LMFDB - Embedded newform 1890.2.bi.b.719.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(719,1890)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1890.719");

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.bi (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.8
Character	$\chi$	$=$	1890.719
Dual form			1890.2.bi.b.899.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-1.47412 - 1.68136i) q^{5} +(1.31170 - 2.29771i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.47412 - 1.68136i) q^{5} +(1.31170 - 2.29771i) q^{7} +1.00000 q^{8} +(-1.47412 - 1.68136i) q^{10} +(-3.56894 - 2.06053i) q^{11} +(1.18566 - 2.05363i) q^{13} +(1.31170 - 2.29771i) q^{14} +1.00000 q^{16} +(-2.28111 + 1.31700i) q^{17} +(0.956982 + 0.552514i) q^{19} +(-1.47412 - 1.68136i) q^{20} +(-3.56894 - 2.06053i) q^{22} +(-0.296239 - 0.513101i) q^{23} +(-0.653922 + 4.95705i) q^{25} +(1.18566 - 2.05363i) q^{26} +(1.31170 - 2.29771i) q^{28} +(-2.36953 + 1.36805i) q^{29} -2.69755i q^{31} +1.00000 q^{32} +(-2.28111 + 1.31700i) q^{34} +(-5.79687 + 1.18167i) q^{35} +(-6.05512 - 3.49593i) q^{37} +(0.956982 + 0.552514i) q^{38} +(-1.47412 - 1.68136i) q^{40} +(-0.257087 + 0.445287i) q^{41} +(-10.4023 + 6.00577i) q^{43} +(-3.56894 - 2.06053i) q^{44} +(-0.296239 - 0.513101i) q^{46} -4.12973i q^{47} +(-3.55890 - 6.02779i) q^{49} +(-0.653922 + 4.95705i) q^{50} +(1.18566 - 2.05363i) q^{52} +(-4.54406 - 7.87055i) q^{53} +(1.79657 + 9.03814i) q^{55} +(1.31170 - 2.29771i) q^{56} +(-2.36953 + 1.36805i) q^{58} +6.93948 q^{59} +4.29324i q^{61} -2.69755i q^{62} +1.00000 q^{64} +(-5.20070 + 1.03378i) q^{65} -13.5150i q^{67} +(-2.28111 + 1.31700i) q^{68} +(-5.79687 + 1.18167i) q^{70} +1.60164i q^{71} +(3.29147 + 5.70100i) q^{73} +(-6.05512 - 3.49593i) q^{74} +(0.956982 + 0.552514i) q^{76} +(-9.41586 + 5.49759i) q^{77} +13.4434 q^{79} +(-1.47412 - 1.68136i) q^{80} +(-0.257087 + 0.445287i) q^{82} +(3.80374 - 2.19609i) q^{83} +(5.57698 + 1.89394i) q^{85} +(-10.4023 + 6.00577i) q^{86} +(-3.56894 - 2.06053i) q^{88} +(7.82648 - 13.5559i) q^{89} +(-3.16341 - 5.41805i) q^{91} +(-0.296239 - 0.513101i) q^{92} -4.12973i q^{94} +(-0.481736 - 2.42350i) q^{95} +(6.92406 + 11.9928i) q^{97} +(-3.55890 - 6.02779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8}+O(q^{10}) $ 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8	$ 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} - 6 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{28} + 3 q^{29} + 48 q^{32} + 18 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49} + 18 q^{50} + 42 q^{55} - 3 q^{56} + 3 q^{58} + 48 q^{64} + 12 q^{65} + 18 q^{70} + 18 q^{73} - 12 q^{77} + 3 q^{82} + 9 q^{83} + 33 q^{85} - 6 q^{88} + 33 q^{89} + 3 q^{92} + 24 q^{97} + 3 q^{98}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 - 6 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^28 + 3 * q^29 + 48 * q^32 + 18 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 + 42 * q^55 - 3 * q^56 + 3 * q^58 + 48 * q^64 + 12 * q^65 + 18 * q^70 + 18 * q^73 - 12 * q^77 + 3 * q^82 + 9 * q^83 + 33 * q^85 - 6 * q^88 + 33 * q^89 + 3 * q^92 + 24 * q^97 + 3 * 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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.47412	−	1.68136i	−0.659248	−	0.751926i
$5$	−1.47412	−	1.68136i	−0.659248	−	0.751926i
$6$		0			0
$7$	1.31170	−	2.29771i	0.495775	−	0.868451i
$7$	1.31170	−	2.29771i	0.495775	−	0.868451i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.47412	−	1.68136i	−0.466159	−	0.531692i
$11$	−3.56894	−	2.06053i	−1.07608	−	0.621273i	−0.146241	−	0.989249i	$-0.546718\pi$
$11$	−3.56894	−	2.06053i	−1.07608	−	0.621273i	−0.929835	+	0.367976i	$0.880051\pi$
$12$		0			0
$13$	1.18566	−	2.05363i	0.328844	−	0.569575i	−0.653439	−	0.756979i	$-0.726674\pi$
$13$	1.18566	−	2.05363i	0.328844	−	0.569575i	0.982283	+	0.187405i	$0.0600076\pi$
$14$	1.31170	−	2.29771i	0.350566	−	0.614088i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.28111	+	1.31700i	−0.553250	+	0.319419i	−0.750432	−	0.660948i	$-0.770154\pi$
$17$	−2.28111	+	1.31700i	−0.553250	+	0.319419i	0.197182	+	0.980367i	$0.436821\pi$
$18$		0			0
$19$	0.956982	+	0.552514i	0.219547	+	0.126755i	0.605740	−	0.795662i	$-0.292877\pi$
$19$	0.956982	+	0.552514i	0.219547	+	0.126755i	−0.386194	+	0.922418i	$0.626210\pi$
$20$	−1.47412	−	1.68136i	−0.329624	−	0.375963i
$21$		0			0
$22$	−3.56894	−	2.06053i	−0.760901	−	0.439306i
$23$	−0.296239	−	0.513101i	−0.0617701	−	0.106989i	0.833487	−	0.552540i	$-0.186341\pi$
$23$	−0.296239	−	0.513101i	−0.0617701	−	0.106989i	−0.895257	+	0.445551i	$0.853008\pi$
$24$		0			0
$25$	−0.653922	+	4.95705i	−0.130784	+	0.991411i
$26$	1.18566	−	2.05363i	0.232528	−	0.402750i
$27$		0			0
$28$	1.31170	−	2.29771i	0.247887	−	0.434226i
$29$	−2.36953	+	1.36805i	−0.440010	+	0.254040i	−0.703602	−	0.710594i	$-0.748426\pi$
$29$	−2.36953	+	1.36805i	−0.440010	+	0.254040i	0.263592	+	0.964634i	$0.415093\pi$
$30$		0			0
$31$		−	2.69755i		−	0.484495i	−0.970215	−	0.242247i	$-0.922115\pi$
$31$		−	2.69755i		−	0.484495i	0.970215	−	0.242247i	$-0.0778845\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.28111	+	1.31700i	−0.391207	+	0.225863i
$35$	−5.79687	+	1.18167i	−0.979849	+	0.199739i
$36$		0			0
$37$	−6.05512	−	3.49593i	−0.995456	−	0.574727i	−0.0885553	−	0.996071i	$-0.528225\pi$
$37$	−6.05512	−	3.49593i	−0.995456	−	0.574727i	−0.906901	+	0.421345i	$0.861558\pi$
$38$	0.956982	+	0.552514i	0.155243	+	0.0896295i
$39$		0			0
$40$	−1.47412	−	1.68136i	−0.233079	−	0.265846i
$41$	−0.257087	+	0.445287i	−0.0401502	+	0.0695422i	−0.885402	−	0.464826i	$-0.846117\pi$
$41$	−0.257087	+	0.445287i	−0.0401502	+	0.0695422i	0.845252	+	0.534368i	$0.179450\pi$
$42$		0			0
$43$	−10.4023	+	6.00577i	−1.58634	+	0.915872i	−0.592432	+	0.805620i	$0.701832\pi$
$43$	−10.4023	+	6.00577i	−1.58634	+	0.915872i	−0.993904	+	0.110251i	$0.964834\pi$
$44$	−3.56894	−	2.06053i	−0.538038	−	0.310636i
$45$		0			0
$46$	−0.296239	−	0.513101i	−0.0436781	−	0.0756527i
$47$		−	4.12973i		−	0.602384i	−0.953564	−	0.301192i	$-0.902616\pi$
$47$		−	4.12973i		−	0.602384i	0.953564	−	0.301192i	$-0.0973844\pi$
$48$		0			0
$49$	−3.55890	−	6.02779i	−0.508414	−	0.861113i
$50$	−0.653922	+	4.95705i	−0.0924786	+	0.701033i
$51$		0			0
$52$	1.18566	−	2.05363i	0.164422	−	0.284787i
$53$	−4.54406	−	7.87055i	−0.624175	−	1.08110i	−0.988700	−	0.149909i	$-0.952102\pi$
$53$	−4.54406	−	7.87055i	−0.624175	−	1.08110i	0.364525	−	0.931194i	$-0.381232\pi$
$54$		0			0
$55$	1.79657	+	9.03814i	0.242250	+	1.21870i
$56$	1.31170	−	2.29771i	0.175283	−	0.307044i
$57$		0			0
$58$	−2.36953	+	1.36805i	−0.311134	+	0.179633i
$59$	6.93948			0.903443			0.451722	−	0.892159i	$-0.350810\pi$
$59$	6.93948			0.903443			0.451722	+	0.892159i	$0.350810\pi$
$60$		0			0
$61$			4.29324i			0.549693i	0.961488	+	0.274847i	$0.0886271\pi$
$61$			4.29324i			0.549693i	−0.961488	+	0.274847i	$0.911373\pi$
$62$		−	2.69755i		−	0.342589i
$63$		0			0
$64$	1.00000			0.125000
$65$	−5.20070	+	1.03378i	−0.645068	+	0.128225i
$66$		0			0
$67$		−	13.5150i		−	1.65112i	−0.564315	−	0.825560i	$-0.690859\pi$
$67$		−	13.5150i		−	1.65112i	0.564315	−	0.825560i	$-0.309141\pi$
$68$	−2.28111	+	1.31700i	−0.276625	+	0.159709i
$69$		0			0
$70$	−5.79687	+	1.18167i	−0.692858	+	0.141237i
$71$			1.60164i			0.190079i	0.995473	+	0.0950396i	$0.0302978\pi$
$71$			1.60164i			0.190079i	−0.995473	+	0.0950396i	$0.969702\pi$
$72$		0			0
$73$	3.29147	+	5.70100i	0.385238	+	0.667252i	0.991802	−	0.127783i	$-0.0407860\pi$
$73$	3.29147	+	5.70100i	0.385238	+	0.667252i	−0.606564	+	0.795035i	$0.707453\pi$
$74$	−6.05512	−	3.49593i	−0.703894	−	0.406393i
$75$		0			0
$76$	0.956982	+	0.552514i	0.109773	+	0.0633777i
$77$	−9.41586	+	5.49759i	−1.07304	+	0.626508i
$78$		0			0
$79$	13.4434			1.51251			0.756253	−	0.654280i	$-0.227028\pi$
$79$	13.4434			1.51251			0.756253	+	0.654280i	$0.227028\pi$
$80$	−1.47412	−	1.68136i	−0.164812	−	0.187981i
$81$		0			0
$82$	−0.257087	+	0.445287i	−0.0283905	+	0.0491738i
$83$	3.80374	−	2.19609i	0.417515	−	0.241052i	−0.276499	−	0.961014i	$-0.589174\pi$
$83$	3.80374	−	2.19609i	0.417515	−	0.241052i	0.694013	+	0.719962i	$0.255841\pi$
$84$		0			0
$85$	5.57698	+	1.89394i	0.604908	+	0.205426i
$86$	−10.4023	+	6.00577i	−1.12171	+	0.647619i
$87$		0			0
$88$	−3.56894	−	2.06053i	−0.380450	−	0.219653i
$89$	7.82648	−	13.5559i	0.829605	−	1.43692i	−0.0687438	−	0.997634i	$-0.521899\pi$
$89$	7.82648	−	13.5559i	0.829605	−	1.43692i	0.898349	−	0.439283i	$-0.144768\pi$
$90$		0			0
$91$	−3.16341	−	5.41805i	−0.331615	−	0.567966i
$92$	−0.296239	−	0.513101i	−0.0308851	−	0.0534945i
$93$		0			0
$94$		−	4.12973i		−	0.425949i
$95$	−0.481736	−	2.42350i	−0.0494251	−	0.248646i
$96$		0			0
$97$	6.92406	+	11.9928i	0.703032	+	1.21769i	0.967397	+	0.253265i	$0.0815044\pi$
$97$	6.92406	+	11.9928i	0.703032	+	1.21769i	−0.264365	+	0.964423i	$0.585162\pi$
$98$	−3.55890	−	6.02779i	−0.359503	−	0.608899i
$99$		0			0
$100$	−0.653922	+	4.95705i	−0.0653922	+	0.495705i
$101$	−1.35453	+	2.34612i	−0.134781	+	0.233448i	−0.925514	−	0.378714i	$-0.876366\pi$
$101$	−1.35453	+	2.34612i	−0.134781	+	0.233448i	0.790733	+	0.612162i	$0.209700\pi$
$102$		0			0
$103$	−9.07239	−	15.7138i	−0.893929	−	1.54833i	−0.835125	−	0.550061i	$-0.814605\pi$
$103$	−9.07239	−	15.7138i	−0.893929	−	1.54833i	−0.0588041	−	0.998270i	$-0.518729\pi$
$104$	1.18566	−	2.05363i	0.116264	−	0.201375i
$105$		0			0
$106$	−4.54406	−	7.87055i	−0.441358	−	0.764455i
$107$	−4.33862	+	7.51471i	−0.419430	+	0.726475i	−0.995882	−	0.0906565i	$-0.971103\pi$
$107$	−4.33862	+	7.51471i	−0.419430	+	0.726475i	0.576452	+	0.817131i	$0.304437\pi$
$108$		0			0
$109$	−7.55567	−	13.0868i	−0.723702	−	1.25349i	−0.959506	−	0.281688i	$-0.909106\pi$
$109$	−7.55567	−	13.0868i	−0.723702	−	1.25349i	0.235804	−	0.971801i	$-0.424228\pi$
$110$	1.79657	+	9.03814i	0.171297	+	0.861753i
$111$		0			0
$112$	1.31170	−	2.29771i	0.123944	−	0.217113i
$113$	0.503287	−	0.871718i	0.0473452	−	0.0820044i	−0.841382	−	0.540441i	$-0.818257\pi$
$113$	0.503287	−	0.871718i	0.0473452	−	0.0820044i	0.888727	+	0.458437i	$0.151591\pi$
$114$		0			0
$115$	−0.426013	+	1.25446i	−0.0397260	+	0.116979i
$116$	−2.36953	+	1.36805i	−0.220005	+	0.127020i
$117$		0			0
$118$	6.93948			0.638831
$119$	0.0339510	+	6.96882i	0.00311228	+	0.638830i
$120$		0			0
$121$	2.99156	+	5.18154i	0.271960	+	0.471049i
$122$			4.29324i			0.388692i
$123$		0			0
$124$		−	2.69755i		−	0.242247i
$125$	9.29854	−	6.20783i	0.831687	−	0.555245i
$126$		0			0
$127$		−	3.12538i		−	0.277333i	−0.990339	−	0.138666i	$-0.955718\pi$
$127$		−	3.12538i		−	0.277333i	0.990339	−	0.138666i	$-0.0442816\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−5.20070	+	1.03378i	−0.456132	+	0.0906685i
$131$	10.7870	+	18.6837i	0.942469	+	1.63240i	0.760742	+	0.649055i	$0.224835\pi$
$131$	10.7870	+	18.6837i	0.942469	+	1.63240i	0.181727	+	0.983349i	$0.441831\pi$
$132$		0			0
$133$	2.52478	−	1.47413i	0.218926	−	0.127823i
$134$		−	13.5150i		−	1.16752i
$135$		0			0
$136$	−2.28111	+	1.31700i	−0.195603	+	0.112932i
$137$	−1.88397	+	3.26314i	−0.160959	+	0.278789i	−0.935213	−	0.354086i	$-0.884792\pi$
$137$	−1.88397	+	3.26314i	−0.160959	+	0.278789i	0.774254	+	0.632875i	$0.218125\pi$
$138$		0			0
$139$	5.20651	+	3.00598i	0.441610	+	0.254964i	0.704280	−	0.709922i	$-0.251270\pi$
$139$	5.20651	+	3.00598i	0.441610	+	0.254964i	−0.262670	+	0.964886i	$0.584603\pi$
$140$	−5.79687	+	1.18167i	−0.489925	+	0.0998693i
$141$		0			0
$142$			1.60164i			0.134406i
$143$	−8.46313	+	4.88619i	−0.707723	+	0.408604i
$144$		0			0
$145$	5.79315	+	1.96735i	0.481095	+	0.163379i
$146$	3.29147	+	5.70100i	0.272404	+	0.471818i
$147$		0			0
$148$	−6.05512	−	3.49593i	−0.497728	−	0.287363i
$149$	9.69236	−	5.59589i	0.794029	−	0.458433i	−0.0473497	−	0.998878i	$-0.515078\pi$
$149$	9.69236	−	5.59589i	0.794029	−	0.458433i	0.841379	+	0.540445i	$0.181744\pi$
$150$		0			0
$151$	9.27469	−	16.0642i	0.754763	−	1.30729i	−0.190729	−	0.981643i	$-0.561085\pi$
$151$	9.27469	−	16.0642i	0.754763	−	1.30729i	0.945492	−	0.325645i	$-0.105582\pi$
$152$	0.956982	+	0.552514i	0.0776215	+	0.0448148i
$153$		0			0
$154$	−9.41586	+	5.49759i	−0.758752	+	0.443008i
$155$	−4.53555	+	3.97652i	−0.364304	+	0.319402i
$156$		0			0
$157$	−11.6703			−0.931389			−0.465695	−	0.884945i	$-0.654196\pi$
$157$	−11.6703			−0.931389			−0.465695	+	0.884945i	$0.654196\pi$
$158$	13.4434			1.06950
$159$		0			0
$160$	−1.47412	−	1.68136i	−0.116540	−	0.132923i
$161$	−1.56753	+	0.00763677i	−0.123539	+	0.000601862i
$162$		0			0
$163$	−10.7728	−	6.21967i	−0.843789	−	0.487162i	0.0147613	−	0.999891i	$-0.495301\pi$
$163$	−10.7728	−	6.21967i	−0.843789	−	0.487162i	−0.858550	+	0.512729i	$0.828634\pi$
$164$	−0.257087	+	0.445287i	−0.0200751	+	0.0347711i
$165$		0			0
$166$	3.80374	−	2.19609i	0.295227	−	0.170450i
$167$	−11.4205	−	6.59363i	−0.883745	−	0.510230i	−0.0118537	−	0.999930i	$-0.503773\pi$
$167$	−11.4205	−	6.59363i	−0.883745	−	0.510230i	−0.871891	+	0.489699i	$0.837107\pi$
$168$		0			0
$169$	3.68840	+	6.38850i	0.283723	+	0.491423i
$170$	5.57698	+	1.89394i	0.427735	+	0.145258i
$171$		0			0
$172$	−10.4023	+	6.00577i	−0.793168	+	0.457936i
$173$		−	14.8129i		−	1.12620i	−0.826387	−	0.563102i	$-0.809608\pi$
$173$		−	14.8129i		−	1.12620i	0.826387	−	0.563102i	$-0.190392\pi$
$174$		0			0
$175$	10.5321	+	8.00467i	0.796152	+	0.605097i
$176$	−3.56894	−	2.06053i	−0.269019	−	0.155318i
$177$		0			0
$178$	7.82648	−	13.5559i	0.586619	−	1.01605i
$179$	−20.6373	+	11.9149i	−1.54250	+	0.890564i	−0.543823	+	0.839200i	$0.683024\pi$
$179$	−20.6373	+	11.9149i	−1.54250	+	0.890564i	−0.998680	+	0.0513644i	$0.983643\pi$
$180$		0			0
$181$		−	11.6911i		−	0.868992i	−0.900674	−	0.434496i	$-0.856926\pi$
$181$		−	11.6911i		−	0.868992i	0.900674	−	0.434496i	$-0.143074\pi$
$182$	−3.16341	−	5.41805i	−0.234487	−	0.401612i
$183$		0			0
$184$	−0.296239	−	0.513101i	−0.0218390	−	0.0378263i
$185$	3.04810	+	15.3342i	0.224100	+	1.12740i
$186$		0			0
$187$	10.8549			0.793785
$188$		−	4.12973i		−	0.301192i
$189$		0			0
$190$	−0.481736	−	2.42350i	−0.0349488	−	0.175819i
$191$			26.0254i			1.88313i	0.336825	+	0.941567i	$0.390647\pi$
$191$			26.0254i			1.88313i	−0.336825	+	0.941567i	$0.609353\pi$
$192$		0			0
$193$		−	18.0736i		−	1.30096i	−0.759522	−	0.650482i	$-0.774567\pi$
$193$		−	18.0736i		−	1.30096i	0.759522	−	0.650482i	$-0.225433\pi$
$194$	6.92406	+	11.9928i	0.497119	+	0.861035i
$195$		0			0
$196$	−3.55890	−	6.02779i	−0.254207	−	0.430556i
$197$	19.0964			1.36056			0.680281	−	0.732951i	$-0.261858\pi$
$197$	19.0964			1.36056			0.680281	+	0.732951i	$0.261858\pi$
$198$		0			0
$199$	21.6198	−	12.4822i	1.53259	−	0.884840i	0.533346	−	0.845897i	$-0.320934\pi$
$199$	21.6198	−	12.4822i	1.53259	−	0.884840i	0.999241	−	0.0389429i	$-0.0123991\pi$
$200$	−0.653922	+	4.95705i	−0.0462393	+	0.350517i
$201$		0			0
$202$	−1.35453	+	2.34612i	−0.0953046	+	0.165072i
$203$	0.0352670	+	7.23893i	0.00247526	+	0.508074i
$204$		0			0
$205$	1.12766	−	0.224154i	0.0787595	−	0.0156556i
$206$	−9.07239	−	15.7138i	−0.632103	−	1.09483i
$207$		0			0
$208$	1.18566	−	2.05363i	0.0822110	−	0.142394i
$209$	−2.27694	−	3.94378i	−0.157499	−	0.272797i
$210$		0			0
$211$	−6.61689	+	11.4608i	−0.455525	+	0.788993i	−0.998718	−	0.0506149i	$-0.983882\pi$
$211$	−6.61689	+	11.4608i	−0.455525	+	0.788993i	0.543193	+	0.839608i	$0.317215\pi$
$212$	−4.54406	−	7.87055i	−0.312088	−	0.540552i
$213$		0			0
$214$	−4.33862	+	7.51471i	−0.296582	+	0.513695i
$215$	25.4321	+	8.63673i	1.73446	+	0.589020i
$216$		0			0
$217$	−6.19818	−	3.53837i	−0.420760	−	0.240200i
$218$	−7.55567	−	13.0868i	−0.511735	−	0.886351i
$219$		0			0
$220$	1.79657	+	9.03814i	0.121125	+	0.609351i
$221$			6.24607i			0.420156i
$222$		0			0
$223$	−2.44383	−	4.23284i	−0.163651	−	0.283452i	0.772524	−	0.634985i	$-0.218994\pi$
$223$	−2.44383	−	4.23284i	−0.163651	−	0.283452i	−0.936175	+	0.351533i	$0.885660\pi$
$224$	1.31170	−	2.29771i	0.0876415	−	0.153522i
$225$		0			0
$226$	0.503287	−	0.871718i	0.0334781	−	0.0579858i
$227$	10.3873	+	5.99711i	0.689429	+	0.398042i	0.803398	−	0.595442i	$-0.203023\pi$
$227$	10.3873	+	5.99711i	0.689429	+	0.398042i	−0.113969	+	0.993484i	$0.536356\pi$
$228$		0			0
$229$	9.16676	−	5.29243i	0.605757	−	0.349734i	−0.165546	−	0.986202i	$-0.552939\pi$
$229$	9.16676	−	5.29243i	0.605757	−	0.349734i	0.771303	+	0.636468i	$0.219605\pi$
$230$	−0.426013	+	1.25446i	−0.0280905	+	0.0827165i
$231$		0			0
$232$	−2.36953	+	1.36805i	−0.155567	+	0.0898166i
$233$	0.259858	−	0.450088i	0.0170239	−	0.0294862i	−0.857388	−	0.514671i	$-0.827914\pi$
$233$	0.259858	−	0.450088i	0.0170239	−	0.0294862i	0.874412	+	0.485184i	$0.161248\pi$
$234$		0			0
$235$	−6.94356	+	6.08774i	−0.452948	+	0.397120i
$236$	6.93948			0.451722
$237$		0			0
$238$	0.0339510	+	6.96882i	0.00220072	+	0.451721i
$239$	2.39886	+	1.38498i	0.155169	+	0.0895869i	0.575574	−	0.817750i	$-0.304779\pi$
$239$	2.39886	+	1.38498i	0.155169	+	0.0895869i	−0.420405	+	0.907337i	$0.638112\pi$
$240$		0			0
$241$	17.4943	+	10.1004i	1.12691	+	0.650621i	0.943156	−	0.332351i	$-0.107842\pi$
$241$	17.4943	+	10.1004i	1.12691	+	0.650621i	0.183753	+	0.982972i	$0.441175\pi$
$242$	2.99156	+	5.18154i	0.192305	+	0.333082i
$243$		0			0
$244$			4.29324i			0.274847i
$245$	−4.88861	+	14.8695i	−0.312322	+	0.949976i
$246$		0			0
$247$	2.26932	−	1.31019i	0.144393	−	0.0833655i
$248$		−	2.69755i		−	0.171295i
$249$		0			0
$250$	9.29854	−	6.20783i	0.588091	−	0.392618i
$251$	20.9869			1.32468			0.662340	−	0.749203i	$-0.269563\pi$
$251$	20.9869			1.32468			0.662340	+	0.749203i	$0.269563\pi$
$252$		0			0
$253$			2.44164i			0.153504i
$254$		−	3.12538i		−	0.196104i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.21246	+	4.74146i	−0.512279	+	0.295764i	−0.733770	−	0.679398i	$-0.762241\pi$
$257$	−8.21246	+	4.74146i	−0.512279	+	0.295764i	0.221491	+	0.975162i	$0.428908\pi$
$258$		0			0
$259$	−15.9751	+	9.32729i	−0.992644	+	0.579570i
$260$	−5.20070	+	1.03378i	−0.322534	+	0.0641123i
$261$		0			0
$262$	10.7870	+	18.6837i	0.666426	+	1.15428i
$263$	5.83660	−	10.1093i	0.359900	−	0.623365i	−0.628044	−	0.778178i	$-0.716144\pi$
$263$	5.83660	−	10.1093i	0.359900	−	0.623365i	0.987944	+	0.154813i	$0.0494774\pi$
$264$		0			0
$265$	−6.53469	+	19.2424i	−0.401423	+	1.18205i
$266$	2.52478	−	1.47413i	0.154804	−	0.0903848i
$267$		0			0
$268$		−	13.5150i		−	0.825560i
$269$	−8.14330	−	14.1046i	−0.496506	−	0.859973i	0.503486	−	0.864003i	$-0.332050\pi$
$269$	−8.14330	−	14.1046i	−0.496506	−	0.859973i	−0.999992	+	0.00403039i	$0.998717\pi$
$270$		0			0
$271$	21.8041	+	12.5886i	1.32450	+	0.764703i	0.984444	−	0.175701i	$-0.0562192\pi$
$271$	21.8041	+	12.5886i	1.32450	+	0.764703i	0.340060	+	0.940404i	$0.389553\pi$
$272$	−2.28111	+	1.31700i	−0.138312	+	0.0798547i
$273$		0			0
$274$	−1.88397	+	3.26314i	−0.113815	+	0.197133i
$275$	12.5480	−	16.3440i	0.756671	−	0.985581i
$276$		0			0
$277$	17.9632	+	10.3710i	1.07930	+	0.623136i	0.930708	−	0.365763i	$-0.119192\pi$
$277$	17.9632	+	10.3710i	1.07930	+	0.623136i	0.148594	+	0.988898i	$0.452525\pi$
$278$	5.20651	+	3.00598i	0.312265	+	0.180287i
$279$		0			0
$280$	−5.79687	+	1.18167i	−0.346429	+	0.0706183i
$281$	−1.17815	+	0.680206i	−0.0702827	+	0.0405777i	−0.534730	−	0.845023i	$-0.679587\pi$
$281$	−1.17815	+	0.680206i	−0.0702827	+	0.0405777i	0.464447	+	0.885601i	$0.346253\pi$
$282$		0			0
$283$	14.9351			0.887802			0.443901	−	0.896076i	$-0.353594\pi$
$283$	14.9351			0.887802			0.443901	+	0.896076i	$0.353594\pi$
$284$			1.60164i			0.0950396i
$285$		0			0
$286$	−8.46313	+	4.88619i	−0.500435	+	0.288927i
$287$	0.685919	+	1.17479i	0.0404885	+	0.0693458i
$288$		0			0
$289$	−5.03103	+	8.71400i	−0.295943	+	0.512589i
$290$	5.79315	+	1.96735i	0.340185	+	0.115527i
$291$		0			0
$292$	3.29147	+	5.70100i	0.192619	+	0.333626i
$293$	9.63607	+	5.56339i	0.562945	+	0.325016i	0.754327	−	0.656499i	$-0.227963\pi$
$293$	9.63607	+	5.56339i	0.562945	+	0.325016i	−0.191382	+	0.981516i	$0.561297\pi$
$294$		0			0
$295$	−10.2296	−	11.6677i	−0.595593	−	0.679322i
$296$	−6.05512	−	3.49593i	−0.351947	−	0.203197i
$297$		0			0
$298$	9.69236	−	5.59589i	0.561464	−	0.324161i
$299$	−1.40496			−0.0812510
$300$		0			0
$301$	0.154823	+	31.7792i	0.00892386	+	1.83172i
$302$	9.27469	−	16.0642i	0.533698	−	0.924392i
$303$		0			0
$304$	0.956982	+	0.552514i	0.0548867	+	0.0316888i
$305$	7.21847	−	6.32877i	0.413329	−	0.362384i
$306$		0			0
$307$	14.1337			0.806651			0.403325	−	0.915057i	$-0.367854\pi$
$307$	14.1337			0.806651			0.403325	+	0.915057i	$0.367854\pi$
$308$	−9.41586	+	5.49759i	−0.536518	+	0.313254i
$309$		0			0
$310$	−4.53555	+	3.97652i	−0.257602	+	0.225851i
$311$	5.87504			0.333143			0.166572	−	0.986029i	$-0.446730\pi$
$311$	5.87504			0.333143			0.166572	+	0.986029i	$0.446730\pi$
$312$		0			0
$313$	−19.0369			−1.07603			−0.538014	−	0.842936i	$-0.680825\pi$
$313$	−19.0369			−1.07603			−0.538014	+	0.842936i	$0.680825\pi$
$314$	−11.6703			−0.658592
$315$		0			0
$316$	13.4434			0.756253
$317$	−15.4166			−0.865882			−0.432941	−	0.901422i	$-0.642524\pi$
$317$	−15.4166			−0.865882			−0.432941	+	0.901422i	$0.642524\pi$
$318$		0			0
$319$	11.2756			0.631312
$320$	−1.47412	−	1.68136i	−0.0824060	−	0.0939907i
$321$		0			0
$322$	−1.56753	+	0.00763677i	−0.0873551	+	0.000425581i
$323$	−2.91064			−0.161952
$324$		0			0
$325$	9.40463	+	7.22032i	0.521675	+	0.400511i
$326$	−10.7728	−	6.21967i	−0.596649	−	0.344475i
$327$		0			0
$328$	−0.257087	+	0.445287i	−0.0141952	+	0.0245869i
$329$	−9.48891	−	5.41696i	−0.523141	−	0.298647i
$330$		0			0
$331$	−30.9300			−1.70007			−0.850033	−	0.526730i	$-0.823418\pi$
$331$	−30.9300			−1.70007			−0.850033	+	0.526730i	$0.823418\pi$
$332$	3.80374	−	2.19609i	0.208757	−	0.120526i
$333$		0			0
$334$	−11.4205	−	6.59363i	−0.624902	−	0.360787i
$335$	−22.7235	+	19.9228i	−1.24152	+	1.08850i
$336$		0			0
$337$	21.3417	+	12.3216i	1.16256	+	0.671202i	0.951915	−	0.306362i	$-0.0991119\pi$
$337$	21.3417	+	12.3216i	1.16256	+	0.671202i	0.210640	+	0.977564i	$0.432445\pi$
$338$	3.68840	+	6.38850i	0.200623	+	0.347489i
$339$		0			0
$340$	5.57698	+	1.89394i	0.302454	+	0.102713i
$341$	−5.55839	+	9.62741i	−0.301003	+	0.521353i
$342$		0			0
$343$	−18.5183	+	0.270672i	−0.999893	+	0.0146149i
$344$	−10.4023	+	6.00577i	−0.560854	+	0.323809i
$345$		0			0
$346$		−	14.8129i		−	0.796347i
$347$	0.546144			0.0293186			0.0146593	−	0.999893i	$-0.495334\pi$
$347$	0.546144			0.0293186			0.0146593	+	0.999893i	$0.495334\pi$
$348$		0			0
$349$	−5.63017	+	3.25058i	−0.301376	+	0.174000i	−0.643061	−	0.765815i	$-0.722336\pi$
$349$	−5.63017	+	3.25058i	−0.301376	+	0.174000i	0.341685	+	0.939815i	$0.389003\pi$
$350$	10.5321	+	8.00467i	0.562965	+	0.427868i
$351$		0			0
$352$	−3.56894	−	2.06053i	−0.190225	−	0.109827i
$353$	−5.67627	−	3.27719i	−0.302117	−	0.174427i	0.341276	−	0.939963i	$-0.389141\pi$
$353$	−5.67627	−	3.27719i	−0.302117	−	0.174427i	−0.643394	+	0.765536i	$0.722474\pi$
$354$		0			0
$355$	2.69292	−	2.36101i	0.142925	−	0.125309i
$356$	7.82648	−	13.5559i	0.414802	−	0.718459i
$357$		0			0
$358$	−20.6373	+	11.9149i	−1.09071	+	0.629724i
$359$	3.55244	+	2.05100i	0.187490	+	0.108248i	0.590807	−	0.806813i	$-0.298809\pi$
$359$	3.55244	+	2.05100i	0.187490	+	0.108248i	−0.403317	+	0.915060i	$0.632143\pi$
$360$		0			0
$361$	−8.88946	−	15.3970i	−0.467866	−	0.810368i
$362$		−	11.6911i		−	0.614470i
$363$		0			0
$364$	−3.16341	−	5.41805i	−0.165807	−	0.283983i
$365$	4.73338	−	13.9381i	0.247756	−	0.729555i
$366$		0			0
$367$	−10.0785	+	17.4565i	−0.526096	+	0.911224i	0.473442	+	0.880825i	$0.343011\pi$
$367$	−10.0785	+	17.4565i	−0.526096	+	0.911224i	−0.999538	+	0.0303995i	$0.990322\pi$
$368$	−0.296239	−	0.513101i	−0.0154425	−	0.0267473i
$369$		0			0
$370$	3.04810	+	15.3342i	0.158463	+	0.797190i
$371$	−24.0446	+	0.117142i	−1.24834	+	0.00608170i
$372$		0			0
$373$	4.94553	−	2.85530i	0.256070	−	0.147842i	−0.366471	−	0.930430i	$-0.619434\pi$
$373$	4.94553	−	2.85530i	0.256070	−	0.147842i	0.622540	+	0.782588i	$0.286101\pi$
$374$	10.8549			0.561291
$375$		0			0
$376$		−	4.12973i		−	0.212975i
$377$			6.48817i			0.334158i
$378$		0			0
$379$	5.42424			0.278624			0.139312	−	0.990249i	$-0.455511\pi$
$379$	5.42424			0.278624			0.139312	+	0.990249i	$0.455511\pi$
$380$	−0.481736	−	2.42350i	−0.0247125	−	0.124323i
$381$		0			0
$382$			26.0254i			1.33158i
$383$	28.8586	−	16.6615i	1.47460	−	0.851363i	0.475013	−	0.879979i	$-0.342443\pi$
$383$	28.8586	−	16.6615i	1.47460	−	0.851363i	0.999590	+	0.0286163i	$0.00911009\pi$
$384$		0			0
$385$	23.1235	+	7.72730i	1.17848	+	0.393820i
$386$		−	18.0736i		−	0.919920i
$387$		0			0
$388$	6.92406	+	11.9928i	0.351516	+	0.608844i
$389$	−25.3567	−	14.6397i	−1.28564	−	0.742263i	−0.307764	−	0.951463i	$-0.599581\pi$
$389$	−25.3567	−	14.6397i	−1.28564	−	0.742263i	−0.977873	+	0.209200i	$0.932914\pi$
$390$		0			0
$391$	1.35151	+	0.780293i	0.0683486	+	0.0394611i
$392$	−3.55890	−	6.02779i	−0.179752	−	0.304449i
$393$		0			0
$394$	19.0964			0.962063
$395$	−19.8173	−	22.6032i	−0.997116	−	1.13729i
$396$		0			0
$397$	−5.42713	+	9.40006i	−0.272380	+	0.471775i	−0.969471	−	0.245207i	$-0.921144\pi$
$397$	−5.42713	+	9.40006i	−0.272380	+	0.471775i	0.697091	+	0.716983i	$0.254477\pi$
$398$	21.6198	−	12.4822i	1.08370	−	0.625676i
$399$		0			0
$400$	−0.653922	+	4.95705i	−0.0326961	+	0.247853i
$401$	15.8321	−	9.14066i	0.790616	−	0.456463i	−0.0495631	−	0.998771i	$-0.515783\pi$
$401$	15.8321	−	9.14066i	0.790616	−	0.456463i	0.840180	+	0.542308i	$0.182450\pi$
$402$		0			0
$403$	−5.53978	−	3.19839i	−0.275956	−	0.159323i
$404$	−1.35453	+	2.34612i	−0.0673905	+	0.116724i
$405$		0			0
$406$	0.0352670	+	7.23893i	0.00175027	+	0.359262i
$407$	14.4069	+	24.9535i	0.714124	+	1.23690i
$408$		0			0
$409$		−	9.67827i		−	0.478560i	−0.970951	−	0.239280i	$-0.923089\pi$
$409$		−	9.67827i		−	0.478560i	0.970951	−	0.239280i	$-0.0769113\pi$
$410$	1.12766	−	0.224154i	0.0556914	−	0.0110702i
$411$		0			0
$412$	−9.07239	−	15.7138i	−0.446964	−	0.774165i
$413$	9.10250	−	15.9449i	0.447905	−	0.784596i
$414$		0			0
$415$	−9.29959	−	3.15814i	−0.456499	−	0.155027i
$416$	1.18566	−	2.05363i	0.0581320	−	0.100688i
$417$		0			0
$418$	−2.27694	−	3.94378i	−0.111369	−	0.192896i
$419$	−5.02659	+	8.70630i	−0.245565	+	0.425331i	−0.962290	−	0.272025i	$-0.912307\pi$
$419$	−5.02659	+	8.70630i	−0.245565	+	0.425331i	0.716725	+	0.697355i	$0.245640\pi$
$420$		0			0
$421$	−6.61761	−	11.4620i	−0.322522	−	0.558625i	0.658485	−	0.752594i	$-0.271197\pi$
$421$	−6.61761	−	11.4620i	−0.322522	−	0.558625i	−0.981008	+	0.193968i	$0.937864\pi$
$422$	−6.61689	+	11.4608i	−0.322105	+	0.557902i
$423$		0			0
$424$	−4.54406	−	7.87055i	−0.220679	−	0.382228i
$425$	−5.03676	−	12.1688i	−0.244319	−	0.590273i
$426$		0			0
$427$	9.86461	+	5.63143i	0.477382	+	0.272524i
$428$	−4.33862	+	7.51471i	−0.209715	+	0.363237i
$429$		0			0
$430$	25.4321	+	8.63673i	1.22645	+	0.416500i
$431$	−4.44716	+	2.56757i	−0.214212	+	0.123675i	−0.603267	−	0.797539i	$-0.706135\pi$
$431$	−4.44716	+	2.56757i	−0.214212	+	0.123675i	0.389055	+	0.921214i	$0.372801\pi$
$432$		0			0
$433$	−7.97362			−0.383188			−0.191594	−	0.981474i	$-0.561366\pi$
$433$	−7.97362			−0.383188			−0.191594	+	0.981474i	$0.561366\pi$
$434$	−6.19818	−	3.53837i	−0.297522	−	0.169847i
$435$		0			0
$436$	−7.55567	−	13.0868i	−0.361851	−	0.626745i
$437$		−	0.654705i		−	0.0313188i
$438$		0			0
$439$			25.8078i			1.23174i	0.787849	+	0.615869i	$0.211195\pi$
$439$			25.8078i			1.23174i	−0.787849	+	0.615869i	$0.788805\pi$
$440$	1.79657	+	9.03814i	0.0856483	+	0.430876i
$441$		0			0
$442$			6.24607i			0.297095i
$443$	31.2880			1.48654			0.743269	−	0.668992i	$-0.233274\pi$
$443$	31.2880			1.48654			0.743269	+	0.668992i	$0.233274\pi$
$444$		0			0
$445$	−34.3294	+	6.82390i	−1.62737	+	0.323484i
$446$	−2.44383	−	4.23284i	−0.115719	−	0.200431i
$447$		0			0
$448$	1.31170	−	2.29771i	0.0619719	−	0.108556i
$449$		−	6.93666i		−	0.327361i	−0.986513	−	0.163681i	$-0.947663\pi$
$449$		−	6.93666i		−	0.327361i	0.986513	−	0.163681i	$-0.0523366\pi$
$450$		0			0
$451$	1.83506	−	1.05947i	0.0864094	−	0.0498885i
$452$	0.503287	−	0.871718i	0.0236726	−	0.0410022i
$453$		0			0
$454$	10.3873	+	5.99711i	0.487500	+	0.281458i
$455$	−4.44642	+	13.3057i	−0.208452	+	0.623780i
$456$		0			0
$457$		−	27.4150i		−	1.28242i	−0.767366	−	0.641209i	$-0.778433\pi$
$457$		−	27.4150i		−	1.28242i	0.767366	−	0.641209i	$-0.221567\pi$
$458$	9.16676	−	5.29243i	0.428335	−	0.247299i
$459$		0			0
$460$	−0.426013	+	1.25446i	−0.0198630	+	0.0584894i
$461$	9.16139	+	15.8680i	0.426689	+	0.739046i	0.996576	−	0.0826762i	$-0.0263467\pi$
$461$	9.16139	+	15.8680i	0.426689	+	0.739046i	−0.569888	+	0.821722i	$0.693013\pi$
$462$		0			0
$463$	16.6964	+	9.63966i	0.775947	+	0.447993i	0.834992	−	0.550262i	$-0.185472\pi$
$463$	16.6964	+	9.63966i	0.775947	+	0.447993i	−0.0590450	+	0.998255i	$0.518806\pi$
$464$	−2.36953	+	1.36805i	−0.110002	+	0.0635099i
$465$		0			0
$466$	0.259858	−	0.450088i	0.0120377	−	0.0208499i
$467$	11.2146	+	6.47476i	0.518951	+	0.299616i	0.736505	−	0.676432i	$-0.236475\pi$
$467$	11.2146	+	6.47476i	0.518951	+	0.299616i	−0.217555	+	0.976048i	$0.569808\pi$
$468$		0			0
$469$	−31.0535	−	17.7276i	−1.43392	−	0.818584i
$470$	−6.94356	+	6.08774i	−0.320282	+	0.280806i
$471$		0			0
$472$	6.93948			0.319415
$473$	49.5003			2.27602
$474$		0			0
$475$	−3.36463	+	4.38251i	−0.154380	+	0.201083i
$476$	0.0339510	+	6.96882i	0.00155614	+	0.319415i
$477$		0			0
$478$	2.39886	+	1.38498i	0.109721	+	0.0633475i
$479$	13.5378	−	23.4482i	0.618560	−	1.07138i	−0.371189	−	0.928557i	$-0.621050\pi$
$479$	13.5378	−	23.4482i	0.618560	−	1.07138i	0.989749	−	0.142820i	$-0.0456169\pi$
$480$		0			0
$481$	−14.3587	+	8.28999i	−0.654700	+	0.377991i
$482$	17.4943	+	10.1004i	0.796845	+	0.460059i
$483$		0			0
$484$	2.99156	+	5.18154i	0.135980	+	0.235524i
$485$	9.95731	−	29.3207i	0.452138	−	1.33139i
$486$		0			0
$487$	−2.98800	+	1.72512i	−0.135399	+	0.0781727i	−0.566169	−	0.824289i	$-0.691575\pi$
$487$	−2.98800	+	1.72512i	−0.135399	+	0.0781727i	0.430770	+	0.902462i	$0.358242\pi$
$488$			4.29324i			0.194346i
$489$		0			0
$490$	−4.88861	+	14.8695i	−0.220845	+	0.671735i
$491$	36.9916	+	21.3571i	1.66941	+	0.963833i	0.967958	+	0.251113i	$0.0807967\pi$
$491$	36.9916	+	21.3571i	1.66941	+	0.963833i	0.701449	+	0.712719i	$0.252537\pi$
$492$		0			0
$493$	3.60343	−	6.24132i	0.162290	−	0.281095i
$494$	2.26932	−	1.31019i	0.102101	−	0.0589483i
$495$		0			0
$496$		−	2.69755i		−	0.121124i
$497$	3.68009	+	2.10086i	0.165075	+	0.0942365i
$498$		0			0
$499$	−18.0193	−	31.2103i	−0.806654	−	1.39717i	−0.915169	−	0.403071i	$-0.867943\pi$
$499$	−18.0193	−	31.2103i	−0.806654	−	1.39717i	0.108514	−	0.994095i	$-0.465391\pi$
$500$	9.29854	−	6.20783i	0.415843	−	0.277623i
$501$		0			0
$502$	20.9869			0.936691
$503$			4.41774i			0.196977i	0.995138	+	0.0984887i	$0.0314008\pi$
$503$			4.41774i			0.196977i	−0.995138	+	0.0984887i	$0.968599\pi$
$504$		0			0
$505$	5.94141	−	1.18102i	0.264389	−	0.0525545i
$506$			2.44164i			0.108544i
$507$		0			0
$508$		−	3.12538i		−	0.138666i
$509$	−12.1022	−	20.9617i	−0.536422	−	0.929110i	−0.999093	−	0.0425803i	$-0.986442\pi$
$509$	−12.1022	−	20.9617i	−0.536422	−	0.929110i	0.462671	−	0.886530i	$-0.346891\pi$
$510$		0			0
$511$	17.4166	−	0.0848512i	0.770467	−	0.00375360i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−8.21246	+	4.74146i	−0.362236	+	0.209137i
$515$	−13.0467	+	38.4180i	−0.574908	+	1.69290i
$516$		0			0
$517$	−8.50944	+	14.7388i	−0.374245	+	0.648211i
$518$	−15.9751	+	9.32729i	−0.701905	+	0.409818i
$519$		0			0
$520$	−5.20070	+	1.03378i	−0.228066	+	0.0453342i
$521$	−7.58138	−	13.1313i	−0.332146	−	0.575294i	0.650786	−	0.759261i	$-0.274439\pi$
$521$	−7.58138	−	13.1313i	−0.332146	−	0.575294i	−0.982932	+	0.183967i	$0.941106\pi$
$522$		0			0
$523$	−0.294517	+	0.510118i	−0.0128783	+	0.0223059i	−0.872393	−	0.488806i	$-0.837433\pi$
$523$	−0.294517	+	0.510118i	−0.0128783	+	0.0223059i	0.859514	+	0.511111i	$0.170766\pi$
$524$	10.7870	+	18.6837i	0.471234	+	0.816202i
$525$		0			0
$526$	5.83660	−	10.1093i	0.254488	−	0.440786i
$527$	3.55267	+	6.15341i	0.154757	+	0.268047i
$528$		0			0
$529$	11.3245	−	19.6146i	0.492369	−	0.852808i
$530$	−6.53469	+	19.2424i	−0.283849	+	0.835834i
$531$		0			0
$532$	2.52478	−	1.47413i	0.109463	−	0.0639117i
$533$	0.609637	+	1.05592i	0.0264063	+	0.0457371i
$534$		0			0
$535$	19.0306	−	3.78284i	0.822763	−	0.163546i
$536$		−	13.5150i		−	0.583759i
$537$		0			0
$538$	−8.14330	−	14.1046i	−0.351082	−	0.608093i
$539$	0.281074	+	28.8460i	0.0121067	+	1.24249i
$540$		0			0
$541$	−21.2555	+	36.8156i	−0.913846	+	1.58283i	−0.105264	+	0.994444i	$0.533569\pi$
$541$	−21.2555	+	36.8156i	−0.913846	+	1.58283i	−0.808582	+	0.588384i	$0.799764\pi$
$542$	21.8041	+	12.5886i	0.936566	+	0.540726i
$543$		0			0
$544$	−2.28111	+	1.31700i	−0.0978017	+	0.0564658i
$545$	−10.8656	+	31.9954i	−0.465431	+	1.37053i
$546$		0			0
$547$	7.46589	−	4.31044i	0.319219	−	0.184301i	−0.331826	−	0.943341i	$-0.607665\pi$
$547$	7.46589	−	4.31044i	0.319219	−	0.184301i	0.651044	+	0.759040i	$0.274331\pi$
$548$	−1.88397	+	3.26314i	−0.0804793	+	0.139394i
$549$		0			0
$550$	12.5480	−	16.3440i	0.535047	−	0.696911i
$551$	−3.02346			−0.128804
$552$		0			0
$553$	17.6337	−	30.8891i	0.749862	−	1.31354i
$554$	17.9632	+	10.3710i	0.763182	+	0.440623i
$555$		0			0
$556$	5.20651	+	3.00598i	0.220805	+	0.127482i
$557$	−3.09319	−	5.35757i	−0.131063	−	0.227007i	0.793024	−	0.609191i	$-0.208506\pi$
$557$	−3.09319	−	5.35757i	−0.131063	−	0.227007i	−0.924087	+	0.382183i	$0.875172\pi$
$558$		0			0
$559$			28.4833i			1.20472i
$560$	−5.79687	+	1.18167i	−0.244962	+	0.0499346i
$561$		0			0
$562$	−1.17815	+	0.680206i	−0.0496974	+	0.0286928i
$563$		−	32.6001i		−	1.37393i	−0.726690	−	0.686966i	$-0.758942\pi$
$563$		−	32.6001i		−	1.37393i	0.726690	−	0.686966i	$-0.241058\pi$
$564$		0			0
$565$	−2.20758	+	0.438815i	−0.0928734	+	0.0184611i
$566$	14.9351			0.627771
$567$		0			0
$568$			1.60164i			0.0672032i
$569$			6.56784i			0.275338i	0.990478	+	0.137669i	$0.0439611\pi$
$569$			6.56784i			0.275338i	−0.990478	+	0.137669i	$0.956039\pi$
$570$		0			0
$571$	−17.9871			−0.752737			−0.376369	−	0.926470i	$-0.622827\pi$
$571$	−17.9871			−0.752737			−0.376369	+	0.926470i	$0.622827\pi$
$572$	−8.46313	+	4.88619i	−0.353861	+	0.204302i
$573$		0			0
$574$	0.685919	+	1.17479i	0.0286297	+	0.0490349i
$575$	2.73719	−	1.13295i	0.114149	−	0.0472471i
$576$		0			0
$577$	−11.8915	−	20.5968i	−0.495051	−	0.857454i	0.504932	−	0.863159i	$-0.331517\pi$
$577$	−11.8915	−	20.5968i	−0.495051	−	0.857454i	−0.999984	+	0.00570479i	$0.998184\pi$
$578$	−5.03103	+	8.71400i	−0.209263	+	0.362455i
$579$		0			0
$580$	5.79315	+	1.96735i	0.240547	+	0.0816897i
$581$	−0.0566132	−	11.6205i	−0.00234871	−	0.482098i
$582$		0			0
$583$			37.4527i			1.55113i
$584$	3.29147	+	5.70100i	0.136202	+	0.235909i
$585$		0			0
$586$	9.63607	+	5.56339i	0.398062	+	0.229821i
$587$	−14.2796	+	8.24435i	−0.589384	+	0.340281i	−0.764854	−	0.644204i	$-0.777189\pi$
$587$	−14.2796	+	8.24435i	−0.589384	+	0.340281i	0.175470	+	0.984485i	$0.443855\pi$
$588$		0			0
$589$	1.49043	−	2.58151i	0.0614123	−	0.106369i
$590$	−10.2296	−	11.6677i	−0.421148	−	0.480353i
$591$		0			0
$592$	−6.05512	−	3.49593i	−0.248864	−	0.143682i
$593$	8.69178	+	5.01820i	0.356928	+	0.206073i	0.667733	−	0.744401i	$-0.267265\pi$
$593$	8.69178	+	5.01820i	0.356928	+	0.206073i	−0.310804	+	0.950474i	$0.600598\pi$
$594$		0			0
$595$	11.6670	−	10.3300i	0.478301	−	0.423488i
$596$	9.69236	−	5.59589i	0.397015	−	0.229217i
$597$		0			0
$598$	−1.40496			−0.0574531
$599$			35.1519i			1.43627i	0.695905	+	0.718134i	$0.255003\pi$
$599$			35.1519i			1.43627i	−0.695905	+	0.718134i	$0.744997\pi$
$600$		0			0
$601$	−32.5093	+	18.7692i	−1.32608	+	0.765613i	−0.984691	−	0.174309i	$-0.944231\pi$
$601$	−32.5093	+	18.7692i	−1.32608	+	0.765613i	−0.341390	+	0.939922i	$0.610898\pi$
$602$	0.154823	+	31.7792i	0.00631013	+	1.29522i
$603$		0			0
$604$	9.27469	−	16.0642i	0.377382	−	0.653644i
$605$	4.30208	−	12.6681i	0.174905	−	0.515032i
$606$		0			0
$607$	12.0927	+	20.9451i	0.490827	+	0.850136i	0.999944	−	0.0105604i	$-0.00336154\pi$
$607$	12.0927	+	20.9451i	0.490827	+	0.850136i	−0.509118	+	0.860697i	$0.670028\pi$
$608$	0.956982	+	0.552514i	0.0388107	+	0.0224074i
$609$		0			0
$610$	7.21847	−	6.32877i	0.292267	−	0.256244i
$611$	−8.48095	−	4.89648i	−0.343102	−	0.198090i
$612$		0			0
$613$	23.6618	−	13.6611i	0.955690	−	0.551768i	0.0608460	−	0.998147i	$-0.480620\pi$
$613$	23.6618	−	13.6611i	0.955690	−	0.551768i	0.894844	+	0.446379i	$0.147287\pi$
$614$	14.1337			0.570388
$615$		0			0
$616$	−9.41586	+	5.49759i	−0.379376	+	0.221504i
$617$	−7.76658	+	13.4521i	−0.312671	+	0.541562i	−0.978940	−	0.204150i	$-0.934557\pi$
$617$	−7.76658	+	13.4521i	−0.312671	+	0.541562i	0.666269	+	0.745712i	$0.267890\pi$
$618$		0			0
$619$	18.4101	+	10.6291i	0.739963	+	0.427218i	0.822056	−	0.569407i	$-0.192827\pi$
$619$	18.4101	+	10.6291i	0.739963	+	0.427218i	−0.0820931	+	0.996625i	$0.526160\pi$
$620$	−4.53555	+	3.97652i	−0.182152	+	0.159701i
$621$		0			0
$622$	5.87504			0.235568
$623$	−20.8814	−	35.7641i	−0.836595	−	1.43286i
$624$		0			0
$625$	−24.1448	−	6.48305i	−0.965791	−	0.259322i
$626$	−19.0369			−0.760866
$627$		0			0
$628$	−11.6703			−0.465695
$629$	18.4165			0.734314
$630$		0			0
$631$	22.0357			0.877226			0.438613	−	0.898676i	$-0.355470\pi$
$631$	22.0357			0.877226			0.438613	+	0.898676i	$0.355470\pi$
$632$	13.4434			0.534751
$633$		0			0
$634$	−15.4166			−0.612271
$635$	−5.25488	+	4.60720i	−0.208534	+	0.182831i
$636$		0			0
$637$	−16.5985	+	0.161735i	−0.657657	+	0.00640816i
$638$	11.2756			0.446405
$639$		0			0
$640$	−1.47412	−	1.68136i	−0.0582698	−	0.0664615i
$641$	−22.2308	−	12.8350i	−0.878065	−	0.506951i	−0.00804523	−	0.999968i	$-0.502561\pi$
$641$	−22.2308	−	12.8350i	−0.878065	−	0.506951i	−0.870020	+	0.493016i	$0.835894\pi$
$642$		0			0
$643$	−0.505064	+	0.874797i	−0.0199178	+	0.0344986i	−0.875813	−	0.482651i	$-0.839674\pi$
$643$	−0.505064	+	0.874797i	−0.0199178	+	0.0344986i	0.855895	+	0.517150i	$0.173007\pi$
$644$	−1.56753	+	0.00763677i	−0.0617694	+	0.000300931i
$645$		0			0
$646$	−2.91064			−0.114517
$647$	12.5056	−	7.22013i	0.491647	−	0.283852i	−0.233611	−	0.972330i	$-0.575054\pi$
$647$	12.5056	−	7.22013i	0.491647	−	0.283852i	0.725257	+	0.688478i	$0.241721\pi$
$648$		0			0
$649$	−24.7666	−	14.2990i	−0.972174	−	0.561285i
$650$	9.40463	+	7.22032i	0.368880	+	0.283204i
$651$		0			0
$652$	−10.7728	−	6.21967i	−0.421895	−	0.243581i
$653$	−22.1117	−	38.2986i	−0.865299	−	1.49874i	−0.866750	−	0.498743i	$-0.833795\pi$
$653$	−22.1117	−	38.2986i	−0.865299	−	1.49874i	0.00145120	−	0.999999i	$-0.499538\pi$
$654$		0			0
$655$	15.5126	−	45.6790i	0.606126	−	1.78483i
$656$	−0.257087	+	0.445287i	−0.0100376	+	0.0173855i
$657$		0			0
$658$	−9.48891	−	5.41696i	−0.369916	−	0.211175i
$659$	24.1702	−	13.9547i	0.941539	−	0.543598i	0.0510965	−	0.998694i	$-0.483728\pi$
$659$	24.1702	−	13.9547i	0.941539	−	0.543598i	0.890442	+	0.455096i	$0.150395\pi$
$660$		0			0
$661$			0.0428492i			0.00166664i	1.00000		0.000833320i	$0.000265254\pi$
$661$			0.0428492i			0.00166664i	−1.00000		0.000833320i	$0.999735\pi$
$662$	−30.9300			−1.20213
$663$		0			0
$664$	3.80374	−	2.19609i	0.147614	−	0.0852248i
$665$	−6.20038	−	2.07201i	−0.240441	−	0.0803492i
$666$		0			0
$667$	1.40389	+	0.810538i	0.0543589	+	0.0313841i
$668$	−11.4205	−	6.59363i	−0.441873	−	0.255115i
$669$		0			0
$670$	−22.7235	+	19.9228i	−0.877887	+	0.769684i
$671$	8.84635	−	15.3223i	0.341510	−	0.591512i
$672$		0			0
$673$	17.4536	−	10.0769i	0.672788	−	0.388434i	−0.124344	−	0.992239i	$-0.539683\pi$
$673$	17.4536	−	10.0769i	0.672788	−	0.388434i	0.797132	+	0.603805i	$0.206349\pi$
$674$	21.3417	+	12.3216i	0.822051	+	0.474611i
$675$		0			0
$676$	3.68840	+	6.38850i	0.141862	+	0.245711i
$677$		−	28.0616i		−	1.07850i	−0.842147	−	0.539248i	$-0.818709\pi$
$677$		−	28.0616i		−	1.07850i	0.842147	−	0.539248i	$-0.181291\pi$
$678$		0			0
$679$	36.6383	−	0.178496i	1.40605	−	0.00685005i
$680$	5.57698	+	1.89394i	0.213867	+	0.0726292i
$681$		0			0
$682$	−5.55839	+	9.62741i	−0.212842	+	0.368652i
$683$	−14.7248	−	25.5040i	−0.563428	−	0.975885i	−0.997194	−	0.0748598i	$-0.976149\pi$
$683$	−14.7248	−	25.5040i	−0.563428	−	0.975885i	0.433767	−	0.901025i	$-0.357184\pi$
$684$		0			0
$685$	8.26371	−	1.64263i	0.315740	−	0.0627618i
$686$	−18.5183	+	0.270672i	−0.707031	+	0.0103343i
$687$		0			0
$688$	−10.4023	+	6.00577i	−0.396584	+	0.228968i
$689$	−21.5509			−0.821025
$690$		0			0
$691$			6.96725i			0.265047i	0.991180	+	0.132523i	$0.0423080\pi$
$691$			6.96725i			0.265047i	−0.991180	+	0.132523i	$0.957692\pi$
$692$		−	14.8129i		−	0.563102i
$693$		0			0
$694$	0.546144			0.0207313
$695$	−2.62091	−	13.1852i	−0.0994168	−	0.500142i
$696$		0			0
$697$		−	1.35433i		−	0.0512989i
$698$	−5.63017	+	3.25058i	−0.213105	+	0.123036i
$699$		0			0
$700$	10.5321	+	8.00467i	0.398076	+	0.302548i
$701$			17.0338i			0.643357i	0.946849	+	0.321678i	$0.104247\pi$
$701$			17.0338i			0.643357i	−0.946849	+	0.321678i	$0.895753\pi$
$702$		0			0
$703$	−3.86309	−	6.69107i	−0.145699	−	0.252359i
$704$	−3.56894	−	2.06053i	−0.134510	−	0.0776591i
$705$		0			0
$706$	−5.67627	−	3.27719i	−0.213629	−	0.123339i
$707$	3.61396	+	6.18972i	0.135917	+	0.232788i
$708$		0			0
$709$	−1.02107			−0.0383470			−0.0191735	−	0.999816i	$-0.506103\pi$
$709$	−1.02107			−0.0383470			−0.0191735	+	0.999816i	$0.506103\pi$
$710$	2.69292	−	2.36101i	0.101064	−	0.0886071i
$711$		0			0
$712$	7.82648	−	13.5559i	0.293310	−	0.508027i
$713$	−1.38412	+	0.799121i	−0.0518356	+	0.0299273i
$714$		0			0
$715$	20.6911	+	7.02670i	0.773804	+	0.262784i
$716$	−20.6373	+	11.9149i	−0.771251	+	0.445282i
$717$		0			0
$718$	3.55244	+	2.05100i	0.132576	+	0.0765426i
$719$	20.6417	−	35.7524i	0.769804	−	1.33334i	−0.167865	−	0.985810i	$-0.553687\pi$
$719$	20.6417	−	35.7524i	0.769804	−	1.33334i	0.937669	−	0.347530i	$-0.112980\pi$
$720$		0			0
$721$	−48.0060	+	0.233878i	−1.78784	+	0.00871006i
$722$	−8.88946	−	15.3970i	−0.330831	−	0.573017i
$723$		0			0
$724$		−	11.6911i		−	0.434496i
$725$	−5.23199	−	12.6405i	−0.194311	−	0.469455i
$726$		0			0
$727$	7.79834	+	13.5071i	0.289224	+	0.500951i	0.973625	−	0.228155i	$-0.0732693\pi$
$727$	7.79834	+	13.5071i	0.289224	+	0.500951i	−0.684400	+	0.729106i	$0.739936\pi$
$728$	−3.16341	−	5.41805i	−0.117244	−	0.200806i
$729$		0			0
$730$	4.73338	−	13.9381i	0.175190	−	0.515873i
$731$	15.8192	−	27.3996i	0.585093	−	1.01341i
$732$		0			0
$733$	−22.3150	−	38.6507i	−0.824222	−	1.42759i	−0.902512	−	0.430664i	$-0.858279\pi$
$733$	−22.3150	−	38.6507i	−0.824222	−	1.42759i	0.0782904	−	0.996931i	$-0.475054\pi$
$734$	−10.0785	+	17.4565i	−0.372006	+	0.644333i
$735$		0			0
$736$	−0.296239	−	0.513101i	−0.0109195	−	0.0189132i
$737$	−27.8480	+	48.2342i	−1.02580	+	1.77673i
$738$		0			0
$739$	−14.6785	−	25.4239i	−0.539957	−	0.935233i	−0.998906	−	0.0467704i	$-0.985107\pi$
$739$	−14.6785	−	25.4239i	−0.539957	−	0.935233i	0.458949	−	0.888463i	$-0.348226\pi$
$740$	3.04810	+	15.3342i	0.112050	+	0.563698i
$741$		0			0
$742$	−24.0446	+	0.117142i	−0.882706	+	0.00430041i
$743$	−20.1964	+	34.9813i	−0.740936	+	1.28334i	0.211134	+	0.977457i	$0.432284\pi$
$743$	−20.1964	+	34.9813i	−0.740936	+	1.28334i	−0.952070	+	0.305881i	$0.901049\pi$
$744$		0			0
$745$	−23.6964	−	8.04729i	−0.868170	−	0.294830i
$746$	4.94553	−	2.85530i	0.181069	−	0.104540i
$747$		0			0
$748$	10.8549			0.396893
$749$	11.5756	+	19.8259i	0.422965	+	0.724423i
$750$		0			0
$751$	10.9318	+	18.9344i	0.398905	+	0.690924i	0.993591	−	0.113034i	$-0.0360568\pi$
$751$	10.9318	+	18.9344i	0.398905	+	0.690924i	−0.594686	+	0.803958i	$0.702724\pi$
$752$		−	4.12973i		−	0.150596i
$753$		0			0
$754$			6.48817i			0.236285i
$755$	−40.6817	+	8.08659i	−1.48056	+	0.294301i
$756$		0			0
$757$			14.0506i			0.510679i	0.966851	+	0.255339i	$0.0821872\pi$
$757$			14.0506i			0.510679i	−0.966851	+	0.255339i	$0.917813\pi$
$758$	5.42424			0.197017
$759$		0			0
$760$	−0.481736	−	2.42350i	−0.0174744	−	0.0879096i
$761$	−19.5919	−	33.9341i	−0.710204	−	1.23011i	−0.964780	−	0.263057i	$-0.915269\pi$
$761$	−19.5919	−	33.9341i	−0.710204	−	1.23011i	0.254576	−	0.967053i	$-0.418064\pi$
$762$		0			0
$763$	−39.9804	+	0.194778i	−1.44739	+	0.00705145i
$764$			26.0254i			0.941567i
$765$		0			0
$766$	28.8586	−	16.6615i	1.04270	−	0.602004i
$767$	8.22789	−	14.2511i	0.297092	−	0.514578i
$768$		0			0
$769$	16.4424	+	9.49301i	0.592927	+	0.342327i	0.766254	−	0.642538i	$-0.222118\pi$
$769$	16.4424	+	9.49301i	0.592927	+	0.342327i	−0.173327	+	0.984864i	$0.555452\pi$
$770$	23.1235	+	7.72730i	0.833315	+	0.278473i
$771$		0			0
$772$		−	18.0736i		−	0.650482i
$773$	−28.9315	+	16.7036i	−1.04060	+	0.600788i	−0.920002	−	0.391914i	$-0.871813\pi$
$773$	−28.9315	+	16.7036i	−1.04060	+	0.600788i	−0.120593	+	0.992702i	$0.538480\pi$
$774$		0			0
$775$	13.3719	+	1.76399i	0.480333	+	0.0633644i
$776$	6.92406	+	11.9928i	0.248559	+	0.430518i
$777$		0			0
$778$	−25.3567	−	14.6397i	−0.909082	−	0.524859i
$779$	−0.492055	+	0.284088i	−0.0176297	+	0.0101785i
$780$		0			0
$781$	3.30022	−	5.71615i	0.118091	−	0.204540i
$782$	1.35151	+	0.780293i	0.0483298	+	0.0279032i
$783$		0			0
$784$	−3.55890	−	6.02779i	−0.127104	−	0.215278i
$785$	17.2034	+	19.6219i	0.614017	+	0.700336i
$786$		0			0
$787$	−0.872685			−0.0311079			−0.0155539	−	0.999879i	$-0.504951\pi$
$787$	−0.872685			−0.0311079			−0.0155539	+	0.999879i	$0.504951\pi$
$788$	19.0964			0.680281
$789$		0			0
$790$	−19.8173	−	22.6032i	−0.705067	−	0.804187i
$791$	−1.34279	−	2.29984i	−0.0477442	−	0.0817727i
$792$		0			0
$793$	8.81673	+	5.09034i	0.313091	+	0.180763i
$794$	−5.42713	+	9.40006i	−0.192601	+	0.333596i
$795$		0			0
$796$	21.6198	−	12.4822i	0.766294	−	0.442420i
$797$	−24.9244	−	14.3901i	−0.882867	−	0.509724i	−0.0112647	−	0.999937i	$-0.503586\pi$
$797$	−24.9244	−	14.3901i	−0.882867	−	0.509724i	−0.871603	+	0.490213i	$0.836919\pi$
$798$		0			0
$799$	5.43885	+	9.42037i	0.192413	+	0.333269i
$800$	−0.653922	+	4.95705i	−0.0231196	+	0.175258i
$801$		0			0
$802$	15.8321	−	9.14066i	0.559050	−	0.322768i
$803$		−	27.1287i		−	0.957352i
$804$		0			0
$805$	2.32358	+	2.62432i	0.0818953	+	0.0924952i
$806$	−5.53978	−	3.19839i	−0.195130	−	0.112659i
$807$		0			0
$808$	−1.35453	+	2.34612i	−0.0476523	+	0.0825362i
$809$	−3.58630	+	2.07055i	−0.126088	+	0.0727967i	−0.561717	−	0.827329i	$-0.689859\pi$
$809$	−3.58630	+	2.07055i	−0.126088	+	0.0727967i	0.435630	+	0.900126i	$0.356526\pi$
$810$		0			0
$811$			17.4383i			0.612342i	0.951977	+	0.306171i	$0.0990479\pi$
$811$			17.4383i			0.612342i	−0.951977	+	0.306171i	$0.900952\pi$
$812$	0.0352670	+	7.23893i	0.00123763	+	0.254037i
$813$		0			0
$814$	14.4069	+	24.9535i	0.504962	+	0.874620i
$815$	5.42292	+	27.2814i	0.189957	+	0.955627i
$816$		0			0
$817$	−13.2731			−0.464366
$818$		−	9.67827i		−	0.338393i
$819$		0			0
$820$	1.12766	−	0.224154i	0.0393797	−	0.00782779i
$821$		−	30.7953i		−	1.07476i	−0.843339	−	0.537381i	$-0.819414\pi$
$821$		−	30.7953i		−	1.07476i	0.843339	−	0.537381i	$-0.180586\pi$
$822$		0			0
$823$			35.0046i			1.22018i	0.792331	+	0.610092i	$0.208867\pi$
$823$			35.0046i			1.22018i	−0.792331	+	0.610092i	$0.791133\pi$
$824$	−9.07239	−	15.7138i	−0.316052	−	0.547417i
$825$		0			0
$826$	9.10250	−	15.9449i	0.316716	−	0.554793i
$827$	−34.7736			−1.20919			−0.604597	−	0.796531i	$-0.706666\pi$
$827$	−34.7736			−1.20919			−0.604597	+	0.796531i	$0.706666\pi$
$828$		0			0
$829$	−7.21777	+	4.16718i	−0.250683	+	0.144732i	−0.620077	−	0.784541i	$-0.712899\pi$
$829$	−7.21777	+	4.16718i	−0.250683	+	0.144732i	0.369394	+	0.929273i	$0.379565\pi$
$830$	−9.29959	−	3.15814i	−0.322793	−	0.109620i
$831$		0			0
$832$	1.18566	−	2.05363i	0.0411055	−	0.0711968i
$833$	16.0568	+	9.06297i	0.556336	+	0.314013i
$834$		0			0
$835$	5.74898	+	28.9218i	0.198952	+	1.00088i
$836$	−2.27694	−	3.94378i	−0.0787496	−	0.136398i
$837$		0			0
$838$	−5.02659	+	8.70630i	−0.173641	+	0.300754i
$839$	15.4855	+	26.8216i	0.534618	+	0.925985i	0.999182	+	0.0404455i	$0.0128777\pi$
$839$	15.4855	+	26.8216i	0.534618	+	0.925985i	−0.464564	+	0.885540i	$0.653789\pi$
$840$		0			0
$841$	−10.7569	+	18.6315i	−0.370928	+	0.642465i
$842$	−6.61761	−	11.4620i	−0.228058	−	0.395008i
$843$		0			0
$844$	−6.61689	+	11.4608i	−0.227763	+	0.394497i
$845$	5.30419	−	15.6190i	0.182470	−	0.537308i
$846$		0			0
$847$	15.8297	−	0.0771197i	0.543914	−	0.00264987i
$848$	−4.54406	−	7.87055i	−0.156044	−	0.270276i
$849$		0			0
$850$	−5.03676	−	12.1688i	−0.172760	−	0.417386i
$851$			4.14252i			0.142004i
$852$		0			0
$853$	−12.6526	−	21.9150i	−0.433217	−	0.750355i	0.563931	−	0.825822i	$-0.309288\pi$
$853$	−12.6526	−	21.9150i	−0.433217	−	0.750355i	−0.997148	+	0.0754673i	$0.975955\pi$
$854$	9.86461	+	5.63143i	0.337560	+	0.192704i
$855$		0			0
$856$	−4.33862	+	7.51471i	−0.148291	+	0.256848i
$857$	12.9904	+	7.50003i	0.443745	+	0.256196i	0.705185	−	0.709023i	$-0.250864\pi$
$857$	12.9904	+	7.50003i	0.443745	+	0.256196i	−0.261440	+	0.965220i	$0.584197\pi$
$858$		0			0
$859$	30.5617	−	17.6448i	1.04275	−	0.602032i	0.122140	−	0.992513i	$-0.461024\pi$
$859$	30.5617	−	17.6448i	1.04275	−	0.602032i	0.920611	+	0.390480i	$0.127691\pi$
$860$	25.4321	+	8.63673i	0.867228	+	0.294510i
$861$		0			0
$862$	−4.44716	+	2.56757i	−0.151471	+	0.0874517i
$863$	8.04268	−	13.9303i	0.273776	−	0.474194i	−0.696050	−	0.717994i	$-0.745061\pi$
$863$	8.04268	−	13.9303i	0.273776	−	0.474194i	0.969826	+	0.243800i	$0.0783940\pi$
$864$		0			0
$865$	−24.9058	+	21.8360i	−0.846822	+	0.742448i
$866$	−7.97362			−0.270955
$867$		0			0
$868$	−6.19818	−	3.53837i	−0.210380	−	0.120100i
$869$	−47.9789	−	27.7006i	−1.62757	−	0.939679i
$870$		0			0
$871$	−27.7548	−	16.0242i	−0.940436	−	0.542961i
$872$	−7.55567	−	13.0868i	−0.255867	−	0.443175i
$873$		0			0
$874$		−	0.654705i		−	0.0221457i
$875$	−2.06690	−	29.5081i	−0.0698740	−	0.997556i
$876$		0			0
$877$	24.0991	−	13.9136i	0.813767	−	0.469829i	−0.0344952	−	0.999405i	$-0.510982\pi$
$877$	24.0991	−	13.9136i	0.813767	−	0.469829i	0.848262	+	0.529576i	$0.177649\pi$
$878$			25.8078i			0.870970i
$879$		0			0
$880$	1.79657	+	9.03814i	0.0605625	+	0.304676i
$881$	36.4477			1.22795			0.613977	−	0.789324i	$-0.289569\pi$
$881$	36.4477			1.22795			0.613977	+	0.789324i	$0.289569\pi$
$882$		0			0
$883$		−	27.9433i		−	0.940367i	−0.882569	−	0.470184i	$-0.844188\pi$
$883$		−	27.9433i		−	0.940367i	0.882569	−	0.470184i	$-0.155812\pi$
$884$			6.24607i			0.210078i
$885$		0			0
$886$	31.2880			1.05114
$887$	−46.0356	+	26.5787i	−1.54572	+	0.892424i	−0.547263	+	0.836961i	$0.684330\pi$
$887$	−46.0356	+	26.5787i	−1.54572	+	0.892424i	−0.998461	+	0.0554632i	$0.982336\pi$
$888$		0			0
$889$	−7.18120	−	4.09955i	−0.240850	−	0.137495i
$890$	−34.3294	+	6.82390i	−1.15072	+	0.228738i
$891$		0			0
$892$	−2.44383	−	4.23284i	−0.0818255	−	0.141726i
$893$	2.28173	−	3.95208i	0.0763553	−	0.132251i
$894$		0			0
$895$	50.4552	+	17.1345i	1.68653	+	0.572745i
$896$	1.31170	−	2.29771i	0.0438207	−	0.0767610i
$897$		0			0
$898$		−	6.93666i		−	0.231479i
$899$	3.69038	+	6.39192i	0.123081	+	0.213182i
$900$		0			0
$901$	20.7310	+	11.9690i	0.690650	+	0.398747i
$902$	1.83506	−	1.05947i	0.0611006	−	0.0352765i
$903$		0			0
$904$	0.503287	−	0.871718i	0.0167391	−	0.0289929i
$905$	−19.6569	+	17.2341i	−0.653417	+	0.572881i
$906$		0			0
$907$	−13.9054	−	8.02828i	−0.461721	−	0.266575i	0.251047	−	0.967975i	$-0.419225\pi$
$907$	−13.9054	−	8.02828i	−0.461721	−	0.266575i	−0.712768	+	0.701400i	$0.752559\pi$
$908$	10.3873	+	5.99711i	0.344714	+	0.199021i
$909$		0			0
$910$	−4.44642	+	13.3057i	−0.147398	+	0.441079i
$911$	36.7577	−	21.2220i	1.21784	−	0.703118i	0.253381	−	0.967367i	$-0.418457\pi$
$911$	36.7577	−	21.2220i	1.21784	−	0.703118i	0.964455	+	0.264249i	$0.0851240\pi$
$912$		0			0
$913$	−18.1004			−0.599037
$914$		−	27.4150i		−	0.906806i
$915$		0			0
$916$	9.16676	−	5.29243i	0.302878	−	0.174867i
$917$	57.0790	−	0.278080i	1.88492	−	0.00918302i
$918$		0			0
$919$	−11.3435	+	19.6475i	−0.374188	+	0.648112i	−0.990205	−	0.139621i	$-0.955412\pi$
$919$	−11.3435	+	19.6475i	−0.374188	+	0.648112i	0.616017	+	0.787732i	$0.288745\pi$
$920$	−0.426013	+	1.25446i	−0.0140452	+	0.0413583i
$921$		0			0
$922$	9.16139	+	15.8680i	0.301714	+	0.522585i
$923$	3.28917	+	1.89900i	0.108264	+	0.0625064i
$924$		0			0
$925$	21.2891	−	27.7295i	0.699980	−	0.911740i
$926$	16.6964	+	9.63966i	0.548677	+	0.316779i
$927$		0			0
$928$	−2.36953	+	1.36805i	−0.0777835	+	0.0449083i
$929$	5.64081			0.185069			0.0925345	−	0.995709i	$-0.470503\pi$
$929$	5.64081			0.185069			0.0925345	+	0.995709i	$0.470503\pi$
$930$		0			0
$931$	−0.0753675	−	7.73482i	−0.00247007	−	0.253499i
$932$	0.259858	−	0.450088i	0.00851194	−	0.0147431i
$933$		0			0
$934$	11.2146	+	6.47476i	0.366953	+	0.211861i
$935$	−16.0014	−	18.2509i	−0.523301	−	0.596868i
$936$		0			0
$937$	−33.6125			−1.09807			−0.549036	−	0.835799i	$-0.685005\pi$
$937$	−33.6125			−1.09807			−0.549036	+	0.835799i	$0.685005\pi$
$938$	−31.0535	−	17.7276i	−1.01393	−	0.578826i
$939$		0			0
$940$	−6.94356	+	6.08774i	−0.226474	+	0.198560i
$941$	−0.233263			−0.00760416			−0.00380208	−	0.999993i	$-0.501210\pi$
$941$	−0.233263			−0.00760416			−0.00380208	+	0.999993i	$0.501210\pi$
$942$		0			0
$943$	0.304637			0.00992033
$944$	6.93948			0.225861
$945$		0			0
$946$	49.5003			1.60939
$947$	−2.62504			−0.0853024			−0.0426512	−	0.999090i	$-0.513580\pi$
$947$	−2.62504			−0.0853024			−0.0426512	+	0.999090i	$0.513580\pi$
$948$		0			0
$949$	15.6103			0.506733
$950$	−3.36463	+	4.38251i	−0.109163	+	0.142187i
$951$		0			0
$952$	0.0339510	+	6.96882i	0.00110036	+	0.225861i
$953$	−15.1772			−0.491637			−0.245818	−	0.969316i	$-0.579057\pi$
$953$	−15.1772			−0.491637			−0.245818	+	0.969316i	$0.579057\pi$
$954$		0			0
$955$	43.7581	−	38.3647i	1.41598	−	1.24145i
$956$	2.39886	+	1.38498i	0.0775846	+	0.0447935i
$957$		0			0
$958$	13.5378	−	23.4482i	0.437388	−	0.757578i
$959$	5.02653	+	8.60906i	0.162315	+	0.278001i
$960$		0			0
$961$	23.7232			0.765265
$962$	−14.3587	+	8.28999i	−0.462942	+	0.267280i
$963$		0			0
$964$	17.4943	+	10.1004i	0.563454	+	0.325310i
$965$	−30.3881	+	26.6427i	−0.978228	+	0.857658i
$966$		0			0
$967$	−11.1551	−	6.44040i	−0.358724	−	0.207109i	0.309797	−	0.950803i	$-0.399739\pi$
$967$	−11.1551	−	6.44040i	−0.358724	−	0.207109i	−0.668521	+	0.743693i	$0.733072\pi$
$968$	2.99156	+	5.18154i	0.0961525	+	0.166541i
$969$		0			0
$970$	9.95731	−	29.3207i	0.319710	−	0.941432i
$971$	−14.3294	+	24.8192i	−0.459851	+	0.796486i	−0.998953	−	0.0457549i	$-0.985431\pi$
$971$	−14.3294	+	24.8192i	−0.459851	+	0.796486i	0.539101	+	0.842241i	$0.318764\pi$
$972$		0			0
$973$	13.7362	−	8.02008i	0.440363	−	0.257112i
$974$	−2.98800	+	1.72512i	−0.0957416	+	0.0552765i
$975$		0			0
$976$			4.29324i			0.137423i
$977$	14.1607			0.453042			0.226521	−	0.974006i	$-0.427265\pi$
$977$	14.1607			0.453042			0.226521	+	0.974006i	$0.427265\pi$
$978$		0			0
$979$	−55.8645	+	32.2534i	−1.78544	+	1.03082i
$980$	−4.88861	+	14.8695i	−0.156161	+	0.474988i
$981$		0			0
$982$	36.9916	+	21.3571i	1.18045	+	0.681533i
$983$	34.2530	+	19.7760i	1.09250	+	0.630755i	0.934241	−	0.356643i	$-0.116079\pi$
$983$	34.2530	+	19.7760i	1.09250	+	0.630755i	0.158259	+	0.987398i	$0.449412\pi$
$984$		0			0
$985$	−28.1505	−	32.1079i	−0.896948	−	1.02304i
$986$	3.60343	−	6.24132i	0.114757	−	0.198764i
$987$		0			0
$988$	2.26932	−	1.31019i	0.0721966	−	0.0416827i
$989$	6.16314	+	3.55829i	0.195976	+	0.113147i
$990$		0			0
$991$	10.3535	+	17.9329i	0.328891	+	0.569656i	0.982292	−	0.187356i	$-0.0599917\pi$
$991$	10.3535	+	17.9329i	0.328891	+	0.569656i	−0.653401	+	0.757012i	$0.726658\pi$
$992$		−	2.69755i		−	0.0856474i
$993$		0			0
$994$	3.68009	+	2.10086i	0.116725	+	0.0666353i
$995$	−52.8573	−	17.9503i	−1.67569	−	0.569063i
$996$		0			0
$997$	−24.8760	+	43.0865i	−0.787831	+	1.36456i	0.139462	+	0.990227i	$0.455463\pi$
$997$	−24.8760	+	43.0865i	−0.787831	+	1.36456i	−0.927293	+	0.374336i	$0.877871\pi$
$998$	−18.0193	−	31.2103i	−0.570391	−	0.987946i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bi.b.719.8		48
3.2	odd	2		630.2.bi.a.509.16	yes	48
5.4	even	2		1890.2.bi.a.719.9		48
7.3	odd	6		1890.2.r.a.1529.3		48
9.2	odd	6		1890.2.r.b.89.3		48
9.7	even	3		630.2.r.a.299.16	yes	48
15.14	odd	2		630.2.bi.b.509.9	yes	48
21.17	even	6		630.2.r.b.59.9	yes	48
35.24	odd	6		1890.2.r.b.1529.3		48
45.29	odd	6		1890.2.r.a.89.3		48
45.34	even	6		630.2.r.b.299.9	yes	48
63.38	even	6		1890.2.bi.a.899.9		48
63.52	odd	6		630.2.bi.b.479.9	yes	48
105.59	even	6		630.2.r.a.59.16	✓	48
315.164	even	6	inner	1890.2.bi.b.899.8		48
315.304	odd	6		630.2.bi.a.479.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.16	✓	48	105.59	even	6
630.2.r.a.299.16	yes	48	9.7	even	3
630.2.r.b.59.9	yes	48	21.17	even	6
630.2.r.b.299.9	yes	48	45.34	even	6
630.2.bi.a.479.16	yes	48	315.304	odd	6
630.2.bi.a.509.16	yes	48	3.2	odd	2
630.2.bi.b.479.9	yes	48	63.52	odd	6
630.2.bi.b.509.9	yes	48	15.14	odd	2
1890.2.r.a.89.3		48	45.29	odd	6
1890.2.r.a.1529.3		48	7.3	odd	6
1890.2.r.b.89.3		48	9.2	odd	6
1890.2.r.b.1529.3		48	35.24	odd	6
1890.2.bi.a.719.9		48	5.4	even	2
1890.2.bi.a.899.9		48	63.38	even	6
1890.2.bi.b.719.8		48	1.1	even	1	trivial
1890.2.bi.b.899.8		48	315.164	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.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.47412 - 1.68136i) q^{5} +(1.31170 - 2.29771i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.47412 - 1.68136i) q^{5} +(1.31170 - 2.29771i) q^{7} +1.00000 q^{8} +(-1.47412 - 1.68136i) q^{10} +(-3.56894 - 2.06053i) q^{11} +(1.18566 - 2.05363i) q^{13} +(1.31170 - 2.29771i) q^{14} +1.00000 q^{16} +(-2.28111 + 1.31700i) q^{17} +(0.956982 + 0.552514i) q^{19} +(-1.47412 - 1.68136i) q^{20} +(-3.56894 - 2.06053i) q^{22} +(-0.296239 - 0.513101i) q^{23} +(-0.653922 + 4.95705i) q^{25} +(1.18566 - 2.05363i) q^{26} +(1.31170 - 2.29771i) q^{28} +(-2.36953 + 1.36805i) q^{29} -2.69755i q^{31} +1.00000 q^{32} +(-2.28111 + 1.31700i) q^{34} +(-5.79687 + 1.18167i) q^{35} +(-6.05512 - 3.49593i) q^{37} +(0.956982 + 0.552514i) q^{38} +(-1.47412 - 1.68136i) q^{40} +(-0.257087 + 0.445287i) q^{41} +(-10.4023 + 6.00577i) q^{43} +(-3.56894 - 2.06053i) q^{44} +(-0.296239 - 0.513101i) q^{46} -4.12973i q^{47} +(-3.55890 - 6.02779i) q^{49} +(-0.653922 + 4.95705i) q^{50} +(1.18566 - 2.05363i) q^{52} +(-4.54406 - 7.87055i) q^{53} +(1.79657 + 9.03814i) q^{55} +(1.31170 - 2.29771i) q^{56} +(-2.36953 + 1.36805i) q^{58} +6.93948 q^{59} +4.29324i q^{61} -2.69755i q^{62} +1.00000 q^{64} +(-5.20070 + 1.03378i) q^{65} -13.5150i q^{67} +(-2.28111 + 1.31700i) q^{68} +(-5.79687 + 1.18167i) q^{70} +1.60164i q^{71} +(3.29147 + 5.70100i) q^{73} +(-6.05512 - 3.49593i) q^{74} +(0.956982 + 0.552514i) q^{76} +(-9.41586 + 5.49759i) q^{77} +13.4434 q^{79} +(-1.47412 - 1.68136i) q^{80} +(-0.257087 + 0.445287i) q^{82} +(3.80374 - 2.19609i) q^{83} +(5.57698 + 1.89394i) q^{85} +(-10.4023 + 6.00577i) q^{86} +(-3.56894 - 2.06053i) q^{88} +(7.82648 - 13.5559i) q^{89} +(-3.16341 - 5.41805i) q^{91} +(-0.296239 - 0.513101i) q^{92} -4.12973i q^{94} +(-0.481736 - 2.42350i) q^{95} +(6.92406 + 11.9928i) q^{97} +(-3.55890 - 6.02779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8}+O(q^{10}) \) 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8	\( 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} - 6 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{28} + 3 q^{29} + 48 q^{32} + 18 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49} + 18 q^{50} + 42 q^{55} - 3 q^{56} + 3 q^{58} + 48 q^{64} + 12 q^{65} + 18 q^{70} + 18 q^{73} - 12 q^{77} + 3 q^{82} + 9 q^{83} + 33 q^{85} - 6 q^{88} + 33 q^{89} + 3 q^{92} + 24 q^{97} + 3 q^{98}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 - 6 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^28 + 3 * q^29 + 48 * q^32 + 18 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 + 42 * q^55 - 3 * q^56 + 3 * q^58 + 48 * q^64 + 12 * q^65 + 18 * q^70 + 18 * q^73 - 12 * q^77 + 3 * q^82 + 9 * q^83 + 33 * q^85 - 6 * q^88 + 33 * q^89 + 3 * q^92 + 24 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more