LMFDB - Embedded newform 224.2.bd.a.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.7
Character	$\chi$	$=$	224.37
Dual form			224.2.bd.a.109.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13266 - 0.846802i) q^{2} +(0.0986144 - 0.128517i) q^{3} +(0.565853 + 1.91828i) q^{4} +(2.39507 - 1.83780i) q^{5} +(-0.220525 + 0.0620594i) q^{6} +(0.134369 + 2.64234i) q^{7} +(0.983485 - 2.65193i) q^{8} +(0.769665 + 2.87243i) q^{9} +O(q^{10})$	\(q+(-1.13266 - 0.846802i) q^{2} +(0.0986144 - 0.128517i) q^{3} +(0.565853 + 1.91828i) q^{4} +(2.39507 - 1.83780i) q^{5} +(-0.220525 + 0.0620594i) q^{6} +(0.134369 + 2.64234i) q^{7} +(0.983485 - 2.65193i) q^{8} +(0.769665 + 2.87243i) q^{9} +(-4.26906 + 0.0534610i) q^{10} +(-0.230980 + 0.0304091i) q^{11} +(0.302333 + 0.116449i) q^{12} +(0.451311 - 0.186939i) q^{13} +(2.08534 - 3.10666i) q^{14} -0.489041i q^{15} +(-3.35962 + 2.17093i) q^{16} +(5.15284 - 2.97500i) q^{17} +(1.56061 - 3.90525i) q^{18} +(0.456233 - 3.46543i) q^{19} +(4.88068 + 3.55450i) q^{20} +(0.352835 + 0.243304i) q^{21} +(0.287373 + 0.161151i) q^{22} +(0.792513 + 2.95770i) q^{23} +(-0.243832 - 0.387913i) q^{24} +(1.06475 - 3.97371i) q^{25} +(-0.669484 - 0.170432i) q^{26} +(0.894039 + 0.370323i) q^{27} +(-4.99272 + 1.75293i) q^{28} +(-3.01331 - 7.27478i) q^{29} +(-0.414121 + 0.553919i) q^{30} +(-1.65406 - 2.86492i) q^{31} +(5.64367 + 0.385998i) q^{32} +(-0.0188699 + 0.0326836i) q^{33} +(-8.35567 - 0.993769i) q^{34} +(5.17792 + 6.08164i) q^{35} +(-5.07462 + 3.10181i) q^{36} +(3.48959 - 2.67766i) q^{37} +(-3.45129 + 3.53883i) q^{38} +(0.0204809 - 0.0764359i) q^{39} +(-2.51822 - 8.15902i) q^{40} +(-7.62359 + 7.62359i) q^{41} +(-0.193614 - 0.574363i) q^{42} +(-3.49397 + 8.43518i) q^{43} +(-0.189034 - 0.425878i) q^{44} +(7.12236 + 5.46518i) q^{45} +(1.60693 - 4.02118i) q^{46} +(-3.11151 - 1.79643i) q^{47} +(-0.0523058 + 0.645853i) q^{48} +(-6.96389 + 0.710095i) q^{49} +(-4.57095 + 3.59924i) q^{50} +(0.125808 - 0.955605i) q^{51} +(0.613978 + 0.759962i) q^{52} +(0.617371 - 0.0812784i) q^{53} +(-0.699055 - 1.17652i) q^{54} +(-0.497328 + 0.497328i) q^{55} +(7.13945 + 2.24236i) q^{56} +(-0.400375 - 0.400375i) q^{57} +(-2.74723 + 10.7916i) q^{58} +(1.44362 + 10.9654i) q^{59} +(0.938119 - 0.276725i) q^{60} +(-1.36236 - 0.179358i) q^{61} +(-0.552525 + 4.64566i) q^{62} +(-7.48651 + 2.41968i) q^{63} +(-6.06551 - 5.21628i) q^{64} +(0.737364 - 1.27715i) q^{65} +(0.0490498 - 0.0210405i) q^{66} +(-1.13554 + 1.47986i) q^{67} +(8.62264 + 8.20120i) q^{68} +(0.458267 + 0.189821i) q^{69} +(-0.714890 - 11.2731i) q^{70} +(-6.13645 - 6.13645i) q^{71} +(8.37445 + 0.783890i) q^{72} +(5.34815 + 1.43303i) q^{73} +(-6.21998 + 0.0778921i) q^{74} +(-0.405688 - 0.528703i) q^{75} +(6.90584 - 1.08574i) q^{76} +(-0.111388 - 0.606241i) q^{77} +(-0.0879241 + 0.0692329i) q^{78} +(-12.7597 - 7.36679i) q^{79} +(-4.05679 + 11.3739i) q^{80} +(-7.59029 + 4.38226i) q^{81} +(15.0906 - 2.17929i) q^{82} +(5.17520 - 2.14364i) q^{83} +(-0.267073 + 0.814512i) q^{84} +(6.87397 - 16.5952i) q^{85} +(11.1004 - 6.59552i) q^{86} +(-1.23209 - 0.330137i) q^{87} +(-0.146523 + 0.642451i) q^{88} +(11.0131 - 2.95095i) q^{89} +(-3.43931 - 12.2214i) q^{90} +(0.554598 + 1.16740i) q^{91} +(-5.22526 + 3.19389i) q^{92} +(-0.531306 - 0.0699477i) q^{93} +(2.00307 + 4.66958i) q^{94} +(-5.27607 - 9.13843i) q^{95} +(0.606154 - 0.687241i) q^{96} -12.8059 q^{97} +(8.48905 + 5.09274i) q^{98} +(-0.265125 - 0.640069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−1.13266	−	0.846802i	−0.800914	−	0.598779i
$2$	−1.13266	−	0.846802i	−0.800914	−	0.598779i
$3$	0.0986144	−	0.128517i	0.0569351	−	0.0741992i	−0.764018	−	0.645195i	$-0.776776\pi$
$3$	0.0986144	−	0.128517i	0.0569351	−	0.0741992i	0.820953	+	0.570996i	$0.193443\pi$
$4$	0.565853	+	1.91828i	0.282926	+	0.959142i
$5$	2.39507	−	1.83780i	1.07111	−	0.821890i	0.0864277	−	0.996258i	$-0.472455\pi$
$5$	2.39507	−	1.83780i	1.07111	−	0.821890i	0.984681	+	0.174368i	$0.0557882\pi$
$6$	−0.220525	+	0.0620594i	−0.0900291	+	0.0253356i
$7$	0.134369	+	2.64234i	0.0507866	+	0.998710i
$7$	0.134369	+	2.64234i	0.0507866	+	0.998710i
$8$	0.983485	−	2.65193i	0.347714	−	0.937600i
$9$	0.769665	+	2.87243i	0.256555	+	0.957477i
$10$	−4.26906	+	0.0534610i	−1.35000	+	0.0169059i
$11$	−0.230980	+	0.0304091i	−0.0696431	+	0.00916869i	−0.165267	−	0.986249i	$-0.552849\pi$
$11$	−0.230980	+	0.0304091i	−0.0696431	+	0.00916869i	0.0956241	+	0.995418i	$0.469515\pi$
$12$	0.302333	+	0.116449i	0.0872760	+	0.0336159i
$13$	0.451311	−	0.186939i	0.125171	−	0.0518476i	−0.319219	−	0.947681i	$-0.603420\pi$
$13$	0.451311	−	0.186939i	0.125171	−	0.0518476i	0.444390	+	0.895833i	$0.353420\pi$
$14$	2.08534	−	3.10666i	0.557331	−	0.830290i
$15$		−	0.489041i		−	0.126270i
$16$	−3.35962	+	2.17093i	−0.839905	+	0.542733i
$17$	5.15284	−	2.97500i	1.24975	−	0.721542i	0.278689	−	0.960381i	$-0.410100\pi$
$17$	5.15284	−	2.97500i	1.24975	−	0.721542i	0.971059	+	0.238839i	$0.0767668\pi$
$18$	1.56061	−	3.90525i	0.367839	−	0.920476i
$19$	0.456233	−	3.46543i	0.104667	−	0.795025i	−0.855932	−	0.517088i	$-0.827016\pi$
$19$	0.456233	−	3.46543i	0.104667	−	0.795025i	0.960599	−	0.277937i	$-0.0896507\pi$
$20$	4.88068	+	3.55450i	1.09135	+	0.794810i
$21$	0.352835	+	0.243304i	0.0769950	+	0.0530933i
$22$	0.287373	+	0.161151i	0.0612682	+	0.0343575i
$23$	0.792513	+	2.95770i	0.165250	+	0.616723i	0.998008	+	0.0630853i	$0.0200940\pi$
$23$	0.792513	+	2.95770i	0.165250	+	0.616723i	−0.832758	+	0.553638i	$0.813239\pi$
$24$	−0.243832	−	0.387913i	−0.0497721	−	0.0791825i
$25$	1.06475	−	3.97371i	0.212950	−	0.794741i
$26$	−0.669484	−	0.170432i	−0.131297	−	0.0334244i
$27$	0.894039	+	0.370323i	0.172058	+	0.0712687i
$28$	−4.99272	+	1.75293i	−0.943535	+	0.331273i
$29$	−3.01331	−	7.27478i	−0.559558	−	1.35089i	−0.910117	−	0.414352i	$-0.864008\pi$
$29$	−3.01331	−	7.27478i	−0.559558	−	1.35089i	0.350558	−	0.936541i	$-0.385992\pi$
$30$	−0.414121	+	0.553919i	−0.0756077	+	0.101131i
$31$	−1.65406	−	2.86492i	−0.297079	−	0.514556i	0.678388	−	0.734704i	$-0.262679\pi$
$31$	−1.65406	−	2.86492i	−0.297079	−	0.514556i	−0.975466	+	0.220149i	$0.929346\pi$
$32$	5.64367	+	0.385998i	0.997669	+	0.0682355i
$33$	−0.0188699	+	0.0326836i	−0.00328483	+	0.00568949i
$34$	−8.35567	−	0.993769i	−1.43299	−	0.170430i
$35$	5.17792	+	6.08164i	0.875228	+	1.02799i
$36$	−5.07462	+	3.10181i	−0.845770	+	0.516968i
$37$	3.48959	−	2.67766i	0.573685	−	0.440204i	−0.280736	−	0.959785i	$-0.590579\pi$
$37$	3.48959	−	2.67766i	0.573685	−	0.440204i	0.854421	+	0.519581i	$0.173912\pi$
$38$	−3.45129	+	3.53883i	−0.559874	+	0.574074i
$39$	0.0204809	−	0.0764359i	0.00327958	−	0.0122395i
$40$	−2.51822	−	8.15902i	−0.398165	−	1.29005i
$41$	−7.62359	+	7.62359i	−1.19060	+	1.19060i	−0.213707	+	0.976898i	$0.568554\pi$
$41$	−7.62359	+	7.62359i	−1.19060	+	1.19060i	−0.976898	+	0.213707i	$0.931446\pi$
$42$	−0.193614	−	0.574363i	−0.0298752	−	0.0886262i
$43$	−3.49397	+	8.43518i	−0.532825	+	1.28635i	0.396820	+	0.917896i	$0.370114\pi$
$43$	−3.49397	+	8.43518i	−0.532825	+	1.28635i	−0.929645	+	0.368456i	$0.879886\pi$
$44$	−0.189034	−	0.425878i	−0.0284980	−	0.0642036i
$45$	7.12236	+	5.46518i	1.06174	+	0.814701i
$46$	1.60693	−	4.02118i	0.236930	−	0.592891i
$47$	−3.11151	−	1.79643i	−0.453860	−	0.262036i	0.255599	−	0.966783i	$-0.417727\pi$
$47$	−3.11151	−	1.79643i	−0.453860	−	0.262036i	−0.709459	+	0.704747i	$0.751061\pi$
$48$	−0.0523058	+	0.645853i	−0.00754969	+	0.0932209i
$49$	−6.96389	+	0.710095i	−0.994841	+	0.101442i
$50$	−4.57095	+	3.59924i	−0.646430	+	0.509009i
$51$	0.125808	−	0.955605i	0.0176166	−	0.133811i
$52$	0.613978	+	0.759962i	0.0851434	+	0.105388i
$53$	0.617371	−	0.0812784i	0.0848024	−	0.0111644i	−0.0880056	−	0.996120i	$-0.528049\pi$
$53$	0.617371	−	0.0812784i	0.0848024	−	0.0111644i	0.172808	+	0.984956i	$0.444716\pi$
$54$	−0.699055	−	1.17652i	−0.0951293	−	0.160105i
$55$	−0.497328	+	0.497328i	−0.0670597	+	0.0670597i
$56$	7.13945	+	2.24236i	0.954050	+	0.299648i
$57$	−0.400375	−	0.400375i	−0.0530310	−	0.0530310i
$58$	−2.74723	+	10.7916i	−0.360729	+	1.41700i
$59$	1.44362	+	10.9654i	0.187943	+	1.42757i	0.782066	+	0.623195i	$0.214166\pi$
$59$	1.44362	+	10.9654i	0.187943	+	1.42757i	−0.594123	+	0.804374i	$0.702501\pi$
$60$	0.938119	−	0.276725i	0.121111	−	0.0357251i
$61$	−1.36236	−	0.179358i	−0.174433	−	0.0229645i	0.0428039	−	0.999083i	$-0.486371\pi$
$61$	−1.36236	−	0.179358i	−0.174433	−	0.0229645i	−0.217236	+	0.976119i	$0.569704\pi$
$62$	−0.552525	+	4.64566i	−0.0701707	+	0.589999i
$63$	−7.48651	+	2.41968i	−0.943212	+	0.304851i
$64$	−6.06551	−	5.21628i	−0.758189	−	0.652035i
$65$	0.737364	−	1.27715i	0.0914588	−	0.158411i
$66$	0.0490498	−	0.0210405i	0.00603761	−	0.00258990i
$67$	−1.13554	+	1.47986i	−0.138728	+	0.180794i	−0.857551	−	0.514400i	$-0.828015\pi$
$67$	−1.13554	+	1.47986i	−0.138728	+	0.180794i	0.718822	+	0.695194i	$0.244681\pi$
$68$	8.62264	+	8.20120i	1.04565	+	0.994542i
$69$	0.458267	+	0.189821i	0.0551689	+	0.0228517i
$70$	−0.714890	−	11.2731i	−0.0854457	−	1.34740i
$71$	−6.13645	−	6.13645i	−0.728263	−	0.728263i	0.242011	−	0.970274i	$-0.422193\pi$
$71$	−6.13645	−	6.13645i	−0.728263	−	0.728263i	−0.970274	+	0.242011i	$0.922193\pi$
$72$	8.37445	+	0.783890i	0.986939	+	0.0923823i
$73$	5.34815	+	1.43303i	0.625953	+	0.167724i	0.557833	−	0.829953i	$-0.311633\pi$
$73$	5.34815	+	1.43303i	0.625953	+	0.167724i	0.0681205	+	0.997677i	$0.478300\pi$
$74$	−6.21998	+	0.0778921i	−0.723058	+	0.00905477i
$75$	−0.405688	−	0.528703i	−0.0468448	−	0.0610494i
$76$	6.90584	−	1.08574i	0.792155	−	0.124543i
$77$	−0.111388	−	0.606241i	−0.0126938	−	0.0690876i
$78$	−0.0879241	+	0.0692329i	−0.00995544	+	0.00783908i
$79$	−12.7597	−	7.36679i	−1.43557	−	0.828829i	−0.438035	−	0.898958i	$-0.644326\pi$
$79$	−12.7597	−	7.36679i	−1.43557	−	0.828829i	−0.997538	+	0.0701291i	$0.977659\pi$
$80$	−4.05679	+	11.3739i	−0.453562	+	1.27164i
$81$	−7.59029	+	4.38226i	−0.843366	+	0.486918i
$82$	15.0906	−	2.17929i	1.66648	−	0.240662i
$83$	5.17520	−	2.14364i	0.568052	−	0.235295i	−0.0801248	−	0.996785i	$-0.525532\pi$
$83$	5.17520	−	2.14364i	0.568052	−	0.235295i	0.648177	+	0.761490i	$0.275532\pi$
$84$	−0.267073	+	0.814512i	−0.0291400	+	0.0888706i
$85$	6.87397	−	16.5952i	0.745587	−	1.80001i
$86$	11.1004	−	6.59552i	1.19699	−	0.711213i
$87$	−1.23209	−	0.330137i	−0.132094	−	0.0353944i
$88$	−0.146523	+	0.642451i	−0.0156194	+	0.0684855i
$89$	11.0131	−	2.95095i	1.16738	−	0.312800i	0.377473	−	0.926021i	$-0.376793\pi$
$89$	11.0131	−	2.95095i	1.16738	−	0.312800i	0.789911	+	0.613221i	$0.210127\pi$
$90$	−3.43931	−	12.2214i	−0.362536	−	1.28825i
$91$	0.554598	+	1.16740i	0.0581377	+	0.122376i
$92$	−5.22526	+	3.19389i	−0.544771	+	0.332986i
$93$	−0.531306	−	0.0699477i	−0.0550938	−	0.00725324i
$94$	2.00307	+	4.66958i	0.206601	+	0.481631i
$95$	−5.27607	−	9.13843i	−0.541314	−	0.937583i
$96$	0.606154	−	0.687241i	0.0618654	−	0.0701413i
$97$	−12.8059			−1.30025			−0.650123	−	0.759829i	$-0.725283\pi$
$97$	−12.8059			−1.30025			−0.650123	+	0.759829i	$0.725283\pi$
$98$	8.48905	+	5.09274i	0.857524	+	0.514444i
$99$	−0.265125	−	0.640069i	−0.0266461	−	0.0643294i
$100$	8.22519	−	0.206038i	0.822519	−	0.0206038i
$101$	−0.643692	−	4.88933i	−0.0640498	−	0.486506i	−0.993165	−	0.116717i	$-0.962763\pi$
$101$	−0.643692	−	4.88933i	−0.0640498	−	0.486506i	0.929115	−	0.369790i	$-0.120570\pi$
$102$	−0.951706	+	0.975844i	−0.0942329	+	0.0966230i
$103$	−4.43413	+	1.18812i	−0.436908	+	0.117069i	−0.470567	−	0.882364i	$-0.655951\pi$
$103$	−4.43413	+	1.18812i	−0.436908	+	0.117069i	0.0336591	+	0.999433i	$0.489284\pi$
$104$	−0.0518927	−	1.38070i	−0.00508850	−	0.135389i
$105$	1.29221	−	0.0657117i	0.126107	−	0.00641281i
$106$	−0.768100	−	0.430730i	−0.0746045	−	0.0418362i
$107$	−12.3164	−	16.0511i	−1.19067	−	1.55172i	−0.761030	−	0.648717i	$-0.775306\pi$
$107$	−12.3164	−	16.0511i	−1.19067	−	1.55172i	−0.429644	−	0.902999i	$-0.641361\pi$
$108$	−0.204490	+	1.92457i	−0.0196771	+	0.185192i
$109$	−0.0997102	−	0.0765104i	−0.00955051	−	0.00732836i	0.603975	−	0.797003i	$-0.293583\pi$
$109$	−0.0997102	−	0.0765104i	−0.00955051	−	0.00732836i	−0.613526	+	0.789675i	$0.710249\pi$
$110$	0.984443	−	0.142167i	0.0938630	−	0.0135551i
$111$		−	0.712527i		−	0.0676300i
$112$	−6.18776	−	8.58555i	−0.584689	−	0.811258i
$113$			9.27096i			0.872139i	0.899913	+	0.436069i	$0.143630\pi$
$113$			9.27096i			0.872139i	−0.899913	+	0.436069i	$0.856370\pi$
$114$	0.114452	+	0.792529i	0.0107194	+	0.0742272i
$115$	7.33379	+	5.62742i	0.683880	+	0.524759i
$116$	12.2500	−	9.89685i	1.13738	−	0.918899i
$117$	0.884328	+	1.15248i	0.0817561	+	0.106547i
$118$	7.65036	−	13.6425i	0.704273	−	1.25590i
$119$	8.55332	+	13.2158i	0.784082	+	1.21149i
$120$	−1.29690	−	0.480964i	−0.118391	−	0.0439058i
$121$	−10.5728	+	2.83296i	−0.961160	+	0.257542i
$122$	1.39122	+	1.35680i	0.125955	+	0.122839i
$123$	0.227964	+	1.73156i	0.0205548	+	0.156129i
$124$	4.55978	−	4.79409i	0.409480	−	0.430522i
$125$	1.02372	+	2.47148i	0.0915645	+	0.221056i
$126$	10.5287	+	3.59891i	0.937970	+	0.320616i
$127$	18.0822			1.60453			0.802266	−	0.596966i	$-0.203627\pi$
$127$	18.0822			1.60453			0.802266	+	0.596966i	$0.203627\pi$
$128$	2.45303	+	11.0446i	0.216820	+	0.976212i
$129$	0.739507	+	1.28086i	0.0651100	+	0.112774i
$130$	−1.91668	+	0.822182i	−0.168104	+	0.0721102i
$131$	19.9200	+	2.62252i	1.74042	+	0.229131i	0.932756	−	0.360509i	$-0.117397\pi$
$131$	19.9200	+	2.62252i	1.74042	+	0.229131i	0.807666	+	0.589640i	$0.200730\pi$
$132$	−0.0733740	−	0.0177037i	−0.00638639	−	0.00154091i
$133$	9.21815	+	0.739876i	0.799315	+	0.0641554i
$134$	2.53934	−	0.714611i	0.219365	−	0.0617330i
$135$	2.82187	−	0.756117i	0.242868	−	0.0650762i
$136$	−2.82175	−	16.5909i	−0.241963	−	1.42266i
$137$	10.8008	+	2.89407i	0.922777	+	0.247257i	0.688772	−	0.724978i	$-0.258150\pi$
$137$	10.8008	+	2.89407i	0.922777	+	0.247257i	0.234005	+	0.972235i	$0.424817\pi$
$138$	−0.358322	−	0.603064i	−0.0305024	−	0.0513362i
$139$	−0.121776	+	0.293993i	−0.0103289	+	0.0249361i	−0.928960	−	0.370181i	$-0.879296\pi$
$139$	−0.121776	+	0.293993i	−0.0103289	+	0.0249361i	0.918631	+	0.395117i	$0.129296\pi$
$140$	−8.73637	+	13.3740i	−0.738358	+	1.13031i
$141$	−0.537711	+	0.222727i	−0.0452835	+	0.0187570i
$142$	1.75418	+	12.1469i	0.147207	+	1.01934i
$143$	−0.0985592	+	0.0569032i	−0.00824193	+	0.00475848i
$144$	−8.82164	−	7.97939i	−0.735136	−	0.664949i
$145$	−20.5867	−	11.8857i	−1.70963	−	0.987058i
$146$	−4.84416	−	6.15196i	−0.400905	−	0.509140i
$147$	−0.595481	+	0.965003i	−0.0491144	+	0.0795921i
$148$	7.11110	+	5.17886i	0.584529	+	0.425700i
$149$	−13.1273	−	17.1078i	−1.07543	−	1.40153i	−0.909655	−	0.415365i	$-0.863654\pi$
$149$	−13.1273	−	17.1078i	−1.07543	−	1.40153i	−0.165775	−	0.986164i	$-0.553013\pi$
$150$	0.0118013	+	0.942380i	0.000963574	+	0.0769450i
$151$	1.63413	+	0.437863i	0.132983	+	0.0356328i	0.324697	−	0.945818i	$-0.394738\pi$
$151$	1.63413	+	0.437863i	0.132983	+	0.0356328i	−0.191713	+	0.981451i	$0.561404\pi$
$152$	−8.74141	−	4.61810i	−0.709022	−	0.374578i
$153$	12.5114	+	12.5114i	1.01149	+	1.01149i
$154$	−0.387202	+	0.780991i	−0.0312016	+	0.0629340i
$155$	−9.22677	−	3.82185i	−0.741112	−	0.306979i
$156$	0.158215	−	0.00396324i	0.0126673	−	0.000317313i
$157$	−11.1037	+	14.4707i	−0.886174	+	1.15488i	0.100945	+	0.994892i	$0.467814\pi$
$157$	−11.1037	+	14.4707i	−0.886174	+	1.15488i	−0.987118	+	0.159992i	$0.948853\pi$
$158$	8.21418	+	19.1490i	0.653485	+	1.52341i
$159$	0.0504360	−	0.0873577i	0.00399984	−	0.00692792i
$160$	14.2264	−	9.44746i	1.12469	−	0.746887i
$161$	−7.70875	+	2.49151i	−0.607535	+	0.196358i
$162$	12.3082	+	1.46385i	0.967020	+	0.115011i
$163$	8.41470	+	1.10782i	0.659090	+	0.0867708i	0.452650	−	0.891688i	$-0.350479\pi$
$163$	8.41470	+	1.10782i	0.659090	+	0.0867708i	0.206440	+	0.978459i	$0.433812\pi$
$164$	−18.9380	−	10.3104i	−1.47881	−	0.805105i
$165$	0.0148713	+	0.112959i	0.00115773	+	0.00879382i
$166$	−7.67699	−	1.95435i	−0.595850	−	0.151687i
$167$	−11.3134	−	11.3134i	−0.875461	−	0.875461i	0.117600	−	0.993061i	$-0.462480\pi$
$167$	−11.3134	−	11.3134i	−0.875461	−	0.875461i	−0.993061	+	0.117600i	$0.962480\pi$
$168$	0.992234	−	0.696411i	0.0765525	−	0.0537293i
$169$	−9.02365	+	9.02365i	−0.694127	+	0.694127i
$170$	−21.8388	+	12.9759i	−1.67496	+	0.995208i
$171$	10.3054	−	1.35673i	0.788071	−	0.103751i
$172$	−18.1581	−	1.92935i	−1.38454	−	0.147111i
$173$	0.681987	−	5.18021i	0.0518505	−	0.393844i	−0.945766	−	0.324848i	$-0.894687\pi$
$173$	0.681987	−	5.18021i	0.0518505	−	0.393844i	0.997617	−	0.0689963i	$-0.0219797\pi$
$174$	1.11598	+	1.41727i	0.0846023	+	0.107443i
$175$	10.6429	+	2.27949i	0.804531	+	0.172313i
$176$	0.709990	−	0.603605i	0.0535175	−	0.0454985i
$177$	1.55160	+	0.895814i	0.116625	+	0.0673335i
$178$	−14.9730	−	5.98347i	−1.12227	−	0.448480i
$179$	−17.3865	−	13.3411i	−1.29953	−	0.997161i	−0.999059	−	0.0433689i	$-0.986191\pi$
$179$	−17.3865	−	13.3411i	−1.29953	−	0.997161i	−0.300467	−	0.953792i	$-0.597142\pi$
$180$	−6.45356	+	16.7552i	−0.481020	+	1.24886i
$181$	−7.84455	+	18.9384i	−0.583081	+	1.40768i	0.306925	+	0.951734i	$0.400700\pi$
$181$	−7.84455	+	18.9384i	−0.583081	+	1.40768i	−0.890006	+	0.455948i	$0.849300\pi$
$182$	0.360381	−	1.79190i	0.0267132	−	0.132825i
$183$	−0.157399	+	0.157399i	−0.0116353	+	0.0116353i
$184$	8.62305	+	0.807160i	0.635700	+	0.0595046i
$185$	3.43681	−	12.8264i	0.252679	−	0.943013i
$186$	0.542559	+	0.529138i	0.0397823	+	0.0387983i
$187$	−1.09974	+	0.843858i	−0.0804208	+	0.0617090i
$188$	1.68541	−	6.98527i	0.122921	−	0.509453i
$189$	−0.858387	+	2.41211i	−0.0624385	+	0.175455i
$190$	−1.76242	+	14.8185i	−0.127860	+	1.07505i
$191$	3.48458	−	6.03547i	0.252135	−	0.436711i	−0.711978	−	0.702201i	$-0.752201\pi$
$191$	3.48458	−	6.03547i	0.252135	−	0.436711i	0.964113	+	0.265491i	$0.0855339\pi$
$192$	−1.26853	+	0.265120i	−0.0915480	+	0.0191334i
$193$	1.89126	+	3.27576i	0.136136	+	0.235794i	0.926031	−	0.377448i	$-0.123198\pi$
$193$	1.89126	+	3.27576i	0.136136	+	0.235794i	−0.789895	+	0.613242i	$0.789865\pi$
$194$	14.5048	+	10.8441i	1.04139	+	0.778561i
$195$	−0.0914208	−	0.220709i	−0.00654678	−	0.0158053i
$196$	−5.30270	−	12.9569i	−0.378764	−	0.925493i
$197$	−2.15459	−	0.892459i	−0.153508	−	0.0635851i	0.304607	−	0.952478i	$-0.401475\pi$
$197$	−2.15459	−	0.892459i	−0.153508	−	0.0635851i	−0.458114	+	0.888893i	$0.651475\pi$
$198$	−0.241714	+	0.949492i	−0.0171779	+	0.0674775i
$199$	3.55082	−	13.2519i	0.251711	−	0.939399i	−0.718179	−	0.695858i	$-0.755024\pi$
$199$	3.55082	−	13.2519i	0.251711	−	0.939399i	0.969891	−	0.243541i	$-0.0783091\pi$
$200$	−9.49084	−	6.73173i	−0.671104	−	0.476005i
$201$	0.0782068	+	0.291872i	0.00551629	+	0.0205871i
$202$	−3.41121	+	6.08304i	−0.240012	+	0.428001i
$203$	18.8175	−	8.93969i	1.32073	−	0.627444i
$204$	1.90431	−	0.299397i	0.133328	−	0.0209620i
$205$	−4.24839	+	32.2697i	−0.296720	+	2.25381i
$206$	6.02848	+	2.40909i	0.420024	+	0.167849i
$207$	−7.88581	+	4.55288i	−0.548102	+	0.316447i
$208$	−1.11040	+	1.60781i	−0.0769925	+	0.111482i
$209$			0.814320i			0.0563277i
$210$	−1.51928	−	1.01982i	−0.104841	−	0.0703741i
$211$	−10.8428	+	4.49125i	−0.746451	+	0.309190i	−0.723293	−	0.690541i	$-0.757372\pi$
$211$	−10.8428	+	4.49125i	−0.746451	+	0.309190i	−0.0231586	+	0.999732i	$0.507372\pi$
$212$	0.505256	+	1.13830i	0.0347011	+	0.0781788i
$213$	−1.39378	+	0.183495i	−0.0955002	+	0.0125728i
$214$	0.358280	+	28.6100i	0.0244915	+	1.95574i
$215$	7.13390	+	26.6241i	0.486528	+	1.81575i
$216$	1.86135	−	2.00673i	0.126649	−	0.136540i
$217$	7.34784	−	4.75555i	0.498804	−	0.322828i
$218$	0.0481490	+	0.171095i	0.00326106	+	0.0115880i
$219$	0.711573	−	0.546009i	0.0480836	−	0.0368959i
$220$	−1.23543	−	0.672601i	−0.0832927	−	0.0453468i
$221$	1.76939	−	2.30592i	0.119022	−	0.155113i
$222$	−0.603369	+	0.807053i	−0.0404955	+	0.0541659i
$223$	18.5303			1.24088			0.620442	−	0.784252i	$-0.286953\pi$
$223$	18.5303			1.24088			0.620442	+	0.784252i	$0.286953\pi$
$224$	−0.261605	+	14.9643i	−0.0174792	+	0.999847i
$225$	12.2337			0.815580
$226$	7.85067	−	10.5009i	0.522219	−	0.698508i
$227$	12.8275	−	16.7171i	0.851391	−	1.10955i	−0.141430	−	0.989948i	$-0.545170\pi$
$227$	12.8275	−	16.7171i	0.851391	−	1.10955i	0.992821	−	0.119606i	$-0.0381632\pi$
$228$	0.541480	−	0.994587i	0.0358604	−	0.0658681i
$229$	2.65261	−	2.03542i	0.175289	−	0.134504i	−0.517391	−	0.855749i	$-0.673097\pi$
$229$	2.65261	−	2.03542i	0.175289	−	0.134504i	0.692680	+	0.721245i	$0.256430\pi$
$230$	−3.54141	−	12.5842i	−0.233514	−	0.829780i
$231$	−0.0888966	−	0.0454690i	−0.00584897	−	0.00299164i
$232$	−22.2558	+	0.836470i	−1.46116	+	0.0549170i
$233$	0.0317046	+	0.118323i	0.00207703	+	0.00775160i	0.966957	−	0.254941i	$-0.0820561\pi$
$233$	0.0317046	+	0.118323i	0.00207703	+	0.00775160i	−0.964880	+	0.262693i	$0.915389\pi$
$234$	−0.0257248	−	2.05422i	−0.00168168	−	0.134289i
$235$	−10.7538	+	1.41576i	−0.701499	+	0.0923541i
$236$	−20.2178	+	8.97405i	−1.31607	+	0.584161i
$237$	−2.20504	+	0.913358i	−0.143233	+	0.0593290i
$238$	1.50313	−	22.2120i	0.0974337	−	1.43979i
$239$		−	15.1118i		−	0.977500i	−0.872424	−	0.488750i	$-0.837453\pi$
$239$		−	15.1118i		−	0.977500i	0.872424	−	0.488750i	$-0.162547\pi$
$240$	1.06167	+	1.64299i	0.0685308	+	0.106055i
$241$	7.72412	−	4.45952i	0.497554	−	0.287263i	−0.230149	−	0.973155i	$-0.573921\pi$
$241$	7.72412	−	4.45952i	0.497554	−	0.287263i	0.727703	+	0.685892i	$0.240588\pi$
$242$	14.3743	+	5.74424i	0.924017	+	0.369254i
$243$	−0.564249	+	4.28590i	−0.0361966	+	0.274941i
$244$	−0.426836	−	2.71489i	−0.0273254	−	0.173803i
$245$	−15.3740	+	14.4990i	−0.982209	+	0.926306i
$246$	1.20808	−	2.15431i	0.0770243	−	0.137354i
$247$	−0.441922	−	1.64928i	−0.0281188	−	0.104941i
$248$	−9.22434	+	1.56886i	−0.585746	+	0.0996228i
$249$	0.234856	−	0.876493i	0.0148834	−	0.0555455i
$250$	0.933325	−	3.66625i	0.0590287	−	0.231874i
$251$	−12.1756	−	5.04331i	−0.768518	−	0.318331i	−0.0362461	−	0.999343i	$-0.511540\pi$
$251$	−12.1756	−	5.04331i	−0.768518	−	0.318331i	−0.732272	+	0.681012i	$0.761540\pi$
$252$	−8.87789	−	12.9921i	−0.559255	−	0.818423i
$253$	−0.272996	−	0.659070i	−0.0171631	−	0.0414354i
$254$	−20.4810	−	15.3120i	−1.28509	−	0.960761i
$255$	−1.45489	−	2.51995i	−0.0911090	−	0.157805i
$256$	6.57411	−	14.5870i	0.410882	−	0.911689i
$257$	3.46931	−	6.00902i	0.216410	−	0.374833i	−0.737298	−	0.675568i	$-0.763899\pi$
$257$	3.46931	−	6.00902i	0.216410	−	0.374833i	0.953708	+	0.300735i	$0.0972320\pi$
$258$	0.247025	−	2.07700i	0.0153791	−	0.129309i
$259$	7.54416	+	8.86088i	0.468772	+	0.550588i
$260$	2.86718	+	0.691793i	0.177815	+	0.0429032i
$261$	18.5771	−	14.2547i	1.14989	−	0.882343i
$262$	−20.3419	−	19.8388i	−1.25673	−	1.22564i
$263$	−5.26790	+	19.6601i	−0.324833	+	1.21229i	0.589647	+	0.807661i	$0.299267\pi$
$263$	−5.26790	+	19.6601i	−0.324833	+	1.21229i	−0.914480	+	0.404631i	$0.867400\pi$
$264$	0.0681165	+	0.0821855i	0.00419228	+	0.00505817i
$265$	1.32927	−	1.32927i	0.0816566	−	0.0816566i
$266$	−9.81453	−	8.64398i	−0.601767	−	0.529996i
$267$	0.706802	−	1.70637i	0.0432556	−	0.104428i
$268$	−3.48135	−	1.34090i	−0.212657	−	0.0819086i
$269$	3.23287	+	2.48067i	0.197112	+	0.151249i	0.702602	−	0.711583i	$-0.252022\pi$
$269$	3.23287	+	2.48067i	0.197112	+	0.151249i	−0.505490	+	0.862832i	$0.668688\pi$
$270$	−3.83651	−	1.53314i	−0.233482	−	0.0933037i
$271$	7.74824	+	4.47345i	0.470672	+	0.271743i	0.716521	−	0.697565i	$-0.245733\pi$
$271$	7.74824	+	4.47345i	0.470672	+	0.271743i	−0.245849	+	0.969308i	$0.579067\pi$
$272$	−10.8531	+	21.1813i	−0.658065	+	1.28431i
$273$	0.204721	+	0.0438470i	0.0123903	+	0.00265374i
$274$	−9.78300	−	12.4242i	−0.591012	−	0.750572i
$275$	−0.125100	+	0.950225i	−0.00754379	+	0.0573007i
$276$	−0.104818	+	0.986497i	−0.00630928	+	0.0593801i
$277$	23.1657	−	3.04982i	1.39189	−	0.183246i	0.602980	−	0.797756i	$-0.293980\pi$
$277$	23.1657	−	3.04982i	1.39189	−	0.183246i	0.788909	+	0.614510i	$0.210646\pi$
$278$	0.386885	−	0.229875i	0.0232038	−	0.0137870i
$279$	6.95622	−	6.95622i	0.416458	−	0.416458i
$280$	21.2205	−	7.75029i	1.26817	−	0.463169i
$281$	13.8956	+	13.8956i	0.828939	+	0.828939i	0.987370	−	0.158431i	$-0.0506434\pi$
$281$	13.8956	+	13.8956i	0.828939	+	0.828939i	−0.158431	+	0.987370i	$0.550643\pi$
$282$	0.797652	+	0.203060i	0.0474995	+	0.0120920i
$283$	1.33074	+	10.1080i	0.0791041	+	0.600855i	0.984383	+	0.176038i	$0.0563283\pi$
$283$	1.33074	+	10.1080i	0.0791041	+	0.600855i	−0.905279	+	0.424817i	$0.860338\pi$
$284$	8.29913	−	15.2438i	0.492463	−	0.904552i
$285$	−1.69474	−	0.223117i	−0.100388	−	0.0132163i
$286$	0.159820	+	0.0190080i	0.00945036	+	0.00112396i
$287$	−21.1685	−	19.1197i	−1.24954	−	1.12860i
$288$	3.23498	+	16.5081i	0.190623	+	0.972751i
$289$	9.20120	−	15.9369i	0.541247	−	0.937467i
$290$	13.2529	+	30.8954i	0.778240	+	1.81424i
$291$	−1.26285	+	1.64578i	−0.0740296	+	0.0964773i
$292$	0.277304	+	11.0701i	0.0162280	+	0.647831i
$293$	−10.6054	−	4.39288i	−0.619571	−	0.256635i	0.0507434	−	0.998712i	$-0.483841\pi$
$293$	−10.6054	−	4.39288i	−0.619571	−	0.256635i	−0.670315	+	0.742077i	$0.733841\pi$
$294$	1.49165	−	0.588769i	0.0869945	−	0.0343377i
$295$	23.6097	+	23.6097i	1.37461	+	1.37461i
$296$	−3.66901	−	11.8876i	−0.213257	−	0.690953i
$297$	−0.217766	−	0.0583503i	−0.0126361	−	0.00338583i
$298$	0.381868	+	30.4936i	0.0221210	+	1.76645i
$299$	0.910579	+	1.18669i	0.0526602	+	0.0686281i
$300$	0.784643	−	1.07739i	0.0453014	−	0.0622033i
$301$	−22.7581	−	8.09881i	−1.31175	−	0.466808i
$302$	−1.48013	−	1.87973i	−0.0851721	−	0.108167i
$303$	−0.691838	−	0.399433i	−0.0397451	−	0.0229468i
$304$	5.99045	+	12.6330i	0.343576	+	0.724552i
$305$	−3.59258	+	2.07418i	−0.205711	+	0.118767i
$306$	−3.57654	−	24.7659i	−0.204457	−	1.41578i
$307$	25.2285	−	10.4500i	1.43987	−	0.596413i	0.480103	−	0.877212i	$-0.340599\pi$
$307$	25.2285	−	10.4500i	1.43987	−	0.596413i	0.959767	+	0.280799i	$0.0905994\pi$
$308$	1.09991	−	0.556716i	0.0626734	−	0.0317219i
$309$	−0.284576	+	0.687026i	−0.0161889	+	0.0390836i
$310$	7.21447	+	12.1421i	0.409754	+	0.689626i
$311$	−10.6381	−	2.85046i	−0.603229	−	0.161635i	−0.0557369	−	0.998445i	$-0.517751\pi$
$311$	−10.6381	−	2.85046i	−0.603229	−	0.161635i	−0.547492	+	0.836811i	$0.684417\pi$
$312$	−0.182560	−	0.129488i	−0.0103354	−	0.00733080i
$313$	−29.2455	+	7.83631i	−1.65305	+	0.442935i	−0.960466	−	0.278398i	$-0.910196\pi$
$313$	−29.2455	+	7.83631i	−1.65305	+	0.442935i	−0.692589	+	0.721333i	$0.743530\pi$
$314$	24.8306	−	6.98773i	1.40127	−	0.394340i
$315$	−13.4838	+	19.5540i	−0.759728	+	1.10174i
$316$	6.91150	−	28.6452i	0.388802	−	1.61142i
$317$	7.58993	+	0.999233i	0.426293	+	0.0561225i	0.340621	−	0.940201i	$-0.389363\pi$
$317$	7.58993	+	0.999233i	0.426293	+	0.0561225i	0.0856723	+	0.996323i	$0.472696\pi$
$318$	−0.131102	+	0.0562376i	−0.00735182	+	0.00315365i
$319$	0.917235	+	1.58870i	0.0513553	+	0.0889500i
$320$	−24.1138	−	1.34613i	−1.34800	−	0.0752512i
$321$	−3.27741			−0.182927
$322$	10.8412	+	3.70574i	0.604158	+	0.206513i
$323$	−7.95875	−	19.2141i	−0.442837	−	1.06910i
$324$	−12.7014	−	12.0806i	−0.705633	−	0.671146i
$325$	−0.262307	−	1.99242i	−0.0145502	−	0.110520i
$326$	−8.59292	−	8.38036i	−0.475918	−	0.464145i
$327$	−0.0196657	+	0.00526942i	−0.00108752	+	0.000291399i
$328$	12.7196	+	27.7150i	0.702321	+	1.53030i
$329$	4.32869	−	8.46304i	0.238648	−	0.466583i
$330$	0.0788095	−	0.140537i	0.00433832	−	0.00773632i
$331$	8.93651	+	11.6463i	0.491195	+	0.640138i	0.971521	−	0.236952i	$-0.0761484\pi$
$331$	8.93651	+	11.6463i	0.491195	+	0.640138i	−0.480326	+	0.877090i	$0.659482\pi$
$332$	7.04050	+	8.71451i	0.386398	+	0.478271i
$333$	10.3772	+	7.96271i	0.568667	+	0.436354i
$334$	3.23408	+	22.3946i	0.176961	+	1.22538i
$335$			5.63128i			0.307670i
$336$	−1.71359	−	0.0514271i	−0.0934840	−	0.00280558i
$337$		−	14.5309i		−	0.791549i	−0.918348	−	0.395775i	$-0.870476\pi$
$337$		−	14.5309i		−	0.791549i	0.918348	−	0.395775i	$-0.129524\pi$
$338$	17.8620	−	2.57951i	0.971565	−	0.140307i
$339$	1.19147	+	0.914251i	0.0647120	+	0.0496553i
$340$	35.7240	+	3.79576i	1.93741	+	0.205854i
$341$	0.469176	+	0.611442i	0.0254073	+	0.0331114i
$342$	−12.8214	−	7.18989i	−0.693301	−	0.388785i
$343$	−2.81204	−	18.3055i	−0.151836	−	0.988406i
$344$	18.9333	+	17.5616i	1.02081	+	0.946860i
$345$	1.44644	−	0.387571i	0.0778735	−	0.0208661i
$346$	−5.15907	+	5.28992i	−0.277353	+	0.284388i
$347$	−1.77627	−	13.4921i	−0.0953550	−	0.724293i	−0.970615	−	0.240640i	$-0.922643\pi$
$347$	−1.77627	−	13.4921i	−0.0953550	−	0.724293i	0.875260	−	0.483653i	$-0.160690\pi$
$348$	−0.0638843	−	2.55030i	−0.00342456	−	0.136711i
$349$	−3.47085	−	8.37938i	−0.185791	−	0.448538i	0.803351	−	0.595506i	$-0.203048\pi$
$349$	−3.47085	−	8.37938i	−0.185791	−	0.448538i	−0.989141	+	0.146968i	$0.953048\pi$
$350$	−10.1246	−	11.5944i	−0.541182	−	0.619745i
$351$	0.472717			0.0252318
$352$	−1.31531	+	0.0824611i	−0.0701064	+	0.00439519i
$353$	9.37055	+	16.2303i	0.498744	+	0.863850i	0.999999	−	0.00144971i	$-0.000461456\pi$
$353$	9.37055	+	16.2303i	0.498744	+	0.863850i	−0.501255	+	0.865300i	$0.667128\pi$
$354$	−0.998859	−	2.32855i	−0.0530887	−	0.123761i
$355$	−25.9748	−	3.41965i	−1.37860	−	0.181496i
$356$	11.8925	+	19.4564i	0.630303	+	1.03119i
$357$	2.54193	+	0.204023i	0.134533	+	0.0107980i
$358$	8.39574	+	29.8339i	0.443729	+	1.57677i
$359$	15.7063	−	4.20850i	0.828949	−	0.222116i	0.180694	−	0.983539i	$-0.442166\pi$
$359$	15.7063	−	4.20850i	0.828949	−	0.222116i	0.648255	+	0.761423i	$0.275499\pi$
$360$	21.4980	−	13.5131i	1.13305	−	0.712204i
$361$	6.55151	+	1.75547i	0.344816	+	0.0923932i
$362$	24.9223	−	14.8081i	1.30989	−	0.778295i
$363$	−0.678543	+	1.63815i	−0.0356143	+	0.0859805i
$364$	−1.92558	+	1.72445i	−0.100928	+	0.0903858i
$365$	15.4428	−	6.39662i	0.808314	−	0.334815i
$366$	0.311566	−	0.0449944i	0.0162858	−	0.00235189i
$367$	6.66599	−	3.84861i	0.347962	−	0.200896i	−0.315825	−	0.948817i	$-0.602281\pi$
$367$	6.66599	−	3.84861i	0.347962	−	0.200896i	0.663787	+	0.747921i	$0.268948\pi$
$368$	−9.08351	−	8.21626i	−0.473511	−	0.428302i
$369$	−27.7658	−	16.0306i	−1.44543	−	0.834521i
$370$	−14.7541	+	11.6176i	−0.767031	+	0.603973i
$371$	0.297720	+	1.62038i	0.0154569	+	0.0841259i
$372$	−0.166461	−	1.05877i	−0.00863062	−	0.0548949i
$373$	−1.06282	−	1.38509i	−0.0550306	−	0.0717173i	0.765027	−	0.643998i	$-0.222725\pi$
$373$	−1.06282	−	1.38509i	−0.0550306	−	0.0717173i	−0.820058	+	0.572281i	$0.806059\pi$
$374$	1.96021	−	0.0245475i	0.101360	−	0.00126932i
$375$	0.418581	+	0.112158i	0.0216154	+	0.00579184i
$376$	−7.82414	+	6.48476i	−0.403499	+	0.334426i
$377$	−2.71988	−	2.71988i	−0.140081	−	0.140081i
$378$	3.01484	−	2.00523i	0.155067	−	0.103138i
$379$	3.51689	+	1.45674i	0.180651	+	0.0748279i	0.471175	−	0.882040i	$-0.343830\pi$
$379$	3.51689	+	1.45674i	0.180651	+	0.0748279i	−0.290525	+	0.956867i	$0.593830\pi$
$380$	14.5446	−	15.2920i	0.746123	−	0.784463i
$381$	1.78316	−	2.32386i	0.0913542	−	0.119055i
$382$	−9.05770	+	3.88540i	−0.463432	+	0.198795i
$383$	−9.64891	+	16.7124i	−0.493036	+	0.853964i	−0.999968	−	0.00802254i	$-0.997446\pi$
$383$	−9.64891	+	16.7124i	−0.493036	+	0.853964i	0.506932	+	0.861986i	$0.330780\pi$
$384$	1.66132	+	0.773898i	0.0847788	+	0.0394928i
$385$	−1.38093	−	1.24728i	−0.0703789	−	0.0635674i
$386$	0.631757	−	5.31185i	0.0321556	−	0.270366i
$387$	−26.9186	−	3.54391i	−1.36835	−	0.180147i
$388$	−7.24628	−	24.5654i	−0.367874	−	1.24712i
$389$	1.95362	+	14.8392i	0.0990526	+	0.752379i	0.966829	+	0.255424i	$0.0822151\pi$
$389$	1.95362	+	14.8392i	0.0990526	+	0.752379i	−0.867777	+	0.496955i	$0.834452\pi$
$390$	−0.0833481	+	0.327405i	−0.00422050	+	0.0165788i
$391$	12.8828	+	12.8828i	0.651513	+	0.651513i
$392$	−4.96576	+	19.1661i	−0.250809	+	0.968037i
$393$	2.30144	−	2.30144i	0.116092	−	0.116092i
$394$	1.68468	+	2.83536i	0.0848732	+	0.142844i
$395$	−44.0990	+	5.80574i	−2.21886	+	0.292119i
$396$	1.07781	−	0.870771i	0.0541621	−	0.0437579i
$397$	−1.21571	+	9.23421i	−0.0610146	+	0.463452i	0.933477	+	0.358637i	$0.116758\pi$
$397$	−1.21571	+	9.23421i	−0.0610146	+	0.463452i	−0.994492	+	0.104815i	$0.966575\pi$
$398$	−15.2436	+	12.0030i	−0.764092	+	0.601659i
$399$	1.00413	−	1.11172i	0.0502693	−	0.0556558i
$400$	5.04949	+	15.6617i	0.252474	+	0.783083i
$401$	17.6143	+	10.1696i	0.879614	+	0.507845i	0.870531	−	0.492114i	$-0.163776\pi$
$401$	17.6143	+	10.1696i	0.879614	+	0.507845i	0.00908270	+	0.999959i	$0.497109\pi$
$402$	0.158576	−	0.396818i	0.00790904	−	0.0197915i
$403$	−1.28206	−	0.983762i	−0.0638641	−	0.0490047i
$404$	9.01488	−	4.00142i	0.448507	−	0.199078i
$405$	−10.1256	+	24.4453i	−0.503143	+	1.21470i
$406$	−28.8841	−	5.80906i	−1.43349	−	0.288299i
$407$	−0.724601	+	0.724601i	−0.0359171	+	0.0359171i
$408$	−2.41047	−	1.27346i	−0.119336	−	0.0630455i
$409$	3.61472	−	13.4903i	0.178736	−	0.667053i	−0.817149	−	0.576427i	$-0.804446\pi$
$409$	3.61472	−	13.4903i	0.178736	−	0.667053i	0.995885	−	0.0906262i	$-0.0288868\pi$
$410$	32.1380	−	32.9532i	1.58718	−	1.62744i
$411$	1.43705	−	1.10269i	0.0708847	−	0.0543917i
$412$	−4.78822	−	7.83362i	−0.235899	−	0.385935i
$413$	−28.7802	+	5.28793i	−1.41618	+	0.260202i
$414$	12.7874	+	1.52085i	0.628464	+	0.0747455i
$415$	8.45538	−	14.6452i	0.415058	−	0.718902i
$416$	2.61921	−	0.880817i	0.128417	−	0.0431856i
$417$	0.0257742	+	0.0446422i	0.00126217	+	0.00218614i
$418$	0.689568	−	0.922350i	0.0337279	−	0.0451136i
$419$	−2.03515	−	4.91330i	−0.0994238	−	0.240030i	0.866339	−	0.499456i	$-0.166467\pi$
$419$	−2.03515	−	4.91330i	−0.0994238	−	0.240030i	−0.965763	+	0.259426i	$0.916467\pi$
$420$	0.857255	+	2.44164i	0.0418297	+	0.119140i
$421$	−10.8099	−	4.47759i	−0.526840	−	0.218224i	0.103378	−	0.994642i	$-0.467035\pi$
$421$	−10.8099	−	4.47759i	−0.526840	−	0.218224i	−0.630219	+	0.776418i	$0.717035\pi$
$422$	16.0845	+	4.09466i	0.782980	+	0.199325i
$423$	2.76530	−	10.3202i	0.134454	−	0.501788i
$424$	0.391630	−	1.71716i	0.0190192	−	0.0833928i
$425$	−6.33526	−	23.6435i	−0.307305	−	1.14688i
$426$	1.73407	+	0.972418i	0.0840158	+	0.0471138i
$427$	0.290867	−	3.62392i	0.0140760	−	0.175374i
$428$	23.8212	−	32.7089i	1.15144	−	1.58105i
$429$	−0.00240634	+	0.0182780i	−0.000116179	+	0.000882469i
$430$	14.4650	−	36.1971i	0.697565	−	1.74558i
$431$	−27.1575	+	15.6794i	−1.30813	+	0.755249i	−0.981784	−	0.190002i	$-0.939151\pi$
$431$	−27.1575	+	15.6794i	−1.30813	+	0.755249i	−0.326345	+	0.945251i	$0.605817\pi$
$432$	−3.80758	+	0.696753i	−0.183192	+	0.0335225i
$433$		−	4.63344i		−	0.222669i	−0.993783	−	0.111334i	$-0.964488\pi$
$433$		−	4.63344i		−	0.222669i	0.993783	−	0.111334i	$-0.0355125\pi$
$434$	−12.3496	−	0.835726i	−0.592802	−	0.0401161i
$435$	−3.55767	+	1.47363i	−0.170577	+	0.0706553i
$436$	0.0903472	−	0.234566i	0.00432685	−	0.0112337i
$437$	10.6113	−	1.39700i	0.507606	−	0.0668276i
$438$	−1.26833	+	0.0158832i	−0.0606034	+	0.000758929i
$439$	3.72032	+	13.8844i	0.177561	+	0.662667i	0.996101	+	0.0882174i	$0.0281170\pi$
$439$	3.72032	+	13.8844i	0.177561	+	0.662667i	−0.818540	+	0.574449i	$0.805216\pi$
$440$	0.829766	+	1.80800i	0.0395576	+	0.0861928i
$441$	−7.39956	−	19.4568i	−0.352360	−	0.926512i
$442$	−3.95678	+	1.11350i	−0.188205	+	0.0529639i
$443$	0.221361	−	0.169856i	0.0105172	−	0.00807011i	−0.603489	−	0.797371i	$-0.706223\pi$
$443$	0.221361	−	0.169856i	0.0105172	−	0.00807011i	0.614007	+	0.789301i	$0.289557\pi$
$444$	1.36683	−	0.403185i	0.0648668	−	0.0191343i
$445$	20.9538	−	27.3076i	0.993308	−	1.29450i
$446$	−20.9886	−	15.6915i	−0.993841	−	0.743016i
$447$	−3.49319			−0.165222
$448$	12.9681	−	16.7280i	0.612687	−	0.790325i
$449$	11.2365			0.530282			0.265141	−	0.964210i	$-0.414581\pi$
$449$	11.2365			0.530282			0.265141	+	0.964210i	$0.414581\pi$
$450$	−13.8567	−	10.3595i	−0.653209	−	0.488352i
$451$	1.52907	−	1.99272i	0.0720012	−	0.0938337i
$452$	−17.7843	+	5.24600i	−0.836505	+	0.246751i
$453$	0.217421	−	0.166833i	0.0102153	−	0.00783851i
$454$	−28.6853	+	8.07252i	−1.34627	+	0.378862i
$455$	3.47375	+	1.77676i	0.162852	+	0.0832956i
$456$	−1.45553	+	0.668006i	−0.0681615	+	0.0312822i
$457$	5.41106	+	20.1943i	0.253118	+	0.944651i	0.969128	+	0.246560i	$0.0793003\pi$
$457$	5.41106	+	20.1943i	0.253118	+	0.944651i	−0.716009	+	0.698091i	$0.754033\pi$
$458$	−4.72811	+	0.0592096i	−0.220930	+	0.00276668i
$459$	5.70855	−	0.751545i	0.266452	−	0.0350791i
$460$	−6.64513	+	17.2526i	−0.309831	+	0.804406i
$461$	−5.18938	+	2.14951i	−0.241693	+	0.100113i	−0.500242	−	0.865886i	$-0.666756\pi$
$461$	−5.18938	+	2.14951i	−0.241693	+	0.100113i	0.258549	+	0.965998i	$0.416756\pi$
$462$	0.0621868	+	0.126779i	0.00289319	+	0.00589829i
$463$			27.0975i			1.25933i	0.776867	+	0.629664i	$0.216808\pi$
$463$			27.0975i			1.25933i	−0.776867	+	0.629664i	$0.783192\pi$
$464$	25.9167	+	17.8988i	1.20315	+	0.830932i
$465$	−1.40106	+	0.808905i	−0.0649728	+	0.0375121i
$466$	0.0642856	−	0.160868i	0.00297797	−	0.00745205i
$467$	3.44943	−	26.2010i	0.159621	−	1.21244i	−0.704703	−	0.709503i	$-0.748920\pi$
$467$	3.44943	−	26.2010i	0.159621	−	1.21244i	0.864323	−	0.502937i	$-0.167747\pi$
$468$	−1.71038	+	2.34852i	−0.0790624	+	0.108561i
$469$	−4.06288	−	2.80163i	−0.187606	−	0.129367i
$470$	13.3793	+	7.50274i	0.617140	+	0.346075i
$471$	0.764735	+	2.85403i	0.0352371	+	0.131507i
$472$	30.4992	+	6.95590i	1.40384	+	0.320171i
$473$	0.550530	−	2.05461i	0.0253134	−	0.0944709i
$474$	3.27100	+	0.832706i	0.150242	+	0.0382475i
$475$	−13.2848	−	5.50276i	−0.609550	−	0.252484i
$476$	−20.5117	+	23.8859i	−0.940154	+	1.09481i
$477$	0.708635	+	1.71080i	0.0324462	+	0.0783320i
$478$	−12.7967	+	17.1166i	−0.585307	+	0.782893i
$479$	19.7905	+	34.2781i	0.904249	+	1.56621i	0.821922	+	0.569600i	$0.192902\pi$
$479$	19.7905	+	34.2781i	0.904249	+	1.56621i	0.0823266	+	0.996605i	$0.473765\pi$
$480$	0.188769	−	2.75998i	0.00861608	−	0.125975i
$481$	1.07433	−	1.86080i	0.0489853	−	0.0848450i
$482$	−12.5252	−	1.48966i	−0.570505	−	0.0678522i
$483$	−0.439993	+	1.23640i	−0.0200204	+	0.0562583i
$484$	−11.4170	−	18.6785i	−0.518957	−	0.849023i
$485$	−30.6711	+	23.5348i	−1.39270	+	1.06866i
$486$	4.26841	−	4.37667i	0.193619	−	0.198530i
$487$	−3.97491	+	14.8346i	−0.180120	+	0.672218i	0.815502	+	0.578754i	$0.196461\pi$
$487$	−3.97491	+	14.8346i	−0.180120	+	0.672218i	−0.995623	+	0.0934643i	$0.970206\pi$
$488$	−1.81551	+	3.43650i	−0.0821843	+	0.155563i
$489$	0.972183	−	0.972183i	0.0439636	−	0.0439636i
$490$	29.6913	−	3.40374i	1.34132	−	0.153765i
$491$	−4.56826	+	11.0288i	−0.206163	+	0.497721i	−0.992813	−	0.119678i	$-0.961814\pi$
$491$	−4.56826	+	11.0288i	−0.206163	+	0.497721i	0.786650	+	0.617399i	$0.211814\pi$
$492$	−3.19262	+	1.41710i	−0.143934	+	0.0638880i
$493$	−37.1696	−	28.5212i	−1.67403	−	1.28453i
$494$	−0.896061	+	2.24229i	−0.0403157	+	0.100886i
$495$	−1.81132	−	1.04576i	−0.0814126	−	0.0470036i
$496$	11.7766	+	6.03420i	0.528784	+	0.270943i
$497$	15.3900	−	17.0391i	0.690337	−	0.764309i
$498$	−1.00823	+	0.793896i	−0.0451798	+	0.0355753i
$499$	−5.33596	+	40.5306i	−0.238870	+	1.81440i	0.280503	+	0.959853i	$0.409499\pi$
$499$	−5.33596	+	40.5306i	−0.238870	+	1.81440i	−0.519373	+	0.854547i	$0.673835\pi$
$500$	−4.16173	+	3.36229i	−0.186118	+	0.150366i
$501$	−2.56964	+	0.338299i	−0.114803	+	0.0151141i
$502$	9.52019	+	16.0227i	0.424907	+	0.715128i
$503$	22.4030	−	22.4030i	0.998901	−	0.998901i	−0.00109823	−	0.999999i	$-0.500350\pi$
$503$	22.4030	−	22.4030i	0.998901	−	0.998901i	0.999999	+	0.00109823i	$0.000349579\pi$
$504$	−0.946038	+	22.2335i	−0.0421399	+	0.990357i
$505$	−10.5273	−	10.5273i	−0.468459	−	0.468459i
$506$	−0.248889	+	0.977678i	−0.0110645	+	0.0434631i
$507$	0.269829	+	2.04955i	0.0119835	+	0.0910239i
$508$	10.2318	+	34.6867i	0.453965	+	1.53897i
$509$	42.8553	+	5.64201i	1.89953	+	0.250078i	0.987213	−	0.159407i	$-0.0509582\pi$
$509$	42.8553	+	5.64201i	1.89953	+	0.250078i	0.912317	+	0.409485i	$0.134291\pi$
$510$	−0.485994	+	4.08626i	−0.0215202	+	0.180943i
$511$	−3.06793	+	14.3242i	−0.135717	+	0.633664i
$512$	−19.7986	+	10.9552i	−0.874981	+	0.484157i
$513$	1.69122	−	2.92928i	0.0746692	−	0.129331i
$514$	−9.01802	+	3.86838i	−0.397768	+	0.170627i
$515$	−8.43653	+	10.9947i	−0.371758	+	0.484484i
$516$	−2.03861	+	2.14336i	−0.0897447	+	0.0943563i
$517$	0.773325	+	0.320322i	0.0340108	+	0.0140877i
$518$	−1.04159	−	16.4248i	−0.0457647	−	0.721665i
$519$	−0.598490	−	0.598490i	−0.0262708	−	0.0262708i
$520$	−2.66174	−	3.21150i	−0.116725	−	0.140834i
$521$	3.63378	+	0.973669i	0.159199	+	0.0426572i	0.337538	−	0.941312i	$-0.390406\pi$
$521$	3.63378	+	0.973669i	0.159199	+	0.0426572i	−0.178339	+	0.983969i	$0.557072\pi$
$522$	−33.1125	+	0.414664i	−1.44929	+	0.0181493i
$523$	2.23284	+	2.90989i	0.0976351	+	0.127241i	0.839616	−	0.543181i	$-0.182780\pi$
$523$	2.23284	+	2.90989i	0.0976351	+	0.127241i	−0.741981	+	0.670421i	$0.766113\pi$
$524$	6.24107	+	39.6962i	0.272642	+	1.73414i
$525$	1.34250	−	1.14301i	0.0585915	−	0.0498849i
$526$	22.6150	−	17.8074i	0.986059	−	0.776439i
$527$	−17.0463	−	9.84167i	−0.742547	−	0.428710i
$528$	−0.00755822	−	0.150770i	−0.000328929	−	0.00656141i
$529$	11.7987	−	6.81197i	0.512986	−	0.296173i
$530$	−2.63125	+	0.379988i	−0.114294	+	0.0165056i
$531$	−30.3862	+	12.5864i	−1.31865	+	0.546201i
$532$	3.79682	+	18.1017i	0.164613	+	0.784807i
$533$	−2.01546	+	4.86576i	−0.0872994	+	0.210759i
$534$	−2.24553	+	1.33422i	−0.0971735	+	0.0577375i
$535$	−58.9974	−	15.8083i	−2.55068	−	0.683453i
$536$	2.80772	+	4.46680i	0.121275	+	0.192936i
$537$	−3.42911	+	0.918828i	−0.147977	+	0.0396504i
$538$	−1.56112	−	5.54737i	−0.0673047	−	0.239164i
$539$	1.58693	−	0.375783i	0.0683538	−	0.0161861i
$540$	3.04721	+	4.98529i	0.131131	+	0.214533i
$541$	−5.35839	−	0.705446i	−0.230375	−	0.0303295i	0.0144547	−	0.999896i	$-0.495399\pi$
$541$	−5.35839	−	0.705446i	−0.230375	−	0.0303295i	−0.244830	+	0.969566i	$0.578732\pi$
$542$	−4.98802	−	11.6281i	−0.214254	−	0.499471i
$543$	1.66032	+	2.87576i	0.0712512	+	0.123411i
$544$	30.2293	−	14.8009i	1.29607	−	0.634584i
$545$	−0.379424			−0.0162527
$546$	−0.194751	−	0.223022i	−0.00833457	−	0.00954448i
$547$	3.07158	+	7.41545i	0.131331	+	0.317062i	0.975842	−	0.218477i	$-0.0701087\pi$
$547$	3.07158	+	7.41545i	0.131331	+	0.317062i	−0.844511	+	0.535538i	$0.820109\pi$
$548$	0.560028	+	22.3567i	0.0239232	+	0.955029i
$549$	−0.533369	−	4.05134i	−0.0227636	−	0.172907i
$550$	0.946348	−	0.970351i	0.0403524	−	0.0413759i
$551$	−26.5851	+	7.12344i	−1.13256	+	0.303469i
$552$	0.954091	−	1.02861i	0.0406088	−	0.0437805i
$553$	17.7510	−	34.7052i	0.754851	−	1.47581i
$554$	−28.8215	−	16.1623i	−1.22451	−	0.686670i
$555$	−1.30948	−	1.70655i	−0.0555845	−	0.0724391i
$556$	−0.632869	−	0.0672438i	−0.0268396	−	0.00285177i
$557$	−0.232128	−	0.178118i	−0.00983559	−	0.00754711i	0.603832	−	0.797112i	$-0.293640\pi$
$557$	−0.232128	−	0.178118i	−0.00983559	−	0.00754711i	−0.613668	+	0.789565i	$0.710306\pi$
$558$	−13.7696	+	1.98851i	−0.582913	+	0.0841806i
$559$			4.46005i			0.188640i
$560$	−30.5987	−	9.19111i	−1.29303	−	0.388395i
$561$			0.224551i			0.00948057i
$562$	−3.97220	−	27.5058i	−0.167557	−	1.16026i
$563$	−15.0810	−	11.5721i	−0.635590	−	0.487705i	0.239992	−	0.970775i	$-0.422855\pi$
$563$	−15.0810	−	11.5721i	−0.635590	−	0.487705i	−0.875582	+	0.483070i	$0.839522\pi$
$564$	−0.731520	−	0.905452i	−0.0308025	−	0.0381264i
$565$	17.0382	+	22.2046i	0.716803	+	0.934155i
$566$	7.05216	−	12.5758i	0.296424	−	0.528599i
$567$	−12.5993	−	19.4673i	−0.529121	−	0.817549i
$568$	−22.3086	+	10.2384i	−0.936047	+	0.429592i
$569$	−3.27356	+	0.877147i	−0.137235	+	0.0367719i	−0.326783	−	0.945100i	$-0.605964\pi$
$569$	−3.27356	+	0.877147i	−0.137235	+	0.0367719i	0.189548	+	0.981871i	$0.439298\pi$
$570$	1.73063	+	1.68782i	0.0724882	+	0.0706951i
$571$	−3.74504	−	28.4464i	−0.156725	−	1.19045i	−0.871251	−	0.490837i	$-0.836691\pi$
$571$	−3.74504	−	28.4464i	−0.156725	−	1.19045i	0.714526	−	0.699609i	$-0.246642\pi$
$572$	−0.164926	−	0.156866i	−0.00689592	−	0.00655888i
$573$	−0.432029	−	1.04301i	−0.0180483	−	0.0435724i
$574$	7.78613	+	39.5817i	0.324987	+	1.65211i
$575$	12.5969			0.525325
$576$	10.3150	−	21.4376i	0.429791	−	0.893231i
$577$	2.58997	+	4.48596i	0.107822	+	0.186753i	0.914888	−	0.403709i	$-0.132279\pi$
$577$	2.58997	+	4.48596i	0.107822	+	0.186753i	−0.807066	+	0.590462i	$0.798946\pi$
$578$	−23.9173	+	10.2596i	−0.994829	+	0.426743i
$579$	0.607495	+	0.0799782i	0.0252466	+	0.00332378i
$580$	11.1512	−	46.2167i	0.463027	−	1.91905i
$581$	6.35960	+	13.3866i	0.263840	+	0.555369i
$582$	2.82403	−	0.794729i	0.117060	−	0.0329426i
$583$	−0.140129	+	0.0375474i	−0.00580354	+	0.00155505i
$584$	9.06013	−	12.7736i	0.374911	−	0.528574i
$585$	4.23606	+	1.13505i	0.175139	+	0.0469284i
$586$	8.29240	+	13.9563i	0.342556	+	0.576529i
$587$	11.2647	−	27.1953i	0.464942	−	1.12247i	−0.501402	−	0.865215i	$-0.667182\pi$
$587$	11.2647	−	27.1953i	0.464942	−	1.12247i	0.966344	−	0.257255i	$-0.0828179\pi$
$588$	−2.18810	−	0.596252i	−0.0902358	−	0.0245890i
$589$	−10.6828	+	4.42498i	−0.440179	+	0.182328i
$590$	−6.74912	−	46.7347i	−0.277857	−	1.92404i
$591$	−0.327169	+	0.188891i	−0.0134579	+	0.00776995i
$592$	−5.91069	+	16.5716i	−0.242928	+	0.681088i
$593$	22.2794	+	12.8630i	0.914906	+	0.528221i	0.882006	−	0.471238i	$-0.156193\pi$
$593$	22.2794	+	12.8630i	0.914906	+	0.528221i	0.0328994	+	0.999459i	$0.489526\pi$
$594$	0.197245	+	0.250496i	0.00809305	+	0.0102780i
$595$	44.7739	+	15.9335i	1.83555	+	0.653209i
$596$	25.3895	−	34.8624i	1.04000	−	1.42802i
$597$	−1.35292	−	1.76316i	−0.0553715	−	0.0721615i
$598$	−0.0264884	−	2.11520i	−0.00108319	−	0.0864970i
$599$	34.2524	+	9.17789i	1.39951	+	0.374998i	0.878170	−	0.478349i	$-0.158764\pi$
$599$	34.2524	+	9.17789i	1.39951	+	0.374998i	0.521343	+	0.853347i	$0.325431\pi$
$600$	−1.80107	+	0.555887i	−0.0735286	+	0.0226940i
$601$	23.2564	+	23.2564i	0.948647	+	0.948647i	0.998744	−	0.0500977i	$-0.0159533\pi$
$601$	23.2564	+	23.2564i	0.948647	+	0.948647i	−0.0500977	+	0.998744i	$0.515953\pi$
$602$	18.9191	+	28.4448i	0.771087	+	1.15932i
$603$	−5.12479	−	2.12276i	−0.208698	−	0.0864454i
$604$	0.0847302	+	3.38248i	0.00344762	+	0.137631i
$605$	−20.1161	+	26.2158i	−0.817835	+	1.06582i
$606$	0.445379	+	1.03827i	0.0180923	+	0.0421770i
$607$	−8.39340	+	14.5378i	−0.340678	+	0.590071i	−0.984559	−	0.175055i	$-0.943990\pi$
$607$	−8.39340	+	14.5378i	−0.340678	+	0.590071i	0.643881	+	0.765126i	$0.277323\pi$
$608$	3.91248	−	19.3817i	0.158672	−	0.786030i
$609$	0.706779	−	3.29995i	0.0286401	−	0.133721i
$610$	5.82560	+	0.692859i	0.235872	+	0.0280531i
$611$	−1.74008	−	0.229086i	−0.0703962	−	0.00926783i
$612$	−16.9208	+	31.0801i	−0.683984	+	1.25634i
$613$	−2.68416	−	20.3882i	−0.108412	−	0.823472i	−0.956113	−	0.292998i	$-0.905347\pi$
$613$	−2.68416	−	20.3882i	−0.108412	−	0.823472i	0.847701	−	0.530475i	$-0.177986\pi$
$614$	−37.4245	−	9.52724i	−1.51033	−	0.384488i
$615$	3.72825	+	3.72825i	0.150337	+	0.150337i
$616$	−1.71726	−	0.300837i	−0.0691904	−	0.0121211i
$617$	−1.22886	+	1.22886i	−0.0494719	+	0.0494719i	−0.731410	−	0.681938i	$-0.761137\pi$
$617$	−1.22886	+	1.22886i	−0.0494719	+	0.0494719i	0.681938	+	0.731410i	$0.261137\pi$
$618$	0.904104	−	0.537190i	0.0363684	−	0.0216090i
$619$	11.2272	−	1.47809i	0.451260	−	0.0594095i	0.0985287	−	0.995134i	$-0.468586\pi$
$619$	11.2272	−	1.47809i	0.451260	−	0.0594095i	0.352731	+	0.935725i	$0.385253\pi$
$620$	2.11040	−	19.8622i	0.0847558	−	0.797684i
$621$	−0.386766	+	2.93778i	−0.0155204	+	0.117889i
$622$	9.63557	+	12.2369i	0.386351	+	0.490657i
$623$	9.27720	+	28.7037i	0.371683	+	1.14999i
$624$	0.0971290	+	0.301258i	0.00388827	+	0.0120600i
$625$	24.8076	+	14.3227i	0.992305	+	0.572908i
$626$	39.7611	+	15.8893i	1.58917	+	0.635062i
$627$	0.104654	+	0.0803037i	0.00417947	+	0.00320702i
$628$	−34.0419	−	13.1118i	−1.35842	−	0.523219i
$629$	10.0153	−	24.1791i	0.399336	−	0.964083i
$630$	31.8310	−	10.7300i	1.26818	−	0.427494i
$631$	−16.3051	+	16.3051i	−0.649097	+	0.649097i	−0.952775	−	0.303678i	$-0.901785\pi$
$631$	−16.3051	+	16.3051i	−0.649097	+	0.649097i	0.303678	+	0.952775i	$0.401785\pi$
$632$	−32.0852	+	26.5926i	−1.27628	+	1.05780i
$633$	−0.492059	+	1.83639i	−0.0195576	+	0.0729899i
$634$	−7.75068	−	7.55896i	−0.307819	−	0.300205i
$635$	43.3081	−	33.2315i	1.71863	−	1.31875i
$636$	0.196116	+	0.0473189i	0.00777651	+	0.00187632i
$637$	−3.01013	+	1.62230i	−0.119266	+	0.0642777i
$638$	0.306394	−	2.57618i	0.0121302	−	0.101992i
$639$	12.9035	−	22.3496i	0.510455	−	0.884135i
$640$	26.1729	+	21.9443i	1.03458	+	0.867427i
$641$	−3.07925	−	5.33342i	−0.121623	−	0.210657i	0.798785	−	0.601617i	$-0.205477\pi$
$641$	−3.07925	−	5.33342i	−0.121623	−	0.210657i	−0.920408	+	0.390959i	$0.872143\pi$
$642$	3.71220	+	2.77532i	0.146509	+	0.109533i
$643$	5.12564	+	12.3744i	0.202135	+	0.487998i	0.992145	−	0.125097i	$-0.0399242\pi$
$643$	5.12564	+	12.3744i	0.202135	+	0.487998i	−0.790009	+	0.613095i	$0.789924\pi$
$644$	−9.14144	−	13.3777i	−0.360223	−	0.527157i
$645$	4.12515	+	1.70869i	0.162427	+	0.0672797i
$646$	−7.25597	+	28.5026i	−0.285482	+	1.12142i
$647$	−3.27222	+	12.2121i	−0.128644	+	0.480106i	−0.999943	−	0.0106459i	$-0.996611\pi$
$647$	−3.27222	+	12.2121i	−0.128644	+	0.480106i	0.871299	+	0.490752i	$0.163278\pi$
$648$	4.15652	+	24.4388i	0.163284	+	0.960049i
$649$	−0.666894	−	2.48888i	−0.0261779	−	0.0976972i
$650$	−1.39008	+	2.47886i	−0.0545234	+	0.0972290i
$651$	0.113435	−	1.41329i	0.00444585	−	0.0553911i
$652$	2.63638	+	16.7686i	0.103248	+	0.656710i
$653$	2.34048	−	17.7777i	0.0915902	−	0.695697i	−0.882625	−	0.470077i	$-0.844226\pi$
$653$	2.34048	−	17.7777i	0.0915902	−	0.695697i	0.974215	−	0.225620i	$-0.0724406\pi$
$654$	0.0267368	+	0.0106845i	0.00104549	+	0.000417797i
$655$	52.5296	−	30.3280i	2.05250	−	1.18501i
$656$	9.06208	−	42.1627i	0.353815	−	1.64618i
$657$			16.4651i			0.642366i
$658$	−12.0695	+	5.92024i	−0.470517	+	0.230795i
$659$	−24.0460	+	9.96017i	−0.936699	+	0.387993i	−0.798216	−	0.602372i	$-0.794223\pi$
$659$	−24.0460	+	9.96017i	−0.936699	+	0.387993i	−0.138483	+	0.990365i	$0.544223\pi$
$660$	−0.208272	+	0.0924454i	−0.00810697	+	0.00359843i
$661$	24.2116	−	3.18752i	0.941723	−	0.123980i	0.355995	−	0.934488i	$-0.384142\pi$
$661$	24.2116	−	3.18752i	0.941723	−	0.123980i	0.585728	+	0.810508i	$0.300809\pi$
$662$	−0.259960	−	20.7588i	−0.0101036	−	0.806813i
$663$	−0.121861	−	0.454793i	−0.00473271	−	0.0176627i
$664$	−0.595055	−	15.8325i	−0.0230926	−	0.614421i
$665$	23.4379	−	15.1691i	0.908881	−	0.588232i
$666$	−5.01104	−	17.8065i	−0.194174	−	0.689988i
$667$	19.1285	−	14.6778i	0.740660	−	0.568328i
$668$	15.3007	−	28.1041i	0.592000	−	1.08738i
$669$	1.82736	−	2.38146i	0.0706498	−	0.0920726i
$670$	4.76858	−	6.37834i	0.184226	−	0.246417i
$671$	0.320133			0.0123586
$672$	1.89737	+	1.50932i	0.0731927	+	0.0582233i
$673$	−21.0532			−0.811541			−0.405770	−	0.913975i	$-0.632997\pi$
$673$	−21.0532			−0.811541			−0.405770	+	0.913975i	$0.632997\pi$
$674$	−12.3048	+	16.4586i	−0.473963	+	0.633963i
$675$	2.42348	−	3.15835i	0.0932799	−	0.121565i
$676$	−22.4160	−	12.2039i	−0.862153	−	0.469379i
$677$	7.37913	−	5.66220i	0.283603	−	0.217616i	−0.457157	−	0.889386i	$-0.651132\pi$
$677$	7.37913	−	5.66220i	0.283603	−	0.217616i	0.740760	+	0.671770i	$0.234466\pi$
$678$	−0.575351	−	2.04448i	−0.0220962	−	0.0785178i
$679$	−1.72072	−	33.8376i	−0.0660351	−	1.29857i
$680$	−37.2490	−	34.5505i	−1.42844	−	1.32495i
$681$	−0.883455	−	3.29710i	−0.0338541	−	0.126345i
$682$	−0.0136482	−	1.08986i	−0.000522615	−	0.0417328i
$683$	24.9846	−	3.28929i	0.956010	−	0.125861i	0.363651	−	0.931535i	$-0.381530\pi$
$683$	24.9846	−	3.28929i	0.956010	−	0.125861i	0.592359	+	0.805674i	$0.298197\pi$
$684$	8.43391	+	19.0009i	0.322478	+	0.726517i
$685$	31.1875	−	12.9183i	1.19161	−	0.493582i
$686$	−12.3161	+	23.1152i	−0.470230	+	0.882544i
$687$		−	0.541627i		−	0.0206643i
$688$	−6.57380	−	35.9242i	−0.250624	−	1.36960i
$689$	0.263432	−	0.152093i	0.0100360	−	0.00579426i
$690$	−1.96652	−	0.785857i	−0.0748642	−	0.0299170i
$691$	2.07939	−	15.7945i	0.0791037	−	0.600852i	−0.905280	−	0.424816i	$-0.860339\pi$
$691$	2.07939	−	15.7945i	0.0791037	−	0.600852i	0.984384	−	0.176037i	$-0.0563277\pi$
$692$	10.3230	−	1.62299i	0.392422	−	0.0616968i
$693$	1.65565	−	0.786556i	0.0628931	−	0.0298788i
$694$	−9.41321	+	16.7861i	−0.357321	+	0.637193i
$695$	0.248639	+	0.927933i	0.00943142	+	0.0351985i
$696$	−2.08724	+	2.94273i	−0.0791167	+	0.111544i
$697$	−16.6030	+	61.9633i	−0.628884	+	2.34703i
$698$	−3.16437	+	12.4301i	−0.119773	+	0.470488i
$699$	0.0183330	+	0.00759379i	0.000693419	+	0.000287223i
$700$	1.64963	+	21.7060i	0.0623502	+	0.820411i
$701$	3.98717	+	9.62588i	0.150593	+	0.363564i	0.981116	−	0.193420i	$-0.0619581\pi$
$701$	3.98717	+	9.62588i	0.150593	+	0.363564i	−0.830523	+	0.556985i	$0.811958\pi$
$702$	−0.535429	−	0.400298i	−0.0202085	−	0.0151083i
$703$	−7.68718	−	13.3146i	−0.289927	−	0.502169i
$704$	1.55964	+	1.02041i	0.0587810	+	0.0384581i
$705$	−0.878528	+	1.52166i	−0.0330873	+	0.0573088i
$706$	3.13014	−	26.3184i	0.117805	−	0.990507i
$707$	12.8328	−	2.35782i	0.482626	−	0.0886751i
$708$	−0.840450	+	3.48330i	−0.0315861	+	0.130910i
$709$	−38.9595	+	29.8946i	−1.46315	+	1.12272i	−0.496062	+	0.868287i	$0.665221\pi$
$709$	−38.9595	+	29.8946i	−1.46315	+	1.12272i	−0.967091	+	0.254430i	$0.918112\pi$
$710$	26.5250	+	25.8689i	0.995465	+	0.970841i
$711$	11.3399	−	42.3212i	0.425280	−	1.58717i
$712$	3.00548	−	32.1082i	0.112635	−	1.20330i
$713$	7.16272	−	7.16272i	0.268246	−	0.268246i
$714$	−2.70639	−	2.38360i	−0.101284	−	0.0892041i
$715$	−0.131479	+	0.317419i	−0.00491705	+	0.0118708i
$716$	15.7538	−	40.9013i	0.588749	−	1.52855i
$717$	−1.94212	−	1.49024i	−0.0725297	−	0.0556540i
$718$	−21.3538	−	8.53334i	−0.796915	−	0.318461i
$719$	20.4741	+	11.8207i	0.763553	+	0.440838i	0.830570	−	0.556914i	$-0.188015\pi$
$719$	20.4741	+	11.8207i	0.763553	+	0.440838i	−0.0670168	+	0.997752i	$0.521348\pi$
$720$	−35.7930	−	2.89877i	−1.33393	−	0.108031i
$721$	−3.73523	−	11.5568i	−0.139107	−	0.430399i
$722$	−5.93412	−	7.53619i	−0.220845	−	0.280468i
$723$	0.188586	−	1.43245i	0.00701358	−	0.0532735i
$724$	−40.7681	−	4.33171i	−1.51514	−	0.160987i
$725$	−32.1163	+	4.22819i	−1.19277	+	0.157031i
$726$	2.15575	−	1.28088i	0.0800073	−	0.0475379i
$727$	23.1640	−	23.1640i	0.859107	−	0.859107i	−0.132126	−	0.991233i	$-0.542180\pi$
$727$	23.1640	−	23.1640i	0.859107	−	0.859107i	0.991233	+	0.132126i	$0.0421804\pi$
$728$	3.64130	−	0.322641i	0.134956	−	0.0119579i
$729$	−18.0972	−	18.0972i	−0.670266	−	0.670266i
$730$	−22.9082	−	5.83179i	−0.847870	−	0.215844i
$731$	7.09076	+	53.8597i	0.262261	+	1.99207i
$732$	−0.391001	−	0.212871i	−0.0144518	−	0.00786795i
$733$	31.0005	+	4.08130i	1.14503	+	0.150746i	0.679080	−	0.734064i	$-0.262379\pi$
$733$	31.0005	+	4.08130i	1.14503	+	0.150746i	0.465951	+	0.884811i	$0.345712\pi$
$734$	−10.8093	−	1.28559i	−0.398980	−	0.0474521i
$735$	0.347265	+	3.40563i	0.0128091	+	0.125618i
$736$	3.33102	+	16.9982i	0.122783	+	0.626561i
$737$	0.217286	−	0.376350i	0.00800382	−	0.0138630i
$738$	17.8746	+	41.6695i	0.657973	+	1.53387i
$739$	−18.8048	+	24.5069i	−0.691746	+	0.901501i	−0.998739	−	0.0502111i	$-0.984011\pi$
$739$	−18.8048	+	24.5069i	−0.691746	+	0.901501i	0.306993	+	0.951712i	$0.400677\pi$
$740$	26.5493	−	0.665053i	0.975972	−	0.0244478i
$741$	−0.255540	−	0.105848i	−0.00938748	−	0.00388842i
$742$	1.03492	−	2.08746i	0.0379933	−	0.0766329i
$743$	−11.1632	−	11.1632i	−0.409537	−	0.409537i	0.472040	−	0.881577i	$-0.343518\pi$
$743$	−11.1632	−	11.1632i	−0.409537	−	0.409537i	−0.881577	+	0.472040i	$0.843518\pi$
$744$	−0.708028	+	1.34020i	−0.0259576	+	0.0491339i
$745$	−62.8816	−	16.8491i	−2.30380	−	0.617303i
$746$	0.0309170	+	2.46884i	0.00113195	+	0.0903906i
$747$	10.1406	+	13.2155i	0.371026	+	0.483530i
$748$	−2.24105	−	1.63211i	−0.0819409	−	0.0596758i
$749$	40.7574	−	34.7009i	1.48924	−	1.26794i
$750$	−0.379136	−	0.481493i	−0.0138441	−	0.0175816i
$751$	21.7475	+	12.5559i	0.793578	+	0.458172i	0.841221	−	0.540692i	$-0.181838\pi$
$751$	21.7475	+	12.5559i	0.793578	+	0.458172i	−0.0476427	+	0.998864i	$0.515171\pi$
$752$	14.3534	−	0.719550i	0.523416	−	0.0262393i
$753$	−1.84884	+	1.06743i	−0.0673755	+	0.0388993i
$754$	0.777510	+	5.38391i	0.0283152	+	0.196071i
$755$	4.71856	−	1.95449i	0.171726	−	0.0711312i
$756$	−5.11283	−	0.281730i	−0.185952	−	0.0102464i
$757$	13.2979	−	32.1039i	0.483320	−	1.16684i	−0.474703	−	0.880146i	$-0.657445\pi$
$757$	13.2979	−	32.1039i	0.483320	−	1.16684i	0.958023	−	0.286691i	$-0.0925554\pi$
$758$	−2.74988	−	4.62811i	−0.0998801	−	0.168101i
$759$	−0.111623	−	0.0299093i	−0.00405165	−	0.00108564i
$760$	−29.4234	+	5.00429i	−1.06730	+	0.181525i
$761$	−41.3619	+	11.0829i	−1.49937	+	0.401754i	−0.912888	−	0.408209i	$-0.866153\pi$
$761$	−41.3619	+	11.0829i	−1.49937	+	0.401754i	−0.586480	+	0.809964i	$0.699487\pi$
$762$	−3.98757	+	1.12217i	−0.144455	+	0.0406519i
$763$	0.188768	−	0.273749i	0.00683387	−	0.00991037i
$764$	13.5495	+	3.26922i	0.490203	+	0.118276i
$765$	52.9593	+	6.97223i	1.91475	+	0.252081i
$766$	25.0811	−	10.7588i	0.906215	−	0.388732i
$767$	2.70138	+	4.67892i	0.0975410	+	0.168946i
$768$	−1.22638	−	2.28337i	−0.0442530	−	0.0823941i
$769$	−38.3304			−1.38223			−0.691115	−	0.722744i	$-0.742880\pi$
$769$	−38.3304			−1.38223			−0.691115	+	0.722744i	$0.742880\pi$
$770$	0.507931	+	2.58213i	0.0183046	+	0.0930534i
$771$	−0.430136	−	1.03844i	−0.0154910	−	0.0373986i
$772$	−5.21365	+	5.48156i	−0.187643	+	0.197286i
$773$	−0.563016	−	4.27653i	−0.0202503	−	0.153816i	0.978332	−	0.207041i	$-0.0663834\pi$
$773$	−0.563016	−	4.27653i	−0.0202503	−	0.153816i	−0.998583	+	0.0532248i	$0.983050\pi$
$774$	27.4888	+	26.8088i	0.988064	+	0.963623i
$775$	−13.1455	+	3.52234i	−0.472202	+	0.126526i
$776$	−12.5945	+	33.9605i	−0.452115	+	1.21911i
$777$	1.88274	−	0.0957413i	0.0675428	−	0.00343470i
$778$	10.3531	−	18.4622i	0.371176	−	0.661901i
$779$	22.9409	+	29.8972i	0.821944	+	1.07118i
$780$	0.371652	−	0.300260i	0.0133073	−	0.0107510i
$781$	1.60400	+	1.23079i	0.0573957	+	0.0440413i
$782$	−3.68271	−	25.5011i	−0.131693	−	0.911919i
$783$		−	7.61984i		−	0.272311i
$784$	21.8545	−	17.5038i	0.780517	−	0.625135i
$785$			55.0647i			1.96534i
$786$	−4.55562	+	0.657894i	−0.162494	+	0.0234663i
$787$	0.788933	+	0.605370i	0.0281224	+	0.0215791i	0.622727	−	0.782439i	$-0.286025\pi$
$787$	0.788933	+	0.605370i	0.0281224	+	0.0215791i	−0.594605	+	0.804018i	$0.702691\pi$
$788$	0.492810	−	4.63811i	0.0175556	−	0.165226i
$789$	2.00716	+	2.61578i	0.0714568	+	0.0931243i
$790$	54.8656	+	30.7672i	1.95203	+	1.09465i
$791$	−24.4970	+	1.24573i	−0.871013	+	0.0442930i
$792$	−1.95817	+	0.0735966i	−0.0695805	+	0.00261514i
$793$	−0.648378	+	0.173732i	−0.0230246	+	0.00616942i
$794$	9.19653	−	9.42979i	0.326373	−	0.334651i
$795$	−0.0397484	−	0.301919i	−0.00140973	−	0.0107080i
$796$	27.4301	−	0.687115i	0.972233	−	0.0243541i
$797$	−14.9969	−	36.2057i	−0.531217	−	1.28247i	−0.930718	−	0.365738i	$-0.880817\pi$
$797$	−14.9969	−	36.2057i	−0.531217	−	1.28247i	0.399501	−	0.916733i	$-0.369183\pi$
$798$	−2.07875	+	0.408912i	−0.0735870	+	0.0144753i
$799$	−21.3775			−0.756282
$800$	7.54295	−	22.0153i	0.266683	−	0.778358i
$801$	16.9528	+	29.3631i	0.598997	+	1.03749i
$802$	−11.3394	−	26.4345i	−0.400408	−	0.933435i
$803$	−1.27889	−	0.168369i	−0.0451311	−	0.00594163i
$804$	−0.515639	+	0.315179i	−0.0181852	+	0.0111155i
$805$	−13.8841	+	20.1345i	−0.489350	+	0.709648i
$806$	0.619095	+	2.19993i	0.0218067	+	0.0774891i
$807$	0.637616	−	0.170849i	0.0224451	−	0.00601416i
$808$	−13.5992	−	3.10155i	−0.478420	−	0.109112i
$809$	−36.8846	−	9.88320i	−1.29679	−	0.347475i	−0.456557	−	0.889694i	$-0.650917\pi$
$809$	−36.8846	−	9.88320i	−1.29679	−	0.347475i	−0.840237	+	0.542219i	$0.817584\pi$
$810$	32.1692	−	19.1139i	1.13031	−	0.671595i
$811$	7.47857	−	18.0549i	0.262608	−	0.633992i	−0.736490	−	0.676448i	$-0.763518\pi$
$811$	7.47857	−	18.0549i	0.262608	−	0.633992i	0.999098	+	0.0424563i	$0.0135183\pi$
$812$	27.7968	+	31.0388i	0.975477	+	1.08925i
$813$	1.33900	−	0.554633i	0.0469608	−	0.0194518i
$814$	1.43432	−	0.207136i	0.0502730	−	0.00726010i
$815$	22.1897	−	12.8113i	0.777273	−	0.448759i
$816$	1.65189	+	3.48359i	0.0578276	+	0.121950i
$817$	27.6375	+	15.9565i	0.966913	+	0.558248i
$818$	−15.5179	+	12.2190i	−0.542570	+	0.427229i
$819$	−2.92641	+	2.49155i	−0.102257	+	0.0870618i
$820$	−64.3064	+	10.1103i	−2.24568	+	0.353067i
$821$	−13.4648	−	17.5476i	−0.469923	−	0.612416i	0.496917	−	0.867798i	$-0.334465\pi$
$821$	−13.4648	−	17.5476i	−0.469923	−	0.612416i	−0.966840	+	0.255382i	$0.917799\pi$
$822$	−2.56146	+	0.0320769i	−0.0893412	+	0.00111881i
$823$	−22.3965	−	6.00112i	−0.780692	−	0.209186i	−0.153602	−	0.988133i	$-0.549088\pi$
$823$	−22.3965	−	6.00112i	−0.780692	−	0.209186i	−0.627090	+	0.778947i	$0.715754\pi$
$824$	−1.21008	+	12.9275i	−0.0421552	+	0.450352i
$825$	0.109783	+	0.109783i	0.00382216	+	0.00382216i
$826$	37.0761	+	18.3817i	1.29004	+	0.639581i
$827$	19.4156	+	8.04219i	0.675145	+	0.279654i	0.693796	−	0.720172i	$-0.255937\pi$
$827$	19.4156	+	8.04219i	0.675145	+	0.279654i	−0.0186507	+	0.999826i	$0.505937\pi$
$828$	−13.1959	−	12.5510i	−0.458590	−	0.436176i
$829$	−30.2212	+	39.3851i	−1.04963	+	1.36790i	−0.122792	+	0.992432i	$0.539185\pi$
$829$	−30.2212	+	39.3851i	−1.04963	+	1.36790i	−0.926835	+	0.375468i	$0.877482\pi$
$830$	−21.9786	+	9.42800i	−0.762890	+	0.327250i
$831$	1.89251	−	3.27793i	0.0656506	−	0.113710i
$832$	−3.71256	−	1.22028i	−0.128710	−	0.0423056i
$833$	−33.7713	+	24.3766i	−1.17011	+	0.844597i
$834$	0.00860962	−	0.0723902i	0.000298127	−	0.00250667i
$835$	−47.8884	−	6.30463i	−1.65725	−	0.218181i
$836$	−1.56210	+	0.460785i	−0.0540262	+	0.0159366i
$837$	−0.417851	−	3.17389i	−0.0144430	−	0.109706i
$838$	−1.85544	+	7.28849i	−0.0640953	+	0.251777i
$839$	−13.7408	−	13.7408i	−0.474384	−	0.474384i	0.428946	−	0.903330i	$-0.358885\pi$
$839$	−13.7408	−	13.7408i	−0.474384	−	0.474384i	−0.903330	+	0.428946i	$0.858885\pi$
$840$	1.09661	−	3.49148i	0.0378365	−	0.120468i
$841$	−23.3363	+	23.3363i	−0.804701	+	0.804701i
$842$	8.45230	+	14.2254i	0.291285	+	0.490240i
$843$	3.15611	−	0.415510i	0.108702	−	0.0143109i
$844$	−14.7509	−	18.2582i	−0.507748	−	0.628475i
$845$	−5.02860	+	38.1960i	−0.172989	+	1.31398i
$846$	−11.8714	+	9.34770i	−0.408146	+	0.321381i
$847$	−8.90629	−	27.5561i	−0.306024	−	0.946840i
$848$	−1.89768	+	1.61333i	−0.0651667	+	0.0554021i
$849$	1.43027	+	0.825768i	0.0490868	+	0.0283403i
$850$	−12.8457	+	32.1449i	−0.440602	+	1.10256i
$851$	10.6853	+	8.19908i	0.366286	+	0.281061i
$852$	−1.14067	−	2.56983i	−0.0390787	−	0.0880411i
$853$	5.39464	−	13.0238i	0.184709	−	0.445927i	−0.804217	−	0.594336i	$-0.797415\pi$
$853$	5.39464	−	13.0238i	0.184709	−	0.445927i	0.988926	+	0.148409i	$0.0474151\pi$
$854$	−3.39820	+	3.85838i	−0.116284	+	0.132031i
$855$	22.1887	−	22.1887i	0.758837	−	0.758837i
$856$	−54.6794	+	16.8764i	−1.86890	+	0.576822i
$857$	6.96695	−	26.0010i	0.237986	−	0.888177i	−0.738793	−	0.673932i	$-0.764604\pi$
$857$	6.96695	−	26.0010i	0.237986	−	0.888177i	0.976780	−	0.214245i	$-0.0687292\pi$
$858$	0.0182034	−	0.0186651i	0.000621454	−	0.000637216i
$859$	34.0759	−	26.1473i	1.16265	−	0.892136i	0.167064	−	0.985946i	$-0.446571\pi$
$859$	34.0759	−	26.1473i	1.16265	−	0.892136i	0.995590	+	0.0938102i	$0.0299047\pi$
$860$	−47.0358	+	28.7501i	−1.60391	+	0.980372i
$861$	−4.54472	+	0.835024i	−0.154884	+	0.0284575i
$862$	44.0376	+	5.23755i	1.49993	+	0.178392i
$863$	−21.5957	+	37.4049i	−0.735128	+	1.27328i	0.219540	+	0.975604i	$0.429544\pi$
$863$	−21.5957	+	37.4049i	−0.735128	+	1.27328i	−0.954667	+	0.297675i	$0.903789\pi$
$864$	4.90271	+	2.43508i	0.166794	+	0.0828430i
$865$	−7.88679	−	13.6603i	−0.268159	−	0.464465i
$866$	−3.92360	+	5.24812i	−0.133329	+	0.178339i
$867$	−1.14079	−	2.75412i	−0.0387434	−	0.0935349i
$868$	13.2803	+	11.4043i	0.450763	+	0.387087i
$869$	3.17124	+	1.31357i	0.107577	+	0.0445599i
$870$	5.27751	+	1.34351i	0.178924	+	0.0455492i
$871$	−0.235837	+	0.880156i	−0.00799103	+	0.0298229i
$872$	−0.300964	+	0.189178i	−0.0101919	+	0.00640638i
$873$	−9.85629	−	36.7842i	−0.333585	−	1.24496i
$874$	−13.2020	−	7.40332i	−0.446564	−	0.250421i
$875$	−6.39294	+	3.03711i	−0.216121	+	0.102673i
$876$	1.45005	+	1.05604i	0.0489925	+	0.0356802i
$877$	5.37481	−	40.8257i	0.181494	−	1.37859i	−0.621880	−	0.783113i	$-0.713631\pi$
$877$	5.37481	−	40.8257i	0.181494	−	1.37859i	0.803374	−	0.595475i	$-0.203036\pi$
$878$	7.54348	−	18.8767i	0.254580	−	0.637059i
$879$	−1.61040	+	0.929765i	−0.0543174	+	0.0313602i
$880$	0.591168	−	2.75050i	0.0199283	−	0.0927193i
$881$			19.2734i			0.649336i	0.945828	+	0.324668i	$0.105253\pi$
$881$			19.2734i			0.649336i	−0.945828	+	0.324668i	$0.894747\pi$
$882$	−8.09480	+	28.3039i	−0.272566	+	0.953042i
$883$	6.38390	−	2.64430i	0.214835	−	0.0889877i	−0.272670	−	0.962108i	$-0.587907\pi$
$883$	6.38390	−	2.64430i	0.214835	−	0.0889877i	0.487506	+	0.873120i	$0.337907\pi$
$884$	5.42461	+	2.08938i	0.182450	+	0.0702736i
$885$	5.36251	−	0.705988i	0.180259	−	0.0237315i
$886$	−0.394562	+	0.00494105i	−0.0132556	+	0.000165998i
$887$	−4.22453	−	15.7662i	−0.141846	−	0.529376i	−0.999876	−	0.0157760i	$-0.994978\pi$
$887$	−4.22453	−	15.7662i	−0.141846	−	0.529376i	0.858030	−	0.513600i	$-0.171689\pi$
$888$	−1.88957	−	0.700759i	−0.0634100	−	0.0235159i
$889$	2.42968	+	47.7792i	0.0814887	+	1.60246i
$890$	−46.8578	+	13.1865i	−1.57068	+	0.442014i
$891$	1.61995	−	1.24303i	0.0542702	−	0.0416430i
$892$	10.4855	+	35.5465i	0.351079	+	1.19018i
$893$	−7.64499	+	9.96314i	−0.255830	+	0.333404i
$894$	3.95660	+	2.95804i	0.132329	+	0.0989315i
$895$	−66.1602			−2.21149
$896$	−28.8539	+	7.96578i	−0.963940	+	0.266118i
$897$	0.242306			0.00809036
$898$	−12.7271	−	9.51507i	−0.424710	−	0.317522i
$899$	−15.8575	+	20.6659i	−0.528877	+	0.689246i
$900$	6.92247	+	23.4677i	0.230749	+	0.782256i
$901$	2.93941	−	2.25549i	0.0979260	−	0.0751413i
$902$	−3.41937	+	0.962266i	−0.113852	+	0.0320399i
$903$	−3.28511	+	2.12613i	−0.109322	+	0.0707533i
$904$	24.5860	+	9.11786i	0.817718	+	0.303255i
$905$	16.0168	+	59.7756i	0.532417	+	1.98701i
$906$	−0.387540	+	0.00485312i	−0.0128751	+	0.000161234i
$907$	−23.0781	+	3.03828i	−0.766294	+	0.100885i	−0.503533	−	0.863976i	$-0.667967\pi$
$907$	−23.0781	+	3.03828i	−0.766294	+	0.100885i	−0.262762	+	0.964861i	$0.584633\pi$
$908$	39.3267	+	15.1473i	1.30510	+	0.502682i
$909$	13.5488	−	5.61211i	0.449386	−	0.186142i
$910$	−2.43003	−	4.95404i	−0.0805545	−	0.164225i
$911$		−	12.7058i		−	0.420962i	−0.977598	−	0.210481i	$-0.932497\pi$
$911$		−	12.7058i		−	0.420962i	0.977598	−	0.210481i	$-0.0675030\pi$
$912$	2.21430	+	0.475922i	0.0733227	+	0.0157593i
$913$	−1.13018	+	0.652511i	−0.0374036	+	0.0215950i
$914$	10.9717	−	27.4555i	0.362911	−	0.908146i
$915$	−0.0877136	+	0.666251i	−0.00289972	+	0.0220256i
$916$	5.40550	+	3.93671i	0.178603	+	0.130073i
$917$	−4.25296	+	52.9879i	−0.140445	+	1.74981i
$918$	−7.10228	−	3.98276i	−0.234410	−	0.131451i
$919$	3.34706	+	12.4914i	0.110409	+	0.412053i	0.998903	−	0.0468366i	$-0.0149140\pi$
$919$	3.34706	+	12.4914i	0.110409	+	0.412053i	−0.888493	+	0.458890i	$0.848247\pi$
$920$	22.1362	−	13.9143i	0.729809	−	0.458739i
$921$	1.14490	−	4.27281i	0.0377256	−	0.140794i
$922$	7.69803	+	1.95970i	0.253521	+	0.0645394i
$923$	−3.91659	−	1.62231i	−0.128916	−	0.0533988i
$924$	0.0369199	−	0.196258i	0.00121458	−	0.00645640i
$925$	−6.92468	−	16.7176i	−0.227682	−	0.549673i
$926$	22.9462	−	30.6924i	0.754060	−	1.00861i
$927$	−6.82560	−	11.8223i	−0.224182	−	0.388295i
$928$	−14.1981	−	42.2196i	−0.466075	−	1.38593i
$929$	13.8912	−	24.0602i	0.455755	−	0.789391i	−0.542976	−	0.839748i	$-0.682703\pi$
$929$	13.8912	−	24.0602i	0.455755	−	0.789391i	0.998731	+	0.0503574i	$0.0160360\pi$
$930$	2.27192	+	0.270207i	0.0744991	+	0.00886044i
$931$	−0.716371	+	24.4569i	−0.0234781	+	0.801541i
$932$	−0.209037	+	0.127772i	−0.00684723	+	0.00418530i
$933$	−1.41540	+	1.08607i	−0.0463381	+	0.0355564i
$934$	−26.0941	+	26.7560i	−0.853826	+	0.875482i
$935$	−1.08310	+	4.04220i	−0.0354213	+	0.132194i
$936$	3.92602	−	1.21173i	0.128326	−	0.0396068i
$937$	24.3942	−	24.3942i	0.796923	−	0.796923i	−0.185686	−	0.982609i	$-0.559451\pi$
$937$	24.3942	−	24.3942i	0.796923	−	0.796923i	0.982609	+	0.185686i	$0.0594508\pi$
$938$	2.22945	+	6.61376i	0.0727941	+	0.215947i
$939$	−1.87693	+	4.53131i	−0.0612513	+	0.147874i
$940$	−8.80088	−	19.8277i	−0.287053	−	0.646707i
$941$	−28.2381	−	21.6679i	−0.920535	−	0.706352i	0.0355722	−	0.999367i	$-0.488675\pi$
$941$	−28.2381	−	21.6679i	−0.920535	−	0.706352i	−0.956108	+	0.293015i	$0.905341\pi$
$942$	1.55061	−	3.88024i	0.0505216	−	0.126425i
$943$	−28.5901	−	16.5065i	−0.931021	−	0.537525i
$944$	−28.6551	−	33.7055i	−0.932643	−	1.09702i
$945$	2.37709	+	7.35472i	0.0773266	+	0.239249i
$946$	−2.36341	+	1.86099i	−0.0768411	+	0.0605059i
$947$	−0.335878	+	2.55125i	−0.0109146	+	0.0829044i	−0.996035	−	0.0889598i	$-0.971646\pi$
$947$	−0.335878	+	2.55125i	−0.0109146	+	0.0829044i	0.985121	+	0.171864i	$0.0549791\pi$
$948$	−2.99981	−	3.71307i	−0.0974293	−	0.120595i
$949$	2.68157	−	0.353035i	0.0870473	−	0.0114600i
$950$	10.3875	+	17.4824i	0.337015	+	0.567204i
$951$	0.876894	−	0.876894i	0.0284353	−	0.0284353i
$952$	43.4595	−	9.68531i	1.40853	−	0.313903i
$953$	13.9233	+	13.9233i	0.451021	+	0.451021i	0.895693	−	0.444672i	$-0.146680\pi$
$953$	13.9233	+	13.9233i	0.451021	+	0.451021i	−0.444672	+	0.895693i	$0.646680\pi$
$954$	0.646061	−	2.53783i	0.0209170	−	0.0821653i
$955$	−2.74618	−	20.8593i	−0.0888644	−	0.674992i
$956$	28.9887	−	8.55105i	0.937561	−	0.276561i
$957$	0.294627	+	0.0387884i	0.00952394	+	0.00125385i
$958$	6.61081	−	55.5841i	0.213586	−	1.79584i
$959$	−6.19582	+	28.9283i	−0.200074	+	0.934143i
$960$	−2.55097	+	2.96628i	−0.0823323	+	0.0957364i
$961$	10.0281	−	17.3692i	0.323488	−	0.560298i
$962$	−2.79258	+	1.19791i	−0.0900365	+	0.0386222i
$963$	36.6261	−	47.7320i	1.18026	−	1.53814i
$964$	12.9253	+	12.2936i	0.416297	+	0.395951i
$965$	10.5499	+	4.36991i	0.339613	+	0.140672i
$966$	1.54535	−	1.02784i	0.0497209	−	0.0330702i
$967$	2.50677	+	2.50677i	0.0806123	+	0.0806123i	0.746263	−	0.665651i	$-0.231846\pi$
$967$	2.50677	+	2.50677i	0.0806123	+	0.0806123i	−0.665651	+	0.746263i	$0.731846\pi$
$968$	−2.88532	+	30.8244i	−0.0927377	+	0.990735i
$969$	−3.25419	−	0.871957i	−0.104540	−	0.0280113i
$970$	54.6694	−	0.684619i	1.75533	−	0.0219818i
$971$	−8.08402	−	10.5353i	−0.259429	−	0.338094i	0.645420	−	0.763828i	$-0.276682\pi$
$971$	−8.08402	−	10.5353i	−0.259429	−	0.338094i	−0.904848	+	0.425734i	$0.860016\pi$
$972$	−8.54085	+	1.34280i	−0.273948	+	0.0430703i
$973$	−0.793191	−	0.282269i	−0.0254285	−	0.00904914i
$974$	17.0642	−	13.4366i	0.546771	−	0.430536i
$975$	−0.281927	−	0.162771i	−0.00902888	−	0.00521283i
$976$	4.96640	−	2.35502i	0.158970	−	0.0753824i
$977$	−2.19706	+	1.26848i	−0.0702903	+	0.0405821i	−0.534733	−	0.845021i	$-0.679588\pi$
$977$	−2.19706	+	1.26848i	−0.0702903	+	0.0405821i	0.464443	+	0.885603i	$0.346255\pi$
$978$	−1.92440	+	0.277910i	−0.0615356	+	0.00888657i
$979$	−2.45407	+	1.01651i	−0.0784323	+	0.0324877i
$980$	−36.5126	−	21.2874i	−1.16635	−	0.680001i
$981$	0.143027	−	0.345298i	0.00456651	−	0.0110245i
$982$	14.5135	−	8.62347i	0.463144	−	0.275186i
$983$	−17.6553	−	4.73072i	−0.563116	−	0.150886i	−0.0339785	−	0.999423i	$-0.510818\pi$
$983$	−17.6553	−	4.73072i	−0.563116	−	0.150886i	−0.529137	+	0.848536i	$0.677484\pi$
$984$	4.81617	+	1.09841i	0.153534	+	0.0350162i
$985$	−6.80055	+	1.82220i	−0.216684	+	0.0580602i
$986$	17.9488	+	63.7802i	0.571606	+	2.03118i
$987$	−0.660772	−	1.39089i	−0.0210326	−	0.0442724i
$988$	2.91371	−	1.78098i	0.0926976	−	0.0566605i
$989$	−27.7177	−	3.64911i	−0.881373	−	0.116035i
$990$	1.16606	+	2.71832i	0.0370597	+	0.0863940i
$991$	10.5563	+	18.2841i	0.335333	+	0.580813i	0.983549	−	0.180643i	$-0.0578180\pi$
$991$	10.5563	+	18.2841i	0.335333	+	0.580813i	−0.648216	+	0.761456i	$0.724485\pi$
$992$	−8.22914	−	16.8072i	−0.261275	−	0.533628i
$993$	2.37801			0.0754640
$994$	−31.8605	+	6.26729i	−1.01055	+	0.198786i
$995$	−15.8498	−	38.2649i	−0.502473	−	1.21308i
$996$	1.81426	−	0.0454466i	0.0574869	−	0.00144003i
$997$	5.88784	+	44.7226i	0.186470	+	1.41638i	0.787087	+	0.616843i	$0.211588\pi$
$997$	5.88784	+	44.7226i	0.186470	+	1.41638i	−0.600617	+	0.799537i	$0.705078\pi$
$998$	40.3653	−	41.3891i	1.27774	−	1.31015i
$999$	4.11143	−	1.10165i	0.130080	−	0.0348548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.37.7	✓	240
4.3	odd	2		896.2.bh.a.625.16		240
7.4	even	3	inner	224.2.bd.a.165.27	yes	240
28.11	odd	6		896.2.bh.a.753.15		240
32.13	even	8	inner	224.2.bd.a.205.27	yes	240
32.19	odd	8		896.2.bh.a.401.15		240
224.109	even	24	inner	224.2.bd.a.109.7	yes	240
224.179	odd	24		896.2.bh.a.529.16		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.7	✓	240	1.1	even	1	trivial
224.2.bd.a.109.7	yes	240	224.109	even	24	inner
224.2.bd.a.165.27	yes	240	7.4	even	3	inner
224.2.bd.a.205.27	yes	240	32.13	even	8	inner
896.2.bh.a.401.15		240	32.19	odd	8
896.2.bh.a.529.16		240	224.179	odd	24
896.2.bh.a.625.16		240	4.3	odd	2
896.2.bh.a.753.15		240	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13266 - 0.846802i) q^{2} +(0.0986144 - 0.128517i) q^{3} +(0.565853 + 1.91828i) q^{4} +(2.39507 - 1.83780i) q^{5} +(-0.220525 + 0.0620594i) q^{6} +(0.134369 + 2.64234i) q^{7} +(0.983485 - 2.65193i) q^{8} +(0.769665 + 2.87243i) q^{9} +O(q^{10})\)	\(q+(-1.13266 - 0.846802i) q^{2} +(0.0986144 - 0.128517i) q^{3} +(0.565853 + 1.91828i) q^{4} +(2.39507 - 1.83780i) q^{5} +(-0.220525 + 0.0620594i) q^{6} +(0.134369 + 2.64234i) q^{7} +(0.983485 - 2.65193i) q^{8} +(0.769665 + 2.87243i) q^{9} +(-4.26906 + 0.0534610i) q^{10} +(-0.230980 + 0.0304091i) q^{11} +(0.302333 + 0.116449i) q^{12} +(0.451311 - 0.186939i) q^{13} +(2.08534 - 3.10666i) q^{14} -0.489041i q^{15} +(-3.35962 + 2.17093i) q^{16} +(5.15284 - 2.97500i) q^{17} +(1.56061 - 3.90525i) q^{18} +(0.456233 - 3.46543i) q^{19} +(4.88068 + 3.55450i) q^{20} +(0.352835 + 0.243304i) q^{21} +(0.287373 + 0.161151i) q^{22} +(0.792513 + 2.95770i) q^{23} +(-0.243832 - 0.387913i) q^{24} +(1.06475 - 3.97371i) q^{25} +(-0.669484 - 0.170432i) q^{26} +(0.894039 + 0.370323i) q^{27} +(-4.99272 + 1.75293i) q^{28} +(-3.01331 - 7.27478i) q^{29} +(-0.414121 + 0.553919i) q^{30} +(-1.65406 - 2.86492i) q^{31} +(5.64367 + 0.385998i) q^{32} +(-0.0188699 + 0.0326836i) q^{33} +(-8.35567 - 0.993769i) q^{34} +(5.17792 + 6.08164i) q^{35} +(-5.07462 + 3.10181i) q^{36} +(3.48959 - 2.67766i) q^{37} +(-3.45129 + 3.53883i) q^{38} +(0.0204809 - 0.0764359i) q^{39} +(-2.51822 - 8.15902i) q^{40} +(-7.62359 + 7.62359i) q^{41} +(-0.193614 - 0.574363i) q^{42} +(-3.49397 + 8.43518i) q^{43} +(-0.189034 - 0.425878i) q^{44} +(7.12236 + 5.46518i) q^{45} +(1.60693 - 4.02118i) q^{46} +(-3.11151 - 1.79643i) q^{47} +(-0.0523058 + 0.645853i) q^{48} +(-6.96389 + 0.710095i) q^{49} +(-4.57095 + 3.59924i) q^{50} +(0.125808 - 0.955605i) q^{51} +(0.613978 + 0.759962i) q^{52} +(0.617371 - 0.0812784i) q^{53} +(-0.699055 - 1.17652i) q^{54} +(-0.497328 + 0.497328i) q^{55} +(7.13945 + 2.24236i) q^{56} +(-0.400375 - 0.400375i) q^{57} +(-2.74723 + 10.7916i) q^{58} +(1.44362 + 10.9654i) q^{59} +(0.938119 - 0.276725i) q^{60} +(-1.36236 - 0.179358i) q^{61} +(-0.552525 + 4.64566i) q^{62} +(-7.48651 + 2.41968i) q^{63} +(-6.06551 - 5.21628i) q^{64} +(0.737364 - 1.27715i) q^{65} +(0.0490498 - 0.0210405i) q^{66} +(-1.13554 + 1.47986i) q^{67} +(8.62264 + 8.20120i) q^{68} +(0.458267 + 0.189821i) q^{69} +(-0.714890 - 11.2731i) q^{70} +(-6.13645 - 6.13645i) q^{71} +(8.37445 + 0.783890i) q^{72} +(5.34815 + 1.43303i) q^{73} +(-6.21998 + 0.0778921i) q^{74} +(-0.405688 - 0.528703i) q^{75} +(6.90584 - 1.08574i) q^{76} +(-0.111388 - 0.606241i) q^{77} +(-0.0879241 + 0.0692329i) q^{78} +(-12.7597 - 7.36679i) q^{79} +(-4.05679 + 11.3739i) q^{80} +(-7.59029 + 4.38226i) q^{81} +(15.0906 - 2.17929i) q^{82} +(5.17520 - 2.14364i) q^{83} +(-0.267073 + 0.814512i) q^{84} +(6.87397 - 16.5952i) q^{85} +(11.1004 - 6.59552i) q^{86} +(-1.23209 - 0.330137i) q^{87} +(-0.146523 + 0.642451i) q^{88} +(11.0131 - 2.95095i) q^{89} +(-3.43931 - 12.2214i) q^{90} +(0.554598 + 1.16740i) q^{91} +(-5.22526 + 3.19389i) q^{92} +(-0.531306 - 0.0699477i) q^{93} +(2.00307 + 4.66958i) q^{94} +(-5.27607 - 9.13843i) q^{95} +(0.606154 - 0.687241i) q^{96} -12.8059 q^{97} +(8.48905 + 5.09274i) q^{98} +(-0.265125 - 0.640069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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