LMFDB - Embedded newform 380.2.d.b.379.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(379,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("380.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.19
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.440015 + 1.34402i) q^{2} +0.562756i q^{3} +(-1.61277 - 1.18278i) q^{4} +(1.40743 - 1.73757i) q^{5} +(-0.756355 - 0.247621i) q^{6} -3.12767 q^{7} +(2.29932 - 1.64716i) q^{8} +2.68331 q^{9} +O(q^{10})$	\(q+(-0.440015 + 1.34402i) q^{2} +0.562756i q^{3} +(-1.61277 - 1.18278i) q^{4} +(1.40743 - 1.73757i) q^{5} +(-0.756355 - 0.247621i) q^{6} -3.12767 q^{7} +(2.29932 - 1.64716i) q^{8} +2.68331 q^{9} +(1.71604 + 2.65617i) q^{10} -3.83819i q^{11} +(0.665615 - 0.907599i) q^{12} +2.34421 q^{13} +(1.37622 - 4.20365i) q^{14} +(0.977829 + 0.792039i) q^{15} +(1.20208 + 3.81510i) q^{16} -0.296420i q^{17} +(-1.18069 + 3.60641i) q^{18} +(4.35567 - 0.167855i) q^{19} +(-4.32502 + 1.13764i) q^{20} -1.76012i q^{21} +(5.15860 + 1.68886i) q^{22} +5.14271 q^{23} +(0.926950 + 1.29396i) q^{24} +(-1.03830 - 4.89101i) q^{25} +(-1.03149 + 3.15066i) q^{26} +3.19832i q^{27} +(5.04423 + 3.69934i) q^{28} -6.81132i q^{29} +(-1.49477 + 0.965712i) q^{30} -4.76184 q^{31} +(-5.65650 - 0.0630825i) q^{32} +2.15997 q^{33} +(0.398394 + 0.130429i) q^{34} +(-4.40197 + 5.43455i) q^{35} +(-4.32756 - 3.17375i) q^{36} +1.81573 q^{37} +(-1.69096 + 5.92796i) q^{38} +1.31922i q^{39} +(0.374068 - 6.31348i) q^{40} +12.0637i q^{41} +(2.36563 + 0.774478i) q^{42} -0.171877 q^{43} +(-4.53972 + 6.19014i) q^{44} +(3.77656 - 4.66243i) q^{45} +(-2.26287 + 6.91190i) q^{46} +6.96079 q^{47} +(-2.14697 + 0.676478i) q^{48} +2.78234 q^{49} +(7.03047 + 0.756623i) q^{50} +0.166812 q^{51} +(-3.78068 - 2.77267i) q^{52} -11.1028 q^{53} +(-4.29860 - 1.40731i) q^{54} +(-6.66913 - 5.40198i) q^{55} +(-7.19152 + 5.15178i) q^{56} +(0.0944615 + 2.45118i) q^{57} +(9.15454 + 2.99708i) q^{58} +7.33191 q^{59} +(-0.640212 - 2.43393i) q^{60} +3.27261 q^{61} +(2.09528 - 6.40000i) q^{62} -8.39250 q^{63} +(2.57373 - 7.57469i) q^{64} +(3.29930 - 4.07322i) q^{65} +(-0.950418 + 2.90304i) q^{66} -9.46955i q^{67} +(-0.350598 + 0.478058i) q^{68} +2.89409i q^{69} +(-5.36721 - 8.30762i) q^{70} -9.45438 q^{71} +(6.16977 - 4.41983i) q^{72} -8.23306i q^{73} +(-0.798946 + 2.44037i) q^{74} +(2.75245 - 0.584309i) q^{75} +(-7.22324 - 4.88107i) q^{76} +12.0046i q^{77} +(-1.77305 - 0.580475i) q^{78} -7.49873 q^{79} +(8.32085 + 3.28078i) q^{80} +6.25004 q^{81} +(-16.2138 - 5.30820i) q^{82} +6.37747 q^{83} +(-2.08183 + 2.83867i) q^{84} +(-0.515050 - 0.417189i) q^{85} +(0.0756284 - 0.231006i) q^{86} +3.83311 q^{87} +(-6.32212 - 8.82523i) q^{88} -3.49224i q^{89} +(4.60465 + 7.12730i) q^{90} -7.33191 q^{91} +(-8.29403 - 6.08267i) q^{92} -2.67975i q^{93} +(-3.06285 + 9.35543i) q^{94} +(5.83862 - 7.80452i) q^{95} +(0.0355001 - 3.18323i) q^{96} -11.9154 q^{97} +(-1.22427 + 3.73952i) q^{98} -10.2990i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.440015	+	1.34402i	−0.311137	+	0.950365i
$2$	−0.440015	+	1.34402i	−0.311137	+	0.950365i
$3$			0.562756i			0.324908i	0.986716	+	0.162454i	$0.0519408\pi$
$3$			0.562756i			0.324908i	−0.986716	+	0.162454i	$0.948059\pi$
$4$	−1.61277	−	1.18278i	−0.806387	−	0.591388i
$5$	1.40743	−	1.73757i	0.629421	−	0.777065i
$5$	1.40743	−	1.73757i	0.629421	−	0.777065i
$6$	−0.756355	−	0.247621i	−0.308781	−	0.101091i
$7$	−3.12767			−1.18215			−0.591075	−	0.806617i	$-0.701296\pi$
$7$	−3.12767			−1.18215			−0.591075	+	0.806617i	$0.701296\pi$
$8$	2.29932	−	1.64716i	0.812932	−	0.582359i
$9$	2.68331			0.894435
$10$	1.71604	+	2.65617i	0.542659	+	0.839953i
$11$		−	3.83819i		−	1.15726i	−0.815591	−	0.578629i	$-0.803588\pi$
$11$		−	3.83819i		−	1.15726i	0.815591	−	0.578629i	$-0.196412\pi$
$12$	0.665615	−	0.907599i	0.192147	−	0.262001i
$13$	2.34421			0.650166			0.325083	−	0.945685i	$-0.394608\pi$
$13$	2.34421			0.650166			0.325083	+	0.945685i	$0.394608\pi$
$14$	1.37622	−	4.20365i	0.367811	−	1.12347i
$15$	0.977829	+	0.792039i	0.252474	+	0.204504i
$16$	1.20208	+	3.81510i	0.300520	+	0.953775i
$17$		−	0.296420i		−	0.0718924i	−0.999354	−	0.0359462i	$-0.988556\pi$
$17$		−	0.296420i		−	0.0718924i	0.999354	−	0.0359462i	$-0.0114445\pi$
$18$	−1.18069	+	3.60641i	−0.278292	+	0.850040i
$19$	4.35567	−	0.167855i	0.999258	−	0.0385086i
$19$	4.35567	−	0.167855i	0.999258	−	0.0385086i
$20$	−4.32502	+	1.13764i	−0.967104	+	0.254383i
$21$		−	1.76012i		−	0.384089i
$22$	5.15860	+	1.68886i	1.09982	+	0.360066i
$23$	5.14271			1.07233			0.536164	−	0.844114i	$-0.319873\pi$
$23$	5.14271			1.07233			0.536164	+	0.844114i	$0.319873\pi$
$24$	0.926950	+	1.29396i	0.189213	+	0.264128i
$25$	−1.03830	−	4.89101i	−0.207660	−	0.978201i
$26$	−1.03149	+	3.15066i	−0.202291	+	0.617895i
$27$			3.19832i			0.615516i
$28$	5.04423	+	3.69934i	0.953270	+	0.699109i
$29$		−	6.81132i		−	1.26483i	−0.774630	−	0.632415i	$-0.782064\pi$
$29$		−	6.81132i		−	1.26483i	0.774630	−	0.632415i	$-0.217936\pi$
$30$	−1.49477	+	0.965712i	−0.272907	+	0.176314i
$31$	−4.76184			−0.855251			−0.427626	−	0.903956i	$-0.640650\pi$
$31$	−4.76184			−0.855251			−0.427626	+	0.903956i	$0.640650\pi$
$32$	−5.65650	−	0.0630825i	−0.999938	−	0.0111515i
$33$	2.15997			0.376002
$34$	0.398394	+	0.130429i	0.0683240	+	0.0223684i
$35$	−4.40197	+	5.43455i	−0.744069	+	0.918607i
$36$	−4.32756	−	3.17375i	−0.721261	−	0.528958i
$37$	1.81573			0.298503			0.149252	−	0.988799i	$-0.452314\pi$
$37$	1.81573			0.298503			0.149252	+	0.988799i	$0.452314\pi$
$38$	−1.69096	+	5.92796i	−0.274309	+	0.961641i
$39$			1.31922i			0.211244i
$40$	0.374068	−	6.31348i	0.0591453	−	0.998249i
$41$			12.0637i			1.88403i	0.335571	+	0.942015i	$0.391071\pi$
$41$			12.0637i			1.88403i	−0.335571	+	0.942015i	$0.608929\pi$
$42$	2.36563	+	0.774478i	0.365025	+	0.119505i
$43$	−0.171877			−0.0262110			−0.0131055	−	0.999914i	$-0.504172\pi$
$43$	−0.171877			−0.0262110			−0.0131055	+	0.999914i	$0.504172\pi$
$44$	−4.53972	+	6.19014i	−0.684389	+	0.933198i
$45$	3.77656	−	4.66243i	0.562976	−	0.695034i
$46$	−2.26287	+	6.91190i	−0.333642	+	1.01910i
$47$	6.96079			1.01534			0.507668	−	0.861553i	$-0.330508\pi$
$47$	6.96079			1.01534			0.507668	+	0.861553i	$0.330508\pi$
$48$	−2.14697	+	0.676478i	−0.309889	+	0.0976412i
$49$	2.78234			0.397477
$50$	7.03047	+	0.756623i	0.994259	+	0.107003i
$51$	0.166812			0.0233584
$52$	−3.78068	−	2.77267i	−0.524285	−	0.384501i
$53$	−11.1028			−1.52508			−0.762542	−	0.646939i	$-0.776049\pi$
$53$	−11.1028			−1.52508			−0.762542	+	0.646939i	$0.776049\pi$
$54$	−4.29860	−	1.40731i	−0.584965	−	0.191510i
$55$	−6.66913	−	5.40198i	−0.899265	−	0.728402i
$56$	−7.19152	+	5.15178i	−0.961007	+	0.688435i
$57$	0.0944615	+	2.45118i	0.0125117	+	0.324667i
$58$	9.15454	+	2.99708i	1.20205	+	0.393536i
$59$	7.33191			0.954534			0.477267	−	0.878758i	$-0.341627\pi$
$59$	7.33191			0.954534			0.477267	+	0.878758i	$0.341627\pi$
$60$	−0.640212	−	2.43393i	−0.0826510	−	0.314219i
$61$	3.27261			0.419015			0.209507	−	0.977807i	$-0.432814\pi$
$61$	3.27261			0.419015			0.209507	+	0.977807i	$0.432814\pi$
$62$	2.09528	−	6.40000i	0.266101	−	0.812801i
$63$	−8.39250			−1.05736
$64$	2.57373	−	7.57469i	0.321716	−	0.946836i
$65$	3.29930	−	4.07322i	0.409228	−	0.505221i
$66$	−0.950418	+	2.90304i	−0.116988	+	0.357339i
$67$		−	9.46955i		−	1.15689i	−0.815722	−	0.578445i	$-0.803660\pi$
$67$		−	9.46955i		−	1.15689i	0.815722	−	0.578445i	$-0.196340\pi$
$68$	−0.350598	+	0.478058i	−0.0425163	+	0.0579731i
$69$			2.89409i			0.348408i
$70$	−5.36721	−	8.30762i	−0.641504	−	0.992950i
$71$	−9.45438			−1.12203			−0.561014	−	0.827806i	$-0.689589\pi$
$71$	−9.45438			−1.12203			−0.561014	+	0.827806i	$0.689589\pi$
$72$	6.16977	−	4.41983i	0.727115	−	0.520882i
$73$		−	8.23306i		−	0.963606i	−0.876279	−	0.481803i	$-0.839982\pi$
$73$		−	8.23306i		−	0.963606i	0.876279	−	0.481803i	$-0.160018\pi$
$74$	−0.798946	+	2.44037i	−0.0928756	+	0.283687i
$75$	2.75245	−	0.584309i	0.317825	−	0.0674702i
$76$	−7.22324	−	4.88107i	−0.828562	−	0.559897i
$77$			12.0046i			1.36805i
$78$	−1.77305	−	0.580475i	−0.200759	−	0.0657259i
$79$	−7.49873			−0.843673			−0.421836	−	0.906672i	$-0.638614\pi$
$79$	−7.49873			−0.843673			−0.421836	+	0.906672i	$0.638614\pi$
$80$	8.32085	+	3.28078i	0.930299	+	0.366802i
$81$	6.25004			0.694449
$82$	−16.2138	−	5.30820i	−1.79052	−	0.586192i
$83$	6.37747			0.700018			0.350009	−	0.936746i	$-0.386179\pi$
$83$	6.37747			0.700018			0.350009	+	0.936746i	$0.386179\pi$
$84$	−2.08183	+	2.83867i	−0.227146	+	0.309725i
$85$	−0.515050	−	0.417189i	−0.0558650	−	0.0452505i
$86$	0.0756284	−	0.231006i	0.00815522	−	0.0249100i
$87$	3.83311			0.410953
$88$	−6.32212	−	8.82523i	−0.673940	−	0.940772i
$89$		−	3.49224i		−	0.370176i	−0.982722	−	0.185088i	$-0.940743\pi$
$89$		−	3.49224i		−	0.370176i	0.982722	−	0.185088i	$-0.0592571\pi$
$90$	4.60465	+	7.12730i	0.485373	+	0.751284i
$91$	−7.33191			−0.768594
$92$	−8.29403	−	6.08267i	−0.864712	−	0.634163i
$93$		−	2.67975i		−	0.277878i
$94$	−3.06285	+	9.35543i	−0.315909	+	0.964939i
$95$	5.83862	−	7.80452i	0.599030	−	0.800727i
$96$	0.0355001	−	3.18323i	0.00362321	−	0.324887i
$97$	−11.9154			−1.20983			−0.604913	−	0.796292i	$-0.706792\pi$
$97$	−11.9154			−1.20983			−0.604913	+	0.796292i	$0.706792\pi$
$98$	−1.22427	+	3.73952i	−0.123670	+	0.377749i
$99$		−	10.2990i		−	1.03509i
$100$	−4.11043	+	9.11616i	−0.411043	+	0.911616i
$101$	−6.01740			−0.598754			−0.299377	−	0.954135i	$-0.596779\pi$
$101$	−6.01740			−0.598754			−0.299377	+	0.954135i	$0.596779\pi$
$102$	−0.0733998	+	0.224199i	−0.00726767	+	0.0221990i
$103$		−	0.989632i		−	0.0975113i	−0.998811	−	0.0487557i	$-0.984474\pi$
$103$		−	0.989632i		−	0.0975113i	0.998811	−	0.0487557i	$-0.0155256\pi$
$104$	5.39008	−	3.86128i	0.528541	−	0.378630i
$105$	−3.05833	−	2.47724i	−0.298462	−	0.241754i
$106$	4.88539	−	14.9223i	0.474511	−	1.44939i
$107$			9.95699i			0.962578i	0.876562	+	0.481289i	$0.159831\pi$
$107$			9.95699i			0.962578i	−0.876562	+	0.481289i	$0.840169\pi$
$108$	3.78289	−	5.15816i	0.364009	−	0.496344i
$109$			13.9205i			1.33334i	0.745351	+	0.666672i	$0.232282\pi$
$109$			13.9205i			1.33334i	−0.745351	+	0.666672i	$0.767718\pi$
$110$	10.1949	−	6.58649i	0.972043	−	0.627997i
$111$			1.02181i			0.0969860i
$112$	−3.75971	−	11.9324i	−0.355260	−	1.12751i
$113$	18.4958			1.73993			0.869967	−	0.493110i	$-0.164140\pi$
$113$	18.4958			1.73993			0.869967	+	0.493110i	$0.164140\pi$
$114$	−3.33600	−	0.951597i	−0.312445	−	0.0891252i
$115$	7.23799	−	8.93581i	0.674946	−	0.833269i
$116$	−8.05627	+	10.9851i	−0.748006	+	1.01994i
$117$	6.29022			0.581531
$118$	−3.22615	+	9.85423i	−0.296991	+	0.907156i
$119$			0.927105i			0.0849875i
$120$	3.55295	+	0.210509i	0.324339	+	0.0192167i
$121$	−3.73173			−0.339248
$122$	−1.44000	+	4.39845i	−0.130371	+	0.398217i
$123$	−6.78891			−0.612136
$124$	7.67977	+	5.63219i	0.689664	+	0.505785i
$125$	−9.95979	−	5.07962i	−0.890831	−	0.454335i
$126$	3.69283	−	11.2797i	0.328983	−	1.00487i
$127$		−	7.85899i		−	0.697372i	−0.937240	−	0.348686i	$-0.886628\pi$
$127$		−	7.85899i		−	0.697372i	0.937240	−	0.348686i	$-0.113372\pi$
$128$	9.04805	+	6.79212i	0.799742	+	0.600344i
$129$		−	0.0967248i		−	0.00851615i
$130$	4.02275	+	6.22660i	0.352818	+	0.546109i
$131$			16.0686i			1.40392i	0.712216	+	0.701960i	$0.247692\pi$
$131$			16.0686i			1.40392i	−0.712216	+	0.701960i	$0.752308\pi$
$132$	−3.48354	−	2.55476i	−0.303203	−	0.222363i
$133$	−13.6231	+	0.524996i	−1.18127	+	0.0455229i
$134$	12.7273	+	4.16674i	1.09947	+	0.359952i
$135$	5.55730	+	4.50140i	0.478296	+	0.387419i
$136$	−0.488251	−	0.681564i	−0.0418672	−	0.0584436i
$137$			18.8105i			1.60709i	0.595247	+	0.803543i	$0.297054\pi$
$137$			18.8105i			1.60709i	−0.595247	+	0.803543i	$0.702946\pi$
$138$	−3.88971	−	1.27344i	−0.331114	−	0.108403i
$139$			15.2280i			1.29162i	0.763498	+	0.645810i	$0.223480\pi$
$139$			15.2280i			1.29162i	−0.763498	+	0.645810i	$0.776520\pi$
$140$	13.5272	−	3.55815i	1.14326	−	0.300719i
$141$			3.91723i			0.329890i
$142$	4.16007	−	12.7069i	0.349105	−	1.06634i
$143$		−	8.99752i		−	0.752410i
$144$	3.22555	+	10.2371i	0.268796	+	0.853090i
$145$	−11.8351	−	9.58644i	−0.982855	−	0.796110i
$146$	11.0654	+	3.62267i	0.915778	+	0.299814i
$147$			1.56578i			0.129143i
$148$	−2.92836	−	2.14760i	−0.240709	−	0.176531i
$149$	−18.8032			−1.54041			−0.770207	−	0.637794i	$-0.779847\pi$
$149$	−18.8032			−1.54041			−0.770207	+	0.637794i	$0.779847\pi$
$150$	−0.425794	+	3.95644i	−0.0347660	+	0.323042i
$151$	−8.71133			−0.708918			−0.354459	−	0.935072i	$-0.615335\pi$
$151$	−8.71133			−0.708918			−0.354459	+	0.935072i	$0.615335\pi$
$152$	9.73858	−	7.56043i	0.789903	−	0.613232i
$153$		−	0.795385i		−	0.0643031i
$154$	−16.1344	−	5.28221i	−1.30015	−	0.425652i
$155$	−6.70194	+	8.27403i	−0.538313	+	0.664586i
$156$	1.56034	−	2.12760i	0.124927	−	0.170344i
$157$			12.8390i			1.02466i	0.858788	+	0.512332i	$0.171218\pi$
$157$			12.8390i			1.02466i	−0.858788	+	0.512332i	$0.828782\pi$
$158$	3.29955	−	10.0784i	0.262498	−	0.801797i
$159$		−	6.24816i		−	0.495511i
$160$	−8.07073	+	9.73978i	−0.638047	+	0.769998i
$161$	−16.0847			−1.26765
$162$	−2.75011	+	8.40018i	−0.216069	+	0.659980i
$163$	−0.411443			−0.0322267			−0.0161133	−	0.999870i	$-0.505129\pi$
$163$	−0.411443			−0.0322267			−0.0161133	+	0.999870i	$0.505129\pi$
$164$	14.2686	−	19.4560i	1.11419	−	1.51926i
$165$	3.04000	−	3.75309i	0.236663	−	0.292178i
$166$	−2.80618	+	8.57144i	−0.217802	+	0.665273i
$167$			1.56210i			0.120879i	0.998172	+	0.0604396i	$0.0192503\pi$
$167$			1.56210i			0.120879i	−0.998172	+	0.0604396i	$0.980750\pi$
$168$	−2.89920	−	4.04707i	−0.223678	−	0.312238i
$169$	−7.50469			−0.577284
$170$	0.787340	−	0.508668i	0.0603862	−	0.0390130i
$171$	11.6876	−	0.450406i	0.893772	−	0.0344434i
$172$	0.277199	+	0.203292i	0.0211362	+	0.0155009i
$173$	11.3997			0.866705			0.433352	−	0.901225i	$-0.357331\pi$
$173$	11.3997			0.866705			0.433352	+	0.901225i	$0.357331\pi$
$174$	−1.68663	+	5.15178i	−0.127863	+	0.390555i
$175$	3.24746	+	15.2975i	0.245485	+	1.15638i
$176$	14.6431	−	4.61382i	1.10377	−	0.347779i
$177$			4.12608i			0.310135i
$178$	4.69363	+	1.53664i	0.351803	+	0.115176i
$179$	8.31107			0.621199			0.310599	−	0.950541i	$-0.399470\pi$
$179$	8.31107			0.621199			0.310599	+	0.950541i	$0.399470\pi$
$180$	−11.6053	+	3.05262i	−0.865011	+	0.227529i
$181$		−	1.46224i		−	0.108687i	−0.998522	−	0.0543437i	$-0.982693\pi$
$181$		−	1.46224i		−	0.108687i	0.998522	−	0.0543437i	$-0.0173067\pi$
$182$	3.22615	−	9.85423i	0.239138	−	0.730444i
$183$			1.84168i			0.136141i
$184$	11.8247	−	8.47086i	0.871730	−	0.624480i
$185$	2.55550	−	3.15495i	0.187884	−	0.231957i
$186$	3.60164	+	1.17913i	0.264085	+	0.0864581i
$187$	−1.13772			−0.0831981
$188$	−11.2262	−	8.23306i	−0.818753	−	0.600457i
$189$		−	10.0033i		−	0.727632i
$190$	7.92034	+	11.2813i	0.574602	+	0.818433i
$191$			4.43480i			0.320891i	0.987045	+	0.160445i	$0.0512930\pi$
$191$			4.43480i			0.320891i	−0.987045	+	0.160445i	$0.948707\pi$
$192$	4.26271	+	1.44838i	0.307634	+	0.104528i
$193$	−6.39281			−0.460164			−0.230082	−	0.973171i	$-0.573899\pi$
$193$	−6.39281			−0.460164			−0.230082	+	0.973171i	$0.573899\pi$
$194$	5.24295	−	16.0145i	0.376422	−	1.14978i
$195$	2.29223	+	1.85670i	0.164150	+	0.132961i
$196$	−4.48729	−	3.29089i	−0.320521	−	0.235063i
$197$			22.3795i			1.59447i	0.603668	+	0.797235i	$0.293705\pi$
$197$			22.3795i			1.59447i	−0.603668	+	0.797235i	$0.706295\pi$
$198$	13.8421	+	4.53173i	0.983716	+	0.322056i
$199$		−	0.591395i		−	0.0419229i	−0.999780	−	0.0209614i	$-0.993327\pi$
$199$		−	0.591395i		−	0.0419229i	0.999780	−	0.0209614i	$-0.00667272\pi$
$200$	−10.4436	−	9.53574i	−0.738477	−	0.674278i
$201$	5.32905			0.375882
$202$	2.64775	−	8.08750i	0.186295	−	0.569035i
$203$			21.3036i			1.49522i
$204$	−0.269030	−	0.197302i	−0.0188359	−	0.0138139i
$205$	20.9615	+	16.9787i	1.46401	+	1.18585i
$206$	1.33008	+	0.435453i	0.0926713	+	0.0303394i
$207$	13.7995			0.959128
$208$	2.81793	+	8.94339i	0.195388	+	0.620112i
$209$	−0.644260	−	16.7179i	−0.0445644	−	1.15640i
$210$	4.67517	−	3.02043i	0.322617	−	0.208430i
$211$	18.8494			1.29765			0.648824	−	0.760938i	$-0.275261\pi$
$211$	18.8494			1.29765			0.648824	+	0.760938i	$0.275261\pi$
$212$	17.9063	+	13.1321i	1.22981	+	0.901916i
$213$		−	5.32052i		−	0.364556i
$214$	−13.3824	−	4.38122i	−0.914801	−	0.299494i
$215$	−0.241904	+	0.298648i	−0.0164977	+	0.0203676i
$216$	5.26814	+	7.35395i	0.358451	+	0.500373i
$217$	14.8935			1.01103
$218$	−18.7094	−	6.12523i	−1.26716	−	0.414853i
$219$	4.63321			0.313083
$220$	4.36647	+	16.6003i	0.294387	+	1.11919i
$221$		−	0.694870i		−	0.0467420i
$222$	−1.37333	−	0.449612i	−0.0921721	−	0.0301760i
$223$		−	15.5731i		−	1.04285i	−0.853296	−	0.521427i	$-0.825400\pi$
$223$		−	15.5731i		−	1.04285i	0.853296	−	0.521427i	$-0.174600\pi$
$224$	17.6917	+	0.197302i	1.18208	+	0.0131828i
$225$	−2.78607	−	13.1241i	−0.185738	−	0.874937i
$226$	−8.13840	+	24.8586i	−0.541359	+	1.65357i
$227$			23.0220i			1.52803i	0.645201	+	0.764013i	$0.276773\pi$
$227$			23.0220i			1.52803i	−0.645201	+	0.764013i	$0.723227\pi$
$228$	2.74685	−	4.06492i	0.181915	−	0.269206i
$229$	14.0599			0.929102			0.464551	−	0.885546i	$-0.346216\pi$
$229$	14.0599			0.929102			0.464551	+	0.885546i	$0.346216\pi$
$230$	8.82508	+	13.6599i	0.581909	+	0.900706i
$231$	−6.75567			−0.444491
$232$	−11.2193	−	15.6614i	−0.736585	−	1.02822i
$233$			18.3115i			1.19963i	0.800140	+	0.599813i	$0.204758\pi$
$233$			18.3115i			1.19963i	−0.800140	+	0.599813i	$0.795242\pi$
$234$	−2.76779	+	8.45418i	−0.180936	+	0.552667i
$235$	9.79680	−	12.0949i	0.639073	−	0.788981i
$236$	−11.8247	−	8.67202i	−0.769724	−	0.564500i
$237$		−	4.21996i		−	0.274116i
$238$	−1.24605	−	0.407940i	−0.0807692	−	0.0264428i
$239$			7.19400i			0.465341i	0.972556	+	0.232671i	$0.0747464\pi$
$239$			7.19400i			0.465341i	−0.972556	+	0.232671i	$0.925254\pi$
$240$	−1.84628	+	4.68261i	−0.119177	+	0.302261i
$241$		−	2.45499i		−	0.158140i	−0.996869	−	0.0790698i	$-0.974805\pi$
$241$		−	2.45499i		−	0.158140i	0.996869	−	0.0790698i	$-0.0251950\pi$
$242$	1.64201	−	5.01551i	0.105553	−	0.322409i
$243$			13.1122i			0.841148i
$244$	−5.27798	−	3.87077i	−0.337888	−	0.247800i
$245$	3.91594	−	4.83451i	0.250180	−	0.308866i
$246$	2.98722	−	9.12443i	0.190458	−	0.581752i
$247$	10.2106	−	0.393487i	0.649684	−	0.0250370i
$248$	−10.9490	+	7.84351i	−0.695261	+	0.498063i
$249$			3.58896i			0.227441i
$250$	11.2096	−	11.1510i	0.708955	−	0.705254i
$251$		−	14.3768i		−	0.907455i	−0.891140	−	0.453728i	$-0.850094\pi$
$251$		−	14.3768i		−	0.907455i	0.891140	−	0.453728i	$-0.149906\pi$
$252$	13.5352	+	9.92645i	0.852638	+	0.625308i
$253$		−	19.7387i		−	1.24096i
$254$	10.5626	+	3.45807i	0.662758	+	0.216979i
$255$	0.234776	−	0.289848i	0.0147022	−	0.0181510i
$256$	−13.1100	+	9.17212i	−0.819375	+	0.573257i
$257$	−13.3686			−0.833913			−0.416956	−	0.908927i	$-0.636903\pi$
$257$	−13.3686			−0.833913			−0.416956	+	0.908927i	$0.636903\pi$
$258$	0.130000	+	0.0425603i	0.00809345	+	0.00264969i
$259$	−5.67900			−0.352876
$260$	−10.1387	+	2.66685i	−0.628778	+	0.165391i
$261$		−	18.2769i		−	1.13131i
$262$	−21.5965	−	7.07042i	−1.33424	−	0.436812i
$263$	−18.3342			−1.13053			−0.565267	−	0.824908i	$-0.691227\pi$
$263$	−18.3342			−1.13053			−0.565267	+	0.824908i	$0.691227\pi$
$264$	4.96645	−	3.55781i	0.305664	−	0.218968i
$265$	−15.6263	+	19.2918i	−0.959919	+	1.18509i
$266$	5.28876	−	18.5407i	0.324275	−	1.13680i
$267$	1.96528			0.120273
$268$	−11.2004	+	15.2722i	−0.684171	+	0.932901i
$269$			3.91723i			0.238838i	0.992844	+	0.119419i	$0.0381031\pi$
$269$			3.91723i			0.238838i	−0.992844	+	0.119419i	$0.961897\pi$
$270$	−8.49526	+	5.48843i	−0.517005	+	0.334015i
$271$		−	32.0793i		−	1.94868i	−0.225079	−	0.974341i	$-0.572264\pi$
$271$		−	32.0793i		−	1.94868i	0.225079	−	0.974341i	$-0.427736\pi$
$272$	1.13087	−	0.356320i	0.0685692	−	0.0216051i
$273$		−	4.12608i		−	0.249722i
$274$	−25.2816	−	8.27688i	−1.52732	−	0.500024i
$275$	−18.7726	+	3.98519i	−1.13203	+	0.240316i
$276$	3.42306	−	4.66752i	0.206044	−	0.280951i
$277$			6.15489i			0.369812i	0.982756	+	0.184906i	$0.0591980\pi$
$277$			6.15489i			0.369812i	−0.982756	+	0.184906i	$0.940802\pi$
$278$	−20.4667	−	6.70054i	−1.22751	−	0.401872i
$279$	−12.7775			−0.764967
$280$	−1.16996	+	19.7465i	−0.0699186	+	1.18008i
$281$			6.21318i			0.370647i	0.982678	+	0.185323i	$0.0593333\pi$
$281$			6.21318i			0.370647i	−0.982678	+	0.185323i	$0.940667\pi$
$282$	−5.26483	−	1.72364i	−0.313516	−	0.102641i
$283$	−13.4604			−0.800136			−0.400068	−	0.916485i	$-0.631014\pi$
$283$	−13.4604			−0.800136			−0.400068	+	0.916485i	$0.631014\pi$
$284$	15.2478	+	11.1824i	0.904790	+	0.663555i
$285$	4.39204	+	3.28572i	0.260162	+	0.194629i
$286$	12.0928	+	3.95904i	0.715064	+	0.234103i
$287$		−	37.7312i		−	2.22720i
$288$	−15.1781	−	0.169270i	−0.894379	−	0.00997431i
$289$	16.9121			0.994831
$290$	18.0920	−	11.6885i	1.06240	−	0.686371i
$291$		−	6.70547i		−	0.393081i
$292$	−9.73786	+	13.2781i	−0.569865	+	0.777040i
$293$	−10.3893			−0.606949			−0.303475	−	0.952840i	$-0.598147\pi$
$293$	−10.3893			−0.606949			−0.303475	+	0.952840i	$0.598147\pi$
$294$	−2.10444	−	0.688967i	−0.122733	−	0.0401814i
$295$	10.3191	−	12.7397i	0.600803	−	0.741735i
$296$	4.17493	−	2.99079i	0.242663	−	0.173836i
$297$	12.2758			0.712312
$298$	8.27367	−	25.2718i	0.479281	−	1.46396i
$299$	12.0556			0.697192
$300$	−5.13018	−	2.31317i	−0.296191	−	0.133551i
$301$	0.537575			0.0309853
$302$	3.83311	−	11.7082i	0.220571	−	0.673731i
$303$		−	3.38633i		−	0.194540i
$304$	5.87624	+	16.4155i	0.337026	+	0.941495i
$305$	4.60596	−	5.68639i	0.263737	−	0.325602i
$306$	1.06901	+	0.349981i	0.0611114	+	0.0200071i
$307$			11.5192i			0.657434i	0.944428	+	0.328717i	$0.106616\pi$
$307$			11.5192i			0.657434i	−0.944428	+	0.328717i	$0.893384\pi$
$308$	14.1988	−	19.3607i	0.809050	−	1.10318i
$309$	0.556922			0.0316822
$310$	−8.17149	−	12.6482i	−0.464110	−	0.718371i
$311$			19.4638i			1.10369i	0.833946	+	0.551847i	$0.186077\pi$
$311$			19.4638i			1.10369i	−0.833946	+	0.551847i	$0.813923\pi$
$312$	2.17296	+	3.03330i	0.123020	+	0.171727i
$313$		−	14.3879i		−	0.813255i	−0.913594	−	0.406628i	$-0.866705\pi$
$313$		−	14.3879i		−	0.813255i	0.913594	−	0.406628i	$-0.133295\pi$
$314$	−17.2559	−	5.64935i	−0.973804	−	0.318811i
$315$	−11.8118	+	14.5826i	−0.665522	+	0.821634i
$316$	12.0938	+	8.86932i	0.680327	+	0.498938i
$317$	−11.3099			−0.635230			−0.317615	−	0.948220i	$-0.602882\pi$
$317$	−11.3099			−0.635230			−0.317615	+	0.948220i	$0.602882\pi$
$318$	8.39764	+	2.74928i	0.470917	+	0.154172i
$319$	−26.1432			−1.46374
$320$	−9.53922	−	15.1329i	−0.533258	−	0.845952i
$321$	−5.60336			−0.312749
$322$	7.07751	−	21.6182i	0.394414	−	1.20473i
$323$	−0.0497555	−	1.29111i	−0.00276847	−	0.0718390i
$324$	−10.0799	−	7.39240i	−0.559995	−	0.410689i
$325$	−2.43399	−	11.4655i	−0.135013	−	0.635993i
$326$	0.181041	−	0.552987i	0.0100269	−	0.0306271i
$327$	−7.83386			−0.433214
$328$	19.8708	+	27.7382i	1.09718	+	1.53159i
$329$	−21.7711			−1.20028
$330$	3.70659	+	5.73723i	0.204041	+	0.315824i
$331$	8.54452			0.469649			0.234825	−	0.972038i	$-0.424548\pi$
$331$	8.54452			0.469649			0.234825	+	0.972038i	$0.424548\pi$
$332$	−10.2854	−	7.54312i	−0.564486	−	0.413982i
$333$	4.87215			0.266992
$334$	−2.09950	−	0.687349i	−0.114879	−	0.0376101i
$335$	−16.4540	−	13.3277i	−0.898978	−	0.728170i
$336$	6.71503	−	2.11580i	0.366335	−	0.115427i
$337$	−9.77305			−0.532372			−0.266186	−	0.963922i	$-0.585764\pi$
$337$	−9.77305			−0.532372			−0.266186	+	0.963922i	$0.585764\pi$
$338$	3.30218	−	10.0864i	0.179615	−	0.548631i
$339$			10.4086i			0.565318i
$340$	0.337218	+	1.28202i	0.0182882	+	0.0695274i
$341$			18.2769i			0.989747i
$342$	−4.53735	+	15.9065i	−0.245352	+	0.860126i
$343$	13.1915			0.712272
$344$	−0.395200	+	0.283109i	−0.0213077	+	0.0152642i
$345$	5.02869	+	4.07322i	0.270735	+	0.219295i
$346$	−5.01605	+	15.3214i	−0.269664	+	0.823686i
$347$	32.2557			1.73158			0.865789	−	0.500408i	$-0.166817\pi$
$347$	32.2557			1.73158			0.865789	+	0.500408i	$0.166817\pi$
$348$	−6.18195	−	4.53372i	−0.331387	−	0.243033i
$349$	12.2964			0.658212			0.329106	−	0.944293i	$-0.393253\pi$
$349$	12.2964			0.658212			0.329106	+	0.944293i	$0.393253\pi$
$350$	−21.9890	−	2.36647i	−1.17536	−	0.126493i
$351$			7.49752i			0.400188i
$352$	−0.242123	+	21.7107i	−0.0129052	+	1.15719i
$353$		−	9.48559i		−	0.504867i	−0.967614	−	0.252434i	$-0.918769\pi$
$353$		−	9.48559i		−	0.504867i	0.967614	−	0.252434i	$-0.0812309\pi$
$354$	−5.54553	−	1.81554i	−0.294742	−	0.0964947i
$355$	−13.3064	+	16.4277i	−0.706228	+	0.871889i
$356$	−4.13053	+	5.63219i	−0.218918	+	0.298505i
$357$	−0.521734			−0.0276131
$358$	−3.65699	+	11.1702i	−0.193278	+	0.590365i
$359$		−	11.7875i		−	0.622118i	−0.950391	−	0.311059i	$-0.899316\pi$
$359$		−	11.7875i		−	0.622118i	0.950391	−	0.311059i	$-0.100684\pi$
$360$	1.00374	−	16.9410i	0.0529016	−	0.892869i
$361$	18.9436	−	1.46224i	0.997034	−	0.0769600i
$362$	1.96528	+	0.643407i	0.103293	+	0.0338167i
$363$		−	2.10005i		−	0.110224i
$364$	11.8247	+	8.67202i	0.619784	+	0.454537i
$365$	−14.3055	−	11.5874i	−0.748785	−	0.606514i
$366$	−2.47526	−	0.810368i	−0.129384	−	0.0423586i
$367$	−27.6424			−1.44292			−0.721460	−	0.692457i	$-0.756528\pi$
$367$	−27.6424			−1.44292			−0.721460	+	0.692457i	$0.756528\pi$
$368$	6.18195	+	19.6200i	0.322256	+	1.02276i
$369$			32.3705i			1.68514i
$370$	3.11585	+	4.82287i	0.161986	+	0.250729i
$371$	34.7259			1.80288
$372$	−3.16955	+	4.32184i	−0.164334	+	0.224077i
$373$	15.2573			0.789991			0.394996	−	0.918683i	$-0.370746\pi$
$373$	15.2573			0.789991			0.394996	+	0.918683i	$0.370746\pi$
$374$	0.500612	−	1.52911i	0.0258860	−	0.0790685i
$375$	2.85859	−	5.60494i	0.147617	−	0.289438i
$376$	16.0051	−	11.4655i	0.825398	−	0.591290i
$377$		−	15.9671i		−	0.822350i
$378$	13.4446	+	4.40160i	0.691516	+	0.226394i
$379$	−29.8592			−1.53376			−0.766882	−	0.641788i	$-0.778193\pi$
$379$	−29.8592			−1.53376			−0.766882	+	0.641788i	$0.778193\pi$
$380$	−18.6474	+	5.68114i	−0.956590	+	0.291436i
$381$	4.42269			0.226582
$382$	−5.96045	−	1.95138i	−0.304963	−	0.0998411i
$383$		−	24.1703i		−	1.23504i	−0.786554	−	0.617521i	$-0.788137\pi$
$383$		−	24.1703i		−	1.23504i	0.786554	−	0.617521i	$-0.211863\pi$
$384$	−3.82231	+	5.09185i	−0.195056	+	0.259842i
$385$	20.8589	+	16.8956i	1.06307	+	0.861081i
$386$	2.81293	−	8.59205i	0.143174	−	0.437324i
$387$	−0.461198			−0.0234440
$388$	19.2168	+	14.0933i	0.975588	+	0.715477i
$389$	14.6644			0.743513			0.371757	−	0.928330i	$-0.378756\pi$
$389$	14.6644			0.743513			0.371757	+	0.928330i	$0.378756\pi$
$390$	−3.50406	+	2.26383i	−0.177435	+	0.114633i
$391$		−	1.52440i		−	0.0770923i
$392$	6.39749	−	4.58296i	0.323122	−	0.231475i
$393$	−9.04271			−0.456144
$394$	−30.0784	−	9.84730i	−1.51533	−	0.496100i
$395$	−10.5539	+	13.0296i	−0.531025	+	0.655588i
$396$	−12.1815	+	16.6100i	−0.612142	+	0.834685i
$397$		−	10.8320i		−	0.543643i	−0.962348	−	0.271821i	$-0.912374\pi$
$397$		−	10.8320i		−	0.543643i	0.962348	−	0.271821i	$-0.0876260\pi$
$398$	0.794846	+	0.260222i	0.0398420	+	0.0130438i
$399$	−0.295445	−	7.66649i	−0.0147907	−	0.383804i
$400$	17.4116	−	9.84059i	0.870578	−	0.492030i
$401$		−	24.3653i		−	1.21675i	−0.793652	−	0.608373i	$-0.791823\pi$
$401$		−	24.3653i		−	1.21675i	0.793652	−	0.608373i	$-0.208177\pi$
$402$	−2.34486	+	7.16234i	−0.116951	+	0.357225i
$403$	−11.1627			−0.556055
$404$	9.70471	+	7.11724i	0.482827	+	0.354096i
$405$	8.79648	−	10.8599i	0.437101	−	0.539632i
$406$	−28.6324	−	9.37389i	−1.42100	−	0.465218i
$407$		−	6.96911i		−	0.345446i
$408$	0.383554	−	0.274766i	0.0189888	−	0.0136030i
$409$		−	14.3876i		−	0.711422i	−0.934596	−	0.355711i	$-0.884239\pi$
$409$		−	14.3876i		−	0.711422i	0.934596	−	0.355711i	$-0.115761\pi$
$410$	−32.0431	+	20.7017i	−1.58250	+	1.02239i
$411$	−10.5857			−0.522154
$412$	−1.17051	+	1.59605i	−0.0576670	+	0.0786319i
$413$	−22.9318			−1.12840
$414$	−6.07196	+	18.5467i	−0.298421	+	0.911522i
$415$	8.97582	−	11.0813i	0.440606	−	0.543959i
$416$	−13.2600	−	0.147878i	−0.650126	−	0.00725034i
$417$	−8.56965			−0.419657
$418$	22.7526	+	6.49022i	1.11287	+	0.317447i
$419$		−	25.9927i		−	1.26983i	−0.772583	−	0.634914i	$-0.781035\pi$
$419$		−	25.9927i		−	1.26983i	0.772583	−	0.634914i	$-0.218965\pi$
$420$	2.00237	+	7.61254i	0.0977059	+	0.371454i
$421$		−	22.3672i		−	1.09011i	−0.838400	−	0.545056i	$-0.816508\pi$
$421$		−	22.3672i		−	1.09011i	0.838400	−	0.545056i	$-0.183492\pi$
$422$	−8.29403	+	25.3340i	−0.403747	+	1.23324i
$423$	18.6779			0.908151
$424$	−25.5288	+	18.2880i	−1.23979	+	0.888146i
$425$	−1.44979	+	0.307772i	−0.0703252	+	0.0149291i
$426$	7.15087	+	2.34111i	0.346461	+	0.113427i
$427$	−10.2357			−0.495338
$428$	11.7769	−	16.0584i	0.569258	−	0.776211i
$429$	5.06341			0.244464
$430$	−0.294947	−	0.456533i	−0.0142236	−	0.0220160i
$431$	−25.7719			−1.24139			−0.620695	−	0.784052i	$-0.713149\pi$
$431$	−25.7719			−1.24139			−0.620695	+	0.784052i	$0.713149\pi$
$432$	−12.2019	+	3.84463i	−0.587064	+	0.184975i
$433$	17.9384			0.862062			0.431031	−	0.902337i	$-0.358150\pi$
$433$	17.9384			0.862062			0.431031	+	0.902337i	$0.358150\pi$
$434$	−6.55335	+	20.0171i	−0.314571	+	0.960852i
$435$	5.39483	−	6.66030i	0.258662	−	0.319337i
$436$	16.4649	−	22.4507i	0.788524	−	1.07519i
$437$	22.3999	−	0.863229i	1.07153	−	0.0412938i
$438$	−2.03868	+	6.22712i	−0.0974118	+	0.297543i
$439$	22.9968			1.09758			0.548790	−	0.835960i	$-0.315089\pi$
$439$	22.9968			1.09758			0.548790	+	0.835960i	$0.315089\pi$
$440$	−24.2324	−	1.43574i	−1.15523	−	0.0684464i
$441$	7.46587			0.355518
$442$	0.933918	+	0.305753i	0.0444219	+	0.0145432i
$443$	24.3789			1.15828			0.579138	−	0.815230i	$-0.303389\pi$
$443$	24.3789			1.15828			0.579138	+	0.815230i	$0.303389\pi$
$444$	1.20857	−	1.64795i	0.0573564	−	0.0782083i
$445$	−6.06801	−	4.91507i	−0.287651	−	0.232997i
$446$	20.9306	+	6.85241i	0.991092	+	0.324471i
$447$		−	10.5816i		−	0.500492i
$448$	−8.04978	+	23.6912i	−0.380317	+	1.11930i
$449$			35.0227i			1.65283i	0.563065	+	0.826413i	$0.309622\pi$
$449$			35.0227i			1.65283i	−0.563065	+	0.826413i	$0.690378\pi$
$450$	18.8649	+	2.03025i	0.889300	+	0.0957069i
$451$	46.3027			2.18031
$452$	−29.8295	−	21.8763i	−1.40306	−	1.02898i
$453$		−	4.90236i		−	0.230333i
$454$	−30.9420	−	10.1300i	−1.45218	−	0.475426i
$455$	−10.3191	+	12.7397i	−0.483769	+	0.597247i
$456$	4.25468	+	5.48045i	0.199244	+	0.256645i
$457$			1.73993i			0.0813904i	0.999172	+	0.0406952i	$0.0129573\pi$
$457$			1.73993i			0.0813904i	−0.999172	+	0.0406952i	$0.987043\pi$
$458$	−6.18655	+	18.8967i	−0.289078	+	0.882986i
$459$	0.948045			0.0442509
$460$	−22.2423	+	5.85053i	−1.03705	+	0.272782i
$461$	20.9737			0.976845			0.488422	−	0.872607i	$-0.337573\pi$
$461$	20.9737			0.976845			0.488422	+	0.872607i	$0.337573\pi$
$462$	2.97260	−	9.07975i	0.138298	−	0.422428i
$463$	−4.36243			−0.202740			−0.101370	−	0.994849i	$-0.532323\pi$
$463$	−4.36243			−0.202740			−0.101370	+	0.994849i	$0.532323\pi$
$464$	25.9859	−	8.18775i	1.20636	−	0.380107i
$465$	−4.65626	−	3.77156i	−0.215929	−	0.174902i
$466$	−24.6110	−	8.05732i	−1.14008	−	0.373248i
$467$	−11.5244			−0.533287			−0.266643	−	0.963795i	$-0.585915\pi$
$467$	−11.5244			−0.533287			−0.266643	+	0.963795i	$0.585915\pi$
$468$	−10.1447	−	7.43993i	−0.468939	−	0.343911i
$469$			29.6177i			1.36762i
$470$	11.9450	+	18.4890i	0.550981	+	0.852834i
$471$	−7.22523			−0.332921
$472$	16.8584	−	12.0768i	0.775971	−	0.555881i
$473$			0.659697i			0.0303329i
$474$	5.67170	+	1.85684i	0.260510	+	0.0852876i
$475$	−5.34346	−	21.1293i	−0.245175	−	0.969479i
$476$	1.09656	−	1.49521i	0.0502606	−	0.0685328i
$477$	−29.7921			−1.36409
$478$	−9.66887	−	3.16547i	−0.442244	−	0.144785i
$479$			11.7269i			0.535817i	0.963444	+	0.267908i	$0.0863324\pi$
$479$			11.7269i			0.535817i	−0.963444	+	0.267908i	$0.913668\pi$
$480$	−5.48113	−	4.54185i	−0.250178	−	0.207306i
$481$	4.25644			0.194077
$482$	3.29955	+	1.08023i	0.150290	+	0.0492032i
$483$		−	9.05178i		−	0.411870i
$484$	6.01843	+	4.41380i	0.273565	+	0.200627i
$485$	−16.7701	+	20.7038i	−0.761489	+	0.940113i
$486$	−17.6230	−	5.76956i	−0.799398	−	0.261713i
$487$			36.4267i			1.65065i	0.564656	+	0.825327i	$0.309009\pi$
$487$			36.4267i			1.65065i	−0.564656	+	0.825327i	$0.690991\pi$
$488$	7.52477	−	5.39051i	0.340631	−	0.244017i
$489$		−	0.231542i		−	0.0104707i
$490$	4.77461	+	7.39036i	0.215695	+	0.333862i
$491$			7.95871i			0.359171i	0.983742	+	0.179586i	$0.0574757\pi$
$491$			7.95871i			0.359171i	−0.983742	+	0.179586i	$0.942524\pi$
$492$	10.9490	+	8.02976i	0.493618	+	0.362010i
$493$	−2.01901			−0.0909317
$494$	−3.96395	+	13.8964i	−0.178347	+	0.625227i
$495$	−17.8953	−	14.4952i	−0.804334	−	0.651509i
$496$	−5.72411	−	18.1669i	−0.257020	−	0.815718i
$497$	29.5702			1.32641
$498$	−4.82363	−	1.57920i	−0.216152	−	0.0707655i
$499$			25.3695i			1.13569i	0.823134	+	0.567847i	$0.192224\pi$
$499$			25.3695i			1.13569i	−0.823134	+	0.567847i	$0.807776\pi$
$500$	10.0548	+	19.9725i	0.449666	+	0.893197i
$501$	−0.879084			−0.0392746
$502$	19.3227	+	6.32600i	0.862414	+	0.282343i
$503$	8.43511			0.376103			0.188052	−	0.982159i	$-0.439783\pi$
$503$	8.43511			0.376103			0.188052	+	0.982159i	$0.439783\pi$
$504$	−19.2970	+	13.8238i	−0.859558	+	0.615761i
$505$	−8.46906	+	10.4557i	−0.376868	+	0.465271i
$506$	26.5292	+	8.68532i	1.17937	+	0.386110i
$507$		−	4.22331i		−	0.187564i
$508$	−9.29542	+	12.6748i	−0.412418	+	0.562352i
$509$		−	38.3457i		−	1.69965i	−0.527069	−	0.849823i	$-0.676709\pi$
$509$		−	38.3457i		−	1.69965i	0.527069	−	0.849823i	$-0.323291\pi$
$510$	0.286256	+	0.443081i	0.0126756	+	0.0196199i
$511$			25.7503i			1.13913i
$512$	−6.55890	−	21.6560i	−0.289865	−	0.957067i
$513$	0.536853	+	13.9308i	0.0237027	+	0.615060i
$514$	5.88240	−	17.9677i	0.259461	−	0.792521i
$515$	−1.71955	−	1.39283i	−0.0757726	−	0.0613756i
$516$	−0.114404	+	0.155995i	−0.00503635	+	0.00686731i
$517$		−	26.7168i		−	1.17501i
$518$	2.49884	−	7.63268i	0.109793	−	0.335361i
$519$			6.41527i			0.281599i
$520$	0.876892	−	14.8001i	0.0384543	−	0.649028i
$521$		−	26.1113i		−	1.14396i	−0.820269	−	0.571979i	$-0.806176\pi$
$521$		−	26.1113i		−	1.14396i	0.820269	−	0.571979i	$-0.193824\pi$
$522$	24.5644	+	8.04208i	1.07516	+	0.351992i
$523$			5.15443i			0.225387i	0.993630	+	0.112694i	$0.0359479\pi$
$523$			5.15443i			0.225387i	−0.993630	+	0.112694i	$0.964052\pi$
$524$	19.0056	−	25.9150i	0.830262	−	1.13210i
$525$	−8.60875	+	1.82753i	−0.375717	+	0.0797598i
$526$	8.06730	−	24.6415i	0.351751	−	1.07442i
$527$			1.41150i			0.0614860i
$528$	2.59645	+	8.24050i	0.112996	+	0.358622i
$529$	3.44744			0.149889
$530$	−19.0528	−	29.4908i	−0.827600	−	1.28100i
$531$	19.6738			0.853769
$532$	22.5919	+	15.2664i	0.979485	+	0.661882i
$533$			28.2798i			1.22493i
$534$	−0.864752	+	2.64137i	−0.0374215	+	0.114303i
$535$	17.3010	+	14.0137i	0.747986	+	0.605867i
$536$	−15.5979	−	21.7735i	−0.673725	−	0.940472i
$537$			4.67711i			0.201832i
$538$	−5.26483	−	1.72364i	−0.226983	−	0.0743113i
$539$		−	10.6792i		−	0.459984i
$540$	−3.63852	−	13.8328i	−0.156577	−	0.595268i
$541$	−8.68410			−0.373359			−0.186679	−	0.982421i	$-0.559773\pi$
$541$	−8.68410			−0.373359			−0.186679	+	0.982421i	$0.559773\pi$
$542$	43.1152	+	14.1154i	1.85196	+	0.606308i
$543$	0.822885			0.0353134
$544$	−0.0186989	+	1.67670i	−0.000801709	+	0.0718879i
$545$	24.1879	+	19.5921i	1.03609	+	0.839234i
$546$	5.54553	+	1.81554i	0.237327	+	0.0776978i
$547$			1.22724i			0.0524731i	0.999656	+	0.0262365i	$0.00835231\pi$
$547$			1.22724i			0.0524731i	−0.999656	+	0.0262365i	$0.991648\pi$
$548$	22.2486	−	30.3370i	0.950411	−	1.29593i
$549$	8.78142			0.374782
$550$	2.90406	−	26.9843i	0.123830	−	1.15061i
$551$	−1.14331	−	29.6678i	−0.0487068	−	1.26389i
$552$	4.76703	+	6.65444i	0.202898	+	0.283232i
$553$	23.4536			0.997347
$554$	−8.27229	−	2.70824i	−0.351456	−	0.115062i
$555$	1.77547	+	1.43813i	0.0753644	+	0.0610450i
$556$	18.0113	−	24.5593i	0.763849	−	1.04155i
$557$		−	10.1755i		−	0.431151i	−0.976487	−	0.215575i	$-0.930837\pi$
$557$		−	10.1755i		−	0.431151i	0.976487	−	0.215575i	$-0.0691627\pi$
$558$	5.62227	−	17.1732i	0.238010	−	0.726998i
$559$	−0.402915			−0.0170415
$560$	−26.0249	−	10.2612i	−1.09975	−	0.433615i
$561$		−	0.640257i		−	0.0270317i
$562$	−8.35063	−	2.73389i	−0.352250	−	0.115322i
$563$			44.1373i			1.86017i	0.367348	+	0.930084i	$0.380266\pi$
$563$			44.1373i			1.86017i	−0.367348	+	0.930084i	$0.619734\pi$
$564$	4.63321	−	6.31760i	0.195093	−	0.266019i
$565$	26.0314	−	32.1377i	1.09515	−	1.35204i
$566$	5.92276	−	18.0910i	0.248952	−	0.760422i
$567$	−19.5481			−0.820943
$568$	−21.7386	+	15.5729i	−0.912133	+	0.653424i
$569$		−	15.7494i		−	0.660248i	−0.943938	−	0.330124i	$-0.892910\pi$
$569$		−	15.7494i		−	0.660248i	0.943938	−	0.330124i	$-0.107090\pi$
$570$	−6.34864	+	4.45722i	−0.265915	+	0.186692i
$571$			29.5903i			1.23832i	0.785266	+	0.619158i	$0.212526\pi$
$571$			29.5903i			1.23832i	−0.785266	+	0.619158i	$0.787474\pi$
$572$	−10.6421	+	14.5110i	−0.444967	+	0.606734i
$573$	−2.49571			−0.104260
$574$	50.7115	+	16.6023i	2.11666	+	0.692967i
$575$	−5.33966	−	25.1530i	−0.222679	−	1.04895i
$576$	6.90610	−	20.3252i	0.287754	−	0.846883i
$577$		−	24.8985i		−	1.03654i	−0.855218	−	0.518269i	$-0.826577\pi$
$577$		−	24.8985i		−	1.03654i	0.855218	−	0.518269i	$-0.173423\pi$
$578$	−7.44159	+	22.7302i	−0.309529	+	0.945453i
$579$		−	3.59759i		−	0.149511i
$580$	7.74880	+	29.4591i	0.321752	+	1.22322i
$581$	−19.9466			−0.827526
$582$	9.01228	+	2.95050i	0.373571	+	0.122302i
$583$			42.6146i			1.76492i
$584$	−13.5612	−	18.9304i	−0.561165	−	0.783346i
$585$	8.85303	−	10.9297i	0.366028	−	0.451888i
$586$	4.57144	−	13.9634i	0.188845	−	0.576823i
$587$	−41.6137			−1.71758			−0.858790	−	0.512327i	$-0.828783\pi$
$587$	−41.6137			−1.71758			−0.858790	+	0.512327i	$0.828783\pi$
$588$	1.85197	−	2.52525i	0.0763739	−	0.104140i
$589$	−20.7410	+	0.799298i	−0.854617	+	0.0329345i
$590$	12.5818	+	19.4748i	0.517986	+	0.801764i
$591$	−12.5942			−0.518056
$592$	2.18265	+	6.92718i	0.0897063	+	0.284705i
$593$			34.0574i			1.39857i	0.714843	+	0.699285i	$0.246498\pi$
$593$			34.0574i			1.39857i	−0.714843	+	0.699285i	$0.753502\pi$
$594$	−5.40151	+	16.4988i	−0.221627	+	0.676956i
$595$	1.61091	+	1.30483i	0.0660408	+	0.0534929i
$596$	30.3252	+	22.2399i	1.24217	+	0.910983i
$597$	0.332811			0.0136211
$598$	−5.30463	+	16.2029i	−0.216922	+	0.662587i
$599$	45.2260			1.84789			0.923943	−	0.382530i	$-0.124947\pi$
$599$	45.2260			1.84789			0.923943	+	0.382530i	$0.124947\pi$
$600$	5.36630	−	5.87723i	0.219078	−	0.239937i
$601$		−	13.7934i		−	0.562645i	−0.959613	−	0.281322i	$-0.909227\pi$
$601$		−	13.7934i		−	0.562645i	0.959613	−	0.281322i	$-0.0907730\pi$
$602$	−0.236541	+	0.722511i	−0.00964068	+	0.0294473i
$603$		−	25.4097i		−	1.03476i
$604$	14.0494	+	10.3036i	0.571662	+	0.419246i
$605$	−5.25213	+	6.48413i	−0.213530	+	0.263618i
$606$	4.55130	+	1.49004i	0.184884	+	0.0605286i
$607$			6.05673i			0.245835i	0.992417	+	0.122918i	$0.0392251\pi$
$607$			6.05673i			0.245835i	−0.992417	+	0.122918i	$0.960775\pi$
$608$	−24.6484	+	0.674706i	−0.999626	+	0.0273629i
$609$	−11.9887			−0.485808
$610$	5.61593	+	8.69260i	0.227382	+	0.351953i
$611$	16.3175			0.660137
$612$	−0.940762	+	1.28278i	−0.0380281	+	0.0518532i
$613$		−	17.6797i		−	0.714074i	−0.934090	−	0.357037i	$-0.883787\pi$
$613$		−	17.6797i		−	0.714074i	0.934090	−	0.357037i	$-0.116213\pi$
$614$	−15.4820	−	5.06861i	−0.624802	−	0.204552i
$615$	−9.55490	+	11.7962i	−0.385291	+	0.475669i
$616$	19.7735	+	27.6024i	0.796698	+	1.11213i
$617$		−	20.4490i		−	0.823245i	−0.911355	−	0.411622i	$-0.864962\pi$
$617$		−	20.4490i		−	0.823245i	0.911355	−	0.411622i	$-0.135038\pi$
$618$	−0.245054	+	0.748513i	−0.00985751	+	0.0301096i
$619$		−	41.3733i		−	1.66293i	−0.555576	−	0.831466i	$-0.687502\pi$
$619$		−	41.3733i		−	1.66293i	0.555576	−	0.831466i	$-0.312498\pi$
$620$	20.5950	−	5.41724i	0.827116	−	0.217561i
$621$			16.4480i			0.660036i
$622$	−26.1598	−	8.56438i	−1.04891	−	0.343400i
$623$			10.9226i			0.437604i
$624$	−5.03295	+	1.58581i	−0.201479	+	0.0634830i
$625$	−22.8439	+	10.1566i	−0.913755	+	0.406266i
$626$	19.3377	+	6.33091i	0.772889	+	0.253034i
$627$	9.40810	−	0.362561i	0.375723	−	0.0144793i
$628$	15.1857	−	20.7064i	0.605974	−	0.826275i
$629$		−	0.538217i		−	0.0214601i
$630$	−14.4019	−	22.2919i	−0.573784	−	0.888129i
$631$			8.70064i			0.346367i	0.984890	+	0.173183i	$0.0554054\pi$
$631$			8.70064i			0.346367i	−0.984890	+	0.173183i	$0.944595\pi$
$632$	−17.2420	+	12.3516i	−0.685848	+	0.491320i
$633$			10.6076i			0.421616i
$634$	4.97654	−	15.2008i	0.197644	−	0.603700i
$635$	−13.6555	−	11.0609i	−0.541903	−	0.438940i
$636$	−7.39017	+	10.0769i	−0.293039	+	0.399574i
$637$	6.52239			0.258426
$638$	11.5034	−	35.1369i	0.455423	−	1.39108i
$639$	−25.3690			−1.00358
$640$	24.5362	−	6.16221i	0.969880	−	0.243583i
$641$			21.0321i			0.830718i	0.909658	+	0.415359i	$0.136344\pi$
$641$			21.0321i			0.830718i	−0.909658	+	0.415359i	$0.863656\pi$
$642$	2.46556	−	7.53102i	0.0973079	−	0.297226i
$643$	28.6196			1.12865			0.564323	−	0.825554i	$-0.309137\pi$
$643$	28.6196			1.12865			0.564323	+	0.825554i	$0.309137\pi$
$644$	25.9410	+	19.0246i	1.02222	+	0.749675i
$645$	−0.168066	−	0.136133i	−0.00661760	−	0.00536024i
$646$	1.75716	+	0.501233i	0.0691347	+	0.0197208i
$647$	15.6384			0.614808			0.307404	−	0.951579i	$-0.400540\pi$
$647$	15.6384			0.614808			0.307404	+	0.951579i	$0.400540\pi$
$648$	14.3708	−	10.2948i	0.564540	−	0.404419i
$649$		−	28.1413i		−	1.10464i
$650$	16.4809	+	1.77368i	0.646433	+	0.0695695i
$651$			8.38140i			0.328493i
$652$	0.663564	+	0.486645i	0.0259872	+	0.0190585i
$653$			21.3458i			0.835324i	0.908602	+	0.417662i	$0.137150\pi$
$653$			21.3458i			0.835324i	−0.908602	+	0.417662i	$0.862850\pi$
$654$	3.44701	−	10.5289i	0.134789	−	0.411711i
$655$	27.9203	+	22.6154i	1.09094	+	0.883656i
$656$	−46.0242	+	14.5015i	−1.79694	+	0.566189i
$657$		−	22.0918i		−	0.861883i
$658$	9.57959	−	29.2607i	0.373451	−	1.14070i
$659$	−27.8535			−1.08502			−0.542510	−	0.840049i	$-0.682526\pi$
$659$	−27.8535			−1.08502			−0.542510	+	0.840049i	$0.682526\pi$
$660$	−9.34190	+	2.45726i	−0.363633	+	0.0956486i
$661$			18.3813i			0.714949i	0.933923	+	0.357474i	$0.116362\pi$
$661$			18.3813i			0.714949i	−0.933923	+	0.357474i	$0.883638\pi$
$662$	−3.75971	+	11.4840i	−0.146125	+	0.446338i
$663$	0.391042			0.0151868
$664$	14.6638	−	10.5047i	0.569067	−	0.407662i
$665$	−18.2613	+	24.4100i	−0.708143	+	0.946579i
$666$	−2.14382	+	6.54826i	−0.0830712	+	0.253740i
$667$		−	35.0286i		−	1.35631i
$668$	1.84762	−	2.51932i	0.0714866	−	0.0974755i
$669$	8.76388			0.338831
$670$	25.1527	−	16.2501i	0.971733	−	0.627796i
$671$		−	12.5609i		−	0.484909i
$672$	−0.111033	+	9.95611i	−0.00428318	+	0.384065i
$673$	−40.0610			−1.54424			−0.772119	−	0.635478i	$-0.780803\pi$
$673$	−40.0610			−1.54424			−0.772119	+	0.635478i	$0.780803\pi$
$674$	4.30029	−	13.1352i	0.165641	−	0.505948i
$675$	15.6430	−	3.32080i	0.602099	−	0.127818i
$676$	12.1034	+	8.87637i	0.465514	+	0.341399i
$677$	27.5660			1.05945			0.529723	−	0.848171i	$-0.322296\pi$
$677$	27.5660			1.05945			0.529723	+	0.848171i	$0.322296\pi$
$678$	−13.9894	−	4.57994i	−0.537258	−	0.175892i
$679$	37.2675			1.43019
$680$	−1.87144	−	0.110881i	−0.0717665	−	0.00425209i
$681$	−12.9558			−0.496467
$682$	−24.5644	−	8.04208i	−0.940621	−	0.307947i
$683$		−	27.6266i		−	1.05710i	−0.848901	−	0.528552i	$-0.822735\pi$
$683$		−	27.6266i		−	1.05710i	0.848901	−	0.528552i	$-0.177265\pi$
$684$	−19.3822	−	13.0974i	−0.741095	−	0.500791i
$685$	32.6845	+	26.4743i	1.24881	+	1.01153i
$686$	−5.80444	+	17.7296i	−0.221614	+	0.676918i
$687$			7.91228i			0.301872i
$688$	−0.206610	−	0.655728i	−0.00787692	−	0.0249994i
$689$	−26.0272			−0.991558
$690$	−7.68719	+	4.96637i	−0.292646	+	0.189067i
$691$		−	16.1536i		−	0.614513i	−0.951627	−	0.307256i	$-0.900589\pi$
$691$		−	16.1536i		−	0.614513i	0.951627	−	0.307256i	$-0.0994109\pi$
$692$	−18.3852	−	13.4833i	−0.698900	−	0.512559i
$693$			32.2120i			1.22363i
$694$	−14.1930	+	43.3523i	−0.538759	+	1.64563i
$695$	26.4597	+	21.4323i	1.00367	+	0.812973i
$696$	8.81355	−	6.31375i	0.334077	−	0.239322i
$697$	3.57591			0.135447
$698$	−5.41060	+	16.5266i	−0.204794	+	0.625541i
$699$	−10.3049			−0.389767
$700$	12.8561	−	28.5124i	0.485914	−	1.07767i
$701$	−10.8798			−0.410923			−0.205461	−	0.978665i	$-0.565869\pi$
$701$	−10.8798			−0.410923			−0.205461	+	0.978665i	$0.565869\pi$
$702$	−10.0768	−	3.29902i	−0.380324	−	0.124513i
$703$	7.90869	−	0.304779i	0.298282	−	0.0114949i
$704$	−29.0731	−	9.87847i	−1.09573	−	0.372309i
$705$	6.80646	+	5.51321i	0.256346	+	0.207640i
$706$	12.7488	+	4.17380i	0.479808	+	0.157083i
$707$	18.8205			0.707817
$708$	4.88023	−	6.65444i	0.183410	−	0.250089i
$709$	−45.2518			−1.69947			−0.849734	−	0.527212i	$-0.823237\pi$
$709$	−45.2518			−1.69947			−0.849734	+	0.527212i	$0.823237\pi$
$710$	−16.2241	−	25.1124i	−0.608879	−	0.942452i
$711$	−20.1214			−0.754610
$712$	−5.75227	−	8.02976i	−0.215576	−	0.300928i
$713$	−24.4887			−0.917110
$714$	0.229571	−	0.701220i	0.00859147	−	0.0262425i
$715$	−15.6338	−	12.6634i	−0.584672	−	0.473583i
$716$	−13.4039	−	9.83014i	−0.500926	−	0.367369i
$717$	−4.04847			−0.151193
$718$	15.8426	+	5.18666i	0.591240	+	0.193564i
$719$			36.6480i			1.36674i	0.730073	+	0.683369i	$0.239486\pi$
$719$			36.6480i			1.36674i	−0.730073	+	0.683369i	$0.760514\pi$
$720$	22.3274	+	8.80333i	0.832092	+	0.328081i
$721$			3.09525i			0.115273i
$722$	−6.37021	+	26.1040i	−0.237075	+	0.971491i
$723$	1.38156			0.0513808
$724$	−1.72950	+	2.35826i	−0.0642765	+	0.0876442i
$725$	−33.3142	+	7.07218i	−1.23726	+	0.262654i
$726$	2.82251	+	0.924054i	0.104753	+	0.0342949i
$727$	−29.9330			−1.11015			−0.555077	−	0.831799i	$-0.687311\pi$
$727$	−29.9330			−1.11015			−0.555077	+	0.831799i	$0.687311\pi$
$728$	−16.8584	+	12.0768i	−0.624814	+	0.447597i
$729$	11.3712			0.421154
$730$	21.8684	−	14.1282i	0.809384	−	0.522910i
$731$			0.0509477i			0.00188437i
$732$	2.17830	−	2.97022i	0.0805123	−	0.109782i
$733$			11.4917i			0.424456i	0.977220	+	0.212228i	$0.0680719\pi$
$733$			11.4917i			0.424456i	−0.977220	+	0.212228i	$0.931928\pi$
$734$	12.1630	−	37.1518i	0.448946	−	1.37130i
$735$	2.72065	+	2.20372i	0.100353	+	0.0812855i
$736$	−29.0897	−	0.324415i	−1.07226	−	0.0119581i
$737$	−36.3460			−1.33882
$738$	−43.5066	−	14.2435i	−1.60150	−	0.524311i
$739$			10.5334i			0.387477i	0.981053	+	0.193739i	$0.0620613\pi$
$739$			10.5334i			0.387477i	−0.981053	+	0.193739i	$0.937939\pi$
$740$	−7.85305	+	2.06563i	−0.288684	+	0.0759342i
$741$	0.221437	+	5.74607i	0.00813470	+	0.211087i
$742$	−15.2799	+	46.6722i	−0.560942	+	1.71339i
$743$		−	0.681568i		−	0.0250043i	−0.999922	−	0.0125022i	$-0.996020\pi$
$743$		−	0.681568i		−	0.0250043i	0.999922	−	0.0125022i	$-0.00397966\pi$
$744$	−4.41398	−	6.16161i	−0.161825	−	0.225896i
$745$	−26.4641	+	32.6718i	−0.969569	+	1.19700i
$746$	−6.71342	+	20.5061i	−0.245796	+	0.750780i
$747$	17.1127			0.626121
$748$	1.83488	+	1.34566i	0.0670898	+	0.0492024i
$749$		−	31.1422i		−	1.13791i
$750$	6.27532	+	6.30825i	0.229142	+	0.230345i
$751$	4.02795			0.146982			0.0734910	−	0.997296i	$-0.476586\pi$
$751$	4.02795			0.146982			0.0734910	+	0.997296i	$0.476586\pi$
$752$	8.36743	+	26.5561i	0.305129	+	0.968402i
$753$	8.09063			0.294839
$754$	21.4601	+	7.02578i	0.781532	+	0.255864i
$755$	−12.2606	+	15.1365i	−0.446208	+	0.550875i
$756$	−11.8317	+	16.1330i	−0.430313	+	0.586753i
$757$			11.3612i			0.412930i	0.978454	+	0.206465i	$0.0661960\pi$
$757$			11.3612i			0.412930i	−0.978454	+	0.206465i	$0.933804\pi$
$758$	13.1385	−	40.1313i	0.477211	−	1.45764i
$759$	11.1081			0.403198
$760$	0.569564	−	27.5622i	0.0206602	−	0.999787i
$761$	−33.0747			−1.19896			−0.599479	−	0.800390i	$-0.704626\pi$
$761$	−33.0747			−1.19896			−0.599479	+	0.800390i	$0.704626\pi$
$762$	−1.94605	+	5.94419i	−0.0704980	+	0.215335i
$763$		−	43.5388i		−	1.57621i
$764$	5.24537	−	7.15232i	0.189771	−	0.258762i
$765$	−1.38204	−	1.11945i	−0.0499676	−	0.0404737i
$766$	32.4853	+	10.6353i	1.17374	+	0.384268i
$767$	17.1875			0.620606
$768$	−5.16167	−	7.37774i	−0.186256	−	0.266221i
$769$	9.24948			0.333545			0.166772	−	0.985995i	$-0.446665\pi$
$769$	9.24948			0.333545			0.166772	+	0.985995i	$0.446665\pi$
$770$	−31.8862	+	20.6004i	−1.14910	+	0.742386i
$771$		−	7.52329i		−	0.270945i
$772$	10.3102	+	7.56126i	0.371071	+	0.272136i
$773$	40.5301			1.45777			0.728884	−	0.684638i	$-0.240040\pi$
$773$	40.5301			1.45777			0.728884	+	0.684638i	$0.240040\pi$
$774$	0.202934	−	0.619859i	0.00729431	−	0.0222804i
$775$	4.94421	+	23.2902i	0.177601	+	0.836608i
$776$	−27.3973	+	19.6266i	−0.983506	+	0.704553i
$777$		−	3.19589i		−	0.114652i
$778$	−6.45254	+	19.7092i	−0.231335	+	0.706609i
$779$	2.02495	+	52.5453i	0.0725513	+	1.88263i
$780$	−1.50079	−	5.70564i	−0.0537369	−	0.204295i
$781$			36.2878i			1.29848i
$782$	2.04882	+	0.670759i	0.0732658	+	0.0239863i
$783$	21.7848			0.778524
$784$	3.34460	+	10.6149i	0.119450	+	0.379104i
$785$	22.3086	+	18.0699i	0.796230	+	0.644944i
$786$	3.97893	−	12.1536i	0.141924	−	0.433504i
$787$			31.2567i			1.11418i	0.830452	+	0.557090i	$0.188082\pi$
$787$			31.2567i			1.11418i	−0.830452	+	0.557090i	$0.811918\pi$
$788$	26.4699	−	36.0930i	0.942951	−	1.28576i
$789$		−	10.3177i		−	0.367319i
$790$	−12.8681	−	19.9179i	−0.457827	−	0.708646i
$791$	−57.8487			−2.05686
$792$	−16.9642	−	23.6808i	−0.602796	−	0.841460i
$793$	7.67168			0.272429
$794$	14.5584	+	4.76624i	0.516659	+	0.169148i
$795$	−10.8566	−	8.79383i	−0.385044	−	0.311885i
$796$	−0.699488	+	0.953786i	−0.0247927	+	0.0338060i
$797$	−2.60336			−0.0922156			−0.0461078	−	0.998936i	$-0.514682\pi$
$797$	−2.60336			−0.0922156			−0.0461078	+	0.998936i	$0.514682\pi$
$798$	10.4339	+	2.97628i	0.369356	+	0.105359i
$799$		−	2.06332i		−	0.0729949i
$800$	5.56460	+	27.7315i	0.196738	+	0.980456i
$801$		−	9.37074i		−	0.331099i
$802$	32.7474	+	10.7211i	1.15635	+	0.378575i
$803$	−31.6001			−1.11514
$804$	−8.59455	−	6.30307i	−0.303106	−	0.222292i
$805$	−22.6381	+	27.9483i	−0.797887	+	0.985048i
$806$	4.91177	−	15.0029i	0.173010	−	0.528456i
$807$	−2.20445			−0.0776002
$808$	−13.8359	+	9.91163i	−0.486746	+	0.348690i
$809$	32.4459			1.14074			0.570368	−	0.821389i	$-0.306800\pi$
$809$	32.4459			1.14074			0.570368	+	0.821389i	$0.306800\pi$
$810$	10.7253	+	16.6011i	0.376849	+	0.583305i
$811$	−36.2431			−1.27267			−0.636333	−	0.771414i	$-0.719550\pi$
$811$	−36.2431			−1.27267			−0.636333	+	0.771414i	$0.719550\pi$
$812$	25.1974	−	34.3579i	0.884255	−	1.20572i
$813$	18.0529			0.633141
$814$	9.36661	+	3.06651i	0.328300	+	0.107481i
$815$	−0.579075	+	0.714910i	−0.0202841	+	0.0250422i
$816$	0.200522	+	0.636405i	0.00701966	+	0.0222786i
$817$	−0.748638	+	0.0288504i	−0.0261915	+	0.00100935i
$818$	19.3372	+	6.33077i	0.676111	+	0.221350i
$819$	−19.6738			−0.687457
$820$	−13.7241	−	52.1756i	−0.479265	−	1.82205i
$821$	−9.80103			−0.342058			−0.171029	−	0.985266i	$-0.554709\pi$
$821$	−9.80103			−0.342058			−0.171029	+	0.985266i	$0.554709\pi$
$822$	4.65787	−	14.2274i	0.162462	−	0.496237i
$823$	−47.5409			−1.65717			−0.828586	−	0.559862i	$-0.810854\pi$
$823$	−47.5409			−1.65717			−0.828586	+	0.559862i	$0.810854\pi$
$824$	−1.63008	−	2.27548i	−0.0567866	−	0.0792700i
$825$	−2.24269	−	10.5644i	−0.0780804	−	0.367806i
$826$	10.0903	−	30.8208i	0.351088	−	1.07239i
$827$		−	29.7178i		−	1.03339i	−0.856169	−	0.516695i	$-0.827162\pi$
$827$		−	29.7178i		−	1.03339i	0.856169	−	0.516695i	$-0.172838\pi$
$828$	−22.2554	−	16.3217i	−0.773429	−	0.567217i
$829$			26.6191i			0.924521i	0.886744	+	0.462260i	$0.152961\pi$
$829$			26.6191i			0.924521i	−0.886744	+	0.462260i	$0.847039\pi$
$830$	10.9440	+	16.9396i	0.379871	+	0.587982i
$831$	−3.46371			−0.120155
$832$	6.03335	−	17.7566i	0.209169	−	0.615601i
$833$		−	0.824741i		−	0.0285756i
$834$	3.77077	−	11.5178i	0.130571	−	0.398828i
$835$	2.71427	+	2.19855i	0.0939310	+	0.0760839i
$836$	−18.7345	+	27.7242i	−0.647945	+	0.958861i
$837$		−	15.2299i		−	0.526421i
$838$	34.9347	+	11.4372i	1.20680	+	0.395091i
$839$	42.7153			1.47470			0.737348	−	0.675513i	$-0.236078\pi$
$839$	42.7153			1.47470			0.737348	+	0.675513i	$0.236078\pi$
$840$	−11.1125	−	0.658403i	−0.383417	−	0.0227171i
$841$	−17.3941			−0.599796
$842$	30.0620	+	9.84191i	1.03600	+	0.339175i
$843$	−3.49650			−0.120426
$844$	−30.3999	−	22.2947i	−1.04641	−	0.767414i
$845$	−10.5623	+	13.0399i	−0.363354	+	0.448587i
$846$	−8.21856	+	25.1035i	−0.282560	+	0.863075i
$847$	11.6716			0.401042
$848$	−13.3464	−	42.3582i	−0.458318	−	1.45459i
$849$		−	7.57491i		−	0.259970i
$850$	0.224278	−	2.08397i	0.00769267	−	0.0714796i
$851$	9.33775			0.320094
$852$	−6.29298	+	8.58079i	−0.215594	+	0.293973i
$853$		−	25.3286i		−	0.867236i	−0.901097	−	0.433618i	$-0.857237\pi$
$853$		−	25.3286i		−	0.867236i	0.901097	−	0.433618i	$-0.142763\pi$
$854$	4.50384	−	13.7569i	0.154118	−	0.470752i
$855$	15.6668	−	20.9419i	0.535793	−	0.716198i
$856$	16.4008	+	22.8943i	0.560566	+	0.782511i
$857$	−20.9648			−0.716146			−0.358073	−	0.933694i	$-0.616566\pi$
$857$	−20.9648			−0.716146			−0.358073	+	0.933694i	$0.616566\pi$
$858$	−2.22798	+	6.80532i	−0.0760618	+	0.232330i
$859$		−	32.2246i		−	1.09949i	−0.835333	−	0.549745i	$-0.814725\pi$
$859$		−	32.2246i		−	1.09949i	0.835333	−	0.549745i	$-0.185275\pi$
$860$	0.743371	−	0.195533i	0.0253487	−	0.00666763i
$861$	21.2335			0.723636
$862$	11.3400	−	34.6379i	0.386243	−	1.17977i
$863$		−	52.0944i		−	1.77331i	−0.462428	−	0.886657i	$-0.653022\pi$
$863$		−	52.0944i		−	1.77331i	0.462428	−	0.886657i	$-0.346978\pi$
$864$	0.201758	−	18.0913i	0.00686394	−	0.615478i
$865$	16.0443	−	19.8078i	0.545522	−	0.673486i
$866$	−7.89314	+	24.1095i	−0.268220	+	0.819274i
$867$			9.51741i			0.323228i
$868$	−24.0198	−	17.6156i	−0.815285	−	0.597914i
$869$			28.7816i			0.976348i
$870$	6.57777	+	10.1814i	0.223007	+	0.345181i
$871$		−	22.1986i		−	0.752170i
$872$	22.9293	+	32.0077i	0.776485	+	1.08392i
$873$	−31.9727			−1.08211
$874$	−8.69610	+	30.4857i	−0.294150	+	1.03120i
$875$	31.1510	+	15.8874i	1.05310	+	0.537092i
$876$	−7.47231	−	5.48005i	−0.252466	−	0.185154i
$877$	−6.22331			−0.210146			−0.105073	−	0.994465i	$-0.533508\pi$
$877$	−6.22331			−0.210146			−0.105073	+	0.994465i	$0.533508\pi$
$878$	−10.1190	+	30.9082i	−0.341498	+	1.04310i
$879$		−	5.84664i		−	0.197202i
$880$	12.5923	−	31.9370i	0.424485	−	1.07660i
$881$	22.3999			0.754672			0.377336	−	0.926076i	$-0.376840\pi$
$881$	22.3999			0.754672			0.377336	+	0.926076i	$0.376840\pi$
$882$	−3.28509	+	10.0343i	−0.110615	+	0.337872i
$883$	−13.1166			−0.441410			−0.220705	−	0.975341i	$-0.570836\pi$
$883$	−13.1166			−0.441410			−0.220705	+	0.975341i	$0.570836\pi$
$884$	−0.821875	+	1.12067i	−0.0276427	+	0.0376921i
$885$	7.16936	+	5.80716i	0.240995	+	0.195206i
$886$	−10.7271	+	32.7657i	−0.360383	+	1.10078i
$887$			8.90724i			0.299076i	0.988756	+	0.149538i	$0.0477786\pi$
$887$			8.90724i			0.299076i	−0.988756	+	0.149538i	$0.952221\pi$
$888$	1.68309	+	2.34947i	0.0564807	+	0.0788430i
$889$			24.5803i			0.824398i
$890$	9.27596	−	5.99281i	0.310931	−	0.200879i
$891$		−	23.9889i		−	0.803657i
$892$	−18.4195	+	25.1160i	−0.616732	+	0.840944i
$893$	30.3189	−	1.16840i	1.01458	−	0.0390991i
$894$	14.2219	+	4.65606i	0.475650	+	0.155722i
$895$	11.6972	−	14.4411i	0.390995	−	0.482712i
$896$	−28.2993	−	21.2435i	−0.945415	−	0.709696i
$897$			6.78435i			0.226523i
$898$	−47.0712	−	15.4105i	−1.57079	−	0.514256i
$899$			32.4344i			1.08175i
$900$	−11.0295	+	24.4614i	−0.367651	+	0.815381i
$901$			3.29108i			0.109642i
$902$	−20.3739	+	62.2317i	−0.678376	+	2.07209i
$903$			0.302524i			0.0100674i
$904$	42.5276	−	30.4655i	1.41445	−	1.01327i
$905$	−2.54074	−	2.05800i	−0.0844572	−	0.0684101i
$906$	6.58886	+	2.15711i	0.218900	+	0.0716652i
$907$		−	33.0139i		−	1.09621i	−0.836410	−	0.548105i	$-0.815350\pi$
$907$		−	33.0139i		−	1.09621i	0.836410	−	0.548105i	$-0.184650\pi$
$908$	27.2299	−	37.1293i	0.903656	−	1.23218i
$909$	−16.1465			−0.535547
$910$	−12.5818	−	19.4748i	−0.417084	−	0.645583i
$911$	−39.2354			−1.29993			−0.649963	−	0.759966i	$-0.725216\pi$
$911$	−39.2354			−1.29993			−0.649963	+	0.759966i	$0.725216\pi$
$912$	−9.23795	+	3.30689i	−0.305899	+	0.109502i
$913$		−	24.4780i		−	0.810102i
$914$	−2.33850	−	0.765594i	−0.0773506	−	0.0253236i
$915$	3.20005	+	2.59203i	0.105790	+	0.0856900i
$916$	−22.6754	−	16.6297i	−0.749215	−	0.549460i
$917$		−	50.2574i		−	1.65964i
$918$	−0.417154	+	1.27419i	−0.0137681	+	0.0420545i
$919$		−	6.07612i		−	0.200433i	−0.994966	−	0.100216i	$-0.968047\pi$
$919$		−	6.07612i		−	0.200433i	0.994966	−	0.100216i	$-0.0319535\pi$
$920$	1.92372	−	32.4684i	0.0634232	−	1.07045i
$921$	−6.48249			−0.213605
$922$	−9.22876	+	28.1891i	−0.303933	+	0.928359i
$923$	−22.1630			−0.729505
$924$	10.8954	+	7.99045i	0.358432	+	0.262867i
$925$	−1.88526	−	8.88073i	−0.0619871	−	0.291996i
$926$	1.91954	−	5.86319i	0.0630798	−	0.192677i
$927$		−	2.65548i		−	0.0872175i
$928$	−0.429675	+	38.5283i	−0.0141048	+	1.26475i
$929$	4.15684			0.136382			0.0681908	−	0.997672i	$-0.478277\pi$
$929$	4.15684			0.136382			0.0681908	+	0.997672i	$0.478277\pi$
$930$	7.11787	−	4.59856i	0.233404	−	0.150793i
$931$	12.1190	−	0.467030i	0.397183	−	0.0153063i
$932$	21.6584	−	29.5323i	0.709444	−	0.967362i
$933$	−10.9534			−0.358598
$934$	5.07091	−	15.4890i	0.165925	−	0.506817i
$935$	−1.60125	+	1.97686i	−0.0523666	+	0.0646503i
$936$	14.4632	−	10.3610i	0.472745	−	0.338660i
$937$		−	37.0667i		−	1.21091i	−0.795878	−	0.605457i	$-0.792990\pi$
$937$		−	37.0667i		−	1.21091i	0.795878	−	0.605457i	$-0.207010\pi$
$938$	−39.8067	−	13.0322i	−1.29973	−	0.425517i
$939$	8.09691			0.264233
$940$	−30.1055	+	7.91884i	−0.981934	+	0.258284i
$941$		−	21.6239i		−	0.704920i	−0.935827	−	0.352460i	$-0.885345\pi$
$941$		−	21.6239i		−	0.704920i	0.935827	−	0.352460i	$-0.114655\pi$
$942$	3.17921	−	9.71084i	0.103584	−	0.316396i
$943$			62.0400i			2.02030i
$944$	8.81355	+	27.9720i	0.286857	+	0.910411i
$945$	−17.3814	−	14.0789i	−0.565417	−	0.457987i
$946$	−0.886645	−	0.290276i	−0.0288273	−	0.00943769i
$947$	−4.46662			−0.145146			−0.0725729	−	0.997363i	$-0.523121\pi$
$947$	−4.46662			−0.145146			−0.0725729	+	0.997363i	$0.523121\pi$
$948$	−4.99127	+	6.80584i	−0.162109	+	0.221043i
$949$		−	19.3000i		−	0.626504i
$950$	30.7494	+	2.11550i	0.997642	+	0.0686358i
$951$		−	6.36474i		−	0.206391i
$952$	1.52709	+	2.13171i	0.0494933	+	0.0690891i
$953$	−47.8624			−1.55041			−0.775207	−	0.631707i	$-0.782355\pi$
$953$	−47.8624			−1.55041			−0.775207	+	0.631707i	$0.782355\pi$
$954$	13.1090	−	40.0412i	0.424419	−	1.29638i
$955$	7.70577	+	6.24165i	0.249353	+	0.201975i
$956$	8.50889	−	11.6023i	0.275197	−	0.375245i
$957$		−	14.7122i		−	0.475579i
$958$	−15.7612	−	5.16002i	−0.509221	−	0.166713i
$959$		−	58.8330i		−	1.89982i
$960$	8.51611	−	5.36826i	0.274856	−	0.173260i
$961$	−8.32490			−0.268545
$962$	−1.87290	+	5.72073i	−0.0603846	+	0.184444i
$963$			26.7176i			0.860964i
$964$	−2.90370	+	3.95934i	−0.0935219	+	0.127522i
$965$	−8.99741	+	11.1079i	−0.289637	+	0.357577i
$966$	12.1658	+	3.98291i	0.391427	+	0.128148i
$967$	23.9769			0.771044			0.385522	−	0.922699i	$-0.374021\pi$
$967$	23.9769			0.771044			0.385522	+	0.922699i	$0.374021\pi$
$968$	−8.58042	+	6.14675i	−0.275785	+	0.197564i
$969$	0.726578	−	0.0280003i	0.0233411	−	0.000899498i
$970$	−20.4473	−	31.6493i	−0.656523	−	1.01620i
$971$	24.6952			0.792508			0.396254	−	0.918141i	$-0.370310\pi$
$971$	24.6952			0.792508			0.396254	+	0.918141i	$0.370310\pi$
$972$	15.5088	−	21.1470i	0.497445	−	0.678291i
$973$		−	47.6282i		−	1.52689i
$974$	−48.9582	−	16.0283i	−1.56872	−	0.513580i
$975$	6.45230	−	1.36974i	0.206639	−	0.0438668i
$976$	3.93394	+	12.4853i	0.125922	+	0.399646i
$977$	4.34630			0.139051			0.0695253	−	0.997580i	$-0.477852\pi$
$977$	4.34630			0.139051			0.0695253	+	0.997580i	$0.477852\pi$
$978$	0.311197	+	0.101882i	0.00995098	+	0.00325782i
$979$	−13.4039			−0.428390
$980$	−12.0337	+	3.16529i	−0.384402	+	0.101112i
$981$			37.3530i			1.19259i
$982$	−10.6967	−	3.50195i	−0.341344	−	0.111752i
$983$			10.7314i			0.342277i	0.985247	+	0.171139i	$0.0547446\pi$
$983$			10.7314i			0.342277i	−0.985247	+	0.171139i	$0.945255\pi$
$984$	−15.6099	+	11.1824i	−0.497624	+	0.356483i
$985$	38.8859	+	31.4975i	1.23901	+	1.00359i
$986$	0.888394	−	2.71359i	0.0282922	−	0.0864183i
$987$		−	12.2518i		−	0.389979i
$988$	−16.9328	−	11.4422i	−0.538703	−	0.364026i
$989$	−0.883913			−0.0281068
$990$	27.3560	−	17.6736i	0.869429	−	0.561702i
$991$	−12.0344			−0.382286			−0.191143	−	0.981562i	$-0.561219\pi$
$991$	−12.0344			−0.382286			−0.191143	+	0.981562i	$0.561219\pi$
$992$	26.9353	+	0.300389i	0.855198	+	0.00953735i
$993$			4.80848i			0.152593i
$994$	−13.0113	+	39.7429i	−0.412695	+	1.26057i
$995$	−1.02759	−	0.832345i	−0.0325768	−	0.0263871i
$996$	4.24494	−	5.78818i	0.134506	−	0.183406i
$997$			34.6145i			1.09625i	0.836396	+	0.548126i	$0.184659\pi$
$997$			34.6145i			1.09625i	−0.836396	+	0.548126i	$0.815341\pi$
$998$	−34.0971	−	11.1630i	−1.07932	−	0.353357i
$999$			5.80727i			0.183734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.d.b.379.19	yes	40
4.3	odd	2	inner	380.2.d.b.379.17	✓	40
5.4	even	2	inner	380.2.d.b.379.22	yes	40
19.18	odd	2	inner	380.2.d.b.379.21	yes	40
20.19	odd	2	inner	380.2.d.b.379.24	yes	40
76.75	even	2	inner	380.2.d.b.379.23	yes	40
95.94	odd	2	inner	380.2.d.b.379.20	yes	40
380.379	even	2	inner	380.2.d.b.379.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.17	✓	40	4.3	odd	2	inner
380.2.d.b.379.18	yes	40	380.379	even	2	inner
380.2.d.b.379.19	yes	40	1.1	even	1	trivial
380.2.d.b.379.20	yes	40	95.94	odd	2	inner
380.2.d.b.379.21	yes	40	19.18	odd	2	inner
380.2.d.b.379.22	yes	40	5.4	even	2	inner
380.2.d.b.379.23	yes	40	76.75	even	2	inner
380.2.d.b.379.24	yes	40	20.19	odd	2	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.440015 + 1.34402i) q^{2} +0.562756i q^{3} +(-1.61277 - 1.18278i) q^{4} +(1.40743 - 1.73757i) q^{5} +(-0.756355 - 0.247621i) q^{6} -3.12767 q^{7} +(2.29932 - 1.64716i) q^{8} +2.68331 q^{9} +O(q^{10})\)	\(q+(-0.440015 + 1.34402i) q^{2} +0.562756i q^{3} +(-1.61277 - 1.18278i) q^{4} +(1.40743 - 1.73757i) q^{5} +(-0.756355 - 0.247621i) q^{6} -3.12767 q^{7} +(2.29932 - 1.64716i) q^{8} +2.68331 q^{9} +(1.71604 + 2.65617i) q^{10} -3.83819i q^{11} +(0.665615 - 0.907599i) q^{12} +2.34421 q^{13} +(1.37622 - 4.20365i) q^{14} +(0.977829 + 0.792039i) q^{15} +(1.20208 + 3.81510i) q^{16} -0.296420i q^{17} +(-1.18069 + 3.60641i) q^{18} +(4.35567 - 0.167855i) q^{19} +(-4.32502 + 1.13764i) q^{20} -1.76012i q^{21} +(5.15860 + 1.68886i) q^{22} +5.14271 q^{23} +(0.926950 + 1.29396i) q^{24} +(-1.03830 - 4.89101i) q^{25} +(-1.03149 + 3.15066i) q^{26} +3.19832i q^{27} +(5.04423 + 3.69934i) q^{28} -6.81132i q^{29} +(-1.49477 + 0.965712i) q^{30} -4.76184 q^{31} +(-5.65650 - 0.0630825i) q^{32} +2.15997 q^{33} +(0.398394 + 0.130429i) q^{34} +(-4.40197 + 5.43455i) q^{35} +(-4.32756 - 3.17375i) q^{36} +1.81573 q^{37} +(-1.69096 + 5.92796i) q^{38} +1.31922i q^{39} +(0.374068 - 6.31348i) q^{40} +12.0637i q^{41} +(2.36563 + 0.774478i) q^{42} -0.171877 q^{43} +(-4.53972 + 6.19014i) q^{44} +(3.77656 - 4.66243i) q^{45} +(-2.26287 + 6.91190i) q^{46} +6.96079 q^{47} +(-2.14697 + 0.676478i) q^{48} +2.78234 q^{49} +(7.03047 + 0.756623i) q^{50} +0.166812 q^{51} +(-3.78068 - 2.77267i) q^{52} -11.1028 q^{53} +(-4.29860 - 1.40731i) q^{54} +(-6.66913 - 5.40198i) q^{55} +(-7.19152 + 5.15178i) q^{56} +(0.0944615 + 2.45118i) q^{57} +(9.15454 + 2.99708i) q^{58} +7.33191 q^{59} +(-0.640212 - 2.43393i) q^{60} +3.27261 q^{61} +(2.09528 - 6.40000i) q^{62} -8.39250 q^{63} +(2.57373 - 7.57469i) q^{64} +(3.29930 - 4.07322i) q^{65} +(-0.950418 + 2.90304i) q^{66} -9.46955i q^{67} +(-0.350598 + 0.478058i) q^{68} +2.89409i q^{69} +(-5.36721 - 8.30762i) q^{70} -9.45438 q^{71} +(6.16977 - 4.41983i) q^{72} -8.23306i q^{73} +(-0.798946 + 2.44037i) q^{74} +(2.75245 - 0.584309i) q^{75} +(-7.22324 - 4.88107i) q^{76} +12.0046i q^{77} +(-1.77305 - 0.580475i) q^{78} -7.49873 q^{79} +(8.32085 + 3.28078i) q^{80} +6.25004 q^{81} +(-16.2138 - 5.30820i) q^{82} +6.37747 q^{83} +(-2.08183 + 2.83867i) q^{84} +(-0.515050 - 0.417189i) q^{85} +(0.0756284 - 0.231006i) q^{86} +3.83311 q^{87} +(-6.32212 - 8.82523i) q^{88} -3.49224i q^{89} +(4.60465 + 7.12730i) q^{90} -7.33191 q^{91} +(-8.29403 - 6.08267i) q^{92} -2.67975i q^{93} +(-3.06285 + 9.35543i) q^{94} +(5.83862 - 7.80452i) q^{95} +(0.0355001 - 3.18323i) q^{96} -11.9154 q^{97} +(-1.22427 + 3.73952i) q^{98} -10.2990i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Introduction

L-functions

Modular forms

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