LMFDB - Embedded newform 930.2.d.h.559.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(559,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("930.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3534400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 $ x^6 - 2x^5 - 3x^4 + 16x^3 + x^2 - 12x + 40
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.5
Root			$-1.81837 - 0.301352i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.2.d.h.559.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.30135 + 1.81837i) q^{5} -1.00000 q^{6} -4.63675i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.30135 + 1.81837i) q^{5} -1.00000 q^{6} -4.63675i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.81837 - 1.30135i) q^{10} +5.23945 q^{11} -1.00000i q^{12} -3.39730i q^{13} +4.63675 q^{14} +(-1.81837 - 1.30135i) q^{15} +1.00000 q^{16} +2.43134i q^{17} -1.00000i q^{18} +7.06808 q^{19} +(1.30135 - 1.81837i) q^{20} +4.63675 q^{21} +5.23945i q^{22} +3.43134i q^{23} +1.00000 q^{24} +(-1.61296 - 4.73269i) q^{25} +3.39730 q^{26} -1.00000i q^{27} +4.63675i q^{28} -0.794590 q^{29} +(1.30135 - 1.81837i) q^{30} +1.00000 q^{31} +1.00000i q^{32} +5.23945i q^{33} -2.43134 q^{34} +(8.43134 + 6.03404i) q^{35} +1.00000 q^{36} +7.06808i q^{38} +3.39730 q^{39} +(1.81837 + 1.30135i) q^{40} +4.41082 q^{41} +4.63675i q^{42} +4.63675i q^{43} -5.23945 q^{44} +(1.30135 - 1.81837i) q^{45} -3.43134 q^{46} -1.56866i q^{47} +1.00000i q^{48} -14.4994 q^{49} +(4.73269 - 1.61296i) q^{50} -2.43134 q^{51} +3.39730i q^{52} -9.43134i q^{53} +1.00000 q^{54} +(-6.81837 + 9.52728i) q^{55} -4.63675 q^{56} +7.06808i q^{57} -0.794590i q^{58} -8.06808 q^{59} +(1.81837 + 1.30135i) q^{60} +8.43134 q^{61} +1.00000i q^{62} +4.63675i q^{63} -1.00000 q^{64} +(6.17755 + 4.42108i) q^{65} -5.23945 q^{66} -7.46538i q^{67} -2.43134i q^{68} -3.43134 q^{69} +(-6.03404 + 8.43134i) q^{70} +14.1021 q^{71} +1.00000i q^{72} +11.4994i q^{73} +(4.73269 - 1.61296i) q^{75} -7.06808 q^{76} -24.2940i q^{77} +3.39730i q^{78} +11.1362 q^{79} +(-1.30135 + 1.81837i) q^{80} +1.00000 q^{81} +4.41082i q^{82} +3.22593i q^{83} -4.63675 q^{84} +(-4.42108 - 3.16403i) q^{85} -4.63675 q^{86} -0.794590i q^{87} -5.23945i q^{88} -5.36325 q^{89} +(1.81837 + 1.30135i) q^{90} -15.7524 q^{91} -3.43134i q^{92} +1.00000i q^{93} +1.56866 q^{94} +(-9.19807 + 12.8524i) q^{95} -1.00000 q^{96} +0.191885i q^{97} -14.4994i q^{98} -5.23945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{14} + 2 q^{15} + 6 q^{16} - 2 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{24} - 4 q^{25} + 24 q^{26} - 12 q^{29} + 6 q^{30} + 6 q^{31} + 4 q^{34} + 32 q^{35} + 6 q^{36} + 24 q^{39} - 2 q^{40} + 12 q^{41} - 2 q^{44} + 6 q^{45} - 2 q^{46} - 24 q^{49} + 8 q^{50} + 4 q^{51} + 6 q^{54} - 28 q^{55} - 2 q^{56} - 4 q^{59} - 2 q^{60} + 32 q^{61} - 6 q^{64} - 20 q^{65} - 2 q^{66} - 2 q^{69} - 14 q^{70} + 18 q^{71} + 8 q^{75} + 2 q^{76} - 22 q^{79} - 6 q^{80} + 6 q^{81} - 2 q^{84} - 10 q^{85} - 2 q^{86} - 58 q^{89} - 2 q^{90} + 16 q^{91} + 28 q^{94} + 6 q^{95} - 6 q^{96} - 2 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^14 + 2 * q^15 + 6 * q^16 - 2 * q^19 + 6 * q^20 + 2 * q^21 + 6 * q^24 - 4 * q^25 + 24 * q^26 - 12 * q^29 + 6 * q^30 + 6 * q^31 + 4 * q^34 + 32 * q^35 + 6 * q^36 + 24 * q^39 - 2 * q^40 + 12 * q^41 - 2 * q^44 + 6 * q^45 - 2 * q^46 - 24 * q^49 + 8 * q^50 + 4 * q^51 + 6 * q^54 - 28 * q^55 - 2 * q^56 - 4 * q^59 - 2 * q^60 + 32 * q^61 - 6 * q^64 - 20 * q^65 - 2 * q^66 - 2 * q^69 - 14 * q^70 + 18 * q^71 + 8 * q^75 + 2 * q^76 - 22 * q^79 - 6 * q^80 + 6 * q^81 - 2 * q^84 - 10 * q^85 - 2 * q^86 - 58 * q^89 - 2 * q^90 + 16 * q^91 + 28 * q^94 + 6 * q^95 - 6 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	−1.30135	+	1.81837i	−0.581983	+	0.813201i
$5$	−1.30135	+	1.81837i	−0.581983	+	0.813201i
$6$	−1.00000			−0.408248
$7$		−	4.63675i		−	1.75253i	−0.481834	−	0.876263i	$-0.660029\pi$
$7$		−	4.63675i		−	1.75253i	0.481834	−	0.876263i	$-0.339971\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−1.81837	−	1.30135i	−0.575020	−	0.411524i
$11$	5.23945			1.57975			0.789877	−	0.613265i	$-0.210144\pi$
$11$	5.23945			1.57975			0.789877	+	0.613265i	$0.210144\pi$
$12$		−	1.00000i		−	0.288675i
$13$		−	3.39730i		−	0.942240i	−0.882069	−	0.471120i	$-0.843850\pi$
$13$		−	3.39730i		−	0.942240i	0.882069	−	0.471120i	$-0.156150\pi$
$14$	4.63675			1.23922
$15$	−1.81837	−	1.30135i	−0.469502	−	0.336008i
$16$	1.00000			0.250000
$17$			2.43134i			0.589686i	0.955546	+	0.294843i	$0.0952673\pi$
$17$			2.43134i			0.589686i	−0.955546	+	0.294843i	$0.904733\pi$
$18$		−	1.00000i		−	0.235702i
$19$	7.06808			1.62153			0.810765	−	0.585372i	$-0.199052\pi$
$19$	7.06808			1.62153			0.810765	+	0.585372i	$0.199052\pi$
$20$	1.30135	−	1.81837i	0.290991	−	0.406601i
$21$	4.63675			1.01182
$22$			5.23945i			1.11705i
$23$			3.43134i			0.715483i	0.933821	+	0.357742i	$0.116453\pi$
$23$			3.43134i			0.715483i	−0.933821	+	0.357742i	$0.883547\pi$
$24$	1.00000			0.204124
$25$	−1.61296	−	4.73269i	−0.322593	−	0.946538i
$26$	3.39730			0.666264
$27$		−	1.00000i		−	0.192450i
$28$			4.63675i			0.876263i
$29$	−0.794590			−0.147552			−0.0737758	−	0.997275i	$-0.523505\pi$
$29$	−0.794590			−0.147552			−0.0737758	+	0.997275i	$0.523505\pi$
$30$	1.30135	−	1.81837i	0.237593	−	0.331988i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$			1.00000i			0.176777i
$33$			5.23945i			0.912071i
$34$	−2.43134			−0.416971
$35$	8.43134	+	6.03404i	1.42516	+	1.01994i
$36$	1.00000			0.166667
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$			7.06808i			1.14659i
$39$	3.39730			0.544003
$40$	1.81837	+	1.30135i	0.287510	+	0.205762i
$41$	4.41082			0.688854			0.344427	−	0.938813i	$-0.388073\pi$
$41$	4.41082			0.688854			0.344427	+	0.938813i	$0.388073\pi$
$42$			4.63675i			0.715466i
$43$			4.63675i			0.707097i	0.935416	+	0.353549i	$0.115025\pi$
$43$			4.63675i			0.707097i	−0.935416	+	0.353549i	$0.884975\pi$
$44$	−5.23945			−0.789877
$45$	1.30135	−	1.81837i	0.193994	−	0.271067i
$46$	−3.43134			−0.505923
$47$		−	1.56866i		−	0.228813i	−0.993434	−	0.114407i	$-0.963503\pi$
$47$		−	1.56866i		−	0.228813i	0.993434	−	0.114407i	$-0.0364966\pi$
$48$			1.00000i			0.144338i
$49$	−14.4994			−2.07135
$50$	4.73269	−	1.61296i	0.669303	−	0.228107i
$51$	−2.43134			−0.340455
$52$			3.39730i			0.471120i
$53$		−	9.43134i		−	1.29549i	−0.761856	−	0.647747i	$-0.775711\pi$
$53$		−	9.43134i		−	1.29549i	0.761856	−	0.647747i	$-0.224289\pi$
$54$	1.00000			0.136083
$55$	−6.81837	+	9.52728i	−0.919389	+	1.28466i
$56$	−4.63675			−0.619611
$57$			7.06808i			0.936191i
$58$		−	0.794590i		−	0.104335i
$59$	−8.06808			−1.05038			−0.525188	−	0.850987i	$-0.676005\pi$
$59$	−8.06808			−1.05038			−0.525188	+	0.850987i	$0.676005\pi$
$60$	1.81837	+	1.30135i	0.234751	+	0.168004i
$61$	8.43134			1.07952			0.539761	−	0.841818i	$-0.318515\pi$
$61$	8.43134			1.07952			0.539761	+	0.841818i	$0.318515\pi$
$62$			1.00000i			0.127000i
$63$			4.63675i			0.584175i
$64$	−1.00000			−0.125000
$65$	6.17755	+	4.42108i	0.766231	+	0.548367i
$66$	−5.23945			−0.644932
$67$		−	7.46538i		−	0.912041i	−0.889969	−	0.456021i	$-0.849274\pi$
$67$		−	7.46538i		−	0.912041i	0.889969	−	0.456021i	$-0.150726\pi$
$68$		−	2.43134i		−	0.294843i
$69$	−3.43134			−0.413084
$70$	−6.03404	+	8.43134i	−0.721206	+	1.00774i
$71$	14.1021			1.67361			0.836807	−	0.547498i	$-0.184420\pi$
$71$	14.1021			1.67361			0.836807	+	0.547498i	$0.184420\pi$
$72$			1.00000i			0.117851i
$73$			11.4994i			1.34591i	0.739686	+	0.672953i	$0.234974\pi$
$73$			11.4994i			1.34591i	−0.739686	+	0.672953i	$0.765026\pi$
$74$		0			0
$75$	4.73269	−	1.61296i	0.546484	−	0.186249i
$76$	−7.06808			−0.810765
$77$		−	24.2940i		−	2.76856i
$78$			3.39730i			0.384668i
$79$	11.1362			1.25292			0.626458	−	0.779455i	$-0.284504\pi$
$79$	11.1362			1.25292			0.626458	+	0.779455i	$0.284504\pi$
$80$	−1.30135	+	1.81837i	−0.145496	+	0.203300i
$81$	1.00000			0.111111
$82$			4.41082i			0.487094i
$83$			3.22593i			0.354091i	0.984203	+	0.177046i	$0.0566541\pi$
$83$			3.22593i			0.354091i	−0.984203	+	0.177046i	$0.943346\pi$
$84$	−4.63675			−0.505911
$85$	−4.42108	−	3.16403i	−0.479533	−	0.343187i
$86$	−4.63675			−0.499993
$87$		−	0.794590i		−	0.0851890i
$88$		−	5.23945i		−	0.558527i
$89$	−5.36325			−0.568504			−0.284252	−	0.958750i	$-0.591745\pi$
$89$	−5.36325			−0.568504			−0.284252	+	0.958750i	$0.591745\pi$
$90$	1.81837	+	1.30135i	0.191673	+	0.137175i
$91$	−15.7524			−1.65130
$92$		−	3.43134i		−	0.357742i
$93$			1.00000i			0.103695i
$94$	1.56866			0.161795
$95$	−9.19807	+	12.8524i	−0.943702	+	1.31863i
$96$	−1.00000			−0.102062
$97$			0.191885i			0.0194830i	0.999953	+	0.00974150i	$0.00310086\pi$
$97$			0.191885i			0.0194830i	−0.999953	+	0.00974150i	$0.996899\pi$
$98$		−	14.4994i		−	1.46466i
$99$	−5.23945			−0.526585
$100$	1.61296	+	4.73269i	0.161296	+	0.473269i
$101$	12.2259			1.21653			0.608263	−	0.793736i	$-0.291867\pi$
$101$	12.2259			1.21653			0.608263	+	0.793736i	$0.291867\pi$
$102$		−	2.43134i		−	0.240738i
$103$		−	15.2735i		−	1.50494i	−0.658625	−	0.752471i	$-0.728862\pi$
$103$		−	15.2735i		−	1.50494i	0.658625	−	0.752471i	$-0.271138\pi$
$104$	−3.39730			−0.333132
$105$	−6.03404	+	8.43134i	−0.588862	+	0.822814i
$106$	9.43134			0.916052
$107$			4.70483i			0.454833i	0.973798	+	0.227417i	$0.0730279\pi$
$107$			4.70483i			0.454833i	−0.973798	+	0.227417i	$0.926972\pi$
$108$			1.00000i			0.0962250i
$109$	13.6573			1.30813			0.654064	−	0.756439i	$-0.273063\pi$
$109$	13.6573			1.30813			0.654064	+	0.756439i	$0.273063\pi$
$110$	−9.52728	−	6.81837i	−0.908390	−	0.650106i
$111$		0			0
$112$		−	4.63675i		−	0.438131i
$113$		−	4.63675i		−	0.436188i	−0.975928	−	0.218094i	$-0.930016\pi$
$113$		−	4.63675i		−	0.436188i	0.975928	−	0.218094i	$-0.0699840\pi$
$114$	−7.06808			−0.661987
$115$	−6.23945	−	4.46538i	−0.581832	−	0.416399i
$116$	0.794590			0.0737758
$117$			3.39730i			0.314080i
$118$		−	8.06808i		−	0.742727i
$119$	11.2735			1.03344
$120$	−1.30135	+	1.81837i	−0.118797	+	0.165994i
$121$	16.4519			1.49562
$122$			8.43134i			0.763337i
$123$			4.41082i			0.397710i
$124$	−1.00000			−0.0898027
$125$	10.7048	+	3.22593i	0.957469	+	0.288536i
$126$	−4.63675			−0.413074
$127$			10.7946i			0.957865i	0.877852	+	0.478932i	$0.158976\pi$
$127$			10.7946i			0.957865i	−0.877852	+	0.478932i	$0.841024\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.63675			−0.408243
$130$	−4.42108	+	6.17755i	−0.387754	+	0.541807i
$131$	16.8897			1.47566			0.737831	−	0.674986i	$-0.235850\pi$
$131$	16.8897			1.47566			0.737831	+	0.674986i	$0.235850\pi$
$132$		−	5.23945i		−	0.456036i
$133$		−	32.7729i		−	2.84177i
$134$	7.46538			0.644910
$135$	1.81837	+	1.30135i	0.156501	+	0.112003i
$136$	2.43134			0.208485
$137$			10.1362i			0.865991i	0.901396	+	0.432996i	$0.142543\pi$
$137$			10.1362i			0.865991i	−0.901396	+	0.432996i	$0.857457\pi$
$138$		−	3.43134i		−	0.292095i
$139$	−1.93192			−0.163863			−0.0819315	−	0.996638i	$-0.526109\pi$
$139$	−1.93192			−0.163863			−0.0819315	+	0.996638i	$0.526109\pi$
$140$	−8.43134	−	6.03404i	−0.712578	−	0.509970i
$141$	1.56866			0.132105
$142$			14.1021i			1.18342i
$143$		−	17.8000i		−	1.48851i
$144$	−1.00000			−0.0833333
$145$	1.03404	−	1.44486i	0.0858725	−	0.119989i
$146$	−11.4994			−0.951699
$147$		−	14.4994i		−	1.19589i
$148$		0			0
$149$	−20.0340			−1.64125			−0.820626	−	0.571465i	$-0.806375\pi$
$149$	−20.0340			−1.64125			−0.820626	+	0.571465i	$0.806375\pi$
$150$	1.61296	+	4.73269i	0.131698	+	0.386422i
$151$	−20.4994			−1.66822			−0.834110	−	0.551599i	$-0.814018\pi$
$151$	−20.4994			−1.66822			−0.834110	+	0.551599i	$0.814018\pi$
$152$		−	7.06808i		−	0.573297i
$153$		−	2.43134i		−	0.196562i
$154$	24.2940			1.95767
$155$	−1.30135	+	1.81837i	−0.104527	+	0.146055i
$156$	−3.39730			−0.272001
$157$			16.7048i			1.33319i	0.745420	+	0.666595i	$0.232249\pi$
$157$			16.7048i			1.33319i	−0.745420	+	0.666595i	$0.767751\pi$
$158$			11.1362i			0.885946i
$159$	9.43134			0.747954
$160$	−1.81837	−	1.30135i	−0.143755	−	0.102881i
$161$	15.9102			1.25390
$162$			1.00000i			0.0785674i
$163$		−	7.53346i		−	0.590066i	−0.955487	−	0.295033i	$-0.904669\pi$
$163$		−	7.53346i		−	0.590066i	0.955487	−	0.295033i	$-0.0953307\pi$
$164$	−4.41082			−0.344427
$165$	−9.52728	−	6.81837i	−0.741698	−	0.530810i
$166$	−3.22593			−0.250380
$167$		−	2.22593i		−	0.172247i	−0.996284	−	0.0861237i	$-0.972552\pi$
$167$		−	2.22593i		−	0.172247i	0.996284	−	0.0861237i	$-0.0274480\pi$
$168$		−	4.63675i		−	0.357733i
$169$	1.45839			0.112184
$170$	3.16403	−	4.42108i	0.242670	−	0.339081i
$171$	−7.06808			−0.540510
$172$		−	4.63675i		−	0.353549i
$173$		−	0.774073i		−	0.0588517i	−0.999567	−	0.0294258i	$-0.990632\pi$
$173$		−	0.774073i		−	0.0588517i	0.999567	−	0.0294258i	$-0.00936789\pi$
$174$	0.794590			0.0602377
$175$	−21.9443	+	7.47890i	−1.65883	+	0.565352i
$176$	5.23945			0.394939
$177$		−	8.06808i		−	0.606434i
$178$		−	5.36325i		−	0.401993i
$179$	−25.4654			−1.90337			−0.951686	−	0.307073i	$-0.900650\pi$
$179$	−25.4654			−1.90337			−0.951686	+	0.307073i	$0.900650\pi$
$180$	−1.30135	+	1.81837i	−0.0969971	+	0.135534i
$181$	13.4584			1.00035			0.500177	−	0.865923i	$-0.333268\pi$
$181$	13.4584			1.00035			0.500177	+	0.865923i	$0.333268\pi$
$182$		−	15.7524i		−	1.16765i
$183$			8.43134i			0.623262i
$184$	3.43134			0.252962
$185$		0			0
$186$	−1.00000			−0.0733236
$187$			12.7389i			0.931559i
$188$			1.56866i			0.114407i
$189$	−4.63675			−0.337274
$190$	−12.8524	−	9.19807i	−0.932412	−	0.667298i
$191$	4.38377			0.317198			0.158599	−	0.987343i	$-0.449302\pi$
$191$	4.38377			0.317198			0.158599	+	0.987343i	$0.449302\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			10.7389i			0.773001i	0.922289	+	0.386500i	$0.126316\pi$
$193$			10.7389i			0.773001i	−0.922289	+	0.386500i	$0.873684\pi$
$194$	−0.191885			−0.0137766
$195$	−4.42108	+	6.17755i	−0.316600	+	0.442384i
$196$	14.4994			1.03567
$197$		−	26.9578i		−	1.92066i	−0.278859	−	0.960332i	$-0.589956\pi$
$197$		−	26.9578i		−	1.92066i	0.278859	−	0.960332i	$-0.410044\pi$
$198$		−	5.23945i		−	0.372352i
$199$	−25.9988			−1.84301			−0.921504	−	0.388368i	$-0.873039\pi$
$199$	−25.9988			−1.84301			−0.921504	+	0.388368i	$0.873039\pi$
$200$	−4.73269	+	1.61296i	−0.334652	+	0.114054i
$201$	7.46538			0.526567
$202$			12.2259i			0.860213i
$203$			3.68431i			0.258588i
$204$	2.43134			0.170228
$205$	−5.74003	+	8.02052i	−0.400901	+	0.560177i
$206$	15.2735			1.06415
$207$		−	3.43134i		−	0.238494i
$208$		−	3.39730i		−	0.235560i
$209$	37.0329			2.56162
$210$	−8.43134	−	6.03404i	−0.581818	−	0.416388i
$211$	−23.9102			−1.64605			−0.823024	−	0.568006i	$-0.807715\pi$
$211$	−23.9102			−1.64605			−0.823024	+	0.568006i	$0.807715\pi$
$212$			9.43134i			0.647747i
$213$			14.1021i			0.966262i
$214$	−4.70483			−0.321616
$215$	−8.43134	−	6.03404i	−0.575012	−	0.411518i
$216$	−1.00000			−0.0680414
$217$		−	4.63675i		−	0.314763i
$218$			13.6573i			0.924987i
$219$	−11.4994			−0.777059
$220$	6.81837	−	9.52728i	0.459695	−	0.642329i
$221$	8.25997			0.555626
$222$		0			0
$223$		−	18.2870i		−	1.22459i	−0.790630	−	0.612295i	$-0.790247\pi$
$223$		−	18.2870i		−	1.22459i	0.790630	−	0.612295i	$-0.209753\pi$
$224$	4.63675			0.309806
$225$	1.61296	+	4.73269i	0.107531	+	0.315513i
$226$	4.63675			0.308432
$227$			17.4313i			1.15696i	0.815697	+	0.578479i	$0.196354\pi$
$227$			17.4313i			1.15696i	−0.815697	+	0.578479i	$0.803646\pi$
$228$		−	7.06808i		−	0.468095i
$229$	−18.3416			−1.21205			−0.606023	−	0.795447i	$-0.707236\pi$
$229$	−18.3416			−1.21205			−0.606023	+	0.795447i	$0.707236\pi$
$230$	4.46538	−	6.23945i	0.294438	−	0.411417i
$231$	24.2940			1.59843
$232$			0.794590i			0.0521674i
$233$		−	18.7729i		−	1.22985i	−0.788584	−	0.614927i	$-0.789185\pi$
$233$		−	18.7729i		−	1.22985i	0.788584	−	0.614927i	$-0.210815\pi$
$234$	−3.39730			−0.222088
$235$	2.85242	+	2.04138i	0.186071	+	0.133165i
$236$	8.06808			0.525188
$237$			11.1362i			0.723372i
$238$			11.2735i			0.730752i
$239$	8.93076			0.577683			0.288841	−	0.957377i	$-0.406730\pi$
$239$	8.93076			0.577683			0.288841	+	0.957377i	$0.406730\pi$
$240$	−1.81837	−	1.30135i	−0.117375	−	0.0840019i
$241$	1.20541			0.0776473			0.0388236	−	0.999246i	$-0.487639\pi$
$241$	1.20541			0.0776473			0.0388236	+	0.999246i	$0.487639\pi$
$242$			16.4519i			1.05757i
$243$			1.00000i			0.0641500i
$244$	−8.43134			−0.539761
$245$	18.8689	−	26.3654i	1.20549	−	1.68442i
$246$	−4.41082			−0.281224
$247$		−	24.0124i		−	1.52787i
$248$		−	1.00000i		−	0.0635001i
$249$	−3.22593			−0.204435
$250$	−3.22593	+	10.7048i	−0.204026	+	0.677033i
$251$	−9.34158			−0.589635			−0.294818	−	0.955554i	$-0.595259\pi$
$251$	−9.34158			−0.589635			−0.294818	+	0.955554i	$0.595259\pi$
$252$		−	4.63675i		−	0.292088i
$253$			17.9783i			1.13029i
$254$	−10.7946			−0.677313
$255$	3.16403	−	4.42108i	0.198139	−	0.276859i
$256$	1.00000			0.0625000
$257$			1.36325i			0.0850374i	0.999096	+	0.0425187i	$0.0135382\pi$
$257$			1.36325i			0.0850374i	−0.999096	+	0.0425187i	$0.986462\pi$
$258$		−	4.63675i		−	0.288671i
$259$		0			0
$260$	−6.17755	−	4.42108i	−0.383115	−	0.274184i
$261$	0.794590			0.0491839
$262$			16.8897i			1.04345i
$263$		−	15.3145i		−	0.944334i	−0.881509	−	0.472167i	$-0.843472\pi$
$263$		−	15.3145i		−	0.944334i	0.881509	−	0.472167i	$-0.156528\pi$
$264$	5.23945			0.322466
$265$	17.1497	+	12.2735i	1.05350	+	0.753955i
$266$	32.7729			2.00944
$267$		−	5.36325i		−	0.328226i
$268$			7.46538i			0.456021i
$269$	−8.41082			−0.512817			−0.256408	−	0.966569i	$-0.582539\pi$
$269$	−8.41082			−0.512817			−0.256408	+	0.966569i	$0.582539\pi$
$270$	−1.30135	+	1.81837i	−0.0791978	+	0.110663i
$271$	−4.27349			−0.259596			−0.129798	−	0.991540i	$-0.541433\pi$
$271$	−4.27349			−0.259596			−0.129798	+	0.991540i	$0.541433\pi$
$272$			2.43134i			0.147421i
$273$		−	15.7524i		−	0.953378i
$274$	−10.1362			−0.612348
$275$	−8.45104	−	24.7967i	−0.509617	−	1.49530i
$276$	3.43134			0.206542
$277$		−	23.9853i		−	1.44114i	−0.693383	−	0.720569i	$-0.743881\pi$
$277$		−	23.9853i		−	1.44114i	0.693383	−	0.720569i	$-0.256119\pi$
$278$		−	1.93192i		−	0.115869i
$279$	−1.00000			−0.0598684
$280$	6.03404	−	8.43134i	0.360603	−	0.503869i
$281$	−20.9988			−1.25269			−0.626343	−	0.779548i	$-0.715449\pi$
$281$	−20.9988			−1.25269			−0.626343	+	0.779548i	$0.715449\pi$
$282$			1.56866i			0.0934125i
$283$		−	18.3961i		−	1.09354i	−0.837284	−	0.546768i	$-0.815858\pi$
$283$		−	18.3961i		−	1.09354i	0.837284	−	0.546768i	$-0.184142\pi$
$284$	−14.1021			−0.836807
$285$	−12.8524	−	9.19807i	−0.761311	−	0.544847i
$286$	17.8000			1.05253
$287$		−	20.4519i		−	1.20723i
$288$		−	1.00000i		−	0.0589256i
$289$	11.0886			0.652271
$290$	1.44486	+	1.03404i	0.0848452	+	0.0607210i
$291$	−0.191885			−0.0112485
$292$		−	11.4994i		−	0.672953i
$293$			19.7253i			1.15237i	0.817320	+	0.576184i	$0.195459\pi$
$293$			19.7253i			1.15237i	−0.817320	+	0.576184i	$0.804541\pi$
$294$	14.4994			0.845623
$295$	10.4994	−	14.6708i	0.611300	−	0.854166i
$296$		0			0
$297$		−	5.23945i		−	0.304024i
$298$		−	20.0340i		−	1.16054i
$299$	11.6573			0.674157
$300$	−4.73269	+	1.61296i	−0.273242	+	0.0931245i
$301$	21.4994			1.23921
$302$		−	20.4994i		−	1.17961i
$303$			12.2259i			0.702361i
$304$	7.06808			0.405382
$305$	−10.9721	+	15.3313i	−0.628263	+	0.877869i
$306$	2.43134			0.138990
$307$		−	10.9308i		−	0.623851i	−0.950107	−	0.311926i	$-0.899026\pi$
$307$		−	10.9308i		−	0.623851i	0.950107	−	0.311926i	$-0.100974\pi$
$308$			24.2940i			1.38428i
$309$	15.2735			0.868879
$310$	−1.81837	−	1.30135i	−0.103277	−	0.0739119i
$311$	−12.6027			−0.714634			−0.357317	−	0.933983i	$-0.616308\pi$
$311$	−12.6027			−0.714634			−0.357317	+	0.933983i	$0.616308\pi$
$312$		−	3.39730i		−	0.192334i
$313$		−	12.4108i		−	0.701501i	−0.936469	−	0.350751i	$-0.885927\pi$
$313$		−	12.4108i		−	0.701501i	0.936469	−	0.350751i	$-0.114073\pi$
$314$	−16.7048			−0.942708
$315$	−8.43134	−	6.03404i	−0.475052	−	0.339980i
$316$	−11.1362			−0.626458
$317$		−	12.7741i		−	0.717463i	−0.933441	−	0.358732i	$-0.883209\pi$
$317$		−	12.7741i		−	0.717463i	0.933441	−	0.358732i	$-0.116791\pi$
$318$			9.43134i			0.528883i
$319$	−4.16322			−0.233095
$320$	1.30135	−	1.81837i	0.0727478	−	0.101650i
$321$	−4.70483			−0.262598
$322$			15.9102i			0.886643i
$323$			17.1849i			0.956193i
$324$	−1.00000			−0.0555556
$325$	−16.0783	+	5.47971i	−0.891866	+	0.303960i
$326$	7.53346			0.417240
$327$			13.6573i			0.755248i
$328$		−	4.41082i		−	0.243547i
$329$	−7.27349			−0.401001
$330$	6.81837	−	9.52728i	0.375339	−	0.524459i
$331$	−6.88972			−0.378693			−0.189347	−	0.981910i	$-0.560637\pi$
$331$	−6.88972			−0.378693			−0.189347	+	0.981910i	$0.560637\pi$
$332$		−	3.22593i		−	0.177046i
$333$		0			0
$334$	2.22593			0.121797
$335$	13.5748	+	9.71509i	0.741673	+	0.530792i
$336$	4.63675			0.252955
$337$			6.72651i			0.366416i	0.983074	+	0.183208i	$0.0586482\pi$
$337$			6.72651i			0.366416i	−0.983074	+	0.183208i	$0.941352\pi$
$338$			1.45839i			0.0793258i
$339$	4.63675			0.251834
$340$	4.42108	+	3.16403i	0.239767	+	0.171593i
$341$	5.23945			0.283732
$342$		−	7.06808i		−	0.382198i
$343$			34.7729i			1.87756i
$344$	4.63675			0.249997
$345$	4.46538	−	6.23945i	0.240408	−	0.335921i
$346$	0.774073			0.0416144
$347$			20.1837i			1.08352i	0.840533	+	0.541760i	$0.182242\pi$
$347$			20.1837i			1.08352i	−0.840533	+	0.541760i	$0.817758\pi$
$348$			0.794590i			0.0425945i
$349$	−32.9578			−1.76419			−0.882095	−	0.471071i	$-0.843868\pi$
$349$	−32.9578			−1.76419			−0.882095	+	0.471071i	$0.843868\pi$
$350$	−7.47890	−	21.9443i	−0.399764	−	1.17297i
$351$	−3.39730			−0.181334
$352$			5.23945i			0.279264i
$353$			32.9373i			1.75308i	0.481334	+	0.876538i	$0.340153\pi$
$353$			32.9373i			1.75308i	−0.481334	+	0.876538i	$0.659847\pi$
$354$	8.06808			0.428814
$355$	−18.3518	+	25.6429i	−0.974014	+	1.36099i
$356$	5.36325			0.284252
$357$			11.2735i			0.596657i
$358$		−	25.4654i		−	1.34589i
$359$	0.444862			0.0234789			0.0117394	−	0.999931i	$-0.496263\pi$
$359$	0.444862			0.0234789			0.0117394	+	0.999931i	$0.496263\pi$
$360$	−1.81837	−	1.30135i	−0.0958367	−	0.0685873i
$361$	30.9578			1.62936
$362$			13.4584i			0.707357i
$363$			16.4519i			0.863498i
$364$	15.7524			0.825650
$365$	−20.9102	−	14.9648i	−1.09449	−	0.783293i
$366$	−8.43134			−0.440713
$367$			22.8750i			1.19407i	0.802216	+	0.597034i	$0.203654\pi$
$367$			22.8750i			1.19407i	−0.802216	+	0.597034i	$0.796346\pi$
$368$			3.43134i			0.178871i
$369$	−4.41082			−0.229618
$370$		0			0
$371$	−43.7307			−2.27039
$372$		−	1.00000i		−	0.0518476i
$373$		−	22.6367i		−	1.17209i	−0.810280	−	0.586043i	$-0.800685\pi$
$373$		−	22.6367i		−	1.17209i	0.810280	−	0.586043i	$-0.199315\pi$
$374$	−12.7389			−0.658711
$375$	−3.22593	+	10.7048i	−0.166586	+	0.552795i
$376$	−1.56866			−0.0808976
$377$			2.69946i			0.139029i
$378$		−	4.63675i		−	0.238489i
$379$	−3.93076			−0.201909			−0.100955	−	0.994891i	$-0.532190\pi$
$379$	−3.93076			−0.201909			−0.100955	+	0.994891i	$0.532190\pi$
$380$	9.19807	−	12.8524i	0.471851	−	0.659315i
$381$	−10.7946			−0.553024
$382$			4.38377i			0.224293i
$383$			29.4777i			1.50624i	0.657882	+	0.753121i	$0.271453\pi$
$383$			29.4777i			1.50624i	−0.657882	+	0.753121i	$0.728547\pi$
$384$	1.00000			0.0510310
$385$	44.1756	+	31.6151i	2.25140	+	1.61125i
$386$	−10.7389			−0.546594
$387$		−	4.63675i		−	0.235699i
$388$		−	0.191885i		−	0.00974150i
$389$	−12.5199			−0.634786			−0.317393	−	0.948294i	$-0.602807\pi$
$389$	−12.5199			−0.634786			−0.317393	+	0.948294i	$0.602807\pi$
$390$	−6.17755	−	4.42108i	−0.312812	−	0.223870i
$391$	−8.34274			−0.421910
$392$			14.4994i			0.732331i
$393$			16.8897i			0.851974i
$394$	26.9578			1.35811
$395$	−14.4921	+	20.2497i	−0.729176	+	1.01887i
$396$	5.23945			0.263292
$397$			11.8422i			0.594341i	0.954824	+	0.297170i	$0.0960429\pi$
$397$			11.8422i			0.594341i	−0.954824	+	0.297170i	$0.903957\pi$
$398$		−	25.9988i		−	1.30320i
$399$	32.7729			1.64070
$400$	−1.61296	−	4.73269i	−0.0806482	−	0.236634i
$401$	−18.9918			−0.948408			−0.474204	−	0.880415i	$-0.657264\pi$
$401$	−18.9918			−0.948408			−0.474204	+	0.880415i	$0.657264\pi$
$402$			7.46538i			0.372339i
$403$		−	3.39730i		−	0.169231i
$404$	−12.2259			−0.608263
$405$	−1.30135	+	1.81837i	−0.0646647	+	0.0903557i
$406$	−3.68431			−0.182849
$407$		0			0
$408$			2.43134i			0.120369i
$409$	26.9308			1.33164			0.665820	−	0.746112i	$-0.268082\pi$
$409$	26.9308			1.33164			0.665820	+	0.746112i	$0.268082\pi$
$410$	−8.02052	−	5.74003i	−0.396105	−	0.283480i
$411$	−10.1362			−0.499980
$412$			15.2735i			0.752471i
$413$			37.4097i			1.84081i
$414$	3.43134			0.168641
$415$	−5.86594	−	4.19807i	−0.287948	−	0.206075i
$416$	3.39730			0.166566
$417$		−	1.93192i		−	0.0946063i
$418$			37.0329i			1.81134i
$419$	−8.10912			−0.396156			−0.198078	−	0.980186i	$-0.563470\pi$
$419$	−8.10912			−0.396156			−0.198078	+	0.980186i	$0.563470\pi$
$420$	6.03404	−	8.43134i	0.294431	−	0.411407i
$421$	−1.17836			−0.0574298			−0.0287149	−	0.999588i	$-0.509141\pi$
$421$	−1.17836			−0.0574298			−0.0287149	+	0.999588i	$0.509141\pi$
$422$		−	23.9102i		−	1.16393i
$423$			1.56866i			0.0762710i
$424$	−9.43134			−0.458026
$425$	11.5068	−	3.92166i	0.558160	−	0.190228i
$426$	−14.1021			−0.683250
$427$		−	39.0940i		−	1.89189i
$428$		−	4.70483i		−	0.227417i
$429$	17.8000			0.859390
$430$	6.03404	−	8.43134i	0.290987	−	0.406595i
$431$	−24.5199			−1.18108			−0.590542	−	0.807007i	$-0.701086\pi$
$431$	−24.5199			−1.18108			−0.590542	+	0.807007i	$0.701086\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			3.91024i			0.187914i	0.995576	+	0.0939571i	$0.0299516\pi$
$433$			3.91024i			0.187914i	−0.995576	+	0.0939571i	$0.970048\pi$
$434$	4.63675			0.222571
$435$	1.44486	+	1.03404i	0.0692758	+	0.0495785i
$436$	−13.6573			−0.654064
$437$			24.2530i			1.16018i
$438$		−	11.4994i		−	0.549464i
$439$	22.8897			1.09247			0.546233	−	0.837633i	$-0.316061\pi$
$439$	22.8897			1.09247			0.546233	+	0.837633i	$0.316061\pi$
$440$	9.52728	+	6.81837i	0.454195	+	0.325053i
$441$	14.4994			0.690449
$442$			8.25997i			0.392887i
$443$			3.22709i			0.153323i	0.997057	+	0.0766617i	$0.0244262\pi$
$443$			3.22709i			0.153323i	−0.997057	+	0.0766617i	$0.975574\pi$
$444$		0			0
$445$	6.97948	−	9.75240i	0.330859	−	0.462308i
$446$	18.2870			0.865915
$447$		−	20.0340i		−	0.947578i
$448$			4.63675i			0.219066i
$449$	−2.94544			−0.139004			−0.0695020	−	0.997582i	$-0.522141\pi$
$449$	−2.94544			−0.139004			−0.0695020	+	0.997582i	$0.522141\pi$
$450$	−4.73269	+	1.61296i	−0.223101	+	0.0760358i
$451$	23.1103			1.08822
$452$			4.63675i			0.218094i
$453$		−	20.4994i		−	0.963147i
$454$	−17.4313			−0.818093
$455$	20.4994	−	28.6437i	0.961028	−	1.34284i
$456$	7.06808			0.330993
$457$			2.61507i			0.122328i	0.998128	+	0.0611639i	$0.0194812\pi$
$457$			2.61507i			0.122328i	−0.998128	+	0.0611639i	$0.980519\pi$
$458$		−	18.3416i		−	0.857046i
$459$	2.43134			0.113485
$460$	6.23945	+	4.46538i	0.290916	+	0.208199i
$461$	6.93076			0.322798			0.161399	−	0.986889i	$-0.448399\pi$
$461$	6.93076			0.322798			0.161399	+	0.986889i	$0.448399\pi$
$462$			24.2940i			1.13026i
$463$			36.7659i			1.70866i	0.519733	+	0.854329i	$0.326031\pi$
$463$			36.7659i			1.70866i	−0.519733	+	0.854329i	$0.673969\pi$
$464$	−0.794590			−0.0368879
$465$	−1.81837	−	1.30135i	−0.0843250	−	0.0603488i
$466$	18.7729			0.869638
$467$			23.3686i			1.08137i	0.841225	+	0.540686i	$0.181835\pi$
$467$			23.3686i			1.08137i	−0.841225	+	0.540686i	$0.818165\pi$
$468$		−	3.39730i		−	0.157040i
$469$	−34.6151			−1.59838
$470$	−2.04138	+	2.85242i	−0.0941620	+	0.131572i
$471$	−16.7048			−0.769718
$472$			8.06808i			0.371364i
$473$			24.2940i			1.11704i
$474$	−11.1362			−0.511501
$475$	−11.4006	−	33.4510i	−0.523094	−	1.53484i
$476$	−11.2735			−0.516720
$477$			9.43134i			0.431831i
$478$			8.93076i			0.408483i
$479$	36.4449			1.66521			0.832604	−	0.553869i	$-0.186849\pi$
$479$	36.4449			1.66521			0.832604	+	0.553869i	$0.186849\pi$
$480$	1.30135	−	1.81837i	0.0593983	−	0.0829970i
$481$		0			0
$482$			1.20541i			0.0549049i
$483$			15.9102i			0.723941i
$484$	−16.4519			−0.747812
$485$	−0.348919	−	0.249710i	−0.0158436	−	0.0113388i
$486$	−1.00000			−0.0453609
$487$			39.3269i			1.78207i	0.453933	+	0.891036i	$0.350021\pi$
$487$			39.3269i			1.78207i	−0.453933	+	0.891036i	$0.649979\pi$
$488$		−	8.43134i		−	0.381669i
$489$	7.53346			0.340675
$490$	26.3654	+	18.8689i	1.19107	+	0.852408i
$491$	8.97948			0.405238			0.202619	−	0.979258i	$-0.435055\pi$
$491$	8.97948			0.405238			0.202619	+	0.979258i	$0.435055\pi$
$492$		−	4.41082i		−	0.198855i
$493$		−	1.93192i		−	0.0870091i
$494$	24.0124			1.08037
$495$	6.81837	−	9.52728i	0.306463	−	0.428219i
$496$	1.00000			0.0449013
$497$		−	65.3880i		−	2.93305i
$498$		−	3.22593i		−	0.144557i
$499$	−7.68431			−0.343997			−0.171999	−	0.985097i	$-0.555022\pi$
$499$	−7.68431			−0.343997			−0.171999	+	0.985097i	$0.555022\pi$
$500$	−10.7048	−	3.22593i	−0.478735	−	0.144268i
$501$	2.22593			0.0994471
$502$		−	9.34158i		−	0.416935i
$503$			25.3891i			1.13205i	0.824389	+	0.566023i	$0.191519\pi$
$503$			25.3891i			1.13205i	−0.824389	+	0.566023i	$0.808481\pi$
$504$	4.63675			0.206537
$505$	−15.9102	+	22.2313i	−0.707996	+	0.989280i
$506$	−17.9783			−0.799234
$507$			1.45839i			0.0647692i
$508$		−	10.7946i		−	0.478932i
$509$	26.4108			1.17064			0.585320	−	0.810803i	$-0.300969\pi$
$509$	26.4108			1.17064			0.585320	+	0.810803i	$0.300969\pi$
$510$	4.42108	+	3.16403i	0.195769	+	0.140105i
$511$	53.3199			2.35873
$512$			1.00000i			0.0441942i
$513$		−	7.06808i		−	0.312064i
$514$	−1.36325			−0.0601305
$515$	27.7729	+	19.8762i	1.22382	+	0.875850i
$516$	4.63675			0.204121
$517$		−	8.21893i		−	0.361468i
$518$		0			0
$519$	0.774073			0.0339780
$520$	4.42108	−	6.17755i	0.193877	−	0.270904i
$521$	−13.3005			−0.582707			−0.291354	−	0.956615i	$-0.594106\pi$
$521$	−13.3005			−0.582707			−0.291354	+	0.956615i	$0.594106\pi$
$522$			0.794590i			0.0347783i
$523$			9.45839i			0.413586i	0.978385	+	0.206793i	$0.0663027\pi$
$523$			9.45839i			0.413586i	−0.978385	+	0.206793i	$0.933697\pi$
$524$	−16.8897			−0.737831
$525$	−7.47890	−	21.9443i	−0.326406	−	0.957727i
$526$	15.3145			0.667745
$527$			2.43134i			0.105911i
$528$			5.23945i			0.228018i
$529$	11.2259			0.488084
$530$	−12.2735	+	17.1497i	−0.533126	+	0.744935i
$531$	8.06808			0.350125
$532$			32.7729i			1.42089i
$533$		−	14.9849i		−	0.649066i
$534$	5.36325			0.232091
$535$	−8.55514	−	6.12264i	−0.369871	−	0.264705i
$536$	−7.46538			−0.322455
$537$		−	25.4654i		−	1.09891i
$538$		−	8.41082i		−	0.362616i
$539$	−75.9690			−3.27222
$540$	−1.81837	−	1.30135i	−0.0782503	−	0.0560013i
$541$	−35.7934			−1.53888			−0.769440	−	0.638719i	$-0.779465\pi$
$541$	−35.7934			−1.53888			−0.769440	+	0.638719i	$0.779465\pi$
$542$		−	4.27349i		−	0.183562i
$543$			13.4584i			0.577555i
$544$	−2.43134			−0.104243
$545$	−17.7729	+	24.8340i	−0.761308	+	1.06377i
$546$	15.7524			0.674140
$547$		−	24.5199i		−	1.04840i	−0.851596	−	0.524198i	$-0.824365\pi$
$547$		−	24.5199i		−	1.04840i	0.851596	−	0.524198i	$-0.175635\pi$
$548$		−	10.1362i		−	0.432996i
$549$	−8.43134			−0.359841
$550$	24.7967	−	8.45104i	1.05733	−	0.360354i
$551$	−5.61623			−0.239259
$552$			3.43134i			0.146047i
$553$		−	51.6356i		−	2.19577i
$554$	23.9853			1.01904
$555$		0			0
$556$	1.93192			0.0819315
$557$			11.4584i			0.485507i	0.970088	+	0.242754i	$0.0780507\pi$
$557$			11.4584i			0.485507i	−0.970088	+	0.242754i	$0.921949\pi$
$558$		−	1.00000i		−	0.0423334i
$559$	15.7524			0.666255
$560$	8.43134	+	6.03404i	0.356289	+	0.254985i
$561$	−12.7389			−0.537836
$562$		−	20.9988i		−	0.885783i
$563$			42.0681i			1.77296i	0.462768	+	0.886479i	$0.346856\pi$
$563$			42.0681i			1.77296i	−0.462768	+	0.886479i	$0.653144\pi$
$564$	−1.56866			−0.0660526
$565$	8.43134	+	6.03404i	0.354709	+	0.253854i
$566$	18.3961			0.773247
$567$		−	4.63675i		−	0.194725i
$568$		−	14.1021i		−	0.591712i
$569$	25.1837			1.05576			0.527879	−	0.849320i	$-0.322988\pi$
$569$	25.1837			1.05576			0.527879	+	0.849320i	$0.322988\pi$
$570$	9.19807	−	12.8524i	0.385265	−	0.538328i
$571$	15.6843			0.656368			0.328184	−	0.944614i	$-0.393563\pi$
$571$	15.6843			0.656368			0.328184	+	0.944614i	$0.393563\pi$
$572$			17.8000i			0.744254i
$573$			4.38377i			0.183135i
$574$	20.4519			0.853644
$575$	16.2395	−	5.53462i	0.677232	−	0.230810i
$576$	1.00000			0.0416667
$577$		−	36.8480i		−	1.53400i	−0.641646	−	0.767001i	$-0.721748\pi$
$577$		−	36.8480i		−	1.53400i	0.641646	−	0.767001i	$-0.278252\pi$
$578$			11.0886i			0.461225i
$579$	−10.7389			−0.446292
$580$	−1.03404	+	1.44486i	−0.0429363	+	0.0599946i
$581$	14.9578			0.620554
$582$		−	0.191885i		−	0.00795390i
$583$		−	49.4150i		−	2.04656i
$584$	11.4994			0.475849
$585$	−6.17755	−	4.42108i	−0.255410	−	0.182789i
$586$	−19.7253			−0.814847
$587$			30.7307i			1.26839i	0.773172	+	0.634196i	$0.218669\pi$
$587$			30.7307i			1.26839i	−0.773172	+	0.634196i	$0.781331\pi$
$588$			14.4994i			0.597946i
$589$	7.06808			0.291235
$590$	14.6708	+	10.4994i	0.603987	+	0.432254i
$591$	26.9578			1.10890
$592$		0			0
$593$		−	29.0259i		−	1.19195i	−0.803003	−	0.595975i	$-0.796766\pi$
$593$		−	29.0259i		−	1.19195i	0.803003	−	0.595975i	$-0.203234\pi$
$594$	5.23945			0.214977
$595$	−14.6708	+	20.4994i	−0.601444	+	0.840394i
$596$	20.0340			0.820626
$597$		−	25.9988i		−	1.06406i
$598$			11.6573i			0.476701i
$599$	−21.7864			−0.890170			−0.445085	−	0.895488i	$-0.646826\pi$
$599$	−21.7864			−0.890170			−0.445085	+	0.895488i	$0.646826\pi$
$600$	−1.61296	−	4.73269i	−0.0658490	−	0.193211i
$601$	40.0951			1.63551			0.817757	−	0.575563i	$-0.195217\pi$
$601$	40.0951			1.63551			0.817757	+	0.575563i	$0.195217\pi$
$602$			21.4994i			0.876251i
$603$			7.46538i			0.304014i
$604$	20.4994			0.834110
$605$	−21.4097	+	29.9156i	−0.870426	+	1.21624i
$606$	−12.2259			−0.496644
$607$		−	3.04757i		−	0.123697i	−0.998086	−	0.0618485i	$-0.980300\pi$
$607$		−	3.04757i		−	0.123697i	0.998086	−	0.0618485i	$-0.0196995\pi$
$608$			7.06808i			0.286649i
$609$	−3.68431			−0.149296
$610$	−15.3313	−	10.9721i	−0.620747	−	0.444249i
$611$	−5.32921			−0.215597
$612$			2.43134i			0.0982810i
$613$		−	13.4243i		−	0.542204i	−0.962551	−	0.271102i	$-0.912612\pi$
$613$		−	13.4243i		−	0.542204i	0.962551	−	0.271102i	$-0.0873881\pi$
$614$	10.9308			0.441129
$615$	−8.02052	−	5.74003i	−0.323418	−	0.231460i
$616$	−24.2940			−0.978834
$617$		−	4.18489i		−	0.168477i	−0.996446	−	0.0842387i	$-0.973154\pi$
$617$		−	4.18489i		−	0.168477i	0.996446	−	0.0842387i	$-0.0268458\pi$
$618$			15.2735i			0.614390i
$619$	−1.45301			−0.0584015			−0.0292008	−	0.999574i	$-0.509296\pi$
$619$	−1.45301			−0.0584015			−0.0292008	+	0.999574i	$0.509296\pi$
$620$	1.30135	−	1.81837i	0.0522636	−	0.0730276i
$621$	3.43134			0.137695
$622$		−	12.6027i		−	0.505322i
$623$			24.8680i			0.996317i
$624$	3.39730			0.136001
$625$	−19.7967	+	15.2673i	−0.791868	+	0.610692i
$626$	12.4108			0.496036
$627$			37.0329i			1.47895i
$628$		−	16.7048i		−	0.666595i
$629$		0			0
$630$	6.03404	−	8.43134i	0.240402	−	0.335913i
$631$	10.9091			0.434284			0.217142	−	0.976140i	$-0.430327\pi$
$631$	10.9091			0.434284			0.217142	+	0.976140i	$0.430327\pi$
$632$		−	11.1362i		−	0.442973i
$633$		−	23.9102i		−	0.950347i
$634$	12.7741			0.507323
$635$	−19.6286	−	14.0476i	−0.778937	−	0.557461i
$636$	−9.43134			−0.373977
$637$			49.2588i			1.95171i
$638$		−	4.16322i		−	0.164823i
$639$	−14.1021			−0.557871
$640$	1.81837	+	1.30135i	0.0718775	+	0.0514405i
$641$	−21.5745			−0.852141			−0.426071	−	0.904690i	$-0.640103\pi$
$641$	−21.5745			−0.852141			−0.426071	+	0.904690i	$0.640103\pi$
$642$		−	4.70483i		−	0.185685i
$643$			48.8410i			1.92610i	0.269321	+	0.963050i	$0.413201\pi$
$643$			48.8410i			1.92610i	−0.269321	+	0.963050i	$0.586799\pi$
$644$	−15.9102			−0.626951
$645$	6.03404	−	8.43134i	0.237590	−	0.331984i
$646$	−17.1849			−0.676131
$647$			20.7729i			0.816668i	0.912833	+	0.408334i	$0.133890\pi$
$647$			20.7729i			0.816668i	−0.912833	+	0.408334i	$0.866110\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−42.2723			−1.65933
$650$	−5.47971	−	16.0783i	−0.214932	−	0.630644i
$651$	4.63675			0.181728
$652$			7.53346i			0.295033i
$653$		−	15.2670i		−	0.597442i	−0.954340	−	0.298721i	$-0.903440\pi$
$653$		−	15.2670i		−	0.597442i	0.954340	−	0.298721i	$-0.0965601\pi$
$654$	−13.6573			−0.534041
$655$	−21.9795	+	30.7118i	−0.858809	+	1.20001i
$656$	4.41082			0.172214
$657$		−	11.4994i		−	0.448635i
$658$		−	7.27349i		−	0.283550i
$659$	−28.6832			−1.11734			−0.558669	−	0.829391i	$-0.688688\pi$
$659$	−28.6832			−1.11734			−0.558669	+	0.829391i	$0.688688\pi$
$660$	9.52728	+	6.81837i	0.370849	+	0.265405i
$661$	4.61507			0.179505			0.0897527	−	0.995964i	$-0.471392\pi$
$661$	4.61507			0.179505			0.0897527	+	0.995964i	$0.471392\pi$
$662$		−	6.88972i		−	0.267777i
$663$			8.25997i			0.320791i
$664$	3.22593			0.125190
$665$	59.5934	+	42.6491i	2.31093	+	1.65386i
$666$		0			0
$667$		−	2.72651i		−	0.105571i
$668$			2.22593i			0.0861237i
$669$	18.2870			0.707017
$670$	−9.71509	+	13.5748i	−0.375327	+	0.524442i
$671$	44.1756			1.70538
$672$			4.63675i			0.178866i
$673$		−	25.7524i		−	0.992682i	−0.868128	−	0.496341i	$-0.834677\pi$
$673$		−	25.7524i		−	0.992682i	0.868128	−	0.496341i	$-0.165323\pi$
$674$	−6.72651			−0.259095
$675$	−4.73269	+	1.61296i	−0.182161	+	0.0620830i
$676$	−1.45839			−0.0560918
$677$			7.45839i			0.286649i	0.989676	+	0.143325i	$0.0457793\pi$
$677$			7.45839i			0.286649i	−0.989676	+	0.143325i	$0.954221\pi$
$678$			4.63675i			0.178073i
$679$	0.889723			0.0341444
$680$	−3.16403	+	4.42108i	−0.121335	+	0.169541i
$681$	−17.4313			−0.667970
$682$			5.23945i			0.200629i
$683$			19.7741i			0.756634i	0.925676	+	0.378317i	$0.123497\pi$
$683$			19.7741i			0.756634i	−0.925676	+	0.378317i	$0.876503\pi$
$684$	7.06808			0.270255
$685$	−18.4313	−	13.1907i	−0.704225	−	0.503992i
$686$	−34.7729			−1.32764
$687$		−	18.3416i		−	0.699775i
$688$			4.63675i			0.176774i
$689$	−32.0410			−1.22067
$690$	6.23945	+	4.46538i	0.237532	+	0.169994i
$691$	30.7934			1.17144			0.585719	−	0.810514i	$-0.300812\pi$
$691$	30.7934			1.17144			0.585719	+	0.810514i	$0.300812\pi$
$692$			0.774073i			0.0294258i
$693$			24.2940i			0.922853i
$694$	−20.1837			−0.766164
$695$	2.51410	−	3.51295i	0.0953654	−	0.133254i
$696$	−0.794590			−0.0301189
$697$			10.7242i			0.406208i
$698$		−	32.9578i		−	1.24747i
$699$	18.7729			0.710057
$700$	21.9443	−	7.47890i	0.829416	−	0.282676i
$701$	−35.6503			−1.34649			−0.673246	−	0.739418i	$-0.735101\pi$
$701$	−35.6503			−1.34649			−0.673246	+	0.739418i	$0.735101\pi$
$702$		−	3.39730i		−	0.128223i
$703$		0			0
$704$	−5.23945			−0.197469
$705$	−2.04138	+	2.85242i	−0.0768830	+	0.107428i
$706$	−32.9373			−1.23961
$707$		−	56.6885i		−	2.13199i
$708$			8.06808i			0.303217i
$709$	−0.931916			−0.0349989			−0.0174994	−	0.999847i	$-0.505571\pi$
$709$	−0.931916			−0.0349989			−0.0174994	+	0.999847i	$0.505571\pi$
$710$	−25.6429	−	18.3518i	−0.962362	−	0.688732i
$711$	−11.1362			−0.417639
$712$			5.36325i			0.200996i
$713$			3.43134i			0.128505i
$714$	−11.2735			−0.421900
$715$	32.3670	+	23.1640i	1.21046	+	0.866285i
$716$	25.4654			0.951686
$717$			8.93076i			0.333525i
$718$			0.444862i			0.0166021i
$719$	3.34158			0.124620			0.0623099	−	0.998057i	$-0.480153\pi$
$719$	3.34158			0.124620			0.0623099	+	0.998057i	$0.480153\pi$
$720$	1.30135	−	1.81837i	0.0484985	−	0.0677668i
$721$	−70.8193			−2.63745
$722$			30.9578i			1.15213i
$723$			1.20541i			0.0448297i
$724$	−13.4584			−0.500177
$725$	1.28164	+	3.76055i	0.0475991	+	0.139663i
$726$	−16.4519			−0.610586
$727$		−	31.0886i		−	1.15301i	−0.817093	−	0.576506i	$-0.804416\pi$
$727$		−	31.0886i		−	1.15301i	0.817093	−	0.576506i	$-0.195584\pi$
$728$			15.7524i			0.583823i
$729$	−1.00000			−0.0370370
$730$	14.9648	−	20.9102i	0.553872	−	0.773923i
$731$	−11.2735			−0.416965
$732$		−	8.43134i		−	0.311631i
$733$		−	9.65726i		−	0.356699i	−0.983967	−	0.178350i	$-0.942924\pi$
$733$		−	9.65726i		−	0.356699i	0.983967	−	0.178350i	$-0.0570758\pi$
$734$	−22.8750			−0.844333
$735$	26.3654	+	18.8689i	0.972501	+	0.695988i
$736$	−3.43134			−0.126481
$737$		−	39.1145i		−	1.44080i
$738$		−	4.41082i		−	0.162365i
$739$	22.5199			0.828409			0.414205	−	0.910184i	$-0.364060\pi$
$739$	22.5199			0.828409			0.414205	+	0.910184i	$0.364060\pi$
$740$		0			0
$741$	24.0124			0.882116
$742$		−	43.7307i		−	1.60541i
$743$		−	40.1826i		−	1.47416i	−0.675808	−	0.737078i	$-0.736205\pi$
$743$		−	40.1826i		−	1.47416i	0.675808	−	0.737078i	$-0.263795\pi$
$744$	1.00000			0.0366618
$745$	26.0713	−	36.4294i	0.955180	−	1.33467i
$746$	22.6367			0.828790
$747$		−	3.22593i		−	0.118030i
$748$		−	12.7389i		−	0.465779i
$749$	21.8151			0.797107
$750$	−10.7048	−	3.22593i	−0.390885	−	0.117794i
$751$	0.410820			0.0149910			0.00749551	−	0.999972i	$-0.497614\pi$
$751$	0.410820			0.0149910			0.00749551	+	0.999972i	$0.497614\pi$
$752$		−	1.56866i		−	0.0572033i
$753$		−	9.34158i		−	0.340426i
$754$	−2.69946			−0.0983084
$755$	26.6770	−	37.2756i	0.970874	−	1.35660i
$756$	4.63675			0.168637
$757$			6.68315i			0.242903i	0.992597	+	0.121452i	$0.0387550\pi$
$757$			6.68315i			0.242903i	−0.992597	+	0.121452i	$0.961245\pi$
$758$		−	3.93076i		−	0.142772i
$759$	−17.9783			−0.652572
$760$	12.8524	+	9.19807i	0.466206	+	0.333649i
$761$	24.2112			0.877657			0.438828	−	0.898571i	$-0.355394\pi$
$761$	24.2112			0.877657			0.438828	+	0.898571i	$0.355394\pi$
$762$		−	10.7946i		−	0.391047i
$763$		−	63.3253i		−	2.29253i
$764$	−4.38377			−0.158599
$765$	4.42108	+	3.16403i	0.159844	+	0.114396i
$766$	−29.4777			−1.06507
$767$			27.4097i			0.989705i
$768$			1.00000i			0.0360844i
$769$	−20.6367			−0.744180			−0.372090	−	0.928197i	$-0.621359\pi$
$769$	−20.6367			−0.744180			−0.372090	+	0.928197i	$0.621359\pi$
$770$	−31.6151	+	44.1756i	−1.13933	+	1.59198i
$771$	−1.36325			−0.0490964
$772$		−	10.7389i		−	0.386500i
$773$		−	38.5934i		−	1.38811i	−0.719923	−	0.694054i	$-0.755823\pi$
$773$		−	38.5934i		−	1.38811i	0.719923	−	0.694054i	$-0.244177\pi$
$774$	4.63675			0.166664
$775$	−1.61296	−	4.73269i	−0.0579394	−	0.170003i
$776$	0.191885			0.00688828
$777$		0			0
$778$		−	12.5199i		−	0.448862i
$779$	31.1760			1.11700
$780$	4.42108	−	6.17755i	0.158300	−	0.221192i
$781$	73.8874			2.64390
$782$		−	8.34274i		−	0.298336i
$783$			0.794590i			0.0283963i
$784$	−14.4994			−0.517836
$785$	−30.3756	−	21.7389i	−1.08415	−	0.775894i
$786$	−16.8897			−0.602436
$787$		−	9.02052i		−	0.321547i	−0.986991	−	0.160773i	$-0.948601\pi$
$787$		−	9.02052i		−	0.321547i	0.986991	−	0.160773i	$-0.0513988\pi$
$788$			26.9578i			0.960332i
$789$	15.3145			0.545212
$790$	−20.2497	−	14.4921i	−0.720452	−	0.515605i
$791$	−21.4994			−0.764431
$792$			5.23945i			0.186176i
$793$		−	28.6437i		−	1.01717i
$794$	−11.8422			−0.420262
$795$	−12.2735	+	17.1497i	−0.435296	+	0.608237i
$796$	25.9988			0.921504
$797$		−	3.20541i		−	0.113541i	−0.998387	−	0.0567707i	$-0.981920\pi$
$797$		−	3.20541i		−	0.113541i	0.998387	−	0.0567707i	$-0.0180804\pi$
$798$			32.7729i			1.16015i
$799$	3.81395			0.134928
$800$	4.73269	−	1.61296i	0.167326	−	0.0570269i
$801$	5.36325			0.189501
$802$		−	18.9918i		−	0.670625i
$803$			60.2507i			2.12620i
$804$	−7.46538			−0.263284
$805$	−20.7048	+	28.9308i	−0.729749	+	1.01968i
$806$	3.39730			0.119665
$807$		−	8.41082i		−	0.296075i
$808$		−	12.2259i		−	0.430107i
$809$	19.1033			0.671636			0.335818	−	0.941927i	$-0.390987\pi$
$809$	19.1033			0.671636			0.335818	+	0.941927i	$0.390987\pi$
$810$	−1.81837	−	1.30135i	−0.0638911	−	0.0457249i
$811$	−51.2248			−1.79874			−0.899372	−	0.437183i	$-0.855976\pi$
$811$	−51.2248			−1.79874			−0.899372	+	0.437183i	$0.855976\pi$
$812$		−	3.68431i		−	0.129294i
$813$		−	4.27349i		−	0.149878i
$814$		0			0
$815$	13.6986	+	9.80369i	0.479843	+	0.343408i
$816$	−2.43134			−0.0851138
$817$			32.7729i			1.14658i
$818$			26.9308i			0.941612i
$819$	15.7524			0.550433
$820$	5.74003	−	8.02052i	0.200451	−	0.280089i
$821$	−33.3145			−1.16269			−0.581343	−	0.813659i	$-0.697472\pi$
$821$	−33.3145			−1.16269			−0.581343	+	0.813659i	$0.697472\pi$
$822$		−	10.1362i		−	0.353539i
$823$			9.66963i			0.337062i	0.985696	+	0.168531i	$0.0539023\pi$
$823$			9.66963i			0.337062i	−0.985696	+	0.168531i	$0.946098\pi$
$824$	−15.2735			−0.532077
$825$	24.7967	−	8.45104i	0.863310	−	0.294228i
$826$	−37.4097			−1.30165
$827$		−	18.3633i		−	0.638553i	−0.947662	−	0.319276i	$-0.896560\pi$
$827$		−	18.3633i		−	0.638553i	0.947662	−	0.319276i	$-0.103440\pi$
$828$			3.43134i			0.119247i
$829$	−12.9091			−0.448351			−0.224175	−	0.974549i	$-0.571969\pi$
$829$	−12.9091			−0.448351			−0.224175	+	0.974549i	$0.571969\pi$
$830$	4.19807	−	5.86594i	0.145717	−	0.203610i
$831$	23.9853			0.832041
$832$			3.39730i			0.117780i
$833$		−	35.2530i		−	1.22144i
$834$	1.93192			0.0668968
$835$	4.04757	+	2.89672i	0.140072	+	0.100245i
$836$	−37.0329			−1.28081
$837$		−	1.00000i		−	0.0345651i
$838$		−	8.10912i		−	0.280125i
$839$	−37.9373			−1.30974			−0.654870	−	0.755741i	$-0.727277\pi$
$839$	−37.9373			−1.30974			−0.654870	+	0.755741i	$0.727277\pi$
$840$	8.43134	+	6.03404i	0.290909	+	0.208194i
$841$	−28.3686			−0.978229
$842$		−	1.17836i		−	0.0406090i
$843$		−	20.9988i		−	0.723239i
$844$	23.9102			0.823024
$845$	−1.89787	+	2.65189i	−0.0652889	+	0.0912278i
$846$	−1.56866			−0.0539317
$847$		−	76.2831i		−	2.62112i
$848$		−	9.43134i		−	0.323873i
$849$	18.3961			0.631354
$850$	3.92166	+	11.5068i	0.134512	+	0.394679i
$851$		0			0
$852$		−	14.1021i		−	0.483131i
$853$			27.4724i			0.940636i	0.882497	+	0.470318i	$0.155861\pi$
$853$			27.4724i			0.940636i	−0.882497	+	0.470318i	$0.844139\pi$
$854$	39.0940			1.33777
$855$	9.19807	−	12.8524i	0.314567	−	0.439543i
$856$	4.70483			0.160808
$857$		−	5.95897i		−	0.203554i	−0.994807	−	0.101777i	$-0.967547\pi$
$857$		−	5.95897i		−	0.203554i	0.994807	−	0.101777i	$-0.0324529\pi$
$858$			17.8000i			0.607681i
$859$	45.0529			1.53719			0.768593	−	0.639738i	$-0.220957\pi$
$859$	45.0529			1.53719			0.768593	+	0.639738i	$0.220957\pi$
$860$	8.43134	+	6.03404i	0.287506	+	0.205759i
$861$	20.4519			0.696997
$862$		−	24.5199i		−	0.835152i
$863$			6.33505i			0.215647i	0.994170	+	0.107824i	$0.0343882\pi$
$863$			6.33505i			0.215647i	−0.994170	+	0.107824i	$0.965612\pi$
$864$	1.00000			0.0340207
$865$	1.40755	+	1.00734i	0.0478583	+	0.0342506i
$866$	−3.91024			−0.132875
$867$			11.0886i			0.376589i
$868$			4.63675i			0.157381i
$869$	58.3474			1.97930
$870$	−1.03404	+	1.44486i	−0.0350573	+	0.0489854i
$871$	−25.3621			−0.859362
$872$		−	13.6573i		−	0.462493i
$873$		−	0.191885i		−	0.00649433i
$874$	−24.2530			−0.820369
$875$	14.9578	−	49.6356i	0.505666	−	1.67799i
$876$	11.4994			0.388529
$877$			27.0692i			0.914063i	0.889450	+	0.457032i	$0.151087\pi$
$877$			27.0692i			0.914063i	−0.889450	+	0.457032i	$0.848913\pi$
$878$			22.8897i			0.772491i
$879$	−19.7253			−0.665319
$880$	−6.81837	+	9.52728i	−0.229847	+	0.321165i
$881$	−25.6286			−0.863449			−0.431725	−	0.902005i	$-0.642095\pi$
$881$	−25.6286			−0.863449			−0.431725	+	0.902005i	$0.642095\pi$
$882$			14.4994i			0.488221i
$883$		−	1.25182i		−	0.0421270i	−0.999778	−	0.0210635i	$-0.993295\pi$
$883$		−	1.25182i		−	0.0421270i	0.999778	−	0.0210635i	$-0.00670522\pi$
$884$	−8.25997			−0.277813
$885$	14.6708	+	10.4994i	0.493153	+	0.352934i
$886$	−3.22709			−0.108416
$887$			48.2723i			1.62083i	0.585859	+	0.810413i	$0.300757\pi$
$887$			48.2723i			1.62083i	−0.585859	+	0.810413i	$0.699243\pi$
$888$		0			0
$889$	50.0518			1.67868
$890$	9.75240	+	6.97948i	0.326901	+	0.233953i
$891$	5.23945			0.175528
$892$			18.2870i			0.612295i
$893$		−	11.0874i		−	0.371027i
$894$	20.0340			0.670039
$895$	33.1394	−	46.3056i	1.10773	−	1.54782i
$896$	−4.63675			−0.154903
$897$			11.6573i			0.389225i
$898$		−	2.94544i		−	0.0982906i
$899$	−0.794590			−0.0265011
$900$	−1.61296	−	4.73269i	−0.0537655	−	0.157756i
$901$	22.9308			0.763934
$902$			23.1103i			0.769488i
$903$			21.4994i			0.715456i
$904$	−4.63675			−0.154216
$905$	−17.5141	+	24.4724i	−0.582189	+	0.813489i
$906$	20.4994			0.681048
$907$		−	4.60270i		−	0.152830i	−0.997076	−	0.0764152i	$-0.975653\pi$
$907$		−	4.60270i		−	0.152830i	0.997076	−	0.0764152i	$-0.0243474\pi$
$908$		−	17.4313i		−	0.578479i
$909$	−12.2259			−0.405508
$910$	28.6437	+	20.4994i	0.949531	+	0.679549i
$911$	−14.9168			−0.494215			−0.247107	−	0.968988i	$-0.579480\pi$
$911$	−14.9168			−0.494215			−0.247107	+	0.968988i	$0.579480\pi$
$912$			7.06808i			0.234048i
$913$			16.9021i			0.559377i
$914$	−2.61507			−0.0864989
$915$	−15.3313	−	10.9721i	−0.506838	−	0.362728i
$916$	18.3416			0.606023
$917$		−	78.3134i		−	2.58614i
$918$			2.43134i			0.0802461i
$919$	−0.615071			−0.0202893			−0.0101447	−	0.999949i	$-0.503229\pi$
$919$	−0.615071			−0.0202893			−0.0101447	+	0.999949i	$0.503229\pi$
$920$	−4.46538	+	6.23945i	−0.147219	+	0.205709i
$921$	10.9308			0.360181
$922$			6.93076i			0.228252i
$923$		−	47.9091i		−	1.57695i
$924$	−24.2940			−0.799214
$925$		0			0
$926$	−36.7659			−1.20820
$927$			15.2735i			0.501647i
$928$		−	0.794590i		−	0.0260837i
$929$	8.45955			0.277549			0.138774	−	0.990324i	$-0.455684\pi$
$929$	8.45955			0.277549			0.138774	+	0.990324i	$0.455684\pi$
$930$	1.30135	−	1.81837i	0.0426730	−	0.0596268i
$931$	−102.483			−3.35875
$932$			18.7729i			0.614927i
$933$		−	12.6027i		−	0.412594i
$934$	−23.3686			−0.764645
$935$	−23.1640	−	16.5778i	−0.757545	−	0.542151i
$936$	3.39730			0.111044
$937$		−	25.2318i		−	0.824286i	−0.911119	−	0.412143i	$-0.864780\pi$
$937$		−	25.2318i		−	0.824286i	0.911119	−	0.412143i	$-0.135220\pi$
$938$		−	34.6151i		−	1.13022i
$939$	12.4108			0.405012
$940$	−2.85242	−	2.04138i	−0.0930355	−	0.0665826i
$941$	4.75124			0.154886			0.0774430	−	0.996997i	$-0.475324\pi$
$941$	4.75124			0.154886			0.0774430	+	0.996997i	$0.475324\pi$
$942$		−	16.7048i		−	0.544273i
$943$			15.1350i			0.492864i
$944$	−8.06808			−0.262594
$945$	6.03404	−	8.43134i	0.196287	−	0.274271i
$946$	−24.2940			−0.789866
$947$			14.3222i			0.465410i	0.972547	+	0.232705i	$0.0747576\pi$
$947$			14.3222i			0.465410i	−0.972547	+	0.232705i	$0.925242\pi$
$948$		−	11.1362i		−	0.361686i
$949$	39.0669			1.26817
$950$	33.4510	−	11.4006i	1.08530	−	0.369883i
$951$	12.7741			0.414228
$952$		−	11.2735i		−	0.365376i
$953$			46.0723i			1.49243i	0.665706	+	0.746214i	$0.268130\pi$
$953$			46.0723i			1.49243i	−0.665706	+	0.746214i	$0.731870\pi$
$954$	−9.43134			−0.305351
$955$	−5.70483	+	7.97133i	−0.184604	+	0.257946i
$956$	−8.93076			−0.288841
$957$		−	4.16322i		−	0.134578i
$958$			36.4449i			1.17748i
$959$	46.9988			1.51767
$960$	1.81837	+	1.30135i	0.0586877	+	0.0420010i
$961$	1.00000			0.0322581
$962$		0			0
$963$		−	4.70483i		−	0.151611i
$964$	−1.20541			−0.0388236
$965$	−19.5273	−	13.9751i	−0.628605	−	0.449873i
$966$	−15.9102			−0.511904
$967$		−	18.6708i		−	0.600412i	−0.953874	−	0.300206i	$-0.902945\pi$
$967$		−	18.6708i		−	0.600412i	0.953874	−	0.300206i	$-0.0970554\pi$
$968$		−	16.4519i		−	0.528783i
$969$	−17.1849			−0.552058
$970$	0.249710	−	0.348919i	0.00801771	−	0.0112031i
$971$	16.9718			0.544651			0.272325	−	0.962205i	$-0.412207\pi$
$971$	16.9718			0.544651			0.272325	+	0.962205i	$0.412207\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			8.95781i			0.287174i
$974$	−39.3269			−1.26011
$975$	−5.47971	−	16.0783i	−0.175491	−	0.514919i
$976$	8.43134			0.269881
$977$			30.9578i			0.990428i	0.868771	+	0.495214i	$0.164910\pi$
$977$			30.9578i			0.990428i	−0.868771	+	0.495214i	$0.835090\pi$
$978$			7.53346i			0.240894i
$979$	−28.1005			−0.898096
$980$	−18.8689	+	26.3654i	−0.602744	+	0.842211i
$981$	−13.6573			−0.436043
$982$			8.97948i			0.286547i
$983$		−	52.7512i		−	1.68250i	−0.540644	−	0.841252i	$-0.681819\pi$
$983$		−	52.7512i		−	1.68250i	0.540644	−	0.841252i	$-0.318181\pi$
$984$	4.41082			0.140612
$985$	49.0194	+	35.0816i	1.56189	+	1.11779i
$986$	1.93192			0.0615247
$987$		−	7.27349i		−	0.231518i
$988$			24.0124i			0.763935i
$989$	−15.9102			−0.505916
$990$	9.52728	+	6.81837i	0.302797	+	0.216702i
$991$	−58.7729			−1.86698			−0.933492	−	0.358599i	$-0.883254\pi$
$991$	−58.7729			−1.86698			−0.933492	+	0.358599i	$0.883254\pi$
$992$			1.00000i			0.0317500i
$993$		−	6.88972i		−	0.218639i
$994$	65.3880			2.07398
$995$	33.8337	−	47.2756i	1.07260	−	1.49874i
$996$	3.22593			0.102217
$997$			25.0259i			0.792578i	0.918126	+	0.396289i	$0.129702\pi$
$997$			25.0259i			0.792578i	−0.918126	+	0.396289i	$0.870298\pi$
$998$		−	7.68431i		−	0.243243i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.d.h.559.5	yes	6
3.2	odd	2		2790.2.d.k.559.2		6
5.2	odd	4		4650.2.a.ck.1.3		3
5.3	odd	4		4650.2.a.cn.1.1		3
5.4	even	2	inner	930.2.d.h.559.2	✓	6
15.14	odd	2		2790.2.d.k.559.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.h.559.2	✓	6	5.4	even	2	inner
930.2.d.h.559.5	yes	6	1.1	even	1	trivial
2790.2.d.k.559.2		6	3.2	odd	2
2790.2.d.k.559.5		6	15.14	odd	2
4650.2.a.ck.1.3		3	5.2	odd	4
4650.2.a.cn.1.1		3	5.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.30135 + 1.81837i) q^{5} -1.00000 q^{6} -4.63675i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.30135 + 1.81837i) q^{5} -1.00000 q^{6} -4.63675i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.81837 - 1.30135i) q^{10} +5.23945 q^{11} -1.00000i q^{12} -3.39730i q^{13} +4.63675 q^{14} +(-1.81837 - 1.30135i) q^{15} +1.00000 q^{16} +2.43134i q^{17} -1.00000i q^{18} +7.06808 q^{19} +(1.30135 - 1.81837i) q^{20} +4.63675 q^{21} +5.23945i q^{22} +3.43134i q^{23} +1.00000 q^{24} +(-1.61296 - 4.73269i) q^{25} +3.39730 q^{26} -1.00000i q^{27} +4.63675i q^{28} -0.794590 q^{29} +(1.30135 - 1.81837i) q^{30} +1.00000 q^{31} +1.00000i q^{32} +5.23945i q^{33} -2.43134 q^{34} +(8.43134 + 6.03404i) q^{35} +1.00000 q^{36} +7.06808i q^{38} +3.39730 q^{39} +(1.81837 + 1.30135i) q^{40} +4.41082 q^{41} +4.63675i q^{42} +4.63675i q^{43} -5.23945 q^{44} +(1.30135 - 1.81837i) q^{45} -3.43134 q^{46} -1.56866i q^{47} +1.00000i q^{48} -14.4994 q^{49} +(4.73269 - 1.61296i) q^{50} -2.43134 q^{51} +3.39730i q^{52} -9.43134i q^{53} +1.00000 q^{54} +(-6.81837 + 9.52728i) q^{55} -4.63675 q^{56} +7.06808i q^{57} -0.794590i q^{58} -8.06808 q^{59} +(1.81837 + 1.30135i) q^{60} +8.43134 q^{61} +1.00000i q^{62} +4.63675i q^{63} -1.00000 q^{64} +(6.17755 + 4.42108i) q^{65} -5.23945 q^{66} -7.46538i q^{67} -2.43134i q^{68} -3.43134 q^{69} +(-6.03404 + 8.43134i) q^{70} +14.1021 q^{71} +1.00000i q^{72} +11.4994i q^{73} +(4.73269 - 1.61296i) q^{75} -7.06808 q^{76} -24.2940i q^{77} +3.39730i q^{78} +11.1362 q^{79} +(-1.30135 + 1.81837i) q^{80} +1.00000 q^{81} +4.41082i q^{82} +3.22593i q^{83} -4.63675 q^{84} +(-4.42108 - 3.16403i) q^{85} -4.63675 q^{86} -0.794590i q^{87} -5.23945i q^{88} -5.36325 q^{89} +(1.81837 + 1.30135i) q^{90} -15.7524 q^{91} -3.43134i q^{92} +1.00000i q^{93} +1.56866 q^{94} +(-9.19807 + 12.8524i) q^{95} -1.00000 q^{96} +0.191885i q^{97} -14.4994i q^{98} -5.23945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{14} + 2 q^{15} + 6 q^{16} - 2 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{24} - 4 q^{25} + 24 q^{26} - 12 q^{29} + 6 q^{30} + 6 q^{31} + 4 q^{34} + 32 q^{35} + 6 q^{36} + 24 q^{39} - 2 q^{40} + 12 q^{41} - 2 q^{44} + 6 q^{45} - 2 q^{46} - 24 q^{49} + 8 q^{50} + 4 q^{51} + 6 q^{54} - 28 q^{55} - 2 q^{56} - 4 q^{59} - 2 q^{60} + 32 q^{61} - 6 q^{64} - 20 q^{65} - 2 q^{66} - 2 q^{69} - 14 q^{70} + 18 q^{71} + 8 q^{75} + 2 q^{76} - 22 q^{79} - 6 q^{80} + 6 q^{81} - 2 q^{84} - 10 q^{85} - 2 q^{86} - 58 q^{89} - 2 q^{90} + 16 q^{91} + 28 q^{94} + 6 q^{95} - 6 q^{96} - 2 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^14 + 2 * q^15 + 6 * q^16 - 2 * q^19 + 6 * q^20 + 2 * q^21 + 6 * q^24 - 4 * q^25 + 24 * q^26 - 12 * q^29 + 6 * q^30 + 6 * q^31 + 4 * q^34 + 32 * q^35 + 6 * q^36 + 24 * q^39 - 2 * q^40 + 12 * q^41 - 2 * q^44 + 6 * q^45 - 2 * q^46 - 24 * q^49 + 8 * q^50 + 4 * q^51 + 6 * q^54 - 28 * q^55 - 2 * q^56 - 4 * q^59 - 2 * q^60 + 32 * q^61 - 6 * q^64 - 20 * q^65 - 2 * q^66 - 2 * q^69 - 14 * q^70 + 18 * q^71 + 8 * q^75 + 2 * q^76 - 22 * q^79 - 6 * q^80 + 6 * q^81 - 2 * q^84 - 10 * q^85 - 2 * q^86 - 58 * q^89 - 2 * q^90 + 16 * q^91 + 28 * q^94 + 6 * q^95 - 6 * q^96 - 2 * q^99

Introduction

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