LMFDB - Embedded newform 1170.2.bp.h.289.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(289,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bp (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,6,0,0,0,0,0,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.3
Root			$-0.147520 - 0.550552i$ of defining polynomial
Character	$\chi$	$=$	1170.289
Dual form			1170.2.bp.h.919.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.67513 - 1.48119i) q^{5} +(1.56410 + 0.903032i) q^{7} +1.00000i q^{8} +(-0.710109 + 2.12032i) q^{10} +(3.22179 + 5.58031i) q^{11} +(-1.98082 + 3.01270i) q^{13} -1.80606 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.416726 - 0.240597i) q^{17} +(-3.14363 + 5.44492i) q^{19} +(-0.445186 - 2.19130i) q^{20} +(-5.58031 - 3.22179i) q^{22} +(-6.16499 + 3.55936i) q^{23} +(0.612127 - 4.96239i) q^{25} +(0.209095 - 3.59948i) q^{26} +(1.56410 - 0.903032i) q^{28} +(-1.15633 - 2.00281i) q^{29} +3.25694 q^{31} +(0.866025 + 0.500000i) q^{32} +0.481194 q^{34} +(3.95763 - 0.804035i) q^{35} +(-2.65264 + 1.53150i) q^{37} -6.28726i q^{38} +(1.48119 + 1.67513i) q^{40} +(3.75329 + 6.50089i) q^{41} +(1.73205 + 1.00000i) q^{43} +6.44358 q^{44} +(3.55936 - 6.16499i) q^{46} +2.19394i q^{47} +(-1.86907 - 3.23732i) q^{49} +(1.95108 + 4.60362i) q^{50} +(1.61866 + 3.22179i) q^{52} +0.906679i q^{53} +(13.6624 + 4.57564i) q^{55} +(-0.903032 + 1.56410i) q^{56} +(2.00281 + 1.15633i) q^{58} +(-3.28726 + 5.69370i) q^{59} +(5.47508 - 9.48313i) q^{61} +(-2.82059 + 1.62847i) q^{62} -1.00000 q^{64} +(1.14425 + 7.98064i) q^{65} +(-0.562690 + 0.324869i) q^{67} +(-0.416726 + 0.240597i) q^{68} +(-3.02539 + 2.67513i) q^{70} +(1.83146 - 3.17217i) q^{71} -2.60720i q^{73} +(1.53150 - 2.65264i) q^{74} +(3.14363 + 5.44492i) q^{76} +11.6375i q^{77} +2.29455 q^{79} +(-2.12032 - 0.710109i) q^{80} +(-6.50089 - 3.75329i) q^{82} -13.3380i q^{83} +(-1.05444 + 0.214221i) q^{85} -2.00000 q^{86} +(-5.58031 + 3.22179i) q^{88} +(0.578163 + 1.00141i) q^{89} +(-5.81876 + 2.92340i) q^{91} +7.11871i q^{92} +(-1.09697 - 1.90000i) q^{94} +(2.79900 + 13.7773i) q^{95} +(11.9784 + 6.91573i) q^{97} +(3.23732 + 1.86907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 2 q^{10} + 6 q^{11} - 20 q^{14} - 6 q^{16} - 26 q^{19} + 4 q^{25} + 28 q^{29} + 24 q^{31} - 16 q^{34} + 6 q^{35} - 4 q^{40} + 4 q^{41} + 12 q^{44} - 4 q^{49} + 8 q^{50} + 12 q^{55} - 10 q^{56}+ \cdots + 8 q^{95}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 6 * q^11 - 20 * q^14 - 6 * q^16 - 26 * q^19 + 4 * q^25 + 28 * q^29 + 24 * q^31 - 16 * q^34 + 6 * q^35 - 4 * q^40 + 4 * q^41 + 12 * q^44 - 4 * q^49 + 8 * q^50 + 12 * q^55 - 10 * q^56 - 16 * q^59 - 8 * q^61 - 12 * q^64 + 10 * q^65 + 24 * q^70 - 40 * q^71 + 10 * q^74 + 26 * q^76 + 56 * q^79 - 16 * q^85 - 24 * q^86 - 14 * q^89 - 38 * q^91 - 14 * q^94 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.67513	−	1.48119i	0.749141	−	0.662410i
$5$	1.67513	−	1.48119i	0.749141	−	0.662410i
$6$		0			0
$7$	1.56410	+	0.903032i	0.591173	+	0.341314i	0.765561	−	0.643363i	$-0.222461\pi$
$7$	1.56410	+	0.903032i	0.591173	+	0.341314i	−0.174388	+	0.984677i	$0.555795\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.710109	+	2.12032i	−0.224556	+	0.670503i
$11$	3.22179	+	5.58031i	0.971407	+	1.68253i	0.691317	+	0.722552i	$0.257031\pi$
$11$	3.22179	+	5.58031i	0.971407	+	1.68253i	0.280090	+	0.959974i	$0.409636\pi$
$12$		0			0
$13$	−1.98082	+	3.01270i	−0.549382	+	0.835572i
$13$	−1.98082	+	3.01270i	−0.549382	+	0.835572i
$14$	−1.80606			−0.482691
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.416726	−	0.240597i	−0.101071	−	0.0583534i	0.448612	−	0.893726i	$-0.351918\pi$
$17$	−0.416726	−	0.240597i	−0.101071	−	0.0583534i	−0.549684	+	0.835373i	$0.685252\pi$
$18$		0			0
$19$	−3.14363	+	5.44492i	−0.721198	+	1.24915i	0.239322	+	0.970940i	$0.423075\pi$
$19$	−3.14363	+	5.44492i	−0.721198	+	1.24915i	−0.960520	+	0.278211i	$0.910258\pi$
$20$	−0.445186	−	2.19130i	−0.0995467	−	0.489990i
$21$		0			0
$22$	−5.58031	−	3.22179i	−1.18973	−	0.686888i
$23$	−6.16499	+	3.55936i	−1.28549	+	0.742177i	−0.977846	−	0.209325i	$-0.932873\pi$
$23$	−6.16499	+	3.55936i	−1.28549	+	0.742177i	−0.307642	+	0.951502i	$0.599540\pi$
$24$		0			0
$25$	0.612127	−	4.96239i	0.122425	−	0.992478i
$26$	0.209095	−	3.59948i	0.0410069	−	0.705917i
$27$		0			0
$28$	1.56410	−	0.903032i	0.295587	−	0.170657i
$29$	−1.15633	−	2.00281i	−0.214724	−	0.371913i	0.738463	−	0.674294i	$-0.235552\pi$
$29$	−1.15633	−	2.00281i	−0.214724	−	0.371913i	−0.953187	+	0.302381i	$0.902219\pi$
$30$		0			0
$31$	3.25694			0.584964			0.292482	−	0.956271i	$-0.405519\pi$
$31$	3.25694			0.584964			0.292482	+	0.956271i	$0.405519\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	0.481194			0.0825241
$35$	3.95763	−	0.804035i	0.668962	−	0.135907i
$36$		0			0
$37$	−2.65264	+	1.53150i	−0.436091	+	0.251777i	−0.701938	−	0.712238i	$-0.747682\pi$
$37$	−2.65264	+	1.53150i	−0.436091	+	0.251777i	0.265847	+	0.964015i	$0.414348\pi$
$38$		−	6.28726i		−	1.01993i
$39$		0			0
$40$	1.48119	+	1.67513i	0.234197	+	0.264861i
$41$	3.75329	+	6.50089i	0.586166	+	1.01527i	0.994729	+	0.102539i	$0.0326967\pi$
$41$	3.75329	+	6.50089i	0.586166	+	1.01527i	−0.408563	+	0.912730i	$0.633970\pi$
$42$		0			0
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$	6.44358			0.971407
$45$		0			0
$46$	3.55936	−	6.16499i	0.524799	−	0.908978i
$47$			2.19394i			0.320019i	0.987116	+	0.160009i	$0.0511524\pi$
$47$			2.19394i			0.320019i	−0.987116	+	0.160009i	$0.948848\pi$
$48$		0			0
$49$	−1.86907	−	3.23732i	−0.267010	−	0.462474i
$50$	1.95108	+	4.60362i	0.275924	+	0.651050i
$51$		0			0
$52$	1.61866	+	3.22179i	0.224468	+	0.446782i
$53$			0.906679i			0.124542i	0.998059	+	0.0622710i	$0.0198343\pi$
$53$			0.906679i			0.124542i	−0.998059	+	0.0622710i	$0.980166\pi$
$54$		0			0
$55$	13.6624	+	4.57564i	1.84224	+	0.616980i
$56$	−0.903032	+	1.56410i	−0.120673	+	0.209011i
$57$		0			0
$58$	2.00281	+	1.15633i	0.262982	+	0.151833i
$59$	−3.28726	+	5.69370i	−0.427965	+	0.741256i	−0.996692	−	0.0812696i	$-0.974103\pi$
$59$	−3.28726	+	5.69370i	−0.427965	+	0.741256i	0.568728	+	0.822526i	$0.307436\pi$
$60$		0			0
$61$	5.47508	−	9.48313i	0.701013	−	1.21419i	−0.267098	−	0.963669i	$-0.586065\pi$
$61$	5.47508	−	9.48313i	0.701013	−	1.21419i	0.968111	−	0.250521i	$-0.0806018\pi$
$62$	−2.82059	+	1.62847i	−0.358216	+	0.206816i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.14425	+	7.98064i	0.141927	+	0.989877i
$66$		0			0
$67$	−0.562690	+	0.324869i	−0.0687435	+	0.0396891i	−0.533978	−	0.845499i	$-0.679303\pi$
$67$	−0.562690	+	0.324869i	−0.0687435	+	0.0396891i	0.465234	+	0.885188i	$0.345970\pi$
$68$	−0.416726	+	0.240597i	−0.0505355	+	0.0291767i
$69$		0			0
$70$	−3.02539	+	2.67513i	−0.361604	+	0.319739i
$71$	1.83146	−	3.17217i	0.217354	−	0.376468i	−0.736644	−	0.676280i	$-0.763591\pi$
$71$	1.83146	−	3.17217i	0.217354	−	0.376468i	0.953998	+	0.299812i	$0.0969241\pi$
$72$		0			0
$73$		−	2.60720i		−	0.305150i	−0.988292	−	0.152575i	$-0.951243\pi$
$73$		−	2.60720i		−	0.305150i	0.988292	−	0.152575i	$-0.0487566\pi$
$74$	1.53150	−	2.65264i	0.178033	−	0.308363i
$75$		0			0
$76$	3.14363	+	5.44492i	0.360599	+	0.624576i
$77$			11.6375i			1.32622i
$78$		0			0
$79$	2.29455			0.258157			0.129079	−	0.991634i	$-0.458798\pi$
$79$	2.29455			0.258157			0.129079	+	0.991634i	$0.458798\pi$
$80$	−2.12032	−	0.710109i	−0.237059	−	0.0793926i
$81$		0			0
$82$	−6.50089	−	3.75329i	−0.717904	−	0.414482i
$83$		−	13.3380i		−	1.46404i	−0.681283	−	0.732020i	$-0.738578\pi$
$83$		−	13.3380i		−	1.46404i	0.681283	−	0.732020i	$-0.261422\pi$
$84$		0			0
$85$	−1.05444	+	0.214221i	−0.114370	+	0.0232356i
$86$	−2.00000			−0.215666
$87$		0			0
$88$	−5.58031	+	3.22179i	−0.594863	+	0.343444i
$89$	0.578163	+	1.00141i	0.0612851	+	0.106149i	0.895040	−	0.445986i	$-0.147147\pi$
$89$	0.578163	+	1.00141i	0.0612851	+	0.106149i	−0.833755	+	0.552135i	$0.813813\pi$
$90$		0			0
$91$	−5.81876	+	2.92340i	−0.609972	+	0.306456i
$92$			7.11871i			0.742177i
$93$		0			0
$94$	−1.09697	−	1.90000i	−0.113144	−	0.195971i
$95$	2.79900	+	13.7773i	0.287172	+	1.41352i
$96$		0			0
$97$	11.9784	+	6.91573i	1.21622	+	0.702186i	0.964108	−	0.265512i	$-0.0855409\pi$
$97$	11.9784	+	6.91573i	1.21622	+	0.702186i	0.252114	+	0.967698i	$0.418874\pi$
$98$	3.23732	+	1.86907i	0.327019	+	0.188804i
$99$		0			0
$100$	−3.99149	−	3.01131i	−0.399149	−	0.301131i
$101$	−4.79995	−	8.31376i	−0.477613	−	0.827250i	0.522057	−	0.852910i	$-0.325165\pi$
$101$	−4.79995	−	8.31376i	−0.477613	−	0.827250i	−0.999671	+	0.0256599i	$0.991831\pi$
$102$		0			0
$103$			3.07522i			0.303011i	0.988456	+	0.151505i	$0.0484121\pi$
$103$			3.07522i			0.303011i	−0.988456	+	0.151505i	$0.951588\pi$
$104$	−3.01270	−	1.98082i	−0.295419	−	0.194236i
$105$		0			0
$106$	−0.453339	−	0.785207i	−0.0440322	−	0.0762660i
$107$	−1.45071	+	0.837565i	−0.140245	+	0.0809705i	−0.568481	−	0.822697i	$-0.692469\pi$
$107$	−1.45071	+	0.837565i	−0.140245	+	0.0809705i	0.428236	+	0.903667i	$0.359135\pi$
$108$		0			0
$109$	−10.8872			−1.04280			−0.521401	−	0.853312i	$-0.674590\pi$
$109$	−10.8872			−1.04280			−0.521401	+	0.853312i	$0.674590\pi$
$110$	−14.1198	+	2.86860i	−1.34627	+	0.273510i
$111$		0			0
$112$		−	1.80606i		−	0.170657i
$113$	12.1244	+	7.00000i	1.14056	+	0.658505i	0.946570	−	0.322498i	$-0.104523\pi$
$113$	12.1244	+	7.00000i	1.14056	+	0.658505i	0.193993	+	0.981003i	$0.437856\pi$
$114$		0			0
$115$	−5.05506	+	15.0939i	−0.471387	+	1.40752i
$116$	−2.31265			−0.214724
$117$		0			0
$118$		−	6.57452i		−	0.605233i
$119$	−0.434534	−	0.752634i	−0.0398336	−	0.0689939i
$120$		0			0
$121$	−15.2599	+	26.4309i	−1.38726	+	2.40281i
$122$			10.9502i			0.991382i
$123$		0			0
$124$	1.62847	−	2.82059i	0.146241	−	0.253297i
$125$	−6.32487	−	9.21933i	−0.565713	−	0.824602i
$126$		0			0
$127$	4.49176	−	2.59332i	0.398580	−	0.230120i	−0.287291	−	0.957843i	$-0.592755\pi$
$127$	4.49176	−	2.59332i	0.398580	−	0.230120i	0.685871	+	0.727723i	$0.259421\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−4.98127	−	6.33932i	−0.436886	−	0.555995i
$131$	10.8011			0.943700			0.471850	−	0.881679i	$-0.343586\pi$
$131$	10.8011			0.943700			0.471850	+	0.881679i	$0.343586\pi$
$132$		0			0
$133$	−9.83388	+	5.67759i	−0.852706	+	0.492310i
$134$	0.324869	−	0.562690i	0.0280644	−	0.0486090i
$135$		0			0
$136$	0.240597	−	0.416726i	0.0206310	−	0.0357340i
$137$	5.32095	+	3.07205i	0.454600	+	0.262463i	0.709771	−	0.704433i	$-0.248798\pi$
$137$	5.32095	+	3.07205i	0.454600	+	0.262463i	−0.255171	+	0.966896i	$0.582132\pi$
$138$		0			0
$139$	5.16902	−	8.95301i	0.438431	−	0.759384i	−0.559138	−	0.829075i	$-0.688868\pi$
$139$	5.16902	−	8.95301i	0.438431	−	0.759384i	0.997569	+	0.0696904i	$0.0222011\pi$
$140$	1.28250	−	3.82943i	0.108391	−	0.323646i
$141$		0			0
$142$			3.66291i			0.307385i
$143$	−23.1936	−	1.34732i	−1.93954	−	0.112669i
$144$		0			0
$145$	−4.90355	−	1.64223i	−0.407218	−	0.136380i
$146$	1.30360	+	2.25790i	0.107887	+	0.186865i
$147$		0			0
$148$			3.06300i			0.251777i
$149$	8.02539	−	13.9004i	0.657466	−	1.13876i	−0.323804	−	0.946124i	$-0.604962\pi$
$149$	8.02539	−	13.9004i	0.657466	−	1.13876i	0.981270	−	0.192640i	$-0.0617049\pi$
$150$		0			0
$151$	9.31757			0.758253			0.379127	−	0.925345i	$-0.376224\pi$
$151$	9.31757			0.758253			0.379127	+	0.925345i	$0.376224\pi$
$152$	−5.44492	−	3.14363i	−0.441642	−	0.254982i
$153$		0			0
$154$	−5.81876	−	10.0784i	−0.468889	−	0.812140i
$155$	5.45580	−	4.82416i	0.438221	−	0.387486i
$156$		0			0
$157$			14.7562i			1.17768i	0.808251	+	0.588838i	$0.200414\pi$
$157$			14.7562i			1.17768i	−0.808251	+	0.588838i	$0.799586\pi$
$158$	−1.98714	+	1.14728i	−0.158088	+	0.0912724i
$159$		0			0
$160$	2.19130	−	0.445186i	0.173238	−	0.0351951i
$161$	−12.8568			−1.01326
$162$		0			0
$163$	11.7127	+	6.76234i	0.917411	+	0.529668i	0.882808	−	0.469734i	$-0.155650\pi$
$163$	11.7127	+	6.76234i	0.917411	+	0.529668i	0.0346029	+	0.999401i	$0.488983\pi$
$164$	7.50659			0.586166
$165$		0			0
$166$	6.66902	+	11.5511i	0.517616	+	0.896538i
$167$	20.2858	−	11.7120i	1.56977	−	0.906304i	0.573570	−	0.819157i	$-0.305558\pi$
$167$	20.2858	−	11.7120i	1.56977	−	0.906304i	0.996195	−	0.0871479i	$-0.0277753\pi$
$168$		0			0
$169$	−5.15268	−	11.9352i	−0.396360	−	0.918095i
$170$	0.806063	−	0.712742i	0.0618222	−	0.0546648i
$171$		0			0
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	−4.00480	−	2.31217i	−0.304479	−	0.175791i	0.339974	−	0.940435i	$-0.389582\pi$
$173$	−4.00480	−	2.31217i	−0.304479	−	0.175791i	−0.644453	+	0.764644i	$0.722915\pi$
$174$		0			0
$175$	5.43862	−	7.20889i	0.411121	−	0.544941i
$176$	3.22179	−	5.58031i	0.242852	−	0.420631i
$177$		0			0
$178$	−1.00141	−	0.578163i	−0.0750586	−	0.0433351i
$179$	4.15633	+	7.19897i	0.310658	+	0.538076i	0.978505	−	0.206223i	$-0.0661172\pi$
$179$	4.15633	+	7.19897i	0.310658	+	0.538076i	−0.667847	+	0.744299i	$0.732784\pi$
$180$		0			0
$181$	−1.02539			−0.0762168			−0.0381084	−	0.999274i	$-0.512133\pi$
$181$	−1.02539			−0.0762168			−0.0381084	+	0.999274i	$0.512133\pi$
$182$	3.57749	−	5.44112i	0.265181	−	0.403323i
$183$		0			0
$184$	−3.55936	−	6.16499i	−0.262399	−	0.454489i
$185$	−2.17507	+	6.49454i	−0.159914	+	0.477488i
$186$		0			0
$187$		−	3.10062i		−	0.226739i
$188$	1.90000	+	1.09697i	0.138572	+	0.0800046i
$189$		0			0
$190$	−9.31265	−	10.5320i	−0.675611	−	0.764070i
$191$	0.177593	−	0.307600i	0.0128502	−	0.0222572i	−0.859529	−	0.511087i	$-0.829243\pi$
$191$	0.177593	−	0.307600i	0.0128502	−	0.0222572i	0.872379	+	0.488830i	$0.162576\pi$
$192$		0			0
$193$	12.1244	−	7.00000i	0.872730	−	0.503871i	0.00447566	−	0.999990i	$-0.498575\pi$
$193$	12.1244	−	7.00000i	0.872730	−	0.503871i	0.868255	+	0.496119i	$0.165242\pi$
$194$	−13.8315			−0.993041
$195$		0			0
$196$	−3.73813			−0.267010
$197$	−12.2166	+	7.05325i	−0.870396	+	0.502523i	−0.867480	−	0.497473i	$-0.834261\pi$
$197$	−12.2166	+	7.05325i	−0.870396	+	0.502523i	−0.00291585	+	0.999996i	$0.500928\pi$
$198$		0			0
$199$	−1.57452	+	2.72714i	−0.111614	+	0.193322i	−0.916421	−	0.400215i	$-0.868935\pi$
$199$	−1.57452	+	2.72714i	−0.111614	+	0.193322i	0.804807	+	0.593537i	$0.202269\pi$
$200$	4.96239	+	0.612127i	0.350894	+	0.0432839i
$201$		0			0
$202$	8.31376	+	4.79995i	0.584954	+	0.337724i
$203$		−	4.17679i		−	0.293153i
$204$		0			0
$205$	15.9163	+	5.33049i	1.11165	+	0.372298i
$206$	−1.53761	−	2.66322i	−0.107130	−	0.185555i
$207$		0			0
$208$	3.59948	+	0.209095i	0.249579	+	0.0144981i
$209$	−40.5125			−2.80231
$210$		0			0
$211$	−1.54666	−	2.67889i	−0.106477	−	0.184423i	0.807864	−	0.589369i	$-0.200624\pi$
$211$	−1.54666	−	2.67889i	−0.106477	−	0.184423i	−0.914340	+	0.404946i	$0.867290\pi$
$212$	0.785207	+	0.453339i	0.0539282	+	0.0311355i
$213$		0			0
$214$	0.837565	−	1.45071i	0.0572548	−	0.0991682i
$215$	4.38261	−	0.890373i	0.298891	−	0.0607229i
$216$		0			0
$217$	5.09417	+	2.94112i	0.345815	+	0.199656i
$218$	9.42856	−	5.44358i	0.638583	−	0.368686i
$219$		0			0
$220$	10.7938	−	9.54420i	0.727721	−	0.643470i
$221$	1.55031	−	0.778890i	0.104285	−	0.0523938i
$222$		0			0
$223$	19.2205	−	11.0970i	1.28710	−	0.743108i	0.308965	−	0.951074i	$-0.400018\pi$
$223$	19.2205	−	11.0970i	1.28710	−	0.743108i	0.978136	+	0.207966i	$0.0666842\pi$
$224$	0.903032	+	1.56410i	0.0603363	+	0.104506i
$225$		0			0
$226$	−14.0000			−0.931266
$227$	11.5490	+	6.66784i	0.766536	+	0.442560i	0.831638	−	0.555319i	$-0.187404\pi$
$227$	11.5490	+	6.66784i	0.766536	+	0.442560i	−0.0651014	+	0.997879i	$0.520737\pi$
$228$		0			0
$229$	−26.1744			−1.72965			−0.864827	−	0.502069i	$-0.832572\pi$
$229$	−26.1744			−1.72965			−0.864827	+	0.502069i	$0.832572\pi$
$230$	−3.16915	−	15.5993i	−0.208968	−	1.02858i
$231$		0			0
$232$	2.00281	−	1.15633i	0.131491	−	0.0759165i
$233$		−	20.8691i		−	1.36718i	−0.729867	−	0.683589i	$-0.760418\pi$
$233$		−	20.8691i		−	1.36718i	0.729867	−	0.683589i	$-0.239582\pi$
$234$		0			0
$235$	3.24965	+	3.67513i	0.211984	+	0.239739i
$236$	3.28726	+	5.69370i	0.213982	+	0.370628i
$237$		0			0
$238$	0.752634	+	0.434534i	0.0487860	+	0.0281666i
$239$	−15.2931			−0.989231			−0.494615	−	0.869112i	$-0.664691\pi$
$239$	−15.2931			−0.989231			−0.494615	+	0.869112i	$0.664691\pi$
$240$		0			0
$241$	6.38423	−	11.0578i	0.411244	−	0.712296i	−0.583782	−	0.811910i	$-0.698428\pi$
$241$	6.38423	−	11.0578i	0.411244	−	0.712296i	0.995026	+	0.0996147i	$0.0317610\pi$
$242$		−	30.5198i		−	1.96188i
$243$		0			0
$244$	−5.47508	−	9.48313i	−0.350506	−	0.607095i
$245$	−7.92603	−	2.65448i	−0.506376	−	0.169589i
$246$		0			0
$247$	−10.1769	−	20.2562i	−0.647543	−	1.28887i
$248$			3.25694i			0.206816i
$249$		0			0
$250$	10.0872	+	4.82174i	0.637968	+	0.304954i
$251$	−2.10602	+	3.64773i	−0.132931	+	0.230243i	−0.924805	−	0.380441i	$-0.875772\pi$
$251$	−2.10602	+	3.64773i	−0.132931	+	0.230243i	0.791874	+	0.610684i	$0.209105\pi$
$252$		0			0
$253$	−39.7246	−	22.9350i	−2.49746	−	1.44191i
$254$	−2.59332	+	4.49176i	−0.162719	+	0.281838i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	16.1300	−	9.31265i	1.00616	−	0.580907i	0.0960955	−	0.995372i	$-0.469365\pi$
$257$	16.1300	−	9.31265i	1.00616	−	0.580907i	0.910065	+	0.414465i	$0.136031\pi$
$258$		0			0
$259$	−5.53198			−0.343740
$260$	7.48357	+	2.99937i	0.464111	+	0.186013i
$261$		0			0
$262$	−9.35406	+	5.40057i	−0.577896	+	0.333648i
$263$	19.9363	−	11.5102i	1.22933	−	0.709751i	0.262437	−	0.964949i	$-0.415474\pi$
$263$	19.9363	−	11.5102i	1.22933	−	0.709751i	0.966889	+	0.255198i	$0.0821406\pi$
$264$		0			0
$265$	1.34297	+	1.51881i	0.0824978	+	0.0932995i
$266$	5.67759	−	9.83388i	0.348116	−	0.602954i
$267$		0			0
$268$			0.649738i			0.0396891i
$269$	6.73695	−	11.6687i	0.410759	−	0.711456i	−0.584214	−	0.811600i	$-0.698597\pi$
$269$	6.73695	−	11.6687i	0.410759	−	0.711456i	0.994973	+	0.100144i	$0.0319304\pi$
$270$		0			0
$271$	8.95017	+	15.5021i	0.543684	+	0.941688i	0.998688	+	0.0511993i	$0.0163044\pi$
$271$	8.95017	+	15.5021i	0.543684	+	0.941688i	−0.455004	+	0.890489i	$0.650362\pi$
$272$			0.481194i			0.0291767i
$273$		0			0
$274$	−6.14411			−0.371179
$275$	29.6638	−	12.5719i	1.78879	−	0.758116i
$276$		0			0
$277$	7.35125	+	4.24424i	0.441694	+	0.255012i	0.704316	−	0.709887i	$-0.251254\pi$
$277$	7.35125	+	4.24424i	0.441694	+	0.255012i	−0.262622	+	0.964899i	$0.584587\pi$
$278$			10.3380i			0.620035i
$279$		0			0
$280$	0.804035	+	3.95763i	0.0480503	+	0.236514i
$281$	16.5296			0.986074			0.493037	−	0.870008i	$-0.335887\pi$
$281$	16.5296			0.986074			0.493037	+	0.870008i	$0.335887\pi$
$282$		0			0
$283$	1.33100	−	0.768452i	0.0791196	−	0.0456797i	−0.459918	−	0.887961i	$-0.652121\pi$
$283$	1.33100	−	0.768452i	0.0791196	−	0.0456797i	0.539038	+	0.842282i	$0.318788\pi$
$284$	−1.83146	−	3.17217i	−0.108677	−	0.188234i
$285$		0			0
$286$	20.7599	−	10.4300i	1.22756	−	0.616737i
$287$			13.5574i			0.800266i
$288$		0			0
$289$	−8.38423	−	14.5219i	−0.493190	−	0.854230i
$290$	5.06772	−	1.02956i	0.297587	−	0.0604579i
$291$		0			0
$292$	−2.25790	−	1.30360i	−0.132134	−	0.0762875i
$293$	5.13527	+	2.96485i	0.300006	+	0.173208i	0.642446	−	0.766331i	$-0.277920\pi$
$293$	5.13527	+	2.96485i	0.300006	+	0.173208i	−0.342440	+	0.939540i	$0.611253\pi$
$294$		0			0
$295$	2.92689	+	14.4068i	0.170410	+	0.838794i
$296$	−1.53150	−	2.65264i	−0.0890167	−	0.154182i
$297$		0			0
$298$			16.0508i			0.929797i
$299$	1.48849	−	25.6237i	0.0860815	−	1.48186i
$300$		0			0
$301$	1.80606	+	3.12819i	0.104100	+	0.180306i
$302$	−8.06926	+	4.65879i	−0.464334	+	0.268083i
$303$		0			0
$304$	6.28726			0.360599
$305$	−4.87487	−	23.9951i	−0.279134	−	1.37396i
$306$		0			0
$307$		−	17.9756i		−	1.02592i	−0.858413	−	0.512960i	$-0.828549\pi$
$307$		−	17.9756i		−	1.02592i	0.858413	−	0.512960i	$-0.171451\pi$
$308$	10.0784	+	5.81876i	0.574269	+	0.331555i
$309$		0			0
$310$	−2.31278	+	6.90575i	−0.131357	+	0.392220i
$311$	−15.9575			−0.904865			−0.452432	−	0.891799i	$-0.649444\pi$
$311$	−15.9575			−0.904865			−0.452432	+	0.891799i	$0.649444\pi$
$312$		0			0
$313$			23.4372i			1.32475i	0.749172	+	0.662376i	$0.230452\pi$
$313$			23.4372i			1.32475i	−0.749172	+	0.662376i	$0.769548\pi$
$314$	−7.37812	−	12.7793i	−0.416371	−	0.721176i
$315$		0			0
$316$	1.14728	−	1.98714i	0.0645393	−	0.111785i
$317$			20.6507i			1.15986i	0.814667	+	0.579929i	$0.196920\pi$
$317$			20.6507i			1.15986i	−0.814667	+	0.579929i	$0.803080\pi$
$318$		0			0
$319$	7.45088	−	12.9053i	0.417169	−	0.722558i
$320$	−1.67513	+	1.48119i	−0.0936427	+	0.0828013i
$321$		0			0
$322$	11.1344	−	6.42842i	0.620493	−	0.358242i
$323$	2.62007	−	1.51270i	0.145784	−	0.0841687i
$324$		0			0
$325$	13.7377	+	11.6738i	0.762028	+	0.647544i
$326$	−13.5247			−0.749063
$327$		0			0
$328$	−6.50089	+	3.75329i	−0.358952	+	0.207241i
$329$	−1.98119	+	3.43153i	−0.109227	+	0.189186i
$330$		0			0
$331$	13.3380	−	23.1022i	0.733125	−	1.26981i	−0.222416	−	0.974952i	$-0.571394\pi$
$331$	13.3380	−	23.1022i	0.733125	−	1.26981i	0.955541	−	0.294858i	$-0.0952724\pi$
$332$	−11.5511	−	6.66902i	−0.633948	−	0.366010i
$333$		0			0
$334$	−11.7120	+	20.2858i	−0.640854	+	1.10999i
$335$	−0.461385	+	1.37765i	−0.0252081	+	0.0752691i
$336$		0			0
$337$		−	8.40597i		−	0.457902i	−0.973438	−	0.228951i	$-0.926470\pi$
$337$		−	8.40597i		−	0.457902i	0.973438	−	0.228951i	$-0.0735296\pi$
$338$	10.4300	+	7.75988i	0.567316	+	0.422082i
$339$		0			0
$340$	−0.341700	+	1.02028i	−0.0185313	+	0.0553327i
$341$	10.4932	+	18.1747i	0.568238	+	0.984217i
$342$		0			0
$343$		−	19.3938i		−	1.04716i
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$		0			0
$346$	4.62435			0.248606
$347$	−18.3177	−	10.5757i	−0.983343	−	0.567733i	−0.0800652	−	0.996790i	$-0.525513\pi$
$347$	−18.3177	−	10.5757i	−0.983343	−	0.567733i	−0.903278	+	0.429056i	$0.858846\pi$
$348$		0			0
$349$	2.73695	+	4.74054i	0.146506	+	0.253755i	0.929934	−	0.367727i	$-0.119864\pi$
$349$	2.73695	+	4.74054i	0.146506	+	0.253755i	−0.783428	+	0.621482i	$0.786531\pi$
$350$	−1.10554	+	8.96239i	−0.0590936	+	0.479060i
$351$		0			0
$352$			6.44358i			0.343444i
$353$	−26.1056	+	15.0721i	−1.38946	+	0.802204i	−0.993254	−	0.115958i	$-0.963006\pi$
$353$	−26.1056	+	15.0721i	−1.38946	+	0.802204i	−0.396205	+	0.918162i	$0.629673\pi$
$354$		0			0
$355$	−1.63068	−	8.02655i	−0.0865474	−	0.426005i
$356$	1.15633			0.0612851
$357$		0			0
$358$	−7.19897	−	4.15633i	−0.380477	−	0.219669i
$359$	−8.38787			−0.442695			−0.221348	−	0.975195i	$-0.571046\pi$
$359$	−8.38787			−0.442695			−0.221348	+	0.975195i	$0.571046\pi$
$360$		0			0
$361$	−10.2648	−	17.7792i	−0.540253	−	0.935745i
$362$	0.888016	−	0.512696i	0.0466731	−	0.0269467i
$363$		0			0
$364$	−0.377639	+	6.50089i	−0.0197937	+	0.340739i
$365$	−3.86177	−	4.36741i	−0.202134	−	0.228600i
$366$		0			0
$367$	−16.8983	+	9.75623i	−0.882084	+	0.509271i	−0.871345	−	0.490671i	$-0.836752\pi$
$367$	−16.8983	+	9.75623i	−0.882084	+	0.509271i	−0.0107388	+	0.999942i	$0.503418\pi$
$368$	6.16499	+	3.55936i	0.321372	+	0.185544i
$369$		0			0
$370$	−1.36361	−	6.71197i	−0.0708906	−	0.348939i
$371$	−0.818760	+	1.41813i	−0.0425079	+	0.0736258i
$372$		0			0
$373$	−7.37324	−	4.25694i	−0.381772	−	0.220416i	0.296817	−	0.954934i	$-0.404075\pi$
$373$	−7.37324	−	4.25694i	−0.381772	−	0.220416i	−0.678589	+	0.734518i	$0.737408\pi$
$374$	1.55031	+	2.68521i	0.0801645	+	0.138849i
$375$		0			0
$376$	−2.19394			−0.113144
$377$	8.32435	+	0.483564i	0.428726	+	0.0249048i
$378$		0			0
$379$	−9.85931	−	17.0768i	−0.506439	−	0.877178i	−0.999972	−	0.00745089i	$-0.997628\pi$
$379$	−9.85931	−	17.0768i	−0.506439	−	0.877178i	0.493533	−	0.869727i	$-0.335705\pi$
$380$	13.3310	+	4.46464i	0.683865	+	0.229031i
$381$		0			0
$382$			0.355186i			0.0181729i
$383$	−24.0059	−	13.8598i	−1.22664	−	0.708202i	−0.260316	−	0.965523i	$-0.583827\pi$
$383$	−24.0059	−	13.8598i	−1.22664	−	0.708202i	−0.966326	+	0.257321i	$0.917160\pi$
$384$		0			0
$385$	17.2374	+	19.4944i	0.878501	+	0.993525i
$386$	−7.00000	+	12.1244i	−0.356291	+	0.617113i
$387$		0			0
$388$	11.9784	−	6.91573i	0.608111	−	0.351093i
$389$	9.15140			0.463994			0.231997	−	0.972716i	$-0.425474\pi$
$389$	9.15140			0.463994			0.231997	+	0.972716i	$0.425474\pi$
$390$		0			0
$391$	3.42548			0.173234
$392$	3.23732	−	1.86907i	0.163509	−	0.0944022i
$393$		0			0
$394$	7.05325	−	12.2166i	0.355337	−	0.615463i
$395$	3.84367	−	3.39868i	0.193396	−	0.171006i
$396$		0			0
$397$	−1.23877	−	0.715205i	−0.0621721	−	0.0358951i	0.468592	−	0.883415i	$-0.344762\pi$
$397$	−1.23877	−	0.715205i	−0.0621721	−	0.0358951i	−0.530764	+	0.847520i	$0.678095\pi$
$398$		−	3.14903i		−	0.157847i
$399$		0			0
$400$	−4.60362	+	1.95108i	−0.230181	+	0.0975538i
$401$	10.8351	+	18.7669i	0.541079	+	0.937177i	0.998842	+	0.0481025i	$0.0153174\pi$
$401$	10.8351	+	18.7669i	0.541079	+	0.937177i	−0.457763	+	0.889074i	$0.651349\pi$
$402$		0			0
$403$	−6.45142	+	9.81217i	−0.321368	+	0.488779i
$404$	−9.59991			−0.477613
$405$		0			0
$406$	2.08840	+	3.61721i	0.103645	+	0.179519i
$407$	−17.0925	−	9.86836i	−0.847244	−	0.489156i
$408$		0			0
$409$	4.54055	−	7.86447i	0.224516	−	0.388873i	−0.731658	−	0.681672i	$-0.761253\pi$
$409$	4.54055	−	7.86447i	0.224516	−	0.388873i	0.956174	+	0.292799i	$0.0945866\pi$
$410$	−16.4492	+	3.34183i	−0.812368	+	0.165041i
$411$		0			0
$412$	2.66322	+	1.53761i	0.131207	+	0.0757527i
$413$	−10.2832	+	5.93700i	−0.506002	+	0.292140i
$414$		0			0
$415$	−19.7562	−	22.3430i	−0.969795	−	1.09677i
$416$	−3.22179	+	1.61866i	−0.157961	+	0.0793613i
$417$		0			0
$418$	35.0848	−	20.2562i	1.71605	−	0.990765i
$419$	7.77139	+	13.4604i	0.379657	+	0.657586i	0.991012	−	0.133771i	$-0.0427086\pi$
$419$	7.77139	+	13.4604i	0.379657	+	0.657586i	−0.611355	+	0.791356i	$0.709375\pi$
$420$		0			0
$421$	−4.96476			−0.241968			−0.120984	−	0.992654i	$-0.538605\pi$
$421$	−4.96476			−0.241968			−0.120984	+	0.992654i	$0.538605\pi$
$422$	2.67889	+	1.54666i	0.130407	+	0.0752903i
$423$		0			0
$424$	−0.906679			−0.0440322
$425$	−1.44903	+	1.92068i	−0.0702881	+	0.0931668i
$426$		0			0
$427$	17.1271	−	9.88835i	0.828840	−	0.478531i
$428$			1.67513i			0.0809705i
$429$		0			0
$430$	−3.35026	+	2.96239i	−0.161564	+	0.142859i
$431$	−16.4853	−	28.5534i	−0.794070	−	1.37537i	−0.923428	−	0.383771i	$-0.874625\pi$
$431$	−16.4853	−	28.5534i	−0.794070	−	1.37537i	0.129358	−	0.991598i	$-0.458708\pi$
$432$		0			0
$433$	−13.9529	−	8.05571i	−0.670534	−	0.387133i	0.125745	−	0.992063i	$-0.459868\pi$
$433$	−13.9529	−	8.05571i	−0.670534	−	0.387133i	−0.796279	+	0.604930i	$0.793201\pi$
$434$	−5.88224			−0.282357
$435$		0			0
$436$	−5.44358	+	9.42856i	−0.260700	+	0.451546i
$437$		−	44.7572i		−	2.14103i
$438$		0			0
$439$	−0.0417360	−	0.0722889i	−0.00199195	−	0.00345016i	0.865028	−	0.501724i	$-0.167301\pi$
$439$	−0.0417360	−	0.0722889i	−0.00199195	−	0.00345016i	−0.867020	+	0.498274i	$0.833967\pi$
$440$	−4.57564	+	13.6624i	−0.218135	+	0.651331i
$441$		0			0
$442$	−0.953161	+	1.44969i	−0.0453372	+	0.0689548i
$443$			40.9135i			1.94386i	0.235271	+	0.971930i	$0.424402\pi$
$443$			40.9135i			1.94386i	−0.235271	+	0.971930i	$0.575598\pi$
$444$		0			0
$445$	2.45178	+	0.821117i	0.116225	+	0.0389247i
$446$	−11.0970	+	19.2205i	−0.525457	+	0.910118i
$447$		0			0
$448$	−1.56410	−	0.903032i	−0.0738966	−	0.0426642i
$449$	14.5659	−	25.2290i	0.687409	−	1.19063i	−0.285264	−	0.958449i	$-0.592081\pi$
$449$	14.5659	−	25.2290i	0.687409	−	1.19063i	0.972673	−	0.232179i	$-0.0745855\pi$
$450$		0			0
$451$	−24.1847	+	41.8891i	−1.13881	+	1.97248i
$452$	12.1244	−	7.00000i	0.570282	−	0.329252i
$453$		0			0
$454$	−13.3357			−0.625874
$455$	−5.41706	+	13.5158i	−0.253956	+	0.633630i
$456$		0			0
$457$	−28.2912	+	16.3339i	−1.32341	+	0.764068i	−0.984270	−	0.176669i	$-0.943468\pi$
$457$	−28.2912	+	16.3339i	−1.32341	+	0.764068i	−0.339135	+	0.940738i	$0.610134\pi$
$458$	22.6677	−	13.0872i	1.05919	−	0.611525i
$459$		0			0
$460$	10.5442	+	11.9248i	0.491626	+	0.555996i
$461$	−9.55031	+	16.5416i	−0.444802	+	0.770420i	−0.998038	−	0.0626044i	$-0.980059\pi$
$461$	−9.55031	+	16.5416i	−0.444802	+	0.770420i	0.553236	+	0.833024i	$0.313393\pi$
$462$		0			0
$463$		−	8.29218i		−	0.385370i	−0.981261	−	0.192685i	$-0.938280\pi$
$463$		−	8.29218i		−	0.385370i	0.981261	−	0.192685i	$-0.0617196\pi$
$464$	−1.15633	+	2.00281i	−0.0536810	+	0.0929783i
$465$		0			0
$466$	10.4345	+	18.0731i	0.483370	+	0.837222i
$467$			23.5369i			1.08916i	0.838710	+	0.544579i	$0.183311\pi$
$467$			23.5369i			1.08916i	−0.838710	+	0.544579i	$0.816689\pi$
$468$		0			0
$469$	−1.17347			−0.0541857
$470$	−4.65184	−	1.55793i	−0.214573	−	0.0718621i
$471$		0			0
$472$	−5.69370	−	3.28726i	−0.262074	−	0.151308i
$473$			12.8872i			0.592553i
$474$		0			0
$475$	25.0955	+	18.9329i	1.15146	+	0.868701i
$476$	−0.869067			−0.0398336
$477$		0			0
$478$	13.2442	−	7.64657i	0.605778	−	0.349746i
$479$	−3.27821	−	5.67802i	−0.149785	−	0.259436i	0.781363	−	0.624077i	$-0.214525\pi$
$479$	−3.27821	−	5.67802i	−0.149785	−	0.259436i	−0.931148	+	0.364642i	$0.881192\pi$
$480$		0			0
$481$	0.640459	−	11.0252i	0.0292024	−	0.502707i
$482$			12.7685i			0.581587i
$483$		0			0
$484$	15.2599	+	26.4309i	0.693631	+	1.20140i
$485$	30.3089	−	6.15758i	1.37626	−	0.279601i
$486$		0			0
$487$	11.7432	+	6.77996i	0.532137	+	0.307229i	0.741886	−	0.670526i	$-0.233931\pi$
$487$	11.7432	+	6.77996i	0.532137	+	0.307229i	−0.209749	+	0.977755i	$0.567265\pi$
$488$	9.48313	+	5.47508i	0.429281	+	0.247845i
$489$		0			0
$490$	8.19139	−	1.66417i	0.370049	−	0.0751794i
$491$	2.47873	+	4.29329i	0.111864	+	0.193753i	0.916522	−	0.399985i	$-0.130985\pi$
$491$	2.47873	+	4.29329i	0.111864	+	0.193753i	−0.804658	+	0.593739i	$0.797651\pi$
$492$		0			0
$493$			1.11283i			0.0501195i
$494$	18.9416	+	12.4539i	0.852223	+	0.560330i
$495$		0			0
$496$	−1.62847	−	2.82059i	−0.0731205	−	0.126648i
$497$	5.72915	−	3.30773i	0.256987	−	0.148372i
$498$		0			0
$499$	13.8700			0.620907			0.310454	−	0.950588i	$-0.399519\pi$
$499$	13.8700			0.620907			0.310454	+	0.950588i	$0.399519\pi$
$500$	−11.1466	+	0.867833i	−0.498491	+	0.0388107i
$501$		0			0
$502$		−	4.21203i		−	0.187992i
$503$	2.98650	+	1.72425i	0.133161	+	0.0768807i	0.565101	−	0.825022i	$-0.308837\pi$
$503$	2.98650	+	1.72425i	0.133161	+	0.0768807i	−0.431940	+	0.901903i	$0.642171\pi$
$504$		0			0
$505$	−20.3549	−	6.81698i	−0.905779	−	0.303352i
$506$	45.8700			2.03917
$507$		0			0
$508$		−	5.18664i		−	0.230120i
$509$	15.4812	+	26.8142i	0.686192	+	1.18852i	0.973061	+	0.230549i	$0.0740523\pi$
$509$	15.4812	+	26.8142i	0.686192	+	1.18852i	−0.286869	+	0.957970i	$0.592614\pi$
$510$		0			0
$511$	2.35439	−	4.07792i	0.104152	−	0.180396i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.31265	+	16.1300i	−0.410763	+	0.711463i
$515$	4.55500	+	5.15140i	0.200717	+	0.226998i
$516$		0			0
$517$	−12.2428	+	7.06841i	−0.538439	+	0.310868i
$518$	4.79083	−	2.76599i	0.210497	−	0.121531i
$519$		0			0
$520$	−7.98064	+	1.14425i	−0.349974	+	0.0501787i
$521$	−14.2506			−0.624330			−0.312165	−	0.950028i	$-0.601054\pi$
$521$	−14.2506			−0.624330			−0.312165	+	0.950028i	$0.601054\pi$
$522$		0			0
$523$	−9.10529	+	5.25694i	−0.398146	+	0.229870i	−0.685684	−	0.727899i	$-0.740497\pi$
$523$	−9.10529	+	5.25694i	−0.398146	+	0.229870i	0.287537	+	0.957769i	$0.407163\pi$
$524$	5.40057	−	9.35406i	0.235925	−	0.408634i
$525$		0			0
$526$	−11.5102	+	19.9363i	−0.501870	+	0.869264i
$527$	−1.35725	−	0.783611i	−0.0591229	−	0.0341346i
$528$		0			0
$529$	13.8380	−	23.9682i	0.601654	−	1.04210i
$530$	−1.92245	−	0.643841i	−0.0835058	−	0.0279666i
$531$		0			0
$532$			11.3552i			0.492310i
$533$	−27.0198	−	1.56959i	−1.17036	−	0.0679865i
$534$		0			0
$535$	−1.18953	+	3.55181i	−0.0514277	+	0.153558i
$536$	−0.324869	−	0.562690i	−0.0140322	−	0.0243045i
$537$		0			0
$538$			13.4739i			0.580901i
$539$	12.0435	−	20.8599i	0.518750	−	0.898501i
$540$		0			0
$541$	15.5345			0.667882			0.333941	−	0.942594i	$-0.391621\pi$
$541$	15.5345			0.667882			0.333941	+	0.942594i	$0.391621\pi$
$542$	−15.5021	−	8.95017i	−0.665874	−	0.384443i
$543$		0			0
$544$	−0.240597	−	0.416726i	−0.0103155	−	0.0178670i
$545$	−18.2374	+	16.1260i	−0.781206	+	0.690762i
$546$		0			0
$547$			23.5515i			1.00699i	0.863998	+	0.503495i	$0.167953\pi$
$547$			23.5515i			1.00699i	−0.863998	+	0.503495i	$0.832047\pi$
$548$	5.32095	−	3.07205i	0.227300	−	0.131232i
$549$		0			0
$550$	−19.4036	+	25.7195i	−0.827374	+	1.09668i
$551$	14.5402			0.619435
$552$		0			0
$553$	3.58890	+	2.07205i	0.152616	+	0.0881127i
$554$	−8.48849			−0.360641
$555$		0			0
$556$	−5.16902	−	8.95301i	−0.219215	−	0.379692i
$557$	17.3602	−	10.0229i	0.735576	−	0.424685i	−0.0848824	−	0.996391i	$-0.527051\pi$
$557$	17.3602	−	10.0229i	0.735576	−	0.424685i	0.820459	+	0.571706i	$0.193718\pi$
$558$		0			0
$559$	−6.44358	+	3.23732i	−0.272535	+	0.136924i
$560$	−2.67513	−	3.02539i	−0.113045	−	0.127846i
$561$		0			0
$562$	−14.3151	+	8.26480i	−0.603844	+	0.348630i
$563$	−10.8898	−	6.28726i	−0.458952	−	0.264976i	0.252651	−	0.967557i	$-0.418697\pi$
$563$	−10.8898	−	6.28726i	−0.458952	−	0.264976i	−0.711604	+	0.702581i	$0.752031\pi$
$564$		0			0
$565$	30.6782	−	6.23261i	1.29064	−	0.262208i
$566$	−0.768452	+	1.33100i	−0.0323004	+	0.0559460i
$567$		0			0
$568$	3.17217	+	1.83146i	0.133102	+	0.0768462i
$569$	−2.14481	−	3.71493i	−0.0899153	−	0.155738i	0.817560	−	0.575844i	$-0.195326\pi$
$569$	−2.14481	−	3.71493i	−0.0899153	−	0.155738i	−0.907475	+	0.420106i	$0.861993\pi$
$570$		0			0
$571$	6.39280			0.267530			0.133765	−	0.991013i	$-0.457293\pi$
$571$	6.39280			0.267530			0.133765	+	0.991013i	$0.457293\pi$
$572$	−12.7636	+	19.4126i	−0.533673	+	0.811680i
$573$		0			0
$574$	−6.77869	−	11.7410i	−0.282937	−	0.490061i
$575$	13.8892	+	32.7718i	0.579218	+	1.36668i
$576$		0			0
$577$		−	37.8169i		−	1.57434i	−0.616738	−	0.787168i	$-0.711546\pi$
$577$		−	37.8169i		−	1.57434i	0.616738	−	0.787168i	$-0.288454\pi$
$578$	14.5219	+	8.38423i	0.604032	+	0.348738i
$579$		0			0
$580$	−3.87399	+	3.42548i	−0.160859	+	0.142236i
$581$	12.0447	−	20.8620i	0.499697	−	0.865501i
$582$		0			0
$583$	−5.05955	+	2.92113i	−0.209545	+	0.120981i
$584$	2.60720			0.107887
$585$		0			0
$586$	−5.92970			−0.244954
$587$	−19.5289	+	11.2750i	−0.806046	+	0.465371i	−0.845581	−	0.533848i	$-0.820746\pi$
$587$	−19.5289	+	11.2750i	−0.806046	+	0.465371i	0.0395351	+	0.999218i	$0.487412\pi$
$588$		0			0
$589$	−10.2386	+	17.7338i	−0.421875	+	0.730708i
$590$	−9.73813	−	11.0132i	−0.400913	−	0.453405i
$591$		0			0
$592$	2.65264	+	1.53150i	0.109023	+	0.0629443i
$593$			8.38787i			0.344449i	0.985058	+	0.172224i	$0.0550954\pi$
$593$			8.38787i			0.344449i	−0.985058	+	0.172224i	$0.944905\pi$
$594$		0			0
$595$	−1.84270	−	0.617132i	−0.0755433	−	0.0253000i
$596$	−8.02539	−	13.9004i	−0.328733	−	0.569382i
$597$		0			0
$598$	11.5228	+	22.9350i	0.471201	+	0.937882i
$599$	29.0884			1.18852			0.594260	−	0.804273i	$-0.297445\pi$
$599$	29.0884			1.18852			0.594260	+	0.804273i	$0.297445\pi$
$600$		0			0
$601$	21.5059	+	37.2493i	0.877243	+	1.51943i	0.854354	+	0.519692i	$0.173953\pi$
$601$	21.5059	+	37.2493i	0.877243	+	1.51943i	0.0228892	+	0.999738i	$0.492713\pi$
$602$	−3.12819	−	1.80606i	−0.127496	−	0.0736097i
$603$		0			0
$604$	4.65879	−	8.06926i	0.189563	−	0.328333i
$605$	13.5870	+	66.8780i	0.552389	+	2.71898i
$606$		0			0
$607$	−18.8372	−	10.8757i	−0.764578	−	0.441429i	0.0663591	−	0.997796i	$-0.478862\pi$
$607$	−18.8372	−	10.8757i	−0.764578	−	0.441429i	−0.830937	+	0.556367i	$0.812195\pi$
$608$	−5.44492	+	3.14363i	−0.220821	+	0.127491i
$609$		0			0
$610$	16.2193	+	18.3430i	0.656701	+	0.742685i
$611$	−6.60966	−	4.34580i	−0.267398	−	0.175812i
$612$		0			0
$613$	−26.6848	+	15.4064i	−1.07779	+	0.622261i	−0.930299	−	0.366803i	$-0.880452\pi$
$613$	−26.6848	+	15.4064i	−1.07779	+	0.622261i	−0.147488	+	0.989064i	$0.547119\pi$
$614$	8.98778	+	15.5673i	0.362717	+	0.628245i
$615$		0			0
$616$	−11.6375			−0.468889
$617$	−39.9125	−	23.0435i	−1.60682	−	0.927696i	−0.990077	−	0.140529i	$-0.955120\pi$
$617$	−39.9125	−	23.0435i	−1.60682	−	0.927696i	−0.616740	−	0.787167i	$-0.711547\pi$
$618$		0			0
$619$	13.5564			0.544878			0.272439	−	0.962173i	$-0.412170\pi$
$619$	13.5564			0.544878			0.272439	+	0.962173i	$0.412170\pi$
$620$	−1.44995	−	7.13694i	−0.0582312	−	0.286627i
$621$		0			0
$622$	13.8196	−	7.97873i	0.554114	−	0.319918i
$623$			2.08840i			0.0836698i
$624$		0			0
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	−11.7186	−	20.2972i	−0.468370	−	0.811241i
$627$		0			0
$628$	12.7793	+	7.37812i	0.509949	+	0.294419i
$629$	1.47390			0.0587682
$630$		0			0
$631$	2.67513	−	4.63346i	0.106495	−	0.184455i	−0.807853	−	0.589384i	$-0.799370\pi$
$631$	2.67513	−	4.63346i	0.106495	−	0.184455i	0.914348	+	0.404929i	$0.132704\pi$
$632$			2.29455i			0.0912724i
$633$		0			0
$634$	−10.3253	−	17.8840i	−0.410072	−	0.710265i
$635$	3.68308	−	10.9973i	0.146159	−	0.436416i
$636$		0			0
$637$	13.4554	+	0.781626i	0.533121	+	0.0309691i
$638$			14.9018i			0.589966i
$639$		0			0
$640$	0.710109	−	2.12032i	0.0280695	−	0.0838129i
$641$	6.19029	−	10.7219i	0.244502	−	0.423489i	−0.717490	−	0.696569i	$-0.754709\pi$
$641$	6.19029	−	10.7219i	0.244502	−	0.423489i	0.961991	+	0.273080i	$0.0880423\pi$
$642$		0			0
$643$	9.98067	+	5.76234i	0.393599	+	0.227245i	0.683718	−	0.729746i	$-0.260362\pi$
$643$	9.98067	+	5.76234i	0.393599	+	0.227245i	−0.290119	+	0.956991i	$0.593695\pi$
$644$	−6.42842	+	11.1344i	−0.253315	+	0.438755i
$645$		0			0
$646$	−1.51270	+	2.62007i	−0.0595162	+	0.103085i
$647$	3.17849	−	1.83510i	0.124959	−	0.0721453i	−0.436217	−	0.899841i	$-0.643682\pi$
$647$	3.17849	−	1.83510i	0.124959	−	0.0721453i	0.561177	+	0.827696i	$0.310349\pi$
$648$		0			0
$649$	−42.3634			−1.66291
$650$	−17.7340	−	3.24095i	−0.695586	−	0.127121i
$651$		0			0
$652$	11.7127	−	6.76234i	0.458706	−	0.264834i
$653$	−7.02043	+	4.05325i	−0.274731	+	0.158616i	−0.631036	−	0.775754i	$-0.717370\pi$
$653$	−7.02043	+	4.05325i	−0.274731	+	0.158616i	0.356305	+	0.934370i	$0.384036\pi$
$654$		0			0
$655$	18.0933	−	15.9986i	0.706965	−	0.625116i
$656$	3.75329	−	6.50089i	0.146541	−	0.253817i
$657$		0			0
$658$		−	3.96239i		−	0.154470i
$659$	−9.27210	+	16.0597i	−0.361190	+	0.625599i	−0.988157	−	0.153447i	$-0.950963\pi$
$659$	−9.27210	+	16.0597i	−0.361190	+	0.625599i	0.626967	+	0.779046i	$0.284296\pi$
$660$		0			0
$661$	−23.2059	−	40.1938i	−0.902606	−	1.56336i	−0.824099	−	0.566446i	$-0.808318\pi$
$661$	−23.2059	−	40.1938i	−0.902606	−	1.56336i	−0.0785068	−	0.996914i	$-0.525015\pi$
$662$			26.6761i			1.03680i
$663$		0			0
$664$	13.3380			0.517616
$665$	−8.06342	+	24.0766i	−0.312686	+	0.933650i
$666$		0			0
$667$	14.2575	+	8.23155i	0.552051	+	0.318727i
$668$		−	23.4241i		−	0.906304i
$669$		0			0
$670$	−0.289255	−	1.42377i	−0.0111749	−	0.0550052i
$671$	70.5583			2.72387
$672$		0			0
$673$	−34.9956	+	20.2047i	−1.34898	+	0.778836i	−0.988105	−	0.153778i	$-0.950856\pi$
$673$	−34.9956	+	20.2047i	−1.34898	+	0.778836i	−0.360877	+	0.932613i	$0.617523\pi$
$674$	4.20299	+	7.27978i	0.161893	+	0.280407i
$675$		0			0
$676$	−12.9126	−	1.50527i	−0.496637	−	0.0578950i
$677$		−	14.2473i		−	0.547567i	−0.961791	−	0.273784i	$-0.911725\pi$
$677$		−	14.2473i		−	0.547567i	0.961791	−	0.273784i	$-0.0882752\pi$
$678$		0			0
$679$	12.4902	+	21.6337i	0.479332	+	0.830227i
$680$	−0.214221	−	1.05444i	−0.00821501	−	0.0404360i
$681$		0			0
$682$	−18.1747	−	10.4932i	−0.695946	−	0.401805i
$683$	5.02599	+	2.90175i	0.192314	+	0.111033i	0.593065	−	0.805154i	$-0.297918\pi$
$683$	5.02599	+	2.90175i	0.192314	+	0.111033i	−0.400751	+	0.916187i	$0.631251\pi$
$684$		0			0
$685$	13.4636	−	2.73527i	0.514418	−	0.104509i
$686$	9.69688	+	16.7955i	0.370228	+	0.641255i
$687$		0			0
$688$		−	2.00000i		−	0.0762493i
$689$	−2.73155	−	1.79597i	−0.104064	−	0.0684210i
$690$		0			0
$691$	9.61990	+	16.6622i	0.365958	+	0.633858i	0.988929	−	0.148387i	$-0.0474080\pi$
$691$	9.61990	+	16.6622i	0.365958	+	0.633858i	−0.622971	+	0.782245i	$0.714075\pi$
$692$	−4.00480	+	2.31217i	−0.152240	+	0.0878956i
$693$		0			0
$694$	21.1514			0.802896
$695$	−4.60236	−	22.6538i	−0.174577	−	0.859307i
$696$		0			0
$697$		−	3.61213i		−	0.136819i
$698$	−4.74054	−	2.73695i	−0.179432	−	0.103595i
$699$		0			0
$700$	−3.52377	−	8.31443i	−0.133186	−	0.314256i
$701$	−45.3742			−1.71376			−0.856881	−	0.515515i	$-0.827601\pi$
$701$	−45.3742			−1.71376			−0.856881	+	0.515515i	$0.827601\pi$
$702$		0			0
$703$		−	19.2579i		−	0.726325i
$704$	−3.22179	−	5.58031i	−0.121426	−	0.210316i
$705$		0			0
$706$	15.0721	−	26.1056i	0.567244	−	0.982496i
$707$		−	17.3380i		−	0.652064i
$708$		0			0
$709$	1.98660	−	3.44089i	0.0746082	−	0.129225i	−0.826308	−	0.563219i	$-0.809563\pi$
$709$	1.98660	−	3.44089i	0.0746082	−	0.129225i	0.900916	+	0.433994i	$0.142896\pi$
$710$	5.42548	+	6.13586i	0.203615	+	0.230275i
$711$		0			0
$712$	−1.00141	+	0.578163i	−0.0375293	+	0.0216676i
$713$	−20.0790	+	11.5926i	−0.751964	+	0.434147i
$714$		0			0
$715$	−40.8479	+	32.0972i	−1.52763	+	1.20037i
$716$	8.31265			0.310658
$717$		0			0
$718$	7.26411	−	4.19394i	0.271094	−	0.156516i
$719$	−22.8496	+	39.5766i	−0.852145	+	1.47596i	0.0271244	+	0.999632i	$0.491365\pi$
$719$	−22.8496	+	39.5766i	−0.852145	+	1.47596i	−0.879269	+	0.476326i	$0.841968\pi$
$720$		0			0
$721$	−2.77702	+	4.80995i	−0.103422	+	0.179132i
$722$	17.7792	+	10.2648i	0.661672	+	0.382016i
$723$		0			0
$724$	−0.512696	+	0.888016i	−0.0190542	+	0.0330029i
$725$	−10.6466	+	4.51216i	−0.395403	+	0.167577i
$726$		0			0
$727$			24.7948i			0.919588i	0.888026	+	0.459794i	$0.152077\pi$
$727$			24.7948i			0.919588i	−0.888026	+	0.459794i	$0.847923\pi$
$728$	−2.92340	−	5.81876i	−0.108349	−	0.215658i
$729$		0			0
$730$	5.52810	+	1.85140i	0.204604	+	0.0685233i
$731$	−0.481194	−	0.833453i	−0.0177976	−	0.0308264i
$732$		0			0
$733$			45.8651i			1.69407i	0.531540	+	0.847033i	$0.321613\pi$
$733$			45.8651i			1.69407i	−0.531540	+	0.847033i	$0.678387\pi$
$734$	9.75623	−	16.8983i	0.360109	−	0.623727i
$735$		0			0
$736$	−7.11871			−0.262399
$737$	−3.62574	−	2.09332i	−0.133556	−	0.0771085i
$738$		0			0
$739$	17.4817	+	30.2791i	0.643074	+	1.11384i	0.984743	+	0.174016i	$0.0556744\pi$
$739$	17.4817	+	30.2791i	0.643074	+	1.11384i	−0.341669	+	0.939820i	$0.610992\pi$
$740$	4.53690	+	5.13093i	0.166780	+	0.188617i
$741$		0			0
$742$		−	1.63752i		−	0.0601152i
$743$	5.94673	−	3.43335i	0.218165	−	0.125957i	−0.386936	−	0.922107i	$-0.626466\pi$
$743$	5.94673	−	3.43335i	0.218165	−	0.125957i	0.605100	+	0.796149i	$0.293133\pi$
$744$		0			0
$745$	−7.14559	−	35.1721i	−0.261794	−	1.28861i
$746$	8.51388			0.311715
$747$		0			0
$748$	−2.68521	−	1.55031i	−0.0981811	−	0.0566849i
$749$	−3.02539			−0.110545
$750$		0			0
$751$	−2.40009	−	4.15708i	−0.0875806	−	0.151694i	0.818907	−	0.573926i	$-0.194580\pi$
$751$	−2.40009	−	4.15708i	−0.0875806	−	0.151694i	−0.906488	+	0.422232i	$0.861247\pi$
$752$	1.90000	−	1.09697i	0.0692860	−	0.0400023i
$753$		0			0
$754$	−7.45088	+	3.74339i	−0.271345	+	0.136326i
$755$	15.6082	−	13.8011i	0.568039	−	0.502275i
$756$		0			0
$757$	24.0541	−	13.8876i	0.874261	−	0.504755i	0.00549931	−	0.999985i	$-0.498250\pi$
$757$	24.0541	−	13.8876i	0.874261	−	0.504755i	0.868762	+	0.495230i	$0.164916\pi$
$758$	17.0768	+	9.85931i	0.620258	+	0.358106i
$759$		0			0
$760$	−13.7773	+	2.79900i	−0.499755	+	0.101530i
$761$	−1.58110	+	2.73855i	−0.0573149	+	0.0992723i	−0.893259	−	0.449542i	$-0.851587\pi$
$761$	−1.58110	+	2.73855i	−0.0573149	+	0.0992723i	0.835944	+	0.548814i	$0.184921\pi$
$762$		0			0
$763$	−17.0286	−	9.83146i	−0.616476	−	0.355923i
$764$	−0.177593	−	0.307600i	−0.00642509	−	0.0111286i
$765$		0			0
$766$	27.7196			1.00155
$767$	−10.6419	−	21.1817i	−0.384257	−	0.764828i
$768$		0			0
$769$	4.07816	+	7.06358i	0.147062	+	0.254719i	0.930140	−	0.367204i	$-0.119685\pi$
$769$	4.07816	+	7.06358i	0.147062	+	0.254719i	−0.783078	+	0.621923i	$0.786352\pi$
$770$	−24.6752	−	8.26390i	−0.889234	−	0.297810i
$771$		0			0
$772$		−	14.0000i		−	0.503871i
$773$	5.09129	+	2.93946i	0.183121	+	0.105725i	0.588758	−	0.808309i	$-0.299617\pi$
$773$	5.09129	+	2.93946i	0.183121	+	0.105725i	−0.405637	+	0.914034i	$0.632950\pi$
$774$		0			0
$775$	1.99366	−	16.1622i	0.0716144	−	0.580564i
$776$	−6.91573	+	11.9784i	−0.248260	+	0.429999i
$777$		0			0
$778$	−7.92535	+	4.57570i	−0.284137	+	0.164047i
$779$	−47.1958			−1.69097
$780$		0			0
$781$	23.6023			0.844556
$782$	−2.96656	+	1.71274i	−0.106084	+	0.0612475i
$783$		0			0
$784$	−1.86907	+	3.23732i	−0.0667524	+	0.115619i
$785$	21.8568	+	24.7186i	0.780104	+	0.882245i
$786$		0			0
$787$	20.5261	+	11.8507i	0.731676	+	0.422433i	0.819035	−	0.573744i	$-0.194509\pi$
$787$	20.5261	+	11.8507i	0.731676	+	0.422433i	−0.0873591	+	0.996177i	$0.527843\pi$
$788$			14.1065i			0.502523i
$789$		0			0
$790$	−1.62938	+	4.86518i	−0.0579708	+	0.173095i
$791$	12.6424	+	21.8974i	0.449514	+	0.778580i
$792$		0			0
$793$	17.7246	+	35.2792i	0.629419	+	1.25280i
$794$	1.43041			0.0507633
$795$		0			0
$796$	1.57452	+	2.72714i	0.0558072	+	0.0966609i
$797$	42.0193	+	24.2599i	1.48840	+	0.859329i	0.999912	−	0.0132409i	$-0.00421482\pi$
$797$	42.0193	+	24.2599i	1.48840	+	0.859329i	0.488489	+	0.872570i	$0.337548\pi$
$798$		0			0
$799$	0.527855	−	0.914271i	0.0186742	−	0.0323446i
$800$	3.01131	−	3.99149i	0.106466	−	0.141121i
$801$		0			0
$802$	−18.7669	−	10.8351i	−0.662684	−	0.382601i
$803$	14.5490	−	8.39986i	0.513423	−	0.296425i
$804$		0			0
$805$	−21.5369	+	19.0435i	−0.759076	+	0.671195i
$806$	0.681010	−	11.7233i	0.0239876	−	0.412936i
$807$		0			0
$808$	8.31376	−	4.79995i	0.292477	−	0.168862i
$809$	8.55936	+	14.8252i	0.300931	+	0.521228i	0.976347	−	0.216209i	$-0.0693693\pi$
$809$	8.55936	+	14.8252i	0.300931	+	0.521228i	−0.675416	+	0.737437i	$0.736036\pi$
$810$		0			0
$811$	−7.67372			−0.269461			−0.134730	−	0.990882i	$-0.543017\pi$
$811$	−7.67372			−0.269461			−0.134730	+	0.990882i	$0.543017\pi$
$812$	−3.61721	−	2.08840i	−0.126939	−	0.0732884i
$813$		0			0
$814$	19.7367			0.691772
$815$	29.6367	−	6.02101i	1.03813	−	0.210907i
$816$		0			0
$817$	−10.8898	+	6.28726i	−0.380988	+	0.219963i
$818$			9.08110i			0.317513i
$819$		0			0
$820$	12.5745	−	11.1187i	0.439121	−	0.388282i
$821$	−26.8933	−	46.5805i	−0.938582	−	1.62567i	−0.768119	−	0.640307i	$-0.778807\pi$
$821$	−26.8933	−	46.5805i	−0.938582	−	1.62567i	−0.170463	−	0.985364i	$-0.554526\pi$
$822$		0			0
$823$	−8.46604	−	4.88787i	−0.295108	−	0.170381i	0.345135	−	0.938553i	$-0.387833\pi$
$823$	−8.46604	−	4.88787i	−0.295108	−	0.170381i	−0.640243	+	0.768172i	$0.721166\pi$
$824$	−3.07522			−0.107130
$825$		0			0
$826$	5.93700	−	10.2832i	0.206575	−	0.357798i
$827$			28.1598i			0.979213i	0.871943	+	0.489607i	$0.162860\pi$
$827$			28.1598i			0.979213i	−0.871943	+	0.489607i	$0.837140\pi$
$828$		0			0
$829$	10.1065	+	17.5050i	0.351013	+	0.607972i	0.986427	−	0.164199i	$-0.0525039\pi$
$829$	10.1065	+	17.5050i	0.351013	+	0.607972i	−0.635414	+	0.772172i	$0.719171\pi$
$830$	28.2809	+	9.47146i	0.981644	+	0.328759i
$831$		0			0
$832$	1.98082	−	3.01270i	0.0686727	−	0.104446i
$833$			1.79877i			0.0623237i
$834$		0			0
$835$	16.6336	−	49.6665i	0.575631	−	1.71878i
$836$	−20.2562	+	35.0848i	−0.700576	+	1.21343i
$837$		0			0
$838$	−13.4604	−	7.77139i	−0.464983	−	0.268458i
$839$	−6.29631	+	10.9055i	−0.217373	+	0.376500i	−0.954004	−	0.299794i	$-0.903082\pi$
$839$	−6.29631	+	10.9055i	−0.217373	+	0.376500i	0.736631	+	0.676295i	$0.236415\pi$
$840$		0			0
$841$	11.8258	−	20.4829i	0.407787	−	0.706308i
$842$	4.29961	−	2.48238i	0.148174	−	0.0855484i
$843$		0			0
$844$	−3.09332			−0.106477
$845$	−26.3098	−	12.3610i	−0.905085	−	0.425230i
$846$		0			0
$847$	−47.7359	+	27.5603i	−1.64022	+	0.946984i
$848$	0.785207	−	0.453339i	0.0269641	−	0.0155677i
$849$		0			0
$850$	0.294552	−	2.38787i	0.0101030	−	0.0819034i
$851$	10.9023	−	18.8834i	0.373727	−	0.647314i
$852$		0			0
$853$		−	45.7704i		−	1.56715i	−0.621299	−	0.783574i	$-0.713395\pi$
$853$		−	45.7704i		−	1.56715i	0.621299	−	0.783574i	$-0.286605\pi$
$854$	−9.88835	+	17.1271i	−0.338372	+	0.586078i
$855$		0			0
$856$	−0.837565	−	1.45071i	−0.0286274	−	0.0495841i
$857$		−	27.8169i		−	0.950206i	−0.879930	−	0.475103i	$-0.842411\pi$
$857$		−	27.8169i		−	0.950206i	0.879930	−	0.475103i	$-0.157589\pi$
$858$		0			0
$859$	−25.9706			−0.886107			−0.443053	−	0.896495i	$-0.646105\pi$
$859$	−25.9706			−0.886107			−0.443053	+	0.896495i	$0.646105\pi$
$860$	1.42022	−	4.24063i	0.0484290	−	0.144604i
$861$		0			0
$862$	28.5534	+	16.4853i	0.972533	+	0.561492i
$863$		−	18.7210i		−	0.637270i	−0.947877	−	0.318635i	$-0.896776\pi$
$863$		−	18.7210i		−	0.637270i	0.947877	−	0.318635i	$-0.103224\pi$
$864$		0			0
$865$	−10.1333	+	2.05870i	−0.344544	+	0.0699978i
$866$	16.1114			0.547488
$867$		0			0
$868$	5.09417	−	2.94112i	0.172907	−	0.0998281i
$869$	7.39257	+	12.8043i	0.250776	+	0.434356i
$870$		0			0
$871$	0.135857	−	2.33872i	0.00460334	−	0.0792446i
$872$		−	10.8872i		−	0.368686i
$873$		0			0
$874$	22.3786	+	38.7609i	0.756967	+	1.31111i
$875$	−1.56736	−	20.1315i	−0.0529865	−	0.680568i
$876$		0			0
$877$	−19.6466	−	11.3430i	−0.663418	−	0.383025i	0.130160	−	0.991493i	$-0.458451\pi$
$877$	−19.6466	−	11.3430i	−0.663418	−	0.383025i	−0.793578	+	0.608468i	$0.791784\pi$
$878$	0.0722889	+	0.0417360i	0.00243963	+	0.00140852i
$879$		0			0
$880$	−2.86860	−	14.1198i	−0.0967003	−	0.475980i
$881$	−1.23813	−	2.14451i	−0.0417138	−	0.0722505i	0.844415	−	0.535690i	$-0.179948\pi$
$881$	−1.23813	−	2.14451i	−0.0417138	−	0.0722505i	−0.886129	+	0.463440i	$0.846615\pi$
$882$		0			0
$883$		−	31.4641i		−	1.05885i	−0.848357	−	0.529425i	$-0.822408\pi$
$883$		−	31.4641i		−	1.05885i	0.848357	−	0.529425i	$-0.177592\pi$
$884$	0.100615	−	1.73205i	0.00338406	−	0.0582552i
$885$		0			0
$886$	−20.4568	−	35.4321i	−0.687258	−	1.19037i
$887$	34.3953	−	19.8581i	1.15488	−	0.666771i	0.204809	−	0.978802i	$-0.434343\pi$
$887$	34.3953	−	19.8581i	1.15488	−	0.666771i	0.950072	+	0.312031i	$0.101009\pi$
$888$		0			0
$889$	9.36741			0.314173
$890$	−2.53386	+	0.514780i	−0.0849351	+	0.0172555i
$891$		0			0
$892$		−	22.1939i		−	0.743108i
$893$	−11.9458	−	6.89692i	−0.399752	−	0.230797i
$894$		0			0
$895$	17.6255	+	5.90289i	0.589154	+	0.197312i
$896$	1.80606			0.0603363
$897$		0			0
$898$			29.1319i			0.972144i
$899$	−3.76608	−	6.52305i	−0.125606	−	0.217556i
$900$		0			0
$901$	0.218144	−	0.377837i	0.00726744	−	0.0125876i
$902$		−	48.3693i		−	1.61052i
$903$		0			0
$904$	−7.00000	+	12.1244i	−0.232817	+	0.403250i
$905$	−1.71767	+	1.51881i	−0.0570972	+	0.0504868i
$906$		0			0
$907$	46.3977	−	26.7877i	1.54061	−	0.889472i	0.541811	−	0.840500i	$-0.317739\pi$
$907$	46.3977	−	26.7877i	1.54061	−	0.889472i	0.998800	−	0.0489717i	$-0.0155944\pi$
$908$	11.5490	−	6.66784i	0.383268	−	0.221280i
$909$		0			0
$910$	−2.06659	−	14.4136i	−0.0685067	−	0.477805i
$911$	−14.6253			−0.484558			−0.242279	−	0.970207i	$-0.577895\pi$
$911$	−14.6253			−0.484558			−0.242279	+	0.970207i	$0.577895\pi$
$912$		0			0
$913$	74.4304	−	42.9724i	2.46329	−	1.42218i
$914$	16.3339	−	28.2912i	0.540278	−	0.935789i
$915$		0			0
$916$	−13.0872	+	22.6677i	−0.432414	+	0.748962i
$917$	16.8940	+	9.75377i	0.557890	+	0.322098i
$918$		0			0
$919$	26.5247	−	45.9421i	0.874969	−	1.51549i	0.0181725	−	0.999835i	$-0.494215\pi$
$919$	26.5247	−	45.9421i	0.874969	−	1.51549i	0.856796	−	0.515655i	$-0.172451\pi$
$920$	−15.0939	−	5.05506i	−0.497632	−	0.166660i
$921$		0			0
$922$		−	19.1006i		−	0.629045i
$923$	5.92901	+	11.8011i	0.195156	+	0.388439i
$924$		0			0
$925$	5.97616	+	14.1009i	0.196495	+	0.463635i
$926$	4.14609	+	7.18124i	0.136249	+	0.235990i
$927$		0			0
$928$		−	2.31265i		−	0.0759165i
$929$	5.22521	−	9.05033i	0.171434	−	0.296932i	−0.767488	−	0.641064i	$-0.778493\pi$
$929$	5.22521	−	9.05033i	0.171434	−	0.296932i	0.938921	+	0.344132i	$0.111827\pi$
$930$		0			0
$931$	23.5026			0.770267
$932$	−18.0731	−	10.4345i	−0.592005	−	0.341795i
$933$		0			0
$934$	−11.7685	−	20.3836i	−0.385076	−	0.666970i
$935$	−4.59261	−	5.19394i	−0.150195	−	0.169860i
$936$		0			0
$937$		−	10.5745i		−	0.345454i	−0.984970	−	0.172727i	$-0.944742\pi$
$937$		−	10.5745i		−	0.345454i	0.984970	−	0.172727i	$-0.0552579\pi$
$938$	1.01625	−	0.586734i	0.0331819	−	0.0191576i
$939$		0			0
$940$	4.80758	−	0.976711i	0.156806	−	0.0318568i
$941$	16.6107			0.541494			0.270747	−	0.962651i	$-0.412729\pi$
$941$	16.6107			0.541494			0.270747	+	0.962651i	$0.412729\pi$
$942$		0			0
$943$	−46.2780	−	26.7186i	−1.50702	−	0.870078i
$944$	6.57452			0.213982
$945$		0			0
$946$	−6.44358	−	11.1606i	−0.209499	−	0.362863i
$947$	−36.7949	+	21.2435i	−1.19567	+	0.690322i	−0.959588	−	0.281410i	$-0.909198\pi$
$947$	−36.7949	+	21.2435i	−1.19567	+	0.690322i	−0.236086	+	0.971732i	$0.575865\pi$
$948$		0			0
$949$	7.85471	+	5.16441i	0.254975	+	0.167644i
$950$	−31.1998	−	3.84860i	−1.01226	−	0.124865i
$951$		0			0
$952$	0.752634	−	0.434534i	0.0243930	−	0.0140833i
$953$	−38.9897	−	22.5107i	−1.26300	−	0.729193i	−0.289346	−	0.957224i	$-0.593438\pi$
$953$	−38.9897	−	22.5107i	−1.26300	−	0.729193i	−0.973654	+	0.228031i	$0.926771\pi$
$954$		0			0
$955$	−0.158124	−	0.778321i	−0.00511678	−	0.0251859i
$956$	−7.64657	+	13.2442i	−0.247308	+	0.428350i
$957$		0			0
$958$	5.67802	+	3.27821i	0.183449	+	0.105914i
$959$	5.54832	+	9.60998i	0.179165	+	0.310322i
$960$		0			0
$961$	−20.3923			−0.657817
$962$	4.95796	+	9.86836i	0.159851	+	0.318169i
$963$		0			0
$964$	−6.38423	−	11.0578i	−0.205622	−	0.356148i
$965$	9.94152	−	29.6844i	0.320029	−	0.955576i
$966$		0			0
$967$		−	24.4763i		−	0.787104i	−0.919302	−	0.393552i	$-0.871246\pi$
$967$		−	24.4763i		−	0.787104i	0.919302	−	0.393552i	$-0.128754\pi$
$968$	−26.4309	−	15.2599i	−0.849521	−	0.490471i
$969$		0			0
$970$	−23.1695	+	20.4871i	−0.743928	+	0.657800i
$971$	−28.2023	+	48.8478i	−0.905054	+	1.56760i	−0.0842097	+	0.996448i	$0.526837\pi$
$971$	−28.2023	+	48.8478i	−0.905054	+	1.56760i	−0.820844	+	0.571152i	$0.806497\pi$
$972$		0			0
$973$	16.1697	−	9.33558i	0.518377	−	0.299285i
$974$	−13.5599			−0.434488
$975$		0			0
$976$	−10.9502			−0.350506
$977$	11.7021	−	6.75623i	0.374385	−	0.216151i	−0.300988	−	0.953628i	$-0.597316\pi$
$977$	11.7021	−	6.75623i	0.374385	−	0.216151i	0.675372	+	0.737477i	$0.263983\pi$
$978$		0			0
$979$	−3.72544	+	6.45265i	−0.119066	+	0.206228i
$980$	−6.26187	+	5.53690i	−0.200028	+	0.176870i
$981$		0			0
$982$	−4.29329	−	2.47873i	−0.137004	−	0.0790995i
$983$		−	30.1187i		−	0.960638i	−0.877094	−	0.480319i	$-0.840521\pi$
$983$		−	30.1187i		−	0.960638i	0.877094	−	0.480319i	$-0.159479\pi$
$984$		0			0
$985$	−10.0171	+	29.9102i	−0.319173	+	0.953020i
$986$	−0.556417	−	0.963743i	−0.0177199	−	0.0306918i
$987$		0			0
$988$	−22.6309	−	1.31464i	−0.719984	−	0.0418241i
$989$	−14.2374			−0.452724
$990$		0			0
$991$	−17.6629	−	30.5931i	−0.561081	−	0.971821i	−0.997402	−	0.0720298i	$-0.977052\pi$
$991$	−17.6629	−	30.5931i	−0.561081	−	0.971821i	0.436322	−	0.899791i	$-0.356281\pi$
$992$	2.82059	+	1.62847i	0.0895539	+	0.0517040i
$993$		0			0
$994$	−3.30773	+	5.72915i	−0.104915	+	0.181718i
$995$	1.40191	+	6.90048i	0.0444434	+	0.218760i
$996$		0			0
$997$	14.5638	+	8.40843i	0.461241	+	0.266298i	0.712566	−	0.701605i	$-0.247533\pi$
$997$	14.5638	+	8.40843i	0.461241	+	0.266298i	−0.251325	+	0.967903i	$0.580866\pi$
$998$	−12.0118	+	6.93501i	−0.380227	+	0.219524i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bp.h.289.3		12
3.2	odd	2		130.2.n.a.29.6	yes	12
5.4	even	2	inner	1170.2.bp.h.289.6		12
12.11	even	2		1040.2.dh.b.289.2		12
13.9	even	3	inner	1170.2.bp.h.919.6		12
15.2	even	4		650.2.e.k.601.1		6
15.8	even	4		650.2.e.j.601.3		6
15.14	odd	2		130.2.n.a.29.1	yes	12
39.2	even	12		1690.2.c.c.1689.5		6
39.11	even	12		1690.2.c.b.1689.5		6
39.23	odd	6		1690.2.b.b.339.3		6
39.29	odd	6		1690.2.b.c.339.6		6
39.35	odd	6		130.2.n.a.9.1	✓	12
60.59	even	2		1040.2.dh.b.289.5		12
65.9	even	6	inner	1170.2.bp.h.919.3		12
156.35	even	6		1040.2.dh.b.529.5		12
195.23	even	12		8450.2.a.bt.1.1		3
195.29	odd	6		1690.2.b.c.339.1		6
195.62	even	12		8450.2.a.ca.1.3		3
195.68	even	12		8450.2.a.cb.1.1		3
195.74	odd	6		130.2.n.a.9.6	yes	12
195.89	even	12		1690.2.c.c.1689.2		6
195.107	even	12		8450.2.a.bu.1.3		3
195.113	even	12		650.2.e.j.451.3		6
195.119	even	12		1690.2.c.b.1689.2		6
195.152	even	12		650.2.e.k.451.1		6
195.179	odd	6		1690.2.b.b.339.4		6
780.659	even	6		1040.2.dh.b.529.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.1	✓	12	39.35	odd	6
130.2.n.a.9.6	yes	12	195.74	odd	6
130.2.n.a.29.1	yes	12	15.14	odd	2
130.2.n.a.29.6	yes	12	3.2	odd	2
650.2.e.j.451.3		6	195.113	even	12
650.2.e.j.601.3		6	15.8	even	4
650.2.e.k.451.1		6	195.152	even	12
650.2.e.k.601.1		6	15.2	even	4
1040.2.dh.b.289.2		12	12.11	even	2
1040.2.dh.b.289.5		12	60.59	even	2
1040.2.dh.b.529.2		12	780.659	even	6
1040.2.dh.b.529.5		12	156.35	even	6
1170.2.bp.h.289.3		12	1.1	even	1	trivial
1170.2.bp.h.289.6		12	5.4	even	2	inner
1170.2.bp.h.919.3		12	65.9	even	6	inner
1170.2.bp.h.919.6		12	13.9	even	3	inner
1690.2.b.b.339.3		6	39.23	odd	6
1690.2.b.b.339.4		6	195.179	odd	6
1690.2.b.c.339.1		6	195.29	odd	6
1690.2.b.c.339.6		6	39.29	odd	6
1690.2.c.b.1689.2		6	195.119	even	12
1690.2.c.b.1689.5		6	39.11	even	12
1690.2.c.c.1689.2		6	195.89	even	12
1690.2.c.c.1689.5		6	39.2	even	12
8450.2.a.bt.1.1		3	195.23	even	12
8450.2.a.bu.1.3		3	195.107	even	12
8450.2.a.ca.1.3		3	195.62	even	12
8450.2.a.cb.1.1		3	195.68	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.67513 - 1.48119i) q^{5} +(1.56410 + 0.903032i) q^{7} +1.00000i q^{8} +(-0.710109 + 2.12032i) q^{10} +(3.22179 + 5.58031i) q^{11} +(-1.98082 + 3.01270i) q^{13} -1.80606 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.416726 - 0.240597i) q^{17} +(-3.14363 + 5.44492i) q^{19} +(-0.445186 - 2.19130i) q^{20} +(-5.58031 - 3.22179i) q^{22} +(-6.16499 + 3.55936i) q^{23} +(0.612127 - 4.96239i) q^{25} +(0.209095 - 3.59948i) q^{26} +(1.56410 - 0.903032i) q^{28} +(-1.15633 - 2.00281i) q^{29} +3.25694 q^{31} +(0.866025 + 0.500000i) q^{32} +0.481194 q^{34} +(3.95763 - 0.804035i) q^{35} +(-2.65264 + 1.53150i) q^{37} -6.28726i q^{38} +(1.48119 + 1.67513i) q^{40} +(3.75329 + 6.50089i) q^{41} +(1.73205 + 1.00000i) q^{43} +6.44358 q^{44} +(3.55936 - 6.16499i) q^{46} +2.19394i q^{47} +(-1.86907 - 3.23732i) q^{49} +(1.95108 + 4.60362i) q^{50} +(1.61866 + 3.22179i) q^{52} +0.906679i q^{53} +(13.6624 + 4.57564i) q^{55} +(-0.903032 + 1.56410i) q^{56} +(2.00281 + 1.15633i) q^{58} +(-3.28726 + 5.69370i) q^{59} +(5.47508 - 9.48313i) q^{61} +(-2.82059 + 1.62847i) q^{62} -1.00000 q^{64} +(1.14425 + 7.98064i) q^{65} +(-0.562690 + 0.324869i) q^{67} +(-0.416726 + 0.240597i) q^{68} +(-3.02539 + 2.67513i) q^{70} +(1.83146 - 3.17217i) q^{71} -2.60720i q^{73} +(1.53150 - 2.65264i) q^{74} +(3.14363 + 5.44492i) q^{76} +11.6375i q^{77} +2.29455 q^{79} +(-2.12032 - 0.710109i) q^{80} +(-6.50089 - 3.75329i) q^{82} -13.3380i q^{83} +(-1.05444 + 0.214221i) q^{85} -2.00000 q^{86} +(-5.58031 + 3.22179i) q^{88} +(0.578163 + 1.00141i) q^{89} +(-5.81876 + 2.92340i) q^{91} +7.11871i q^{92} +(-1.09697 - 1.90000i) q^{94} +(2.79900 + 13.7773i) q^{95} +(11.9784 + 6.91573i) q^{97} +(3.23732 + 1.86907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 2 q^{10} + 6 q^{11} - 20 q^{14} - 6 q^{16} - 26 q^{19} + 4 q^{25} + 28 q^{29} + 24 q^{31} - 16 q^{34} + 6 q^{35} - 4 q^{40} + 4 q^{41} + 12 q^{44} - 4 q^{49} + 8 q^{50} + 12 q^{55} - 10 q^{56}+ \cdots + 8 q^{95}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 6 * q^11 - 20 * q^14 - 6 * q^16 - 26 * q^19 + 4 * q^25 + 28 * q^29 + 24 * q^31 - 16 * q^34 + 6 * q^35 - 4 * q^40 + 4 * q^41 + 12 * q^44 - 4 * q^49 + 8 * q^50 + 12 * q^55 - 10 * q^56 - 16 * q^59 - 8 * q^61 - 12 * q^64 + 10 * q^65 + 24 * q^70 - 40 * q^71 + 10 * q^74 + 26 * q^76 + 56 * q^79 - 16 * q^85 - 24 * q^86 - 14 * q^89 - 38 * q^91 - 14 * q^94 + 8 * q^95

Introduction

L-functions

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