LMFDB - Embedded newform 1890.2.bq.a.289.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(289,1890)]

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([4, 3, 2]))

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

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

chi := DirichletCharacter("1890.289");

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.bq (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:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.47
Character	$\chi$	$=$	1890.289
Dual form			1890.2.bq.a.739.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.15250 + 0.605607i) q^{5} +(-1.94150 + 1.79738i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.15250 + 0.605607i) q^{5} +(-1.94150 + 1.79738i) q^{7} -1.00000i q^{8} +(2.16692 - 0.551777i) q^{10} -4.10584 q^{11} +(-3.36239 + 1.94128i) q^{13} +(-0.782695 + 2.52733i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.40480 + 1.38841i) q^{17} +(-1.40977 + 2.44179i) q^{19} +(1.60072 - 1.56131i) q^{20} +(-3.55576 + 2.05292i) q^{22} +5.92553i q^{23} +(4.26648 + 2.60714i) q^{25} +(-1.94128 + 3.36239i) q^{26} +(0.585831 + 2.58008i) q^{28} +(-2.36090 + 4.08921i) q^{29} +(1.94744 - 3.37307i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.38841 + 2.40480i) q^{34} +(-5.26758 + 2.69307i) q^{35} +(-0.356887 - 0.206049i) q^{37} +2.81954i q^{38} +(0.605607 - 2.15250i) q^{40} +(3.43052 + 5.94183i) q^{41} +(1.08691 + 0.627530i) q^{43} +(-2.05292 + 3.55576i) q^{44} +(2.96277 + 5.13166i) q^{46} +(-4.42203 + 2.55306i) q^{47} +(0.538827 - 6.97923i) q^{49} +(4.99845 + 0.124606i) q^{50} +3.88256i q^{52} +(-4.20182 + 2.42592i) q^{53} +(-8.83781 - 2.48653i) q^{55} +(1.79738 + 1.94150i) q^{56} +4.72181i q^{58} +(6.24051 - 10.8089i) q^{59} +(0.544252 + 0.942671i) q^{61} -3.89489i q^{62} -1.00000 q^{64} +(-8.41319 + 2.14230i) q^{65} +(10.8485 + 6.26339i) q^{67} +2.77682i q^{68} +(-3.21532 + 4.96606i) q^{70} -16.3189 q^{71} +(11.1123 - 6.41567i) q^{73} -0.412097 q^{74} +(1.40977 + 2.44179i) q^{76} +(7.97148 - 7.37977i) q^{77} +(-3.01373 - 5.21993i) q^{79} +(-0.551777 - 2.16692i) q^{80} +(5.94183 + 3.43052i) q^{82} +(-13.4228 - 7.74967i) q^{83} +(-6.01715 + 1.53218i) q^{85} +1.25506 q^{86} +4.10584i q^{88} +(-3.68803 + 6.38786i) q^{89} +(3.03886 - 9.81250i) q^{91} +(5.13166 + 2.96277i) q^{92} +(-2.55306 + 4.42203i) q^{94} +(-4.51329 + 4.40219i) q^{95} +(3.62553 + 2.09320i) q^{97} +(-3.02298 - 6.31361i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4}+O(q^{10}) $ 96 * q + 48 * q^4	$ 96 q + 48 q^{4} + 8 q^{11} + 2 q^{14} - 48 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} + 12 q^{49} + 12 q^{50} + 12 q^{55} + 4 q^{56} + 24 q^{59} - 6 q^{61} - 96 q^{64} - 18 q^{65} + 6 q^{70} + 32 q^{71} + 8 q^{86} + 66 q^{89} - 12 q^{94} - 30 q^{95}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^11 + 2 * q^14 - 48 * q^16 - 24 * q^26 - 10 * q^29 + 34 * q^35 - 30 * q^41 + 4 * q^44 - 6 * q^46 + 12 * q^49 + 12 * q^50 + 12 * q^55 + 4 * q^56 + 24 * q^59 - 6 * q^61 - 96 * q^64 - 18 * q^65 + 6 * q^70 + 32 * q^71 + 8 * q^86 + 66 * q^89 - 12 * q^94 - 30 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.15250	+	0.605607i	0.962626	+	0.270836i
$5$	2.15250	+	0.605607i	0.962626	+	0.270836i
$6$		0			0
$7$	−1.94150	+	1.79738i	−0.733817	+	0.679347i
$7$	−1.94150	+	1.79738i	−0.733817	+	0.679347i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.16692	−	0.551777i	0.685240	−	0.174487i
$11$	−4.10584			−1.23796			−0.618979	−	0.785408i	$-0.712453\pi$
$11$	−4.10584			−1.23796			−0.618979	+	0.785408i	$0.712453\pi$
$12$		0			0
$13$	−3.36239	+	1.94128i	−0.932560	+	0.538414i	−0.887620	−	0.460576i	$-0.847643\pi$
$13$	−3.36239	+	1.94128i	−0.932560	+	0.538414i	−0.0449397	+	0.998990i	$0.514310\pi$
$14$	−0.782695	+	2.52733i	−0.209184	+	0.675457i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.40480	+	1.38841i	−0.583249	+	0.336739i	−0.762424	−	0.647078i	$-0.775991\pi$
$17$	−2.40480	+	1.38841i	−0.583249	+	0.336739i	0.179175	+	0.983817i	$0.442657\pi$
$18$		0			0
$19$	−1.40977	+	2.44179i	−0.323424	+	0.560186i	−0.981192	−	0.193034i	$-0.938167\pi$
$19$	−1.40977	+	2.44179i	−0.323424	+	0.560186i	0.657768	+	0.753220i	$0.271501\pi$
$20$	1.60072	−	1.56131i	0.357932	−	0.349120i
$21$		0			0
$22$	−3.55576	+	2.05292i	−0.758091	+	0.437684i
$23$			5.92553i			1.23556i	0.786351	+	0.617780i	$0.211968\pi$
$23$			5.92553i			1.23556i	−0.786351	+	0.617780i	$0.788032\pi$
$24$		0			0
$25$	4.26648	+	2.60714i	0.853296	+	0.521427i
$26$	−1.94128	+	3.36239i	−0.380716	+	0.659420i
$27$		0			0
$28$	0.585831	+	2.58008i	0.110712	+	0.487589i
$29$	−2.36090	+	4.08921i	−0.438409	+	0.759346i	−0.997567	−	0.0697147i	$-0.977791\pi$
$29$	−2.36090	+	4.08921i	−0.438409	+	0.759346i	0.559158	+	0.829061i	$0.311124\pi$
$30$		0			0
$31$	1.94744	−	3.37307i	0.349771	−	0.605821i	−0.636438	−	0.771328i	$-0.719593\pi$
$31$	1.94744	−	3.37307i	0.349771	−	0.605821i	0.986209	+	0.165507i	$0.0529260\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−1.38841	+	2.40480i	−0.238110	+	0.412419i
$35$	−5.26758	+	2.69307i	−0.890383	+	0.455213i
$36$		0			0
$37$	−0.356887	−	0.206049i	−0.0586718	−	0.0338742i	0.470377	−	0.882465i	$-0.344118\pi$
$37$	−0.356887	−	0.206049i	−0.0586718	−	0.0338742i	−0.529049	+	0.848591i	$0.677451\pi$
$38$			2.81954i			0.457390i
$39$		0			0
$40$	0.605607	−	2.15250i	0.0957549	−	0.340340i
$41$	3.43052	+	5.94183i	0.535757	+	0.927958i	0.999126	+	0.0417929i	$0.0133070\pi$
$41$	3.43052	+	5.94183i	0.535757	+	0.927958i	−0.463369	+	0.886165i	$0.653360\pi$
$42$		0			0
$43$	1.08691	+	0.627530i	0.165753	+	0.0956975i	0.580582	−	0.814202i	$-0.302825\pi$
$43$	1.08691	+	0.627530i	0.165753	+	0.0956975i	−0.414829	+	0.909899i	$0.636159\pi$
$44$	−2.05292	+	3.55576i	−0.309489	+	0.536051i
$45$		0			0
$46$	2.96277	+	5.13166i	0.436836	+	0.756622i
$47$	−4.42203	+	2.55306i	−0.645019	+	0.372402i	−0.786545	−	0.617533i	$-0.788132\pi$
$47$	−4.42203	+	2.55306i	−0.645019	+	0.372402i	0.141526	+	0.989935i	$0.454799\pi$
$48$		0			0
$49$	0.538827	−	6.97923i	0.0769753	−	0.997033i
$50$	4.99845	+	0.124606i	0.706887	+	0.0176219i
$51$		0			0
$52$			3.88256i			0.538414i
$53$	−4.20182	+	2.42592i	−0.577164	+	0.333226i	−0.760006	−	0.649917i	$-0.774804\pi$
$53$	−4.20182	+	2.42592i	−0.577164	+	0.333226i	0.182842	+	0.983142i	$0.441470\pi$
$54$		0			0
$55$	−8.83781	−	2.48653i	−1.19169	−	0.335283i
$56$	1.79738	+	1.94150i	0.240185	+	0.259444i
$57$		0			0
$58$			4.72181i			0.620004i
$59$	6.24051	−	10.8089i	0.812445	−	1.40720i	−0.0987028	−	0.995117i	$-0.531469\pi$
$59$	6.24051	−	10.8089i	0.812445	−	1.40720i	0.911148	−	0.412079i	$-0.135197\pi$
$60$		0			0
$61$	0.544252	+	0.942671i	0.0696843	+	0.120697i	0.898762	−	0.438436i	$-0.144467\pi$
$61$	0.544252	+	0.942671i	0.0696843	+	0.120697i	−0.829078	+	0.559133i	$0.811134\pi$
$62$		−	3.89489i		−	0.494651i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.41319	+	2.14230i	−1.04353	+	0.265720i
$66$		0			0
$67$	10.8485	+	6.26339i	1.32536	+	0.765195i	0.984578	−	0.174949i	$-0.0559759\pi$
$67$	10.8485	+	6.26339i	1.32536	+	0.765195i	0.340779	+	0.940143i	$0.389309\pi$
$68$			2.77682i			0.336739i
$69$		0			0
$70$	−3.21532	+	4.96606i	−0.384304	+	0.593558i
$71$	−16.3189			−1.93669			−0.968346	−	0.249611i	$-0.919697\pi$
$71$	−16.3189			−1.93669			−0.968346	+	0.249611i	$0.919697\pi$
$72$		0			0
$73$	11.1123	−	6.41567i	1.30059	−	0.750897i	0.320086	−	0.947389i	$-0.396288\pi$
$73$	11.1123	−	6.41567i	1.30059	−	0.750897i	0.980505	+	0.196492i	$0.0629549\pi$
$74$	−0.412097			−0.0479053
$75$		0			0
$76$	1.40977	+	2.44179i	0.161712	+	0.280093i
$77$	7.97148	−	7.37977i	0.908435	−	0.841003i
$78$		0			0
$79$	−3.01373	−	5.21993i	−0.339071	−	0.587288i	0.645187	−	0.764024i	$-0.276779\pi$
$79$	−3.01373	−	5.21993i	−0.339071	−	0.587288i	−0.984258	+	0.176736i	$0.943446\pi$
$80$	−0.551777	−	2.16692i	−0.0616905	−	0.242269i
$81$		0			0
$82$	5.94183	+	3.43052i	0.656165	+	0.378837i
$83$	−13.4228	−	7.74967i	−1.47335	−	0.850637i	−0.473796	−	0.880635i	$-0.657116\pi$
$83$	−13.4228	−	7.74967i	−1.47335	−	0.850637i	−0.999550	+	0.0299982i	$0.990450\pi$
$84$		0			0
$85$	−6.01715	+	1.53218i	−0.652651	+	0.166189i
$86$	1.25506			0.135337
$87$		0			0
$88$			4.10584i			0.437684i
$89$	−3.68803	+	6.38786i	−0.390931	+	0.677112i	−0.992573	−	0.121654i	$-0.961180\pi$
$89$	−3.68803	+	6.38786i	−0.390931	+	0.677112i	0.601642	+	0.798766i	$0.294513\pi$
$90$		0			0
$91$	3.03886	−	9.81250i	0.318559	−	1.02863i
$92$	5.13166	+	2.96277i	0.535013	+	0.308890i
$93$		0			0
$94$	−2.55306	+	4.42203i	−0.263328	+	0.456097i
$95$	−4.51329	+	4.40219i	−0.463054	+	0.451655i
$96$		0			0
$97$	3.62553	+	2.09320i	0.368117	+	0.212532i	0.672635	−	0.739974i	$-0.265162\pi$
$97$	3.62553	+	2.09320i	0.368117	+	0.212532i	−0.304519	+	0.952506i	$0.598496\pi$
$98$	−3.02298	−	6.31361i	−0.305367	−	0.637770i
$99$		0			0
$100$	4.39109	−	2.39131i	0.439109	−	0.239131i
$101$	12.6639			1.26011			0.630053	−	0.776552i	$-0.283033\pi$
$101$	12.6639			1.26011			0.630053	+	0.776552i	$0.283033\pi$
$102$		0			0
$103$			4.37970i			0.431545i	0.976444	+	0.215772i	$0.0692270\pi$
$103$			4.37970i			0.431545i	−0.976444	+	0.215772i	$0.930773\pi$
$104$	1.94128	+	3.36239i	0.190358	+	0.329710i
$105$		0			0
$106$	−2.42592	+	4.20182i	−0.235626	+	0.408117i
$107$	−2.83265	−	1.63543i	−0.273843	−	0.158103i	0.356790	−	0.934185i	$-0.383871\pi$
$107$	−2.83265	−	1.63543i	−0.273843	−	0.158103i	−0.630633	+	0.776081i	$0.717205\pi$
$108$		0			0
$109$	−1.65955	−	2.87443i	−0.158956	−	0.275321i	0.775536	−	0.631303i	$-0.217480\pi$
$109$	−1.65955	−	2.87443i	−0.158956	−	0.275321i	−0.934493	+	0.355983i	$0.884146\pi$
$110$	−8.89703	+	2.26551i	−0.848299	+	0.216008i
$111$		0			0
$112$	2.52733	+	0.782695i	0.238810	+	0.0739577i
$113$	6.85140	−	3.95566i	0.644526	−	0.372117i	−0.141830	−	0.989891i	$-0.545299\pi$
$113$	6.85140	−	3.95566i	0.644526	−	0.372117i	0.786356	+	0.617774i	$0.211965\pi$
$114$		0			0
$115$	−3.58855	+	12.7547i	−0.334634	+	1.18938i
$116$	2.36090	+	4.08921i	0.219204	+	0.379673i
$117$		0			0
$118$		−	12.4810i		−	1.14897i
$119$	2.17340	−	7.01794i	0.199236	−	0.643333i
$120$		0			0
$121$	5.85793			0.532539
$122$	0.942671	+	0.544252i	0.0853455	+	0.0492742i
$123$		0			0
$124$	−1.94744	−	3.37307i	−0.174886	−	0.302911i
$125$	7.60468	+	8.19566i	0.680183	+	0.733042i
$126$		0			0
$127$			7.37701i			0.654604i	0.944920	+	0.327302i	$0.106139\pi$
$127$			7.37701i			0.654604i	−0.944920	+	0.327302i	$0.893861\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−6.21488	+	6.06189i	−0.545081	+	0.531663i
$131$	−11.9234			−1.04175			−0.520874	−	0.853633i	$-0.674394\pi$
$131$	−11.9234			−1.04175			−0.520874	+	0.853633i	$0.674394\pi$
$132$		0			0
$133$	−1.65177	−	7.27464i	−0.143227	−	0.630791i
$134$	12.5268			1.08215
$135$		0			0
$136$	1.38841	+	2.40480i	0.119055	+	0.206210i
$137$			19.8145i			1.69287i	0.532492	+	0.846435i	$0.321256\pi$
$137$			19.8145i			1.69287i	−0.532492	+	0.846435i	$0.678744\pi$
$138$		0			0
$139$	2.84915	+	4.93488i	0.241662	+	0.418571i	0.961188	−	0.275895i	$-0.0889741\pi$
$139$	2.84915	+	4.93488i	0.241662	+	0.418571i	−0.719526	+	0.694466i	$0.755641\pi$
$140$	−0.301516	+	5.90839i	−0.0254828	+	0.499350i
$141$		0			0
$142$	−14.1325	+	8.15943i	−1.18598	+	0.684724i
$143$	13.8055	−	7.97058i	1.15447	−	0.666534i
$144$		0			0
$145$	−7.55829	+	7.37222i	−0.627682	+	0.612229i
$146$	6.41567	−	11.1123i	0.530964	−	0.919657i
$147$		0			0
$148$	−0.356887	+	0.206049i	−0.0293359	+	0.0169371i
$149$	20.8041			1.70434			0.852169	−	0.523266i	$-0.175287\pi$
$149$	20.8041			1.70434			0.852169	+	0.523266i	$0.175287\pi$
$150$		0			0
$151$	16.2643			1.32357			0.661786	−	0.749692i	$-0.269799\pi$
$151$	16.2643			1.32357			0.661786	+	0.749692i	$0.269799\pi$
$152$	2.44179	+	1.40977i	0.198056	+	0.114347i
$153$		0			0
$154$	3.21362	−	10.3768i	0.258961	−	0.836187i
$155$	6.23462	−	6.08113i	0.500777	−	0.488448i
$156$		0			0
$157$	−17.5445	−	10.1293i	−1.40020	−	0.808406i	−0.405788	−	0.913967i	$-0.633003\pi$
$157$	−17.5445	−	10.1293i	−1.40020	−	0.808406i	−0.994413	+	0.105561i	$0.966336\pi$
$158$	−5.21993	−	3.01373i	−0.415275	−	0.239759i
$159$		0			0
$160$	−1.56131	−	1.60072i	−0.123433	−	0.126548i
$161$	−10.6505	−	11.5044i	−0.839373	−	0.906674i
$162$		0			0
$163$	−6.81431	−	3.93424i	−0.533738	−	0.308154i	0.208799	−	0.977958i	$-0.433044\pi$
$163$	−6.81431	−	3.93424i	−0.533738	−	0.308154i	−0.742537	+	0.669805i	$0.766378\pi$
$164$	6.86104			0.535757
$165$		0			0
$166$	−15.4993			−1.20298
$167$	−18.3747	+	10.6086i	−1.42187	+	0.820919i	−0.996459	−	0.0840795i	$-0.973205\pi$
$167$	−18.3747	+	10.6086i	−1.42187	+	0.820919i	−0.425415	+	0.904999i	$0.639872\pi$
$168$		0			0
$169$	1.03712	−	1.79635i	0.0797788	−	0.138181i
$170$	−4.44491	+	4.33549i	−0.340909	+	0.332517i
$171$		0			0
$172$	1.08691	−	0.627530i	0.0828764	−	0.0478487i
$173$	4.27136	−	2.46607i	0.324745	−	0.187492i	−0.328760	−	0.944413i	$-0.606631\pi$
$173$	4.27136	−	2.46607i	0.324745	−	0.187492i	0.653506	+	0.756922i	$0.273298\pi$
$174$		0			0
$175$	−12.9694	+	2.60675i	−0.980393	+	0.197052i
$176$	2.05292	+	3.55576i	0.154745	+	0.268026i
$177$		0			0
$178$			7.37607i			0.552860i
$179$	2.63272	+	4.56000i	0.196779	+	0.340831i	0.947482	−	0.319809i	$-0.103619\pi$
$179$	2.63272	+	4.56000i	0.196779	+	0.340831i	−0.750703	+	0.660639i	$0.770285\pi$
$180$		0			0
$181$	20.1029			1.49423			0.747117	−	0.664692i	$-0.231437\pi$
$181$	20.1029			1.49423			0.747117	+	0.664692i	$0.231437\pi$
$182$	−2.27452	−	10.0173i	−0.168599	−	0.742532i
$183$		0			0
$184$	5.92553			0.436836
$185$	−0.643412	−	0.659652i	−0.0473046	−	0.0484986i
$186$		0			0
$187$	9.87372	−	5.70059i	0.722038	−	0.416869i
$188$			5.10612i			0.372402i
$189$		0			0
$190$	−1.70754	+	6.06905i	−0.123878	+	0.440295i
$191$	−1.49644	−	2.59190i	−0.108278	−	0.187543i	0.806795	−	0.590832i	$-0.201200\pi$
$191$	−1.49644	−	2.59190i	−0.108278	−	0.187543i	−0.915073	+	0.403289i	$0.867867\pi$
$192$		0			0
$193$	18.5687	+	10.7206i	1.33660	+	0.771687i	0.986302	−	0.164951i	$-0.0527466\pi$
$193$	18.5687	+	10.7206i	1.33660	+	0.771687i	0.350299	+	0.936638i	$0.386080\pi$
$194$	4.18640			0.300566
$195$		0			0
$196$	−5.77478	−	3.95625i	−0.412484	−	0.282590i
$197$			3.13660i			0.223474i	0.993738	+	0.111737i	$0.0356414\pi$
$197$			3.13660i			0.223474i	−0.993738	+	0.111737i	$0.964359\pi$
$198$		0			0
$199$	−7.45046	−	12.9046i	−0.528149	−	0.914781i	−0.999461	−	0.0328145i	$-0.989553\pi$
$199$	−7.45046	−	12.9046i	−0.528149	−	0.914781i	0.471313	−	0.881966i	$-0.343780\pi$
$200$	2.60714	−	4.26648i	0.184352	−	0.301686i
$201$		0			0
$202$	10.9673	−	6.33196i	0.771655	−	0.445515i
$203$	−2.76618	−	12.1826i	−0.194148	−	0.855053i
$204$		0			0
$205$	3.78576	+	14.8673i	0.264409	+	1.03838i
$206$	2.18985	+	3.79293i	0.152574	+	0.264266i
$207$		0			0
$208$	3.36239	+	1.94128i	0.233140	+	0.134603i
$209$	5.78829	−	10.0256i	0.400385	−	0.693487i
$210$		0			0
$211$	7.20990	+	12.4879i	0.496350	+	0.859704i	0.999991	−	0.00420922i	$-0.00133984\pi$
$211$	7.20990	+	12.4879i	0.496350	+	0.859704i	−0.503641	+	0.863913i	$0.668007\pi$
$212$			4.85184i			0.333226i
$213$		0			0
$214$	−3.27086			−0.223592
$215$	1.95954	+	2.00900i	0.133640	+	0.137013i
$216$		0			0
$217$	2.28174	+	10.0491i	0.154895	+	0.682178i
$218$	−2.87443	−	1.65955i	−0.194681	−	0.112399i
$219$		0			0
$220$	−6.57230	+	6.41050i	−0.443104	+	0.432196i
$221$	5.39058	−	9.33676i	0.362610	−	0.628059i
$222$		0			0
$223$	−15.8455	−	9.14843i	−1.06110	−	0.612624i	−0.135361	−	0.990796i	$-0.543219\pi$
$223$	−15.8455	−	9.14843i	−1.06110	−	0.612624i	−0.925735	+	0.378172i	$0.876553\pi$
$224$	2.58008	−	0.585831i	0.172389	−	0.0391425i
$225$		0			0
$226$	3.95566	−	6.85140i	0.263126	−	0.455748i
$227$			9.02500i			0.599010i	0.954095	+	0.299505i	$0.0968215\pi$
$227$			9.02500i			0.599010i	−0.954095	+	0.299505i	$0.903178\pi$
$228$		0			0
$229$	17.1853			1.13564			0.567819	−	0.823153i	$-0.307787\pi$
$229$	17.1853			1.13564			0.567819	+	0.823153i	$0.307787\pi$
$230$	3.26957	+	12.8402i	0.215589	+	0.846655i
$231$		0			0
$232$	4.08921	+	2.36090i	0.268469	+	0.155001i
$233$	4.18657	+	2.41712i	0.274272	+	0.158351i	0.630827	−	0.775923i	$-0.282716\pi$
$233$	4.18657	+	2.41712i	0.274272	+	0.158351i	−0.356556	+	0.934274i	$0.616049\pi$
$234$		0			0
$235$	−11.0645	+	2.81744i	−0.721772	+	0.183789i
$236$	−6.24051	−	10.8089i	−0.406223	−	0.703598i
$237$		0			0
$238$	−1.62675	−	7.16441i	−0.105446	−	0.464400i
$239$	8.08215	+	13.9987i	0.522791	+	0.905500i	0.999648	+	0.0265194i	$0.00844237\pi$
$239$	8.08215	+	13.9987i	0.522791	+	0.905500i	−0.476858	+	0.878981i	$0.658224\pi$
$240$		0			0
$241$	−9.67745			−0.623380			−0.311690	−	0.950184i	$-0.600895\pi$
$241$	−9.67745			−0.623380			−0.311690	+	0.950184i	$0.600895\pi$
$242$	5.07312	−	2.92897i	0.326113	−	0.188281i
$243$		0			0
$244$	1.08850			0.0696843
$245$	5.38650	−	14.6964i	0.344131	−	0.938922i
$246$		0			0
$247$		−	10.9470i		−	0.696543i
$248$	−3.37307	−	1.94744i	−0.214190	−	0.123663i
$249$		0			0
$250$	10.6837	+	3.29531i	0.675695	+	0.208414i
$251$	−17.3945			−1.09793			−0.548967	−	0.835844i	$-0.684979\pi$
$251$	−17.3945			−1.09793			−0.548967	+	0.835844i	$0.684979\pi$
$252$		0			0
$253$		−	24.3293i		−	1.52957i
$254$	3.68851	+	6.38868i	0.231437	+	0.400861i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$			4.64656i			0.289845i	0.989443	+	0.144922i	$0.0462932\pi$
$257$			4.64656i			0.289845i	−0.989443	+	0.144922i	$0.953707\pi$
$258$		0			0
$259$	1.06324	−	0.241419i	0.0660667	−	0.0150011i
$260$	−2.35131	+	8.35719i	−0.145822	+	0.518291i
$261$		0			0
$262$	−10.3259	+	5.96168i	−0.637938	+	0.368314i
$263$		−	28.1073i		−	1.73317i	−0.499029	−	0.866586i	$-0.666310\pi$
$263$		−	28.1073i		−	1.73317i	0.499029	−	0.866586i	$-0.333690\pi$
$264$		0			0
$265$	−10.5136	+	2.67713i	−0.645842	+	0.164455i
$266$	−5.06780	−	5.47413i	−0.310727	−	0.335641i
$267$		0			0
$268$	10.8485	−	6.26339i	0.662678	−	0.382597i
$269$	−14.0809	−	24.3889i	−0.858529	−	1.48702i	−0.873332	−	0.487125i	$-0.838046\pi$
$269$	−14.0809	−	24.3889i	−0.858529	−	1.48702i	0.0148033	−	0.999890i	$-0.495288\pi$
$270$		0			0
$271$	−10.1408	+	17.5644i	−0.616009	+	1.06696i	0.374197	+	0.927349i	$0.377918\pi$
$271$	−10.1408	+	17.5644i	−0.616009	+	1.06696i	−0.990207	+	0.139610i	$0.955415\pi$
$272$	2.40480	+	1.38841i	0.145812	+	0.0841847i
$273$		0			0
$274$	9.90727	+	17.1599i	0.598520	+	1.03667i
$275$	−17.5175	−	10.7045i	−1.05634	−	0.645505i
$276$		0			0
$277$		−	10.2372i		−	0.615092i	−0.951533	−	0.307546i	$-0.900492\pi$
$277$		−	10.2372i		−	0.615092i	0.951533	−	0.307546i	$-0.0995077\pi$
$278$	4.93488	+	2.84915i	0.295974	+	0.170881i
$279$		0			0
$280$	2.69307	+	5.26758i	0.160942	+	0.314798i
$281$	−10.5038	+	18.1931i	−0.626604	+	1.08531i	0.361625	+	0.932324i	$0.382222\pi$
$281$	−10.5038	+	18.1931i	−0.626604	+	1.08531i	−0.988228	+	0.152986i	$0.951111\pi$
$282$		0			0
$283$	4.22732	+	2.44064i	0.251288	+	0.145081i	0.620354	−	0.784322i	$-0.286989\pi$
$283$	4.22732	+	2.44064i	0.251288	+	0.145081i	−0.369066	+	0.929403i	$0.620322\pi$
$284$	−8.15943	+	14.1325i	−0.484173	+	0.838612i
$285$		0			0
$286$	7.97058	−	13.8055i	0.471310	−	0.816334i
$287$	−17.3401	−	5.37010i	−1.02355	−	0.316987i
$288$		0			0
$289$	−4.64463	+	8.04474i	−0.273214	+	0.473220i
$290$	−2.85956	+	10.1637i	−0.167919	+	0.596831i
$291$		0			0
$292$		−	12.8313i		−	0.750897i
$293$	−3.55724	+	2.05377i	−0.207816	+	0.119983i	−0.600296	−	0.799778i	$-0.704951\pi$
$293$	−3.55724	+	2.05377i	−0.207816	+	0.119983i	0.392480	+	0.919761i	$0.371617\pi$
$294$		0			0
$295$	19.9786	−	19.4868i	1.16320	−	1.13456i
$296$	−0.206049	+	0.356887i	−0.0119763	+	0.0207436i
$297$		0			0
$298$	18.0169	−	10.4021i	1.04369	−	0.602575i
$299$	−11.5031	−	19.9240i	−0.665242	−	1.15223i
$300$		0			0
$301$	−3.23815	+	0.735253i	−0.186644	+	0.0423793i
$302$	14.0853	−	8.13217i	0.810520	−	0.467954i
$303$		0			0
$304$	2.81954			0.161712
$305$	0.600611	+	2.35870i	0.0343909	+	0.135059i
$306$		0			0
$307$			7.22215i			0.412190i	0.978532	+	0.206095i	$0.0660755\pi$
$307$			7.22215i			0.412190i	−0.978532	+	0.206095i	$0.933924\pi$
$308$	−2.40533	−	10.5934i	−0.137056	−	0.603614i
$309$		0			0
$310$	2.35877	−	8.38373i	0.133969	−	0.476164i
$311$	−11.6444	+	20.1688i	−0.660296	+	1.14367i	0.320242	+	0.947336i	$0.396236\pi$
$311$	−11.6444	+	20.1688i	−0.660296	+	1.14367i	−0.980538	+	0.196331i	$0.937097\pi$
$312$		0			0
$313$	15.7359	−	9.08510i	0.889443	−	0.513520i	0.0156827	−	0.999877i	$-0.495008\pi$
$313$	15.7359	−	9.08510i	0.889443	−	0.513520i	0.873760	+	0.486357i	$0.161675\pi$
$314$	−20.2586			−1.14326
$315$		0			0
$316$	−6.02746			−0.339071
$317$	−0.588683	+	0.339876i	−0.0330637	+	0.0190893i	−0.516441	−	0.856323i	$-0.672743\pi$
$317$	−0.588683	+	0.339876i	−0.0330637	+	0.0190893i	0.483377	+	0.875412i	$0.339410\pi$
$318$		0			0
$319$	9.69350	−	16.7896i	0.542732	−	0.940039i
$320$	−2.15250	−	0.605607i	−0.120328	−	0.0338545i
$321$		0			0
$322$	−14.9758	−	4.63788i	−0.834567	−	0.258459i
$323$		−	7.82936i		−	0.435637i
$324$		0			0
$325$	−19.4068	−	0.483790i	−1.07649	−	0.0268358i
$326$	−7.86848			−0.435795
$327$		0			0
$328$	5.94183	−	3.43052i	0.328083	−	0.189419i
$329$	3.99653	−	12.9048i	0.220336	−	0.711467i
$330$		0			0
$331$	−6.36098	−	11.0175i	−0.349631	−	0.605579i	0.636553	−	0.771233i	$-0.280360\pi$
$331$	−6.36098	−	11.0175i	−0.349631	−	0.605579i	−0.986184	+	0.165654i	$0.947026\pi$
$332$	−13.4228	+	7.74967i	−0.736673	+	0.425318i
$333$		0			0
$334$	−10.6086	+	18.3747i	−0.580477	+	1.00542i
$335$	19.5582	+	20.0519i	1.06858	+	1.09555i
$336$		0			0
$337$	−14.7645	+	8.52431i	−0.804276	+	0.464349i	−0.844964	−	0.534823i	$-0.820378\pi$
$337$	−14.7645	+	8.52431i	−0.804276	+	0.464349i	0.0406882	+	0.999172i	$0.487045\pi$
$338$		−	2.07425i		−	0.112824i
$339$		0			0
$340$	−1.68166	+	5.97710i	−0.0912010	+	0.324154i
$341$	−7.99589	+	13.8493i	−0.433002	+	0.749981i
$342$		0			0
$343$	11.4982	+	14.5186i	0.620846	+	0.783933i
$344$	0.627530	−	1.08691i	0.0338342	−	0.0586025i
$345$		0			0
$346$	2.46607	−	4.27136i	0.132577	−	0.229630i
$347$	21.7602	+	12.5633i	1.16815	+	0.674431i	0.953244	−	0.302203i	$-0.0977221\pi$
$347$	21.7602	+	12.5633i	1.16815	+	0.674431i	0.214906	+	0.976635i	$0.431055\pi$
$348$		0			0
$349$	4.80323	−	8.31944i	0.257111	−	0.445329i	−0.708356	−	0.705856i	$-0.750563\pi$
$349$	4.80323	−	8.31944i	0.257111	−	0.445329i	0.965467	+	0.260526i	$0.0838961\pi$
$350$	−9.92844	+	8.74220i	−0.530697	+	0.467290i
$351$		0			0
$352$	3.55576	+	2.05292i	0.189523	+	0.109421i
$353$		−	27.0566i		−	1.44008i	−0.693933	−	0.720040i	$-0.744124\pi$
$353$		−	27.0566i		−	1.44008i	0.693933	−	0.720040i	$-0.255876\pi$
$354$		0			0
$355$	−35.1263	−	9.88282i	−1.86431	−	0.524526i
$356$	3.68803	+	6.38786i	0.195465	+	0.338556i
$357$		0			0
$358$	4.56000	+	2.63272i	0.241004	+	0.139144i
$359$	4.43043	−	7.67373i	0.233829	−	0.405004i	−0.725103	−	0.688641i	$-0.758208\pi$
$359$	4.43043	−	7.67373i	0.233829	−	0.405004i	0.958932	+	0.283637i	$0.0915410\pi$
$360$		0			0
$361$	5.52509	+	9.56974i	0.290794	+	0.503671i
$362$	17.4096	−	10.0514i	0.915028	−	0.528292i
$363$		0			0
$364$	−6.97844	−	7.53798i	−0.365770	−	0.395097i
$365$	27.8045	−	7.08003i	1.45535	−	0.370586i
$366$		0			0
$367$		−	10.7689i		−	0.562130i	−0.959689	−	0.281065i	$-0.909312\pi$
$367$		−	10.7689i		−	0.562130i	0.959689	−	0.281065i	$-0.0906877\pi$
$368$	5.13166	−	2.96277i	0.267506	−	0.154445i
$369$		0			0
$370$	−0.887037	−	0.249569i	−0.0461149	−	0.0129745i
$371$	3.79751	−	12.2622i	0.197157	−	0.636621i
$372$		0			0
$373$		−	4.91686i		−	0.254585i	−0.991865	−	0.127293i	$-0.959371\pi$
$373$		−	4.91686i		−	0.254585i	0.991865	−	0.127293i	$-0.0406287\pi$
$374$	5.70059	−	9.87372i	0.294771	−	0.510558i
$375$		0			0
$376$	2.55306	+	4.42203i	0.131664	+	0.228049i
$377$		−	18.3327i		−	0.944181i
$378$		0			0
$379$	36.3873			1.86909			0.934544	−	0.355848i	$-0.115808\pi$
$379$	36.3873			1.86909			0.934544	+	0.355848i	$0.115808\pi$
$380$	1.55576	+	6.10972i	0.0798086	+	0.313422i
$381$		0			0
$382$	−2.59190	−	1.49644i	−0.132613	−	0.0765643i
$383$		−	9.36356i		−	0.478456i	−0.970963	−	0.239228i	$-0.923106\pi$
$383$		−	9.36356i		−	0.478456i	0.970963	−	0.239228i	$-0.0768943\pi$
$384$		0			0
$385$	21.6278	−	11.0573i	1.10226	−	0.563534i
$386$	21.4412			1.09133
$387$		0			0
$388$	3.62553	−	2.09320i	0.184058	−	0.106266i
$389$	2.04857			0.103866			0.0519332	−	0.998651i	$-0.483462\pi$
$389$	2.04857			0.103866			0.0519332	+	0.998651i	$0.483462\pi$
$390$		0			0
$391$	−8.22707	−	14.2497i	−0.416061	−	0.720639i
$392$	−6.97923	−	0.538827i	−0.352504	−	0.0272149i
$393$		0			0
$394$	1.56830	+	2.71638i	0.0790099	+	0.136849i
$395$	−3.32581	−	13.0610i	−0.167340	−	0.657171i
$396$		0			0
$397$	−25.1640	−	14.5284i	−1.26294	−	0.729161i	−0.289302	−	0.957238i	$-0.593423\pi$
$397$	−25.1640	−	14.5284i	−1.26294	−	0.729161i	−0.973643	+	0.228077i	$0.926756\pi$
$398$	−12.9046	−	7.45046i	−0.646848	−	0.373458i
$399$		0			0
$400$	0.124606	−	4.99845i	0.00623030	−	0.249922i
$401$	20.0009			0.998798			0.499399	−	0.866372i	$-0.333554\pi$
$401$	20.0009			0.998798			0.499399	+	0.866372i	$0.333554\pi$
$402$		0			0
$403$			15.1221i			0.753286i
$404$	6.33196	−	10.9673i	0.315027	−	0.545642i
$405$		0			0
$406$	−8.48690	−	9.16738i	−0.421198	−	0.454969i
$407$	1.46532	+	0.846003i	0.0726332	+	0.0419348i
$408$		0			0
$409$	10.5357	−	18.2484i	0.520959	−	0.902327i	−0.478744	−	0.877955i	$-0.658908\pi$
$409$	10.5357	−	18.2484i	0.520959	−	0.902327i	0.999703	−	0.0243728i	$-0.00775888\pi$
$410$	10.7122	+	10.9826i	0.529039	+	0.542392i
$411$		0			0
$412$	3.79293	+	2.18985i	0.186864	+	0.107886i
$413$	7.31176	+	32.2020i	0.359788	+	1.58456i
$414$		0			0
$415$	−24.1993	−	24.8101i	−1.18790	−	1.21788i
$416$	3.88256			0.190358
$417$		0			0
$418$		−	11.5766i		−	0.566230i
$419$	10.8551	+	18.8016i	0.530306	+	0.918517i	0.999375	+	0.0353551i	$0.0112562\pi$
$419$	10.8551	+	18.8016i	0.530306	+	0.918517i	−0.469069	+	0.883162i	$0.655410\pi$
$420$		0			0
$421$	−10.3520	+	17.9301i	−0.504524	+	0.873861i	0.495463	+	0.868629i	$0.334999\pi$
$421$	−10.3520	+	17.9301i	−0.504524	+	0.873861i	−0.999986	+	0.00523148i	$0.998335\pi$
$422$	12.4879	+	7.20990i	0.607902	+	0.350973i
$423$		0			0
$424$	2.42592	+	4.20182i	0.117813	+	0.204058i
$425$	−13.8798	−	0.346008i	−0.673269	−	0.0167839i
$426$		0			0
$427$	−2.75101	−	0.851966i	−0.133130	−	0.0412295i
$428$	−2.83265	+	1.63543i	−0.136921	+	0.0790516i
$429$		0			0
$430$	2.70151	+	0.760074i	0.130279	+	0.0366540i
$431$	1.15807	+	2.00583i	0.0557821	+	0.0966174i	0.892568	−	0.450913i	$-0.148901\pi$
$431$	1.15807	+	2.00583i	0.0557821	+	0.0966174i	−0.836786	+	0.547530i	$0.815568\pi$
$432$		0			0
$433$		−	22.2752i		−	1.07048i	−0.844701	−	0.535238i	$-0.820222\pi$
$433$		−	22.2752i		−	1.07048i	0.844701	−	0.535238i	$-0.179778\pi$
$434$	7.00060	+	7.56191i	0.336040	+	0.362983i
$435$		0			0
$436$	−3.31911			−0.158956
$437$	−14.4689	−	8.35364i	−0.692143	−	0.399609i
$438$		0			0
$439$	−10.3774	−	17.9742i	−0.495287	−	0.857863i	0.504698	−	0.863296i	$-0.331604\pi$
$439$	−10.3774	−	17.9742i	−0.495287	−	0.857863i	−0.999985	+	0.00543326i	$0.998271\pi$
$440$	−2.48653	+	8.83781i	−0.118541	+	0.421326i
$441$		0			0
$442$		−	10.7812i		−	0.512808i
$443$	16.2494	−	9.38160i	0.772033	−	0.445733i	−0.0615666	−	0.998103i	$-0.519610\pi$
$443$	16.2494	−	9.38160i	0.772033	−	0.445733i	0.833599	+	0.552370i	$0.186276\pi$
$444$		0			0
$445$	−11.8070	+	11.5163i	−0.559706	+	0.545927i
$446$	−18.2969			−0.866382
$447$		0			0
$448$	1.94150	−	1.79738i	0.0917271	−	0.0849184i
$449$	−4.33662			−0.204658			−0.102329	−	0.994751i	$-0.532629\pi$
$449$	−4.33662			−0.204658			−0.102329	+	0.994751i	$0.532629\pi$
$450$		0			0
$451$	−14.0852	−	24.3962i	−0.663244	−	1.14877i
$452$		−	7.91132i		−	0.372117i
$453$		0			0
$454$	4.51250	+	7.81588i	0.211782	+	0.366817i
$455$	12.4837	−	19.2810i	0.585243	−	0.903908i
$456$		0			0
$457$	19.6734	−	11.3584i	0.920282	−	0.531325i	0.0365568	−	0.999332i	$-0.488361\pi$
$457$	19.6734	−	11.3584i	0.920282	−	0.531325i	0.883725	+	0.468007i	$0.155028\pi$
$458$	14.8829	−	8.59266i	0.695434	−	0.401509i
$459$		0			0
$460$	9.25161	+	9.48512i	0.431358	+	0.442246i
$461$	−8.41648	+	14.5778i	−0.391995	+	0.678955i	−0.992713	−	0.120506i	$-0.961548\pi$
$461$	−8.41648	+	14.5778i	−0.391995	+	0.678955i	0.600718	+	0.799461i	$0.294882\pi$
$462$		0			0
$463$	24.0438	−	13.8817i	1.11741	−	0.645138i	0.176673	−	0.984270i	$-0.443467\pi$
$463$	24.0438	−	13.8817i	1.11741	−	0.645138i	0.940739	+	0.339132i	$0.110133\pi$
$464$	4.72181			0.219204
$465$		0			0
$466$	4.83424			0.223942
$467$	29.8191	+	17.2161i	1.37986	+	0.796665i	0.992143	−	0.125112i	$-0.0399291\pi$
$467$	29.8191	+	17.2161i	1.37986	+	0.796665i	0.387721	+	0.921777i	$0.373262\pi$
$468$		0			0
$469$	−32.3201	+	7.33857i	−1.49240	+	0.338864i
$470$	−8.17346	+	7.97225i	−0.377014	+	0.367732i
$471$		0			0
$472$	−10.8089	−	6.24051i	−0.497519	−	0.287243i
$473$	−4.46270	−	2.57654i	−0.205195	−	0.118469i
$474$		0			0
$475$	−12.3808	+	6.74240i	−0.568072	+	0.309363i
$476$	−4.99101	−	5.39119i	−0.228763	−	0.247105i
$477$		0			0
$478$	13.9987	+	8.08215i	0.640285	+	0.369669i
$479$	11.2870			0.515717			0.257859	−	0.966183i	$-0.416983\pi$
$479$	11.2870			0.515717			0.257859	+	0.966183i	$0.416983\pi$
$480$		0			0
$481$	1.59999			0.0729533
$482$	−8.38092	+	4.83873i	−0.381740	+	0.220398i
$483$		0			0
$484$	2.92897	−	5.07312i	0.133135	−	0.230596i
$485$	6.53628	+	6.70125i	0.296797	+	0.304288i
$486$		0			0
$487$	−21.2703	+	12.2804i	−0.963848	+	0.556478i	−0.897355	−	0.441309i	$-0.854514\pi$
$487$	−21.2703	+	12.2804i	−0.963848	+	0.556478i	−0.0664931	+	0.997787i	$0.521181\pi$
$488$	0.942671	−	0.544252i	0.0426727	−	0.0246371i
$489$		0			0
$490$	−2.68338	−	15.4207i	−0.121223	−	0.696638i
$491$	9.08350	+	15.7331i	0.409933	+	0.710024i	0.994882	−	0.101046i	$-0.0322188\pi$
$491$	9.08350	+	15.7331i	0.409933	+	0.710024i	−0.584949	+	0.811070i	$0.698885\pi$
$492$		0			0
$493$		−	13.1116i		−	0.590517i
$494$	−5.47352	−	9.48041i	−0.246265	−	0.426544i
$495$		0			0
$496$	−3.89489			−0.174886
$497$	31.6830	−	29.3312i	1.42118	−	1.31569i
$498$		0			0
$499$	−11.3838			−0.509609			−0.254805	−	0.966993i	$-0.582011\pi$
$499$	−11.3838			−0.509609			−0.254805	+	0.966993i	$0.582011\pi$
$500$	10.9000	−	2.48802i	0.487462	−	0.111267i
$501$		0			0
$502$	−15.0641	+	8.69727i	−0.672345	+	0.388178i
$503$		−	7.11598i		−	0.317286i	−0.987336	−	0.158643i	$-0.949288\pi$
$503$		−	7.11598i		−	0.317286i	0.987336	−	0.158643i	$-0.0507118\pi$
$504$		0			0
$505$	27.2590	+	7.66936i	1.21301	+	0.341282i
$506$	−12.1646	−	21.0698i	−0.540785	−	0.936666i
$507$		0			0
$508$	6.38868	+	3.68851i	0.283452	+	0.163651i
$509$	−24.4003			−1.08152			−0.540762	−	0.841176i	$-0.681864\pi$
$509$	−24.4003			−1.08152			−0.540762	+	0.841176i	$0.681864\pi$
$510$		0			0
$511$	−10.0430	+	32.4290i	−0.444277	+	1.43457i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	2.32328	+	4.02404i	0.102476	+	0.177493i
$515$	−2.65238	+	9.42729i	−0.116878	+	0.415416i
$516$		0			0
$517$	18.1561	−	10.4825i	0.798506	−	0.461018i
$518$	0.800086	−	0.740696i	0.0351537	−	0.0325443i
$519$		0			0
$520$	2.14230	+	8.41319i	0.0939463	+	0.368943i
$521$	10.6836	+	18.5046i	0.468058	+	0.810701i	0.999334	−	0.0364984i	$-0.0116204\pi$
$521$	10.6836	+	18.5046i	0.468058	+	0.810701i	−0.531275	+	0.847199i	$0.678287\pi$
$522$		0			0
$523$	22.4124	+	12.9398i	0.980028	+	0.565819i	0.902278	−	0.431154i	$-0.141893\pi$
$523$	22.4124	+	12.9398i	0.980028	+	0.565819i	0.0777491	+	0.996973i	$0.475227\pi$
$524$	−5.96168	+	10.3259i	−0.260437	+	0.451090i
$525$		0			0
$526$	−14.0537	−	24.3416i	−0.612769	−	1.06135i
$527$			10.8154i			0.471126i
$528$		0			0
$529$	−12.1119			−0.526606
$530$	−7.76644	+	7.57524i	−0.337352	+	0.329047i
$531$		0			0
$532$	−7.12591	−	2.20684i	−0.308947	−	0.0956787i
$533$	−23.0695	−	13.3192i	−0.999251	−	0.576918i
$534$		0			0
$535$	−5.10684	−	5.23574i	−0.220788	−	0.226361i
$536$	6.26339	−	10.8485i	0.270537	−	0.468584i
$537$		0			0
$538$	−24.3889	−	14.0809i	−1.05148	−	0.607072i
$539$	−2.21234	+	28.6556i	−0.0952922	+	1.23428i
$540$		0			0
$541$	−18.0736	+	31.3045i	−0.777047	+	1.34588i	0.156590	+	0.987664i	$0.449950\pi$
$541$	−18.0736	+	31.3045i	−0.777047	+	1.34588i	−0.933637	+	0.358221i	$0.883384\pi$
$542$			20.2816i			0.871169i
$543$		0			0
$544$	2.77682			0.119055
$545$	−1.83141	−	7.19224i	−0.0784488	−	0.308082i
$546$		0			0
$547$	−8.13044	−	4.69411i	−0.347633	−	0.200706i	0.316010	−	0.948756i	$-0.397657\pi$
$547$	−8.13044	−	4.69411i	−0.347633	−	0.200706i	−0.663642	+	0.748050i	$0.730990\pi$
$548$	17.1599	+	9.90727i	0.733034	+	0.423218i
$549$		0			0
$550$	−20.5228	−	0.511612i	−0.875096	−	0.0218152i
$551$	−6.65667	−	11.5297i	−0.283583	−	0.491181i
$552$		0			0
$553$	15.2334	+	4.71766i	0.647789	+	0.200615i
$554$	−5.11858	−	8.86564i	−0.217468	−	0.376665i
$555$		0			0
$556$	5.69831			0.241662
$557$	−18.3702	+	10.6060i	−0.778370	+	0.449392i	−0.835852	−	0.548955i	$-0.815026\pi$
$557$	−18.3702	+	10.6060i	−0.778370	+	0.449392i	0.0574826	+	0.998347i	$0.481693\pi$
$558$		0			0
$559$	−4.87284			−0.206099
$560$	4.96606	+	3.21532i	0.209854	+	0.135872i
$561$		0			0
$562$			21.0076i			0.886151i
$563$	−19.5334	−	11.2776i	−0.823233	−	0.475294i	0.0282970	−	0.999600i	$-0.490992\pi$
$563$	−19.5334	−	11.2776i	−0.823233	−	0.475294i	−0.851530	+	0.524306i	$0.824325\pi$
$564$		0			0
$565$	17.1432	−	4.36528i	0.721220	−	0.183649i
$566$	4.88129			0.205176
$567$		0			0
$568$			16.3189i			0.684724i
$569$	4.56567	+	7.90797i	0.191403	+	0.331519i	0.945715	−	0.324996i	$-0.105363\pi$
$569$	4.56567	+	7.90797i	0.191403	+	0.331519i	−0.754313	+	0.656515i	$0.772030\pi$
$570$		0			0
$571$	−21.9988	+	38.1030i	−0.920621	+	1.59456i	−0.122165	+	0.992510i	$0.538984\pi$
$571$	−21.9988	+	38.1030i	−0.920621	+	1.59456i	−0.798456	+	0.602053i	$0.794350\pi$
$572$		−	15.9412i		−	0.666534i
$573$		0			0
$574$	−17.7020	+	4.01940i	−0.738867	+	0.167767i
$575$	−15.4487	+	25.2812i	−0.644254	+	1.05430i
$576$		0			0
$577$	16.2964	−	9.40875i	0.678429	−	0.391691i	−0.120834	−	0.992673i	$-0.538557\pi$
$577$	16.2964	−	9.40875i	0.678429	−	0.391691i	0.799263	+	0.600981i	$0.205223\pi$
$578$			9.28927i			0.386383i
$579$		0			0
$580$	2.60538	+	10.2318i	0.108183	+	0.424852i
$581$	39.9895	−	9.07998i	1.65904	−	0.376701i
$582$		0			0
$583$	17.2520	−	9.96044i	0.714505	−	0.412519i
$584$	−6.41567	−	11.1123i	−0.265482	−	0.459828i
$585$		0			0
$586$	−2.05377	+	3.55724i	−0.0848405	+	0.146948i
$587$	13.2631	+	7.65744i	0.547426	+	0.316056i	0.748083	−	0.663605i	$-0.230974\pi$
$587$	13.2631	+	7.65744i	0.547426	+	0.316056i	−0.200657	+	0.979661i	$0.564308\pi$
$588$		0			0
$589$	5.49090	+	9.51051i	0.226248	+	0.391874i
$590$	7.55860	−	26.8653i	0.311183	−	1.10603i
$591$		0			0
$592$			0.412097i			0.0169371i
$593$	−18.6589	−	10.7727i	−0.766231	−	0.442384i	0.0652975	−	0.997866i	$-0.479200\pi$
$593$	−18.6589	−	10.7727i	−0.766231	−	0.442384i	−0.831528	+	0.555482i	$0.812534\pi$
$594$		0			0
$595$	8.92836	−	13.7899i	0.366027	−	0.565329i
$596$	10.4021	−	18.0169i	0.426085	−	0.738000i
$597$		0			0
$598$	−19.9240	−	11.5031i	−0.814752	−	0.470397i
$599$	−18.9338	+	32.7942i	−0.773612	+	1.33994i	0.161959	+	0.986797i	$0.448219\pi$
$599$	−18.9338	+	32.7942i	−0.773612	+	1.33994i	−0.935571	+	0.353138i	$0.885115\pi$
$600$		0			0
$601$	−16.2700	+	28.1804i	−0.663666	+	1.14950i	0.315979	+	0.948766i	$0.397667\pi$
$601$	−16.2700	+	28.1804i	−0.663666	+	1.14950i	−0.979645	+	0.200737i	$0.935666\pi$
$602$	−2.43670	+	2.25582i	−0.0993124	+	0.0919405i
$603$		0			0
$604$	8.13217	−	14.0853i	0.330893	−	0.573124i
$605$	12.6092	+	3.54761i	0.512636	+	0.144231i
$606$		0			0
$607$			33.4534i			1.35783i	0.734216	+	0.678916i	$0.237550\pi$
$607$			33.4534i			1.35783i	−0.734216	+	0.678916i	$0.762450\pi$
$608$	2.44179	−	1.40977i	0.0990278	−	0.0571737i
$609$		0			0
$610$	1.69949	+	1.74239i	0.0688105	+	0.0705472i
$611$	9.91240	−	17.1688i	0.401013	−	0.694574i
$612$		0			0
$613$	−14.1077	+	8.14510i	−0.569806	+	0.328978i	−0.757072	−	0.653332i	$-0.773371\pi$
$613$	−14.1077	+	8.14510i	−0.569806	+	0.328978i	0.187266	+	0.982309i	$0.440037\pi$
$614$	3.61107	+	6.25456i	0.145731	+	0.252414i
$615$		0			0
$616$	−7.37977	−	7.97148i	−0.297339	−	0.321180i
$617$	3.39147	−	1.95807i	0.136536	−	0.0788289i	−0.430176	−	0.902745i	$-0.641549\pi$
$617$	3.39147	−	1.95807i	0.136536	−	0.0788289i	0.566712	+	0.823916i	$0.308215\pi$
$618$		0			0
$619$	−23.1487			−0.930424			−0.465212	−	0.885199i	$-0.654022\pi$
$619$	−23.1487			−0.930424			−0.465212	+	0.885199i	$0.654022\pi$
$620$	−2.14911	−	8.43991i	−0.0863102	−	0.338955i
$621$		0			0
$622$			23.2889i			0.933800i
$623$	−4.32113	−	19.0308i	−0.173122	−	0.762454i
$624$		0			0
$625$	11.4057	+	22.2466i	0.456228	+	0.889863i
$626$	9.08510	−	15.7359i	0.363114	−	0.628931i
$627$		0			0
$628$	−17.5445	+	10.1293i	−0.700100	+	0.404203i
$629$	1.14432			0.0456270
$630$		0			0
$631$	29.9516			1.19235			0.596177	−	0.802853i	$-0.296686\pi$
$631$	29.9516			1.19235			0.596177	+	0.802853i	$0.296686\pi$
$632$	−5.21993	+	3.01373i	−0.207638	+	0.119880i
$633$		0			0
$634$	−0.339876	+	0.588683i	−0.0134982	+	0.0233796i
$635$	−4.46757	+	15.8790i	−0.177290	+	0.630138i
$636$		0			0
$637$	11.7369	+	24.5129i	0.465032	+	0.971238i
$638$		−	19.3870i		−	0.767538i
$639$		0			0
$640$	−2.16692	+	0.551777i	−0.0856550	+	0.0218109i
$641$	14.7671			0.583266			0.291633	−	0.956530i	$-0.405801\pi$
$641$	14.7671			0.583266			0.291633	+	0.956530i	$0.405801\pi$
$642$		0			0
$643$	−6.76719	+	3.90704i	−0.266872	+	0.154078i	−0.627465	−	0.778645i	$-0.715908\pi$
$643$	−6.76719	+	3.90704i	−0.266872	+	0.154078i	0.360593	+	0.932723i	$0.382574\pi$
$644$	−15.2883	+	3.47136i	−0.602445	+	0.136791i
$645$		0			0
$646$	−3.91468	−	6.78043i	−0.154021	−	0.266772i
$647$	21.1027	−	12.1837i	0.829634	−	0.478989i	−0.0240933	−	0.999710i	$-0.507670\pi$
$647$	21.1027	−	12.1837i	0.829634	−	0.478989i	0.853727	+	0.520720i	$0.174337\pi$
$648$		0			0
$649$	−25.6225	+	44.3795i	−1.00577	+	1.74205i
$650$	−17.0486	+	9.28440i	−0.668703	+	0.364164i
$651$		0			0
$652$	−6.81431	+	3.93424i	−0.266869	+	0.154077i
$653$			20.4980i			0.802147i	0.916046	+	0.401074i	$0.131363\pi$
$653$			20.4980i			0.802147i	−0.916046	+	0.401074i	$0.868637\pi$
$654$		0			0
$655$	−25.6650	−	7.22087i	−1.00281	−	0.282143i
$656$	3.43052	−	5.94183i	0.133939	−	0.231990i
$657$		0			0
$658$	−2.99132	−	13.1742i	−0.116614	−	0.513583i
$659$	5.19823	−	9.00360i	0.202494	−	0.350731i	−0.746837	−	0.665007i	$-0.768429\pi$
$659$	5.19823	−	9.00360i	0.202494	−	0.350731i	0.949332	+	0.314276i	$0.101762\pi$
$660$		0			0
$661$	12.8594	−	22.2732i	0.500174	−	0.866327i	−0.499826	−	0.866126i	$-0.666603\pi$
$661$	12.8594	−	22.2732i	0.500174	−	0.866327i	1.00000		0.000201292i	$-6.40733e-5\pi$
$662$	−11.0175	−	6.36098i	−0.428209	−	0.247226i
$663$		0			0
$664$	−7.74967	+	13.4228i	−0.300745	+	0.520906i
$665$	0.850138	−	16.6590i	0.0329669	−	0.646006i
$666$		0			0
$667$	−24.2307	−	13.9896i	−0.938217	−	0.541680i
$668$			21.2172i			0.820919i
$669$		0			0
$670$	26.9638	+	7.58631i	1.04170	+	0.293085i
$671$	−2.23461	−	3.87046i	−0.0862662	−	0.149417i
$672$		0			0
$673$	−12.4068	−	7.16309i	−0.478248	−	0.276117i	0.241438	−	0.970416i	$-0.422381\pi$
$673$	−12.4068	−	7.16309i	−0.478248	−	0.276117i	−0.719686	+	0.694300i	$0.755714\pi$
$674$	−8.52431	+	14.7645i	−0.328344	+	0.568709i
$675$		0			0
$676$	−1.03712	−	1.79635i	−0.0398894	−	0.0690905i
$677$	−0.775475	+	0.447721i	−0.0298039	+	0.0172073i	−0.514828	−	0.857294i	$-0.672144\pi$
$677$	−0.775475	+	0.447721i	−0.0298039	+	0.0172073i	0.485024	+	0.874501i	$0.338811\pi$
$678$		0			0
$679$	−10.8012	+	2.45252i	−0.414513	+	0.0941191i
$680$	1.53218	+	6.01715i	0.0587566	+	0.230747i
$681$		0			0
$682$			15.9918i			0.612357i
$683$	17.0207	−	9.82692i	0.651280	−	0.376016i	−0.137667	−	0.990479i	$-0.543960\pi$
$683$	17.0207	−	9.82692i	0.651280	−	0.376016i	0.788946	+	0.614462i	$0.210627\pi$
$684$		0			0
$685$	−11.9998	+	42.6507i	−0.458490	+	1.62960i
$686$	17.2171	+	6.82440i	0.657351	+	0.260557i
$687$		0			0
$688$		−	1.25506i		−	0.0478487i
$689$	9.41877	−	16.3138i	0.358827	−	0.621506i
$690$		0			0
$691$	−9.66268	−	16.7363i	−0.367586	−	0.636677i	0.621602	−	0.783333i	$-0.286482\pi$
$691$	−9.66268	−	16.7363i	−0.367586	−	0.636677i	−0.989188	+	0.146656i	$0.953149\pi$
$692$		−	4.93214i		−	0.187492i
$693$		0			0
$694$	25.1265			0.953790
$695$	3.14419	+	12.3478i	0.119266	+	0.468378i
$696$		0			0
$697$	−16.4994	−	9.52593i	−0.624959	−	0.360820i
$698$		−	9.60646i		−	0.363610i
$699$		0			0
$700$	−4.22718	+	12.5352i	−0.159772	+	0.473786i
$701$	37.8106			1.42809			0.714044	−	0.700101i	$-0.246862\pi$
$701$	37.8106			1.42809			0.714044	+	0.700101i	$0.246862\pi$
$702$		0			0
$703$	1.00626	−	0.580962i	0.0379517	−	0.0219114i
$704$	4.10584			0.154745
$705$		0			0
$706$	−13.5283	−	23.4317i	−0.509145	−	0.881865i
$707$	−24.5870	+	22.7619i	−0.924688	+	0.856050i
$708$		0			0
$709$	−21.7380	−	37.6513i	−0.816387	−	1.41402i	−0.908328	−	0.418260i	$-0.862640\pi$
$709$	−21.7380	−	37.6513i	−0.816387	−	1.41402i	0.0919403	−	0.995765i	$-0.470693\pi$
$710$	−35.3617	+	9.00437i	−1.32710	+	0.337928i
$711$		0			0
$712$	6.38786	+	3.68803i	0.239395	+	0.138215i
$713$	19.9872	+	11.5396i	0.748528	+	0.432163i
$714$		0			0
$715$	34.5432	−	8.79596i	1.29184	−	0.328950i
$716$	5.26544			0.196779
$717$		0			0
$718$		−	8.86086i		−	0.330684i
$719$	−14.5195	+	25.1485i	−0.541486	+	0.937881i	0.457333	+	0.889295i	$0.348805\pi$
$719$	−14.5195	+	25.1485i	−0.541486	+	0.937881i	−0.998819	+	0.0485854i	$0.984529\pi$
$720$		0			0
$721$	−7.87200	−	8.50318i	−0.293169	−	0.316675i
$722$	9.56974	+	5.52509i	0.356149	+	0.205623i
$723$		0			0
$724$	10.0514	−	17.4096i	0.373559	−	0.647023i
$725$	−20.7339	+	11.2913i	−0.770036	+	0.419349i
$726$		0			0
$727$	−1.94247	−	1.12149i	−0.0720423	−	0.0415936i	0.463546	−	0.886073i	$-0.346577\pi$
$727$	−1.94247	−	1.12149i	−0.0720423	−	0.0415936i	−0.535588	+	0.844479i	$0.679910\pi$
$728$	−9.81250	−	3.03886i	−0.363675	−	0.112628i
$729$		0			0
$730$	20.5394	−	20.0337i	0.760196	−	0.741481i
$731$	−3.48508			−0.128900
$732$		0			0
$733$		−	0.870582i		−	0.0321557i	−0.999871	−	0.0160778i	$-0.994882\pi$
$733$		−	0.870582i		−	0.0321557i	0.999871	−	0.0160778i	$-0.00511795\pi$
$734$	−5.38443	−	9.32611i	−0.198743	−	0.344233i
$735$		0			0
$736$	2.96277	−	5.13166i	0.109209	−	0.189156i
$737$	−44.5423	−	25.7165i	−1.64074	−	0.947279i
$738$		0			0
$739$	9.25114	+	16.0234i	0.340309	+	0.589432i	0.984490	−	0.175441i	$-0.0561351\pi$
$739$	9.25114	+	16.0234i	0.340309	+	0.589432i	−0.644181	+	0.764873i	$0.722802\pi$
$740$	−0.892982	+	0.227386i	−0.0328267	+	0.00835886i
$741$		0			0
$742$	−2.84236	−	12.5181i	−0.104346	−	0.459555i
$743$	7.22866	−	4.17347i	0.265194	−	0.153110i	−0.361508	−	0.932369i	$-0.617738\pi$
$743$	7.22866	−	4.17347i	0.265194	−	0.153110i	0.626701	+	0.779259i	$0.284405\pi$
$744$		0			0
$745$	44.7807	+	12.5991i	1.64064	+	0.461596i
$746$	−2.45843	−	4.25812i	−0.0900095	−	0.155901i
$747$		0			0
$748$		−	11.4012i		−	0.416869i
$749$	8.43909	−	1.91617i	0.308357	−	0.0700154i
$750$		0			0
$751$	39.0062			1.42336			0.711678	−	0.702505i	$-0.247935\pi$
$751$	39.0062			1.42336			0.711678	+	0.702505i	$0.247935\pi$
$752$	4.42203	+	2.55306i	0.161255	+	0.0931005i
$753$		0			0
$754$	−9.16634	−	15.8766i	−0.333819	−	0.578191i
$755$	35.0089	+	9.84980i	1.27410	+	0.358471i
$756$		0			0
$757$		−	37.6562i		−	1.36864i	−0.729182	−	0.684320i	$-0.760099\pi$
$757$		−	37.6562i		−	1.36864i	0.729182	−	0.684320i	$-0.239901\pi$
$758$	31.5123	−	18.1936i	1.14458	−	0.660822i
$759$		0			0
$760$	4.40219	+	4.51329i	0.159684	+	0.163714i
$761$	−36.2325			−1.31343			−0.656714	−	0.754140i	$-0.728054\pi$
$761$	−36.2325			−1.31343			−0.656714	+	0.754140i	$0.728054\pi$
$762$		0			0
$763$	8.38847	+	2.59785i	0.303683	+	0.0940484i
$764$	−2.99287			−0.108278
$765$		0			0
$766$	−4.68178	−	8.10908i	−0.169160	−	0.292993i
$767$			48.4583i			1.74973i
$768$		0			0
$769$	6.17687	+	10.6986i	0.222744	+	0.385803i	0.955640	−	0.294537i	$-0.0951654\pi$
$769$	6.17687	+	10.6986i	0.222744	+	0.385803i	−0.732897	+	0.680340i	$0.761832\pi$
$770$	13.2016	−	20.3899i	0.475752	−	0.734799i
$771$		0			0
$772$	18.5687	−	10.7206i	0.668300	−	0.385843i
$773$	37.1712	−	21.4608i	1.33695	−	0.771891i	0.350600	−	0.936525i	$-0.385978\pi$
$773$	37.1712	−	21.4608i	1.33695	−	0.771891i	0.986355	+	0.164634i	$0.0526443\pi$
$774$		0			0
$775$	17.1028	−	9.31389i	0.614350	−	0.334565i
$776$	2.09320	−	3.62553i	0.0751415	−	0.130149i
$777$		0			0
$778$	1.77411	−	1.02428i	0.0636049	−	0.0367223i
$779$	−19.3450			−0.693106
$780$		0			0
$781$	67.0027			2.39754
$782$	−14.2497	−	8.22707i	−0.509568	−	0.294199i
$783$		0			0
$784$	−6.31361	+	3.02298i	−0.225486	+	0.107963i
$785$	−31.6300	−	32.4283i	−1.12892	−	1.15742i
$786$		0			0
$787$	27.8257	+	16.0652i	0.991879	+	0.572662i	0.905835	−	0.423630i	$-0.139244\pi$
$787$	27.8257	+	16.0652i	0.991879	+	0.572662i	0.0860435	+	0.996291i	$0.472578\pi$
$788$	2.71638	+	1.56830i	0.0967669	+	0.0558684i
$789$		0			0
$790$	−9.41074	−	9.64827i	−0.334819	−	0.343270i
$791$	−6.19215	+	19.9945i	−0.220167	+	0.710922i
$792$		0			0
$793$	−3.65998	−	2.11309i	−0.129970	−	0.0750380i
$794$	−29.0569			−1.03119
$795$		0			0
$796$	−14.9009			−0.528149
$797$	−31.8223	+	18.3726i	−1.12720	+	0.650791i	−0.943230	−	0.332140i	$-0.892229\pi$
$797$	−31.8223	+	18.3726i	−1.12720	+	0.650791i	−0.183973	+	0.982931i	$0.558896\pi$
$798$		0			0
$799$	7.08939	−	12.2792i	0.250805	−	0.434406i
$800$	−2.39131	−	4.39109i	−0.0845456	−	0.155248i
$801$		0			0
$802$	17.3213	−	10.0005i	0.611637	−	0.353129i
$803$	−45.6252	+	26.3417i	−1.61008	+	0.929579i
$804$		0			0
$805$	−15.9579	−	31.2132i	−0.562442	−	1.10012i
$806$	7.56106	+	13.0961i	0.266327	+	0.461292i
$807$		0			0
$808$		−	12.6639i		−	0.445515i
$809$	−1.13309	−	1.96256i	−0.0398372	−	0.0690001i	0.845419	−	0.534103i	$-0.179351\pi$
$809$	−1.13309	−	1.96256i	−0.0398372	−	0.0690001i	−0.885257	+	0.465103i	$0.846017\pi$
$810$		0			0
$811$	27.0434			0.949622			0.474811	−	0.880088i	$-0.342516\pi$
$811$	27.0434			0.949622			0.474811	+	0.880088i	$0.342516\pi$
$812$	−11.9336	−	3.69573i	−0.418786	−	0.129695i
$813$		0			0
$814$	1.69201			0.0593048
$815$	−12.2852	−	12.5952i	−0.430331	−	0.441192i
$816$		0			0
$817$	−3.06460	+	1.76935i	−0.107217	+	0.0619016i
$818$		−	21.0715i		−	0.736747i
$819$		0			0
$820$	14.7684	+	4.15509i	0.515733	+	0.145102i
$821$	5.07500	+	8.79016i	0.177119	+	0.306779i	0.940893	−	0.338705i	$-0.109989\pi$
$821$	5.07500	+	8.79016i	0.177119	+	0.306779i	−0.763774	+	0.645484i	$0.776656\pi$
$822$		0			0
$823$	−7.04401	−	4.06686i	−0.245539	−	0.141762i	0.372181	−	0.928160i	$-0.378610\pi$
$823$	−7.04401	−	4.06686i	−0.245539	−	0.141762i	−0.617720	+	0.786398i	$0.711943\pi$
$824$	4.37970			0.152574
$825$		0			0
$826$	22.4332	+	24.2319i	0.780550	+	0.843135i
$827$			2.64164i			0.0918589i	0.998945	+	0.0459294i	$0.0146249\pi$
$827$			2.64164i			0.0918589i	−0.998945	+	0.0459294i	$0.985375\pi$
$828$		0			0
$829$	14.6215	+	25.3252i	0.507827	+	0.879582i	0.999959	+	0.00906143i	$0.00288438\pi$
$829$	14.6215	+	25.3252i	0.507827	+	0.879582i	−0.492132	+	0.870521i	$0.663782\pi$
$830$	−33.3623	−	9.38651i	−1.15802	−	0.325811i
$831$		0			0
$832$	3.36239	−	1.94128i	0.116570	−	0.0673017i
$833$	8.39427	+	17.5317i	0.290844	+	0.607439i
$834$		0			0
$835$	−45.9760	+	11.7072i	−1.59107	+	0.405143i
$836$	−5.78829	−	10.0256i	−0.200192	−	0.346743i
$837$		0			0
$838$	18.8016	+	10.8551i	0.649489	+	0.374983i
$839$	3.93007	−	6.80707i	0.135681	−	0.235006i	−0.790176	−	0.612879i	$-0.790011\pi$
$839$	3.93007	−	6.80707i	0.135681	−	0.235006i	0.925857	+	0.377873i	$0.123344\pi$
$840$		0			0
$841$	3.35227	+	5.80630i	0.115595	+	0.200217i
$842$			20.7039i			0.713504i
$843$		0			0
$844$	14.4198			0.496350
$845$	3.32029	−	3.23855i	0.114222	−	0.111410i
$846$		0			0
$847$	−11.3732	+	10.5290i	−0.390787	+	0.361779i
$848$	4.20182	+	2.42592i	0.144291	+	0.0833064i
$849$		0			0
$850$	−12.1933	+	6.64024i	−0.418225	+	0.227758i
$851$	1.22095	−	2.11474i	0.0418535	−	0.0724925i
$852$		0			0
$853$	6.09946	+	3.52152i	0.208841	+	0.120575i	0.600773	−	0.799420i	$-0.294860\pi$
$853$	6.09946	+	3.52152i	0.208841	+	0.120575i	−0.391931	+	0.919994i	$0.628193\pi$
$854$	−2.80842	+	0.637678i	−0.0961023	+	0.0218209i
$855$		0			0
$856$	−1.63543	+	2.83265i	−0.0558979	+	0.0968180i
$857$			3.13485i			0.107084i	0.998566	+	0.0535422i	$0.0170512\pi$
$857$			3.13485i			0.107084i	−0.998566	+	0.0535422i	$0.982949\pi$
$858$		0			0
$859$	30.7265			1.04837			0.524187	−	0.851603i	$-0.324369\pi$
$859$	30.7265			1.04837			0.524187	+	0.851603i	$0.324369\pi$
$860$	2.71962	−	0.692513i	0.0927381	−	0.0236145i
$861$		0			0
$862$	2.00583	+	1.15807i	0.0683188	+	0.0394439i
$863$	−26.0574	−	15.0443i	−0.887004	−	0.512112i	−0.0140430	−	0.999901i	$-0.504470\pi$
$863$	−26.0574	−	15.0443i	−0.887004	−	0.512112i	−0.872962	+	0.487789i	$0.837804\pi$
$864$		0			0
$865$	10.6876	−	2.72144i	0.363388	−	0.0925317i
$866$	−11.1376	−	19.2909i	−0.378470	−	0.655530i
$867$		0			0
$868$	9.84365	+	3.04851i	0.334115	+	0.103473i
$869$	12.3739	+	21.4322i	0.419756	+	0.727038i
$870$		0			0
$871$	−48.6359			−1.64797
$872$	−2.87443	+	1.65955i	−0.0973405	+	0.0561996i
$873$		0			0
$874$	−16.7073			−0.565132
$875$	−29.4952	−	2.24333i	−0.997120	−	0.0758385i
$876$		0			0
$877$			16.4269i			0.554698i	0.960769	+	0.277349i	$0.0894559\pi$
$877$			16.4269i			0.554698i	−0.960769	+	0.277349i	$0.910544\pi$
$878$	−17.9742	−	10.3774i	−0.606601	−	0.350221i
$879$		0			0
$880$	2.26551	+	8.89703i	0.0763702	+	0.299919i
$881$	33.4780			1.12790			0.563951	−	0.825808i	$-0.309281\pi$
$881$	33.4780			1.12790			0.563951	+	0.825808i	$0.309281\pi$
$882$		0			0
$883$		−	44.7104i		−	1.50462i	−0.658807	−	0.752312i	$-0.728939\pi$
$883$		−	44.7104i		−	1.50462i	0.658807	−	0.752312i	$-0.271061\pi$
$884$	−5.39058	−	9.33676i	−0.181305	−	0.314029i
$885$		0			0
$886$	9.38160	−	16.2494i	0.315181	−	0.545910i
$887$		−	23.6328i		−	0.793511i	−0.917924	−	0.396755i	$-0.870136\pi$
$887$		−	23.6328i		−	0.793511i	0.917924	−	0.396755i	$-0.129864\pi$
$888$		0			0
$889$	−13.2593	−	14.3225i	−0.444703	−	0.480360i
$890$	−4.46700	+	15.8770i	−0.149734	+	0.532197i
$891$		0			0
$892$	−15.8455	+	9.14843i	−0.530548	+	0.306312i
$893$		−	14.3969i		−	0.481774i
$894$		0			0
$895$	2.90535	+	11.4098i	0.0971150	+	0.381387i
$896$	0.782695	−	2.52733i	0.0261480	−	0.0844321i
$897$		0			0
$898$	−3.75563	+	2.16831i	−0.125327	+	0.0723575i
$899$	9.19545	+	15.9270i	0.306685	+	0.531195i
$900$		0			0
$901$	6.73635	−	11.6677i	0.224420	−	0.388707i
$902$	−24.3962	−	14.0852i	−0.812305	−	0.468985i
$903$		0			0
$904$	−3.95566	−	6.85140i	−0.131563	−	0.227874i
$905$	43.2713	+	12.1744i	1.43839	+	0.404692i
$906$		0			0
$907$		−	50.9921i		−	1.69316i	−0.532258	−	0.846582i	$-0.678656\pi$
$907$		−	50.9921i		−	1.69316i	0.532258	−	0.846582i	$-0.321344\pi$
$908$	7.81588	+	4.51250i	0.259379	+	0.149753i
$909$		0			0
$910$	1.17065	−	22.9397i	0.0388068	−	0.760443i
$911$	−23.6679	+	40.9939i	−0.784151	+	1.35819i	0.145354	+	0.989380i	$0.453568\pi$
$911$	−23.6679	+	40.9939i	−0.784151	+	1.35819i	−0.929505	+	0.368810i	$0.879765\pi$
$912$		0			0
$913$	55.1120	+	31.8189i	1.82394	+	1.05305i
$914$	11.3584	−	19.6734i	0.375703	−	0.650737i
$915$		0			0
$916$	8.59266	−	14.8829i	0.283910	−	0.491746i
$917$	23.1492	−	21.4308i	0.764453	−	0.707709i
$918$		0			0
$919$	−25.2990	+	43.8191i	−0.834536	+	1.44546i	0.0598717	+	0.998206i	$0.480931\pi$
$919$	−25.2990	+	43.8191i	−0.834536	+	1.44546i	−0.894408	+	0.447253i	$0.852402\pi$
$920$	12.7547	+	3.58855i	0.420510	+	0.118311i
$921$		0			0
$922$			16.8330i			0.554364i
$923$	54.8704	−	31.6795i	1.80608	−	1.04274i
$924$		0			0
$925$	−0.985453	−	1.80955i	−0.0324015	−	0.0594978i
$926$	13.8817	−	24.0438i	0.456181	−	0.790129i
$927$		0			0
$928$	4.08921	−	2.36090i	0.134235	−	0.0775005i
$929$	−0.531701	−	0.920934i	−0.0174446	−	0.0302149i	0.857171	−	0.515031i	$-0.172220\pi$
$929$	−0.531701	−	0.920934i	−0.0174446	−	0.0302149i	−0.874616	+	0.484816i	$0.838886\pi$
$930$		0			0
$931$	16.2822	+	11.1548i	0.533628	+	0.365584i
$932$	4.18657	−	2.41712i	0.137136	−	0.0791754i
$933$		0			0
$934$	34.4321			1.12665
$935$	24.7055	−	6.29091i	0.807955	−	0.205735i
$936$		0			0
$937$			39.6086i			1.29396i	0.762508	+	0.646978i	$0.223968\pi$
$937$			39.6086i			1.29396i	−0.762508	+	0.646978i	$0.776032\pi$
$938$	−24.3207	+	22.5154i	−0.794100	+	0.735155i
$939$		0			0
$940$	−3.09230	+	10.9909i	−0.100860	+	0.358484i
$941$	−1.20918	+	2.09436i	−0.0394182	+	0.0682743i	−0.885061	−	0.465474i	$-0.845884\pi$
$941$	−1.20918	+	2.09436i	−0.0394182	+	0.0682743i	0.845643	+	0.533749i	$0.179217\pi$
$942$		0			0
$943$	−35.2085	+	20.3276i	−1.14655	+	0.661959i
$944$	−12.4810			−0.406223
$945$		0			0
$946$	−5.15308			−0.167541
$947$	−30.7095	+	17.7301i	−0.997923	+	0.576151i	−0.907633	−	0.419764i	$-0.862113\pi$
$947$	−30.7095	+	17.7301i	−0.997923	+	0.576151i	−0.0902900	+	0.995916i	$0.528779\pi$
$948$		0			0
$949$	−24.9092	+	43.1440i	−0.808586	+	1.40051i
$950$	−7.35093	+	12.0295i	−0.238496	+	0.390289i
$951$		0			0
$952$	−7.01794	−	2.17340i	−0.227453	−	0.0704404i
$953$			50.6918i			1.64207i	0.570878	+	0.821035i	$0.306603\pi$
$953$			50.6918i			1.64207i	−0.570878	+	0.821035i	$0.693397\pi$
$954$		0			0
$955$	−1.65140	−	6.48531i	−0.0534379	−	0.209860i
$956$	16.1643			0.522791
$957$		0			0
$958$	9.77485	−	5.64351i	0.315811	−	0.182334i
$959$	−35.6143	−	38.4699i	−1.15005	−	1.24226i
$960$		0			0
$961$	7.91493	+	13.7091i	0.255320	+	0.442228i
$962$	1.38563	−	0.799995i	0.0446746	−	0.0257929i
$963$		0			0
$964$	−4.83873	+	8.38092i	−0.155845	+	0.269931i
$965$	33.4765	+	34.3214i	1.07765	+	1.10484i
$966$		0			0
$967$	18.4021	−	10.6245i	0.591772	−	0.341659i	−0.174026	−	0.984741i	$-0.555678\pi$
$967$	18.4021	−	10.6245i	0.591772	−	0.341659i	0.765798	+	0.643082i	$0.222344\pi$
$968$		−	5.85793i		−	0.188281i
$969$		0			0
$970$	9.01121	+	2.53531i	0.289332	+	0.0814040i
$971$	3.26795	−	5.66026i	0.104874	−	0.181646i	−0.808813	−	0.588066i	$-0.799890\pi$
$971$	3.26795	−	5.66026i	0.104874	−	0.181646i	0.913687	+	0.406420i	$0.133223\pi$
$972$		0			0
$973$	−14.4015	−	4.46003i	−0.461691	−	0.142982i
$974$	−12.2804	+	21.2703i	−0.393489	+	0.681544i
$975$		0			0
$976$	0.544252	−	0.942671i	0.0174211	−	0.0301742i
$977$	28.8203	+	16.6394i	0.922044	+	0.532342i	0.884286	−	0.466945i	$-0.154645\pi$
$977$	28.8203	+	16.6394i	0.922044	+	0.532342i	0.0377572	+	0.999287i	$0.487979\pi$
$978$		0			0
$979$	15.1425	−	26.2275i	0.483956	−	0.838236i
$980$	−10.0342	−	12.0131i	−0.320532	−	0.383743i
$981$		0			0
$982$	15.7331	+	9.08350i	0.502063	+	0.289866i
$983$			23.5480i			0.751064i	0.926809	+	0.375532i	$0.122540\pi$
$983$			23.5480i			0.751064i	−0.926809	+	0.375532i	$0.877460\pi$
$984$		0			0
$985$	−1.89955	+	6.75152i	−0.0605247	+	0.215121i
$986$	−6.55581	−	11.3550i	−0.208779	−	0.361617i
$987$		0			0
$988$	−9.48041	−	5.47352i	−0.301612	−	0.174136i
$989$	−3.71845	+	6.44055i	−0.118240	+	0.204797i
$990$		0			0
$991$	−17.3486	−	30.0487i	−0.551097	−	0.954527i	−0.998196	−	0.0600429i	$-0.980876\pi$
$991$	−17.3486	−	30.0487i	−0.551097	−	0.954527i	0.447099	−	0.894484i	$-0.352457\pi$
$992$	−3.37307	+	1.94744i	−0.107095	+	0.0618314i
$993$		0			0
$994$	12.7727	−	41.2431i	0.405125	−	1.30815i
$995$	−8.22198	−	32.2891i	−0.260654	−	1.02363i
$996$		0			0
$997$			49.3413i			1.56266i	0.624121	+	0.781328i	$0.285457\pi$
$997$			49.3413i			1.56266i	−0.624121	+	0.781328i	$0.714543\pi$
$998$	−9.85866	+	5.69190i	−0.312071	+	0.180174i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bq.a.289.47		96
3.2	odd	2		630.2.bq.a.79.6	yes	96
5.4	even	2	inner	1890.2.bq.a.289.18		96
7.4	even	3		1890.2.ba.a.1369.7		96
9.4	even	3		1890.2.ba.a.1549.46		96
9.5	odd	6		630.2.ba.a.499.15	✓	96
15.14	odd	2		630.2.bq.a.79.43	yes	96
21.11	odd	6		630.2.ba.a.529.10	yes	96
35.4	even	6		1890.2.ba.a.1369.46		96
45.4	even	6		1890.2.ba.a.1549.7		96
45.14	odd	6		630.2.ba.a.499.34	yes	96
63.4	even	3	inner	1890.2.bq.a.739.18		96
63.32	odd	6		630.2.bq.a.319.43	yes	96
105.74	odd	6		630.2.ba.a.529.39	yes	96
315.4	even	6	inner	1890.2.bq.a.739.47		96
315.284	odd	6		630.2.bq.a.319.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ba.a.499.15	✓	96	9.5	odd	6
630.2.ba.a.499.34	yes	96	45.14	odd	6
630.2.ba.a.529.10	yes	96	21.11	odd	6
630.2.ba.a.529.39	yes	96	105.74	odd	6
630.2.bq.a.79.6	yes	96	3.2	odd	2
630.2.bq.a.79.43	yes	96	15.14	odd	2
630.2.bq.a.319.6	yes	96	315.284	odd	6
630.2.bq.a.319.43	yes	96	63.32	odd	6
1890.2.ba.a.1369.7		96	7.4	even	3
1890.2.ba.a.1369.46		96	35.4	even	6
1890.2.ba.a.1549.7		96	45.4	even	6
1890.2.ba.a.1549.46		96	9.4	even	3
1890.2.bq.a.289.18		96	5.4	even	2	inner
1890.2.bq.a.289.47		96	1.1	even	1	trivial
1890.2.bq.a.739.18		96	63.4	even	3	inner
1890.2.bq.a.739.47		96	315.4	even	6	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.15250 + 0.605607i) q^{5} +(-1.94150 + 1.79738i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.15250 + 0.605607i) q^{5} +(-1.94150 + 1.79738i) q^{7} -1.00000i q^{8} +(2.16692 - 0.551777i) q^{10} -4.10584 q^{11} +(-3.36239 + 1.94128i) q^{13} +(-0.782695 + 2.52733i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.40480 + 1.38841i) q^{17} +(-1.40977 + 2.44179i) q^{19} +(1.60072 - 1.56131i) q^{20} +(-3.55576 + 2.05292i) q^{22} +5.92553i q^{23} +(4.26648 + 2.60714i) q^{25} +(-1.94128 + 3.36239i) q^{26} +(0.585831 + 2.58008i) q^{28} +(-2.36090 + 4.08921i) q^{29} +(1.94744 - 3.37307i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.38841 + 2.40480i) q^{34} +(-5.26758 + 2.69307i) q^{35} +(-0.356887 - 0.206049i) q^{37} +2.81954i q^{38} +(0.605607 - 2.15250i) q^{40} +(3.43052 + 5.94183i) q^{41} +(1.08691 + 0.627530i) q^{43} +(-2.05292 + 3.55576i) q^{44} +(2.96277 + 5.13166i) q^{46} +(-4.42203 + 2.55306i) q^{47} +(0.538827 - 6.97923i) q^{49} +(4.99845 + 0.124606i) q^{50} +3.88256i q^{52} +(-4.20182 + 2.42592i) q^{53} +(-8.83781 - 2.48653i) q^{55} +(1.79738 + 1.94150i) q^{56} +4.72181i q^{58} +(6.24051 - 10.8089i) q^{59} +(0.544252 + 0.942671i) q^{61} -3.89489i q^{62} -1.00000 q^{64} +(-8.41319 + 2.14230i) q^{65} +(10.8485 + 6.26339i) q^{67} +2.77682i q^{68} +(-3.21532 + 4.96606i) q^{70} -16.3189 q^{71} +(11.1123 - 6.41567i) q^{73} -0.412097 q^{74} +(1.40977 + 2.44179i) q^{76} +(7.97148 - 7.37977i) q^{77} +(-3.01373 - 5.21993i) q^{79} +(-0.551777 - 2.16692i) q^{80} +(5.94183 + 3.43052i) q^{82} +(-13.4228 - 7.74967i) q^{83} +(-6.01715 + 1.53218i) q^{85} +1.25506 q^{86} +4.10584i q^{88} +(-3.68803 + 6.38786i) q^{89} +(3.03886 - 9.81250i) q^{91} +(5.13166 + 2.96277i) q^{92} +(-2.55306 + 4.42203i) q^{94} +(-4.51329 + 4.40219i) q^{95} +(3.62553 + 2.09320i) q^{97} +(-3.02298 - 6.31361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4}+O(q^{10}) \) 96 * q + 48 * q^4	\( 96 q + 48 q^{4} + 8 q^{11} + 2 q^{14} - 48 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} + 12 q^{49} + 12 q^{50} + 12 q^{55} + 4 q^{56} + 24 q^{59} - 6 q^{61} - 96 q^{64} - 18 q^{65} + 6 q^{70} + 32 q^{71} + 8 q^{86} + 66 q^{89} - 12 q^{94} - 30 q^{95}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^11 + 2 * q^14 - 48 * q^16 - 24 * q^26 - 10 * q^29 + 34 * q^35 - 30 * q^41 + 4 * q^44 - 6 * q^46 + 12 * q^49 + 12 * q^50 + 12 * q^55 + 4 * q^56 + 24 * q^59 - 6 * q^61 - 96 * q^64 - 18 * q^65 + 6 * q^70 + 32 * q^71 + 8 * q^86 + 66 * q^89 - 12 * q^94 - 30 * q^95

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