LMFDB - Embedded newform 804.2.i.e.565.4

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			565.4
Root			$-0.150216 + 0.260181i$ of defining polynomial
Character	$\chi$	$=$	804.565
Dual form			804.2.i.e.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +2.90974 q^{5} +(-0.217351 - 0.376462i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +2.90974 q^{5} +(-0.217351 - 0.376462i) q^{7} +1.00000 q^{9} +(2.53795 + 4.39586i) q^{11} +(-1.58730 + 2.74929i) q^{13} +2.90974 q^{15} +(0.150216 - 0.260181i) q^{17} +(-1.17039 + 2.02717i) q^{19} +(-0.217351 - 0.376462i) q^{21} +(1.50000 - 2.59808i) q^{23} +3.46659 q^{25} +1.00000 q^{27} +(-2.95487 - 5.11799i) q^{29} +(0.937089 + 1.62309i) q^{31} +(2.53795 + 4.39586i) q^{33} +(-0.632434 - 1.09541i) q^{35} +(4.62287 - 8.00704i) q^{37} +(-1.58730 + 2.74929i) q^{39} +(-1.18817 - 2.05797i) q^{41} -2.77547 q^{43} +2.90974 q^{45} +(3.88774 + 6.73376i) q^{47} +(3.40552 - 5.89853i) q^{49} +(0.150216 - 0.260181i) q^{51} -13.4644 q^{53} +(7.38478 + 12.7908i) q^{55} +(-1.17039 + 2.02717i) q^{57} -3.34077 q^{59} +(3.82666 - 6.62797i) q^{61} +(-0.217351 - 0.376462i) q^{63} +(-4.61864 + 7.99973i) q^{65} +(8.16321 + 0.601709i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-3.57590 - 6.19364i) q^{71} +(-6.22612 + 10.7840i) q^{73} +3.46659 q^{75} +(1.10325 - 1.91089i) q^{77} +(0.188167 + 0.325915i) q^{79} +1.00000 q^{81} +(1.62526 - 2.81503i) q^{83} +(0.437089 - 0.757060i) q^{85} +(-2.95487 - 5.11799i) q^{87} +13.9357 q^{89} +1.38001 q^{91} +(0.937089 + 1.62309i) q^{93} +(-3.40552 + 5.89853i) q^{95} +(-0.127092 + 0.220129i) q^{97} +(2.53795 + 4.39586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.90974			1.30128			0.650638	−	0.759388i	$-0.274502\pi$
$5$	2.90974			1.30128			0.650638	+	0.759388i	$0.274502\pi$
$6$		0			0
$7$	−0.217351	−	0.376462i	−0.0821508	−	0.142289i	0.822023	−	0.569455i	$-0.192846\pi$
$7$	−0.217351	−	0.376462i	−0.0821508	−	0.142289i	−0.904174	+	0.427165i	$0.859512\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.53795	+	4.39586i	0.765221	+	1.32540i	0.940130	+	0.340817i	$0.110704\pi$
$11$	2.53795	+	4.39586i	0.765221	+	1.32540i	−0.174909	+	0.984585i	$0.555963\pi$
$12$		0			0
$13$	−1.58730	+	2.74929i	−0.440239	+	0.762516i	−0.997707	−	0.0676821i	$-0.978440\pi$
$13$	−1.58730	+	2.74929i	−0.440239	+	0.762516i	0.557468	+	0.830198i	$0.311773\pi$
$14$		0			0
$15$	2.90974			0.751292
$16$		0			0
$17$	0.150216	−	0.260181i	0.0364326	−	0.0631032i	−0.847234	−	0.531220i	$-0.821734\pi$
$17$	0.150216	−	0.260181i	0.0364326	−	0.0631032i	0.883667	+	0.468116i	$0.155067\pi$
$18$		0			0
$19$	−1.17039	+	2.02717i	−0.268505	+	0.465064i	−0.968476	−	0.249107i	$-0.919863\pi$
$19$	−1.17039	+	2.02717i	−0.268505	+	0.465064i	0.699971	+	0.714171i	$0.253196\pi$
$20$		0			0
$21$	−0.217351	−	0.376462i	−0.0474298	−	0.0821508i
$22$		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
$25$	3.46659			0.693319
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.95487	−	5.11799i	−0.548706	−	0.950386i	−0.998364	−	0.0571853i	$-0.981787\pi$
$29$	−2.95487	−	5.11799i	−0.548706	−	0.950386i	0.449658	−	0.893201i	$-0.351546\pi$
$30$		0			0
$31$	0.937089	+	1.62309i	0.168306	+	0.291515i	0.937824	−	0.347110i	$-0.112837\pi$
$31$	0.937089	+	1.62309i	0.168306	+	0.291515i	−0.769518	+	0.638625i	$0.779504\pi$
$32$		0			0
$33$	2.53795	+	4.39586i	0.441801	+	0.765221i
$34$		0			0
$35$	−0.632434	−	1.09541i	−0.106901	−	0.185158i
$36$		0			0
$37$	4.62287	−	8.00704i	0.759995	−	1.31635i	−0.182858	−	0.983139i	$-0.558535\pi$
$37$	4.62287	−	8.00704i	0.759995	−	1.31635i	0.942853	−	0.333210i	$-0.108132\pi$
$38$		0			0
$39$	−1.58730	+	2.74929i	−0.254172	+	0.440239i
$40$		0			0
$41$	−1.18817	−	2.05797i	−0.185561	−	0.321400i	0.758205	−	0.652017i	$-0.226077\pi$
$41$	−1.18817	−	2.05797i	−0.185561	−	0.321400i	−0.943765	+	0.330616i	$0.892743\pi$
$42$		0			0
$43$	−2.77547			−0.423255			−0.211628	−	0.977350i	$-0.567876\pi$
$43$	−2.77547			−0.423255			−0.211628	+	0.977350i	$0.567876\pi$
$44$		0			0
$45$	2.90974			0.433759
$46$		0			0
$47$	3.88774	+	6.73376i	0.567085	+	0.982219i	0.996852	+	0.0792798i	$0.0252621\pi$
$47$	3.88774	+	6.73376i	0.567085	+	0.982219i	−0.429768	+	0.902939i	$0.641405\pi$
$48$		0			0
$49$	3.40552	−	5.89853i	0.486502	−	0.842647i
$50$		0			0
$51$	0.150216	−	0.260181i	0.0210344	−	0.0364326i
$52$		0			0
$53$	−13.4644			−1.84947			−0.924736	−	0.380610i	$-0.875714\pi$
$53$	−13.4644			−1.84947			−0.924736	+	0.380610i	$0.875714\pi$
$54$		0			0
$55$	7.38478	+	12.7908i	0.995764	+	1.72471i
$56$		0			0
$57$	−1.17039	+	2.02717i	−0.155021	+	0.268505i
$58$		0			0
$59$	−3.34077			−0.434931			−0.217466	−	0.976068i	$-0.569779\pi$
$59$	−3.34077			−0.434931			−0.217466	+	0.976068i	$0.569779\pi$
$60$		0			0
$61$	3.82666	−	6.62797i	0.489954	−	0.848625i	−0.509980	−	0.860187i	$-0.670347\pi$
$61$	3.82666	−	6.62797i	0.489954	−	0.848625i	0.999933	+	0.0115619i	$0.00368036\pi$
$62$		0			0
$63$	−0.217351	−	0.376462i	−0.0273836	−	0.0474298i
$64$		0			0
$65$	−4.61864	+	7.99973i	−0.572872	+	0.992244i
$66$		0			0
$67$	8.16321	+	0.601709i	0.997294	+	0.0735104i
$67$	8.16321	+	0.601709i	0.997294	+	0.0735104i
$68$		0			0
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$	−3.57590	−	6.19364i	−0.424382	−	0.735050i	0.571981	−	0.820267i	$-0.306175\pi$
$71$	−3.57590	−	6.19364i	−0.424382	−	0.735050i	−0.996362	+	0.0852165i	$0.972842\pi$
$72$		0			0
$73$	−6.22612	+	10.7840i	−0.728712	+	1.26217i	0.228716	+	0.973493i	$0.426547\pi$
$73$	−6.22612	+	10.7840i	−0.728712	+	1.26217i	−0.957428	+	0.288673i	$0.906786\pi$
$74$		0			0
$75$	3.46659			0.400288
$76$		0			0
$77$	1.10325	−	1.91089i	0.125727	−	0.217766i
$78$		0			0
$79$	0.188167	+	0.325915i	0.0211704	+	0.0366683i	0.876417	−	0.481554i	$-0.159927\pi$
$79$	0.188167	+	0.325915i	0.0211704	+	0.0366683i	−0.855246	+	0.518222i	$0.826594\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	1.62526	−	2.81503i	0.178395	−	0.308989i	−0.762936	−	0.646474i	$-0.776243\pi$
$83$	1.62526	−	2.81503i	0.178395	−	0.308989i	0.941331	+	0.337485i	$0.109576\pi$
$84$		0			0
$85$	0.437089	−	0.757060i	0.0474089	−	0.0821147i
$86$		0			0
$87$	−2.95487	−	5.11799i	−0.316795	−	0.548706i
$88$		0			0
$89$	13.9357			1.47718			0.738592	−	0.674153i	$-0.235491\pi$
$89$	13.9357			1.47718			0.738592	+	0.674153i	$0.235491\pi$
$90$		0			0
$91$	1.38001			0.144664
$92$		0			0
$93$	0.937089	+	1.62309i	0.0971716	+	0.168306i
$94$		0			0
$95$	−3.40552	+	5.89853i	−0.349399	+	0.605176i
$96$		0			0
$97$	−0.127092	+	0.220129i	−0.0129042	+	0.0223507i	−0.872405	−	0.488783i	$-0.837441\pi$
$97$	−0.127092	+	0.220129i	−0.0129042	+	0.0223507i	0.859501	+	0.511134i	$0.170774\pi$
$98$		0			0
$99$	2.53795	+	4.39586i	0.255074	+	0.441801i
$100$		0			0
$101$	−3.58124	−	6.20290i	−0.356347	−	0.617211i	0.631000	−	0.775783i	$-0.282645\pi$
$101$	−3.58124	−	6.20290i	−0.356347	−	0.617211i	−0.987348	+	0.158571i	$0.949311\pi$
$102$		0			0
$103$	2.26064	+	3.91555i	0.222748	+	0.385811i	0.955641	−	0.294533i	$-0.0951640\pi$
$103$	2.26064	+	3.91555i	0.222748	+	0.385811i	−0.732894	+	0.680343i	$0.761831\pi$
$104$		0			0
$105$	−0.632434	−	1.09541i	−0.0617192	−	0.106901i
$106$		0			0
$107$	−14.8099			−1.43173			−0.715864	−	0.698240i	$-0.753967\pi$
$107$	−14.8099			−1.43173			−0.715864	+	0.698240i	$0.753967\pi$
$108$		0			0
$109$	19.2362			1.84249			0.921245	−	0.388983i	$-0.127174\pi$
$109$	19.2362			1.84249			0.921245	+	0.388983i	$0.127174\pi$
$110$		0			0
$111$	4.62287	−	8.00704i	0.438783	−	0.759995i
$112$		0			0
$113$	−10.3336	−	17.8983i	−0.972103	−	1.68373i	−0.689183	−	0.724587i	$-0.742030\pi$
$113$	−10.3336	−	17.8983i	−0.972103	−	1.68373i	−0.282920	−	0.959144i	$-0.591303\pi$
$114$		0			0
$115$	4.36461	−	7.55973i	0.407002	−	0.704948i
$116$		0			0
$117$	−1.58730	+	2.74929i	−0.146746	+	0.254172i
$118$		0			0
$119$	−0.130598			−0.0119719
$120$		0			0
$121$	−7.38239	+	12.7867i	−0.671127	+	1.16243i
$122$		0			0
$123$	−1.18817	−	2.05797i	−0.107133	−	0.185561i
$124$		0			0
$125$	−4.46182			−0.399077
$126$		0			0
$127$	1.03612	+	1.79460i	0.0919404	+	0.159245i	0.908328	−	0.418260i	$-0.137360\pi$
$127$	1.03612	+	1.79460i	0.0919404	+	0.159245i	−0.816387	+	0.577505i	$0.804026\pi$
$128$		0			0
$129$	−2.77547			−0.244367
$130$		0			0
$131$	2.64855			0.231404			0.115702	−	0.993284i	$-0.463088\pi$
$131$	2.64855			0.231404			0.115702	+	0.993284i	$0.463088\pi$
$132$		0			0
$133$	1.01754			0.0882315
$134$		0			0
$135$	2.90974			0.250431
$136$		0			0
$137$	−7.37156			−0.629795			−0.314897	−	0.949126i	$-0.601970\pi$
$137$	−7.37156			−0.629795			−0.314897	+	0.949126i	$0.601970\pi$
$138$		0			0
$139$	−8.79301			−0.745813			−0.372907	−	0.927869i	$-0.621639\pi$
$139$	−8.79301			−0.745813			−0.372907	+	0.927869i	$0.621639\pi$
$140$		0			0
$141$	3.88774	+	6.73376i	0.327406	+	0.567085i
$142$		0			0
$143$	−16.1140			−1.34752
$144$		0			0
$145$	−8.59791	−	14.8920i	−0.714017	−	1.23671i
$146$		0			0
$147$	3.40552	−	5.89853i	0.280882	−	0.486502i
$148$		0			0
$149$	−8.92186			−0.730907			−0.365454	−	0.930830i	$-0.619086\pi$
$149$	−8.92186			−0.730907			−0.365454	+	0.930830i	$0.619086\pi$
$150$		0			0
$151$	−7.08619	+	12.2736i	−0.576666	+	0.998814i	0.419193	+	0.907897i	$0.362313\pi$
$151$	−7.08619	+	12.2736i	−0.576666	+	0.998814i	−0.995858	+	0.0909169i	$0.971020\pi$
$152$		0			0
$153$	0.150216	−	0.260181i	0.0121442	−	0.0210344i
$154$		0			0
$155$	2.72669	+	4.72276i	0.219013	+	0.379341i
$156$		0			0
$157$	−0.628210	+	1.08809i	−0.0501366	+	0.0868392i	−0.890005	−	0.455952i	$-0.849299\pi$
$157$	−0.628210	+	1.08809i	−0.0501366	+	0.0868392i	0.839868	+	0.542791i	$0.182632\pi$
$158$		0			0
$159$	−13.4644			−1.06779
$160$		0			0
$161$	−1.30410			−0.102778
$162$		0			0
$163$	0.479831	+	0.831091i	0.0375832	+	0.0650961i	0.884205	−	0.467099i	$-0.154701\pi$
$163$	0.479831	+	0.831091i	0.0375832	+	0.0650961i	−0.846622	+	0.532195i	$0.821367\pi$
$164$		0			0
$165$	7.38478	+	12.7908i	0.574904	+	0.995764i
$166$		0			0
$167$	−2.61681	−	4.53245i	−0.202495	−	0.350731i	0.746837	−	0.665007i	$-0.231572\pi$
$167$	−2.61681	−	4.53245i	−0.202495	−	0.350731i	−0.949332	+	0.314276i	$0.898238\pi$
$168$		0			0
$169$	1.46093	+	2.53041i	0.112379	+	0.194647i
$170$		0			0
$171$	−1.17039	+	2.02717i	−0.0895016	+	0.155021i
$172$		0			0
$173$	−0.912144	+	1.57988i	−0.0693490	+	0.120116i	−0.898615	−	0.438738i	$-0.855426\pi$
$173$	−0.912144	+	1.57988i	−0.0693490	+	0.120116i	0.829266	+	0.558854i	$0.188759\pi$
$174$		0			0
$175$	−0.753466	−	1.30504i	−0.0569567	−	0.0986518i
$176$		0			0
$177$	−3.34077			−0.251108
$178$		0			0
$179$	−17.5323			−1.31042			−0.655212	−	0.755445i	$-0.727421\pi$
$179$	−17.5323			−1.31042			−0.655212	+	0.755445i	$0.727421\pi$
$180$		0			0
$181$	−5.18282	−	8.97692i	−0.385236	−	0.667249i	0.606566	−	0.795033i	$-0.292547\pi$
$181$	−5.18282	−	8.97692i	−0.385236	−	0.667249i	−0.991802	+	0.127785i	$0.959213\pi$
$182$		0			0
$183$	3.82666	−	6.62797i	0.282875	−	0.489954i
$184$		0			0
$185$	13.4513	−	23.2984i	0.988963	−	1.71293i
$186$		0			0
$187$	1.52496			0.111516
$188$		0			0
$189$	−0.217351	−	0.376462i	−0.0158099	−	0.0273836i
$190$		0			0
$191$	−0.771248	+	1.33584i	−0.0558055	+	0.0966580i	−0.892579	−	0.450892i	$-0.851106\pi$
$191$	−0.771248	+	1.33584i	−0.0558055	+	0.0966580i	0.836773	+	0.547550i	$0.184439\pi$
$192$		0			0
$193$	−26.1587			−1.88294			−0.941471	−	0.337095i	$-0.890556\pi$
$193$	−26.1587			−1.88294			−0.941471	+	0.337095i	$0.890556\pi$
$194$		0			0
$195$	−4.61864	+	7.99973i	−0.330748	+	0.572872i
$196$		0			0
$197$	−5.54672	−	9.60720i	−0.395187	−	0.684485i	0.597938	−	0.801543i	$-0.295987\pi$
$197$	−5.54672	−	9.60720i	−0.395187	−	0.684485i	−0.993125	+	0.117058i	$0.962654\pi$
$198$		0			0
$199$	5.55573	−	9.62281i	0.393835	−	0.682143i	−0.599116	−	0.800662i	$-0.704481\pi$
$199$	5.55573	−	9.62281i	0.393835	−	0.682143i	0.992952	+	0.118519i	$0.0378146\pi$
$200$		0			0
$201$	8.16321	+	0.601709i	0.575788	+	0.0424413i
$202$		0			0
$203$	−1.28449	+	2.22479i	−0.0901532	+	0.156150i
$204$		0			0
$205$	−3.45726	−	5.98815i	−0.241465	−	0.418230i
$206$		0			0
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$		0			0
$209$	−11.8815			−0.821862
$210$		0			0
$211$	5.41213	−	9.37408i	0.372586	−	0.645338i	−0.617376	−	0.786668i	$-0.711804\pi$
$211$	5.41213	−	9.37408i	0.372586	−	0.645338i	0.989963	+	0.141330i	$0.0451377\pi$
$212$		0			0
$213$	−3.57590	−	6.19364i	−0.245017	−	0.424382i
$214$		0			0
$215$	−8.07590			−0.550772
$216$		0			0
$217$	0.407353	−	0.705557i	0.0276530	−	0.0478963i
$218$		0			0
$219$	−6.22612	+	10.7840i	−0.420722	+	0.728712i
$220$		0			0
$221$	0.476876	+	0.825973i	0.0320781	+	0.0555610i
$222$		0			0
$223$	2.65332			0.177679			0.0888397	−	0.996046i	$-0.471684\pi$
$223$	2.65332			0.177679			0.0888397	+	0.996046i	$0.471684\pi$
$224$		0			0
$225$	3.46659			0.231106
$226$		0			0
$227$	12.9821	+	22.4857i	0.861655	+	1.49243i	0.870331	+	0.492467i	$0.163905\pi$
$227$	12.9821	+	22.4857i	0.861655	+	1.49243i	−0.00867618	+	0.999962i	$0.502762\pi$
$228$		0			0
$229$	8.83782	−	15.3075i	0.584019	−	1.01155i	−0.410978	−	0.911645i	$-0.634813\pi$
$229$	8.83782	−	15.3075i	0.584019	−	1.01155i	0.994997	−	0.0999056i	$-0.0318541\pi$
$230$		0			0
$231$	1.10325	−	1.91089i	0.0725885	−	0.125727i
$232$		0			0
$233$	−0.711843	−	1.23295i	−0.0466344	−	0.0807731i	0.841766	−	0.539843i	$-0.181516\pi$
$233$	−0.711843	−	1.23295i	−0.0466344	−	0.0807731i	−0.888400	+	0.459069i	$0.848183\pi$
$234$		0			0
$235$	11.3123	+	19.5935i	0.737933	+	1.27814i
$236$		0			0
$237$	0.188167	+	0.325915i	0.0122228	+	0.0211704i
$238$		0			0
$239$	11.3662	+	19.6868i	0.735218	+	1.27344i	0.954627	+	0.297803i	$0.0962538\pi$
$239$	11.3662	+	19.6868i	0.735218	+	1.27344i	−0.219409	+	0.975633i	$0.570413\pi$
$240$		0			0
$241$	2.39069			0.153998			0.0769989	−	0.997031i	$-0.475466\pi$
$241$	2.39069			0.153998			0.0769989	+	0.997031i	$0.475466\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	9.90917	−	17.1632i	0.633074	−	1.09652i
$246$		0			0
$247$	−3.71551	−	6.43546i	−0.236413	−	0.409479i
$248$		0			0
$249$	1.62526	−	2.81503i	0.102996	−	0.178395i
$250$		0			0
$251$	−3.69167	+	6.39417i	−0.233016	+	0.403596i	−0.958694	−	0.284438i	$-0.908193\pi$
$251$	−3.69167	+	6.39417i	−0.233016	+	0.403596i	0.725678	+	0.688034i	$0.241526\pi$
$252$		0			0
$253$	15.2277			0.957358
$254$		0			0
$255$	0.437089	−	0.757060i	0.0273716	−	0.0474089i
$256$		0			0
$257$	0.691673	+	1.19801i	0.0431454	+	0.0747300i	0.886792	−	0.462169i	$-0.152929\pi$
$257$	0.691673	+	1.19801i	0.0431454	+	0.0747300i	−0.843646	+	0.536899i	$0.819595\pi$
$258$		0			0
$259$	−4.01913			−0.249737
$260$		0			0
$261$	−2.95487	−	5.11799i	−0.182902	−	0.316795i
$262$		0			0
$263$	7.31733			0.451206			0.225603	−	0.974219i	$-0.427565\pi$
$263$	7.31733			0.451206			0.225603	+	0.974219i	$0.427565\pi$
$264$		0			0
$265$	−39.1778			−2.40667
$266$		0			0
$267$	13.9357			0.852852
$268$		0			0
$269$	3.82426			0.233169			0.116585	−	0.993181i	$-0.462805\pi$
$269$	3.82426			0.233169			0.116585	+	0.993181i	$0.462805\pi$
$270$		0			0
$271$	0.320204			0.0194510			0.00972550	−	0.999953i	$-0.496904\pi$
$271$	0.320204			0.0194510			0.00972550	+	0.999953i	$0.496904\pi$
$272$		0			0
$273$	1.38001			0.0835218
$274$		0			0
$275$	8.79804	+	15.2387i	0.530542	+	0.918926i
$276$		0			0
$277$	−15.2079			−0.913756			−0.456878	−	0.889529i	$-0.651032\pi$
$277$	−15.2079			−0.913756			−0.456878	+	0.889529i	$0.651032\pi$
$278$		0			0
$279$	0.937089	+	1.62309i	0.0561020	+	0.0971716i
$280$		0			0
$281$	3.80888	−	6.59717i	0.227219	−	0.393554i	−0.729764	−	0.683699i	$-0.760370\pi$
$281$	3.80888	−	6.59717i	0.227219	−	0.393554i	0.956983	+	0.290145i	$0.0937035\pi$
$282$		0			0
$283$	−22.2695			−1.32378			−0.661892	−	0.749600i	$-0.730246\pi$
$283$	−22.2695			−1.32378			−0.661892	+	0.749600i	$0.730246\pi$
$284$		0			0
$285$	−3.40552	+	5.89853i	−0.201725	+	0.349399i
$286$		0			0
$287$	−0.516497	+	0.894600i	−0.0304879	+	0.0528066i
$288$		0			0
$289$	8.45487	+	14.6443i	0.497345	+	0.861427i
$290$		0			0
$291$	−0.127092	+	0.220129i	−0.00745024	+	0.0129042i
$292$		0			0
$293$	−13.0509			−0.762439			−0.381220	−	0.924484i	$-0.624496\pi$
$293$	−13.0509			−0.762439			−0.381220	+	0.924484i	$0.624496\pi$
$294$		0			0
$295$	−9.72078			−0.565965
$296$		0			0
$297$	2.53795	+	4.39586i	0.147267	+	0.255074i
$298$		0			0
$299$	4.76191	+	8.24788i	0.275389	+	0.476987i
$300$		0			0
$301$	0.603250	+	1.04486i	0.0347708	+	0.0602247i
$302$		0			0
$303$	−3.58124	−	6.20290i	−0.205737	−	0.356347i
$304$		0			0
$305$	11.1346	−	19.2857i	0.637565	−	1.10429i
$306$		0			0
$307$	−3.45646	+	5.98676i	−0.197271	+	0.341683i	−0.947643	−	0.319333i	$-0.896541\pi$
$307$	−3.45646	+	5.98676i	−0.197271	+	0.341683i	0.750372	+	0.661016i	$0.229874\pi$
$308$		0			0
$309$	2.26064	+	3.91555i	0.128604	+	0.222748i
$310$		0			0
$311$	−19.7673			−1.12090			−0.560451	−	0.828188i	$-0.689372\pi$
$311$	−19.7673			−1.12090			−0.560451	+	0.828188i	$0.689372\pi$
$312$		0			0
$313$	11.3825			0.643379			0.321690	−	0.946845i	$-0.395749\pi$
$313$	11.3825			0.643379			0.321690	+	0.946845i	$0.395749\pi$
$314$		0			0
$315$	−0.632434	−	1.09541i	−0.0356336	−	0.0617192i
$316$		0			0
$317$	1.78098	−	3.08475i	0.100030	−	0.173257i	−0.811667	−	0.584121i	$-0.801440\pi$
$317$	1.78098	−	3.08475i	0.100030	−	0.173257i	0.911697	+	0.410864i	$0.134773\pi$
$318$		0			0
$319$	14.9986	−	25.9784i	0.839762	−	1.45451i
$320$		0			0
$321$	−14.8099			−0.826608
$322$		0			0
$323$	0.351620	+	0.609024i	0.0195647	+	0.0338870i
$324$		0			0
$325$	−5.50254	+	9.53067i	−0.305226	+	0.528667i
$326$		0			0
$327$	19.2362			1.06376
$328$		0			0
$329$	1.69000	−	2.92717i	0.0931729	−	0.161380i
$330$		0			0
$331$	−3.46252	−	5.99726i	−0.190317	−	0.329639i	0.755038	−	0.655681i	$-0.227618\pi$
$331$	−3.46252	−	5.99726i	−0.190317	−	0.329639i	−0.945355	+	0.326042i	$0.894285\pi$
$332$		0			0
$333$	4.62287	−	8.00704i	0.253332	−	0.438783i
$334$		0			0
$335$	23.7528	+	1.75082i	1.29776	+	0.0956574i
$336$		0			0
$337$	2.20356	−	3.81668i	0.120036	−	0.207908i	−0.799746	−	0.600339i	$-0.795032\pi$
$337$	2.20356	−	3.81668i	0.120036	−	0.207908i	0.919781	+	0.392431i	$0.128366\pi$
$338$		0			0
$339$	−10.3336	−	17.8983i	−0.561244	−	0.972103i
$340$		0			0
$341$	−4.75657	+	8.23862i	−0.257583	+	0.446146i
$342$		0			0
$343$	−6.00367			−0.324168
$344$		0			0
$345$	4.36461	−	7.55973i	0.234983	−	0.407002i
$346$		0			0
$347$	1.07007	+	1.85342i	0.0574446	+	0.0994969i	0.893318	−	0.449426i	$-0.148371\pi$
$347$	1.07007	+	1.85342i	0.0574446	+	0.0994969i	−0.835873	+	0.548923i	$0.815038\pi$
$348$		0			0
$349$	−12.8238			−0.686442			−0.343221	−	0.939255i	$-0.611518\pi$
$349$	−12.8238			−0.686442			−0.343221	+	0.939255i	$0.611518\pi$
$350$		0			0
$351$	−1.58730	+	2.74929i	−0.0847240	+	0.146746i
$352$		0			0
$353$	9.45407	−	16.3749i	0.503190	−	0.871550i	−0.496804	−	0.867863i	$-0.665493\pi$
$353$	9.45407	−	16.3749i	0.503190	−	0.871550i	0.999993	−	0.00368684i	$-0.00117356\pi$
$354$		0			0
$355$	−10.4050	−	18.0219i	−0.552237	−	0.956503i
$356$		0			0
$357$	−0.130598			−0.00691197
$358$		0			0
$359$	33.4999			1.76806			0.884029	−	0.467432i	$-0.154821\pi$
$359$	33.4999			1.76806			0.884029	+	0.467432i	$0.154821\pi$
$360$		0			0
$361$	6.76040	+	11.7094i	0.355810	+	0.616282i
$362$		0			0
$363$	−7.38239	+	12.7867i	−0.387475	+	0.671127i
$364$		0			0
$365$	−18.1164	+	31.3785i	−0.948255	+	1.64243i
$366$		0			0
$367$	18.6892	+	32.3706i	0.975568	+	1.68973i	0.678049	+	0.735017i	$0.262826\pi$
$367$	18.6892	+	32.3706i	0.975568	+	1.68973i	0.297519	+	0.954716i	$0.403841\pi$
$368$		0			0
$369$	−1.18817	−	2.05797i	−0.0618535	−	0.107133i
$370$		0			0
$371$	2.92649	+	5.06882i	0.151936	+	0.263160i
$372$		0			0
$373$	11.5188	+	19.9512i	0.596422	+	1.03303i	0.993345	+	0.115181i	$0.0367448\pi$
$373$	11.5188	+	19.9512i	0.596422	+	1.03303i	−0.396923	+	0.917852i	$0.629922\pi$
$374$		0			0
$375$	−4.46182			−0.230407
$376$		0			0
$377$	18.7611			0.966247
$378$		0			0
$379$	−5.35910	+	9.28224i	−0.275279	+	0.476797i	−0.970205	−	0.242284i	$-0.922103\pi$
$379$	−5.35910	+	9.28224i	−0.275279	+	0.476797i	0.694927	+	0.719081i	$0.255437\pi$
$380$		0			0
$381$	1.03612	+	1.79460i	0.0530818	+	0.0919404i
$382$		0			0
$383$	6.66688	−	11.5474i	0.340662	−	0.590043i	−0.643894	−	0.765115i	$-0.722682\pi$
$383$	6.66688	−	11.5474i	0.340662	−	0.590043i	0.984556	+	0.175071i	$0.0560156\pi$
$384$		0			0
$385$	3.21017	−	5.56018i	0.163606	−	0.283373i
$386$		0			0
$387$	−2.77547			−0.141085
$388$		0			0
$389$	6.72214	−	11.6431i	0.340826	−	0.590328i	−0.643760	−	0.765227i	$-0.722627\pi$
$389$	6.72214	−	11.6431i	0.340826	−	0.590328i	0.984586	+	0.174899i	$0.0559599\pi$
$390$		0			0
$391$	−0.450647	−	0.780543i	−0.0227902	−	0.0394738i
$392$		0			0
$393$	2.64855			0.133601
$394$		0			0
$395$	0.547517	+	0.948327i	0.0275486	+	0.0477155i
$396$		0			0
$397$	33.1033			1.66141			0.830704	−	0.556714i	$-0.187938\pi$
$397$	33.1033			1.66141			0.830704	+	0.556714i	$0.187938\pi$
$398$		0			0
$399$	1.01754			0.0509405
$400$		0			0
$401$	−1.48031			−0.0739231			−0.0369615	−	0.999317i	$-0.511768\pi$
$401$	−1.48031			−0.0739231			−0.0369615	+	0.999317i	$0.511768\pi$
$402$		0			0
$403$	−5.94978			−0.296380
$404$		0			0
$405$	2.90974			0.144586
$406$		0			0
$407$	46.9305			2.32626
$408$		0			0
$409$	3.04880	+	5.28068i	0.150754	+	0.261113i	0.931505	−	0.363729i	$-0.118497\pi$
$409$	3.04880	+	5.28068i	0.150754	+	0.261113i	−0.780751	+	0.624842i	$0.785163\pi$
$410$		0			0
$411$	−7.37156			−0.363612
$412$		0			0
$413$	0.726118	+	1.25767i	0.0357299	+	0.0618861i
$414$		0			0
$415$	4.72907	−	8.19099i	0.232141	−	0.402080i
$416$		0			0
$417$	−8.79301			−0.430595
$418$		0			0
$419$	−17.3216	+	30.0019i	−0.846217	+	1.46569i	0.0383437	+	0.999265i	$0.487792\pi$
$419$	−17.3216	+	30.0019i	−0.846217	+	1.46569i	−0.884560	+	0.466426i	$0.845542\pi$
$420$		0			0
$421$	2.79477	−	4.84068i	0.136209	−	0.235920i	−0.789850	−	0.613300i	$-0.789842\pi$
$421$	2.79477	−	4.84068i	0.136209	−	0.235920i	0.926059	+	0.377380i	$0.123175\pi$
$422$		0			0
$423$	3.88774	+	6.73376i	0.189028	+	0.327406i
$424$		0			0
$425$	0.520737	−	0.901942i	0.0252594	−	0.0437506i
$426$		0			0
$427$	−3.32691			−0.161000
$428$		0			0
$429$	−16.1140			−0.777991
$430$		0			0
$431$	6.76701	+	11.7208i	0.325955	+	0.564571i	0.981705	−	0.190407i	$-0.0609808\pi$
$431$	6.76701	+	11.7208i	0.325955	+	0.564571i	−0.655750	+	0.754978i	$0.727647\pi$
$432$		0			0
$433$	4.28392	+	7.41996i	0.205872	+	0.356581i	0.950410	−	0.310999i	$-0.100664\pi$
$433$	4.28392	+	7.41996i	0.205872	+	0.356581i	−0.744538	+	0.667580i	$0.767330\pi$
$434$		0			0
$435$	−8.59791	−	14.8920i	−0.412238	−	0.714017i
$436$		0			0
$437$	3.51116	+	6.08150i	0.167961	+	0.290918i
$438$		0			0
$439$	12.4306	−	21.5305i	0.593281	−	1.02759i	−0.400505	−	0.916294i	$-0.631165\pi$
$439$	12.4306	−	21.5305i	0.593281	−	1.02759i	0.993787	−	0.111299i	$-0.0355012\pi$
$440$		0			0
$441$	3.40552	−	5.89853i	0.162167	−	0.280882i
$442$		0			0
$443$	−7.60691	−	13.1755i	−0.361415	−	0.625989i	0.626779	−	0.779197i	$-0.284373\pi$
$443$	−7.60691	−	13.1755i	−0.361415	−	0.625989i	−0.988194	+	0.153208i	$0.951040\pi$
$444$		0			0
$445$	40.5493			1.92222
$446$		0			0
$447$	−8.92186			−0.421990
$448$		0			0
$449$	10.9950	+	19.0438i	0.518884	+	0.898734i	0.999759	+	0.0219448i	$0.00698582\pi$
$449$	10.9950	+	19.0438i	0.518884	+	0.898734i	−0.480875	+	0.876789i	$0.659681\pi$
$450$		0			0
$451$	6.03102	−	10.4460i	0.283990	−	0.491884i
$452$		0			0
$453$	−7.08619	+	12.2736i	−0.332938	+	0.576666i
$454$		0			0
$455$	4.01546			0.188248
$456$		0			0
$457$	19.2040	+	33.2624i	0.898327	+	1.55595i	0.829633	+	0.558310i	$0.188550\pi$
$457$	19.2040	+	33.2624i	0.898327	+	1.55595i	0.0686942	+	0.997638i	$0.478117\pi$
$458$		0			0
$459$	0.150216	−	0.260181i	0.00701147	−	0.0121442i
$460$		0			0
$461$	29.9544			1.39512			0.697558	−	0.716529i	$-0.254270\pi$
$461$	29.9544			1.39512			0.697558	+	0.716529i	$0.254270\pi$
$462$		0			0
$463$	16.8105	−	29.1166i	0.781248	−	1.35316i	−0.149967	−	0.988691i	$-0.547917\pi$
$463$	16.8105	−	29.1166i	0.781248	−	1.35316i	0.931215	−	0.364470i	$-0.118750\pi$
$464$		0			0
$465$	2.72669	+	4.72276i	0.126447	+	0.219013i
$466$		0			0
$467$	1.22669	−	2.12468i	0.0567642	−	0.0983185i	−0.836247	−	0.548353i	$-0.815255\pi$
$467$	1.22669	−	2.12468i	0.0567642	−	0.0983185i	0.893011	+	0.450035i	$0.148588\pi$
$468$		0			0
$469$	−1.54776	−	3.20392i	−0.0714688	−	0.147943i
$470$		0			0
$471$	−0.628210	+	1.08809i	−0.0289464	+	0.0501366i
$472$		0			0
$473$	−7.04401	−	12.2006i	−0.323884	−	0.560983i
$474$		0			0
$475$	−4.05725	+	7.02736i	−0.186159	+	0.322437i
$476$		0			0
$477$	−13.4644			−0.616490
$478$		0			0
$479$	−9.55149	+	16.5437i	−0.436419	+	0.755900i	−0.997410	−	0.0719219i	$-0.977087\pi$
$479$	−9.55149	+	16.5437i	−0.436419	+	0.755900i	0.560991	+	0.827822i	$0.310420\pi$
$480$		0			0
$481$	14.6758	+	25.4192i	0.669159	+	1.15902i
$482$		0			0
$483$	−1.30410			−0.0593388
$484$		0			0
$485$	−0.369804	+	0.640519i	−0.0167919	+	0.0290844i
$486$		0			0
$487$	11.6116	−	20.1119i	0.526173	−	0.911358i	−0.473363	−	0.880868i	$-0.656960\pi$
$487$	11.6116	−	20.1119i	0.526173	−	0.911358i	0.999535	−	0.0304899i	$-0.00970674\pi$
$488$		0			0
$489$	0.479831	+	0.831091i	0.0216987	+	0.0375832i
$490$		0			0
$491$	5.12726			0.231390			0.115695	−	0.993285i	$-0.463091\pi$
$491$	5.12726			0.231390			0.115695	+	0.993285i	$0.463091\pi$
$492$		0			0
$493$	−1.77547			−0.0799632
$494$		0			0
$495$	7.38478	+	12.7908i	0.331921	+	0.574904i
$496$		0			0
$497$	−1.55445	+	2.69238i	−0.0697266	+	0.120770i
$498$		0			0
$499$	−15.0962	+	26.1475i	−0.675800	+	1.17052i	0.300434	+	0.953803i	$0.402869\pi$
$499$	−15.0962	+	26.1475i	−0.675800	+	1.17052i	−0.976234	+	0.216718i	$0.930465\pi$
$500$		0			0
$501$	−2.61681	−	4.53245i	−0.116910	−	0.202495i
$502$		0			0
$503$	−13.8731	−	24.0288i	−0.618569	−	1.07139i	−0.989747	−	0.142831i	$-0.954379\pi$
$503$	−13.8731	−	24.0288i	−0.618569	−	1.07139i	0.371178	−	0.928562i	$-0.378954\pi$
$504$		0			0
$505$	−10.4205	−	18.0488i	−0.463706	−	0.803162i
$506$		0			0
$507$	1.46093	+	2.53041i	0.0648822	+	0.112379i
$508$		0			0
$509$	0.402809			0.0178542			0.00892710	−	0.999960i	$-0.497158\pi$
$509$	0.402809			0.0178542			0.00892710	+	0.999960i	$0.497158\pi$
$510$		0			0
$511$	5.41300			0.239457
$512$		0			0
$513$	−1.17039	+	2.02717i	−0.0516738	+	0.0895016i
$514$		0			0
$515$	6.57789	+	11.3932i	0.289856	+	0.502046i
$516$		0			0
$517$	−19.7338	+	34.1799i	−0.867890	+	1.50323i
$518$		0			0
$519$	−0.912144	+	1.57988i	−0.0400387	+	0.0693490i
$520$		0			0
$521$	−3.64010			−0.159476			−0.0797378	−	0.996816i	$-0.525408\pi$
$521$	−3.64010			−0.159476			−0.0797378	+	0.996816i	$0.525408\pi$
$522$		0			0
$523$	5.45599	−	9.45005i	0.238574	−	0.413222i	−0.721732	−	0.692173i	$-0.756653\pi$
$523$	5.45599	−	9.45005i	0.238574	−	0.413222i	0.960305	+	0.278951i	$0.0899868\pi$
$524$		0			0
$525$	−0.753466	−	1.30504i	−0.0328839	−	0.0569567i
$526$		0			0
$527$	0.563062			0.0245273
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	−3.34077			−0.144977
$532$		0			0
$533$	7.54393			0.326764
$534$		0			0
$535$	−43.0930			−1.86307
$536$		0			0
$537$	−17.5323			−0.756573
$538$		0			0
$539$	34.5721			1.48913
$540$		0			0
$541$	35.9727			1.54659			0.773294	−	0.634048i	$-0.218608\pi$
$541$	35.9727			1.54659			0.773294	+	0.634048i	$0.218608\pi$
$542$		0			0
$543$	−5.18282	−	8.97692i	−0.222416	−	0.385236i
$544$		0			0
$545$	55.9722			2.39759
$546$		0			0
$547$	−8.32219	−	14.4145i	−0.355831	−	0.616318i	0.631429	−	0.775434i	$-0.282469\pi$
$547$	−8.32219	−	14.4145i	−0.355831	−	0.616318i	−0.987260	+	0.159116i	$0.949136\pi$
$548$		0			0
$549$	3.82666	−	6.62797i	0.163318	−	0.282875i
$550$		0			0
$551$	13.8333			0.589320
$552$		0			0
$553$	0.0817964	−	0.141675i	0.00347834	−	0.00602465i
$554$		0			0
$555$	13.4513	−	23.2984i	0.570978	−	0.988963i
$556$		0			0
$557$	−0.0958410	−	0.166001i	−0.00406091	−	0.00703371i	0.863988	−	0.503513i	$-0.167959\pi$
$557$	−0.0958410	−	0.166001i	−0.00406091	−	0.00703371i	−0.868049	+	0.496479i	$0.834626\pi$
$558$		0			0
$559$	4.40552	−	7.63058i	0.186334	−	0.322739i
$560$		0			0
$561$	1.52496			0.0643839
$562$		0			0
$563$	−8.09871			−0.341320			−0.170660	−	0.985330i	$-0.554590\pi$
$563$	−8.09871			−0.341320			−0.170660	+	0.985330i	$0.554590\pi$
$564$		0			0
$565$	−30.0681	−	52.0794i	−1.26497	−	2.19100i
$566$		0			0
$567$	−0.217351	−	0.376462i	−0.00912786	−	0.0158099i
$568$		0			0
$569$	−3.45941	−	5.99188i	−0.145026	−	0.251193i	0.784357	−	0.620310i	$-0.212993\pi$
$569$	−3.45941	−	5.99188i	−0.145026	−	0.251193i	−0.929383	+	0.369118i	$0.879660\pi$
$570$		0			0
$571$	−6.51960	−	11.2923i	−0.272837	−	0.472567i	0.696750	−	0.717314i	$-0.254629\pi$
$571$	−6.51960	−	11.2923i	−0.272837	−	0.472567i	−0.969587	+	0.244746i	$0.921295\pi$
$572$		0			0
$573$	−0.771248	+	1.33584i	−0.0322193	+	0.0558055i
$574$		0			0
$575$	5.19989	−	9.00647i	0.216850	−	0.375596i
$576$		0			0
$577$	16.7298	+	28.9768i	0.696470	+	1.20632i	0.969683	+	0.244367i	$0.0785802\pi$
$577$	16.7298	+	28.9768i	0.696470	+	1.20632i	−0.273213	+	0.961954i	$0.588086\pi$
$578$		0			0
$579$	−26.1587			−1.08712
$580$		0			0
$581$	−1.41300			−0.0586211
$582$		0			0
$583$	−34.1719	−	59.1874i	−1.41525	−	2.45129i
$584$		0			0
$585$	−4.61864	+	7.99973i	−0.190957	+	0.330748i
$586$		0			0
$587$	−12.8675	+	22.2871i	−0.531097	+	0.919888i	0.468244	+	0.883599i	$0.344887\pi$
$587$	−12.8675	+	22.2871i	−0.531097	+	0.919888i	−0.999341	+	0.0362884i	$0.988447\pi$
$588$		0			0
$589$	−4.38702			−0.180764
$590$		0			0
$591$	−5.54672	−	9.60720i	−0.228162	−	0.395187i
$592$		0			0
$593$	−13.2624	+	22.9711i	−0.544621	+	0.943312i	0.454009	+	0.890997i	$0.349993\pi$
$593$	−13.2624	+	22.9711i	−0.544621	+	0.943312i	−0.998631	+	0.0523150i	$0.983340\pi$
$594$		0			0
$595$	−0.380006			−0.0155787
$596$		0			0
$597$	5.55573	−	9.62281i	0.227381	−	0.393835i
$598$		0			0
$599$	14.8026	+	25.6388i	0.604817	+	1.04757i	0.992080	+	0.125604i	$0.0400870\pi$
$599$	14.8026	+	25.6388i	0.604817	+	1.04757i	−0.387264	+	0.921969i	$0.626580\pi$
$600$		0			0
$601$	−23.6469	+	40.9577i	−0.964579	+	1.67070i	−0.253835	+	0.967247i	$0.581692\pi$
$601$	−23.6469	+	40.9577i	−0.964579	+	1.67070i	−0.710743	+	0.703452i	$0.751641\pi$
$602$		0			0
$603$	8.16321	+	0.601709i	0.332431	+	0.0245035i
$604$		0			0
$605$	−21.4809	+	37.2059i	−0.873321	+	1.51264i
$606$		0			0
$607$	−16.6546	−	28.8466i	−0.675989	−	1.17085i	−0.976179	−	0.216968i	$-0.930383\pi$
$607$	−16.6546	−	28.8466i	−0.675989	−	1.17085i	0.300190	−	0.953879i	$-0.402950\pi$
$608$		0			0
$609$	−1.28449	+	2.22479i	−0.0520500	+	0.0901532i
$610$		0			0
$611$	−24.6841			−0.998611
$612$		0			0
$613$	−10.0794	+	17.4580i	−0.407103	+	0.705124i	−0.994564	−	0.104129i	$-0.966794\pi$
$613$	−10.0794	+	17.4580i	−0.407103	+	0.705124i	0.587460	+	0.809253i	$0.300128\pi$
$614$		0			0
$615$	−3.45726	−	5.98815i	−0.139410	−	0.241465i
$616$		0			0
$617$	−33.4753			−1.34767			−0.673833	−	0.738883i	$-0.735353\pi$
$617$	−33.4753			−1.34767			−0.673833	+	0.738883i	$0.735353\pi$
$618$		0			0
$619$	−14.9123	+	25.8289i	−0.599376	+	1.03815i	0.393538	+	0.919309i	$0.371251\pi$
$619$	−14.9123	+	25.8289i	−0.599376	+	1.03815i	−0.992913	+	0.118841i	$0.962082\pi$
$620$		0			0
$621$	1.50000	−	2.59808i	0.0601929	−	0.104257i
$622$		0			0
$623$	−3.02894	−	5.24627i	−0.121352	−	0.210187i
$624$		0			0
$625$	−30.3157			−1.21263
$626$		0			0
$627$	−11.8815			−0.474502
$628$		0			0
$629$	−1.38885	−	2.40557i	−0.0553772	−	0.0959162i
$630$		0			0
$631$	19.7314	−	34.1758i	0.785494	−	1.36052i	−0.143210	−	0.989692i	$-0.545742\pi$
$631$	19.7314	−	34.1758i	0.785494	−	1.36052i	0.928704	−	0.370823i	$-0.120924\pi$
$632$		0			0
$633$	5.41213	−	9.37408i	0.215113	−	0.372586i
$634$		0			0
$635$	3.01483	+	5.22183i	0.119640	+	0.207222i
$636$		0			0
$637$	10.8112	+	18.7255i	0.428355	+	0.741932i
$638$		0			0
$639$	−3.57590	−	6.19364i	−0.141461	−	0.245017i
$640$		0			0
$641$	−14.8662	−	25.7490i	−0.587180	−	1.01703i	−0.994600	−	0.103785i	$-0.966905\pi$
$641$	−14.8662	−	25.7490i	−0.587180	−	1.01703i	0.407420	−	0.913241i	$-0.366429\pi$
$642$		0			0
$643$	−31.6155			−1.24679			−0.623397	−	0.781905i	$-0.714248\pi$
$643$	−31.6155			−1.24679			−0.623397	+	0.781905i	$0.714248\pi$
$644$		0			0
$645$	−8.07590			−0.317988
$646$		0			0
$647$	18.1353	−	31.4112i	0.712972	−	1.23490i	−0.250765	−	0.968048i	$-0.580682\pi$
$647$	18.1353	−	31.4112i	0.712972	−	1.23490i	0.963737	−	0.266855i	$-0.0859846\pi$
$648$		0			0
$649$	−8.47871	−	14.6856i	−0.332819	−	0.576459i
$650$		0			0
$651$	0.407353	−	0.705557i	0.0159654	−	0.0276530i
$652$		0			0
$653$	−0.594252	+	1.02927i	−0.0232549	+	0.0402786i	−0.877419	−	0.479725i	$-0.840736\pi$
$653$	−0.594252	+	1.02927i	−0.0232549	+	0.0402786i	0.854164	+	0.520004i	$0.174070\pi$
$654$		0			0
$655$	7.70658			0.301121
$656$		0			0
$657$	−6.22612	+	10.7840i	−0.242904	+	0.420722i
$658$		0			0
$659$	−20.5325	−	35.5634i	−0.799833	−	1.38535i	−0.919724	−	0.392565i	$-0.871588\pi$
$659$	−20.5325	−	35.5634i	−0.799833	−	1.38535i	0.119891	−	0.992787i	$-0.461745\pi$
$660$		0			0
$661$	−25.5334			−0.993134			−0.496567	−	0.867998i	$-0.665406\pi$
$661$	−25.5334			−0.993134			−0.496567	+	0.867998i	$0.665406\pi$
$662$		0			0
$663$	0.476876	+	0.825973i	0.0185203	+	0.0320781i
$664$		0			0
$665$	2.96076			0.114814
$666$		0			0
$667$	−17.7292			−0.686478
$668$		0			0
$669$	2.65332			0.102583
$670$		0			0
$671$	38.8475			1.49969
$672$		0			0
$673$	−33.4532			−1.28953			−0.644763	−	0.764383i	$-0.723044\pi$
$673$	−33.4532			−1.28953			−0.644763	+	0.764383i	$0.723044\pi$
$674$		0			0
$675$	3.46659			0.133429
$676$		0			0
$677$	−11.1122	−	19.2468i	−0.427075	−	0.739716i	0.569536	−	0.821966i	$-0.307123\pi$
$677$	−11.1122	−	19.2468i	−0.427075	−	0.739716i	−0.996612	+	0.0822500i	$0.973789\pi$
$678$		0			0
$679$	0.110494			0.00424036
$680$		0			0
$681$	12.9821	+	22.4857i	0.497477	+	0.861655i
$682$		0			0
$683$	0.452467	−	0.783697i	0.0173132	−	0.0299873i	−0.857239	−	0.514919i	$-0.827822\pi$
$683$	0.452467	−	0.783697i	0.0173132	−	0.0299873i	0.874552	+	0.484931i	$0.161155\pi$
$684$		0			0
$685$	−21.4493			−0.819537
$686$		0			0
$687$	8.83782	−	15.3075i	0.337184	−	0.584019i
$688$		0			0
$689$	21.3720	−	37.0174i	0.814209	−	1.41025i
$690$		0			0
$691$	17.1711	+	29.7412i	0.653220	+	1.13141i	0.982337	+	0.187120i	$0.0599155\pi$
$691$	17.1711	+	29.7412i	0.653220	+	1.13141i	−0.329117	+	0.944289i	$0.606751\pi$
$692$		0			0
$693$	1.10325	−	1.91089i	0.0419090	−	0.0725885i
$694$		0			0
$695$	−25.5854			−0.970508
$696$		0			0
$697$	−0.713925			−0.0270418
$698$		0			0
$699$	−0.711843	−	1.23295i	−0.0269244	−	0.0466344i
$700$		0			0
$701$	16.5971	+	28.7470i	0.626864	+	1.08576i	0.988177	+	0.153316i	$0.0489953\pi$
$701$	16.5971	+	28.7470i	0.626864	+	1.08576i	−0.361313	+	0.932445i	$0.617671\pi$
$702$		0			0
$703$	10.8211	+	18.7426i	0.408124	+	0.706892i
$704$		0			0
$705$	11.3123	+	19.5935i	0.426046	+	0.737933i
$706$		0			0
$707$	−1.55677	+	2.69641i	−0.0585484	+	0.101409i
$708$		0			0
$709$	−19.6615	+	34.0548i	−0.738405	+	1.27895i	0.214809	+	0.976656i	$0.431087\pi$
$709$	−19.6615	+	34.0548i	−0.738405	+	1.27895i	−0.953213	+	0.302298i	$0.902246\pi$
$710$		0			0
$711$	0.188167	+	0.325915i	0.00705681	+	0.0122228i
$712$		0			0
$713$	5.62253			0.210565
$714$		0			0
$715$	−46.8876			−1.75350
$716$		0			0
$717$	11.3662	+	19.6868i	0.424479	+	0.735218i
$718$		0			0
$719$	24.9506	−	43.2156i	0.930499	−	1.61167i	0.148029	−	0.988983i	$-0.452707\pi$
$719$	24.9506	−	43.2156i	0.930499	−	1.61167i	0.782470	−	0.622689i	$-0.213960\pi$
$720$		0			0
$721$	0.982704	−	1.70209i	0.0365978	−	0.0633893i
$722$		0			0
$723$	2.39069			0.0889107
$724$		0			0
$725$	−10.2433	−	17.7420i	−0.380428	−	0.658920i
$726$		0			0
$727$	20.3578	−	35.2607i	0.755027	−	1.30775i	−0.190333	−	0.981719i	$-0.560957\pi$
$727$	20.3578	−	35.2607i	0.755027	−	1.30775i	0.945361	−	0.326026i	$-0.105710\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.416919	+	0.722125i	−0.0154203	+	0.0267088i
$732$		0			0
$733$	−13.5865	−	23.5325i	−0.501828	−	0.869192i	−0.999998	−	0.00211264i	$-0.999328\pi$
$733$	−13.5865	−	23.5325i	−0.501828	−	0.869192i	0.498169	−	0.867080i	$-0.334006\pi$
$734$		0			0
$735$	9.90917	−	17.1632i	0.365505	−	0.633074i
$736$		0			0
$737$	18.0728	+	37.4114i	0.665720	+	1.37807i
$738$		0			0
$739$	−1.90345	+	3.29687i	−0.0700196	+	0.121277i	−0.898910	−	0.438134i	$-0.855640\pi$
$739$	−1.90345	+	3.29687i	−0.0700196	+	0.121277i	0.828890	+	0.559412i	$0.188973\pi$
$740$		0			0
$741$	−3.71551	−	6.43546i	−0.136493	−	0.236413i
$742$		0			0
$743$	−7.09680	+	12.2920i	−0.260357	+	0.450951i	−0.966337	−	0.257281i	$-0.917173\pi$
$743$	−7.09680	+	12.2920i	−0.260357	+	0.450951i	0.705980	+	0.708232i	$0.250507\pi$
$744$		0			0
$745$	−25.9603			−0.951112
$746$		0			0
$747$	1.62526	−	2.81503i	0.0594650	−	0.102996i
$748$		0			0
$749$	3.21894	+	5.57537i	0.117618	+	0.203719i
$750$		0			0
$751$	47.6064			1.73718			0.868591	−	0.495529i	$-0.165026\pi$
$751$	47.6064			1.73718			0.868591	+	0.495529i	$0.165026\pi$
$752$		0			0
$753$	−3.69167	+	6.39417i	−0.134532	+	0.233016i
$754$		0			0
$755$	−20.6190	+	35.7131i	−0.750401	+	1.29973i
$756$		0			0
$757$	9.17054	+	15.8838i	0.333309	+	0.577308i	0.983158	−	0.182755i	$-0.0585015\pi$
$757$	9.17054	+	15.8838i	0.333309	+	0.577308i	−0.649850	+	0.760063i	$0.725168\pi$
$758$		0			0
$759$	15.2277			0.552731
$760$		0			0
$761$	28.7755			1.04311			0.521555	−	0.853218i	$-0.325352\pi$
$761$	28.7755			1.04311			0.521555	+	0.853218i	$0.325352\pi$
$762$		0			0
$763$	−4.18099	−	7.24168i	−0.151362	−	0.262167i
$764$		0			0
$765$	0.437089	−	0.757060i	0.0158030	−	0.0273716i
$766$		0			0
$767$	5.30282	−	9.18475i	0.191474	−	0.331642i
$768$		0			0
$769$	−25.9595	−	44.9633i	−0.936125	−	1.62142i	−0.772615	−	0.634875i	$-0.781052\pi$
$769$	−25.9595	−	44.9633i	−0.936125	−	1.62142i	−0.163510	−	0.986542i	$-0.552282\pi$
$770$		0			0
$771$	0.691673	+	1.19801i	0.0249100	+	0.0431454i
$772$		0			0
$773$	14.2311	+	24.6489i	0.511856	+	0.886561i	0.999906	+	0.0137449i	$0.00437527\pi$
$773$	14.2311	+	24.6489i	0.511856	+	0.886561i	−0.488049	+	0.872816i	$0.662291\pi$
$774$		0			0
$775$	3.24850	+	5.62658i	0.116690	+	0.202113i
$776$		0			0
$777$	−4.01913			−0.144186
$778$		0			0
$779$	5.56245			0.199296
$780$		0			0
$781$	18.1509	−	31.4383i	0.649491	−	1.12495i
$782$		0			0
$783$	−2.95487	−	5.11799i	−0.105598	−	0.182902i
$784$		0			0
$785$	−1.82793	+	3.16607i	−0.0652416	+	0.113002i
$786$		0			0
$787$	22.8874	−	39.6421i	0.815847	−	1.41309i	−0.0928704	−	0.995678i	$-0.529604\pi$
$787$	22.8874	−	39.6421i	0.815847	−	1.41309i	0.908718	−	0.417411i	$-0.137062\pi$
$788$		0			0
$789$	7.31733			0.260504
$790$		0			0
$791$	−4.49202	+	7.78041i	−0.159718	+	0.276640i
$792$		0			0
$793$	12.1481	+	21.0412i	0.431393	+	0.747195i
$794$		0			0
$795$	−39.1778			−1.38949
$796$		0			0
$797$	−14.1803	−	24.5611i	−0.502293	−	0.869998i	−0.999996	−	0.00265027i	$-0.999156\pi$
$797$	−14.1803	−	24.5611i	−0.502293	−	0.869998i	0.497703	−	0.867347i	$-0.334177\pi$
$798$		0			0
$799$	2.33600			0.0826416
$800$		0			0
$801$	13.9357			0.492395
$802$		0			0
$803$	−63.2063			−2.23050
$804$		0			0
$805$	−3.79460			−0.133742
$806$		0			0
$807$	3.82426			0.134620
$808$		0			0
$809$	21.6070			0.759663			0.379832	−	0.925056i	$-0.375982\pi$
$809$	21.6070			0.759663			0.379832	+	0.925056i	$0.375982\pi$
$810$		0			0
$811$	14.8808	+	25.7743i	0.522535	+	0.905057i	0.999656	+	0.0262198i	$0.00834699\pi$
$811$	14.8808	+	25.7743i	0.522535	+	0.905057i	−0.477121	+	0.878838i	$0.658320\pi$
$812$		0			0
$813$	0.320204			0.0112300
$814$		0			0
$815$	1.39618	+	2.41826i	0.0489061	+	0.0847079i
$816$		0			0
$817$	3.24837	−	5.62634i	0.113646	−	0.196841i
$818$		0			0
$819$	1.38001			0.0482213
$820$		0			0
$821$	−20.5642	+	35.6182i	−0.717695	+	1.24308i	0.244216	+	0.969721i	$0.421469\pi$
$821$	−20.5642	+	35.6182i	−0.717695	+	1.24308i	−0.961911	+	0.273363i	$0.911864\pi$
$822$		0			0
$823$	−2.38847	+	4.13695i	−0.0832568	+	0.144205i	−0.904647	−	0.426162i	$-0.859866\pi$
$823$	−2.38847	+	4.13695i	−0.0832568	+	0.144205i	0.821390	+	0.570367i	$0.193199\pi$
$824$		0			0
$825$	8.79804	+	15.2387i	0.306309	+	0.530542i
$826$		0			0
$827$	10.2251	−	17.7104i	0.355561	−	0.615850i	−0.631653	−	0.775251i	$-0.717623\pi$
$827$	10.2251	−	17.7104i	0.355561	−	0.615850i	0.987214	+	0.159402i	$0.0509565\pi$
$828$		0			0
$829$	21.3455			0.741361			0.370681	−	0.928760i	$-0.379124\pi$
$829$	21.3455			0.741361			0.370681	+	0.928760i	$0.379124\pi$
$830$		0			0
$831$	−15.2079			−0.527557
$832$		0			0
$833$	−1.02312	−	1.77210i	−0.0354491	−	0.0613997i
$834$		0			0
$835$	−7.61424	−	13.1882i	−0.263501	−	0.456398i
$836$		0			0
$837$	0.937089	+	1.62309i	0.0323905	+	0.0561020i
$838$		0			0
$839$	−5.21735	−	9.03672i	−0.180123	−	0.311982i	0.761799	−	0.647813i	$-0.224316\pi$
$839$	−5.21735	−	9.03672i	−0.180123	−	0.311982i	−0.941922	+	0.335831i	$0.890983\pi$
$840$		0			0
$841$	−2.96252	+	5.13123i	−0.102156	+	0.176939i
$842$		0			0
$843$	3.80888	−	6.59717i	0.131185	−	0.227219i
$844$		0			0
$845$	4.25093	+	7.36282i	0.146236	+	0.253289i
$846$		0			0
$847$	6.41827			0.220534
$848$		0			0
$849$	−22.2695			−0.764287
$850$		0			0
$851$	−13.8686	−	24.0211i	−0.475410	−	0.823434i
$852$		0			0
$853$	13.6529	−	23.6475i	0.467467	−	0.809676i	−0.531842	−	0.846843i	$-0.678500\pi$
$853$	13.6529	−	23.6475i	0.467467	−	0.809676i	0.999309	+	0.0371673i	$0.0118335\pi$
$854$		0			0
$855$	−3.40552	+	5.89853i	−0.116466	+	0.201725i
$856$		0			0
$857$	28.6339			0.978114			0.489057	−	0.872252i	$-0.337341\pi$
$857$	28.6339			0.978114			0.489057	+	0.872252i	$0.337341\pi$
$858$		0			0
$859$	0.984375	+	1.70499i	0.0335864	+	0.0581734i	0.882330	−	0.470631i	$-0.155974\pi$
$859$	0.984375	+	1.70499i	0.0335864	+	0.0581734i	−0.848744	+	0.528805i	$0.822640\pi$
$860$		0			0
$861$	−0.516497	+	0.894600i	−0.0176022	+	0.0304879i
$862$		0			0
$863$	−34.6863			−1.18074			−0.590368	−	0.807134i	$-0.701017\pi$
$863$	−34.6863			−1.18074			−0.590368	+	0.807134i	$0.701017\pi$
$864$		0			0
$865$	−2.65410	+	4.59704i	−0.0902422	+	0.156304i
$866$		0			0
$867$	8.45487	+	14.6443i	0.287142	+	0.497345i
$868$		0			0
$869$	−0.955117	+	1.65431i	−0.0324001	+	0.0561187i
$870$		0			0
$871$	−14.6118	+	21.4879i	−0.495101	+	0.728091i
$872$		0			0
$873$	−0.127092	+	0.220129i	−0.00430140	+	0.00745024i
$874$		0			0
$875$	0.969779	+	1.67971i	0.0327845	+	0.0567844i
$876$		0			0
$877$	0.718866	−	1.24511i	0.0242744	−	0.0420445i	−0.853633	−	0.520875i	$-0.825606\pi$
$877$	0.718866	−	1.24511i	0.0242744	−	0.0420445i	0.877907	+	0.478830i	$0.158939\pi$
$878$		0			0
$879$	−13.0509			−0.440195
$880$		0			0
$881$	7.39571	−	12.8097i	0.249168	−	0.431571i	−0.714127	−	0.700016i	$-0.753176\pi$
$881$	7.39571	−	12.8097i	0.249168	−	0.431571i	0.963295	+	0.268445i	$0.0865097\pi$
$882$		0			0
$883$	19.7664	+	34.2364i	0.665192	+	1.15215i	0.979233	+	0.202736i	$0.0649834\pi$
$883$	19.7664	+	34.2364i	0.665192	+	1.15215i	−0.314042	+	0.949409i	$0.601683\pi$
$884$		0			0
$885$	−9.72078			−0.326760
$886$		0			0
$887$	−27.5854	+	47.7793i	−0.926227	+	1.60427i	−0.136650	+	0.990619i	$0.543634\pi$
$887$	−27.5854	+	47.7793i	−0.926227	+	1.60427i	−0.789576	+	0.613652i	$0.789700\pi$
$888$		0			0
$889$	0.450400	−	0.780116i	0.0151059	−	0.0261643i
$890$		0			0
$891$	2.53795	+	4.39586i	0.0850246	+	0.147267i
$892$		0			0
$893$	−18.2006			−0.609060
$894$		0			0
$895$	−51.0144			−1.70522
$896$		0			0
$897$	4.76191	+	8.24788i	0.158996	+	0.275389i
$898$		0			0
$899$	5.53795	−	9.59201i	0.184701	−	0.319912i
$900$		0			0
$901$	−2.02256	+	3.50317i	−0.0673811	+	0.116708i
$902$		0			0
$903$	0.603250	+	1.04486i	0.0200749	+	0.0347708i
$904$		0			0
$905$	−15.0807	−	26.1205i	−0.501299	−	0.868275i
$906$		0			0
$907$	−24.8295	−	43.0060i	−0.824451	−	1.42799i	−0.902338	−	0.431028i	$-0.858151\pi$
$907$	−24.8295	−	43.0060i	−0.824451	−	1.42799i	0.0778878	−	0.996962i	$-0.475182\pi$
$908$		0			0
$909$	−3.58124	−	6.20290i	−0.118782	−	0.205737i
$910$		0			0
$911$	−13.6028			−0.450680			−0.225340	−	0.974280i	$-0.572349\pi$
$911$	−13.6028			−0.450680			−0.225340	+	0.974280i	$0.572349\pi$
$912$		0			0
$913$	16.4993			0.546046
$914$		0			0
$915$	11.1346	−	19.2857i	0.368098	−	0.637565i
$916$		0			0
$917$	−0.575663	−	0.997077i	−0.0190101	−	0.0329264i
$918$		0			0
$919$	−11.1893	+	19.3804i	−0.369100	+	0.639300i	−0.989425	−	0.145045i	$-0.953667\pi$
$919$	−11.1893	+	19.3804i	−0.369100	+	0.639300i	0.620325	+	0.784345i	$0.287001\pi$
$920$		0			0
$921$	−3.45646	+	5.98676i	−0.113894	+	0.197271i
$922$		0			0
$923$	22.7042			0.747317
$924$		0			0
$925$	16.0256	−	27.7572i	0.526919	−	0.912650i
$926$		0			0
$927$	2.26064	+	3.91555i	0.0742493	+	0.128604i
$928$		0			0
$929$	3.15177			0.103406			0.0517032	−	0.998662i	$-0.483535\pi$
$929$	3.15177			0.103406			0.0517032	+	0.998662i	$0.483535\pi$
$930$		0			0
$931$	7.97153	+	13.8071i	0.261256	+	0.452509i
$932$		0			0
$933$	−19.7673			−0.647153
$934$		0			0
$935$	4.43724			0.145113
$936$		0			0
$937$	16.2579			0.531121			0.265560	−	0.964094i	$-0.414443\pi$
$937$	16.2579			0.531121			0.265560	+	0.964094i	$0.414443\pi$
$938$		0			0
$939$	11.3825			0.371455
$940$		0			0
$941$	52.3945			1.70801			0.854006	−	0.520263i	$-0.174166\pi$
$941$	52.3945			1.70801			0.854006	+	0.520263i	$0.174166\pi$
$942$		0			0
$943$	−7.12900			−0.232152
$944$		0			0
$945$	−0.632434	−	1.09541i	−0.0205731	−	0.0356336i
$946$		0			0
$947$	−35.5324			−1.15465			−0.577324	−	0.816515i	$-0.695903\pi$
$947$	−35.5324			−1.15465			−0.577324	+	0.816515i	$0.695903\pi$
$948$		0			0
$949$	−19.7655	−	34.2348i	−0.641615	−	1.11131i
$950$		0			0
$951$	1.78098	−	3.08475i	0.0577522	−	0.100030i
$952$		0			0
$953$	−47.3376			−1.53341			−0.766707	−	0.641997i	$-0.778106\pi$
$953$	−47.3376			−1.53341			−0.766707	+	0.641997i	$0.778106\pi$
$954$		0			0
$955$	−2.24413	+	3.88695i	−0.0726184	+	0.125779i
$956$		0			0
$957$	14.9986	−	25.9784i	0.484837	−	0.839762i
$958$		0			0
$959$	1.60221	+	2.77511i	0.0517381	+	0.0896131i
$960$		0			0
$961$	13.7437	−	23.8048i	0.443346	−	0.767898i
$962$		0			0
$963$	−14.8099			−0.477242
$964$		0			0
$965$	−76.1149			−2.45023
$966$		0			0
$967$	25.3757	+	43.9520i	0.816027	+	1.41340i	0.908588	+	0.417693i	$0.137161\pi$
$967$	25.3757	+	43.9520i	0.816027	+	1.41340i	−0.0925610	+	0.995707i	$0.529505\pi$
$968$		0			0
$969$	0.351620	+	0.609024i	0.0112957	+	0.0195647i
$970$		0			0
$971$	28.4140	+	49.2144i	0.911847	+	1.57937i	0.811453	+	0.584418i	$0.198677\pi$
$971$	28.4140	+	49.2144i	0.911847	+	1.57937i	0.100395	+	0.994948i	$0.467989\pi$
$972$		0			0
$973$	1.91116	+	3.31023i	0.0612691	+	0.106121i
$974$		0			0
$975$	−5.50254	+	9.53067i	−0.176222	+	0.305226i
$976$		0			0
$977$	15.7712	−	27.3166i	0.504567	−	0.873936i	−0.495419	−	0.868654i	$-0.664986\pi$
$977$	15.7712	−	27.3166i	0.504567	−	0.873936i	0.999986	−	0.00528147i	$-0.00168115\pi$
$978$		0			0
$979$	35.3682	+	61.2595i	1.13037	+	1.95786i
$980$		0			0
$981$	19.2362			0.614163
$982$		0			0
$983$	−36.4599			−1.16289			−0.581445	−	0.813586i	$-0.697513\pi$
$983$	−36.4599			−1.16289			−0.581445	+	0.813586i	$0.697513\pi$
$984$		0			0
$985$	−16.1395	−	27.9545i	−0.514248	−	0.890703i
$986$		0			0
$987$	1.69000	−	2.92717i	0.0537934	−	0.0931729i
$988$		0			0
$989$	−4.16321	+	7.21089i	−0.132382	+	0.229293i
$990$		0			0
$991$	55.2848			1.75618			0.878089	−	0.478497i	$-0.158818\pi$
$991$	55.2848			1.75618			0.878089	+	0.478497i	$0.158818\pi$
$992$		0			0
$993$	−3.46252	−	5.99726i	−0.109880	−	0.190317i
$994$		0			0
$995$	16.1657	−	27.9999i	0.512489	−	0.887656i
$996$		0			0
$997$	21.5575			0.682733			0.341366	−	0.939930i	$-0.389110\pi$
$997$	21.5575			0.682733			0.341366	+	0.939930i	$0.389110\pi$
$998$		0			0
$999$	4.62287	−	8.00704i	0.146261	−	0.253332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.i.e.565.4	yes	8
3.2	odd	2		2412.2.l.f.1369.1		8
67.37	even	3	inner	804.2.i.e.37.4	✓	8
201.104	odd	6		2412.2.l.f.37.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.e.37.4	✓	8	67.37	even	3	inner
804.2.i.e.565.4	yes	8	1.1	even	1	trivial
2412.2.l.f.37.1		8	201.104	odd	6
2412.2.l.f.1369.1		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +2.90974 q^{5} +(-0.217351 - 0.376462i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +2.90974 q^{5} +(-0.217351 - 0.376462i) q^{7} +1.00000 q^{9} +(2.53795 + 4.39586i) q^{11} +(-1.58730 + 2.74929i) q^{13} +2.90974 q^{15} +(0.150216 - 0.260181i) q^{17} +(-1.17039 + 2.02717i) q^{19} +(-0.217351 - 0.376462i) q^{21} +(1.50000 - 2.59808i) q^{23} +3.46659 q^{25} +1.00000 q^{27} +(-2.95487 - 5.11799i) q^{29} +(0.937089 + 1.62309i) q^{31} +(2.53795 + 4.39586i) q^{33} +(-0.632434 - 1.09541i) q^{35} +(4.62287 - 8.00704i) q^{37} +(-1.58730 + 2.74929i) q^{39} +(-1.18817 - 2.05797i) q^{41} -2.77547 q^{43} +2.90974 q^{45} +(3.88774 + 6.73376i) q^{47} +(3.40552 - 5.89853i) q^{49} +(0.150216 - 0.260181i) q^{51} -13.4644 q^{53} +(7.38478 + 12.7908i) q^{55} +(-1.17039 + 2.02717i) q^{57} -3.34077 q^{59} +(3.82666 - 6.62797i) q^{61} +(-0.217351 - 0.376462i) q^{63} +(-4.61864 + 7.99973i) q^{65} +(8.16321 + 0.601709i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-3.57590 - 6.19364i) q^{71} +(-6.22612 + 10.7840i) q^{73} +3.46659 q^{75} +(1.10325 - 1.91089i) q^{77} +(0.188167 + 0.325915i) q^{79} +1.00000 q^{81} +(1.62526 - 2.81503i) q^{83} +(0.437089 - 0.757060i) q^{85} +(-2.95487 - 5.11799i) q^{87} +13.9357 q^{89} +1.38001 q^{91} +(0.937089 + 1.62309i) q^{93} +(-3.40552 + 5.89853i) q^{95} +(-0.127092 + 0.220129i) q^{97} +(2.53795 + 4.39586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 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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