LMFDB - Embedded newform 1805.2.b.f.1084.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1805,2,Mod(1084,1805)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1805, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1805.1084"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-2,2,12,0,0,-8,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.4227136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 7x^{2} + 1 $ x^6 + 6x^4 + 7x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.1
Root			$-0.407132i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.f.1084.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.45620i q^{2} +1.56104i q^{3} -4.03293 q^{4} +(2.19869 - 0.407132i) q^{5} +3.83424 q^{6} -4.50527i q^{7} +4.99330i q^{8} +0.563139 q^{9} +(-1.00000 - 5.40043i) q^{10} +2.19869 q^{11} -6.29559i q^{12} -3.75849i q^{13} -11.0659 q^{14} +(0.635552 + 3.43226i) q^{15} +4.19869 q^{16} -0.665886i q^{17} -1.38318i q^{18} +(-8.86718 + 1.64194i) q^{20} +7.03293 q^{21} -5.40043i q^{22} -0.488026i q^{23} -7.79476 q^{24} +(4.66849 - 1.79032i) q^{25} -9.23163 q^{26} +5.56222i q^{27} +18.1695i q^{28} -3.59607 q^{29} +(8.43032 - 1.56104i) q^{30} +6.83424 q^{31} -0.326239i q^{32} +3.43226i q^{33} -1.63555 q^{34} +(-1.83424 - 9.90571i) q^{35} -2.27110 q^{36} +3.01171i q^{37} +5.86718 q^{39} +(2.03293 + 10.9787i) q^{40} +0.0724126 q^{41} -17.2743i q^{42} +0.420541i q^{43} -8.86718 q^{44} +(1.23817 - 0.229272i) q^{45} -1.19869 q^{46} -5.02278i q^{47} +6.55434i q^{48} -13.2975 q^{49} +(-4.39738 - 11.4668i) q^{50} +1.03948 q^{51} +15.1578i q^{52} +2.61799i q^{53} +13.6619 q^{54} +(4.83424 - 0.895159i) q^{55} +22.4962 q^{56} +8.83269i q^{58} -12.5357 q^{59} +(-2.56314 - 13.8421i) q^{60} +7.06587 q^{61} -16.7863i q^{62} -2.53710i q^{63} +7.59607 q^{64} +(-1.53020 - 8.26377i) q^{65} +8.43032 q^{66} -5.72667i q^{67} +2.68548i q^{68} +0.761831 q^{69} +(-24.3304 + 4.50527i) q^{70} +6.97252 q^{71} +2.81192i q^{72} -2.95764i q^{73} +7.39738 q^{74} +(2.79476 + 7.28772i) q^{75} -9.90571i q^{77} -14.4110i q^{78} -11.3370 q^{79} +(9.23163 - 1.70942i) q^{80} -6.99346 q^{81} -0.177860i q^{82} -15.6999i q^{83} -28.3634 q^{84} +(-0.271104 - 1.46408i) q^{85} +1.03293 q^{86} -5.61363i q^{87} +10.9787i q^{88} +1.33697 q^{89} +(-0.563139 - 3.04120i) q^{90} -16.9330 q^{91} +1.96818i q^{92} +10.6686i q^{93} -12.3370 q^{94} +0.509273 q^{96} -4.38638i q^{97} +32.6613i q^{98} +1.23817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9} - 6 q^{10} + 2 q^{11} - 22 q^{14} + 4 q^{15} + 14 q^{16} - 20 q^{20} + 20 q^{21} - 2 q^{24} + 6 q^{25} - 22 q^{26} + 12 q^{29} + 6 q^{30} + 30 q^{31} - 10 q^{34}+ \cdots + 30 q^{99}+O(q^{100}) $ 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9 - 6 * q^10 + 2 * q^11 - 22 * q^14 + 4 * q^15 + 14 * q^16 - 20 * q^20 + 20 * q^21 - 2 * q^24 + 6 * q^25 - 22 * q^26 + 12 * q^29 + 6 * q^30 + 30 * q^31 - 10 * q^34 - 14 * q^36 + 2 * q^39 - 10 * q^40 + 12 * q^41 - 20 * q^44 + 30 * q^45 + 4 * q^46 - 2 * q^49 - 4 * q^50 + 40 * q^51 + 4 * q^54 + 18 * q^55 + 46 * q^56 - 20 * q^59 - 4 * q^60 - 2 * q^61 + 12 * q^64 - 20 * q^65 + 6 * q^66 - 18 * q^69 - 46 * q^70 - 2 * q^71 + 22 * q^74 - 28 * q^75 - 24 * q^79 + 22 * q^80 + 14 * q^81 - 48 * q^84 - 2 * q^85 - 16 * q^86 - 36 * q^89 + 8 * q^90 - 24 * q^91 - 30 * q^94 + 26 * q^96 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.45620i		−	1.73680i	−0.495866	−	0.868399i	$-0.665149\pi$
$2$		−	2.45620i		−	1.73680i	0.495866	−	0.868399i	$-0.334851\pi$
$3$			1.56104i			0.901270i	0.892708	+	0.450635i	$0.148802\pi$
$3$			1.56104i			0.901270i	−0.892708	+	0.450635i	$0.851198\pi$
$4$	−4.03293			−2.01647
$5$	2.19869	−	0.407132i	0.983285	−	0.182075i
$5$	2.19869	−	0.407132i	0.983285	−	0.182075i
$6$	3.83424			1.56532
$7$		−	4.50527i		−	1.70283i	−0.524490	−	0.851417i	$-0.675744\pi$
$7$		−	4.50527i		−	1.70283i	0.524490	−	0.851417i	$-0.324256\pi$
$8$			4.99330i			1.76540i
$9$	0.563139			0.187713
$10$	−1.00000	−	5.40043i	−0.316228	−	1.70777i
$11$	2.19869			0.662930			0.331465	−	0.943467i	$-0.392457\pi$
$11$	2.19869			0.662930			0.331465	+	0.943467i	$0.392457\pi$
$12$		−	6.29559i		−	1.81738i
$13$		−	3.75849i		−	1.04242i	−0.853429	−	0.521209i	$-0.825481\pi$
$13$		−	3.75849i		−	1.04242i	0.853429	−	0.521209i	$-0.174519\pi$
$14$	−11.0659			−2.95748
$15$	0.635552	+	3.43226i	0.164099	+	0.886205i
$16$	4.19869			1.04967
$17$		−	0.665886i		−	0.161501i	−0.996734	−	0.0807506i	$-0.974268\pi$
$17$		−	0.665886i		−	0.161501i	0.996734	−	0.0807506i	$-0.0257317\pi$
$18$		−	1.38318i		−	0.326020i
$19$		0			0
$19$		0			0
$20$	−8.86718	+	1.64194i	−1.98276	+	0.367149i
$21$	7.03293			1.53471
$22$		−	5.40043i		−	1.15138i
$23$		−	0.488026i		−	0.101760i	−0.998705	−	0.0508802i	$-0.983797\pi$
$23$		−	0.488026i		−	0.101760i	0.998705	−	0.0508802i	$-0.0162027\pi$
$24$	−7.79476			−1.59110
$25$	4.66849	−	1.79032i	0.933697	−	0.358063i
$26$	−9.23163			−1.81047
$27$			5.56222i			1.07045i
$28$			18.1695i			3.43371i
$29$	−3.59607			−0.667774			−0.333887	−	0.942613i	$-0.608360\pi$
$29$	−3.59607			−0.667774			−0.333887	+	0.942613i	$0.608360\pi$
$30$	8.43032	−	1.56104i	1.53916	−	0.285006i
$31$	6.83424			1.22747			0.613733	−	0.789514i	$-0.289667\pi$
$31$	6.83424			1.22747			0.613733	+	0.789514i	$0.289667\pi$
$32$		−	0.326239i		−	0.0576714i
$33$			3.43226i			0.597479i
$34$	−1.63555			−0.280495
$35$	−1.83424	−	9.90571i	−0.310044	−	1.67437i
$36$	−2.27110			−0.378517
$37$			3.01171i			0.495123i	0.968872	+	0.247561i	$0.0796292\pi$
$37$			3.01171i			0.495123i	−0.968872	+	0.247561i	$0.920371\pi$
$38$		0			0
$39$	5.86718			0.939500
$40$	2.03293	+	10.9787i	0.321435	+	1.73589i
$41$	0.0724126			0.0113090			0.00565448	−	0.999984i	$-0.498200\pi$
$41$	0.0724126			0.0113090			0.00565448	+	0.999984i	$0.498200\pi$
$42$		−	17.2743i		−	2.66548i
$43$			0.420541i			0.0641319i	0.999486	+	0.0320660i	$0.0102087\pi$
$43$			0.420541i			0.0641319i	−0.999486	+	0.0320660i	$0.989791\pi$
$44$	−8.86718			−1.33678
$45$	1.23817	−	0.229272i	0.184575	−	0.0341779i
$46$	−1.19869			−0.176737
$47$		−	5.02278i		−	0.732648i	−0.930487	−	0.366324i	$-0.880616\pi$
$47$		−	5.02278i		−	0.732648i	0.930487	−	0.366324i	$-0.119384\pi$
$48$			6.55434i			0.946038i
$49$	−13.2975			−1.89964
$50$	−4.39738	−	11.4668i	−0.621884	−	1.62164i
$51$	1.03948			0.145556
$52$			15.1578i			2.10200i
$53$			2.61799i			0.359609i	0.983702	+	0.179804i	$0.0575465\pi$
$53$			2.61799i			0.359609i	−0.983702	+	0.179804i	$0.942454\pi$
$54$	13.6619			1.85915
$55$	4.83424	−	0.895159i	0.651849	−	0.120703i
$56$	22.4962			3.00618
$57$		0			0
$58$			8.83269i			1.15979i
$59$	−12.5357			−1.63200			−0.816002	−	0.578049i	$-0.803814\pi$
$59$	−12.5357			−1.63200			−0.816002	+	0.578049i	$0.803814\pi$
$60$	−2.56314	−	13.8421i	−0.330900	−	1.78700i
$61$	7.06587			0.904692			0.452346	−	0.891843i	$-0.350587\pi$
$61$	7.06587			0.904692			0.452346	+	0.891843i	$0.350587\pi$
$62$		−	16.7863i		−	2.13186i
$63$		−	2.53710i		−	0.319644i
$64$	7.59607			0.949509
$65$	−1.53020	−	8.26377i	−0.189799	−	1.02499i
$66$	8.43032			1.03770
$67$		−	5.72667i		−	0.699624i	−0.936820	−	0.349812i	$-0.886245\pi$
$67$		−	5.72667i		−	0.699624i	0.936820	−	0.349812i	$-0.113755\pi$
$68$			2.68548i			0.325662i
$69$	0.761831			0.0917136
$70$	−24.3304	+	4.50527i	−2.90804	+	0.538483i
$71$	6.97252			0.827486			0.413743	−	0.910394i	$-0.364221\pi$
$71$	6.97252			0.827486			0.413743	+	0.910394i	$0.364221\pi$
$72$			2.81192i			0.331388i
$73$		−	2.95764i		−	0.346165i	−0.984907	−	0.173083i	$-0.944627\pi$
$73$		−	2.95764i		−	0.346165i	0.984907	−	0.173083i	$-0.0553728\pi$
$74$	7.39738			0.859928
$75$	2.79476	+	7.28772i	0.322712	+	0.841513i
$76$		0			0
$77$		−	9.90571i		−	1.12886i
$78$		−	14.4110i		−	1.63172i
$79$	−11.3370			−1.27551			−0.637755	−	0.770240i	$-0.720137\pi$
$79$	−11.3370			−1.27551			−0.637755	+	0.770240i	$0.720137\pi$
$80$	9.23163	−	1.70942i	1.03213	−	0.191119i
$81$	−6.99346			−0.777051
$82$		−	0.177860i		−	0.0196414i
$83$		−	15.6999i		−	1.72328i	−0.507517	−	0.861642i	$-0.669436\pi$
$83$		−	15.6999i		−	1.72328i	0.507517	−	0.861642i	$-0.330564\pi$
$84$	−28.3634			−3.09470
$85$	−0.271104	−	1.46408i	−0.0294053	−	0.158802i
$86$	1.03293			0.111384
$87$		−	5.61363i		−	0.601845i
$88$			10.9787i			1.17034i
$89$	1.33697			0.141719			0.0708594	−	0.997486i	$-0.477426\pi$
$89$	1.33697			0.141719			0.0708594	+	0.997486i	$0.477426\pi$
$90$	−0.563139	−	3.04120i	−0.0593601	−	0.320570i
$91$	−16.9330			−1.77507
$92$			1.96818i			0.205197i
$93$			10.6686i			1.10628i
$94$	−12.3370			−1.27246
$95$		0			0
$96$	0.509273			0.0519775
$97$		−	4.38638i		−	0.445369i	−0.974891	−	0.222685i	$-0.928518\pi$
$97$		−	4.38638i		−	0.445369i	0.974891	−	0.222685i	$-0.0714820\pi$
$98$			32.6613i			3.29929i
$99$	1.23817			0.124441
$100$	−18.8277	+	7.22023i	−1.88277	+	0.722023i
$101$	−10.5686			−1.05161			−0.525807	−	0.850604i	$-0.676237\pi$
$101$	−10.5686			−1.05161			−0.525807	+	0.850604i	$0.676237\pi$
$102$		−	2.55317i		−	0.252801i
$103$			5.75615i			0.567171i	0.958947	+	0.283585i	$0.0915239\pi$
$103$			5.75615i			0.567171i	−0.958947	+	0.283585i	$0.908476\pi$
$104$	18.7673			1.84028
$105$	15.4633	−	2.86334i	1.50906	−	0.279433i
$106$	6.43032			0.624568
$107$			1.30229i			0.125897i	0.998017	+	0.0629486i	$0.0200504\pi$
$107$			1.30229i			0.125897i	−0.998017	+	0.0629486i	$0.979950\pi$
$108$		−	22.4321i		−	2.15853i
$109$	12.0329			1.15255			0.576273	−	0.817257i	$-0.304506\pi$
$109$	12.0329			1.15255			0.576273	+	0.817257i	$0.304506\pi$
$110$	−2.19869	−	11.8739i	−0.209637	−	1.13213i
$111$	−4.70142			−0.446239
$112$		−	18.9163i		−	1.78742i
$113$			7.74626i			0.728707i	0.931261	+	0.364353i	$0.118710\pi$
$113$			7.74626i			0.728707i	−0.931261	+	0.364353i	$0.881290\pi$
$114$		0			0
$115$	−0.198691	−	1.07302i	−0.0185281	−	0.100060i
$116$	14.5027			1.34654
$117$		−	2.11656i		−	0.195676i
$118$			30.7901i			2.83446i
$119$	−3.00000			−0.275010
$120$	−17.1383	+	3.17350i	−1.56450	+	0.289700i
$121$	−6.16576			−0.560523
$122$		−	17.3552i		−	1.57127i
$123$			0.113039i			0.0101924i
$124$	−27.5621			−2.47515
$125$	9.53566	−	5.83705i	0.852896	−	0.522081i
$126$	−6.23163			−0.555157
$127$			3.93635i			0.349295i	0.984631	+	0.174647i	$0.0558786\pi$
$127$			3.93635i			0.349295i	−0.984631	+	0.174647i	$0.944121\pi$
$128$		−	19.3100i		−	1.70678i
$129$	−0.656483			−0.0578001
$130$	−20.2975	+	3.75849i	−1.78021	+	0.329642i
$131$	−16.3250			−1.42632			−0.713160	−	0.701002i	$-0.752737\pi$
$131$	−16.3250			−1.42632			−0.713160	+	0.701002i	$0.752737\pi$
$132$		−	13.8421i		−	1.20480i
$133$		0			0
$134$	−14.0659			−1.21511
$135$	2.26456	+	12.2296i	0.194902	+	1.05256i
$136$	3.32497			0.285114
$137$			16.4306i			1.40376i	0.712296	+	0.701879i	$0.247655\pi$
$137$			16.4306i			1.40376i	−0.712296	+	0.701879i	$0.752345\pi$
$138$		−	1.87121i		−	0.159288i
$139$	2.66849			0.226338			0.113169	−	0.993576i	$-0.463900\pi$
$139$	2.66849			0.226338			0.113169	+	0.993576i	$0.463900\pi$
$140$	7.39738	+	39.9491i	0.625193	+	3.37631i
$141$	7.84079			0.660313
$142$		−	17.1259i		−	1.43718i
$143$		−	8.26377i		−	0.691051i
$144$	2.36445			0.197037
$145$	−7.90666	+	1.46408i	−0.656612	+	0.121585i
$146$	−7.26456			−0.601219
$147$		−	20.7580i		−	1.71209i
$148$		−	12.1460i		−	0.998399i
$149$	17.9660			1.47183			0.735915	−	0.677074i	$-0.236752\pi$
$149$	17.9660			1.47183			0.735915	+	0.677074i	$0.236752\pi$
$150$	17.9001	−	6.86451i	1.46154	−	0.560485i
$151$	−12.7344			−1.03631			−0.518154	−	0.855288i	$-0.673380\pi$
$151$	−12.7344			−1.03631			−0.518154	+	0.855288i	$0.673380\pi$
$152$		0			0
$153$		−	0.374987i		−	0.0303159i
$154$	−24.3304			−1.96060
$155$	15.0264	−	2.78244i	1.20695	−	0.223491i
$156$	−23.6619			−1.89447
$157$			20.0541i			1.60049i	0.599673	+	0.800245i	$0.295298\pi$
$157$			20.0541i			1.60049i	−0.599673	+	0.800245i	$0.704702\pi$
$158$			27.8459i			2.21530i
$159$	−4.08680			−0.324104
$160$	−0.132822	−	0.717298i	−0.0105005	−	0.0567074i
$161$	−2.19869			−0.173281
$162$			17.1773i			1.34958i
$163$		−	14.2331i		−	1.11482i	−0.830236	−	0.557412i	$-0.811794\pi$
$163$		−	14.2331i		−	1.11482i	0.830236	−	0.557412i	$-0.188206\pi$
$164$	−0.292035			−0.0228041
$165$	1.39738	+	7.54647i	0.108786	+	0.587492i
$166$	−38.5621			−2.99300
$167$		−	5.61630i		−	0.434602i	−0.976105	−	0.217301i	$-0.930275\pi$
$167$		−	5.61630i		−	0.434602i	0.976105	−	0.217301i	$-0.0697253\pi$
$168$			35.1176i			2.70938i
$169$	−1.12628			−0.0866368
$170$	−3.59607	+	0.665886i	−0.275806	+	0.0510711i
$171$		0			0
$172$		−	1.69601i		−	0.129320i
$173$		−	10.6905i		−	0.812783i	−0.913699	−	0.406391i	$-0.866787\pi$
$173$		−	10.6905i		−	0.812783i	0.913699	−	0.406391i	$-0.133213\pi$
$174$	−13.7882			−1.04528
$175$	−8.06587	−	21.0328i	−0.609722	−	1.58993i
$176$	9.23163			0.695860
$177$		−	19.5687i		−	1.47088i
$178$		−	3.28388i		−	0.246137i
$179$	−7.68942			−0.574734			−0.287367	−	0.957821i	$-0.592780\pi$
$179$	−7.68942			−0.574734			−0.287367	+	0.957821i	$0.592780\pi$
$180$	−4.99346	+	0.924640i	−0.372190	+	0.0689186i
$181$	−6.12628			−0.455363			−0.227681	−	0.973736i	$-0.573114\pi$
$181$	−6.12628			−0.455363			−0.227681	+	0.973736i	$0.573114\pi$
$182$			41.5910i			3.08293i
$183$			11.0301i			0.815371i
$184$	2.43686			0.179648
$185$	1.22617	+	6.62183i	0.0901496	+	0.486847i
$186$	26.2042			1.92138
$187$		−	1.46408i		−	0.107064i
$188$			20.2565i			1.47736i
$189$	25.0593			1.82280
$190$		0			0
$191$	5.85517			0.423666			0.211833	−	0.977306i	$-0.432057\pi$
$191$	5.85517			0.423666			0.211833	+	0.977306i	$0.432057\pi$
$192$			11.8578i			0.855764i
$193$			2.59117i			0.186517i	0.995642	+	0.0932584i	$0.0297283\pi$
$193$			2.59117i			0.186517i	−0.995642	+	0.0932584i	$0.970272\pi$
$194$	−10.7738			−0.773516
$195$	12.9001	−	2.38872i	0.923796	−	0.171060i
$196$	53.6279			3.83057
$197$			19.8628i			1.41517i	0.706629	+	0.707584i	$0.250215\pi$
$197$			19.8628i			1.41517i	−0.706629	+	0.707584i	$0.749785\pi$
$198$		−	3.04120i		−	0.216128i
$199$	12.7618			0.904662			0.452331	−	0.891850i	$-0.350593\pi$
$199$	12.7618			0.904662			0.452331	+	0.891850i	$0.350593\pi$
$200$	8.93959	+	23.3112i	0.632124	+	1.64835i
$201$	8.93959			0.630550
$202$			25.9586i			1.82644i
$203$			16.2013i			1.13711i
$204$	−4.19215			−0.293509
$205$	0.159213	−	0.0294815i	0.0111199	−	0.00205908i
$206$	14.1383			0.985061
$207$		−	0.274827i		−	0.0191018i
$208$		−	15.7808i		−	1.09420i
$209$		0			0
$210$	−7.03293	−	37.9809i	−0.485319	−	2.62093i
$211$	13.8552			0.953830			0.476915	−	0.878950i	$-0.341755\pi$
$211$	13.8552			0.953830			0.476915	+	0.878950i	$0.341755\pi$
$212$		−	10.5582i		−	0.725139i
$213$			10.8844i			0.745788i
$214$	3.19869			0.218658
$215$	0.171216	+	0.924640i	0.0116768	+	0.0630599i
$216$	−27.7738			−1.88977
$217$		−	30.7901i		−	2.09017i
$218$		−	29.5553i		−	2.00174i
$219$	4.61701			0.311988
$220$	−19.4962	+	3.61012i	−1.31443	+	0.243394i
$221$	−2.50273			−0.168352
$222$			11.5476i			0.775027i
$223$		−	21.6960i		−	1.45287i	−0.687233	−	0.726437i	$-0.741175\pi$
$223$		−	21.6960i		−	1.45287i	0.687233	−	0.726437i	$-0.258825\pi$
$224$	−1.46980			−0.0982048
$225$	2.62901	−	1.00820i	0.175267	−	0.0672132i
$226$	19.0264			1.26562
$227$			8.19628i			0.544006i	0.962296	+	0.272003i	$0.0876861\pi$
$227$			8.19628i			0.544006i	−0.962296	+	0.272003i	$0.912314\pi$
$228$		0			0
$229$	16.6619			1.10105			0.550526	−	0.834818i	$-0.314427\pi$
$229$	16.6619			1.10105			0.550526	+	0.834818i	$0.314427\pi$
$230$	−2.63555	+	0.488026i	−0.173783	+	0.0321795i
$231$	15.4633			1.01741
$232$		−	17.9563i		−	1.17889i
$233$		−	12.2135i		−	0.800135i	−0.916486	−	0.400068i	$-0.868987\pi$
$233$		−	12.2135i		−	0.800135i	0.916486	−	0.400068i	$-0.131013\pi$
$234$	−5.19869			−0.339849
$235$	−2.04494	−	11.0435i	−0.133397	−	0.720402i
$236$	50.5555			3.29088
$237$		−	17.6975i		−	1.14958i
$238$			7.36861i			0.477636i
$239$	−2.03948			−0.131923			−0.0659614	−	0.997822i	$-0.521011\pi$
$239$	−2.03948			−0.131923			−0.0659614	+	0.997822i	$0.521011\pi$
$240$	2.66849	+	14.4110i	0.172250	+	0.930225i
$241$	17.5237			1.12880			0.564399	−	0.825502i	$-0.309108\pi$
$241$	17.5237			1.12880			0.564399	+	0.825502i	$0.309108\pi$
$242$			15.1444i			0.973516i
$243$			5.76956i			0.370118i
$244$	−28.4962			−1.82428
$245$	−29.2371	+	5.41384i	−1.86789	+	0.345878i
$246$	0.277648			0.0177022
$247$		0			0
$248$			34.1254i			2.16697i
$249$	24.5082			1.55314
$250$	−14.3370	−	23.4215i	−0.906750	−	1.48131i
$251$	−3.33806			−0.210696			−0.105348	−	0.994435i	$-0.533596\pi$
$251$	−3.33806			−0.210696			−0.105348	+	0.994435i	$0.533596\pi$
$252$			10.2319i			0.644552i
$253$		−	1.07302i		−	0.0674601i
$254$	9.66849			0.606655
$255$	2.28549	−	0.423205i	0.143123	−	0.0265021i
$256$	−32.2371			−2.01482
$257$		−	27.5845i		−	1.72067i	−0.509726	−	0.860337i	$-0.670253\pi$
$257$		−	27.5845i		−	1.72067i	0.509726	−	0.860337i	$-0.329747\pi$
$258$			1.61246i			0.100387i
$259$	13.5686			0.843112
$260$	6.17122	+	33.3272i	0.382723	+	2.06687i
$261$	−2.02509			−0.125350
$262$			40.0974i			2.47723i
$263$			13.6262i			0.840227i	0.907471	+	0.420114i	$0.138010\pi$
$263$			13.6262i			0.840227i	−0.907471	+	0.420114i	$0.861990\pi$
$264$	−17.1383			−1.05479
$265$	1.06587	+	5.75615i	0.0654758	+	0.353598i
$266$		0			0
$267$			2.08707i			0.127727i
$268$			23.0953i			1.41077i
$269$	3.60808			0.219988			0.109994	−	0.993932i	$-0.464917\pi$
$269$	3.60808			0.219988			0.109994	+	0.993932i	$0.464917\pi$
$270$	30.0384	−	5.56222i	1.82808	−	0.338506i
$271$	10.5631			0.641665			0.320833	−	0.947136i	$-0.396037\pi$
$271$	10.5631			0.641665			0.320833	+	0.947136i	$0.396037\pi$
$272$		−	2.79585i		−	0.169523i
$273$		−	26.4332i		−	1.59981i
$274$	40.3568			2.43804
$275$	10.2646	−	3.93635i	0.618976	−	0.237371i
$276$	−3.07241			−0.184938
$277$		−	6.73487i		−	0.404659i	−0.979317	−	0.202330i	$-0.935149\pi$
$277$		−	6.73487i		−	0.404659i	0.979317	−	0.202330i	$-0.0648512\pi$
$278$		−	6.55434i		−	0.393103i
$279$	3.84863			0.230412
$280$	49.4622	−	9.15893i	2.95593	−	0.547351i
$281$	23.4303			1.39774			0.698868	−	0.715251i	$-0.253688\pi$
$281$	23.4303			1.39774			0.698868	+	0.715251i	$0.253688\pi$
$282$		−	19.2586i		−	1.14683i
$283$			14.6831i			0.872822i	0.899747	+	0.436411i	$0.143751\pi$
$283$			14.6831i			0.872822i	−0.899747	+	0.436411i	$0.856249\pi$
$284$	−28.1197			−1.66860
$285$		0			0
$286$	−20.2975			−1.20022
$287$		−	0.326239i		−	0.0192573i
$288$		−	0.183718i		−	0.0108257i
$289$	16.5566			0.973917
$290$	3.59607	+	19.4204i	0.211169	+	1.14040i
$291$	6.84733			0.401398
$292$			11.9280i			0.698031i
$293$			18.1855i			1.06241i	0.847243	+	0.531206i	$0.178261\pi$
$293$			18.1855i			1.06241i	−0.847243	+	0.531206i	$0.821739\pi$
$294$	−50.9858			−2.97355
$295$	−27.5621	+	5.10368i	−1.60472	+	0.297147i
$296$	−15.0384			−0.874089
$297$			12.2296i			0.709634i
$298$		−	44.1281i		−	2.55627i
$299$	−1.83424			−0.106077
$300$	−11.2711	−	29.3909i	−0.650737	−	1.69688i
$301$	1.89465			0.109206
$302$			31.2782i			1.79986i
$303$		−	16.4981i		−	0.947788i
$304$		0			0
$305$	15.5357	−	2.87674i	0.889570	−	0.164722i
$306$	−0.921044			−0.0526526
$307$			29.3801i			1.67681i	0.545045	+	0.838406i	$0.316512\pi$
$307$			29.3801i			1.67681i	−0.545045	+	0.838406i	$0.683488\pi$
$308$			39.9491i			2.27631i
$309$	−8.98561			−0.511174
$310$	−6.83424	−	36.9079i	−0.388159	−	2.09623i
$311$	−0.193232			−0.0109572			−0.00547859	−	0.999985i	$-0.501744\pi$
$311$	−0.193232			−0.0109572			−0.00547859	+	0.999985i	$0.501744\pi$
$312$			29.2966i			1.65859i
$313$			21.2755i			1.20256i	0.799038	+	0.601281i	$0.205343\pi$
$313$			21.2755i			1.20256i	−0.799038	+	0.601281i	$0.794657\pi$
$314$	49.2569			2.77973
$315$	−1.03293	−	5.57829i	−0.0581993	−	0.314301i
$316$	45.7213			2.57202
$317$			19.1701i			1.07670i	0.842721	+	0.538351i	$0.180952\pi$
$317$			19.1701i			1.07670i	−0.842721	+	0.538351i	$0.819048\pi$
$318$			10.0380i			0.562904i
$319$	−7.90666			−0.442688
$320$	16.7014	−	3.09261i	0.933638	−	0.172882i
$321$	−2.03293			−0.113467
$322$			5.40043i			0.300954i
$323$		0			0
$324$	28.2042			1.56690
$325$	−6.72890	−	17.5465i	−0.373252	−	0.973304i
$326$	−34.9594			−1.93622
$327$			18.7839i			1.03875i
$328$			0.361578i			0.0199648i
$329$	−22.6290			−1.24758
$330$	18.5357	−	3.43226i	1.02035	−	0.188939i
$331$	−20.6070			−1.13266			−0.566331	−	0.824178i	$-0.691638\pi$
$331$	−20.6070			−1.13266			−0.566331	+	0.824178i	$0.691638\pi$
$332$			63.3165i			3.47495i
$333$			1.69601i			0.0929410i
$334$	−13.7948			−0.754816
$335$	−2.33151	−	12.5912i	−0.127384	−	0.687930i
$336$	29.5291			1.61095
$337$		−	10.2074i		−	0.556030i	−0.960577	−	0.278015i	$-0.910324\pi$
$337$		−	10.2074i		−	0.556030i	0.960577	−	0.278015i	$-0.0896765\pi$
$338$			2.76637i			0.150471i
$339$	−12.0923			−0.656761
$340$	1.09334	+	5.90453i	0.0592949	+	0.320218i
$341$	15.0264			0.813725
$342$		0			0
$343$			28.3719i			1.53194i
$344$	−2.09989			−0.113218
$345$	1.67503	−	0.310166i	0.0901806	−	0.0166988i
$346$	−26.2580			−1.41164
$347$			5.44110i			0.292094i	0.989278	+	0.146047i	$0.0466550\pi$
$347$			5.44110i			0.292094i	−0.989278	+	0.146047i	$0.953345\pi$
$348$			22.6394i			1.21360i
$349$	1.55114			0.0830304			0.0415152	−	0.999138i	$-0.486781\pi$
$349$	1.55114			0.0830304			0.0415152	+	0.999138i	$0.486781\pi$
$350$	−51.6609	+	19.8114i	−2.76139	+	1.05896i
$351$	20.9056			1.11586
$352$		−	0.717298i		−	0.0382321i
$353$			32.9335i			1.75287i	0.481517	+	0.876437i	$0.340086\pi$
$353$			32.9335i			1.75287i	−0.481517	+	0.876437i	$0.659914\pi$
$354$	−48.0648			−2.55461
$355$	15.3304	−	2.83874i	0.813655	−	0.150665i
$356$	−5.39192			−0.285771
$357$		−	4.68313i		−	0.247858i
$358$			18.8868i			0.998197i
$359$	3.49727			0.184579			0.0922894	−	0.995732i	$-0.470581\pi$
$359$	3.49727			0.184579			0.0922894	+	0.995732i	$0.470581\pi$
$360$	1.14483	+	6.18255i	0.0603376	+	0.325849i
$361$		0			0
$362$			15.0474i			0.790873i
$363$		−	9.62502i		−	0.505183i
$364$	68.2899			3.57936
$365$	−1.20415	−	6.50293i	−0.0630281	−	0.340379i
$366$	27.0923			1.41614
$367$			19.5039i			1.01810i	0.860738	+	0.509048i	$0.170002\pi$
$367$			19.5039i			1.01810i	−0.860738	+	0.509048i	$0.829998\pi$
$368$		−	2.04907i		−	0.106815i
$369$	0.0407784			0.00212284
$370$	16.2646	−	3.01171i	0.845554	−	0.156572i
$371$	11.7948			0.612354
$372$		−	43.0256i		−	2.23077i
$373$		−	23.5158i		−	1.21760i	−0.793322	−	0.608802i	$-0.791650\pi$
$373$		−	23.5158i		−	1.21760i	0.793322	−	0.608802i	$-0.208350\pi$
$374$	−3.59607			−0.185949
$375$	9.11189	+	14.8856i	0.470536	+	0.768689i
$376$	25.0803			1.29342
$377$			13.5158i			0.696100i
$378$		−	61.5508i		−	3.16583i
$379$	7.05148			0.362210			0.181105	−	0.983464i	$-0.442033\pi$
$379$	7.05148			0.362210			0.181105	+	0.983464i	$0.442033\pi$
$380$		0			0
$381$	−6.14483			−0.314809
$382$		−	14.3815i		−	0.735822i
$383$		−	3.08409i		−	0.157589i	−0.996891	−	0.0787947i	$-0.974893\pi$
$383$		−	3.08409i		−	0.157589i	0.996891	−	0.0787947i	$-0.0251072\pi$
$384$	30.1437			1.53827
$385$	−4.03293	−	21.7796i	−0.205537	−	1.10999i
$386$	6.36445			0.323942
$387$			0.236823i			0.0120384i
$388$			17.6900i			0.898072i
$389$	−9.39084			−0.476134			−0.238067	−	0.971249i	$-0.576514\pi$
$389$	−9.39084			−0.476134			−0.238067	+	0.971249i	$0.576514\pi$
$390$	−5.86718	−	31.6853i	−0.297096	−	1.60445i
$391$	−0.324970			−0.0164344
$392$		−	66.3984i		−	3.35362i
$393$		−	25.4840i		−	1.28550i
$394$	48.7871			2.45786
$395$	−24.9265	+	4.61565i	−1.25419	+	0.232239i
$396$	−4.99346			−0.250931
$397$		−	26.7595i		−	1.34302i	−0.740996	−	0.671510i	$-0.765646\pi$
$397$		−	26.7595i		−	1.34302i	0.740996	−	0.671510i	$-0.234354\pi$
$398$		−	31.3456i		−	1.57122i
$399$		0			0
$400$	19.6015	−	7.51699i	0.980077	−	0.375849i
$401$	−25.1701			−1.25694			−0.628468	−	0.777835i	$-0.716318\pi$
$401$	−25.1701			−1.25694			−0.628468	+	0.777835i	$0.716318\pi$
$402$		−	21.9575i		−	1.09514i
$403$		−	25.6865i		−	1.27953i
$404$	42.6225			2.12055
$405$	−15.3765	+	2.84726i	−0.764062	+	0.141482i
$406$	39.7937			1.97493
$407$			6.62183i			0.328232i
$408$			5.19043i			0.256964i
$409$	28.3215			1.40041			0.700204	−	0.713943i	$-0.253092\pi$
$409$	28.3215			1.40041			0.700204	+	0.713943i	$0.253092\pi$
$410$	−0.0724126	−	0.391060i	−0.00357621	−	0.0193131i
$411$	−25.6489			−1.26516
$412$		−	23.2142i		−	1.14368i
$413$			56.4766i			2.77903i
$414$	−0.675030			−0.0331759
$415$	−6.39192	−	34.5192i	−0.313767	−	1.69448i
$416$	−1.22617			−0.0601178
$417$			4.16563i			0.203992i
$418$		0			0
$419$	−13.0449			−0.637287			−0.318643	−	0.947875i	$-0.603227\pi$
$419$	−13.0449			−0.637287			−0.318643	+	0.947875i	$0.603227\pi$
$420$	−62.3623	+	11.5476i	−3.04297	+	0.563467i
$421$	3.32497			0.162049			0.0810246	−	0.996712i	$-0.474181\pi$
$421$	3.32497			0.162049			0.0810246	+	0.996712i	$0.474181\pi$
$422$		−	34.0311i		−	1.65661i
$423$		−	2.82853i		−	0.137528i
$424$	−13.0724			−0.634852
$425$	−1.19215	−	3.10868i	−0.0578276	−	0.150793i
$426$	26.7344			1.29528
$427$		−	31.8337i		−	1.54054i
$428$		−	5.25205i		−	0.253868i
$429$	12.9001			0.622823
$430$	2.27110	−	0.420541i	0.109522	−	0.0202803i
$431$	0.0484069			0.00233168			0.00116584	−	0.999999i	$-0.499629\pi$
$431$	0.0484069			0.00233168			0.00116584	+	0.999999i	$0.499629\pi$
$432$			23.3540i			1.12362i
$433$			9.56872i			0.459844i	0.973209	+	0.229922i	$0.0738470\pi$
$433$			9.56872i			0.459844i	−0.973209	+	0.229922i	$0.926153\pi$
$434$	−75.6268			−3.63020
$435$	−2.28549	−	12.3426i	−0.109581	−	0.591784i
$436$	−48.5280			−2.32407
$437$		0			0
$438$		−	11.3403i		−	0.541861i
$439$	22.2515			1.06200			0.531002	−	0.847370i	$-0.321816\pi$
$439$	22.2515			1.06200			0.531002	+	0.847370i	$0.321816\pi$
$440$	4.46980	+	24.1388i	0.213089	+	1.15077i
$441$	−7.48834			−0.356588
$442$			6.14721i			0.292393i
$443$		−	20.1157i		−	0.955727i	−0.878434	−	0.477863i	$-0.841411\pi$
$443$		−	20.1157i		−	0.955727i	0.878434	−	0.477863i	$-0.158589\pi$
$444$	18.9605			0.899827
$445$	2.93959	−	0.544325i	0.139350	−	0.0258035i
$446$	−53.2899			−2.52335
$447$			28.0457i			1.32652i
$448$		−	34.2224i		−	1.61686i
$449$	12.4973			0.589783			0.294891	−	0.955531i	$-0.404717\pi$
$449$	12.4973			0.589783			0.294891	+	0.955531i	$0.404717\pi$
$450$	−2.47634	−	6.45738i	−0.116736	−	0.304404i
$451$	0.159213			0.00749705
$452$		−	31.2402i		−	1.46941i
$453$		−	19.8789i		−	0.933992i
$454$	20.1317			0.944829
$455$	−37.2305	+	6.89399i	−1.74539	+	0.323195i
$456$		0			0
$457$		−	28.3179i		−	1.32465i	−0.749215	−	0.662327i	$-0.769569\pi$
$457$		−	28.3179i		−	1.32465i	0.749215	−	0.662327i	$-0.230431\pi$
$458$		−	40.9251i		−	1.91231i
$459$	3.70381			0.172879
$460$	0.801309	+	4.32741i	0.0373612	+	0.201767i
$461$	5.31951			0.247754			0.123877	−	0.992298i	$-0.460467\pi$
$461$	5.31951			0.247754			0.123877	+	0.992298i	$0.460467\pi$
$462$		−	37.9809i		−	1.76703i
$463$			17.9327i			0.833401i	0.909044	+	0.416701i	$0.136814\pi$
$463$			17.9327i			0.833401i	−0.909044	+	0.416701i	$0.863186\pi$
$464$	−15.0988			−0.700944
$465$	4.34352	+	23.4569i	0.201426	+	1.08779i
$466$	−29.9989			−1.38967
$467$			28.7791i			1.33174i	0.746069	+	0.665868i	$0.231939\pi$
$467$			28.7791i			1.33174i	−0.746069	+	0.665868i	$0.768061\pi$
$468$			8.53593i			0.394574i
$469$	−25.8002			−1.19134
$470$	−27.1252	+	5.02278i	−1.25119	+	0.231684i
$471$	−31.3053			−1.44247
$472$		−	62.5943i		−	2.88114i
$473$			0.924640i			0.0425150i
$474$	−43.4687			−1.99658
$475$		0			0
$476$	12.0988			0.554548
$477$			1.47429i			0.0675033i
$478$			5.00937i			0.229123i
$479$	8.05148			0.367882			0.183941	−	0.982937i	$-0.441115\pi$
$479$	8.05148			0.367882			0.183941	+	0.982937i	$0.441115\pi$
$480$	1.11973	−	0.207342i	0.0511087	−	0.00946381i
$481$	11.3195			0.516125
$482$		−	43.0417i		−	1.96049i
$483$		−	3.43226i		−	0.156173i
$484$	24.8661			1.13028
$485$	−1.78584	−	9.64429i	−0.0810907	−	0.437925i
$486$	14.1712			0.642819
$487$			1.09761i			0.0497376i	0.999691	+	0.0248688i	$0.00791680\pi$
$487$			1.09761i			0.0497376i	−0.999691	+	0.0248688i	$0.992083\pi$
$488$			35.2820i			1.59714i
$489$	22.2185			1.00476
$490$	13.2975	+	71.8122i	0.600720	+	3.24415i
$491$	13.1053			0.591436			0.295718	−	0.955275i	$-0.404441\pi$
$491$	13.1053			0.591436			0.295718	+	0.955275i	$0.404441\pi$
$492$		−	0.455880i		−	0.0205527i
$493$			2.39458i			0.107846i
$494$		0			0
$495$	2.72235	−	0.504099i	0.122361	−	0.0226576i
$496$	28.6949			1.28844
$497$		−	31.4131i		−	1.40907i
$498$		−	60.1971i		−	2.69750i
$499$	−24.1407			−1.08068			−0.540342	−	0.841445i	$-0.681705\pi$
$499$	−24.1407			−1.08068			−0.540342	+	0.841445i	$0.681705\pi$
$500$	−38.4567	+	23.5404i	−1.71984	+	1.05276i
$501$	8.76729			0.391694
$502$			8.19895i			0.365937i
$503$			18.9618i			0.845465i	0.906254	+	0.422733i	$0.138929\pi$
$503$			18.9618i			0.845465i	−0.906254	+	0.422733i	$0.861071\pi$
$504$	12.6685			0.564299
$505$	−23.2371	+	4.30282i	−1.03404	+	0.191473i
$506$	−2.63555			−0.117165
$507$		−	1.75817i		−	0.0780831i
$508$		−	15.8751i		−	0.704342i
$509$	−21.9605			−0.973383			−0.486692	−	0.873574i	$-0.661796\pi$
$509$	−21.9605			−0.973383			−0.486692	+	0.873574i	$0.661796\pi$
$510$	−1.03948	−	5.61363i	−0.0460289	−	0.248576i
$511$	−13.3250			−0.589462
$512$			40.5609i			1.79255i
$513$		0			0
$514$	−67.7531			−2.98846
$515$	2.34352	+	12.6560i	0.103268	+	0.557690i
$516$	2.64755			0.116552
$517$		−	11.0435i		−	0.485695i
$518$		−	33.3272i		−	1.46431i
$519$	16.6883			0.732537
$520$	41.2635	−	7.64077i	1.80952	−	0.335070i
$521$	6.56968			0.287823			0.143912	−	0.989591i	$-0.454032\pi$
$521$	6.56968			0.287823			0.143912	+	0.989591i	$0.454032\pi$
$522$			4.97403i			0.217708i
$523$		−	4.19777i		−	0.183556i	−0.995780	−	0.0917779i	$-0.970745\pi$
$523$		−	4.19777i		−	0.183556i	0.995780	−	0.0917779i	$-0.0292550\pi$
$524$	65.8375			2.87613
$525$	32.8332	−	12.5912i	1.43296	−	0.549524i
$526$	33.4687			1.45931
$527$		−	4.55083i		−	0.198237i
$528$			14.4110i			0.627157i
$529$	22.7618			0.989645
$530$	14.1383	−	2.61799i	0.614128	−	0.113718i
$531$	−7.05933			−0.306349
$532$		0			0
$533$		−	0.272162i		−	0.0117887i
$534$	5.12628			0.221836
$535$	0.530205	+	2.86334i	0.0229228	+	0.123793i
$536$	28.5950			1.23512
$537$		−	12.0035i		−	0.517990i
$538$		−	8.86217i		−	0.382075i
$539$	−29.2371			−1.25933
$540$	−9.13282	−	49.3212i	−0.393014	−	2.12245i
$541$	−4.63009			−0.199063			−0.0995316	−	0.995034i	$-0.531734\pi$
$541$	−4.63009			−0.199063			−0.0995316	+	0.995034i	$0.531734\pi$
$542$		−	25.9452i		−	1.11444i
$543$		−	9.56340i		−	0.410405i
$544$	−0.217238			−0.00931400
$545$	26.4567	−	4.89900i	1.13328	−	0.209850i
$546$	−64.9254			−2.77855
$547$		−	38.0399i		−	1.62647i	−0.581938	−	0.813233i	$-0.697705\pi$
$547$		−	38.0399i		−	1.62647i	0.581938	−	0.813233i	$-0.302295\pi$
$548$		−	66.2634i		−	2.83063i
$549$	3.97907			0.169823
$550$	−9.66849	−	25.2118i	−0.412266	−	1.07504i
$551$		0			0
$552$			3.80405i			0.161911i
$553$			51.0762i			2.17198i
$554$	−16.5422			−0.702811
$555$	−10.3370	+	1.91410i	−0.438780	+	0.0812491i
$556$	−10.7618			−0.456403
$557$			36.4306i			1.54361i	0.635857	+	0.771807i	$0.280647\pi$
$557$			36.4306i			1.54361i	−0.635857	+	0.771807i	$0.719353\pi$
$558$		−	9.45302i		−	0.400178i
$559$	1.58060			0.0668523
$560$	−7.70142	−	41.5910i	−0.325444	−	1.75754i
$561$	2.28549			0.0964935
$562$		−	57.5496i		−	2.42758i
$563$		−	20.6856i		−	0.871795i	−0.899996	−	0.435897i	$-0.856431\pi$
$563$		−	20.6856i		−	0.871795i	0.899996	−	0.435897i	$-0.143569\pi$
$564$	−31.6214			−1.33150
$565$	3.15375	+	17.0316i	0.132679	+	0.716526i
$566$	36.0648			1.51592
$567$			31.5074i			1.32319i
$568$			34.8159i			1.46084i
$569$	27.1132			1.13664			0.568322	−	0.822806i	$-0.307593\pi$
$569$	27.1132			1.13664			0.568322	+	0.822806i	$0.307593\pi$
$570$		0			0
$571$	46.4687			1.94466			0.972328	−	0.233622i	$-0.0750578\pi$
$571$	46.4687			1.94466			0.972328	+	0.233622i	$0.0750578\pi$
$572$			33.3272i			1.39348i
$573$			9.14019i			0.381837i
$574$	−0.801309			−0.0334460
$575$	−0.873721	−	2.27834i	−0.0364367	−	0.0950135i
$576$	4.27765			0.178235
$577$			18.0398i			0.751008i	0.926821	+	0.375504i	$0.122530\pi$
$577$			18.0398i			0.751008i	−0.926821	+	0.375504i	$0.877470\pi$
$578$		−	40.6664i		−	1.69150i
$579$	−4.04494			−0.168102
$580$	31.8870	−	5.90453i	1.32404	−	0.245172i
$581$	−70.7322			−2.93447
$582$		−	16.8184i		−	0.697147i
$583$			5.75615i			0.238395i
$584$	14.7684			0.611120
$585$	−0.861719	−	4.65365i	−0.0356277	−	0.192405i
$586$	44.6674			1.84519
$587$			26.0337i			1.07452i	0.843415	+	0.537262i	$0.180541\pi$
$587$			26.0337i			1.07452i	−0.843415	+	0.537262i	$0.819459\pi$
$588$			83.7156i			3.45237i
$589$		0			0
$590$	12.5357	+	67.6980i	0.516085	+	2.78708i
$591$	−31.0068			−1.27545
$592$			12.6453i			0.519717i
$593$			18.1561i			0.745580i	0.927916	+	0.372790i	$0.121599\pi$
$593$			18.1561i			0.745580i	−0.927916	+	0.372790i	$0.878401\pi$
$594$	30.0384			1.23249
$595$	−6.59607	+	1.22140i	−0.270413	+	0.0500724i
$596$	−72.4556			−2.96790
$597$			19.9218i			0.815345i
$598$			4.50527i			0.184234i
$599$	−40.0713			−1.63727			−0.818635	−	0.574314i	$-0.805269\pi$
$599$	−40.0713			−1.63727			−0.818635	+	0.574314i	$0.805269\pi$
$600$	−36.3898	+	13.9551i	−1.48561	+	0.569715i
$601$	15.0473			0.613793			0.306897	−	0.951743i	$-0.400709\pi$
$601$	15.0473			0.613793			0.306897	+	0.951743i	$0.400709\pi$
$602$		−	4.65365i		−	0.189669i
$603$		−	3.22491i		−	0.131329i
$604$	51.3568			2.08968
$605$	−13.5566	+	2.51028i	−0.551154	+	0.102057i
$606$	−40.5226			−1.64612
$607$		−	29.3860i		−	1.19274i	−0.802709	−	0.596370i	$-0.796609\pi$
$607$		−	29.3860i		−	1.19274i	0.802709	−	0.596370i	$-0.203391\pi$
$608$		0			0
$609$	−25.2910			−1.02484
$610$	−7.06587	−	38.1587i	−0.286089	−	1.54500i
$611$	−18.8781			−0.763726
$612$			1.51230i			0.0611310i
$613$			34.7078i			1.40183i	0.713243	+	0.700917i	$0.247225\pi$
$613$			34.7078i			1.40183i	−0.713243	+	0.700917i	$0.752775\pi$
$614$	72.1636			2.91229
$615$	0.0460220	+	0.248539i	0.00185579	+	0.0100220i
$616$	49.4622			1.99289
$617$			10.7275i			0.431874i	0.976407	+	0.215937i	$0.0692805\pi$
$617$			10.7275i			0.431874i	−0.976407	+	0.215937i	$0.930719\pi$
$618$			22.0705i			0.887805i
$619$	36.1437			1.45274			0.726370	−	0.687304i	$-0.241206\pi$
$619$	36.1437			1.45274			0.726370	+	0.687304i	$0.241206\pi$
$620$	−60.6004	+	11.2214i	−2.43377	+	0.450663i
$621$	2.71451			0.108929
$622$			0.474617i			0.0190304i
$623$		−	6.02343i		−	0.241324i
$624$	24.6345			0.986168
$625$	18.5895	−	16.7161i	0.743581	−	0.668646i
$626$	52.2569			2.08861
$627$		0			0
$628$		−	80.8768i		−	3.22734i
$629$	2.00546			0.0799629
$630$	−13.7014	+	2.53710i	−0.545878	+	0.101080i
$631$	−31.5764			−1.25704			−0.628519	−	0.777794i	$-0.716339\pi$
$631$	−31.5764			−1.25704			−0.628519	+	0.777794i	$0.716339\pi$
$632$		−	56.6089i		−	2.25178i
$633$			21.6285i			0.859658i
$634$	47.0857			1.87001
$635$	1.60262	+	8.65483i	0.0635979	+	0.343456i
$636$	16.4818			0.653546
$637$			49.9786i			1.98022i
$638$			19.4204i			0.768859i
$639$	3.92650			0.155330
$640$	−7.86172	−	42.4567i	−0.310762	−	1.67825i
$641$	19.8266			0.783104			0.391552	−	0.920156i	$-0.371938\pi$
$641$	19.8266			0.783104			0.391552	+	0.920156i	$0.371938\pi$
$642$			4.99330i			0.197070i
$643$		−	13.4569i		−	0.530687i	−0.964154	−	0.265343i	$-0.914515\pi$
$643$		−	13.4569i		−	0.530687i	0.964154	−	0.265343i	$-0.0854853\pi$
$644$	8.86718			0.349416
$645$	−1.44340	+	0.267276i	−0.0568340	+	0.0105240i
$646$		0			0
$647$			4.19511i			0.164927i	0.996594	+	0.0824634i	$0.0262787\pi$
$647$			4.19511i			0.164927i	−0.996594	+	0.0824634i	$0.973721\pi$
$648$		−	34.9204i		−	1.37180i
$649$	−27.5621			−1.08191
$650$	−43.0977	+	16.5275i	−1.69043	+	0.648263i
$651$	48.0648			1.88381
$652$			57.4012i			2.24801i
$653$			12.1680i			0.476170i	0.971244	+	0.238085i	$0.0765196\pi$
$653$			12.1680i			0.476170i	−0.971244	+	0.238085i	$0.923480\pi$
$654$	46.1372			1.80411
$655$	−35.8936	+	6.64642i	−1.40248	+	0.259697i
$656$	0.304038			0.0118707
$657$		−	1.66556i		−	0.0649798i
$658$			55.5814i			2.16679i
$659$	−8.24471			−0.321168			−0.160584	−	0.987022i	$-0.551338\pi$
$659$	−8.24471			−0.321168			−0.160584	+	0.987022i	$0.551338\pi$
$660$	−5.63555	−	30.4344i	−0.219364	−	1.18466i
$661$	21.1197			0.821462			0.410731	−	0.911756i	$-0.365273\pi$
$661$	21.1197			0.821462			0.410731	+	0.911756i	$0.365273\pi$
$662$			50.6150i			1.96721i
$663$		−	3.90687i		−	0.151730i
$664$	78.3941			3.04228
$665$		0			0
$666$	4.16576			0.161420
$667$			1.75498i			0.0679530i
$668$			22.6502i			0.876361i
$669$	33.8685			1.30943
$670$	−30.9265	+	5.72667i	−1.19480	+	0.221241i
$671$	15.5357			0.599748
$672$		−	2.29442i		−	0.0885090i
$673$			30.2802i			1.16722i	0.812036	+	0.583608i	$0.198359\pi$
$673$			30.2802i			1.16722i	−0.812036	+	0.583608i	$0.801641\pi$
$674$	−25.0713			−0.965711
$675$	9.95814	+	25.9671i	0.383289	+	0.999476i
$676$	4.54221			0.174700
$677$			49.9003i			1.91783i	0.283701	+	0.958913i	$0.408438\pi$
$677$			49.9003i			1.91783i	−0.283701	+	0.958913i	$0.591562\pi$
$678$			29.7010i			1.14066i
$679$	−19.7618			−0.758389
$680$	7.31058	−	1.35370i	0.280348	−	0.0519121i
$681$	−12.7948			−0.490296
$682$		−	36.9079i		−	1.41328i
$683$		−	3.11357i		−	0.119137i	−0.998224	−	0.0595687i	$-0.981027\pi$
$683$		−	3.11357i		−	0.119137i	0.998224	−	0.0595687i	$-0.0189725\pi$
$684$		0			0
$685$	6.68942	+	36.1258i	0.255590	+	1.38029i
$686$	69.6872			2.66067
$687$			26.0100i			0.992345i
$688$			1.76572i			0.0673175i
$689$	9.83970			0.374863
$690$	−0.761831	−	4.11421i	−0.0290024	−	0.156625i
$691$	−30.2831			−1.15202			−0.576012	−	0.817441i	$-0.695392\pi$
$691$	−30.2831			−1.15202			−0.576012	+	0.817441i	$0.695392\pi$
$692$			43.1140i			1.63895i
$693$		−	5.57829i		−	0.211902i
$694$	13.3644			0.507308
$695$	5.86718	−	1.08643i	0.222555	−	0.0412105i
$696$	28.0305			1.06250
$697$		−	0.0482186i		−	0.00182641i
$698$		−	3.80991i		−	0.144207i
$699$	19.0659			0.721137
$700$	32.5291	+	84.8239i	1.22949	+	3.20604i
$701$	44.5699			1.68338			0.841691	−	0.539960i	$-0.181561\pi$
$701$	44.5699			1.68338			0.841691	+	0.539960i	$0.181561\pi$
$702$		−	51.3483i		−	1.93802i
$703$		0			0
$704$	16.7014			0.629458
$705$	17.2395	−	3.19224i	0.649276	−	0.120227i
$706$	80.8914			3.04439
$707$			47.6144i			1.79073i
$708$			78.9194i			2.96597i
$709$	−9.34352			−0.350903			−0.175452	−	0.984488i	$-0.556139\pi$
$709$	−9.34352			−0.350903			−0.175452	+	0.984488i	$0.556139\pi$
$710$	−6.97252	−	37.6546i	−0.261674	−	1.41315i
$711$	−6.38429			−0.239430
$712$			6.67591i			0.250190i
$713$		−	3.33529i		−	0.124908i
$714$	−11.5027			−0.430479
$715$	−3.36445	−	18.1695i	−0.125823	−	0.679500i
$716$	31.0109			1.15893
$717$		−	3.18372i		−	0.118898i
$718$		−	8.59001i		−	0.320576i
$719$	−25.3974			−0.947163			−0.473581	−	0.880750i	$-0.657039\pi$
$719$	−25.3974			−0.947163			−0.473581	+	0.880750i	$0.657039\pi$
$720$	5.19869	−	0.962643i	0.193744	−	0.0358756i
$721$	25.9330			0.965797
$722$		0			0
$723$			27.3552i			1.01735i
$724$	24.7069			0.918224
$725$	−16.7882	+	6.43811i	−0.623499	+	0.239105i
$726$	−23.6410			−0.877400
$727$		−	31.4377i		−	1.16596i	−0.812486	−	0.582980i	$-0.801886\pi$
$727$		−	31.4377i		−	1.16596i	0.812486	−	0.582980i	$-0.198114\pi$
$728$		−	84.5518i		−	3.13370i
$729$	−29.9869			−1.11063
$730$	−15.9725	+	2.95764i	−0.591170	+	0.109467i
$731$	0.280033			0.0103574
$732$		−	44.4838i		−	1.64417i
$733$			25.3946i			0.937971i	0.883206	+	0.468985i	$0.155380\pi$
$733$			25.3946i			0.937971i	−0.883206	+	0.468985i	$0.844620\pi$
$734$	47.9056			1.76823
$735$	−8.45125	−	45.6404i	−0.311729	−	1.68347i
$736$	−0.159213			−0.00586867
$737$		−	12.5912i		−	0.463802i
$738$		−	0.100160i		−	0.00368694i
$739$	−35.5082			−1.30619			−0.653095	−	0.757276i	$-0.726530\pi$
$739$	−35.5082			−1.30619			−0.653095	+	0.757276i	$0.726530\pi$
$740$	−4.94505	−	26.7054i	−0.181784	−	0.981710i
$741$		0			0
$742$		−	28.9703i		−	1.06353i
$743$		−	17.1099i		−	0.627700i	−0.949473	−	0.313850i	$-0.898381\pi$
$743$		−	17.1099i		−	0.627700i	0.949473	−	0.313850i	$-0.101619\pi$
$744$	−53.2713			−1.95302
$745$	39.5016	−	7.31453i	1.44723	−	0.267984i
$746$	−57.7597			−2.11473
$747$		−	8.84121i		−	0.323483i
$748$			5.90453i			0.215891i
$749$	5.86718			0.214382
$750$	36.5621	−	22.3807i	1.33506	−	0.817226i
$751$	−7.45125			−0.271900			−0.135950	−	0.990716i	$-0.543409\pi$
$751$	−7.45125			−0.271900			−0.135950	+	0.990716i	$0.543409\pi$
$752$		−	21.0891i		−	0.769041i
$753$		−	5.21086i		−	0.189894i
$754$	33.1976			1.20899
$755$	−27.9989	+	5.18457i	−1.01898	+	0.188686i
$756$	−101.063			−3.67561
$757$			53.7675i			1.95421i	0.212750	+	0.977107i	$0.431758\pi$
$757$			53.7675i			1.95421i	−0.212750	+	0.977107i	$0.568242\pi$
$758$		−	17.3199i		−	0.629086i
$759$	1.67503			0.0607997
$760$		0			0
$761$	23.3939			0.848029			0.424014	−	0.905655i	$-0.360621\pi$
$761$	23.3939			0.848029			0.424014	+	0.905655i	$0.360621\pi$
$762$			15.0929i			0.546760i
$763$		−	54.2117i		−	1.96259i
$764$	−23.6135			−0.854308
$765$	−0.152669	−	0.824480i	−0.00551977	−	0.0298091i
$766$	−7.57514			−0.273701
$767$			47.1152i			1.70123i
$768$		−	50.3235i		−	1.81589i
$769$	13.2447			0.477617			0.238808	−	0.971067i	$-0.423243\pi$
$769$	13.2447			0.477617			0.238808	+	0.971067i	$0.423243\pi$
$770$	−53.4951	+	9.90571i	−1.92783	+	0.356977i
$771$	43.0606			1.55079
$772$		−	10.4500i		−	0.376105i
$773$			17.8052i			0.640410i	0.947348	+	0.320205i	$0.103752\pi$
$773$			17.8052i			0.640410i	−0.947348	+	0.320205i	$0.896248\pi$
$774$	0.581686			0.0209083
$775$	31.9056	−	12.2355i	1.14608	−	0.439511i
$776$	21.9025			0.786254
$777$			21.1812i			0.759871i
$778$			23.0658i			0.826949i
$779$		0			0
$780$	−52.0253	+	9.63354i	−1.86280	+	0.344936i
$781$	15.3304			0.548566
$782$			0.798192i			0.0285433i
$783$		−	20.0022i		−	0.714819i
$784$	−55.8321			−1.99400
$785$	8.16467	+	44.0928i	0.291410	+	1.57374i
$786$	−62.5939			−2.23265
$787$		−	43.5779i		−	1.55339i	−0.629880	−	0.776693i	$-0.716896\pi$
$787$		−	43.5779i		−	1.55339i	0.629880	−	0.776693i	$-0.283104\pi$
$788$		−	80.1055i		−	2.85364i
$789$	−21.2711			−0.757271
$790$	11.3370	+	61.2246i	0.403351	+	2.17827i
$791$	34.8990			1.24087
$792$			6.18255i			0.219687i
$793$		−	26.5570i		−	0.943068i
$794$	−65.7267			−2.33255
$795$	−8.98561	+	1.66387i	−0.318687	+	0.0590114i
$796$	−51.4676			−1.82422
$797$		−	16.1311i		−	0.571395i	−0.958320	−	0.285697i	$-0.907775\pi$
$797$		−	16.1311i		−	0.571395i	0.958320	−	0.285697i	$-0.0922252\pi$
$798$		0			0
$799$	−3.34460			−0.118323
$800$	−0.584071	−	1.52304i	−0.0206500	−	0.0538476i
$801$	0.752902			0.0266025
$802$			61.8230i			2.18304i
$803$		−	6.50293i		−	0.229484i
$804$	−36.0528			−1.27148
$805$	−4.83424	+	0.895159i	−0.170385	+	0.0315502i
$806$	−63.0912			−2.22229
$807$			5.63237i			0.198269i
$808$		−	52.7722i		−	1.85652i
$809$	−28.7134			−1.00951			−0.504755	−	0.863263i	$-0.668417\pi$
$809$	−28.7134			−1.00951			−0.504755	+	0.863263i	$0.668417\pi$
$810$	6.99346	+	37.7677i	0.245725	+	1.32702i
$811$	21.5422			0.756449			0.378225	−	0.925714i	$-0.376535\pi$
$811$	21.5422			0.756449			0.378225	+	0.925714i	$0.376535\pi$
$812$		−	65.3388i		−	2.29294i
$813$			16.4895i			0.578313i
$814$	16.2646			0.570073
$815$	−5.79476	−	31.2942i	−0.202982	−	1.09619i
$816$	4.36445			0.152786
$817$		0			0
$818$		−	69.5634i		−	2.43223i
$819$	−9.53566			−0.333203
$820$	−0.642096	+	0.118897i	−0.0224230	+	0.00415207i
$821$	33.3204			1.16289			0.581445	−	0.813586i	$-0.302487\pi$
$821$	33.3204			1.16289			0.581445	+	0.813586i	$0.302487\pi$
$822$			62.9988i			2.19734i
$823$		−	37.2390i		−	1.29807i	−0.760759	−	0.649035i	$-0.775173\pi$
$823$		−	37.2390i		−	1.29807i	0.760759	−	0.649035i	$-0.224827\pi$
$824$	−28.7422			−1.00128
$825$	6.14483	+	16.0234i	0.213935	+	0.557864i
$826$	138.718			4.82662
$827$			29.0512i			1.01021i	0.863058	+	0.505105i	$0.168546\pi$
$827$			29.0512i			1.01021i	−0.863058	+	0.505105i	$0.831454\pi$
$828$			1.10836i			0.0385181i
$829$	−34.5380			−1.19956			−0.599778	−	0.800166i	$-0.704744\pi$
$829$	−34.5380			−1.19956			−0.599778	+	0.800166i	$0.704744\pi$
$830$	−84.7861	+	15.6999i	−2.94297	+	0.544950i
$831$	10.5134			0.364707
$832$		−	28.5498i		−	0.989786i
$833$			8.85462i			0.306794i
$834$	10.2316			0.354292
$835$	−2.28658	−	12.3485i	−0.0791302	−	0.427338i
$836$		0			0
$837$			38.0136i			1.31394i
$838$			32.0410i			1.10684i
$839$	44.7243			1.54406			0.772028	−	0.635589i	$-0.219243\pi$
$839$	44.7243			1.54406			0.772028	+	0.635589i	$0.219243\pi$
$840$	14.2975	+	77.2127i	0.493310	+	2.66409i
$841$	−16.0683			−0.554078
$842$		−	8.16680i		−	0.281447i
$843$			36.5758i			1.25974i
$844$	−55.8770			−1.92337
$845$	−2.47634	+	0.458545i	−0.0851886	+	0.0157744i
$846$	−6.94743			−0.238858
$847$			27.7784i			0.954478i
$848$			10.9921i			0.377471i
$849$	−22.9210			−0.786648
$850$	−7.63555	+	2.92816i	−0.261897	+	0.100435i
$851$	1.46980			0.0503839
$852$		−	43.8962i		−	1.50386i
$853$		−	16.2603i		−	0.556741i	−0.960474	−	0.278370i	$-0.910206\pi$
$853$		−	16.2603i		−	0.556741i	0.960474	−	0.278370i	$-0.0897943\pi$
$854$	−78.1900			−2.67561
$855$		0			0
$856$	−6.50273			−0.222259
$857$			16.6379i			0.568340i	0.958774	+	0.284170i	$0.0917181\pi$
$857$			16.6379i			0.568340i	−0.958774	+	0.284170i	$0.908282\pi$
$858$		−	31.6853i		−	1.08172i
$859$	−40.2724			−1.37408			−0.687038	−	0.726621i	$-0.741090\pi$
$859$	−40.2724			−1.37408			−0.687038	+	0.726621i	$0.741090\pi$
$860$	−0.690503	−	3.72901i	−0.0235459	−	0.127158i
$861$	0.509273			0.0173560
$862$		−	0.118897i		−	0.00404965i
$863$		−	32.9634i		−	1.12209i	−0.827786	−	0.561044i	$-0.810400\pi$
$863$		−	32.9634i		−	1.12209i	0.827786	−	0.561044i	$-0.189600\pi$
$864$	1.81461			0.0617343
$865$	−4.35245	−	23.5051i	−0.147988	−	0.799197i
$866$	23.5027			0.798655
$867$			25.8456i			0.877762i
$868$			124.175i			4.21476i
$869$	−24.9265			−0.845574
$870$	−30.3160	+	5.61363i	−1.02781	+	0.190320i
$871$	−21.5237			−0.729301
$872$			60.0841i			2.03470i
$873$		−	2.47014i		−	0.0836016i
$874$		0			0
$875$	−26.2975	−	42.9608i	−0.889018	−	1.45234i
$876$	−18.6201			−0.629114
$877$		−	0.213199i		−	0.00719923i	−0.999994	−	0.00359962i	$-0.998854\pi$
$877$		−	0.213199i		−	0.00719923i	0.999994	−	0.00359962i	$-0.00114580\pi$
$878$		−	54.6541i		−	1.84449i
$879$	−28.3885			−0.957519
$880$	20.2975	−	3.75849i	0.684228	−	0.126699i
$881$	51.8661			1.74741			0.873707	−	0.486453i	$-0.161710\pi$
$881$	51.8661			1.74741			0.873707	+	0.486453i	$0.161710\pi$
$882$			18.3929i			0.619321i
$883$			41.6451i			1.40147i	0.713422	+	0.700734i	$0.247144\pi$
$883$			41.6451i			1.40147i	−0.713422	+	0.700734i	$0.752856\pi$
$884$	10.0933			0.339476
$885$	−7.96707	−	43.0256i	−0.267810	−	1.44629i
$886$	−49.4083			−1.65990
$887$		−	4.09325i		−	0.137438i	−0.997636	−	0.0687190i	$-0.978109\pi$
$887$		−	4.09325i		−	0.137438i	0.997636	−	0.0687190i	$-0.0218912\pi$
$888$		−	23.4756i		−	0.787790i
$889$	17.7344			0.594791
$890$	−1.33697	−	7.22023i	−0.0448154	−	0.242023i
$891$	−15.3765			−0.515130
$892$			87.4987i			2.92967i
$893$		0			0
$894$	68.8859			2.30389
$895$	−16.9067	+	3.13061i	−0.565127	+	0.104645i
$896$	−86.9967			−2.90636
$897$		−	2.86334i		−	0.0956040i
$898$		−	30.6958i		−	1.02433i
$899$	−24.5764			−0.819670
$900$	−10.6026	+	4.06600i	−0.353421	+	0.135533i
$901$	1.74328			0.0580772
$902$		−	0.391060i		−	0.0130209i
$903$			2.95764i			0.0984240i
$904$	−38.6794			−1.28646
$905$	−13.4698	+	2.49421i	−0.447751	+	0.0829102i
$906$	−48.8266			−1.62216
$907$		−	8.40726i		−	0.279158i	−0.990211	−	0.139579i	$-0.955425\pi$
$907$		−	8.40726i		−	0.279158i	0.990211	−	0.139579i	$-0.0445750\pi$
$908$		−	33.0551i		−	1.09697i
$909$	−5.95159			−0.197402
$910$	16.9330	+	91.4458i	0.561325	+	3.03140i
$911$	8.87918			0.294180			0.147090	−	0.989123i	$-0.453009\pi$
$911$	8.87918			0.294180			0.147090	+	0.989123i	$0.453009\pi$
$912$		0			0
$913$		−	34.5192i		−	1.14242i
$914$	−69.5544			−2.30066
$915$	4.49073	+	24.2519i	0.148459	+	0.801742i
$916$	−67.1965			−2.22024
$917$			73.5485i			2.42878i
$918$		−	9.09730i		−	0.300256i
$919$	45.9834			1.51685			0.758427	−	0.651758i	$-0.225968\pi$
$919$	45.9834			1.51685			0.758427	+	0.651758i	$0.225968\pi$
$920$	5.35790	−	0.992125i	0.176645	−	0.0327094i
$921$	−45.8637			−1.51126
$922$		−	13.0658i		−	0.430299i
$923$		−	26.2062i		−	0.862587i
$924$	−62.3623			−2.05157
$925$	5.39192	+	14.0601i	0.177285	+	0.462295i
$926$	44.0462			1.44745
$927$			3.24152i			0.106465i
$928$			1.17318i			0.0385115i
$929$	22.1778			0.727629			0.363814	−	0.931471i	$-0.381474\pi$
$929$	22.1778			0.727629			0.363814	+	0.931471i	$0.381474\pi$
$930$	57.6148	−	10.6686i	1.88926	−	0.349836i
$931$		0			0
$932$			49.2564i			1.61345i
$933$		−	0.301644i		−	0.00987538i
$934$	70.6872			2.31296
$935$	−0.596074	−	3.21906i	−0.0194937	−	0.105274i
$936$	10.5686			0.345445
$937$		−	34.3274i		−	1.12143i	−0.828009	−	0.560714i	$-0.810527\pi$
$937$		−	34.3274i		−	1.12143i	0.828009	−	0.560714i	$-0.189473\pi$
$938$			63.3706i			2.06912i
$939$	−33.2120			−1.08383
$940$	8.24710	+	44.5379i	0.268991	+	1.45267i
$941$	33.7213			1.09928			0.549641	−	0.835401i	$-0.314765\pi$
$941$	33.7213			1.09928			0.549641	+	0.835401i	$0.314765\pi$
$942$			76.8923i			2.50529i
$943$		−	0.0353393i		−	0.00115080i
$944$	−52.6334			−1.71307
$945$	55.0977	−	10.2025i	1.79233	−	0.331886i
$946$	2.27110			0.0738400
$947$			22.1465i			0.719664i	0.933017	+	0.359832i	$0.117166\pi$
$947$			22.1465i			0.719664i	−0.933017	+	0.359832i	$0.882834\pi$
$948$			71.3729i			2.31809i
$949$	−11.1163			−0.360849
$950$		0			0
$951$	−29.9254			−0.970398
$952$		−	14.9799i		−	0.485501i
$953$		−	37.2967i		−	1.20816i	−0.796924	−	0.604079i	$-0.793541\pi$
$953$		−	37.2967i		−	1.20816i	0.796924	−	0.604079i	$-0.206459\pi$
$954$	3.62116			0.117240
$955$	12.8737	−	2.38383i	0.416584	−	0.0771390i
$956$	8.22508			0.266018
$957$		−	12.3426i		−	0.398981i
$958$		−	19.7761i		−	0.638936i
$959$	74.0242			2.39037
$960$	4.82770	+	26.0717i	0.155813	+	0.841459i
$961$	15.7069			0.506674
$962$		−	27.8030i		−	0.896405i
$963$			0.733371i			0.0236326i
$964$	−70.6718			−2.27618
$965$	1.05495	+	5.69719i	0.0339601	+	0.183399i
$966$	−8.43032			−0.271241
$967$			18.6736i			0.600502i	0.953860	+	0.300251i	$0.0970704\pi$
$967$			18.6736i			0.600502i	−0.953860	+	0.300251i	$0.902930\pi$
$968$		−	30.7875i		−	0.989547i
$969$		0			0
$970$	−23.6883	+	4.38638i	−0.760587	+	0.140838i
$971$	28.5806			0.917195			0.458598	−	0.888644i	$-0.348352\pi$
$971$	28.5806			0.917195			0.458598	+	0.888644i	$0.348352\pi$
$972$		−	23.2683i		−	0.746330i
$973$		−	12.0223i		−	0.385416i
$974$	2.69596			0.0863842
$975$	27.3908	−	10.5041i	0.877209	−	0.336401i
$976$	29.6674			0.949630
$977$		−	58.1909i		−	1.86169i	−0.365411	−	0.930846i	$-0.619072\pi$
$977$		−	58.1909i		−	1.86169i	0.365411	−	0.930846i	$-0.380928\pi$
$978$		−	54.5732i		−	1.74506i
$979$	2.93959			0.0939497
$980$	117.911	−	21.8337i	3.76654	−	0.697451i
$981$	6.77622			0.216348
$982$		−	32.1894i		−	1.02720i
$983$			48.0725i			1.53328i	0.642080	+	0.766638i	$0.278072\pi$
$983$			48.0725i			1.53328i	−0.642080	+	0.766638i	$0.721928\pi$
$984$	−0.564439			−0.0179937
$985$	8.08680	+	43.6722i	0.257667	+	1.39151i
$986$	5.88157			0.187307
$987$		−	35.3249i		−	1.12440i
$988$		0			0
$989$	0.205235			0.00652609
$990$	−1.23817	−	6.68665i	−0.0393516	−	0.212516i
$991$	38.3952			1.21966			0.609832	−	0.792531i	$-0.291237\pi$
$991$	38.3952			1.21966			0.609832	+	0.792531i	$0.291237\pi$
$992$		−	2.22960i		−	0.0707897i
$993$		−	32.1684i		−	1.02083i
$994$	−77.1570			−2.44727
$995$	28.0593	−	5.19576i	0.889540	−	0.164717i
$996$	−98.8399			−3.13186
$997$		−	37.8218i		−	1.19783i	−0.800814	−	0.598914i	$-0.795599\pi$
$997$		−	37.8218i		−	1.19783i	0.800814	−	0.598914i	$-0.204401\pi$
$998$			59.2944i			1.87693i
$999$	−16.7518			−0.530004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.f.1084.1		6
5.2	odd	4		9025.2.a.bu.1.6		6
5.3	odd	4		9025.2.a.bu.1.1		6
5.4	even	2	inner	1805.2.b.f.1084.6		6
19.7	even	3		95.2.i.b.49.6	yes	12
19.11	even	3		95.2.i.b.64.1	yes	12
19.18	odd	2		1805.2.b.g.1084.6		6
57.11	odd	6		855.2.be.d.64.6		12
57.26	odd	6		855.2.be.d.334.1		12
95.7	odd	12		475.2.e.g.201.1		12
95.18	even	4		9025.2.a.bt.1.6		6
95.37	even	4		9025.2.a.bt.1.1		6
95.49	even	6		95.2.i.b.64.6	yes	12
95.64	even	6		95.2.i.b.49.1	✓	12
95.68	odd	12		475.2.e.g.26.6		12
95.83	odd	12		475.2.e.g.201.6		12
95.87	odd	12		475.2.e.g.26.1		12
95.94	odd	2		1805.2.b.g.1084.1		6
285.239	odd	6		855.2.be.d.64.1		12
285.254	odd	6		855.2.be.d.334.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.1	✓	12	95.64	even	6
95.2.i.b.49.6	yes	12	19.7	even	3
95.2.i.b.64.1	yes	12	19.11	even	3
95.2.i.b.64.6	yes	12	95.49	even	6
475.2.e.g.26.1		12	95.87	odd	12
475.2.e.g.26.6		12	95.68	odd	12
475.2.e.g.201.1		12	95.7	odd	12
475.2.e.g.201.6		12	95.83	odd	12
855.2.be.d.64.1		12	285.239	odd	6
855.2.be.d.64.6		12	57.11	odd	6
855.2.be.d.334.1		12	57.26	odd	6
855.2.be.d.334.6		12	285.254	odd	6
1805.2.b.f.1084.1		6	1.1	even	1	trivial
1805.2.b.f.1084.6		6	5.4	even	2	inner
1805.2.b.g.1084.1		6	95.94	odd	2
1805.2.b.g.1084.6		6	19.18	odd	2
9025.2.a.bt.1.1		6	95.37	even	4
9025.2.a.bt.1.6		6	95.18	even	4
9025.2.a.bu.1.1		6	5.3	odd	4
9025.2.a.bu.1.6		6	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.45620i q^{2} +1.56104i q^{3} -4.03293 q^{4} +(2.19869 - 0.407132i) q^{5} +3.83424 q^{6} -4.50527i q^{7} +4.99330i q^{8} +0.563139 q^{9} +(-1.00000 - 5.40043i) q^{10} +2.19869 q^{11} -6.29559i q^{12} -3.75849i q^{13} -11.0659 q^{14} +(0.635552 + 3.43226i) q^{15} +4.19869 q^{16} -0.665886i q^{17} -1.38318i q^{18} +(-8.86718 + 1.64194i) q^{20} +7.03293 q^{21} -5.40043i q^{22} -0.488026i q^{23} -7.79476 q^{24} +(4.66849 - 1.79032i) q^{25} -9.23163 q^{26} +5.56222i q^{27} +18.1695i q^{28} -3.59607 q^{29} +(8.43032 - 1.56104i) q^{30} +6.83424 q^{31} -0.326239i q^{32} +3.43226i q^{33} -1.63555 q^{34} +(-1.83424 - 9.90571i) q^{35} -2.27110 q^{36} +3.01171i q^{37} +5.86718 q^{39} +(2.03293 + 10.9787i) q^{40} +0.0724126 q^{41} -17.2743i q^{42} +0.420541i q^{43} -8.86718 q^{44} +(1.23817 - 0.229272i) q^{45} -1.19869 q^{46} -5.02278i q^{47} +6.55434i q^{48} -13.2975 q^{49} +(-4.39738 - 11.4668i) q^{50} +1.03948 q^{51} +15.1578i q^{52} +2.61799i q^{53} +13.6619 q^{54} +(4.83424 - 0.895159i) q^{55} +22.4962 q^{56} +8.83269i q^{58} -12.5357 q^{59} +(-2.56314 - 13.8421i) q^{60} +7.06587 q^{61} -16.7863i q^{62} -2.53710i q^{63} +7.59607 q^{64} +(-1.53020 - 8.26377i) q^{65} +8.43032 q^{66} -5.72667i q^{67} +2.68548i q^{68} +0.761831 q^{69} +(-24.3304 + 4.50527i) q^{70} +6.97252 q^{71} +2.81192i q^{72} -2.95764i q^{73} +7.39738 q^{74} +(2.79476 + 7.28772i) q^{75} -9.90571i q^{77} -14.4110i q^{78} -11.3370 q^{79} +(9.23163 - 1.70942i) q^{80} -6.99346 q^{81} -0.177860i q^{82} -15.6999i q^{83} -28.3634 q^{84} +(-0.271104 - 1.46408i) q^{85} +1.03293 q^{86} -5.61363i q^{87} +10.9787i q^{88} +1.33697 q^{89} +(-0.563139 - 3.04120i) q^{90} -16.9330 q^{91} +1.96818i q^{92} +10.6686i q^{93} -12.3370 q^{94} +0.509273 q^{96} -4.38638i q^{97} +32.6613i q^{98} +1.23817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9} - 6 q^{10} + 2 q^{11} - 22 q^{14} + 4 q^{15} + 14 q^{16} - 20 q^{20} + 20 q^{21} - 2 q^{24} + 6 q^{25} - 22 q^{26} + 12 q^{29} + 6 q^{30} + 30 q^{31} - 10 q^{34}+ \cdots + 30 q^{99}+O(q^{100}) \) 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9 - 6 * q^10 + 2 * q^11 - 22 * q^14 + 4 * q^15 + 14 * q^16 - 20 * q^20 + 20 * q^21 - 2 * q^24 + 6 * q^25 - 22 * q^26 + 12 * q^29 + 6 * q^30 + 30 * q^31 - 10 * q^34 - 14 * q^36 + 2 * q^39 - 10 * q^40 + 12 * q^41 - 20 * q^44 + 30 * q^45 + 4 * q^46 - 2 * q^49 - 4 * q^50 + 40 * q^51 + 4 * q^54 + 18 * q^55 + 46 * q^56 - 20 * q^59 - 4 * q^60 - 2 * q^61 + 12 * q^64 - 20 * q^65 + 6 * q^66 - 18 * q^69 - 46 * q^70 - 2 * q^71 + 22 * q^74 - 28 * q^75 - 24 * q^79 + 22 * q^80 + 14 * q^81 - 48 * q^84 - 2 * q^85 - 16 * q^86 - 36 * q^89 + 8 * q^90 - 24 * q^91 - 30 * q^94 + 26 * q^96 + 30 * q^99

Introduction

L-functions

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Database

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