.19543	−	8.19347i	0.108824	−	0.406135i
$408$	1.34812	−	4.45052i	0.0667419	−	0.220334i
$409$			3.65826i			0.180889i	0.995901	+	0.0904446i	$0.0288288\pi$
$409$			3.65826i			0.180889i	−0.995901	+	0.0904446i	$0.971171\pi$
$410$	3.35454	−	0.306671i	0.165669	−	0.0151454i
$411$	−13.0406	−	8.10199i	−0.643245	−	0.399641i
$412$	−12.5330	−	3.35821i	−0.617458	−	0.165447i
$413$	32.3228	−	8.22594i	1.59050	−	0.404772i
$414$	−2.39134	+	1.18164i	−0.117528	+	0.0580746i
$415$	−15.2343	+	33.0056i	−0.747823	+	1.62018i
$416$	2.88537	+	1.66587i	0.141467	+	0.0816761i
$417$	5.20510	+	22.2834i	0.254895	+	1.09122i
$418$	−0.353680	+	1.31995i	−0.0172991	+	0.0645609i
$419$	11.7629	−	20.3739i	0.574655	−	0.995331i	−0.421424	−	0.906864i	$-0.638470\pi$
$419$	11.7629	−	20.3739i	0.574655	−	0.995331i	0.996079	−	0.0884676i	$-0.0281970\pi$
$420$	7.57288	+	6.90300i	0.369519	+	0.336832i
$421$	−4.56136	−	7.90050i	−0.222307	−	0.385047i	0.733201	−	0.680012i	$-0.238025\pi$
$421$	−4.56136	−	7.90050i	−0.222307	−	0.385047i	−0.955508	+	0.294965i	$0.904692\pi$
$422$	−9.71720	+	2.60372i	−0.473026	+	0.126747i
$423$	−14.1921	+	12.4661i	−0.690041	+	0.606121i
$424$	0.135622	−	0.0783014i	0.00658639	−	0.00380265i
$425$	−7.61371	+	11.0560i	−0.369319	+	0.536297i
$426$	7.18890	+	0.232481i	0.348303	+	0.0112638i
$427$	−4.04485	+	1.02939i	−0.195744	+	0.0498156i
$428$	4.21428	+	15.7279i	0.203705	+	0.760237i
$429$	−3.81142	−	7.12386i	−0.184017	−	0.343943i
$430$	2.84196	+	7.71449i	0.137052	+	0.372026i
$431$	24.5878	−	14.1958i	1.18435	−	0.683786i	0.227335	−	0.973817i	$-0.426999\pi$
$431$	24.5878	−	14.1958i	1.18435	−	0.683786i	0.957017	+	0.290031i	$0.0936655\pi$
$432$	4.01275	−	3.30119i	0.193063	−	0.158829i
$433$	−9.01561	−	9.01561i	−0.433262	−	0.433262i	0.456474	−	0.889737i	$-0.349112\pi$
$433$	−9.01561	−	9.01561i	−0.433262	−	0.433262i	−0.889737	+	0.456474i	$0.849112\pi$
$434$	−14.2178	−	8.44919i	−0.682476	−	0.405574i
$435$	−11.0218	−	5.52623i	−0.528454	−	0.264962i
$436$	−10.2817	−	17.8085i	−0.492405	−	0.852871i
$437$	−0.613640	−	0.613640i	−0.0293544	−	0.0293544i
$438$	15.9565	+	4.83342i	0.762430	+	0.230950i
$439$			34.5255i			1.64781i	0.566727	+	0.823906i	$0.308209\pi$
$439$			34.5255i			1.64781i	−0.566727	+	0.823906i	$0.691791\pi$
$440$	0.285013	+	3.11762i	0.0135874	+	0.148627i
$441$	8.82584	+	19.0553i	0.420278	+	0.907395i
$442$	−6.32513	+	6.32513i	−0.300856	+	0.300856i
$443$	−1.77010	+	1.77010i	−0.0841000	+	0.0841000i	−0.747905	−	0.663805i	$-0.768940\pi$
$443$	−1.77010	+	1.77010i	−0.0841000	+	0.0841000i	0.663805	+	0.747905i	$0.268940\pi$
$444$	−8.91368	−	5.53798i	−0.423025	−	0.262821i
$445$	−23.8142	−	19.8247i	−1.12890	−	0.939782i
$446$	−18.9520	+	10.9419i	−0.897403	+	0.518116i
$447$	−3.95645	+	13.0613i	−0.187134	+	0.617781i
$448$	−0.652527	−	2.56402i	−0.0308290	−	0.121139i
$449$	30.7956			1.45334			0.726668	−	0.686989i	$-0.241068\pi$
$449$	30.7956			1.45334			0.726668	+	0.686989i	$0.241068\pi$
$450$	−13.9329	+	5.55652i	−0.656802	+	0.261937i
$451$	1.05456	+	1.82655i	0.0496572	+	0.0860087i
$452$	−16.2428	+	4.35225i	−0.763998	+	0.204713i
$453$	19.6987	−	4.60134i	0.925524	−	0.216190i
$454$	3.94419	+	2.27718i	0.185110	+	0.106873i
$455$	−6.58019	−	18.5801i	−0.308484	−	0.871047i
$456$	1.43598	+	0.892157i	0.0672458	+	0.0417791i
$457$	18.3360	−	18.3360i	0.857724	−	0.857724i	−0.133346	−	0.991070i	$-0.542572\pi$
$457$	18.3360	−	18.3360i	0.857724	−	0.857724i	0.991070	+	0.133346i	$0.0425721\pi$
$458$	−11.9975	−	3.21471i	−0.560605	−	0.150214i
$459$	5.77268	+	12.7003i	0.269446	+	0.592799i
$460$	−1.80512	−	0.833187i	−0.0841643	−	0.0388475i
$461$	−8.95950	+	5.17277i	−0.417286	+	0.240920i	−0.693915	−	0.720057i	$-0.744116\pi$
$461$	−8.95950	+	5.17277i	−0.417286	+	0.240920i	0.276630	+	0.960977i	$0.410782\pi$
$462$	−1.93718	+	6.11642i	−0.0901259	+	0.284562i
$463$	−2.20354	+	0.590436i	−0.102407	+	0.0274399i	−0.309659	−	0.950848i	$-0.600215\pi$
$463$	−2.20354	+	0.590436i	−0.102407	+	0.0274399i	0.207252	+	0.978288i	$0.433548\pi$
$464$	1.59174	+	2.75698i	0.0738949	+	0.127990i
$465$	20.2187	−	13.3172i	0.937621	−	0.617571i
$466$	1.51109	−	2.61728i	0.0699998	−	0.121243i
$467$	4.89886	−	1.31265i	0.226692	−	0.0607420i	−0.143685	−	0.989623i	$-0.545895\pi$
$467$	4.89886	−	1.31265i	0.226692	−	0.0607420i	0.370377	+	0.928882i	$0.379228\pi$
$468$	−9.80162	+	1.95776i	−0.453080	+	0.0904975i
$469$	−7.32656	+	12.3287i	−0.338309	+	0.569287i
$470$	−13.8750	−	2.39078i	−0.640006	−	0.110279i
$471$	−13.0142	−	0.420866i	−0.599663	−	0.0193925i
$472$	8.91398	−	8.91398i	0.410299	−	0.410299i
$473$	−3.63988	+	3.63988i	−0.167362	+	0.167362i
$474$	−6.70779	−	0.216923i	−0.308099	−	0.00996360i
$475$	−3.16600	−	3.71388i	−0.145266	−	0.170404i
$476$	7.10277	+	0.0894708i	0.325555	+	0.00410089i
$477$	−0.150661	+	0.444996i	−0.00689832	+	0.0203749i
$478$	−6.12811	+	1.64202i	−0.280293	+	0.0751043i
$479$	−8.12035	+	14.0649i	−0.371028	+	0.642640i	−0.989724	−	0.142991i	$-0.954328\pi$
$479$	−8.12035	+	14.0649i	−0.371028	+	0.642640i	0.618696	+	0.785631i	$0.287661\pi$
$480$	3.79349	+	0.780677i	0.173148	+	0.0356329i
$481$	10.0930	+	17.4816i	0.460201	+	0.797091i
$482$	5.66837	−	1.51883i	0.258187	−	0.0691810i
$483$	−2.74878	−	3.00755i	−0.125074	−	0.136848i
$484$	7.82873	−	4.51992i	0.355851	−	0.205451i
$485$	−11.9550	+	25.9007i	−0.542846	+	1.17609i
$486$	−2.50874	+	15.3853i	−0.113799	+	0.697890i
$487$	20.8211	+	5.57899i	0.943494	+	0.252808i	0.697599	−	0.716488i	$-0.254252\pi$
$487$	20.8211	+	5.57899i	0.943494	+	0.252808i	0.245894	+	0.969297i	$0.420918\pi$
$488$	−1.11549	+	1.11549i	−0.0504958	+	0.0504958i
$489$	−16.5223	−	10.2651i	−0.747165	−	0.464205i
$490$	−6.91555	+	14.0419i	−0.312413	+	0.634349i
$491$	7.58826	+	4.38108i	0.342453	+	0.197716i	0.661356	−	0.750072i	$-0.269981\pi$
$491$	7.58826	+	4.38108i	0.342453	+	0.197716i	−0.318903	+	0.947787i	$0.603314\pi$
$492$	2.54085	−	0.593508i	0.114550	−	0.0267574i
$493$	−8.25582	+	2.21214i	−0.371823	+	0.0996298i
$494$	−1.62596	−	2.81625i	−0.0731555	−	0.126709i
$495$	−6.81476	−	6.46268i	−0.306301	−	0.290476i
$496$	−6.25111			−0.280683
$497$	2.70974	+	10.6476i	0.121548	+	0.477609i
$498$	−8.16312	+	26.9487i	−0.365798	+	1.20760i
$499$	15.7604	−	9.09927i	0.705532	−	0.407339i	−0.103872	−	0.994591i	$-0.533123\pi$
$499$	15.7604	−	9.09927i	0.705532	−	0.407339i	0.809405	+	0.587251i	$0.199790\pi$
$500$	−9.74720	−	5.47650i	−0.435908	−	0.244917i
$501$	−37.8233	−	23.4992i	−1.68982	−	1.04987i
$502$	1.07748	−	1.07748i	0.0480902	−	0.0480902i
$503$	−4.37850	+	4.37850i	−0.195228	+	0.195228i	−0.797951	−	0.602723i	$-0.794082\pi$
$503$	−4.37850	+	4.37850i	−0.195228	+	0.195228i	0.602723	+	0.797951i	$0.294082\pi$
$504$	6.54709	+	4.48728i	0.291630	+	0.199879i
$505$	−21.6925	+	26.0579i	−0.965306	+	1.15956i
$506$		−	1.24482i		−	0.0553389i
$507$	−3.14872	−	0.953788i	−0.139840	−	0.0423592i
$508$	8.08485	+	8.08485i	0.358707	+	0.358707i
$509$	−19.0132	−	32.9317i	−0.842743	−	1.45967i	−0.887567	−	0.460679i	$-0.847606\pi$
$509$	−19.0132	−	32.9317i	−0.842743	−	1.45967i	0.0448236	−	0.998995i	$-0.485727\pi$
$510$	−4.66056	+	9.29527i	−0.206373	+	0.411601i
$511$	−0.320780	+	25.4656i	−0.0141905	+	1.12653i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−5.00294	+	0.832114i	−0.220885	+	0.0367387i
$514$	17.7034	−	10.2211i	0.780865	−	0.450833i
$515$	26.3426	+	12.1589i	1.16079	+	0.535786i
$516$	3.00418	+	5.61506i	0.132252	+	0.247189i
$517$	−2.28162	−	8.51512i	−0.100346	−	0.374495i
$518$	4.34351	−	15.4301i	0.190843	−	0.677959i
$519$	−44.9502	−	1.45364i	−1.97310	−	0.0638078i
$520$	−5.72567	−	4.76648i	−0.251087	−	0.209024i
$521$	−9.69959	+	5.60006i	−0.424947	+	0.245343i	−0.697191	−	0.716885i	$-0.745567\pi$
$521$	−9.69959	+	5.60006i	−0.424947	+	0.245343i	0.272245	+	0.962228i	$0.412234\pi$
$522$	−9.04606	−	3.06271i	−0.395935	−	0.134051i
$523$	42.6224	−	11.4206i	1.86375	−	0.499389i	0.863756	−	0.503911i	$-0.168106\pi$
$523$	42.6224	−	11.4206i	1.86375	−	0.499389i	0.999990	+	0.00452171i	$0.00143931\pi$
$524$	−9.92846	−	17.1966i	−0.433727	−	0.751237i
$525$	−14.0665	−	18.0868i	−0.613913	−	0.789374i
$526$	8.90693	−	15.4273i	0.388360	−	0.672660i
$527$	4.34376	−	16.2111i	0.189217	−	0.706169i
$528$	0.551591	+	2.36140i	0.0240049	+	0.102767i
$529$	−19.2340	−	11.1047i	−0.836259	−	0.482814i
$530$	−0.328587	+	0.121049i	−0.0142729	+	0.00525804i
$531$	−2.44349	+	37.7398i	−0.106038	+	1.63777i
$532$	−0.699730	+	2.48576i	−0.0303372	+	0.107771i
$533$	−4.84808	−	1.29904i	−0.209994	−	0.0562677i
$534$	−20.3873	−	12.6664i	−0.882246	−	0.548130i
$535$	−3.31471	−	36.2581i	−0.143307	−	1.56757i
$536$			5.42054i			0.234131i
$537$	1.40598	−	4.64152i	0.0606723	−	0.200296i
$538$	2.95883	−	11.0425i	0.127564	−	0.476076i
$539$	−9.79729	−	0.246864i	−0.421999	−	0.0106332i
$540$	−10.0959	+	5.75085i	−0.434460	+	0.247477i
$541$	−10.1448	+	17.5713i	−0.436160	+	0.755451i	−0.997390	−	0.0722090i	$-0.976995\pi$
$541$	−10.1448	+	17.5713i	−0.436160	+	0.755451i	0.561230	+	0.827660i	$0.310328\pi$
$542$	−12.1236	+	3.24851i	−0.520753	+	0.139535i
$543$	3.21320	+	3.42797i	0.137892	+	0.147108i
$544$	2.32511	−	1.34240i	0.0996883	−	0.0575551i
$545$	15.8949	+	43.1466i	0.680863	+	1.84820i
$546$	−7.03248	−	13.5519i	−0.300962	−	0.579969i
$547$	29.7796	+	7.97943i	1.27329	+	0.341176i	0.831289	−	0.555841i	$-0.187604\pi$
$547$	29.7796	+	7.97943i	1.27329	+	0.341176i	0.441997	+	0.897017i	$0.354270\pi$
$548$	−2.29411	−	8.56175i	−0.0979997	−	0.365740i
$549$	0.305776	−	4.72273i	0.0130502	−	0.201561i
$550$	0.555702	−	6.97819i	0.0236952	−	0.297551i
$551$		−	3.10722i		−	0.132372i
$552$	−1.47387	−	0.446453i	−0.0627319	−	0.0190023i
$553$	−2.52839	−	9.93499i	−0.107518	−	0.422479i
$554$	−7.09497	+	12.2888i	−0.301436	+	0.522103i
$555$	17.5394	+	15.5880i	0.744506	+	0.661672i
$556$	−6.60583	+	11.4416i	−0.280150	+	0.485233i
$557$	−5.38615	+	20.1014i	−0.228219	+	0.851724i	0.752871	+	0.658168i	$0.228669\pi$
$557$	−5.38615	+	20.1014i	−0.228219	+	0.851724i	−0.981089	+	0.193555i	$0.937998\pi$
$558$	14.0897	−	12.3761i	0.596463	−	0.523923i
$559$		−	12.2498i		−	0.518110i
$560$	0.464351	+	5.89783i	0.0196224	+	0.249229i
$561$	−6.50717	−	0.210435i	−0.274733	−	0.00888458i
$562$	−11.8852	−	3.18462i	−0.501345	−	0.134335i
$563$	0.855993	−	0.855993i	0.0360758	−	0.0360758i	−0.688839	−	0.724915i	$-0.741879\pi$
$563$	0.855993	−	0.855993i	0.0360758	−	0.0360758i	0.724915	+	0.688839i	$0.241879\pi$
$564$	−10.9002	−	0.352502i	−0.458982	−	0.0148430i
$565$	37.4451	−	3.42323i	1.57533	−	0.144016i
$566$			26.6950i			1.12208i
$567$	−23.6408	+	2.84802i	−0.992821	+	0.119606i
$568$	2.93639	+	2.93639i	0.123208	+	0.123208i
$569$	−0.715639			−0.0300011			−0.0150006	−	0.999887i	$-0.504775\pi$
$569$	−0.715639			−0.0300011			−0.0150006	+	0.999887i	$0.504775\pi$
$570$	−2.82556	−	2.51119i	−0.118350	−	0.105182i
$571$	43.2511			1.81000			0.905001	−	0.425410i	$-0.139870\pi$
$571$	43.2511			1.81000			0.905001	+	0.425410i	$0.139870\pi$
$572$	1.20729	−	4.50569i	0.0504795	−	0.188392i
$573$	10.5240	−	9.86467i	0.439647	−	0.412102i
$574$	1.94921	+	3.47654i	0.0813585	+	0.145108i
$575$	3.66140	+	2.52141i	0.152691	+	0.105150i
$576$	2.99373	+	0.193831i	0.124739	+	0.00807629i
$577$	−22.0276	−	5.90228i	−0.917021	−	0.245715i	−0.230710	−	0.973023i	$-0.574105\pi$
$577$	−22.0276	−	5.90228i	−0.917021	−	0.245715i	−0.686312	+	0.727308i	$0.740771\pi$
$578$	−2.53431	−	9.45816i	−0.105413	−	0.393408i
$579$	−0.473981	+	14.6567i	−0.0196980	+	0.609111i
$580$	−2.46074	−	6.67965i	−0.102177	−	0.277358i
$581$	−43.0086	−	0.541762i	−1.78430	−	0.0224761i
$582$	−6.40591	+	21.1477i	−0.265534	+	0.876601i
$583$	−0.155035	−	0.155035i	−0.00642090	−	0.00642090i
$584$	4.81293	+	8.33623i	0.199160	+	0.344956i
$585$	22.3422	−	0.592454i	0.923735	−	0.0244950i
$586$	4.10997	−	7.11868i	0.169781	−	0.294070i
$587$	2.13948	−	7.98463i	0.0883056	−	0.329561i	−0.907614	−	0.419806i	$-0.862098\pi$
$587$	2.13948	−	7.98463i	0.0883056	−	0.329561i	0.995920	+	0.0902447i	$0.0287649\pi$
$588$	−3.80608	+	11.5115i	−0.156960	+	0.474725i
$589$	5.28392	+	3.05067i	0.217720	+	0.125701i
$590$	−23.0274	+	16.2582i	−0.948024	+	0.669339i
$591$	−0.182537	+	5.64450i	−0.00750858	+	0.232184i
$592$	−1.56810	−	5.85224i	−0.0644486	−	0.240526i
$593$	9.35349	+	34.9077i	0.384102	+	1.43349i	0.839578	+	0.543239i	$0.182802\pi$
$593$	9.35349	+	34.9077i	0.384102	+	1.43349i	−0.455476	+	0.890248i	$0.650531\pi$
$594$	−5.91843	−	4.23042i	−0.242836	−	0.173576i
$595$	−15.6176	−	2.89406i	−0.640261	−	0.118645i
$596$	−6.82371	+	3.93967i	−0.279510	+	0.161375i
$597$	−18.9500	−	5.74020i	−0.775572	−	0.234931i
$598$	2.09468	+	2.09468i	0.0856576	+	0.0856576i
$599$	27.1856			1.11077			0.555386	−	0.831593i	$-0.312570\pi$
$599$	27.1856			1.11077			0.555386	+	0.831593i	$0.312570\pi$
$600$	−8.06289	−	3.16068i	−0.329166	−	0.129034i
$601$	19.0237	+	32.9499i	0.775991	+	1.34406i	0.934236	+	0.356656i	$0.116083\pi$
$601$	19.0237	+	32.9499i	0.775991	+	1.34406i	−0.158245	+	0.987400i	$0.550584\pi$
$602$	−6.96454	+	6.79126i	−0.283853	+	0.276791i
$603$	−10.7317	−	12.2176i	−0.437030	−	0.497539i
$604$	10.1145	+	5.83959i	0.411552	+	0.237610i
$605$	−18.9676	+	6.98752i	−0.771141	+	0.284083i
$606$	−13.8598	+	22.3081i	−0.563016	+	0.906207i
$607$	15.9730	+	4.27996i	0.648325	+	0.173718i	0.567971	−	0.823048i	$-0.307728\pi$
$607$	15.9730	+	4.27996i	0.648325	+	0.173718i	0.0803535	+	0.996766i	$0.474395\pi$
$608$	0.252618	+	0.942785i	0.0102450	+	0.0382350i
$609$	0.655151	−	14.5739i	0.0265481	−	0.590563i
$610$	2.88164	−	2.03454i	0.116674	−	0.0823760i
$611$	18.1679	+	10.4892i	0.734993	+	0.424348i
$612$	−2.58295	+	7.62903i	−0.104409	+	0.308385i
$613$	7.83235	−	29.2307i	0.316346	−	1.18062i	−0.606385	−	0.795171i	$-0.707381\pi$
$613$	7.83235	−	29.2307i	0.316346	−	1.18062i	0.922730	−	0.385446i	$-0.125952\pi$
$614$	−23.7998			−0.960480
$615$	−5.82436	+	0.343094i	−0.234861	+	0.0138349i
$616$	−3.23101	+	1.81155i	−0.130181	+	0.0729893i
$617$	17.9218	−	4.80213i	0.721504	−	0.193326i	0.120661	−	0.992694i	$-0.461499\pi$
$617$	17.9218	−	4.80213i	0.721504	−	0.193326i	0.600843	+	0.799367i	$0.294832\pi$
$618$	21.5085	+	6.51520i	0.865199	+	0.262080i
$619$	16.7228	+	9.65489i	0.672145	+	0.388063i	0.796889	−	0.604126i	$-0.206478\pi$
$619$	16.7228	+	9.65489i	0.672145	+	0.388063i	−0.124744	+	0.992189i	$0.539811\pi$
$620$	13.7749	+	2.37353i	0.553214	+	0.0953234i
$621$	4.20592	−	1.91172i	0.168778	−	0.0767147i
$622$	−3.65365	+	3.65365i	−0.146498	+	0.146498i
$623$	9.93444	−	35.2916i	0.398015	−	1.41393i
$624$	−4.90174	−	3.04540i	−0.196227	−	0.121914i
$625$	19.3995	+	15.7690i	0.775978	+	0.630760i
$626$		−	32.4780i		−	1.29808i
$627$	0.686167	−	2.26523i	0.0274029	−	0.0904645i
$628$	−5.31581	−	5.31581i	−0.212124	−	0.212124i
$629$	16.2664			0.648584
$630$	−12.7233	−	12.3741i	−0.506909	−	0.492994i
$631$	−43.1479			−1.71769			−0.858846	−	0.512234i	$-0.828818\pi$
$631$	−43.1479			−1.71769			−0.858846	+	0.512234i	$0.828818\pi$
$632$	−2.73988	−	2.73988i	−0.108986	−	0.108986i
$633$	16.9677	−	3.96341i	0.674404	−	0.157531i
$634$			4.23676i			0.168263i
$635$	−14.7459	−	20.8855i	−0.585175	−	0.828817i
$636$	−0.239165	+	0.127959i	−0.00948351	+	0.00507389i
$637$	16.9015	−	16.0707i	0.669660	−	0.636742i
$638$	3.15162	−	3.15162i	0.124774	−	0.124774i
$639$	−12.4320	−	0.804918i	−0.491803	−	0.0318421i
$640$	1.28969	+	1.82666i	0.0509795	+	0.0722052i
$641$	1.20018	+	0.692925i	0.0474043	+	0.0273689i	0.523515	−	0.852017i	$-0.324620\pi$
$641$	1.20018	+	0.692925i	0.0474043	+	0.0273689i	−0.476111	+	0.879385i	$0.657954\pi$
$642$	−6.41503	−	27.4632i	−0.253181	−	1.08389i
$643$	2.09081	−	0.560231i	0.0824535	−	0.0220933i	−0.217356	−	0.976092i	$-0.569743\pi$
$643$	2.09081	−	0.560231i	0.0824535	−	0.0220933i	0.299810	+	0.953999i	$0.403077\pi$
$644$	0.0296298	−	2.35220i	0.00116758	−	0.0926898i
$645$	−4.48797	−	13.5140i	−0.176714	−	0.532113i
$646$	−2.62049			−0.103102
$647$	3.66341	−	13.6720i	0.144024	−	0.537503i	−0.855773	−	0.517351i	$-0.826918\pi$
$647$	3.66341	−	13.6720i	0.144024	−	0.537503i	0.999797	−	0.0201523i	$-0.00641512\pi$
$648$	−7.13147	+	5.49019i	−0.280150	+	0.215675i
$649$	−15.2849	−	8.82475i	−0.599985	−	0.346402i
$650$	10.8072	+	12.6774i	0.423894	+	0.497249i
$651$	24.1401	+	15.4227i	0.946123	+	0.604465i
$652$	−2.90662	−	10.8476i	−0.113832	−	0.424827i
$653$	19.8112	+	5.30840i	0.775273	+	0.207734i	0.624700	−	0.780865i	$-0.285221\pi$
$653$	19.8112	+	5.30840i	0.775273	+	0.207734i	0.150573	+	0.988599i	$0.451888\pi$
$654$	16.8022	+	31.4046i	0.657017	+	1.22802i
$655$	15.3488	+	41.6641i	0.599727	+	1.62795i
$656$	1.30462	+	0.753225i	0.0509370	+	0.0294085i
$657$	−27.3524	−	9.26066i	−1.06712	−	0.361293i
$658$	−4.10866	−	16.1445i	−0.160172	−	0.629376i
$659$	−11.0170	−	19.0819i	−0.429159	−	0.743326i	0.567639	−	0.823277i	$-0.307857\pi$
$659$	−11.0170	−	19.0819i	−0.429159	−	0.743326i	−0.996799	+	0.0799514i	$0.974524\pi$
$660$	−0.318863	−	5.41301i	−0.0124117	−	0.210701i
$661$	−44.3466			−1.72488			−0.862442	−	0.506156i	$-0.831066\pi$
$661$	−44.3466			−1.72488			−0.862442	+	0.506156i	$0.831066\pi$
$662$	16.8313	+	16.8313i	0.654169	+	0.654169i
$663$	11.3038	−	10.5956i	0.439004	−	0.411500i
$664$	−14.0790	+	8.12850i	−0.546370	+	0.315447i
$665$	2.48576	−	5.21191i	0.0963936	−	0.202109i
$666$	15.1209	+	10.0861i	0.585921	+	0.390827i
$667$	0.732588	+	2.73406i	0.0283659	+	0.105863i
$668$	−6.65391	−	24.8327i	−0.257448	−	0.960807i
$669$	33.4213	−	17.8811i	1.29214	−	0.691323i
$670$	2.05817	−	11.9447i	0.0795139	−	0.461463i
$671$	1.91274	+	1.10432i	0.0738406	+	0.0426319i
$672$	0.986077	+	4.47523i	0.0380387	+	0.172636i
$673$	−0.181145	+	0.676043i	−0.00698263	+	0.0260595i	−0.969329	−	0.245766i	$-0.920961\pi$
$673$	−0.181145	+	0.676043i	−0.00698263	+	0.0260595i	0.962347	+	0.271825i	$0.0876273\pi$
$674$	−16.9534	+	29.3641i	−0.653020	+	1.13106i
$675$	24.4309	−	8.83914i	0.940346	−	0.340219i
$676$	−0.949743	−	1.64500i	−0.0365286	−	0.0632694i
$677$	4.07994	+	4.07994i	0.156805	+	0.156805i	0.781149	−	0.624344i	$-0.214634\pi$
$677$	4.07994	+	4.07994i	0.156805	+	0.156805i	−0.624344	+	0.781149i	$0.714634\pi$
$678$	28.3624	−	6.62505i	1.08925	−	0.254434i
$679$	−33.7505	−	0.425142i	−1.29522	−	0.0163154i
$680$	−5.63331	+	2.07527i	−0.216028	+	0.0795831i
$681$	−6.70048	−	4.16294i	−0.256763	−	0.159524i
$682$	2.26516	+	8.45369i	0.0867374	+	0.323709i
$683$	−36.0556	−	9.66107i	−1.37963	−	0.369671i	−0.508643	−	0.860977i	$-0.669853\pi$
$683$	−36.0556	−	9.66107i	−1.37963	−	0.369671i	−0.870987	+	0.491307i	$0.836519\pi$
$684$	−2.43594	−	1.62485i	−0.0931405	−	0.0621275i
$685$	1.80442	+	19.7377i	0.0689432	+	0.754138i
$686$	−18.5070	−	0.699674i	−0.706602	−	0.0267137i
$687$	20.5894	+	6.23680i	0.785535	+	0.237949i
$688$	−0.951596	+	3.55140i	−0.0362793	+	0.135396i
$689$	0.521760			0.0198775
$690$	3.07829	+	1.54343i	0.117188	+	0.0587572i
$691$	12.3658			0.470415			0.235208	−	0.971945i	$-0.424423\pi$
$691$	12.3658			0.470415			0.235208	+	0.971945i	$0.424423\pi$
$692$	−18.3604	−	18.3604i	−0.697959	−	0.697959i
$693$	3.69596	−	10.4800i	0.140398	−	0.398101i
$694$			15.4290i			0.585678i
$695$	18.9009	−	22.7045i	0.716953	−	0.861231i
$696$	−2.60120	−	4.86185i	−0.0985981	−	0.184288i
$697$	−2.85991	+	2.85991i	−0.108327	+	0.108327i
$698$	−12.2578	−	3.28446i	−0.463964	−	0.124319i
$699$	−2.76244	+	4.44630i	−0.104485	+	0.168174i
$700$	1.21615	−	13.1727i	0.0459662	−	0.497883i
$701$		−	8.90880i		−	0.336481i	−0.985746	−	0.168240i	$-0.946192\pi$
$701$		−	8.90880i		−	0.336481i	0.985746	−	0.168240i	$-0.0538085\pi$
$702$	17.0776	−	2.84044i	0.644554	−	0.107206i
$703$	−1.53053	+	5.71203i	−0.0577252	+	0.215433i
$704$	−0.700028	+	1.21248i	−0.0263833	+	0.0456972i
$705$	23.8858	+	4.91556i	0.899592	+	0.185131i
$706$	11.9016	−	20.6141i	0.447922	−	0.775824i
$707$	−38.6166	−	10.8704i	−1.45233	−	0.408825i
$708$	−15.9304	+	14.9324i	−0.598703	+	0.561193i
$709$		−	26.9039i		−	1.01040i	−0.863004	−	0.505198i	$-0.831420\pi$
$709$		−	26.9039i		−	1.01040i	0.863004	−	0.505198i	$-0.168580\pi$
$710$	−5.35567	−	7.58555i	−0.200995	−	0.284681i
$711$	11.6000	+	0.751050i	0.435035	+	0.0281666i
$712$	−3.58655	−	13.3852i	−0.134412	−	0.501632i
$713$	−5.36860	−	1.43851i	−0.201056	−	0.0538727i
$714$	−12.2909	−	0.552524i	−0.459976	−	0.0206777i
$715$	−4.37119	+	9.47030i	−0.163473	+	0.354169i
$716$	2.42489	−	1.40001i	0.0906225	−	0.0523209i
$717$	10.7006	−	2.49951i	0.399620	−	0.0933457i
$718$	−14.9838	+	4.01490i	−0.559191	+	0.149835i
$719$	12.2314	−	21.1855i	0.456156	−	0.790085i	−0.542598	−	0.839993i	$-0.682559\pi$
$719$	12.2314	−	21.1855i	0.456156	−	0.790085i	0.998754	+	0.0499071i	$0.0158925\pi$
$720$	−6.52337	−	1.56384i	−0.243112	−	0.0582808i
$721$	−0.432395	+	34.3263i	−0.0161032	+	1.27838i
$722$	−4.67100	+	17.4324i	−0.173836	+	0.648766i
$723$	−9.89780	+	2.31199i	−0.368103	+	0.0859838i
$724$			2.71266i			0.100815i
$725$	2.88622	+	15.6536i	0.107192	+	0.581360i
$726$	−13.8057	+	7.38636i	−0.512378	+	0.274134i
$727$	−28.6866	−	7.68656i	−1.06393	−	0.285079i	−0.315932	−	0.948782i	$-0.602317\pi$
$727$	−28.6866	−	7.68656i	−1.06393	−	0.285079i	−0.747996	+	0.663703i	$0.768984\pi$
$728$	2.38855	−	8.48519i	0.0885254	−	0.314482i
$729$	5.20431	−	26.4937i	0.192752	−	0.981247i
$730$	−7.44049	−	20.1971i	−0.275385	−	0.747529i
$731$	−8.54870	−	4.93559i	−0.316185	−	0.182550i
$732$	1.99352	−	1.86863i	0.0736828	−	0.0690664i
$733$	−0.504403	+	1.88246i	−0.0186305	+	0.0695301i	−0.974615	−	0.223886i	$-0.928126\pi$
$733$	−0.504403	+	1.88246i	−0.0186305	+	0.0695301i	0.955985	+	0.293416i	$0.0947922\pi$
$734$	12.1450	−	21.0358i	0.448281	−	0.776446i
$735$	12.7579	−	23.9214i	0.470583	−	0.882356i
$736$	−0.444560	−	0.770000i	−0.0163867	−	0.0283826i
$737$	7.33047	−	1.96419i	0.270021	−	0.0723520i
$738$	−4.43181	+	0.885203i	−0.163137	+	0.0325848i
$739$	−5.90884	+	3.41147i	−0.217360	+	0.125493i	−0.604727	−	0.796433i	$-0.706718\pi$
$739$	−5.90884	+	3.41147i	−0.217360	+	0.125493i	0.387367	+	0.921926i	$0.373385\pi$
$740$	1.23338	+	13.4914i	0.0453399	+	0.495953i
$741$	2.65711	+	4.96636i	0.0976115	+	0.182444i
$742$	−0.289264	−	0.296644i	−0.0106192	−	0.0108901i
$743$	9.88034	+	36.8739i	0.362474	+	1.35277i	0.870812	+	0.491615i	$0.163593\pi$
$743$	9.88034	+	36.8739i	0.362474	+	1.35277i	−0.508338	+	0.861158i	$0.669740\pi$
$744$	10.8216	+	0.349958i	0.396738	+	0.0128301i
$745$	16.5326	−	6.09049i	0.605707	−	0.223138i
$746$	−4.05095	+	2.33882i	−0.148316	+	0.0856301i
$747$	15.6402	−	46.1952i	0.572246	−	1.69019i
$748$	−2.65793	−	2.65793i	−0.0971836	−	0.0971836i
$749$	37.5767	−	21.0684i	1.37302	−	0.769822i
$750$	16.5672	+	10.0263i	0.604950	+	0.366109i
$751$	3.79091	+	6.56604i	0.138332	+	0.239598i	0.926865	−	0.375394i	$-0.122493\pi$
$751$	3.79091	+	6.56604i	0.138332	+	0.239598i	−0.788533	+	0.614992i	$0.789159\pi$
$752$	−4.45232	−	4.45232i	−0.162359	−	0.162359i
$753$	−1.92559	+	1.80495i	−0.0701725	+	0.0657761i
$754$			10.6066i			0.386268i
$755$	−20.0709	−	16.7085i	−0.730455	−	0.608086i
$756$	−11.0827	−	8.13466i	−0.403076	−	0.295855i
$757$	0.229660	−	0.229660i	0.00834713	−	0.00834713i	−0.702921	−	0.711268i	$-0.748121\pi$
$757$	0.229660	−	0.229660i	0.00834713	−	0.00834713i	0.711268	+	0.702921i	$0.248121\pi$
$758$	8.12499	−	8.12499i	0.295113	−	0.295113i
$759$	−0.0696892	+	2.15496i	−0.00252956	+	0.0782201i
$760$	−0.198695	−	2.17343i	−0.00720743	−	0.0788387i
$761$	−23.0735	+	13.3215i	−0.836414	+	0.482904i	−0.856044	−	0.516903i	$-0.827085\pi$
$761$	−23.0735	+	13.3215i	−0.836414	+	0.482904i	0.0196296	+	0.999807i	$0.493751\pi$
$762$	−13.5434	−	14.4487i	−0.490627	−	0.523420i
$763$	−38.9522	+	37.9831i	−1.41016	+	1.37508i
$764$	8.32800			0.301296
$765$	8.58850	−	15.8305i	0.310518	−	0.572355i
$766$	−4.23849	−	7.34127i	−0.153143	−	0.265251i
$767$	40.5697	−	10.8706i	1.46489	−	0.392516i
$768$	1.18452	+	1.26369i	0.0427426	+	0.0455995i
$769$	−25.3689	−	14.6467i	−0.914824	−	0.528174i	−0.0328440	−	0.999460i	$-0.510456\pi$
$769$	−25.3689	−	14.6467i	−0.914824	−	0.528174i	−0.881980	+	0.471287i	$0.843790\pi$
$770$	7.80767	−	2.76511i	0.281369	−	0.0996477i
$771$	−31.2194	+	16.7031i	−1.12434	+	0.601547i
$772$	−5.98669	+	5.98669i	−0.215466	+	0.215466i
$773$	−38.0890	−	10.2059i	−1.36997	−	0.367081i	−0.502500	−	0.864577i	$-0.667586\pi$
$773$	−38.0890	−	10.2059i	−1.36997	−	0.367081i	−0.867466	+	0.497496i	$0.834253\pi$
$774$	−4.88633	−	9.88868i	−0.175635	−	0.355441i
$775$	−29.4531	−	10.4606i	−1.05799	−	0.375756i
$776$	−11.0483	+	6.37875i	−0.396611	+	0.228984i
$777$	−8.38307	+	26.4686i	−0.300741	+	0.949554i
$778$	29.3288	−	7.85864i	1.05149	−	0.281746i
$779$	−0.735179	−	1.27337i	−0.0263405	−	0.0456231i
$780$	9.64512	+	8.57201i	0.345351	+	0.306927i
$781$	2.90700	−	5.03506i	0.104020	−	0.180169i
$782$	2.30578	−	0.617831i	0.0824544	−	0.0220936i
$783$	15.4886	+	5.80843i	0.553517	+	0.207576i
$784$	−6.14842	+	3.34619i	−0.219586	+	0.119507i
$785$	9.69548	+	13.7323i	0.346047	+	0.490126i
$786$	16.2249	+	30.3256i	0.578723	+	1.08168i
$787$	−30.5419	+	30.5419i	−1.08870	+	1.08870i	−0.0930383	+	0.995663i	$0.529658\pi$
$787$	−30.5419	+	30.5419i	−1.08870	+	1.08870i	−0.995663	+	0.0930383i	$0.970342\pi$
$788$	−2.30556	+	2.30556i	−0.0821323	+	0.0821323i
$789$	−16.2829	+	26.2082i	−0.579685	+	0.933036i
$790$	4.99725	+	7.07790i	0.177794	+	0.251820i
$791$	21.7582	+	38.8070i	0.773631	+	1.37982i
$792$	−0.822685	−	4.11881i	−0.0292328	−	0.146356i
$793$	−5.07687	+	1.36034i	−0.180285	+	0.0483072i
$794$	−2.05647	+	3.56190i	−0.0729812	+	0.126407i
$795$	0.575608	−	0.191158i	0.0204147	−	0.00677969i
$796$	−5.71586	−	9.90016i	−0.202593	−	0.350902i
$797$	−12.2459	+	3.28128i	−0.433772	+	0.116229i	−0.469096	−	0.883147i	$-0.655420\pi$
$797$	−12.2459	+	3.28128i	−0.433772	+	0.116229i	0.0353244	+	0.999376i	$0.488754\pi$
$798$	1.35050	−	4.26403i	0.0478071	−	0.150945i
$799$	14.6401	−	8.45249i	0.517931	−	0.299028i
$800$	−2.14837	−	4.51492i	−0.0759564	−	0.159626i
$801$	34.5843	+	23.0688i	1.22198	+	0.815095i
$802$	10.4435	+	2.79831i	0.368771	+	0.0988119i
$803$	9.52949	−	9.52949i	0.336288	−	0.336288i
$804$	0.303460	−	9.38374i	0.0107022	−	0.330939i
$805$	−0.958419	+	5.17205i	−0.0337798	+	0.182291i
$806$	−18.0368	−	10.4135i	−0.635319	−	0.366801i
$807$	−5.74036	+	18.9505i	−0.202070	+	0.667090i
$808$	−14.6463	+	3.92447i	−0.515255	+	0.138062i
$809$	−3.93638	−	6.81801i	−0.138396	−	0.239708i	0.788494	−	0.615043i	$-0.210861\pi$
$809$	−3.93638	−	6.81801i	−0.138396	−	0.239708i	−0.926890	+	0.375334i	$0.877528\pi$
$810$	17.7995	−	9.39035i	0.625410	−	0.329943i
$811$	29.0830			1.02124			0.510621	−	0.859806i	$-0.329415\pi$
$811$	29.0830			1.02124			0.510621	+	0.859806i	$0.329415\pi$
$812$	6.03031	−	5.88027i	0.211622	−	0.206357i
$813$	21.1696	−	4.94492i	0.742449	−	0.173426i
$814$	−7.34606	+	4.24125i	−0.257479	+	0.148656i
$815$	2.28618	+	25.0075i	0.0800813	+	0.875973i
$816$	−4.10026	+	2.19373i	−0.143538	+	0.0767959i
$817$	2.53752	−	2.53752i	0.0887767	−	0.0887767i
$818$	2.58678	−	2.58678i	0.0904446	−	0.0904446i
$819$	11.4156	+	23.8541i	0.398892	+	0.833529i
$820$	−2.58886	−	2.15517i	−0.0904071	−	0.0752616i
$821$		−	21.2668i		−	0.742216i	−0.928590	−	0.371108i	$-0.878978\pi$
$821$		−	21.2668i		−	0.742216i	0.928590	−	0.371108i	$-0.121022\pi$
$822$	3.49213	+	14.9501i	0.121802	+	0.521443i
$823$	14.8479	+	14.8479i	0.517564	+	0.517564i	0.916834	−	0.399269i	$-0.130736\pi$
$823$	14.8479	+	14.8479i	0.517564	+	0.517564i	−0.399269	+	0.916834i	$0.630736\pi$
$824$	6.48757	+	11.2368i	0.226005	+	0.391453i
$825$	−1.35266	+	12.0492i	−0.0470937	+	0.419498i
$826$	−28.6723	−	17.0390i	−0.997636	−	0.592864i
$827$	−15.3137	−	15.3137i	−0.532511	−	0.532511i	0.388808	−	0.921319i	$-0.372887\pi$
$827$	−15.3137	−	15.3137i	−0.532511	−	0.532511i	−0.921319	+	0.388808i	$0.872887\pi$
$828$	2.52648	+	0.855387i	0.0878013	+	0.0297268i
$829$	−47.3861	+	27.3584i	−1.64579	+	0.950196i	−0.667067	+	0.744998i	$0.732450\pi$
$829$	−47.3861	+	27.3584i	−1.64579	+	0.950196i	−0.978721	+	0.205198i	$0.934216\pi$
$830$	34.1107	−	12.5662i	1.18400	−	0.436178i
$831$	12.9704	−	20.8766i	0.449938	−	0.724200i
$832$	−0.862319	−	3.21822i	−0.0298955	−	0.111572i
$833$	−4.40534	−	18.2700i	−0.152636	−	0.633019i
$834$	12.0762	−	19.4373i	0.418164	−	0.673059i
$835$	5.23358	+	57.2478i	0.181116	+	1.98114i
$836$	1.18344	−	0.683257i	0.0409300	−	0.0236309i
$837$	−25.0841	+	20.6361i	−0.867034	+	0.713287i
$838$	−22.7242	+	6.08892i	−0.784993	+	0.210338i
$839$	15.7307	+	27.2463i	0.543083	+	0.940647i	0.998725	+	0.0504839i	$0.0160764\pi$
$839$	15.7307	+	27.2463i	0.543083	+	0.940647i	−0.455642	+	0.890163i	$0.650590\pi$
$840$	−0.473679	−	10.2360i	−0.0163435	−	0.353175i
$841$	9.43270	−	16.3379i	0.325265	−	0.563376i
$842$	−2.36113	+	8.81187i	−0.0813700	+	0.303677i
$843$	20.3966	+	6.17841i	0.702498	+	0.212796i
$844$	8.71220	+	5.02999i	0.299886	+	0.173139i
$845$	1.46824	+	3.98554i	0.0505092	+	0.137107i
$846$	18.8501	+	1.22046i	0.648081	+	0.0419604i
$847$	−16.6976	−	17.1237i	−0.573738	−	0.588376i
$848$	−0.151267	−	0.0405318i	−0.00519452	−	0.00139187i
$849$	1.49448	−	46.2130i	0.0512904	−	1.58603i
$850$	13.2015	−	2.43410i	0.452808	−	0.0834891i
$851$		−	5.38689i		−	0.184660i
$852$	−4.91893	−	5.24771i	−0.168520	−	0.179784i
$853$	4.43850	−	16.5647i	0.151971	−	0.567165i	−0.847374	−	0.530996i	$-0.821818\pi$
$853$	4.43850	−	16.5647i	0.151971	−	0.567165i	0.999346	−	0.0361687i	$-0.0115154\pi$
$854$	3.58803	+	2.13225i	0.122780	+	0.0729642i
$855$	4.75087	+	4.50542i	0.162476	+	0.154082i
$856$	8.14136	−	14.1012i	0.278266	−	0.481971i
$857$	23.7431	−	6.36193i	0.811047	−	0.217319i	0.170619	−	0.985337i	$-0.445423\pi$
$857$	23.7431	−	6.36193i	0.811047	−	0.217319i	0.640429	+	0.768018i	$0.278757\pi$
$858$	−2.34225	+	7.73241i	−0.0799630	+	0.263980i
$859$	−22.9251	+	13.2358i	−0.782195	+	0.451600i	−0.837208	−	0.546885i	$-0.815813\pi$
$859$	−22.9251	+	13.2358i	−0.782195	+	0.451600i	0.0550128	+	0.998486i	$0.482480\pi$
$860$	3.44539	−	7.46454i	0.117487	−	0.254539i
$861$	−3.17974	−	6.12752i	−0.108365	−	0.208825i
$862$	−27.4241	−	7.34827i	−0.934069	−	0.250283i
$863$	5.10131	+	19.0383i	0.173651	+	0.648073i	0.996778	+	0.0802153i	$0.0255608\pi$
$863$	5.10131	+	19.0383i	0.173651	+	0.648073i	−0.823127	+	0.567857i	$0.807773\pi$
$864$	−5.17173	−	0.503149i	−0.175946	−	0.0171175i
$865$	33.4875	+	47.4304i	1.13861	+	1.61268i
$866$			12.7500i			0.433262i
$867$	3.85776	+	16.5153i	0.131016	+	0.560890i
$868$	4.07902	+	16.0280i	0.138451	+	0.544025i
$869$	−2.71245	+	4.69810i	−0.0920135	+	0.159372i
$870$	3.88595	+	11.7012i	0.131746	+	0.396708i
$871$	−9.02992	+	15.6403i	−0.305967	+	0.529950i
$872$	−5.32221	+	19.8628i	−0.180233	+	0.672638i
$873$	12.2735	−	36.2511i	0.415395	−	1.22692i
$874$			0.867818i			0.0293544i
$875$	−7.68157	+	28.5656i	−0.259684	+	0.965694i
$876$	−7.86519	−	14.7007i	−0.265740	−	0.496690i
$877$	−52.7573	−	14.1363i	−1.78149	−	0.477348i	−0.790634	−	0.612290i	$-0.790249\pi$
$877$	−52.7573	−	14.1363i	−1.78149	−	0.477348i	−0.990854	+	0.134942i	$0.956915\pi$
$878$	24.4132	−	24.4132i	0.823906	−	0.823906i
$879$	−7.51349	+	12.0934i	−0.253424	+	0.407900i
$880$	2.00296	−	2.40603i	0.0675196	−	0.0811071i
$881$		−	38.5826i		−	1.29988i	−0.759985	−	0.649940i	$-0.774794\pi$
$881$		−	38.5826i		−	1.29988i	0.759985	−	0.649940i	$-0.225206\pi$
$882$	7.23333	−	19.7149i	0.243559	−	0.663837i
$883$	23.3647	+	23.3647i	0.786284	+	0.786284i	0.980883	−	0.194599i	$-0.0623404\pi$
$883$	23.3647	+	23.3647i	0.786284	+	0.786284i	−0.194599	+	0.980883i	$0.562340\pi$
$884$	8.94509			0.300856
$885$	40.7740	−	26.8561i	1.37060	−	0.902759i
$886$	2.50330			0.0841000
$887$	−0.836905	+	3.12337i	−0.0281005	+	0.104873i	−0.978552	−	0.206001i	$-0.933955\pi$
$887$	−0.836905	+	3.12337i	−0.0281005	+	0.104873i	0.950451	+	0.310874i	$0.100622\pi$
$888$	2.38699	+	10.2189i	0.0801020	+	0.342923i
$889$	15.4542	−	26.0053i	0.518316	−	0.872191i
$890$	2.82098	+	30.8574i	0.0945594	+	1.03434i
$891$	10.0088	+	7.65481i	0.335308	+	0.256446i
$892$	21.1382	+	5.66397i	0.707760	+	0.189644i
$893$	1.59062	+	5.93627i	0.0532281	+	0.198650i
$894$	12.0334	−	6.43813i	0.402457	−	0.215323i
$895$	−5.87507	+	2.16433i	−0.196382	+	0.0723457i
$896$	−1.35163	+	2.27444i	−0.0451548	+	0.0759838i
$897$	−3.50892	−	3.74346i	−0.117159	−	0.124990i
$898$	−21.7758	−	21.7758i	−0.726668	−	0.726668i
$899$	−9.95017	−	17.2342i	−0.331857	−	0.574793i
$900$	13.7811	+	5.92298i	0.459370	+	0.197433i
$901$	0.210224	−	0.364119i	0.00700358	−	0.0121306i
$902$	0.545879	−	2.03725i	0.0181758	−	0.0678330i
$903$	12.4368	−	11.3668i	0.413872	−	0.378262i
$904$	14.5629	+	8.40791i	0.484355	+	0.279643i
$905$	1.02999	−	5.97761i	0.0342381	−	0.198702i
$906$	−17.1827	−	10.6754i	−0.570857	−	0.354667i
$907$	−11.6723	−	43.5616i	−0.387572	−	1.44644i	−0.834072	−	0.551656i	$-0.813996\pi$
$907$	−11.6723	−	43.5616i	−0.387572	−	1.44644i	0.446500	−	0.894784i	$-0.352670\pi$
$908$	−1.17875	−	4.39917i	−0.0391184	−	0.145992i
$909$	25.2422	−	37.8427i	0.837232	−	1.25516i
$910$	−8.48520	+	17.7910i	−0.281282	+	0.589766i
$911$	23.2044	−	13.3971i	0.768797	−	0.443865i	−0.0636484	−	0.997972i	$-0.520274\pi$
$911$	23.2044	−	13.3971i	0.768797	−	0.443865i	0.832445	+	0.554107i	$0.186940\pi$
$912$	−0.384539	−	1.64624i	−0.0127334	−	0.0545125i
$913$	16.0943	+	16.0943i	0.532642	+	0.532642i
$914$	−25.9311			−0.857724
$915$	−5.10243	+	3.36076i	−0.168681	+	0.111103i
$916$	6.21035	+	10.7566i	0.205196	+	0.355409i
$917$	−37.6139	+	36.6780i	−1.24212	+	1.21122i
$918$	4.89856	−	13.0624i	0.161677	−	0.431122i
$919$	−13.6927	−	7.90548i	−0.451680	−	0.260778i	0.256859	−	0.966449i	$-0.417312\pi$
$919$	−13.6927	−	7.90548i	−0.451680	−	0.260778i	−0.708539	+	0.705671i	$0.750646\pi$
$920$	0.687262	+	1.86557i	0.0226584	+	0.0615059i
$921$	41.2009	+	1.33239i	1.35761	+	0.0439038i
$922$	9.99303	+	2.67762i	0.329103	+	0.0881828i
$923$	3.58094	+	13.3642i	0.117868	+	0.439889i
$924$	5.69476	−	2.95517i	0.187344	−	0.0972180i
$925$	2.40478	−	30.1978i	0.0790686	−	0.992898i
$926$	1.97564	+	1.14063i	0.0649235	+	0.0374836i
$927$	−36.8696	−	12.4829i	−1.21096	−	0.409992i
$928$	0.823948	−	3.07501i	0.0270474	−	0.100942i
$929$	−9.49245			−0.311437			−0.155719	−	0.987801i	$-0.549769\pi$
$929$	−9.49245			−0.311437			−0.155719	+	0.987801i	$0.549769\pi$
$930$	−23.7135	−	4.88010i	−0.777596	−	0.160025i
$931$	6.83013	+	0.172100i	0.223848	+	0.00564036i
$932$	−2.91920	+	0.782196i	−0.0956215	+	0.0256217i
$933$	6.52955	−	6.12046i	0.213768	−	0.200375i
$934$	−4.39220	−	2.53584i	−0.143717	−	0.0829751i
$935$	4.84779	+	6.86621i	0.158540	+	0.224549i
$936$	8.31514	+	5.54645i	0.271789	+	0.181291i
$937$	9.11713	−	9.11713i	0.297844	−	0.297844i	−0.542325	−	0.840169i	$-0.682456\pi$
$937$	9.11713	−	9.11713i	0.297844	−	0.297844i	0.840169	+	0.542325i	$0.182456\pi$
$938$	13.8984	−	3.53705i	0.453798	−	0.115489i
$939$	−1.81823	+	56.2242i	−0.0593357	+	1.83481i
$940$	8.12057	+	11.5017i	0.264864	+	0.375142i
$941$		−	44.1047i		−	1.43777i	−0.695128	−	0.718886i	$-0.744652\pi$
$941$		−	44.1047i		−	1.43777i	0.695128	−	0.718886i	$-0.255348\pi$
$942$	8.90484	+	9.50003i	0.290135	+	0.309528i
$943$	0.947109	+	0.947109i	0.0308421	+	0.0308421i
$944$	−12.6063			−0.410299
$945$	21.3332	+	22.1336i	0.693968	+	0.720006i
$946$	5.14757			0.167362
$947$	9.83253	+	9.83253i	0.319514	+	0.319514i	0.848581	−	0.529066i	$-0.177458\pi$
$947$	9.83253	+	9.83253i	0.319514	+	0.319514i	−0.529066	+	0.848581i	$0.677458\pi$
$948$	4.58974	+	4.89651i	0.149068	+	0.159031i
$949$			32.0709i			1.04106i
$950$	−0.387405	+	4.86481i	−0.0125691	+	0.157835i
$951$	0.237189	−	7.33446i	0.00769137	−	0.237836i
$952$	−4.95915	−	5.08568i	−0.160727	−	0.164828i
$953$	38.6288	−	38.6288i	1.25131	−	1.25131i	0.296177	−	0.955133i	$-0.404288\pi$
$953$	38.6288	−	38.6288i	1.25131	−	1.25131i	0.955133	−	0.296177i	$-0.0957119\pi$
$954$	0.421193	−	0.208126i	0.0136366	−	0.00673832i
$955$	−18.3515	−	3.16212i	−0.593842	−	0.102324i
$956$	5.49431	+	3.17214i	0.177699	+	0.102594i
$957$	−5.63235	+	5.27948i	−0.182068	+	0.170661i
$958$	15.6873	−	4.20340i	0.506834	−	0.135806i
$959$	−20.4555	+	11.4689i	−0.660544	+	0.370351i
$960$	−2.13038	−	3.23442i	−0.0687577	−	0.104391i
$961$	8.07635			0.260527
$962$	5.22452	−	19.4982i	0.168445	−	0.628646i
$963$	9.56786	+	47.9020i	0.308320	+	1.54362i
$964$	−5.08212	−	2.93416i	−0.163684	−	0.0945030i
$965$	15.4654	−	10.9191i	0.497848	−	0.351498i
$966$	−0.182978	+	4.07035i	−0.00588721	+	0.130961i
$967$	10.0035	+	37.3334i	0.321690	+	1.20056i	0.917598	+	0.397509i	$0.130125\pi$
$967$	10.0035	+	37.3334i	0.321690	+	1.20056i	−0.595909	+	0.803052i	$0.703208\pi$
$968$	−8.73182	−	2.33968i	−0.280651	−	0.0752003i
$969$	4.53644	+	0.146704i	0.145732	+	0.00471280i
$970$	26.7680	−	9.86115i	0.859469	−	0.316623i
$971$	−45.4479	−	26.2393i	−1.45849	−	0.842060i	−0.459554	−	0.888150i	$-0.651991\pi$
$971$	−45.4479	−	26.2393i	−1.45849	−	0.842060i	−0.998937	+	0.0460897i	$0.985324\pi$
$972$	12.6530	−	9.10508i	0.405844	−	0.292046i
$973$	33.6471	+	9.47151i	1.07868	+	0.303643i
$974$	−10.7778	−	18.6677i	−0.345343	−	0.598151i
$975$	−17.9992	−	22.5515i	−0.576435	−	0.722225i
$976$	1.57754			0.0504958
$977$	39.2541	+	39.2541i	1.25585	+	1.25585i	0.953056	+	0.302796i	$0.0979200\pi$
$977$	39.2541	+	39.2541i	1.25585	+	1.25585i	0.302796	+	0.953056i	$0.402080\pi$
$978$	4.42449	+	18.9416i	0.141480	+	0.605685i
$979$	−16.8019	+	9.70056i	−0.536990	+	0.310031i
$980$	14.8192	−	5.03910i	0.473381	−	0.160968i
$981$	−27.3289	−	55.3067i	−0.872544	−	1.76581i
$982$	−2.26782	−	8.46361i	−0.0723689	−	0.270084i
$983$	2.60742	+	9.73104i	0.0831639	+	0.310372i	0.994960	−	0.100271i	$-0.0319710\pi$
$983$	2.60742	+	9.73104i	0.0831639	+	0.310372i	−0.911796	+	0.410643i	$0.865304\pi$
$984$	−2.21633	−	1.37698i	−0.0706539	−	0.0438965i
$985$	5.95594	−	4.20511i	0.189772	−	0.133986i
$986$	7.40197	+	4.27353i	0.235727	+	0.136097i
$987$	6.20887	+	28.1784i	0.197630	+	0.896929i
$988$	−0.841659	+	3.14112i	−0.0267768	+	0.0999322i
$989$	−1.63451	+	2.83105i	−0.0519743	+	0.0900221i
$990$	0.248960	+	9.38856i	0.00791246	+	0.298388i
$991$	14.8773	+	25.7683i	0.472594	+	0.818556i	0.999508	−	0.0313623i	$-0.00998456\pi$
$991$	14.8773	+	25.7683i	0.472594	+	0.818556i	−0.526915	+	0.849918i	$0.676651\pi$
$992$	4.42020	+	4.42020i	0.140342	+	0.140342i
$993$	−28.1952	−	30.0798i	−0.894749	−	0.954553i
$994$	5.61289	−	9.44504i	0.178030	−	0.299579i
$995$	8.83636	+	23.9862i	0.280132	+	0.760415i
$996$	24.8278	−	13.2834i	0.786700	−	0.420902i
$997$	−10.5589	−	39.4063i	−0.334403	−	1.24801i	−0.904515	−	0.426443i	$-0.859767\pi$
$997$	−10.5589	−	39.4063i	−0.334403	−	1.24801i	0.570111	−	0.821568i	$-0.306900\pi$
$998$	−17.5784	−	4.71013i	−0.556436	−	0.149096i
$999$	−25.6117	−	18.3070i	−0.810320	−	0.579207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.23.18	yes	192
5.2	odd	4	inner	630.2.cd.a.527.41	yes	192
7.4	even	3		630.2.bt.a.473.38	yes	192
9.2	odd	6		630.2.bt.a.443.26	yes	192
35.32	odd	12		630.2.bt.a.347.26	yes	192
45.2	even	12		630.2.bt.a.317.38	✓	192
63.11	odd	6	inner	630.2.cd.a.263.41	yes	192
315.137	even	12	inner	630.2.cd.a.137.18	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.38	✓	192	45.2	even	12
630.2.bt.a.347.26	yes	192	35.32	odd	12
630.2.bt.a.443.26	yes	192	9.2	odd	6
630.2.bt.a.473.38	yes	192	7.4	even	3
630.2.cd.a.23.18	yes	192	1.1	even	1	trivial
630.2.cd.a.137.18	yes	192	315.137	even	12	inner
630.2.cd.a.263.41	yes	192	63.11	odd	6	inner
630.2.cd.a.527.41	yes	192	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.18452 + 1.26369i) q^{3} +1.00000i q^{4} +(0.379698 - 2.20359i) q^{5} +(0.0559834 - 1.73115i) q^{6} +(2.56402 - 0.652527i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.193831 + 2.99373i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.18452 + 1.26369i) q^{3} +1.00000i q^{4} +(0.379698 - 2.20359i) q^{5} +(0.0559834 - 1.73115i) q^{6} +(2.56402 - 0.652527i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.193831 + 2.99373i) q^{9} +(-1.82666 + 1.28969i) q^{10} +(-1.21248 - 0.700028i) q^{11} +(-1.26369 + 1.18452i) q^{12} +(3.21822 - 0.862319i) q^{13} +(-2.27444 - 1.35163i) q^{14} +(3.23442 - 2.13038i) q^{15} -1.00000 q^{16} +(0.694879 - 2.59332i) q^{17} +(2.25395 - 1.97983i) q^{18} +(0.845277 + 0.488021i) q^{19} +(2.20359 + 0.379698i) q^{20} +(3.86172 + 2.46720i) q^{21} +(0.362361 + 1.35235i) q^{22} +(-0.858823 - 0.230121i) q^{23} +(1.73115 + 0.0559834i) q^{24} +(-4.71166 - 1.67340i) q^{25} +(-2.88537 - 1.66587i) q^{26} +(-4.01275 + 3.30119i) q^{27} +(0.652527 + 2.56402i) q^{28} +(-1.59174 - 2.75698i) q^{29} +(-3.79349 - 0.780677i) q^{30} +6.25111 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.551591 - 2.36140i) q^{33} +(-2.32511 + 1.34240i) q^{34} +(-0.464351 - 5.89783i) q^{35} +(-2.99373 - 0.193831i) q^{36} +(1.56810 + 5.85224i) q^{37} +(-0.252618 - 0.942785i) q^{38} +(4.90174 + 3.04540i) q^{39} +(-1.28969 - 1.82666i) q^{40} +(-1.30462 - 0.753225i) q^{41} +(-0.986077 - 4.47523i) q^{42} +(0.951596 - 3.55140i) q^{43} +(0.700028 - 1.21248i) q^{44} +(6.52337 + 1.56384i) q^{45} +(0.444560 + 0.770000i) q^{46} +(4.45232 + 4.45232i) q^{47} +(-1.18452 - 1.26369i) q^{48} +(6.14842 - 3.34619i) q^{49} +(2.14837 + 4.51492i) q^{50} +(4.10026 - 2.19373i) q^{51} +(0.862319 + 3.21822i) q^{52} +(0.151267 + 0.0405318i) q^{53} +(5.17173 + 0.503149i) q^{54} +(-2.00296 + 2.40603i) q^{55} +(1.35163 - 2.27444i) q^{56} +(0.384539 + 1.64624i) q^{57} +(-0.823948 + 3.07501i) q^{58} +12.6063 q^{59} +(2.13038 + 3.23442i) q^{60} -1.57754 q^{61} +(-4.42020 - 4.42020i) q^{62} +(1.45650 + 7.80247i) q^{63} -1.00000i q^{64} +(-0.678250 - 7.41907i) q^{65} +(-1.27973 + 2.05980i) q^{66} +(-3.83290 + 3.83290i) q^{67} +(2.59332 + 0.694879i) q^{68} +(-0.726491 - 1.35787i) q^{69} +(-3.84205 + 4.49874i) q^{70} +4.15268i q^{71} +(1.97983 + 2.25395i) q^{72} +(-2.49135 + 9.29786i) q^{73} +(3.02934 - 5.24697i) q^{74} +(-3.46639 - 7.93626i) q^{75} +(-0.488021 + 0.845277i) q^{76} +(-3.56562 - 1.00371i) q^{77} +(-1.31263 - 5.61948i) q^{78} -3.87477i q^{79} +(-0.379698 + 2.20359i) q^{80} +(-8.92486 - 1.16056i) q^{81} +(0.389898 + 1.45512i) q^{82} +(-15.7031 - 4.20762i) q^{83} +(-2.46720 + 3.86172i) q^{84} +(-5.45079 - 2.51591i) q^{85} +(-3.18410 + 1.83834i) q^{86} +(1.59852 - 5.27717i) q^{87} +(-1.35235 + 0.362361i) q^{88} +(6.92869 - 12.0008i) q^{89} +(-3.50692 - 5.71852i) q^{90} +(7.68889 - 4.31098i) q^{91} +(0.230121 - 0.858823i) q^{92} +(7.40455 + 7.89947i) q^{93} -6.29653i q^{94} +(1.39635 - 1.67735i) q^{95} +(-0.0559834 + 1.73115i) q^{96} +(-12.3228 - 3.30188i) q^{97} +(-6.71370 - 1.98147i) q^{98} +(2.33071 - 3.49417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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