LMFDB - Embedded newform 804.2.y.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	804.73
Dual form			804.2.y.b.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{3} +(-3.13336 - 0.920039i) q^{5} +(-2.56141 + 0.493671i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{3} +(-3.13336 - 0.920039i) q^{5} +(-2.56141 + 0.493671i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-1.04793 + 0.999195i) q^{11} +(-0.0752496 + 1.57968i) q^{13} +(2.13854 - 2.46801i) q^{15} +(6.09133 - 4.79027i) q^{17} +(6.41011 + 1.23545i) q^{19} +(0.614989 - 2.53502i) q^{21} +(2.94684 - 0.281389i) q^{23} +(4.76523 + 3.06243i) q^{25} +(0.959493 - 0.281733i) q^{27} +(2.68992 - 4.65909i) q^{29} +(-0.0686466 - 1.44107i) q^{31} +(-0.473576 - 1.36831i) q^{33} +(8.48003 + 0.809745i) q^{35} +(-0.917976 - 1.58998i) q^{37} +(-1.40567 - 0.724673i) q^{39} +(-0.463871 - 0.185706i) q^{41} +(0.294267 + 2.04667i) q^{43} +(1.35660 + 2.97054i) q^{45} +(-4.84236 - 6.80014i) q^{47} +(-0.181462 + 0.0726464i) q^{49} +(1.82696 + 7.53082i) q^{51} +(1.33800 - 9.30602i) q^{53} +(4.20283 - 2.16671i) q^{55} +(-3.78666 + 5.31762i) q^{57} +(-0.211108 + 0.135671i) q^{59} +(5.09947 + 4.86234i) q^{61} +(2.05046 + 1.61250i) q^{63} +(1.68915 - 4.88049i) q^{65} +(-1.16988 + 8.10132i) q^{67} +(-0.968202 + 2.79744i) q^{69} +(0.989232 + 0.777940i) q^{71} +(1.98241 + 1.89022i) q^{73} +(-4.76523 + 3.06243i) q^{75} +(2.19089 - 3.07668i) q^{77} +(12.0326 - 6.20325i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(3.33870 + 13.7623i) q^{83} +(-23.4936 + 9.40541i) q^{85} +(3.12062 + 4.38230i) q^{87} +(-3.98045 - 8.71598i) q^{89} +(-0.587099 - 4.08336i) q^{91} +(1.33936 + 0.536198i) q^{93} +(-18.9485 - 9.76865i) q^{95} +(-6.62571 - 11.4761i) q^{97} +(1.44139 + 0.137636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{20}{33}\right)$	$1$

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
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$		0			0
$5$	−3.13336	−	0.920039i	−1.40128	−	0.411454i	−0.508159	−	0.861264i	$-0.669674\pi$
$5$	−3.13336	−	0.920039i	−1.40128	−	0.411454i	−0.893124	+	0.449810i	$0.851492\pi$
$6$		0			0
$7$	−2.56141	+	0.493671i	−0.968122	+	0.186590i	−0.648719	−	0.761028i	$-0.724695\pi$
$7$	−2.56141	+	0.493671i	−0.968122	+	0.186590i	−0.319404	+	0.947619i	$0.603483\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	−1.04793	+	0.999195i	−0.315962	+	0.301269i	−0.831418	−	0.555647i	$-0.812471\pi$
$11$	−1.04793	+	0.999195i	−0.315962	+	0.301269i	0.515457	+	0.856916i	$0.327622\pi$
$12$		0			0
$13$	−0.0752496	+	1.57968i	−0.0208705	+	0.438125i	0.964115	+	0.265486i	$0.0855324\pi$
$13$	−0.0752496	+	1.57968i	−0.0208705	+	0.438125i	−0.984985	+	0.172639i	$0.944771\pi$
$14$		0			0
$15$	2.13854	−	2.46801i	0.552169	−	0.637237i
$16$		0			0
$17$	6.09133	−	4.79027i	1.47736	−	1.16181i	0.527331	−	0.849660i	$-0.323193\pi$
$17$	6.09133	−	4.79027i	1.47736	−	1.16181i	0.950032	−	0.312152i	$-0.101050\pi$
$18$		0			0
$19$	6.41011	+	1.23545i	1.47058	+	0.283431i	0.860720	−	0.509078i	$-0.170014\pi$
$19$	6.41011	+	1.23545i	1.47058	+	0.283431i	0.609860	+	0.792509i	$0.291226\pi$
$20$		0			0
$21$	0.614989	−	2.53502i	0.134202	−	0.553187i
$22$		0			0
$23$	2.94684	−	0.281389i	0.614459	−	0.0586737i	0.216814	−	0.976213i	$-0.430434\pi$
$23$	2.94684	−	0.281389i	0.614459	−	0.0586737i	0.397645	+	0.917539i	$0.369827\pi$
$24$		0			0
$25$	4.76523	+	3.06243i	0.953046	+	0.612486i
$26$		0			0
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$		0			0
$29$	2.68992	−	4.65909i	0.499506	−	0.865170i	−0.500493	−	0.865740i	$-0.666848\pi$
$29$	2.68992	−	4.65909i	0.499506	−	0.865170i	1.00000		0.000569879i	$0.000181398\pi$
$30$		0			0
$31$	−0.0686466	−	1.44107i	−0.0123293	−	0.258824i	−0.996613	−	0.0822309i	$-0.973796\pi$
$31$	−0.0686466	−	1.44107i	−0.0123293	−	0.258824i	0.984284	−	0.176593i	$-0.0565075\pi$
$32$		0			0
$33$	−0.473576	−	1.36831i	−0.0824390	−	0.238192i
$34$		0			0
$35$	8.48003	+	0.809745i	1.43339	+	0.136872i
$36$		0			0
$37$	−0.917976	−	1.58998i	−0.150914	−	0.261391i	0.780649	−	0.624969i	$-0.214888\pi$
$37$	−0.917976	−	1.58998i	−0.150914	−	0.261391i	−0.931564	+	0.363578i	$0.881555\pi$
$38$		0			0
$39$	−1.40567	−	0.724673i	−0.225087	−	0.116041i
$40$		0			0
$41$	−0.463871	−	0.185706i	−0.0724444	−	0.0290024i	0.335157	−	0.942162i	$-0.391211\pi$
$41$	−0.463871	−	0.185706i	−0.0724444	−	0.0290024i	−0.407602	+	0.913160i	$0.633635\pi$
$42$		0			0
$43$	0.294267	+	2.04667i	0.0448753	+	0.312114i	0.999880	+	0.0155222i	$0.00494106\pi$
$43$	0.294267	+	2.04667i	0.0448753	+	0.312114i	−0.955004	+	0.296592i	$0.904150\pi$
$44$		0			0
$45$	1.35660	+	2.97054i	0.202230	+	0.442821i
$46$		0			0
$47$	−4.84236	−	6.80014i	−0.706330	−	0.991902i	−0.999359	−	0.0357983i	$-0.988603\pi$
$47$	−4.84236	−	6.80014i	−0.706330	−	0.991902i	0.293029	−	0.956104i	$-0.405337\pi$
$48$		0			0
$49$	−0.181462	+	0.0726464i	−0.0259231	+	0.0103781i
$50$		0			0
$51$	1.82696	+	7.53082i	0.255825	+	1.05453i
$52$		0			0
$53$	1.33800	−	9.30602i	0.183789	−	1.27828i	−0.663914	−	0.747809i	$-0.731106\pi$
$53$	1.33800	−	9.30602i	0.183789	−	1.27828i	0.847703	−	0.530471i	$-0.177985\pi$
$54$		0			0
$55$	4.20283	−	2.16671i	0.566710	−	0.292159i
$56$		0			0
$57$	−3.78666	+	5.31762i	−0.501555	+	0.704336i
$58$		0			0
$59$	−0.211108	+	0.135671i	−0.0274839	+	0.0176628i	−0.554311	−	0.832310i	$-0.687018\pi$
$59$	−0.211108	+	0.135671i	−0.0274839	+	0.0176628i	0.526827	+	0.849973i	$0.323382\pi$
$60$		0			0
$61$	5.09947	+	4.86234i	0.652921	+	0.622559i	0.942345	−	0.334642i	$-0.108615\pi$
$61$	5.09947	+	4.86234i	0.652921	+	0.622559i	−0.289424	+	0.957201i	$0.593464\pi$
$62$		0			0
$63$	2.05046	+	1.61250i	0.258334	+	0.203156i
$64$		0			0
$65$	1.68915	−	4.88049i	0.209514	−	0.605350i
$66$		0			0
$67$	−1.16988	+	8.10132i	−0.142924	+	0.989734i
$67$	−1.16988	+	8.10132i	−0.142924	+	0.989734i
$68$		0			0
$69$	−0.968202	+	2.79744i	−0.116558	+	0.336772i
$70$		0			0
$71$	0.989232	+	0.777940i	0.117400	+	0.0923245i	0.675133	−	0.737696i	$-0.264086\pi$
$71$	0.989232	+	0.777940i	0.117400	+	0.0923245i	−0.557733	+	0.830021i	$0.688329\pi$
$72$		0			0
$73$	1.98241	+	1.89022i	0.232023	+	0.221234i	0.797167	−	0.603759i	$-0.206331\pi$
$73$	1.98241	+	1.89022i	0.232023	+	0.221234i	−0.565144	+	0.824992i	$0.691179\pi$
$74$		0			0
$75$	−4.76523	+	3.06243i	−0.550241	+	0.353619i
$76$		0			0
$77$	2.19089	−	3.07668i	0.249676	−	0.350620i
$78$		0			0
$79$	12.0326	−	6.20325i	1.35378	−	0.697920i	0.379906	−	0.925025i	$-0.375956\pi$
$79$	12.0326	−	6.20325i	1.35378	−	0.697920i	0.973870	+	0.227104i	$0.0729259\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	3.33870	+	13.7623i	0.366470	+	1.51061i	0.794735	+	0.606956i	$0.207610\pi$
$83$	3.33870	+	13.7623i	0.366470	+	1.51061i	−0.428266	+	0.903653i	$0.640875\pi$
$84$		0			0
$85$	−23.4936	+	9.40541i	−2.54824	+	1.02016i
$86$		0			0
$87$	3.12062	+	4.38230i	0.334565	+	0.469831i
$88$		0			0
$89$	−3.98045	−	8.71598i	−0.421927	−	0.923892i	−0.994568	−	0.104086i	$-0.966808\pi$
$89$	−3.98045	−	8.71598i	−0.421927	−	0.923892i	0.572641	−	0.819806i	$-0.305919\pi$
$90$		0			0
$91$	−0.587099	−	4.08336i	−0.0615447	−	0.428053i
$92$		0			0
$93$	1.33936	+	0.536198i	0.138885	+	0.0556012i
$94$		0			0
$95$	−18.9485	−	9.76865i	−1.94408	−	1.00224i
$96$		0			0
$97$	−6.62571	−	11.4761i	−0.672739	−	1.16522i	−0.977124	−	0.212669i	$-0.931784\pi$
$97$	−6.62571	−	11.4761i	−0.672739	−	1.16522i	0.304385	−	0.952549i	$-0.401549\pi$
$98$		0			0
$99$	1.44139	+	0.137636i	0.144865	+	0.0138329i
$100$		0			0
$101$	2.98089	+	8.61270i	0.296609	+	0.856996i	0.990573	+	0.136986i	$0.0437416\pi$
$101$	2.98089	+	8.61270i	0.296609	+	0.856996i	−0.693964	+	0.720010i	$0.744137\pi$
$102$		0			0
$103$	−0.181157	−	3.80296i	−0.0178500	−	0.374717i	−0.990064	−	0.140621i	$-0.955090\pi$
$103$	−0.181157	−	3.80296i	−0.0178500	−	0.374717i	0.972214	−	0.234096i	$-0.0752129\pi$
$104$		0			0
$105$	−4.25930	+	7.37733i	−0.415665	+	0.719953i
$106$		0			0
$107$	15.6956	−	4.60864i	1.51735	−	0.445534i	0.586198	−	0.810168i	$-0.300624\pi$
$107$	15.6956	−	4.60864i	1.51735	−	0.445534i	0.931151	+	0.364635i	$0.118806\pi$
$108$		0			0
$109$	−4.58320	−	2.94544i	−0.438991	−	0.282122i	0.302419	−	0.953175i	$-0.402206\pi$
$109$	−4.58320	−	2.94544i	−0.438991	−	0.282122i	−0.741409	+	0.671053i	$0.765842\pi$
$110$		0			0
$111$	1.82764	−	0.174518i	0.173472	−	0.0165646i
$112$		0			0
$113$	2.16272	−	8.91484i	0.203451	−	0.838638i	−0.774967	−	0.632002i	$-0.782233\pi$
$113$	2.16272	−	8.91484i	0.203451	−	0.838638i	0.978418	−	0.206636i	$-0.0662515\pi$
$114$		0			0
$115$	−9.49242	−	1.82951i	−0.885173	−	0.170603i
$116$		0			0
$117$	1.24312	−	0.977602i	0.114927	−	0.0903794i
$118$		0			0
$119$	−13.2376	+	15.2770i	−1.21349	+	1.40044i
$120$		0			0
$121$	−0.423644	+	8.89337i	−0.0385131	+	0.808489i
$122$		0			0
$123$	0.361623	−	0.344807i	0.0326064	−	0.0310902i
$124$		0			0
$125$	−1.42093	−	1.63985i	−0.127092	−	0.146672i
$126$		0			0
$127$	17.7596	−	3.42288i	1.57591	−	0.303732i	0.675026	−	0.737794i	$-0.264132\pi$
$127$	17.7596	−	3.42288i	1.57591	−	0.303732i	0.900883	+	0.434062i	$0.142920\pi$
$128$		0			0
$129$	−1.98396	−	0.582543i	−0.174678	−	0.0512901i
$130$		0			0
$131$	3.24732	−	7.11064i	0.283720	−	0.621259i	−0.713090	−	0.701072i	$-0.752705\pi$
$131$	3.24732	−	7.11064i	0.283720	−	0.621259i	0.996810	+	0.0798129i	$0.0254323\pi$
$132$		0			0
$133$	−17.0288			−1.47659
$134$		0			0
$135$	−3.26565			−0.281062
$136$		0			0
$137$	2.33755	−	5.11851i	0.199710	−	0.437304i	−0.783107	−	0.621887i	$-0.786366\pi$
$137$	2.33755	−	5.11851i	0.199710	−	0.437304i	0.982817	+	0.184583i	$0.0590935\pi$
$138$		0			0
$139$	17.1653	+	5.04019i	1.45594	+	0.427503i	0.911501	−	0.411297i	$-0.134924\pi$
$139$	17.1653	+	5.04019i	1.45594	+	0.427503i	0.544440	+	0.838800i	$0.316742\pi$
$140$		0			0
$141$	8.19721	−	1.57988i	0.690330	−	0.133050i
$142$		0			0
$143$	−1.49956	−	1.73058i	−0.125399	−	0.144718i
$144$		0			0
$145$	−12.7151	+	12.1238i	−1.05593	+	1.00682i
$146$		0			0
$147$	0.00930053	−	0.195242i	0.000767095	−	0.0161033i
$148$		0			0
$149$	6.53331	−	7.53984i	0.535230	−	0.617688i	−0.422148	−	0.906527i	$-0.638724\pi$
$149$	6.53331	−	7.53984i	0.535230	−	0.617688i	0.957378	+	0.288839i	$0.0932692\pi$
$150$		0			0
$151$	−1.76274	+	1.38624i	−0.143450	+	0.112810i	−0.687305	−	0.726369i	$-0.741206\pi$
$151$	−1.76274	+	1.38624i	−0.143450	+	0.112810i	0.543855	+	0.839179i	$0.316964\pi$
$152$		0			0
$153$	−7.60922	−	1.46656i	−0.615169	−	0.118564i
$154$		0			0
$155$	−1.11074	+	4.57855i	−0.0892171	+	0.367758i
$156$		0			0
$157$	−15.6810	+	1.49735i	−1.25148	+	0.119502i	−0.699669	−	0.714468i	$-0.746669\pi$
$157$	−15.6810	+	1.49735i	−1.25148	+	0.119502i	−0.551811	+	0.833969i	$0.686063\pi$
$158$		0			0
$159$	7.90923	+	5.08295i	0.627242	+	0.403104i
$160$		0			0
$161$	−7.40916	+	2.17553i	−0.583924	+	0.171455i
$162$		0			0
$163$	6.47975	−	11.2233i	0.507533	−	0.879074i	−0.492429	−	0.870353i	$-0.663891\pi$
$163$	6.47975	−	11.2233i	0.507533	−	0.879074i	0.999962	−	0.00872084i	$-0.00277596\pi$
$164$		0			0
$165$	0.224990	+	4.72311i	0.0175154	+	0.367694i
$166$		0			0
$167$	−1.54251	−	4.45680i	−0.119363	−	0.344878i	0.869453	−	0.494016i	$-0.164471\pi$
$167$	−1.54251	−	4.45680i	−0.119363	−	0.344878i	−0.988816	+	0.149138i	$0.952350\pi$
$168$		0			0
$169$	10.4514	+	0.997988i	0.803954	+	0.0767683i
$170$		0			0
$171$	−3.26404	−	5.65348i	−0.249607	−	0.432333i
$172$		0			0
$173$	−22.5992	−	11.6507i	−1.71818	−	0.885784i	−0.976641	−	0.214876i	$-0.931065\pi$
$173$	−22.5992	−	11.6507i	−1.71818	−	0.885784i	−0.741541	−	0.670908i	$-0.765905\pi$
$174$		0			0
$175$	−13.7175	−	5.49168i	−1.03695	−	0.415132i
$176$		0			0
$177$	−0.0357131	−	0.248390i	−0.00268436	−	0.0186702i
$178$		0			0
$179$	1.58074	+	3.46134i	0.118150	+	0.258713i	0.959462	−	0.281837i	$-0.0909436\pi$
$179$	1.58074	+	3.46134i	0.118150	+	0.258713i	−0.841312	+	0.540550i	$0.818216\pi$
$180$		0			0
$181$	−3.03436	−	4.26116i	−0.225542	−	0.316730i	0.686262	−	0.727354i	$-0.259250\pi$
$181$	−3.03436	−	4.26116i	−0.225542	−	0.316730i	−0.911805	+	0.410624i	$0.865311\pi$
$182$		0			0
$183$	−6.54134	+	2.61876i	−0.483550	+	0.193584i
$184$		0			0
$185$	1.41351	+	5.82656i	0.103923	+	0.428378i
$186$		0			0
$187$	−1.59684	+	11.1063i	−0.116773	+	0.812171i
$188$		0			0
$189$	−2.31857	+	1.19531i	−0.168651	+	0.0869458i
$190$		0			0
$191$	0.669604	−	0.940327i	0.0484508	−	0.0680396i	−0.789640	−	0.613571i	$-0.789733\pi$
$191$	0.669604	−	0.940327i	0.0484508	−	0.0680396i	0.838091	+	0.545531i	$0.183672\pi$
$192$		0			0
$193$	−13.1371	+	8.44270i	−0.945629	+	0.607719i	−0.919986	−	0.391952i	$-0.871800\pi$
$193$	−13.1371	+	8.44270i	−0.945629	+	0.607719i	−0.0256434	+	0.999671i	$0.508163\pi$
$194$		0			0
$195$	3.73775	+	3.56394i	0.267666	+	0.255219i
$196$		0			0
$197$	−10.7577	−	8.45995i	−0.766454	−	0.602746i	0.156490	−	0.987679i	$-0.449982\pi$
$197$	−10.7577	−	8.45995i	−0.766454	−	0.602746i	−0.922944	+	0.384933i	$0.874224\pi$
$198$		0			0
$199$	−1.30128	+	3.75980i	−0.0922453	+	0.266525i	−0.981680	−	0.190537i	$-0.938977\pi$
$199$	−1.30128	+	3.75980i	−0.0922453	+	0.266525i	0.889435	+	0.457062i	$0.151098\pi$
$200$		0			0
$201$	−6.88323	−	4.42957i	−0.485506	−	0.312438i
$202$		0			0
$203$	−4.58994	+	13.2618i	−0.322151	+	0.930794i
$204$		0			0
$205$	1.28262	+	1.00866i	0.0895820	+	0.0704481i
$206$		0			0
$207$	−2.14243	−	2.04280i	−0.148909	−	0.141985i
$208$		0			0
$209$	−7.95177	+	5.11029i	−0.550036	+	0.353486i
$210$		0			0
$211$	7.63412	−	10.7206i	0.525554	−	0.738038i	−0.463418	−	0.886140i	$-0.653377\pi$
$211$	7.63412	−	10.7206i	0.525554	−	0.738038i	0.988972	+	0.148102i	$0.0473164\pi$
$212$		0			0
$213$	−1.11858	+	0.576669i	−0.0766439	+	0.0395127i
$214$		0			0
$215$	0.960971	−	6.68370i	0.0655377	−	0.455824i
$216$		0			0
$217$	0.887246	+	3.65728i	0.0602302	+	0.248272i
$218$		0			0
$219$	−2.54293	+	1.01804i	−0.171835	+	0.0687924i
$220$		0			0
$221$	7.10874	+	9.98283i	0.478186	+	0.671518i
$222$		0			0
$223$	−4.15036	−	9.08803i	−0.277929	−	0.608580i	0.718262	−	0.695772i	$-0.244938\pi$
$223$	−4.15036	−	9.08803i	−0.277929	−	0.608580i	−0.996191	+	0.0871926i	$0.972210\pi$
$224$		0			0
$225$	−0.806134	−	5.60678i	−0.0537423	−	0.373786i
$226$		0			0
$227$	14.1563	+	5.66734i	0.939589	+	0.376155i	0.790356	−	0.612647i	$-0.209895\pi$
$227$	14.1563	+	5.66734i	0.939589	+	0.376155i	0.149233	+	0.988802i	$0.452320\pi$
$228$		0			0
$229$	−0.389309	−	0.200703i	−0.0257262	−	0.0132628i	0.445315	−	0.895374i	$-0.353092\pi$
$229$	−0.389309	−	0.200703i	−0.0257262	−	0.0132628i	−0.471042	+	0.882111i	$0.656122\pi$
$230$		0			0
$231$	1.88852	+	3.27101i	0.124255	+	0.215216i
$232$		0			0
$233$	−10.8167	−	1.03287i	−0.708626	−	0.0676656i	−0.265482	−	0.964116i	$-0.585531\pi$
$233$	−10.8167	−	1.03287i	−0.708626	−	0.0676656i	−0.443144	+	0.896450i	$0.646137\pi$
$234$		0			0
$235$	8.91647	+	25.7625i	0.581647	+	1.68056i
$236$		0			0
$237$	0.644141	+	13.5222i	0.0418415	+	0.878361i
$238$		0			0
$239$	−6.65017	+	11.5184i	−0.430164	+	0.745065i	−0.996887	−	0.0788429i	$-0.974877\pi$
$239$	−6.65017	+	11.5184i	−0.430164	+	0.745065i	0.566723	+	0.823908i	$0.308211\pi$
$240$		0			0
$241$	28.5539	−	8.38417i	1.83932	−	0.540072i	0.839322	−	0.543634i	$-0.182952\pi$
$241$	28.5539	−	8.38417i	1.83932	−	0.540072i	0.999994	+	0.00356255i	$0.00113400\pi$
$242$		0			0
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$		0			0
$245$	0.635424	−	0.0606756i	0.0405958	−	0.00387642i
$246$		0			0
$247$	−2.43397	+	10.0330i	−0.154870	+	0.638383i
$248$		0			0
$249$	−13.9056	−	2.68008i	−0.881230	−	0.169843i
$250$		0			0
$251$	2.31948	−	1.82406i	0.146404	−	0.115134i	−0.542270	−	0.840204i	$-0.682435\pi$
$251$	2.31948	−	1.82406i	0.146404	−	0.115134i	0.688675	+	0.725070i	$0.258193\pi$
$252$		0			0
$253$	−2.80691	+	3.23935i	−0.176469	+	0.203656i
$254$		0			0
$255$	1.20412	−	25.2777i	0.0754051	−	1.58295i
$256$		0			0
$257$	15.9495	−	15.2078i	0.994902	−	0.948637i	−0.00377826	−	0.999993i	$-0.501203\pi$
$257$	15.9495	−	15.2078i	0.994902	−	0.948637i	0.998680	+	0.0513556i	$0.0163542\pi$
$258$		0			0
$259$	3.13624	+	3.61942i	0.194877	+	0.224900i
$260$		0			0
$261$	−5.28263	+	1.01814i	−0.326986	+	0.0630215i
$262$		0			0
$263$	−22.1647	−	6.50814i	−1.36673	−	0.401309i	−0.485601	−	0.874180i	$-0.661399\pi$
$263$	−22.1647	−	6.50814i	−1.36673	−	0.401309i	−0.881131	+	0.472871i	$0.843218\pi$
$264$		0			0
$265$	−12.7543	+	27.9281i	−0.783493	+	1.71561i
$266$		0			0
$267$	9.58187			0.586401
$268$		0			0
$269$	4.21819			0.257187			0.128594	−	0.991697i	$-0.458954\pi$
$269$	4.21819			0.257187			0.128594	+	0.991697i	$0.458954\pi$
$270$		0			0
$271$	−8.39041	+	18.3724i	−0.509681	+	1.11605i	0.463519	+	0.886087i	$0.346586\pi$
$271$	−8.39041	+	18.3724i	−0.509681	+	1.11605i	−0.973200	+	0.229959i	$0.926141\pi$
$272$		0			0
$273$	3.95825	+	1.16225i	0.239564	+	0.0703424i
$274$		0			0
$275$	−8.05357	+	1.55220i	−0.485649	+	0.0936011i
$276$		0			0
$277$	20.1606	+	23.2666i	1.21133	+	1.39795i	0.893050	+	0.449958i	$0.148561\pi$
$277$	20.1606	+	23.2666i	1.21133	+	1.39795i	0.318284	+	0.947995i	$0.396894\pi$
$278$		0			0
$279$	−1.04413	+	0.995579i	−0.0625106	+	0.0596037i
$280$		0			0
$281$	−1.11268	+	23.3581i	−0.0663772	+	1.39343i	0.682580	+	0.730811i	$0.260858\pi$
$281$	−1.11268	+	23.3581i	−0.0663772	+	1.39343i	−0.748957	+	0.662618i	$0.769445\pi$
$282$		0			0
$283$	−13.8593	+	15.9945i	−0.823852	+	0.950776i	−0.999432	−	0.0336893i	$-0.989274\pi$
$283$	−13.8593	+	15.9945i	−0.823852	+	0.950776i	0.175580	+	0.984465i	$0.443820\pi$
$284$		0			0
$285$	16.7574	−	13.1782i	0.992622	−	0.780607i
$286$		0			0
$287$	1.27984	+	0.246669i	0.0755466	+	0.0145604i
$288$		0			0
$289$	10.1496	−	41.8374i	0.597038	−	2.46102i
$290$		0			0
$291$	13.1914	−	1.25963i	0.773295	−	0.0738407i
$292$		0			0
$293$	6.75619	+	4.34194i	0.394701	+	0.253659i	0.722904	−	0.690948i	$-0.242807\pi$
$293$	6.75619	+	4.34194i	0.394701	+	0.253659i	−0.328204	+	0.944607i	$0.606443\pi$
$294$		0			0
$295$	0.786300	−	0.230879i	0.0457802	−	0.0134423i
$296$		0			0
$297$	−0.723972	+	1.25396i	−0.0420091	+	0.0727619i
$298$		0			0
$299$	0.222757	+	4.67625i	0.0128824	+	0.270435i
$300$		0			0
$301$	−1.76412	−	5.09709i	−0.101682	−	0.293791i
$302$		0			0
$303$	−9.07270	−	0.866337i	−0.521213	−	0.0497698i
$304$		0			0
$305$	−11.5050	−	19.9272i	−0.658773	−	1.14103i
$306$		0			0
$307$	−19.3729	−	9.98743i	−1.10567	−	0.570013i	−0.194028	−	0.980996i	$-0.562155\pi$
$307$	−19.3729	−	9.98743i	−1.10567	−	0.570013i	−0.911643	+	0.410983i	$0.865185\pi$
$308$		0			0
$309$	3.53455	+	1.41502i	0.201073	+	0.0804977i
$310$		0			0
$311$	−2.43610	−	16.9434i	−0.138138	−	0.960774i	−0.934503	−	0.355956i	$-0.884155\pi$
$311$	−2.43610	−	16.9434i	−0.138138	−	0.960774i	0.796364	−	0.604817i	$-0.206754\pi$
$312$		0			0
$313$	−5.53583	−	12.1218i	−0.312903	−	0.685163i	0.686204	−	0.727409i	$-0.259276\pi$
$313$	−5.53583	−	12.1218i	−0.312903	−	0.685163i	−0.999107	+	0.0422465i	$0.986549\pi$
$314$		0			0
$315$	−4.94127	−	6.93905i	−0.278409	−	0.390971i
$316$		0			0
$317$	8.26345	−	3.30819i	0.464121	−	0.185806i	−0.127803	−	0.991800i	$-0.540793\pi$
$317$	8.26345	−	3.30819i	0.464121	−	0.185806i	0.591925	+	0.805993i	$0.298368\pi$
$318$		0			0
$319$	1.83650	+	7.57014i	0.102824	+	0.423846i
$320$		0			0
$321$	−2.32801	+	16.1917i	−0.129937	+	0.903732i
$322$		0			0
$323$	44.9642	−	23.1807i	2.50187	−	1.28981i
$324$		0			0
$325$	−5.19625	+	7.29711i	−0.288236	+	0.404771i
$326$		0			0
$327$	4.58320	−	2.94544i	0.253451	−	0.162883i
$328$		0			0
$329$	15.7603	+	15.0274i	0.868893	+	0.828488i
$330$		0			0
$331$	−1.20696	−	0.949162i	−0.0663404	−	0.0521707i	0.584438	−	0.811438i	$-0.301315\pi$
$331$	−1.20696	−	0.949162i	−0.0663404	−	0.0521707i	−0.650779	+	0.759268i	$0.725557\pi$
$332$		0			0
$333$	−0.600481	+	1.73498i	−0.0329062	+	0.0950761i
$334$		0			0
$335$	11.1192	−	24.3080i	0.607506	−	1.32809i
$336$		0			0
$337$	11.6806	−	33.7488i	0.636281	−	1.83841i	0.0988583	−	0.995102i	$-0.468481\pi$
$337$	11.6806	−	33.7488i	0.636281	−	1.83841i	0.537423	−	0.843313i	$-0.319398\pi$
$338$		0			0
$339$	7.21080	+	5.67064i	0.391637	+	0.307987i
$340$		0			0
$341$	1.51185	+	1.44154i	0.0818710	+	0.0780639i
$342$		0			0
$343$	15.7901	−	10.1477i	0.852585	−	0.547923i
$344$		0			0
$345$	5.60748	−	7.87460i	0.301897	−	0.423954i
$346$		0			0
$347$	12.6669	−	6.53024i	0.679995	−	0.350562i	−0.0833797	−	0.996518i	$-0.526571\pi$
$347$	12.6669	−	6.53024i	0.679995	−	0.350562i	0.763375	+	0.645956i	$0.223541\pi$
$348$		0			0
$349$	−2.17786	+	15.1474i	−0.116578	+	0.810819i	0.844700	+	0.535240i	$0.179779\pi$
$349$	−2.17786	+	15.1474i	−0.116578	+	0.810819i	−0.961278	+	0.275579i	$0.911130\pi$
$350$		0			0
$351$	0.372847	+	1.53689i	0.0199011	+	0.0820334i
$352$		0			0
$353$	−27.0313	+	10.8217i	−1.43873	+	0.575981i	−0.954301	−	0.298848i	$-0.903397\pi$
$353$	−27.0313	+	10.8217i	−1.43873	+	0.575981i	−0.484431	+	0.874830i	$0.660973\pi$
$354$		0			0
$355$	−2.38389	−	3.34770i	−0.126524	−	0.177678i
$356$		0			0
$357$	−8.39733	−	18.3876i	−0.444434	−	0.973175i
$358$		0			0
$359$	0.297374	+	2.06828i	0.0156948	+	0.109160i	0.996163	−	0.0875185i	$-0.0278937\pi$
$359$	0.297374	+	2.06828i	0.0156948	+	0.109160i	−0.980468	+	0.196678i	$0.936985\pi$
$360$		0			0
$361$	21.9242	+	8.77712i	1.15390	+	0.461954i
$362$		0			0
$363$	−7.91371	−	4.07980i	−0.415362	−	0.214134i
$364$		0			0
$365$	−4.47253	−	7.74665i	−0.234103	−	0.405478i
$366$		0			0
$367$	−32.5434	−	3.10752i	−1.69875	−	0.162211i	−0.799803	−	0.600262i	$-0.795063\pi$
$367$	−32.5434	−	3.10752i	−1.69875	−	0.162211i	−0.898950	+	0.438051i	$0.855669\pi$
$368$		0			0
$369$	0.163424	+	0.472182i	0.00850749	+	0.0245808i
$370$		0			0
$371$	1.16694	+	24.4971i	0.0605845	+	1.27182i
$372$		0			0
$373$	12.5938	−	21.8131i	0.652081	−	1.12944i	−0.330536	−	0.943794i	$-0.607229\pi$
$373$	12.5938	−	21.8131i	0.652081	−	1.12944i	0.982617	−	0.185645i	$-0.0594373\pi$
$374$		0			0
$375$	2.08193	−	0.611311i	0.107511	−	0.0315680i
$376$		0			0
$377$	7.15746	+	4.59982i	0.368628	+	0.236903i
$378$		0			0
$379$	23.4114	−	2.23552i	1.20256	−	0.114831i	0.525525	−	0.850778i	$-0.323869\pi$
$379$	23.4114	−	2.23552i	1.20256	−	0.114831i	0.677039	+	0.735947i	$0.263263\pi$
$380$		0			0
$381$	−4.26404	+	17.5766i	−0.218453	+	0.900477i
$382$		0			0
$383$	12.7154	+	2.45069i	0.649727	+	0.125225i	0.503457	−	0.864020i	$-0.332061\pi$
$383$	12.7154	+	2.45069i	0.649727	+	0.125225i	0.146270	+	0.989245i	$0.453273\pi$
$384$		0			0
$385$	−9.69554	+	7.62465i	−0.494130	+	0.388588i
$386$		0			0
$387$	1.35407	−	1.56268i	0.0688311	−	0.0794353i
$388$		0			0
$389$	−0.689242	+	14.4690i	−0.0349460	+	0.733606i	0.911608	+	0.411061i	$0.134842\pi$
$389$	−0.689242	+	14.4690i	−0.0349460	+	0.733606i	−0.946554	+	0.322545i	$0.895461\pi$
$390$		0			0
$391$	16.6022	−	15.8302i	0.839612	−	0.800568i
$392$		0			0
$393$	5.11908	+	5.90773i	0.258223	+	0.298006i
$394$		0			0
$395$	−43.4098	+	8.36656i	−2.18419	+	0.420967i
$396$		0			0
$397$	11.6107	+	3.40921i	0.582725	+	0.171103i	0.559791	−	0.828634i	$-0.310881\pi$
$397$	11.6107	+	3.40921i	0.582725	+	0.171103i	0.0229334	+	0.999737i	$0.492699\pi$
$398$		0			0
$399$	7.07403	−	15.4900i	0.354145	−	0.775468i
$400$		0			0
$401$	34.2575			1.71074			0.855370	−	0.518017i	$-0.173330\pi$
$401$	34.2575			1.71074			0.855370	+	0.518017i	$0.173330\pi$
$402$		0			0
$403$	2.28160			0.113654
$404$		0			0
$405$	1.35660	−	2.97054i	0.0674099	−	0.147607i
$406$		0			0
$407$	2.55067	+	0.748945i	0.126432	+	0.0371238i
$408$		0			0
$409$	19.1084	−	3.68283i	0.944848	−	0.182104i	0.306516	−	0.951866i	$-0.400837\pi$
$409$	19.1084	−	3.68283i	0.944848	−	0.182104i	0.638332	+	0.769761i	$0.279625\pi$
$410$		0			0
$411$	3.68491	+	4.25261i	0.181763	+	0.209766i
$412$		0			0
$413$	0.473757	−	0.451727i	0.0233121	−	0.0222280i
$414$		0			0
$415$	2.20049	−	46.1940i	0.108018	−	2.26758i
$416$		0			0
$417$	−11.7154	+	13.5203i	−0.573707	+	0.662094i
$418$		0			0
$419$	−21.0453	+	16.5502i	−1.02813	+	0.808531i	−0.981708	−	0.190391i	$-0.939025\pi$
$419$	−21.0453	+	16.5502i	−1.02813	+	0.808531i	−0.0464226	+	0.998922i	$0.514782\pi$
$420$		0			0
$421$	−7.73690	−	1.49117i	−0.377074	−	0.0726750i	−0.00280679	−	0.999996i	$-0.500893\pi$
$421$	−7.73690	−	1.49117i	−0.377074	−	0.0726750i	−0.374267	+	0.927321i	$0.622106\pi$
$422$		0			0
$423$	−1.96813	+	8.11275i	−0.0956939	+	0.394455i
$424$		0			0
$425$	43.6964	−	4.17250i	2.11959	−	0.202396i
$426$		0			0
$427$	−15.4622	−	9.93698i	−0.748271	−	0.480884i
$428$		0			0
$429$	2.19713	−	0.645135i	0.106078	−	0.0311474i
$430$		0			0
$431$	0.473650	−	0.820386i	0.0228149	−	0.0395166i	−0.854393	−	0.519628i	$-0.826070\pi$
$431$	0.473650	−	0.820386i	0.0228149	−	0.0395166i	0.877207	+	0.480112i	$0.159404\pi$
$432$		0			0
$433$	−1.51637	−	31.8326i	−0.0728722	−	1.52977i	−0.678840	−	0.734286i	$-0.737517\pi$
$433$	−1.51637	−	31.8326i	−0.0728722	−	1.52977i	0.605968	−	0.795489i	$-0.292786\pi$
$434$		0			0
$435$	−5.74615	−	16.6024i	−0.275507	−	0.796025i
$436$		0			0
$437$	19.2372	+	1.83693i	0.920241	+	0.0878724i
$438$		0			0
$439$	−9.22634	−	15.9805i	−0.440349	−	0.762707i	0.557366	−	0.830267i	$-0.311812\pi$
$439$	−9.22634	−	15.9805i	−0.440349	−	0.762707i	−0.997715	+	0.0675599i	$0.978479\pi$
$440$		0			0
$441$	0.173735	+	0.0895666i	0.00827309	+	0.00426507i
$442$		0			0
$443$	−20.2637	−	8.11238i	−0.962759	−	0.385431i	−0.163584	−	0.986529i	$-0.552306\pi$
$443$	−20.2637	−	8.11238i	−0.962759	−	0.385431i	−0.799175	+	0.601099i	$0.794730\pi$
$444$		0			0
$445$	4.45317	+	30.9725i	0.211101	+	1.46824i
$446$		0			0
$447$	4.14445	+	9.07507i	0.196026	+	0.429236i
$448$		0			0
$449$	−9.90699	−	13.9124i	−0.467540	−	0.656568i	0.511726	−	0.859149i	$-0.329006\pi$
$449$	−9.90699	−	13.9124i	−0.467540	−	0.656568i	−0.979266	+	0.202581i	$0.935067\pi$
$450$		0			0
$451$	0.671659	−	0.268892i	0.0316272	−	0.0126616i
$452$		0			0
$453$	−0.528695	−	2.17931i	−0.0248402	−	0.102393i
$454$		0			0
$455$	−1.91726	+	13.3348i	−0.0898824	+	0.625146i
$456$		0			0
$457$	13.1520	−	6.78034i	0.615226	−	0.317171i	−0.122297	−	0.992494i	$-0.539026\pi$
$457$	13.1520	−	6.78034i	0.615226	−	0.317171i	0.737522	+	0.675323i	$0.235996\pi$
$458$		0			0
$459$	4.49501	−	6.31236i	0.209809	−	0.294636i
$460$		0			0
$461$	7.14839	−	4.59399i	0.332934	−	0.213963i	−0.363484	−	0.931601i	$-0.618413\pi$
$461$	7.14839	−	4.59399i	0.332934	−	0.213963i	0.696417	+	0.717637i	$0.254776\pi$
$462$		0			0
$463$	4.89240	+	4.66489i	0.227369	+	0.216796i	0.795197	−	0.606352i	$-0.207368\pi$
$463$	4.89240	+	4.66489i	0.227369	+	0.216796i	−0.567828	+	0.823147i	$0.692216\pi$
$464$		0			0
$465$	−3.70338	−	2.91237i	−0.171740	−	0.135058i
$466$		0			0
$467$	−11.9568	+	34.5470i	−0.553297	+	1.59865i	0.227444	+	0.973791i	$0.426963\pi$
$467$	−11.9568	+	34.5470i	−0.553297	+	1.59865i	−0.780741	+	0.624855i	$0.785158\pi$
$468$		0			0
$469$	−1.00285	−	21.3283i	−0.0463072	−	0.984851i
$470$		0			0
$471$	5.15208	−	14.8860i	0.237395	−	0.685909i
$472$		0			0
$473$	−2.35339	−	1.85073i	−0.108209	−	0.0850966i
$474$		0			0
$475$	26.7622	+	25.5177i	1.22793	+	1.17083i
$476$		0			0
$477$	−7.90923	+	5.08295i	−0.362139	+	0.232732i
$478$		0			0
$479$	−20.2881	+	28.4906i	−0.926985	+	1.30177i	0.0262866	+	0.999654i	$0.491632\pi$
$479$	−20.2881	+	28.4906i	−0.926985	+	1.30177i	−0.953272	+	0.302114i	$0.902308\pi$
$480$		0			0
$481$	2.58074	−	1.33047i	0.117672	−	0.0606640i
$482$		0			0
$483$	1.09895	−	7.64336i	0.0500039	−	0.347785i
$484$		0			0
$485$	10.2023	+	42.0546i	0.463264	+	1.90960i
$486$		0			0
$487$	13.6293	−	5.45636i	0.617604	−	0.247251i	−0.0416972	−	0.999130i	$-0.513276\pi$
$487$	13.6293	−	5.45636i	0.617604	−	0.247251i	0.659301	+	0.751879i	$0.270852\pi$
$488$		0			0
$489$	7.51725	+	10.5565i	0.339942	+	0.477382i
$490$		0			0
$491$	14.1188	+	30.9158i	0.637171	+	1.39521i	0.902347	+	0.431010i	$0.141843\pi$
$491$	14.1188	+	30.9158i	0.637171	+	1.39521i	−0.265176	+	0.964200i	$0.585430\pi$
$492$		0			0
$493$	−5.93308	−	41.2655i	−0.267212	−	1.85850i
$494$		0			0
$495$	−4.38976	−	1.75739i	−0.197305	−	0.0789890i
$496$		0			0
$497$	−2.91788	−	1.50427i	−0.130885	−	0.0674757i
$498$		0			0
$499$	−16.8927	−	29.2590i	−0.756220	−	1.30981i	−0.944765	−	0.327747i	$-0.893711\pi$
$499$	−16.8927	−	29.2590i	−0.756220	−	1.30981i	0.188545	−	0.982064i	$-0.439623\pi$
$500$		0			0
$501$	4.69483	+	0.448302i	0.209750	+	0.0200287i
$502$		0			0
$503$	10.2003	+	29.4718i	0.454809	+	1.31408i	0.906612	+	0.421966i	$0.138660\pi$
$503$	10.2003	+	29.4718i	0.454809	+	1.31408i	−0.451803	+	0.892118i	$0.649219\pi$
$504$		0			0
$505$	−1.41618	−	29.7293i	−0.0630192	−	1.32293i
$506$		0			0
$507$	−5.24947	+	9.09235i	−0.233137	+	0.403805i
$508$		0			0
$509$	−15.6075	+	4.58278i	−0.691790	+	0.203128i	−0.608684	−	0.793413i	$-0.708302\pi$
$509$	−15.6075	+	4.58278i	−0.691790	+	0.203128i	−0.0831062	+	0.996541i	$0.526484\pi$
$510$		0			0
$511$	−6.01091	−	3.86298i	−0.265907	−	0.170888i
$512$		0			0
$513$	6.49852	−	0.620533i	0.286917	−	0.0273972i
$514$		0			0
$515$	−2.93124	+	12.0827i	−0.129166	+	0.532429i
$516$		0			0
$517$	11.8691	+	2.28758i	0.522002	+	0.100608i
$518$		0			0
$519$	19.9859	−	15.7170i	0.877282	−	0.689902i
$520$		0			0
$521$	−3.04015	+	3.50852i	−0.133191	+	0.153711i	−0.818427	−	0.574610i	$-0.805154\pi$
$521$	−3.04015	+	3.50852i	−0.133191	+	0.153711i	0.685236	+	0.728321i	$0.259699\pi$
$522$		0			0
$523$	−1.52352	+	31.9827i	−0.0666190	+	1.39850i	0.679980	+	0.733230i	$0.261988\pi$
$523$	−1.52352	+	31.9827i	−0.0666190	+	1.39850i	−0.746599	+	0.665274i	$0.768315\pi$
$524$		0			0
$525$	10.6939	−	10.1966i	0.466719	−	0.445016i
$526$		0			0
$527$	−7.32126	−	8.44918i	−0.318919	−	0.368052i
$528$		0			0
$529$	−13.9797	+	2.69436i	−0.607811	+	0.117146i
$530$		0			0
$531$	0.240779	+	0.0706992i	0.0104489	+	0.00306809i
$532$		0			0
$533$	0.328262	−	0.718794i	0.0142186	−	0.0311344i
$534$		0			0
$535$	−53.4201			−2.30955
$536$		0			0
$537$	−3.80521			−0.164207
$538$		0			0
$539$	0.117571	−	0.257444i	0.00506413	−	0.0110889i
$540$		0			0
$541$	32.9875	+	9.68602i	1.41825	+	0.416434i	0.898909	−	0.438135i	$-0.144361\pi$
$541$	32.9875	+	9.68602i	1.41825	+	0.416434i	0.519337	+	0.854570i	$0.326179\pi$
$542$		0			0
$543$	5.13661	−	0.990000i	0.220433	−	0.0424850i
$544$		0			0
$545$	11.6509	+	13.4459i	0.499070	+	0.575957i
$546$		0			0
$547$	10.8132	−	10.3103i	0.462338	−	0.440839i	−0.422761	−	0.906241i	$-0.638939\pi$
$547$	10.8132	−	10.3103i	0.462338	−	0.440839i	0.885099	+	0.465403i	$0.154090\pi$
$548$		0			0
$549$	0.335265	−	7.03808i	0.0143088	−	0.300378i
$550$		0			0
$551$	22.9988	−	26.5420i	0.979780	−	1.13073i
$552$		0			0
$553$	−27.7581	+	21.8292i	−1.18040	+	0.928274i
$554$		0			0
$555$	−5.88722	−	1.13467i	−0.249899	−	0.0481640i
$556$		0			0
$557$	−5.77505	+	23.8051i	−0.244697	+	1.00865i	0.708358	+	0.705854i	$0.249436\pi$
$557$	−5.77505	+	23.8051i	−0.244697	+	1.00865i	−0.953054	+	0.302800i	$0.902079\pi$
$558$		0			0
$559$	−3.25523	+	0.310837i	−0.137682	+	0.0131470i
$560$		0			0
$561$	−9.43927	−	6.06625i	−0.398526	−	0.256117i
$562$		0			0
$563$	−40.1465	+	11.7881i	−1.69197	+	0.496808i	−0.978910	−	0.204292i	$-0.934511\pi$
$563$	−40.1465	+	11.7881i	−1.69197	+	0.496808i	−0.713063	+	0.701100i	$0.752693\pi$
$564$		0			0
$565$	−14.9786	+	25.9437i	−0.630154	+	1.09146i
$566$		0			0
$567$	−0.124120	−	2.60560i	−0.00521254	−	0.109425i
$568$		0			0
$569$	−5.63472	−	16.2805i	−0.236220	−	0.682513i	−0.999342	−	0.0362588i	$-0.988456\pi$
$569$	−5.63472	−	16.2805i	−0.236220	−	0.682513i	0.763123	−	0.646254i	$-0.223665\pi$
$570$		0			0
$571$	0.105016	+	0.0100279i	0.00439480	+	0.000419653i	0.0972532	−	0.995260i	$-0.468994\pi$
$571$	0.105016	+	0.0100279i	0.00439480	+	0.000419653i	−0.0928584	+	0.995679i	$0.529600\pi$
$572$		0			0
$573$	0.577188	+	0.999719i	0.0241124	+	0.0417638i
$574$		0			0
$575$	14.9041	+	7.68361i	0.621545	+	0.320429i
$576$		0			0
$577$	−17.5885	−	7.04136i	−0.732218	−	0.293136i	−0.0245669	−	0.999698i	$-0.507821\pi$
$577$	−17.5885	−	7.04136i	−0.732218	−	0.293136i	−0.707651	+	0.706562i	$0.750245\pi$
$578$		0			0
$579$	−2.22240	−	15.4571i	−0.0923599	−	0.642377i
$580$		0			0
$581$	−15.3458	−	33.6027i	−0.636652	−	1.39407i
$582$		0			0
$583$	7.89640	+	11.0889i	0.327036	+	0.459257i
$584$		0			0
$585$	−4.79459	+	1.91946i	−0.198232	+	0.0793600i
$586$		0			0
$587$	5.67917	+	23.4099i	0.234405	+	0.966229i	0.960421	+	0.278552i	$0.0898544\pi$
$587$	5.67917	+	23.4099i	0.234405	+	0.966229i	−0.726017	+	0.687677i	$0.758630\pi$
$588$		0			0
$589$	1.34033	−	9.32222i	0.0552274	−	0.384115i
$590$		0			0
$591$	12.1643	−	6.27116i	0.500374	−	0.257961i
$592$		0			0
$593$	14.0341	−	19.7081i	0.576311	−	0.809315i	−0.418800	−	0.908078i	$-0.637549\pi$
$593$	14.0341	−	19.7081i	0.576311	−	0.809315i	0.995111	+	0.0987632i	$0.0314886\pi$
$594$		0			0
$595$	55.5335	−	35.6892i	2.27665	−	1.46312i
$596$		0			0
$597$	−2.87946	−	2.74556i	−0.117849	−	0.112368i
$598$		0			0
$599$	20.0397	+	15.7594i	0.818799	+	0.643911i	0.937098	−	0.349067i	$-0.113502\pi$
$599$	20.0397	+	15.7594i	0.818799	+	0.643911i	−0.118299	+	0.992978i	$0.537744\pi$
$600$		0			0
$601$	−8.15764	+	23.5699i	−0.332757	+	0.961438i	0.647216	+	0.762307i	$0.275933\pi$
$601$	−8.15764	+	23.5699i	−0.332757	+	0.961438i	−0.979973	+	0.199131i	$0.936188\pi$
$602$		0			0
$603$	6.88868	−	4.42110i	0.280529	−	0.180041i
$604$		0			0
$605$	9.50968	−	27.4764i	0.386623	−	1.11707i
$606$		0			0
$607$	22.7708	+	17.9071i	0.924237	+	0.726828i	0.962169	−	0.272452i	$-0.0878347\pi$
$607$	22.7708	+	17.9071i	0.924237	+	0.726828i	−0.0379323	+	0.999280i	$0.512077\pi$
$608$		0			0
$609$	−10.1566	−	9.68430i	−0.411566	−	0.392428i
$610$		0			0
$611$	11.1064	−	7.13768i	0.449319	−	0.288760i
$612$		0			0
$613$	5.45314	−	7.65787i	0.220250	−	0.309298i	−0.689636	−	0.724156i	$-0.742229\pi$
$613$	5.45314	−	7.65787i	0.220250	−	0.309298i	0.909886	+	0.414858i	$0.136169\pi$
$614$		0			0
$615$	−1.45033	+	0.747698i	−0.0584830	+	0.0301501i
$616$		0			0
$617$	−2.72317	+	18.9401i	−0.109631	+	0.762499i	0.858637	+	0.512584i	$0.171312\pi$
$617$	−2.72317	+	18.9401i	−0.109631	+	0.762499i	−0.968268	+	0.249915i	$0.919597\pi$
$618$		0			0
$619$	−3.22226	−	13.2824i	−0.129514	−	0.533863i	−0.999190	−	0.0402405i	$-0.987188\pi$
$619$	−3.22226	−	13.2824i	−0.129514	−	0.533863i	0.869676	−	0.493623i	$-0.164328\pi$
$620$		0			0
$621$	2.74820	−	1.10021i	0.110281	−	0.0441500i
$622$		0			0
$623$	14.4984	+	20.3602i	0.580866	+	0.815713i
$624$		0			0
$625$	−8.82189	−	19.3172i	−0.352875	−	0.772689i
$626$		0			0
$627$	−1.34520	−	9.35608i	−0.0537222	−	0.373646i
$628$		0			0
$629$	−13.2081	−	5.28774i	−0.526643	−	0.210836i
$630$		0			0
$631$	18.9727	+	9.78113i	0.755293	+	0.389380i	0.792456	−	0.609929i	$-0.208802\pi$
$631$	18.9727	+	9.78113i	0.755293	+	0.389380i	−0.0371635	+	0.999309i	$0.511832\pi$
$632$		0			0
$633$	6.58049	+	11.3977i	0.261551	+	0.453020i
$634$		0			0
$635$	−58.7965	−	5.61438i	−2.33327	−	0.222800i
$636$		0			0
$637$	−0.101103	−	0.292119i	−0.00400586	−	0.0115742i
$638$		0			0
$639$	−0.0598809	−	1.25705i	−0.00236885	−	0.0497283i
$640$		0			0
$641$	−5.38009	+	9.31859i	−0.212501	+	0.368062i	−0.952497	−	0.304549i	$-0.901494\pi$
$641$	−5.38009	+	9.31859i	−0.212501	+	0.368062i	0.739996	+	0.672612i	$0.234827\pi$
$642$		0			0
$643$	−35.2525	+	10.3511i	−1.39022	+	0.408207i	−0.889316	−	0.457293i	$-0.848819\pi$
$643$	−35.2525	+	10.3511i	−1.39022	+	0.408207i	−0.500909	+	0.865500i	$0.667001\pi$
$644$		0			0
$645$	5.68050	+	3.65064i	0.223670	+	0.143744i
$646$		0			0
$647$	−16.0942	+	1.53681i	−0.632729	+	0.0604183i	−0.406493	−	0.913654i	$-0.633248\pi$
$647$	−16.0942	+	1.53681i	−0.632729	+	0.0604183i	−0.226237	+	0.974072i	$0.572642\pi$
$648$		0			0
$649$	0.0856638	−	0.353111i	0.00336260	−	0.0138608i
$650$		0			0
$651$	−3.69535	−	0.712221i	−0.144832	−	0.0279141i
$652$		0			0
$653$	1.61501	−	1.27006i	0.0632002	−	0.0497012i	−0.586059	−	0.810268i	$-0.699321\pi$
$653$	1.61501	−	1.27006i	0.0632002	−	0.0497012i	0.649259	+	0.760567i	$0.275079\pi$
$654$		0			0
$655$	−16.7171	+	19.2926i	−0.653191	+	0.753823i
$656$		0			0
$657$	0.130333	−	2.73604i	0.00508479	−	0.106743i
$658$		0			0
$659$	24.9131	−	23.7545i	0.970475	−	0.925346i	−0.0267616	−	0.999642i	$-0.508519\pi$
$659$	24.9131	−	23.7545i	0.970475	−	0.925346i	0.997236	+	0.0742961i	$0.0236710\pi$
$660$		0			0
$661$	27.1637	+	31.3486i	1.05655	+	1.21932i	0.974897	+	0.222657i	$0.0714731\pi$
$661$	27.1637	+	31.3486i	1.05655	+	1.21932i	0.0816489	+	0.996661i	$0.473981\pi$
$662$		0			0
$663$	−12.0338	+	2.31932i	−0.467353	+	0.0900749i
$664$		0			0
$665$	53.3575	+	15.6672i	2.06912	+	0.607547i
$666$		0			0
$667$	6.61577	−	14.4865i	0.256164	−	0.560920i
$668$		0			0
$669$	9.99089			0.386270
$670$		0			0
$671$	−10.2023			−0.393855
$672$		0			0
$673$	−7.05263	+	15.4431i	−0.271859	+	0.595288i	−0.995487	−	0.0949024i	$-0.969746\pi$
$673$	−7.05263	+	15.4431i	−0.271859	+	0.595288i	0.723628	+	0.690191i	$0.242473\pi$
$674$		0			0
$675$	5.43499	+	1.59586i	0.209193	+	0.0614246i
$676$		0			0
$677$	−5.42785	+	1.04613i	−0.208609	+	0.0402061i	−0.292485	−	0.956270i	$-0.594482\pi$
$677$	−5.42785	+	1.04613i	−0.208609	+	0.0402061i	0.0838759	+	0.996476i	$0.473270\pi$
$678$		0			0
$679$	22.6366	+	26.1240i	0.868712	+	1.00255i
$680$		0			0
$681$	−11.0360	+	10.5228i	−0.422899	+	0.403233i
$682$		0			0
$683$	0.483723	−	10.1546i	0.0185092	−	0.388555i	−0.970537	−	0.240951i	$-0.922541\pi$
$683$	0.483723	−	10.1546i	0.0185092	−	0.388555i	0.989047	−	0.147604i	$-0.0471562\pi$
$684$		0			0
$685$	−12.0336	+	13.8875i	−0.459780	+	0.530615i
$686$		0			0
$687$	0.344290	−	0.270753i	0.0131355	−	0.0103299i
$688$		0			0
$689$	14.5999	+	2.81389i	0.556211	+	0.107201i
$690$		0			0
$691$	−3.22504	+	13.2938i	−0.122686	+	0.505719i	0.876996	+	0.480498i	$0.159544\pi$
$691$	−3.22504	+	13.2938i	−0.122686	+	0.505719i	−0.999682	+	0.0252210i	$0.991971\pi$
$692$		0			0
$693$	−3.75993	+	0.359030i	−0.142828	+	0.0136384i
$694$		0			0
$695$	−49.1480	−	31.5855i	−1.86429	−	1.19811i
$696$		0			0
$697$	−3.71517	+	1.09087i	−0.140722	+	0.0413197i
$698$		0			0
$699$	5.43295	−	9.41015i	0.205493	−	0.355925i
$700$		0			0
$701$	1.37646	+	28.8954i	0.0519881	+	1.09137i	0.862634	+	0.505829i	$0.168813\pi$
$701$	1.37646	+	28.8954i	0.0519881	+	1.09137i	−0.810646	+	0.585537i	$0.800884\pi$
$702$		0			0
$703$	−3.91999	−	11.3261i	−0.147845	−	0.427171i
$704$		0			0
$705$	−27.1384	−	2.59140i	−1.02209	−	0.0975979i
$706$		0			0
$707$	−11.8871	−	20.5891i	−0.447061	−	0.774333i
$708$		0			0
$709$	−34.0170	−	17.5370i	−1.27754	−	0.658616i	−0.320134	−	0.947372i	$-0.603728\pi$
$709$	−34.0170	−	17.5370i	−1.27754	−	0.658616i	−0.957403	+	0.288756i	$0.906758\pi$
$710$		0			0
$711$	−12.5678	−	5.03139i	−0.471329	−	0.188692i
$712$		0			0
$713$	−0.607792	−	4.22729i	−0.0227620	−	0.158313i
$714$		0			0
$715$	3.10645	+	6.80218i	0.116175	+	0.254387i
$716$		0			0
$717$	−7.71495	−	10.8341i	−0.288120	−	0.404608i
$718$		0			0
$719$	−28.7557	+	11.5121i	−1.07241	+	0.429327i	−0.839605	−	0.543197i	$-0.817214\pi$
$719$	−28.7557	+	11.5121i	−1.07241	+	0.429327i	−0.232802	+	0.972524i	$0.574790\pi$
$720$		0			0
$721$	2.34143	+	9.65151i	0.0871994	+	0.359441i
$722$		0			0
$723$	−4.23519	+	29.4564i	−0.157509	+	1.09550i
$724$		0			0
$725$	27.0862	−	13.9639i	1.00596	−	0.518607i
$726$		0			0
$727$	26.5408	−	37.2713i	0.984344	−	1.38232i	0.0610880	−	0.998132i	$-0.480543\pi$
$727$	26.5408	−	37.2713i	0.984344	−	1.38232i	0.923256	−	0.384185i	$-0.125518\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	11.5966	+	11.0573i	0.428915	+	0.408970i
$732$		0			0
$733$	−1.25121	−	0.983964i	−0.0462146	−	0.0363435i	0.594785	−	0.803885i	$-0.297237\pi$
$733$	−1.25121	−	0.983964i	−0.0462146	−	0.0363435i	−0.640999	+	0.767542i	$0.721480\pi$
$734$		0			0
$735$	−0.208772	+	0.603208i	−0.00770068	+	0.0222497i
$736$		0			0
$737$	−6.86885	−	9.65852i	−0.253018	−	0.355776i
$738$		0			0
$739$	7.45587	−	21.5423i	0.274269	−	0.792447i	−0.720790	−	0.693154i	$-0.756221\pi$
$739$	7.45587	−	21.5423i	0.274269	−	0.792447i	0.995058	−	0.0992933i	$-0.0316582\pi$
$740$		0			0
$741$	−8.11520	−	6.38187i	−0.298119	−	0.234444i
$742$		0			0
$743$	−27.9119	−	26.6140i	−1.02399	−	0.976372i	−0.0242613	−	0.999706i	$-0.507723\pi$
$743$	−27.9119	−	26.6140i	−1.02399	−	0.976372i	−0.999728	+	0.0233341i	$0.992572\pi$
$744$		0			0
$745$	−27.4082	+	17.6142i	−1.00416	+	0.645333i
$746$		0			0
$747$	8.21447	−	11.5356i	0.300552	−	0.422066i
$748$		0			0
$749$	−37.9277	+	19.5531i	−1.38585	+	0.714453i
$750$		0			0
$751$	−3.85366	+	26.8028i	−0.140622	+	0.978048i	0.790271	+	0.612757i	$0.209940\pi$
$751$	−3.85366	+	26.8028i	−0.140622	+	0.978048i	−0.930893	+	0.365291i	$0.880970\pi$
$752$		0			0
$753$	0.695677	+	2.86762i	0.0253519	+	0.104502i
$754$		0			0
$755$	6.79870	−	2.72179i	0.247430	−	0.0990561i
$756$		0			0
$757$	2.73926	+	3.84676i	0.0995603	+	0.139813i	0.861351	−	0.508011i	$-0.169619\pi$
$757$	2.73926	+	3.84676i	0.0995603	+	0.139813i	−0.761791	+	0.647823i	$0.775680\pi$
$758$		0			0
$759$	−1.78058	−	3.89893i	−0.0646310	−	0.141522i
$760$		0			0
$761$	−1.67124	−	11.6237i	−0.0605823	−	0.421359i	−0.997432	−	0.0716258i	$-0.977181\pi$
$761$	−1.67124	−	11.6237i	−0.0605823	−	0.421359i	0.936849	−	0.349733i	$-0.113728\pi$
$762$		0			0
$763$	13.1935	+	5.28189i	0.477638	+	0.191217i
$764$		0			0
$765$	22.4932	+	11.5960i	0.813242	+	0.419255i
$766$		0			0
$767$	−0.198431	−	0.343693i	−0.00716493	−	0.0124100i
$768$		0			0
$769$	−36.5556	−	3.49064i	−1.31823	−	0.125876i	−0.587879	−	0.808949i	$-0.700037\pi$
$769$	−36.5556	−	3.49064i	−1.31823	−	0.125876i	−0.730350	+	0.683073i	$0.760643\pi$
$770$		0			0
$771$	7.20785	+	20.8257i	0.259585	+	0.750020i
$772$		0			0
$773$	1.43729	+	30.1725i	0.0516958	+	1.08523i	0.864481	+	0.502666i	$0.167647\pi$
$773$	1.43729	+	30.1725i	0.0516958	+	1.08523i	−0.812785	+	0.582564i	$0.802050\pi$
$774$		0			0
$775$	4.08605	−	7.07725i	0.146775	−	0.254222i
$776$		0			0
$777$	−4.59518	+	1.34927i	−0.164851	+	0.0484047i
$778$		0			0
$779$	−2.74403	−	1.76348i	−0.0983152	−	0.0631833i
$780$		0			0
$781$	−1.81396	+	0.173212i	−0.0649084	+	0.00619801i
$782$		0			0
$783$	1.26835	−	5.22820i	0.0453270	−	0.186841i
$784$		0			0
$785$	50.5119	+	9.73537i	1.80285	+	0.347470i
$786$		0			0
$787$	−38.3404	+	30.1512i	−1.36669	+	1.07478i	−0.377837	+	0.925872i	$0.623332\pi$
$787$	−38.3404	+	30.1512i	−1.36669	+	1.07478i	−0.988852	+	0.148904i	$0.952426\pi$
$788$		0			0
$789$	15.1276	−	17.4581i	0.538555	−	0.621526i
$790$		0			0
$791$	−1.13860	+	23.9022i	−0.0404841	+	0.849866i
$792$		0			0
$793$	−8.06469	+	7.68966i	−0.286385	+	0.273068i
$794$		0			0
$795$	−20.1060	−	23.2035i	−0.713085	−	0.822944i
$796$		0			0
$797$	−49.8367	+	9.60524i	−1.76531	+	0.340235i	−0.965576	−	0.260123i	$-0.916237\pi$
$797$	−49.8367	+	9.60524i	−1.76531	+	0.340235i	−0.799731	+	0.600358i	$0.795025\pi$
$798$		0			0
$799$	−62.0709	−	18.2257i	−2.19591	−	0.644777i
$800$		0			0
$801$	−3.98045	+	8.71598i	−0.140642	+	0.307964i
$802$		0			0
$803$	−3.96612			−0.139961
$804$		0			0
$805$	25.2172			0.888788
$806$		0			0
$807$	−1.75230	+	3.83700i	−0.0616838	+	0.135069i
$808$		0			0
$809$	−47.0583	−	13.8176i	−1.65448	−	0.485800i	−0.684508	−	0.729005i	$-0.739983\pi$
$809$	−47.0583	−	13.8176i	−1.65448	−	0.485800i	−0.969975	+	0.243205i	$0.921801\pi$
$810$		0			0
$811$	−21.5069	+	4.14512i	−0.755211	+	0.145555i	−0.552304	−	0.833643i	$-0.686251\pi$
$811$	−21.5069	+	4.14512i	−0.755211	+	0.145555i	−0.202907	+	0.979198i	$0.565039\pi$
$812$		0			0
$813$	−13.2267	−	15.2644i	−0.463879	−	0.535345i
$814$		0			0
$815$	−30.6293	+	29.2049i	−1.07290	+	1.02300i
$816$		0			0
$817$	−0.642271	+	13.4829i	−0.0224702	+	0.471708i
$818$		0			0
$819$	−2.70153	+	3.11774i	−0.0943992	+	0.108942i
$820$		0			0
$821$	37.5496	−	29.5294i	1.31049	−	1.03058i	0.313785	−	0.949494i	$-0.398403\pi$
$821$	37.5496	−	29.5294i	1.31049	−	1.03058i	0.996707	−	0.0810878i	$-0.0258394\pi$
$822$		0			0
$823$	−52.4348	−	10.1060i	−1.82776	−	0.352272i	−0.844656	−	0.535310i	$-0.820195\pi$
$823$	−52.4348	−	10.1060i	−1.82776	−	0.352272i	−0.983106	+	0.183037i	$0.941407\pi$
$824$		0			0
$825$	1.93365	−	7.97059i	0.0673209	−	0.277500i
$826$		0			0
$827$	−3.13497	+	0.299353i	−0.109014	+	0.0104095i	−0.149420	−	0.988774i	$-0.547741\pi$
$827$	−3.13497	+	0.299353i	−0.109014	+	0.0104095i	0.0404067	+	0.999183i	$0.487135\pi$
$828$		0			0
$829$	24.2703	+	15.5975i	0.842941	+	0.541725i	0.889366	−	0.457197i	$-0.151146\pi$
$829$	24.2703	+	15.5975i	0.842941	+	0.541725i	−0.0464248	+	0.998922i	$0.514783\pi$
$830$		0			0
$831$	−29.5390	+	8.67345i	−1.02470	+	0.300879i
$832$		0			0
$833$	−0.757348	+	1.31177i	−0.0262406	+	0.0454500i
$834$		0			0
$835$	0.732828	+	15.3840i	0.0253606	+	0.532384i
$836$		0			0
$837$	−0.471862	−	1.36336i	−0.0163099	−	0.0471244i
$838$		0			0
$839$	−13.5196	−	1.29096i	−0.466747	−	0.0445689i	−0.140967	−	0.990014i	$-0.545021\pi$
$839$	−13.5196	−	1.29096i	−0.466747	−	0.0445689i	−0.325781	+	0.945445i	$0.605627\pi$
$840$		0			0
$841$	0.0286153	+	0.0495631i	0.000986734	+	0.00170907i
$842$		0			0
$843$	−20.7851	−	10.7155i	−0.715876	−	0.369060i
$844$		0			0
$845$	−31.8299	−	12.7428i	−1.09498	−	0.438364i
$846$		0			0
$847$	−3.30528	−	22.9887i	−0.113571	−	0.789902i
$848$		0			0
$849$	−8.79176	−	19.2513i	−0.301732	−	0.660702i
$850$		0			0
$851$	−3.15254	−	4.42712i	−0.108068	−	0.151760i
$852$		0			0
$853$	15.3240	−	6.13481i	0.524684	−	0.210052i	−0.0941725	−	0.995556i	$-0.530021\pi$
$853$	15.3240	−	6.13481i	0.524684	−	0.210052i	0.618856	+	0.785504i	$0.287596\pi$
$854$		0			0
$855$	5.02600	+	20.7175i	0.171886	+	0.708522i
$856$		0			0
$857$	3.63753	−	25.2996i	0.124256	−	0.864217i	−0.828394	−	0.560146i	$-0.810745\pi$
$857$	3.63753	−	25.2996i	0.124256	−	0.864217i	0.952649	−	0.304071i	$-0.0983460\pi$
$858$		0			0
$859$	−5.58395	+	2.87872i	−0.190522	+	0.0982208i	−0.550848	−	0.834606i	$-0.685696\pi$
$859$	−5.58395	+	2.87872i	−0.190522	+	0.0982208i	0.360326	+	0.932826i	$0.382665\pi$
$860$		0			0
$861$	−0.756043	+	1.06171i	−0.0257659	+	0.0361831i
$862$		0			0
$863$	19.3582	−	12.4407i	0.658960	−	0.423488i	−0.167971	−	0.985792i	$-0.553721\pi$
$863$	19.3582	−	12.4407i	0.658960	−	0.423488i	0.826930	+	0.562304i	$0.190085\pi$
$864$		0			0
$865$	60.0923	+	57.2979i	2.04320	+	1.94819i
$866$		0			0
$867$	33.8403	+	26.6123i	1.14928	+	0.903802i
$868$		0			0
$869$	−6.41105	+	18.5235i	−0.217480	+	0.628367i
$870$		0			0
$871$	−12.7095	−	2.45766i	−0.430644	−	0.0832746i
$872$		0			0
$873$	−4.33411	+	12.5226i	−0.146688	+	0.423826i
$874$		0			0
$875$	4.44914	+	3.49884i	0.150408	+	0.118282i
$876$		0			0
$877$	39.6941	+	37.8482i	1.34037	+	1.27804i	0.930686	+	0.365818i	$0.119211\pi$
$877$	39.6941	+	37.8482i	1.34037	+	1.27804i	0.409688	+	0.912226i	$0.365638\pi$
$878$		0			0
$879$	−6.75619	+	4.34194i	−0.227881	+	0.146450i
$880$		0			0
$881$	20.1277	−	28.2654i	0.678119	−	0.952285i	−0.321866	−	0.946785i	$-0.604310\pi$
$881$	20.1277	−	28.2654i	0.678119	−	0.952285i	0.999985	−	0.00549960i	$-0.00175058\pi$
$882$		0			0
$883$	−26.9275	+	13.8821i	−0.906183	+	0.467170i	−0.847312	−	0.531096i	$-0.821780\pi$
$883$	−26.9275	+	13.8821i	−0.906183	+	0.467170i	−0.0588712	+	0.998266i	$0.518750\pi$
$884$		0			0
$885$	−0.116626	+	0.811154i	−0.00392035	+	0.0272667i
$886$		0			0
$887$	9.21904	+	38.0014i	0.309545	+	1.27596i	0.887847	+	0.460139i	$0.152200\pi$
$887$	9.21904	+	38.0014i	0.309545	+	1.27596i	−0.578302	+	0.815823i	$0.696284\pi$
$888$		0			0
$889$	−43.7998	+	17.5348i	−1.46900	+	0.588099i
$890$		0			0
$891$	−0.839890	−	1.17946i	−0.0281374	−	0.0395134i
$892$		0			0
$893$	−22.6388	−	49.5721i	−0.757579	−	1.65887i
$894$		0			0
$895$	−1.76847	−	12.3000i	−0.0591135	−	0.411143i
$896$		0			0
$897$	−4.34620	−	1.73996i	−0.145116	−	0.0580955i
$898$		0			0
$899$	−6.89872	−	3.55653i	−0.230085	−	0.118617i
$900$		0			0
$901$	−36.4281	−	63.0954i	−1.21360	−	2.10201i
$902$		0			0
$903$	5.36932	+	0.512708i	0.178680	+	0.0170618i
$904$		0			0
$905$	5.58732	+	16.1435i	0.185729	+	0.536628i
$906$		0			0
$907$	−0.884522	−	18.5684i	−0.0293701	−	0.616553i	−0.964791	−	0.263018i	$-0.915282\pi$
$907$	−0.884522	−	18.5684i	−0.0293701	−	0.616553i	0.935421	−	0.353536i	$-0.115021\pi$
$908$		0			0
$909$	4.55698	−	7.89292i	0.151146	−	0.261792i
$910$		0			0
$911$	−1.76949	+	0.519570i	−0.0586259	+	0.0172141i	−0.310914	−	0.950438i	$-0.600635\pi$
$911$	−1.76949	+	0.519570i	−0.0586259	+	0.0172141i	0.252288	+	0.967652i	$0.418817\pi$
$912$		0			0
$913$	−17.2499	−	11.0859i	−0.570890	−	0.366889i
$914$		0			0
$915$	22.9057	−	2.18723i	0.757241	−	0.0723077i
$916$		0			0
$917$	−4.80740	+	19.8164i	−0.158754	+	0.654394i
$918$		0			0
$919$	32.0803	+	6.18297i	1.05823	+	0.203957i	0.688541	−	0.725198i	$-0.258252\pi$
$919$	32.0803	+	6.18297i	1.05823	+	0.203957i	0.369691	+	0.929155i	$0.379464\pi$
$920$		0			0
$921$	17.1327	−	13.4733i	0.564541	−	0.443960i
$922$		0			0
$923$	−1.30334	+	1.50413i	−0.0428999	+	0.0495091i
$924$		0			0
$925$	0.494835	−	10.3879i	0.0162701	−	0.341551i
$926$		0			0
$927$	−2.75545	+	2.62732i	−0.0905009	+	0.0862925i
$928$		0			0
$929$	34.1034	+	39.3575i	1.11890	+	1.29128i	0.952270	+	0.305257i	$0.0987422\pi$
$929$	34.1034	+	39.3575i	1.11890	+	1.29128i	0.166627	+	0.986020i	$0.446712\pi$
$930$		0			0
$931$	−1.25294	+	0.241485i	−0.0410635	+	0.00791435i
$932$		0			0
$933$	16.4243	+	4.82260i	0.537707	+	0.157885i
$934$		0			0
$935$	15.2217	−	33.3308i	0.497802	−	1.09004i
$936$		0			0
$937$	36.2389			1.18387			0.591937	−	0.805984i	$-0.298363\pi$
$937$	36.2389			1.18387			0.591937	+	0.805984i	$0.298363\pi$
$938$		0			0
$939$	13.3260			0.434878
$940$		0			0
$941$	17.4545	−	38.2200i	0.569001	−	1.24594i	−0.378327	−	0.925672i	$-0.623501\pi$
$941$	17.4545	−	38.2200i	0.569001	−	1.24594i	0.947328	−	0.320266i	$-0.103772\pi$
$942$		0			0
$943$	−1.41921	−	0.416718i	−0.0462158	−	0.0135702i
$944$		0			0
$945$	8.36466	−	1.61216i	0.272102	−	0.0524434i
$946$		0			0
$947$	−18.1706	−	20.9700i	−0.590465	−	0.681433i	0.379356	−	0.925251i	$-0.376146\pi$
$947$	−18.1706	−	20.9700i	−0.590465	−	0.681433i	−0.969821	+	0.243818i	$0.921600\pi$
$948$		0			0
$949$	−3.13513	+	2.98934i	−0.101771	+	0.0970380i
$950$		0			0
$951$	−0.423529	+	8.89097i	−0.0137339	+	0.288309i
$952$		0			0
$953$	−29.1912	+	33.6885i	−0.945597	+	1.09128i	0.0501128	+	0.998744i	$0.484042\pi$
$953$	−29.1912	+	33.6885i	−0.945597	+	1.09128i	−0.995710	+	0.0925333i	$0.970504\pi$
$954$		0			0
$955$	−2.96325	+	2.33032i	−0.0958885	+	0.0754075i
$956$		0			0
$957$	−7.64895	−	1.47421i	−0.247255	−	0.0476546i
$958$		0			0
$959$	−3.46055	+	14.2646i	−0.111747	+	0.460627i
$960$		0			0
$961$	28.7877	−	2.74889i	0.928634	−	0.0886738i
$962$		0			0
$963$	−13.7614	−	8.84391i	−0.443455	−	0.284991i
$964$		0			0
$965$	48.9309	−	14.3674i	1.57514	−	0.462503i
$966$		0			0
$967$	24.1305	−	41.7952i	0.775984	−	1.34404i	−0.158256	−	0.987398i	$-0.550587\pi$
$967$	24.1305	−	41.7952i	0.775984	−	1.34404i	0.934240	−	0.356646i	$-0.116080\pi$
$968$		0			0
$969$	2.40706	+	50.5305i	0.0773260	+	1.62327i
$970$		0			0
$971$	1.37373	+	3.96914i	0.0440852	+	0.127376i	0.964895	−	0.262636i	$-0.0845920\pi$
$971$	1.37373	+	3.96914i	0.0440852	+	0.127376i	−0.920810	+	0.390012i	$0.872471\pi$
$972$		0			0
$973$	−46.4556	−	4.43597i	−1.48930	−	0.142211i
$974$		0			0
$975$	−4.47908	−	7.75800i	−0.143445	−	0.248455i
$976$		0			0
$977$	1.29407	+	0.667142i	0.0414011	+	0.0213438i	0.478803	−	0.877922i	$-0.341071\pi$
$977$	1.29407	+	0.667142i	0.0414011	+	0.0213438i	−0.437402	+	0.899266i	$0.644101\pi$
$978$		0			0
$979$	12.8802	+	5.15645i	0.411653	+	0.164801i
$980$		0			0
$981$	0.775339	+	5.39260i	0.0247547	+	0.172173i
$982$		0			0
$983$	−11.8758	−	26.0045i	−0.378780	−	0.829413i	−0.998988	−	0.0449757i	$-0.985679\pi$
$983$	−11.8758	−	26.0045i	−0.378780	−	0.829413i	0.620208	−	0.784438i	$-0.287048\pi$
$984$		0			0
$985$	25.9243	+	36.4056i	0.826017	+	1.15998i
$986$		0			0
$987$	−20.2165	+	8.09346i	−0.643498	+	0.257618i
$988$		0			0
$989$	1.44307	+	5.94841i	0.0458869	+	0.189148i
$990$		0			0
$991$	3.68374	−	25.6209i	0.117018	−	0.813876i	−0.843793	−	0.536669i	$-0.819682\pi$
$991$	3.68374	−	25.6209i	0.117018	−	0.813876i	0.960810	−	0.277207i	$-0.0894087\pi$
$992$		0			0
$993$	1.36478	−	0.703591i	0.0433099	−	0.0223278i
$994$		0			0
$995$	7.53655	−	10.5836i	0.238925	−	0.335523i
$996$		0			0
$997$	12.8091	−	8.23193i	0.405670	−	0.260708i	−0.321856	−	0.946789i	$-0.604307\pi$
$997$	12.8091	−	8.23193i	0.405670	−	0.260708i	0.727525	+	0.686081i	$0.240670\pi$
$998$		0			0
$999$	−1.32874	−	1.26695i	−0.0420395	−	0.0400846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.73.1	✓	120
67.56	even	33	inner	804.2.y.b.793.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.73.1	✓	120	1.1	even	1	trivial
804.2.y.b.793.1	yes	120	67.56	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{3} +(-3.13336 - 0.920039i) q^{5} +(-2.56141 + 0.493671i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{3} +(-3.13336 - 0.920039i) q^{5} +(-2.56141 + 0.493671i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-1.04793 + 0.999195i) q^{11} +(-0.0752496 + 1.57968i) q^{13} +(2.13854 - 2.46801i) q^{15} +(6.09133 - 4.79027i) q^{17} +(6.41011 + 1.23545i) q^{19} +(0.614989 - 2.53502i) q^{21} +(2.94684 - 0.281389i) q^{23} +(4.76523 + 3.06243i) q^{25} +(0.959493 - 0.281733i) q^{27} +(2.68992 - 4.65909i) q^{29} +(-0.0686466 - 1.44107i) q^{31} +(-0.473576 - 1.36831i) q^{33} +(8.48003 + 0.809745i) q^{35} +(-0.917976 - 1.58998i) q^{37} +(-1.40567 - 0.724673i) q^{39} +(-0.463871 - 0.185706i) q^{41} +(0.294267 + 2.04667i) q^{43} +(1.35660 + 2.97054i) q^{45} +(-4.84236 - 6.80014i) q^{47} +(-0.181462 + 0.0726464i) q^{49} +(1.82696 + 7.53082i) q^{51} +(1.33800 - 9.30602i) q^{53} +(4.20283 - 2.16671i) q^{55} +(-3.78666 + 5.31762i) q^{57} +(-0.211108 + 0.135671i) q^{59} +(5.09947 + 4.86234i) q^{61} +(2.05046 + 1.61250i) q^{63} +(1.68915 - 4.88049i) q^{65} +(-1.16988 + 8.10132i) q^{67} +(-0.968202 + 2.79744i) q^{69} +(0.989232 + 0.777940i) q^{71} +(1.98241 + 1.89022i) q^{73} +(-4.76523 + 3.06243i) q^{75} +(2.19089 - 3.07668i) q^{77} +(12.0326 - 6.20325i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(3.33870 + 13.7623i) q^{83} +(-23.4936 + 9.40541i) q^{85} +(3.12062 + 4.38230i) q^{87} +(-3.98045 - 8.71598i) q^{89} +(-0.587099 - 4.08336i) q^{91} +(1.33936 + 0.536198i) q^{93} +(-18.9485 - 9.76865i) q^{95} +(-6.62571 - 11.4761i) q^{97} +(1.44139 + 0.137636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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