LMFDB - Embedded newform 1890.2.t.b.1601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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, 1]))

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

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

chi := DirichletCharacter("1890.1151");

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.t (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			1601.1
Character	$\chi$	$=$	1890.1601
Dual form			1890.2.t.b.1151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.555567 + 2.58676i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.555567 + 2.58676i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} -4.07809i q^{11} +(-5.20173 + 3.00322i) q^{13} +(-0.812247 - 2.51799i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.641724 + 1.11150i) q^{17} +(2.90701 + 1.67836i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.03904 + 3.53173i) q^{22} +2.18864i q^{23} +1.00000 q^{25} +(3.00322 - 5.20173i) q^{26} +(1.96242 + 1.77452i) q^{28} +(-6.21856 - 3.59029i) q^{29} +(-6.79271 - 3.92178i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.11150 - 0.641724i) q^{34} +(-0.555567 + 2.58676i) q^{35} +(-2.90160 + 5.02572i) q^{37} -3.35672 q^{38} +1.00000i q^{40} +(-1.36925 - 2.37162i) q^{41} +(-2.43768 + 4.22219i) q^{43} +(-3.53173 - 2.03904i) q^{44} +(-1.09432 - 1.89542i) q^{46} +(-4.13613 - 7.16398i) q^{47} +(-6.38269 - 2.87424i) q^{49} +(-0.866025 + 0.500000i) q^{50} +6.00644i q^{52} +(7.48689 - 4.32256i) q^{53} -4.07809i q^{55} +(-2.58676 - 0.555567i) q^{56} +7.18058 q^{58} +(0.630579 - 1.09220i) q^{59} +(-2.56956 + 1.48353i) q^{61} +7.84355 q^{62} -1.00000 q^{64} +(-5.20173 + 3.00322i) q^{65} +(4.31098 - 7.46684i) q^{67} +1.28345 q^{68} +(-0.812247 - 2.51799i) q^{70} +14.1375i q^{71} +(-6.02332 + 3.47757i) q^{73} -5.80320i q^{74} +(2.90701 - 1.67836i) q^{76} +(10.5490 + 2.26565i) q^{77} +(6.09277 + 10.5530i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(2.37162 + 1.36925i) q^{82} +(-6.87948 + 11.9156i) q^{83} +(0.641724 + 1.11150i) q^{85} -4.87537i q^{86} +4.07809 q^{88} +(7.29497 - 12.6353i) q^{89} +(-4.87871 - 15.1241i) q^{91} +(1.89542 + 1.09432i) q^{92} +(7.16398 + 4.13613i) q^{94} +(2.90701 + 1.67836i) q^{95} +(-16.8723 - 9.74120i) q^{97} +(6.96469 - 0.702180i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−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
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.555567	+	2.58676i	−0.209985	+	0.977705i
$7$	−0.555567	+	2.58676i	−0.209985	+	0.977705i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$		−	4.07809i		−	1.22959i	−0.788687	−	0.614795i	$-0.789239\pi$
$11$		−	4.07809i		−	1.22959i	0.788687	−	0.614795i	$-0.210761\pi$
$12$		0			0
$13$	−5.20173	+	3.00322i	−1.44270	+	0.832943i	−0.998029	−	0.0627507i	$-0.980013\pi$
$13$	−5.20173	+	3.00322i	−1.44270	+	0.832943i	−0.444671	+	0.895694i	$0.646679\pi$
$14$	−0.812247	−	2.51799i	−0.217082	−	0.672960i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.641724	+	1.11150i	0.155641	+	0.269578i	0.933292	−	0.359118i	$-0.116922\pi$
$17$	0.641724	+	1.11150i	0.155641	+	0.269578i	−0.777651	+	0.628696i	$0.783589\pi$
$18$		0			0
$19$	2.90701	+	1.67836i	0.666913	+	0.385043i	0.794906	−	0.606733i	$-0.207520\pi$
$19$	2.90701	+	1.67836i	0.666913	+	0.385043i	−0.127993	+	0.991775i	$0.540853\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	2.03904	+	3.53173i	0.434726	+	0.752967i
$23$			2.18864i			0.456363i	0.973619	+	0.228182i	$0.0732780\pi$
$23$			2.18864i			0.456363i	−0.973619	+	0.228182i	$0.926722\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	3.00322	−	5.20173i	0.588980	−	1.02014i
$27$		0			0
$28$	1.96242	+	1.77452i	0.370862	+	0.335352i
$29$	−6.21856	−	3.59029i	−1.15476	−	0.666700i	−0.204716	−	0.978821i	$-0.565627\pi$
$29$	−6.21856	−	3.59029i	−1.15476	−	0.666700i	−0.950042	+	0.312122i	$0.898960\pi$
$30$		0			0
$31$	−6.79271	−	3.92178i	−1.22001	−	0.704372i	−0.255088	−	0.966918i	$-0.582104\pi$
$31$	−6.79271	−	3.92178i	−1.22001	−	0.704372i	−0.964919	+	0.262546i	$0.915438\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−1.11150	−	0.641724i	−0.190621	−	0.110055i
$35$	−0.555567	+	2.58676i	−0.0939079	+	0.437243i
$36$		0			0
$37$	−2.90160	+	5.02572i	−0.477020	+	0.826223i	−0.999653	−	0.0263347i	$-0.991616\pi$
$37$	−2.90160	+	5.02572i	−0.477020	+	0.826223i	0.522633	+	0.852558i	$0.324950\pi$
$38$	−3.35672			−0.544532
$39$		0			0
$40$			1.00000i			0.158114i
$41$	−1.36925	−	2.37162i	−0.213842	−	0.370384i	0.739072	−	0.673626i	$-0.235264\pi$
$41$	−1.36925	−	2.37162i	−0.213842	−	0.370384i	−0.952914	+	0.303242i	$0.901931\pi$
$42$		0			0
$43$	−2.43768	+	4.22219i	−0.371743	+	0.643878i	−0.989834	−	0.142229i	$-0.954573\pi$
$43$	−2.43768	+	4.22219i	−0.371743	+	0.643878i	0.618091	+	0.786107i	$0.287906\pi$
$44$	−3.53173	−	2.03904i	−0.532428	−	0.307397i
$45$		0			0
$46$	−1.09432	−	1.89542i	−0.161349	−	0.279464i
$47$	−4.13613	−	7.16398i	−0.603316	−	1.04497i	−0.992315	−	0.123736i	$-0.960512\pi$
$47$	−4.13613	−	7.16398i	−0.603316	−	1.04497i	0.388999	−	0.921238i	$-0.372821\pi$
$48$		0			0
$49$	−6.38269	−	2.87424i	−0.911813	−	0.410606i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$			6.00644i			0.832943i
$53$	7.48689	−	4.32256i	1.02840	−	0.593749i	0.111877	−	0.993722i	$-0.464314\pi$
$53$	7.48689	−	4.32256i	1.02840	−	0.593749i	0.916527	+	0.399973i	$0.130980\pi$
$54$		0			0
$55$		−	4.07809i		−	0.549889i
$56$	−2.58676	−	0.555567i	−0.345671	−	0.0742407i
$57$		0			0
$58$	7.18058			0.942856
$59$	0.630579	−	1.09220i	0.0820944	−	0.142192i	−0.822055	−	0.569408i	$-0.807172\pi$
$59$	0.630579	−	1.09220i	0.0820944	−	0.142192i	0.904149	+	0.427216i	$0.140506\pi$
$60$		0			0
$61$	−2.56956	+	1.48353i	−0.328998	+	0.189947i	−0.655396	−	0.755285i	$-0.727498\pi$
$61$	−2.56956	+	1.48353i	−0.328998	+	0.189947i	0.326398	+	0.945232i	$0.394165\pi$
$62$	7.84355			0.996132
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.20173	+	3.00322i	−0.645195	+	0.372504i
$66$		0			0
$67$	4.31098	−	7.46684i	0.526670	−	0.912220i	−0.472847	−	0.881145i	$-0.656774\pi$
$67$	4.31098	−	7.46684i	0.526670	−	0.912220i	0.999517	−	0.0310753i	$-0.00989316\pi$
$68$	1.28345			0.155641
$69$		0			0
$70$	−0.812247	−	2.51799i	−0.0970821	−	0.300957i
$71$			14.1375i			1.67781i	0.544277	+	0.838906i	$0.316804\pi$
$71$			14.1375i			1.67781i	−0.544277	+	0.838906i	$0.683196\pi$
$72$		0			0
$73$	−6.02332	+	3.47757i	−0.704977	+	0.407018i	−0.809198	−	0.587536i	$-0.800098\pi$
$73$	−6.02332	+	3.47757i	−0.704977	+	0.407018i	0.104222	+	0.994554i	$0.466765\pi$
$74$		−	5.80320i		−	0.674608i
$75$		0			0
$76$	2.90701	−	1.67836i	0.333457	−	0.192521i
$77$	10.5490	+	2.26565i	1.20218	+	0.258195i
$78$		0			0
$79$	6.09277	+	10.5530i	0.685490	+	1.18730i	0.973283	+	0.229610i	$0.0737452\pi$
$79$	6.09277	+	10.5530i	0.685490	+	1.18730i	−0.287793	+	0.957693i	$0.592921\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	2.37162	+	1.36925i	0.261901	+	0.151209i
$83$	−6.87948	+	11.9156i	−0.755121	+	1.30791i	0.190194	+	0.981747i	$0.439088\pi$
$83$	−6.87948	+	11.9156i	−0.755121	+	1.30791i	−0.945314	+	0.326161i	$0.894245\pi$
$84$		0			0
$85$	0.641724	+	1.11150i	0.0696048	+	0.120559i
$86$		−	4.87537i		−	0.525724i
$87$		0			0
$88$	4.07809			0.434726
$89$	7.29497	−	12.6353i	0.773265	−	1.33933i	−0.162499	−	0.986709i	$-0.551955\pi$
$89$	7.29497	−	12.6353i	0.773265	−	1.33933i	0.935764	−	0.352626i	$-0.114711\pi$
$90$		0			0
$91$	−4.87871	−	15.1241i	−0.511428	−	1.58544i
$92$	1.89542	+	1.09432i	0.197611	+	0.114091i
$93$		0			0
$94$	7.16398	+	4.13613i	0.738908	+	0.426609i
$95$	2.90701	+	1.67836i	0.298253	+	0.172196i
$96$		0			0
$97$	−16.8723	−	9.74120i	−1.71312	−	0.989069i	−0.930285	−	0.366837i	$-0.880441\pi$
$97$	−16.8723	−	9.74120i	−1.71312	−	0.989069i	−0.782832	−	0.622233i	$-0.786226\pi$
$98$	6.96469	−	0.702180i	0.703540	−	0.0709309i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−8.53717			−0.849480			−0.424740	−	0.905315i	$-0.639635\pi$
$101$	−8.53717			−0.849480			−0.424740	+	0.905315i	$0.639635\pi$
$102$		0			0
$103$		−	3.61248i		−	0.355948i	−0.984035	−	0.177974i	$-0.943046\pi$
$103$		−	3.61248i		−	0.355948i	0.984035	−	0.177974i	$-0.0569543\pi$
$104$	−3.00322	−	5.20173i	−0.294490	−	0.510072i
$105$		0			0
$106$	−4.32256	+	7.48689i	−0.419844	+	0.727191i
$107$	−11.5596	−	6.67392i	−1.11751	−	0.645192i	−0.176743	−	0.984257i	$-0.556556\pi$
$107$	−11.5596	−	6.67392i	−1.11751	−	0.645192i	−0.940763	+	0.339065i	$0.889889\pi$
$108$		0			0
$109$	5.38583	+	9.32854i	0.515869	+	0.893512i	0.999830	+	0.0184222i	$0.00586429\pi$
$109$	5.38583	+	9.32854i	0.515869	+	0.893512i	−0.483961	+	0.875090i	$0.660802\pi$
$110$	2.03904	+	3.53173i	0.194415	+	0.336737i
$111$		0			0
$112$	2.51799	−	0.812247i	0.237927	−	0.0767501i
$113$	2.45659	−	1.41832i	0.231097	−	0.133424i	−0.379981	−	0.924994i	$-0.624070\pi$
$113$	2.45659	−	1.41832i	0.231097	−	0.133424i	0.611078	+	0.791570i	$0.290736\pi$
$114$		0			0
$115$			2.18864i			0.204092i
$116$	−6.21856	+	3.59029i	−0.577379	+	0.333350i
$117$		0			0
$118$			1.26116i			0.116099i
$119$	−3.23171	+	1.04248i	−0.296250	+	0.0955637i
$120$		0			0
$121$	−5.63079			−0.511890
$122$	1.48353	−	2.56956i	0.134313	−	0.232637i
$123$		0			0
$124$	−6.79271	+	3.92178i	−0.610004	+	0.352186i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−10.9625			−0.972768			−0.486384	−	0.873745i	$-0.661684\pi$
$127$	−10.9625			−0.972768			−0.486384	+	0.873745i	$0.661684\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	3.00322	−	5.20173i	0.263400	−	0.456222i
$131$	−20.7312			−1.81129			−0.905647	−	0.424032i	$-0.860614\pi$
$131$	−20.7312			−1.81129			−0.905647	+	0.424032i	$0.860614\pi$
$132$		0			0
$133$	−5.95656	+	6.58730i	−0.516499	+	0.571191i
$134$			8.62197i			0.744825i
$135$		0			0
$136$	−1.11150	+	0.641724i	−0.0953103	+	0.0550274i
$137$			9.67432i			0.826533i	0.910610	+	0.413267i	$0.135612\pi$
$137$			9.67432i			0.826533i	−0.910610	+	0.413267i	$0.864388\pi$
$138$		0			0
$139$	−4.57137	+	2.63928i	−0.387739	+	0.223861i	−0.681180	−	0.732116i	$-0.738533\pi$
$139$	−4.57137	+	2.63928i	−0.387739	+	0.223861i	0.293441	+	0.955977i	$0.405200\pi$
$140$	1.96242	+	1.77452i	0.165855	+	0.149974i
$141$		0			0
$142$	−7.06874	−	12.2434i	−0.593196	−	1.02745i
$143$	12.2474	+	21.2131i	1.02418	+	1.77393i
$144$		0			0
$145$	−6.21856	−	3.59029i	−0.516423	−	0.298157i
$146$	3.47757	−	6.02332i	0.287806	−	0.498494i
$147$		0			0
$148$	2.90160	+	5.02572i	0.238510	+	0.413112i
$149$		−	4.37779i		−	0.358642i	−0.983791	−	0.179321i	$-0.942610\pi$
$149$		−	4.37779i		−	0.358642i	0.983791	−	0.179321i	$-0.0573901\pi$
$150$		0			0
$151$	−5.57316			−0.453538			−0.226769	−	0.973949i	$-0.572816\pi$
$151$	−5.57316			−0.453538			−0.226769	+	0.973949i	$0.572816\pi$
$152$	−1.67836	+	2.90701i	−0.136133	+	0.235789i
$153$		0			0
$154$	−10.2686	+	3.31241i	−0.827465	+	0.266922i
$155$	−6.79271	−	3.92178i	−0.545604	−	0.315005i
$156$		0			0
$157$	−0.243649	−	0.140671i	−0.0194453	−	0.0112267i	0.490246	−	0.871584i	$-0.336907\pi$
$157$	−0.243649	−	0.140671i	−0.0194453	−	0.0112267i	−0.509691	+	0.860357i	$0.670240\pi$
$158$	−10.5530	−	6.09277i	−0.839550	−	0.484714i
$159$		0			0
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−5.66149	−	1.21594i	−0.446188	−	0.0958292i
$162$		0			0
$163$	−3.76577	+	6.52251i	−0.294958	+	0.510882i	−0.974975	−	0.222314i	$-0.928639\pi$
$163$	−3.76577	+	6.52251i	−0.294958	+	0.510882i	0.680017	+	0.733196i	$0.261972\pi$
$164$	−2.73851			−0.213842
$165$		0			0
$166$		−	13.7590i		−	1.06790i
$167$	4.87241	+	8.43926i	0.377039	+	0.653050i	0.990630	−	0.136574i	$-0.0436091\pi$
$167$	4.87241	+	8.43926i	0.377039	+	0.653050i	−0.613591	+	0.789624i	$0.710276\pi$
$168$		0			0
$169$	11.5387	−	19.9855i	0.887589	−	1.53735i
$170$	−1.11150	−	0.641724i	−0.0852481	−	0.0492180i
$171$		0			0
$172$	2.43768	+	4.22219i	0.185872	+	0.321939i
$173$	−7.13345	−	12.3555i	−0.542346	−	0.939370i	−0.998769	−	0.0496076i	$-0.984203\pi$
$173$	−7.13345	−	12.3555i	−0.542346	−	0.939370i	0.456423	−	0.889763i	$-0.349130\pi$
$174$		0			0
$175$	−0.555567	+	2.58676i	−0.0419969	+	0.195541i
$176$	−3.53173	+	2.03904i	−0.266214	+	0.153699i
$177$		0			0
$178$			14.5899i			1.09356i
$179$	−7.42444	+	4.28650i	−0.554928	+	0.320388i	−0.751107	−	0.660180i	$-0.770480\pi$
$179$	−7.42444	+	4.28650i	−0.554928	+	0.320388i	0.196179	+	0.980568i	$0.437147\pi$
$180$		0			0
$181$		−	1.70947i		−	0.127064i	−0.997980	−	0.0635319i	$-0.979764\pi$
$181$		−	1.70947i		−	0.127064i	0.997980	−	0.0635319i	$-0.0202365\pi$
$182$	11.7872	+	10.6585i	0.873722	+	0.790063i
$183$		0			0
$184$	−2.18864			−0.161349
$185$	−2.90160	+	5.02572i	−0.213330	+	0.369498i
$186$		0			0
$187$	4.53279	−	2.61701i	0.331470	−	0.191375i
$188$	−8.27225			−0.603316
$189$		0			0
$190$	−3.35672			−0.243522
$191$	8.02069	−	4.63075i	0.580357	−	0.335069i	−0.180918	−	0.983498i	$-0.557907\pi$
$191$	8.02069	−	4.63075i	0.580357	−	0.335069i	0.761275	+	0.648429i	$0.224574\pi$
$192$		0			0
$193$	12.1247	−	21.0006i	0.872756	−	1.51166i	0.0136221	−	0.999907i	$-0.495664\pi$
$193$	12.1247	−	21.0006i	0.872756	−	1.51166i	0.859134	−	0.511751i	$-0.171003\pi$
$194$	19.4824			1.39875
$195$		0			0
$196$	−5.68051	+	4.09045i	−0.405751	+	0.292175i
$197$		−	18.8947i		−	1.34619i	−0.739554	−	0.673097i	$-0.764964\pi$
$197$		−	18.8947i		−	1.34619i	0.739554	−	0.673097i	$-0.235036\pi$
$198$		0			0
$199$	2.25502	−	1.30194i	0.159854	−	0.0922919i	−0.417939	−	0.908475i	$-0.637247\pi$
$199$	2.25502	−	1.30194i	0.159854	−	0.0922919i	0.577793	+	0.816183i	$0.303914\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	7.39341	−	4.26859i	0.520198	−	0.300337i
$203$	12.7421	−	14.0913i	0.894317	−	0.989016i
$204$		0			0
$205$	−1.36925	−	2.37162i	−0.0956329	−	0.165641i
$206$	1.80624	+	3.12850i	0.125847	+	0.217973i
$207$		0			0
$208$	5.20173	+	3.00322i	0.360675	+	0.208236i
$209$	6.84450	−	11.8550i	0.473444	−	0.820029i
$210$		0			0
$211$	−3.12513	−	5.41288i	−0.215143	−	0.372638i	0.738174	−	0.674610i	$-0.235688\pi$
$211$	−3.12513	−	5.41288i	−0.215143	−	0.372638i	−0.953317	+	0.301972i	$0.902355\pi$
$212$		−	8.64512i		−	0.593749i
$213$		0			0
$214$	13.3478			0.912440
$215$	−2.43768	+	4.22219i	−0.166249	+	0.287951i
$216$		0			0
$217$	13.9185	−	15.3923i	0.944850	−	1.04490i
$218$	−9.32854	−	5.38583i	−0.631808	−	0.364775i
$219$		0			0
$220$	−3.53173	−	2.03904i	−0.238109	−	0.137472i
$221$	−6.67615	−	3.85448i	−0.449087	−	0.259280i
$222$		0			0
$223$	4.24320	+	2.44981i	0.284145	+	0.164051i	0.635299	−	0.772267i	$-0.280877\pi$
$223$	4.24320	+	2.44981i	0.284145	+	0.164051i	−0.351153	+	0.936318i	$0.614210\pi$
$224$	−1.77452	+	1.96242i	−0.118565	+	0.131120i
$225$		0			0
$226$	−1.41832	+	2.45659i	−0.0943449	+	0.163410i
$227$	−17.4808			−1.16024			−0.580121	−	0.814531i	$-0.696995\pi$
$227$	−17.4808			−1.16024			−0.580121	+	0.814531i	$0.696995\pi$
$228$		0			0
$229$			14.5924i			0.964292i	0.876091	+	0.482146i	$0.160143\pi$
$229$			14.5924i			0.964292i	−0.876091	+	0.482146i	$0.839857\pi$
$230$	−1.09432	−	1.89542i	−0.0721573	−	0.124980i
$231$		0			0
$232$	3.59029	−	6.21856i	0.235714	−	0.408269i
$233$	−3.42360	−	1.97662i	−0.224288	−	0.129493i	0.383646	−	0.923480i	$-0.374668\pi$
$233$	−3.42360	−	1.97662i	−0.224288	−	0.129493i	−0.607934	+	0.793988i	$0.708002\pi$
$234$		0			0
$235$	−4.13613	−	7.16398i	−0.269811	−	0.467327i
$236$	−0.630579	−	1.09220i	−0.0410472	−	0.0710959i
$237$		0			0
$238$	2.27750	−	2.51866i	0.147628	−	0.163261i
$239$	−16.0317	+	9.25590i	−1.03700	+	0.598714i	−0.918983	−	0.394297i	$-0.870988\pi$
$239$	−16.0317	+	9.25590i	−1.03700	+	0.598714i	−0.118021	+	0.993011i	$0.537655\pi$
$240$		0			0
$241$			21.9366i			1.41306i	0.707681	+	0.706532i	$0.249741\pi$
$241$			21.9366i			1.41306i	−0.707681	+	0.706532i	$0.750259\pi$
$242$	4.87641	−	2.81540i	0.313468	−	0.180981i
$243$		0			0
$244$			2.96707i			0.189947i
$245$	−6.38269	−	2.87424i	−0.407775	−	0.183628i
$246$		0			0
$247$	−20.1620			−1.28287
$248$	3.92178	−	6.79271i	0.249033	−	0.431338i
$249$		0			0
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−15.6773			−0.989540			−0.494770	−	0.869024i	$-0.664748\pi$
$251$	−15.6773			−0.989540			−0.494770	+	0.869024i	$0.664748\pi$
$252$		0			0
$253$	8.92547			0.561139
$254$	9.49383	−	5.48127i	0.595696	−	0.343925i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.5872			0.660411			0.330206	−	0.943909i	$-0.392882\pi$
$257$	10.5872			0.660411			0.330206	+	0.943909i	$0.392882\pi$
$258$		0			0
$259$	−11.3883	−	10.2979i	−0.707635	−	0.639879i
$260$			6.00644i			0.372504i
$261$		0			0
$262$	17.9538	−	10.3656i	1.10919	−	0.640389i
$263$			24.2649i			1.49624i	0.663564	+	0.748120i	$0.269043\pi$
$263$			24.2649i			1.49624i	−0.663564	+	0.748120i	$0.730957\pi$
$264$		0			0
$265$	7.48689	−	4.32256i	0.459916	−	0.265533i
$266$	1.86488	−	8.68305i	0.114343	−	0.532392i
$267$		0			0
$268$	−4.31098	−	7.46684i	−0.263335	−	0.456110i
$269$	9.04616	+	15.6684i	0.551554	+	0.955320i	0.998163	+	0.0605906i	$0.0192984\pi$
$269$	9.04616	+	15.6684i	0.551554	+	0.955320i	−0.446608	+	0.894730i	$0.647368\pi$
$270$		0			0
$271$	−3.07389	−	1.77471i	−0.186725	−	0.107806i	0.403723	−	0.914881i	$-0.367716\pi$
$271$	−3.07389	−	1.77471i	−0.186725	−	0.107806i	−0.590449	+	0.807075i	$0.701049\pi$
$272$	0.641724	−	1.11150i	0.0389102	−	0.0673945i
$273$		0			0
$274$	−4.83716	−	8.37821i	−0.292224	−	0.506146i
$275$		−	4.07809i		−	0.245918i
$276$		0			0
$277$	2.30895			0.138732			0.0693658	−	0.997591i	$-0.477902\pi$
$277$	2.30895			0.138732			0.0693658	+	0.997591i	$0.477902\pi$
$278$	2.63928	−	4.57137i	0.158294	−	0.274173i
$279$		0			0
$280$	−2.58676	−	0.555567i	−0.154589	−	0.0332015i
$281$	0.186637	+	0.107755i	0.0111338	+	0.00642812i	0.505557	−	0.862793i	$-0.331287\pi$
$281$	0.186637	+	0.107755i	0.0111338	+	0.00642812i	−0.494423	+	0.869222i	$0.664621\pi$
$282$		0			0
$283$	13.3787	+	7.72421i	0.795283	+	0.459157i	0.841819	−	0.539760i	$-0.181485\pi$
$283$	13.3787	+	7.72421i	0.795283	+	0.459157i	−0.0465363	+	0.998917i	$0.514818\pi$
$284$	12.2434	+	7.06874i	0.726514	+	0.419453i
$285$		0			0
$286$	−21.2131	−	12.2474i	−1.25436	−	0.724203i
$287$	6.89553	−	2.22434i	0.407030	−	0.131299i
$288$		0			0
$289$	7.67638	−	13.2959i	0.451552	−	0.782111i
$290$	7.18058			0.421658
$291$		0			0
$292$			6.95513i			0.407018i
$293$	−0.347292	−	0.601528i	−0.0202890	−	0.0351417i	0.855703	−	0.517468i	$-0.173125\pi$
$293$	−0.347292	−	0.601528i	−0.0202890	−	0.0351417i	−0.875992	+	0.482326i	$0.839792\pi$
$294$		0			0
$295$	0.630579	−	1.09220i	0.0367137	−	0.0635901i
$296$	−5.02572	−	2.90160i	−0.292114	−	0.168652i
$297$		0			0
$298$	2.18889	+	3.79127i	0.126799	+	0.219623i
$299$	−6.57297	−	11.3847i	−0.380125	−	0.658395i
$300$		0			0
$301$	−9.56751	−	8.65142i	−0.551462	−	0.498659i
$302$	4.82650	−	2.78658i	0.277734	−	0.160350i
$303$		0			0
$304$		−	3.35672i		−	0.192521i
$305$	−2.56956	+	1.48353i	−0.147132	+	0.0849469i
$306$		0			0
$307$			34.0796i			1.94502i	0.232853	+	0.972512i	$0.425194\pi$
$307$			34.0796i			1.94502i	−0.232853	+	0.972512i	$0.574806\pi$
$308$	7.23663	−	8.00292i	0.412345	−	0.456009i
$309$		0			0
$310$	7.84355			0.445484
$311$	4.24381	−	7.35049i	0.240644	−	0.416808i	−0.720254	−	0.693711i	$-0.755975\pi$
$311$	4.24381	−	7.35049i	0.240644	−	0.416808i	0.960898	+	0.276903i	$0.0893080\pi$
$312$		0			0
$313$	23.6250	−	13.6399i	1.33536	−	0.770973i	0.349248	−	0.937030i	$-0.386437\pi$
$313$	23.6250	−	13.6399i	1.33536	−	0.770973i	0.986116	+	0.166057i	$0.0531037\pi$
$314$	0.281341			0.0158770
$315$		0			0
$316$	12.1855			0.685490
$317$	−0.0390775	+	0.0225614i	−0.00219481	+	0.00126717i	−0.501097	−	0.865391i	$-0.667070\pi$
$317$	−0.0390775	+	0.0225614i	−0.00219481	+	0.00126717i	0.498902	+	0.866658i	$0.333737\pi$
$318$		0			0
$319$	−14.6415	+	25.3598i	−0.819767	+	1.41988i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	5.51097	−	1.77772i	0.307114	−	0.0990682i
$323$			4.30818i			0.239714i
$324$		0			0
$325$	−5.20173	+	3.00322i	−0.288540	+	0.166589i
$326$		−	7.53154i		−	0.417134i
$327$		0			0
$328$	2.37162	−	1.36925i	0.130951	−	0.0756044i
$329$	20.8294	−	6.71911i	1.14836	−	0.370437i
$330$		0			0
$331$	−9.23258	−	15.9913i	−0.507468	−	0.878961i	−0.999963	−	0.00864533i	$-0.997248\pi$
$331$	−9.23258	−	15.9913i	−0.507468	−	0.878961i	0.492494	−	0.870316i	$-0.336085\pi$
$332$	6.87948	+	11.9156i	0.377560	+	0.653954i
$333$		0			0
$334$	−8.43926	−	4.87241i	−0.461776	−	0.266607i
$335$	4.31098	−	7.46684i	0.235534	−	0.407957i
$336$		0			0
$337$	11.5293	+	19.9693i	0.628041	+	1.08780i	0.987944	+	0.154810i	$0.0494764\pi$
$337$	11.5293	+	19.9693i	0.628041	+	1.08780i	−0.359903	+	0.932990i	$0.617190\pi$
$338$			23.0773i			1.25524i
$339$		0			0
$340$	1.28345			0.0696048
$341$	−15.9933	+	27.7013i	−0.866088	+	1.50011i
$342$		0			0
$343$	10.9810	−	14.9137i	0.592918	−	0.805263i
$344$	−4.22219	−	2.43768i	−0.227645	−	0.131431i
$345$		0			0
$346$	12.3555	+	7.13345i	0.664235	+	0.383496i
$347$	19.3393	+	11.1655i	1.03819	+	0.599398i	0.919319	−	0.393512i	$-0.128740\pi$
$347$	19.3393	+	11.1655i	1.03819	+	0.599398i	0.118868	+	0.992910i	$0.462073\pi$
$348$		0			0
$349$	−8.01876	−	4.62963i	−0.429235	−	0.247819i	0.269786	−	0.962920i	$-0.413047\pi$
$349$	−8.01876	−	4.62963i	−0.429235	−	0.247819i	−0.699020	+	0.715102i	$0.746380\pi$
$350$	−0.812247	−	2.51799i	−0.0434164	−	0.134592i
$351$		0			0
$352$	2.03904	−	3.53173i	0.108681	−	0.188242i
$353$	−13.1868			−0.701860			−0.350930	−	0.936402i	$-0.614135\pi$
$353$	−13.1868			−0.701860			−0.350930	+	0.936402i	$0.614135\pi$
$354$		0			0
$355$			14.1375i			0.750340i
$356$	−7.29497	−	12.6353i	−0.386633	−	0.669667i
$357$		0			0
$358$	4.28650	−	7.42444i	0.226549	−	0.392394i
$359$	−9.81294	−	5.66550i	−0.517907	−	0.299014i	0.218171	−	0.975911i	$-0.429991\pi$
$359$	−9.81294	−	5.66550i	−0.517907	−	0.299014i	−0.736078	+	0.676897i	$0.763324\pi$
$360$		0			0
$361$	−3.86621	−	6.69647i	−0.203485	−	0.352446i
$362$	0.854734	+	1.48044i	0.0449238	+	0.0778104i
$363$		0			0
$364$	−15.5372	−	3.33698i	−0.814373	−	0.174905i
$365$	−6.02332	+	3.47757i	−0.315275	+	0.182024i
$366$		0			0
$367$			24.3474i			1.27092i	0.772133	+	0.635461i	$0.219190\pi$
$367$			24.3474i			1.27092i	−0.772133	+	0.635461i	$0.780810\pi$
$368$	1.89542	−	1.09432i	0.0988055	−	0.0570454i
$369$		0			0
$370$		−	5.80320i		−	0.301694i
$371$	7.02197	+	21.7683i	0.364563	+	1.13015i
$372$		0			0
$373$	−27.4626			−1.42196			−0.710979	−	0.703214i	$-0.751748\pi$
$373$	−27.4626			−1.42196			−0.710979	+	0.703214i	$0.751748\pi$
$374$	−2.61701	+	4.53279i	−0.135322	+	0.234385i
$375$		0			0
$376$	7.16398	−	4.13613i	0.369454	−	0.213304i
$377$	43.1297			2.22129
$378$		0			0
$379$	32.0033			1.64390			0.821948	−	0.569562i	$-0.192887\pi$
$379$	32.0033			1.64390			0.821948	+	0.569562i	$0.192887\pi$
$380$	2.90701	−	1.67836i	0.149126	−	0.0860981i
$381$		0			0
$382$	−4.63075	+	8.02069i	−0.236930	+	0.410374i
$383$	−14.2705			−0.729191			−0.364595	−	0.931166i	$-0.618793\pi$
$383$	−14.2705			−0.729191			−0.364595	+	0.931166i	$0.618793\pi$
$384$		0			0
$385$	10.5490	+	2.26565i	0.537629	+	0.115468i
$386$			24.2494i			1.23426i
$387$		0			0
$388$	−16.8723	+	9.74120i	−0.856559	+	0.494535i
$389$			10.7610i			0.545604i	0.962070	+	0.272802i	$0.0879504\pi$
$389$			10.7610i			0.545604i	−0.962070	+	0.272802i	$0.912050\pi$
$390$		0			0
$391$	−2.43267	+	1.40450i	−0.123025	+	0.0710288i
$392$	2.87424	−	6.38269i	0.145171	−	0.322375i
$393$		0			0
$394$	9.44736	+	16.3633i	0.475951	+	0.824372i
$395$	6.09277	+	10.5530i	0.306560	+	0.530978i
$396$		0			0
$397$	19.3500	+	11.1717i	0.971150	+	0.560694i	0.899587	−	0.436742i	$-0.143868\pi$
$397$	19.3500	+	11.1717i	0.971150	+	0.560694i	0.0715634	+	0.997436i	$0.477201\pi$
$398$	−1.30194	+	2.25502i	−0.0652602	+	0.113034i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	18.9839i		−	0.948009i	−0.880522	−	0.474005i	$-0.842808\pi$
$401$		−	18.9839i		−	0.948009i	0.880522	−	0.474005i	$-0.157192\pi$
$402$		0			0
$403$	47.1118			2.34681
$404$	−4.26859	+	7.39341i	−0.212370	+	0.367836i
$405$		0			0
$406$	−3.98929	+	18.5745i	−0.197985	+	0.921835i
$407$	20.4953	+	11.8330i	1.01592	+	0.586539i
$408$		0			0
$409$	22.5328	+	13.0093i	1.11418	+	0.643270i	0.939908	−	0.341428i	$-0.110910\pi$
$409$	22.5328	+	13.0093i	1.11418	+	0.643270i	0.174269	+	0.984698i	$0.444244\pi$
$410$	2.37162	+	1.36925i	0.117126	+	0.0676226i
$411$		0			0
$412$	−3.12850	−	1.80624i	−0.154130	−	0.0889869i
$413$	2.47492	+	2.23795i	0.121783	+	0.110122i
$414$		0			0
$415$	−6.87948	+	11.9156i	−0.337700	+	0.584914i
$416$	−6.00644			−0.294490
$417$		0			0
$418$			13.6890i			0.669551i
$419$	−3.75114	−	6.49717i	−0.183255	−	0.317407i	0.759732	−	0.650236i	$-0.225330\pi$
$419$	−3.75114	−	6.49717i	−0.183255	−	0.317407i	−0.942987	+	0.332829i	$0.891997\pi$
$420$		0			0
$421$	−7.94926	+	13.7685i	−0.387423	+	0.671037i	−0.992102	−	0.125433i	$-0.959968\pi$
$421$	−7.94926	+	13.7685i	−0.387423	+	0.671037i	0.604679	+	0.796469i	$0.293301\pi$
$422$	5.41288	+	3.12513i	0.263495	+	0.152129i
$423$		0			0
$424$	4.32256	+	7.48689i	0.209922	+	0.363596i
$425$	0.641724	+	1.11150i	0.0311282	+	0.0539156i
$426$		0			0
$427$	−2.40999	−	7.47104i	−0.116628	−	0.361549i
$428$	−11.5596	+	6.67392i	−0.558753	+	0.322596i
$429$		0			0
$430$		−	4.87537i		−	0.235111i
$431$	19.4232	−	11.2140i	0.935581	−	0.540158i	0.0470087	−	0.998894i	$-0.485031\pi$
$431$	19.4232	−	11.2140i	0.935581	−	0.540158i	0.888572	+	0.458737i	$0.151698\pi$
$432$		0			0
$433$		−	1.97195i		−	0.0947659i	−0.998877	−	0.0473830i	$-0.984912\pi$
$433$		−	1.97195i		−	0.0947659i	0.998877	−	0.0473830i	$-0.0150881\pi$
$434$	−4.35762	+	20.2894i	−0.209172	+	0.973923i
$435$		0			0
$436$	10.7717			0.515869
$437$	−3.67333	+	6.36239i	−0.175719	+	0.304355i
$438$		0			0
$439$	9.15130	−	5.28351i	0.436768	−	0.252168i	−0.265458	−	0.964122i	$-0.585523\pi$
$439$	9.15130	−	5.28351i	0.436768	−	0.252168i	0.702226	+	0.711954i	$0.252190\pi$
$440$	4.07809			0.194415
$441$		0			0
$442$	7.70896			0.366678
$443$	5.85561	−	3.38074i	0.278208	−	0.160624i	−0.354404	−	0.935093i	$-0.615316\pi$
$443$	5.85561	−	3.38074i	0.278208	−	0.160624i	0.632612	+	0.774469i	$0.281983\pi$
$444$		0			0
$445$	7.29497	−	12.6353i	0.345815	−	0.598969i
$446$	−4.89962			−0.232004
$447$		0			0
$448$	0.555567	−	2.58676i	0.0262481	−	0.122213i
$449$		−	3.97534i		−	0.187608i	−0.995591	−	0.0938039i	$-0.970097\pi$
$449$		−	3.97534i		−	0.187608i	0.995591	−	0.0938039i	$-0.0299027\pi$
$450$		0			0
$451$	−9.67166	+	5.58394i	−0.455421	+	0.262937i
$452$		−	2.83663i		−	0.133424i
$453$		0			0
$454$	15.1388	−	8.74040i	0.710500	−	0.410207i
$455$	−4.87871	−	15.1241i	−0.228717	−	0.709030i
$456$		0			0
$457$	3.26014	+	5.64673i	0.152503	+	0.264143i	0.932147	−	0.362080i	$-0.117933\pi$
$457$	3.26014	+	5.64673i	0.152503	+	0.264143i	−0.779644	+	0.626223i	$0.784600\pi$
$458$	−7.29619	−	12.6374i	−0.340929	−	0.590506i
$459$		0			0
$460$	1.89542	+	1.09432i	0.0883743	+	0.0510229i
$461$	−4.69303	+	8.12857i	−0.218576	+	0.378585i	−0.954373	−	0.298617i	$-0.903475\pi$
$461$	−4.69303	+	8.12857i	−0.218576	+	0.378585i	0.735797	+	0.677203i	$0.236808\pi$
$462$		0			0
$463$	16.8709	+	29.2212i	0.784056	+	1.35803i	0.929561	+	0.368668i	$0.120186\pi$
$463$	16.8709	+	29.2212i	0.784056	+	1.35803i	−0.145505	+	0.989357i	$0.546481\pi$
$464$			7.18058i			0.333350i
$465$		0			0
$466$	3.95324			0.183130
$467$	−17.9147	+	31.0293i	−0.828996	+	1.43586i	0.0698312	+	0.997559i	$0.477754\pi$
$467$	−17.9147	+	31.0293i	−0.828996	+	1.43586i	−0.898827	+	0.438304i	$0.855579\pi$
$468$		0			0
$469$	16.9199	+	15.2998i	0.781289	+	0.706480i
$470$	7.16398	+	4.13613i	0.330450	+	0.190785i
$471$		0			0
$472$	1.09220	+	0.630579i	0.0502724	+	0.0290248i
$473$	17.2185	+	9.94108i	0.791706	+	0.457092i
$474$		0			0
$475$	2.90701	+	1.67836i	0.133383	+	0.0770085i
$476$	−0.713041	+	3.31998i	−0.0326822	+	0.152171i
$477$		0			0
$478$	9.25590	−	16.0317i	0.423355	−	0.733272i
$479$	13.8779			0.634096			0.317048	−	0.948409i	$-0.397308\pi$
$479$	13.8779			0.634096			0.317048	+	0.948409i	$0.397308\pi$
$480$		0			0
$481$		−	34.8566i		−	1.58932i
$482$	−10.9683	−	18.9977i	−0.499593	−	0.865321i
$483$		0			0
$484$	−2.81540	+	4.87641i	−0.127973	+	0.221655i
$485$	−16.8723	−	9.74120i	−0.766130	−	0.442325i
$486$		0			0
$487$	13.8002	+	23.9026i	0.625345	+	1.08313i	0.988474	+	0.151390i	$0.0483750\pi$
$487$	13.8002	+	23.9026i	0.625345	+	1.08313i	−0.363129	+	0.931739i	$0.618292\pi$
$488$	−1.48353	−	2.56956i	−0.0671564	−	0.116318i
$489$		0			0
$490$	6.96469	−	0.702180i	0.314633	−	0.0317213i
$491$	18.1949	−	10.5048i	0.821122	−	0.474075i	−0.0296811	−	0.999559i	$-0.509449\pi$
$491$	18.1949	−	10.5048i	0.821122	−	0.474075i	0.850803	+	0.525484i	$0.176116\pi$
$492$		0			0
$493$		−	9.21590i		−	0.415063i
$494$	17.4608	−	10.0810i	0.785597	−	0.453565i
$495$		0			0
$496$			7.84355i			0.352186i
$497$	−36.5703	−	7.85432i	−1.64040	−	0.352314i
$498$		0			0
$499$	0.395326			0.0176972			0.00884862	−	0.999961i	$-0.497183\pi$
$499$	0.395326			0.0176972			0.00884862	+	0.999961i	$0.497183\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	13.5769	−	7.83863i	0.605967	−	0.349855i
$503$	10.3934			0.463418			0.231709	−	0.972785i	$-0.425568\pi$
$503$	10.3934			0.463418			0.231709	+	0.972785i	$0.425568\pi$
$504$		0			0
$505$	−8.53717			−0.379899
$506$	−7.72968	+	4.46273i	−0.343626	+	0.198393i
$507$		0			0
$508$	−5.48127	+	9.49383i	−0.243192	+	0.421221i
$509$	40.5347			1.79667			0.898334	−	0.439313i	$-0.144778\pi$
$509$	40.5347			1.79667			0.898334	+	0.439313i	$0.144778\pi$
$510$		0			0
$511$	−5.64928	−	17.5129i	−0.249910	−	0.774727i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.16878	+	5.29360i	−0.404417	+	0.233491i
$515$		−	3.61248i		−	0.159185i
$516$		0			0
$517$	−29.2153	+	16.8675i	−1.28489	+	0.741831i
$518$	15.0115	+	3.22407i	0.659568	+	0.141657i
$519$		0			0
$520$	−3.00322	−	5.20173i	−0.131700	−	0.228111i
$521$	−4.80694	−	8.32586i	−0.210596	−	0.364763i	0.741305	−	0.671168i	$-0.234207\pi$
$521$	−4.80694	−	8.32586i	−0.210596	−	0.364763i	−0.951901	+	0.306405i	$0.900874\pi$
$522$		0			0
$523$	−14.2342	−	8.21809i	−0.622416	−	0.359352i	0.155393	−	0.987853i	$-0.450336\pi$
$523$	−14.2342	−	8.21809i	−0.622416	−	0.359352i	−0.777809	+	0.628501i	$0.783669\pi$
$524$	−10.3656	+	17.9538i	−0.452824	+	0.784313i
$525$		0			0
$526$	−12.1325	−	21.0140i	−0.529001	−	0.916256i
$527$		−	10.0668i		−	0.438516i
$528$		0			0
$529$	18.2099			0.791733
$530$	−4.32256	+	7.48689i	−0.187760	+	0.325210i
$531$		0			0
$532$	2.72649	+	8.45218i	0.118208	+	0.366449i
$533$	14.2450	+	8.22434i	0.617019	+	0.356236i
$534$		0			0
$535$	−11.5596	−	6.67392i	−0.499764	−	0.288539i
$536$	7.46684	+	4.31098i	0.322518	+	0.186206i
$537$		0			0
$538$	−15.6684	−	9.04616i	−0.675513	−	0.390008i
$539$	−11.7214	+	26.0292i	−0.504877	+	1.12116i
$540$		0			0
$541$	16.1578	−	27.9861i	0.694678	−	1.20322i	−0.275612	−	0.961269i	$-0.588880\pi$
$541$	16.1578	−	27.9861i	0.694678	−	1.20322i	0.970289	−	0.241948i	$-0.0777863\pi$
$542$	3.54942			0.152461
$543$		0			0
$544$			1.28345i			0.0550274i
$545$	5.38583	+	9.32854i	0.230704	+	0.399591i
$546$		0			0
$547$	−3.41985	+	5.92335i	−0.146222	+	0.253264i	−0.929828	−	0.367994i	$-0.880045\pi$
$547$	−3.41985	+	5.92335i	−0.146222	+	0.253264i	0.783606	+	0.621258i	$0.213378\pi$
$548$	8.37821	+	4.83716i	0.357899	+	0.206633i
$549$		0			0
$550$	2.03904	+	3.53173i	0.0869451	+	0.150593i
$551$	−12.0516	−	20.8740i	−0.513416	−	0.889262i
$552$		0			0
$553$	−30.6830	+	9.89766i	−1.30477	+	0.420891i
$554$	−1.99961	+	1.15448i	−0.0849554	+	0.0490490i
$555$		0			0
$556$			5.27856i			0.223861i
$557$	5.91206	−	3.41333i	0.250502	−	0.144627i	−0.369492	−	0.929234i	$-0.620468\pi$
$557$	5.91206	−	3.41333i	0.250502	−	0.144627i	0.619994	+	0.784607i	$0.287135\pi$
$558$		0			0
$559$		−	29.2836i		−	1.23856i
$560$	2.51799	−	0.812247i	0.106404	−	0.0343237i
$561$		0			0
$562$	−0.215510			−0.00909074
$563$	5.41857	−	9.38524i	0.228366	−	0.395541i	−0.728958	−	0.684558i	$-0.759995\pi$
$563$	5.41857	−	9.38524i	0.228366	−	0.395541i	0.957324	+	0.289017i	$0.0933285\pi$
$564$		0			0
$565$	2.45659	−	1.41832i	0.103350	−	0.0596690i
$566$	−15.4484			−0.649346
$567$		0			0
$568$	−14.1375			−0.593196
$569$	12.0811	−	6.97501i	0.506465	−	0.292408i	−0.224914	−	0.974379i	$-0.572210\pi$
$569$	12.0811	−	6.97501i	0.506465	−	0.292408i	0.731379	+	0.681971i	$0.238877\pi$
$570$		0			0
$571$	13.6060	−	23.5662i	0.569393	−	0.986217i	−0.427234	−	0.904141i	$-0.640512\pi$
$571$	13.6060	−	23.5662i	0.569393	−	0.986217i	0.996626	−	0.0820756i	$-0.0261549\pi$
$572$	24.4948			1.02418
$573$		0			0
$574$	−4.85953	+	5.37410i	−0.202833	+	0.224311i
$575$			2.18864i			0.0912726i
$576$		0			0
$577$	13.2438	−	7.64631i	0.551346	−	0.318320i	−0.198318	−	0.980138i	$-0.563548\pi$
$577$	13.2438	−	7.64631i	0.551346	−	0.318320i	0.749665	+	0.661818i	$0.230215\pi$
$578$			15.3528i			0.638591i
$579$		0			0
$580$	−6.21856	+	3.59029i	−0.258212	+	0.149079i
$581$	−27.0008	−	24.4155i	−1.12018	−	1.01293i
$582$		0			0
$583$	−17.6278	−	30.5322i	−0.730068	−	1.26451i
$584$	−3.47757	−	6.02332i	−0.143903	−	0.249247i
$585$		0			0
$586$	0.601528	+	0.347292i	0.0248489	+	0.0143465i
$587$	7.16231	−	12.4055i	0.295620	−	0.512029i	−0.679509	−	0.733667i	$-0.737807\pi$
$587$	7.16231	−	12.4055i	0.295620	−	0.512029i	0.975129	+	0.221638i	$0.0711404\pi$
$588$		0			0
$589$	−13.1643	−	22.8013i	−0.542426	−	0.939509i
$590$			1.26116i			0.0519211i
$591$		0			0
$592$	5.80320			0.238510
$593$	−0.594674	+	1.03001i	−0.0244203	+	0.0422973i	−0.877977	−	0.478702i	$-0.841107\pi$
$593$	−0.594674	+	1.03001i	−0.0244203	+	0.0422973i	0.853557	+	0.521000i	$0.174441\pi$
$594$		0			0
$595$	−3.23171	+	1.04248i	−0.132487	+	0.0427374i
$596$	−3.79127	−	2.18889i	−0.155297	−	0.0896606i
$597$		0			0
$598$	11.3847	+	6.57297i	0.465556	+	0.268789i
$599$	39.8059	+	22.9819i	1.62642	+	0.939016i	0.985148	+	0.171706i	$0.0549280\pi$
$599$	39.8059	+	22.9819i	1.62642	+	0.939016i	0.641276	+	0.767310i	$0.278405\pi$
$600$		0			0
$601$	−14.0543	−	8.11427i	−0.573288	−	0.330988i	0.185173	−	0.982706i	$-0.440715\pi$
$601$	−14.0543	−	8.11427i	−0.573288	−	0.330988i	−0.758462	+	0.651718i	$0.774049\pi$
$602$	12.6114	+	2.70859i	0.514003	+	0.110394i
$603$		0			0
$604$	−2.78658	+	4.82650i	−0.113384	+	0.196387i
$605$	−5.63079			−0.228924
$606$		0			0
$607$			6.95304i			0.282215i	0.989994	+	0.141108i	$0.0450664\pi$
$607$			6.95304i			0.282215i	−0.989994	+	0.141108i	$0.954934\pi$
$608$	1.67836	+	2.90701i	0.0680665	+	0.117895i
$609$		0			0
$610$	1.48353	−	2.56956i	0.0600665	−	0.104038i
$611$	43.0300	+	24.8434i	1.74081	+	1.00506i
$612$		0			0
$613$	−20.0114	−	34.6608i	−0.808253	−	1.39993i	−0.914073	−	0.405549i	$-0.867080\pi$
$613$	−20.0114	−	34.6608i	−0.808253	−	1.39993i	0.105821	−	0.994385i	$-0.466253\pi$
$614$	−17.0398	−	29.5138i	−0.687670	−	1.19108i
$615$		0			0
$616$	−2.26565	+	10.5490i	−0.0912856	+	0.425033i
$617$	−7.94775	+	4.58864i	−0.319964	+	0.184732i	−0.651377	−	0.758754i	$-0.725808\pi$
$617$	−7.94775	+	4.58864i	−0.319964	+	0.184732i	0.331412	+	0.943486i	$0.392475\pi$
$618$		0			0
$619$			38.3260i			1.54045i	0.637770	+	0.770227i	$0.279857\pi$
$619$			38.3260i			1.54045i	−0.637770	+	0.770227i	$0.720143\pi$
$620$	−6.79271	+	3.92178i	−0.272802	+	0.157502i
$621$		0			0
$622$			8.48761i			0.340322i
$623$	28.6316	+	25.8901i	1.14710	+	1.03726i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−13.6399	+	23.6250i	−0.545160	+	0.944245i
$627$		0			0
$628$	−0.243649	+	0.140671i	−0.00972264	+	0.00561337i
$629$	−7.44811			−0.296976
$630$		0			0
$631$	−21.4220			−0.852797			−0.426399	−	0.904535i	$-0.640218\pi$
$631$	−21.4220			−0.852797			−0.426399	+	0.904535i	$0.640218\pi$
$632$	−10.5530	+	6.09277i	−0.419775	+	0.242357i
$633$		0			0
$634$	0.0225614	−	0.0390775i	0.000896027	−	0.00155196i
$635$	−10.9625			−0.435035
$636$		0			0
$637$	41.8330	−	4.21760i	1.65748	−	0.167108i
$638$		−	29.2830i		−	1.15933i
$639$		0			0
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$			23.8349i			0.941421i	0.882288	+	0.470710i	$0.156002\pi$
$641$			23.8349i			0.941421i	−0.882288	+	0.470710i	$0.843998\pi$
$642$		0			0
$643$	10.6419	−	6.14411i	0.419676	−	0.242300i	−0.275263	−	0.961369i	$-0.588765\pi$
$643$	10.6419	−	6.14411i	0.419676	−	0.242300i	0.694939	+	0.719069i	$0.255432\pi$
$644$	−3.88378	+	4.29503i	−0.153042	+	0.169248i
$645$		0			0
$646$	−2.15409	−	3.73099i	−0.0847516	−	0.146794i
$647$	−8.50175	−	14.7255i	−0.334238	−	0.578917i	0.649100	−	0.760703i	$-0.275146\pi$
$647$	−8.50175	−	14.7255i	−0.334238	−	0.578917i	−0.983338	+	0.181786i	$0.941812\pi$
$648$		0			0
$649$	−4.45407	−	2.57156i	−0.174837	−	0.100942i
$650$	3.00322	−	5.20173i	0.117796	−	0.204029i
$651$		0			0
$652$	3.76577	+	6.52251i	0.147479	+	0.255441i
$653$			11.0926i			0.434087i	0.976162	+	0.217044i	$0.0696414\pi$
$653$			11.0926i			0.434087i	−0.976162	+	0.217044i	$0.930359\pi$
$654$		0			0
$655$	−20.7312			−0.810035
$656$	−1.36925	+	2.37162i	−0.0534604	+	0.0925961i
$657$		0			0
$658$	−14.6793	+	16.2336i	−0.572257	+	0.632853i
$659$	39.7712	+	22.9619i	1.54927	+	0.894470i	0.998198	+	0.0600103i	$0.0191133\pi$
$659$	39.7712	+	22.9619i	1.54927	+	0.894470i	0.551069	+	0.834459i	$0.314220\pi$
$660$		0			0
$661$	−18.0299	−	10.4096i	−0.701281	−	0.404885i	0.106543	−	0.994308i	$-0.466022\pi$
$661$	−18.0299	−	10.4096i	−0.701281	−	0.404885i	−0.807824	+	0.589423i	$0.799355\pi$
$662$	15.9913	+	9.23258i	0.621519	+	0.358834i
$663$		0			0
$664$	−11.9156	−	6.87948i	−0.462415	−	0.266975i
$665$	−5.95656	+	6.58730i	−0.230986	+	0.255444i
$666$		0			0
$667$	7.85785	−	13.6102i	0.304257	−	0.526989i
$668$	9.74482			0.377039
$669$		0			0
$670$			8.62197i			0.333096i
$671$	6.04998	+	10.4789i	0.233557	+	0.404532i
$672$		0			0
$673$	14.6307	−	25.3410i	0.563970	−	0.976825i	−0.433175	−	0.901310i	$-0.642607\pi$
$673$	14.6307	−	25.3410i	0.563970	−	0.976825i	0.997145	−	0.0755149i	$-0.0240600\pi$
$674$	−19.9693	−	11.5293i	−0.769190	−	0.444092i
$675$		0			0
$676$	−11.5387	−	19.9855i	−0.443795	−	0.768675i
$677$	−12.3058	−	21.3142i	−0.472949	−	0.819172i	0.526571	−	0.850131i	$-0.323477\pi$
$677$	−12.3058	−	21.3142i	−0.472949	−	0.819172i	−0.999521	+	0.0309588i	$0.990144\pi$
$678$		0			0
$679$	34.5718	−	38.2326i	1.32675	−	1.46723i
$680$	−1.11150	+	0.641724i	−0.0426240	+	0.0246090i
$681$		0			0
$682$		−	31.9867i		−	1.22483i
$683$	4.84830	−	2.79917i	0.185515	−	0.107107i	−0.404366	−	0.914597i	$-0.632508\pi$
$683$	4.84830	−	2.79917i	0.185515	−	0.107107i	0.589881	+	0.807490i	$0.299175\pi$
$684$		0			0
$685$			9.67432i			0.369637i
$686$	−2.05298	+	18.4061i	−0.0783831	+	0.702749i
$687$		0			0
$688$	4.87537			0.185872
$689$	−25.9632	+	44.9696i	−0.989119	+	1.71320i
$690$		0			0
$691$	−28.6519	+	16.5422i	−1.08997	+	0.629294i	−0.933568	−	0.358399i	$-0.883323\pi$
$691$	−28.6519	+	16.5422i	−1.08997	+	0.629294i	−0.156401	+	0.987694i	$0.549989\pi$
$692$	−14.2669			−0.542346
$693$		0			0
$694$	−22.3311			−0.847677
$695$	−4.57137	+	2.63928i	−0.173402	+	0.100114i
$696$		0			0
$697$	1.75737	−	3.04385i	0.0665650	−	0.115294i
$698$	9.25927			0.350469
$699$		0			0
$700$	1.96242	+	1.77452i	0.0741725	+	0.0670704i
$701$			3.12417i			0.117998i	0.998258	+	0.0589992i	$0.0187909\pi$
$701$			3.12417i			0.117998i	−0.998258	+	0.0589992i	$0.981209\pi$
$702$		0			0
$703$	−16.8699	+	9.73987i	−0.636262	+	0.367346i
$704$			4.07809i			0.153699i
$705$		0			0
$706$	11.4201	−	6.59338i	0.429800	−	0.248145i
$707$	4.74297	−	22.0836i	0.178378	−	0.830541i
$708$		0			0
$709$	21.7411	+	37.6567i	0.816504	+	1.41423i	0.908243	+	0.418443i	$0.137424\pi$
$709$	21.7411	+	37.6567i	0.816504	+	1.41423i	−0.0917396	+	0.995783i	$0.529243\pi$
$710$	−7.06874	−	12.2434i	−0.265285	−	0.459487i
$711$		0			0
$712$	12.6353	+	7.29497i	0.473526	+	0.273391i
$713$	8.58336	−	14.8668i	0.321449	−	0.556766i
$714$		0			0
$715$	12.2474	+	21.2131i	0.458026	+	0.793325i
$716$			8.57300i			0.320388i
$717$		0			0
$718$	11.3310			0.422869
$719$	2.21764	−	3.84106i	0.0827039	−	0.143247i	−0.821707	−	0.569911i	$-0.806978\pi$
$719$	2.21764	−	3.84106i	0.0827039	−	0.143247i	0.904411	+	0.426663i	$0.140311\pi$
$720$		0			0
$721$	9.34462	+	2.00697i	0.348012	+	0.0747435i
$722$	6.69647	+	3.86621i	0.249217	+	0.143885i
$723$		0			0
$724$	−1.48044	−	0.854734i	−0.0550202	−	0.0317659i
$725$	−6.21856	−	3.59029i	−0.230952	−	0.133340i
$726$		0			0
$727$	36.5068	+	21.0772i	1.35396	+	0.781711i	0.988802	−	0.149233i	$-0.0476803\pi$
$727$	36.5068	+	21.0772i	1.35396	+	0.781711i	0.365162	+	0.930944i	$0.381014\pi$
$728$	15.1241	−	4.87871i	0.560538	−	0.180817i
$729$		0			0
$730$	3.47757	−	6.02332i	0.128711	−	0.222933i
$731$	−6.25728			−0.231434
$732$		0			0
$733$			46.2254i			1.70738i	0.520785	+	0.853688i	$0.325639\pi$
$733$			46.2254i			1.70738i	−0.520785	+	0.853688i	$0.674361\pi$
$734$	−12.1737	−	21.0854i	−0.449339	−	0.778278i
$735$		0			0
$736$	−1.09432	+	1.89542i	−0.0403372	+	0.0698660i
$737$	−30.4504	−	17.5806i	−1.12166	−	0.647589i
$738$		0			0
$739$	−14.2820	−	24.7371i	−0.525371	−	0.909969i	−0.999563	−	0.0295478i	$-0.990593\pi$
$739$	−14.2820	−	24.7371i	−0.525371	−	0.909969i	0.474193	−	0.880421i	$-0.342740\pi$
$740$	2.90160	+	5.02572i	0.106665	+	0.184749i
$741$		0			0
$742$	−16.9654	−	15.3409i	−0.622818	−	0.563183i
$743$	−3.36454	+	1.94252i	−0.123433	+	0.0712640i	−0.560445	−	0.828192i	$-0.689370\pi$
$743$	−3.36454	+	1.94252i	−0.123433	+	0.0712640i	0.437012	+	0.899456i	$0.356037\pi$
$744$		0			0
$745$		−	4.37779i		−	0.160390i
$746$	23.7833	−	13.7313i	0.870767	−	0.502738i
$747$		0			0
$748$		−	5.23401i		−	0.191375i
$749$	23.6860	−	26.1941i	0.865467	−	0.957111i
$750$		0			0
$751$	21.2885			0.776829			0.388415	−	0.921485i	$-0.373023\pi$
$751$	21.2885			0.776829			0.388415	+	0.921485i	$0.373023\pi$
$752$	−4.13613	+	7.16398i	−0.150829	+	0.261244i
$753$		0			0
$754$	−37.3514	+	21.5649i	−1.36026	+	0.785346i
$755$	−5.57316			−0.202828
$756$		0			0
$757$	−42.1251			−1.53106			−0.765531	−	0.643399i	$-0.777524\pi$
$757$	−42.1251			−1.53106			−0.765531	+	0.643399i	$0.777524\pi$
$758$	−27.7156	+	16.0016i	−1.00668	+	0.581205i
$759$		0			0
$760$	−1.67836	+	2.90701i	−0.0608806	+	0.105448i
$761$	−48.8379			−1.77037			−0.885187	−	0.465236i	$-0.845970\pi$
$761$	−48.8379			−1.77037			−0.885187	+	0.465236i	$0.845970\pi$
$762$		0			0
$763$	−27.1229	+	8.74925i	−0.981915	+	0.316744i
$764$		−	9.26150i		−	0.335069i
$765$		0			0
$766$	12.3587	−	7.13527i	0.446536	−	0.257808i
$767$			7.57507i			0.273520i
$768$		0			0
$769$	−41.1583	+	23.7627i	−1.48420	+	0.856906i	−0.999839	−	0.0179596i	$-0.994283\pi$
$769$	−41.1583	+	23.7627i	−1.48420	+	0.856906i	−0.484366	+	0.874866i	$0.660950\pi$
$770$	−10.2686	+	3.31241i	−0.370053	+	0.119371i
$771$		0			0
$772$	−12.1247	−	21.0006i	−0.436378	−	0.755829i
$773$	−2.07497	−	3.59395i	−0.0746314	−	0.129265i	0.826295	−	0.563238i	$-0.190445\pi$
$773$	−2.07497	−	3.59395i	−0.0746314	−	0.129265i	−0.900926	+	0.433973i	$0.857111\pi$
$774$		0			0
$775$	−6.79271	−	3.92178i	−0.244001	−	0.140874i
$776$	9.74120	−	16.8723i	0.349689	−	0.605679i
$777$		0			0
$778$	−5.38049	−	9.31929i	−0.192900	−	0.334113i
$779$		−	9.19241i		−	0.329352i
$780$		0			0
$781$	57.6539			2.06302
$782$	1.40450	−	2.43267i	0.0502249	−	0.0869922i
$783$		0			0
$784$	0.702180	+	6.96469i	0.0250779	+	0.248739i
$785$	−0.243649	−	0.140671i	−0.00869619	−	0.00502075i
$786$		0			0
$787$	23.6630	+	13.6618i	0.843495	+	0.486992i	0.858451	−	0.512896i	$-0.171427\pi$
$787$	23.6630	+	13.6618i	0.843495	+	0.486992i	−0.0149557	+	0.999888i	$0.504761\pi$
$788$	−16.3633	−	9.44736i	−0.582919	−	0.336548i
$789$		0			0
$790$	−10.5530	−	6.09277i	−0.375458	−	0.216771i
$791$	2.30404	+	7.14260i	0.0819224	+	0.253961i
$792$		0			0
$793$	8.91076	−	15.4339i	0.316430	−	0.548073i
$794$	−22.3435			−0.792941
$795$		0			0
$796$		−	2.60387i		−	0.0922919i
$797$	−14.7404	−	25.5311i	−0.522132	−	0.904359i	−0.999668	−	0.0257473i	$-0.991803\pi$
$797$	−14.7404	−	25.5311i	−0.522132	−	0.904359i	0.477536	−	0.878612i	$-0.341530\pi$
$798$		0			0
$799$	5.30850	−	9.19460i	0.187801	−	0.325282i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	9.49194	+	16.4405i	0.335172	+	0.580535i
$803$	14.1818	+	24.5636i	0.500466	+	0.866832i
$804$		0			0
$805$	−5.66149	−	1.21594i	−0.199541	−	0.0428561i
$806$	−40.8000	+	23.5559i	−1.43712	+	0.829721i
$807$		0			0
$808$		−	8.53717i		−	0.300337i
$809$	−1.53294	+	0.885046i	−0.0538955	+	0.0311166i	−0.526706	−	0.850048i	$-0.676573\pi$
$809$	−1.53294	+	0.885046i	−0.0538955	+	0.0311166i	0.472810	+	0.881164i	$0.343240\pi$
$810$		0			0
$811$		−	21.7821i		−	0.764872i	−0.923982	−	0.382436i	$-0.875085\pi$
$811$		−	21.7821i		−	0.764872i	0.923982	−	0.382436i	$-0.124915\pi$
$812$	−5.83240	−	18.0806i	−0.204677	−	0.634504i
$813$		0			0
$814$	−23.6660			−0.829491
$815$	−3.76577	+	6.52251i	−0.131909	+	0.228473i
$816$		0			0
$817$	−14.1727	+	8.18263i	−0.495841	+	0.286274i
$818$	−26.0187			−0.909722
$819$		0			0
$820$	−2.73851			−0.0956329
$821$	21.5112	−	12.4195i	0.750746	−	0.433443i	−0.0752177	−	0.997167i	$-0.523965\pi$
$821$	21.5112	−	12.4195i	0.750746	−	0.433443i	0.825963	+	0.563724i	$0.190632\pi$
$822$		0			0
$823$	−22.3540	+	38.7182i	−0.779210	+	1.34963i	0.153187	+	0.988197i	$0.451046\pi$
$823$	−22.3540	+	38.7182i	−0.779210	+	1.34963i	−0.932398	+	0.361434i	$0.882287\pi$
$824$	3.61248			0.125847
$825$		0			0
$826$	−3.26232	−	0.700658i	−0.113511	−	0.0243790i
$827$		−	43.9883i		−	1.52962i	−0.644255	−	0.764811i	$-0.722832\pi$
$827$		−	43.9883i		−	1.52962i	0.644255	−	0.764811i	$-0.277168\pi$
$828$		0			0
$829$	23.3072	−	13.4564i	0.809492	−	0.467360i	−0.0372876	−	0.999305i	$-0.511872\pi$
$829$	23.3072	−	13.4564i	0.809492	−	0.467360i	0.846779	+	0.531944i	$0.178538\pi$
$830$		−	13.7590i		−	0.477580i
$831$		0			0
$832$	5.20173	−	3.00322i	0.180338	−	0.104118i
$833$	−0.901212	−	8.93882i	−0.0312252	−	0.309712i
$834$		0			0
$835$	4.87241	+	8.43926i	0.168617	+	0.292053i
$836$	−6.84450	−	11.8550i	−0.236722	−	0.410015i
$837$		0			0
$838$	6.49717	+	3.75114i	0.224441	+	0.129581i
$839$	−7.52241	+	13.0292i	−0.259702	+	0.449818i	−0.966162	−	0.257935i	$-0.916958\pi$
$839$	−7.52241	+	13.0292i	−0.259702	+	0.449818i	0.706460	+	0.707753i	$0.250291\pi$
$840$		0			0
$841$	11.2803	+	19.5381i	0.388977	+	0.673728i
$842$		−	15.8985i		−	0.547899i
$843$		0			0
$844$	−6.25025			−0.215143
$845$	11.5387	−	19.9855i	0.396942	−	0.687524i
$846$		0			0
$847$	3.12828	−	14.5655i	0.107489	−	0.500478i
$848$	−7.48689	−	4.32256i	−0.257101	−	0.148437i
$849$		0			0
$850$	−1.11150	−	0.641724i	−0.0381241	−	0.0220110i
$851$	−10.9995	−	6.35056i	−0.377058	−	0.217694i
$852$		0			0
$853$	11.0905	+	6.40312i	0.379732	+	0.219239i	0.677702	−	0.735337i	$-0.262976\pi$
$853$	11.0905	+	6.40312i	0.379732	+	0.219239i	−0.297970	+	0.954575i	$0.596309\pi$
$854$	5.82263	+	5.26511i	0.199246	+	0.180168i
$855$		0			0
$856$	6.67392	−	11.5596i	0.228110	−	0.395098i
$857$	42.5215			1.45251			0.726254	−	0.687426i	$-0.241260\pi$
$857$	42.5215			1.45251			0.726254	+	0.687426i	$0.241260\pi$
$858$		0			0
$859$			7.34964i			0.250767i	0.992108	+	0.125383i	$0.0400161\pi$
$859$			7.34964i			0.250767i	−0.992108	+	0.125383i	$0.959984\pi$
$860$	2.43768	+	4.22219i	0.0831243	+	0.143976i
$861$		0			0
$862$	−11.2140	+	19.4232i	−0.381949	+	0.661556i
$863$	−3.64790	−	2.10612i	−0.124176	−	0.0716930i	0.436625	−	0.899643i	$-0.356174\pi$
$863$	−3.64790	−	2.10612i	−0.124176	−	0.0716930i	−0.560801	+	0.827950i	$0.689507\pi$
$864$		0			0
$865$	−7.13345	−	12.3555i	−0.242544	−	0.420099i
$866$	0.985975	+	1.70776i	0.0335048	+	0.0580320i
$867$		0			0
$868$	−6.37090	−	19.7500i	−0.216242	−	0.670357i
$869$	43.0360	−	24.8468i	1.45990	−	0.842871i
$870$		0			0
$871$			51.7873i			1.75475i
$872$	−9.32854	+	5.38583i	−0.315904	+	0.182387i
$873$		0			0
$874$		−	7.34666i		−	0.248504i
$875$	−0.555567	+	2.58676i	−0.0187816	+	0.0874486i
$876$		0			0
$877$	−26.7236			−0.902390			−0.451195	−	0.892425i	$-0.649002\pi$
$877$	−26.7236			−0.902390			−0.451195	+	0.892425i	$0.649002\pi$
$878$	−5.28351	+	9.15130i	−0.178310	+	0.308842i
$879$		0			0
$880$	−3.53173	+	2.03904i	−0.119054	+	0.0687361i
$881$	−5.40270			−0.182022			−0.0910109	−	0.995850i	$-0.529010\pi$
$881$	−5.40270			−0.182022			−0.0910109	+	0.995850i	$0.529010\pi$
$882$		0			0
$883$	−27.9671			−0.941169			−0.470584	−	0.882355i	$-0.655957\pi$
$883$	−27.9671			−0.941169			−0.470584	+	0.882355i	$0.655957\pi$
$884$	−6.67615	+	3.85448i	−0.224543	+	0.129640i
$885$		0			0
$886$	−3.38074	+	5.85561i	−0.113578	+	0.196723i
$887$	−21.4552			−0.720395			−0.360198	−	0.932876i	$-0.617291\pi$
$887$	−21.4552			−0.720395			−0.360198	+	0.932876i	$0.617291\pi$
$888$		0			0
$889$	6.09042	−	28.3575i	0.204266	−	0.951079i
$890$			14.5899i			0.489056i
$891$		0			0
$892$	4.24320	−	2.44981i	0.142073	−	0.0820257i
$893$		−	27.7677i		−	0.929209i
$894$		0			0
$895$	−7.42444	+	4.28650i	−0.248172	+	0.143282i
$896$	0.812247	+	2.51799i	0.0271353	+	0.0841200i
$897$		0			0
$898$	1.98767	+	3.44275i	0.0663294	+	0.114886i
$899$	28.1606	+	48.7756i	0.939209	+	1.62676i
$900$		0			0
$901$	9.60904	+	5.54778i	0.320124	+	0.184823i
$902$	5.58394	−	9.67166i	0.185925	−	0.322031i
$903$		0			0
$904$	1.41832	+	2.45659i	0.0471725	+	0.0817051i
$905$		−	1.70947i		−	0.0568247i
$906$		0			0
$907$	−21.1006			−0.700634			−0.350317	−	0.936631i	$-0.613926\pi$
$907$	−21.1006			−0.700634			−0.350317	+	0.936631i	$0.613926\pi$
$908$	−8.74040	+	15.1388i	−0.290060	+	0.502399i
$909$		0			0
$910$	11.7872	+	10.6585i	0.390740	+	0.353327i
$911$	−18.9423	−	10.9363i	−0.627585	−	0.362337i	0.152231	−	0.988345i	$-0.451354\pi$
$911$	−18.9423	−	10.9363i	−0.627585	−	0.362337i	−0.779816	+	0.626008i	$0.784688\pi$
$912$		0			0
$913$	48.5929	+	28.0551i	1.60819	+	0.928488i
$914$	−5.64673	−	3.26014i	−0.186777	−	0.107836i
$915$		0			0
$916$	12.6374	+	7.29619i	0.417551	+	0.241073i
$917$	11.5176	−	53.6267i	0.380344	−	1.77091i
$918$		0			0
$919$	−10.9564	+	18.9770i	−0.361418	+	0.625994i	−0.988194	−	0.153205i	$-0.951040\pi$
$919$	−10.9564	+	18.9770i	−0.361418	+	0.625994i	0.626777	+	0.779199i	$0.284374\pi$
$920$	−2.18864			−0.0721573
$921$		0			0
$922$		−	9.38607i		−	0.309114i
$923$	−42.4580	−	73.5394i	−1.39752	−	2.42058i
$924$		0			0
$925$	−2.90160	+	5.02572i	−0.0954040	+	0.165245i
$926$	−29.2212	−	16.8709i	−0.960269	−	0.554411i
$927$		0			0
$928$	−3.59029	−	6.21856i	−0.117857	−	0.204134i
$929$	−12.1080	−	20.9717i	−0.397251	−	0.688059i	0.596135	−	0.802884i	$-0.296702\pi$
$929$	−12.1080	−	20.9717i	−0.397251	−	0.688059i	−0.993386	+	0.114826i	$0.963369\pi$
$930$		0			0
$931$	−13.7305	−	19.0679i	−0.449999	−	0.624925i
$932$	−3.42360	+	1.97662i	−0.112144	+	0.0647463i
$933$		0			0
$934$		−	35.8295i		−	1.17238i
$935$	4.53279	−	2.61701i	0.148238	−	0.0855853i
$936$		0			0
$937$			38.1815i			1.24733i	0.781690	+	0.623667i	$0.214358\pi$
$937$			38.1815i			1.24733i	−0.781690	+	0.623667i	$0.785642\pi$
$938$	−22.3030	−	4.79008i	−0.728218	−	0.156402i
$939$		0			0
$940$	−8.27225			−0.269811
$941$	−3.96611	+	6.86950i	−0.129291	+	0.223939i	−0.923402	−	0.383834i	$-0.874604\pi$
$941$	−3.96611	+	6.86950i	−0.129291	+	0.223939i	0.794111	+	0.607773i	$0.207937\pi$
$942$		0			0
$943$	5.19062	−	2.99680i	0.169030	−	0.0975894i
$944$	−1.26116			−0.0410472
$945$		0			0
$946$	−19.8822			−0.646425
$947$	2.86322	−	1.65308i	0.0930421	−	0.0537179i	−0.452757	−	0.891634i	$-0.649560\pi$
$947$	2.86322	−	1.65308i	0.0930421	−	0.0537179i	0.545799	+	0.837916i	$0.316226\pi$
$948$		0			0
$949$	20.8878	−	36.1787i	0.678047	−	1.17441i
$950$	−3.35672			−0.108906
$951$		0			0
$952$	−1.04248	−	3.23171i	−0.0337869	−	0.104740i
$953$		−	53.6699i		−	1.73854i	−0.494339	−	0.869269i	$-0.664590\pi$
$953$		−	53.6699i		−	1.73854i	0.494339	−	0.869269i	$-0.335410\pi$
$954$		0			0
$955$	8.02069	−	4.63075i	0.259543	−	0.149847i
$956$			18.5118i			0.598714i
$957$		0			0
$958$	−12.0186	+	6.93894i	−0.388303	+	0.224187i
$959$	−25.0252	−	5.37473i	−0.808105	−	0.173559i
$960$		0			0
$961$	15.2606	+	26.4322i	0.492279	+	0.852652i
$962$	17.4283	+	30.1867i	0.561910	+	0.973257i
$963$		0			0
$964$	18.9977	+	10.9683i	0.611874	+	0.353266i
$965$	12.1247	−	21.0006i	0.390308	−	0.676034i
$966$		0			0
$967$	8.76620	+	15.1835i	0.281902	+	0.488268i	0.971853	−	0.235587i	$-0.0757014\pi$
$967$	8.76620	+	15.1835i	0.281902	+	0.488268i	−0.689951	+	0.723856i	$0.742368\pi$
$968$		−	5.63079i		−	0.180981i
$969$		0			0
$970$	19.4824			0.625542
$971$	−1.13150	+	1.95981i	−0.0363115	+	0.0628933i	−0.883610	−	0.468224i	$-0.844894\pi$
$971$	−1.13150	+	1.95981i	−0.0363115	+	0.0628933i	0.847299	+	0.531117i	$0.178228\pi$
$972$		0			0
$973$	−4.28750	−	13.2914i	−0.137451	−	0.426101i
$974$	−23.9026	−	13.8002i	−0.765888	−	0.442186i
$975$		0			0
$976$	2.56956	+	1.48353i	0.0822495	+	0.0474868i
$977$	−39.2275	−	22.6480i	−1.25500	−	0.724574i	−0.282901	−	0.959149i	$-0.591297\pi$
$977$	−39.2275	−	22.6480i	−1.25500	−	0.724574i	−0.972098	+	0.234575i	$0.924630\pi$
$978$		0			0
$979$	−51.5277	−	29.7495i	−1.64683	−	0.950799i
$980$	−5.68051	+	4.09045i	−0.181457	+	0.130665i
$981$		0			0
$982$	−10.5048	+	18.1949i	−0.335222	+	0.580621i
$983$	−27.1875			−0.867145			−0.433572	−	0.901119i	$-0.642747\pi$
$983$	−27.1875			−0.867145			−0.433572	+	0.901119i	$0.642747\pi$
$984$		0			0
$985$		−	18.8947i		−	0.602036i
$986$	4.60795	+	7.98120i	0.146747	+	0.254173i
$987$		0			0
$988$	−10.0810	+	17.4608i	−0.320719	+	0.555501i
$989$	−9.24086	−	5.33521i	−0.293842	−	0.169650i
$990$		0			0
$991$	−13.1793	−	22.8272i	−0.418654	−	0.725130i	0.577150	−	0.816638i	$-0.304165\pi$
$991$	−13.1793	−	22.8272i	−0.418654	−	0.725130i	−0.995804	+	0.0915077i	$0.970831\pi$
$992$	−3.92178	−	6.79271i	−0.124516	−	0.215669i
$993$		0			0
$994$	35.5980	−	11.4831i	1.12910	−	0.364223i
$995$	2.25502	−	1.30194i	0.0714890	−	0.0412742i
$996$		0			0
$997$			51.3611i			1.62662i	0.581828	+	0.813312i	$0.302338\pi$
$997$			51.3611i			1.62662i	−0.581828	+	0.813312i	$0.697662\pi$
$998$	−0.342363	+	0.197663i	−0.0108373	+	0.00625692i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1601.1		28
3.2	odd	2		630.2.t.b.551.9	yes	28
7.3	odd	6		1890.2.bk.b.521.13		28
9.4	even	3		630.2.bk.b.131.5	yes	28
9.5	odd	6		1890.2.bk.b.341.13		28
21.17	even	6		630.2.bk.b.101.12	yes	28
63.31	odd	6		630.2.t.b.311.9	✓	28
63.59	even	6	inner	1890.2.t.b.1151.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.9	✓	28	63.31	odd	6
630.2.t.b.551.9	yes	28	3.2	odd	2
630.2.bk.b.101.12	yes	28	21.17	even	6
630.2.bk.b.131.5	yes	28	9.4	even	3
1890.2.t.b.1151.1		28	63.59	even	6	inner
1890.2.t.b.1601.1		28	1.1	even	1	trivial
1890.2.bk.b.341.13		28	9.5	odd	6
1890.2.bk.b.521.13		28	7.3	odd	6

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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.555567 + 2.58676i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.555567 + 2.58676i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} -4.07809i q^{11} +(-5.20173 + 3.00322i) q^{13} +(-0.812247 - 2.51799i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.641724 + 1.11150i) q^{17} +(2.90701 + 1.67836i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.03904 + 3.53173i) q^{22} +2.18864i q^{23} +1.00000 q^{25} +(3.00322 - 5.20173i) q^{26} +(1.96242 + 1.77452i) q^{28} +(-6.21856 - 3.59029i) q^{29} +(-6.79271 - 3.92178i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.11150 - 0.641724i) q^{34} +(-0.555567 + 2.58676i) q^{35} +(-2.90160 + 5.02572i) q^{37} -3.35672 q^{38} +1.00000i q^{40} +(-1.36925 - 2.37162i) q^{41} +(-2.43768 + 4.22219i) q^{43} +(-3.53173 - 2.03904i) q^{44} +(-1.09432 - 1.89542i) q^{46} +(-4.13613 - 7.16398i) q^{47} +(-6.38269 - 2.87424i) q^{49} +(-0.866025 + 0.500000i) q^{50} +6.00644i q^{52} +(7.48689 - 4.32256i) q^{53} -4.07809i q^{55} +(-2.58676 - 0.555567i) q^{56} +7.18058 q^{58} +(0.630579 - 1.09220i) q^{59} +(-2.56956 + 1.48353i) q^{61} +7.84355 q^{62} -1.00000 q^{64} +(-5.20173 + 3.00322i) q^{65} +(4.31098 - 7.46684i) q^{67} +1.28345 q^{68} +(-0.812247 - 2.51799i) q^{70} +14.1375i q^{71} +(-6.02332 + 3.47757i) q^{73} -5.80320i q^{74} +(2.90701 - 1.67836i) q^{76} +(10.5490 + 2.26565i) q^{77} +(6.09277 + 10.5530i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(2.37162 + 1.36925i) q^{82} +(-6.87948 + 11.9156i) q^{83} +(0.641724 + 1.11150i) q^{85} -4.87537i q^{86} +4.07809 q^{88} +(7.29497 - 12.6353i) q^{89} +(-4.87871 - 15.1241i) q^{91} +(1.89542 + 1.09432i) q^{92} +(7.16398 + 4.13613i) q^{94} +(2.90701 + 1.67836i) q^{95} +(-16.8723 - 9.74120i) q^{97} +(6.96469 - 0.702180i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more