LMFDB - Embedded newform 380.3.h.a.39.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(39,380)]

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, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("380.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.h (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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$108$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.18
Character	$\chi$	$=$	380.39
Dual form			380.3.h.a.39.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70952 + 1.03804i) q^{2} +1.20444 q^{3} +(1.84495 - 3.54911i) q^{4} +(3.17819 + 3.85994i) q^{5} +(-2.05903 + 1.25026i) q^{6} +6.44137 q^{7} +(0.530130 + 7.98242i) q^{8} -7.54932 q^{9} +O(q^{10})$	\(q+(-1.70952 + 1.03804i) q^{2} +1.20444 q^{3} +(1.84495 - 3.54911i) q^{4} +(3.17819 + 3.85994i) q^{5} +(-2.05903 + 1.25026i) q^{6} +6.44137 q^{7} +(0.530130 + 7.98242i) q^{8} -7.54932 q^{9} +(-9.43996 - 3.29958i) q^{10} +4.38090i q^{11} +(2.22214 - 4.27470i) q^{12} +18.5880i q^{13} +(-11.0117 + 6.68640i) q^{14} +(3.82795 + 4.64908i) q^{15} +(-9.19233 - 13.0958i) q^{16} -10.0468i q^{17} +(12.9057 - 7.83649i) q^{18} +4.35890i q^{19} +(19.5629 - 4.15833i) q^{20} +7.75827 q^{21} +(-4.54754 - 7.48925i) q^{22} +16.8137 q^{23} +(0.638512 + 9.61437i) q^{24} +(-4.79828 + 24.5352i) q^{25} +(-19.2951 - 31.7766i) q^{26} -19.9327 q^{27} +(11.8840 - 22.8611i) q^{28} +14.9419 q^{29} +(-11.3699 - 3.97416i) q^{30} -10.3268i q^{31} +(29.3085 + 12.8457i) q^{32} +5.27654i q^{33} +(10.4289 + 17.1752i) q^{34} +(20.4719 + 24.8633i) q^{35} +(-13.9281 + 26.7933i) q^{36} +32.8822i q^{37} +(-4.52471 - 7.45164i) q^{38} +22.3882i q^{39} +(-29.1268 + 27.4159i) q^{40} +33.0801 q^{41} +(-13.2630 + 8.05339i) q^{42} -77.3574 q^{43} +(15.5483 + 8.08253i) q^{44} +(-23.9931 - 29.1399i) q^{45} +(-28.7434 + 17.4532i) q^{46} +77.0608 q^{47} +(-11.0716 - 15.7732i) q^{48} -7.50874 q^{49} +(-17.2657 - 46.9243i) q^{50} -12.1008i q^{51} +(65.9707 + 34.2939i) q^{52} +77.3006i q^{53} +(34.0755 - 20.6909i) q^{54} +(-16.9100 + 13.9233i) q^{55} +(3.41477 + 51.4177i) q^{56} +5.25005i q^{57} +(-25.5436 + 15.5103i) q^{58} +41.4208i q^{59} +(23.5624 - 5.00848i) q^{60} -5.37481 q^{61} +(10.7196 + 17.6539i) q^{62} -48.6279 q^{63} +(-63.4379 + 8.46344i) q^{64} +(-71.7485 + 59.0760i) q^{65} +(-5.47726 - 9.02038i) q^{66} -33.9875 q^{67} +(-35.6571 - 18.5358i) q^{68} +20.2511 q^{69} +(-60.8063 - 21.2538i) q^{70} -65.9277i q^{71} +(-4.00212 - 60.2618i) q^{72} +12.9194i q^{73} +(-34.1330 - 56.2129i) q^{74} +(-5.77926 + 29.5513i) q^{75} +(15.4702 + 8.04194i) q^{76} +28.2190i q^{77} +(-23.2398 - 38.2731i) q^{78} +49.5948i q^{79} +(21.3342 - 77.1029i) q^{80} +43.9360 q^{81} +(-56.5512 + 34.3384i) q^{82} -131.312 q^{83} +(14.3136 - 27.5349i) q^{84} +(38.7799 - 31.9305i) q^{85} +(132.244 - 80.3000i) q^{86} +17.9967 q^{87} +(-34.9701 + 2.32245i) q^{88} +146.244 q^{89} +(71.2652 + 24.9096i) q^{90} +119.732i q^{91} +(31.0203 - 59.6735i) q^{92} -12.4381i q^{93} +(-131.737 + 79.9922i) q^{94} +(-16.8251 + 13.8534i) q^{95} +(35.3005 + 15.4719i) q^{96} -58.5847i q^{97} +(12.8364 - 7.79437i) q^{98} -33.0728i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) $ 108 * q + 4 * q^5 + 324 * q^9	$ 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) $ 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * 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 $

$2$	−1.70952	+	1.03804i	−0.854762	+	0.519020i
$2$	−1.70952	+	1.03804i	−0.854762	+	0.519020i
$3$	1.20444			0.401481			0.200741	−	0.979644i	$-0.435665\pi$
$3$	1.20444			0.401481			0.200741	+	0.979644i	$0.435665\pi$
$4$	1.84495	−	3.54911i	0.461237	−	0.887277i
$5$	3.17819	+	3.85994i	0.635637	+	0.771988i
$5$	3.17819	+	3.85994i	0.635637	+	0.771988i
$6$	−2.05903	+	1.25026i	−0.343171	+	0.208377i
$7$	6.44137			0.920196			0.460098	−	0.887868i	$-0.347814\pi$
$7$	6.44137			0.920196			0.460098	+	0.887868i	$0.347814\pi$
$8$	0.530130	+	7.98242i	0.0662663	+	0.997802i
$9$	−7.54932			−0.838813
$10$	−9.43996	−	3.29958i	−0.943996	−	0.329958i
$11$			4.38090i			0.398263i	0.979973	+	0.199132i	$0.0638122\pi$
$11$			4.38090i			0.398263i	−0.979973	+	0.199132i	$0.936188\pi$
$12$	2.22214	−	4.27470i	0.185178	−	0.356225i
$13$			18.5880i			1.42984i	0.699204	+	0.714922i	$0.253538\pi$
$13$			18.5880i			1.42984i	−0.699204	+	0.714922i	$0.746462\pi$
$14$	−11.0117	+	6.68640i	−0.786549	+	0.477600i
$15$	3.82795	+	4.64908i	0.255196	+	0.309939i
$16$	−9.19233	−	13.0958i	−0.574521	−	0.818490i
$17$		−	10.0468i		−	0.590987i	−0.955345	−	0.295493i	$-0.904516\pi$
$17$		−	10.0468i		−	0.590987i	0.955345	−	0.295493i	$-0.0954840\pi$
$18$	12.9057	−	7.83649i	0.716986	−	0.435360i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	19.5629	−	4.15833i	0.978147	−	0.207917i
$21$	7.75827			0.369441
$22$	−4.54754	−	7.48925i	−0.206707	−	0.340421i
$23$	16.8137			0.731029			0.365514	−	0.930806i	$-0.380893\pi$
$23$	16.8137			0.731029			0.365514	+	0.930806i	$0.380893\pi$
$24$	0.638512	+	9.61437i	0.0266047	+	0.400599i
$25$	−4.79828	+	24.5352i	−0.191931	+	0.981408i
$26$	−19.2951	−	31.7766i	−0.742118	−	1.22218i
$27$	−19.9327			−0.738249
$28$	11.8840	−	22.8611i	0.424428	−	0.816469i
$29$	14.9419			0.515239			0.257619	−	0.966246i	$-0.417062\pi$
$29$	14.9419			0.515239			0.257619	+	0.966246i	$0.417062\pi$
$30$	−11.3699	−	3.97416i	−0.378997	−	0.132472i
$31$		−	10.3268i		−	0.333123i	−0.986031	−	0.166562i	$-0.946734\pi$
$31$		−	10.3268i		−	0.333123i	0.986031	−	0.166562i	$-0.0532664\pi$
$32$	29.3085	+	12.8457i	0.915891	+	0.401427i
$33$			5.27654i			0.159895i
$34$	10.4289	+	17.1752i	0.306734	+	0.505153i
$35$	20.4719	+	24.8633i	0.584911	+	0.710380i
$36$	−13.9281	+	26.7933i	−0.386892	+	0.744259i
$37$			32.8822i			0.888708i	0.895851	+	0.444354i	$0.146567\pi$
$37$			32.8822i			0.888708i	−0.895851	+	0.444354i	$0.853433\pi$
$38$	−4.52471	−	7.45164i	−0.119071	−	0.196096i
$39$			22.3882i			0.574056i
$40$	−29.1268	+	27.4159i	−0.728170	+	0.685397i
$41$	33.0801			0.806832			0.403416	−	0.915017i	$-0.367823\pi$
$41$	33.0801			0.806832			0.403416	+	0.915017i	$0.367823\pi$
$42$	−13.2630	+	8.05339i	−0.315785	+	0.191747i
$43$	−77.3574			−1.79901			−0.899505	−	0.436911i	$-0.856072\pi$
$43$	−77.3574			−1.79901			−0.899505	+	0.436911i	$0.856072\pi$
$44$	15.5483	+	8.08253i	0.353370	+	0.183694i
$45$	−23.9931	−	29.1399i	−0.533180	−	0.647553i
$46$	−28.7434	+	17.4532i	−0.624856	+	0.379418i
$47$	77.0608			1.63959			0.819796	−	0.572655i	$-0.194087\pi$
$47$	77.0608			1.63959			0.819796	+	0.572655i	$0.194087\pi$
$48$	−11.0716	−	15.7732i	−0.230659	−	0.328608i
$49$	−7.50874			−0.153240
$50$	−17.2657	−	46.9243i	−0.345315	−	0.938487i
$51$		−	12.1008i		−	0.237270i
$52$	65.9707	+	34.2939i	1.26867	+	0.659497i
$53$			77.3006i			1.45850i	0.684246	+	0.729251i	$0.260131\pi$
$53$			77.3006i			1.45850i	−0.684246	+	0.729251i	$0.739869\pi$
$54$	34.0755	−	20.6909i	0.631027	−	0.383166i
$55$	−16.9100	+	13.9233i	−0.307455	+	0.253151i
$56$	3.41477	+	51.4177i	0.0609780	+	0.918173i
$57$			5.25005i			0.0921061i
$58$	−25.5436	+	15.5103i	−0.440407	+	0.267419i
$59$			41.4208i			0.702047i	0.936367	+	0.351023i	$0.114166\pi$
$59$			41.4208i			0.702047i	−0.936367	+	0.351023i	$0.885834\pi$
$60$	23.5624	−	5.00848i	0.392707	−	0.0834746i
$61$	−5.37481			−0.0881116			−0.0440558	−	0.999029i	$-0.514028\pi$
$61$	−5.37481			−0.0881116			−0.0440558	+	0.999029i	$0.514028\pi$
$62$	10.7196	+	17.6539i	0.172897	+	0.284741i
$63$	−48.6279			−0.771872
$64$	−63.4379	+	8.46344i	−0.991218	+	0.132241i
$65$	−71.7485	+	59.0760i	−1.10382	+	0.908862i
$66$	−5.47726	−	9.02038i	−0.0829888	−	0.136672i
$67$	−33.9875			−0.507276			−0.253638	−	0.967299i	$-0.581627\pi$
$67$	−33.9875			−0.507276			−0.253638	+	0.967299i	$0.581627\pi$
$68$	−35.6571	−	18.5358i	−0.524369	−	0.272585i
$69$	20.2511			0.293494
$70$	−60.8063	−	21.2538i	−0.868661	−	0.303626i
$71$		−	65.9277i		−	0.928560i	−0.885689	−	0.464280i	$-0.846313\pi$
$71$		−	65.9277i		−	0.928560i	0.885689	−	0.464280i	$-0.153687\pi$
$72$	−4.00212	−	60.2618i	−0.0555850	−	0.836969i
$73$			12.9194i			0.176979i	0.996077	+	0.0884893i	$0.0282039\pi$
$73$			12.9194i			0.176979i	−0.996077	+	0.0884893i	$0.971796\pi$
$74$	−34.1330	−	56.2129i	−0.461257	−	0.759634i
$75$	−5.77926	+	29.5513i	−0.0770567	+	0.394017i
$76$	15.4702	+	8.04194i	0.203555	+	0.105815i
$77$			28.2190i			0.366480i
$78$	−23.2398	−	38.2731i	−0.297946	−	0.490681i
$79$			49.5948i			0.627782i	0.949459	+	0.313891i	$0.101633\pi$
$79$			49.5948i			0.627782i	−0.949459	+	0.313891i	$0.898367\pi$
$80$	21.3342	−	77.1029i	0.266678	−	0.963786i
$81$	43.9360			0.542420
$82$	−56.5512	+	34.3384i	−0.689649	+	0.418762i
$83$	−131.312			−1.58207			−0.791037	−	0.611768i	$-0.790459\pi$
$83$	−131.312			−1.58207			−0.791037	+	0.611768i	$0.790459\pi$
$84$	14.3136	−	27.5349i	0.170400	−	0.327797i
$85$	38.7799	−	31.9305i	0.456235	−	0.375653i
$86$	132.244	−	80.3000i	1.53773	−	0.933721i
$87$	17.9967			0.206859
$88$	−34.9701	+	2.32245i	−0.397388	+	0.0263914i
$89$	146.244			1.64319			0.821596	−	0.570070i	$-0.193084\pi$
$89$	146.244			1.64319			0.821596	+	0.570070i	$0.193084\pi$
$90$	71.2652	+	24.9096i	0.791836	+	0.276773i
$91$			119.732i			1.31574i
$92$	31.0203	−	59.6735i	0.337177	−	0.648625i
$93$		−	12.4381i		−	0.133743i
$94$	−131.737	+	79.9922i	−1.40146	+	0.850981i
$95$	−16.8251	+	13.8534i	−0.177106	+	0.145825i
$96$	35.3005	+	15.4719i	0.367713	+	0.161165i
$97$		−	58.5847i		−	0.603966i	−0.953313	−	0.301983i	$-0.902351\pi$
$97$		−	58.5847i		−	0.603966i	0.953313	−	0.301983i	$-0.0976485\pi$
$98$	12.8364	−	7.79437i	0.130983	−	0.0795344i
$99$		−	33.0728i		−	0.334068i
$100$	78.2255	+	62.2958i	0.782255	+	0.622958i
$101$	164.046			1.62421			0.812107	−	0.583508i	$-0.198320\pi$
$101$	164.046			1.62421			0.812107	+	0.583508i	$0.198320\pi$
$102$	12.5611	+	20.6866i	0.123148	+	0.202809i
$103$	−13.2411			−0.128554			−0.0642770	−	0.997932i	$-0.520474\pi$
$103$	−13.2411			−0.128554			−0.0642770	+	0.997932i	$0.520474\pi$
$104$	−148.377	+	9.85405i	−1.42670	+	0.0947505i
$105$	24.6572	+	29.9465i	0.234831	+	0.285204i
$106$	−80.2411	−	132.147i	−0.756991	−	1.24667i
$107$	55.1237			0.515174			0.257587	−	0.966255i	$-0.417073\pi$
$107$	55.1237			0.515174			0.257587	+	0.966255i	$0.417073\pi$
$108$	−36.7748	+	70.7434i	−0.340508	+	0.655031i
$109$	128.952			1.18304			0.591522	−	0.806289i	$-0.298527\pi$
$109$	128.952			1.18304			0.591522	+	0.806289i	$0.298527\pi$
$110$	14.4551	−	41.3555i	0.131410	−	0.375959i
$111$			39.6047i			0.356800i
$112$	−59.2112	−	84.3552i	−0.528672	−	0.753171i
$113$		−	127.923i		−	1.13206i	−0.824384	−	0.566032i	$-0.808478\pi$
$113$		−	127.923i		−	1.13206i	0.824384	−	0.566032i	$-0.191522\pi$
$114$	−5.44976	−	8.97509i	−0.0478049	−	0.0787288i
$115$	53.4369	+	64.8997i	0.464669	+	0.564345i
$116$	27.5671	−	53.0305i	0.237647	−	0.457159i
$117$		−	140.327i		−	1.19937i
$118$	−42.9964	−	70.8098i	−0.364376	−	0.600083i
$119$		−	64.7150i		−	0.543823i
$120$	−35.0816	+	33.0209i	−0.292347	+	0.275174i
$121$	101.808			0.841386
$122$	9.18836	−	5.57926i	0.0753144	−	0.0457316i
$123$	39.8431			0.323928
$124$	−36.6510	−	19.0524i	−0.295572	−	0.153649i
$125$	−109.954	+	59.4564i	−0.879634	+	0.475651i
$126$	83.1307	−	50.4777i	0.659767	−	0.400617i
$127$	7.74382			0.0609749			0.0304875	−	0.999535i	$-0.490294\pi$
$127$	7.74382			0.0609749			0.0304875	+	0.999535i	$0.490294\pi$
$128$	99.6633	−	80.3195i	0.778620	−	0.627496i
$129$	−93.1726			−0.722268
$130$	61.3325	−	175.470i	0.471789	−	1.34977i
$131$		−	161.434i		−	1.23232i	−0.787622	−	0.616159i	$-0.788688\pi$
$131$		−	161.434i		−	1.23232i	0.787622	−	0.616159i	$-0.211312\pi$
$132$	18.7270	+	9.73495i	0.141871	+	0.0737496i
$133$			28.0773i			0.211107i
$134$	58.1024	−	35.2803i	0.433600	−	0.263286i
$135$	−63.3499	−	76.9391i	−0.469258	−	0.569919i
$136$	80.1975	−	5.32610i	0.589688	−	0.0391625i
$137$		−	70.5190i		−	0.514737i	−0.966313	−	0.257369i	$-0.917145\pi$
$137$		−	70.5190i		−	0.514737i	0.966313	−	0.257369i	$-0.0828554\pi$
$138$	−34.6198	+	21.0214i	−0.250868	+	0.152329i
$139$		−	215.827i		−	1.55271i	−0.630295	−	0.776356i	$-0.717066\pi$
$139$		−	215.827i		−	1.55271i	0.630295	−	0.776356i	$-0.282934\pi$
$140$	126.012	−	26.7854i	0.900086	−	0.191324i
$141$	92.8154			0.658266
$142$	68.4356	+	112.705i	0.481941	+	0.793698i
$143$	−81.4320			−0.569455
$144$	69.3958	+	98.8646i	0.481915	+	0.686560i
$145$	47.4882	+	57.6749i	0.327505	+	0.397758i
$146$	−13.4109	−	22.0861i	−0.0918554	−	0.151275i
$147$	−9.04385			−0.0615228
$148$	116.702	+	60.6659i	0.788530	+	0.409905i
$149$	−244.215			−1.63903			−0.819513	−	0.573061i	$-0.805756\pi$
$149$	−244.215			−1.63903			−0.819513	+	0.573061i	$0.805756\pi$
$150$	−20.7956	−	56.5177i	−0.138637	−	0.376785i
$151$		−	173.692i		−	1.15028i	−0.818056	−	0.575139i	$-0.804948\pi$
$151$		−	173.692i		−	1.15028i	0.818056	−	0.575139i	$-0.195052\pi$
$152$	−34.7945	+	2.31078i	−0.228911	+	0.0152025i
$153$			75.8462i			0.495727i
$154$	−29.2924	−	48.2410i	−0.190211	−	0.313254i
$155$	39.8609	−	32.8205i	0.257167	−	0.211745i
$156$	79.4581	+	41.3050i	0.509346	+	0.264776i
$157$		−	30.1229i		−	0.191866i	−0.995388	−	0.0959328i	$-0.969417\pi$
$157$		−	30.1229i		−	0.191866i	0.995388	−	0.0959328i	$-0.0305834\pi$
$158$	−51.4813	−	84.7835i	−0.325831	−	0.536604i
$159$			93.1042i			0.585561i
$160$	43.5644	+	153.955i	0.272278	+	0.962219i
$161$	108.303			0.672689
$162$	−75.1097	+	45.6073i	−0.463640	+	0.281527i
$163$	100.884			0.618918			0.309459	−	0.950913i	$-0.399852\pi$
$163$	100.884			0.618918			0.309459	+	0.950913i	$0.399852\pi$
$164$	61.0311	−	117.405i	0.372141	−	0.715883i
$165$	−20.3671	+	16.7698i	−0.123437	+	0.101635i
$166$	224.481	−	136.307i	1.35230	−	0.821128i
$167$	158.441			0.948749			0.474375	−	0.880323i	$-0.342674\pi$
$167$	158.441			0.948749			0.474375	+	0.880323i	$0.342674\pi$
$168$	4.11289	+	61.9297i	0.0244815	+	0.368629i
$169$	−176.513			−1.04446
$170$	−33.1501	+	94.8411i	−0.195001	+	0.557889i
$171$		−	32.9067i		−	0.192437i
$172$	−142.720	+	274.550i	−0.829770	+	1.59622i
$173$		−	52.4672i		−	0.303279i	−0.988436	−	0.151639i	$-0.951545\pi$
$173$		−	52.4672i		−	0.303279i	0.988436	−	0.151639i	$-0.0484552\pi$
$174$	−30.7658	+	18.6813i	−0.176815	+	0.107364i
$175$	−30.9075	+	158.040i	−0.176614	+	0.903088i
$176$	57.3715	−	40.2707i	0.325975	−	0.228811i
$177$			49.8890i			0.281859i
$178$	−250.008	+	151.807i	−1.40454	+	0.852849i
$179$			30.3539i			0.169575i	0.996399	+	0.0847875i	$0.0270211\pi$
$179$			30.3539i			0.169575i	−0.996399	+	0.0847875i	$0.972979\pi$
$180$	−147.687	+	31.3926i	−0.820482	+	0.174403i
$181$	−300.899			−1.66242			−0.831212	−	0.555956i	$-0.812352\pi$
$181$	−300.899			−1.66242			−0.831212	+	0.555956i	$0.812352\pi$
$182$	−124.287	−	204.685i	−0.682894	−	1.12464i
$183$	−6.47365			−0.0353751
$184$	8.91343	+	134.214i	0.0484425	+	0.729422i
$185$	−126.923	+	104.506i	−0.686072	+	0.564896i
$186$	12.9112	+	21.2632i	0.0694151	+	0.114318i
$187$	44.0139			0.235368
$188$	142.173	−	273.497i	0.756241	−	1.45477i
$189$	−128.394			−0.679334
$190$	14.3825	−	41.1478i	0.0756976	−	0.216567i
$191$			240.190i			1.25754i	0.777593	+	0.628768i	$0.216441\pi$
$191$			240.190i			1.25754i	−0.777593	+	0.628768i	$0.783559\pi$
$192$	−76.4074	+	10.1937i	−0.397955	+	0.0530924i
$193$		−	81.0689i		−	0.420046i	−0.977696	−	0.210023i	$-0.932646\pi$
$193$		−	81.0689i		−	0.420046i	0.977696	−	0.210023i	$-0.0673539\pi$
$194$	60.8132	+	100.152i	0.313470	+	0.516247i
$195$	−86.4170	+	71.1538i	−0.443164	+	0.364891i
$196$	−13.8532	+	26.6493i	−0.0706798	+	0.135966i
$197$		−	265.088i		−	1.34563i	−0.739812	−	0.672813i	$-0.765086\pi$
$197$		−	265.088i		−	1.34563i	0.739812	−	0.672813i	$-0.234914\pi$
$198$	34.3308	+	56.5387i	0.173388	+	0.285549i
$199$		−	78.0268i		−	0.392094i	−0.980594	−	0.196047i	$-0.937189\pi$
$199$		−	78.0268i		−	0.392094i	0.980594	−	0.196047i	$-0.0628106\pi$
$200$	−198.394	−	25.2950i	−0.991970	−	0.126475i
$201$	−40.9360			−0.203662
$202$	−280.440	+	170.286i	−1.38832	+	0.843000i
$203$	96.2465			0.474120
$204$	−42.9469	−	22.3253i	−0.210524	−	0.109438i
$205$	105.135	+	127.687i	0.512852	+	0.622864i
$206$	22.6359	−	13.7447i	0.109883	−	0.0667221i
$207$	−126.932			−0.613196
$208$	243.425	−	170.867i	1.17031	−	0.821476i
$209$	−19.0959			−0.0913679
$210$	−73.2377	−	25.5990i	−0.348751	−	0.121900i
$211$			225.442i			1.06845i	0.845343	+	0.534224i	$0.179396\pi$
$211$			225.442i			1.06845i	−0.845343	+	0.534224i	$0.820604\pi$
$212$	274.348	+	142.616i	1.29410	+	0.672715i
$213$		−	79.4062i		−	0.372799i
$214$	−94.2353	+	57.2205i	−0.440352	+	0.267386i
$215$	−245.856	−	298.595i	−1.14352	−	1.38881i
$216$	−10.5669	−	159.111i	−0.0489210	−	0.736626i
$217$		−	66.5188i		−	0.306538i
$218$	−220.446	+	133.857i	−1.01122	+	0.614024i
$219$			15.5607i			0.0710536i
$220$	18.2172	+	85.7032i	0.0828056	+	0.389560i
$221$	186.749			0.845019
$222$	−41.1113	−	67.7053i	−0.185186	−	0.304979i
$223$	213.433			0.957099			0.478550	−	0.878060i	$-0.341163\pi$
$223$	213.433			0.957099			0.478550	+	0.878060i	$0.341163\pi$
$224$	188.787	+	82.7436i	0.842799	+	0.369391i
$225$	36.2237	−	185.224i	0.160994	−	0.823218i
$226$	132.789	+	218.688i	0.587563	+	0.967645i
$227$	33.4439			0.147330			0.0736650	−	0.997283i	$-0.476530\pi$
$227$	33.4439			0.147330			0.0736650	+	0.997283i	$0.476530\pi$
$228$	18.6330	+	9.68607i	0.0817236	+	0.0424827i
$229$	−44.7554			−0.195439			−0.0977193	−	0.995214i	$-0.531155\pi$
$229$	−44.7554			−0.195439			−0.0977193	+	0.995214i	$0.531155\pi$
$230$	−158.720	−	55.4780i	−0.690088	−	0.241209i
$231$			33.9882i			0.147135i
$232$	7.92116	+	119.273i	0.0341430	+	0.514106i
$233$			215.494i			0.924866i	0.886654	+	0.462433i	$0.153023\pi$
$233$			215.494i			0.924866i	−0.886654	+	0.462433i	$0.846977\pi$
$234$	145.664	+	239.892i	0.622498	+	1.02518i
$235$	244.914	+	297.450i	1.04219	+	1.26575i
$236$	147.007	+	76.4192i	0.622910	+	0.323810i
$237$			59.7341i			0.252043i
$238$	67.1767	+	110.632i	0.282255	+	0.464840i
$239$		−	305.842i		−	1.27968i	−0.768510	−	0.639838i	$-0.779002\pi$
$239$		−	305.842i		−	1.27968i	0.768510	−	0.639838i	$-0.220998\pi$
$240$	25.6959	−	92.8661i	0.107066	−	0.386942i
$241$	−149.888			−0.621943			−0.310971	−	0.950419i	$-0.600654\pi$
$241$	−149.888			−0.621943			−0.310971	+	0.950419i	$0.600654\pi$
$242$	−174.043	+	105.680i	−0.719185	+	0.436696i
$243$	232.313			0.956020
$244$	−9.91624	+	19.0758i	−0.0406403	+	0.0781794i
$245$	−23.8642	−	28.9833i	−0.0974047	−	0.118299i
$246$	−68.1128	+	41.3587i	−0.276881	+	0.168125i
$247$	−81.0231			−0.328029
$248$	82.4329	−	5.47456i	0.332391	−	0.0220748i
$249$	−158.158			−0.635173
$250$	126.251	−	215.779i	0.505006	−	0.863116i
$251$			79.7048i			0.317549i	0.987315	+	0.158774i	$0.0507543\pi$
$251$			79.7048i			0.317549i	−0.987315	+	0.158774i	$0.949246\pi$
$252$	−89.7160	+	172.586i	−0.356016	+	0.684864i
$253$			73.6589i			0.291142i
$254$	−13.2382	+	8.03839i	−0.0521191	+	0.0316472i
$255$	46.7082	−	38.4585i	0.183170	−	0.150818i
$256$	−87.0020	+	240.763i	−0.339852	+	0.940479i
$257$		−	112.477i		−	0.437653i	−0.975764	−	0.218827i	$-0.929777\pi$
$257$		−	112.477i		−	0.437653i	0.975764	−	0.218827i	$-0.0702230\pi$
$258$	159.281	−	96.7169i	0.617368	−	0.374872i
$259$			211.806i			0.817785i
$260$	77.2950	+	363.635i	0.297289	+	1.39860i
$261$	−112.801			−0.432189
$262$	167.575	+	275.975i	0.639598	+	1.05334i
$263$	−399.362			−1.51849			−0.759244	−	0.650806i	$-0.774431\pi$
$263$	−399.362			−1.51849			−0.759244	+	0.650806i	$0.774431\pi$
$264$	−42.1196	+	2.79726i	−0.159544	+	0.0105957i
$265$	−298.376	+	245.676i	−1.12595	+	0.927078i
$266$	−29.1453	−	47.9988i	−0.109569	−	0.180447i
$267$	176.143			0.659711
$268$	−62.7051	+	120.625i	−0.233974	+	0.450094i
$269$	−49.1692			−0.182785			−0.0913925	−	0.995815i	$-0.529132\pi$
$269$	−49.1692			−0.182785			−0.0913925	+	0.995815i	$0.529132\pi$
$270$	188.164	+	65.7696i	0.696904	+	0.243591i
$271$		−	477.297i		−	1.76124i	−0.473819	−	0.880622i	$-0.657125\pi$
$271$		−	477.297i		−	1.76124i	0.473819	−	0.880622i	$-0.342875\pi$
$272$	−131.571	+	92.3533i	−0.483717	+	0.339534i
$273$			144.211i			0.528244i
$274$	73.2015	+	120.554i	0.267159	+	0.439978i
$275$	−107.486	−	21.0208i	−0.390859	−	0.0764391i
$276$	37.3622	−	71.8734i	0.135370	−	0.260411i
$277$		−	373.269i		−	1.34754i	−0.738940	−	0.673771i	$-0.764673\pi$
$277$		−	373.269i		−	1.34754i	0.738940	−	0.673771i	$-0.235327\pi$
$278$	224.037	+	368.961i	0.805888	+	1.32720i
$279$			77.9604i			0.279428i
$280$	−187.617	+	176.596i	−0.670059	+	0.630699i
$281$	308.449			1.09768			0.548842	−	0.835926i	$-0.315069\pi$
$281$	308.449			1.09768			0.548842	+	0.835926i	$0.315069\pi$
$282$	−158.670	+	96.3461i	−0.562661	+	0.341653i
$283$	178.424			0.630472			0.315236	−	0.949013i	$-0.397916\pi$
$283$	178.424			0.630472			0.315236	+	0.949013i	$0.397916\pi$
$284$	−233.985	−	121.633i	−0.823890	−	0.428286i
$285$	−20.2649	+	16.6856i	−0.0711048	+	0.0585461i
$286$	139.210	−	84.5297i	0.486748	−	0.295558i
$287$	213.081			0.742443
$288$	−221.259	−	96.9759i	−0.768261	−	0.336722i
$289$	188.062			0.650735
$290$	−141.051	−	49.3021i	−0.486383	−	0.170007i
$291$		−	70.5619i		−	0.242481i
$292$	45.8525	+	23.8357i	0.157029	+	0.0816291i
$293$			383.511i			1.30891i	0.756100	+	0.654456i	$0.227102\pi$
$293$			383.511i			1.30891i	−0.756100	+	0.654456i	$0.772898\pi$
$294$	15.4607	−	9.38788i	0.0525874	−	0.0319316i
$295$	−159.882	+	131.643i	−0.541972	+	0.446247i
$296$	−262.479	+	17.4318i	−0.886754	+	0.0588914i
$297$		−	87.3232i		−	0.294017i
$298$	417.491	−	253.505i	1.40098	−	0.850687i
$299$			312.532i			1.04526i
$300$	94.2182	+	75.0318i	0.314061	+	0.250106i
$301$	−498.288			−1.65544
$302$	180.299	+	296.931i	0.597017	+	0.983214i
$303$	197.584			0.652092
$304$	57.0834	−	40.0685i	0.187774	−	0.131804i
$305$	−17.0821	−	20.7464i	−0.0560070	−	0.0680211i
$306$	−78.7314	−	129.661i	−0.257292	−	0.423729i
$307$	89.1480			0.290384			0.145192	−	0.989403i	$-0.453620\pi$
$307$	89.1480			0.290384			0.145192	+	0.989403i	$0.453620\pi$
$308$	100.152	+	52.0626i	0.325170	+	0.169034i
$309$	−15.9481			−0.0516120
$310$	−34.0742	+	97.4847i	−0.109917	+	0.314467i
$311$		−	494.211i		−	1.58910i	−0.607198	−	0.794551i	$-0.707706\pi$
$311$		−	494.211i		−	1.58910i	0.607198	−	0.794551i	$-0.292294\pi$
$312$	−178.712	+	11.8687i	−0.572794	+	0.0380405i
$313$		−	193.158i		−	0.617117i	−0.951205	−	0.308559i	$-0.900153\pi$
$313$		−	193.158i		−	0.617117i	0.951205	−	0.308559i	$-0.0998466\pi$
$314$	31.2688	+	51.4959i	0.0995821	+	0.164000i
$315$	−154.549	−	187.701i	−0.490630	−	0.595876i
$316$	176.017	+	91.4998i	0.557017	+	0.289556i
$317$		−	619.732i		−	1.95499i	−0.210954	−	0.977496i	$-0.567657\pi$
$317$		−	619.732i		−	1.95499i	0.210954	−	0.977496i	$-0.432343\pi$
$318$	−96.6459	−	159.164i	−0.303918	−	0.500516i
$319$			65.4590i			0.205201i
$320$	−234.286	−	217.968i	−0.732143	−	0.681151i
$321$	66.3933			0.206833
$322$	−185.147	+	112.423i	−0.574990	+	0.349139i
$323$	43.7929			0.135582
$324$	81.0596	−	155.934i	0.250184	−	0.481277i
$325$	−456.060	−	89.1903i	−1.40326	−	0.274432i
$326$	−172.463	+	104.721i	−0.529028	+	0.321231i
$327$	155.315			0.474970
$328$	17.5368	+	264.059i	0.0534657	+	0.805058i
$329$	496.377			1.50875
$330$	17.4104	−	49.8103i	0.0527587	−	0.150940i
$331$		−	155.301i		−	0.469186i	−0.972094	−	0.234593i	$-0.924624\pi$
$331$		−	155.301i		−	0.469186i	0.972094	−	0.234593i	$-0.0753757\pi$
$332$	−242.264	+	466.041i	−0.729711	+	1.40374i
$333$		−	248.238i		−	0.745460i
$334$	−270.859	+	164.468i	−0.810955	+	0.492420i
$335$	−108.018	−	131.190i	−0.322443	−	0.391611i
$336$	−71.3166	−	101.601i	−0.212252	−	0.302384i
$337$			182.187i			0.540615i	0.962774	+	0.270308i	$0.0871254\pi$
$337$			182.187i			0.540615i	−0.962774	+	0.270308i	$0.912875\pi$
$338$	301.753	−	183.228i	0.892761	−	0.542093i
$339$		−	154.076i		−	0.454502i
$340$	−41.7778	−	196.544i	−0.122876	−	0.578071i
$341$	45.2407			0.132671
$342$	34.1585	+	56.2548i	0.0998785	+	0.164488i
$343$	−363.994			−1.06121
$344$	−41.0095	−	617.499i	−0.119214	−	1.79505i
$345$	64.3618	+	78.1681i	0.186556	+	0.226574i
$346$	54.4631	+	89.6940i	0.157408	+	0.259231i
$347$	−37.0704			−0.106831			−0.0534156	−	0.998572i	$-0.517011\pi$
$347$	−37.0704			−0.106831			−0.0534156	+	0.998572i	$0.517011\pi$
$348$	33.2030	−	63.8722i	0.0954109	−	0.183541i
$349$	−244.060			−0.699311			−0.349656	−	0.936878i	$-0.613701\pi$
$349$	−244.060			−0.699311			−0.349656	+	0.936878i	$0.613701\pi$
$350$	−111.215	−	302.257i	−0.317757	−	0.863592i
$351$		−	370.509i		−	1.05558i
$352$	−56.2755	+	128.398i	−0.159874	+	0.364766i
$353$			48.4139i			0.137150i	0.997646	+	0.0685750i	$0.0218452\pi$
$353$			48.4139i			0.137150i	−0.997646	+	0.0685750i	$0.978155\pi$
$354$	−51.7867	−	85.2864i	−0.146290	−	0.240922i
$355$	254.477	−	209.531i	0.716837	−	0.590227i
$356$	269.813	−	519.036i	0.757901	−	1.45797i
$357$		−	77.9456i		−	0.218335i
$358$	−31.5086	−	51.8908i	−0.0880128	−	0.144946i
$359$			191.649i			0.533842i	0.963718	+	0.266921i	$0.0860062\pi$
$359$			191.649i			0.533842i	−0.963718	+	0.266921i	$0.913994\pi$
$360$	219.887	−	206.971i	0.610798	−	0.574920i
$361$	−19.0000			−0.0526316
$362$	514.394	−	312.345i	1.42098	−	0.862831i
$363$	122.622			0.337801
$364$	424.942	+	220.899i	1.16742	+	0.606867i
$365$	−49.8683	+	41.0604i	−0.136625	+	0.112494i
$366$	11.0669	−	6.71991i	0.0302373	−	0.0183604i
$367$	276.491			0.753381			0.376690	−	0.926339i	$-0.377062\pi$
$367$	276.491			0.753381			0.376690	+	0.926339i	$0.377062\pi$
$368$	−154.557	−	220.189i	−0.419991	−	0.598340i
$369$	−249.732			−0.676781
$370$	108.497	−	310.406i	0.293236	−	0.838936i
$371$			497.922i			1.34211i
$372$	−44.1440	−	22.9476i	−0.118667	−	0.0616871i
$373$			671.067i			1.79911i	0.436811	+	0.899553i	$0.356108\pi$
$373$			671.067i			1.79911i	−0.436811	+	0.899553i	$0.643892\pi$
$374$	−75.2428	+	45.6881i	−0.201184	+	0.122161i
$375$	−132.434	+	71.6119i	−0.353157	+	0.190965i
$376$	40.8523	+	615.132i	0.108650	+	1.63599i
$377$			277.740i			0.736711i
$378$	219.493	−	133.278i	0.580669	−	0.352588i
$379$			291.027i			0.767880i	0.923358	+	0.383940i	$0.125433\pi$
$379$			291.027i			0.767880i	−0.923358	+	0.383940i	$0.874567\pi$
$380$	18.1258	+	85.2728i	0.0476993	+	0.224402i
$381$	9.32699			0.0244803
$382$	−249.326	−	410.610i	−0.652686	−	1.07490i
$383$	−60.6356			−0.158318			−0.0791588	−	0.996862i	$-0.525223\pi$
$383$	−60.6356			−0.158318			−0.0791588	+	0.996862i	$0.525223\pi$
$384$	120.039	−	96.7403i	0.312601	−	0.251928i
$385$	−108.924	+	89.6852i	−0.282918	+	0.232948i
$386$	84.1527	+	138.589i	0.218012	+	0.359039i
$387$	583.995			1.50903
$388$	−207.923	−	108.086i	−0.535885	−	0.278571i
$389$	435.068			1.11843			0.559214	−	0.829024i	$-0.311103\pi$
$389$	435.068			1.11843			0.559214	+	0.829024i	$0.311103\pi$
$390$	73.8716	−	211.343i	0.189414	−	0.541906i
$391$		−	168.923i		−	0.432028i
$392$	−3.98061	−	59.9379i	−0.0101546	−	0.152903i
$393$		−	194.438i		−	0.494753i
$394$	275.172	+	453.175i	0.698407	+	1.15019i
$395$	−191.433	+	157.621i	−0.484640	+	0.399041i
$396$	−117.379	−	61.0176i	−0.296411	−	0.154085i
$397$		−	169.633i		−	0.427286i	−0.976912	−	0.213643i	$-0.931467\pi$
$397$		−	169.633i		−	0.427286i	0.976912	−	0.213643i	$-0.0685330\pi$
$398$	80.9949	+	133.389i	0.203505	+	0.335147i
$399$			33.8175i			0.0847557i
$400$	365.417	−	162.698i	0.913541	−	0.406746i
$401$	8.07776			0.0201441			0.0100720	−	0.999949i	$-0.496794\pi$
$401$	8.07776			0.0201441			0.0100720	+	0.999949i	$0.496794\pi$
$402$	69.9811	−	42.4932i	0.174082	−	0.105704i
$403$	191.955			0.476314
$404$	302.656	−	582.216i	0.749148	−	1.44113i
$405$	139.637	+	169.590i	0.344782	+	0.418742i
$406$	−164.536	+	99.9076i	−0.405260	+	0.246078i
$407$	−144.054			−0.353940
$408$	96.5934	−	6.41498i	0.236748	−	0.0157230i
$409$	−101.139			−0.247284			−0.123642	−	0.992327i	$-0.539457\pi$
$409$	−101.139			−0.247284			−0.123642	+	0.992327i	$0.539457\pi$
$410$	−312.275	−	109.150i	−0.761646	−	0.266221i
$411$		−	84.9361i		−	0.206657i
$412$	−24.4291	+	46.9940i	−0.0592939	+	0.114063i
$413$			266.807i			0.646021i
$414$	216.993	−	131.760i	0.524137	−	0.318261i
$415$	−417.334	−	506.857i	−1.00563	−	1.22134i
$416$	−238.775	+	544.786i	−0.573978	+	1.30958i
$417$		−	259.951i		−	0.623385i
$418$	32.6449	−	19.8223i	0.0780978	−	0.0474217i
$419$		−	598.543i		−	1.42850i	−0.699889	−	0.714251i	$-0.746767\pi$
$419$		−	598.543i		−	1.42850i	0.699889	−	0.714251i	$-0.253233\pi$
$420$	151.774	−	32.2615i	0.361368	−	0.0768130i
$421$	625.523			1.48580			0.742901	−	0.669401i	$-0.233449\pi$
$421$	625.523			1.48580			0.742901	+	0.669401i	$0.233449\pi$
$422$	−234.018	−	385.399i	−0.554545	−	0.913269i
$423$	−581.757			−1.37531
$424$	−617.046	+	40.9794i	−1.45530	+	0.0966495i
$425$	246.500	+	48.2072i	0.579999	+	0.113429i
$426$	82.4268	+	135.747i	0.193490	+	0.318655i
$427$	−34.6211			−0.0810799
$428$	101.700	−	195.640i	0.237618	−	0.457102i
$429$	−98.0803			−0.228625
$430$	730.250	+	255.247i	1.69826	+	0.593598i
$431$			594.626i			1.37964i	0.723980	+	0.689821i	$0.242311\pi$
$431$			594.626i			1.37964i	−0.723980	+	0.689821i	$0.757689\pi$
$432$	183.228	+	261.036i	0.424139	+	0.604249i
$433$		−	263.306i		−	0.608098i	−0.952656	−	0.304049i	$-0.901661\pi$
$433$		−	263.306i		−	0.608098i	0.952656	−	0.304049i	$-0.0983386\pi$
$434$	69.0492	+	113.716i	0.159099	+	0.262017i
$435$	57.1969	+	69.4662i	0.131487	+	0.159692i
$436$	237.910	−	457.664i	0.545664	−	1.04969i
$437$			73.2890i			0.167709i
$438$	−16.1527	−	26.6015i	−0.0368782	−	0.0607339i
$439$			316.778i			0.721590i	0.932645	+	0.360795i	$0.117495\pi$
$439$			316.778i			0.721590i	−0.932645	+	0.360795i	$0.882505\pi$
$440$	−120.106	−	127.602i	−0.272968	−	0.290003i
$441$	56.6858			0.128539
$442$	−319.252	+	193.853i	−0.722290	+	0.438582i
$443$	291.631			0.658309			0.329155	−	0.944276i	$-0.393236\pi$
$443$	291.631			0.658309			0.329155	+	0.944276i	$0.393236\pi$
$444$	140.562	+	73.0687i	0.316580	+	0.164569i
$445$	464.791	+	564.494i	1.04447	+	1.26853i
$446$	−364.869	+	221.552i	−0.818092	+	0.496753i
$447$	−294.143			−0.658038
$448$	−408.627	+	54.5162i	−0.912114	+	0.121688i
$449$	−15.5790			−0.0346971			−0.0173486	−	0.999850i	$-0.505522\pi$
$449$	−15.5790			−0.0346971			−0.0173486	+	0.999850i	$0.505522\pi$
$450$	130.345	+	354.247i	0.289655	+	0.787215i
$451$			144.921i			0.321332i
$452$	−454.013	−	236.012i	−1.00445	−	0.522149i
$453$		−	209.202i		−	0.461815i
$454$	−57.1732	+	34.7161i	−0.125932	+	0.0764672i
$455$	−462.159	+	380.531i	−1.01573	+	0.836331i
$456$	−41.9081	+	2.78321i	−0.0919037	+	0.00610353i
$457$		−	422.833i		−	0.925237i	−0.886558	−	0.462618i	$-0.846910\pi$
$457$		−	422.833i		−	0.925237i	0.886558	−	0.462618i	$-0.153090\pi$
$458$	76.5105	−	46.4579i	0.167054	−	0.101437i
$459$			200.259i			0.436295i
$460$	328.924	−	69.9168i	0.715053	−	0.151993i
$461$	548.488			1.18978			0.594889	−	0.803808i	$-0.297196\pi$
$461$	548.488			1.18978			0.594889	+	0.803808i	$0.297196\pi$
$462$	−35.2811	−	58.1036i	−0.0763660	−	0.125765i
$463$	366.269			0.791078			0.395539	−	0.918449i	$-0.370558\pi$
$463$	366.269			0.791078			0.395539	+	0.918449i	$0.370558\pi$
$464$	−137.351	−	195.677i	−0.296015	−	0.421718i
$465$	48.0102	−	39.5305i	0.103248	−	0.0850118i
$466$	−223.691	−	368.392i	−0.480024	−	0.790540i
$467$	−223.999			−0.479656			−0.239828	−	0.970815i	$-0.577091\pi$
$467$	−223.999			−0.479656			−0.239828	+	0.970815i	$0.577091\pi$
$468$	−498.034	−	258.895i	−1.06418	−	0.553195i
$469$	−218.926			−0.466793
$470$	−727.451	−	254.268i	−1.54777	−	0.540997i
$471$		−	36.2814i		−	0.0770305i
$472$	−330.638	+	21.9584i	−0.700504	+	0.0465220i
$473$		−	338.895i		−	0.716480i
$474$	−62.0064	−	102.117i	−0.130815	−	0.215437i
$475$	−106.947	−	20.9152i	−0.225151	−	0.0440320i
$476$	−229.680	−	119.396i	−0.482522	−	0.250831i
$477$		−	583.567i		−	1.22341i
$478$	317.476	+	522.845i	0.664177	+	1.09382i
$479$			763.448i			1.59384i	0.604087	+	0.796918i	$0.293538\pi$
$479$			763.448i			1.59384i	−0.604087	+	0.796918i	$0.706462\pi$
$480$	52.4709	+	185.430i	0.109314	+	0.386313i
$481$	−611.214			−1.27071
$482$	256.238	−	155.590i	0.531613	−	0.322801i
$483$	130.445			0.270072
$484$	187.830	−	361.327i	0.388078	−	0.746543i
$485$	226.133	−	186.193i	0.466254	−	0.383903i
$486$	−397.145	+	241.150i	−0.817170	+	0.496193i
$487$	−630.562			−1.29479			−0.647394	−	0.762155i	$-0.724141\pi$
$487$	−630.562			−1.29479			−0.647394	+	0.762155i	$0.724141\pi$
$488$	−2.84935	−	42.9039i	−0.00583883	−	0.0879179i
$489$	121.509			0.248484
$490$	70.8822	+	24.7757i	0.144657	+	0.0505626i
$491$			441.165i			0.898503i	0.893405	+	0.449251i	$0.148309\pi$
$491$			441.165i			0.898503i	−0.893405	+	0.449251i	$0.851691\pi$
$492$	73.5085	−	141.408i	0.149407	−	0.287414i
$493$		−	150.118i		−	0.304499i
$494$	138.511	−	84.1052i	0.280387	−	0.170253i
$495$	127.659	−	105.111i	0.257897	−	0.212346i
$496$	−135.238	+	94.9275i	−0.272658	+	0.191386i
$497$		−	424.665i		−	0.854457i
$498$	270.375	−	164.174i	0.542922	−	0.329667i
$499$		−	181.530i		−	0.363788i	−0.983318	−	0.181894i	$-0.941777\pi$
$499$		−	181.530i		−	0.363788i	0.983318	−	0.181894i	$-0.0582228\pi$
$500$	8.15719	+	499.933i	0.0163144	+	0.999867i
$501$	190.833			0.380905
$502$	−82.7367	−	136.257i	−0.164814	−	0.271429i
$503$	−863.536			−1.71677			−0.858386	−	0.513005i	$-0.828532\pi$
$503$	−863.536			−1.71677			−0.858386	+	0.513005i	$0.828532\pi$
$504$	−25.7791	−	388.168i	−0.0511491	−	0.770176i
$505$	521.368	+	633.207i	1.03241	+	1.25387i
$506$	−76.4609	−	125.922i	−0.151108	−	0.248857i
$507$	−212.600			−0.419329
$508$	14.2869	−	27.4836i	0.0281239	−	0.0541017i
$509$	774.848			1.52229			0.761147	−	0.648579i	$-0.224636\pi$
$509$	774.848			1.52229			0.761147	+	0.648579i	$0.224636\pi$
$510$	−39.9275	+	114.231i	−0.0782892	+	0.223982i
$511$			83.2189i			0.162855i
$512$	−101.189	−	501.901i	−0.197635	−	0.980276i
$513$		−	86.8847i		−	0.169366i
$514$	116.756	+	192.282i	0.227151	+	0.374090i
$515$	−42.0825	−	51.1097i	−0.0817137	−	0.0992422i
$516$	−171.899	+	330.680i	−0.333137	+	0.640852i
$517$			337.596i			0.652990i
$518$	−219.863	−	362.088i	−0.424447	−	0.699012i
$519$		−	63.1938i		−	0.121761i
$520$	−509.606	−	541.408i	−0.980011	−	1.04117i
$521$	279.159			0.535813			0.267906	−	0.963445i	$-0.413668\pi$
$521$	279.159			0.535813			0.267906	+	0.963445i	$0.413668\pi$
$522$	192.837	−	117.092i	0.369419	−	0.224315i
$523$	328.355			0.627830			0.313915	−	0.949451i	$-0.398359\pi$
$523$	328.355			0.627830			0.313915	+	0.949451i	$0.398359\pi$
$524$	−572.946	−	297.837i	−1.09341	−	0.568391i
$525$	−37.2263	+	190.351i	−0.0709073	+	0.362573i
$526$	682.720	−	414.554i	1.29795	−	0.788125i
$527$	−103.751			−0.196871
$528$	69.1008	−	48.5038i	0.130873	−	0.0918632i
$529$	−246.301			−0.465597
$530$	255.060	−	729.714i	0.481245	−	1.37682i
$531$		−	312.698i		−	0.588886i
$532$	99.6493	+	51.8011i	0.187311	+	0.0973706i
$533$			614.892i			1.15364i
$534$	−301.120	+	182.843i	−0.563896	+	0.342403i
$535$	175.193	+	212.774i	0.327464	+	0.397709i
$536$	−18.0178	−	271.302i	−0.0336153	−	0.506161i
$537$			36.5596i			0.0680812i
$538$	84.0559	−	51.0395i	0.156238	−	0.0948690i
$539$		−	32.8950i		−	0.0610297i
$540$	−389.942	+	82.8869i	−0.722116	+	0.153494i
$541$	−520.625			−0.962337			−0.481169	−	0.876628i	$-0.659788\pi$
$541$	−520.625			−0.962337			−0.481169	+	0.876628i	$0.659788\pi$
$542$	495.454	+	815.952i	0.914121	+	1.50545i
$543$	−362.415			−0.667432
$544$	129.057	−	294.456i	0.237238	−	0.541279i
$545$	409.833	+	497.747i	0.751987	+	0.913296i
$546$	−149.696	−	246.531i	−0.274169	−	0.451523i
$547$	972.376			1.77765			0.888827	−	0.458244i	$-0.151521\pi$
$547$	972.376			1.77765			0.888827	+	0.458244i	$0.151521\pi$
$548$	−250.279	−	130.104i	−0.456714	−	0.237416i
$549$	40.5761			0.0739091
$550$	205.571	−	75.6394i	0.373765	−	0.137526i
$551$			65.1303i			0.118204i
$552$	10.7357	+	161.653i	0.0194488	+	0.292849i
$553$			319.458i			0.577682i
$554$	387.468	+	638.113i	0.699401	+	1.15183i
$555$	−152.872	+	125.871i	−0.275445	+	0.226795i
$556$	−765.993	−	398.189i	−1.37769	−	0.716168i
$557$			704.353i			1.26455i	0.774745	+	0.632274i	$0.217878\pi$
$557$			704.353i			1.26455i	−0.774745	+	0.632274i	$0.782122\pi$
$558$	−80.9259	−	133.275i	−0.145029	−	0.238844i
$559$		−	1437.92i		−	2.57230i
$560$	137.422	−	496.648i	0.245396	−	0.886872i
$561$	53.0122			0.0944960
$562$	−527.302	+	320.183i	−0.938260	+	0.569720i
$563$	−741.155			−1.31644			−0.658220	−	0.752826i	$-0.728690\pi$
$563$	−741.155			−1.31644			−0.658220	+	0.752826i	$0.728690\pi$
$564$	171.240	−	329.412i	0.303616	−	0.584064i
$565$	493.776	−	406.563i	0.873939	−	0.719581i
$566$	−305.020	+	185.211i	−0.538904	+	0.327228i
$567$	283.008			0.499132
$568$	526.263	−	34.9503i	0.926519	−	0.0615322i
$569$	355.408			0.624618			0.312309	−	0.949980i	$-0.398897\pi$
$569$	355.408			0.624618			0.312309	+	0.949980i	$0.398897\pi$
$570$	17.3230	−	49.5602i	0.0303912	−	0.0869478i
$571$			1057.10i			1.85131i	0.378364	+	0.925657i	$0.376487\pi$
$571$			1057.10i			1.85131i	−0.378364	+	0.925657i	$0.623513\pi$
$572$	−150.238	+	289.011i	−0.262654	+	0.505264i
$573$			289.295i			0.504877i
$574$	−364.268	+	221.187i	−0.634612	+	0.385343i
$575$	−80.6766	+	412.527i	−0.140307	+	0.717438i
$576$	478.913	−	63.8932i	0.831446	−	0.110926i
$577$			270.911i			0.469516i	0.972054	+	0.234758i	$0.0754297\pi$
$577$			270.911i			0.469516i	−0.972054	+	0.234758i	$0.924570\pi$
$578$	−321.497	+	195.216i	−0.556224	+	0.337744i
$579$		−	97.6429i		−	0.168641i
$580$	292.308	−	62.1335i	0.503979	−	0.107127i
$581$	−845.831			−1.45582
$582$	73.2461	+	120.627i	0.125852	+	0.207263i
$583$	−338.646			−0.580868
$584$	−103.128	+	6.84898i	−0.176590	+	0.0117277i
$585$	541.652	−	445.984i	0.925901	−	0.762365i
$586$	−398.100	−	655.621i	−0.679351	−	1.11881i
$587$	727.172			1.23879			0.619397	−	0.785078i	$-0.287377\pi$
$587$	727.172			1.23879			0.619397	+	0.785078i	$0.287377\pi$
$588$	−16.6854	+	32.0976i	−0.0283766	+	0.0545878i
$589$	45.0135			0.0764237
$590$	136.671	−	391.010i	0.231646	−	0.662729i
$591$		−	319.284i		−	0.540244i
$592$	430.620	−	302.264i	0.727398	−	0.510581i
$593$			148.946i			0.251174i	0.992083	+	0.125587i	$0.0400815\pi$
$593$			148.946i			0.251174i	−0.992083	+	0.125587i	$0.959919\pi$
$594$	90.6449	+	149.281i	0.152601	+	0.251315i
$595$	249.796	−	205.676i	0.419825	−	0.345674i
$596$	−450.564	+	866.745i	−0.755979	+	1.45427i
$597$		−	93.9788i		−	0.157418i
$598$	−324.421	−	534.281i	−0.542509	−	0.893447i
$599$		−	145.115i		−	0.242262i	−0.992637	−	0.121131i	$-0.961348\pi$
$599$		−	145.115i		−	0.242262i	0.992637	−	0.121131i	$-0.0386522\pi$
$600$	−238.954	−	30.4664i	−0.398257	−	0.0507773i
$601$	−785.811			−1.30751			−0.653753	−	0.756708i	$-0.726807\pi$
$601$	−785.811			−1.30751			−0.653753	+	0.756708i	$0.726807\pi$
$602$	851.835	−	517.242i	1.41501	−	0.859207i
$603$	256.582			0.425509
$604$	−616.452	−	320.453i	−1.02062	−	0.530551i
$605$	323.564	+	392.972i	0.534816	+	0.649540i
$606$	−337.774	+	205.100i	−0.557383	+	0.338448i
$607$	−383.971			−0.632572			−0.316286	−	0.948664i	$-0.602436\pi$
$607$	−383.971			−0.632572			−0.316286	+	0.948664i	$0.602436\pi$
$608$	−55.9929	+	127.753i	−0.0920936	+	0.210120i
$609$	115.923			0.190350
$610$	50.7379	+	17.7346i	0.0831769	+	0.0290731i
$611$			1432.41i			2.34436i
$612$	269.187	+	139.932i	0.439847	+	0.228648i
$613$		−	303.034i		−	0.494345i	−0.968971	−	0.247173i	$-0.920499\pi$
$613$		−	303.034i		−	0.494345i	0.968971	−	0.247173i	$-0.0795015\pi$
$614$	−152.401	+	92.5391i	−0.248209	+	0.150715i
$615$	126.629	+	153.792i	0.205900	+	0.250068i
$616$	−225.256	+	14.9597i	−0.365675	+	0.0242853i
$617$			847.375i			1.37338i	0.726951	+	0.686690i	$0.240937\pi$
$617$			847.375i			1.37338i	−0.726951	+	0.686690i	$0.759063\pi$
$618$	27.2637	−	16.5548i	0.0441160	−	0.0267877i
$619$		−	316.706i		−	0.511642i	−0.966724	−	0.255821i	$-0.917654\pi$
$619$		−	316.706i		−	0.511642i	0.966724	−	0.255821i	$-0.0823458\pi$
$620$	−42.9423	−	202.023i	−0.0692618	−	0.325843i
$621$	−335.142			−0.539681
$622$	513.010	+	844.865i	0.824775	+	1.35830i
$623$	942.013			1.51206
$624$	293.192	−	205.800i	0.469859	−	0.329807i
$625$	−578.953	−	235.454i	−0.926325	−	0.376726i
$626$	200.505	+	330.208i	0.320296	+	0.527488i
$627$	−22.9999			−0.0366825
$628$	−106.909	−	55.5752i	−0.170238	−	0.0884956i
$629$	330.360			0.525214
$630$	459.046	+	160.452i	0.728644	+	0.254685i
$631$		−	319.937i		−	0.507032i	−0.967331	−	0.253516i	$-0.918413\pi$
$631$		−	319.937i		−	0.507032i	0.967331	−	0.253516i	$-0.0815871\pi$
$632$	−395.886	+	26.2917i	−0.626402	+	0.0416008i
$633$			271.533i			0.428962i
$634$	643.307	+	1059.45i	1.01468	+	1.67105i
$635$	24.6113	+	29.8907i	0.0387579	+	0.0470719i
$636$	330.437	+	171.772i	0.519555	+	0.270082i
$637$		−	139.572i		−	0.219109i
$638$	−67.9490	−	111.904i	−0.106503	−	0.175398i
$639$			497.709i			0.778888i
$640$	626.777	+	129.424i	0.979339	+	0.202225i
$641$	262.847			0.410057			0.205029	−	0.978756i	$-0.434271\pi$
$641$	262.847			0.410057			0.205029	+	0.978756i	$0.434271\pi$
$642$	−113.501	+	68.9189i	−0.176793	+	0.107350i
$643$	−385.615			−0.599713			−0.299856	−	0.953984i	$-0.596939\pi$
$643$	−385.615			−0.599713			−0.299856	+	0.953984i	$0.596939\pi$
$644$	199.813	−	384.379i	0.310269	−	0.596862i
$645$	−296.120	−	359.641i	−0.459101	−	0.557583i
$646$	−74.8650	+	45.4587i	−0.115890	+	0.0703695i
$647$	−101.900			−0.157496			−0.0787482	−	0.996895i	$-0.525092\pi$
$647$	−101.900			−0.157496			−0.0787482	+	0.996895i	$0.525092\pi$
$648$	23.2918	+	350.715i	0.0359441	+	0.541228i
$649$	−181.460			−0.279600
$650$	872.229	−	320.935i	1.34189	−	0.493747i
$651$		−	80.1182i		−	0.123069i
$652$	186.125	−	358.047i	0.285468	−	0.549152i
$653$			500.908i			0.767088i	0.923523	+	0.383544i	$0.125297\pi$
$653$			500.908i			0.767088i	−0.923523	+	0.383544i	$0.874703\pi$
$654$	−265.515	+	161.223i	−0.405987	+	0.246519i
$655$	623.124	−	513.066i	0.951335	−	0.783307i
$656$	−304.083	−	433.212i	−0.463542	−	0.660384i
$657$		−	97.5329i		−	0.148452i
$658$	−848.569	+	515.259i	−1.28962	+	0.783069i
$659$			552.028i			0.837675i	0.908061	+	0.418837i	$0.137562\pi$
$659$			552.028i			0.837675i	−0.908061	+	0.418837i	$0.862438\pi$
$660$	21.9416	+	103.225i	0.0332449	+	0.156401i
$661$	29.9077			0.0452461			0.0226231	−	0.999744i	$-0.492798\pi$
$661$	29.9077			0.0452461			0.0226231	+	0.999744i	$0.492798\pi$
$662$	161.208	+	265.490i	0.243517	+	0.401042i
$663$	224.929			0.339259
$664$	−69.6126	−	1048.19i	−0.104838	−	1.57860i
$665$	−108.377	+	89.2348i	−0.162972	+	0.134188i
$666$	257.681	+	424.369i	0.386908	+	0.637191i
$667$	251.228			0.376654
$668$	292.316	−	562.325i	0.437598	−	0.841803i
$669$	257.068			0.384257
$670$	320.840	+	112.144i	0.478866	+	0.167380i
$671$		−	23.5465i		−	0.0350916i
$672$	227.383	+	99.6600i	0.338368	+	0.148304i
$673$		−	540.570i		−	0.803225i	−0.915810	−	0.401612i	$-0.868450\pi$
$673$		−	540.570i		−	0.803225i	0.915810	−	0.401612i	$-0.131550\pi$
$674$	−189.118	−	311.454i	−0.280590	−	0.462097i
$675$	95.6427	−	489.053i	0.141693	−	0.724524i
$676$	−325.657	+	626.464i	−0.481742	+	0.926722i
$677$			257.178i			0.379880i	0.981796	+	0.189940i	$0.0608293\pi$
$677$			257.178i			0.379880i	−0.981796	+	0.189940i	$0.939171\pi$
$678$	159.937	+	263.397i	0.235896	+	0.388491i
$679$		−	377.366i		−	0.555767i
$680$	275.441	+	292.630i	0.405060	+	0.430339i
$681$	40.2813			0.0591502
$682$	−77.3401	+	46.9616i	−0.113402	+	0.0688587i
$683$	−1357.92			−1.98817			−0.994086	−	0.108593i	$-0.965365\pi$
$683$	−1357.92			−1.98817			−0.994086	+	0.108593i	$0.965365\pi$
$684$	−116.789	−	60.7112i	−0.170745	−	0.0887590i
$685$	272.199	−	224.122i	0.397371	−	0.327186i
$686$	622.256	−	377.840i	0.907079	−	0.550787i
$687$	−53.9054			−0.0784649
$688$	711.095	+	1013.06i	1.03357	+	1.47247i
$689$	−1436.86			−2.08543
$690$	−191.170	−	66.8202i	−0.277057	−	0.0968408i
$691$		−	1073.44i		−	1.55346i	−0.629834	−	0.776730i	$-0.716877\pi$
$691$		−	1073.44i		−	1.55346i	0.629834	−	0.776730i	$-0.283123\pi$
$692$	−186.212	−	96.7993i	−0.269092	−	0.139883i
$693$		−	213.034i		−	0.307408i
$694$	63.3728	−	38.4806i	0.0913153	−	0.0554475i
$695$	833.079	−	685.938i	1.19867	−	0.986961i
$696$	9.54060	+	143.657i	0.0137078	+	0.206404i
$697$		−	332.348i		−	0.476827i
$698$	417.226	−	253.343i	0.597745	−	0.362956i
$699$			259.550i			0.371316i
$700$	503.880	+	401.270i	0.719828	+	0.573243i
$701$	−543.051			−0.774680			−0.387340	−	0.921937i	$-0.626606\pi$
$701$	−543.051			−0.774680			−0.387340	+	0.921937i	$0.626606\pi$
$702$	384.603	+	633.394i	0.547867	+	0.902271i
$703$	−143.330			−0.203884
$704$	−37.0775	−	277.915i	−0.0526669	−	0.394766i
$705$	294.985	+	358.262i	0.418418	+	0.508173i
$706$	−50.2556	−	82.7648i	−0.0711835	−	0.117231i
$707$	1056.68			1.49460
$708$	177.061	+	92.0426i	0.250087	+	0.130004i
$709$	428.058			0.603748			0.301874	−	0.953348i	$-0.402388\pi$
$709$	428.058			0.603748			0.301874	+	0.953348i	$0.402388\pi$
$710$	−217.534	+	622.355i	−0.306386	+	0.876556i
$711$		−	374.407i		−	0.526592i
$712$	77.5284	+	1167.38i	0.108888	+	1.63958i
$713$		−	173.631i		−	0.243522i
$714$	80.9106	+	133.250i	0.113320	+	0.186624i
$715$	−258.806	−	314.323i	−0.361967	−	0.439612i
$716$	107.729	+	56.0014i	0.150460	+	0.0782143i
$717$		−	368.370i		−	0.513766i
$718$	−198.939	−	327.629i	−0.277074	−	0.456308i
$719$		−	566.186i		−	0.787463i	−0.919226	−	0.393731i	$-0.871184\pi$
$719$		−	566.186i		−	0.787463i	0.919226	−	0.393731i	$-0.128816\pi$
$720$	−161.059	+	582.074i	−0.223693	+	0.808436i
$721$	−85.2906			−0.118295
$722$	32.4810	−	19.7228i	0.0449875	−	0.0273168i
$723$	−180.532			−0.249698
$724$	−555.142	+	1067.92i	−0.766771	+	1.47503i
$725$	−71.6955	+	366.603i	−0.0988903	+	0.505660i
$726$	−209.625	+	127.286i	−0.288739	+	0.175325i
$727$	−1178.55			−1.62112			−0.810560	−	0.585656i	$-0.800837\pi$
$727$	−1178.55			−1.62112			−0.810560	+	0.585656i	$0.800837\pi$
$728$	−955.751	+	63.4736i	−1.31285	+	0.0871890i
$729$	−115.616			−0.158596
$730$	42.6287	−	121.959i	0.0583955	−	0.167067i
$731$			777.192i			1.06319i
$732$	−11.9435	+	22.9757i	−0.0163163	+	0.0313875i
$733$			999.534i			1.36362i	0.731529	+	0.681810i	$0.238807\pi$
$733$			999.534i			1.36362i	−0.731529	+	0.681810i	$0.761193\pi$
$734$	−472.668	+	287.008i	−0.643961	+	0.391019i
$735$	−28.7430	−	34.9087i	−0.0391062	−	0.0474949i
$736$	492.783	+	215.982i	0.669543	+	0.293454i
$737$		−	148.896i		−	0.202029i
$738$	426.923	−	259.232i	0.578487	−	0.351263i
$739$			855.820i			1.15808i	0.815300	+	0.579039i	$0.196572\pi$
$739$			855.820i			1.15808i	−0.815300	+	0.579039i	$0.803428\pi$
$740$	136.735	+	643.272i	0.184777	+	0.869287i
$741$	−97.5878			−0.131697
$742$	−516.863	−	851.210i	−0.696580	−	1.14718i
$743$	−972.675			−1.30912			−0.654559	−	0.756011i	$-0.727146\pi$
$743$	−972.675			−1.30912			−0.654559	+	0.756011i	$0.727146\pi$
$744$	99.2858	−	6.59379i	0.133449	−	0.00886263i
$745$	−776.160	−	942.655i	−1.04183	−	1.26531i
$746$	−696.594	−	1147.20i	−0.933772	−	1.53781i
$747$	991.317			1.32706
$748$	81.2033	−	156.210i	0.108561	−	0.208837i
$749$	355.072			0.474061
$750$	152.063	−	259.894i	0.202750	−	0.346525i
$751$			1107.31i			1.47445i	0.675647	+	0.737225i	$0.263864\pi$
$751$			1107.31i			1.47445i	−0.675647	+	0.737225i	$0.736136\pi$
$752$	−708.369	−	1009.18i	−0.941980	−	1.34199i
$753$			95.9999i			0.127490i
$754$	−288.305	−	474.804i	−0.382368	−	0.629713i
$755$	670.441	−	552.025i	0.888001	−	0.731159i
$756$	−236.880	+	455.684i	−0.313334	+	0.602757i
$757$			620.597i			0.819811i	0.912128	+	0.409906i	$0.134438\pi$
$757$			620.597i			0.819811i	−0.912128	+	0.409906i	$0.865562\pi$
$758$	−302.097	−	497.517i	−0.398545	−	0.656355i
$759$			88.7180i			0.116888i
$760$	−119.503	−	126.961i	−0.157241	−	0.167054i
$761$	−925.617			−1.21632			−0.608159	−	0.793816i	$-0.708092\pi$
$761$	−925.617			−1.21632			−0.608159	+	0.793816i	$0.708092\pi$
$762$	−15.9447	+	9.68178i	−0.0209248	+	0.0127058i
$763$	830.627			1.08863
$764$	852.459	+	443.137i	1.11578	+	0.580023i
$765$	−292.762	+	241.053i	−0.382695	+	0.315102i
$766$	103.658	−	62.9422i	0.135324	−	0.0821700i
$767$	−769.928			−1.00382
$768$	−104.789	+	289.985i	−0.136444	+	0.377585i
$769$	−262.821			−0.341770			−0.170885	−	0.985291i	$-0.554663\pi$
$769$	−262.821			−0.341770			−0.170885	+	0.985291i	$0.554663\pi$
$770$	93.1108	−	266.386i	0.120923	−	0.345956i
$771$		−	135.472i		−	0.175710i
$772$	−287.722	−	149.568i	−0.372697	−	0.193741i
$773$		−	62.4348i		−	0.0807694i	−0.999184	−	0.0403847i	$-0.987142\pi$
$773$		−	62.4348i		−	0.0807694i	0.999184	−	0.0403847i	$-0.0128583\pi$
$774$	−998.354	+	606.210i	−1.28986	+	0.783217i
$775$	253.371	+	49.5509i	0.326930	+	0.0639367i
$776$	467.647	−	31.0575i	0.602638	−	0.0400226i
$777$			255.109i			0.328325i
$778$	−743.760	+	451.618i	−0.955989	+	0.580486i
$779$			144.193i			0.185100i
$780$	93.0975	+	437.978i	0.119356	+	0.561511i
$781$	288.823			0.369811
$782$	175.349	+	288.778i	0.224231	+	0.369281i
$783$	−297.833			−0.380374
$784$	69.0228	+	98.3332i	0.0880393	+	0.125425i
$785$	116.273	−	95.7362i	0.148118	−	0.121957i
$786$	201.834	+	332.396i	0.256786	+	0.422896i
$787$	−703.356			−0.893718			−0.446859	−	0.894605i	$-0.647457\pi$
$787$	−703.356			−0.893718			−0.446859	+	0.894605i	$0.647457\pi$
$788$	−940.828	−	489.074i	−1.19394	−	0.620653i
$789$	−481.009			−0.609644
$790$	163.642	−	468.173i	0.207142	−	0.592623i
$791$		−	824.000i		−	1.04172i
$792$	264.001	−	17.5329i	0.333334	−	0.0221375i
$793$		−	99.9068i		−	0.125986i
$794$	176.085	+	289.991i	0.221770	+	0.365228i
$795$	−359.377	+	295.902i	−0.452046	+	0.372204i
$796$	−276.925	−	143.955i	−0.347896	−	0.180848i
$797$		−	594.908i		−	0.746435i	−0.927744	−	0.373217i	$-0.878255\pi$
$797$		−	594.908i		−	0.746435i	0.927744	−	0.373217i	$-0.121745\pi$
$798$	−35.1039	−	57.8119i	−0.0439899	−	0.0724459i
$799$		−	774.213i		−	0.968977i
$800$	−455.801	+	657.454i	−0.569752	+	0.821817i
$801$	−1104.04			−1.37833
$802$	−13.8091	+	8.38504i	−0.0172184	+	0.0104552i
$803$	−56.5987			−0.0704841
$804$	−75.5248	+	145.286i	−0.0939363	+	0.180704i
$805$	344.207	+	418.043i	0.427586	+	0.519308i
$806$	−328.151	+	199.256i	−0.407135	+	0.247216i
$807$	−59.2215			−0.0733848
$808$	86.9656	+	1309.48i	0.107631	+	1.62064i
$809$	1546.99			1.91222			0.956112	−	0.293001i	$-0.0946538\pi$
$809$	1546.99			1.91222			0.956112	+	0.293001i	$0.0946538\pi$
$810$	−414.754	−	144.970i	−0.512042	−	0.178976i
$811$			1456.80i			1.79630i	0.439686	+	0.898152i	$0.355090\pi$
$811$			1456.80i			1.79630i	−0.439686	+	0.898152i	$0.644910\pi$
$812$	177.570	−	341.589i	0.218682	−	0.420676i
$813$		−	574.878i		−	0.707107i
$814$	246.263	−	149.533i	0.302534	−	0.183702i
$815$	320.627	+	389.405i	0.393407	+	0.477797i
$816$	−158.470	+	111.234i	−0.194203	+	0.136317i
$817$		−	337.193i		−	0.412721i
$818$	172.900	−	104.986i	0.211369	−	0.128345i
$819$		−	903.895i		−	1.10366i
$820$	647.144	−	137.558i	0.789200	−	0.167754i
$821$	576.233			0.701867			0.350934	−	0.936400i	$-0.385864\pi$
$821$	576.233			0.701867			0.350934	+	0.936400i	$0.385864\pi$
$822$	88.1671	+	145.200i	0.107259	+	0.176643i
$823$	−12.5467			−0.0152451			−0.00762255	−	0.999971i	$-0.502426\pi$
$823$	−12.5467			−0.0152451			−0.00762255	+	0.999971i	$0.502426\pi$
$824$	−7.01949	−	105.696i	−0.00851880	−	0.128271i
$825$	−129.461	−	25.3183i	−0.156923	−	0.0306889i
$826$	−276.956	−	456.112i	−0.335297	−	0.552194i
$827$	−1258.03			−1.52120			−0.760600	−	0.649221i	$-0.775095\pi$
$827$	−1258.03			−1.52120			−0.760600	+	0.649221i	$0.775095\pi$
$828$	−234.182	+	450.494i	−0.282829	+	0.544075i
$829$	592.821			0.715104			0.357552	−	0.933893i	$-0.383611\pi$
$829$	592.821			0.715104			0.357552	+	0.933893i	$0.383611\pi$
$830$	1239.58	+	433.275i	1.49347	+	0.522018i
$831$		−	449.582i		−	0.541013i
$832$	−157.318	−	1179.18i	−0.189084	−	1.41729i
$833$			75.4386i			0.0905625i
$834$	269.840	+	444.393i	0.323549	+	0.532846i
$835$	503.555	+	611.573i	0.603060	+	0.732423i
$836$	−35.2309	+	67.7734i	−0.0421423	+	0.0810686i
$837$			205.841i			0.245928i
$838$	621.311	+	1023.22i	0.741421	+	1.22103i
$839$			1194.78i			1.42405i	0.702152	+	0.712027i	$0.252223\pi$
$839$			1194.78i			1.42405i	−0.702152	+	0.712027i	$0.747777\pi$
$840$	−225.974	+	212.700i	−0.269016	+	0.253214i
$841$	−617.739			−0.734529
$842$	−1069.35	+	649.317i	−1.27001	+	0.771161i
$843$	371.510			0.440700
$844$	800.120	+	415.930i	0.948009	+	0.492808i
$845$	−560.991	−	681.330i	−0.663895	−	0.806307i
$846$	994.527	−	603.886i	1.17556	−	0.713814i
$847$	655.781			0.774240
$848$	1012.32	−	710.573i	1.19377	−	0.837940i
$849$	214.901			0.253123
$850$	−471.438	+	173.465i	−0.554633	+	0.204076i
$851$			552.870i			0.649671i
$852$	−281.821	−	146.500i	−0.330776	−	0.171949i
$853$		−	566.396i		−	0.664005i	−0.943279	−	0.332002i	$-0.892276\pi$
$853$		−	566.396i		−	0.664005i	0.943279	−	0.332002i	$-0.107724\pi$
$854$	59.1857	−	35.9381i	0.0693040	−	0.0420821i
$855$	127.018	−	104.584i	0.148559	−	0.122320i
$856$	29.2227	+	440.020i	0.0341387	+	0.514042i
$857$			1029.47i			1.20125i	0.799530	+	0.600626i	$0.205082\pi$
$857$			1029.47i			1.20125i	−0.799530	+	0.600626i	$0.794918\pi$
$858$	167.671	−	101.811i	0.195420	−	0.118661i
$859$			274.430i			0.319476i	0.987159	+	0.159738i	$0.0510650\pi$
$859$			274.430i			0.319476i	−0.987159	+	0.159738i	$0.948935\pi$
$860$	−1513.34	+	321.678i	−1.75969	+	0.374044i
$861$	256.644			0.298077
$862$	−617.245	−	1016.53i	−0.716062	−	1.17927i
$863$	1475.75			1.71002			0.855012	−	0.518608i	$-0.173550\pi$
$863$	1475.75			1.71002			0.855012	+	0.518608i	$0.173550\pi$
$864$	−584.198	−	256.049i	−0.676156	−	0.296353i
$865$	202.520	−	166.751i	0.234128	−	0.192775i
$866$	273.322	+	450.129i	0.315615	+	0.519779i
$867$	226.511			0.261258
$868$	−236.083	−	122.724i	−0.271984	−	0.141387i
$869$	−217.270			−0.250023
$870$	−169.888	−	59.3816i	−0.195274	−	0.0682547i
$871$		−	631.758i		−	0.725325i
$872$	68.3613	+	1029.35i	0.0783960	+	1.18044i
$873$			442.274i			0.506614i
$874$	−76.0769	−	125.289i	−0.0870445	−	0.143352i
$875$	−708.256	+	382.981i	−0.809436	+	0.437692i
$876$	55.2267	+	28.7087i	0.0630442	+	0.0327725i
$877$		−	1390.07i		−	1.58503i	−0.609851	−	0.792516i	$-0.708771\pi$
$877$		−	1390.07i		−	1.58503i	0.609851	−	0.792516i	$-0.291229\pi$
$878$	−328.828	−	541.540i	−0.374520	−	0.616788i
$879$			461.917i			0.525503i
$880$	337.780	+	93.4630i	0.383841	+	0.106208i
$881$	601.667			0.682936			0.341468	−	0.939893i	$-0.389076\pi$
$881$	601.667			0.682936			0.341468	+	0.939893i	$0.389076\pi$
$882$	−96.9058	+	58.8421i	−0.109871	+	0.0667144i
$883$	822.025			0.930946			0.465473	−	0.885062i	$-0.345884\pi$
$883$	822.025			0.930946			0.465473	+	0.885062i	$0.345884\pi$
$884$	344.543	−	662.793i	0.389754	−	0.749766i
$885$	−192.568	+	158.556i	−0.217592	+	0.179160i
$886$	−498.550	+	302.724i	−0.562698	+	0.341675i
$887$	1146.80			1.29289			0.646446	−	0.762959i	$-0.276254\pi$
$887$	1146.80			1.29289			0.646446	+	0.762959i	$0.276254\pi$
$888$	−316.142	+	20.9957i	−0.356015	+	0.0236438i
$889$	49.8808			0.0561089
$890$	−1380.54	−	482.544i	−1.55117	−	0.542185i
$891$			192.479i			0.216026i
$892$	393.773	−	757.497i	0.441450	−	0.849212i
$893$			335.900i			0.376148i
$894$	502.845	−	305.332i	0.562466	−	0.341535i
$895$	−117.164	+	96.4704i	−0.130910	+	0.107788i
$896$	641.968	−	517.368i	0.716482	−	0.577420i
$897$			376.427i			0.419651i
$898$	26.6327	−	16.1716i	0.0296578	−	0.0180085i
$899$		−	154.302i		−	0.171638i
$900$	−590.549	−	470.291i	−0.656166	−	0.522545i
$901$	776.622			0.861955
$902$	−150.433	−	247.745i	−0.166777	−	0.274662i
$903$	−600.159			−0.664628
$904$	1021.14	−	67.8159i	1.12957	−	0.0750176i
$905$	−956.312	−	1161.45i	−1.05670	−	1.28337i
$906$	217.160	+	357.636i	0.239691	+	0.394742i
$907$	−329.375			−0.363148			−0.181574	−	0.983377i	$-0.558119\pi$
$907$	−329.375			−0.363148			−0.181574	+	0.983377i	$0.558119\pi$
$908$	61.7023	−	118.696i	0.0679541	−	0.130723i
$909$	−1238.43			−1.36241
$910$	395.066	−	1130.27i	0.434138	−	1.24205i
$911$		−	1242.65i		−	1.36405i	−0.731327	−	0.682027i	$-0.761099\pi$
$911$		−	1242.65i		−	1.36405i	0.731327	−	0.682027i	$-0.238901\pi$
$912$	68.7538	−	48.2602i	0.0753879	−	0.0529169i
$913$		−	575.265i		−	0.630082i
$914$	438.917	+	722.844i	0.480216	+	0.790857i
$915$	−20.5745	−	24.9879i	−0.0224858	−	0.0273092i
$916$	−82.5715	+	158.842i	−0.0901435	+	0.173408i
$917$		−	1039.85i		−	1.13397i
$918$	−207.877	−	342.348i	−0.226446	−	0.372929i
$919$		−	1254.84i		−	1.36544i	−0.730682	−	0.682718i	$-0.760798\pi$
$919$		−	1254.84i		−	1.36544i	0.730682	−	0.682718i	$-0.239202\pi$
$920$	−489.728	+	460.961i	−0.532313	+	0.501045i
$921$	107.374			0.116584
$922$	−937.654	+	569.352i	−1.01698	+	0.617519i
$923$	1225.46			1.32770
$924$	120.628	+	62.7064i	0.130549	+	0.0678641i
$925$	−806.771	−	157.778i	−0.872185	−	0.170571i
$926$	−626.146	+	380.202i	−0.676184	+	0.410585i
$927$	99.9610			0.107833
$928$	437.926	+	191.939i	0.471903	+	0.206831i
$929$	1699.39			1.82927			0.914635	−	0.404281i	$-0.132478\pi$
$929$	1699.39			1.82927			0.914635	+	0.404281i	$0.132478\pi$
$930$	−41.0404	+	117.415i	−0.0441295	+	0.126252i
$931$		−	32.7298i		−	0.0351556i
$932$	764.810	+	397.575i	0.820612	+	0.426582i
$933$		−	595.249i		−	0.637994i
$934$	382.932	−	232.520i	0.409992	−	0.248951i
$935$	139.884	+	169.891i	0.149609	+	0.181702i
$936$	1120.14	−	74.3913i	1.19674	−	0.0794779i
$937$		−	80.2211i		−	0.0856148i	−0.999083	−	0.0428074i	$-0.986370\pi$
$937$		−	80.2211i		−	0.0856148i	0.999083	−	0.0428074i	$-0.0136302\pi$
$938$	374.259	−	227.254i	0.398997	−	0.242275i
$939$		−	232.648i		−	0.247761i
$940$	1507.54	−	320.445i	1.60376	−	0.340899i
$941$	−1490.89			−1.58437			−0.792185	−	0.610281i	$-0.791057\pi$
$941$	−1490.89			−1.58437			−0.792185	+	0.610281i	$0.791057\pi$
$942$	37.6615	+	62.0239i	0.0399803	+	0.0658427i
$943$	556.197			0.589817
$944$	542.440	−	380.753i	0.574618	−	0.403341i
$945$	−408.060	−	495.593i	−0.431810	−	0.524437i
$946$	351.786	+	579.349i	0.371867	+	0.612420i
$947$	−641.294			−0.677184			−0.338592	−	0.940933i	$-0.609951\pi$
$947$	−641.294			−0.677184			−0.338592	+	0.940933i	$0.609951\pi$
$948$	212.003	+	110.206i	0.223632	+	0.116251i
$949$	−240.146			−0.253052
$950$	204.538	−	75.2596i	0.215304	−	0.0792207i
$951$		−	746.433i		−	0.784893i
$952$	516.582	−	34.3074i	0.542628	−	0.0360372i
$953$		−	1570.96i		−	1.64844i	−0.566273	−	0.824218i	$-0.691615\pi$
$953$		−	1570.96i		−	1.64844i	0.566273	−	0.824218i	$-0.308385\pi$
$954$	605.765	+	997.622i	0.634974	+	1.04572i
$955$	−927.117	+	763.367i	−0.970803	+	0.799337i
$956$	−1085.47	−	564.263i	−1.13543	−	0.590234i
$957$			78.8417i			0.0823842i
$958$	−792.489	−	1305.13i	−0.827233	−	1.36235i
$959$		−	454.239i		−	0.473659i
$960$	−282.184	−	262.530i	−0.293942	−	0.273469i
$961$	854.357			0.889029
$962$	1044.88	−	634.464i	1.08616	−	0.659526i
$963$	−416.146			−0.432135
$964$	−276.536	+	531.970i	−0.286863	+	0.551836i
$965$	312.921	−	257.652i	0.324270	−	0.266997i
$966$	−222.999	+	135.407i	−0.230848	+	0.140173i
$967$	−549.309			−0.568055			−0.284028	−	0.958816i	$-0.591671\pi$
$967$	−549.309			−0.568055			−0.284028	+	0.958816i	$0.591671\pi$
$968$	53.9714	+	812.672i	0.0557555	+	0.839537i
$969$	52.7460			0.0544335
$970$	−193.305	+	553.037i	−0.199283	+	0.570141i
$971$		−	1755.93i		−	1.80837i	−0.427136	−	0.904187i	$-0.640478\pi$
$971$		−	1755.93i		−	1.80837i	0.427136	−	0.904187i	$-0.359522\pi$
$972$	428.605	−	824.504i	0.440952	−	0.848255i
$973$		−	1390.22i		−	1.42880i
$974$	1077.96	−	654.548i	1.10674	−	0.672021i
$975$	−549.299	−	107.425i	−0.563383	−	0.110179i
$976$	49.4070	+	70.3876i	0.0506219	+	0.0721184i
$977$			993.873i			1.01727i	0.860982	+	0.508635i	$0.169850\pi$
$977$			993.873i			1.01727i	−0.860982	+	0.508635i	$0.830150\pi$
$978$	−207.722	+	126.131i	−0.212395	+	0.128968i
$979$			640.681i			0.654423i
$980$	−146.893	+	31.2238i	−0.149891	+	0.0318611i
$981$	−973.498			−0.992353
$982$	−457.946	−	754.182i	−0.466341	−	0.768006i
$983$	237.419			0.241525			0.120763	−	0.992681i	$-0.461466\pi$
$983$	237.419			0.241525			0.120763	+	0.992681i	$0.461466\pi$
$984$	21.1220	+	318.044i	0.0214655	+	0.323216i
$985$	1023.23	−	842.500i	1.03881	−	0.855330i
$986$	155.828	+	256.630i	0.158041	+	0.260274i
$987$	597.859			0.605733
$988$	−149.483	+	287.560i	−0.151299	+	0.291052i
$989$	−1300.66			−1.31513
$990$	−109.126	+	312.206i	−0.110229	+	0.315359i
$991$		−	235.754i		−	0.237895i	−0.992901	−	0.118948i	$-0.962048\pi$
$991$		−	235.754i		−	0.237895i	0.992901	−	0.118948i	$-0.0379520\pi$
$992$	132.655	−	302.664i	0.133724	−	0.305104i
$993$		−	187.051i		−	0.188369i
$994$	440.819	+	725.975i	0.443480	+	0.730357i
$995$	301.179	−	247.983i	0.302692	−	0.249230i
$996$	−291.794	+	561.320i	−0.292965	+	0.563575i
$997$			1880.76i			1.88642i	0.332202	+	0.943208i	$0.392208\pi$
$997$			1880.76i			1.88642i	−0.332202	+	0.943208i	$0.607792\pi$
$998$	188.436	+	310.331i	0.188813	+	0.310952i
$999$		−	655.431i		−	0.656088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.h.a.39.18	yes	108
4.3	odd	2	inner	380.3.h.a.39.92	yes	108
5.4	even	2	inner	380.3.h.a.39.91	yes	108
20.19	odd	2	inner	380.3.h.a.39.17	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.h.a.39.17	✓	108	20.19	odd	2	inner
380.3.h.a.39.18	yes	108	1.1	even	1	trivial
380.3.h.a.39.91	yes	108	5.4	even	2	inner
380.3.h.a.39.92	yes	108	4.3	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70952 + 1.03804i) q^{2} +1.20444 q^{3} +(1.84495 - 3.54911i) q^{4} +(3.17819 + 3.85994i) q^{5} +(-2.05903 + 1.25026i) q^{6} +6.44137 q^{7} +(0.530130 + 7.98242i) q^{8} -7.54932 q^{9} +O(q^{10})\)	\(q+(-1.70952 + 1.03804i) q^{2} +1.20444 q^{3} +(1.84495 - 3.54911i) q^{4} +(3.17819 + 3.85994i) q^{5} +(-2.05903 + 1.25026i) q^{6} +6.44137 q^{7} +(0.530130 + 7.98242i) q^{8} -7.54932 q^{9} +(-9.43996 - 3.29958i) q^{10} +4.38090i q^{11} +(2.22214 - 4.27470i) q^{12} +18.5880i q^{13} +(-11.0117 + 6.68640i) q^{14} +(3.82795 + 4.64908i) q^{15} +(-9.19233 - 13.0958i) q^{16} -10.0468i q^{17} +(12.9057 - 7.83649i) q^{18} +4.35890i q^{19} +(19.5629 - 4.15833i) q^{20} +7.75827 q^{21} +(-4.54754 - 7.48925i) q^{22} +16.8137 q^{23} +(0.638512 + 9.61437i) q^{24} +(-4.79828 + 24.5352i) q^{25} +(-19.2951 - 31.7766i) q^{26} -19.9327 q^{27} +(11.8840 - 22.8611i) q^{28} +14.9419 q^{29} +(-11.3699 - 3.97416i) q^{30} -10.3268i q^{31} +(29.3085 + 12.8457i) q^{32} +5.27654i q^{33} +(10.4289 + 17.1752i) q^{34} +(20.4719 + 24.8633i) q^{35} +(-13.9281 + 26.7933i) q^{36} +32.8822i q^{37} +(-4.52471 - 7.45164i) q^{38} +22.3882i q^{39} +(-29.1268 + 27.4159i) q^{40} +33.0801 q^{41} +(-13.2630 + 8.05339i) q^{42} -77.3574 q^{43} +(15.5483 + 8.08253i) q^{44} +(-23.9931 - 29.1399i) q^{45} +(-28.7434 + 17.4532i) q^{46} +77.0608 q^{47} +(-11.0716 - 15.7732i) q^{48} -7.50874 q^{49} +(-17.2657 - 46.9243i) q^{50} -12.1008i q^{51} +(65.9707 + 34.2939i) q^{52} +77.3006i q^{53} +(34.0755 - 20.6909i) q^{54} +(-16.9100 + 13.9233i) q^{55} +(3.41477 + 51.4177i) q^{56} +5.25005i q^{57} +(-25.5436 + 15.5103i) q^{58} +41.4208i q^{59} +(23.5624 - 5.00848i) q^{60} -5.37481 q^{61} +(10.7196 + 17.6539i) q^{62} -48.6279 q^{63} +(-63.4379 + 8.46344i) q^{64} +(-71.7485 + 59.0760i) q^{65} +(-5.47726 - 9.02038i) q^{66} -33.9875 q^{67} +(-35.6571 - 18.5358i) q^{68} +20.2511 q^{69} +(-60.8063 - 21.2538i) q^{70} -65.9277i q^{71} +(-4.00212 - 60.2618i) q^{72} +12.9194i q^{73} +(-34.1330 - 56.2129i) q^{74} +(-5.77926 + 29.5513i) q^{75} +(15.4702 + 8.04194i) q^{76} +28.2190i q^{77} +(-23.2398 - 38.2731i) q^{78} +49.5948i q^{79} +(21.3342 - 77.1029i) q^{80} +43.9360 q^{81} +(-56.5512 + 34.3384i) q^{82} -131.312 q^{83} +(14.3136 - 27.5349i) q^{84} +(38.7799 - 31.9305i) q^{85} +(132.244 - 80.3000i) q^{86} +17.9967 q^{87} +(-34.9701 + 2.32245i) q^{88} +146.244 q^{89} +(71.2652 + 24.9096i) q^{90} +119.732i q^{91} +(31.0203 - 59.6735i) q^{92} -12.4381i q^{93} +(-131.737 + 79.9922i) q^{94} +(-16.8251 + 13.8534i) q^{95} +(35.3005 + 15.4719i) q^{96} -58.5847i q^{97} +(12.8364 - 7.79437i) q^{98} -33.0728i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) \) 108 * q + 4 * q^5 + 324 * q^9	\( 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) \) 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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