LMFDB - Embedded newform 912.2.bo.c.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("912.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			529.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	912.529
Dual form			912.2.bo.c.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{3} +(-0.0812519 + 0.460802i) q^{5} +(-2.20574 - 3.82045i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{3} +(-0.0812519 + 0.460802i) q^{5} +(-2.20574 - 3.82045i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-2.76604 + 4.79093i) q^{11} +(-5.62449 - 2.04715i) q^{13} +(0.0812519 + 0.460802i) q^{15} +(-3.33022 - 2.79439i) q^{17} +(-4.34002 + 0.405223i) q^{19} +(-3.37939 - 2.83564i) q^{21} +(0.549163 + 3.11446i) q^{23} +(4.49273 + 1.63522i) q^{25} +(0.500000 - 0.866025i) q^{27} +(-1.15657 + 0.970481i) q^{29} +(-1.09240 - 1.89209i) q^{31} +(-0.960637 + 5.44804i) q^{33} +(1.93969 - 0.705990i) q^{35} -2.75877 q^{37} -5.98545 q^{39} +(1.84002 - 0.669713i) q^{41} +(-0.624485 + 3.54163i) q^{43} +(0.233956 + 0.405223i) q^{45} +(7.08512 - 5.94512i) q^{47} +(-6.23055 + 10.7916i) q^{49} +(-4.08512 - 1.48686i) q^{51} +(-0.464508 - 2.63435i) q^{53} +(-1.98293 - 1.66387i) q^{55} +(-3.93969 + 1.86516i) q^{57} +(-1.01707 - 0.853427i) q^{59} +(-1.15270 - 6.53731i) q^{61} +(-4.14543 - 1.50881i) q^{63} +(1.40033 - 2.42544i) q^{65} +(1.90760 - 1.60067i) q^{67} +(1.58125 + 2.73881i) q^{69} +(1.31908 - 7.48086i) q^{71} +(-2.97431 + 1.08256i) q^{73} +4.78106 q^{75} +24.4047 q^{77} +(1.18732 - 0.432149i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-8.96838 - 15.5337i) q^{83} +(1.55825 - 1.30753i) q^{85} +(-0.754900 + 1.30753i) q^{87} +(-11.7280 - 4.26865i) q^{89} +(4.58512 + 26.0035i) q^{91} +(-1.67365 - 1.40436i) q^{93} +(0.165907 - 2.03282i) q^{95} +(-6.36618 - 5.34186i) q^{97} +(0.960637 + 5.44804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q - 3 * q^5 - 3 * q^7	$ 6 q - 3 q^{5} - 3 q^{7} - 12 q^{11} - 21 q^{13} + 3 q^{15} + 3 q^{17} - 6 q^{19} - 9 q^{21} + 15 q^{23} + 9 q^{25} + 3 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 9 q^{43} + 6 q^{45} + 21 q^{47} - 3 q^{51} + 30 q^{53} + 9 q^{55} - 18 q^{57} - 27 q^{59} - 9 q^{61} - 9 q^{63} - 6 q^{65} + 15 q^{67} + 12 q^{69} - 9 q^{71} + 12 q^{73} - 6 q^{75} + 42 q^{77} - 15 q^{79} + 3 q^{83} - 36 q^{85} - 6 q^{87} - 48 q^{89} + 6 q^{91} - 9 q^{93} + 48 q^{95} + 18 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 3 * q^7 - 12 * q^11 - 21 * q^13 + 3 * q^15 + 3 * q^17 - 6 * q^19 - 9 * q^21 + 15 * q^23 + 9 * q^25 + 3 * q^27 + 15 * q^29 - 3 * q^31 + 3 * q^33 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 9 * q^43 + 6 * q^45 + 21 * q^47 - 3 * q^51 + 30 * q^53 + 9 * q^55 - 18 * q^57 - 27 * q^59 - 9 * q^61 - 9 * q^63 - 6 * q^65 + 15 * q^67 + 12 * q^69 - 9 * q^71 + 12 * q^73 - 6 * q^75 + 42 * q^77 - 15 * q^79 + 3 * q^83 - 36 * q^85 - 6 * q^87 - 48 * q^89 + 6 * q^91 - 9 * q^93 + 48 * q^95 + 18 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$4$		0			0
$5$	−0.0812519	+	0.460802i	−0.0363370	+	0.206077i	−0.997571	−	0.0696565i	$-0.977810\pi$
$5$	−0.0812519	+	0.460802i	−0.0363370	+	0.206077i	0.961234	+	0.275734i	$0.0889208\pi$
$6$		0			0
$7$	−2.20574	−	3.82045i	−0.833690	−	1.44399i	−0.895092	−	0.445881i	$-0.852891\pi$
$7$	−2.20574	−	3.82045i	−0.833690	−	1.44399i	0.0614021	−	0.998113i	$-0.480443\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	−2.76604	+	4.79093i	−0.833994	+	1.44452i	0.0608533	+	0.998147i	$0.480618\pi$
$11$	−2.76604	+	4.79093i	−0.833994	+	1.44452i	−0.894847	+	0.446373i	$0.852716\pi$
$12$		0			0
$13$	−5.62449	−	2.04715i	−1.55995	−	0.567776i	−0.589226	−	0.807968i	$-0.700567\pi$
$13$	−5.62449	−	2.04715i	−1.55995	−	0.567776i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	0.0812519	+	0.460802i	0.0209792	+	0.118979i
$16$		0			0
$17$	−3.33022	−	2.79439i	−0.807698	−	0.677739i	0.142360	−	0.989815i	$-0.454531\pi$
$17$	−3.33022	−	2.79439i	−0.807698	−	0.677739i	−0.950057	+	0.312076i	$0.898976\pi$
$18$		0			0
$19$	−4.34002	+	0.405223i	−0.995669	+	0.0929645i
$19$	−4.34002	+	0.405223i	−0.995669	+	0.0929645i
$20$		0			0
$21$	−3.37939	−	2.83564i	−0.737442	−	0.618788i
$22$		0			0
$23$	0.549163	+	3.11446i	0.114508	+	0.649409i	0.986992	+	0.160767i	$0.0513967\pi$
$23$	0.549163	+	3.11446i	0.114508	+	0.649409i	−0.872484	+	0.488643i	$0.837492\pi$
$24$		0			0
$25$	4.49273	+	1.63522i	0.898545	+	0.327044i
$26$		0			0
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$		0			0
$29$	−1.15657	+	0.970481i	−0.214770	+	0.180214i	−0.743826	−	0.668374i	$-0.766991\pi$
$29$	−1.15657	+	0.970481i	−0.214770	+	0.180214i	0.529055	+	0.848587i	$0.322546\pi$
$30$		0			0
$31$	−1.09240	−	1.89209i	−0.196200	−	0.339829i	0.751093	−	0.660196i	$-0.229527\pi$
$31$	−1.09240	−	1.89209i	−0.196200	−	0.339829i	−0.947293	+	0.320368i	$0.896194\pi$
$32$		0			0
$33$	−0.960637	+	5.44804i	−0.167225	+	0.948383i
$34$		0			0
$35$	1.93969	−	0.705990i	0.327868	−	0.119334i
$36$		0			0
$37$	−2.75877			−0.453539			−0.226770	−	0.973948i	$-0.572816\pi$
$37$	−2.75877			−0.453539			−0.226770	+	0.973948i	$0.572816\pi$
$38$		0			0
$39$	−5.98545			−0.958439
$40$		0			0
$41$	1.84002	−	0.669713i	0.287363	−	0.104592i	−0.194317	−	0.980939i	$-0.562249\pi$
$41$	1.84002	−	0.669713i	0.287363	−	0.104592i	0.481680	+	0.876347i	$0.340027\pi$
$42$		0			0
$43$	−0.624485	+	3.54163i	−0.0952331	+	0.540094i	0.899443	+	0.437039i	$0.143973\pi$
$43$	−0.624485	+	3.54163i	−0.0952331	+	0.540094i	−0.994676	+	0.103055i	$0.967138\pi$
$44$		0			0
$45$	0.233956	+	0.405223i	0.0348760	+	0.0604071i
$46$		0			0
$47$	7.08512	−	5.94512i	1.03347	−	0.867185i	0.0422114	−	0.999109i	$-0.486560\pi$
$47$	7.08512	−	5.94512i	1.03347	−	0.867185i	0.991260	+	0.131923i	$0.0421153\pi$
$48$		0			0
$49$	−6.23055	+	10.7916i	−0.890079	+	1.54166i
$50$		0			0
$51$	−4.08512	−	1.48686i	−0.572032	−	0.208202i
$52$		0			0
$53$	−0.464508	−	2.63435i	−0.0638050	−	0.361856i	−0.999948	−	0.0102357i	$-0.996742\pi$
$53$	−0.464508	−	2.63435i	−0.0638050	−	0.361856i	0.936143	−	0.351621i	$-0.114369\pi$
$54$		0			0
$55$	−1.98293	−	1.66387i	−0.267378	−	0.224357i
$56$		0			0
$57$	−3.93969	+	1.86516i	−0.521825	+	0.247046i
$58$		0			0
$59$	−1.01707	−	0.853427i	−0.132412	−	0.111107i	0.574177	−	0.818731i	$-0.305322\pi$
$59$	−1.01707	−	0.853427i	−0.132412	−	0.111107i	−0.706588	+	0.707625i	$0.749767\pi$
$60$		0			0
$61$	−1.15270	−	6.53731i	−0.147589	−	0.837016i	−0.965252	−	0.261320i	$-0.915842\pi$
$61$	−1.15270	−	6.53731i	−0.147589	−	0.837016i	0.817664	−	0.575696i	$-0.195269\pi$
$62$		0			0
$63$	−4.14543	−	1.50881i	−0.522275	−	0.190093i
$64$		0			0
$65$	1.40033	−	2.42544i	0.173690	−	0.300839i
$66$		0			0
$67$	1.90760	−	1.60067i	0.233051	−	0.195553i	−0.518782	−	0.854907i	$-0.673614\pi$
$67$	1.90760	−	1.60067i	0.233051	−	0.195553i	0.751833	+	0.659354i	$0.229170\pi$
$68$		0			0
$69$	1.58125	+	2.73881i	0.190360	+	0.329714i
$70$		0			0
$71$	1.31908	−	7.48086i	0.156546	−	0.887815i	−0.800813	−	0.598914i	$-0.795599\pi$
$71$	1.31908	−	7.48086i	0.156546	−	0.887815i	0.957359	−	0.288901i	$-0.0932898\pi$
$72$		0			0
$73$	−2.97431	+	1.08256i	−0.348116	+	0.126704i	−0.510160	−	0.860080i	$-0.670414\pi$
$73$	−2.97431	+	1.08256i	−0.348116	+	0.126704i	0.162043	+	0.986784i	$0.448192\pi$
$74$		0			0
$75$	4.78106			0.552069
$76$		0			0
$77$	24.4047			2.78117
$78$		0			0
$79$	1.18732	−	0.432149i	0.133584	−	0.0486205i	−0.274363	−	0.961626i	$-0.588467\pi$
$79$	1.18732	−	0.432149i	0.133584	−	0.0486205i	0.407947	+	0.913006i	$0.366245\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	−8.96838	−	15.5337i	−0.984407	−	1.70504i	−0.644541	−	0.764570i	$-0.722951\pi$
$83$	−8.96838	−	15.5337i	−0.984407	−	1.70504i	−0.339867	−	0.940474i	$-0.610382\pi$
$84$		0			0
$85$	1.55825	−	1.30753i	0.169016	−	0.141821i
$86$		0			0
$87$	−0.754900	+	1.30753i	−0.0809338	+	0.140181i
$88$		0			0
$89$	−11.7280	−	4.26865i	−1.24317	−	0.452476i	−0.365081	−	0.930976i	$-0.618959\pi$
$89$	−11.7280	−	4.26865i	−1.24317	−	0.452476i	−0.878088	+	0.478500i	$0.841181\pi$
$90$		0			0
$91$	4.58512	+	26.0035i	0.480651	+	2.72591i
$92$		0			0
$93$	−1.67365	−	1.40436i	−0.173549	−	0.145625i
$94$		0			0
$95$	0.165907	−	2.03282i	0.0170217	−	0.208563i
$96$		0			0
$97$	−6.36618	−	5.34186i	−0.646388	−	0.542384i	0.259585	−	0.965720i	$-0.416414\pi$
$97$	−6.36618	−	5.34186i	−0.646388	−	0.542384i	−0.905972	+	0.423337i	$0.860859\pi$
$98$		0			0
$99$	0.960637	+	5.44804i	0.0965477	+	0.547549i
$100$		0			0
$101$	−1.16637	−	0.424525i	−0.116059	−	0.0422419i	0.283338	−	0.959020i	$-0.408558\pi$
$101$	−1.16637	−	0.424525i	−0.116059	−	0.0422419i	−0.399397	+	0.916778i	$0.630780\pi$
$102$		0			0
$103$	1.69207	−	2.93075i	0.166724	−	0.288775i	−0.770542	−	0.637389i	$-0.780014\pi$
$103$	1.69207	−	2.93075i	0.166724	−	0.288775i	0.937266	+	0.348614i	$0.113348\pi$
$104$		0			0
$105$	1.58125	−	1.32683i	0.154314	−	0.129485i
$106$		0			0
$107$	7.90807	+	13.6972i	0.764502	+	1.32416i	0.940509	+	0.339768i	$0.110348\pi$
$107$	7.90807	+	13.6972i	0.764502	+	1.32416i	−0.176007	+	0.984389i	$0.556318\pi$
$108$		0			0
$109$	−1.00980	+	5.72686i	−0.0967213	+	0.548534i	0.897485	+	0.441045i	$0.145392\pi$
$109$	−1.00980	+	5.72686i	−0.0967213	+	0.548534i	−0.994206	+	0.107489i	$0.965719\pi$
$110$		0			0
$111$	−2.59240	+	0.943555i	−0.246059	+	0.0895583i
$112$		0			0
$113$	12.1361			1.14167			0.570834	−	0.821066i	$-0.306620\pi$
$113$	12.1361			1.14167			0.570834	+	0.821066i	$0.306620\pi$
$114$		0			0
$115$	−1.47977			−0.137989
$116$		0			0
$117$	−5.62449	+	2.04715i	−0.519984	+	0.189259i
$118$		0			0
$119$	−3.33022	+	18.8866i	−0.305281	+	1.73133i
$120$		0			0
$121$	−9.80200	−	16.9776i	−0.891091	−	1.54342i
$122$		0			0
$123$	1.50000	−	1.25865i	0.135250	−	0.113489i
$124$		0			0
$125$	−2.28833	+	3.96351i	−0.204675	+	0.354507i
$126$		0			0
$127$	0.426022	+	0.155059i	0.0378033	+	0.0137593i	0.360853	−	0.932623i	$-0.382486\pi$
$127$	0.426022	+	0.155059i	0.0378033	+	0.0137593i	−0.323049	+	0.946382i	$0.604708\pi$
$128$		0			0
$129$	0.624485	+	3.54163i	0.0549829	+	0.311823i
$130$		0			0
$131$	8.27972	+	6.94751i	0.723402	+	0.607006i	0.928324	−	0.371772i	$-0.121250\pi$
$131$	8.27972	+	6.94751i	0.723402	+	0.607006i	−0.204922	+	0.978778i	$0.565694\pi$
$132$		0			0
$133$	11.1211	+	15.6870i	0.964320	+	1.36024i
$134$		0			0
$135$	0.358441	+	0.300767i	0.0308497	+	0.0258859i
$136$		0			0
$137$	1.90508	+	10.8042i	0.162762	+	0.923068i	0.951342	+	0.308136i	$0.0997053\pi$
$137$	1.90508	+	10.8042i	0.162762	+	0.923068i	−0.788580	+	0.614932i	$0.789184\pi$
$138$		0			0
$139$	−12.6493	−	4.60397i	−1.07290	−	0.390504i	−0.255639	−	0.966772i	$-0.582286\pi$
$139$	−12.6493	−	4.60397i	−1.07290	−	0.390504i	−0.817260	+	0.576269i	$0.804508\pi$
$140$		0			0
$141$	4.62449	−	8.00984i	0.389452	−	0.674550i
$142$		0			0
$143$	25.3653	−	21.2840i	2.12115	−	1.77986i
$144$		0			0
$145$	−0.353226	−	0.611806i	−0.0293338	−	0.0508077i
$146$		0			0
$147$	−2.16385	+	12.2718i	−0.178471	+	1.01216i
$148$		0			0
$149$	−7.69594	+	2.80109i	−0.630476	+	0.229474i	−0.637438	−	0.770501i	$-0.720006\pi$
$149$	−7.69594	+	2.80109i	−0.630476	+	0.229474i	0.00696263	+	0.999976i	$0.497784\pi$
$150$		0			0
$151$	−21.1411			−1.72044			−0.860221	−	0.509921i	$-0.829675\pi$
$151$	−21.1411			−1.72044			−0.860221	+	0.509921i	$0.829675\pi$
$152$		0			0
$153$	−4.34730			−0.351458
$154$		0			0
$155$	0.960637	−	0.349643i	0.0771602	−	0.0280840i
$156$		0			0
$157$	3.41013	−	19.3398i	0.272158	−	1.54348i	−0.475689	−	0.879614i	$-0.657801\pi$
$157$	3.41013	−	19.3398i	0.272158	−	1.54348i	0.747847	−	0.663871i	$-0.231088\pi$
$158$		0			0
$159$	−1.33750	−	2.31661i	−0.106070	−	0.183719i
$160$		0			0
$161$	10.6873	−	8.96773i	0.842279	−	0.706756i
$162$		0			0
$163$	2.27584	−	3.94188i	0.178258	−	0.308752i	−0.763026	−	0.646368i	$-0.776287\pi$
$163$	2.27584	−	3.94188i	0.178258	−	0.308752i	0.941284	+	0.337616i	$0.109621\pi$
$164$		0			0
$165$	−2.43242	−	0.885328i	−0.189364	−	0.0689227i
$166$		0			0
$167$	−3.32383	−	18.8504i	−0.257205	−	1.45868i	−0.790348	−	0.612658i	$-0.790100\pi$
$167$	−3.32383	−	18.8504i	−0.257205	−	1.45868i	0.533142	−	0.846026i	$-0.321011\pi$
$168$		0			0
$169$	17.4855	+	14.6720i	1.34503	+	1.12862i
$170$		0			0
$171$	−3.06418	+	3.10013i	−0.234324	+	0.237073i
$172$		0			0
$173$	4.25284	+	3.56856i	0.323337	+	0.271312i	0.789979	−	0.613134i	$-0.210092\pi$
$173$	4.25284	+	3.56856i	0.323337	+	0.271312i	−0.466641	+	0.884447i	$0.654536\pi$
$174$		0			0
$175$	−3.66250	−	20.7711i	−0.276859	−	1.57015i
$176$		0			0
$177$	−1.24763	−	0.454099i	−0.0937773	−	0.0341322i
$178$		0			0
$179$	−4.17499	+	7.23130i	−0.312054	+	0.540493i	−0.978807	−	0.204786i	$-0.934350\pi$
$179$	−4.17499	+	7.23130i	−0.312054	+	0.540493i	0.666753	+	0.745279i	$0.267684\pi$
$180$		0			0
$181$	−9.64337	+	8.09175i	−0.716786	+	0.601455i	−0.926494	−	0.376309i	$-0.877193\pi$
$181$	−9.64337	+	8.09175i	−0.716786	+	0.601455i	0.209708	+	0.977764i	$0.432749\pi$
$182$		0			0
$183$	−3.31908	−	5.74881i	−0.245353	−	0.424964i
$184$		0			0
$185$	0.224155	−	1.27125i	0.0164802	−	0.0934640i
$186$		0			0
$187$	22.5993	−	8.22546i	1.65262	−	0.601505i
$188$		0			0
$189$	−4.41147			−0.320888
$190$		0			0
$191$	6.71688			0.486016			0.243008	−	0.970024i	$-0.421866\pi$
$191$	6.71688			0.486016			0.243008	+	0.970024i	$0.421866\pi$
$192$		0			0
$193$	11.7763	−	4.28623i	0.847677	−	0.308529i	0.118584	−	0.992944i	$-0.462164\pi$
$193$	11.7763	−	4.28623i	0.847677	−	0.308529i	0.729093	+	0.684415i	$0.239942\pi$
$194$		0			0
$195$	0.486329	−	2.75811i	0.0348268	−	0.197512i
$196$		0			0
$197$	2.03596	+	3.52638i	0.145056	+	0.251245i	0.929394	−	0.369089i	$-0.120330\pi$
$197$	2.03596	+	3.52638i	0.145056	+	0.251245i	−0.784338	+	0.620334i	$0.786997\pi$
$198$		0			0
$199$	5.48158	−	4.59959i	0.388579	−	0.326057i	−0.427480	−	0.904025i	$-0.640599\pi$
$199$	5.48158	−	4.59959i	0.388579	−	0.326057i	0.816059	+	0.577968i	$0.196154\pi$
$200$		0			0
$201$	1.24510	−	2.15658i	0.0878226	−	0.152113i
$202$		0			0
$203$	6.25877	+	2.27801i	0.439280	+	0.159885i
$204$		0			0
$205$	0.159100	+	0.902302i	0.0111120	+	0.0630195i
$206$		0			0
$207$	2.42262	+	2.03282i	0.168384	+	0.141291i
$208$		0			0
$209$	10.0633	−	21.9136i	0.696093	−	1.51580i
$210$		0			0
$211$	2.03209	+	1.70513i	0.139895	+	0.117386i	0.710050	−	0.704151i	$-0.248672\pi$
$211$	2.03209	+	1.70513i	0.139895	+	0.117386i	−0.570155	+	0.821537i	$0.693117\pi$
$212$		0			0
$213$	−1.31908	−	7.48086i	−0.0903817	−	0.512580i
$214$		0			0
$215$	−1.58125	−	0.575529i	−0.107840	−	0.0392507i
$216$		0			0
$217$	−4.81908	+	8.34689i	−0.327140	+	0.566624i
$218$		0			0
$219$	−2.42468	+	2.03455i	−0.163845	+	0.137482i
$220$		0			0
$221$	13.0103	+	22.5344i	0.875165	+	1.51583i
$222$		0			0
$223$	−2.42246	+	13.7384i	−0.162220	+	0.919993i	0.789665	+	0.613538i	$0.210254\pi$
$223$	−2.42246	+	13.7384i	−0.162220	+	0.919993i	−0.951885	+	0.306456i	$0.900857\pi$
$224$		0			0
$225$	4.49273	−	1.63522i	0.299515	−	0.109015i
$226$		0			0
$227$	23.6117			1.56717			0.783583	−	0.621287i	$-0.213390\pi$
$227$	23.6117			1.56717			0.783583	+	0.621287i	$0.213390\pi$
$228$		0			0
$229$	8.61081			0.569019			0.284509	−	0.958673i	$-0.408169\pi$
$229$	8.61081			0.569019			0.284509	+	0.958673i	$0.408169\pi$
$230$		0			0
$231$	22.9329	−	8.34689i	1.50887	−	0.549185i
$232$		0			0
$233$	−2.68139	+	15.2069i	−0.175664	+	0.996238i	0.761711	+	0.647916i	$0.224359\pi$
$233$	−2.68139	+	15.2069i	−0.175664	+	0.996238i	−0.937375	+	0.348322i	$0.886752\pi$
$234$		0			0
$235$	2.16385	+	3.74789i	0.141154	+	0.244486i
$236$		0			0
$237$	0.967911	−	0.812174i	0.0628726	−	0.0527564i
$238$		0			0
$239$	3.87939	−	6.71929i	0.250937	−	0.434635i	−0.712847	−	0.701319i	$-0.752595\pi$
$239$	3.87939	−	6.71929i	0.250937	−	0.434635i	0.963784	+	0.266684i	$0.0859281\pi$
$240$		0			0
$241$	12.4846	+	4.54401i	0.804202	+	0.292706i	0.711227	−	0.702963i	$-0.248140\pi$
$241$	12.4846	+	4.54401i	0.804202	+	0.292706i	0.0929755	+	0.995668i	$0.470362\pi$
$242$		0			0
$243$	−0.173648	−	0.984808i	−0.0111395	−	0.0631754i
$244$		0			0
$245$	−4.46657	−	3.74789i	−0.285358	−	0.239444i
$246$		0			0
$247$	25.2399	+	6.60549i	1.60598	+	0.420297i
$248$		0			0
$249$	−13.7404	−	11.5295i	−0.870759	−	0.730654i
$250$		0			0
$251$	3.06506	+	17.3828i	0.193465	+	1.09719i	0.914588	+	0.404386i	$0.132515\pi$
$251$	3.06506	+	17.3828i	0.193465	+	1.09719i	−0.721124	+	0.692806i	$0.756374\pi$
$252$		0			0
$253$	−16.4402	−	5.98373i	−1.03358	−	0.376194i
$254$		0			0
$255$	1.01707	−	1.76162i	0.0636917	−	0.110317i
$256$		0			0
$257$	6.05303	−	5.07910i	0.377578	−	0.316825i	−0.434173	−	0.900830i	$-0.642959\pi$
$257$	6.05303	−	5.07910i	0.377578	−	0.316825i	0.811751	+	0.584004i	$0.198515\pi$
$258$		0			0
$259$	6.08512	+	10.5397i	0.378111	+	0.654908i
$260$		0			0
$261$	−0.262174	+	1.48686i	−0.0162282	+	0.0920345i
$262$		0			0
$263$	−23.8405	+	8.67723i	−1.47007	+	0.535061i	−0.948119	−	0.317916i	$-0.897017\pi$
$263$	−23.8405	+	8.67723i	−1.47007	+	0.535061i	−0.521949	+	0.852977i	$0.674795\pi$
$264$		0			0
$265$	1.25166			0.0768888
$266$		0			0
$267$	−12.4807			−0.763807
$268$		0			0
$269$	−18.9538	+	6.89863i	−1.15564	+	0.420617i	−0.847536	−	0.530737i	$-0.821915\pi$
$269$	−18.9538	+	6.89863i	−1.15564	+	0.420617i	−0.308099	+	0.951354i	$0.599693\pi$
$270$		0			0
$271$	−3.56165	+	20.1991i	−0.216355	+	1.22701i	0.662185	+	0.749341i	$0.269629\pi$
$271$	−3.56165	+	20.1991i	−0.216355	+	1.22701i	−0.878540	+	0.477669i	$0.841482\pi$
$272$		0			0
$273$	13.2023	+	22.8671i	0.799042	+	1.38398i
$274$		0			0
$275$	−20.2613	+	17.0012i	−1.22180	+	1.02521i
$276$		0			0
$277$	−4.56758	+	7.91128i	−0.274439	+	0.475343i	−0.969994	−	0.243131i	$-0.921826\pi$
$277$	−4.56758	+	7.91128i	−0.274439	+	0.475343i	0.695554	+	0.718474i	$0.255159\pi$
$278$		0			0
$279$	−2.05303	−	0.747243i	−0.122912	−	0.0447363i
$280$		0			0
$281$	−0.595800	−	3.37895i	−0.0355424	−	0.201571i	0.961866	−	0.273522i	$-0.0881886\pi$
$281$	−0.595800	−	3.37895i	−0.0355424	−	0.201571i	−0.997408	+	0.0719508i	$0.977078\pi$
$282$		0			0
$283$	−8.61200	−	7.22632i	−0.511930	−	0.429560i	0.349878	−	0.936795i	$-0.386223\pi$
$283$	−8.61200	−	7.22632i	−0.511930	−	0.429560i	−0.861808	+	0.507235i	$0.830668\pi$
$284$		0			0
$285$	−0.539363	−	1.96697i	−0.0319491	−	0.116513i
$286$		0			0
$287$	−6.61721	−	5.55250i	−0.390602	−	0.327754i
$288$		0			0
$289$	0.329755	+	1.87014i	0.0193974	+	0.110008i
$290$		0			0
$291$	−7.80928	−	2.84234i	−0.457788	−	0.166621i
$292$		0			0
$293$	7.26604	−	12.5852i	0.424487	−	0.735233i	−0.571886	−	0.820333i	$-0.693788\pi$
$293$	7.26604	−	12.5852i	0.424487	−	0.735233i	0.996372	+	0.0851007i	$0.0271212\pi$
$294$		0			0
$295$	0.475900	−	0.399328i	0.0277080	−	0.0232498i
$296$		0			0
$297$	2.76604	+	4.79093i	0.160502	+	0.277998i
$298$		0			0
$299$	3.28699	−	18.6414i	0.190091	−	1.07806i
$300$		0			0
$301$	14.9081	−	5.42609i	0.859287	−	0.312755i
$302$		0			0
$303$	−1.24123			−0.0713068
$304$		0			0
$305$	3.10607			0.177853
$306$		0			0
$307$	−24.1532	+	8.79104i	−1.37849	+	0.501731i	−0.921721	−	0.387853i	$-0.873217\pi$
$307$	−24.1532	+	8.79104i	−1.37849	+	0.501731i	−0.456773	+	0.889583i	$0.650995\pi$
$308$		0			0
$309$	0.587649	−	3.33272i	0.0334302	−	0.189592i
$310$		0			0
$311$	2.91875	+	5.05542i	0.165507	+	0.286667i	0.936835	−	0.349771i	$-0.113741\pi$
$311$	2.91875	+	5.05542i	0.165507	+	0.286667i	−0.771328	+	0.636438i	$0.780407\pi$
$312$		0			0
$313$	−12.6480	+	10.6129i	−0.714905	+	0.599876i	−0.925971	−	0.377596i	$-0.876751\pi$
$313$	−12.6480	+	10.6129i	−0.714905	+	0.599876i	0.211066	+	0.977472i	$0.432307\pi$
$314$		0			0
$315$	1.03209	−	1.78763i	0.0581516	−	0.100722i
$316$		0			0
$317$	25.3243	+	9.21729i	1.42235	+	0.517695i	0.934730	−	0.355359i	$-0.115641\pi$
$317$	25.3243	+	9.21729i	1.42235	+	0.517695i	0.487624	+	0.873054i	$0.337864\pi$
$318$		0			0
$319$	−1.45037	−	8.22546i	−0.0812051	−	0.460537i
$320$		0			0
$321$	12.1159	+	10.1664i	0.676242	+	0.567434i
$322$		0			0
$323$	15.5856	+	10.7782i	0.867205	+	0.599716i
$324$		0			0
$325$	−21.9217	−	18.3945i	−1.21600	−	1.02034i
$326$		0			0
$327$	1.00980	+	5.72686i	0.0558421	+	0.316696i
$328$		0			0
$329$	−38.3410	−	13.9550i	−2.11381	−	0.769362i
$330$		0			0
$331$	14.2442	−	24.6717i	0.782933	−	1.35608i	−0.147293	−	0.989093i	$-0.547056\pi$
$331$	14.2442	−	24.6717i	0.782933	−	1.35608i	0.930226	−	0.366987i	$-0.119611\pi$
$332$		0			0
$333$	−2.11334	+	1.77330i	−0.115810	+	0.0971764i
$334$		0			0
$335$	0.582596	+	1.00909i	0.0318306	+	0.0551323i
$336$		0			0
$337$	2.89780	−	16.4343i	0.157853	−	0.895231i	−0.798277	−	0.602290i	$-0.794255\pi$
$337$	2.89780	−	16.4343i	0.157853	−	0.895231i	0.956131	−	0.292941i	$-0.0946339\pi$
$338$		0			0
$339$	11.4042	−	4.15079i	0.619391	−	0.225440i
$340$		0			0
$341$	12.0865			0.654519
$342$		0			0
$343$	24.0915			1.30082
$344$		0			0
$345$	−1.39053	+	0.506111i	−0.0748636	+	0.0272481i
$346$		0			0
$347$	3.25237	−	18.4451i	0.174597	−	0.990186i	−0.764012	−	0.645202i	$-0.776773\pi$
$347$	3.25237	−	18.4451i	0.174597	−	0.990186i	0.938608	−	0.344984i	$-0.112116\pi$
$348$		0			0
$349$	0.820422	+	1.42101i	0.0439162	+	0.0760651i	0.887148	−	0.461485i	$-0.152683\pi$
$349$	0.820422	+	1.42101i	0.0439162	+	0.0760651i	−0.843232	+	0.537550i	$0.819350\pi$
$350$		0			0
$351$	−4.58512	+	3.84737i	−0.244736	+	0.205358i
$352$		0			0
$353$	5.95336	−	10.3115i	0.316866	−	0.548827i	−0.662967	−	0.748649i	$-0.730703\pi$
$353$	5.95336	−	10.3115i	0.316866	−	0.548827i	0.979832	+	0.199822i	$0.0640363\pi$
$354$		0			0
$355$	3.34002	+	1.21567i	0.177270	+	0.0645210i
$356$		0			0
$357$	3.33022	+	18.8866i	0.176254	+	0.999586i
$358$		0			0
$359$	−1.75877	−	1.47578i	−0.0928244	−	0.0778889i	0.595195	−	0.803582i	$-0.297075\pi$
$359$	−1.75877	−	1.47578i	−0.0928244	−	0.0778889i	−0.688019	+	0.725693i	$0.741519\pi$
$360$		0			0
$361$	18.6716	−	3.51735i	0.982715	−	0.185124i
$362$		0			0
$363$	−15.0175	−	12.6012i	−0.788216	−	0.661392i
$364$		0			0
$365$	−0.257178	−	1.45853i	−0.0134613	−	0.0763429i
$366$		0			0
$367$	−20.1989	−	7.35181i	−1.05438	−	0.383761i	−0.244063	−	0.969759i	$-0.578480\pi$
$367$	−20.1989	−	7.35181i	−1.05438	−	0.383761i	−0.810312	+	0.585998i	$0.800703\pi$
$368$		0			0
$369$	0.979055	−	1.69577i	0.0509676	−	0.0882785i
$370$		0			0
$371$	−9.03983	+	7.58532i	−0.469325	+	0.393810i
$372$		0			0
$373$	−13.9907	−	24.2325i	−0.724409	−	1.25471i	−0.959217	−	0.282672i	$-0.908779\pi$
$373$	−13.9907	−	24.2325i	−0.724409	−	1.25471i	0.234807	−	0.972042i	$-0.424554\pi$
$374$		0			0
$375$	−0.794730	+	4.50714i	−0.0410397	+	0.232748i
$376$		0			0
$377$	8.49185	−	3.09078i	0.437352	−	0.159183i
$378$		0			0
$379$	−8.88981			−0.456639			−0.228320	−	0.973586i	$-0.573323\pi$
$379$	−8.88981			−0.456639			−0.228320	+	0.973586i	$0.573323\pi$
$380$		0			0
$381$	0.453363			0.0232265
$382$		0			0
$383$	−23.5069	+	8.55580i	−1.20114	+	0.437181i	−0.863624	−	0.504137i	$-0.831811\pi$
$383$	−23.5069	+	8.55580i	−1.20114	+	0.437181i	−0.337521	+	0.941318i	$0.609588\pi$
$384$		0			0
$385$	−1.98293	+	11.2457i	−0.101059	+	0.573136i
$386$		0			0
$387$	1.79813	+	3.11446i	0.0914043	+	0.158317i
$388$		0			0
$389$	−17.8739	+	14.9980i	−0.906244	+	0.760429i	−0.971401	−	0.237446i	$-0.923690\pi$
$389$	−17.8739	+	14.9980i	−0.906244	+	0.760429i	0.0651569	+	0.997875i	$0.479245\pi$
$390$		0			0
$391$	6.87417	−	11.9064i	0.347642	−	0.602133i
$392$		0			0
$393$	10.1566	+	3.69669i	0.512331	+	0.186473i
$394$		0			0
$395$	0.102663	+	0.582232i	0.00516555	+	0.0292953i
$396$		0			0
$397$	2.90239	+	2.43539i	0.145667	+	0.122229i	0.712709	−	0.701460i	$-0.247468\pi$
$397$	2.90239	+	2.43539i	0.145667	+	0.122229i	−0.567042	+	0.823689i	$0.691912\pi$
$398$		0			0
$399$	15.8157	+	10.9373i	0.791774	+	0.547552i
$400$		0			0
$401$	−16.7456	−	14.0512i	−0.836234	−	0.701683i	0.120479	−	0.992716i	$-0.461557\pi$
$401$	−16.7456	−	14.0512i	−0.836234	−	0.701683i	−0.956713	+	0.291032i	$0.906001\pi$
$402$		0			0
$403$	2.27079	+	12.8783i	0.113116	+	0.641514i
$404$		0			0
$405$	0.439693	+	0.160035i	0.0218485	+	0.00795220i
$406$		0			0
$407$	7.63088	−	13.2171i	0.378249	−	0.655146i
$408$		0			0
$409$	−6.06418	+	5.08845i	−0.299854	+	0.251608i	−0.780284	−	0.625426i	$-0.784925\pi$
$409$	−6.06418	+	5.08845i	−0.299854	+	0.251608i	0.480429	+	0.877033i	$0.340481\pi$
$410$		0			0
$411$	5.48545	+	9.50108i	0.270577	+	0.468654i
$412$		0			0
$413$	−1.01707	+	5.76811i	−0.0500469	+	0.283830i
$414$		0			0
$415$	7.88666	−	2.87051i	0.387141	−	0.140908i
$416$		0			0
$417$	−13.4611			−0.659193
$418$		0			0
$419$	−6.22937			−0.304325			−0.152162	−	0.988356i	$-0.548624\pi$
$419$	−6.22937			−0.304325			−0.152162	+	0.988356i	$0.548624\pi$
$420$		0			0
$421$	3.35591	−	1.22145i	0.163557	−	0.0595300i	−0.258944	−	0.965892i	$-0.583374\pi$
$421$	3.35591	−	1.22145i	0.163557	−	0.0595300i	0.422501	+	0.906362i	$0.361152\pi$
$422$		0			0
$423$	1.60607	−	9.10846i	0.0780896	−	0.442868i
$424$		0			0
$425$	−10.3923	−	18.0001i	−0.504103	−	0.873131i
$426$		0			0
$427$	−22.4329	+	18.8234i	−1.08560	+	0.910929i
$428$		0			0
$429$	16.5560	−	28.6759i	0.799332	−	1.38448i
$430$		0			0
$431$	−24.2520	−	8.82699i	−1.16818	−	0.425181i	−0.316164	−	0.948704i	$-0.602395\pi$
$431$	−24.2520	−	8.82699i	−1.16818	−	0.425181i	−0.852011	+	0.523523i	$0.824617\pi$
$432$		0			0
$433$	4.53209	+	25.7028i	0.217798	+	1.23520i	0.875984	+	0.482340i	$0.160213\pi$
$433$	4.53209	+	25.7028i	0.217798	+	1.23520i	−0.658186	+	0.752856i	$0.728676\pi$
$434$		0			0
$435$	−0.541174	−	0.454099i	−0.0259473	−	0.0217724i
$436$		0			0
$437$	−3.64543	−	13.2943i	−0.174385	−	0.635952i
$438$		0			0
$439$	−17.3366	−	14.5472i	−0.827432	−	0.694298i	0.127268	−	0.991868i	$-0.459379\pi$
$439$	−17.3366	−	14.5472i	−0.827432	−	0.694298i	−0.954700	+	0.297571i	$0.903824\pi$
$440$		0			0
$441$	2.16385	+	12.2718i	0.103040	+	0.584371i
$442$		0			0
$443$	13.5432	+	4.92933i	0.643458	+	0.234200i	0.643079	−	0.765800i	$-0.277657\pi$
$443$	13.5432	+	4.92933i	0.643458	+	0.234200i	0.000379869		1.00000i	$0.499879\pi$
$444$		0			0
$445$	2.91993	−	5.05747i	0.138418	−	0.239747i
$446$		0			0
$447$	−6.27379	+	5.26433i	−0.296740	+	0.248994i
$448$		0			0
$449$	−18.1361	−	31.4126i	−0.855895	−	1.48245i	−0.875812	−	0.482653i	$-0.839673\pi$
$449$	−18.1361	−	31.4126i	−0.855895	−	1.48245i	0.0199166	−	0.999802i	$-0.493660\pi$
$450$		0			0
$451$	−1.88103	+	10.6679i	−0.0885744	+	0.502331i
$452$		0			0
$453$	−19.8662	+	7.23070i	−0.933395	+	0.339728i
$454$		0			0
$455$	−12.3550			−0.579213
$456$		0			0
$457$	−40.4543			−1.89237			−0.946186	−	0.323623i	$-0.895099\pi$
$457$	−40.4543			−1.89237			−0.946186	+	0.323623i	$0.895099\pi$
$458$		0			0
$459$	−4.08512	+	1.48686i	−0.190677	+	0.0694008i
$460$		0			0
$461$	−6.81996	+	38.6779i	−0.317637	+	1.80141i	0.239400	+	0.970921i	$0.423049\pi$
$461$	−6.81996	+	38.6779i	−0.317637	+	1.80141i	−0.557037	+	0.830488i	$0.688062\pi$
$462$		0			0
$463$	10.4167	+	18.0422i	0.484105	+	0.838494i	0.999833	−	0.0182582i	$-0.00581209\pi$
$463$	10.4167	+	18.0422i	0.484105	+	0.838494i	−0.515729	+	0.856752i	$0.672479\pi$
$464$		0			0
$465$	0.783119	−	0.657115i	0.0363163	−	0.0304730i
$466$		0			0
$467$	−5.96198	+	10.3265i	−0.275888	+	0.477851i	−0.970359	−	0.241669i	$-0.922305\pi$
$467$	−5.96198	+	10.3265i	−0.275888	+	0.477851i	0.694471	+	0.719521i	$0.255638\pi$
$468$		0			0
$469$	−10.3229	−	3.75725i	−0.476669	−	0.173493i
$470$		0			0
$471$	−3.41013	−	19.3398i	−0.157130	−	0.891131i
$472$		0			0
$473$	−15.2404	−	12.7882i	−0.700752	−	0.588001i
$474$		0			0
$475$	−20.1612	−	5.27633i	−0.925057	−	0.242095i
$476$		0			0
$477$	−2.04916	−	1.71945i	−0.0938247	−	0.0787283i
$478$		0			0
$479$	1.28564	+	7.29125i	0.0587426	+	0.333146i	0.999990	−	0.00457323i	$-0.00145571\pi$
$479$	1.28564	+	7.29125i	0.0587426	+	0.333146i	−0.941247	+	0.337719i	$0.890345\pi$
$480$		0			0
$481$	15.5167	+	5.64760i	0.707499	+	0.257509i
$482$		0			0
$483$	6.97565	−	12.0822i	0.317403	−	0.549758i
$484$		0			0
$485$	2.97881	−	2.49952i	0.135261	−	0.113497i
$486$		0			0
$487$	−11.2934	−	19.5607i	−0.511752	−	0.886381i	−0.999907	−	0.0136238i	$-0.995663\pi$
$487$	−11.2934	−	19.5607i	−0.511752	−	0.886381i	0.488155	−	0.872757i	$-0.337670\pi$
$488$		0			0
$489$	0.790393	−	4.48254i	0.0357428	−	0.202707i
$490$		0			0
$491$	15.0680	−	5.48432i	0.680011	−	0.247504i	0.0211590	−	0.999776i	$-0.493264\pi$
$491$	15.0680	−	5.48432i	0.680011	−	0.247504i	0.658852	+	0.752272i	$0.271042\pi$
$492$		0			0
$493$	6.56355			0.295607
$494$		0			0
$495$	−2.58853			−0.116346
$496$		0			0
$497$	−31.4898	+	11.4613i	−1.41251	+	0.514112i
$498$		0			0
$499$	6.09879	−	34.5880i	0.273019	−	1.54837i	−0.472164	−	0.881511i	$-0.656527\pi$
$499$	6.09879	−	34.5880i	0.273019	−	1.54837i	0.745183	−	0.666860i	$-0.232362\pi$
$500$		0			0
$501$	−9.57057	−	16.5767i	−0.427582	−	0.740593i
$502$		0			0
$503$	−30.7395	+	25.7935i	−1.37061	+	1.15007i	−0.398061	+	0.917359i	$0.630317\pi$
$503$	−30.7395	+	25.7935i	−1.37061	+	1.15007i	−0.972545	+	0.232715i	$0.925239\pi$
$504$		0			0
$505$	0.290393	−	0.502975i	0.0129223	−	0.0223821i
$506$		0			0
$507$	21.4491	+	7.80683i	0.952587	+	0.346713i
$508$		0			0
$509$	0.745100	+	4.22567i	0.0330260	+	0.187300i	0.996858	−	0.0792114i	$-0.0252402\pi$
$509$	0.745100	+	4.22567i	0.0330260	+	0.187300i	−0.963832	+	0.266511i	$0.914129\pi$
$510$		0			0
$511$	10.6964	+	8.97535i	0.473181	+	0.397046i
$512$		0			0
$513$	−1.81908	+	3.96118i	−0.0803142	+	0.174890i
$514$		0			0
$515$	1.21301	+	1.01784i	0.0534517	+	0.0448513i
$516$		0			0
$517$	8.88490	+	50.3888i	0.390758	+	2.21610i
$518$		0			0
$519$	5.21688	+	1.89879i	0.228996	+	0.0833476i
$520$		0			0
$521$	−4.38532	+	7.59559i	−0.192124	+	0.332769i	−0.945954	−	0.324301i	$-0.894871\pi$
$521$	−4.38532	+	7.59559i	−0.192124	+	0.332769i	0.753830	+	0.657070i	$0.228204\pi$
$522$		0			0
$523$	−22.9800	+	19.2825i	−1.00484	+	0.843165i	−0.987648	−	0.156687i	$-0.949919\pi$
$523$	−22.9800	+	19.2825i	−1.00484	+	0.843165i	−0.0171965	+	0.999852i	$0.505474\pi$
$524$		0			0
$525$	−10.5458	−	18.2658i	−0.460255	−	0.797184i
$526$		0			0
$527$	−1.64930	+	9.35365i	−0.0718446	+	0.407451i
$528$		0			0
$529$	12.2147	−	4.44577i	0.531072	−	0.193294i
$530$		0			0
$531$	−1.32770			−0.0576171
$532$		0			0
$533$	−11.7202			−0.507657
$534$		0			0
$535$	−6.95424	+	2.53114i	−0.300658	+	0.109431i
$536$		0			0
$537$	−1.44996	+	8.22313i	−0.0625704	+	0.354854i
$538$		0			0
$539$	−34.4680	−	59.7003i	−1.48464	−	2.57147i
$540$		0			0
$541$	3.83544	−	3.21831i	0.164898	−	0.138366i	−0.556605	−	0.830778i	$-0.687896\pi$
$541$	3.83544	−	3.21831i	0.164898	−	0.138366i	0.721503	+	0.692411i	$0.243452\pi$
$542$		0			0
$543$	−6.29426	+	10.9020i	−0.270113	+	0.467849i
$544$		0			0
$545$	−2.55690	−	0.930637i	−0.109526	−	0.0398641i
$546$		0			0
$547$	−2.35803	−	13.3731i	−0.100822	−	0.571790i	−0.992807	−	0.119725i	$-0.961799\pi$
$547$	−2.35803	−	13.3731i	−0.100822	−	0.571790i	0.891985	−	0.452065i	$-0.149313\pi$
$548$		0			0
$549$	−5.08512	−	4.26692i	−0.217028	−	0.182108i
$550$		0			0
$551$	4.62630	−	4.68058i	0.197087	−	0.199399i
$552$		0			0
$553$	−4.26991	−	3.58288i	−0.181575	−	0.152360i
$554$		0			0
$555$	−0.224155	−	1.27125i	−0.00951487	−	0.0539615i
$556$		0			0
$557$	22.2961	+	8.11511i	0.944715	+	0.343848i	0.768026	−	0.640419i	$-0.221239\pi$
$557$	22.2961	+	8.11511i	0.944715	+	0.343848i	0.176689	+	0.984267i	$0.443461\pi$
$558$		0			0
$559$	10.7626	−	18.6414i	0.455211	−	0.788449i
$560$		0			0
$561$	18.4231	−	15.4588i	0.777823	−	0.652671i
$562$		0			0
$563$	−7.37211	−	12.7689i	−0.310697	−	0.538144i	0.667816	−	0.744326i	$-0.267229\pi$
$563$	−7.37211	−	12.7689i	−0.310697	−	0.538144i	−0.978514	+	0.206183i	$0.933896\pi$
$564$		0			0
$565$	−0.986081	+	5.59234i	−0.0414847	+	0.235272i
$566$		0			0
$567$	−4.14543	+	1.50881i	−0.174092	+	0.0633642i
$568$		0			0
$569$	23.9668			1.00474			0.502370	−	0.864653i	$-0.332462\pi$
$569$	23.9668			1.00474			0.502370	+	0.864653i	$0.332462\pi$
$570$		0			0
$571$	41.0847			1.71934			0.859671	−	0.510848i	$-0.170669\pi$
$571$	41.0847			1.71934			0.859671	+	0.510848i	$0.170669\pi$
$572$		0			0
$573$	6.31180	−	2.29731i	0.263679	−	0.0959714i
$574$		0			0
$575$	−2.62558	+	14.8904i	−0.109494	+	0.620973i
$576$		0			0
$577$	3.72756	+	6.45632i	0.155180	+	0.268780i	0.933125	−	0.359553i	$-0.117071\pi$
$577$	3.72756	+	6.45632i	0.155180	+	0.268780i	−0.777944	+	0.628333i	$0.783737\pi$
$578$		0			0
$579$	9.60014	−	8.05547i	0.398968	−	0.334774i
$580$		0			0
$581$	−39.5638	+	68.5265i	−1.64138	+	2.84296i
$582$		0			0
$583$	13.9058	+	5.06132i	0.575921	+	0.209618i
$584$		0			0
$585$	−0.486329	−	2.75811i	−0.0201072	−	0.114034i
$586$		0			0
$587$	−4.53462	−	3.80499i	−0.187164	−	0.157049i	0.544391	−	0.838831i	$-0.316761\pi$
$587$	−4.53462	−	3.80499i	−0.187164	−	0.157049i	−0.731555	+	0.681782i	$0.761205\pi$
$588$		0			0
$589$	5.50774	+	7.76903i	0.226943	+	0.320117i
$590$		0			0
$591$	3.11927	+	2.61738i	0.128310	+	0.107665i
$592$		0			0
$593$	−0.870767	−	4.93837i	−0.0357581	−	0.202794i	0.961695	−	0.274122i	$-0.0883874\pi$
$593$	−0.870767	−	4.93837i	−0.0357581	−	0.202794i	−0.997453	+	0.0713281i	$0.977276\pi$
$594$		0			0
$595$	−8.43242	−	3.06915i	−0.345695	−	0.125823i
$596$		0			0
$597$	3.57785	−	6.19702i	0.146432	−	0.253627i
$598$		0			0
$599$	−3.68164	+	3.08926i	−0.150428	+	0.126224i	−0.714896	−	0.699231i	$-0.753526\pi$
$599$	−3.68164	+	3.08926i	−0.150428	+	0.126224i	0.564468	+	0.825455i	$0.309081\pi$
$600$		0			0
$601$	−4.42468	−	7.66377i	−0.180486	−	0.312612i	0.761560	−	0.648095i	$-0.224434\pi$
$601$	−4.42468	−	7.66377i	−0.180486	−	0.312612i	−0.942046	+	0.335483i	$0.891101\pi$
$602$		0			0
$603$	0.432419	−	2.45237i	0.0176094	−	0.0998681i
$604$		0			0
$605$	8.61974	−	3.13733i	0.350442	−	0.127551i
$606$		0			0
$607$	−0.715948			−0.0290594			−0.0145297	−	0.999894i	$-0.504625\pi$
$607$	−0.715948			−0.0290594			−0.0145297	+	0.999894i	$0.504625\pi$
$608$		0			0
$609$	6.66044			0.269895
$610$		0			0
$611$	−52.0207	+	18.9340i	−2.10453	+	0.765987i
$612$		0			0
$613$	4.23870	−	24.0389i	0.171200	−	0.970921i	−0.771240	−	0.636545i	$-0.780363\pi$
$613$	4.23870	−	24.0389i	0.171200	−	0.970921i	0.942440	−	0.334377i	$-0.108526\pi$
$614$		0			0
$615$	0.458111	+	0.793471i	0.0184728	+	0.0319959i
$616$		0			0
$617$	−33.2918	+	27.9351i	−1.34028	+	1.12463i	−0.358722	+	0.933444i	$0.616788\pi$
$617$	−33.2918	+	27.9351i	−1.34028	+	1.12463i	−0.981555	+	0.191182i	$0.938768\pi$
$618$		0			0
$619$	11.8648	−	20.5505i	0.476888	−	0.825994i	−0.522761	−	0.852479i	$-0.675098\pi$
$619$	11.8648	−	20.5505i	0.476888	−	0.825994i	0.999649	+	0.0264848i	$0.00843137\pi$
$620$		0			0
$621$	2.97178	+	1.08164i	0.119253	+	0.0434047i
$622$		0			0
$623$	9.56077	+	54.2218i	0.383044	+	2.17235i
$624$		0			0
$625$	16.6721	+	13.9895i	0.666882	+	0.559581i
$626$		0			0
$627$	1.96151	−	24.0339i	0.0783353	−	0.959822i
$628$		0			0
$629$	9.18732	+	7.70908i	0.366322	+	0.307381i
$630$		0			0
$631$	4.48293	+	25.4239i	0.178462	+	1.01211i	0.934071	+	0.357087i	$0.116230\pi$
$631$	4.48293	+	25.4239i	0.178462	+	1.01211i	−0.755609	+	0.655023i	$0.772659\pi$
$632$		0			0
$633$	2.49273	+	0.907278i	0.0990770	+	0.0360611i
$634$		0			0
$635$	−0.106067	+	0.183713i	−0.00420913	+	0.00729043i
$636$		0			0
$637$	57.1357	−	47.9425i	2.26380	−	1.89955i
$638$		0			0
$639$	−3.79813	−	6.57856i	−0.150252	−	0.260244i
$640$		0			0
$641$	−1.87645	+	10.6419i	−0.0741153	+	0.420329i	0.925064	+	0.379812i	$0.124011\pi$
$641$	−1.87645	+	10.6419i	−0.0741153	+	0.420329i	−0.999179	+	0.0405163i	$0.987100\pi$
$642$		0			0
$643$	13.5360	−	4.92669i	0.533806	−	0.194290i	−0.0610309	−	0.998136i	$-0.519439\pi$
$643$	13.5360	−	4.92669i	0.533806	−	0.194290i	0.594837	+	0.803846i	$0.297217\pi$
$644$		0			0
$645$	−1.68273			−0.0662576
$646$		0			0
$647$	24.9463			0.980738			0.490369	−	0.871515i	$-0.336862\pi$
$647$	24.9463			0.980738			0.490369	+	0.871515i	$0.336862\pi$
$648$		0			0
$649$	6.90198	−	2.51211i	0.270926	−	0.0986091i
$650$		0			0
$651$	−1.67365	+	9.49173i	−0.0655954	+	0.372010i
$652$		0			0
$653$	−17.8071	−	30.8427i	−0.696844	−	1.20697i	−0.969555	−	0.244873i	$-0.921254\pi$
$653$	−17.8071	−	30.8427i	−0.696844	−	1.20697i	0.272711	−	0.962096i	$-0.412080\pi$
$654$		0			0
$655$	−3.87417	+	3.25082i	−0.151376	+	0.127020i
$656$		0			0
$657$	−1.58260	+	2.74114i	−0.0617430	+	0.106942i
$658$		0			0
$659$	−46.0163	−	16.7485i	−1.79254	−	0.652431i	−0.999038	−	0.0438619i	$-0.986034\pi$
$659$	−46.0163	−	16.7485i	−1.79254	−	0.652431i	−0.793501	−	0.608569i	$-0.791744\pi$
$660$		0			0
$661$	−5.90966	−	33.5154i	−0.229859	−	1.30360i	−0.853174	−	0.521626i	$-0.825326\pi$
$661$	−5.90966	−	33.5154i	−0.229859	−	1.30360i	0.623315	−	0.781971i	$-0.285785\pi$
$662$		0			0
$663$	19.9329	+	16.7257i	0.774129	+	0.649571i
$664$		0			0
$665$	−8.13223	+	3.85002i	−0.315354	+	0.149297i
$666$		0			0
$667$	−3.65767	−	3.06915i	−0.141626	−	0.118838i
$668$		0			0
$669$	2.42246	+	13.7384i	0.0936576	+	0.531158i
$670$		0			0
$671$	34.5082	+	12.5600i	1.33217	+	0.484872i
$672$		0			0
$673$	14.1493	−	24.5073i	0.545415	−	0.944687i	−0.453165	−	0.891427i	$-0.649705\pi$
$673$	14.1493	−	24.5073i	0.545415	−	0.944687i	0.998581	−	0.0532607i	$-0.0169614\pi$
$674$		0			0
$675$	3.66250	−	3.07321i	0.140970	−	0.118288i
$676$		0			0
$677$	−12.5025	−	21.6550i	−0.480511	−	0.832270i	0.519239	−	0.854629i	$-0.326215\pi$
$677$	−12.5025	−	21.6550i	−0.480511	−	0.832270i	−0.999750	+	0.0223595i	$0.992882\pi$
$678$		0			0
$679$	−6.36618	+	36.1044i	−0.244312	+	1.38556i
$680$		0			0
$681$	22.1878	−	8.07569i	0.850238	−	0.309461i
$682$		0			0
$683$	40.1284			1.53547			0.767734	−	0.640768i	$-0.221384\pi$
$683$	40.1284			1.53547			0.767734	+	0.640768i	$0.221384\pi$
$684$		0			0
$685$	−5.13341			−0.196137
$686$		0			0
$687$	8.09152	−	2.94507i	0.308711	−	0.112362i
$688$		0			0
$689$	−2.78029	+	15.7678i	−0.105921	+	0.600705i
$690$		0			0
$691$	1.44087	+	2.49567i	0.0548135	+	0.0949397i	0.892130	−	0.451778i	$-0.149210\pi$
$691$	1.44087	+	2.49567i	0.0548135	+	0.0949397i	−0.837317	+	0.546718i	$0.815877\pi$
$692$		0			0
$693$	18.6951	−	15.6870i	0.710167	−	0.595901i
$694$		0			0
$695$	3.14930	−	5.45475i	0.119460	−	0.206910i
$696$		0			0
$697$	−7.99912	−	2.91144i	−0.302988	−	0.110279i
$698$		0			0
$699$	2.68139	+	15.2069i	0.101419	+	0.575178i
$700$		0			0
$701$	11.8491	+	9.94258i	0.447535	+	0.375526i	0.838520	−	0.544871i	$-0.183421\pi$
$701$	11.8491	+	9.94258i	0.447535	+	0.375526i	−0.390985	+	0.920397i	$0.627866\pi$
$702$		0			0
$703$	11.9731	−	1.11792i	0.451575	−	0.0421630i
$704$		0			0
$705$	3.31521	+	2.78179i	0.124858	+	0.104768i
$706$		0			0
$707$	0.950837	+	5.39246i	0.0357599	+	0.202804i
$708$		0			0
$709$	−43.8353	−	15.9548i	−1.64627	−	0.599193i	−0.658152	−	0.752885i	$-0.728661\pi$
$709$	−43.8353	−	15.9548i	−1.64627	−	0.599193i	−0.988119	+	0.153692i	$0.950884\pi$
$710$		0			0
$711$	0.631759	−	1.09424i	0.0236928	−	0.0410372i
$712$		0			0
$713$	5.29292	−	4.44129i	0.198221	−	0.166327i
$714$		0			0
$715$	7.74675	+	13.4178i	0.289712	+	0.501796i
$716$		0			0
$717$	1.34730	−	7.64090i	0.0503157	−	0.285355i
$718$		0			0
$719$	−10.8020	+	3.93161i	−0.402847	+	0.146624i	−0.535494	−	0.844539i	$-0.679875\pi$
$719$	−10.8020	+	3.93161i	−0.402847	+	0.146624i	0.132647	+	0.991163i	$0.457652\pi$
$720$		0			0
$721$	−14.9290			−0.555986
$722$		0			0
$723$	13.2858			0.494104
$724$		0			0
$725$	−6.78312	+	2.46885i	−0.251919	+	0.0916909i
$726$		0			0
$727$	−3.02687	+	17.1663i	−0.112261	+	0.636661i	0.875810	+	0.482657i	$0.160328\pi$
$727$	−3.02687	+	17.1663i	−0.112261	+	0.636661i	−0.988070	+	0.154004i	$0.950783\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	11.9764	−	10.0494i	0.442962	−	0.371689i
$732$		0			0
$733$	21.9393	−	38.0000i	0.810346	−	1.40356i	−0.102276	−	0.994756i	$-0.532613\pi$
$733$	21.9393	−	38.0000i	0.810346	−	1.40356i	0.912622	−	0.408804i	$-0.134054\pi$
$734$		0			0
$735$	−5.47906	−	1.99421i	−0.202098	−	0.0735577i
$736$		0			0
$737$	2.39218	+	13.5667i	0.0881170	+	0.499736i
$738$		0			0
$739$	13.6040	+	11.4151i	0.500432	+	0.419912i	0.857747	−	0.514072i	$-0.171864\pi$
$739$	13.6040	+	11.4151i	0.500432	+	0.419912i	−0.357316	+	0.933984i	$0.616308\pi$
$740$		0			0
$741$	25.9770	−	2.42544i	0.954289	−	0.0891008i
$742$		0			0
$743$	−7.98751	−	6.70232i	−0.293033	−	0.245884i	0.484404	−	0.874844i	$-0.339036\pi$
$743$	−7.98751	−	6.70232i	−0.293033	−	0.245884i	−0.777438	+	0.628960i	$0.783481\pi$
$744$		0			0
$745$	−0.665441	−	3.77390i	−0.0243799	−	0.138265i
$746$		0			0
$747$	−16.8550	−	6.13473i	−0.616694	−	0.224458i
$748$		0			0
$749$	34.8862	−	60.4248i	1.27472	−	2.20787i
$750$		0			0
$751$	26.0915	−	21.8934i	0.952093	−	0.798901i	−0.0275557	−	0.999620i	$-0.508772\pi$
$751$	26.0915	−	21.8934i	0.952093	−	0.798901i	0.979649	+	0.200719i	$0.0643279\pi$
$752$		0			0
$753$	8.82547	+	15.2862i	0.321618	+	0.557059i
$754$		0			0
$755$	1.71776	−	9.74189i	0.0625156	−	0.354544i
$756$		0			0
$757$	−40.6664	+	14.8014i	−1.47805	+	0.537965i	−0.950272	−	0.311420i	$-0.899195\pi$
$757$	−40.6664	+	14.8014i	−1.47805	+	0.537965i	−0.527774	+	0.849385i	$0.676973\pi$
$758$		0			0
$759$	−17.4953			−0.635037
$760$		0			0
$761$	14.1679			0.513585			0.256793	−	0.966467i	$-0.417334\pi$
$761$	14.1679			0.513585			0.256793	+	0.966467i	$0.417334\pi$
$762$		0			0
$763$	24.1065	−	8.77406i	0.872715	−	0.317642i
$764$		0			0
$765$	0.353226	−	2.00324i	0.0127709	−	0.0724275i
$766$		0			0
$767$	3.97343	+	6.88218i	0.143472	+	0.248501i
$768$		0			0
$769$	−13.9722	+	11.7241i	−0.503852	+	0.422782i	−0.858960	−	0.512043i	$-0.828889\pi$
$769$	−13.9722	+	11.7241i	−0.503852	+	0.422782i	0.355107	+	0.934825i	$0.384444\pi$
$770$		0			0
$771$	3.95084	−	6.84305i	0.142286	−	0.246446i
$772$		0			0
$773$	26.5437	+	9.66112i	0.954711	+	0.347486i	0.771959	−	0.635673i	$-0.219277\pi$
$773$	26.5437	+	9.66112i	0.954711	+	0.347486i	0.182752	+	0.983159i	$0.441499\pi$
$774$		0			0
$775$	−1.81386	−	10.2869i	−0.0651559	−	0.369517i
$776$		0			0
$777$	9.32295	+	7.82288i	0.334459	+	0.280644i
$778$		0			0
$779$	−7.71436	+	3.65219i	−0.276395	+	0.130853i
$780$		0			0
$781$	32.1917	+	27.0120i	1.15191	+	0.966566i
$782$		0			0
$783$	0.262174	+	1.48686i	0.00936934	+	0.0531361i
$784$		0			0
$785$	8.63475	+	3.14279i	0.308188	+	0.112171i
$786$		0			0
$787$	9.07057	−	15.7107i	0.323331	−	0.560026i	−0.657842	−	0.753156i	$-0.728531\pi$
$787$	9.07057	−	15.7107i	0.323331	−	0.560026i	0.981173	+	0.193130i	$0.0618639\pi$
$788$		0			0
$789$	−19.4349	+	16.3079i	−0.691902	+	0.580575i
$790$		0			0
$791$	−26.7690	−	46.3653i	−0.951797	−	1.64856i
$792$		0			0
$793$	−6.89945	+	39.1287i	−0.245007	+	1.38950i
$794$		0			0
$795$	1.17617	−	0.428092i	0.0417146	−	0.0151829i
$796$		0			0
$797$	−32.8111			−1.16223			−0.581114	−	0.813822i	$-0.697383\pi$
$797$	−32.8111			−1.16223			−0.581114	+	0.813822i	$0.697383\pi$
$798$		0			0
$799$	−40.2080			−1.42246
$800$		0			0
$801$	−11.7280	+	4.26865i	−0.414389	+	0.150825i
$802$		0			0
$803$	3.04060	−	17.2441i	0.107300	−	0.608531i
$804$		0			0
$805$	3.26399	+	5.65339i	0.115040	+	0.199256i
$806$		0			0
$807$	−15.4513	+	12.9652i	−0.543912	+	0.456396i
$808$		0			0
$809$	4.67112	−	8.09062i	0.164228	−	0.284451i	−0.772153	−	0.635437i	$-0.780820\pi$
$809$	4.67112	−	8.09062i	0.164228	−	0.284451i	0.936381	+	0.350986i	$0.114153\pi$
$810$		0			0
$811$	−14.1027	−	5.13295i	−0.495211	−	0.180242i	0.0823275	−	0.996605i	$-0.473765\pi$
$811$	−14.1027	−	5.13295i	−0.495211	−	0.180242i	−0.577539	+	0.816363i	$0.695987\pi$
$812$		0			0
$813$	3.56165	+	20.1991i	0.124913	+	0.708414i
$814$		0			0
$815$	1.63151	+	1.36900i	0.0571493	+	0.0479540i
$816$		0			0
$817$	1.27513	−	15.6238i	0.0446111	−	0.546608i
$818$		0			0
$819$	20.2271	+	16.9726i	0.706794	+	0.593070i
$820$		0			0
$821$	6.34760	+	35.9990i	0.221533	+	1.25637i	0.869203	+	0.494455i	$0.164632\pi$
$821$	6.34760	+	35.9990i	0.221533	+	1.25637i	−0.647671	+	0.761920i	$0.724257\pi$
$822$		0			0
$823$	21.4595	+	7.81060i	0.748030	+	0.272261i	0.687776	−	0.725923i	$-0.258587\pi$
$823$	21.4595	+	7.81060i	0.748030	+	0.272261i	0.0602532	+	0.998183i	$0.480809\pi$
$824$		0			0
$825$	−13.2246	+	22.9057i	−0.460422	+	0.797475i
$826$		0			0
$827$	−1.86303	+	1.56326i	−0.0647838	+	0.0543600i	−0.674605	−	0.738179i	$-0.735686\pi$
$827$	−1.86303	+	1.56326i	−0.0647838	+	0.0543600i	0.609821	+	0.792539i	$0.291241\pi$
$828$		0			0
$829$	11.6702	+	20.2135i	0.405324	+	0.702042i	0.994359	−	0.106065i	$-0.0338253\pi$
$829$	11.6702	+	20.2135i	0.405324	+	0.702042i	−0.589035	+	0.808108i	$0.700492\pi$
$830$		0			0
$831$	−1.58630	+	8.99638i	−0.0550283	+	0.312081i
$832$		0			0
$833$	50.9051	−	18.5280i	1.76376	−	0.641956i
$834$		0			0
$835$	8.95636			0.309947
$836$		0			0
$837$	−2.18479			−0.0755175
$838$		0			0
$839$	−1.37851	+	0.501736i	−0.0475914	+	0.0173218i	−0.365706	−	0.930730i	$-0.619172\pi$
$839$	−1.37851	+	0.501736i	−0.0475914	+	0.0173218i	0.318115	+	0.948052i	$0.396950\pi$
$840$		0			0
$841$	−4.63997	+	26.3146i	−0.159999	+	0.907399i
$842$		0			0
$843$	−1.71554	−	2.97140i	−0.0590862	−	0.102340i
$844$		0			0
$845$	−8.18164	+	6.86521i	−0.281457	+	0.236170i
$846$		0			0
$847$	−43.2413	+	74.8961i	−1.48579	+	2.57346i
$848$		0			0
$849$	−10.5642	−	3.84505i	−0.362562	−	0.131962i
$850$		0			0
$851$	−1.51501	−	8.59208i	−0.0519340	−	0.294533i
$852$		0			0
$853$	−7.15207	−	6.00130i	−0.244882	−	0.205481i	0.512083	−	0.858936i	$-0.328874\pi$
$853$	−7.15207	−	6.00130i	−0.244882	−	0.205481i	−0.756965	+	0.653456i	$0.773319\pi$
$854$		0			0
$855$	−1.17958	−	1.66387i	−0.0403407	−	0.0569032i
$856$		0			0
$857$	26.6930	+	22.3981i	0.911816	+	0.765104i	0.972464	−	0.233055i	$-0.0748723\pi$
$857$	26.6930	+	22.3981i	0.911816	+	0.765104i	−0.0606480	+	0.998159i	$0.519317\pi$
$858$		0			0
$859$	4.00758	+	22.7281i	0.136737	+	0.775473i	0.973635	+	0.228114i	$0.0732558\pi$
$859$	4.00758	+	22.7281i	0.136737	+	0.775473i	−0.836898	+	0.547359i	$0.815633\pi$
$860$		0			0
$861$	−8.11721	−	2.95442i	−0.276634	−	0.100686i
$862$		0			0
$863$	21.5788	−	37.3755i	0.734550	−	1.27228i	−0.220370	−	0.975416i	$-0.570727\pi$
$863$	21.5788	−	37.3755i	0.734550	−	1.27228i	0.954920	−	0.296862i	$-0.0959402\pi$
$864$		0			0
$865$	−1.98995	+	1.66977i	−0.0676604	+	0.0567738i
$866$		0			0
$867$	0.949493	+	1.64457i	0.0322465	+	0.0558525i
$868$		0			0
$869$	−1.21378	+	6.88370i	−0.0411748	+	0.233514i
$870$		0			0
$871$	−14.0061	+	5.09780i	−0.474578	+	0.172732i
$872$		0			0
$873$	−8.31046			−0.281266
$874$		0			0
$875$	20.1898			0.682541
$876$		0			0
$877$	−42.1374	+	15.3368i	−1.42288	+	0.517886i	−0.934882	−	0.354959i	$-0.884495\pi$
$877$	−42.1374	+	15.3368i	−1.42288	+	0.517886i	−0.487998	+	0.872845i	$0.662273\pi$
$878$		0			0
$879$	2.52347	−	14.3113i	0.0851146	−	0.482709i
$880$		0			0
$881$	2.29932	+	3.98253i	0.0774659	+	0.134175i	0.902156	−	0.431410i	$-0.141984\pi$
$881$	2.29932	+	3.98253i	0.0774659	+	0.134175i	−0.824690	+	0.565585i	$0.808650\pi$
$882$		0			0
$883$	5.53524	−	4.64462i	0.186276	−	0.156304i	−0.544881	−	0.838513i	$-0.683425\pi$
$883$	5.53524	−	4.64462i	0.186276	−	0.156304i	0.731157	+	0.682209i	$0.238981\pi$
$884$		0			0
$885$	0.310622	−	0.538013i	0.0104414	−	0.0180851i
$886$		0			0
$887$	43.5676	+	15.8573i	1.46286	+	0.532437i	0.946151	−	0.323725i	$-0.104935\pi$
$887$	43.5676	+	15.8573i	1.46286	+	0.532437i	0.516707	+	0.856162i	$0.327158\pi$
$888$		0			0
$889$	−0.347296	−	1.96962i	−0.0116479	−	0.0660588i
$890$		0			0
$891$	4.23783	+	3.55596i	0.141973	+	0.119129i
$892$		0			0
$893$	−28.3405	+	28.6730i	−0.948378	+	0.959506i
$894$		0			0
$895$	−2.99297	−	2.51140i	−0.100044	−	0.0839470i
$896$		0			0
$897$	−3.28699	−	18.6414i	−0.109749	−	0.622420i
$898$		0			0
$899$	3.09967	+	1.12819i	0.103380	+	0.0376272i
$900$		0			0
$901$	−5.81449	+	10.0710i	−0.193709	+	0.335514i
$902$		0			0
$903$	12.1532	−	10.1977i	0.404432	−	0.339359i
$904$		0			0
$905$	−2.94516	−	5.10116i	−0.0979003	−	0.169568i
$906$		0			0
$907$	9.44222	−	53.5495i	0.313524	−	1.77808i	−0.266857	−	0.963736i	$-0.585985\pi$
$907$	9.44222	−	53.5495i	0.313524	−	1.77808i	0.580381	−	0.814345i	$-0.302904\pi$
$908$		0			0
$909$	−1.16637	+	0.424525i	−0.0386862	+	0.0140806i
$910$		0			0
$911$	16.8993			0.559899			0.279950	−	0.960015i	$-0.409682\pi$
$911$	16.8993			0.559899			0.279950	+	0.960015i	$0.409682\pi$
$912$		0			0
$913$	99.2277			3.28396
$914$		0			0
$915$	2.91875	−	1.06234i	0.0964908	−	0.0351198i
$916$		0			0
$917$	8.27972	−	46.9566i	0.273420	−	1.55064i
$918$		0			0
$919$	−3.85100	−	6.67014i	−0.127033	−	0.220027i	0.795493	−	0.605963i	$-0.207212\pi$
$919$	−3.85100	−	6.67014i	−0.127033	−	0.220027i	−0.922526	+	0.385936i	$0.873879\pi$
$920$		0			0
$921$	−19.6898	+	16.5217i	−0.648802	+	0.544410i
$922$		0			0
$923$	−22.7335	+	39.3757i	−0.748284	+	1.29607i
$924$		0			0
$925$	−12.3944	−	4.51119i	−0.407525	−	0.148327i
$926$		0			0
$927$	−0.587649	−	3.33272i	−0.0193009	−	0.109461i
$928$		0			0
$929$	−13.9010	−	11.6644i	−0.456078	−	0.382695i	0.385607	−	0.922663i	$-0.373992\pi$
$929$	−13.9010	−	11.6644i	−0.456078	−	0.382695i	−0.841686	+	0.539968i	$0.818436\pi$
$930$		0			0
$931$	22.6677	−	49.3607i	0.742904	−	1.61773i
$932$		0			0
$933$	4.47178	+	3.75227i	0.146400	+	0.122844i
$934$		0			0
$935$	1.95408	+	11.0821i	0.0639052	+	0.362424i
$936$		0			0
$937$	9.71436	+	3.53574i	0.317354	+	0.115507i	0.495786	−	0.868445i	$-0.334880\pi$
$937$	9.71436	+	3.53574i	0.317354	+	0.115507i	−0.178432	+	0.983952i	$0.557102\pi$
$938$		0			0
$939$	−8.25537	+	14.2987i	−0.269404	+	0.466621i
$940$		0			0
$941$	34.5808	−	29.0168i	1.12730	−	0.945920i	0.128353	−	0.991729i	$-0.459031\pi$
$941$	34.5808	−	29.0168i	1.12730	−	0.945920i	0.998950	+	0.0458088i	$0.0145865\pi$
$942$		0			0
$943$	3.09627	+	5.36289i	0.100828	+	0.174640i
$944$		0			0
$945$	0.358441	−	2.03282i	0.0116601	−	0.0661276i
$946$		0			0
$947$	−18.9561	+	6.89944i	−0.615989	+	0.224202i	−0.631122	−	0.775684i	$-0.717405\pi$
$947$	−18.9561	+	6.89944i	−0.615989	+	0.224202i	0.0151327	+	0.999885i	$0.495183\pi$
$948$		0			0
$949$	18.9451			0.614984
$950$		0			0
$951$	26.9495			0.873899
$952$		0			0
$953$	42.0232	−	15.2952i	1.36127	−	0.495460i	0.444820	−	0.895620i	$-0.353268\pi$
$953$	42.0232	−	15.2952i	1.36127	−	0.495460i	0.916445	+	0.400160i	$0.131045\pi$
$954$		0			0
$955$	−0.545759	+	3.09516i	−0.0176604	+	0.100157i
$956$		0			0
$957$	−4.17617	−	7.23335i	−0.134997	−	0.233821i
$958$		0			0
$959$	37.0749	−	31.1095i	1.19721	−	1.00458i
$960$		0			0
$961$	13.1133	−	22.7130i	0.423011	−	0.732677i
$962$		0			0
$963$	14.8623	+	5.40944i	0.478931	+	0.174317i
$964$		0			0
$965$	1.01826	+	5.77482i	0.0327788	+	0.185898i
$966$		0			0
$967$	8.96270	+	7.52060i	0.288221	+	0.241846i	0.775421	−	0.631444i	$-0.217537\pi$
$967$	8.96270	+	7.52060i	0.288221	+	0.241846i	−0.487201	+	0.873290i	$0.661982\pi$
$968$		0			0
$969$	18.3320	+	4.79763i	0.588910	+	0.154122i
$970$		0			0
$971$	−27.9786	−	23.4769i	−0.897877	−	0.753409i	0.0718969	−	0.997412i	$-0.477095\pi$
$971$	−27.9786	−	23.4769i	−0.897877	−	0.753409i	−0.969774	+	0.244003i	$0.921539\pi$
$972$		0			0
$973$	10.3118	+	58.4811i	0.330581	+	1.87482i
$974$		0			0
$975$	−26.8910	−	9.78752i	−0.861201	−	0.313452i
$976$		0			0
$977$	25.0219	−	43.3392i	0.800521	−	1.38654i	−0.118753	−	0.992924i	$-0.537890\pi$
$977$	25.0219	−	43.3392i	0.800521	−	1.38654i	0.919274	−	0.393619i	$-0.128777\pi$
$978$		0			0
$979$	52.8911	−	44.3809i	1.69041	−	1.41842i
$980$		0			0
$981$	2.90760	+	5.03612i	0.0928326	+	0.160791i
$982$		0			0
$983$	−1.71317	+	9.71589i	−0.0546417	+	0.309889i	−0.999863	−	0.0165411i	$-0.994735\pi$
$983$	−1.71317	+	9.71589i	−0.0546417	+	0.309889i	0.945221	+	0.326430i	$0.105846\pi$
$984$		0			0
$985$	−1.79039	+	0.651650i	−0.0570466	+	0.0207633i
$986$		0			0
$987$	−40.8016			−1.29873
$988$		0			0
$989$	−11.3732			−0.361647
$990$		0			0
$991$	32.1596	−	11.7051i	1.02158	−	0.371826i	0.223712	−	0.974655i	$-0.428182\pi$
$991$	32.1596	−	11.7051i	1.02158	−	0.371826i	0.797870	+	0.602830i	$0.205960\pi$
$992$		0			0
$993$	4.94697	−	28.0556i	0.156987	−	0.890319i
$994$		0			0
$995$	1.67412	+	2.89965i	0.0530730	+	0.0919252i
$996$		0			0
$997$	30.4818	−	25.5773i	0.965368	−	0.810040i	−0.0164497	−	0.999865i	$-0.505236\pi$
$997$	30.4818	−	25.5773i	0.965368	−	0.810040i	0.981818	+	0.189825i	$0.0607919\pi$
$998$		0			0
$999$	−1.37939	+	2.38917i	−0.0436418	+	0.0755898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.c.529.1		6
4.3	odd	2		114.2.i.b.73.1	yes	6
12.11	even	2		342.2.u.d.73.1		6
19.6	even	9	inner	912.2.bo.c.481.1		6
76.43	odd	18		2166.2.a.t.1.3		3
76.63	odd	18		114.2.i.b.25.1	✓	6
76.71	even	18		2166.2.a.n.1.3		3
228.71	odd	18		6498.2.a.bt.1.1		3
228.119	even	18		6498.2.a.bo.1.1		3
228.215	even	18		342.2.u.d.253.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.25.1	✓	6	76.63	odd	18
114.2.i.b.73.1	yes	6	4.3	odd	2
342.2.u.d.73.1		6	12.11	even	2
342.2.u.d.253.1		6	228.215	even	18
912.2.bo.c.481.1		6	19.6	even	9	inner
912.2.bo.c.529.1		6	1.1	even	1	trivial
2166.2.a.n.1.3		3	76.71	even	18
2166.2.a.t.1.3		3	76.43	odd	18
6498.2.a.bo.1.1		3	228.119	even	18
6498.2.a.bt.1.1		3	228.71	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{3} +(-0.0812519 + 0.460802i) q^{5} +(-2.20574 - 3.82045i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{3} +(-0.0812519 + 0.460802i) q^{5} +(-2.20574 - 3.82045i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-2.76604 + 4.79093i) q^{11} +(-5.62449 - 2.04715i) q^{13} +(0.0812519 + 0.460802i) q^{15} +(-3.33022 - 2.79439i) q^{17} +(-4.34002 + 0.405223i) q^{19} +(-3.37939 - 2.83564i) q^{21} +(0.549163 + 3.11446i) q^{23} +(4.49273 + 1.63522i) q^{25} +(0.500000 - 0.866025i) q^{27} +(-1.15657 + 0.970481i) q^{29} +(-1.09240 - 1.89209i) q^{31} +(-0.960637 + 5.44804i) q^{33} +(1.93969 - 0.705990i) q^{35} -2.75877 q^{37} -5.98545 q^{39} +(1.84002 - 0.669713i) q^{41} +(-0.624485 + 3.54163i) q^{43} +(0.233956 + 0.405223i) q^{45} +(7.08512 - 5.94512i) q^{47} +(-6.23055 + 10.7916i) q^{49} +(-4.08512 - 1.48686i) q^{51} +(-0.464508 - 2.63435i) q^{53} +(-1.98293 - 1.66387i) q^{55} +(-3.93969 + 1.86516i) q^{57} +(-1.01707 - 0.853427i) q^{59} +(-1.15270 - 6.53731i) q^{61} +(-4.14543 - 1.50881i) q^{63} +(1.40033 - 2.42544i) q^{65} +(1.90760 - 1.60067i) q^{67} +(1.58125 + 2.73881i) q^{69} +(1.31908 - 7.48086i) q^{71} +(-2.97431 + 1.08256i) q^{73} +4.78106 q^{75} +24.4047 q^{77} +(1.18732 - 0.432149i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-8.96838 - 15.5337i) q^{83} +(1.55825 - 1.30753i) q^{85} +(-0.754900 + 1.30753i) q^{87} +(-11.7280 - 4.26865i) q^{89} +(4.58512 + 26.0035i) q^{91} +(-1.67365 - 1.40436i) q^{93} +(0.165907 - 2.03282i) q^{95} +(-6.36618 - 5.34186i) q^{97} +(0.960637 + 5.44804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q - 3 * q^5 - 3 * q^7	\( 6 q - 3 q^{5} - 3 q^{7} - 12 q^{11} - 21 q^{13} + 3 q^{15} + 3 q^{17} - 6 q^{19} - 9 q^{21} + 15 q^{23} + 9 q^{25} + 3 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 9 q^{43} + 6 q^{45} + 21 q^{47} - 3 q^{51} + 30 q^{53} + 9 q^{55} - 18 q^{57} - 27 q^{59} - 9 q^{61} - 9 q^{63} - 6 q^{65} + 15 q^{67} + 12 q^{69} - 9 q^{71} + 12 q^{73} - 6 q^{75} + 42 q^{77} - 15 q^{79} + 3 q^{83} - 36 q^{85} - 6 q^{87} - 48 q^{89} + 6 q^{91} - 9 q^{93} + 48 q^{95} + 18 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 3 * q^7 - 12 * q^11 - 21 * q^13 + 3 * q^15 + 3 * q^17 - 6 * q^19 - 9 * q^21 + 15 * q^23 + 9 * q^25 + 3 * q^27 + 15 * q^29 - 3 * q^31 + 3 * q^33 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 9 * q^43 + 6 * q^45 + 21 * q^47 - 3 * q^51 + 30 * q^53 + 9 * q^55 - 18 * q^57 - 27 * q^59 - 9 * q^61 - 9 * q^63 - 6 * q^65 + 15 * q^67 + 12 * q^69 - 9 * q^71 + 12 * q^73 - 6 * q^75 + 42 * q^77 - 15 * q^79 + 3 * q^83 - 36 * q^85 - 6 * q^87 - 48 * q^89 + 6 * q^91 - 9 * q^93 + 48 * q^95 + 18 * q^97 - 3 * q^99

Introduction

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