LMFDB - Embedded newform 1890.2.bk.b.341.12

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			341.12
Character	$\chi$	$=$	1890.341
Dual form			1890.2.bk.b.521.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.408654 + 2.61400i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.408654 + 2.61400i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +(-3.42673 - 1.97842i) q^{11} +(2.82686 + 1.63209i) q^{13} +(2.61400 - 0.408654i) q^{14} +1.00000 q^{16} +(0.497322 + 0.861388i) q^{17} +(-4.90846 - 2.83390i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.97842 + 3.42673i) q^{22} +(6.67695 - 3.85494i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.63209 - 2.82686i) q^{26} +(-0.408654 - 2.61400i) q^{28} +(4.10273 - 2.36871i) q^{29} +5.58041i q^{31} -1.00000i q^{32} +(0.861388 - 0.497322i) q^{34} +(-2.05946 + 1.66090i) q^{35} +(-5.05548 + 8.75634i) q^{37} +(-2.83390 + 4.90846i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-5.16567 + 8.94721i) q^{41} +(5.10292 + 8.83852i) q^{43} +(3.42673 + 1.97842i) q^{44} +(-3.85494 - 6.67695i) q^{46} +4.73926 q^{47} +(-6.66600 + 2.13644i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-2.82686 - 1.63209i) q^{52} +(-8.82289 + 5.09390i) q^{53} -3.95684i q^{55} +(-2.61400 + 0.408654i) q^{56} +(-2.36871 - 4.10273i) q^{58} +3.40720 q^{59} +6.29939i q^{61} +5.58041 q^{62} -1.00000 q^{64} +3.26418i q^{65} +9.22190 q^{67} +(-0.497322 - 0.861388i) q^{68} +(1.66090 + 2.05946i) q^{70} -2.74965i q^{71} +(-12.7539 + 7.36348i) q^{73} +(8.75634 + 5.05548i) q^{74} +(4.90846 + 2.83390i) q^{76} +(3.77125 - 9.76595i) q^{77} -1.84147 q^{79} +(0.500000 + 0.866025i) q^{80} +(8.94721 + 5.16567i) q^{82} +(0.789829 + 1.36802i) q^{83} +(-0.497322 + 0.861388i) q^{85} +(8.83852 - 5.10292i) q^{86} +(1.97842 - 3.42673i) q^{88} +(-6.92781 + 11.9993i) q^{89} +(-3.11107 + 8.05637i) q^{91} +(-6.67695 + 3.85494i) q^{92} -4.73926i q^{94} -5.66780i q^{95} +(-0.776974 + 0.448586i) q^{97} +(2.13644 + 6.66600i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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
$7$	0.408654	+	2.61400i	0.154457	+	0.988000i
$7$	0.408654	+	2.61400i	0.154457	+	0.988000i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	−3.42673	−	1.97842i	−1.03320	−	0.596516i	−0.115298	−	0.993331i	$-0.536782\pi$
$11$	−3.42673	−	1.97842i	−1.03320	−	0.596516i	−0.917899	+	0.396815i	$0.870116\pi$
$12$		0			0
$13$	2.82686	+	1.63209i	0.784030	+	0.452660i	0.837857	−	0.545890i	$-0.183809\pi$
$13$	2.82686	+	1.63209i	0.784030	+	0.452660i	−0.0538267	+	0.998550i	$0.517142\pi$
$14$	2.61400	−	0.408654i	0.698621	−	0.109217i
$15$		0			0
$16$	1.00000			0.250000
$17$	0.497322	+	0.861388i	0.120618	+	0.208917i	0.920012	−	0.391891i	$-0.128179\pi$
$17$	0.497322	+	0.861388i	0.120618	+	0.208917i	−0.799393	+	0.600808i	$0.794846\pi$
$18$		0			0
$19$	−4.90846	−	2.83390i	−1.12608	−	0.650141i	−0.183132	−	0.983088i	$-0.558624\pi$
$19$	−4.90846	−	2.83390i	−1.12608	−	0.650141i	−0.942945	+	0.332947i	$0.891957\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−1.97842	+	3.42673i	−0.421801	+	0.730580i
$23$	6.67695	−	3.85494i	1.39224	−	0.803810i	0.398677	−	0.917092i	$-0.369470\pi$
$23$	6.67695	−	3.85494i	1.39224	−	0.803810i	0.993563	+	0.113282i	$0.0361363\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.63209	−	2.82686i	0.320079	−	0.554393i
$27$		0			0
$28$	−0.408654	−	2.61400i	−0.0772283	−	0.494000i
$29$	4.10273	−	2.36871i	0.761858	−	0.439859i	−0.0681041	−	0.997678i	$-0.521695\pi$
$29$	4.10273	−	2.36871i	0.761858	−	0.439859i	0.829963	+	0.557819i	$0.188362\pi$
$30$		0			0
$31$			5.58041i			1.00227i	0.865369	+	0.501135i	$0.167084\pi$
$31$			5.58041i			1.00227i	−0.865369	+	0.501135i	$0.832916\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	0.861388	−	0.497322i	0.147727	−	0.0852901i
$35$	−2.05946	+	1.66090i	−0.348113	+	0.280744i
$36$		0			0
$37$	−5.05548	+	8.75634i	−0.831115	+	1.43953i	0.0660393	+	0.997817i	$0.478964\pi$
$37$	−5.05548	+	8.75634i	−0.831115	+	1.43953i	−0.897155	+	0.441717i	$0.854370\pi$
$38$	−2.83390	+	4.90846i	−0.459719	+	0.796257i
$39$		0			0
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	−5.16567	+	8.94721i	−0.806743	+	1.39732i	0.108365	+	0.994111i	$0.465438\pi$
$41$	−5.16567	+	8.94721i	−0.806743	+	1.39732i	−0.915108	+	0.403208i	$0.867895\pi$
$42$		0			0
$43$	5.10292	+	8.83852i	0.778188	+	1.34786i	0.932985	+	0.359915i	$0.117194\pi$
$43$	5.10292	+	8.83852i	0.778188	+	1.34786i	−0.154797	+	0.987946i	$0.549472\pi$
$44$	3.42673	+	1.97842i	0.516598	+	0.298258i
$45$		0			0
$46$	−3.85494	−	6.67695i	−0.568379	−	0.984462i
$47$	4.73926			0.691293			0.345646	−	0.938365i	$-0.387660\pi$
$47$	4.73926			0.691293			0.345646	+	0.938365i	$0.387660\pi$
$48$		0			0
$49$	−6.66600	+	2.13644i	−0.952286	+	0.305206i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$	−2.82686	−	1.63209i	−0.392015	−	0.226330i
$53$	−8.82289	+	5.09390i	−1.21192	+	0.699701i	−0.963177	−	0.268869i	$-0.913350\pi$
$53$	−8.82289	+	5.09390i	−1.21192	+	0.699701i	−0.248741	+	0.968570i	$0.580017\pi$
$54$		0			0
$55$		−	3.95684i		−	0.533540i
$56$	−2.61400	+	0.408654i	−0.349311	+	0.0546086i
$57$		0			0
$58$	−2.36871	−	4.10273i	−0.311027	−	0.538715i
$59$	3.40720			0.443580			0.221790	−	0.975094i	$-0.428810\pi$
$59$	3.40720			0.443580			0.221790	+	0.975094i	$0.428810\pi$
$60$		0			0
$61$			6.29939i			0.806554i	0.915078	+	0.403277i	$0.132129\pi$
$61$			6.29939i			0.806554i	−0.915078	+	0.403277i	$0.867871\pi$
$62$	5.58041			0.708713
$63$		0			0
$64$	−1.00000			−0.125000
$65$			3.26418i			0.404871i
$66$		0			0
$67$	9.22190			1.12663			0.563317	−	0.826241i	$-0.309525\pi$
$67$	9.22190			1.12663			0.563317	+	0.826241i	$0.309525\pi$
$68$	−0.497322	−	0.861388i	−0.0603092	−	0.104459i
$69$		0			0
$70$	1.66090	+	2.05946i	0.198516	+	0.246153i
$71$		−	2.74965i		−	0.326324i	−0.986599	−	0.163162i	$-0.947831\pi$
$71$		−	2.74965i		−	0.326324i	0.986599	−	0.163162i	$-0.0521693\pi$
$72$		0			0
$73$	−12.7539	+	7.36348i	−1.49273	+	0.861830i	−0.999965	−	0.00833139i	$-0.997348\pi$
$73$	−12.7539	+	7.36348i	−1.49273	+	0.861830i	−0.492767	+	0.870161i	$0.664015\pi$
$74$	8.75634	+	5.05548i	1.01790	+	0.587687i
$75$		0			0
$76$	4.90846	+	2.83390i	0.563039	+	0.325071i
$77$	3.77125	−	9.76595i	0.429774	−	1.11293i
$78$		0			0
$79$	−1.84147			−0.207182			−0.103591	−	0.994620i	$-0.533033\pi$
$79$	−1.84147			−0.207182			−0.103591	+	0.994620i	$0.533033\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	8.94721	+	5.16567i	0.988054	+	0.570453i
$83$	0.789829	+	1.36802i	0.0866950	+	0.150160i	0.906112	−	0.423037i	$-0.139036\pi$
$83$	0.789829	+	1.36802i	0.0866950	+	0.150160i	−0.819417	+	0.573198i	$0.805703\pi$
$84$		0			0
$85$	−0.497322	+	0.861388i	−0.0539422	+	0.0934306i
$86$	8.83852	−	5.10292i	0.953082	−	0.550262i
$87$		0			0
$88$	1.97842	−	3.42673i	0.210900	−	0.365290i
$89$	−6.92781	+	11.9993i	−0.734347	+	1.27193i	0.220663	+	0.975350i	$0.429178\pi$
$89$	−6.92781	+	11.9993i	−0.734347	+	1.27193i	−0.955009	+	0.296576i	$0.904155\pi$
$90$		0			0
$91$	−3.11107	+	8.05637i	−0.326129	+	0.844537i
$92$	−6.67695	+	3.85494i	−0.696120	+	0.401905i
$93$		0			0
$94$		−	4.73926i		−	0.488818i
$95$		−	5.66780i		−	0.581504i
$96$		0			0
$97$	−0.776974	+	0.448586i	−0.0788897	+	0.0455470i	−0.538926	−	0.842353i	$-0.681170\pi$
$97$	−0.776974	+	0.448586i	−0.0788897	+	0.0455470i	0.460036	+	0.887900i	$0.347836\pi$
$98$	2.13644	+	6.66600i	0.215813	+	0.673368i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	0.107847	−	0.186797i	0.0107312	−	0.0185870i	−0.860610	−	0.509265i	$-0.829917\pi$
$101$	0.107847	−	0.186797i	0.0107312	−	0.0185870i	0.871341	+	0.490678i	$0.163251\pi$
$102$		0			0
$103$	−9.83240	+	5.67674i	−0.968816	+	0.559346i	−0.898875	−	0.438205i	$-0.855614\pi$
$103$	−9.83240	+	5.67674i	−0.968816	+	0.559346i	−0.0699406	+	0.997551i	$0.522281\pi$
$104$	−1.63209	+	2.82686i	−0.160039	+	0.277196i
$105$		0			0
$106$	5.09390	+	8.82289i	0.494763	+	0.856955i
$107$	−5.53564	−	3.19600i	−0.535151	−	0.308969i	0.207961	−	0.978137i	$-0.433317\pi$
$107$	−5.53564	−	3.19600i	−0.535151	−	0.308969i	−0.743111	+	0.669168i	$0.766651\pi$
$108$		0			0
$109$	0.615666	+	1.06636i	0.0589701	+	0.102139i	0.894003	−	0.448060i	$-0.147885\pi$
$109$	0.615666	+	1.06636i	0.0589701	+	0.102139i	−0.835033	+	0.550199i	$0.814552\pi$
$110$	−3.95684			−0.377270
$111$		0			0
$112$	0.408654	+	2.61400i	0.0386141	+	0.247000i
$113$	7.32005	+	4.22623i	0.688612	+	0.397571i	0.803092	−	0.595855i	$-0.203187\pi$
$113$	7.32005	+	4.22623i	0.688612	+	0.397571i	−0.114480	+	0.993426i	$0.536520\pi$
$114$		0			0
$115$	6.67695	+	3.85494i	0.622628	+	0.359475i
$116$	−4.10273	+	2.36871i	−0.380929	+	0.219930i
$117$		0			0
$118$		−	3.40720i		−	0.313658i
$119$	−2.04844	+	1.65201i	−0.187780	+	0.151440i
$120$		0			0
$121$	2.32830	+	4.03273i	0.211664	+	0.366612i
$122$	6.29939			0.570320
$123$		0			0
$124$		−	5.58041i		−	0.501135i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	20.5777			1.82598			0.912988	−	0.407985i	$-0.133769\pi$
$127$	20.5777			1.82598			0.912988	+	0.407985i	$0.133769\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	3.26418			0.286287
$131$	−2.50459	−	4.33807i	−0.218827	−	0.379019i	0.735623	−	0.677391i	$-0.236890\pi$
$131$	−2.50459	−	4.33807i	−0.218827	−	0.379019i	−0.954450	+	0.298372i	$0.903556\pi$
$132$		0			0
$133$	5.40196	−	13.9888i	0.468409	−	1.21298i
$134$		−	9.22190i		−	0.796651i
$135$		0			0
$136$	−0.861388	+	0.497322i	−0.0738634	+	0.0426450i
$137$	−7.99924	−	4.61836i	−0.683421	−	0.394573i	0.117722	−	0.993047i	$-0.462441\pi$
$137$	−7.99924	−	4.61836i	−0.683421	−	0.394573i	−0.801143	+	0.598473i	$0.795774\pi$
$138$		0			0
$139$	11.2919	+	6.51936i	0.957763	+	0.552965i	0.895484	−	0.445094i	$-0.146830\pi$
$139$	11.2919	+	6.51936i	0.957763	+	0.552965i	0.0622791	+	0.998059i	$0.480163\pi$
$140$	2.05946	−	1.66090i	0.174057	−	0.140372i
$141$		0			0
$142$	−2.74965			−0.230746
$143$	−6.45792	−	11.1854i	−0.540038	−	0.935373i
$144$		0			0
$145$	4.10273	+	2.36871i	0.340713	+	0.196711i
$146$	7.36348	+	12.7539i	0.609406	+	1.05552i
$147$		0			0
$148$	5.05548	−	8.75634i	0.415558	−	0.719767i
$149$	19.1098	−	11.0331i	1.56554	−	0.903863i	0.568858	−	0.822436i	$-0.307385\pi$
$149$	19.1098	−	11.0331i	1.56554	−	0.903863i	0.996679	−	0.0814277i	$-0.0259480\pi$
$150$		0			0
$151$	−2.76891	+	4.79589i	−0.225331	+	0.390284i	−0.956419	−	0.291999i	$-0.905680\pi$
$151$	−2.76891	+	4.79589i	−0.225331	+	0.390284i	0.731088	+	0.682283i	$0.239013\pi$
$152$	2.83390	−	4.90846i	0.229860	−	0.398128i
$153$		0			0
$154$	−9.76595	−	3.77125i	−0.786963	−	0.303896i
$155$	−4.83278	+	2.79020i	−0.388178	+	0.224115i
$156$		0			0
$157$		−	16.7972i		−	1.34056i	−0.742107	−	0.670281i	$-0.766173\pi$
$157$		−	16.7972i		−	1.34056i	0.742107	−	0.670281i	$-0.233827\pi$
$158$			1.84147i			0.146500i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	12.8054	+	15.8782i	1.00920	+	1.25138i
$162$		0			0
$163$	0.864749	−	1.49779i	0.0677324	−	0.117316i	−0.830170	−	0.557510i	$-0.811757\pi$
$163$	0.864749	−	1.49779i	0.0677324	−	0.117316i	0.897903	+	0.440194i	$0.145090\pi$
$164$	5.16567	−	8.94721i	0.403371	−	0.698660i
$165$		0			0
$166$	1.36802	−	0.789829i	0.106179	−	0.0613026i
$167$	−0.371022	+	0.642629i	−0.0287105	+	0.0497281i	−0.880024	−	0.474930i	$-0.842473\pi$
$167$	−0.371022	+	0.642629i	−0.0287105	+	0.0497281i	0.851313	+	0.524658i	$0.175807\pi$
$168$		0			0
$169$	−1.17257	−	2.03096i	−0.0901981	−	0.156228i
$170$	0.861388	+	0.497322i	0.0660654	+	0.0381429i
$171$		0			0
$172$	−5.10292	−	8.83852i	−0.389094	−	0.673930i
$173$	−0.964238			−0.0733097			−0.0366548	−	0.999328i	$-0.511670\pi$
$173$	−0.964238			−0.0733097			−0.0366548	+	0.999328i	$0.511670\pi$
$174$		0			0
$175$	−2.46812	−	0.953096i	−0.186572	−	0.0720473i
$176$	−3.42673	−	1.97842i	−0.258299	−	0.149129i
$177$		0			0
$178$	11.9993	+	6.92781i	0.899387	+	0.519262i
$179$	−0.186006	+	0.107391i	−0.0139028	+	0.00802676i	−0.506935	−	0.861984i	$-0.669222\pi$
$179$	−0.186006	+	0.107391i	−0.0139028	+	0.00802676i	0.493033	+	0.870011i	$0.335888\pi$
$180$		0			0
$181$			11.1757i			0.830681i	0.909666	+	0.415341i	$0.136338\pi$
$181$			11.1757i			0.830681i	−0.909666	+	0.415341i	$0.863662\pi$
$182$	8.05637	+	3.11107i	0.597178	+	0.230608i
$183$		0			0
$184$	3.85494	+	6.67695i	0.284190	+	0.492231i
$185$	−10.1110			−0.743372
$186$		0			0
$187$		−	3.93565i		−	0.287803i
$188$	−4.73926			−0.345646
$189$		0			0
$190$	−5.66780			−0.411185
$191$			18.8822i			1.36627i	0.730294	+	0.683133i	$0.239383\pi$
$191$			18.8822i			1.36627i	−0.730294	+	0.683133i	$0.760617\pi$
$192$		0			0
$193$	−5.89018			−0.423985			−0.211992	−	0.977271i	$-0.567995\pi$
$193$	−5.89018			−0.423985			−0.211992	+	0.977271i	$0.567995\pi$
$194$	0.448586	+	0.776974i	0.0322066	+	0.0557835i
$195$		0			0
$196$	6.66600	−	2.13644i	0.476143	−	0.152603i
$197$		−	24.0786i		−	1.71553i	−0.514043	−	0.857764i	$-0.671853\pi$
$197$		−	24.0786i		−	1.71553i	0.514043	−	0.857764i	$-0.328147\pi$
$198$		0			0
$199$	13.1750	−	7.60658i	0.933950	−	0.539216i	0.0458914	−	0.998946i	$-0.485387\pi$
$199$	13.1750	−	7.60658i	0.933950	−	0.539216i	0.888059	+	0.459730i	$0.152054\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$		0			0
$202$	−0.186797	−	0.107847i	−0.0131430	−	0.00758812i
$203$	7.86842	+	9.75657i	0.552255	+	0.684777i
$204$		0			0
$205$	−10.3313			−0.721573
$206$	5.67674	+	9.83240i	0.395517	+	0.685056i
$207$		0			0
$208$	2.82686	+	1.63209i	0.196007	+	0.113165i
$209$	11.2133	+	19.4220i	0.775640	+	1.34345i
$210$		0			0
$211$	−3.11109	+	5.38856i	−0.214176	+	0.370964i	−0.953017	−	0.302916i	$-0.902040\pi$
$211$	−3.11109	+	5.38856i	−0.214176	+	0.370964i	0.738841	+	0.673879i	$0.235373\pi$
$212$	8.82289	−	5.09390i	0.605959	−	0.349850i
$213$		0			0
$214$	−3.19600	+	5.53564i	−0.218474	+	0.378409i
$215$	−5.10292	+	8.83852i	−0.348016	+	0.602782i
$216$		0			0
$217$	−14.5872	+	2.28045i	−0.990243	+	0.154807i
$218$	1.06636	−	0.615666i	0.0722233	−	0.0416982i
$219$		0			0
$220$			3.95684i			0.266770i
$221$			3.24670i			0.218396i
$222$		0			0
$223$	4.37102	−	2.52361i	0.292705	−	0.168994i	−0.346456	−	0.938066i	$-0.612615\pi$
$223$	4.37102	−	2.52361i	0.292705	−	0.168994i	0.639161	+	0.769073i	$0.279282\pi$
$224$	2.61400	−	0.408654i	0.174655	−	0.0273043i
$225$		0			0
$226$	4.22623	−	7.32005i	0.281125	−	0.486922i
$227$	2.53981	−	4.39908i	0.168573	−	0.291977i	−0.769345	−	0.638833i	$-0.779417\pi$
$227$	2.53981	−	4.39908i	0.168573	−	0.291977i	0.937918	+	0.346856i	$0.112751\pi$
$228$		0			0
$229$	25.6828	−	14.8280i	1.69716	−	0.979859i	0.748736	−	0.662868i	$-0.230661\pi$
$229$	25.6828	−	14.8280i	1.69716	−	0.979859i	0.948429	−	0.316991i	$-0.102672\pi$
$230$	3.85494	−	6.67695i	0.254187	−	0.440265i
$231$		0			0
$232$	2.36871	+	4.10273i	0.155514	+	0.269358i
$233$	−15.8420	−	9.14639i	−1.03784	−	0.599200i	−0.118622	−	0.992939i	$-0.537848\pi$
$233$	−15.8420	−	9.14639i	−1.03784	−	0.599200i	−0.919222	+	0.393740i	$0.871181\pi$
$234$		0			0
$235$	2.36963	+	4.10432i	0.154578	+	0.267737i
$236$	−3.40720			−0.221790
$237$		0			0
$238$	1.65201	+	2.04844i	0.107084	+	0.132780i
$239$	−6.05638	−	3.49665i	−0.391755	−	0.226180i	0.291165	−	0.956673i	$-0.405957\pi$
$239$	−6.05638	−	3.49665i	−0.391755	−	0.226180i	−0.682920	+	0.730493i	$0.739290\pi$
$240$		0			0
$241$	4.77687	+	2.75793i	0.307705	+	0.177654i	0.645899	−	0.763423i	$-0.276483\pi$
$241$	4.77687	+	2.75793i	0.307705	+	0.177654i	−0.338194	+	0.941076i	$0.609816\pi$
$242$	4.03273	−	2.32830i	0.259234	−	0.149669i
$243$		0			0
$244$		−	6.29939i		−	0.403277i
$245$	−5.18322	−	4.70471i	−0.331143	−	0.300573i
$246$		0			0
$247$	−9.25035	−	16.0221i	−0.588586	−	1.01946i
$248$	−5.58041			−0.354356
$249$		0			0
$250$			1.00000i			0.0632456i
$251$	0.276363			0.0174439			0.00872195	−	0.999962i	$-0.497224\pi$
$251$	0.276363			0.0174439			0.00872195	+	0.999962i	$0.497224\pi$
$252$		0			0
$253$	−30.5068			−1.91794
$254$		−	20.5777i		−	1.29116i
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.24562	+	14.2818i	0.514348	+	0.890876i	0.999861	+	0.0166473i	$0.00529924\pi$
$257$	8.24562	+	14.2818i	0.514348	+	0.890876i	−0.485514	+	0.874229i	$0.661367\pi$
$258$		0			0
$259$	−24.9550	−	9.63671i	−1.55063	−	0.598796i
$260$		−	3.26418i		−	0.202436i
$261$		0			0
$262$	−4.33807	+	2.50459i	−0.268007	+	0.154734i
$263$	2.17310	+	1.25464i	0.133999	+	0.0773646i	0.565501	−	0.824748i	$-0.308683\pi$
$263$	2.17310	+	1.25464i	0.133999	+	0.0773646i	−0.431502	+	0.902112i	$0.642016\pi$
$264$		0			0
$265$	−8.82289	−	5.09390i	−0.541986	−	0.312916i
$266$	−13.9888	−	5.40196i	−0.857708	−	0.331215i
$267$		0			0
$268$	−9.22190			−0.563317
$269$	−13.3603	−	23.1408i	−0.814594	−	1.41092i	−0.909619	−	0.415444i	$-0.863626\pi$
$269$	−13.3603	−	23.1408i	−0.814594	−	1.41092i	0.0950245	−	0.995475i	$-0.469707\pi$
$270$		0			0
$271$	12.9500	+	7.47668i	0.786656	+	0.454176i	0.838784	−	0.544464i	$-0.183267\pi$
$271$	12.9500	+	7.47668i	0.786656	+	0.454176i	−0.0521278	+	0.998640i	$0.516600\pi$
$272$	0.497322	+	0.861388i	0.0301546	+	0.0522293i
$273$		0			0
$274$	−4.61836	+	7.99924i	−0.279005	+	0.483252i
$275$	3.42673	−	1.97842i	0.206639	−	0.119303i
$276$		0			0
$277$	7.11465	−	12.3229i	0.427478	−	0.740414i	−0.569170	−	0.822220i	$-0.692735\pi$
$277$	7.11465	−	12.3229i	0.427478	−	0.740414i	0.996648	+	0.0818060i	$0.0260688\pi$
$278$	6.51936	−	11.2919i	0.391005	−	0.677241i
$279$		0			0
$280$	−1.66090	−	2.05946i	−0.0992581	−	0.123077i
$281$	−21.5588	+	12.4470i	−1.28609	+	0.742524i	−0.977954	−	0.208819i	$-0.933038\pi$
$281$	−21.5588	+	12.4470i	−1.28609	+	0.742524i	−0.308135	+	0.951343i	$0.599705\pi$
$282$		0			0
$283$		−	17.1797i		−	1.02122i	−0.859811	−	0.510612i	$-0.829419\pi$
$283$		−	17.1797i		−	1.02122i	0.859811	−	0.510612i	$-0.170581\pi$
$284$			2.74965i			0.163162i
$285$		0			0
$286$	−11.1854	+	6.45792i	−0.661409	+	0.381865i
$287$	−25.4990	−	9.84677i	−1.50516	−	0.581236i
$288$		0			0
$289$	8.00534	−	13.8657i	0.470902	−	0.815627i
$290$	2.36871	−	4.10273i	0.139096	−	0.240921i
$291$		0			0
$292$	12.7539	−	7.36348i	0.746366	−	0.430915i
$293$	−3.98706	+	6.90578i	−0.232926	+	0.403440i	−0.958668	−	0.284527i	$-0.908163\pi$
$293$	−3.98706	+	6.90578i	−0.232926	+	0.403440i	0.725742	+	0.687967i	$0.241497\pi$
$294$		0			0
$295$	1.70360	+	2.95072i	0.0991875	+	0.171798i
$296$	−8.75634	−	5.05548i	−0.508952	−	0.293844i
$297$		0			0
$298$	−11.0331	−	19.1098i	−0.639128	−	1.10700i
$299$	25.1664			1.45541
$300$		0			0
$301$	−21.0186	+	16.9509i	−1.21149	+	0.977035i
$302$	4.79589	+	2.76891i	0.275973	+	0.159333i
$303$		0			0
$304$	−4.90846	−	2.83390i	−0.281519	−	0.162535i
$305$	−5.45543	+	3.14969i	−0.312377	+	0.180351i
$306$		0			0
$307$			15.5665i			0.888429i	0.895920	+	0.444215i	$0.146517\pi$
$307$			15.5665i			0.888429i	−0.895920	+	0.444215i	$0.853483\pi$
$308$	−3.77125	+	9.76595i	−0.214887	+	0.556467i
$309$		0			0
$310$	2.79020	+	4.83278i	0.158473	+	0.274483i
$311$	20.1669			1.14356			0.571779	−	0.820408i	$-0.306253\pi$
$311$	20.1669			1.14356			0.571779	+	0.820408i	$0.306253\pi$
$312$		0			0
$313$		−	6.67203i		−	0.377125i	−0.982061	−	0.188563i	$-0.939617\pi$
$313$		−	6.67203i		−	0.377125i	0.982061	−	0.188563i	$-0.0603829\pi$
$314$	−16.7972			−0.947921
$315$		0			0
$316$	1.84147			0.103591
$317$			25.5416i			1.43456i	0.696786	+	0.717279i	$0.254613\pi$
$317$			25.5416i			1.43456i	−0.696786	+	0.717279i	$0.745387\pi$
$318$		0			0
$319$	−18.7453			−1.04953
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	15.8782	−	12.8054i	0.884858	−	0.713615i
$323$		−	5.63745i		−	0.313676i
$324$		0			0
$325$	−2.82686	+	1.63209i	−0.156806	+	0.0905320i
$326$	−1.49779	−	0.864749i	−0.0829549	−	0.0478940i
$327$		0			0
$328$	−8.94721	−	5.16567i	−0.494027	−	0.285227i
$329$	1.93672	+	12.3884i	0.106775	+	0.682997i
$330$		0			0
$331$	1.81278			0.0996394			0.0498197	−	0.998758i	$-0.484135\pi$
$331$	1.81278			0.0996394			0.0498197	+	0.998758i	$0.484135\pi$
$332$	−0.789829	−	1.36802i	−0.0433475	−	0.0750801i
$333$		0			0
$334$	0.642629	+	0.371022i	0.0351631	+	0.0203014i
$335$	4.61095	+	7.98640i	0.251923	+	0.436344i
$336$		0			0
$337$	7.15488	−	12.3926i	0.389751	−	0.675069i	−0.602665	−	0.797995i	$-0.705894\pi$
$337$	7.15488	−	12.3926i	0.389751	−	0.675069i	0.992416	+	0.122926i	$0.0392277\pi$
$338$	−2.03096	+	1.17257i	−0.110470	+	0.0637797i
$339$		0			0
$340$	0.497322	−	0.861388i	0.0269711	−	0.0467153i
$341$	11.0404	−	19.1225i	0.597871	−	1.03554i
$342$		0			0
$343$	−8.30875	−	16.5519i	−0.448630	−	0.893717i
$344$	−8.83852	+	5.10292i	−0.476541	+	0.275131i
$345$		0			0
$346$			0.964238i			0.0518378i
$347$			6.00500i			0.322365i	0.986925	+	0.161183i	$0.0515308\pi$
$347$			6.00500i			0.322365i	−0.986925	+	0.161183i	$0.948469\pi$
$348$		0			0
$349$	11.6157	−	6.70633i	0.621775	−	0.358982i	−0.155785	−	0.987791i	$-0.549791\pi$
$349$	11.6157	−	6.70633i	0.621775	−	0.358982i	0.777560	+	0.628809i	$0.216457\pi$
$350$	−0.953096	+	2.46812i	−0.0509451	+	0.131926i
$351$		0			0
$352$	−1.97842	+	3.42673i	−0.105450	+	0.182645i
$353$	0.252692	−	0.437675i	0.0134494	−	0.0232951i	−0.859222	−	0.511602i	$-0.829052\pi$
$353$	0.252692	−	0.437675i	0.0134494	−	0.0232951i	0.872672	+	0.488307i	$0.162385\pi$
$354$		0			0
$355$	2.38127	−	1.37483i	0.126385	−	0.0729683i
$356$	6.92781	−	11.9993i	0.367173	−	0.635963i
$357$		0			0
$358$	0.107391	+	0.186006i	0.00567578	+	0.00983073i
$359$	11.2748	+	6.50952i	0.595062	+	0.343559i	0.767097	−	0.641532i	$-0.221701\pi$
$359$	11.2748	+	6.50952i	0.595062	+	0.343559i	−0.172034	+	0.985091i	$0.555034\pi$
$360$		0			0
$361$	6.56197	+	11.3657i	0.345367	+	0.598193i
$362$	11.1757			0.587380
$363$		0			0
$364$	3.11107	−	8.05637i	0.163065	−	0.422269i
$365$	−12.7539	−	7.36348i	−0.667570	−	0.385422i
$366$		0			0
$367$	−27.7376	−	16.0143i	−1.44789	−	0.835942i	−0.449537	−	0.893262i	$-0.648411\pi$
$367$	−27.7376	−	16.0143i	−1.44789	−	0.835942i	−0.998356	+	0.0573200i	$0.981744\pi$
$368$	6.67695	−	3.85494i	0.348060	−	0.200952i
$369$		0			0
$370$			10.1110i			0.525643i
$371$	−16.9210	−	20.9814i	−0.878493	−	1.08930i
$372$		0			0
$373$	−3.40038	−	5.88964i	−0.176065	−	0.304954i	0.764464	−	0.644666i	$-0.223004\pi$
$373$	−3.40038	−	5.88964i	−0.176065	−	0.304954i	−0.940529	+	0.339712i	$0.889670\pi$
$374$	−3.93565			−0.203508
$375$		0			0
$376$			4.73926i			0.244409i
$377$	15.4638			0.796426
$378$		0			0
$379$	2.14646			0.110256			0.0551281	−	0.998479i	$-0.482443\pi$
$379$	2.14646			0.110256			0.0551281	+	0.998479i	$0.482443\pi$
$380$			5.66780i			0.290752i
$381$		0			0
$382$	18.8822			0.966096
$383$	−0.355273	−	0.615351i	−0.0181536	−	0.0314430i	0.856806	−	0.515639i	$-0.172445\pi$
$383$	−0.355273	−	0.615351i	−0.0181536	−	0.0314430i	−0.874959	+	0.484196i	$0.839112\pi$
$384$		0			0
$385$	10.3432	−	1.61698i	0.527138	−	0.0824088i
$386$			5.89018i			0.299802i
$387$		0			0
$388$	0.776974	−	0.448586i	0.0394449	−	0.0227735i
$389$	−16.9870	−	9.80747i	−0.861277	−	0.497258i	0.00316299	−	0.999995i	$-0.498993\pi$
$389$	−16.9870	−	9.80747i	−0.861277	−	0.497258i	−0.864440	+	0.502737i	$0.832327\pi$
$390$		0			0
$391$	6.64119	+	3.83429i	0.335859	+	0.193908i
$392$	−2.13644	−	6.66600i	−0.107907	−	0.336684i
$393$		0			0
$394$	−24.0786			−1.21306
$395$	−0.920736	−	1.59476i	−0.0463273	−	0.0802412i
$396$		0			0
$397$	20.7322	+	11.9697i	1.04052	+	0.600743i	0.919980	−	0.391965i	$-0.128205\pi$
$397$	20.7322	+	11.9697i	1.04052	+	0.600743i	0.120538	+	0.992709i	$0.461538\pi$
$398$	−7.60658	−	13.1750i	−0.381284	−	0.660402i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−0.585108	+	0.337812i	−0.0292189	+	0.0168696i	−0.514538	−	0.857467i	$-0.672037\pi$
$401$	−0.585108	+	0.337812i	−0.0292189	+	0.0168696i	0.485319	+	0.874337i	$0.338703\pi$
$402$		0			0
$403$	−9.10772	+	15.7750i	−0.453688	+	0.785810i
$404$	−0.107847	+	0.186797i	−0.00536561	+	0.00929351i
$405$		0			0
$406$	9.75657	−	7.86842i	0.484210	−	0.390503i
$407$	34.6475	−	20.0037i	1.71741	−	0.991548i
$408$		0			0
$409$			30.3557i			1.50099i	0.660874	+	0.750497i	$0.270186\pi$
$409$			30.3557i			1.50099i	−0.660874	+	0.750497i	$0.729814\pi$
$410$			10.3313i			0.510229i
$411$		0			0
$412$	9.83240	−	5.67674i	0.484408	−	0.279673i
$413$	1.39237	+	8.90643i	0.0685138	+	0.438257i
$414$		0			0
$415$	−0.789829	+	1.36802i	−0.0387712	+	0.0671537i
$416$	1.63209	−	2.82686i	0.0800197	−	0.138598i
$417$		0			0
$418$	19.4220	−	11.2133i	0.949961	−	0.548460i
$419$	−5.87786	+	10.1808i	−0.287152	+	0.497363i	−0.973129	−	0.230261i	$-0.926042\pi$
$419$	−5.87786	+	10.1808i	−0.287152	+	0.497363i	0.685976	+	0.727624i	$0.259375\pi$
$420$		0			0
$421$	14.4557	+	25.0380i	0.704526	+	1.22028i	0.966862	+	0.255299i	$0.0821739\pi$
$421$	14.4557	+	25.0380i	0.704526	+	1.22028i	−0.262336	+	0.964977i	$0.584493\pi$
$422$	5.38856	+	3.11109i	0.262311	+	0.151445i
$423$		0			0
$424$	−5.09390	−	8.82289i	−0.247382	−	0.428477i
$425$	−0.994645			−0.0482474
$426$		0			0
$427$	−16.4666	+	2.57427i	−0.796875	+	0.124577i
$428$	5.53564	+	3.19600i	0.267575	+	0.154485i
$429$		0			0
$430$	8.83852	+	5.10292i	0.426231	+	0.246085i
$431$	−17.2762	+	9.97444i	−0.832167	+	0.480452i	−0.854594	−	0.519297i	$-0.826194\pi$
$431$	−17.2762	+	9.97444i	−0.832167	+	0.480452i	0.0224273	+	0.999748i	$0.492861\pi$
$432$		0			0
$433$			28.8157i			1.38479i	0.721517	+	0.692397i	$0.243445\pi$
$433$			28.8157i			1.38479i	−0.721517	+	0.692397i	$0.756555\pi$
$434$	2.28045	+	14.5872i	0.109465	+	0.700208i
$435$		0			0
$436$	−0.615666	−	1.06636i	−0.0294851	−	0.0510696i
$437$	−43.6980			−2.09036
$438$		0			0
$439$			8.17520i			0.390181i	0.980785	+	0.195091i	$0.0625001\pi$
$439$			8.17520i			0.390181i	−0.980785	+	0.195091i	$0.937500\pi$
$440$	3.95684			0.188635
$441$		0			0
$442$	3.24670			0.154430
$443$		−	26.2700i		−	1.24813i	−0.781374	−	0.624063i	$-0.785481\pi$
$443$		−	26.2700i		−	1.24813i	0.781374	−	0.624063i	$-0.214519\pi$
$444$		0			0
$445$	−13.8556			−0.656820
$446$	−2.52361	−	4.37102i	−0.119496	−	0.206974i
$447$		0			0
$448$	−0.408654	−	2.61400i	−0.0193071	−	0.123500i
$449$		−	6.39690i		−	0.301888i	−0.988542	−	0.150944i	$-0.951769\pi$
$449$		−	6.39690i		−	0.301888i	0.988542	−	0.150944i	$-0.0482314\pi$
$450$		0			0
$451$	35.4027	−	20.4398i	1.66705	−	0.962471i
$452$	−7.32005	−	4.22623i	−0.344306	−	0.198785i
$453$		0			0
$454$	−4.39908	−	2.53981i	−0.206459	−	0.119199i
$455$	−8.53256	+	1.33392i	−0.400013	+	0.0625350i
$456$		0			0
$457$	−10.3267			−0.483065			−0.241532	−	0.970393i	$-0.577650\pi$
$457$	−10.3267			−0.483065			−0.241532	+	0.970393i	$0.577650\pi$
$458$	−14.8280	−	25.6828i	−0.692865	−	1.20008i
$459$		0			0
$460$	−6.67695	−	3.85494i	−0.311314	−	0.179737i
$461$	4.00379	+	6.93476i	0.186475	+	0.322984i	0.944073	−	0.329738i	$-0.106960\pi$
$461$	4.00379	+	6.93476i	0.186475	+	0.322984i	−0.757598	+	0.652722i	$0.773627\pi$
$462$		0			0
$463$	15.2865	−	26.4770i	0.710425	−	1.23049i	−0.254273	−	0.967132i	$-0.581836\pi$
$463$	15.2865	−	26.4770i	0.710425	−	1.23049i	0.964698	−	0.263359i	$-0.0848304\pi$
$464$	4.10273	−	2.36871i	0.190465	−	0.109965i
$465$		0			0
$466$	−9.14639	+	15.8420i	−0.423698	+	0.733867i
$467$	3.61017	−	6.25300i	0.167059	−	0.289354i	−0.770326	−	0.637651i	$-0.779906\pi$
$467$	3.61017	−	6.25300i	0.167059	−	0.289354i	0.937385	+	0.348296i	$0.113240\pi$
$468$		0			0
$469$	3.76856	+	24.1061i	0.174016	+	1.11311i
$470$	4.10432	−	2.36963i	0.189318	−	0.109303i
$471$		0			0
$472$			3.40720i			0.156829i
$473$		−	40.3829i		−	1.85681i
$474$		0			0
$475$	4.90846	−	2.83390i	0.225215	−	0.130028i
$476$	2.04844	−	1.65201i	0.0938899	−	0.0757198i
$477$		0			0
$478$	−3.49665	+	6.05638i	−0.159933	+	0.277012i
$479$	−9.13594	+	15.8239i	−0.417432	+	0.723013i	−0.995680	−	0.0928475i	$-0.970403\pi$
$479$	−9.13594	+	15.8239i	−0.417432	+	0.723013i	0.578248	+	0.815861i	$0.303736\pi$
$480$		0			0
$481$	−28.5822	+	16.5020i	−1.30324	+	0.752425i
$482$	2.75793	−	4.77687i	0.125620	−	0.217581i
$483$		0			0
$484$	−2.32830	−	4.03273i	−0.105832	−	0.183306i
$485$	−0.776974	−	0.448586i	−0.0352806	−	0.0203692i
$486$		0			0
$487$	−19.2868	−	33.4057i	−0.873967	−	1.51375i	−0.857859	−	0.513885i	$-0.828206\pi$
$487$	−19.2868	−	33.4057i	−0.873967	−	1.51375i	−0.0161074	−	0.999870i	$-0.505127\pi$
$488$	−6.29939			−0.285160
$489$		0			0
$490$	−4.70471	+	5.18322i	−0.212537	+	0.234154i
$491$	−21.3449	−	12.3235i	−0.963282	−	0.556151i	−0.0661005	−	0.997813i	$-0.521056\pi$
$491$	−21.3449	−	12.3235i	−0.963282	−	0.556151i	−0.897182	+	0.441662i	$0.854389\pi$
$492$		0			0
$493$	4.08076	+	2.35603i	0.183788	+	0.106110i
$494$	−16.0221	+	9.25035i	−0.720867	+	0.416193i
$495$		0			0
$496$			5.58041i			0.250568i
$497$	7.18760	−	1.12366i	0.322408	−	0.0504029i
$498$		0			0
$499$	−5.25899	−	9.10884i	−0.235425	−	0.407768i	0.723971	−	0.689830i	$-0.242315\pi$
$499$	−5.25899	−	9.10884i	−0.235425	−	0.407768i	−0.959396	+	0.282062i	$0.908981\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$		−	0.276363i		−	0.0123347i
$503$	19.4315			0.866406			0.433203	−	0.901296i	$-0.357383\pi$
$503$	19.4315			0.866406			0.433203	+	0.901296i	$0.357383\pi$
$504$		0			0
$505$	0.215695			0.00959830
$506$			30.5068i			1.35619i
$507$		0			0
$508$	−20.5777			−0.912988
$509$	−11.6664	−	20.2068i	−0.517105	−	0.895652i	−0.999803	−	0.0198652i	$-0.993676\pi$
$509$	−11.6664	−	20.2068i	−0.517105	−	0.895652i	0.482698	−	0.875787i	$-0.339657\pi$
$510$		0			0
$511$	−24.4601	−	30.3296i	−1.08205	−	1.34170i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	14.2818	−	8.24562i	0.629945	−	0.363699i
$515$	−9.83240	−	5.67674i	−0.433268	−	0.250147i
$516$		0			0
$517$	−16.2402	−	9.37626i	−0.714241	−	0.412367i
$518$	−9.63671	+	24.9550i	−0.423413	+	1.09646i
$519$		0			0
$520$	−3.26418			−0.143144
$521$	−11.8637	−	20.5486i	−0.519759	−	0.900249i	−0.999736	−	0.0229682i	$-0.992688\pi$
$521$	−11.8637	−	20.5486i	−0.519759	−	0.900249i	0.479977	−	0.877281i	$-0.340645\pi$
$522$		0			0
$523$	15.7239	+	9.07818i	0.687556	+	0.396961i	0.802696	−	0.596388i	$-0.203398\pi$
$523$	15.7239	+	9.07818i	0.687556	+	0.396961i	−0.115140	+	0.993349i	$0.536732\pi$
$524$	2.50459	+	4.33807i	0.109413	+	0.189510i
$525$		0			0
$526$	1.25464	−	2.17310i	0.0547050	−	0.0947519i
$527$	−4.80689	+	2.77526i	−0.209392	+	0.120892i
$528$		0			0
$529$	18.2211	−	31.5598i	0.792221	−	1.37217i
$530$	−5.09390	+	8.82289i	−0.221265	+	0.383242i
$531$		0			0
$532$	−5.40196	+	13.9888i	−0.234205	+	0.606491i
$533$	−29.2053	+	16.8617i	−1.26502	+	0.730360i
$534$		0			0
$535$		−	6.39201i		−	0.276351i
$536$			9.22190i			0.398325i
$537$		0			0
$538$	−23.1408	+	13.3603i	−0.997670	+	0.576005i
$539$	27.0694	+	5.86716i	1.16596	+	0.252717i
$540$		0			0
$541$	5.56494	−	9.63875i	0.239255	−	0.414402i	−0.721245	−	0.692680i	$-0.756430\pi$
$541$	5.56494	−	9.63875i	0.239255	−	0.414402i	0.960501	+	0.278277i	$0.0897634\pi$
$542$	7.47668	−	12.9500i	0.321151	−	0.556250i
$543$		0			0
$544$	0.861388	−	0.497322i	0.0369317	−	0.0213225i
$545$	−0.615666	+	1.06636i	−0.0263722	+	0.0456781i
$546$		0			0
$547$	−15.8512	−	27.4550i	−0.677747	−	1.17389i	−0.975658	−	0.219299i	$-0.929623\pi$
$547$	−15.8512	−	27.4550i	−0.677747	−	1.17389i	0.297911	−	0.954594i	$-0.403710\pi$
$548$	7.99924	+	4.61836i	0.341711	+	0.197287i
$549$		0			0
$550$	−1.97842	−	3.42673i	−0.0843602	−	0.146116i
$551$	−26.8508			−1.14388
$552$		0			0
$553$	−0.752524	−	4.81361i	−0.0320006	−	0.204696i
$554$	−12.3229	−	7.11465i	−0.523552	−	0.302273i
$555$		0			0
$556$	−11.2919	−	6.51936i	−0.478881	−	0.276482i
$557$	−28.2949	+	16.3360i	−1.19889	+	0.692181i	−0.960308	−	0.278941i	$-0.910016\pi$
$557$	−28.2949	+	16.3360i	−1.19889	+	0.692181i	−0.238584	+	0.971122i	$0.576683\pi$
$558$		0			0
$559$			33.3137i			1.40902i
$560$	−2.05946	+	1.66090i	−0.0870283	+	0.0701860i
$561$		0			0
$562$	12.4470	+	21.5588i	0.525044	+	0.909402i
$563$	24.4996			1.03253			0.516267	−	0.856428i	$-0.327321\pi$
$563$	24.4996			1.03253			0.516267	+	0.856428i	$0.327321\pi$
$564$		0			0
$565$			8.45246i			0.355598i
$566$	−17.1797			−0.722115
$567$		0			0
$568$	2.74965			0.115373
$569$			21.3621i			0.895548i	0.894147	+	0.447774i	$0.147783\pi$
$569$			21.3621i			0.895548i	−0.894147	+	0.447774i	$0.852217\pi$
$570$		0			0
$571$	−16.4486			−0.688354			−0.344177	−	0.938905i	$-0.611842\pi$
$571$	−16.4486			−0.688354			−0.344177	+	0.938905i	$0.611842\pi$
$572$	6.45792	+	11.1854i	0.270019	+	0.467687i
$573$		0			0
$574$	−9.84677	+	25.4990i	−0.410996	+	1.06431i
$575$			7.70987i			0.321524i
$576$		0			0
$577$	17.2606	−	9.96542i	0.718569	−	0.414866i	−0.0956570	−	0.995414i	$-0.530495\pi$
$577$	17.2606	−	9.96542i	0.718569	−	0.414866i	0.814226	+	0.580549i	$0.197162\pi$
$578$	−13.8657	−	8.00534i	−0.576735	−	0.332978i
$579$		0			0
$580$	−4.10273	−	2.36871i	−0.170357	−	0.0983555i
$581$	−3.25325	+	2.62366i	−0.134968	+	0.108848i
$582$		0			0
$583$	40.3115			1.66953
$584$	−7.36348	−	12.7539i	−0.304703	−	0.527761i
$585$		0			0
$586$	6.90578	+	3.98706i	0.285275	+	0.164704i
$587$	1.94532	+	3.36939i	0.0802918	+	0.139070i	0.903375	−	0.428851i	$-0.141081\pi$
$587$	1.94532	+	3.36939i	0.0802918	+	0.139070i	−0.823083	+	0.567920i	$0.807748\pi$
$588$		0			0
$589$	15.8143	−	27.3912i	0.651618	−	1.12863i
$590$	2.95072	−	1.70360i	0.121479	−	0.0701362i
$591$		0			0
$592$	−5.05548	+	8.75634i	−0.207779	+	0.359883i
$593$	−7.52066	+	13.0262i	−0.308836	+	0.534920i	−0.978108	−	0.208097i	$-0.933273\pi$
$593$	−7.52066	+	13.0262i	−0.308836	+	0.534920i	0.669272	+	0.743018i	$0.266606\pi$
$594$		0			0
$595$	−2.45490	−	0.947992i	−0.100641	−	0.0388639i
$596$	−19.1098	+	11.0331i	−0.782769	+	0.451932i
$597$		0			0
$598$		−	25.1664i		−	1.02913i
$599$		−	27.3275i		−	1.11657i	−0.829649	−	0.558286i	$-0.811459\pi$
$599$		−	27.3275i		−	1.11657i	0.829649	−	0.558286i	$-0.188541\pi$
$600$		0			0
$601$	10.2307	−	5.90670i	0.417319	−	0.240939i	−0.276610	−	0.960982i	$-0.589211\pi$
$601$	10.2307	−	5.90670i	0.417319	−	0.240939i	0.693930	+	0.720043i	$0.255878\pi$
$602$	16.9509	+	21.0186i	0.690868	+	0.856653i
$603$		0			0
$604$	2.76891	−	4.79589i	0.112665	−	0.195142i
$605$	−2.32830	+	4.03273i	−0.0946589	+	0.163954i
$606$		0			0
$607$	0.641040	−	0.370104i	0.0260190	−	0.0150221i	−0.486934	−	0.873439i	$-0.661885\pi$
$607$	0.641040	−	0.370104i	0.0260190	−	0.0150221i	0.512953	+	0.858417i	$0.328551\pi$
$608$	−2.83390	+	4.90846i	−0.114930	+	0.199064i
$609$		0			0
$610$	3.14969	+	5.45543i	0.127527	+	0.220884i
$611$	13.3972	+	7.73490i	0.541994	+	0.312920i
$612$		0			0
$613$	8.29710	+	14.3710i	0.335117	+	0.580439i	0.983507	−	0.180869i	$-0.0578909\pi$
$613$	8.29710	+	14.3710i	0.335117	+	0.580439i	−0.648390	+	0.761308i	$0.724558\pi$
$614$	15.5665			0.628214
$615$		0			0
$616$	9.76595	+	3.77125i	0.393482	+	0.151948i
$617$	40.0027	+	23.0956i	1.61045	+	0.929793i	0.989266	+	0.146128i	$0.0466813\pi$
$617$	40.0027	+	23.0956i	1.61045	+	0.929793i	0.621184	+	0.783665i	$0.286652\pi$
$618$		0			0
$619$	15.6722	+	9.04833i	0.629917	+	0.363683i	0.780720	−	0.624881i	$-0.214852\pi$
$619$	15.6722	+	9.04833i	0.629917	+	0.363683i	−0.150803	+	0.988564i	$0.548186\pi$
$620$	4.83278	−	2.79020i	0.194089	−	0.112057i
$621$		0			0
$622$		−	20.1669i		−	0.808618i
$623$	−34.1973	−	13.2057i	−1.37009	−	0.529077i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.67203			−0.266668
$627$		0			0
$628$			16.7972i			0.670281i
$629$	−10.0568			−0.400991
$630$		0			0
$631$	8.36756			0.333107			0.166554	−	0.986032i	$-0.446736\pi$
$631$	8.36756			0.333107			0.166554	+	0.986032i	$0.446736\pi$
$632$		−	1.84147i		−	0.0732498i
$633$		0			0
$634$	25.5416			1.01439
$635$	10.2889	+	17.8208i	0.408301	+	0.707198i
$636$		0			0
$637$	−22.3307	−	4.84009i	−0.884775	−	0.191771i
$638$			18.7453i			0.742132i
$639$		0			0
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$	−14.8984	−	8.60160i	−0.588451	−	0.339743i	0.176034	−	0.984384i	$-0.443673\pi$
$641$	−14.8984	−	8.60160i	−0.588451	−	0.339743i	−0.764485	+	0.644642i	$0.777007\pi$
$642$		0			0
$643$	33.1046	+	19.1129i	1.30552	+	0.753740i	0.981344	−	0.192258i	$-0.0615809\pi$
$643$	33.1046	+	19.1129i	1.30552	+	0.753740i	0.324172	+	0.945998i	$0.394914\pi$
$644$	−12.8054	−	15.8782i	−0.504602	−	0.625689i
$645$		0			0
$646$	−5.63745			−0.221802
$647$	−7.26184	−	12.5779i	−0.285492	−	0.494487i	0.687236	−	0.726434i	$-0.258824\pi$
$647$	−7.26184	−	12.5779i	−0.285492	−	0.494487i	−0.972728	+	0.231947i	$0.925490\pi$
$648$		0			0
$649$	−11.6755	−	6.74088i	−0.458305	−	0.264603i
$650$	1.63209	+	2.82686i	0.0640158	+	0.110879i
$651$		0			0
$652$	−0.864749	+	1.49779i	−0.0338662	+	0.0586580i
$653$	−18.0580	+	10.4258i	−0.706666	+	0.407994i	−0.809825	−	0.586671i	$-0.800438\pi$
$653$	−18.0580	+	10.4258i	−0.706666	+	0.407994i	0.103160	+	0.994665i	$0.467105\pi$
$654$		0			0
$655$	2.50459	−	4.33807i	0.0978623	−	0.169502i
$656$	−5.16567	+	8.94721i	−0.201686	+	0.349330i
$657$		0			0
$658$	12.3884	−	1.93672i	0.482952	−	0.0755011i
$659$	19.3743	−	11.1857i	0.754715	−	0.435735i	−0.0726801	−	0.997355i	$-0.523155\pi$
$659$	19.3743	−	11.1857i	0.754715	−	0.435735i	0.827395	+	0.561621i	$0.189822\pi$
$660$		0			0
$661$			44.5340i			1.73217i	0.499894	+	0.866086i	$0.333372\pi$
$661$			44.5340i			1.73217i	−0.499894	+	0.866086i	$0.666628\pi$
$662$		−	1.81278i		−	0.0704557i
$663$		0			0
$664$	−1.36802	+	0.789829i	−0.0530896	+	0.0306513i
$665$	14.8156	−	2.31617i	0.574526	−	0.0898171i
$666$		0			0
$667$	18.2625	−	31.6316i	0.707126	−	1.22478i
$668$	0.371022	−	0.642629i	0.0143553	−	0.0248641i
$669$		0			0
$670$	7.98640	−	4.61095i	0.308542	−	0.178137i
$671$	12.4628	−	21.5863i	0.481123	−	0.833329i
$672$		0			0
$673$	−2.10536	−	3.64659i	−0.0811557	−	0.140566i	0.822591	−	0.568634i	$-0.192528\pi$
$673$	−2.10536	−	3.64659i	−0.0811557	−	0.140566i	−0.903747	+	0.428068i	$0.859194\pi$
$674$	−12.3926	−	7.15488i	−0.477346	−	0.275596i
$675$		0			0
$676$	1.17257	+	2.03096i	0.0450990	+	0.0781138i
$677$	39.6564			1.52412			0.762059	−	0.647508i	$-0.224189\pi$
$677$	39.6564			1.52412			0.762059	+	0.647508i	$0.224189\pi$
$678$		0			0
$679$	−1.49012	−	1.84769i	−0.0571855	−	0.0709080i
$680$	−0.861388	−	0.497322i	−0.0330327	−	0.0190714i
$681$		0			0
$682$	−19.1225	−	11.0404i	−0.732240	−	0.422759i
$683$	39.4682	−	22.7869i	1.51021	−	0.871918i	0.510278	−	0.860010i	$-0.329543\pi$
$683$	39.4682	−	22.7869i	1.51021	−	0.871918i	0.999929	−	0.0119087i	$-0.00379073\pi$
$684$		0			0
$685$		−	9.23672i		−	0.352917i
$686$	−16.5519	+	8.30875i	−0.631954	+	0.317229i
$687$		0			0
$688$	5.10292	+	8.83852i	0.194547	+	0.336965i
$689$	−33.2548			−1.26691
$690$		0			0
$691$		−	19.7402i		−	0.750952i	−0.926832	−	0.375476i	$-0.877479\pi$
$691$		−	19.7402i		−	0.750952i	0.926832	−	0.375476i	$-0.122521\pi$
$692$	0.964238			0.0366548
$693$		0			0
$694$	6.00500			0.227947
$695$			13.0387i			0.494587i
$696$		0			0
$697$	−10.2760			−0.389232
$698$	−6.70633	−	11.6157i	−0.253838	−	0.439661i
$699$		0			0
$700$	2.46812	+	0.953096i	0.0932861	+	0.0360237i
$701$			13.6845i			0.516855i	0.966031	+	0.258427i	$0.0832043\pi$
$701$			13.6845i			0.516855i	−0.966031	+	0.258427i	$0.916796\pi$
$702$		0			0
$703$	49.6292	−	28.6534i	1.87180	−	1.08068i
$704$	3.42673	+	1.97842i	0.129150	+	0.0745646i
$705$		0			0
$706$	−0.437675	−	0.252692i	−0.0164721	−	0.00951017i
$707$	0.532361	+	0.205578i	0.0200215	+	0.00773156i
$708$		0			0
$709$	−6.98123			−0.262185			−0.131093	−	0.991370i	$-0.541849\pi$
$709$	−6.98123			−0.262185			−0.131093	+	0.991370i	$0.541849\pi$
$710$	−1.37483	−	2.38127i	−0.0515963	−	0.0893675i
$711$		0			0
$712$	−11.9993	−	6.92781i	−0.449694	−	0.259631i
$713$	21.5121	+	37.2601i	0.805635	+	1.39540i
$714$		0			0
$715$	6.45792	−	11.1854i	0.241512	−	0.418312i
$716$	0.186006	−	0.107391i	0.00695138	−	0.00401338i
$717$		0			0
$718$	6.50952	−	11.2748i	0.242933	−	0.420773i
$719$	−7.49920	+	12.9890i	−0.279673	+	0.484408i	−0.971303	−	0.237844i	$-0.923559\pi$
$719$	−7.49920	+	12.9890i	−0.279673	+	0.484408i	0.691630	+	0.722252i	$0.256893\pi$
$720$		0			0
$721$	−18.8571	−	23.3821i	−0.702273	−	0.870795i
$722$	11.3657	−	6.56197i	0.422986	−	0.244211i
$723$		0			0
$724$		−	11.1757i		−	0.415341i
$725$			4.73743i			0.175944i
$726$		0			0
$727$	−22.4642	+	12.9697i	−0.833152	+	0.481020i	−0.854931	−	0.518742i	$-0.826400\pi$
$727$	−22.4642	+	12.9697i	−0.833152	+	0.481020i	0.0217788	+	0.999763i	$0.493067\pi$
$728$	−8.05637	−	3.11107i	−0.298589	−	0.115304i
$729$		0			0
$730$	−7.36348	+	12.7539i	−0.272534	+	0.472044i
$731$	−5.07559	+	8.79118i	−0.187728	+	0.325154i
$732$		0			0
$733$	−19.6712	+	11.3572i	−0.726572	+	0.419486i	−0.817167	−	0.576401i	$-0.804456\pi$
$733$	−19.6712	+	11.3572i	−0.726572	+	0.419486i	0.0905950	+	0.995888i	$0.471123\pi$
$734$	−16.0143	+	27.7376i	−0.591100	+	1.02382i
$735$		0			0
$736$	−3.85494	−	6.67695i	−0.142095	−	0.246116i
$737$	−31.6009	−	18.2448i	−1.16404	−	0.672056i
$738$		0			0
$739$	−6.74623	−	11.6848i	−0.248164	−	0.429833i	0.714852	−	0.699275i	$-0.246494\pi$
$739$	−6.74623	−	11.6848i	−0.248164	−	0.429833i	−0.963016	+	0.269443i	$0.913161\pi$
$740$	10.1110			0.371686
$741$		0			0
$742$	−20.9814	+	16.9210i	−0.770252	+	0.621188i
$743$	32.3371	+	18.6698i	1.18633	+	0.684930i	0.957471	−	0.288529i	$-0.0931662\pi$
$743$	32.3371	+	18.6698i	1.18633	+	0.684930i	0.228862	+	0.973459i	$0.426500\pi$
$744$		0			0
$745$	19.1098	+	11.0331i	0.700130	+	0.404220i
$746$	−5.88964	+	3.40038i	−0.215635	+	0.124497i
$747$		0			0
$748$			3.93565i			0.143902i
$749$	6.09220	−	15.7762i	0.222604	−	0.576451i
$750$		0			0
$751$	15.3349	+	26.5609i	0.559579	+	0.969220i	0.997531	+	0.0702215i	$0.0223706\pi$
$751$	15.3349	+	26.5609i	0.559579	+	0.969220i	−0.437952	+	0.898998i	$0.644296\pi$
$752$	4.73926			0.172823
$753$		0			0
$754$		−	15.4638i		−	0.563159i
$755$	−5.53782			−0.201542
$756$		0			0
$757$	−22.5697			−0.820308			−0.410154	−	0.912016i	$-0.634525\pi$
$757$	−22.5697			−0.820308			−0.410154	+	0.912016i	$0.634525\pi$
$758$		−	2.14646i		−	0.0779630i
$759$		0			0
$760$	5.66780			0.205593
$761$	−10.1156	−	17.5208i	−0.366691	−	0.635127i	0.622355	−	0.782735i	$-0.286176\pi$
$761$	−10.1156	−	17.5208i	−0.366691	−	0.635127i	−0.989046	+	0.147608i	$0.952843\pi$
$762$		0			0
$763$	−2.53588	+	2.04513i	−0.0918052	+	0.0740385i
$764$		−	18.8822i		−	0.683133i
$765$		0			0
$766$	−0.615351	+	0.355273i	−0.0222335	+	0.0128365i
$767$	9.63168	+	5.56086i	0.347780	+	0.200791i
$768$		0			0
$769$	29.9888	+	17.3140i	1.08142	+	0.624359i	0.931280	−	0.364305i	$-0.118693\pi$
$769$	29.9888	+	17.3140i	1.08142	+	0.624359i	0.150143	+	0.988664i	$0.452027\pi$
$770$	−1.61698	−	10.3432i	−0.0582718	−	0.372743i
$771$		0			0
$772$	5.89018			0.211992
$773$	9.02636	+	15.6341i	0.324656	+	0.562320i	0.981443	−	0.191756i	$-0.0614183\pi$
$773$	9.02636	+	15.6341i	0.324656	+	0.562320i	−0.656787	+	0.754076i	$0.728085\pi$
$774$		0			0
$775$	−4.83278	−	2.79020i	−0.173598	−	0.100227i
$776$	−0.448586	−	0.776974i	−0.0161033	−	0.0278917i
$777$		0			0
$778$	−9.80747	+	16.9870i	−0.351615	+	0.609015i
$779$	50.7110	−	29.2780i	1.81691	−	1.04899i
$780$		0			0
$781$	−5.43997	+	9.42231i	−0.194658	+	0.337157i
$782$	3.83429	−	6.64119i	0.137114	−	0.237488i
$783$		0			0
$784$	−6.66600	+	2.13644i	−0.238072	+	0.0763015i
$785$	14.5468	−	8.39860i	0.519198	−	0.299759i
$786$		0			0
$787$		−	1.78725i		−	0.0637087i	−0.999493	−	0.0318544i	$-0.989859\pi$
$787$		−	1.78725i		−	0.0637087i	0.999493	−	0.0318544i	$-0.0101413\pi$
$788$			24.0786i			0.857764i
$789$		0			0
$790$	−1.59476	+	0.920736i	−0.0567391	+	0.0327583i
$791$	−8.05601	+	20.8617i	−0.286439	+	0.741756i
$792$		0			0
$793$	−10.2812	+	17.8075i	−0.365094	+	0.632362i
$794$	11.9697	−	20.7322i	0.424790	−	0.735757i
$795$		0			0
$796$	−13.1750	+	7.60658i	−0.466975	+	0.269608i
$797$	21.5468	−	37.3202i	0.763227	−	1.32195i	−0.177951	−	0.984039i	$-0.556947\pi$
$797$	21.5468	−	37.3202i	0.763227	−	1.32195i	0.941179	−	0.337909i	$-0.109720\pi$
$798$		0			0
$799$	2.35694	+	4.08234i	0.0833826	+	0.144423i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	0.337812	+	0.585108i	0.0119286	+	0.0206609i
$803$	58.2722			2.05638
$804$		0			0
$805$	−7.34825	+	19.0289i	−0.258992	+	0.670680i
$806$	15.7750	+	9.10772i	0.555652	+	0.320806i
$807$		0			0
$808$	0.186797	+	0.107847i	0.00657151	+	0.00379406i
$809$	−31.6514	+	18.2739i	−1.11280	+	0.642478i	−0.939554	−	0.342400i	$-0.888760\pi$
$809$	−31.6514	+	18.2739i	−1.11280	+	0.642478i	−0.173250	+	0.984878i	$0.555427\pi$
$810$		0			0
$811$			0.856906i			0.0300900i	0.999887	+	0.0150450i	$0.00478916\pi$
$811$			0.856906i			0.0300900i	−0.999887	+	0.0150450i	$0.995211\pi$
$812$	−7.86842	−	9.75657i	−0.276127	−	0.342388i
$813$		0			0
$814$	−20.0037	−	34.6475i	−0.701130	−	1.21439i
$815$	1.72950			0.0605817
$816$		0			0
$817$		−	57.8446i		−	2.02373i
$818$	30.3557			1.06136
$819$		0			0
$820$	10.3313			0.360786
$821$		−	13.5165i		−	0.471728i	−0.971786	−	0.235864i	$-0.924208\pi$
$821$		−	13.5165i		−	0.471728i	0.971786	−	0.235864i	$-0.0757921\pi$
$822$		0			0
$823$	−14.9733			−0.521935			−0.260968	−	0.965348i	$-0.584042\pi$
$823$	−14.9733			−0.521935			−0.260968	+	0.965348i	$0.584042\pi$
$824$	−5.67674	−	9.83240i	−0.197759	−	0.342528i
$825$		0			0
$826$	8.90643	−	1.39237i	0.309894	−	0.0484466i
$827$		−	14.6192i		−	0.508361i	−0.967157	−	0.254180i	$-0.918194\pi$
$827$		−	14.6192i		−	0.508361i	0.967157	−	0.254180i	$-0.0818057\pi$
$828$		0			0
$829$	3.40972	−	1.96860i	0.118425	−	0.0683724i	−0.439618	−	0.898185i	$-0.644886\pi$
$829$	3.40972	−	1.96860i	0.118425	−	0.0683724i	0.558042	+	0.829813i	$0.311553\pi$
$830$	1.36802	+	0.789829i	0.0474848	+	0.0274154i
$831$		0			0
$832$	−2.82686	−	1.63209i	−0.0980037	−	0.0565825i
$833$	−5.15546	−	4.67951i	−0.178626	−	0.162136i
$834$		0			0
$835$	−0.742044			−0.0256795
$836$	−11.2133	−	19.4220i	−0.387820	−	0.671724i
$837$		0			0
$838$	10.1808	+	5.87786i	0.351688	+	0.203047i
$839$	−16.9706	−	29.3940i	−0.585891	−	1.01479i	−0.994764	−	0.102202i	$-0.967411\pi$
$839$	−16.9706	−	29.3940i	−0.585891	−	1.01479i	0.408872	−	0.912592i	$-0.365922\pi$
$840$		0			0
$841$	−3.27839	+	5.67833i	−0.113048	+	0.195804i
$842$	25.0380	−	14.4557i	0.862865	−	0.498175i
$843$		0			0
$844$	3.11109	−	5.38856i	0.107088	−	0.185482i
$845$	1.17257	−	2.03096i	0.0403378	−	0.0698671i
$846$		0			0
$847$	−9.59010	+	7.73417i	−0.329520	+	0.265749i
$848$	−8.82289	+	5.09390i	−0.302979	+	0.174925i
$849$		0			0
$850$			0.994645i			0.0341160i
$851$			77.9542i			2.67223i
$852$		0			0
$853$	27.7997	−	16.0501i	0.951843	−	0.549547i	0.0581898	−	0.998306i	$-0.481467\pi$
$853$	27.7997	−	16.0501i	0.951843	−	0.549547i	0.893653	+	0.448759i	$0.148134\pi$
$854$	2.57427	+	16.4666i	0.0880896	+	0.563476i
$855$		0			0
$856$	3.19600	−	5.53564i	0.109237	−	0.189204i
$857$	7.37024	−	12.7656i	0.251763	−	0.436066i	−0.712249	−	0.701927i	$-0.752323\pi$
$857$	7.37024	−	12.7656i	0.251763	−	0.436066i	0.964011	+	0.265862i	$0.0856564\pi$
$858$		0			0
$859$	−1.36977	+	0.790839i	−0.0467360	+	0.0269831i	−0.523186	−	0.852219i	$-0.675257\pi$
$859$	−1.36977	+	0.790839i	−0.0467360	+	0.0269831i	0.476450	+	0.879202i	$0.341923\pi$
$860$	5.10292	−	8.83852i	0.174008	−	0.301391i
$861$		0			0
$862$	9.97444	+	17.2762i	0.339731	+	0.588431i
$863$	−5.03980	−	2.90973i	−0.171557	−	0.0990483i	0.411763	−	0.911291i	$-0.364913\pi$
$863$	−5.03980	−	2.90973i	−0.171557	−	0.0990483i	−0.583320	+	0.812243i	$0.698247\pi$
$864$		0			0
$865$	−0.482119	−	0.835055i	−0.0163925	−	0.0283927i
$866$	28.8157			0.979197
$867$		0			0
$868$	14.5872	−	2.28045i	0.495122	−	0.0774036i
$869$	6.31022	+	3.64321i	0.214060	+	0.123587i
$870$		0			0
$871$	26.0690	+	15.0510i	0.883315	+	0.509982i
$872$	−1.06636	+	0.615666i	−0.0361117	+	0.0208491i
$873$		0			0
$874$			43.6980i			1.47811i
$875$	−0.408654	−	2.61400i	−0.0138150	−	0.0883694i
$876$		0			0
$877$	24.0873	+	41.7204i	0.813369	+	1.40880i	0.910493	+	0.413524i	$0.135702\pi$
$877$	24.0873	+	41.7204i	0.813369	+	1.40880i	−0.0971239	+	0.995272i	$0.530964\pi$
$878$	8.17520			0.275900
$879$		0			0
$880$		−	3.95684i		−	0.133385i
$881$	53.9354			1.81713			0.908566	−	0.417742i	$-0.137178\pi$
$881$	53.9354			1.81713			0.908566	+	0.417742i	$0.137178\pi$
$882$		0			0
$883$	−42.9089			−1.44400			−0.722000	−	0.691893i	$-0.756777\pi$
$883$	−42.9089			−1.44400			−0.722000	+	0.691893i	$0.756777\pi$
$884$		−	3.24670i		−	0.109198i
$885$		0			0
$886$	−26.2700			−0.882558
$887$	−9.55424	−	16.5484i	−0.320800	−	0.555642i	0.659853	−	0.751394i	$-0.270618\pi$
$887$	−9.55424	−	16.5484i	−0.320800	−	0.555642i	−0.980653	+	0.195753i	$0.937285\pi$
$888$		0			0
$889$	8.40916	+	53.7902i	0.282034	+	1.80406i
$890$			13.8556i			0.464442i
$891$		0			0
$892$	−4.37102	+	2.52361i	−0.146353	+	0.0844968i
$893$	−23.2625	−	13.4306i	−0.778449	−	0.449438i
$894$		0			0
$895$	−0.186006	−	0.107391i	−0.00621750	−	0.00358968i
$896$	−2.61400	+	0.408654i	−0.0873277	+	0.0136522i
$897$		0			0
$898$	−6.39690			−0.213467
$899$	13.2184	+	22.8949i	0.440858	+	0.763589i
$900$		0			0
$901$	−8.77564	−	5.06662i	−0.292359	−	0.168794i
$902$	−20.4398	−	35.4027i	−0.680570	−	1.17878i
$903$		0			0
$904$	−4.22623	+	7.32005i	−0.140562	+	0.243461i
$905$	−9.67842	+	5.58784i	−0.321721	+	0.185746i
$906$		0			0
$907$	13.5228	−	23.4221i	0.449016	−	0.777718i	−0.549306	−	0.835621i	$-0.685108\pi$
$907$	13.5228	−	23.4221i	0.449016	−	0.777718i	0.998322	+	0.0579028i	$0.0184413\pi$
$908$	−2.53981	+	4.39908i	−0.0842865	+	0.145989i
$909$		0			0
$910$	1.33392	+	8.53256i	0.0442189	+	0.282852i
$911$	−4.11941	+	2.37834i	−0.136482	+	0.0787979i	−0.566686	−	0.823934i	$-0.691775\pi$
$911$	−4.11941	+	2.37834i	−0.136482	+	0.0787979i	0.430204	+	0.902732i	$0.358442\pi$
$912$		0			0
$913$		−	6.25046i		−	0.206860i
$914$			10.3267i			0.341578i
$915$		0			0
$916$	−25.6828	+	14.8280i	−0.848582	+	0.489929i
$917$	10.3162	−	8.31976i	0.340671	−	0.274743i
$918$		0			0
$919$	−17.3173	+	29.9945i	−0.571245	+	0.989426i	0.425193	+	0.905103i	$0.360206\pi$
$919$	−17.3173	+	29.9945i	−0.571245	+	0.989426i	−0.996438	+	0.0843232i	$0.973127\pi$
$920$	−3.85494	+	6.67695i	−0.127094	+	0.220132i
$921$		0			0
$922$	6.93476	−	4.00379i	0.228384	−	0.131858i
$923$	4.48768	−	7.77289i	0.147714	−	0.255848i
$924$		0			0
$925$	−5.05548	−	8.75634i	−0.166223	−	0.287907i
$926$	−26.4770	−	15.2865i	−0.870089	−	0.502346i
$927$		0			0
$928$	−2.36871	−	4.10273i	−0.0777569	−	0.134679i
$929$	29.2791			0.960615			0.480307	−	0.877100i	$-0.340525\pi$
$929$	29.2791			0.960615			0.480307	+	0.877100i	$0.340525\pi$
$930$		0			0
$931$	38.7743	+	8.40415i	1.27078	+	0.275435i
$932$	15.8420	+	9.14639i	0.518922	+	0.299600i
$933$		0			0
$934$	−6.25300	−	3.61017i	−0.204604	−	0.118128i
$935$	3.40837	−	1.96783i	0.111466	−	0.0643548i
$936$		0			0
$937$		−	25.3740i		−	0.828932i	−0.910065	−	0.414466i	$-0.863968\pi$
$937$		−	25.3740i		−	0.828932i	0.910065	−	0.414466i	$-0.136032\pi$
$938$	24.1061	−	3.76856i	0.787091	−	0.123048i
$939$		0			0
$940$	−2.36963	−	4.10432i	−0.0772889	−	0.133868i
$941$	12.1904			0.397397			0.198699	−	0.980061i	$-0.436329\pi$
$941$	12.1904			0.397397			0.198699	+	0.980061i	$0.436329\pi$
$942$		0			0
$943$			79.6534i			2.59387i
$944$	3.40720			0.110895
$945$		0			0
$946$	−40.3829			−1.31296
$947$			16.2933i			0.529461i	0.964322	+	0.264731i	$0.0852831\pi$
$947$			16.2933i			0.529461i	−0.964322	+	0.264731i	$0.914717\pi$
$948$		0			0
$949$	−48.0714			−1.56046
$950$	−2.83390	−	4.90846i	−0.0919438	−	0.159251i
$951$		0			0
$952$	−1.65201	−	2.04844i	−0.0535420	−	0.0663902i
$953$		−	58.2513i		−	1.88695i	−0.331449	−	0.943473i	$-0.607538\pi$
$953$		−	58.2513i		−	1.88695i	0.331449	−	0.943473i	$-0.392462\pi$
$954$		0			0
$955$	−16.3524	+	9.44109i	−0.529153	+	0.305506i
$956$	6.05638	+	3.49665i	0.195877	+	0.113090i
$957$		0			0
$958$	15.8239	+	9.13594i	0.511248	+	0.295169i
$959$	8.80349	−	22.7973i	0.284279	−	0.736164i
$960$		0			0
$961$	−0.140960			−0.00454711
$962$	16.5020	+	28.5822i	0.532045	+	0.921529i
$963$		0			0
$964$	−4.77687	−	2.75793i	−0.153853	−	0.0888269i
$965$	−2.94509	−	5.10105i	−0.0948058	−	0.164209i
$966$		0			0
$967$	5.61342	−	9.72273i	0.180515	−	0.312662i	−0.761541	−	0.648117i	$-0.775557\pi$
$967$	5.61342	−	9.72273i	0.180515	−	0.312662i	0.942056	+	0.335455i	$0.108890\pi$
$968$	−4.03273	+	2.32830i	−0.129617	+	0.0748344i
$969$		0			0
$970$	−0.448586	+	0.776974i	−0.0144032	+	0.0249471i
$971$	−8.18607	+	14.1787i	−0.262704	+	0.455016i	−0.966959	−	0.254930i	$-0.917947\pi$
$971$	−8.18607	+	14.1787i	−0.262704	+	0.455016i	0.704256	+	0.709946i	$0.251281\pi$
$972$		0			0
$973$	−12.4272	+	32.1811i	−0.398396	+	1.03168i
$974$	−33.4057	+	19.2868i	−1.07039	+	0.617988i
$975$		0			0
$976$			6.29939i			0.201638i
$977$			58.4624i			1.87038i	0.354149	+	0.935189i	$0.384770\pi$
$977$			58.4624i			1.87038i	−0.354149	+	0.935189i	$0.615230\pi$
$978$		0			0
$979$	47.4794	−	27.4123i	1.51745	−	0.876100i
$980$	5.18322	+	4.70471i	0.165572	+	0.150286i
$981$		0			0
$982$	−12.3235	+	21.3449i	−0.393258	+	0.681143i
$983$	12.6833	−	21.9682i	0.404535	−	0.700675i	−0.589732	−	0.807599i	$-0.700767\pi$
$983$	12.6833	−	21.9682i	0.404535	−	0.700675i	0.994267	+	0.106924i	$0.0341000\pi$
$984$		0			0
$985$	20.8527	−	12.0393i	0.664421	−	0.383604i
$986$	2.35603	−	4.08076i	0.0750312	−	0.129958i
$987$		0			0
$988$	9.25035	+	16.0221i	0.294293	+	0.509730i
$989$	68.1438	+	39.3429i	2.16685	+	1.25103i
$990$		0			0
$991$	−11.2022	−	19.4028i	−0.355850	−	0.616349i	0.631413	−	0.775446i	$-0.282475\pi$
$991$	−11.2022	−	19.4028i	−0.355850	−	0.616349i	−0.987263	+	0.159097i	$0.949142\pi$
$992$	5.58041			0.177178
$993$		0			0
$994$	−1.12366	−	7.18760i	−0.0356402	−	0.227977i
$995$	13.1750	+	7.60658i	0.417675	+	0.241145i
$996$		0			0
$997$	21.1293	+	12.1990i	0.669172	+	0.386346i	0.795763	−	0.605609i	$-0.207070\pi$
$997$	21.1293	+	12.1990i	0.669172	+	0.386346i	−0.126591	+	0.991955i	$0.540404\pi$
$998$	−9.10884	+	5.25899i	−0.288335	+	0.166470i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bk.b.341.12		28
3.2	odd	2		630.2.bk.b.131.8	yes	28
7.3	odd	6		1890.2.t.b.1151.9		28
9.2	odd	6		1890.2.t.b.1601.9		28
9.7	even	3		630.2.t.b.551.2	yes	28
21.17	even	6		630.2.t.b.311.2	✓	28
63.38	even	6	inner	1890.2.bk.b.521.12		28
63.52	odd	6		630.2.bk.b.101.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.2	✓	28	21.17	even	6
630.2.t.b.551.2	yes	28	9.7	even	3
630.2.bk.b.101.1	yes	28	63.52	odd	6
630.2.bk.b.131.8	yes	28	3.2	odd	2
1890.2.t.b.1151.9		28	7.3	odd	6
1890.2.t.b.1601.9		28	9.2	odd	6
1890.2.bk.b.341.12		28	1.1	even	1	trivial
1890.2.bk.b.521.12		28	63.38	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.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.408654 + 2.61400i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.408654 + 2.61400i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +(-3.42673 - 1.97842i) q^{11} +(2.82686 + 1.63209i) q^{13} +(2.61400 - 0.408654i) q^{14} +1.00000 q^{16} +(0.497322 + 0.861388i) q^{17} +(-4.90846 - 2.83390i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.97842 + 3.42673i) q^{22} +(6.67695 - 3.85494i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.63209 - 2.82686i) q^{26} +(-0.408654 - 2.61400i) q^{28} +(4.10273 - 2.36871i) q^{29} +5.58041i q^{31} -1.00000i q^{32} +(0.861388 - 0.497322i) q^{34} +(-2.05946 + 1.66090i) q^{35} +(-5.05548 + 8.75634i) q^{37} +(-2.83390 + 4.90846i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-5.16567 + 8.94721i) q^{41} +(5.10292 + 8.83852i) q^{43} +(3.42673 + 1.97842i) q^{44} +(-3.85494 - 6.67695i) q^{46} +4.73926 q^{47} +(-6.66600 + 2.13644i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-2.82686 - 1.63209i) q^{52} +(-8.82289 + 5.09390i) q^{53} -3.95684i q^{55} +(-2.61400 + 0.408654i) q^{56} +(-2.36871 - 4.10273i) q^{58} +3.40720 q^{59} +6.29939i q^{61} +5.58041 q^{62} -1.00000 q^{64} +3.26418i q^{65} +9.22190 q^{67} +(-0.497322 - 0.861388i) q^{68} +(1.66090 + 2.05946i) q^{70} -2.74965i q^{71} +(-12.7539 + 7.36348i) q^{73} +(8.75634 + 5.05548i) q^{74} +(4.90846 + 2.83390i) q^{76} +(3.77125 - 9.76595i) q^{77} -1.84147 q^{79} +(0.500000 + 0.866025i) q^{80} +(8.94721 + 5.16567i) q^{82} +(0.789829 + 1.36802i) q^{83} +(-0.497322 + 0.861388i) q^{85} +(8.83852 - 5.10292i) q^{86} +(1.97842 - 3.42673i) q^{88} +(-6.92781 + 11.9993i) q^{89} +(-3.11107 + 8.05637i) q^{91} +(-6.67695 + 3.85494i) q^{92} -4.73926i q^{94} -5.66780i q^{95} +(-0.776974 + 0.448586i) q^{97} +(2.13644 + 6.66600i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) \) 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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