LMFDB - Embedded newform 930.2.d.h.559.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(559,930)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [6,0,0,-6,-6,-6,0,0,-6,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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			559.1
Root			$0.627553 + 1.14620i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.2.d.h.559.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.14620 + 0.627553i) q^{5} -1.00000 q^{6} -0.255105i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(0.627553 + 2.14620i) q^{10} +2.03730 q^{11} +1.00000i q^{12} +1.70760i q^{13} -0.255105 q^{14} +(0.627553 + 2.14620i) q^{15} +1.00000 q^{16} +5.83991i q^{17} +1.00000i q^{18} -6.09501 q^{19} +(2.14620 - 0.627553i) q^{20} -0.255105 q^{21} -2.03730i q^{22} +4.83991i q^{23} +1.00000 q^{24} +(4.21236 - 2.69371i) q^{25} +1.70760 q^{26} +1.00000i q^{27} +0.255105i q^{28} +2.58480 q^{29} +(2.14620 - 0.627553i) q^{30} +1.00000 q^{31} -1.00000i q^{32} -2.03730i q^{33} +5.83991 q^{34} +(0.160092 + 0.547507i) q^{35} +1.00000 q^{36} +6.09501i q^{38} +1.70760 q^{39} +(-0.627553 - 2.14620i) q^{40} +11.1696 q^{41} +0.255105i q^{42} +0.255105i q^{43} -2.03730 q^{44} +(2.14620 - 0.627553i) q^{45} +4.83991 q^{46} +9.83991i q^{47} -1.00000i q^{48} +6.93492 q^{49} +(-2.69371 - 4.21236i) q^{50} +5.83991 q^{51} -1.70760i q^{52} +1.16009i q^{53} +1.00000 q^{54} +(-4.37245 + 1.27851i) q^{55} +0.255105 q^{56} +6.09501i q^{57} -2.58480i q^{58} +5.09501 q^{59} +(-0.627553 - 2.14620i) q^{60} +0.160092 q^{61} -1.00000i q^{62} +0.255105i q^{63} -1.00000 q^{64} +(-1.07161 - 3.66485i) q^{65} -2.03730 q^{66} -7.38741i q^{67} -5.83991i q^{68} +4.83991 q^{69} +(0.547507 - 0.160092i) q^{70} -5.64252 q^{71} -1.00000i q^{72} +9.93492i q^{73} +(-2.69371 - 4.21236i) q^{75} +6.09501 q^{76} -0.519725i q^{77} -1.70760i q^{78} -15.1900 q^{79} +(-2.14620 + 0.627553i) q^{80} +1.00000 q^{81} -11.1696i q^{82} +8.42471i q^{83} +0.255105 q^{84} +(-3.66485 - 12.5336i) q^{85} +0.255105 q^{86} -2.58480i q^{87} +2.03730i q^{88} -10.2551 q^{89} +(-0.627553 - 2.14620i) q^{90} +0.435617 q^{91} -4.83991i q^{92} -1.00000i q^{93} +9.83991 q^{94} +(13.0811 - 3.82494i) q^{95} -1.00000 q^{96} +4.87720i q^{97} -6.93492i q^{98} -2.03730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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
$5$	−2.14620	+	0.627553i	−0.959810	+	0.280650i
$5$	−2.14620	+	0.627553i	−0.959810	+	0.280650i
$6$	−1.00000			−0.408248
$7$		−	0.255105i		−	0.0964206i	−0.998837	−	0.0482103i	$-0.984648\pi$
$7$		−	0.255105i		−	0.0964206i	0.998837	−	0.0482103i	$-0.0153518\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	0.627553	+	2.14620i	0.198450	+	0.678688i
$11$	2.03730			0.614268			0.307134	−	0.951666i	$-0.400630\pi$
$11$	2.03730			0.614268			0.307134	+	0.951666i	$0.400630\pi$
$12$			1.00000i			0.288675i
$13$			1.70760i			0.473603i	0.971558	+	0.236801i	$0.0760990\pi$
$13$			1.70760i			0.473603i	−0.971558	+	0.236801i	$0.923901\pi$
$14$	−0.255105			−0.0681797
$15$	0.627553	+	2.14620i	0.162033	+	0.554147i
$16$	1.00000			0.250000
$17$			5.83991i			1.41639i	0.706019	+	0.708193i	$0.250489\pi$
$17$			5.83991i			1.41639i	−0.706019	+	0.708193i	$0.749511\pi$
$18$			1.00000i			0.235702i
$19$	−6.09501			−1.39829			−0.699146	−	0.714979i	$-0.746436\pi$
$19$	−6.09501			−1.39829			−0.699146	+	0.714979i	$0.746436\pi$
$20$	2.14620	−	0.627553i	0.479905	−	0.140325i
$21$	−0.255105			−0.0556685
$22$		−	2.03730i		−	0.434353i
$23$			4.83991i			1.00919i	0.863356	+	0.504595i	$0.168358\pi$
$23$			4.83991i			1.00919i	−0.863356	+	0.504595i	$0.831642\pi$
$24$	1.00000			0.204124
$25$	4.21236	−	2.69371i	0.842471	−	0.538741i
$26$	1.70760			0.334888
$27$			1.00000i			0.192450i
$28$			0.255105i			0.0482103i
$29$	2.58480			0.479986			0.239993	−	0.970775i	$-0.422855\pi$
$29$	2.58480			0.479986			0.239993	+	0.970775i	$0.422855\pi$
$30$	2.14620	−	0.627553i	0.391841	−	0.114575i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$		−	1.00000i		−	0.176777i
$33$		−	2.03730i		−	0.354648i
$34$	5.83991			1.00154
$35$	0.160092	+	0.547507i	0.0270605	+	0.0925455i
$36$	1.00000			0.166667
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$			6.09501i			0.988742i
$39$	1.70760			0.273435
$40$	−0.627553	−	2.14620i	−0.0992248	−	0.339344i
$41$	11.1696			1.74440			0.872200	−	0.489150i	$-0.162693\pi$
$41$	11.1696			1.74440			0.872200	+	0.489150i	$0.162693\pi$
$42$			0.255105i			0.0393636i
$43$			0.255105i			0.0389032i	0.999811	+	0.0194516i	$0.00619202\pi$
$43$			0.255105i			0.0389032i	−0.999811	+	0.0194516i	$0.993808\pi$
$44$	−2.03730			−0.307134
$45$	2.14620	−	0.627553i	0.319937	−	0.0935500i
$46$	4.83991			0.713606
$47$			9.83991i			1.43530i	0.696405	+	0.717649i	$0.254782\pi$
$47$			9.83991i			1.43530i	−0.696405	+	0.717649i	$0.745218\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.93492			0.990703
$50$	−2.69371	−	4.21236i	−0.380948	−	0.595717i
$51$	5.83991			0.817751
$52$		−	1.70760i		−	0.236801i
$53$			1.16009i			0.159351i	0.996821	+	0.0796754i	$0.0253884\pi$
$53$			1.16009i			0.159351i	−0.996821	+	0.0796754i	$0.974612\pi$
$54$	1.00000			0.136083
$55$	−4.37245	+	1.27851i	−0.589581	+	0.172394i
$56$	0.255105			0.0340898
$57$			6.09501i			0.807304i
$58$		−	2.58480i		−	0.339401i
$59$	5.09501			0.663314			0.331657	−	0.943400i	$-0.392392\pi$
$59$	5.09501			0.663314			0.331657	+	0.943400i	$0.392392\pi$
$60$	−0.627553	−	2.14620i	−0.0810167	−	0.277073i
$61$	0.160092			0.0204977			0.0102488	−	0.999947i	$-0.496738\pi$
$61$	0.160092			0.0204977			0.0102488	+	0.999947i	$0.496738\pi$
$62$		−	1.00000i		−	0.127000i
$63$			0.255105i			0.0321402i
$64$	−1.00000			−0.125000
$65$	−1.07161	−	3.66485i	−0.132917	−	0.454569i
$66$	−2.03730			−0.250774
$67$		−	7.38741i		−	0.902516i	−0.892393	−	0.451258i	$-0.850975\pi$
$67$		−	7.38741i		−	0.902516i	0.892393	−	0.451258i	$-0.149025\pi$
$68$		−	5.83991i		−	0.708193i
$69$	4.83991			0.582656
$70$	0.547507	−	0.160092i	0.0654396	−	0.0191346i
$71$	−5.64252			−0.669644			−0.334822	−	0.942281i	$-0.608676\pi$
$71$	−5.64252			−0.669644			−0.334822	+	0.942281i	$0.608676\pi$
$72$		−	1.00000i		−	0.117851i
$73$			9.93492i			1.16279i	0.813620	+	0.581397i	$0.197494\pi$
$73$			9.93492i			1.16279i	−0.813620	+	0.581397i	$0.802506\pi$
$74$		0			0
$75$	−2.69371	−	4.21236i	−0.311043	−	0.486401i
$76$	6.09501			0.699146
$77$		−	0.519725i		−	0.0592281i
$78$		−	1.70760i		−	0.193347i
$79$	−15.1900			−1.70901			−0.854506	−	0.519442i	$-0.826140\pi$
$79$	−15.1900			−1.70901			−0.854506	+	0.519442i	$0.826140\pi$
$80$	−2.14620	+	0.627553i	−0.239953	+	0.0701625i
$81$	1.00000			0.111111
$82$		−	11.1696i		−	1.23348i
$83$			8.42471i			0.924732i	0.886689	+	0.462366i	$0.152999\pi$
$83$			8.42471i			0.924732i	−0.886689	+	0.462366i	$0.847001\pi$
$84$	0.255105			0.0278342
$85$	−3.66485	−	12.5336i	−0.397509	−	1.35946i
$86$	0.255105			0.0275087
$87$		−	2.58480i		−	0.277120i
$88$			2.03730i			0.217177i
$89$	−10.2551			−1.08704			−0.543519	−	0.839397i	$-0.682909\pi$
$89$	−10.2551			−1.08704			−0.543519	+	0.839397i	$0.682909\pi$
$90$	−0.627553	−	2.14620i	−0.0661498	−	0.226229i
$91$	0.435617			0.0456651
$92$		−	4.83991i		−	0.504595i
$93$		−	1.00000i		−	0.103695i
$94$	9.83991			1.01491
$95$	13.0811	−	3.82494i	1.34209	−	0.392431i
$96$	−1.00000			−0.102062
$97$			4.87720i			0.495205i	0.968862	+	0.247603i	$0.0796427\pi$
$97$			4.87720i			0.495205i	−0.968862	+	0.247603i	$0.920357\pi$
$98$		−	6.93492i		−	0.700533i
$99$	−2.03730			−0.204756
$100$	−4.21236	+	2.69371i	−0.421236	+	0.269371i
$101$	0.575289			0.0572434			0.0286217	−	0.999590i	$-0.490888\pi$
$101$	0.575289			0.0572434			0.0286217	+	0.999590i	$0.490888\pi$
$102$		−	5.83991i		−	0.578237i
$103$			5.48979i			0.540925i	0.962730	+	0.270463i	$0.0871766\pi$
$103$			5.48979i			0.540925i	−0.962730	+	0.270463i	$0.912823\pi$
$104$	−1.70760			−0.167444
$105$	0.547507	−	0.160092i	0.0534312	−	0.0156234i
$106$	1.16009			0.112678
$107$			13.3501i			1.29060i	0.763927	+	0.645302i	$0.223269\pi$
$107$			13.3501i			1.29060i	−0.763927	+	0.645302i	$0.776731\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−6.26462			−0.600042			−0.300021	−	0.953933i	$-0.596994\pi$
$109$	−6.26462			−0.600042			−0.300021	+	0.953933i	$0.596994\pi$
$110$	1.27851	+	4.37245i	0.121901	+	0.416897i
$111$		0			0
$112$		−	0.255105i		−	0.0241052i
$113$		−	0.255105i		−	0.0239983i	−0.999928	−	0.0119991i	$-0.996180\pi$
$113$		−	0.255105i		−	0.0239983i	0.999928	−	0.0119991i	$-0.00381953\pi$
$114$	6.09501			0.570850
$115$	−3.03730	−	10.3874i	−0.283229	−	0.968631i
$116$	−2.58480			−0.239993
$117$		−	1.70760i		−	0.157868i
$118$		−	5.09501i		−	0.469034i
$119$	1.48979			0.136569
$120$	−2.14620	+	0.627553i	−0.195920	+	0.0572874i
$121$	−6.84942			−0.622675
$122$		−	0.160092i		−	0.0144940i
$123$		−	11.1696i		−	1.00713i
$124$	−1.00000			−0.0898027
$125$	−7.35012	+	8.42471i	−0.657415	+	0.753529i
$126$	0.255105			0.0227266
$127$		−	7.41520i		−	0.657992i	−0.944331	−	0.328996i	$-0.893290\pi$
$127$		−	7.41520i		−	0.657992i	0.944331	−	0.328996i	$-0.106710\pi$
$128$			1.00000i			0.0883883i
$129$	0.255105			0.0224607
$130$	−3.66485	+	1.07161i	−0.321429	+	0.0939862i
$131$	17.2442			1.50663			0.753316	−	0.657658i	$-0.228453\pi$
$131$	17.2442			1.50663			0.753316	+	0.657658i	$0.228453\pi$
$132$			2.03730i			0.177324i
$133$			1.55487i			0.134824i
$134$	−7.38741			−0.638175
$135$	−0.627553	−	2.14620i	−0.0540111	−	0.184716i
$136$	−5.83991			−0.500768
$137$			16.1900i			1.38321i	0.722277	+	0.691604i	$0.243095\pi$
$137$			16.1900i			1.38321i	−0.722277	+	0.691604i	$0.756905\pi$
$138$		−	4.83991i		−	0.412000i
$139$	−15.0950			−1.28034			−0.640171	−	0.768232i	$-0.721137\pi$
$139$	−15.0950			−1.28034			−0.640171	+	0.768232i	$0.721137\pi$
$140$	−0.160092	−	0.547507i	−0.0135302	−	0.0462728i
$141$	9.83991			0.828670
$142$			5.64252i			0.473510i
$143$			3.47888i			0.290919i
$144$	−1.00000			−0.0833333
$145$	−5.54751	+	1.62210i	−0.460695	+	0.134708i
$146$	9.93492			0.822220
$147$		−	6.93492i		−	0.571983i
$148$		0			0
$149$	−13.4525			−1.10207			−0.551036	−	0.834482i	$-0.685767\pi$
$149$	−13.4525			−1.10207			−0.551036	+	0.834482i	$0.685767\pi$
$150$	−4.21236	+	2.69371i	−0.343937	+	0.219940i
$151$	0.934921			0.0760828			0.0380414	−	0.999276i	$-0.487888\pi$
$151$	0.934921			0.0760828			0.0380414	+	0.999276i	$0.487888\pi$
$152$		−	6.09501i		−	0.494371i
$153$		−	5.83991i		−	0.472129i
$154$	−0.519725			−0.0418806
$155$	−2.14620	+	0.627553i	−0.172387	+	0.0504062i
$156$	−1.70760			−0.136717
$157$			1.35012i			0.107751i	0.998548	+	0.0538756i	$0.0171574\pi$
$157$			1.35012i			0.107751i	−0.998548	+	0.0538756i	$0.982843\pi$
$158$			15.1900i			1.20845i
$159$	1.16009			0.0920013
$160$	0.627553	+	2.14620i	0.0496124	+	0.169672i
$161$	1.23468			0.0973068
$162$		−	1.00000i		−	0.0785674i
$163$		−	20.4824i		−	1.60431i	−0.597117	−	0.802154i	$-0.703687\pi$
$163$		−	20.4824i		−	1.60431i	0.597117	−	0.802154i	$-0.296313\pi$
$164$	−11.1696			−0.872200
$165$	1.27851	+	4.37245i	0.0995319	+	0.340395i
$166$	8.42471			0.653884
$167$		−	9.42471i		−	0.729306i	−0.931143	−	0.364653i	$-0.881188\pi$
$167$		−	9.42471i		−	0.729306i	0.931143	−	0.364653i	$-0.118812\pi$
$168$		−	0.255105i		−	0.0196818i
$169$	10.0841			0.775701
$170$	−12.5336	+	3.66485i	−0.961284	+	0.281081i
$171$	6.09501			0.466097
$172$		−	0.255105i		−	0.0194516i
$173$			12.4247i			0.944633i	0.881429	+	0.472317i	$0.156582\pi$
$173$			12.4247i			0.944633i	−0.881429	+	0.472317i	$0.843418\pi$
$174$	−2.58480			−0.195953
$175$	−0.687178	−	1.07459i	−0.0519458	−	0.0812316i
$176$	2.03730			0.153567
$177$		−	5.09501i		−	0.382965i
$178$			10.2551i			0.768653i
$179$	−10.6126			−0.793222			−0.396611	−	0.917987i	$-0.629814\pi$
$179$	−10.6126			−0.793222			−0.396611	+	0.917987i	$0.629814\pi$
$180$	−2.14620	+	0.627553i	−0.159968	+	0.0467750i
$181$	22.0841			1.64150			0.820749	−	0.571288i	$-0.193556\pi$
$181$	22.0841			1.64150			0.820749	+	0.571288i	$0.193556\pi$
$182$		−	0.435617i		−	0.0322901i
$183$		−	0.160092i		−	0.0118343i
$184$	−4.83991			−0.356803
$185$		0			0
$186$	−1.00000			−0.0733236
$187$			11.8976i			0.870040i
$188$		−	9.83991i		−	0.717649i
$189$	0.255105			0.0185562
$190$	−3.82494	−	13.0811i	−0.277490	−	0.949004i
$191$	−5.75441			−0.416374			−0.208187	−	0.978089i	$-0.566756\pi$
$191$	−5.75441			−0.416374			−0.208187	+	0.978089i	$0.566756\pi$
$192$			1.00000i			0.0721688i
$193$			13.8976i			1.00037i	0.865918	+	0.500186i	$0.166735\pi$
$193$			13.8976i			1.00037i	−0.865918	+	0.500186i	$0.833265\pi$
$194$	4.87720			0.350163
$195$	−3.66485	+	1.07161i	−0.262445	+	0.0767394i
$196$	−6.93492			−0.495352
$197$			14.1492i			1.00809i	0.863678	+	0.504044i	$0.168155\pi$
$197$			14.1492i			1.00809i	−0.863678	+	0.504044i	$0.831845\pi$
$198$			2.03730i			0.144784i
$199$	16.8698			1.19587			0.597936	−	0.801544i	$-0.295988\pi$
$199$	16.8698			1.19587			0.597936	+	0.801544i	$0.295988\pi$
$200$	2.69371	+	4.21236i	0.190474	+	0.297859i
$201$	−7.38741			−0.521068
$202$		−	0.575289i		−	0.0404772i
$203$		−	0.659396i		−	0.0462805i
$204$	−5.83991			−0.408875
$205$	−23.9722	+	7.00951i	−1.67429	+	0.489566i
$206$	5.48979			0.382492
$207$		−	4.83991i		−	0.336397i
$208$			1.70760i			0.118401i
$209$	−12.4173			−0.858926
$210$	−0.160092	−	0.547507i	−0.0110474	−	0.0377815i
$211$	−9.23468			−0.635742			−0.317871	−	0.948134i	$-0.602968\pi$
$211$	−9.23468			−0.635742			−0.317871	+	0.948134i	$0.602968\pi$
$212$		−	1.16009i		−	0.0796754i
$213$			5.64252i			0.386619i
$214$	13.3501			0.912595
$215$	−0.160092	−	0.547507i	−0.0109182	−	0.0373396i
$216$	−1.00000			−0.0680414
$217$		−	0.255105i		−	0.0173177i
$218$			6.26462i			0.424294i
$219$	9.93492			0.671340
$220$	4.37245	−	1.27851i	0.294790	−	0.0861972i
$221$	−9.97222			−0.670804
$222$		0			0
$223$			16.9518i			1.13518i	0.823313	+	0.567588i	$0.192123\pi$
$223$			16.9518i			1.13518i	−0.823313	+	0.567588i	$0.807877\pi$
$224$	−0.255105			−0.0170449
$225$	−4.21236	+	2.69371i	−0.280824	+	0.179580i
$226$	−0.255105			−0.0169693
$227$		−	9.16009i		−	0.607977i	−0.952676	−	0.303988i	$-0.901682\pi$
$227$		−	9.16009i		−	0.607977i	0.952676	−	0.303988i	$-0.0983184\pi$
$228$		−	6.09501i		−	0.403652i
$229$	4.60522			0.304322			0.152161	−	0.988356i	$-0.451377\pi$
$229$	4.60522			0.304322			0.152161	+	0.988356i	$0.451377\pi$
$230$	−10.3874	+	3.03730i	−0.684926	+	0.200273i
$231$	−0.519725			−0.0341954
$232$			2.58480i			0.169701i
$233$		−	12.4451i		−	0.815308i	−0.913137	−	0.407654i	$-0.866347\pi$
$233$		−	12.4451i		−	0.815308i	0.913137	−	0.407654i	$-0.133653\pi$
$234$	−1.70760			−0.111629
$235$	−6.17506	−	21.1184i	−0.402816	−	1.37761i
$236$	−5.09501			−0.331657
$237$			15.1900i			0.986698i
$238$		−	1.48979i		−	0.0965687i
$239$	−20.7748			−1.34381			−0.671906	−	0.740636i	$-0.734524\pi$
$239$	−20.7748			−1.34381			−0.671906	+	0.740636i	$0.734524\pi$
$240$	0.627553	+	2.14620i	0.0405083	+	0.138537i
$241$	4.58480			0.295333			0.147667	−	0.989037i	$-0.452824\pi$
$241$	4.58480			0.295333			0.147667	+	0.989037i	$0.452824\pi$
$242$			6.84942i			0.440298i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.160092			−0.0102488
$245$	−14.8837	+	4.35203i	−0.950887	+	0.278041i
$246$	−11.1696			−0.712148
$247$		−	10.4078i		−	0.662235i
$248$			1.00000i			0.0635001i
$249$	8.42471			0.533894
$250$	8.42471	+	7.35012i	0.532826	+	0.464862i
$251$	13.6052			0.858754			0.429377	−	0.903125i	$-0.358733\pi$
$251$	13.6052			0.858754			0.429377	+	0.903125i	$0.358733\pi$
$252$		−	0.255105i		−	0.0160701i
$253$			9.86033i			0.619914i
$254$	−7.41520			−0.465271
$255$	−12.5336	+	3.66485i	−0.784885	+	0.229502i
$256$	1.00000			0.0625000
$257$		−	6.25511i		−	0.390183i	−0.980785	−	0.195091i	$-0.937500\pi$
$257$		−	6.25511i		−	0.390183i	0.980785	−	0.195091i	$-0.0625003\pi$
$258$		−	0.255105i		−	0.0158821i
$259$		0			0
$260$	1.07161	+	3.66485i	0.0664583	+	0.227284i
$261$	−2.58480			−0.159995
$262$		−	17.2442i		−	1.06535i
$263$		−	24.5292i		−	1.51254i	−0.654261	−	0.756269i	$-0.727020\pi$
$263$		−	24.5292i		−	1.51254i	0.654261	−	0.756269i	$-0.272980\pi$
$264$	2.03730			0.125387
$265$	−0.728019	−	2.48979i	−0.0447218	−	0.152947i
$266$	1.55487			0.0953351
$267$			10.2551i			0.627602i
$268$			7.38741i			0.451258i
$269$	−15.1696			−0.924907			−0.462454	−	0.886643i	$-0.653031\pi$
$269$	−15.1696			−0.924907			−0.462454	+	0.886643i	$0.653031\pi$
$270$	−2.14620	+	0.627553i	−0.130614	+	0.0381916i
$271$	5.51021			0.334721			0.167361	−	0.985896i	$-0.446476\pi$
$271$	5.51021			0.334721			0.167361	+	0.985896i	$0.446476\pi$
$272$			5.83991i			0.354096i
$273$		−	0.435617i		−	0.0263647i
$274$	16.1900			0.978075
$275$	8.58182	−	5.48788i	0.517503	−	0.330932i
$276$	−4.83991			−0.291328
$277$		−	27.3319i		−	1.64221i	−0.570776	−	0.821106i	$-0.693357\pi$
$277$		−	27.3319i		−	1.64221i	0.570776	−	0.821106i	$-0.306643\pi$
$278$			15.0950i			0.905339i
$279$	−1.00000			−0.0598684
$280$	−0.547507	+	0.160092i	−0.0327198	+	0.00956732i
$281$	21.8698			1.30465			0.652323	−	0.757941i	$-0.273795\pi$
$281$	21.8698			1.30465			0.652323	+	0.757941i	$0.273795\pi$
$282$		−	9.83991i		−	0.585958i
$283$		−	26.1622i		−	1.55518i	−0.628769	−	0.777592i	$-0.716441\pi$
$283$		−	26.1622i		−	1.55518i	0.628769	−	0.777592i	$-0.283559\pi$
$284$	5.64252			0.334822
$285$	−3.82494	−	13.0811i	−0.226570	−	0.774859i
$286$	3.47888			0.205711
$287$		−	2.84942i		−	0.168196i
$288$			1.00000i			0.0589256i
$289$	−17.1045			−1.00615
$290$	1.62210	+	5.54751i	0.0952530	+	0.325761i
$291$	4.87720			0.285907
$292$		−	9.93492i		−	0.581397i
$293$			13.3596i			0.780478i	0.920714	+	0.390239i	$0.127608\pi$
$293$			13.3596i			0.780478i	−0.920714	+	0.390239i	$0.872392\pi$
$294$	−6.93492			−0.404453
$295$	−10.9349	+	3.19739i	−0.636656	+	0.186159i
$296$		0			0
$297$			2.03730i			0.118216i
$298$			13.4525i			0.779282i
$299$	−8.26462			−0.477955
$300$	2.69371	+	4.21236i	0.155521	+	0.243200i
$301$	0.0650786			0.00375107
$302$		−	0.934921i		−	0.0537987i
$303$		−	0.575289i		−	0.0330495i
$304$	−6.09501			−0.349573
$305$	−0.343589	+	0.100466i	−0.0196739	+	0.00575267i
$306$	−5.83991			−0.333845
$307$		−	18.7748i		−	1.07154i	−0.844365	−	0.535768i	$-0.820022\pi$
$307$		−	18.7748i		−	1.07154i	0.844365	−	0.535768i	$-0.179978\pi$
$308$			0.519725i			0.0296141i
$309$	5.48979			0.312303
$310$	0.627553	+	2.14620i	0.0356426	+	0.121896i
$311$	−14.2924			−0.810448			−0.405224	−	0.914217i	$-0.632806\pi$
$311$	−14.2924			−0.810448			−0.405224	+	0.914217i	$0.632806\pi$
$312$			1.70760i			0.0966737i
$313$			19.1696i			1.08353i	0.840530	+	0.541765i	$0.182244\pi$
$313$			19.1696i			1.08353i	−0.840530	+	0.541765i	$0.817756\pi$
$314$	1.35012			0.0761916
$315$	−0.160092	−	0.547507i	−0.00902015	−	0.0308485i
$316$	15.1900			0.854506
$317$			24.4247i			1.37183i	0.727682	+	0.685914i	$0.240597\pi$
$317$			24.4247i			1.37183i	−0.727682	+	0.685914i	$0.759403\pi$
$318$		−	1.16009i		−	0.0650547i
$319$	5.26601			0.294840
$320$	2.14620	−	0.627553i	0.119976	−	0.0350813i
$321$	13.3501			0.745131
$322$		−	1.23468i		−	0.0688063i
$323$		−	35.5943i		−	1.98052i
$324$	−1.00000			−0.0555556
$325$	4.59977	+	7.19301i	0.255149	+	0.398997i
$326$	−20.4824			−1.13442
$327$			6.26462i			0.346434i
$328$			11.1696i			0.616738i
$329$	2.51021			0.138392
$330$	4.37245	−	1.27851i	0.240695	−	0.0703797i
$331$	−7.24420			−0.398177			−0.199089	−	0.979981i	$-0.563798\pi$
$331$	−7.24420			−0.398177			−0.199089	+	0.979981i	$0.563798\pi$
$332$		−	8.42471i		−	0.462366i
$333$		0			0
$334$	−9.42471			−0.515697
$335$	4.63599	+	15.8549i	0.253291	+	0.866244i
$336$	−0.255105			−0.0139171
$337$		−	16.5102i		−	0.899368i	−0.893188	−	0.449684i	$-0.851537\pi$
$337$		−	16.5102i		−	0.899368i	0.893188	−	0.449684i	$-0.148463\pi$
$338$		−	10.0841i		−	0.548503i
$339$	−0.255105			−0.0138554
$340$	3.66485	+	12.5336i	0.198754	+	0.679731i
$341$	2.03730			0.110326
$342$		−	6.09501i		−	0.329581i
$343$		−	3.55487i		−	0.191945i
$344$	−0.255105			−0.0137543
$345$	−10.3874	+	3.03730i	−0.559240	+	0.163523i
$346$	12.4247			0.667957
$347$			4.27553i			0.229522i	0.993393	+	0.114761i	$0.0366103\pi$
$347$			4.27553i			0.229522i	−0.993393	+	0.114761i	$0.963390\pi$
$348$			2.58480i			0.138560i
$349$	−20.1492			−1.07856			−0.539281	−	0.842126i	$-0.681304\pi$
$349$	−20.1492			−1.07856			−0.539281	+	0.842126i	$0.681304\pi$
$350$	−1.07459	+	0.687178i	−0.0574394	+	0.0367312i
$351$	−1.70760			−0.0911449
$352$		−	2.03730i		−	0.108588i
$353$		−	35.1587i		−	1.87131i	−0.352918	−	0.935654i	$-0.614810\pi$
$353$		−	35.1587i		−	1.87131i	0.352918	−	0.935654i	$-0.385190\pi$
$354$	−5.09501			−0.270797
$355$	12.1100	−	3.54098i	0.642731	−	0.187936i
$356$	10.2551			0.543519
$357$		−	1.48979i		−	0.0788480i
$358$			10.6126i			0.560893i
$359$	0.622100			0.0328332			0.0164166	−	0.999865i	$-0.494774\pi$
$359$	0.622100			0.0328332			0.0164166	+	0.999865i	$0.494774\pi$
$360$	0.627553	+	2.14620i	0.0330749	+	0.113115i
$361$	18.1492			0.955220
$362$		−	22.0841i		−	1.16071i
$363$			6.84942i			0.359501i
$364$	−0.435617			−0.0228325
$365$	−6.23468	−	21.3223i	−0.326338	−	1.11606i
$366$	−0.160092			−0.00836813
$367$			28.0877i			1.46616i	0.680141	+	0.733082i	$0.261919\pi$
$367$			28.0877i			1.46616i	−0.680141	+	0.733082i	$0.738081\pi$
$368$			4.83991i			0.252298i
$369$	−11.1696			−0.581466
$370$		0			0
$371$	0.295945			0.0153647
$372$			1.00000i			0.0518476i
$373$			17.7449i			0.918796i	0.888231	+	0.459398i	$0.151935\pi$
$373$			17.7449i			0.918796i	−0.888231	+	0.459398i	$0.848065\pi$
$374$	11.8976			0.615212
$375$	8.42471	+	7.35012i	0.435050	+	0.379558i
$376$	−9.83991			−0.507455
$377$			4.41381i			0.227323i
$378$		−	0.255105i		−	0.0131212i
$379$	25.7748			1.32396			0.661982	−	0.749520i	$-0.269716\pi$
$379$	25.7748			1.32396			0.661982	+	0.749520i	$0.269716\pi$
$380$	−13.0811	+	3.82494i	−0.671047	+	0.196215i
$381$	−7.41520			−0.379892
$382$			5.75441i			0.294421i
$383$			19.7952i			1.01149i	0.862683	+	0.505745i	$0.168782\pi$
$383$			19.7952i			1.01149i	−0.862683	+	0.505745i	$0.831218\pi$
$384$	1.00000			0.0510310
$385$	0.326154	+	1.11543i	0.0166224	+	0.0568477i
$386$	13.8976			0.707370
$387$		−	0.255105i		−	0.0129677i
$388$		−	4.87720i		−	0.247603i
$389$	23.9444			1.21403			0.607016	−	0.794690i	$-0.292367\pi$
$389$	23.9444			1.21403			0.607016	+	0.794690i	$0.292367\pi$
$390$	1.07161	+	3.66485i	0.0542630	+	0.185577i
$391$	−28.2646			−1.42940
$392$			6.93492i			0.350266i
$393$		−	17.2442i		−	0.869855i
$394$	14.1492			0.712826
$395$	32.6008	−	9.53254i	1.64033	−	0.479634i
$396$	2.03730			0.102378
$397$		−	10.3297i		−	0.518433i	−0.965819	−	0.259216i	$-0.916536\pi$
$397$		−	10.3297i		−	0.518433i	0.965819	−	0.259216i	$-0.0834643\pi$
$398$		−	16.8698i		−	0.845609i
$399$	1.55487			0.0778408
$400$	4.21236	−	2.69371i	0.210618	−	0.134685i
$401$	0.398320			0.0198912			0.00994559	−	0.999951i	$-0.496834\pi$
$401$	0.398320			0.0198912			0.00994559	+	0.999951i	$0.496834\pi$
$402$			7.38741i			0.368451i
$403$			1.70760i			0.0850615i
$404$	−0.575289			−0.0286217
$405$	−2.14620	+	0.627553i	−0.106646	+	0.0311833i
$406$	−0.659396			−0.0327253
$407$		0			0
$408$			5.83991i			0.289119i
$409$	−2.77483			−0.137206			−0.0686032	−	0.997644i	$-0.521854\pi$
$409$	−2.77483			−0.137206			−0.0686032	+	0.997644i	$0.521854\pi$
$410$	7.00951	+	23.9722i	0.346175	+	1.18390i
$411$	16.1900			0.798595
$412$		−	5.48979i		−	0.270463i
$413$		−	1.29976i		−	0.0639572i
$414$	−4.83991			−0.237869
$415$	−5.28695	−	18.0811i	−0.259526	−	0.887567i
$416$	1.70760			0.0837219
$417$			15.0950i			0.739206i
$418$			12.4173i			0.607352i
$419$	35.1140			1.71543			0.857717	−	0.514123i	$-0.171882\pi$
$419$	35.1140			1.71543			0.857717	+	0.514123i	$0.171882\pi$
$420$	−0.547507	+	0.160092i	−0.0267156	+	0.00781168i
$421$	12.3392			0.601376			0.300688	−	0.953722i	$-0.402784\pi$
$421$	12.3392			0.601376			0.300688	+	0.953722i	$0.402784\pi$
$422$			9.23468i			0.449537i
$423$		−	9.83991i		−	0.478433i
$424$	−1.16009			−0.0563390
$425$	15.7310	+	24.5998i	0.763066	+	1.19326i
$426$	5.64252			0.273381
$427$		−	0.0408402i		−	0.00197640i
$428$		−	13.3501i		−	0.645302i
$429$	3.47888			0.167962
$430$	−0.547507	+	0.160092i	−0.0264031	+	0.00772031i
$431$	11.9444			0.575343			0.287672	−	0.957729i	$-0.407119\pi$
$431$	11.9444			0.575343			0.287672	+	0.957729i	$0.407119\pi$
$432$			1.00000i			0.0481125i
$433$			10.7653i			0.517348i	0.965965	+	0.258674i	$0.0832855\pi$
$433$			10.7653i			0.517348i	−0.965965	+	0.258674i	$0.916714\pi$
$434$	−0.255105			−0.0122454
$435$	1.62210	+	5.54751i	0.0777737	+	0.265983i
$436$	6.26462			0.300021
$437$		−	29.4993i		−	1.41114i
$438$		−	9.93492i		−	0.474709i
$439$	23.2442			1.10939			0.554693	−	0.832055i	$-0.312836\pi$
$439$	23.2442			1.10939			0.554693	+	0.832055i	$0.312836\pi$
$440$	−1.27851	−	4.37245i	−0.0609506	−	0.208448i
$441$	−6.93492			−0.330234
$442$			9.97222i			0.474330i
$443$		−	34.4451i		−	1.63654i	−0.574836	−	0.818269i	$-0.694934\pi$
$443$		−	34.4451i		−	1.63654i	0.574836	−	0.818269i	$-0.305066\pi$
$444$		0			0
$445$	22.0095	−	6.43562i	1.04335	−	0.305078i
$446$	16.9518			0.802691
$447$			13.4525i			0.636281i
$448$			0.255105i			0.0120526i
$449$	−24.5570			−1.15892			−0.579459	−	0.815002i	$-0.696736\pi$
$449$	−24.5570			−1.15892			−0.579459	+	0.815002i	$0.696736\pi$
$450$	2.69371	+	4.21236i	0.126983	+	0.198572i
$451$	22.7558			1.07153
$452$			0.255105i			0.0119991i
$453$		−	0.934921i		−	0.0439264i
$454$	−9.16009			−0.429904
$455$	−0.934921	+	0.273373i	−0.0438298	+	0.0128159i
$456$	−6.09501			−0.285425
$457$			30.1154i			1.40874i	0.709833	+	0.704370i	$0.248771\pi$
$457$			30.1154i			1.40874i	−0.709833	+	0.704370i	$0.751229\pi$
$458$		−	4.60522i		−	0.215188i
$459$	−5.83991			−0.272584
$460$	3.03730	+	10.3874i	0.141615	+	0.484316i
$461$	−22.7748			−1.06073			−0.530365	−	0.847770i	$-0.677945\pi$
$461$	−22.7748			−1.06073			−0.530365	+	0.847770i	$0.677945\pi$
$462$			0.519725i			0.0241798i
$463$		−	29.0264i		−	1.34897i	−0.738288	−	0.674485i	$-0.764366\pi$
$463$		−	29.0264i		−	1.34897i	0.738288	−	0.674485i	$-0.235634\pi$
$464$	2.58480			0.119996
$465$	0.627553	+	2.14620i	0.0291021	+	0.0995277i
$466$	−12.4451			−0.576510
$467$		−	17.3188i		−	0.801418i	−0.916205	−	0.400709i	$-0.868764\pi$
$467$		−	17.3188i		−	0.801418i	0.916205	−	0.400709i	$-0.131236\pi$
$468$			1.70760i			0.0789338i
$469$	−1.88457			−0.0870212
$470$	−21.1184	+	6.17506i	−0.974120	+	0.284834i
$471$	1.35012			0.0622102
$472$			5.09501i			0.234517i
$473$			0.519725i			0.0238970i
$474$	15.1900			0.697701
$475$	−25.6744	+	16.4182i	−1.17802	+	0.753318i
$476$	−1.48979			−0.0682844
$477$		−	1.16009i		−	0.0531170i
$478$			20.7748i			0.950219i
$479$	36.6221			1.67331			0.836653	−	0.547733i	$-0.184509\pi$
$479$	36.6221			1.67331			0.836653	+	0.547733i	$0.184509\pi$
$480$	2.14620	−	0.627553i	0.0979602	−	0.0286437i
$481$		0			0
$482$		−	4.58480i		−	0.208832i
$483$		−	1.23468i		−	0.0561801i
$484$	6.84942			0.311337
$485$	−3.06070	−	10.4675i	−0.138979	−	0.475303i
$486$	−1.00000			−0.0453609
$487$			34.9371i			1.58315i	0.611072	+	0.791575i	$0.290739\pi$
$487$			34.9371i			1.58315i	−0.611072	+	0.791575i	$0.709261\pi$
$488$			0.160092i			0.00724702i
$489$	−20.4824			−0.926247
$490$	4.35203	+	14.8837i	0.196605	+	0.672379i
$491$	24.0095			1.08353			0.541767	−	0.840529i	$-0.317755\pi$
$491$	24.0095			1.08353			0.541767	+	0.840529i	$0.317755\pi$
$492$			11.1696i			0.503565i
$493$			15.0950i			0.679845i
$494$	−10.4078			−0.468271
$495$	4.37245	−	1.27851i	0.196527	−	0.0574648i
$496$	1.00000			0.0449013
$497$			1.43944i			0.0645675i
$498$		−	8.42471i		−	0.377520i
$499$	−4.65940			−0.208583			−0.104292	−	0.994547i	$-0.533258\pi$
$499$	−4.65940			−0.208583			−0.104292	+	0.994547i	$0.533258\pi$
$500$	7.35012	−	8.42471i	0.328707	−	0.376765i
$501$	−9.42471			−0.421065
$502$		−	13.6052i		−	0.607231i
$503$		−	4.30928i		−	0.192141i	−0.995375	−	0.0960706i	$-0.969373\pi$
$503$		−	4.30928i		−	0.192141i	0.995375	−	0.0960706i	$-0.0306275\pi$
$504$	−0.255105			−0.0113633
$505$	−1.23468	+	0.361024i	−0.0549428	+	0.0160653i
$506$	9.86033			0.438345
$507$		−	10.0841i		−	0.447851i
$508$			7.41520i			0.328996i
$509$	33.1696			1.47022			0.735108	−	0.677950i	$-0.237131\pi$
$509$	33.1696			1.47022			0.735108	+	0.677950i	$0.237131\pi$
$510$	3.66485	+	12.5336i	0.162282	+	0.554998i
$511$	2.53445			0.112117
$512$		−	1.00000i		−	0.0441942i
$513$		−	6.09501i		−	0.269101i
$514$	−6.25511			−0.275901
$515$	−3.44513	−	11.7822i	−0.151811	−	0.519185i
$516$	−0.255105			−0.0112304
$517$			20.0468i			0.881658i
$518$		0			0
$519$	12.4247			0.545384
$520$	3.66485	−	1.07161i	0.160714	−	0.0469931i
$521$	−20.4138			−0.894345			−0.447173	−	0.894448i	$-0.647569\pi$
$521$	−20.4138			−0.894345			−0.447173	+	0.894448i	$0.647569\pi$
$522$			2.58480i			0.113134i
$523$		−	18.0841i		−	0.790763i	−0.918517	−	0.395381i	$-0.870612\pi$
$523$		−	18.0841i		−	0.790763i	0.918517	−	0.395381i	$-0.129388\pi$
$524$	−17.2442			−0.753316
$525$	−1.07459	+	0.687178i	−0.0468991	+	0.0299909i
$526$	−24.5292			−1.06953
$527$			5.83991i			0.254390i
$528$		−	2.03730i		−	0.0886620i
$529$	−0.424711			−0.0184657
$530$	−2.48979	+	0.728019i	−0.108150	+	0.0316231i
$531$	−5.09501			−0.221105
$532$		−	1.55487i		−	0.0674121i
$533$			19.0732i			0.826152i
$534$	10.2551			0.443782
$535$	−8.37790	−	28.6520i	−0.362208	−	1.23874i
$536$	7.38741			0.319088
$537$			10.6126i			0.457967i
$538$			15.1696i			0.654008i
$539$	14.1285			0.608557
$540$	0.627553	+	2.14620i	0.0270056	+	0.0923578i
$541$	10.4546			0.449480			0.224740	−	0.974419i	$-0.427847\pi$
$541$	10.4546			0.449480			0.224740	+	0.974419i	$0.427847\pi$
$542$		−	5.51021i		−	0.236684i
$543$		−	22.0841i		−	0.947720i
$544$	5.83991			0.250384
$545$	13.4451	−	3.93138i	0.575926	−	0.168402i
$546$	−0.435617			−0.0186427
$547$		−	11.9444i		−	0.510707i	−0.966848	−	0.255354i	$-0.917808\pi$
$547$		−	11.9444i		−	0.510707i	0.966848	−	0.255354i	$-0.0821919\pi$
$548$		−	16.1900i		−	0.691604i
$549$	−0.160092			−0.00683255
$550$	−5.48788	−	8.58182i	−0.234004	−	0.365930i
$551$	−15.7544			−0.671160
$552$			4.83991i			0.206000i
$553$			3.87505i			0.164784i
$554$	−27.3319			−1.16122
$555$		0			0
$556$	15.0950			0.640171
$557$		−	20.0841i		−	0.850991i	−0.904961	−	0.425495i	$-0.860100\pi$
$557$		−	20.0841i		−	0.850991i	0.904961	−	0.425495i	$-0.139900\pi$
$558$			1.00000i			0.0423334i
$559$	−0.435617			−0.0184246
$560$	0.160092	+	0.547507i	0.00676511	+	0.0231364i
$561$	11.8976			0.502318
$562$		−	21.8698i		−	0.922524i
$563$		−	28.9050i		−	1.21820i	−0.793093	−	0.609100i	$-0.791531\pi$
$563$		−	28.9050i		−	1.21820i	0.793093	−	0.609100i	$-0.208469\pi$
$564$	−9.83991			−0.414335
$565$	0.160092	+	0.547507i	0.00673511	+	0.0230338i
$566$	−26.1622			−1.09968
$567$		−	0.255105i		−	0.0107134i
$568$		−	5.64252i		−	0.236755i
$569$	0.724475			0.0303716			0.0151858	−	0.999885i	$-0.495166\pi$
$569$	0.724475			0.0303716			0.0151858	+	0.999885i	$0.495166\pi$
$570$	−13.0811	+	3.82494i	−0.547908	+	0.160209i
$571$	12.6594			0.529779			0.264890	−	0.964279i	$-0.414664\pi$
$571$	12.6594			0.529779			0.264890	+	0.964279i	$0.414664\pi$
$572$		−	3.47888i		−	0.145459i
$573$			5.75441i			0.240394i
$574$	−2.84942			−0.118933
$575$	13.0373	+	20.3874i	0.543693	+	0.850214i
$576$	1.00000			0.0416667
$577$		−	31.0117i		−	1.29103i	−0.763746	−	0.645516i	$-0.776642\pi$
$577$		−	31.0117i		−	1.29103i	0.763746	−	0.645516i	$-0.223358\pi$
$578$			17.1045i			0.711455i
$579$	13.8976			0.577566
$580$	5.54751	−	1.62210i	0.230348	−	0.0673540i
$581$	2.14919			0.0891633
$582$		−	4.87720i		−	0.202167i
$583$			2.36345i			0.0978841i
$584$	−9.93492			−0.411110
$585$	1.07161	+	3.66485i	0.0443055	+	0.151523i
$586$	13.3596			0.551881
$587$			13.2959i			0.548782i	0.961618	+	0.274391i	$0.0884763\pi$
$587$			13.2959i			0.548782i	−0.961618	+	0.274391i	$0.911524\pi$
$588$			6.93492i			0.285991i
$589$	−6.09501			−0.251141
$590$	3.19739	+	10.9349i	0.131634	+	0.450184i
$591$	14.1492			0.582020
$592$		0			0
$593$			3.05417i			0.125420i	0.998032	+	0.0627099i	$0.0199743\pi$
$593$			3.05417i			0.125420i	−0.998032	+	0.0627099i	$0.980026\pi$
$594$	2.03730			0.0835913
$595$	−3.19739	+	0.934921i	−0.131080	+	0.0383280i
$596$	13.4525			0.551036
$597$		−	16.8698i		−	0.690437i
$598$			8.26462i			0.337965i
$599$	0.983124			0.0401693			0.0200847	−	0.999798i	$-0.493606\pi$
$599$	0.983124			0.0401693			0.0200847	+	0.999798i	$0.493606\pi$
$600$	4.21236	−	2.69371i	0.171969	−	0.109970i
$601$	43.8290			1.78782			0.893911	−	0.448244i	$-0.147950\pi$
$601$	43.8290			1.78782			0.893911	+	0.448244i	$0.147950\pi$
$602$		−	0.0650786i		−	0.00265240i
$603$			7.38741i			0.300839i
$604$	−0.934921			−0.0380414
$605$	14.7002	−	4.29837i	0.597650	−	0.174754i
$606$	−0.575289			−0.0233695
$607$			4.91450i			0.199473i	0.995014	+	0.0997367i	$0.0318001\pi$
$607$			4.91450i			0.199473i	−0.995014	+	0.0997367i	$0.968200\pi$
$608$			6.09501i			0.247185i
$609$	−0.659396			−0.0267201
$610$	0.100466	+	0.343589i	0.00406775	+	0.0139115i
$611$	−16.8026			−0.679761
$612$			5.83991i			0.236064i
$613$			28.6316i			1.15642i	0.815888	+	0.578210i	$0.196249\pi$
$613$			28.6316i			1.15642i	−0.815888	+	0.578210i	$0.803751\pi$
$614$	−18.7748			−0.757690
$615$	7.00951	+	23.9722i	0.282651	+	0.966653i
$616$	0.519725			0.0209403
$617$			22.5943i			0.909613i	0.890590	+	0.454806i	$0.150292\pi$
$617$			22.5943i			0.909613i	−0.890590	+	0.454806i	$0.849708\pi$
$618$		−	5.48979i		−	0.220832i
$619$	−21.0204			−0.844882			−0.422441	−	0.906390i	$-0.638827\pi$
$619$	−21.0204			−0.844882			−0.422441	+	0.906390i	$0.638827\pi$
$620$	2.14620	−	0.627553i	0.0861935	−	0.0252031i
$621$	−4.83991			−0.194219
$622$			14.2924i			0.573073i
$623$			2.61613i			0.104813i
$624$	1.70760			0.0683586
$625$	10.4879	−	22.6937i	0.419515	−	0.907748i
$626$	19.1696			0.766172
$627$			12.4173i			0.495901i
$628$		−	1.35012i		−	0.0538756i
$629$		0			0
$630$	−0.547507	+	0.160092i	−0.0218132	+	0.00637821i
$631$	−46.6352			−1.85652			−0.928258	−	0.371937i	$-0.878694\pi$
$631$	−46.6352			−1.85652			−0.928258	+	0.371937i	$0.878694\pi$
$632$		−	15.1900i		−	0.604227i
$633$			9.23468i			0.367046i
$634$	24.4247			0.970029
$635$	4.65343	+	15.9145i	0.184666	+	0.631548i
$636$	−1.16009			−0.0460006
$637$			11.8421i			0.469200i
$638$		−	5.26601i		−	0.208483i
$639$	5.64252			0.223215
$640$	−0.627553	−	2.14620i	−0.0248062	−	0.0848360i
$641$	36.5015			1.44172			0.720860	−	0.693080i	$-0.243747\pi$
$641$	36.5015			1.44172			0.720860	+	0.693080i	$0.243747\pi$
$642$		−	13.3501i		−	0.526887i
$643$		−	4.45986i		−	0.175880i	−0.996126	−	0.0879398i	$-0.971972\pi$
$643$		−	4.45986i		−	0.175880i	0.996126	−	0.0879398i	$-0.0280283\pi$
$644$	−1.23468			−0.0486534
$645$	−0.547507	+	0.160092i	−0.0215581	+	0.00630361i
$646$	−35.5943			−1.40044
$647$			10.4451i			0.410640i	0.978695	+	0.205320i	$0.0658236\pi$
$647$			10.4451i			0.410640i	−0.978695	+	0.205320i	$0.934176\pi$
$648$			1.00000i			0.0392837i
$649$	10.3801			0.407453
$650$	7.19301	−	4.59977i	0.282133	−	0.180418i
$651$	−0.255105			−0.00999835
$652$			20.4824i			0.802154i
$653$		−	26.4437i		−	1.03482i	−0.855737	−	0.517412i	$-0.826896\pi$
$653$		−	26.4437i		−	1.03482i	0.855737	−	0.517412i	$-0.173104\pi$
$654$	6.26462			0.244966
$655$	−37.0095	+	10.8216i	−1.44608	+	0.422836i
$656$	11.1696			0.436100
$657$		−	9.93492i		−	0.387598i
$658$		−	2.51021i		−	0.0978582i
$659$	17.2104			0.670424			0.335212	−	0.942143i	$-0.391192\pi$
$659$	17.2104			0.670424			0.335212	+	0.942143i	$0.391192\pi$
$660$	−1.27851	−	4.37245i	−0.0497660	−	0.170197i
$661$	−28.1154			−1.09356			−0.546782	−	0.837275i	$-0.684147\pi$
$661$	−28.1154			−1.09356			−0.546782	+	0.837275i	$0.684147\pi$
$662$			7.24420i			0.281554i
$663$			9.97222i			0.387289i
$664$	−8.42471			−0.326942
$665$	−0.975762	−	3.33706i	−0.0378384	−	0.129406i
$666$		0			0
$667$			12.5102i			0.484397i
$668$			9.42471i			0.364653i
$669$	16.9518			0.655394
$670$	15.8549	−	4.63599i	0.612527	−	0.179104i
$671$	0.326154			0.0125911
$672$			0.255105i			0.00984089i
$673$			9.56438i			0.368680i	0.982863	+	0.184340i	$0.0590147\pi$
$673$			9.56438i			0.368680i	−0.982863	+	0.184340i	$0.940985\pi$
$674$	−16.5102			−0.635950
$675$	2.69371	+	4.21236i	0.103681	+	0.162134i
$676$	−10.0841			−0.387850
$677$		−	16.0841i		−	0.618162i	−0.951036	−	0.309081i	$-0.899978\pi$
$677$		−	16.0841i		−	0.618162i	0.951036	−	0.309081i	$-0.100022\pi$
$678$			0.255105i			0.00979725i
$679$	1.24420			0.0477480
$680$	12.5336	−	3.66485i	0.480642	−	0.140541i
$681$	−9.16009			−0.351015
$682$		−	2.03730i		−	0.0780121i
$683$		−	31.4247i		−	1.20243i	−0.799086	−	0.601217i	$-0.794683\pi$
$683$		−	31.4247i		−	1.20243i	0.799086	−	0.601217i	$-0.205317\pi$
$684$	−6.09501			−0.233049
$685$	−10.1601	−	34.7470i	−0.388197	−	1.32762i
$686$	−3.55487			−0.135726
$687$		−	4.60522i		−	0.175700i
$688$			0.255105i			0.00972579i
$689$	−1.98097			−0.0754690
$690$	3.03730	+	10.3874i	0.115628	+	0.395442i
$691$	−15.4546			−0.587922			−0.293961	−	0.955817i	$-0.594974\pi$
$691$	−15.4546			−0.587922			−0.293961	+	0.955817i	$0.594974\pi$
$692$		−	12.4247i		−	0.472317i
$693$			0.519725i			0.0197427i
$694$	4.27553			0.162297
$695$	32.3969	−	9.47291i	1.22889	−	0.359328i
$696$	2.58480			0.0979767
$697$			65.2295i			2.47074i
$698$			20.1492i			0.762658i
$699$	−12.4451			−0.470718
$700$	0.687178	+	1.07459i	0.0259729	+	0.0406158i
$701$	−39.2069			−1.48082			−0.740412	−	0.672153i	$-0.765370\pi$
$701$	−39.2069			−1.48082			−0.740412	+	0.672153i	$0.765370\pi$
$702$			1.70760i			0.0644491i
$703$		0			0
$704$	−2.03730			−0.0767835
$705$	−21.1184	+	6.17506i	−0.795366	+	0.232566i
$706$	−35.1587			−1.32322
$707$		−	0.146759i		−	0.00551944i
$708$			5.09501i			0.191482i
$709$	−14.0950			−0.529349			−0.264675	−	0.964338i	$-0.585265\pi$
$709$	−14.0950			−0.529349			−0.264675	+	0.964338i	$0.585265\pi$
$710$	−3.54098	−	12.1100i	−0.132891	−	0.454479i
$711$	15.1900			0.569670
$712$		−	10.2551i		−	0.384326i
$713$			4.83991i			0.181256i
$714$	−1.48979			−0.0557540
$715$	−2.18318	−	7.46638i	−0.0816464	−	0.279227i
$716$	10.6126			0.396611
$717$			20.7748i			0.775850i
$718$		−	0.622100i		−	0.0232166i
$719$	−19.6052			−0.731151			−0.365576	−	0.930782i	$-0.619128\pi$
$719$	−19.6052			−0.731151			−0.365576	+	0.930782i	$0.619128\pi$
$720$	2.14620	−	0.627553i	0.0799842	−	0.0233875i
$721$	1.40047			0.0521563
$722$		−	18.1492i		−	0.675443i
$723$		−	4.58480i		−	0.170511i
$724$	−22.0841			−0.820749
$725$	10.8881	−	6.96270i	0.404374	−	0.258588i
$726$	6.84942			0.254206
$727$			2.89547i			0.107387i	0.998557	+	0.0536936i	$0.0170994\pi$
$727$			2.89547i			0.107387i	−0.998557	+	0.0536936i	$0.982901\pi$
$728$			0.435617i			0.0161450i
$729$	−1.00000			−0.0370370
$730$	−21.3223	+	6.23468i	−0.789175	+	0.230756i
$731$	−1.48979			−0.0551019
$732$			0.160092i			0.00591716i
$733$		−	10.2646i		−	0.379132i	−0.981868	−	0.189566i	$-0.939292\pi$
$733$		−	10.2646i		−	0.379132i	0.981868	−	0.189566i	$-0.0607082\pi$
$734$	28.0877			1.03673
$735$	4.35203	+	14.8837i	0.160527	+	0.548995i
$736$	4.83991			0.178401
$737$		−	15.0504i		−	0.554387i
$738$			11.1696i			0.411159i
$739$	−13.9444			−0.512954			−0.256477	−	0.966550i	$-0.582562\pi$
$739$	−13.9444			−0.512954			−0.256477	+	0.966550i	$0.582562\pi$
$740$		0			0
$741$	−10.4078			−0.382341
$742$		−	0.295945i		−	0.0108645i
$743$		−	27.1454i		−	0.995867i	−0.867215	−	0.497933i	$-0.834092\pi$
$743$		−	27.1454i		−	0.995867i	0.867215	−	0.497933i	$-0.165908\pi$
$744$	1.00000			0.0366618
$745$	28.8718	−	8.44215i	1.05778	−	0.309296i
$746$	17.7449			0.649687
$747$		−	8.42471i		−	0.308244i
$748$		−	11.8976i		−	0.435020i
$749$	3.40568			0.124441
$750$	7.35012	−	8.42471i	0.268388	−	0.307627i
$751$	7.16961			0.261623			0.130811	−	0.991407i	$-0.458242\pi$
$751$	7.16961			0.261623			0.130811	+	0.991407i	$0.458242\pi$
$752$			9.83991i			0.358825i
$753$		−	13.6052i		−	0.495802i
$754$	4.41381			0.160741
$755$	−2.00653	+	0.586712i	−0.0730251	+	0.0213526i
$756$	−0.255105			−0.00927808
$757$			39.2104i			1.42513i	0.701607	+	0.712564i	$0.252466\pi$
$757$			39.2104i			1.42513i	−0.701607	+	0.712564i	$0.747534\pi$
$758$		−	25.7748i		−	0.936184i
$759$	9.86033			0.357907
$760$	3.82494	+	13.0811i	0.138745	+	0.474502i
$761$	−38.7566			−1.40492			−0.702462	−	0.711721i	$-0.747916\pi$
$761$	−38.7566			−1.40492			−0.702462	+	0.711721i	$0.747916\pi$
$762$			7.41520i			0.268624i
$763$			1.59814i			0.0578564i
$764$	5.75441			0.208187
$765$	3.66485	+	12.5336i	0.132503	+	0.453154i
$766$	19.7952			0.715231
$767$			8.70024i			0.314147i
$768$		−	1.00000i		−	0.0360844i
$769$	−15.7449			−0.567775			−0.283888	−	0.958858i	$-0.591624\pi$
$769$	−15.7449			−0.567775			−0.283888	+	0.958858i	$0.591624\pi$
$770$	1.11543	−	0.326154i	0.0401974	−	0.0117538i
$771$	−6.25511			−0.225272
$772$		−	13.8976i		−	0.500186i
$773$		−	21.9758i		−	0.790413i	−0.918592	−	0.395207i	$-0.870673\pi$
$773$		−	21.9758i		−	0.790413i	0.918592	−	0.395207i	$-0.129327\pi$
$774$	−0.255105			−0.00916956
$775$	4.21236	−	2.69371i	0.151312	−	0.0967608i
$776$	−4.87720			−0.175081
$777$		0			0
$778$		−	23.9444i		−	0.858450i
$779$	−68.0789			−2.43918
$780$	3.66485	−	1.07161i	0.131223	−	0.0383697i
$781$	−11.4955			−0.411341
$782$			28.2646i			1.01074i
$783$			2.58480i			0.0923733i
$784$	6.93492			0.247676
$785$	−0.847270	−	2.89762i	−0.0302404	−	0.103421i
$786$	−17.2442			−0.615080
$787$		−	6.00951i		−	0.214216i	−0.994247	−	0.107108i	$-0.965841\pi$
$787$		−	6.00951i		−	0.214216i	0.994247	−	0.107108i	$-0.0341591\pi$
$788$		−	14.1492i		−	0.504044i
$789$	−24.5292			−0.873264
$790$	−9.53254	−	32.6008i	−0.339153	−	1.15989i
$791$	−0.0650786			−0.00231393
$792$		−	2.03730i		−	0.0723922i
$793$			0.273373i			0.00970774i
$794$	−10.3297			−0.366587
$795$	−2.48979	+	0.728019i	−0.0883037	+	0.0258202i
$796$	−16.8698			−0.597936
$797$			6.58480i			0.233246i	0.993176	+	0.116623i	$0.0372069\pi$
$797$			6.58480i			0.233246i	−0.993176	+	0.116623i	$0.962793\pi$
$798$		−	1.55487i		−	0.0550417i
$799$	−57.4642			−2.03294
$800$	−2.69371	−	4.21236i	−0.0952369	−	0.148929i
$801$	10.2551			0.362346
$802$		−	0.398320i		−	0.0140652i
$803$			20.2404i			0.714268i
$804$	7.38741			0.260534
$805$	−2.64988	+	0.774830i	−0.0933961	+	0.0273092i
$806$	1.70760			0.0601476
$807$			15.1696i			0.533995i
$808$			0.575289i			0.0202386i
$809$	42.2273			1.48463			0.742317	−	0.670049i	$-0.233727\pi$
$809$	42.2273			1.48463			0.742317	+	0.670049i	$0.233727\pi$
$810$	0.627553	+	2.14620i	0.0220499	+	0.0754098i
$811$	3.29455			0.115687			0.0578437	−	0.998326i	$-0.481577\pi$
$811$	3.29455			0.115687			0.0578437	+	0.998326i	$0.481577\pi$
$812$			0.659396i			0.0231403i
$813$		−	5.51021i		−	0.193252i
$814$		0			0
$815$	12.8538	+	43.9594i	0.450249	+	1.53983i
$816$	5.83991			0.204438
$817$		−	1.55487i		−	0.0543980i
$818$			2.77483i			0.0970196i
$819$	−0.435617			−0.0152217
$820$	23.9722	−	7.00951i	0.837146	−	0.244783i
$821$	6.52924			0.227872			0.113936	−	0.993488i	$-0.463654\pi$
$821$	6.52924			0.227872			0.113936	+	0.993488i	$0.463654\pi$
$822$		−	16.1900i		−	0.564692i
$823$			44.6725i			1.55718i	0.627531	+	0.778592i	$0.284066\pi$
$823$			44.6725i			1.55718i	−0.627531	+	0.778592i	$0.715934\pi$
$824$	−5.48979			−0.191246
$825$	−5.48788	−	8.58182i	−0.191063	−	0.298781i
$826$	−1.29976			−0.0452246
$827$			23.2551i			0.808659i	0.914613	+	0.404330i	$0.132495\pi$
$827$			23.2551i			0.808659i	−0.914613	+	0.404330i	$0.867505\pi$
$828$			4.83991i			0.168198i
$829$	44.6352			1.55024			0.775122	−	0.631812i	$-0.217689\pi$
$829$	44.6352			1.55024			0.775122	+	0.631812i	$0.217689\pi$
$830$	−18.0811	+	5.28695i	−0.627605	+	0.183513i
$831$	−27.3319			−0.948131
$832$		−	1.70760i		−	0.0592003i
$833$			40.4993i			1.40322i
$834$	15.0950			0.522698
$835$	5.91450	+	20.2273i	0.204680	+	0.699995i
$836$	12.4173			0.429463
$837$			1.00000i			0.0345651i
$838$		−	35.1140i		−	1.21299i
$839$	−40.1587			−1.38643			−0.693216	−	0.720730i	$-0.743807\pi$
$839$	−40.1587			−1.38643			−0.693216	+	0.720730i	$0.743807\pi$
$840$	0.160092	+	0.547507i	0.00552369	+	0.0188908i
$841$	−22.3188			−0.769614
$842$		−	12.3392i		−	0.425237i
$843$		−	21.8698i		−	0.753237i
$844$	9.23468			0.317871
$845$	−21.6425	+	6.32831i	−0.744525	+	0.217700i
$846$	−9.83991			−0.338303
$847$			1.74732i			0.0600387i
$848$			1.16009i			0.0398377i
$849$	−26.1622			−0.897886
$850$	24.5998	−	15.7310i	0.843765	−	0.539569i
$851$		0			0
$852$		−	5.64252i		−	0.193310i
$853$			10.8589i			0.371803i	0.982568	+	0.185901i	$0.0595205\pi$
$853$			10.8589i			0.371803i	−0.982568	+	0.185901i	$0.940479\pi$
$854$	−0.0408402			−0.00139752
$855$	−13.0811	+	3.82494i	−0.447365	+	0.130810i
$856$	−13.3501			−0.456298
$857$			36.0190i			1.23039i	0.788376	+	0.615193i	$0.210922\pi$
$857$			36.0190i			1.23039i	−0.788376	+	0.615193i	$0.789078\pi$
$858$		−	3.47888i		−	0.118767i
$859$	35.9782			1.22756			0.613780	−	0.789477i	$-0.289648\pi$
$859$	35.9782			1.22756			0.613780	+	0.789477i	$0.289648\pi$
$860$	0.160092	+	0.547507i	0.00545909	+	0.0186698i
$861$	−2.84942			−0.0971081
$862$		−	11.9444i		−	0.406829i
$863$			48.5388i			1.65228i	0.563466	+	0.826139i	$0.309468\pi$
$863$			48.5388i			1.65228i	−0.563466	+	0.826139i	$0.690532\pi$
$864$	1.00000			0.0340207
$865$	−7.79716	−	26.6659i	−0.265111	−	0.906669i
$866$	10.7653			0.365820
$867$			17.1045i			0.580900i
$868$			0.255105i			0.00865883i
$869$	−30.9466			−1.04979
$870$	5.54751	−	1.62210i	0.188078	−	0.0549943i
$871$	12.6147			0.427434
$872$		−	6.26462i		−	0.212147i
$873$		−	4.87720i		−	0.165068i
$874$	−29.4993			−0.997829
$875$	2.14919	+	1.87505i	0.0726558	+	0.0633883i
$876$	−9.93492			−0.335670
$877$		−	56.7748i		−	1.91715i	−0.284841	−	0.958575i	$-0.591941\pi$
$877$		−	56.7748i		−	1.91715i	0.284841	−	0.958575i	$-0.408059\pi$
$878$		−	23.2442i		−	0.784454i
$879$	13.3596			0.450609
$880$	−4.37245	+	1.27851i	−0.147395	+	0.0430986i
$881$	−1.34657			−0.0453673			−0.0226836	−	0.999743i	$-0.507221\pi$
$881$	−1.34657			−0.0453673			−0.0226836	+	0.999743i	$0.507221\pi$
$882$			6.93492i			0.233511i
$883$		−	36.3705i		−	1.22397i	−0.790871	−	0.611983i	$-0.790372\pi$
$883$		−	36.3705i		−	1.22397i	0.790871	−	0.611983i	$-0.209628\pi$
$884$	9.97222			0.335402
$885$	3.19739	+	10.9349i	0.107479	+	0.367573i
$886$	−34.4451			−1.15721
$887$			4.38005i			0.147068i	0.997293	+	0.0735339i	$0.0234277\pi$
$887$			4.38005i			0.147068i	−0.997293	+	0.0735339i	$0.976572\pi$
$888$		0			0
$889$	−1.89165			−0.0634440
$890$	−6.43562	−	22.0095i	−0.215722	−	0.737761i
$891$	2.03730			0.0682520
$892$		−	16.9518i		−	0.567588i
$893$		−	59.9744i		−	2.00697i
$894$	13.4525			0.449919
$895$	22.7767	−	6.65995i	0.761342	−	0.222618i
$896$	0.255105			0.00852246
$897$			8.26462i			0.275948i
$898$			24.5570i			0.819478i
$899$	2.58480			0.0862080
$900$	4.21236	−	2.69371i	0.140412	−	0.0897902i
$901$	−6.77483			−0.225702
$902$		−	22.7558i		−	0.757685i
$903$		−	0.0650786i		−	0.00216568i
$904$	0.255105			0.00848467
$905$	−47.3969	+	13.8589i	−1.57553	+	0.460687i
$906$	−0.934921			−0.0310607
$907$			6.29240i			0.208936i	0.994528	+	0.104468i	$0.0333139\pi$
$907$			6.29240i			0.208936i	−0.994528	+	0.104468i	$0.966686\pi$
$908$			9.16009i			0.303988i
$909$	−0.575289			−0.0190811
$910$	0.273373	+	0.934921i	0.00906221	+	0.0309923i
$911$	−32.1682			−1.06578			−0.532890	−	0.846184i	$-0.678894\pi$
$911$	−32.1682			−1.06578			−0.532890	+	0.846184i	$0.678894\pi$
$912$			6.09501i			0.201826i
$913$			17.1636i			0.568033i
$914$	30.1154			0.996130
$915$	0.100466	+	0.343589i	0.00332130	+	0.0113587i
$916$	−4.60522			−0.152161
$917$		−	4.39908i		−	0.145270i
$918$			5.83991i			0.192746i
$919$	32.1154			1.05939			0.529695	−	0.848188i	$-0.322306\pi$
$919$	32.1154			1.05939			0.529695	+	0.848188i	$0.322306\pi$
$920$	10.3874	−	3.03730i	0.342463	−	0.100137i
$921$	−18.7748			−0.618652
$922$			22.7748i			0.750049i
$923$		−	9.63516i		−	0.317145i
$924$	0.519725			0.0170977
$925$		0			0
$926$	−29.0264			−0.953866
$927$		−	5.48979i		−	0.180308i
$928$		−	2.58480i		−	0.0848503i
$929$	59.9540			1.96703			0.983513	−	0.180839i	$-0.0578814\pi$
$929$	59.9540			1.96703			0.983513	+	0.180839i	$0.0578814\pi$
$930$	2.14620	−	0.627553i	0.0703767	−	0.0205783i
$931$	−42.2684			−1.38529
$932$			12.4451i			0.407654i
$933$			14.2924i			0.467912i
$934$	−17.3188			−0.566688
$935$	−7.46638	−	25.5347i	−0.244177	−	0.835074i
$936$	1.70760			0.0558146
$937$		−	52.7661i		−	1.72379i	−0.507085	−	0.861896i	$-0.669277\pi$
$937$		−	52.7661i		−	1.72379i	0.507085	−	0.861896i	$-0.330723\pi$
$938$			1.88457i			0.0615333i
$939$	19.1696			0.625576
$940$	6.17506	+	21.1184i	0.201408	+	0.688807i
$941$	−54.3055			−1.77031			−0.885154	−	0.465299i	$-0.845947\pi$
$941$	−54.3055			−1.77031			−0.885154	+	0.465299i	$0.845947\pi$
$942$		−	1.35012i		−	0.0439892i
$943$			54.0599i			1.76043i
$944$	5.09501			0.165829
$945$	−0.547507	+	0.160092i	−0.0178104	+	0.00520779i
$946$	0.519725			0.0168977
$947$		−	49.2741i		−	1.60119i	−0.599203	−	0.800597i	$-0.704516\pi$
$947$		−	49.2741i		−	1.60119i	0.599203	−	0.800597i	$-0.295484\pi$
$948$		−	15.1900i		−	0.493349i
$949$	−16.9649			−0.550703
$950$	16.4182	+	25.6744i	0.532676	+	0.832986i
$951$	24.4247			0.792026
$952$			1.48979i			0.0482844i
$953$			20.9012i			0.677055i	0.940956	+	0.338528i	$0.109929\pi$
$953$			20.9012i			0.677055i	−0.940956	+	0.338528i	$0.890071\pi$
$954$	−1.16009			−0.0375594
$955$	12.3501	−	3.61119i	0.399640	−	0.116855i
$956$	20.7748			0.671906
$957$		−	5.26601i		−	0.170226i
$958$		−	36.6221i		−	1.18321i
$959$	4.13016			0.133370
$960$	−0.627553	−	2.14620i	−0.0202542	−	0.0692683i
$961$	1.00000			0.0322581
$962$		0			0
$963$		−	13.3501i		−	0.430202i
$964$	−4.58480			−0.147667
$965$	−8.72149	−	29.8271i	−0.280755	−	0.960168i
$966$	−1.23468			−0.0397253
$967$			7.19739i			0.231452i	0.993281	+	0.115726i	$0.0369195\pi$
$967$			7.19739i			0.231452i	−0.993281	+	0.115726i	$0.963080\pi$
$968$		−	6.84942i		−	0.220149i
$969$	−35.5943			−1.14345
$970$	−10.4675	+	3.06070i	−0.336090	+	0.0982732i
$971$	−42.7939			−1.37332			−0.686660	−	0.726979i	$-0.740924\pi$
$971$	−42.7939			−1.37332			−0.686660	+	0.726979i	$0.740924\pi$
$972$			1.00000i			0.0320750i
$973$			3.85081i			0.123451i
$974$	34.9371			1.11946
$975$	7.19301	−	4.59977i	0.230361	−	0.147311i
$976$	0.160092			0.00512441
$977$		−	18.1492i		−	0.580644i	−0.956929	−	0.290322i	$-0.906238\pi$
$977$		−	18.1492i		−	0.580644i	0.956929	−	0.290322i	$-0.0937624\pi$
$978$			20.4824i			0.654956i
$979$	−20.8927			−0.667733
$980$	14.8837	−	4.35203i	0.475443	−	0.139020i
$981$	6.26462			0.200014
$982$		−	24.0095i		−	0.766174i
$983$		−	6.30546i		−	0.201113i	−0.994931	−	0.100556i	$-0.967938\pi$
$983$		−	6.30546i		−	0.201113i	0.994931	−	0.100556i	$-0.0320623\pi$
$984$	11.1696			0.356074
$985$	−8.87936	−	30.3670i	−0.282920	−	0.967573i
$986$	15.0950			0.480723
$987$		−	2.51021i		−	0.0799009i
$988$			10.4078i			0.331117i
$989$	−1.23468			−0.0392607
$990$	−1.27851	−	4.37245i	−0.0406337	−	0.138966i
$991$	−27.5549			−0.875309			−0.437655	−	0.899143i	$-0.644191\pi$
$991$	−27.5549			−0.875309			−0.437655	+	0.899143i	$0.644191\pi$
$992$		−	1.00000i		−	0.0317500i
$993$			7.24420i			0.229888i
$994$	1.43944			0.0456561
$995$	−36.2061	+	10.5867i	−1.14781	+	0.335621i
$996$	−8.42471			−0.266947
$997$			0.945827i			0.0299546i	0.999888	+	0.0149773i	$0.00476761\pi$
$997$			0.945827i			0.0299546i	−0.999888	+	0.0149773i	$0.995232\pi$
$998$			4.65940i			0.147491i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.d.h.559.1	✓	6
3.2	odd	2		2790.2.d.k.559.6		6
5.2	odd	4		4650.2.a.cn.1.2		3
5.3	odd	4		4650.2.a.ck.1.2		3
5.4	even	2	inner	930.2.d.h.559.4	yes	6
15.14	odd	2		2790.2.d.k.559.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.h.559.1	✓	6	1.1	even	1	trivial
930.2.d.h.559.4	yes	6	5.4	even	2	inner
2790.2.d.k.559.3		6	15.14	odd	2
2790.2.d.k.559.6		6	3.2	odd	2
4650.2.a.ck.1.2		3	5.3	odd	4
4650.2.a.cn.1.2		3	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.14620 + 0.627553i) q^{5} -1.00000 q^{6} -0.255105i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(0.627553 + 2.14620i) q^{10} +2.03730 q^{11} +1.00000i q^{12} +1.70760i q^{13} -0.255105 q^{14} +(0.627553 + 2.14620i) q^{15} +1.00000 q^{16} +5.83991i q^{17} +1.00000i q^{18} -6.09501 q^{19} +(2.14620 - 0.627553i) q^{20} -0.255105 q^{21} -2.03730i q^{22} +4.83991i q^{23} +1.00000 q^{24} +(4.21236 - 2.69371i) q^{25} +1.70760 q^{26} +1.00000i q^{27} +0.255105i q^{28} +2.58480 q^{29} +(2.14620 - 0.627553i) q^{30} +1.00000 q^{31} -1.00000i q^{32} -2.03730i q^{33} +5.83991 q^{34} +(0.160092 + 0.547507i) q^{35} +1.00000 q^{36} +6.09501i q^{38} +1.70760 q^{39} +(-0.627553 - 2.14620i) q^{40} +11.1696 q^{41} +0.255105i q^{42} +0.255105i q^{43} -2.03730 q^{44} +(2.14620 - 0.627553i) q^{45} +4.83991 q^{46} +9.83991i q^{47} -1.00000i q^{48} +6.93492 q^{49} +(-2.69371 - 4.21236i) q^{50} +5.83991 q^{51} -1.70760i q^{52} +1.16009i q^{53} +1.00000 q^{54} +(-4.37245 + 1.27851i) q^{55} +0.255105 q^{56} +6.09501i q^{57} -2.58480i q^{58} +5.09501 q^{59} +(-0.627553 - 2.14620i) q^{60} +0.160092 q^{61} -1.00000i q^{62} +0.255105i q^{63} -1.00000 q^{64} +(-1.07161 - 3.66485i) q^{65} -2.03730 q^{66} -7.38741i q^{67} -5.83991i q^{68} +4.83991 q^{69} +(0.547507 - 0.160092i) q^{70} -5.64252 q^{71} -1.00000i q^{72} +9.93492i q^{73} +(-2.69371 - 4.21236i) q^{75} +6.09501 q^{76} -0.519725i q^{77} -1.70760i q^{78} -15.1900 q^{79} +(-2.14620 + 0.627553i) q^{80} +1.00000 q^{81} -11.1696i q^{82} +8.42471i q^{83} +0.255105 q^{84} +(-3.66485 - 12.5336i) q^{85} +0.255105 q^{86} -2.58480i q^{87} +2.03730i q^{88} -10.2551 q^{89} +(-0.627553 - 2.14620i) q^{90} +0.435617 q^{91} -4.83991i q^{92} -1.00000i q^{93} +9.83991 q^{94} +(13.0811 - 3.82494i) q^{95} -1.00000 q^{96} +4.87720i q^{97} -6.93492i q^{98} -2.03730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{14} + 2 q^{15} + 6 q^{16} - 2 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{24} - 4 q^{25} + 24 q^{26} - 12 q^{29} + 6 q^{30} + 6 q^{31} + 4 q^{34}+ \cdots - 2 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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