LMFDB - Embedded newform 804.2.i.e.565.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(37,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("804.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.i (of order $3$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} - 9x^{5} + 54x^{4} - 50x^{3} + 85x^{2} + 24x + 9 $ x^8 - x^7 + 8x^6 - 9x^5 + 54x^4 - 50x^3 + 85x^2 + 24x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			565.3
Root			$0.830946 - 1.43924i$ of defining polynomial
Character	$\chi$	$=$	804.565
Dual form			804.2.i.e.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +0.238118 q^{5} +(-1.47881 - 2.56138i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +0.238118 q^{5} +(-1.47881 - 2.56138i) q^{7} +1.00000 q^{9} +(-2.02165 - 3.50159i) q^{11} +(0.0288087 - 0.0498982i) q^{13} +0.238118 q^{15} +(-0.830946 + 1.43924i) q^{17} +(3.66951 - 6.35578i) q^{19} +(-1.47881 - 2.56138i) q^{21} +(1.50000 - 2.59808i) q^{23} -4.94330 q^{25} +1.00000 q^{27} +(-1.61906 - 2.80429i) q^{29} +(0.302137 + 0.523316i) q^{31} +(-2.02165 - 3.50159i) q^{33} +(-0.352132 - 0.609911i) q^{35} +(1.60504 - 2.78000i) q^{37} +(0.0288087 - 0.0498982i) q^{39} +(4.35259 + 7.53891i) q^{41} +4.38140 q^{43} +0.238118 q^{45} +(0.309300 + 0.535724i) q^{47} +(-0.873778 + 1.51343i) q^{49} +(-0.830946 + 1.43924i) q^{51} -6.01009 q^{53} +(-0.481390 - 0.833793i) q^{55} +(3.66951 - 6.35578i) q^{57} +6.33903 q^{59} +(4.37882 - 7.58434i) q^{61} +(-1.47881 - 2.56138i) q^{63} +(0.00685988 - 0.0118817i) q^{65} +(-2.57210 + 7.77073i) q^{67} +(1.50000 - 2.59808i) q^{69} +(5.54329 + 9.60126i) q^{71} +(3.87424 - 6.71037i) q^{73} -4.94330 q^{75} +(-5.97927 + 10.3564i) q^{77} +(-5.35259 - 9.27096i) q^{79} +1.00000 q^{81} +(-4.55045 + 7.88162i) q^{83} +(-0.197863 + 0.342709i) q^{85} +(-1.61906 - 2.80429i) q^{87} -8.24419 q^{89} -0.170411 q^{91} +(0.302137 + 0.523316i) q^{93} +(0.873778 - 1.51343i) q^{95} +(1.28307 - 2.22234i) q^{97} +(-2.02165 - 3.50159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 - 6 * q^5 + 8 * q^9	$ 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9} + 3 q^{11} - 2 q^{13} - 6 q^{15} - q^{17} + 4 q^{19} + 12 q^{23} + 18 q^{25} + 8 q^{27} - 9 q^{29} - q^{31} + 3 q^{33} - 9 q^{35} + 14 q^{37} - 2 q^{39} + 10 q^{41} + 8 q^{43} - 6 q^{45} + 16 q^{47} + 6 q^{49} - q^{51} - 12 q^{53} + 4 q^{55} + 4 q^{57} + 4 q^{61} - 22 q^{65} + 20 q^{67} + 12 q^{69} + 6 q^{71} - 13 q^{73} + 18 q^{75} - 5 q^{77} - 18 q^{79} + 8 q^{81} - 15 q^{83} - 5 q^{85} - 9 q^{87} - 4 q^{89} - 34 q^{91} - q^{93} - 6 q^{95} + 30 q^{97} + 3 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 6 * q^5 + 8 * q^9 + 3 * q^11 - 2 * q^13 - 6 * q^15 - q^17 + 4 * q^19 + 12 * q^23 + 18 * q^25 + 8 * q^27 - 9 * q^29 - q^31 + 3 * q^33 - 9 * q^35 + 14 * q^37 - 2 * q^39 + 10 * q^41 + 8 * q^43 - 6 * q^45 + 16 * q^47 + 6 * q^49 - q^51 - 12 * q^53 + 4 * q^55 + 4 * q^57 + 4 * q^61 - 22 * q^65 + 20 * q^67 + 12 * q^69 + 6 * q^71 - 13 * q^73 + 18 * q^75 - 5 * q^77 - 18 * q^79 + 8 * q^81 - 15 * q^83 - 5 * q^85 - 9 * q^87 - 4 * q^89 - 34 * q^91 - q^93 - 6 * q^95 + 30 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	0.238118			0.106490			0.0532448	−	0.998581i	$-0.483044\pi$
$5$	0.238118			0.106490			0.0532448	+	0.998581i	$0.483044\pi$
$6$		0			0
$7$	−1.47881	−	2.56138i	−0.558939	−	0.968111i	−0.997585	−	0.0694509i	$-0.977875\pi$
$7$	−1.47881	−	2.56138i	−0.558939	−	0.968111i	0.438646	−	0.898660i	$-0.355458\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.02165	−	3.50159i	−0.609549	−	1.05577i	−0.991315	−	0.131511i	$-0.958017\pi$
$11$	−2.02165	−	3.50159i	−0.609549	−	1.05577i	0.381766	−	0.924259i	$-0.375316\pi$
$12$		0			0
$13$	0.0288087	−	0.0498982i	0.00799010	−	0.0138393i	−0.862003	−	0.506904i	$-0.830790\pi$
$13$	0.0288087	−	0.0498982i	0.00799010	−	0.0138393i	0.869993	+	0.493064i	$0.164123\pi$
$14$		0			0
$15$	0.238118			0.0614818
$16$		0			0
$17$	−0.830946	+	1.43924i	−0.201534	+	0.349067i	−0.949023	−	0.315207i	$-0.897926\pi$
$17$	−0.830946	+	1.43924i	−0.201534	+	0.349067i	0.747489	+	0.664274i	$0.231259\pi$
$18$		0			0
$19$	3.66951	−	6.35578i	0.841844	−	1.45812i	−0.0464900	−	0.998919i	$-0.514804\pi$
$19$	3.66951	−	6.35578i	0.841844	−	1.45812i	0.888334	−	0.459198i	$-0.151863\pi$
$20$		0			0
$21$	−1.47881	−	2.56138i	−0.322704	−	0.558939i
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−4.94330			−0.988660
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−1.61906	−	2.80429i	−0.300652	−	0.520744i	0.675632	−	0.737239i	$-0.263871\pi$
$29$	−1.61906	−	2.80429i	−0.300652	−	0.520744i	−0.976284	+	0.216495i	$0.930538\pi$
$30$		0			0
$31$	0.302137	+	0.523316i	0.0542654	+	0.0939904i	0.891882	−	0.452268i	$-0.149385\pi$
$31$	0.302137	+	0.523316i	0.0542654	+	0.0939904i	−0.837617	+	0.546258i	$0.816052\pi$
$32$		0			0
$33$	−2.02165	−	3.50159i	−0.351923	−	0.609549i
$34$		0			0
$35$	−0.352132	−	0.609911i	−0.0595212	−	0.103094i
$36$		0			0
$37$	1.60504	−	2.78000i	0.263866	−	0.457030i	−0.703400	−	0.710795i	$-0.748336\pi$
$37$	1.60504	−	2.78000i	0.263866	−	0.457030i	0.967266	+	0.253765i	$0.0816689\pi$
$38$		0			0
$39$	0.0288087	−	0.0498982i	0.00461309	−	0.00799010i
$40$		0			0
$41$	4.35259	+	7.53891i	0.679760	+	1.17738i	0.975053	+	0.221973i	$0.0712496\pi$
$41$	4.35259	+	7.53891i	0.679760	+	1.17738i	−0.295292	+	0.955407i	$0.595417\pi$
$42$		0			0
$43$	4.38140			0.668157			0.334079	−	0.942545i	$-0.391575\pi$
$43$	4.38140			0.668157			0.334079	+	0.942545i	$0.391575\pi$
$44$		0			0
$45$	0.238118			0.0354966
$46$		0			0
$47$	0.309300	+	0.535724i	0.0451161	+	0.0781433i	0.887702	−	0.460419i	$-0.152301\pi$
$47$	0.309300	+	0.535724i	0.0451161	+	0.0781433i	−0.842586	+	0.538563i	$0.818968\pi$
$48$		0			0
$49$	−0.873778	+	1.51343i	−0.124825	+	0.216204i
$50$		0			0
$51$	−0.830946	+	1.43924i	−0.116356	+	0.201534i
$52$		0			0
$53$	−6.01009			−0.825549			−0.412775	−	0.910833i	$-0.635440\pi$
$53$	−6.01009			−0.825549			−0.412775	+	0.910833i	$0.635440\pi$
$54$		0			0
$55$	−0.481390	−	0.833793i	−0.0649107	−	0.112429i
$56$		0			0
$57$	3.66951	−	6.35578i	0.486039	−	0.841844i
$58$		0			0
$59$	6.33903			0.825271			0.412635	−	0.910896i	$-0.364608\pi$
$59$	6.33903			0.825271			0.412635	+	0.910896i	$0.364608\pi$
$60$		0			0
$61$	4.37882	−	7.58434i	0.560651	−	0.971076i	−0.436789	−	0.899564i	$-0.643884\pi$
$61$	4.37882	−	7.58434i	0.560651	−	0.971076i	0.997440	−	0.0715116i	$-0.0227823\pi$
$62$		0			0
$63$	−1.47881	−	2.56138i	−0.186313	−	0.322704i
$64$		0			0
$65$	0.00685988	−	0.0118817i	0.000850863	−	0.00147374i
$66$		0			0
$67$	−2.57210	+	7.77073i	−0.314232	+	0.949346i
$67$	−2.57210	+	7.77073i	−0.314232	+	0.949346i
$68$		0			0
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$	5.54329	+	9.60126i	0.657868	+	1.13946i	0.981167	+	0.193163i	$0.0618747\pi$
$71$	5.54329	+	9.60126i	0.657868	+	1.13946i	−0.323299	+	0.946297i	$0.604792\pi$
$72$		0			0
$73$	3.87424	−	6.71037i	0.453445	−	0.785390i	−0.545152	−	0.838337i	$-0.683528\pi$
$73$	3.87424	−	6.71037i	0.453445	−	0.785390i	0.998597	+	0.0529472i	$0.0168615\pi$
$74$		0			0
$75$	−4.94330			−0.570803
$76$		0			0
$77$	−5.97927	+	10.3564i	−0.681401	+	1.18022i
$78$		0			0
$79$	−5.35259	−	9.27096i	−0.602214	−	1.04306i	−0.992485	−	0.122365i	$-0.960952\pi$
$79$	−5.35259	−	9.27096i	−0.602214	−	1.04306i	0.390272	−	0.920700i	$-0.372381\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−4.55045	+	7.88162i	−0.499477	+	0.865120i	−1.00000		0.000603553i	$-0.999808\pi$
$83$	−4.55045	+	7.88162i	−0.499477	+	0.865120i	0.500523	+	0.865723i	$0.333141\pi$
$84$		0			0
$85$	−0.197863	+	0.342709i	−0.0214613	+	0.0371720i
$86$		0			0
$87$	−1.61906	−	2.80429i	−0.173581	−	0.300652i
$88$		0			0
$89$	−8.24419			−0.873882			−0.436941	−	0.899490i	$-0.643938\pi$
$89$	−8.24419			−0.873882			−0.436941	+	0.899490i	$0.643938\pi$
$90$		0			0
$91$	−0.170411			−0.0178639
$92$		0			0
$93$	0.302137	+	0.523316i	0.0313301	+	0.0542654i
$94$		0			0
$95$	0.873778	−	1.51343i	0.0896477	−	0.155274i
$96$		0			0
$97$	1.28307	−	2.22234i	0.130276	−	0.225644i	−0.793507	−	0.608561i	$-0.791747\pi$
$97$	1.28307	−	2.22234i	0.130276	−	0.225644i	0.923783	+	0.382917i	$0.125080\pi$
$98$		0			0
$99$	−2.02165	−	3.50159i	−0.203183	−	0.351923i
$100$		0			0
$101$	4.40809	+	7.63504i	0.438621	+	0.759714i	0.997583	−	0.0694788i	$-0.0221336\pi$
$101$	4.40809	+	7.63504i	0.438621	+	0.759714i	−0.558962	+	0.829193i	$0.688800\pi$
$102$		0			0
$103$	0.0923688	+	0.159987i	0.00910137	+	0.0157640i	0.870540	−	0.492097i	$-0.163770\pi$
$103$	0.0923688	+	0.159987i	0.00910137	+	0.0157640i	−0.861439	+	0.507861i	$0.830436\pi$
$104$		0			0
$105$	−0.352132	−	0.609911i	−0.0343646	−	0.0595212i
$106$		0			0
$107$	8.63992			0.835252			0.417626	−	0.908619i	$-0.362862\pi$
$107$	8.63992			0.835252			0.417626	+	0.908619i	$0.362862\pi$
$108$		0			0
$109$	−4.90608			−0.469917			−0.234959	−	0.972005i	$-0.575495\pi$
$109$	−4.90608			−0.469917			−0.234959	+	0.972005i	$0.575495\pi$
$110$		0			0
$111$	1.60504	−	2.78000i	0.152343	−	0.263866i
$112$		0			0
$113$	5.24161	+	9.07874i	0.493089	+	0.854056i	0.999968	−	0.00796136i	$-0.00253421\pi$
$113$	5.24161	+	9.07874i	0.493089	+	0.854056i	−0.506879	+	0.862017i	$0.669201\pi$
$114$		0			0
$115$	0.357177	−	0.618649i	0.0333069	−	0.0576893i
$116$		0			0
$117$	0.0288087	−	0.0498982i	0.00266337	−	0.00461309i
$118$		0			0
$119$	4.91525			0.450581
$120$		0			0
$121$	−2.67410	+	4.63168i	−0.243100	+	0.421061i
$122$		0			0
$123$	4.35259	+	7.53891i	0.392460	+	0.679760i
$124$		0			0
$125$	−2.36768			−0.211772
$126$		0			0
$127$	−8.28903	−	14.3570i	−0.735533	−	1.27398i	−0.954489	−	0.298245i	$-0.903599\pi$
$127$	−8.28903	−	14.3570i	−0.735533	−	1.27398i	0.218957	−	0.975735i	$-0.429735\pi$
$128$		0			0
$129$	4.38140			0.385761
$130$		0			0
$131$	10.0686			0.879700			0.439850	−	0.898071i	$-0.355032\pi$
$131$	10.0686			0.879700			0.439850	+	0.898071i	$0.355032\pi$
$132$		0			0
$133$	−21.7061			−1.88216
$134$		0			0
$135$	0.238118			0.0204939
$136$		0			0
$137$	−2.60580			−0.222628			−0.111314	−	0.993785i	$-0.535506\pi$
$137$	−2.60580			−0.222628			−0.111314	+	0.993785i	$0.535506\pi$
$138$		0			0
$139$	21.0875			1.78862			0.894309	−	0.447450i	$-0.147668\pi$
$139$	21.0875			1.78862			0.894309	+	0.447450i	$0.147668\pi$
$140$		0			0
$141$	0.309300	+	0.535724i	0.0260478	+	0.0451161i
$142$		0			0
$143$	−0.232964			−0.0194814
$144$		0			0
$145$	−0.385527	−	0.667753i	−0.0320163	−	0.0554539i
$146$		0			0
$147$	−0.873778	+	1.51343i	−0.0720680	+	0.124825i
$148$		0			0
$149$	−18.9967			−1.55627			−0.778134	−	0.628098i	$-0.783834\pi$
$149$	−18.9967			−1.55627			−0.778134	+	0.628098i	$0.783834\pi$
$150$		0			0
$151$	−5.94789	+	10.3020i	−0.484032	+	0.838368i	−0.999832	−	0.0183410i	$-0.994162\pi$
$151$	−5.94789	+	10.3020i	−0.484032	+	0.838368i	0.515800	+	0.856709i	$0.327495\pi$
$152$		0			0
$153$	−0.830946	+	1.43924i	−0.0671780	+	0.116356i
$154$		0			0
$155$	0.0719442	+	0.124611i	0.00577870	+	0.0100090i
$156$		0			0
$157$	1.25976	−	2.18197i	0.100540	−	0.174141i	−0.811367	−	0.584537i	$-0.801276\pi$
$157$	1.25976	−	2.18197i	0.100540	−	0.174141i	0.911907	+	0.410396i	$0.134610\pi$
$158$		0			0
$159$	−6.01009			−0.476631
$160$		0			0
$161$	−8.87288			−0.699281
$162$		0			0
$163$	4.33857	+	7.51462i	0.339823	+	0.588590i	0.984399	−	0.175950i	$-0.0562996\pi$
$163$	4.33857	+	7.51462i	0.339823	+	0.588590i	−0.644576	+	0.764540i	$0.722966\pi$
$164$		0			0
$165$	−0.481390	−	0.833793i	−0.0374762	−	0.0649107i
$166$		0			0
$167$	6.77425	+	11.7333i	0.524207	+	0.907953i	0.999603	+	0.0281810i	$0.00897146\pi$
$167$	6.77425	+	11.7333i	0.524207	+	0.907953i	−0.475396	+	0.879772i	$0.657695\pi$
$168$		0			0
$169$	6.49834	+	11.2555i	0.499872	+	0.865804i
$170$		0			0
$171$	3.66951	−	6.35578i	0.280615	−	0.486039i
$172$		0			0
$173$	−10.4517	+	18.1028i	−0.794627	+	1.37633i	0.128449	+	0.991716i	$0.459000\pi$
$173$	−10.4517	+	18.1028i	−0.794627	+	1.37633i	−0.923076	+	0.384618i	$0.874333\pi$
$174$		0			0
$175$	7.31022	+	12.6617i	0.552600	+	0.957132i
$176$		0			0
$177$	6.33903			0.476470
$178$		0			0
$179$	−11.0509			−0.825986			−0.412993	−	0.910734i	$-0.635517\pi$
$179$	−11.0509			−0.825986			−0.412993	+	0.910734i	$0.635517\pi$
$180$		0			0
$181$	1.48779	+	2.57693i	0.110587	+	0.191542i	0.916007	−	0.401162i	$-0.131394\pi$
$181$	1.48779	+	2.57693i	0.110587	+	0.191542i	−0.805420	+	0.592704i	$0.798060\pi$
$182$		0			0
$183$	4.37882	−	7.58434i	0.323692	−	0.560651i
$184$		0			0
$185$	0.382188	−	0.661969i	0.0280990	−	0.0486689i
$186$		0			0
$187$	6.71951			0.491379
$188$		0			0
$189$	−1.47881	−	2.56138i	−0.107568	−	0.186313i
$190$		0			0
$191$	7.99330	−	13.8448i	0.578375	−	1.00177i	−0.417291	−	0.908773i	$-0.637021\pi$
$191$	7.99330	−	13.8448i	0.578375	−	1.00177i	0.995666	−	0.0930014i	$-0.0296461\pi$
$192$		0			0
$193$	17.0631			1.22823			0.614114	−	0.789218i	$-0.289514\pi$
$193$	17.0631			1.22823			0.614114	+	0.789218i	$0.289514\pi$
$194$		0			0
$195$	0.00685988	−	0.0118817i	0.000491246	−	0.000850863i
$196$		0			0
$197$	10.3747	+	17.9695i	0.739166	+	1.28027i	0.952871	+	0.303375i	$0.0981136\pi$
$197$	10.3747	+	17.9695i	0.739166	+	1.28027i	−0.213705	+	0.976898i	$0.568553\pi$
$198$		0			0
$199$	0.295277	−	0.511435i	0.0209316	−	0.0362546i	−0.855370	−	0.518018i	$-0.826670\pi$
$199$	0.295277	−	0.511435i	0.0209316	−	0.0362546i	0.876301	+	0.481763i	$0.160003\pi$
$200$		0			0
$201$	−2.57210	+	7.77073i	−0.181422	+	0.548105i
$202$		0			0
$203$	−4.78857	+	8.29405i	−0.336092	+	0.582128i
$204$		0			0
$205$	1.03643	+	1.79515i	0.0723875	+	0.125379i
$206$		0			0
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$		0			0
$209$	−29.6738			−2.05258
$210$		0			0
$211$	−0.417372	+	0.722909i	−0.0287331	+	0.0497671i	−0.880034	−	0.474910i	$-0.842481\pi$
$211$	−0.417372	+	0.722909i	−0.0287331	+	0.0497671i	0.851301	+	0.524677i	$0.175814\pi$
$212$		0			0
$213$	5.54329	+	9.60126i	0.379820	+	0.657868i
$214$		0			0
$215$	1.04329			0.0711518
$216$		0			0
$217$	0.893608	−	1.54777i	0.0606621	−	0.105070i
$218$		0			0
$219$	3.87424	−	6.71037i	0.261797	−	0.453445i
$220$		0			0
$221$	0.0478769	+	0.0829253i	0.00322055	+	0.00557816i
$222$		0			0
$223$	3.75764			0.251631			0.125815	−	0.992054i	$-0.459845\pi$
$223$	3.75764			0.251631			0.125815	+	0.992054i	$0.459845\pi$
$224$		0			0
$225$	−4.94330			−0.329553
$226$		0			0
$227$	4.82701	+	8.36063i	0.320380	+	0.554915i	0.980566	−	0.196187i	$-0.0628561\pi$
$227$	4.82701	+	8.36063i	0.320380	+	0.554915i	−0.660186	+	0.751102i	$0.729523\pi$
$228$		0			0
$229$	−5.12972	+	8.88493i	−0.338981	+	0.587133i	−0.984241	−	0.176830i	$-0.943416\pi$
$229$	−5.12972	+	8.88493i	−0.338981	+	0.587133i	0.645260	+	0.763963i	$0.276749\pi$
$230$		0			0
$231$	−5.97927	+	10.3564i	−0.393407	+	0.681401i
$232$		0			0
$233$	12.3233	+	21.3447i	0.807329	+	1.39833i	0.914707	+	0.404117i	$0.132421\pi$
$233$	12.3233	+	21.3447i	0.807329	+	1.39833i	−0.107378	+	0.994218i	$0.534246\pi$
$234$		0			0
$235$	0.0736500	+	0.127566i	0.00480440	+	0.00832146i
$236$		0			0
$237$	−5.35259	−	9.27096i	−0.347688	−	0.602214i
$238$		0			0
$239$	−9.89846	−	17.1446i	−0.640278	−	1.10899i	−0.985371	−	0.170425i	$-0.945486\pi$
$239$	−9.89846	−	17.1446i	−0.640278	−	1.10899i	0.345093	−	0.938569i	$-0.387848\pi$
$240$		0			0
$241$	3.09999			0.199688			0.0998440	−	0.995003i	$-0.468166\pi$
$241$	3.09999			0.199688			0.0998440	+	0.995003i	$0.468166\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−0.208062	+	0.360374i	−0.0132926	+	0.0230235i
$246$		0			0
$247$	−0.211428	−	0.366204i	−0.0134528	−	0.0233010i
$248$		0			0
$249$	−4.55045	+	7.88162i	−0.288373	+	0.499477i
$250$		0			0
$251$	5.48478	−	9.49991i	0.346196	−	0.599629i	−0.639374	−	0.768896i	$-0.720807\pi$
$251$	5.48478	−	9.49991i	0.346196	−	0.599629i	0.985570	+	0.169267i	$0.0541399\pi$
$252$		0			0
$253$	−12.1299			−0.762599
$254$		0			0
$255$	−0.197863	+	0.342709i	−0.0123907	+	0.0214613i
$256$		0			0
$257$	−8.48478	−	14.6961i	−0.529266	−	0.916715i	−0.999417	−	0.0341295i	$-0.989134\pi$
$257$	−8.48478	−	14.6961i	−0.529266	−	0.916715i	0.470152	−	0.882586i	$-0.344199\pi$
$258$		0			0
$259$	−9.49419			−0.589940
$260$		0			0
$261$	−1.61906	−	2.80429i	−0.100217	−	0.173581i
$262$		0			0
$263$	11.7857			0.726737			0.363368	−	0.931646i	$-0.381627\pi$
$263$	11.7857			0.726737			0.363368	+	0.931646i	$0.381627\pi$
$264$		0			0
$265$	−1.43111			−0.0879125
$266$		0			0
$267$	−8.24419			−0.504536
$268$		0			0
$269$	−7.83474			−0.477693			−0.238846	−	0.971057i	$-0.576769\pi$
$269$	−7.83474			−0.477693			−0.238846	+	0.971057i	$0.576769\pi$
$270$		0			0
$271$	−25.3214			−1.53816			−0.769082	−	0.639150i	$-0.779286\pi$
$271$	−25.3214			−1.53816			−0.769082	+	0.639150i	$0.779286\pi$
$272$		0			0
$273$	−0.170411			−0.0103137
$274$		0			0
$275$	9.99360	+	17.3094i	0.602637	+	1.04380i
$276$		0			0
$277$	−11.5296			−0.692748			−0.346374	−	0.938097i	$-0.612587\pi$
$277$	−11.5296			−0.692748			−0.346374	+	0.938097i	$0.612587\pi$
$278$		0			0
$279$	0.302137	+	0.523316i	0.0180885	+	0.0313301i
$280$		0			0
$281$	5.06190	−	8.76747i	0.301968	−	0.523023i	−0.674614	−	0.738171i	$-0.735690\pi$
$281$	5.06190	−	8.76747i	0.301968	−	0.523023i	0.976582	+	0.215147i	$0.0690232\pi$
$282$		0			0
$283$	2.31885			0.137841			0.0689206	−	0.997622i	$-0.478045\pi$
$283$	2.31885			0.137841			0.0689206	+	0.997622i	$0.478045\pi$
$284$		0			0
$285$	0.873778	−	1.51343i	0.0517581	−	0.0896477i
$286$		0			0
$287$	12.8733	−	22.2973i	0.759889	−	1.31617i
$288$		0			0
$289$	7.11906	+	12.3306i	0.418768	+	0.725328i
$290$		0			0
$291$	1.28307	−	2.22234i	0.0752148	−	0.130276i
$292$		0			0
$293$	10.1189			0.591150			0.295575	−	0.955319i	$-0.404489\pi$
$293$	10.1189			0.591150			0.295575	+	0.955319i	$0.404489\pi$
$294$		0			0
$295$	1.50944			0.0878828
$296$		0			0
$297$	−2.02165	−	3.50159i	−0.117308	−	0.203183i
$298$		0			0
$299$	−0.0864261	−	0.149694i	−0.00499815	−	0.00865705i
$300$		0			0
$301$	−6.47927	−	11.2224i	−0.373459	−	0.646850i
$302$		0			0
$303$	4.40809	+	7.63504i	0.253238	+	0.438621i
$304$		0			0
$305$	1.04268	−	1.80597i	0.0597035	−	0.103410i
$306$		0			0
$307$	15.1366	−	26.2173i	0.863890	−	1.49630i	−0.00425501	−	0.999991i	$-0.501354\pi$
$307$	15.1366	−	26.2173i	0.863890	−	1.49630i	0.868145	−	0.496311i	$-0.165312\pi$
$308$		0			0
$309$	0.0923688	+	0.159987i	0.00525468	+	0.00910137i
$310$		0			0
$311$	−4.99061			−0.282991			−0.141496	−	0.989939i	$-0.545191\pi$
$311$	−4.99061			−0.282991			−0.141496	+	0.989939i	$0.545191\pi$
$312$		0			0
$313$	4.47200			0.252772			0.126386	−	0.991981i	$-0.459662\pi$
$313$	4.47200			0.252772			0.126386	+	0.991981i	$0.459662\pi$
$314$		0			0
$315$	−0.352132	−	0.609911i	−0.0198404	−	0.0343646i
$316$		0			0
$317$	8.92076	−	15.4512i	0.501040	−	0.867826i	−0.498960	−	0.866625i	$-0.666284\pi$
$317$	8.92076	−	15.4512i	0.501040	−	0.867826i	0.999999	−	0.00120086i	$-0.000382246\pi$
$318$		0			0
$319$	−6.54633	+	11.3386i	−0.366524	+	0.634838i
$320$		0			0
$321$	8.63992			0.482233
$322$		0			0
$323$	6.09833	+	10.5626i	0.339320	+	0.587720i
$324$		0			0
$325$	−0.142410	+	0.246662i	−0.00789949	+	0.0136823i
$326$		0			0
$327$	−4.90608			−0.271307
$328$		0			0
$329$	0.914795	−	1.58447i	0.0504343	−	0.0873547i
$330$		0			0
$331$	8.75730	+	15.1681i	0.481344	+	0.833713i	0.999771	−	0.0214092i	$-0.00681528\pi$
$331$	8.75730	+	15.1681i	0.481344	+	0.833713i	−0.518426	+	0.855122i	$0.673482\pi$
$332$		0			0
$333$	1.60504	−	2.78000i	0.0879554	−	0.152343i
$334$		0			0
$335$	−0.612463	+	1.85035i	−0.0334625	+	0.101096i
$336$		0			0
$337$	−0.880179	+	1.52451i	−0.0479464	+	0.0830456i	−0.889003	−	0.457902i	$-0.848601\pi$
$337$	−0.880179	+	1.52451i	−0.0479464	+	0.0830456i	0.841056	+	0.540948i	$0.181934\pi$
$338$		0			0
$339$	5.24161	+	9.07874i	0.284685	+	0.493089i
$340$		0			0
$341$	1.22163	−	2.11592i	0.0661548	−	0.114583i
$342$		0			0
$343$	−15.5348			−0.838799
$344$		0			0
$345$	0.357177	−	0.618649i	0.0192298	−	0.0333069i
$346$		0			0
$347$	−7.76861	−	13.4556i	−0.417041	−	0.722336i	0.578600	−	0.815612i	$-0.303599\pi$
$347$	−7.76861	−	13.4556i	−0.417041	−	0.722336i	−0.995640	+	0.0932761i	$0.970266\pi$
$348$		0			0
$349$	12.1427			0.649982			0.324991	−	0.945717i	$-0.394639\pi$
$349$	12.1427			0.649982			0.324991	+	0.945717i	$0.394639\pi$
$350$		0			0
$351$	0.0288087	−	0.0498982i	0.00153770	−	0.00266337i
$352$		0			0
$353$	−5.98109	+	10.3595i	−0.318341	+	0.551383i	−0.980142	−	0.198297i	$-0.936459\pi$
$353$	−5.98109	+	10.3595i	−0.318341	+	0.551383i	0.661801	+	0.749680i	$0.269792\pi$
$354$		0			0
$355$	1.31996	+	2.28623i	0.0700561	+	0.121341i
$356$		0			0
$357$	4.91525			0.260143
$358$		0			0
$359$	24.6439			1.30066			0.650329	−	0.759653i	$-0.274631\pi$
$359$	24.6439			1.30066			0.650329	+	0.759653i	$0.274631\pi$
$360$		0			0
$361$	−17.4307	−	30.1908i	−0.917403	−	1.58899i
$362$		0			0
$363$	−2.67410	+	4.63168i	−0.140354	+	0.243100i
$364$		0			0
$365$	0.922526	−	1.59786i	0.0482872	−	0.0836359i
$366$		0			0
$367$	−11.5544	−	20.0128i	−0.603135	−	1.04466i	−0.992343	−	0.123511i	$-0.960585\pi$
$367$	−11.5544	−	20.0128i	−0.603135	−	1.04466i	0.389208	−	0.921150i	$-0.372749\pi$
$368$		0			0
$369$	4.35259	+	7.53891i	0.226587	+	0.392460i
$370$		0			0
$371$	8.88780	+	15.3941i	0.461432	+	0.799223i
$372$		0			0
$373$	1.48416	+	2.57064i	0.0768470	+	0.133103i	0.901888	−	0.431970i	$-0.142181\pi$
$373$	1.48416	+	2.57064i	0.0768470	+	0.133103i	−0.825041	+	0.565073i	$0.808848\pi$
$374$		0			0
$375$	−2.36768			−0.122266
$376$		0			0
$377$	−0.186572			−0.00960895
$378$		0			0
$379$	12.9450	−	22.4214i	0.664939	−	1.15171i	−0.314363	−	0.949303i	$-0.601791\pi$
$379$	12.9450	−	22.4214i	0.664939	−	1.15171i	0.979302	−	0.202405i	$-0.0648758\pi$
$380$		0			0
$381$	−8.28903	−	14.3570i	−0.424660	−	0.735533i
$382$		0			0
$383$	5.46267	−	9.46162i	0.279129	−	0.483466i	−0.692039	−	0.721860i	$-0.743287\pi$
$383$	5.46267	−	9.46162i	0.279129	−	0.483466i	0.971169	+	0.238394i	$0.0766208\pi$
$384$		0			0
$385$	−1.42377	+	2.46605i	−0.0725622	+	0.125681i
$386$		0			0
$387$	4.38140			0.222719
$388$		0			0
$389$	17.0369	−	29.5088i	0.863805	−	1.49615i	−0.00442470	−	0.999990i	$-0.501408\pi$
$389$	17.0369	−	29.5088i	0.863805	−	1.49615i	0.868229	−	0.496163i	$-0.165258\pi$
$390$		0			0
$391$	2.49284	+	4.31772i	0.126068	+	0.218356i
$392$		0			0
$393$	10.0686			0.507895
$394$		0			0
$395$	−1.27455	−	2.20758i	−0.0641295	−	0.111076i
$396$		0			0
$397$	14.9626			0.750949			0.375475	−	0.926833i	$-0.377480\pi$
$397$	14.9626			0.750949			0.375475	+	0.926833i	$0.377480\pi$
$398$		0			0
$399$	−21.7061			−1.08666
$400$		0			0
$401$	−34.0156			−1.69866			−0.849328	−	0.527866i	$-0.822992\pi$
$401$	−34.0156			−1.69866			−0.849328	+	0.527866i	$0.822992\pi$
$402$		0			0
$403$	0.0348167			0.00173434
$404$		0			0
$405$	0.238118			0.0118322
$406$		0			0
$407$	−12.9793			−0.643358
$408$		0			0
$409$	13.9157	+	24.1027i	0.688088	+	1.19180i	0.972456	+	0.233088i	$0.0748829\pi$
$409$	13.9157	+	24.1027i	0.688088	+	1.19180i	−0.284368	+	0.958715i	$0.591784\pi$
$410$		0			0
$411$	−2.60580			−0.128535
$412$		0			0
$413$	−9.37424	−	16.2367i	−0.461276	−	0.798953i
$414$		0			0
$415$	−1.08355	+	1.87676i	−0.0531892	+	0.0921263i
$416$		0			0
$417$	21.0875			1.03266
$418$		0			0
$419$	13.2023	−	22.8670i	0.644973	−	1.11713i	−0.339334	−	0.940666i	$-0.610202\pi$
$419$	13.2023	−	22.8670i	0.644973	−	1.11713i	0.984308	−	0.176461i	$-0.0564649\pi$
$420$		0			0
$421$	14.2797	−	24.7333i	0.695952	−	1.20542i	−0.273906	−	0.961756i	$-0.588316\pi$
$421$	14.2797	−	24.7333i	0.695952	−	1.20542i	0.969859	−	0.243668i	$-0.0783509\pi$
$422$		0			0
$423$	0.309300	+	0.535724i	0.0150387	+	0.0260478i
$424$		0			0
$425$	4.10761	−	7.11459i	0.199248	−	0.345109i
$426$		0			0
$427$	−25.9018			−1.25348
$428$		0			0
$429$	−0.232964			−0.0112476
$430$		0			0
$431$	−18.9742	−	32.8644i	−0.913957	−	1.58302i	−0.808421	−	0.588605i	$-0.799677\pi$
$431$	−18.9742	−	32.8644i	−0.913957	−	1.58302i	−0.105537	−	0.994415i	$-0.533656\pi$
$432$		0			0
$433$	0.342392	+	0.593040i	0.0164543	+	0.0284997i	0.874135	−	0.485682i	$-0.161429\pi$
$433$	0.342392	+	0.593040i	0.0164543	+	0.0284997i	−0.857681	+	0.514182i	$0.828096\pi$
$434$		0			0
$435$	−0.385527	−	0.667753i	−0.0184846	−	0.0320163i
$436$		0			0
$437$	−11.0085	−	19.0673i	−0.526610	−	0.912115i
$438$		0			0
$439$	11.1436	−	19.3013i	0.531856	−	0.921202i	−0.467452	−	0.884018i	$-0.654828\pi$
$439$	11.1436	−	19.3013i	0.531856	−	0.921202i	0.999308	−	0.0371840i	$-0.0118388\pi$
$440$		0			0
$441$	−0.873778	+	1.51343i	−0.0416085	+	0.0720680i
$442$		0			0
$443$	5.31356	+	9.20335i	0.252455	+	0.437264i	0.964201	−	0.265172i	$-0.0854288\pi$
$443$	5.31356	+	9.20335i	0.252455	+	0.437264i	−0.711746	+	0.702437i	$0.752095\pi$
$444$		0			0
$445$	−1.96309			−0.0930594
$446$		0			0
$447$	−18.9967			−0.898512
$448$		0			0
$449$	−20.0811	−	34.7815i	−0.947686	−	1.64144i	−0.750283	−	0.661117i	$-0.770083\pi$
$449$	−20.0811	−	34.7815i	−0.947686	−	1.64144i	−0.197403	−	0.980322i	$-0.563251\pi$
$450$		0			0
$451$	17.5988	−	30.4820i	0.828695	−	1.43534i
$452$		0			0
$453$	−5.94789	+	10.3020i	−0.279456	+	0.484032i
$454$		0			0
$455$	−0.0405779			−0.00190232
$456$		0			0
$457$	−0.659120	−	1.14163i	−0.0308323	−	0.0534031i	0.850198	−	0.526464i	$-0.176482\pi$
$457$	−0.659120	−	1.14163i	−0.0308323	−	0.0534031i	−0.881030	+	0.473061i	$0.843149\pi$
$458$		0			0
$459$	−0.830946	+	1.43924i	−0.0387852	+	0.0671780i
$460$		0			0
$461$	−0.0579275			−0.00269795			−0.00134898	−	0.999999i	$-0.500429\pi$
$461$	−0.0579275			−0.00269795			−0.00134898	+	0.999999i	$0.500429\pi$
$462$		0			0
$463$	−14.5628	+	25.2235i	−0.676790	+	1.17224i	0.299152	+	0.954206i	$0.403296\pi$
$463$	−14.5628	+	25.2235i	−0.676790	+	1.17224i	−0.975942	+	0.218030i	$0.930037\pi$
$464$		0			0
$465$	0.0719442	+	0.124611i	0.00333633	+	0.00577870i
$466$		0			0
$467$	−1.42806	+	2.47347i	−0.0660825	+	0.114458i	−0.897174	−	0.441678i	$-0.854383\pi$
$467$	−1.42806	+	2.47347i	−0.0660825	+	0.114458i	0.831091	+	0.556136i	$0.187717\pi$
$468$		0			0
$469$	23.7075	−	4.90334i	1.09471	−	0.226415i
$470$		0			0
$471$	1.25976	−	2.18197i	0.0580468	−	0.100540i
$472$		0			0
$473$	−8.85764	−	15.3419i	−0.407275	−	0.705420i
$474$		0			0
$475$	−18.1395	+	31.4185i	−0.832297	+	1.44158i
$476$		0			0
$477$	−6.01009			−0.275183
$478$		0			0
$479$	12.6857	−	21.9722i	0.579623	−	1.00394i	−0.415899	−	0.909411i	$-0.636533\pi$
$479$	12.6857	−	21.9722i	0.579623	−	1.00394i	0.995522	−	0.0945262i	$-0.0301336\pi$
$480$		0			0
$481$	−0.0924780	−	0.160177i	−0.00421663	−	0.00730343i
$482$		0			0
$483$	−8.87288			−0.403730
$484$		0			0
$485$	0.305522	−	0.529179i	0.0138730	−	0.0240288i
$486$		0			0
$487$	−1.11155	+	1.92525i	−0.0503690	+	0.0872416i	−0.890111	−	0.455745i	$-0.849373\pi$
$487$	−1.11155	+	1.92525i	−0.0503690	+	0.0872416i	0.839742	+	0.542986i	$0.182706\pi$
$488$		0			0
$489$	4.33857	+	7.51462i	0.196197	+	0.339823i
$490$		0			0
$491$	16.8839			0.761959			0.380980	−	0.924583i	$-0.375587\pi$
$491$	16.8839			0.761959			0.380980	+	0.924583i	$0.375587\pi$
$492$		0			0
$493$	5.38140			0.242366
$494$		0			0
$495$	−0.481390	−	0.833793i	−0.0216369	−	0.0374762i
$496$		0			0
$497$	16.3950	−	28.3969i	0.735416	−	1.27378i
$498$		0			0
$499$	−15.2851	+	26.4746i	−0.684255	+	1.18516i	0.289415	+	0.957204i	$0.406539\pi$
$499$	−15.2851	+	26.4746i	−0.684255	+	1.18516i	−0.973670	+	0.227961i	$0.926794\pi$
$500$		0			0
$501$	6.77425	+	11.7333i	0.302651	+	0.524207i
$502$		0			0
$503$	−13.0810	−	22.6569i	−0.583252	−	1.01022i	−0.995091	−	0.0989649i	$-0.968447\pi$
$503$	−13.0810	−	22.6569i	−0.583252	−	1.01022i	0.411839	−	0.911256i	$-0.364886\pi$
$504$		0			0
$505$	1.04965	+	1.81804i	0.0467086	+	0.0809017i
$506$		0			0
$507$	6.49834	+	11.2555i	0.288601	+	0.499872i
$508$		0			0
$509$	13.8586			0.614270			0.307135	−	0.951666i	$-0.400630\pi$
$509$	13.8586			0.614270			0.307135	+	0.951666i	$0.400630\pi$
$510$		0			0
$511$	−22.9171			−1.01379
$512$		0			0
$513$	3.66951	−	6.35578i	0.162013	−	0.280615i
$514$		0			0
$515$	0.0219947	+	0.0380959i	0.000969202	+	0.00167871i
$516$		0			0
$517$	1.25059	−	2.16609i	0.0550009	−	0.0952644i
$518$		0			0
$519$	−10.4517	+	18.1028i	−0.458778	+	0.794627i
$520$		0			0
$521$	−7.84483			−0.343688			−0.171844	−	0.985124i	$-0.554973\pi$
$521$	−7.84483			−0.343688			−0.171844	+	0.985124i	$0.554973\pi$
$522$		0			0
$523$	3.64236	−	6.30876i	0.159269	−	0.275863i	−0.775336	−	0.631549i	$-0.782419\pi$
$523$	3.64236	−	6.30876i	0.159269	−	0.275863i	0.934605	+	0.355686i	$0.115753\pi$
$524$		0			0
$525$	7.31022	+	12.6617i	0.319044	+	0.552600i
$526$		0			0
$527$	−1.00424			−0.0437452
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	6.33903			0.275090
$532$		0			0
$533$	0.501570			0.0217254
$534$		0			0
$535$	2.05732			0.0889457
$536$		0			0
$537$	−11.0509			−0.476883
$538$		0			0
$539$	7.06587			0.304349
$540$		0			0
$541$	22.8778			0.983594			0.491797	−	0.870710i	$-0.336340\pi$
$541$	22.8778			0.983594			0.491797	+	0.870710i	$0.336340\pi$
$542$		0			0
$543$	1.48779	+	2.57693i	0.0638473	+	0.110587i
$544$		0			0
$545$	−1.16823			−0.0500413
$546$		0			0
$547$	14.7561	+	25.5583i	0.630925	+	1.09279i	0.987363	+	0.158475i	$0.0506578\pi$
$547$	14.7561	+	25.5583i	0.630925	+	1.09279i	−0.356438	+	0.934319i	$0.616009\pi$
$548$		0			0
$549$	4.37882	−	7.58434i	0.186884	−	0.323692i
$550$		0			0
$551$	−23.7646			−1.01241
$552$		0			0
$553$	−15.8310	+	27.4200i	−0.673201	+	1.16602i
$554$		0			0
$555$	0.382188	−	0.661969i	0.0162230	−	0.0280990i
$556$		0			0
$557$	19.5358	+	33.8370i	0.827759	+	1.43372i	0.899792	+	0.436319i	$0.143718\pi$
$557$	19.5358	+	33.8370i	0.827759	+	1.43372i	−0.0720326	+	0.997402i	$0.522949\pi$
$558$		0			0
$559$	0.126222	−	0.218624i	0.00533864	−	0.00924680i
$560$		0			0
$561$	6.71951			0.283698
$562$		0			0
$563$	−13.9857			−0.589426			−0.294713	−	0.955586i	$-0.595224\pi$
$563$	−13.9857			−0.589426			−0.294713	+	0.955586i	$0.595224\pi$
$564$		0			0
$565$	1.24812	+	2.16181i	0.0525089	+	0.0909481i
$566$		0			0
$567$	−1.47881	−	2.56138i	−0.0621043	−	0.107568i
$568$		0			0
$569$	10.8459	+	18.7856i	0.454683	+	0.787534i	0.998670	−	0.0515594i	$-0.0164192\pi$
$569$	10.8459	+	18.7856i	0.454683	+	0.787534i	−0.543987	+	0.839094i	$0.683086\pi$
$570$		0			0
$571$	4.78475	+	8.28743i	0.200235	+	0.346818i	0.948604	−	0.316465i	$-0.102496\pi$
$571$	4.78475	+	8.28743i	0.200235	+	0.346818i	−0.748369	+	0.663283i	$0.769163\pi$
$572$		0			0
$573$	7.99330	−	13.8448i	0.333925	−	0.578375i
$574$		0			0
$575$	−7.41495	+	12.8431i	−0.309225	+	0.535593i
$576$		0			0
$577$	0.791479	+	1.37088i	0.0329497	+	0.0570706i	0.882030	−	0.471193i	$-0.156177\pi$
$577$	0.791479	+	1.37088i	0.0329497	+	0.0570706i	−0.849080	+	0.528264i	$0.822843\pi$
$578$		0			0
$579$	17.0631			0.709117
$580$		0			0
$581$	26.9171			1.11671
$582$		0			0
$583$	12.1503	+	21.0449i	0.503213	+	0.871590i
$584$		0			0
$585$	0.00685988	−	0.0118817i	0.000283621	−	0.000491246i
$586$		0			0
$587$	11.0773	−	19.1864i	0.457207	−	0.791906i	−0.541605	−	0.840633i	$-0.682183\pi$
$587$	11.0773	−	19.1864i	0.457207	−	0.791906i	0.998812	+	0.0487271i	$0.0155165\pi$
$588$		0			0
$589$	4.43478			0.182732
$590$		0			0
$591$	10.3747	+	17.9695i	0.426758	+	0.739166i
$592$		0			0
$593$	−7.00369	+	12.1307i	−0.287607	+	0.498150i	−0.973238	−	0.229799i	$-0.926193\pi$
$593$	−7.00369	+	12.1307i	−0.287607	+	0.498150i	0.685631	+	0.727949i	$0.259526\pi$
$594$		0			0
$595$	1.17041			0.0479822
$596$		0			0
$597$	0.295277	−	0.511435i	0.0120849	−	0.0209316i
$598$		0			0
$599$	−12.3404	−	21.3742i	−0.504215	−	0.873326i	−0.999988	−	0.00487410i	$-0.998449\pi$
$599$	−12.3404	−	21.3742i	−0.504215	−	0.873326i	0.495773	−	0.868452i	$-0.334885\pi$
$600$		0			0
$601$	12.5007	−	21.6519i	0.509915	−	0.883199i	−0.490019	−	0.871712i	$-0.663010\pi$
$601$	12.5007	−	21.6519i	0.509915	−	0.883199i	0.999934	−	0.0114871i	$-0.00365653\pi$
$602$		0			0
$603$	−2.57210	+	7.77073i	−0.104744	+	0.316449i
$604$		0			0
$605$	−0.636752	+	1.10289i	−0.0258876	+	0.0448387i
$606$		0			0
$607$	−15.0788	−	26.1173i	−0.612032	−	1.06007i	−0.990898	−	0.134618i	$-0.957019\pi$
$607$	−15.0788	−	26.1173i	−0.612032	−	1.06007i	0.378866	−	0.925452i	$-0.376314\pi$
$608$		0			0
$609$	−4.78857	+	8.29405i	−0.194043	+	0.336092i
$610$		0			0
$611$	0.0356422			0.00144193
$612$		0			0
$613$	2.67548	−	4.63406i	0.108061	−	0.187168i	−0.806923	−	0.590656i	$-0.798869\pi$
$613$	2.67548	−	4.63406i	0.108061	−	0.187168i	0.914985	+	0.403488i	$0.132202\pi$
$614$		0			0
$615$	1.03643	+	1.79515i	0.0417929	+	0.0723875i
$616$		0			0
$617$	−23.8763			−0.961223			−0.480612	−	0.876934i	$-0.659585\pi$
$617$	−23.8763			−0.961223			−0.480612	+	0.876934i	$0.659585\pi$
$618$		0			0
$619$	−22.2496	+	38.5374i	−0.894286	+	1.54895i	−0.0596008	+	0.998222i	$0.518983\pi$
$619$	−22.2496	+	38.5374i	−0.894286	+	1.54895i	−0.834685	+	0.550727i	$0.814351\pi$
$620$		0			0
$621$	1.50000	−	2.59808i	0.0601929	−	0.104257i
$622$		0			0
$623$	12.1916	+	21.1165i	0.488447	+	0.846015i
$624$		0			0
$625$	24.1527			0.966108
$626$		0			0
$627$	−29.6738			−1.18506
$628$		0			0
$629$	2.66739	+	4.62006i	0.106356	+	0.184214i
$630$		0			0
$631$	1.90490	−	3.29938i	0.0758328	−	0.131346i	−0.825615	−	0.564233i	$-0.809172\pi$
$631$	1.90490	−	3.29938i	0.0758328	−	0.131346i	0.901448	+	0.432887i	$0.142505\pi$
$632$		0			0
$633$	−0.417372	+	0.722909i	−0.0165890	+	0.0287331i
$634$		0			0
$635$	−1.97377	−	3.41867i	−0.0783266	−	0.135666i
$636$		0			0
$637$	0.0503448	+	0.0871998i	0.00199473	+	0.00345498i
$638$		0			0
$639$	5.54329	+	9.60126i	0.219289	+	0.379820i
$640$		0			0
$641$	−8.97060	−	15.5375i	−0.354317	−	0.613696i	0.632684	−	0.774410i	$-0.281953\pi$
$641$	−8.97060	−	15.5375i	−0.354317	−	0.613696i	−0.987001	+	0.160715i	$0.948620\pi$
$642$		0			0
$643$	−35.0772			−1.38331			−0.691655	−	0.722228i	$-0.743118\pi$
$643$	−35.0772			−1.38331			−0.691655	+	0.722228i	$0.743118\pi$
$644$		0			0
$645$	1.04329			0.0410795
$646$		0			0
$647$	−2.08230	+	3.60665i	−0.0818636	+	0.141792i	−0.904050	−	0.427426i	$-0.859421\pi$
$647$	−2.08230	+	3.60665i	−0.0818636	+	0.141792i	0.822187	+	0.569218i	$0.192754\pi$
$648$		0			0
$649$	−12.8153	−	22.1967i	−0.503043	−	0.871296i
$650$		0			0
$651$	0.893608	−	1.54777i	0.0350233	−	0.0606621i
$652$		0			0
$653$	1.78019	−	3.08338i	0.0696641	−	0.120662i	−0.829089	−	0.559116i	$-0.811141\pi$
$653$	1.78019	−	3.08338i	0.0696641	−	0.120662i	0.898753	+	0.438454i	$0.144474\pi$
$654$		0			0
$655$	2.39752			0.0936789
$656$		0			0
$657$	3.87424	−	6.71037i	0.151148	−	0.261797i
$658$		0			0
$659$	9.38197	+	16.2500i	0.365470	+	0.633012i	0.988851	−	0.148906i	$-0.0475751\pi$
$659$	9.38197	+	16.2500i	0.365470	+	0.633012i	−0.623382	+	0.781918i	$0.714242\pi$
$660$		0			0
$661$	−33.9433			−1.32024			−0.660121	−	0.751160i	$-0.729495\pi$
$661$	−33.9433			−1.32024			−0.660121	+	0.751160i	$0.729495\pi$
$662$		0			0
$663$	0.0478769	+	0.0829253i	0.00185939	+	0.00322055i
$664$		0			0
$665$	−5.16862			−0.200430
$666$		0			0
$667$	−9.71435			−0.376141
$668$		0			0
$669$	3.75764			0.145279
$670$		0			0
$671$	−35.4097			−1.36698
$672$		0			0
$673$	20.3064			0.782752			0.391376	−	0.920231i	$-0.371999\pi$
$673$	20.3064			0.782752			0.391376	+	0.920231i	$0.371999\pi$
$674$		0			0
$675$	−4.94330			−0.190268
$676$		0			0
$677$	9.53442	+	16.5141i	0.366438	+	0.634689i	0.989006	−	0.147877i	$-0.0472440\pi$
$677$	9.53442	+	16.5141i	0.366438	+	0.634689i	−0.622568	+	0.782566i	$0.713911\pi$
$678$		0			0
$679$	−7.58968			−0.291265
$680$		0			0
$681$	4.82701	+	8.36063i	0.184972	+	0.320380i
$682$		0			0
$683$	−13.0945	+	22.6804i	−0.501047	+	0.867840i	0.498952	+	0.866630i	$0.333718\pi$
$683$	−13.0945	+	22.6804i	−0.501047	+	0.867840i	−0.999999	+	0.00120983i	$0.999615\pi$
$684$		0			0
$685$	−0.620488			−0.0237076
$686$		0			0
$687$	−5.12972	+	8.88493i	−0.195711	+	0.338981i
$688$		0			0
$689$	−0.173143	+	0.299892i	−0.00659622	+	0.0114250i
$690$		0			0
$691$	17.5746	+	30.4400i	0.668568	+	1.15799i	0.978305	+	0.207171i	$0.0664258\pi$
$691$	17.5746	+	30.4400i	0.668568	+	1.15799i	−0.309737	+	0.950822i	$0.600241\pi$
$692$		0			0
$693$	−5.97927	+	10.3564i	−0.227134	+	0.393407i
$694$		0			0
$695$	5.02132			0.190469
$696$		0			0
$697$	−14.4671			−0.547979
$698$		0			0
$699$	12.3233	+	21.3447i	0.466112	+	0.807329i
$700$		0			0
$701$	−5.71462	−	9.89801i	−0.215838	−	0.373843i	0.737693	−	0.675136i	$-0.235915\pi$
$701$	−5.71462	−	9.89801i	−0.215838	−	0.373843i	−0.953532	+	0.301293i	$0.902582\pi$
$702$		0			0
$703$	−11.7794	−	20.4025i	−0.444268	−	0.769496i
$704$		0			0
$705$	0.0736500	+	0.127566i	0.00277382	+	0.00480440i
$706$		0			0
$707$	13.0375	−	22.5816i	0.490325	−	0.849268i
$708$		0			0
$709$	−17.3275	+	30.0121i	−0.650747	+	1.12713i	0.332195	+	0.943211i	$0.392211\pi$
$709$	−17.3275	+	30.0121i	−0.650747	+	1.12713i	−0.982942	+	0.183916i	$0.941123\pi$
$710$		0			0
$711$	−5.35259	−	9.27096i	−0.200738	−	0.347688i
$712$		0			0
$713$	1.81282			0.0678907
$714$		0			0
$715$	−0.0554729			−0.00207457
$716$		0			0
$717$	−9.89846	−	17.1446i	−0.369665	−	0.640278i
$718$		0			0
$719$	13.1511	−	22.7784i	0.490453	−	0.849490i	−0.509486	−	0.860479i	$-0.670165\pi$
$719$	13.1511	−	22.7784i	0.490453	−	0.849490i	0.999940	+	0.0109888i	$0.00349793\pi$
$720$		0			0
$721$	0.273192	−	0.473183i	0.0101742	−	0.0176223i
$722$		0			0
$723$	3.09999			0.115290
$724$		0			0
$725$	8.00349	+	13.8625i	0.297242	+	0.514839i
$726$		0			0
$727$	−4.12225	+	7.13995i	−0.152886	+	0.264806i	−0.932287	−	0.361719i	$-0.882190\pi$
$727$	−4.12225	+	7.13995i	−0.152886	+	0.264806i	0.779401	+	0.626525i	$0.215523\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.64070	+	6.30588i	−0.134656	+	0.233232i
$732$		0			0
$733$	17.4980	+	30.3074i	0.646304	+	1.11943i	0.983999	+	0.178175i	$0.0570194\pi$
$733$	17.4980	+	30.3074i	0.646304	+	1.11943i	−0.337695	+	0.941256i	$0.609647\pi$
$734$		0			0
$735$	−0.208062	+	0.360374i	−0.00767449	+	0.0132926i
$736$		0			0
$737$	32.4098	−	6.70322i	1.19383	−	0.246916i
$738$		0			0
$739$	13.7951	−	23.8939i	0.507462	−	0.878950i	−0.492501	−	0.870312i	$-0.663917\pi$
$739$	13.7951	−	23.8939i	0.507462	−	0.878950i	0.999963	−	0.00863792i	$-0.00274957\pi$
$740$		0			0
$741$	−0.211428	−	0.366204i	−0.00776700	−	0.0134528i
$742$		0			0
$743$	−14.7313	+	25.5153i	−0.540438	+	0.936066i	0.458441	+	0.888725i	$0.348408\pi$
$743$	−14.7313	+	25.5153i	−0.540438	+	0.936066i	−0.998879	+	0.0473413i	$0.984925\pi$
$744$		0			0
$745$	−4.52345			−0.165727
$746$		0			0
$747$	−4.55045	+	7.88162i	−0.166492	+	0.288373i
$748$		0			0
$749$	−12.7768	−	22.1301i	−0.466855	−	0.808616i
$750$		0			0
$751$	−13.9048			−0.507392			−0.253696	−	0.967284i	$-0.581646\pi$
$751$	−13.9048			−0.507392			−0.253696	+	0.967284i	$0.581646\pi$
$752$		0			0
$753$	5.48478	−	9.49991i	0.199876	−	0.346196i
$754$		0			0
$755$	−1.41630	+	2.45310i	−0.0515444	+	0.0892775i
$756$		0			0
$757$	2.12839	+	3.68647i	0.0773575	+	0.133987i	0.902109	−	0.431508i	$-0.142018\pi$
$757$	2.12839	+	3.68647i	0.0773575	+	0.133987i	−0.824752	+	0.565495i	$0.808685\pi$
$758$		0			0
$759$	−12.1299			−0.440286
$760$		0			0
$761$	21.6186			0.783674			0.391837	−	0.920035i	$-0.371840\pi$
$761$	21.6186			0.783674			0.391837	+	0.920035i	$0.371840\pi$
$762$		0			0
$763$	7.25518	+	12.5663i	0.262655	+	0.454932i
$764$		0			0
$765$	−0.197863	+	0.342709i	−0.00715376	+	0.0123907i
$766$		0			0
$767$	0.182619	−	0.316306i	0.00659400	−	0.0114211i
$768$		0			0
$769$	5.91704	+	10.2486i	0.213374	+	0.369575i	0.952768	−	0.303698i	$-0.0982214\pi$
$769$	5.91704	+	10.2486i	0.213374	+	0.369575i	−0.739394	+	0.673273i	$0.764888\pi$
$770$		0			0
$771$	−8.48478	−	14.6961i	−0.305572	−	0.529266i
$772$		0			0
$773$	26.3508	+	45.6409i	0.947772	+	1.64159i	0.750103	+	0.661321i	$0.230004\pi$
$773$	26.3508	+	45.6409i	0.947772	+	1.64159i	0.197669	+	0.980269i	$0.436663\pi$
$774$		0			0
$775$	−1.49355	−	2.58691i	−0.0536500	−	0.0929245i
$776$		0			0
$777$	−9.49419			−0.340602
$778$		0			0
$779$	63.8876			2.28901
$780$		0			0
$781$	22.4131	−	38.8207i	0.802005	−	1.38911i
$782$		0			0
$783$	−1.61906	−	2.80429i	−0.0578605	−	0.100217i
$784$		0			0
$785$	0.299972	−	0.519568i	0.0107065	−	0.0185442i
$786$		0			0
$787$	−26.9388	+	46.6594i	−0.960266	+	1.66323i	−0.238437	+	0.971158i	$0.576635\pi$
$787$	−26.9388	+	46.6594i	−0.960266	+	1.66323i	−0.721829	+	0.692072i	$0.756698\pi$
$788$		0			0
$789$	11.7857			0.419582
$790$		0			0
$791$	15.5027	−	26.8515i	0.551214	−	0.954730i
$792$		0			0
$793$	−0.252296	−	0.436990i	−0.00895931	−	0.0155180i
$794$		0			0
$795$	−1.43111			−0.0507563
$796$		0			0
$797$	13.5574	+	23.4821i	0.480229	+	0.831780i	0.999743	−	0.0226816i	$-0.00722038\pi$
$797$	13.5574	+	23.4821i	0.480229	+	0.831780i	−0.519514	+	0.854462i	$0.673887\pi$
$798$		0			0
$799$	−1.02805			−0.0363697
$800$		0			0
$801$	−8.24419			−0.291294
$802$		0			0
$803$	−31.3293			−1.10559
$804$		0			0
$805$	−2.11279			−0.0744662
$806$		0			0
$807$	−7.83474			−0.275796
$808$		0			0
$809$	−8.88471			−0.312370			−0.156185	−	0.987728i	$-0.549920\pi$
$809$	−8.88471			−0.312370			−0.156185	+	0.987728i	$0.549920\pi$
$810$		0			0
$811$	12.0607	+	20.8897i	0.423508	+	0.733537i	0.996280	−	0.0861778i	$-0.0274653\pi$
$811$	12.0607	+	20.8897i	0.423508	+	0.733537i	−0.572772	+	0.819715i	$0.694132\pi$
$812$		0			0
$813$	−25.3214			−0.888060
$814$		0			0
$815$	1.03309	+	1.78937i	0.0361876	+	0.0626788i
$816$		0			0
$817$	16.0776	−	27.8472i	0.562484	−	0.974251i
$818$		0			0
$819$	−0.170411			−0.00595464
$820$		0			0
$821$	−18.5191	+	32.0760i	−0.646320	+	1.11946i	0.337675	+	0.941263i	$0.390360\pi$
$821$	−18.5191	+	32.0760i	−0.646320	+	1.11946i	−0.983995	+	0.178196i	$0.942974\pi$
$822$		0			0
$823$	−19.4224	+	33.6406i	−0.677024	+	1.17264i	0.298849	+	0.954300i	$0.403397\pi$
$823$	−19.4224	+	33.6406i	−0.677024	+	1.17264i	−0.975873	+	0.218339i	$0.929936\pi$
$824$		0			0
$825$	9.99360	+	17.3094i	0.347932	+	0.602637i
$826$		0			0
$827$	9.45852	−	16.3826i	0.328905	−	0.569680i	−0.653390	−	0.757022i	$-0.726654\pi$
$827$	9.45852	−	16.3826i	0.328905	−	0.569680i	0.982295	+	0.187341i	$0.0599870\pi$
$828$		0			0
$829$	5.34999			0.185813			0.0929065	−	0.995675i	$-0.470384\pi$
$829$	5.34999			0.185813			0.0929065	+	0.995675i	$0.470384\pi$
$830$		0			0
$831$	−11.5296			−0.399958
$832$		0			0
$833$	−1.45212	−	2.51515i	−0.0503131	−	0.0871448i
$834$		0			0
$835$	1.61307	+	2.79392i	0.0558226	+	0.0966876i
$836$		0			0
$837$	0.302137	+	0.523316i	0.0104434	+	0.0180885i
$838$		0			0
$839$	−6.47881	−	11.2216i	−0.223673	−	0.387414i	0.732247	−	0.681039i	$-0.238472\pi$
$839$	−6.47881	−	11.2216i	−0.223673	−	0.387414i	−0.955921	+	0.293625i	$0.905138\pi$
$840$		0			0
$841$	9.25730	−	16.0341i	0.319217	−	0.552900i
$842$		0			0
$843$	5.06190	−	8.76747i	0.174341	−	0.301968i
$844$		0			0
$845$	1.54737	+	2.68013i	0.0532312	+	0.0921992i
$846$		0			0
$847$	15.8180			0.543512
$848$		0			0
$849$	2.31885			0.0795826
$850$		0			0
$851$	−4.81511	−	8.34001i	−0.165060	−	0.285892i
$852$		0			0
$853$	−20.4323	+	35.3898i	−0.699590	+	1.21172i	0.269019	+	0.963135i	$0.413301\pi$
$853$	−20.4323	+	35.3898i	−0.699590	+	1.21172i	−0.968609	+	0.248590i	$0.920033\pi$
$854$		0			0
$855$	0.873778	−	1.51343i	0.0298826	−	0.0517581i
$856$		0			0
$857$	−2.07046			−0.0707255			−0.0353628	−	0.999375i	$-0.511259\pi$
$857$	−2.07046			−0.0707255			−0.0353628	+	0.999375i	$0.511259\pi$
$858$		0			0
$859$	−8.12638	−	14.0753i	−0.277268	−	0.480243i	0.693436	−	0.720518i	$-0.256096\pi$
$859$	−8.12638	−	14.0753i	−0.277268	−	0.480243i	−0.970705	+	0.240275i	$0.922762\pi$
$860$		0			0
$861$	12.8733	−	22.2973i	0.438722	−	0.759889i
$862$		0			0
$863$	−9.01097			−0.306737			−0.153368	−	0.988169i	$-0.549012\pi$
$863$	−9.01097			−0.306737			−0.153368	+	0.988169i	$0.549012\pi$
$864$		0			0
$865$	−2.48874	+	4.31062i	−0.0846195	+	0.146565i
$866$		0			0
$867$	7.11906	+	12.3306i	0.241776	+	0.418768i
$868$		0			0
$869$	−21.6421	+	37.4852i	−0.734157	+	1.27160i
$870$		0			0
$871$	0.313646	+	0.352208i	0.0106275	+	0.0119341i
$872$		0			0
$873$	1.28307	−	2.22234i	0.0434253	−	0.0752148i
$874$		0			0
$875$	3.50136	+	6.06453i	0.118367	+	0.205018i
$876$		0			0
$877$	21.3230	−	36.9326i	0.720028	−	1.24712i	−0.240960	−	0.970535i	$-0.577462\pi$
$877$	21.3230	−	36.9326i	0.720028	−	1.24712i	0.960988	−	0.276590i	$-0.0892043\pi$
$878$		0			0
$879$	10.1189			0.341301
$880$		0			0
$881$	−21.6439	+	37.4883i	−0.729201	+	1.26301i	0.228020	+	0.973656i	$0.426775\pi$
$881$	−21.6439	+	37.4883i	−0.729201	+	1.26301i	−0.957221	+	0.289357i	$0.906558\pi$
$882$		0			0
$883$	−6.90744	−	11.9640i	−0.232454	−	0.402622i	0.726076	−	0.687615i	$-0.241342\pi$
$883$	−6.90744	−	11.9640i	−0.232454	−	0.402622i	−0.958530	+	0.284993i	$0.908009\pi$
$884$		0			0
$885$	1.50944			0.0507392
$886$		0			0
$887$	−12.3477	+	21.3869i	−0.414597	+	0.718102i	−0.995386	−	0.0959515i	$-0.969411\pi$
$887$	−12.3477	+	21.3869i	−0.414597	+	0.718102i	0.580789	+	0.814054i	$0.302744\pi$
$888$		0			0
$889$	−24.5159	+	42.4627i	−0.822235	+	1.42415i
$890$		0			0
$891$	−2.02165	−	3.50159i	−0.0677277	−	0.117308i
$892$		0			0
$893$	4.53992			0.151923
$894$		0			0
$895$	−2.63143			−0.0879590
$896$		0			0
$897$	−0.0864261	−	0.149694i	−0.00288568	−	0.00499815i
$898$		0			0
$899$	0.978355	−	1.69456i	0.0326300	−	0.0565167i
$900$		0			0
$901$	4.99406	−	8.64996i	0.166376	−	0.288172i
$902$		0			0
$903$	−6.47927	−	11.2224i	−0.215617	−	0.373459i
$904$		0			0
$905$	0.354270	+	0.613614i	0.0117763	+	0.0203972i
$906$		0			0
$907$	−5.44439	−	9.42996i	−0.180778	−	0.313117i	0.761368	−	0.648320i	$-0.224528\pi$
$907$	−5.44439	−	9.42996i	−0.180778	−	0.313117i	−0.942146	+	0.335204i	$0.891195\pi$
$908$		0			0
$909$	4.40809	+	7.63504i	0.146207	+	0.253238i
$910$		0			0
$911$	−33.4723			−1.10899			−0.554494	−	0.832188i	$-0.687088\pi$
$911$	−33.4723			−1.10899			−0.554494	+	0.832188i	$0.687088\pi$
$912$		0			0
$913$	36.7976			1.21782
$914$		0			0
$915$	1.04268	−	1.80597i	0.0344698	−	0.0597035i
$916$		0			0
$917$	−14.8896	−	25.7896i	−0.491698	−	0.851647i
$918$		0			0
$919$	10.1983	−	17.6640i	0.336412	−	0.582683i	−0.647343	−	0.762199i	$-0.724120\pi$
$919$	10.1983	−	17.6640i	0.336412	−	0.582683i	0.983755	+	0.179516i	$0.0574531\pi$
$920$		0			0
$921$	15.1366	−	26.2173i	0.498767	−	0.863890i
$922$		0			0
$923$	0.638780			0.0210257
$924$		0			0
$925$	−7.93417	+	13.7424i	−0.260874	+	0.451847i
$926$		0			0
$927$	0.0923688	+	0.159987i	0.00303379	+	0.00525468i
$928$		0			0
$929$	−45.8247			−1.50346			−0.751730	−	0.659471i	$-0.770780\pi$
$929$	−45.8247			−1.50346			−0.751730	+	0.659471i	$0.770780\pi$
$930$		0			0
$931$	6.41268	+	11.1071i	0.210167	+	0.364020i
$932$		0			0
$933$	−4.99061			−0.163385
$934$		0			0
$935$	1.60004			0.0523268
$936$		0			0
$937$	22.9686			0.750353			0.375176	−	0.926953i	$-0.377582\pi$
$937$	22.9686			0.750353			0.375176	+	0.926953i	$0.377582\pi$
$938$		0			0
$939$	4.47200			0.145938
$940$		0			0
$941$	40.5184			1.32086			0.660432	−	0.750886i	$-0.270373\pi$
$941$	40.5184			1.32086			0.660432	+	0.750886i	$0.270373\pi$
$942$		0			0
$943$	26.1155			0.850439
$944$		0			0
$945$	−0.352132	−	0.609911i	−0.0114549	−	0.0198404i
$946$		0			0
$947$	44.1488			1.43464			0.717321	−	0.696742i	$-0.245368\pi$
$947$	44.1488			1.43464			0.717321	+	0.696742i	$0.245368\pi$
$948$		0			0
$949$	−0.223223	−	0.386634i	−0.00724614	−	0.0125507i
$950$		0			0
$951$	8.92076	−	15.4512i	0.289275	−	0.501040i
$952$		0			0
$953$	18.7396			0.607036			0.303518	−	0.952826i	$-0.401839\pi$
$953$	18.7396			0.607036			0.303518	+	0.952826i	$0.401839\pi$
$954$		0			0
$955$	1.90335	−	3.29670i	0.0615909	−	0.106679i
$956$		0			0
$957$	−6.54633	+	11.3386i	−0.211613	+	0.366524i
$958$		0			0
$959$	3.85349	+	6.67444i	0.124436	+	0.215529i
$960$		0			0
$961$	15.3174	−	26.5306i	0.494111	−	0.855825i
$962$		0			0
$963$	8.63992			0.278417
$964$		0			0
$965$	4.06303			0.130794
$966$		0			0
$967$	−2.00743	−	3.47697i	−0.0645545	−	0.111812i	0.831942	−	0.554863i	$-0.187229\pi$
$967$	−2.00743	−	3.47697i	−0.0645545	−	0.111812i	−0.896496	+	0.443051i	$0.853896\pi$
$968$		0			0
$969$	6.09833	+	10.5626i	0.195907	+	0.339320i
$970$		0			0
$971$	−18.1059	−	31.3604i	−0.581046	−	1.00640i	−0.995356	−	0.0962658i	$-0.969310\pi$
$971$	−18.1059	−	31.3604i	−0.581046	−	1.00640i	0.414309	−	0.910136i	$-0.364023\pi$
$972$		0			0
$973$	−31.1845	−	54.0131i	−0.999728	−	1.73158i
$974$		0			0
$975$	−0.142410	+	0.246662i	−0.00456077	+	0.00789949i
$976$		0			0
$977$	7.00670	−	12.1360i	0.224164	−	0.388264i	−0.731904	−	0.681408i	$-0.761368\pi$
$977$	7.00670	−	12.1360i	0.224164	−	0.388264i	0.956068	+	0.293144i	$0.0947014\pi$
$978$		0			0
$979$	16.6668	+	28.8678i	0.532674	+	0.922619i
$980$		0			0
$981$	−4.90608			−0.156639
$982$		0			0
$983$	−61.6550			−1.96649			−0.983244	−	0.182293i	$-0.941648\pi$
$983$	−61.6550			−1.96649			−0.983244	+	0.182293i	$0.941648\pi$
$984$		0			0
$985$	2.47040	+	4.27886i	0.0787136	+	0.136336i
$986$		0			0
$987$	0.914795	−	1.58447i	0.0291182	−	0.0504343i
$988$		0			0
$989$	6.57210	−	11.3832i	0.208981	−	0.361965i
$990$		0			0
$991$	8.92844			0.283621			0.141811	−	0.989894i	$-0.454708\pi$
$991$	8.92844			0.283621			0.141811	+	0.989894i	$0.454708\pi$
$992$		0			0
$993$	8.75730	+	15.1681i	0.277904	+	0.481344i
$994$		0			0
$995$	0.0703108	−	0.121782i	0.00222900	−	0.00386074i
$996$		0			0
$997$	−13.3351			−0.422327			−0.211163	−	0.977451i	$-0.567725\pi$
$997$	−13.3351			−0.422327			−0.211163	+	0.977451i	$0.567725\pi$
$998$		0			0
$999$	1.60504	−	2.78000i	0.0507811	−	0.0879554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.i.e.565.3	yes	8
3.2	odd	2		2412.2.l.f.1369.2		8
67.37	even	3	inner	804.2.i.e.37.3	✓	8
201.104	odd	6		2412.2.l.f.37.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.e.37.3	✓	8	67.37	even	3	inner
804.2.i.e.565.3	yes	8	1.1	even	1	trivial
2412.2.l.f.37.2		8	201.104	odd	6
2412.2.l.f.1369.2		8	3.2	odd	2

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +0.238118 q^{5} +(-1.47881 - 2.56138i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +0.238118 q^{5} +(-1.47881 - 2.56138i) q^{7} +1.00000 q^{9} +(-2.02165 - 3.50159i) q^{11} +(0.0288087 - 0.0498982i) q^{13} +0.238118 q^{15} +(-0.830946 + 1.43924i) q^{17} +(3.66951 - 6.35578i) q^{19} +(-1.47881 - 2.56138i) q^{21} +(1.50000 - 2.59808i) q^{23} -4.94330 q^{25} +1.00000 q^{27} +(-1.61906 - 2.80429i) q^{29} +(0.302137 + 0.523316i) q^{31} +(-2.02165 - 3.50159i) q^{33} +(-0.352132 - 0.609911i) q^{35} +(1.60504 - 2.78000i) q^{37} +(0.0288087 - 0.0498982i) q^{39} +(4.35259 + 7.53891i) q^{41} +4.38140 q^{43} +0.238118 q^{45} +(0.309300 + 0.535724i) q^{47} +(-0.873778 + 1.51343i) q^{49} +(-0.830946 + 1.43924i) q^{51} -6.01009 q^{53} +(-0.481390 - 0.833793i) q^{55} +(3.66951 - 6.35578i) q^{57} +6.33903 q^{59} +(4.37882 - 7.58434i) q^{61} +(-1.47881 - 2.56138i) q^{63} +(0.00685988 - 0.0118817i) q^{65} +(-2.57210 + 7.77073i) q^{67} +(1.50000 - 2.59808i) q^{69} +(5.54329 + 9.60126i) q^{71} +(3.87424 - 6.71037i) q^{73} -4.94330 q^{75} +(-5.97927 + 10.3564i) q^{77} +(-5.35259 - 9.27096i) q^{79} +1.00000 q^{81} +(-4.55045 + 7.88162i) q^{83} +(-0.197863 + 0.342709i) q^{85} +(-1.61906 - 2.80429i) q^{87} -8.24419 q^{89} -0.170411 q^{91} +(0.302137 + 0.523316i) q^{93} +(0.873778 - 1.51343i) q^{95} +(1.28307 - 2.22234i) q^{97} +(-2.02165 - 3.50159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 - 6 * q^5 + 8 * q^9	\( 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9} + 3 q^{11} - 2 q^{13} - 6 q^{15} - q^{17} + 4 q^{19} + 12 q^{23} + 18 q^{25} + 8 q^{27} - 9 q^{29} - q^{31} + 3 q^{33} - 9 q^{35} + 14 q^{37} - 2 q^{39} + 10 q^{41} + 8 q^{43} - 6 q^{45} + 16 q^{47} + 6 q^{49} - q^{51} - 12 q^{53} + 4 q^{55} + 4 q^{57} + 4 q^{61} - 22 q^{65} + 20 q^{67} + 12 q^{69} + 6 q^{71} - 13 q^{73} + 18 q^{75} - 5 q^{77} - 18 q^{79} + 8 q^{81} - 15 q^{83} - 5 q^{85} - 9 q^{87} - 4 q^{89} - 34 q^{91} - q^{93} - 6 q^{95} + 30 q^{97} + 3 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 6 * q^5 + 8 * q^9 + 3 * q^11 - 2 * q^13 - 6 * q^15 - q^17 + 4 * q^19 + 12 * q^23 + 18 * q^25 + 8 * q^27 - 9 * q^29 - q^31 + 3 * q^33 - 9 * q^35 + 14 * q^37 - 2 * q^39 + 10 * q^41 + 8 * q^43 - 6 * q^45 + 16 * q^47 + 6 * q^49 - q^51 - 12 * q^53 + 4 * q^55 + 4 * q^57 + 4 * q^61 - 22 * q^65 + 20 * q^67 + 12 * q^69 + 6 * q^71 - 13 * q^73 + 18 * q^75 - 5 * q^77 - 18 * q^79 + 8 * q^81 - 15 * q^83 - 5 * q^85 - 9 * q^87 - 4 * q^89 - 34 * q^91 - q^93 - 6 * q^95 + 30 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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