LMFDB - Embedded newform 1890.2.bk.b.521.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(341,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 5]))

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

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

chi := DirichletCharacter("1890.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bk (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.3
Character	$\chi$	$=$	1890.521
Dual form			1890.2.bk.b.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.21694 + 1.44401i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.21694 + 1.44401i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +(4.20911 - 2.43013i) q^{11} +(-3.42136 + 1.97532i) q^{13} +(1.44401 + 2.21694i) q^{14} +1.00000 q^{16} +(-1.25228 + 2.16902i) q^{17} +(-0.962409 + 0.555647i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-2.43013 - 4.20911i) q^{22} +(-2.86139 - 1.65202i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.97532 + 3.42136i) q^{26} +(2.21694 - 1.44401i) q^{28} +(-3.70789 - 2.14075i) q^{29} +7.39752i q^{31} -1.00000i q^{32} +(2.16902 + 1.25228i) q^{34} +(0.142082 + 2.64193i) q^{35} +(-1.82085 - 3.15380i) q^{37} +(0.555647 + 0.962409i) q^{38} +(0.866025 + 0.500000i) q^{40} +(3.91000 + 6.77231i) q^{41} +(-3.62690 + 6.28198i) q^{43} +(-4.20911 + 2.43013i) q^{44} +(-1.65202 + 2.86139i) q^{46} -11.6852 q^{47} +(2.82965 - 6.40258i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.42136 - 1.97532i) q^{52} +(-4.92292 - 2.84225i) q^{53} -4.86026i q^{55} +(-1.44401 - 2.21694i) q^{56} +(-2.14075 + 3.70789i) q^{58} +1.39292 q^{59} +9.20374i q^{61} +7.39752 q^{62} -1.00000 q^{64} +3.95064i q^{65} +6.01448 q^{67} +(1.25228 - 2.16902i) q^{68} +(2.64193 - 0.142082i) q^{70} +9.66386i q^{71} +(12.0570 + 6.96114i) q^{73} +(-3.15380 + 1.82085i) q^{74} +(0.962409 - 0.555647i) q^{76} +(-5.82221 + 11.4655i) q^{77} -7.83821 q^{79} +(0.500000 - 0.866025i) q^{80} +(6.77231 - 3.91000i) q^{82} +(-0.393868 + 0.682199i) q^{83} +(1.25228 + 2.16902i) q^{85} +(6.28198 + 3.62690i) q^{86} +(2.43013 + 4.20911i) q^{88} +(7.49361 + 12.9793i) q^{89} +(4.73255 - 9.31966i) q^{91} +(2.86139 + 1.65202i) q^{92} +11.6852i q^{94} +1.11129i q^{95} +(-14.9781 - 8.64760i) q^{97} +(-6.40258 - 2.82965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) $ 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7	$ 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) $ 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7 + 28 * q^16 - 6 * q^17 - 6 * q^19 - 14 * q^20 - 6 * q^22 - 30 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 + 4 * q^35 + 4 * q^37 + 6 * q^38 + 18 * q^41 + 28 * q^43 - 18 * q^46 - 60 * q^47 - 20 * q^49 - 42 * q^53 + 6 * q^58 + 48 * q^59 - 12 * q^62 - 28 * q^64 + 80 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^73 + 6 * q^76 + 18 * q^77 - 4 * q^79 + 14 * q^80 + 24 * q^82 - 18 * q^83 + 6 * q^85 + 96 * q^86 + 6 * q^88 + 6 * q^89 + 66 * q^91 + 30 * q^92 + 72 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−2.21694	+	1.44401i	−0.837925	+	0.545786i
$7$	−2.21694	+	1.44401i	−0.837925	+	0.545786i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	4.20911	−	2.43013i	1.26909	−	0.732712i	0.294278	−	0.955720i	$-0.404921\pi$
$11$	4.20911	−	2.43013i	1.26909	−	0.732712i	0.974817	+	0.223008i	$0.0715875\pi$
$12$		0			0
$13$	−3.42136	+	1.97532i	−0.948914	+	0.547856i	−0.892743	−	0.450566i	$-0.851222\pi$
$13$	−3.42136	+	1.97532i	−0.948914	+	0.547856i	−0.0561705	+	0.998421i	$0.517889\pi$
$14$	1.44401	+	2.21694i	0.385929	+	0.592502i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.25228	+	2.16902i	−0.303723	+	0.526064i	−0.976976	−	0.213348i	$-0.931563\pi$
$17$	−1.25228	+	2.16902i	−0.303723	+	0.526064i	0.673253	+	0.739412i	$0.264896\pi$
$18$		0			0
$19$	−0.962409	+	0.555647i	−0.220792	+	0.127474i	−0.606317	−	0.795223i	$-0.707354\pi$
$19$	−0.962409	+	0.555647i	−0.220792	+	0.127474i	0.385525	+	0.922697i	$0.374020\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−2.43013	−	4.20911i	−0.518106	−	0.897385i
$23$	−2.86139	−	1.65202i	−0.596640	−	0.344470i	0.171079	−	0.985257i	$-0.445275\pi$
$23$	−2.86139	−	1.65202i	−0.596640	−	0.344470i	−0.767719	+	0.640787i	$0.778608\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.97532	+	3.42136i	0.387392	+	0.670983i
$27$		0			0
$28$	2.21694	−	1.44401i	0.418962	−	0.272893i
$29$	−3.70789	−	2.14075i	−0.688537	−	0.397527i	0.114527	−	0.993420i	$-0.463465\pi$
$29$	−3.70789	−	2.14075i	−0.688537	−	0.397527i	−0.803064	+	0.595893i	$0.796798\pi$
$30$		0			0
$31$			7.39752i			1.32863i	0.747451	+	0.664317i	$0.231277\pi$
$31$			7.39752i			1.32863i	−0.747451	+	0.664317i	$0.768723\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	2.16902	+	1.25228i	0.371983	+	0.214765i
$35$	0.142082	+	2.64193i	0.0240163	+	0.446568i
$36$		0			0
$37$	−1.82085	−	3.15380i	−0.299345	−	0.518482i	0.676641	−	0.736313i	$-0.263435\pi$
$37$	−1.82085	−	3.15380i	−0.299345	−	0.518482i	−0.975986	+	0.217832i	$0.930102\pi$
$38$	0.555647	+	0.962409i	0.0901378	+	0.156123i
$39$		0			0
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	3.91000	+	6.77231i	0.610639	+	1.05766i	0.991133	+	0.132874i	$0.0424206\pi$
$41$	3.91000	+	6.77231i	0.610639	+	1.05766i	−0.380494	+	0.924783i	$0.624246\pi$
$42$		0			0
$43$	−3.62690	+	6.28198i	−0.553098	+	0.957993i	0.444951	+	0.895555i	$0.353221\pi$
$43$	−3.62690	+	6.28198i	−0.553098	+	0.957993i	−0.998049	+	0.0624384i	$0.980112\pi$
$44$	−4.20911	+	2.43013i	−0.634547	+	0.366356i
$45$		0			0
$46$	−1.65202	+	2.86139i	−0.243577	+	0.421888i
$47$	−11.6852			−1.70445			−0.852227	−	0.523172i	$-0.824749\pi$
$47$	−11.6852			−1.70445			−0.852227	+	0.523172i	$0.824749\pi$
$48$		0			0
$49$	2.82965	−	6.40258i	0.404236	−	0.914655i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	3.42136	−	1.97532i	0.474457	−	0.273928i
$53$	−4.92292	−	2.84225i	−0.676216	−	0.390413i	0.122212	−	0.992504i	$-0.461001\pi$
$53$	−4.92292	−	2.84225i	−0.676216	−	0.390413i	−0.798428	+	0.602091i	$0.794335\pi$
$54$		0			0
$55$		−	4.86026i		−	0.655358i
$56$	−1.44401	−	2.21694i	−0.192964	−	0.296251i
$57$		0			0
$58$	−2.14075	+	3.70789i	−0.281094	+	0.486869i
$59$	1.39292			0.181343			0.0906716	−	0.995881i	$-0.471099\pi$
$59$	1.39292			0.181343			0.0906716	+	0.995881i	$0.471099\pi$
$60$		0			0
$61$			9.20374i			1.17842i	0.807981	+	0.589209i	$0.200561\pi$
$61$			9.20374i			1.17842i	−0.807981	+	0.589209i	$0.799439\pi$
$62$	7.39752			0.939486
$63$		0			0
$64$	−1.00000			−0.125000
$65$			3.95064i			0.490017i
$66$		0			0
$67$	6.01448			0.734786			0.367393	−	0.930066i	$-0.380250\pi$
$67$	6.01448			0.734786			0.367393	+	0.930066i	$0.380250\pi$
$68$	1.25228	−	2.16902i	0.151862	−	0.263032i
$69$		0			0
$70$	2.64193	−	0.142082i	0.315771	−	0.0169821i
$71$			9.66386i			1.14689i	0.819244	+	0.573445i	$0.194393\pi$
$71$			9.66386i			1.14689i	−0.819244	+	0.573445i	$0.805607\pi$
$72$		0			0
$73$	12.0570	+	6.96114i	1.41117	+	0.814739i	0.995499	−	0.0947757i	$-0.0302134\pi$
$73$	12.0570	+	6.96114i	1.41117	+	0.814739i	0.415671	+	0.909515i	$0.363547\pi$
$74$	−3.15380	+	1.82085i	−0.366622	+	0.211669i
$75$		0			0
$76$	0.962409	−	0.555647i	0.110396	−	0.0637371i
$77$	−5.82221	+	11.4655i	−0.663502	+	1.30661i
$78$		0			0
$79$	−7.83821			−0.881868			−0.440934	−	0.897540i	$-0.645353\pi$
$79$	−7.83821			−0.881868			−0.440934	+	0.897540i	$0.645353\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	6.77231	−	3.91000i	0.747877	−	0.431787i
$83$	−0.393868	+	0.682199i	−0.0432326	+	0.0748811i	−0.886832	−	0.462092i	$-0.847099\pi$
$83$	−0.393868	+	0.682199i	−0.0432326	+	0.0748811i	0.843599	+	0.536973i	$0.180432\pi$
$84$		0			0
$85$	1.25228	+	2.16902i	0.135829	+	0.235263i
$86$	6.28198	+	3.62690i	0.677404	+	0.391099i
$87$		0			0
$88$	2.43013	+	4.20911i	0.259053	+	0.448693i
$89$	7.49361	+	12.9793i	0.794321	+	1.37580i	0.923270	+	0.384153i	$0.125506\pi$
$89$	7.49361	+	12.9793i	0.794321	+	1.37580i	−0.128949	+	0.991651i	$0.541160\pi$
$90$		0			0
$91$	4.73255	−	9.31966i	0.496106	−	0.976966i
$92$	2.86139	+	1.65202i	0.298320	+	0.172235i
$93$		0			0
$94$			11.6852i			1.20523i
$95$			1.11129i			0.114016i
$96$		0			0
$97$	−14.9781	−	8.64760i	−1.52079	−	0.878031i	−0.999699	−	0.0245323i	$-0.992190\pi$
$97$	−14.9781	−	8.64760i	−1.52079	−	0.878031i	−0.521095	−	0.853499i	$-0.674476\pi$
$98$	−6.40258	−	2.82965i	−0.646759	−	0.285838i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−1.46643	−	2.53993i	−0.145915	−	0.252733i	0.783799	−	0.621015i	$-0.213279\pi$
$101$	−1.46643	−	2.53993i	−0.145915	−	0.252733i	−0.929714	+	0.368282i	$0.879946\pi$
$102$		0			0
$103$	2.23884	+	1.29260i	0.220600	+	0.127363i	0.606228	−	0.795291i	$-0.292682\pi$
$103$	2.23884	+	1.29260i	0.220600	+	0.127363i	−0.385628	+	0.922654i	$0.626015\pi$
$104$	−1.97532	−	3.42136i	−0.193696	−	0.335492i
$105$		0			0
$106$	−2.84225	+	4.92292i	−0.276064	+	0.478157i
$107$	−6.46896	+	3.73486i	−0.625378	+	0.361062i	−0.778960	−	0.627074i	$-0.784252\pi$
$107$	−6.46896	+	3.73486i	−0.625378	+	0.361062i	0.153582	+	0.988136i	$0.450919\pi$
$108$		0			0
$109$	−8.23189	+	14.2581i	−0.788472	+	1.36567i	0.138430	+	0.990372i	$0.455794\pi$
$109$	−8.23189	+	14.2581i	−0.788472	+	1.36567i	−0.926903	+	0.375302i	$0.877539\pi$
$110$	−4.86026			−0.463408
$111$		0			0
$112$	−2.21694	+	1.44401i	−0.209481	+	0.136446i
$113$	−2.91952	+	1.68559i	−0.274646	+	0.158567i	−0.630997	−	0.775785i	$-0.717354\pi$
$113$	−2.91952	+	1.68559i	−0.274646	+	0.158567i	0.356351	+	0.934352i	$0.384021\pi$
$114$		0			0
$115$	−2.86139	+	1.65202i	−0.266826	+	0.154052i
$116$	3.70789	+	2.14075i	0.344269	+	0.198764i
$117$		0			0
$118$		−	1.39292i		−	0.128229i
$119$	−0.355855	−	6.61690i	−0.0326211	−	0.606570i
$120$		0			0
$121$	6.31108	−	10.9311i	0.573734	−	0.993737i
$122$	9.20374			0.833267
$123$		0			0
$124$		−	7.39752i		−	0.664317i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	14.4595			1.28307			0.641535	−	0.767093i	$-0.278298\pi$
$127$	14.4595			1.28307			0.641535	+	0.767093i	$0.278298\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	3.95064			0.346494
$131$	6.59248	−	11.4185i	0.575988	−	0.997640i	−0.419946	−	0.907549i	$-0.637951\pi$
$131$	6.59248	−	11.4185i	0.575988	−	0.997640i	0.995934	−	0.0900907i	$-0.0287157\pi$
$132$		0			0
$133$	1.33124	−	2.62157i	0.115433	−	0.227319i
$134$		−	6.01448i		−	0.519572i
$135$		0			0
$136$	−2.16902	−	1.25228i	−0.185992	−	0.107382i
$137$	−8.98722	+	5.18877i	−0.767830	+	0.443307i	−0.832100	−	0.554626i	$-0.812861\pi$
$137$	−8.98722	+	5.18877i	−0.767830	+	0.443307i	0.0642701	+	0.997933i	$0.479528\pi$
$138$		0			0
$139$	7.92494	−	4.57547i	0.672185	−	0.388086i	−0.124719	−	0.992192i	$-0.539803\pi$
$139$	7.92494	−	4.57547i	0.672185	−	0.388086i	0.796904	+	0.604106i	$0.206470\pi$
$140$	−0.142082	−	2.64193i	−0.0120081	−	0.223284i
$141$		0			0
$142$	9.66386			0.810974
$143$	−9.60058	+	16.6287i	−0.802841	+	1.39056i
$144$		0			0
$145$	−3.70789	+	2.14075i	−0.307923	+	0.177780i
$146$	6.96114	−	12.0570i	0.576108	−	0.997848i
$147$		0			0
$148$	1.82085	+	3.15380i	0.149673	+	0.259241i
$149$	−20.9438	−	12.0919i	−1.71578	−	0.990606i	−0.926263	−	0.376878i	$-0.876998\pi$
$149$	−20.9438	−	12.0919i	−1.71578	−	0.990606i	−0.789517	−	0.613728i	$-0.789669\pi$
$150$		0			0
$151$	11.4978	+	19.9148i	0.935679	+	1.62064i	0.773418	+	0.633897i	$0.218546\pi$
$151$	11.4978	+	19.9148i	0.935679	+	1.62064i	0.162262	+	0.986748i	$0.448121\pi$
$152$	−0.555647	−	0.962409i	−0.0450689	−	0.0780617i
$153$		0			0
$154$	11.4655	+	5.82221i	0.923914	+	0.469167i
$155$	6.40644	+	3.69876i	0.514578	+	0.297091i
$156$		0			0
$157$			8.09026i			0.645673i	0.946455	+	0.322836i	$0.104636\pi$
$157$			8.09026i			0.645673i	−0.946455	+	0.322836i	$0.895364\pi$
$158$			7.83821i			0.623575i
$159$		0			0
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	8.72906	−	0.469446i	0.687947	−	0.0369975i
$162$		0			0
$163$	−0.616736	−	1.06822i	−0.0483065	−	0.0836693i	0.840861	−	0.541251i	$-0.182049\pi$
$163$	−0.616736	−	1.06822i	−0.0483065	−	0.0836693i	−0.889168	+	0.457582i	$0.848716\pi$
$164$	−3.91000	−	6.77231i	−0.305319	−	0.528829i
$165$		0			0
$166$	0.682199	+	0.393868i	0.0529489	+	0.0305701i
$167$	5.43643	+	9.41617i	0.420683	+	0.728645i	0.996006	−	0.0892813i	$-0.0284570\pi$
$167$	5.43643	+	9.41617i	0.420683	+	0.728645i	−0.575323	+	0.817926i	$0.695124\pi$
$168$		0			0
$169$	1.30379	−	2.25823i	0.100292	−	0.173710i
$170$	2.16902	−	1.25228i	0.166356	−	0.0960457i
$171$		0			0
$172$	3.62690	−	6.28198i	0.276549	−	0.478997i
$173$	−5.77390			−0.438981			−0.219491	−	0.975615i	$-0.570440\pi$
$173$	−5.77390			−0.438981			−0.219491	+	0.975615i	$0.570440\pi$
$174$		0			0
$175$	2.35902	+	1.19792i	0.178325	+	0.0905542i
$176$	4.20911	−	2.43013i	0.317274	−	0.183178i
$177$		0			0
$178$	12.9793	−	7.49361i	0.972840	−	0.561670i
$179$	−4.85812	−	2.80484i	−0.363113	−	0.209643i	0.307332	−	0.951602i	$-0.400564\pi$
$179$	−4.85812	−	2.80484i	−0.363113	−	0.209643i	−0.670445	+	0.741959i	$0.733897\pi$
$180$		0			0
$181$		−	24.0589i		−	1.78828i	−0.447784	−	0.894142i	$-0.647787\pi$
$181$		−	24.0589i		−	1.78828i	0.447784	−	0.894142i	$-0.352213\pi$
$182$	−9.31966	−	4.73255i	−0.690819	−	0.350800i
$183$		0			0
$184$	1.65202	−	2.86139i	0.121789	−	0.210944i
$185$	−3.64170			−0.267743
$186$		0			0
$187$			12.1728i			0.890167i
$188$	11.6852			0.852227
$189$		0			0
$190$	1.11129			0.0806217
$191$		−	24.2354i		−	1.75361i	−0.480843	−	0.876807i	$-0.659669\pi$
$191$		−	24.2354i		−	1.75361i	0.480843	−	0.876807i	$-0.340331\pi$
$192$		0			0
$193$	−0.617476			−0.0444469			−0.0222235	−	0.999753i	$-0.507075\pi$
$193$	−0.617476			−0.0444469			−0.0222235	+	0.999753i	$0.507075\pi$
$194$	−8.64760	+	14.9781i	−0.620862	+	1.07536i
$195$		0			0
$196$	−2.82965	+	6.40258i	−0.202118	+	0.457327i
$197$			2.28650i			0.162906i	0.996677	+	0.0814531i	$0.0259561\pi$
$197$			2.28650i			0.162906i	−0.996677	+	0.0814531i	$0.974044\pi$
$198$		0			0
$199$	−3.60562	−	2.08171i	−0.255596	−	0.147568i	0.366728	−	0.930328i	$-0.380478\pi$
$199$	−3.60562	−	2.08171i	−0.255596	−	0.147568i	−0.622324	+	0.782760i	$0.713811\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$		0			0
$202$	−2.53993	+	1.46643i	−0.178709	+	0.103178i
$203$	11.3114	−	0.608325i	0.793907	−	0.0426961i
$204$		0			0
$205$	7.81999			0.546172
$206$	1.29260	−	2.23884i	0.0900595	−	0.155988i
$207$		0			0
$208$	−3.42136	+	1.97532i	−0.237228	+	0.136964i
$209$	−2.70059	+	4.67756i	−0.186804	+	0.323554i
$210$		0			0
$211$	1.26573	+	2.19231i	0.0871365	+	0.150925i	0.906300	−	0.422636i	$-0.138895\pi$
$211$	1.26573	+	2.19231i	0.0871365	+	0.150925i	−0.819163	+	0.573561i	$0.805562\pi$
$212$	4.92292	+	2.84225i	0.338108	+	0.195207i
$213$		0			0
$214$	3.73486	+	6.46896i	0.255309	+	0.442209i
$215$	3.62690	+	6.28198i	0.247353	+	0.428428i
$216$		0			0
$217$	−10.6821	−	16.3999i	−0.725149	−	1.11329i
$218$	14.2581	+	8.23189i	0.965677	+	0.557534i
$219$		0			0
$220$			4.86026i			0.327679i
$221$		−	9.89465i		−	0.665586i
$222$		0			0
$223$	9.62445	+	5.55668i	0.644501	+	0.372103i	0.786346	−	0.617786i	$-0.211970\pi$
$223$	9.62445	+	5.55668i	0.644501	+	0.372103i	−0.141845	+	0.989889i	$0.545304\pi$
$224$	1.44401	+	2.21694i	0.0964822	+	0.148126i
$225$		0			0
$226$	1.68559	+	2.91952i	0.112124	+	0.194204i
$227$	5.76421	+	9.98390i	0.382584	+	0.662655i	0.991431	−	0.130633i	$-0.0417010\pi$
$227$	5.76421	+	9.98390i	0.382584	+	0.662655i	−0.608847	+	0.793288i	$0.708368\pi$
$228$		0			0
$229$	−22.7387	−	13.1282i	−1.50262	−	0.867535i	−0.999995	−	0.00302766i	$-0.999036\pi$
$229$	−22.7387	−	13.1282i	−1.50262	−	0.867535i	−0.502620	−	0.864508i	$-0.667630\pi$
$230$	1.65202	+	2.86139i	0.108931	+	0.188674i
$231$		0			0
$232$	2.14075	−	3.70789i	0.140547	−	0.243435i
$233$	−0.657636	+	0.379686i	−0.0430832	+	0.0248741i	−0.521387	−	0.853320i	$-0.674585\pi$
$233$	−0.657636	+	0.379686i	−0.0430832	+	0.0248741i	0.478304	+	0.878194i	$0.341252\pi$
$234$		0			0
$235$	−5.84258	+	10.1196i	−0.381128	+	0.660132i
$236$	−1.39292			−0.0906716
$237$		0			0
$238$	−6.61690	+	0.355855i	−0.428910	+	0.0230666i
$239$	21.2951	−	12.2947i	1.37746	−	0.795280i	0.385611	−	0.922661i	$-0.373991\pi$
$239$	21.2951	−	12.2947i	1.37746	−	0.795280i	0.991854	+	0.127382i	$0.0406573\pi$
$240$		0			0
$241$	−11.6664	+	6.73558i	−0.751497	+	0.433877i	−0.826235	−	0.563326i	$-0.809521\pi$
$241$	−11.6664	+	6.73558i	−0.751497	+	0.433877i	0.0747375	+	0.997203i	$0.476188\pi$
$242$	−10.9311	−	6.31108i	−0.702678	−	0.405691i
$243$		0			0
$244$		−	9.20374i		−	0.589209i
$245$	−4.12998	−	5.65184i	−0.263854	−	0.361083i
$246$		0			0
$247$	2.19516	−	3.80213i	0.139675	−	0.241924i
$248$	−7.39752			−0.469743
$249$		0			0
$250$			1.00000i			0.0632456i
$251$	−1.02268			−0.0645513			−0.0322756	−	0.999479i	$-0.510275\pi$
$251$	−1.02268			−0.0645513			−0.0322756	+	0.999479i	$0.510275\pi$
$252$		0			0
$253$	−16.0585			−1.00959
$254$		−	14.4595i		−	0.907268i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−11.9035	+	20.6174i	−0.742517	+	1.28608i	0.208829	+	0.977952i	$0.433035\pi$
$257$	−11.9035	+	20.6174i	−0.742517	+	1.28608i	−0.951346	+	0.308125i	$0.900298\pi$
$258$		0			0
$259$	8.59084	+	4.36246i	0.533809	+	0.271070i
$260$		−	3.95064i		−	0.245008i
$261$		0			0
$262$	−11.4185	−	6.59248i	−0.705438	−	0.407285i
$263$	−6.57942	+	3.79863i	−0.405704	+	0.234234i	−0.688942	−	0.724816i	$-0.741925\pi$
$263$	−6.57942	+	3.79863i	−0.405704	+	0.234234i	0.283238	+	0.959050i	$0.408591\pi$
$264$		0			0
$265$	−4.92292	+	2.84225i	−0.302413	+	0.174598i
$266$	−2.62157	−	1.33124i	−0.160739	−	0.0816236i
$267$		0			0
$268$	−6.01448			−0.367393
$269$	−3.58635	+	6.21175i	−0.218664	+	0.378737i	−0.954400	−	0.298532i	$-0.903503\pi$
$269$	−3.58635	+	6.21175i	−0.218664	+	0.378737i	0.735736	+	0.677269i	$0.236836\pi$
$270$		0			0
$271$	−3.19806	+	1.84640i	−0.194268	+	0.112161i	−0.593979	−	0.804480i	$-0.702444\pi$
$271$	−3.19806	+	1.84640i	−0.194268	+	0.112161i	0.399711	+	0.916641i	$0.369111\pi$
$272$	−1.25228	+	2.16902i	−0.0759308	+	0.131516i
$273$		0			0
$274$	5.18877	+	8.98722i	0.313465	+	0.542938i
$275$	−4.20911	−	2.43013i	−0.253819	−	0.146542i
$276$		0			0
$277$	−12.4545	−	21.5718i	−0.748317	−	1.29612i	−0.948629	−	0.316392i	$-0.897529\pi$
$277$	−12.4545	−	21.5718i	−0.748317	−	1.29612i	0.200311	−	0.979732i	$-0.435805\pi$
$278$	−4.57547	−	7.92494i	−0.274418	−	0.475306i
$279$		0			0
$280$	−2.64193	+	0.142082i	−0.157886	+	0.00849104i
$281$	12.6865	+	7.32455i	0.756813	+	0.436946i	0.828150	−	0.560506i	$-0.189393\pi$
$281$	12.6865	+	7.32455i	0.756813	+	0.436946i	−0.0713375	+	0.997452i	$0.522727\pi$
$282$		0			0
$283$			6.34995i			0.377465i	0.982029	+	0.188733i	$0.0604380\pi$
$283$			6.34995i			0.377465i	−0.982029	+	0.188733i	$0.939562\pi$
$284$		−	9.66386i		−	0.573445i
$285$		0			0
$286$	16.6287	+	9.60058i	0.983275	+	0.567694i
$287$	−18.4475	−	9.36772i	−1.08892	−	0.552959i
$288$		0			0
$289$	5.36358	+	9.28999i	0.315504	+	0.546470i
$290$	2.14075	+	3.70789i	0.125709	+	0.217735i
$291$		0			0
$292$	−12.0570	−	6.96114i	−0.705585	−	0.407370i
$293$	1.79507	+	3.10915i	0.104869	+	0.181638i	0.913685	−	0.406424i	$-0.133224\pi$
$293$	1.79507	+	3.10915i	0.104869	+	0.181638i	−0.808816	+	0.588062i	$0.799891\pi$
$294$		0			0
$295$	0.696461	−	1.20631i	0.0405496	−	0.0702339i
$296$	3.15380	−	1.82085i	0.183311	−	0.105835i
$297$		0			0
$298$	−12.0919	+	20.9438i	−0.700464	+	1.21324i
$299$	13.0531			0.754880
$300$		0			0
$301$	−1.03064	−	19.1641i	−0.0594050	−	1.10460i
$302$	19.9148	−	11.4978i	1.14597	−	0.661625i
$303$		0			0
$304$	−0.962409	+	0.555647i	−0.0551979	+	0.0318685i
$305$	7.97067	+	4.60187i	0.456399	+	0.263502i
$306$		0			0
$307$		−	11.0589i		−	0.631166i	−0.948898	−	0.315583i	$-0.897800\pi$
$307$		−	11.0589i		−	0.631166i	0.948898	−	0.315583i	$-0.102200\pi$
$308$	5.82221	−	11.4655i	0.331751	−	0.653306i
$309$		0			0
$310$	3.69876	−	6.40644i	0.210075	−	0.363861i
$311$	13.9447			0.790729			0.395364	−	0.918524i	$-0.370618\pi$
$311$	13.9447			0.790729			0.395364	+	0.918524i	$0.370618\pi$
$312$		0			0
$313$		−	13.2712i		−	0.750130i	−0.926999	−	0.375065i	$-0.877620\pi$
$313$		−	13.2712i		−	0.750130i	0.926999	−	0.375065i	$-0.122380\pi$
$314$	8.09026			0.456560
$315$		0			0
$316$	7.83821			0.440934
$317$		−	4.45055i		−	0.249968i	−0.992159	−	0.124984i	$-0.960112\pi$
$317$		−	4.45055i		−	0.249968i	0.992159	−	0.124984i	$-0.0398879\pi$
$318$		0			0
$319$	−20.8092			−1.16509
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	−0.469446	−	8.72906i	−0.0261612	−	0.486452i
$323$		−	2.78331i		−	0.154867i
$324$		0			0
$325$	3.42136	+	1.97532i	0.189783	+	0.109571i
$326$	−1.06822	+	0.616736i	−0.0591631	+	0.0341578i
$327$		0			0
$328$	−6.77231	+	3.91000i	−0.373938	+	0.215893i
$329$	25.9053	−	16.8735i	1.42820	−	0.930267i
$330$		0			0
$331$	7.83959			0.430903			0.215451	−	0.976515i	$-0.430878\pi$
$331$	7.83959			0.430903			0.215451	+	0.976515i	$0.430878\pi$
$332$	0.393868	−	0.682199i	0.0216163	−	0.0374405i
$333$		0			0
$334$	9.41617	−	5.43643i	0.515230	−	0.297468i
$335$	3.00724	−	5.20869i	0.164303	−	0.284581i
$336$		0			0
$337$	−4.66042	−	8.07208i	−0.253869	−	0.439714i	0.710719	−	0.703476i	$-0.248370\pi$
$337$	−4.66042	−	8.07208i	−0.253869	−	0.439714i	−0.964588	+	0.263762i	$0.915037\pi$
$338$	−2.25823	−	1.30379i	−0.122832	−	0.0709169i
$339$		0			0
$340$	−1.25228	−	2.16902i	−0.0679146	−	0.117631i
$341$	17.9769	+	31.1370i	0.973506	+	1.68616i
$342$		0			0
$343$	2.97226	+	18.2802i	0.160487	+	0.987038i
$344$	−6.28198	−	3.62690i	−0.338702	−	0.195550i
$345$		0			0
$346$			5.77390i			0.310407i
$347$		−	29.6538i		−	1.59190i	−0.605361	−	0.795951i	$-0.706971\pi$
$347$		−	29.6538i		−	1.59190i	0.605361	−	0.795951i	$-0.293029\pi$
$348$		0			0
$349$	−28.0322	−	16.1844i	−1.50053	−	0.866330i	−1.00000		0.000609911i	$-0.999806\pi$
$349$	−28.0322	−	16.1844i	−1.50053	−	0.866330i	−0.500528	−	0.865720i	$-0.666861\pi$
$350$	1.19792	−	2.35902i	0.0640315	−	0.126095i
$351$		0			0
$352$	−2.43013	−	4.20911i	−0.129526	−	0.224346i
$353$	−3.02849	−	5.24551i	−0.161191	−	0.279190i	0.774105	−	0.633057i	$-0.218200\pi$
$353$	−3.02849	−	5.24551i	−0.161191	−	0.279190i	−0.935296	+	0.353867i	$0.884867\pi$
$354$		0			0
$355$	8.36915	+	4.83193i	0.444188	+	0.256452i
$356$	−7.49361	−	12.9793i	−0.397160	−	0.687902i
$357$		0			0
$358$	−2.80484	+	4.85812i	−0.148240	+	0.256760i
$359$	11.4661	−	6.61995i	0.605157	−	0.349388i	−0.165911	−	0.986141i	$-0.553056\pi$
$359$	11.4661	−	6.61995i	0.605157	−	0.349388i	0.771068	+	0.636753i	$0.219723\pi$
$360$		0			0
$361$	−8.88251	+	15.3850i	−0.467501	+	0.809735i
$362$	−24.0589			−1.26451
$363$		0			0
$364$	−4.73255	+	9.31966i	−0.248053	+	0.488483i
$365$	12.0570	−	6.96114i	0.631094	−	0.364362i
$366$		0			0
$367$	15.5018	−	8.94994i	0.809185	−	0.467183i	−0.0374878	−	0.999297i	$-0.511936\pi$
$367$	15.5018	−	8.94994i	0.809185	−	0.467183i	0.846673	+	0.532114i	$0.178602\pi$
$368$	−2.86139	−	1.65202i	−0.149160	−	0.0861176i
$369$		0			0
$370$			3.64170i			0.189323i
$371$	15.0181	−	0.807668i	0.779700	−	0.0419320i
$372$		0			0
$373$	2.26234	−	3.91848i	0.117139	−	0.202891i	−0.801494	−	0.598003i	$-0.795961\pi$
$373$	2.26234	−	3.91848i	0.117139	−	0.202891i	0.918633	+	0.395112i	$0.129294\pi$
$374$	12.1728			0.629443
$375$		0			0
$376$		−	11.6852i		−	0.602616i
$377$	16.9147			0.871150
$378$		0			0
$379$	−7.47021			−0.383719			−0.191860	−	0.981422i	$-0.561452\pi$
$379$	−7.47021			−0.383719			−0.191860	+	0.981422i	$0.561452\pi$
$380$		−	1.11129i		−	0.0570082i
$381$		0			0
$382$	−24.2354			−1.23999
$383$	16.5416	−	28.6508i	0.845234	−	1.46399i	−0.0401839	−	0.999192i	$-0.512794\pi$
$383$	16.5416	−	28.6508i	0.845234	−	1.46399i	0.885418	−	0.464796i	$-0.153872\pi$
$384$		0			0
$385$	7.01829	+	10.7749i	0.357685	+	0.549140i
$386$			0.617476i			0.0314287i
$387$		0			0
$388$	14.9781	+	8.64760i	0.760397	+	0.439015i
$389$	−31.5651	+	18.2241i	−1.60041	+	0.923999i	−0.609009	+	0.793163i	$0.708433\pi$
$389$	−31.5651	+	18.2241i	−1.60041	+	0.923999i	−0.991404	+	0.130836i	$0.958234\pi$
$390$		0			0
$391$	7.16653	−	4.13760i	0.362427	−	0.209247i
$392$	6.40258	+	2.82965i	0.323379	+	0.142919i
$393$		0			0
$394$	2.28650			0.115192
$395$	−3.91911	+	6.78809i	−0.197192	+	0.341546i
$396$		0			0
$397$	−13.3331	+	7.69789i	−0.669171	+	0.386346i	−0.795762	−	0.605609i	$-0.792930\pi$
$397$	−13.3331	+	7.69789i	−0.669171	+	0.386346i	0.126592	+	0.991955i	$0.459596\pi$
$398$	−2.08171	+	3.60562i	−0.104346	+	0.180733i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−14.2091	−	8.20364i	−0.709570	−	0.409670i	0.101332	−	0.994853i	$-0.467690\pi$
$401$	−14.2091	−	8.20364i	−0.709570	−	0.409670i	−0.810902	+	0.585182i	$0.801023\pi$
$402$		0			0
$403$	−14.6125	−	25.3096i	−0.727899	−	1.26076i
$404$	1.46643	+	2.53993i	0.0729576	+	0.126366i
$405$		0			0
$406$	−0.608325	−	11.3114i	−0.0301907	−	0.561377i
$407$	−15.3283	−	8.84980i	−0.759796	−	0.438668i
$408$		0			0
$409$		−	21.1331i		−	1.04496i	−0.852651	−	0.522481i	$-0.825006\pi$
$409$		−	21.1331i		−	1.04496i	0.852651	−	0.522481i	$-0.174994\pi$
$410$		−	7.81999i		−	0.386202i
$411$		0			0
$412$	−2.23884	−	1.29260i	−0.110300	−	0.0636817i
$413$	−3.08803	+	2.01140i	−0.151952	+	0.0989745i
$414$		0			0
$415$	0.393868	+	0.682199i	0.0193342	+	0.0334878i
$416$	1.97532	+	3.42136i	0.0968481	+	0.167746i
$417$		0			0
$418$	4.67756	+	2.70059i	0.228787	+	0.132090i
$419$	2.31087	+	4.00254i	0.112893	+	0.195537i	0.916936	−	0.399035i	$-0.130655\pi$
$419$	2.31087	+	4.00254i	0.112893	+	0.195537i	−0.804042	+	0.594572i	$0.797322\pi$
$420$		0			0
$421$	1.15555	−	2.00148i	0.0563183	−	0.0975461i	−0.836492	−	0.547979i	$-0.815397\pi$
$421$	1.15555	−	2.00148i	0.0563183	−	0.0975461i	0.892810	+	0.450433i	$0.148731\pi$
$422$	2.19231	−	1.26573i	0.106720	−	0.0616148i
$423$		0			0
$424$	2.84225	−	4.92292i	0.138032	−	0.239078i
$425$	2.50457			0.121489
$426$		0			0
$427$	−13.2903	−	20.4041i	−0.643164	−	0.987426i
$428$	6.46896	−	3.73486i	0.312689	−	0.180531i
$429$		0			0
$430$	6.28198	−	3.62690i	0.302944	−	0.174905i
$431$	−21.3345	−	12.3175i	−1.02765	−	0.593313i	−0.111338	−	0.993783i	$-0.535514\pi$
$431$	−21.3345	−	12.3175i	−1.02765	−	0.593313i	−0.916310	+	0.400469i	$0.868847\pi$
$432$		0			0
$433$		−	6.55773i		−	0.315144i	−0.987507	−	0.157572i	$-0.949633\pi$
$433$		−	6.55773i		−	0.315144i	0.987507	−	0.157572i	$-0.0503667\pi$
$434$	−16.3999	+	10.6821i	−0.787218	+	0.512758i
$435$		0			0
$436$	8.23189	−	14.2581i	0.394236	−	0.682837i
$437$	3.67176			0.175644
$438$		0			0
$439$		−	32.4291i		−	1.54776i	−0.633335	−	0.773878i	$-0.718314\pi$
$439$		−	32.4291i		−	1.54776i	0.633335	−	0.773878i	$-0.281686\pi$
$440$	4.86026			0.231704
$441$		0			0
$442$	−9.89465			−0.470640
$443$		−	0.235686i		−	0.0111978i	−0.999984	−	0.00559888i	$-0.998218\pi$
$443$		−	0.235686i		−	0.0111978i	0.999984	−	0.00559888i	$-0.00178219\pi$
$444$		0			0
$445$	14.9872			0.710462
$446$	5.55668	−	9.62445i	0.263116	−	0.455731i
$447$		0			0
$448$	2.21694	−	1.44401i	0.104741	−	0.0682232i
$449$		−	18.8068i		−	0.887549i	−0.896139	−	0.443774i	$-0.853639\pi$
$449$		−	18.8068i		−	0.887549i	0.896139	−	0.443774i	$-0.146361\pi$
$450$		0			0
$451$	32.9152	+	19.0036i	1.54992	+	0.894845i
$452$	2.91952	−	1.68559i	0.137323	−	0.0792833i
$453$		0			0
$454$	9.98390	−	5.76421i	0.468568	−	0.270528i
$455$	−5.70478	−	8.75834i	−0.267444	−	0.410597i
$456$		0			0
$457$	−18.6117			−0.870617			−0.435308	−	0.900281i	$-0.643361\pi$
$457$	−18.6117			−0.870617			−0.435308	+	0.900281i	$0.643361\pi$
$458$	−13.1282	+	22.7387i	−0.613440	+	1.06251i
$459$		0			0
$460$	2.86139	−	1.65202i	0.133413	−	0.0770259i
$461$	13.7720	−	23.8538i	0.641426	−	1.11098i	−0.343689	−	0.939084i	$-0.611677\pi$
$461$	13.7720	−	23.8538i	0.641426	−	1.11098i	0.985115	−	0.171898i	$-0.0549901\pi$
$462$		0			0
$463$	0.239162	+	0.414241i	0.0111148	+	0.0192514i	0.871529	−	0.490343i	$-0.163129\pi$
$463$	0.239162	+	0.414241i	0.0111148	+	0.0192514i	−0.860415	+	0.509595i	$0.829795\pi$
$464$	−3.70789	−	2.14075i	−0.172134	−	0.0993818i
$465$		0			0
$466$	0.379686	+	0.657636i	0.0175886	+	0.0304644i
$467$	−6.08486	−	10.5393i	−0.281574	−	0.487700i	0.690199	−	0.723620i	$-0.257523\pi$
$467$	−6.08486	−	10.5393i	−0.281574	−	0.487700i	−0.971773	+	0.235920i	$0.924190\pi$
$468$		0			0
$469$	−13.3337	+	8.68499i	−0.615695	+	0.401036i
$470$	10.1196	+	5.84258i	0.466784	+	0.269498i
$471$		0			0
$472$			1.39292i			0.0641145i
$473$			35.2554i			1.62105i
$474$		0			0
$475$	0.962409	+	0.555647i	0.0441583	+	0.0254948i
$476$	0.355855	+	6.61690i	0.0163106	+	0.303285i
$477$		0			0
$478$	−12.2947	−	21.2951i	−0.562348	−	0.974015i
$479$	20.1769	+	34.9474i	0.921906	+	1.59679i	0.796462	+	0.604688i	$0.206702\pi$
$479$	20.1769	+	34.9474i	0.921906	+	1.59679i	0.125444	+	0.992101i	$0.459964\pi$
$480$		0			0
$481$	12.4595	+	7.19352i	0.568106	+	0.327996i
$482$	6.73558	+	11.6664i	0.306797	+	0.531389i
$483$		0			0
$484$	−6.31108	+	10.9311i	−0.286867	+	0.496868i
$485$	−14.9781	+	8.64760i	−0.680120	+	0.392667i
$486$		0			0
$487$	−4.11277	+	7.12353i	−0.186367	+	0.322798i	−0.944036	−	0.329841i	$-0.893005\pi$
$487$	−4.11277	+	7.12353i	−0.186367	+	0.322798i	0.757669	+	0.652639i	$0.226338\pi$
$488$	−9.20374			−0.416634
$489$		0			0
$490$	−5.65184	+	4.12998i	−0.255324	+	0.186573i
$491$	−9.11388	+	5.26190i	−0.411303	+	0.237466i	−0.691350	−	0.722520i	$-0.742984\pi$
$491$	−9.11388	+	5.26190i	−0.411303	+	0.237466i	0.280046	+	0.959987i	$0.409650\pi$
$492$		0			0
$493$	9.28664	−	5.36165i	0.418249	−	0.241476i
$494$	−3.80213	−	2.19516i	−0.171066	−	0.0987650i
$495$		0			0
$496$			7.39752i			0.332158i
$497$	−13.9548	−	21.4242i	−0.625956	−	0.961007i
$498$		0			0
$499$	−0.425242	+	0.736540i	−0.0190364	+	0.0329721i	−0.875387	−	0.483423i	$-0.839393\pi$
$499$	−0.425242	+	0.736540i	−0.0190364	+	0.0329721i	0.856350	+	0.516395i	$0.172727\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$			1.02268i			0.0456446i
$503$	−21.5476			−0.960759			−0.480380	−	0.877061i	$-0.659501\pi$
$503$	−21.5476			−0.960759			−0.480380	+	0.877061i	$0.659501\pi$
$504$		0			0
$505$	−2.93286			−0.130511
$506$			16.0585i			0.713888i
$507$		0			0
$508$	−14.4595			−0.641535
$509$	1.10449	−	1.91303i	0.0489556	−	0.0847936i	−0.840509	−	0.541797i	$-0.817744\pi$
$509$	1.10449	−	1.91303i	0.0489556	−	0.0847936i	0.889465	+	0.457004i	$0.151077\pi$
$510$		0			0
$511$	−36.7817	+	1.97811i	−1.62713	+	0.0875064i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	20.6174	+	11.9035i	0.909394	+	0.525039i
$515$	2.23884	−	1.29260i	0.0986552	−	0.0569586i
$516$		0			0
$517$	−49.1841	+	28.3965i	−2.16311	+	1.24887i
$518$	4.36246	−	8.59084i	0.191675	−	0.377460i
$519$		0			0
$520$	−3.95064			−0.173247
$521$	−12.0872	+	20.9356i	−0.529548	+	0.917204i	0.469858	+	0.882742i	$0.344305\pi$
$521$	−12.0872	+	20.9356i	−0.529548	+	0.917204i	−0.999406	+	0.0344623i	$0.989028\pi$
$522$		0			0
$523$	−10.3393	+	5.96937i	−0.452104	+	0.261022i	−0.708718	−	0.705492i	$-0.750726\pi$
$523$	−10.3393	+	5.96937i	−0.452104	+	0.261022i	0.256614	+	0.966514i	$0.417393\pi$
$524$	−6.59248	+	11.4185i	−0.287994	+	0.498820i
$525$		0			0
$526$	3.79863	+	6.57942i	0.165628	+	0.286876i
$527$	−16.0453	−	9.26378i	−0.698946	−	0.403537i
$528$		0			0
$529$	−6.04165	−	10.4644i	−0.262680	−	0.454976i
$530$	2.84225	+	4.92292i	0.123460	+	0.213838i
$531$		0			0
$532$	−1.33124	+	2.62157i	−0.0577166	+	0.113659i
$533$	−26.7550	−	15.4470i	−1.15889	−	0.669084i
$534$		0			0
$535$			7.46971i			0.322944i
$536$			6.01448i			0.259786i
$537$		0			0
$538$	6.21175	+	3.58635i	0.267807	+	0.154619i
$539$	−3.64881	−	33.8256i	−0.157166	−	1.45697i
$540$		0			0
$541$	7.35700	+	12.7427i	0.316302	+	0.547852i	0.979713	−	0.200403i	$-0.0642253\pi$
$541$	7.35700	+	12.7427i	0.316302	+	0.547852i	−0.663411	+	0.748255i	$0.730892\pi$
$542$	1.84640	+	3.19806i	0.0793098	+	0.137369i
$543$		0			0
$544$	2.16902	+	1.25228i	0.0929959	+	0.0536912i
$545$	8.23189	+	14.2581i	0.352616	+	0.610748i
$546$		0			0
$547$	8.78526	−	15.2165i	0.375631	−	0.650611i	−0.614791	−	0.788690i	$-0.710759\pi$
$547$	8.78526	−	15.2165i	0.375631	−	0.650611i	0.990421	+	0.138079i	$0.0440928\pi$
$548$	8.98722	−	5.18877i	0.383915	−	0.221653i
$549$		0			0
$550$	−2.43013	+	4.20911i	−0.103621	+	0.179477i
$551$	4.75800			0.202698
$552$		0			0
$553$	17.3769	−	11.3185i	0.738939	−	0.481311i
$554$	−21.5718	+	12.4545i	−0.916498	+	0.529140i
$555$		0			0
$556$	−7.92494	+	4.57547i	−0.336092	+	0.194043i
$557$	−16.7457	−	9.66812i	−0.709537	−	0.409652i	0.101352	−	0.994851i	$-0.467683\pi$
$557$	−16.7457	−	9.66812i	−0.709537	−	0.409652i	−0.810890	+	0.585199i	$0.801016\pi$
$558$		0			0
$559$		−	28.6572i		−	1.21207i
$560$	0.142082	+	2.64193i	0.00600407	+	0.111642i
$561$		0			0
$562$	7.32455	−	12.6865i	0.308968	−	0.535147i
$563$	24.0647			1.01421			0.507103	−	0.861886i	$-0.330717\pi$
$563$	24.0647			1.01421			0.507103	+	0.861886i	$0.330717\pi$
$564$		0			0
$565$			3.37117i			0.141826i
$566$	6.34995			0.266908
$567$		0			0
$568$	−9.66386			−0.405487
$569$			37.2930i			1.56341i	0.623651	+	0.781703i	$0.285649\pi$
$569$			37.2930i			1.56341i	−0.623651	+	0.781703i	$0.714351\pi$
$570$		0			0
$571$	7.65139			0.320201			0.160100	−	0.987101i	$-0.448818\pi$
$571$	7.65139			0.320201			0.160100	+	0.987101i	$0.448818\pi$
$572$	9.60058	−	16.6287i	0.401421	−	0.695281i
$573$		0			0
$574$	−9.36772	+	18.4475i	−0.391001	+	0.769985i
$575$			3.30404i			0.137788i
$576$		0			0
$577$	34.5692	+	19.9585i	1.43913	+	0.830884i	0.997789	−	0.0664543i	$-0.0211687\pi$
$577$	34.5692	+	19.9585i	1.43913	+	0.830884i	0.441344	+	0.897338i	$0.354502\pi$
$578$	9.28999	−	5.36358i	0.386412	−	0.223095i
$579$		0			0
$580$	3.70789	−	2.14075i	0.153962	−	0.0888898i
$581$	−0.111923	−	2.08115i	−0.00464336	−	0.0863404i
$582$		0			0
$583$	−27.6282			−1.14424
$584$	−6.96114	+	12.0570i	−0.288054	+	0.498924i
$585$		0			0
$586$	3.10915	−	1.79507i	0.128438	−	0.0741535i
$587$	−12.0540	+	20.8782i	−0.497523	+	0.861734i	−0.999996	−	0.00285838i	$-0.999090\pi$
$587$	−12.0540	+	20.8782i	−0.497523	+	0.861734i	0.502473	+	0.864593i	$0.332423\pi$
$588$		0			0
$589$	−4.11041	−	7.11944i	−0.169366	−	0.293351i
$590$	−1.20631	−	0.696461i	−0.0496629	−	0.0286729i
$591$		0			0
$592$	−1.82085	−	3.15380i	−0.0748364	−	0.129620i
$593$	−7.23840	−	12.5373i	−0.297246	−	0.514844i	0.678259	−	0.734823i	$-0.262735\pi$
$593$	−7.23840	−	12.5373i	−0.297246	−	0.514844i	−0.975505	+	0.219978i	$0.929401\pi$
$594$		0			0
$595$	−5.90833	−	3.00027i	−0.242218	−	0.122999i
$596$	20.9438	+	12.0919i	0.857890	+	0.495303i
$597$		0			0
$598$		−	13.0531i		−	0.533781i
$599$			17.0187i			0.695367i	0.937612	+	0.347683i	$0.113032\pi$
$599$			17.0187i			0.695367i	−0.937612	+	0.347683i	$0.886968\pi$
$600$		0			0
$601$	23.0713	+	13.3202i	0.941099	+	0.543344i	0.890305	−	0.455365i	$-0.150491\pi$
$601$	23.0713	+	13.3202i	0.941099	+	0.543344i	0.0507942	+	0.998709i	$0.483825\pi$
$602$	−19.1641	+	1.03064i	−0.781070	+	0.0420057i
$603$		0			0
$604$	−11.4978	−	19.9148i	−0.467840	−	0.810322i
$605$	−6.31108	−	10.9311i	−0.256582	−	0.444413i
$606$		0			0
$607$	26.1917	+	15.1218i	1.06309	+	0.613774i	0.926285	−	0.376824i	$-0.122984\pi$
$607$	26.1917	+	15.1218i	1.06309	+	0.613774i	0.136803	+	0.990598i	$0.456317\pi$
$608$	0.555647	+	0.962409i	0.0225345	+	0.0390308i
$609$		0			0
$610$	4.60187	−	7.97067i	0.186324	−	0.322723i
$611$	39.9791	−	23.0819i	1.61738	−	0.933795i
$612$		0			0
$613$	−10.5704	+	18.3085i	−0.426934	+	0.739472i	−0.996599	−	0.0824054i	$-0.973740\pi$
$613$	−10.5704	+	18.3085i	−0.426934	+	0.739472i	0.569665	+	0.821877i	$0.307073\pi$
$614$	−11.0589			−0.446301
$615$		0			0
$616$	−11.4655	−	5.82221i	−0.461957	−	0.234583i
$617$	−27.0032	+	15.5903i	−1.08711	+	0.627641i	−0.932805	−	0.360382i	$-0.882646\pi$
$617$	−27.0032	+	15.5903i	−1.08711	+	0.627641i	−0.154302	+	0.988024i	$0.549313\pi$
$618$		0			0
$619$	−15.0635	+	8.69694i	−0.605455	+	0.349559i	−0.771184	−	0.636612i	$-0.780335\pi$
$619$	−15.0635	+	8.69694i	−0.605455	+	0.349559i	0.165730	+	0.986171i	$0.447002\pi$
$620$	−6.40644	−	3.69876i	−0.257289	−	0.148546i
$621$		0			0
$622$		−	13.9447i		−	0.559130i
$623$	−35.3552	−	17.9535i	−1.41648	−	0.719291i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.2712			−0.530422
$627$		0			0
$628$		−	8.09026i		−	0.322836i
$629$	9.12086			0.363673
$630$		0			0
$631$	−2.59501			−0.103306			−0.0516529	−	0.998665i	$-0.516449\pi$
$631$	−2.59501			−0.103306			−0.0516529	+	0.998665i	$0.516449\pi$
$632$		−	7.83821i		−	0.311787i
$633$		0			0
$634$	−4.45055			−0.176754
$635$	7.22974	−	12.5223i	0.286903	−	0.496931i
$636$		0			0
$637$	2.96592	+	27.4950i	0.117514	+	1.08939i
$638$			20.8092i			0.823844i
$639$		0			0
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	4.66393	−	2.69272i	0.184214	−	0.106356i	−0.405057	−	0.914291i	$-0.632748\pi$
$641$	4.66393	−	2.69272i	0.184214	−	0.106356i	0.589271	+	0.807935i	$0.299415\pi$
$642$		0			0
$643$	16.1682	−	9.33469i	0.637610	−	0.368124i	−0.146083	−	0.989272i	$-0.546667\pi$
$643$	16.1682	−	9.33469i	0.637610	−	0.368124i	0.783693	+	0.621148i	$0.213333\pi$
$644$	−8.72906	+	0.469446i	−0.343973	+	0.0184988i
$645$		0			0
$646$	−2.78331			−0.109508
$647$	−2.10117	+	3.63934i	−0.0826056	+	0.143077i	−0.904368	−	0.426753i	$-0.859658\pi$
$647$	−2.10117	+	3.63934i	−0.0826056	+	0.143077i	0.821763	+	0.569830i	$0.192991\pi$
$648$		0			0
$649$	5.86297	−	3.38499i	0.230142	−	0.132872i
$650$	1.97532	−	3.42136i	0.0774785	−	0.134197i
$651$		0			0
$652$	0.616736	+	1.06822i	0.0241532	+	0.0418346i
$653$	23.0433	+	13.3041i	0.901755	+	0.520628i	0.877769	−	0.479084i	$-0.159031\pi$
$653$	23.0433	+	13.3041i	0.901755	+	0.520628i	0.0239858	+	0.999712i	$0.492364\pi$
$654$		0			0
$655$	−6.59248	−	11.4185i	−0.257589	−	0.446158i
$656$	3.91000	+	6.77231i	0.152660	+	0.264414i
$657$		0			0
$658$	−16.8735	−	25.9053i	−0.657798	−	1.00989i
$659$	−35.1130	−	20.2725i	−1.36781	−	0.789704i	−0.377160	−	0.926148i	$-0.623099\pi$
$659$	−35.1130	−	20.2725i	−1.36781	−	0.789704i	−0.990648	+	0.136444i	$0.956433\pi$
$660$		0			0
$661$		−	27.7557i		−	1.07957i	−0.841803	−	0.539785i	$-0.818505\pi$
$661$		−	27.7557i		−	1.07957i	0.841803	−	0.539785i	$-0.181495\pi$
$662$		−	7.83959i		−	0.304694i
$663$		0			0
$664$	−0.682199	−	0.393868i	−0.0264745	−	0.0152850i
$665$	−1.60472	−	2.46367i	−0.0622285	−	0.0955371i
$666$		0			0
$667$	7.07313	+	12.2510i	0.273873	+	0.474361i
$668$	−5.43643	−	9.41617i	−0.210342	−	0.364323i
$669$		0			0
$670$	−5.20869	−	3.00724i	−0.201229	−	0.116180i
$671$	22.3663	+	38.7396i	0.863441	+	1.49552i
$672$		0			0
$673$	19.5469	−	33.8562i	0.753477	−	1.30506i	−0.192650	−	0.981267i	$-0.561708\pi$
$673$	19.5469	−	33.8562i	0.753477	−	1.30506i	0.946128	−	0.323794i	$-0.104958\pi$
$674$	−8.07208	+	4.66042i	−0.310925	+	0.179513i
$675$		0			0
$676$	−1.30379	+	2.25823i	−0.0501458	+	0.0868551i
$677$	38.0245			1.46140			0.730700	−	0.682698i	$-0.239194\pi$
$677$	38.0245			1.46140			0.730700	+	0.682698i	$0.239194\pi$
$678$		0			0
$679$	45.6928	−	2.45734i	1.75353	−	0.0943042i
$680$	−2.16902	+	1.25228i	−0.0831780	+	0.0480229i
$681$		0			0
$682$	31.1370	−	17.9769i	1.19230	−	0.688373i
$683$	−27.3258	−	15.7765i	−1.04559	−	0.603673i	−0.124180	−	0.992260i	$-0.539630\pi$
$683$	−27.3258	−	15.7765i	−1.04559	−	0.603673i	−0.921412	+	0.388587i	$0.872963\pi$
$684$		0			0
$685$			10.3775i			0.396506i
$686$	18.2802	−	2.97226i	0.697941	−	0.113481i
$687$		0			0
$688$	−3.62690	+	6.28198i	−0.138274	+	0.239498i
$689$	22.4574			0.855561
$690$		0			0
$691$			48.4845i			1.84444i	0.386671	+	0.922218i	$0.373625\pi$
$691$			48.4845i			1.84444i	−0.386671	+	0.922218i	$0.626375\pi$
$692$	5.77390			0.219491
$693$		0			0
$694$	−29.6538			−1.12564
$695$		−	9.15093i		−	0.347115i
$696$		0			0
$697$	−19.5857			−0.741861
$698$	−16.1844	+	28.0322i	−0.612588	+	1.06103i
$699$		0			0
$700$	−2.35902	−	1.19792i	−0.0891627	−	0.0452771i
$701$		−	48.2125i		−	1.82096i	−0.413553	−	0.910480i	$-0.635712\pi$
$701$		−	48.2125i		−	1.82096i	0.413553	−	0.910480i	$-0.364288\pi$
$702$		0			0
$703$	3.50480	+	2.02350i	0.132186	+	0.0763176i
$704$	−4.20911	+	2.43013i	−0.158637	+	0.0915890i
$705$		0			0
$706$	−5.24551	+	3.02849i	−0.197417	+	0.113979i
$707$	6.91868	+	3.51333i	0.260204	+	0.132132i
$708$		0			0
$709$	38.7382			1.45484			0.727422	−	0.686190i	$-0.240718\pi$
$709$	38.7382			1.45484			0.727422	+	0.686190i	$0.240718\pi$
$710$	4.83193	−	8.36915i	0.181339	−	0.314089i
$711$		0			0
$712$	−12.9793	+	7.49361i	−0.486420	+	0.280835i
$713$	12.2209	−	21.1672i	0.457675	−	0.792716i
$714$		0			0
$715$	9.60058	+	16.6287i	0.359041	+	0.621878i
$716$	4.85812	+	2.80484i	0.181557	+	0.104822i
$717$		0			0
$718$	−6.61995	−	11.4661i	−0.247054	−	0.427911i
$719$	8.83033	+	15.2946i	0.329316	+	0.570392i	0.982376	−	0.186914i	$-0.0598486\pi$
$719$	8.83033	+	15.2946i	0.329316	+	0.570392i	−0.653060	+	0.757306i	$0.726515\pi$
$720$		0			0
$721$	−6.82991	+	0.367310i	−0.254359	+	0.0136794i
$722$	15.3850	+	8.88251i	0.572569	+	0.330573i
$723$		0			0
$724$			24.0589i			0.894142i
$725$			4.28150i			0.159011i
$726$		0			0
$727$	−15.3445	−	8.85913i	−0.569094	−	0.328567i	0.187693	−	0.982228i	$-0.439899\pi$
$727$	−15.3445	−	8.85913i	−0.569094	−	0.328567i	−0.756788	+	0.653661i	$0.773232\pi$
$728$	9.31966	+	4.73255i	0.345409	+	0.175400i
$729$		0			0
$730$	−6.96114	−	12.0570i	−0.257643	−	0.446251i
$731$	−9.08382	−	15.7336i	−0.335977	−	0.581930i
$732$		0			0
$733$	33.4413	+	19.3074i	1.23518	+	0.713133i	0.968106	−	0.250542i	$-0.0806087\pi$
$733$	33.4413	+	19.3074i	1.23518	+	0.713133i	0.267078	+	0.963675i	$0.413942\pi$
$734$	−8.94994	−	15.5018i	−0.330348	−	0.572180i
$735$		0			0
$736$	−1.65202	+	2.86139i	−0.0608943	+	0.105472i
$737$	25.3156	−	14.6160i	0.932513	−	0.538386i
$738$		0			0
$739$	18.1858	−	31.4988i	0.668976	−	1.15870i	−0.309215	−	0.950992i	$-0.600066\pi$
$739$	18.1858	−	31.4988i	0.668976	−	1.15870i	0.978191	−	0.207708i	$-0.0666004\pi$
$740$	3.64170			0.133871
$741$		0			0
$742$	−0.807668	−	15.0181i	−0.0296504	−	0.551331i
$743$	−28.2741	+	16.3241i	−1.03728	+	0.598872i	−0.919061	−	0.394116i	$-0.871051\pi$
$743$	−28.2741	+	16.3241i	−1.03728	+	0.598872i	−0.118216	+	0.992988i	$0.537717\pi$
$744$		0			0
$745$	−20.9438	+	12.0919i	−0.767320	+	0.443013i
$746$	−3.91848	−	2.26234i	−0.143466	−	0.0828300i
$747$		0			0
$748$		−	12.1728i		−	0.445083i
$749$	8.94812	−	17.6212i	0.326957	−	0.643865i
$750$		0			0
$751$	−6.19350	+	10.7274i	−0.226004	+	0.391450i	−0.956620	−	0.291338i	$-0.905900\pi$
$751$	−6.19350	+	10.7274i	−0.226004	+	0.391450i	0.730616	+	0.682788i	$0.239233\pi$
$752$	−11.6852			−0.426114
$753$		0			0
$754$		−	16.9147i		−	0.615996i
$755$	22.9956			0.836897
$756$		0			0
$757$	39.2473			1.42647			0.713234	−	0.700926i	$-0.247230\pi$
$757$	39.2473			1.42647			0.713234	+	0.700926i	$0.247230\pi$
$758$			7.47021i			0.271330i
$759$		0			0
$760$	−1.11129			−0.0403109
$761$	7.03390	−	12.1831i	0.254979	−	0.441636i	−0.709911	−	0.704291i	$-0.751265\pi$
$761$	7.03390	−	12.1831i	0.254979	−	0.441636i	0.964890	+	0.262655i	$0.0845983\pi$
$762$		0			0
$763$	−2.33921	−	43.4962i	−0.0846852	−	1.57467i
$764$			24.2354i			0.876807i
$765$		0			0
$766$	−28.6508	−	16.5416i	−1.03520	−	0.597671i
$767$	−4.76569	+	2.75147i	−0.172079	+	0.0993498i
$768$		0			0
$769$	12.1581	−	7.01950i	0.438434	−	0.253130i	−0.264499	−	0.964386i	$-0.585207\pi$
$769$	12.1581	−	7.01950i	0.438434	−	0.253130i	0.702933	+	0.711256i	$0.251873\pi$
$770$	10.7749	−	7.01829i	0.388301	−	0.252921i
$771$		0			0
$772$	0.617476			0.0222235
$773$	−8.57207	+	14.8473i	−0.308316	+	0.534019i	−0.977994	−	0.208632i	$-0.933099\pi$
$773$	−8.57207	+	14.8473i	−0.308316	+	0.534019i	0.669678	+	0.742652i	$0.266432\pi$
$774$		0			0
$775$	6.40644	−	3.69876i	0.230126	−	0.132863i
$776$	8.64760	−	14.9781i	0.310431	−	0.537682i
$777$		0			0
$778$	18.2241	+	31.5651i	0.653366	+	1.13166i
$779$	−7.52603	−	4.34515i	−0.269648	−	0.155681i
$780$		0			0
$781$	23.4845	+	40.6763i	0.840340	+	1.45551i
$782$	−4.13760	−	7.16653i	−0.147960	−	0.256275i
$783$		0			0
$784$	2.82965	−	6.40258i	0.101059	−	0.228664i
$785$	7.00637	+	4.04513i	0.250068	+	0.144377i
$786$		0			0
$787$			33.0686i			1.17877i	0.807853	+	0.589384i	$0.200629\pi$
$787$			33.0686i			1.17877i	−0.807853	+	0.589384i	$0.799371\pi$
$788$		−	2.28650i		−	0.0814531i
$789$		0			0
$790$	6.78809	+	3.91911i	0.241509	+	0.139436i
$791$	4.03840	−	7.95268i	0.143589	−	0.282765i
$792$		0			0
$793$	−18.1803	−	31.4893i	−0.645603	−	1.11822i
$794$	7.69789	+	13.3331i	0.273188	+	0.473175i
$795$		0			0
$796$	3.60562	+	2.08171i	0.127798	+	0.0737841i
$797$	−9.84860	−	17.0583i	−0.348855	−	0.604235i	0.637191	−	0.770706i	$-0.280096\pi$
$797$	−9.84860	−	17.0583i	−0.348855	−	0.604235i	−0.986046	+	0.166471i	$0.946763\pi$
$798$		0			0
$799$	14.6331	−	25.3453i	0.517682	−	0.896652i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−8.20364	+	14.2091i	−0.289681	+	0.501742i
$803$	67.6659			2.38788
$804$		0			0
$805$	3.95798	−	7.79431i	0.139500	−	0.274713i
$806$	−25.3096	+	14.6125i	−0.891491	+	0.514703i
$807$		0			0
$808$	2.53993	−	1.46643i	0.0893545	−	0.0515888i
$809$	21.6772	+	12.5154i	0.762131	+	0.440017i	0.830060	−	0.557674i	$-0.188306\pi$
$809$	21.6772	+	12.5154i	0.762131	+	0.440017i	−0.0679294	+	0.997690i	$0.521639\pi$
$810$		0			0
$811$			12.0504i			0.423146i	0.977362	+	0.211573i	$0.0678586\pi$
$811$			12.0504i			0.423146i	−0.977362	+	0.211573i	$0.932141\pi$
$812$	−11.3114	+	0.608325i	−0.396953	+	0.0213480i
$813$		0			0
$814$	−8.84980	+	15.3283i	−0.310185	+	0.537257i
$815$	−1.23347			−0.0432066
$816$		0			0
$817$		−	8.06111i		−	0.282023i
$818$	−21.1331			−0.738900
$819$		0			0
$820$	−7.81999			−0.273086
$821$			41.8882i			1.46191i	0.682427	+	0.730953i	$0.260924\pi$
$821$			41.8882i			1.46191i	−0.682427	+	0.730953i	$0.739076\pi$
$822$		0			0
$823$	27.6822			0.964940			0.482470	−	0.875912i	$-0.339740\pi$
$823$	27.6822			0.964940			0.482470	+	0.875912i	$0.339740\pi$
$824$	−1.29260	+	2.23884i	−0.0450297	+	0.0779938i
$825$		0			0
$826$	2.01140	+	3.08803i	0.0699855	+	0.107446i
$827$			36.8335i			1.28083i	0.768031	+	0.640413i	$0.221237\pi$
$827$			36.8335i			1.28083i	−0.768031	+	0.640413i	$0.778763\pi$
$828$		0			0
$829$	44.8357	+	25.8859i	1.55721	+	0.899055i	0.997522	+	0.0703515i	$0.0224121\pi$
$829$	44.8357	+	25.8859i	1.55721	+	0.899055i	0.559687	+	0.828704i	$0.310921\pi$
$830$	0.682199	−	0.393868i	0.0236795	−	0.0136714i
$831$		0			0
$832$	3.42136	−	1.97532i	0.118614	−	0.0684820i
$833$	10.3438	+	14.1554i	0.358391	+	0.490456i
$834$		0			0
$835$	10.8729			0.376271
$836$	2.70059	−	4.67756i	0.0934019	−	0.161777i
$837$		0			0
$838$	4.00254	−	2.31087i	0.138265	−	0.0798276i
$839$	4.77807	−	8.27587i	0.164957	−	0.285715i	−0.771683	−	0.636008i	$-0.780585\pi$
$839$	4.77807	−	8.27587i	0.164957	−	0.285715i	0.936640	+	0.350293i	$0.113918\pi$
$840$		0			0
$841$	−5.33439	−	9.23943i	−0.183944	−	0.318601i
$842$	−2.00148	−	1.15555i	−0.0689755	−	0.0398230i
$843$		0			0
$844$	−1.26573	−	2.19231i	−0.0435682	−	0.0754624i
$845$	−1.30379	−	2.25823i	−0.0448518	−	0.0776855i
$846$		0			0
$847$	1.79339	+	33.3469i	0.0616214	+	1.14581i
$848$	−4.92292	−	2.84225i	−0.169054	−	0.0976033i
$849$		0			0
$850$		−	2.50457i		−	0.0859059i
$851$			12.0323i			0.412463i
$852$		0			0
$853$	−6.13810	−	3.54384i	−0.210165	−	0.121339i	0.391223	−	0.920296i	$-0.372052\pi$
$853$	−6.13810	−	3.54384i	−0.210165	−	0.121339i	−0.601388	+	0.798957i	$0.705385\pi$
$854$	−20.4041	+	13.2903i	−0.698215	+	0.454786i
$855$		0			0
$856$	−3.73486	−	6.46896i	−0.127655	−	0.221104i
$857$	18.7513	+	32.4782i	0.640531	+	1.10943i	0.985314	+	0.170750i	$0.0546191\pi$
$857$	18.7513	+	32.4782i	0.640531	+	1.10943i	−0.344783	+	0.938682i	$0.612048\pi$
$858$		0			0
$859$	−10.1182	−	5.84175i	−0.345229	−	0.199318i	0.317353	−	0.948307i	$-0.397206\pi$
$859$	−10.1182	−	5.84175i	−0.345229	−	0.199318i	−0.662582	+	0.748990i	$0.730539\pi$
$860$	−3.62690	−	6.28198i	−0.123676	−	0.214214i
$861$		0			0
$862$	−12.3175	+	21.3345i	−0.419536	+	0.726657i
$863$	41.4770	−	23.9467i	1.41189	−	0.815157i	0.416326	−	0.909215i	$-0.363317\pi$
$863$	41.4770	−	23.9467i	1.41189	−	0.815157i	0.995567	+	0.0940587i	$0.0299841\pi$
$864$		0			0
$865$	−2.88695	+	5.00034i	−0.0981592	+	0.170017i
$866$	−6.55773			−0.222841
$867$		0			0
$868$	10.6821	+	16.3999i	0.362575	+	0.556647i
$869$	−32.9919	+	19.0479i	−1.11917	+	0.646155i
$870$		0			0
$871$	−20.5777	+	11.8805i	−0.697248	+	0.402557i
$872$	−14.2581	−	8.23189i	−0.482839	−	0.278767i
$873$		0			0
$874$		−	3.67176i		−	0.124199i
$875$	2.21694	−	1.44401i	0.0749463	−	0.0488166i
$876$		0			0
$877$	16.6303	−	28.8045i	0.561564	−	0.972658i	−0.435796	−	0.900046i	$-0.643533\pi$
$877$	16.6303	−	28.8045i	0.561564	−	0.972658i	0.997360	−	0.0726125i	$-0.0231336\pi$
$878$	−32.4291			−1.09443
$879$		0			0
$880$		−	4.86026i		−	0.163839i
$881$	−39.7345			−1.33869			−0.669344	−	0.742953i	$-0.733425\pi$
$881$	−39.7345			−1.33869			−0.669344	+	0.742953i	$0.733425\pi$
$882$		0			0
$883$	−20.3226			−0.683910			−0.341955	−	0.939716i	$-0.611089\pi$
$883$	−20.3226			−0.683910			−0.341955	+	0.939716i	$0.611089\pi$
$884$			9.89465i			0.332793i
$885$		0			0
$886$	−0.235686			−0.00791802
$887$	1.35913	−	2.35408i	0.0456351	−	0.0790424i	−0.842306	−	0.539000i	$-0.818802\pi$
$887$	1.35913	−	2.35408i	0.0456351	−	0.0790424i	0.887941	+	0.459958i	$0.152136\pi$
$888$		0			0
$889$	−32.0558	+	20.8797i	−1.07512	+	0.700282i
$890$		−	14.9872i		−	0.502373i
$891$		0			0
$892$	−9.62445	−	5.55668i	−0.322250	−	0.186051i
$893$	11.2459	−	6.49282i	0.376329	−	0.217274i
$894$		0			0
$895$	−4.85812	+	2.80484i	−0.162389	+	0.0937554i
$896$	−1.44401	−	2.21694i	−0.0482411	−	0.0740628i
$897$		0			0
$898$	−18.8068			−0.627592
$899$	15.8362	−	27.4292i	0.528168	−	0.914813i
$900$		0			0
$901$	12.3298	−	7.11861i	0.410765	−	0.237155i
$902$	19.0036	−	32.9152i	0.632751	−	1.09596i
$903$		0			0
$904$	−1.68559	−	2.91952i	−0.0560618	−	0.0971019i
$905$	−20.8356	−	12.0294i	−0.692599	−	0.399872i
$906$		0			0
$907$	23.1327	+	40.0670i	0.768109	+	1.33040i	0.938587	+	0.345042i	$0.112135\pi$
$907$	23.1327	+	40.0670i	0.768109	+	1.33040i	−0.170479	+	0.985361i	$0.554531\pi$
$908$	−5.76421	−	9.98390i	−0.191292	−	0.331327i
$909$		0			0
$910$	−8.75834	+	5.70478i	−0.290336	+	0.189112i
$911$	33.8272	+	19.5301i	1.12074	+	0.647062i	0.941591	−	0.336759i	$-0.109331\pi$
$911$	33.8272	+	19.5301i	1.12074	+	0.647062i	0.179154	+	0.983821i	$0.442664\pi$
$912$		0			0
$913$			3.82860i			0.126708i
$914$			18.6117i			0.615619i
$915$		0			0
$916$	22.7387	+	13.1282i	0.751308	+	0.433768i
$917$	1.87335	+	34.8338i	0.0618635	+	1.15031i
$918$		0			0
$919$	19.6509	+	34.0363i	0.648223	+	1.12276i	0.983547	+	0.180652i	$0.0578209\pi$
$919$	19.6509	+	34.0363i	0.648223	+	1.12276i	−0.335324	+	0.942103i	$0.608846\pi$
$920$	−1.65202	−	2.86139i	−0.0544655	−	0.0943371i
$921$		0			0
$922$	−23.8538	−	13.7720i	−0.785583	−	0.453556i
$923$	−19.0892	−	33.0635i	−0.628330	−	1.08830i
$924$		0			0
$925$	−1.82085	+	3.15380i	−0.0598691	+	0.103696i
$926$	0.414241	−	0.239162i	0.0136128	−	0.00785935i
$927$		0			0
$928$	−2.14075	+	3.70789i	−0.0702735	+	0.121717i
$929$	−45.7542			−1.50115			−0.750574	−	0.660787i	$-0.770223\pi$
$929$	−45.7542			−1.50115			−0.750574	+	0.660787i	$0.770223\pi$
$930$		0			0
$931$	0.834297	+	7.73419i	0.0273430	+	0.253478i
$932$	0.657636	−	0.379686i	0.0215416	−	0.0124370i
$933$		0			0
$934$	−10.5393	+	6.08486i	−0.344856	+	0.199103i
$935$	10.5420	+	6.08642i	0.344760	+	0.199047i
$936$		0			0
$937$			52.1498i			1.70366i	0.523819	+	0.851830i	$0.324507\pi$
$937$			52.1498i			1.70366i	−0.523819	+	0.851830i	$0.675493\pi$
$938$	8.68499	+	13.3337i	0.283575	+	0.435362i
$939$		0			0
$940$	5.84258	−	10.1196i	0.190564	−	0.330066i
$941$	−26.7510			−0.872058			−0.436029	−	0.899933i	$-0.643616\pi$
$941$	−26.7510			−0.872058			−0.436029	+	0.899933i	$0.643616\pi$
$942$		0			0
$943$		−	25.8376i		−	0.841388i
$944$	1.39292			0.0453358
$945$		0			0
$946$	35.2554			1.14625
$947$		−	9.85468i		−	0.320234i	−0.987098	−	0.160117i	$-0.948813\pi$
$947$		−	9.85468i		−	0.320234i	0.987098	−	0.160117i	$-0.0511872\pi$
$948$		0			0
$949$	−55.0019			−1.78544
$950$	0.555647	−	0.962409i	0.0180276	−	0.0312247i
$951$		0			0
$952$	6.61690	−	0.355855i	0.214455	−	0.0115333i
$953$		−	18.8568i		−	0.610830i	−0.952219	−	0.305415i	$-0.901205\pi$
$953$		−	18.8568i		−	0.610830i	0.952219	−	0.305415i	$-0.0987952\pi$
$954$		0			0
$955$	−20.9885	−	12.1177i	−0.679172	−	0.392120i
$956$	−21.2951	+	12.2947i	−0.688732	+	0.397640i
$957$		0			0
$958$	34.9474	−	20.1769i	1.12910	−	0.651886i
$959$	12.4315	−	24.4809i	0.401433	−	0.790528i
$960$		0			0
$961$	−23.7233			−0.765267
$962$	7.19352	−	12.4595i	0.231928	−	0.401712i
$963$		0			0
$964$	11.6664	−	6.73558i	0.375749	−	0.216939i
$965$	−0.308738	+	0.534750i	−0.00993863	+	0.0172142i
$966$		0			0
$967$	27.7839	+	48.1232i	0.893471	+	1.54754i	0.835686	+	0.549208i	$0.185070\pi$
$967$	27.7839	+	48.1232i	0.893471	+	1.54754i	0.0577849	+	0.998329i	$0.481596\pi$
$968$	10.9311	+	6.31108i	0.351339	+	0.202846i
$969$		0			0
$970$	8.64760	+	14.9781i	0.277658	+	0.480917i
$971$	26.8589	+	46.5210i	0.861944	+	1.49293i	0.870050	+	0.492963i	$0.164086\pi$
$971$	26.8589	+	46.5210i	0.861944	+	1.49293i	−0.00810628	+	0.999967i	$0.502580\pi$
$972$		0			0
$973$	−10.9621	+	21.5873i	−0.351428	+	0.692056i
$974$	7.12353	+	4.11277i	0.228253	+	0.131782i
$975$		0			0
$976$			9.20374i			0.294605i
$977$			17.1964i			0.550162i	0.961421	+	0.275081i	$0.0887046\pi$
$977$			17.1964i			0.550162i	−0.961421	+	0.275081i	$0.911295\pi$
$978$		0			0
$979$	63.0829	+	36.4209i	2.01614	+	1.16402i
$980$	4.12998	+	5.65184i	0.131927	+	0.180541i
$981$		0			0
$982$	5.26190	+	9.11388i	0.167914	+	0.290835i
$983$	14.2867	+	24.7453i	0.455676	+	0.789254i	0.998727	−	0.0504459i	$-0.0160642\pi$
$983$	14.2867	+	24.7453i	0.455676	+	0.789254i	−0.543051	+	0.839700i	$0.682731\pi$
$984$		0			0
$985$	1.98016	+	1.14325i	0.0630933	+	0.0364269i
$986$	−5.36165	−	9.28664i	−0.170750	−	0.295747i
$987$		0			0
$988$	−2.19516	+	3.80213i	−0.0698374	+	0.120962i
$989$	20.7559	−	11.9834i	0.660001	−	0.381052i
$990$		0			0
$991$	−9.29023	+	16.0912i	−0.295114	+	0.511152i	−0.975011	−	0.222155i	$-0.928691\pi$
$991$	−9.29023	+	16.0912i	−0.295114	+	0.511152i	0.679897	+	0.733307i	$0.262024\pi$
$992$	7.39752			0.234871
$993$		0			0
$994$	−21.4242	+	13.9548i	−0.679535	+	0.442618i
$995$	−3.60562	+	2.08171i	−0.114306	+	0.0659945i
$996$		0			0
$997$	−6.69547	+	3.86563i	−0.212048	+	0.122426i	−0.602263	−	0.798298i	$-0.705734\pi$
$997$	−6.69547	+	3.86563i	−0.212048	+	0.122426i	0.390215	+	0.920724i	$0.372401\pi$
$998$	0.736540	+	0.425242i	0.0233148	+	0.0134608i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bk.b.521.3		28
3.2	odd	2		630.2.bk.b.101.14	yes	28
7.5	odd	6		1890.2.t.b.1601.7		28
9.4	even	3		630.2.t.b.311.13	✓	28
9.5	odd	6		1890.2.t.b.1151.7		28
21.5	even	6		630.2.t.b.551.13	yes	28
63.5	even	6	inner	1890.2.bk.b.341.3		28
63.40	odd	6		630.2.bk.b.131.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.13	✓	28	9.4	even	3
630.2.t.b.551.13	yes	28	21.5	even	6
630.2.bk.b.101.14	yes	28	3.2	odd	2
630.2.bk.b.131.7	yes	28	63.40	odd	6
1890.2.t.b.1151.7		28	9.5	odd	6
1890.2.t.b.1601.7		28	7.5	odd	6
1890.2.bk.b.341.3		28	63.5	even	6	inner
1890.2.bk.b.521.3		28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.21694 + 1.44401i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.21694 + 1.44401i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +(4.20911 - 2.43013i) q^{11} +(-3.42136 + 1.97532i) q^{13} +(1.44401 + 2.21694i) q^{14} +1.00000 q^{16} +(-1.25228 + 2.16902i) q^{17} +(-0.962409 + 0.555647i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-2.43013 - 4.20911i) q^{22} +(-2.86139 - 1.65202i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.97532 + 3.42136i) q^{26} +(2.21694 - 1.44401i) q^{28} +(-3.70789 - 2.14075i) q^{29} +7.39752i q^{31} -1.00000i q^{32} +(2.16902 + 1.25228i) q^{34} +(0.142082 + 2.64193i) q^{35} +(-1.82085 - 3.15380i) q^{37} +(0.555647 + 0.962409i) q^{38} +(0.866025 + 0.500000i) q^{40} +(3.91000 + 6.77231i) q^{41} +(-3.62690 + 6.28198i) q^{43} +(-4.20911 + 2.43013i) q^{44} +(-1.65202 + 2.86139i) q^{46} -11.6852 q^{47} +(2.82965 - 6.40258i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.42136 - 1.97532i) q^{52} +(-4.92292 - 2.84225i) q^{53} -4.86026i q^{55} +(-1.44401 - 2.21694i) q^{56} +(-2.14075 + 3.70789i) q^{58} +1.39292 q^{59} +9.20374i q^{61} +7.39752 q^{62} -1.00000 q^{64} +3.95064i q^{65} +6.01448 q^{67} +(1.25228 - 2.16902i) q^{68} +(2.64193 - 0.142082i) q^{70} +9.66386i q^{71} +(12.0570 + 6.96114i) q^{73} +(-3.15380 + 1.82085i) q^{74} +(0.962409 - 0.555647i) q^{76} +(-5.82221 + 11.4655i) q^{77} -7.83821 q^{79} +(0.500000 - 0.866025i) q^{80} +(6.77231 - 3.91000i) q^{82} +(-0.393868 + 0.682199i) q^{83} +(1.25228 + 2.16902i) q^{85} +(6.28198 + 3.62690i) q^{86} +(2.43013 + 4.20911i) q^{88} +(7.49361 + 12.9793i) q^{89} +(4.73255 - 9.31966i) q^{91} +(2.86139 + 1.65202i) q^{92} +11.6852i q^{94} +1.11129i q^{95} +(-14.9781 - 8.64760i) q^{97} +(-6.40258 - 2.82965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) \) 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) \) 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7 + 28 * q^16 - 6 * q^17 - 6 * q^19 - 14 * q^20 - 6 * q^22 - 30 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 + 4 * q^35 + 4 * q^37 + 6 * q^38 + 18 * q^41 + 28 * q^43 - 18 * q^46 - 60 * q^47 - 20 * q^49 - 42 * q^53 + 6 * q^58 + 48 * q^59 - 12 * q^62 - 28 * q^64 + 80 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^73 + 6 * q^76 + 18 * q^77 - 4 * q^79 + 14 * q^80 + 24 * q^82 - 18 * q^83 + 6 * q^85 + 96 * q^86 + 6 * q^88 + 6 * q^89 + 66 * q^91 + 30 * q^92 + 72 * q^97 - 24 * q^98

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