LMFDB - Embedded newform 380.2.i.c.201.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [380,2,Mod(121,380)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(380, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("380.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$380 = 2^{2} \cdot 5 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	380.i (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4$ x^8 - x^7 + 9x^6 + 2x^5 + 65x^4 - 20x^3 + 25x^2 + 6x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$3$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$1.58253 - 2.74101i$ of defining polynomial
Character	$\chi$	$=$	380.201
Dual form			380.2.i.c.121.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58253 + 2.74101i) q^{3} +(-0.500000 + 0.866025i) q^{5} -1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} -3.79695 q^{11} +(3.34910 + 5.80081i) q^{13} +(-1.58253 - 2.74101i) q^{15} +(3.00877 - 5.21135i) q^{17} +(-3.93502 - 1.87499i) q^{19} +(2.42625 - 4.20239i) q^{21} +(-2.19282 - 3.79808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +12.7158 q^{27} +(0.549376 + 0.951547i) q^{29} -1.05555 q^{31} +(6.00877 - 10.4075i) q^{33} +(0.766575 - 1.32775i) q^{35} -10.7970 q^{37} -21.2002 q^{39} +(-1.76658 + 3.05980i) q^{41} +(-2.77535 + 4.80705i) q^{43} +7.01755 q^{45} +(5.61907 + 9.73252i) q^{47} -4.64945 q^{49} +(9.52293 + 16.4942i) q^{51} +(-0.788178 - 1.36516i) q^{53} +(1.89848 - 3.28826i) q^{55} +(11.3667 - 7.81874i) q^{57} +(-1.61568 + 2.79843i) q^{59} +(-0.0331500 - 0.0574175i) q^{61} +(5.37948 + 9.31753i) q^{63} -6.69820 q^{65} +(2.85250 + 4.94067i) q^{67} +13.8808 q^{69} +(3.23880 - 5.60977i) q^{71} +(-6.98978 + 12.1066i) q^{73} +3.16505 q^{75} +5.82130 q^{77} +(0.996602 - 1.72617i) q^{79} +(-9.59668 + 16.6219i) q^{81} -10.3477 q^{83} +(3.00877 + 5.21135i) q^{85} -3.47760 q^{87} +(-1.53655 - 2.66138i) q^{89} +(-5.13467 - 8.89352i) q^{91} +(1.67043 - 2.89327i) q^{93} +(3.59130 - 2.47034i) q^{95} +(-4.43502 + 7.68169i) q^{97} +(13.3227 + 23.0755i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - q^{3} - 4 q^{5} - 5 q^{9} + 4 q^{11} + 9 q^{13} - q^{15} + q^{17} + 3 q^{19} + 8 q^{21} - 4 q^{25} + 20 q^{27} + 5 q^{29} - 20 q^{31} + 25 q^{33} - 52 q^{37} - 54 q^{39} - 8 q^{41} + 7 q^{43} + 10 q^{45}+ \cdots + 24 q^{99}+O(q^{100})$ 8 * q - q^3 - 4 * q^5 - 5 * q^9 + 4 * q^11 + 9 * q^13 - q^15 + q^17 + 3 * q^19 + 8 * q^21 - 4 * q^25 + 20 * q^27 + 5 * q^29 - 20 * q^31 + 25 * q^33 - 52 * q^37 - 54 * q^39 - 8 * q^41 + 7 * q^43 + 10 * q^45 + 16 * q^47 + 20 * q^49 + 12 * q^51 + 5 * q^53 - 2 * q^55 + 27 * q^57 + 11 * q^59 + 12 * q^61 - 3 * q^63 - 18 * q^65 + 6 * q^69 + 14 * q^71 - 4 * q^73 + 2 * q^75 - 44 * q^77 + 13 * q^79 - 24 * q^81 + 10 * q^83 + q^85 - 4 * q^87 + 5 * q^89 - 46 * q^91 - 28 * q^93 - 6 * q^95 - q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$ .

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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

)

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

$2$		0			0
$2$		0			0
$3$	−1.58253	+	2.74101i	−0.913672	+	1.58253i	−0.104837	+	0.994489i	$0.533432\pi$
$3$	−1.58253	+	2.74101i	−0.913672	+	1.58253i	−0.808835	+	0.588036i	$0.799901\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−1.53315			−0.579476			−0.289738	−	0.957106i	$-0.593568\pi$
$7$	−1.53315			−0.579476			−0.289738	+	0.957106i	$0.593568\pi$
$8$		0			0
$9$	−3.50877	−	6.07738i	−1.16959	−	2.02579i
$10$		0			0
$11$	−3.79695			−1.14482			−0.572412	−	0.819966i	$-0.693992\pi$
$11$	−3.79695			−1.14482			−0.572412	+	0.819966i	$0.693992\pi$
$12$		0			0
$13$	3.34910	+	5.80081i	0.928873	+	1.60886i	0.785210	+	0.619229i	$0.212555\pi$
$13$	3.34910	+	5.80081i	0.928873	+	1.60886i	0.143663	+	0.989627i	$0.454112\pi$
$14$		0			0
$15$	−1.58253	−	2.74101i	−0.408606	−	0.707727i
$16$		0			0
$17$	3.00877	−	5.21135i	0.729735	−	1.26394i	−0.227260	−	0.973834i	$-0.572977\pi$
$17$	3.00877	−	5.21135i	0.729735	−	1.26394i	0.956995	−	0.290104i	$-0.0936899\pi$
$18$		0			0
$19$	−3.93502	−	1.87499i	−0.902756	−	0.430152i
$19$	−3.93502	−	1.87499i	−0.902756	−	0.430152i
$20$		0			0
$21$	2.42625	−	4.20239i	0.529451	−	0.917036i
$22$		0			0
$23$	−2.19282	−	3.79808i	−0.457235	−	0.791955i	0.541578	−	0.840650i	$-0.317827\pi$
$23$	−2.19282	−	3.79808i	−0.457235	−	0.791955i	−0.998814	+	0.0486953i	$0.984494\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	12.7158			2.44715
$28$		0			0
$29$	0.549376	+	0.951547i	0.102016	+	0.176698i	0.912515	−	0.409042i	$-0.134137\pi$
$29$	0.549376	+	0.951547i	0.102016	+	0.176698i	−0.810499	+	0.585740i	$0.800804\pi$
$30$		0			0
$31$	−1.05555			−0.189582			−0.0947908	−	0.995497i	$-0.530218\pi$
$31$	−1.05555			−0.189582			−0.0947908	+	0.995497i	$0.530218\pi$
$32$		0			0
$33$	6.00877	−	10.4075i	1.04599	−	1.81171i
$34$		0			0
$35$	0.766575	−	1.32775i	0.129575	−	0.224430i
$36$		0			0
$37$	−10.7970			−1.77501			−0.887504	−	0.460800i	$-0.847563\pi$
$37$	−10.7970			−1.77501			−0.887504	+	0.460800i	$0.847563\pi$
$38$		0			0
$39$	−21.2002			−3.39474
$40$		0			0
$41$	−1.76658	+	3.05980i	−0.275893	+	0.477860i	−0.970360	−	0.241664i	$-0.922307\pi$
$41$	−1.76658	+	3.05980i	−0.275893	+	0.477860i	0.694467	+	0.719524i	$0.255640\pi$
$42$		0			0
$43$	−2.77535	+	4.80705i	−0.423237	+	0.733068i	−0.996254	−	0.0864756i	$-0.972440\pi$
$43$	−2.77535	+	4.80705i	−0.423237	+	0.733068i	0.573017	+	0.819543i	$0.305773\pi$
$44$		0			0
$45$	7.01755			1.04611
$46$		0			0
$47$	5.61907	+	9.73252i	0.819626	+	1.41963i	0.905958	+	0.423368i	$0.139152\pi$
$47$	5.61907	+	9.73252i	0.819626	+	1.41963i	−0.0863319	+	0.996266i	$0.527515\pi$
$48$		0			0
$49$	−4.64945			−0.664207
$50$		0			0
$51$	9.52293	+	16.4942i	1.33348	+	2.30965i
$52$		0			0
$53$	−0.788178	−	1.36516i	−0.108265	−	0.187520i	0.806803	−	0.590821i	$-0.201196\pi$
$53$	−0.788178	−	1.36516i	−0.108265	−	0.187520i	−0.915067	+	0.403301i	$0.867863\pi$
$54$		0			0
$55$	1.89848	−	3.28826i	0.255990	−	0.443389i
$56$		0			0
$57$	11.3667	−	7.81874i	1.50555	−	1.03562i
$58$		0			0
$59$	−1.61568	+	2.79843i	−0.210343	+	0.364325i	−0.951822	−	0.306651i	$-0.900791\pi$
$59$	−1.61568	+	2.79843i	−0.210343	+	0.364325i	0.741479	+	0.670976i	$0.234125\pi$
$60$		0			0
$61$	−0.0331500	−	0.0574175i	−0.00424442	−	0.00735156i	0.863895	−	0.503671i	$-0.168018\pi$
$61$	−0.0331500	−	0.0574175i	−0.00424442	−	0.00735156i	−0.868140	+	0.496320i	$0.834684\pi$
$62$		0			0
$63$	5.37948	+	9.31753i	0.677751	+	1.17390i
$64$		0			0
$65$	−6.69820			−0.830810
$66$		0			0
$67$	2.85250	+	4.94067i	0.348488	+	0.603599i	0.985981	−	0.166857i	$-0.0533618\pi$
$67$	2.85250	+	4.94067i	0.348488	+	0.603599i	−0.637493	+	0.770456i	$0.720028\pi$
$68$		0			0
$69$	13.8808			1.67105
$70$		0			0
$71$	3.23880	−	5.60977i	0.384375	−	0.665757i	−0.607307	−	0.794467i	$-0.707750\pi$
$71$	3.23880	−	5.60977i	0.384375	−	0.665757i	0.991682	+	0.128710i	$0.0410836\pi$
$72$		0			0
$73$	−6.98978	+	12.1066i	−0.818091	+	1.41698i	0.0889951	+	0.996032i	$0.471634\pi$
$73$	−6.98978	+	12.1066i	−0.818091	+	1.41698i	−0.907087	+	0.420944i	$0.861699\pi$
$74$		0			0
$75$	3.16505			0.365469
$76$		0			0
$77$	5.82130			0.663398
$78$		0			0
$79$	0.996602	−	1.72617i	0.112127	−	0.194209i	−0.804501	−	0.593951i	$-0.797567\pi$
$79$	0.996602	−	1.72617i	0.112127	−	0.194209i	0.916627	+	0.399743i	$0.130900\pi$
$80$		0			0
$81$	−9.59668	+	16.6219i	−1.06630	+	1.84688i
$82$		0			0
$83$	−10.3477			−1.13580			−0.567901	−	0.823097i	$-0.692244\pi$
$83$	−10.3477			−1.13580			−0.567901	+	0.823097i	$0.692244\pi$
$84$		0			0
$85$	3.00877	+	5.21135i	0.326347	+	0.565250i
$86$		0			0
$87$	−3.47760			−0.372838
$88$		0			0
$89$	−1.53655	−	2.66138i	−0.162874	−	0.282106i	0.773024	−	0.634376i	$-0.218743\pi$
$89$	−1.53655	−	2.66138i	−0.162874	−	0.282106i	−0.935898	+	0.352271i	$0.885410\pi$
$90$		0			0
$91$	−5.13467	−	8.89352i	−0.538260	−	0.932294i
$92$		0			0
$93$	1.67043	−	2.89327i	0.173215	−	0.300018i
$94$		0			0
$95$	3.59130	−	2.47034i	0.368460	−	0.253451i
$96$		0			0
$97$	−4.43502	+	7.68169i	−0.450308	+	0.779957i	−0.998405	−	0.0564579i	$-0.982019\pi$
$97$	−4.43502	+	7.68169i	−0.450308	+	0.779957i	0.548097	+	0.836415i	$0.315353\pi$
$98$		0			0
$99$	13.3227	+	23.0755i	1.33898	+	2.31918i
$100$		0			0
$101$	−3.10413	−	5.37651i	−0.308872	−	0.534983i	0.669244	−	0.743043i	$-0.266618\pi$
$101$	−3.10413	−	5.37651i	−0.308872	−	0.534983i	−0.978116	+	0.208060i	$0.933285\pi$
$102$		0			0
$103$	−0.253048			−0.0249336			−0.0124668	−	0.999922i	$-0.503968\pi$
$103$	−0.253048			−0.0249336			−0.0124668	+	0.999922i	$0.503968\pi$
$104$		0			0
$105$	2.42625	+	4.20239i	0.236778	+	0.410111i
$106$		0			0
$107$	−6.05555			−0.585412			−0.292706	−	0.956203i	$-0.594556\pi$
$107$	−6.05555			−0.585412			−0.292706	+	0.956203i	$0.594556\pi$
$108$		0			0
$109$	−2.62445	+	4.54568i	−0.251377	+	0.435397i	−0.963905	−	0.266246i	$-0.914217\pi$
$109$	−2.62445	+	4.54568i	−0.251377	+	0.435397i	0.712528	+	0.701643i	$0.247550\pi$
$110$		0			0
$111$	17.0865	−	29.5946i	1.62177	−	2.80900i
$112$		0			0
$113$	2.42885			0.228487			0.114244	−	0.993453i	$-0.463556\pi$
$113$	2.42885			0.228487			0.114244	+	0.993453i	$0.463556\pi$
$114$		0			0
$115$	4.38565			0.408964
$116$		0			0
$117$	23.5025	−	40.7075i	2.17281	−	3.76341i
$118$		0			0
$119$	−4.61290	+	7.98978i	−0.422864	+	0.732422i
$120$		0			0
$121$	3.41685			0.310623
$122$		0			0
$123$	−5.59130	−	9.68442i	−0.504151	−	0.873214i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	9.64945	+	16.7133i	0.856250	+	1.48307i	0.875480	+	0.483254i	$0.160545\pi$
$127$	9.64945	+	16.7133i	0.856250	+	1.48307i	−0.0192299	+	0.999815i	$0.506121\pi$
$128$		0			0
$129$	−8.78412	−	15.2146i	−0.773399	−	1.33957i
$130$		0			0
$131$	6.62983	−	11.4832i	0.579251	−	1.00329i	−0.416315	−	0.909221i	$-0.636679\pi$
$131$	6.62983	−	11.4832i	0.579251	−	1.00329i	0.995565	−	0.0940711i	$-0.0299881\pi$
$132$		0			0
$133$	6.03298	+	2.87464i	0.523126	+	0.249263i
$134$		0			0
$135$	−6.35788	+	11.0122i	−0.547199	+	0.947776i
$136$		0			0
$137$	7.77535	+	13.4673i	0.664293	+	1.15059i	0.979476	+	0.201558i	$0.0646006\pi$
$137$	7.77535	+	13.4673i	0.664293	+	1.15059i	−0.315184	+	0.949031i	$0.602066\pi$
$138$		0			0
$139$	9.31110	+	16.1273i	0.789758	+	1.36790i	0.926115	+	0.377241i	$0.123127\pi$
$139$	9.31110	+	16.1273i	0.789758	+	1.36790i	−0.136358	+	0.990660i	$0.543540\pi$
$140$		0			0
$141$	−35.5693			−2.99548
$142$		0			0
$143$	−12.7164	−	22.0254i	−1.06340	−	1.84186i
$144$		0			0
$145$	−1.09875			−0.0912463
$146$		0			0
$147$	7.35788	−	12.7442i	0.606867	−	1.05113i
$148$		0			0
$149$	2.34372	−	4.05945i	0.192005	−	0.332563i	−0.753909	−	0.656978i	$-0.771834\pi$
$149$	2.34372	−	4.05945i	0.192005	−	0.332563i	0.945915	+	0.324415i	$0.105168\pi$
$150$		0			0
$151$	−5.93370			−0.482878			−0.241439	−	0.970416i	$-0.577619\pi$
$151$	−5.93370			−0.482878			−0.241439	+	0.970416i	$0.577619\pi$
$152$		0			0
$153$	−42.2285			−3.41397
$154$		0			0
$155$	0.527773	−	0.914130i	0.0423917	−	0.0734247i
$156$		0			0
$157$	4.64685	−	8.04857i	0.370859	−	0.642346i	−0.618839	−	0.785518i	$-0.712397\pi$
$157$	4.64685	−	8.04857i	0.370859	−	0.642346i	0.989698	+	0.143172i	$0.0457301\pi$
$158$		0			0
$159$	4.98925			0.395673
$160$		0			0
$161$	3.36193	+	5.82303i	0.264957	+	0.458919i
$162$		0			0
$163$	5.88495			0.460945			0.230472	−	0.973079i	$-0.425973\pi$
$163$	5.88495			0.460945			0.230472	+	0.973079i	$0.425973\pi$
$164$		0			0
$165$	6.00877	+	10.4075i	0.467782	+	0.810223i
$166$		0			0
$167$	−6.39848	−	11.0825i	−0.495129	−	0.857589i	0.504855	−	0.863204i	$-0.331546\pi$
$167$	−6.39848	−	11.0825i	−0.495129	−	0.857589i	−0.999984	+	0.00561549i	$0.998213\pi$
$168$		0			0
$169$	−15.9330	+	27.5967i	−1.22561	+	2.12282i
$170$		0			0
$171$	2.41210	+	30.4935i	0.184458	+	2.33190i
$172$		0			0
$173$	7.52032	−	13.0256i	0.571760	−	0.990317i	−0.424626	−	0.905369i	$-0.639594\pi$
$173$	7.52032	−	13.0256i	0.571760	−	0.990317i	0.996385	−	0.0849476i	$-0.0270723\pi$
$174$		0			0
$175$	0.766575	+	1.32775i	0.0579476	+	0.100368i
$176$		0			0
$177$	−5.11370	−	8.85718i	−0.384369	−	0.665747i
$178$		0			0
$179$	21.5452			1.61036			0.805180	−	0.593030i	$-0.202069\pi$
$179$	21.5452			1.61036			0.805180	+	0.593030i	$0.202069\pi$
$180$		0			0
$181$	−2.13530	−	3.69845i	−0.158716	−	0.274903i	0.775690	−	0.631114i	$-0.217402\pi$
$181$	−2.13530	−	3.69845i	−0.158716	−	0.274903i	−0.934406	+	0.356210i	$0.884069\pi$
$182$		0			0
$183$	0.209843			0.0155120
$184$		0			0
$185$	5.39848	−	9.35044i	0.396904	−	0.687458i
$186$		0			0
$187$	−11.4242	+	19.7873i	−0.835418	+	1.44699i
$188$		0			0
$189$	−19.4952			−1.41806
$190$		0			0
$191$	−6.30180			−0.455982			−0.227991	−	0.973663i	$-0.573216\pi$
$191$	−6.30180			−0.455982			−0.227991	+	0.973663i	$0.573216\pi$
$192$		0			0
$193$	7.68943	−	13.3185i	0.553497	−	0.958685i	−0.444522	−	0.895768i	$-0.646626\pi$
$193$	7.68943	−	13.3185i	0.553497	−	0.958685i	0.998019	−	0.0629169i	$-0.0200403\pi$
$194$		0			0
$195$	10.6001	−	18.3599i	0.759087	−	1.31478i
$196$		0			0
$197$	−12.7210			−0.906331			−0.453165	−	0.891426i	$-0.649705\pi$
$197$	−12.7210			−0.906331			−0.453165	+	0.891426i	$0.649705\pi$
$198$		0			0
$199$	−5.10885	−	8.84879i	−0.362157	−	0.627274i	0.626159	−	0.779696i	$-0.284626\pi$
$199$	−5.10885	−	8.84879i	−0.362157	−	0.627274i	−0.988316	+	0.152422i	$0.951293\pi$
$200$		0			0
$201$	−18.0566			−1.27361
$202$		0			0
$203$	−0.842275	−	1.45886i	−0.0591161	−	0.102392i
$204$		0			0
$205$	−1.76658	−	3.05980i	−0.123383	−	0.213706i
$206$		0			0
$207$	−15.3883	+	26.6532i	−1.06956	+	1.85253i
$208$		0			0
$209$	14.9411	+	7.11925i	1.03350	+	0.492449i
$210$		0			0
$211$	−2.53655	+	4.39343i	−0.174623	+	0.302456i	−0.940031	−	0.341090i	$-0.889204\pi$
$211$	−2.53655	+	4.39343i	−0.174623	+	0.302456i	0.765408	+	0.643546i	$0.222537\pi$
$212$		0			0
$213$	10.2510	+	17.7552i	0.702385	+	1.21657i
$214$		0			0
$215$	−2.77535	−	4.80705i	−0.189277	−	0.327838i
$216$		0			0
$217$	1.61831			0.109858
$218$		0			0
$219$	−22.1230	−	38.3182i	−1.49493	−	2.58930i
$220$		0			0
$221$	40.3068			2.71133
$222$		0			0
$223$	4.26318	−	7.38404i	0.285483	−	0.494472i	−0.687243	−	0.726428i	$-0.741179\pi$
$223$	4.26318	−	7.38404i	0.285483	−	0.494472i	0.972726	+	0.231956i	$0.0745125\pi$
$224$		0			0
$225$	−3.50877	+	6.07738i	−0.233918	+	0.405158i
$226$		0			0
$227$	−20.0566			−1.33120			−0.665602	−	0.746307i	$-0.731825\pi$
$227$	−20.0566			−1.33120			−0.665602	+	0.746307i	$0.731825\pi$
$228$		0			0
$229$	7.92955			0.524000			0.262000	−	0.965068i	$-0.415618\pi$
$229$	7.92955			0.524000			0.262000	+	0.965068i	$0.415618\pi$
$230$		0			0
$231$	−9.21235	+	15.9563i	−0.606128	+	1.04985i
$232$		0			0
$233$	−5.28950	+	9.16169i	−0.346527	+	0.600202i	−0.985630	−	0.168919i	$-0.945972\pi$
$233$	−5.28950	+	9.16169i	−0.346527	+	0.600202i	0.639103	+	0.769121i	$0.279306\pi$
$234$		0			0
$235$	−11.2381			−0.733096
$236$		0			0
$237$	3.15430	+	5.46340i	0.204894	+	0.354886i
$238$		0			0
$239$	−5.68065			−0.367451			−0.183725	−	0.982978i	$-0.558816\pi$
$239$	−5.68065			−0.367451			−0.183725	+	0.982978i	$0.558816\pi$
$240$		0			0
$241$	−4.75714	−	8.23962i	−0.306435	−	0.530760i	0.671145	−	0.741326i	$-0.265803\pi$
$241$	−4.75714	−	8.23962i	−0.306435	−	0.530760i	−0.977580	+	0.210566i	$0.932469\pi$
$242$		0			0
$243$	−11.3004	−	19.5728i	−0.724918	−	1.25559i
$244$		0			0
$245$	2.32473	−	4.02654i	0.148521	−	0.257246i
$246$		0			0
$247$	−2.30233	−	29.1059i	−0.146494	−	1.85196i
$248$		0			0
$249$	16.3754	−	28.3631i	1.03775	−	1.79744i
$250$		0			0
$251$	−6.26658	−	10.8540i	−0.395543	−	0.685100i	0.597628	−	0.801774i	$-0.296110\pi$
$251$	−6.26658	−	10.8540i	−0.395543	−	0.685100i	−0.993170	+	0.116674i	$0.962777\pi$
$252$		0			0
$253$	8.32605	+	14.4211i	0.523454	+	0.906649i
$254$		0			0
$255$	−19.0459			−1.19270
$256$		0			0
$257$	8.54453	+	14.7996i	0.532993	+	0.923171i	0.999258	+	0.0385258i	$0.0122662\pi$
$257$	8.54453	+	14.7996i	0.532993	+	0.923171i	−0.466264	+	0.884645i	$0.654400\pi$
$258$		0			0
$259$	16.5533			1.02857
$260$		0			0
$261$	3.85527	−	6.67753i	0.238635	−	0.413328i
$262$		0			0
$263$	−0.460054	+	0.796838i	−0.0283682	+	0.0491351i	−0.879861	−	0.475231i	$-0.842364\pi$
$263$	−0.460054	+	0.796838i	−0.0283682	+	0.0491351i	0.851493	+	0.524366i	$0.175698\pi$
$264$		0			0
$265$	1.57636			0.0968347
$266$		0			0
$267$	9.72651			0.595252
$268$		0			0
$269$	−12.6826	+	21.9669i	−0.773272	+	1.33935i	0.162489	+	0.986710i	$0.448048\pi$
$269$	−12.6826	+	21.9669i	−0.773272	+	1.33935i	−0.935761	+	0.352636i	$0.885285\pi$
$270$		0			0
$271$	5.61828	−	9.73115i	0.341286	−	0.591125i	−0.643386	−	0.765542i	$-0.722471\pi$
$271$	5.61828	−	9.73115i	0.341286	−	0.591125i	0.984672	+	0.174417i	$0.0558041\pi$
$272$		0			0
$273$	32.5030			1.96717
$274$		0			0
$275$	1.89848	+	3.28826i	0.114482	+	0.198289i
$276$		0			0
$277$	16.5491			0.994340			0.497170	−	0.867653i	$-0.334373\pi$
$277$	16.5491			0.994340			0.497170	+	0.867653i	$0.334373\pi$
$278$		0			0
$279$	3.70367	+	6.41495i	0.221733	+	0.384053i
$280$		0			0
$281$	5.28950	+	9.16169i	0.315545	+	0.546540i	0.979553	−	0.201185i	$-0.0644793\pi$
$281$	5.28950	+	9.16169i	0.315545	+	0.546540i	−0.664008	+	0.747725i	$0.731146\pi$
$282$		0			0
$283$	−10.3707	+	17.9626i	−0.616474	+	1.06776i	0.373650	+	0.927570i	$0.378106\pi$
$283$	−10.3707	+	17.9626i	−0.616474	+	1.06776i	−0.990124	+	0.140195i	$0.955227\pi$
$284$		0			0
$285$	1.08790	+	13.7532i	0.0644418	+	0.814668i
$286$		0			0
$287$	2.70842	−	4.69113i	0.159873	−	0.276909i
$288$		0			0
$289$	−9.60545	−	16.6371i	−0.565027	−	0.978655i
$290$		0			0
$291$	−14.0371	−	24.3129i	−0.822868	−	1.42525i
$292$		0			0
$293$	13.6846			0.799460			0.399730	−	0.916633i	$-0.369104\pi$
$293$	13.6846			0.799460			0.399730	+	0.916633i	$0.369104\pi$
$294$		0			0
$295$	−1.61568	−	2.79843i	−0.0940683	−	0.162931i
$296$		0			0
$297$	−48.2811			−2.80155
$298$		0			0
$299$	14.6880	−	25.4403i	0.849428	−	1.47125i
$300$		0			0
$301$	4.25503	−	7.36992i	0.245256	−	0.424795i
$302$		0			0
$303$	19.6495			1.12883
$304$		0			0
$305$	0.0663000			0.00379633
$306$		0			0
$307$	4.31872	−	7.48025i	0.246483	−	0.426920i	−0.716065	−	0.698034i	$-0.754059\pi$
$307$	4.31872	−	7.48025i	0.246483	−	0.426920i	0.962547	+	0.271113i	$0.0873919\pi$
$308$		0			0
$309$	0.400456	−	0.693609i	0.0227811	−	0.0394581i
$310$		0			0
$311$	29.7658			1.68786			0.843930	−	0.536453i	$-0.180236\pi$
$311$	29.7658			1.68786			0.843930	+	0.536453i	$0.180236\pi$
$312$		0			0
$313$	−5.60413	−	9.70664i	−0.316764	−	0.548651i	0.663047	−	0.748578i	$-0.269263\pi$
$313$	−5.60413	−	9.70664i	−0.316764	−	0.548651i	−0.979811	+	0.199926i	$0.935930\pi$
$314$		0			0
$315$	−10.7590			−0.606199
$316$		0			0
$317$	2.34650	+	4.06425i	0.131792	+	0.228271i	0.924368	−	0.381503i	$-0.124593\pi$
$317$	2.34650	+	4.06425i	0.131792	+	0.228271i	−0.792575	+	0.609774i	$0.791260\pi$
$318$		0			0
$319$	−2.08595	−	3.61298i	−0.116791	−	0.202288i
$320$		0			0
$321$	9.58306	−	16.5983i	0.534874	−	0.926429i
$322$		0			0
$323$	−21.6108	+	14.8654i	−1.20246	+	0.827131i
$324$		0			0
$325$	3.34910	−	5.80081i	0.185775	−	0.321771i
$326$		0			0
$327$	−8.30652	−	14.3873i	−0.459352	−	0.795620i
$328$		0			0
$329$	−8.61488	−	14.9214i	−0.474954	−	0.822644i
$330$		0			0
$331$	29.1137			1.60024			0.800118	−	0.599843i	$-0.204770\pi$
$331$	29.1137			1.60024			0.800118	+	0.599843i	$0.204770\pi$
$332$		0			0
$333$	37.8841	+	65.6171i	2.07603	+	3.59580i
$334$		0			0
$335$	−5.70500			−0.311697
$336$		0			0
$337$	−11.5790	+	20.0554i	−0.630749	+	1.09249i	0.356650	+	0.934238i	$0.383919\pi$
$337$	−11.5790	+	20.0554i	−0.630749	+	1.09249i	−0.987399	+	0.158251i	$0.949415\pi$
$338$		0			0
$339$	−3.84372	+	6.65752i	−0.208762	+	0.361587i
$340$		0			0
$341$	4.00786			0.217038
$342$		0			0
$343$	17.8604			0.964369
$344$		0			0
$345$	−6.94040	+	12.0211i	−0.373659	+	0.647196i
$346$		0			0
$347$	−7.83090	+	13.5635i	−0.420385	+	0.728127i	−0.995977	−	0.0896094i	$-0.971438\pi$
$347$	−7.83090	+	13.5635i	−0.420385	+	0.728127i	0.575592	+	0.817737i	$0.304771\pi$
$348$		0			0
$349$	−9.72130			−0.520369			−0.260185	−	0.965559i	$-0.583783\pi$
$349$	−9.72130			−0.520369			−0.260185	+	0.965559i	$0.583783\pi$
$350$		0			0
$351$	42.5863	+	73.7617i	2.27309	+	3.93711i
$352$		0			0
$353$	11.3789			0.605635			0.302818	−	0.953049i	$-0.402073\pi$
$353$	11.3789			0.605635			0.302818	+	0.953049i	$0.402073\pi$
$354$		0			0
$355$	3.23880	+	5.60977i	0.171898	+	0.297736i
$356$		0			0
$357$	−14.6001	−	25.2881i	−0.772718	−	1.33839i
$358$		0			0
$359$	−14.3876	+	24.9201i	−0.759350	+	1.31523i	0.183833	+	0.982958i	$0.441150\pi$
$359$	−14.3876	+	24.9201i	−0.759350	+	1.31523i	−0.943183	+	0.332275i	$0.892184\pi$
$360$		0			0
$361$	11.9688	+	14.7563i	0.629938	+	0.776645i
$362$		0			0
$363$	−5.40725	+	9.36563i	−0.283807	+	0.491568i
$364$		0			0
$365$	−6.98978	−	12.1066i	−0.365862	−	0.633691i
$366$		0			0
$367$	12.0649	+	20.8969i	0.629780	+	1.09081i	0.987596	+	0.157019i	$0.0501884\pi$
$367$	12.0649	+	20.8969i	0.629780	+	1.09081i	−0.357815	+	0.933792i	$0.616478\pi$
$368$		0			0
$369$	24.7941			1.29073
$370$		0			0
$371$	1.20839	+	2.09300i	0.0627367	+	0.108663i
$372$		0			0
$373$	−26.7281			−1.38393			−0.691964	−	0.721932i	$-0.743254\pi$
$373$	−26.7281			−1.38393			−0.691964	+	0.721932i	$0.743254\pi$
$374$		0			0
$375$	−1.58253	+	2.74101i	−0.0817213	+	0.141545i
$376$		0			0
$377$	−3.67983	+	6.37365i	−0.189521	+	0.328260i
$378$		0			0
$379$	4.29369			0.220552			0.110276	−	0.993901i	$-0.464826\pi$
$379$	4.29369			0.220552			0.110276	+	0.993901i	$0.464826\pi$
$380$		0			0
$381$	−61.0820			−3.12933
$382$		0			0
$383$	−2.78610	+	4.82567i	−0.142363	+	0.246580i	−0.928386	−	0.371617i	$-0.878803\pi$
$383$	−2.78610	+	4.82567i	−0.142363	+	0.246580i	0.786023	+	0.618197i	$0.212137\pi$
$384$		0			0
$385$	−2.91065	+	5.04139i	−0.148340	+	0.256933i
$386$		0			0
$387$	38.9523			1.98006
$388$		0			0
$389$	−14.0743	−	24.3774i	−0.713594	−	1.23598i	−0.963499	−	0.267711i	$-0.913733\pi$
$389$	−14.0743	−	24.3774i	−0.713594	−	1.23598i	0.249905	−	0.968270i	$-0.419601\pi$
$390$		0			0
$391$	−26.3909			−1.33464
$392$		0			0
$393$	20.9837	+	36.3449i	1.05849	+	1.83336i
$394$		0			0
$395$	0.996602	+	1.72617i	0.0501445	+	0.0868528i
$396$		0			0
$397$	−17.3712	+	30.0879i	−0.871837	+	1.51007i	−0.0117431	+	0.999931i	$0.503738\pi$
$397$	−17.3712	+	30.0879i	−0.871837	+	1.51007i	−0.860094	+	0.510135i	$0.829595\pi$
$398$		0			0
$399$	−17.4268	+	11.9873i	−0.872430	+	0.600116i
$400$		0			0
$401$	11.9370	−	20.6755i	0.596106	−	1.03249i	−0.397284	−	0.917696i	$-0.630047\pi$
$401$	11.9370	−	20.6755i	0.596106	−	1.03249i	0.993390	−	0.114789i	$-0.0366193\pi$
$402$		0			0
$403$	−3.53513	−	6.12302i	−0.176097	−	0.305010i
$404$		0			0
$405$	−9.59668	−	16.6219i	−0.476863	−	0.825951i
$406$		0			0
$407$	40.9955			2.03207
$408$		0			0
$409$	18.7346	+	32.4492i	0.926365	+	1.60451i	0.789350	+	0.613943i	$0.210418\pi$
$409$	18.7346	+	32.4492i	0.926365	+	1.60451i	0.137015	+	0.990569i	$0.456249\pi$
$410$		0			0
$411$	−49.2188			−2.42778
$412$		0			0
$413$	2.47707	−	4.29042i	0.121889	−	0.211118i
$414$		0			0
$415$	5.17383	−	8.96133i	0.253973	−	0.439894i
$416$		0			0
$417$	−58.9402			−2.88632
$418$		0			0
$419$	−0.360241			−0.0175989			−0.00879947	−	0.999961i	$-0.502801\pi$
$419$	−0.360241			−0.0175989			−0.00879947	+	0.999961i	$0.502801\pi$
$420$		0			0
$421$	−12.1243	+	20.9999i	−0.590901	+	1.02347i	0.403210	+	0.915108i	$0.367894\pi$
$421$	−12.1243	+	20.9999i	−0.590901	+	1.02347i	−0.994111	+	0.108364i	$0.965439\pi$
$422$		0			0
$423$	39.4321	−	68.2984i	1.91726	−	3.32078i
$424$		0			0
$425$	−6.01755			−0.291894
$426$		0			0
$427$	0.0508239	+	0.0880297i	0.00245954	+	0.00426005i
$428$		0			0
$429$	80.4960			3.88638
$430$		0			0
$431$	6.32067	+	10.9477i	0.304456	+	0.527333i	0.977140	−	0.212596i	$-0.0681920\pi$
$431$	6.32067	+	10.9477i	0.304456	+	0.527333i	−0.672684	+	0.739930i	$0.734859\pi$
$432$		0			0
$433$	12.2320	+	21.1864i	0.587831	+	1.01815i	0.994516	+	0.104585i	$0.0333514\pi$
$433$	12.2320	+	21.1864i	0.587831	+	1.01815i	−0.406685	+	0.913569i	$0.633315\pi$
$434$		0			0
$435$	1.73880	−	3.01169i	0.0833692	−	0.144400i
$436$		0			0
$437$	1.50745	+	19.0571i	0.0721111	+	0.911623i
$438$		0			0
$439$	12.4004	−	21.4782i	0.591840	−	1.02510i	−0.402144	−	0.915576i	$-0.631735\pi$
$439$	12.4004	−	21.4782i	0.591840	−	1.02510i	0.993985	−	0.109521i	$-0.0349316\pi$
$440$		0			0
$441$	16.3139	+	28.2565i	0.776851	+	1.34555i
$442$		0			0
$443$	−15.1318	−	26.2090i	−0.718932	−	1.24523i	−0.961423	−	0.275074i	$-0.911298\pi$
$443$	−15.1318	−	26.2090i	−0.718932	−	1.24523i	0.242491	−	0.970154i	$-0.422036\pi$
$444$		0			0
$445$	3.07310			0.145679
$446$		0			0
$447$	7.41801	+	12.8484i	0.350860	+	0.607707i
$448$		0			0
$449$	−29.0742			−1.37209			−0.686047	−	0.727557i	$-0.740656\pi$
$449$	−29.0742			−1.37209			−0.686047	+	0.727557i	$0.740656\pi$
$450$		0			0
$451$	6.70760	−	11.6179i	0.315849	−	0.547066i
$452$		0			0
$453$	9.39023	−	16.2644i	0.441192	−	0.764166i
$454$		0			0
$455$	10.2693			0.481434
$456$		0			0
$457$	−3.06234			−0.143250			−0.0716251	−	0.997432i	$-0.522819\pi$
$457$	−3.06234			−0.143250			−0.0716251	+	0.997432i	$0.522819\pi$
$458$		0			0
$459$	38.2588	−	66.2662i	1.78577	−	3.09304i
$460$		0			0
$461$	13.2934	−	23.0249i	0.619137	−	1.07238i	−0.370507	−	0.928830i	$-0.620816\pi$
$461$	13.2934	−	23.0249i	0.619137	−	1.07238i	0.989644	−	0.143547i	$-0.0458507\pi$
$462$		0			0
$463$	4.82684			0.224322			0.112161	−	0.993690i	$-0.464223\pi$
$463$	4.82684			0.224322			0.112161	+	0.993690i	$0.464223\pi$
$464$		0			0
$465$	1.67043	+	2.89327i	0.0774643	+	0.134172i
$466$		0			0
$467$	−1.31539			−0.0608690			−0.0304345	−	0.999537i	$-0.509689\pi$
$467$	−1.31539			−0.0608690			−0.0304345	+	0.999537i	$0.509689\pi$
$468$		0			0
$469$	−4.37331	−	7.57479i	−0.201941	−	0.349771i
$470$		0			0
$471$	14.7075	+	25.4741i	0.677686	+	1.17379i
$472$		0			0
$473$	10.5379	−	18.2521i	0.484532	−	0.839234i
$474$		0			0
$475$	0.343724	+	4.34533i	0.0157711	+	0.199377i
$476$		0			0
$477$	−5.53108	+	9.58011i	−0.253251	+	0.438643i
$478$		0			0
$479$	−9.53915	−	16.5223i	−0.435855	−	0.754923i	0.561510	−	0.827470i	$-0.310221\pi$
$479$	−9.53915	−	16.5223i	−0.435855	−	0.754923i	−0.997365	+	0.0725469i	$0.976887\pi$
$480$		0			0
$481$	−36.1601	−	62.6311i	−1.64876	−	2.85573i
$482$		0			0
$483$	−21.2814			−0.968335
$484$		0			0
$485$	−4.43502	−	7.68169i	−0.201384	−	0.348807i
$486$		0			0
$487$	−8.23656			−0.373234			−0.186617	−	0.982433i	$-0.559752\pi$
$487$	−8.23656			−0.373234			−0.186617	+	0.982433i	$0.559752\pi$
$488$		0			0
$489$	−9.31308	+	16.1307i	−0.421152	+	0.729457i
$490$		0			0
$491$	−15.4776	+	26.8079i	−0.698493	+	1.20983i	0.270496	+	0.962721i	$0.412812\pi$
$491$	−15.4776	+	26.8079i	−0.698493	+	1.20983i	−0.968989	+	0.247104i	$0.920521\pi$
$492$		0			0
$493$	6.61179			0.297780
$494$		0			0
$495$	−26.6453			−1.19762
$496$		0			0
$497$	−4.96557	+	8.60062i	−0.222736	+	0.385790i
$498$		0			0
$499$	−0.554753	+	0.960860i	−0.0248341	+	0.0430140i	−0.878175	−	0.478339i	$-0.841239\pi$
$499$	−0.554753	+	0.960860i	−0.0248341	+	0.0430140i	0.853341	+	0.521353i	$0.174572\pi$
$500$		0			0
$501$	40.5030			1.80954
$502$		0			0
$503$	−4.32552	−	7.49202i	−0.192865	−	0.334053i	0.753333	−	0.657639i	$-0.228445\pi$
$503$	−4.32552	−	7.49202i	−0.192865	−	0.334053i	−0.946199	+	0.323586i	$0.895111\pi$
$504$		0			0
$505$	6.20826			0.276264
$506$		0			0
$507$	−50.4286	−	87.3449i	−2.23961	−	3.87912i
$508$		0			0
$509$	10.3944	+	18.0037i	0.460725	+	0.797999i	0.998997	−	0.0447722i	$-0.0142562\pi$
$509$	10.3944	+	18.0037i	0.460725	+	0.797999i	−0.538273	+	0.842771i	$0.680923\pi$
$510$		0			0
$511$	10.7164	−	18.5613i	0.474065	−	0.821104i
$512$		0			0
$513$	−50.0368	−	23.8419i	−2.20918	−	1.05265i
$514$		0			0
$515$	0.126524	−	0.219146i	0.00557532	−	0.00965674i
$516$		0			0
$517$	−21.3354	−	36.9539i	−0.938328	−	1.62523i
$518$		0			0
$519$	23.8022	+	41.2266i	1.04480	+	1.80965i
$520$		0			0
$521$	−24.5098			−1.07379			−0.536897	−	0.843648i	$-0.680404\pi$
$521$	−24.5098			−1.07379			−0.536897	+	0.843648i	$0.680404\pi$
$522$		0			0
$523$	−9.03447	−	15.6482i	−0.395050	−	0.684247i	0.598058	−	0.801453i	$-0.295939\pi$
$523$	−9.03447	−	15.6482i	−0.395050	−	0.684247i	−0.993108	+	0.117207i	$0.962606\pi$
$524$		0			0
$525$	−4.85250			−0.211780
$526$		0			0
$527$	−3.17590	+	5.50082i	−0.138344	+	0.239619i
$528$		0			0
$529$	1.88304	−	3.26153i	0.0818715	−	0.141806i
$530$		0			0
$531$	22.6762			0.984062
$532$		0			0
$533$	−23.6658			−1.02508
$534$		0			0
$535$	3.02777	−	5.24426i	0.130902	−	0.226729i
$536$		0			0
$537$	−34.0958	+	59.0556i	−1.47134	+	2.54844i
$538$		0			0
$539$	17.6537			0.760401
$540$		0			0
$541$	8.75440	+	15.1631i	0.376381	+	0.651911i	0.990533	−	0.137277i	$-0.0438350\pi$
$541$	8.75440	+	15.1631i	0.376381	+	0.651911i	−0.614152	+	0.789188i	$0.710502\pi$
$542$		0			0
$543$	13.5167			0.580055
$544$		0			0
$545$	−2.62445	−	4.54568i	−0.112419	−	0.194716i
$546$		0			0
$547$	−13.4864	−	23.3591i	−0.576636	−	0.998763i	−0.995862	−	0.0908807i	$-0.971032\pi$
$547$	−13.4864	−	23.3591i	−0.576636	−	0.998763i	0.419226	−	0.907882i	$-0.362302\pi$
$548$		0			0
$549$	−0.232632	+	0.402930i	−0.00992849	+	0.0171966i
$550$		0			0
$551$	−0.377667	−	4.77443i	−0.0160891	−	0.203398i
$552$		0			0
$553$	−1.52794	+	2.64647i	−0.0649746	+	0.112539i
$554$		0			0
$555$	17.0865	+	29.5946i	0.725280	+	1.25622i
$556$		0			0
$557$	7.98361	+	13.8280i	0.338276	+	0.585912i	0.984109	−	0.177568i	$-0.0568228\pi$
$557$	7.98361	+	13.8280i	0.338276	+	0.585912i	−0.645832	+	0.763479i	$0.723490\pi$
$558$		0			0
$559$	−37.1797			−1.57253
$560$		0			0
$561$	−36.1581	−	62.6277i	−1.52660	−	2.64414i
$562$		0			0
$563$	−8.58711			−0.361904			−0.180952	−	0.983492i	$-0.557918\pi$
$563$	−8.58711			−0.361904			−0.180952	+	0.983492i	$0.557918\pi$
$564$		0			0
$565$	−1.21443	+	2.10345i	−0.0510913	+	0.0884928i
$566$		0			0
$567$	14.7131	−	25.4839i	0.617894	−	1.07022i
$568$		0			0
$569$	22.5910			0.947064			0.473532	−	0.880777i	$-0.342979\pi$
$569$	22.5910			0.947064			0.473532	+	0.880777i	$0.342979\pi$
$570$		0			0
$571$	17.1000			0.715613			0.357806	−	0.933796i	$-0.383525\pi$
$571$	17.1000			0.715613			0.357806	+	0.933796i	$0.383525\pi$
$572$		0			0
$573$	9.97276	−	17.2733i	0.416618	−	0.721603i
$574$		0			0
$575$	−2.19282	+	3.79808i	−0.0914471	+	0.158391i
$576$		0			0
$577$	−0.677755			−0.0282153			−0.0141077	−	0.999900i	$-0.504491\pi$
$577$	−0.677755			−0.0282153			−0.0141077	+	0.999900i	$0.504491\pi$
$578$		0			0
$579$	24.3374	+	42.1537i	1.01143	+	1.75185i
$580$		0			0
$581$	15.8645			0.658171
$582$		0			0
$583$	2.99267	+	5.18346i	0.123944	+	0.214677i
$584$		0			0
$585$	23.5025	+	40.7075i	0.971708	+	1.68305i
$586$		0			0
$587$	−13.6859	+	23.7047i	−0.564878	+	0.978397i	0.432183	+	0.901786i	$0.357743\pi$
$587$	−13.6859	+	23.7047i	−0.564878	+	0.978397i	−0.997061	+	0.0766112i	$0.975590\pi$
$588$		0			0
$589$	4.15360	+	1.97914i	0.171146	+	0.0815489i
$590$		0			0
$591$	20.1312	−	34.8683i	0.828089	−	1.43429i
$592$		0			0
$593$	−4.18940	−	7.25625i	−0.172038	−	0.297978i	0.767094	−	0.641534i	$-0.221702\pi$
$593$	−4.18940	−	7.25625i	−0.172038	−	0.297978i	−0.939132	+	0.343556i	$0.888368\pi$
$594$		0			0
$595$	−4.61290	−	7.98978i	−0.189111	−	0.327549i
$596$		0			0
$597$	32.3395			1.32357
$598$		0			0
$599$	16.9553	+	29.3675i	0.692777	+	1.19992i	0.970924	+	0.239386i	$0.0769462\pi$
$599$	16.9553	+	29.3675i	0.692777	+	1.19992i	−0.278148	+	0.960538i	$0.589720\pi$
$600$		0			0
$601$	−5.74951			−0.234528			−0.117264	−	0.993101i	$-0.537412\pi$
$601$	−5.74951			−0.234528			−0.117264	+	0.993101i	$0.537412\pi$
$602$		0			0
$603$	20.0175	−	34.6714i	0.815178	−	1.41193i
$604$		0			0
$605$	−1.70842	+	2.95908i	−0.0694573	+	0.120304i
$606$		0			0
$607$	−8.87815			−0.360353			−0.180177	−	0.983634i	$-0.557667\pi$
$607$	−8.87815			−0.360353			−0.180177	+	0.983634i	$0.557667\pi$
$608$		0			0
$609$	5.33169			0.216051
$610$		0			0
$611$	−37.6377	+	65.1904i	−1.52266	+	2.63732i
$612$		0			0
$613$	6.02098	−	10.4286i	0.243185	−	0.421209i	−0.718435	−	0.695594i	$-0.755141\pi$
$613$	6.02098	−	10.4286i	0.243185	−	0.421209i	0.961620	+	0.274386i	$0.0884745\pi$
$614$		0			0
$615$	11.1826			0.450926
$616$		0			0
$617$	−23.4362	−	40.5927i	−0.943505	−	1.63420i	−0.758717	−	0.651420i	$-0.774173\pi$
$617$	−23.4362	−	40.5927i	−0.943505	−	1.63420i	−0.184788	−	0.982778i	$-0.559160\pi$
$618$		0			0
$619$	14.8700			0.597678			0.298839	−	0.954304i	$-0.403401\pi$
$619$	14.8700			0.597678			0.298839	+	0.954304i	$0.403401\pi$
$620$		0			0
$621$	−27.8834	−	48.2955i	−1.11892	−	1.93803i
$622$		0			0
$623$	2.35576	+	4.08029i	0.0943815	+	0.163473i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−43.1586	+	29.6874i	−1.72359	+	1.18560i
$628$		0			0
$629$	−32.4856	+	56.2667i	−1.29529	+	2.24350i
$630$		0			0
$631$	−8.71235	−	15.0902i	−0.346833	−	0.600733i	0.638852	−	0.769330i	$-0.279410\pi$
$631$	−8.71235	−	15.0902i	−0.346833	−	0.600733i	−0.985685	+	0.168597i	$0.946076\pi$
$632$		0			0
$633$	−8.02830	−	13.9054i	−0.319096	−	0.552691i
$634$		0			0
$635$	−19.2989			−0.765854
$636$		0			0
$637$	−15.5715	−	26.9706i	−0.616964	−	1.06861i
$638$		0			0
$639$	−45.4569			−1.79825
$640$		0			0
$641$	−15.9973	+	27.7081i	−0.631854	+	1.09440i	0.355318	+	0.934745i	$0.384373\pi$
$641$	−15.9973	+	27.7081i	−0.631854	+	1.09440i	−0.987172	+	0.159658i	$0.948961\pi$
$642$		0			0
$643$	−17.5203	+	30.3461i	−0.690934	+	1.19673i	0.280598	+	0.959825i	$0.409467\pi$
$643$	−17.5203	+	30.3461i	−0.690934	+	1.19673i	−0.971532	+	0.236908i	$0.923866\pi$
$644$		0			0
$645$	17.5682			0.691749
$646$		0			0
$647$	17.4260			0.685087			0.342544	−	0.939502i	$-0.388712\pi$
$647$	17.4260			0.685087			0.342544	+	0.939502i	$0.388712\pi$
$648$		0			0
$649$	6.13464	−	10.6255i	0.240806	−	0.417088i
$650$		0			0
$651$	−2.56102	+	4.43581i	−0.100374	+	0.173853i
$652$		0			0
$653$	−49.1457			−1.92322			−0.961609	−	0.274422i	$-0.911513\pi$
$653$	−49.1457			−1.92322			−0.961609	+	0.274422i	$0.911513\pi$
$654$		0			0
$655$	6.62983	+	11.4832i	0.259049	+	0.448686i
$656$		0			0
$657$	98.1022			3.82733
$658$		0			0
$659$	−0.862722	−	1.49428i	−0.0336069	−	0.0582088i	0.848733	−	0.528822i	$-0.177366\pi$
$659$	−0.862722	−	1.49428i	−0.0336069	−	0.0582088i	−0.882340	+	0.470613i	$0.844033\pi$
$660$		0			0
$661$	−10.9594	−	18.9822i	−0.426270	−	0.738321i	0.570268	−	0.821459i	$-0.306839\pi$
$661$	−10.9594	−	18.9822i	−0.426270	−	0.738321i	−0.996538	+	0.0831373i	$0.973506\pi$
$662$		0			0
$663$	−63.7865	+	110.481i	−2.47726	+	4.29074i
$664$		0			0
$665$	−5.50600	+	3.78740i	−0.213514	+	0.146869i
$666$		0			0
$667$	2.40937	−	4.17315i	0.0932911	−	0.161585i
$668$		0			0
$669$	13.4932	+	23.3709i	0.521676	+	0.903570i
$670$		0			0
$671$	0.125869	+	0.218012i	0.00485912	+	0.00841624i
$672$		0			0
$673$	6.63165			0.255631			0.127816	−	0.991798i	$-0.459203\pi$
$673$	6.63165			0.255631			0.127816	+	0.991798i	$0.459203\pi$
$674$		0			0
$675$	−6.35788	−	11.0122i	−0.244715	−	0.423858i
$676$		0			0
$677$	32.7008			1.25679			0.628397	−	0.777893i	$-0.283711\pi$
$677$	32.7008			1.25679			0.628397	+	0.777893i	$0.283711\pi$
$678$		0			0
$679$	6.79956	−	11.7772i	0.260943	−	0.451967i
$680$		0			0
$681$	31.7401	−	54.9755i	1.21628	−	2.10666i
$682$		0			0
$683$	−51.9872			−1.98923			−0.994617	−	0.103622i	$-0.966957\pi$
$683$	−51.9872			−1.98923			−0.994617	+	0.103622i	$0.966957\pi$
$684$		0			0
$685$	−15.5507			−0.594162
$686$		0			0
$687$	−12.5487	+	21.7350i	−0.478764	+	0.829243i
$688$		0			0
$689$	5.27937	−	9.14414i	0.201128	−	0.348364i
$690$		0			0
$691$	−8.93635			−0.339955			−0.169977	−	0.985448i	$-0.554369\pi$
$691$	−8.93635			−0.339955			−0.169977	+	0.985448i	$0.554369\pi$
$692$		0			0
$693$	−20.4256	−	35.3782i	−0.775905	−	1.34391i
$694$		0			0
$695$	−18.6222			−0.706381
$696$		0			0
$697$	10.6305	+	18.4125i	0.402657	+	0.697423i
$698$		0			0
$699$	−16.7415	−	28.9972i	−0.633223	−	1.09678i
$700$		0			0
$701$	−1.12927	+	1.95595i	−0.0426518	+	0.0738751i	−0.886563	−	0.462607i	$-0.846914\pi$
$701$	−1.12927	+	1.95595i	−0.0426518	+	0.0738751i	0.843911	+	0.536483i	$0.180247\pi$
$702$		0			0
$703$	42.4863	+	20.2442i	1.60240	+	0.763523i
$704$		0			0
$705$	17.7847	−	30.8039i	0.669809	−	1.16014i
$706$		0			0
$707$	4.75909	+	8.24299i	0.178984	+	0.310010i
$708$		0			0
$709$	−23.4045	−	40.5378i	−0.878975	−	1.52243i	−0.852467	−	0.522781i	$-0.824894\pi$
$709$	−23.4045	−	40.5378i	−0.878975	−	1.52243i	−0.0265084	−	0.999649i	$-0.508439\pi$
$710$		0			0
$711$	−13.9874			−0.524569
$712$		0			0
$713$	2.31463	+	4.00905i	0.0866834	+	0.150140i
$714$		0			0
$715$	25.4328			0.951131
$716$		0			0
$717$	8.98978	−	15.5708i	0.335729	−	0.581500i
$718$		0			0
$719$	11.7570	−	20.3637i	0.438462	−	0.759439i	−0.559109	−	0.829094i	$-0.688857\pi$
$719$	11.7570	−	20.3637i	0.438462	−	0.759439i	0.997571	+	0.0696552i	$0.0221899\pi$
$720$		0			0
$721$	0.387961			0.0144484
$722$		0			0
$723$	30.1132			1.11992
$724$		0			0
$725$	0.549376	−	0.951547i	0.0204033	−	0.0353396i
$726$		0			0
$727$	12.7374	−	22.0617i	0.472402	−	0.818225i	−0.527099	−	0.849804i	$-0.676720\pi$
$727$	12.7374	−	22.0617i	0.472402	−	0.818225i	0.999501	+	0.0315791i	$0.0100536\pi$
$728$		0			0
$729$	13.9523			0.516752
$730$		0			0
$731$	16.7008	+	28.9266i	0.617702	+	1.06989i
$732$		0			0
$733$	−1.41916			−0.0524179			−0.0262090	−	0.999656i	$-0.508344\pi$
$733$	−1.41916			−0.0524179			−0.0262090	+	0.999656i	$0.508344\pi$
$734$		0			0
$735$	7.35788	+	12.7442i	0.271399	+	0.470077i
$736$		0			0
$737$	−10.8308	−	18.7595i	−0.398958	−	0.691015i
$738$		0			0
$739$	10.7699	−	18.6540i	0.396176	−	0.686198i	−0.597074	−	0.802186i	$-0.703670\pi$
$739$	10.7699	−	18.6540i	0.396176	−	0.686198i	0.993251	+	0.115988i	$0.0370035\pi$
$740$		0			0
$741$	83.4231	+	39.7501i	3.06462	+	1.46025i
$742$		0			0
$743$	21.2813	−	36.8602i	0.780734	−	1.35227i	−0.150781	−	0.988567i	$-0.548179\pi$
$743$	21.2813	−	36.8602i	0.780734	−	1.35227i	0.931515	−	0.363703i	$-0.118488\pi$
$744$		0			0
$745$	2.34372	+	4.05945i	0.0858674	+	0.148727i
$746$		0			0
$747$	36.3076	+	62.8866i	1.32842	+	2.30090i
$748$		0			0
$749$	9.28406			0.339232
$750$		0			0
$751$	−9.30708	−	16.1203i	−0.339620	−	0.588239i	0.644741	−	0.764401i	$-0.276965\pi$
$751$	−9.30708	−	16.1203i	−0.339620	−	0.588239i	−0.984361	+	0.176162i	$0.943632\pi$
$752$		0			0
$753$	39.6681			1.44558
$754$		0			0
$755$	2.96685	−	5.13873i	0.107975	−	0.187018i
$756$		0			0
$757$	15.3842	−	26.6462i	0.559148	−	0.968473i	−0.438420	−	0.898770i	$-0.644462\pi$
$757$	15.3842	−	26.6462i	0.559148	−	0.968473i	0.997568	−	0.0697028i	$-0.0222051\pi$
$758$		0			0
$759$	−52.7047			−1.91306
$760$		0			0
$761$	13.9270			0.504853			0.252427	−	0.967616i	$-0.418771\pi$
$761$	13.9270			0.504853			0.252427	+	0.967616i	$0.418771\pi$
$762$		0			0
$763$	4.02368	−	6.96921i	0.145667	−	0.252302i
$764$		0			0
$765$	21.1142	−	36.5709i	0.763387	−	1.32222i
$766$		0			0
$767$	−21.6442			−0.781528
$768$		0			0
$769$	24.3166	+	42.1176i	0.876880	+	1.51880i	0.854747	+	0.519045i	$0.173712\pi$
$769$	24.3166	+	42.1176i	0.876880	+	1.51880i	0.0221329	+	0.999755i	$0.492954\pi$
$770$		0			0
$771$	−54.0877			−1.94792
$772$		0			0
$773$	9.79276	+	16.9616i	0.352221	+	0.610065i	0.986638	−	0.162926i	$-0.0520932\pi$
$773$	9.79276	+	16.9616i	0.352221	+	0.610065i	−0.634417	+	0.772991i	$0.718760\pi$
$774$		0			0
$775$	0.527773	+	0.914130i	0.0189582	+	0.0328365i
$776$		0			0
$777$	−26.1961	+	45.3730i	−0.939780	+	1.62775i
$778$		0			0
$779$	12.6886	−	8.72807i	0.454616	−	0.312715i
$780$		0			0
$781$	−12.2976	+	21.3000i	−0.440042	+	0.762175i
$782$		0			0
$783$	6.98572	+	12.0996i	0.249649	+	0.432405i
$784$		0			0
$785$	4.64685	+	8.04857i	0.165853	+	0.287266i
$786$		0			0
$787$	13.4029			0.477760			0.238880	−	0.971049i	$-0.423220\pi$
$787$	13.4029			0.477760			0.238880	+	0.971049i	$0.423220\pi$
$788$		0			0
$789$	−1.45610	−	2.52203i	−0.0518384	−	0.0897867i
$790$		0			0
$791$	−3.72380			−0.132403
$792$		0			0
$793$	0.222045	−	0.384594i	0.00788507	−	0.0136573i
$794$		0			0
$795$	−2.49462	+	4.32081i	−0.0884752	+	0.153243i
$796$		0			0
$797$	30.0201			1.06337			0.531684	−	0.846943i	$-0.321559\pi$
$797$	30.0201			1.06337			0.531684	+	0.846943i	$0.321559\pi$
$798$		0			0
$799$	67.6261			2.39244
$800$		0			0
$801$	−10.7828	+	18.6764i	−0.380992	+	0.659897i
$802$		0			0
$803$	26.5399	−	45.9684i	0.936571	−	1.62219i
$804$		0			0
$805$	−6.72386			−0.236985
$806$		0			0
$807$	−40.1411	−	69.5264i	−1.41303	−	2.44745i
$808$		0			0
$809$	−13.4967			−0.474520			−0.237260	−	0.971446i	$-0.576249\pi$
$809$	−13.4967			−0.474520			−0.237260	+	0.971446i	$0.576249\pi$
$810$		0			0
$811$	2.63260	+	4.55980i	0.0924431	+	0.160116i	0.908539	−	0.417801i	$-0.137199\pi$
$811$	2.63260	+	4.55980i	0.0924431	+	0.160116i	−0.816096	+	0.577917i	$0.803866\pi$
$812$		0			0
$813$	17.7821	+	30.7996i	0.623647	+	1.08019i
$814$		0			0
$815$	−2.94247	+	5.09652i	−0.103070	+	0.178523i
$816$		0			0
$817$	19.9342	−	13.7121i	0.697410	−	0.479725i
$818$		0			0
$819$	−36.0328	+	62.4107i	−1.25909	+	2.18081i
$820$		0			0
$821$	16.4147	+	28.4312i	0.572879	+	0.992255i	0.996269	+	0.0863073i	$0.0275067\pi$
$821$	16.4147	+	28.4312i	0.572879	+	0.992255i	−0.423390	+	0.905948i	$0.639160\pi$
$822$		0			0
$823$	−20.8577	−	36.1266i	−0.727054	−	1.25929i	−0.958123	−	0.286357i	$-0.907556\pi$
$823$	−20.8577	−	36.1266i	−0.727054	−	1.25929i	0.231069	−	0.972937i	$-0.425778\pi$
$824$		0			0
$825$	−12.0175			−0.418397
$826$		0			0
$827$	6.09523	+	10.5572i	0.211952	+	0.367111i	0.952325	−	0.305084i	$-0.0986847\pi$
$827$	6.09523	+	10.5572i	0.211952	+	0.367111i	−0.740373	+	0.672196i	$0.765351\pi$
$828$		0			0
$829$	−52.9958			−1.84062			−0.920310	−	0.391190i	$-0.872064\pi$
$829$	−52.9958			−1.84062			−0.920310	+	0.391190i	$0.872064\pi$
$830$		0			0
$831$	−26.1894	+	45.3614i	−0.908500	+	1.57357i
$832$		0			0
$833$	−13.9892	+	24.2299i	−0.484695	+	0.839517i
$834$		0			0
$835$	12.7970			0.442857
$836$		0			0
$837$	−13.4221			−0.463934
$838$		0			0
$839$	7.60822	−	13.1778i	0.262665	−	0.454949i	−0.704284	−	0.709918i	$-0.748732\pi$
$839$	7.60822	−	13.1778i	0.262665	−	0.454949i	0.966949	+	0.254969i	$0.0820652\pi$
$840$		0			0
$841$	13.8964	−	24.0692i	0.479185	−	0.829973i
$842$		0			0
$843$	−33.4831			−1.15322
$844$		0			0
$845$	−15.9330	−	27.5967i	−0.548110	−	0.949355i
$846$		0			0
$847$	−5.23854			−0.179998
$848$		0			0
$849$	−32.8238	−	56.8525i	−1.12651	−	1.95117i
$850$		0			0
$851$	23.6758	+	41.0077i	0.811597	+	1.40573i
$852$		0			0
$853$	23.5729	−	40.8295i	0.807122	−	1.39798i	−0.107728	−	0.994180i	$-0.534357\pi$
$853$	23.5729	−	40.8295i	0.807122	−	1.39798i	0.914849	−	0.403795i	$-0.132309\pi$
$854$		0			0
$855$	−27.6142	−	13.1578i	−0.944387	−	0.449988i
$856$		0			0
$857$	25.6906	−	44.4974i	0.877574	−	1.52000i	0.0235779	−	0.999722i	$-0.492494\pi$
$857$	25.6906	−	44.4974i	0.877574	−	1.52000i	0.853996	−	0.520280i	$-0.174172\pi$
$858$		0			0
$859$	−1.03055	−	1.78496i	−0.0351618	−	0.0609019i	0.847909	−	0.530142i	$-0.177861\pi$
$859$	−1.03055	−	1.78496i	−0.0351618	−	0.0609019i	−0.883071	+	0.469240i	$0.844528\pi$
$860$		0			0
$861$	8.57230	+	14.8477i	0.292143	+	0.506007i
$862$		0			0
$863$	−35.8646			−1.22084			−0.610422	−	0.792076i	$-0.709000\pi$
$863$	−35.8646			−1.22084			−0.610422	+	0.792076i	$0.709000\pi$
$864$		0			0
$865$	7.52032	+	13.0256i	0.255699	+	0.442883i
$866$		0			0
$867$	60.8035			2.06500
$868$		0			0
$869$	−3.78405	+	6.55417i	−0.128365	+	0.222335i
$870$		0			0
$871$	−19.1066	+	33.0936i	−0.647403	+	1.12133i
$872$		0			0
$873$	62.2460			2.10671
$874$		0			0
$875$	−1.53315			−0.0518299
$876$		0			0
$877$	−6.54598	+	11.3380i	−0.221042	+	0.382856i	−0.955125	−	0.296204i	$-0.904279\pi$
$877$	−6.54598	+	11.3380i	−0.221042	+	0.382856i	0.734083	+	0.679060i	$0.237612\pi$
$878$		0			0
$879$	−21.6562	+	37.5096i	−0.730444	+	1.26517i
$880$		0			0
$881$	−26.9322			−0.907369			−0.453684	−	0.891162i	$-0.649891\pi$
$881$	−26.9322			−0.907369			−0.453684	+	0.891162i	$0.649891\pi$
$882$		0			0
$883$	14.8172	+	25.6642i	0.498640	+	0.863670i	0.999999	−	0.00156969i	$-0.000499648\pi$
$883$	14.8172	+	25.6642i	0.498640	+	0.863670i	−0.501359	+	0.865239i	$0.667166\pi$
$884$		0			0
$885$	10.2274			0.343790
$886$		0			0
$887$	15.2151	+	26.3533i	0.510873	+	0.884858i	0.999921	+	0.0126008i	$0.00401107\pi$
$887$	15.2151	+	26.3533i	0.510873	+	0.884858i	−0.489048	+	0.872257i	$0.662656\pi$
$888$		0			0
$889$	−14.7941	−	25.6241i	−0.496177	−	0.859403i
$890$		0			0
$891$	36.4381	−	63.1127i	1.22072	−	2.11435i
$892$		0			0
$893$	−3.86282	−	48.8334i	−0.129264	−	1.63415i
$894$		0			0
$895$	−10.7726	+	18.6587i	−0.360088	+	0.623690i
$896$		0			0
$897$	46.4882	+	80.5199i	1.55220	+	2.68848i
$898$		0			0
$899$	−0.579891	−	1.00440i	−0.0193405	−	0.0334986i
$900$		0			0
$901$	−9.48580			−0.316018
$902$		0			0
$903$	13.4674	+	23.3262i	0.448166	+	0.776247i
$904$		0			0
$905$	4.27060			0.141959
$906$		0			0
$907$	−5.59680	+	9.69395i	−0.185839	+	0.321882i	−0.943859	−	0.330349i	$-0.892834\pi$
$907$	−5.59680	+	9.69395i	−0.185839	+	0.321882i	0.758020	+	0.652231i	$0.226167\pi$
$908$		0			0
$909$	−21.7834	+	37.7299i	−0.722509	+	1.25142i
$910$		0			0
$911$	−0.339795			−0.0112579			−0.00562895	−	0.999984i	$-0.501792\pi$
$911$	−0.339795			−0.0112579			−0.00562895	+	0.999984i	$0.501792\pi$
$912$		0			0
$913$	39.2895			1.30029
$914$		0			0
$915$	−0.104921	+	0.181729i	−0.00346860	+	0.00600779i
$916$		0			0
$917$	−10.1645	+	17.6055i	−0.335662	+	0.581384i
$918$		0			0
$919$	−15.0715			−0.497163			−0.248582	−	0.968611i	$-0.579964\pi$
$919$	−15.0715			−0.497163			−0.248582	+	0.968611i	$0.579964\pi$
$920$		0			0
$921$	13.6690	+	23.6754i	0.450408	+	0.780130i
$922$		0			0
$923$	43.3883			1.42814
$924$		0			0
$925$	5.39848	+	9.35044i	0.177501	+	0.307440i
$926$		0			0
$927$	0.887890	+	1.53787i	0.0291621	+	0.0505103i
$928$		0			0
$929$	−11.3279	+	19.6204i	−0.371655	+	0.643725i	−0.989820	−	0.142323i	$-0.954543\pi$
$929$	−11.3279	+	19.6204i	−0.371655	+	0.643725i	0.618165	+	0.786048i	$0.287876\pi$
$930$		0			0
$931$	18.2957	+	8.71767i	0.599617	+	0.285710i
$932$		0			0
$933$	−47.1051	+	81.5884i	−1.54215	+	2.67108i
$934$		0			0
$935$	−11.4242	−	19.7873i	−0.373610	−	0.647112i
$936$		0			0
$937$	−9.41266	−	16.3032i	−0.307498	−	0.532602i	0.670316	−	0.742076i	$-0.266158\pi$
$937$	−9.41266	−	16.3032i	−0.307498	−	0.532602i	−0.977814	+	0.209473i	$0.932825\pi$
$938$		0			0
$939$	35.4747			1.15767
$940$		0			0
$941$	6.91540	+	11.9778i	0.225436	+	0.390466i	0.956450	−	0.291896i	$-0.0942861\pi$
$941$	6.91540	+	11.9778i	0.225436	+	0.390466i	−0.731014	+	0.682362i	$0.760953\pi$
$942$		0			0
$943$	15.4952			0.504592
$944$		0			0
$945$	9.74758	−	16.8833i	0.317089	−	0.549214i
$946$		0			0
$947$	−23.0053	+	39.8463i	−0.747570	+	1.29483i	0.201414	+	0.979506i	$0.435446\pi$
$947$	−23.0053	+	39.8463i	−0.747570	+	1.29483i	−0.948984	+	0.315323i	$0.897887\pi$
$948$		0			0
$949$	−93.6379			−3.03961
$950$		0			0
$951$	−14.8536			−0.481660
$952$		0			0
$953$	3.72192	−	6.44656i	0.120565	−	0.208824i	−0.799426	−	0.600765i	$-0.794863\pi$
$953$	3.72192	−	6.44656i	0.120565	−	0.208824i	0.919991	+	0.391940i	$0.128196\pi$
$954$		0			0
$955$	3.15090	−	5.45752i	0.101961	−	0.176601i
$956$		0			0
$957$	13.2043			0.426834
$958$		0			0
$959$	−11.9208	−	20.6474i	−0.384942	−	0.666739i
$960$		0			0
$961$	−29.8858			−0.964059
$962$		0			0
$963$	21.2475	+	36.8018i	0.684693	+	1.18592i
$964$		0			0
$965$	7.68943	+	13.3185i	0.247531	+	0.428737i
$966$		0			0
$967$	20.8376	−	36.0918i	0.670092	−	1.16063i	−0.307786	−	0.951456i	$-0.599588\pi$
$967$	20.8376	−	36.0918i	0.670092	−	1.16063i	0.977878	−	0.209178i	$-0.0670787\pi$
$968$		0			0
$969$	−6.54651	−	82.7604i	−0.210304	−	2.65865i
$970$		0			0
$971$	9.63451	−	16.6875i	0.309186	−	0.535526i	−0.668999	−	0.743264i	$-0.733277\pi$
$971$	9.63451	−	16.6875i	0.309186	−	0.535526i	0.978185	+	0.207738i	$0.0666101\pi$
$972$		0			0
$973$	−14.2753	−	24.7256i	−0.457646	−	0.792666i
$974$		0			0
$975$	10.6001	+	18.3599i	0.339474	+	0.587986i
$976$		0			0
$977$	19.7307			0.631242			0.315621	−	0.948885i	$-0.397787\pi$
$977$	19.7307			0.631242			0.315621	+	0.948885i	$0.397787\pi$
$978$		0			0
$979$	5.83420	+	10.1051i	0.186462	+	0.322961i
$980$		0			0
$981$	36.8344			1.17603
$982$		0			0
$983$	−16.6318	+	28.8071i	−0.530472	+	0.918805i	0.468896	+	0.883254i	$0.344652\pi$
$983$	−16.6318	+	28.8071i	−0.530472	+	0.918805i	−0.999368	+	0.0355513i	$0.988681\pi$
$984$		0			0
$985$	6.36048	−	11.0167i	0.202662	−	0.351020i
$986$		0			0
$987$	54.5331			1.73581
$988$		0			0
$989$	24.3434			0.774076
$990$		0			0
$991$	8.90804	−	15.4292i	0.282973	−	0.490124i	−0.689142	−	0.724626i	$-0.742013\pi$
$991$	8.90804	−	15.4292i	0.282973	−	0.490124i	0.972116	+	0.234502i	$0.0753459\pi$
$992$		0			0
$993$	−46.0732	+	79.8012i	−1.46209	+	2.53241i
$994$		0			0
$995$	10.2177			0.323923
$996$		0			0
$997$	−10.6048	−	18.3680i	−0.335857	−	0.581722i	0.647792	−	0.761817i	$-0.275693\pi$
$997$	−10.6048	−	18.3680i	−0.335857	−	0.581722i	−0.983649	+	0.180095i	$0.942359\pi$
$998$		0			0
$999$	−137.291			−4.34371

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.i.c.201.1	yes	8
3.2	odd	2		3420.2.t.w.3241.2		8
4.3	odd	2		1520.2.q.m.961.4		8
5.2	odd	4		1900.2.s.d.49.8		16
5.3	odd	4		1900.2.s.d.49.1		16
5.4	even	2		1900.2.i.d.201.4		8
19.7	even	3	inner	380.2.i.c.121.1	✓	8
19.8	odd	6		7220.2.a.p.1.1		4
19.11	even	3		7220.2.a.r.1.4		4
57.26	odd	6		3420.2.t.w.1261.2		8
76.7	odd	6		1520.2.q.m.881.4		8
95.7	odd	12		1900.2.s.d.349.1		16
95.64	even	6		1900.2.i.d.501.4		8
95.83	odd	12		1900.2.s.d.349.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.c.121.1	✓	8	19.7	even	3	inner
380.2.i.c.201.1	yes	8	1.1	even	1	trivial
1520.2.q.m.881.4		8	76.7	odd	6
1520.2.q.m.961.4		8	4.3	odd	2
1900.2.i.d.201.4		8	5.4	even	2
1900.2.i.d.501.4		8	95.64	even	6
1900.2.s.d.49.1		16	5.3	odd	4
1900.2.s.d.49.8		16	5.2	odd	4
1900.2.s.d.349.1		16	95.7	odd	12
1900.2.s.d.349.8		16	95.83	odd	12
3420.2.t.w.1261.2		8	57.26	odd	6
3420.2.t.w.3241.2		8	3.2	odd	2
7220.2.a.p.1.1		4	19.8	odd	6
7220.2.a.r.1.4		4	19.11	even	3

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	380.2.i.c.201.1

Level	$380$
Weight	$2$
Character	380.201
Analytic conductor	$3.034$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$