LMFDB - Embedded newform 39.3.g.a.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,3,Mod(31,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("39.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	39.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.06267303101$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1579585536.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 4x^{6} + 28x^{5} - 38x^{4} + 8x^{3} + 200x^{2} - 352x + 484 $ x^8 - 2x^7 - 4x^6 + 28x^5 - 38x^4 + 8x^3 + 200x^2 - 352*x + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.2
Root			$1.11361 + 1.42401i$ of defining polynomial
Character	$\chi$	$=$	39.34
Dual form			39.3.g.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.676424 - 0.676424i) q^{2} +1.73205 q^{3} -3.08490i q^{4} +(1.58008 + 1.58008i) q^{5} +(-1.17160 - 1.17160i) q^{6} +(3.96400 - 3.96400i) q^{7} +(-4.79240 + 4.79240i) q^{8} +3.00000 q^{9} -2.13761i q^{10} +(-10.0345 + 10.0345i) q^{11} -5.34320i q^{12} +(-5.41846 + 11.8170i) q^{13} -5.36270 q^{14} +(2.73677 + 2.73677i) q^{15} -5.85621 q^{16} +6.40175i q^{17} +(-2.02927 - 2.02927i) q^{18} +(7.73551 + 7.73551i) q^{19} +(4.87438 - 4.87438i) q^{20} +(6.86585 - 6.86585i) q^{21} +13.5752 q^{22} -34.8297i q^{23} +(-8.30068 + 8.30068i) q^{24} -20.0067i q^{25} +(11.6585 - 4.32810i) q^{26} +5.19615 q^{27} +(-12.2285 - 12.2285i) q^{28} +8.25124 q^{29} -3.70244i q^{30} +(13.8633 + 13.8633i) q^{31} +(23.1309 + 23.1309i) q^{32} +(-17.3803 + 17.3803i) q^{33} +(4.33030 - 4.33030i) q^{34} +12.5269 q^{35} -9.25470i q^{36} +(-37.2522 + 37.2522i) q^{37} -10.4650i q^{38} +(-9.38504 + 20.4676i) q^{39} -15.1447 q^{40} +(-28.7020 - 28.7020i) q^{41} -9.28846 q^{42} -42.7195i q^{43} +(30.9555 + 30.9555i) q^{44} +(4.74023 + 4.74023i) q^{45} +(-23.5597 + 23.5597i) q^{46} +(37.5964 - 37.5964i) q^{47} -10.1432 q^{48} +17.5734i q^{49} +(-13.5330 + 13.5330i) q^{50} +11.0882i q^{51} +(36.4541 + 16.7154i) q^{52} -96.7934 q^{53} +(-3.51480 - 3.51480i) q^{54} -31.7107 q^{55} +37.9942i q^{56} +(13.3983 + 13.3983i) q^{57} +(-5.58134 - 5.58134i) q^{58} +(37.8935 - 37.8935i) q^{59} +(8.44267 - 8.44267i) q^{60} +91.2864 q^{61} -18.7549i q^{62} +(11.8920 - 11.8920i) q^{63} -7.86776i q^{64} +(-27.2333 + 10.1101i) q^{65} +23.5129 q^{66} +(-42.4500 - 42.4500i) q^{67} +19.7488 q^{68} -60.3268i q^{69} +(-8.47347 - 8.47347i) q^{70} +(29.8579 + 29.8579i) q^{71} +(-14.3772 + 14.3772i) q^{72} +(-10.9949 + 10.9949i) q^{73} +50.3966 q^{74} -34.6526i q^{75} +(23.8633 - 23.8633i) q^{76} +79.5538i q^{77} +(20.1930 - 7.49649i) q^{78} +102.031 q^{79} +(-9.25326 - 9.25326i) q^{80} +9.00000 q^{81} +38.8295i q^{82} +(-85.2758 - 85.2758i) q^{83} +(-21.1805 - 21.1805i) q^{84} +(-10.1153 + 10.1153i) q^{85} +(-28.8965 + 28.8965i) q^{86} +14.2916 q^{87} -96.1790i q^{88} +(-63.8510 + 63.8510i) q^{89} -6.41282i q^{90} +(25.3636 + 68.3212i) q^{91} -107.446 q^{92} +(24.0119 + 24.0119i) q^{93} -50.8623 q^{94} +24.4454i q^{95} +(40.0639 + 40.0639i) q^{96} +(-58.7023 - 58.7023i) q^{97} +(11.8871 - 11.8871i) q^{98} +(-30.1036 + 30.1036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 20 q^{5} + 8 q^{7} - 24 q^{8} + 24 q^{9} - 20 q^{11} + 8 q^{13} - 16 q^{14} + 12 q^{15} + 56 q^{16} + 12 q^{18} - 40 q^{19} + 44 q^{20} - 48 q^{21} - 128 q^{22} + 36 q^{24} - 32 q^{26} + 32 q^{28}+ \cdots - 60 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 20 * q^5 + 8 * q^7 - 24 * q^8 + 24 * q^9 - 20 * q^11 + 8 * q^13 - 16 * q^14 + 12 * q^15 + 56 * q^16 + 12 * q^18 - 40 * q^19 + 44 * q^20 - 48 * q^21 - 128 * q^22 + 36 * q^24 - 32 * q^26 + 32 * q^28 + 56 * q^29 + 32 * q^31 + 148 * q^32 - 36 * q^33 + 96 * q^34 + 104 * q^35 - 16 * q^37 + 24 * q^39 + 48 * q^40 - 116 * q^41 - 216 * q^42 - 92 * q^44 - 60 * q^45 - 264 * q^46 + 100 * q^47 + 20 * q^50 + 72 * q^52 - 232 * q^53 - 176 * q^55 + 120 * q^57 - 104 * q^58 + 316 * q^59 + 12 * q^60 + 160 * q^61 + 24 * q^63 - 92 * q^65 + 312 * q^66 + 176 * q^67 + 168 * q^68 + 184 * q^70 + 4 * q^71 - 72 * q^72 - 64 * q^73 - 64 * q^74 + 112 * q^76 + 180 * q^78 + 208 * q^79 - 332 * q^80 + 72 * q^81 - 212 * q^83 - 240 * q^84 - 168 * q^85 - 24 * q^87 - 452 * q^89 - 400 * q^91 - 720 * q^92 - 24 * q^93 + 16 * q^94 + 24 * q^96 + 128 * q^97 + 724 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.676424	−	0.676424i	−0.338212	−	0.338212i	0.517482	−	0.855694i	$-0.326869\pi$
$2$	−0.676424	−	0.676424i	−0.338212	−	0.338212i	−0.855694	+	0.517482i	$0.826869\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$		−	3.08490i		−	0.771225i
$5$	1.58008	+	1.58008i	0.316015	+	0.316015i	0.847234	−	0.531219i	$-0.178266\pi$
$5$	1.58008	+	1.58008i	0.316015	+	0.316015i	−0.531219	+	0.847234i	$0.678266\pi$
$6$	−1.17160	−	1.17160i	−0.195267	−	0.195267i
$7$	3.96400	−	3.96400i	0.566286	−	0.566286i	−0.364800	−	0.931086i	$-0.618863\pi$
$7$	3.96400	−	3.96400i	0.566286	−	0.566286i	0.931086	+	0.364800i	$0.118863\pi$
$8$	−4.79240	+	4.79240i	−0.599050	+	0.599050i
$9$	3.00000			0.333333
$10$		−	2.13761i		−	0.213761i
$11$	−10.0345	+	10.0345i	−0.912230	+	0.912230i	−0.996447	−	0.0842172i	$-0.973161\pi$
$11$	−10.0345	+	10.0345i	−0.912230	+	0.912230i	0.0842172	+	0.996447i	$0.473161\pi$
$12$		−	5.34320i		−	0.445267i
$13$	−5.41846	+	11.8170i	−0.416804	+	0.908996i
$13$	−5.41846	+	11.8170i	−0.416804	+	0.908996i
$14$	−5.36270			−0.383050
$15$	2.73677	+	2.73677i	0.182452	+	0.182452i
$16$	−5.85621			−0.366013
$17$			6.40175i			0.376574i	0.982114	+	0.188287i	$0.0602934\pi$
$17$			6.40175i			0.376574i	−0.982114	+	0.188287i	$0.939707\pi$
$18$	−2.02927	−	2.02927i	−0.112737	−	0.112737i
$19$	7.73551	+	7.73551i	0.407132	+	0.407132i	0.880737	−	0.473605i	$-0.157048\pi$
$19$	7.73551	+	7.73551i	0.407132	+	0.407132i	−0.473605	+	0.880737i	$0.657048\pi$
$20$	4.87438	−	4.87438i	0.243719	−	0.243719i
$21$	6.86585	−	6.86585i	0.326945	−	0.326945i
$22$	13.5752			0.617055
$23$		−	34.8297i		−	1.51434i	−0.653221	−	0.757168i	$-0.726583\pi$
$23$		−	34.8297i		−	1.51434i	0.653221	−	0.757168i	$-0.273417\pi$
$24$	−8.30068	+	8.30068i	−0.345862	+	0.345862i
$25$		−	20.0067i		−	0.800269i
$26$	11.6585	−	4.32810i	0.448402	−	0.166465i
$27$	5.19615			0.192450
$28$	−12.2285	−	12.2285i	−0.436734	−	0.436734i
$29$	8.25124			0.284526			0.142263	−	0.989829i	$-0.454562\pi$
$29$	8.25124			0.284526			0.142263	+	0.989829i	$0.454562\pi$
$30$		−	3.70244i		−	0.123415i
$31$	13.8633	+	13.8633i	0.447202	+	0.447202i	0.894423	−	0.447221i	$-0.147586\pi$
$31$	13.8633	+	13.8633i	0.447202	+	0.447202i	−0.447221	+	0.894423i	$0.647586\pi$
$32$	23.1309	+	23.1309i	0.722840	+	0.722840i
$33$	−17.3803	+	17.3803i	−0.526676	+	0.526676i
$34$	4.33030	−	4.33030i	0.127362	−	0.127362i
$35$	12.5269			0.357910
$36$		−	9.25470i		−	0.257075i
$37$	−37.2522	+	37.2522i	−1.00682	+	1.00682i	−0.00683875	+	0.999977i	$0.502177\pi$
$37$	−37.2522	+	37.2522i	−1.00682	+	1.00682i	−0.999977	+	0.00683875i	$0.997823\pi$
$38$		−	10.4650i		−	0.275394i
$39$	−9.38504	+	20.4676i	−0.240642	+	0.524809i
$40$	−15.1447			−0.378618
$41$	−28.7020	−	28.7020i	−0.700050	−	0.700050i	0.264371	−	0.964421i	$-0.414836\pi$
$41$	−28.7020	−	28.7020i	−0.700050	−	0.700050i	−0.964421	+	0.264371i	$0.914836\pi$
$42$	−9.28846			−0.221154
$43$		−	42.7195i		−	0.993477i	−0.867900	−	0.496739i	$-0.834531\pi$
$43$		−	42.7195i		−	0.993477i	0.867900	−	0.496739i	$-0.165469\pi$
$44$	30.9555	+	30.9555i	0.703535	+	0.703535i
$45$	4.74023	+	4.74023i	0.105338	+	0.105338i
$46$	−23.5597	+	23.5597i	−0.512167	+	0.512167i
$47$	37.5964	−	37.5964i	0.799924	−	0.799924i	−0.183159	−	0.983083i	$-0.558632\pi$
$47$	37.5964	−	37.5964i	0.799924	−	0.799924i	0.983083	+	0.183159i	$0.0586323\pi$
$48$	−10.1432			−0.211318
$49$			17.5734i			0.358641i
$50$	−13.5330	+	13.5330i	−0.270661	+	0.270661i
$51$			11.0882i			0.217415i
$52$	36.4541	+	16.7154i	0.701041	+	0.321450i
$53$	−96.7934			−1.82629			−0.913145	−	0.407635i	$-0.866354\pi$
$53$	−96.7934			−1.82629			−0.913145	+	0.407635i	$0.866354\pi$
$54$	−3.51480	−	3.51480i	−0.0650890	−	0.0650890i
$55$	−31.7107			−0.576558
$56$			37.9942i			0.678467i
$57$	13.3983	+	13.3983i	0.235058	+	0.235058i
$58$	−5.58134	−	5.58134i	−0.0962300	−	0.0962300i
$59$	37.8935	−	37.8935i	0.642262	−	0.642262i	−0.308849	−	0.951111i	$-0.599944\pi$
$59$	37.8935	−	37.8935i	0.642262	−	0.642262i	0.951111	+	0.308849i	$0.0999437\pi$
$60$	8.44267	−	8.44267i	0.140711	−	0.140711i
$61$	91.2864			1.49650			0.748249	−	0.663418i	$-0.230895\pi$
$61$	91.2864			1.49650			0.748249	+	0.663418i	$0.230895\pi$
$62$		−	18.7549i		−	0.302499i
$63$	11.8920	−	11.8920i	0.188762	−	0.188762i
$64$		−	7.86776i		−	0.122934i
$65$	−27.2333	+	10.1101i	−0.418973	+	0.155540i
$66$	23.5129			0.356257
$67$	−42.4500	−	42.4500i	−0.633581	−	0.633581i	0.315383	−	0.948964i	$-0.397867\pi$
$67$	−42.4500	−	42.4500i	−0.633581	−	0.633581i	−0.948964	+	0.315383i	$0.897867\pi$
$68$	19.7488			0.290423
$69$		−	60.3268i		−	0.874302i
$70$	−8.47347	−	8.47347i	−0.121050	−	0.121050i
$71$	29.8579	+	29.8579i	0.420534	+	0.420534i	0.885388	−	0.464853i	$-0.153893\pi$
$71$	29.8579	+	29.8579i	0.420534	+	0.420534i	−0.464853	+	0.885388i	$0.653893\pi$
$72$	−14.3772	+	14.3772i	−0.199683	+	0.199683i
$73$	−10.9949	+	10.9949i	−0.150615	+	0.150615i	−0.778393	−	0.627777i	$-0.783965\pi$
$73$	−10.9949	+	10.9949i	−0.150615	+	0.150615i	0.627777	+	0.778393i	$0.283965\pi$
$74$	50.3966			0.681035
$75$		−	34.6526i		−	0.462035i
$76$	23.8633	−	23.8633i	0.313990	−	0.313990i
$77$			79.5538i			1.03317i
$78$	20.1930	−	7.49649i	0.258885	−	0.0961088i
$79$	102.031			1.29153			0.645764	−	0.763537i	$-0.276539\pi$
$79$	102.031			1.29153			0.645764	+	0.763537i	$0.276539\pi$
$80$	−9.25326	−	9.25326i	−0.115666	−	0.115666i
$81$	9.00000			0.111111
$82$			38.8295i			0.473531i
$83$	−85.2758	−	85.2758i	−1.02742	−	1.02742i	−0.999613	−	0.0278064i	$-0.991148\pi$
$83$	−85.2758	−	85.2758i	−1.02742	−	1.02742i	−0.0278064	−	0.999613i	$-0.508852\pi$
$84$	−21.1805	−	21.1805i	−0.252148	−	0.252148i
$85$	−10.1153	+	10.1153i	−0.119003	+	0.119003i
$86$	−28.8965	+	28.8965i	−0.336006	+	0.336006i
$87$	14.2916			0.164271
$88$		−	96.1790i		−	1.09294i
$89$	−63.8510	+	63.8510i	−0.717427	+	0.717427i	−0.968078	−	0.250651i	$-0.919355\pi$
$89$	−63.8510	+	63.8510i	−0.717427	+	0.717427i	0.250651	+	0.968078i	$0.419355\pi$
$90$		−	6.41282i		−	0.0712535i
$91$	25.3636	+	68.3212i	0.278721	+	0.750782i
$92$	−107.446			−1.16789
$93$	24.0119	+	24.0119i	0.258192	+	0.258192i
$94$	−50.8623			−0.541088
$95$			24.4454i			0.257320i
$96$	40.0639	+	40.0639i	0.417332	+	0.417332i
$97$	−58.7023	−	58.7023i	−0.605178	−	0.605178i	0.336504	−	0.941682i	$-0.390755\pi$
$97$	−58.7023	−	58.7023i	−0.605178	−	0.605178i	−0.941682	+	0.336504i	$0.890755\pi$
$98$	11.8871	−	11.8871i	0.121297	−	0.121297i
$99$	−30.1036	+	30.1036i	−0.304077	+	0.304077i
$100$	−61.7187			−0.617187
$101$			130.126i			1.28837i	0.764869	+	0.644186i	$0.222804\pi$
$101$			130.126i			1.28837i	−0.764869	+	0.644186i	$0.777196\pi$
$102$	7.50030	−	7.50030i	0.0735324	−	0.0735324i
$103$			27.9217i			0.271085i	0.990772	+	0.135542i	$0.0432777\pi$
$103$			27.9217i			0.271085i	−0.990772	+	0.135542i	$0.956722\pi$
$104$	−30.6641	−	82.5990i	−0.294847	−	0.794221i
$105$	21.6971			0.206640
$106$	65.4734	+	65.4734i	0.617674	+	0.617674i
$107$	166.168			1.55297			0.776486	−	0.630134i	$-0.217000\pi$
$107$	166.168			1.55297			0.776486	+	0.630134i	$0.217000\pi$
$108$		−	16.0296i		−	0.148422i
$109$	−4.56393	−	4.56393i	−0.0418709	−	0.0418709i	0.685861	−	0.727732i	$-0.259426\pi$
$109$	−4.56393	−	4.56393i	−0.0418709	−	0.0418709i	−0.727732	+	0.685861i	$0.759426\pi$
$110$	21.4499	+	21.4499i	0.194999	+	0.194999i
$111$	−64.5226	+	64.5226i	−0.581285	+	0.581285i
$112$	−23.2140	+	23.2140i	−0.207268	+	0.207268i
$113$	−60.7525			−0.537633			−0.268817	−	0.963191i	$-0.586633\pi$
$113$	−60.7525			−0.537633			−0.268817	+	0.963191i	$0.586633\pi$
$114$		−	18.1259i		−	0.158999i
$115$	55.0336	−	55.0336i	0.478553	−	0.478553i
$116$		−	25.4543i		−	0.219433i
$117$	−16.2554	+	35.4509i	−0.138935	+	0.302999i
$118$	−51.2641			−0.434442
$119$	25.3765	+	25.3765i	0.213248	+	0.213248i
$120$	−26.2314			−0.218595
$121$		−	80.3837i		−	0.664328i
$122$	−61.7484	−	61.7484i	−0.506134	−	0.506134i
$123$	−49.7134	−	49.7134i	−0.404174	−	0.404174i
$124$	42.7668	−	42.7668i	0.344893	−	0.344893i
$125$	71.1141	−	71.1141i	0.568913	−	0.568913i
$126$	−16.0881			−0.127683
$127$			130.207i			1.02525i	0.858613	+	0.512624i	$0.171327\pi$
$127$			130.207i			1.02525i	−0.858613	+	0.512624i	$0.828673\pi$
$128$	87.2016	−	87.2016i	0.681262	−	0.681262i
$129$		−	73.9924i		−	0.573584i
$130$	25.2600	+	11.5825i	0.194308	+	0.0890963i
$131$	135.531			1.03459			0.517293	−	0.855809i	$-0.326940\pi$
$131$	135.531			1.03459			0.517293	+	0.855809i	$0.326940\pi$
$132$	53.6165	+	53.6165i	0.406186	+	0.406186i
$133$	61.3271			0.461106
$134$			57.4284i			0.428570i
$135$	8.21032	+	8.21032i	0.0608172	+	0.0608172i
$136$	−30.6797	−	30.6797i	−0.225586	−	0.225586i
$137$	135.519	−	135.519i	0.989190	−	0.989190i	−0.0107526	−	0.999942i	$-0.503423\pi$
$137$	135.519	−	135.519i	0.989190	−	0.989190i	0.999942	+	0.0107526i	$0.00342272\pi$
$138$	−40.8065	+	40.8065i	−0.295700	+	0.295700i
$139$	−244.006			−1.75544			−0.877720	−	0.479174i	$-0.840936\pi$
$139$	−244.006			−1.75544			−0.877720	+	0.479174i	$0.840936\pi$
$140$		−	38.6441i		−	0.276029i
$141$	65.1189	−	65.1189i	0.461836	−	0.461836i
$142$		−	40.3933i		−	0.284460i
$143$	−64.2059	−	172.949i	−0.448992	−	1.20944i
$144$	−17.5686			−0.122004
$145$	13.0376	+	13.0376i	0.0899145	+	0.0899145i
$146$	14.8745			0.101880
$147$			30.4380i			0.207061i
$148$	114.919	+	114.919i	0.776481	+	0.776481i
$149$	174.887	+	174.887i	1.17374	+	1.17374i	0.981312	+	0.192425i	$0.0616351\pi$
$149$	174.887	+	174.887i	1.17374	+	1.17374i	0.192425	+	0.981312i	$0.438365\pi$
$150$	−23.4399	+	23.4399i	−0.156266	+	0.156266i
$151$	−38.1095	+	38.1095i	−0.252381	+	0.252381i	−0.821946	−	0.569565i	$-0.807112\pi$
$151$	−38.1095	+	38.1095i	−0.252381	+	0.252381i	0.569565	+	0.821946i	$0.307112\pi$
$152$	−74.1433			−0.487785
$153$			19.2053i			0.125525i
$154$	53.8121	−	53.8121i	0.349429	−	0.349429i
$155$			43.8101i			0.282646i
$156$	63.1404	+	28.9519i	0.404746	+	0.185589i
$157$	150.359			0.957699			0.478849	−	0.877897i	$-0.341054\pi$
$157$	150.359			0.957699			0.478849	+	0.877897i	$0.341054\pi$
$158$	−69.0161	−	69.0161i	−0.436810	−	0.436810i
$159$	−167.651			−1.05441
$160$			73.0971i			0.456857i
$161$	−138.065	−	138.065i	−0.857547	−	0.857547i
$162$	−6.08782	−	6.08782i	−0.0375791	−	0.0375791i
$163$	−167.544	+	167.544i	−1.02788	+	1.02788i	−0.0282759	+	0.999600i	$0.509002\pi$
$163$	−167.544	+	167.544i	−1.02788	+	1.02788i	−0.999600	+	0.0282759i	$0.990998\pi$
$164$	−88.5429	+	88.5429i	−0.539896	+	0.539896i
$165$	−54.9245			−0.332876
$166$			115.365i			0.694972i
$167$	−33.7608	+	33.7608i	−0.202160	+	0.202160i	−0.800925	−	0.598765i	$-0.795658\pi$
$167$	−33.7608	+	33.7608i	−0.202160	+	0.202160i	0.598765	+	0.800925i	$0.295658\pi$
$168$			65.8078i			0.391713i
$169$	−110.281	−	128.059i	−0.652548	−	0.757747i
$170$	13.6844			0.0804966
$171$	23.2065	+	23.2065i	0.135711	+	0.135711i
$172$	−131.785			−0.766195
$173$			150.230i			0.868383i	0.900821	+	0.434191i	$0.142966\pi$
$173$			150.230i			0.868383i	−0.900821	+	0.434191i	$0.857034\pi$
$174$	−9.66717	−	9.66717i	−0.0555584	−	0.0555584i
$175$	−79.3066	−	79.3066i	−0.453181	−	0.453181i
$176$	58.7643	−	58.7643i	0.333888	−	0.333888i
$177$	65.6334	−	65.6334i	0.370810	−	0.370810i
$178$	86.3808			0.485285
$179$			247.106i			1.38048i	0.723582	+	0.690239i	$0.242495\pi$
$179$			247.106i			1.38048i	−0.723582	+	0.690239i	$0.757505\pi$
$180$	14.6231	−	14.6231i	0.0812396	−	0.0812396i
$181$		−	111.674i		−	0.616986i	−0.951227	−	0.308493i	$-0.900175\pi$
$181$		−	111.674i		−	0.616986i	0.951227	−	0.308493i	$-0.0998247\pi$
$182$	29.0575	−	63.3707i	0.159657	−	0.348191i
$183$	158.113			0.864004
$184$	166.918	+	166.918i	0.907162	+	0.907162i
$185$	−117.723			−0.636338
$186$		−	32.4845i		−	0.174648i
$187$	−64.2386	−	64.2386i	−0.343522	−	0.343522i
$188$	−115.981	−	115.981i	−0.616921	−	0.616921i
$189$	20.5976	−	20.5976i	0.108982	−	0.108982i
$190$	16.5355	−	16.5355i	0.0870288	−	0.0870288i
$191$	−64.6991			−0.338739			−0.169369	−	0.985553i	$-0.554173\pi$
$191$	−64.6991			−0.338739			−0.169369	+	0.985553i	$0.554173\pi$
$192$		−	13.6274i		−	0.0709759i
$193$	97.0986	−	97.0986i	0.503102	−	0.503102i	−0.409299	−	0.912400i	$-0.634227\pi$
$193$	97.0986	−	97.0986i	0.503102	−	0.503102i	0.912400	+	0.409299i	$0.134227\pi$
$194$			79.4153i			0.409357i
$195$	−47.1694	+	17.5112i	−0.241894	+	0.0898012i
$196$	54.2121			0.276593
$197$	48.8725	+	48.8725i	0.248084	+	0.248084i	0.820184	−	0.572100i	$-0.193871\pi$
$197$	48.8725	+	48.8725i	0.248084	+	0.248084i	−0.572100	+	0.820184i	$0.693871\pi$
$198$	40.7256			0.205685
$199$		−	139.570i		−	0.701358i	−0.936496	−	0.350679i	$-0.885951\pi$
$199$		−	139.570i		−	0.701358i	0.936496	−	0.350679i	$-0.114049\pi$
$200$	95.8802	+	95.8802i	0.479401	+	0.479401i
$201$	−73.5255	−	73.5255i	−0.365798	−	0.365798i
$202$	88.0201	−	88.0201i	0.435743	−	0.435743i
$203$	32.7079	−	32.7079i	0.161123	−	0.161123i
$204$	34.2059			0.167676
$205$		−	90.7029i		−	0.442453i
$206$	18.8869	−	18.8869i	0.0916842	−	0.0916842i
$207$		−	104.489i		−	0.504778i
$208$	31.7316	−	69.2025i	0.152556	−	0.332704i
$209$	−155.244			−0.742796
$210$	−14.6765	−	14.6765i	−0.0698880	−	0.0698880i
$211$	52.9556			0.250975			0.125487	−	0.992095i	$-0.459951\pi$
$211$	52.9556			0.250975			0.125487	+	0.992095i	$0.459951\pi$
$212$			298.598i			1.40848i
$213$	51.7154	+	51.7154i	0.242796	+	0.242796i
$214$	−112.400	−	112.400i	−0.525234	−	0.525234i
$215$	67.5001	−	67.5001i	0.313954	−	0.313954i
$216$	−24.9020	+	24.9020i	−0.115287	+	0.115287i
$217$	109.908			0.506489
$218$			6.17430i			0.0283225i
$219$	−19.0438	+	19.0438i	−0.0869578	+	0.0869578i
$220$			97.8242i			0.444656i
$221$	−75.6492	−	34.6876i	−0.342304	−	0.156958i
$222$	87.2894			0.393195
$223$	70.4483	+	70.4483i	0.315912	+	0.315912i	0.847195	−	0.531283i	$-0.178290\pi$
$223$	70.4483	+	70.4483i	0.315912	+	0.315912i	−0.531283	+	0.847195i	$0.678290\pi$
$224$	183.382			0.818668
$225$		−	60.0201i		−	0.266756i
$226$	41.0945	+	41.0945i	0.181834	+	0.181834i
$227$	−95.0195	−	95.0195i	−0.418588	−	0.418588i	0.466129	−	0.884717i	$-0.345648\pi$
$227$	−95.0195	−	95.0195i	−0.418588	−	0.418588i	−0.884717	+	0.466129i	$0.845648\pi$
$228$	41.3324	−	41.3324i	0.181282	−	0.181282i
$229$	66.9011	−	66.9011i	0.292144	−	0.292144i	−0.545782	−	0.837927i	$-0.683767\pi$
$229$	66.9011	−	66.9011i	0.292144	−	0.292144i	0.837927	+	0.545782i	$0.183767\pi$
$230$	−74.4522			−0.323705
$231$			137.791i			0.596499i
$232$	−39.5433	+	39.5433i	−0.170445	+	0.170445i
$233$			81.9200i			0.351588i	0.984427	+	0.175794i	$0.0562493\pi$
$233$			81.9200i			0.351588i	−0.984427	+	0.175794i	$0.943751\pi$
$234$	34.9754	−	12.9843i	0.149467	−	0.0554884i
$235$	118.811			0.505577
$236$	−116.898	−	116.898i	−0.495329	−	0.495329i
$237$	176.722			0.745664
$238$		−	34.3306i		−	0.144246i
$239$	5.12005	+	5.12005i	0.0214228	+	0.0214228i	0.717737	−	0.696314i	$-0.245178\pi$
$239$	5.12005	+	5.12005i	0.0214228	+	0.0214228i	−0.696314	+	0.717737i	$0.745178\pi$
$240$	−16.0271	−	16.0271i	−0.0667796	−	0.0667796i
$241$	−152.203	+	152.203i	−0.631546	+	0.631546i	−0.948456	−	0.316910i	$-0.897355\pi$
$241$	−152.203	+	152.203i	−0.631546	+	0.631546i	0.316910	+	0.948456i	$0.397355\pi$
$242$	−54.3735	+	54.3735i	−0.224684	+	0.224684i
$243$	15.5885			0.0641500
$244$		−	281.609i		−	1.15414i
$245$	−27.7673	+	27.7673i	−0.113336	+	0.113336i
$246$			67.2547i			0.273393i
$247$	−133.325	+	49.4956i	−0.539776	+	0.200387i
$248$	−132.877			−0.535793
$249$	−147.702	−	147.702i	−0.593181	−	0.593181i
$250$	−96.2066			−0.384826
$251$		−	221.877i		−	0.883974i	−0.897022	−	0.441987i	$-0.854274\pi$
$251$		−	221.877i		−	0.883974i	0.897022	−	0.441987i	$-0.145726\pi$
$252$	−36.6856	−	36.6856i	−0.145578	−	0.145578i
$253$	349.500	+	349.500i	1.38142	+	1.38142i
$254$	88.0749	−	88.0749i	0.346751	−	0.346751i
$255$	−17.5201	+	17.5201i	−0.0687064	+	0.0687064i
$256$	−149.442			−0.583756
$257$		−	15.0363i		−	0.0585068i	−0.999572	−	0.0292534i	$-0.990687\pi$
$257$		−	15.0363i		−	0.0585068i	0.999572	−	0.0292534i	$-0.00931298\pi$
$258$	−50.0503	+	50.0503i	−0.193993	+	0.193993i
$259$			295.335i			1.14029i
$260$	31.1887	+	84.0119i	0.119956	+	0.323123i
$261$	24.7537			0.0948419
$262$	−91.6763	−	91.6763i	−0.349909	−	0.349909i
$263$	−105.723			−0.401990			−0.200995	−	0.979592i	$-0.564418\pi$
$263$	−105.723			−0.401990			−0.200995	+	0.979592i	$0.564418\pi$
$264$		−	166.587i		−	0.631011i
$265$	−152.941	−	152.941i	−0.577136	−	0.577136i
$266$	−41.4832	−	41.4832i	−0.155952	−	0.155952i
$267$	−110.593	+	110.593i	−0.414207	+	0.414207i
$268$	−130.954	+	130.954i	−0.488634	+	0.488634i
$269$	168.740			0.627286			0.313643	−	0.949541i	$-0.398451\pi$
$269$	168.740			0.627286			0.313643	+	0.949541i	$0.398451\pi$
$270$		−	11.1073i		−	0.0411382i
$271$	−52.4787	+	52.4787i	−0.193648	+	0.193648i	−0.797271	−	0.603622i	$-0.793724\pi$
$271$	−52.4787	+	52.4787i	−0.193648	+	0.193648i	0.603622	+	0.797271i	$0.293724\pi$
$272$		−	37.4900i		−	0.137831i
$273$	43.9311	+	118.336i	0.160920	+	0.433464i
$274$	−183.337			−0.669112
$275$	200.758	+	200.758i	0.730029	+	0.730029i
$276$	−186.102			−0.674283
$277$			153.018i			0.552412i	0.961098	+	0.276206i	$0.0890772\pi$
$277$			153.018i			0.552412i	−0.961098	+	0.276206i	$0.910923\pi$
$278$	165.052	+	165.052i	0.593711	+	0.593711i
$279$	41.5898	+	41.5898i	0.149067	+	0.149067i
$280$	−60.0337	+	60.0337i	−0.214406	+	0.214406i
$281$	37.8887	−	37.8887i	0.134835	−	0.134835i	−0.636468	−	0.771303i	$-0.719605\pi$
$281$	37.8887	−	37.8887i	0.134835	−	0.134835i	0.771303	+	0.636468i	$0.219605\pi$
$282$	−88.0961			−0.312397
$283$		−	34.7222i		−	0.122693i	−0.998117	−	0.0613467i	$-0.980460\pi$
$283$		−	34.7222i		−	0.122693i	0.998117	−	0.0613467i	$-0.0195395\pi$
$284$	92.1087	−	92.1087i	0.324326	−	0.324326i
$285$			42.3407i			0.148564i
$286$	−73.5567	+	160.418i	−0.257191	+	0.560901i
$287$	−227.550			−0.792857
$288$	69.3926	+	69.3926i	0.240947	+	0.240947i
$289$	248.018			0.858192
$290$		−	17.6379i		−	0.0608203i
$291$	−101.675	−	101.675i	−0.349400	−	0.349400i
$292$	33.9182	+	33.9182i	0.116158	+	0.116158i
$293$	54.4668	−	54.4668i	0.185894	−	0.185894i	−0.608025	−	0.793918i	$-0.708038\pi$
$293$	54.4668	−	54.4668i	0.185894	−	0.185894i	0.793918	+	0.608025i	$0.208038\pi$
$294$	20.5890	−	20.5890i	0.0700306	−	0.0700306i
$295$	119.749			0.405929
$296$		−	357.055i		−	1.20627i
$297$	−52.1410	+	52.1410i	−0.175559	+	0.175559i
$298$		−	236.595i		−	0.793944i
$299$	411.581	+	188.723i	1.37652	+	0.631182i
$300$	−106.900			−0.356333
$301$	−169.340	−	169.340i	−0.562592	−	0.562592i
$302$	51.5565			0.170717
$303$			225.384i			0.743842i
$304$	−45.3007	−	45.3007i	−0.149016	−	0.149016i
$305$	144.240	+	144.240i	0.472916	+	0.472916i
$306$	12.9909	−	12.9909i	0.0424539	−	0.0424539i
$307$	223.385	−	223.385i	0.727639	−	0.727639i	−0.242510	−	0.970149i	$-0.577971\pi$
$307$	223.385	−	223.385i	0.727639	−	0.727639i	0.970149	+	0.242510i	$0.0779707\pi$
$308$	245.416			0.796804
$309$			48.3619i			0.156511i
$310$	29.6342	−	29.6342i	0.0955942	−	0.0955942i
$311$		−	516.479i		−	1.66070i	−0.557240	−	0.830352i	$-0.688140\pi$
$311$		−	516.479i		−	1.66070i	0.557240	−	0.830352i	$-0.311860\pi$
$312$	−53.1118	−	143.066i	−0.170230	−	0.458544i
$313$	−149.235			−0.476788			−0.238394	−	0.971169i	$-0.576621\pi$
$313$	−149.235			−0.476788			−0.238394	+	0.971169i	$0.576621\pi$
$314$	−101.706	−	101.706i	−0.323905	−	0.323905i
$315$	37.5806			0.119303
$316$		−	314.754i		−	0.996058i
$317$	−188.163	−	188.163i	−0.593574	−	0.593574i	0.345021	−	0.938595i	$-0.387872\pi$
$317$	−188.163	−	188.163i	−0.593574	−	0.593574i	−0.938595	+	0.345021i	$0.887872\pi$
$318$	113.403	+	113.403i	0.356614	+	0.356614i
$319$	−82.7974	+	82.7974i	−0.259553	+	0.259553i
$320$	12.4317	−	12.4317i	0.0388490	−	0.0388490i
$321$	287.811			0.896609
$322$			186.781i			0.580066i
$323$	−49.5208	+	49.5208i	−0.153315	+	0.153315i
$324$		−	27.7641i		−	0.0856917i
$325$	236.418	+	108.406i	0.727441	+	0.333555i
$326$	226.661			0.695281
$327$	−7.90495	−	7.90495i	−0.0241742	−	0.0241742i
$328$	275.103			0.838730
$329$		−	298.065i		−	0.905972i
$330$	37.1523	+	37.1523i	0.112583	+	0.112583i
$331$	−133.749	−	133.749i	−0.404074	−	0.404074i	0.475592	−	0.879666i	$-0.342234\pi$
$331$	−133.749	−	133.749i	−0.404074	−	0.404074i	−0.879666	+	0.475592i	$0.842234\pi$
$332$	−263.067	+	263.067i	−0.792372	+	0.792372i
$333$	−111.757	+	111.757i	−0.335605	+	0.335605i
$334$	45.6732			0.136746
$335$		−	134.148i		−	0.400443i
$336$	−40.2078	+	40.2078i	−0.119666	+	0.119666i
$337$		−	202.419i		−	0.600651i	−0.953837	−	0.300325i	$-0.902905\pi$
$337$		−	202.419i		−	0.600651i	0.953837	−	0.300325i	$-0.0970952\pi$
$338$	−12.0259	+	161.219i	−0.0355796	+	0.476979i
$339$	−105.226			−0.310403
$340$	31.2046	+	31.2046i	0.0917781	+	0.0917781i
$341$	−278.223			−0.815903
$342$		−	31.3949i		−	0.0917980i
$343$	263.897	+	263.897i	0.769379	+	0.769379i
$344$	204.729	+	204.729i	0.595143	+	0.595143i
$345$	95.3210	−	95.3210i	0.276293	−	0.276293i
$346$	101.619	−	101.619i	0.293698	−	0.293698i
$347$	190.870			0.550059			0.275029	−	0.961436i	$-0.411312\pi$
$347$	190.870			0.550059			0.275029	+	0.961436i	$0.411312\pi$
$348$		−	44.0881i		−	0.126690i
$349$	−472.034	+	472.034i	−1.35253	+	1.35253i	−0.469713	+	0.882819i	$0.655643\pi$
$349$	−472.034	+	472.034i	−1.35253	+	1.35253i	−0.882819	+	0.469713i	$0.844357\pi$
$350$			107.290i			0.306543i
$351$	−28.1551	+	61.4027i	−0.0802140	+	0.174936i
$352$	−464.215			−1.31879
$353$	−298.499	−	298.499i	−0.845606	−	0.845606i	0.143975	−	0.989581i	$-0.454012\pi$
$353$	−298.499	−	298.499i	−0.845606	−	0.845606i	−0.989581	+	0.143975i	$0.954012\pi$
$354$	−88.7921			−0.250825
$355$			94.3556i			0.265791i
$356$	196.974	+	196.974i	0.553298	+	0.553298i
$357$	43.9535	+	43.9535i	0.123119	+	0.123119i
$358$	167.148	−	167.148i	0.466894	−	0.466894i
$359$	−86.3614	+	86.3614i	−0.240561	+	0.240561i	−0.817082	−	0.576521i	$-0.804410\pi$
$359$	−86.3614	+	86.3614i	−0.240561	+	0.240561i	0.576521	+	0.817082i	$0.304410\pi$
$360$	−45.4342			−0.126206
$361$		−	241.324i		−	0.668487i
$362$	−75.5394	+	75.5394i	−0.208672	+	0.208672i
$363$		−	139.229i		−	0.383550i
$364$	210.764	−	78.2443i	0.579022	−	0.214957i
$365$	−34.7456			−0.0951935
$366$	−106.951	−	106.951i	−0.292217	−	0.292217i
$367$	−54.1950			−0.147670			−0.0738352	−	0.997270i	$-0.523524\pi$
$367$	−54.1950			−0.147670			−0.0738352	+	0.997270i	$0.523524\pi$
$368$			203.970i			0.554266i
$369$	−86.1061	−	86.1061i	−0.233350	−	0.233350i
$370$	79.6304	+	79.6304i	0.215217	+	0.215217i
$371$	−383.689	+	383.689i	−1.03420	+	1.03420i
$372$	74.0743	−	74.0743i	0.199124	−	0.199124i
$373$	−17.9362			−0.0480862			−0.0240431	−	0.999711i	$-0.507654\pi$
$373$	−17.9362			−0.0480862			−0.0240431	+	0.999711i	$0.507654\pi$
$374$			86.9051i			0.232367i
$375$	123.173	−	123.173i	0.328462	−	0.328462i
$376$			360.354i			0.958389i
$377$	−44.7090	+	97.5045i	−0.118592	+	0.258633i
$378$	−27.8654			−0.0737179
$379$	−281.565	−	281.565i	−0.742916	−	0.742916i	0.230222	−	0.973138i	$-0.426055\pi$
$379$	−281.565	−	281.565i	−0.742916	−	0.742916i	−0.973138	+	0.230222i	$0.926055\pi$
$380$	75.4116			0.198452
$381$			225.524i			0.591927i
$382$	43.7641	+	43.7641i	0.114566	+	0.114566i
$383$	−244.827	−	244.827i	−0.639236	−	0.639236i	0.311131	−	0.950367i	$-0.399292\pi$
$383$	−244.827	−	244.827i	−0.639236	−	0.639236i	−0.950367	+	0.311131i	$0.899292\pi$
$384$	151.038	−	151.038i	0.393327	−	0.393327i
$385$	−125.701	+	125.701i	−0.326496	+	0.326496i
$386$	−131.360			−0.340310
$387$		−	128.159i		−	0.331159i
$388$	−181.091	+	181.091i	−0.466728	+	0.466728i
$389$			582.261i			1.49681i	0.663240	+	0.748407i	$0.269181\pi$
$389$			582.261i			1.49681i	−0.663240	+	0.748407i	$0.730819\pi$
$390$	43.7516	+	20.0615i	0.112184	+	0.0514398i
$391$	222.971			0.570259
$392$	−84.2187	−	84.2187i	−0.214844	−	0.214844i
$393$	234.746			0.597318
$394$		−	66.1171i		−	0.167810i
$395$	161.216	+	161.216i	0.408143	+	0.408143i
$396$	92.8666	+	92.8666i	0.234512	+	0.234512i
$397$	372.060	−	372.060i	0.937179	−	0.937179i	−0.0609613	−	0.998140i	$-0.519417\pi$
$397$	372.060	−	372.060i	0.937179	−	0.937179i	0.998140	+	0.0609613i	$0.0194166\pi$
$398$	−94.4087	+	94.4087i	−0.237208	+	0.237208i
$399$	106.222			0.266220
$400$			117.163i			0.292909i
$401$	−380.251	+	380.251i	−0.948258	+	0.948258i	−0.998726	−	0.0504677i	$-0.983929\pi$
$401$	−380.251	+	380.251i	−0.948258	+	0.948258i	0.0504677	+	0.998726i	$0.483929\pi$
$402$			99.4689i			0.247435i
$403$	−238.939	+	88.7040i	−0.592901	+	0.220109i
$404$	401.424			0.993625
$405$	14.2207	+	14.2207i	0.0351128	+	0.0351128i
$406$	−44.2489			−0.108987
$407$		−	747.616i		−	1.83689i
$408$	−53.1389	−	53.1389i	−0.130242	−	0.130242i
$409$	58.5825	+	58.5825i	0.143233	+	0.143233i	0.775087	−	0.631854i	$-0.217706\pi$
$409$	58.5825	+	58.5825i	0.143233	+	0.143233i	−0.631854	+	0.775087i	$0.717706\pi$
$410$	−61.3537	+	61.3537i	−0.149643	+	0.149643i
$411$	234.726	−	234.726i	0.571109	−	0.571109i
$412$	86.1358			0.209067
$413$		−	300.420i		−	0.727408i
$414$	−70.6790	+	70.6790i	−0.170722	+	0.170722i
$415$		−	269.485i		−	0.649361i
$416$	−398.670	+	148.003i	−0.958342	+	0.355776i
$417$	−422.631			−1.01350
$418$	105.011	+	105.011i	0.251223	+	0.251223i
$419$	−451.990			−1.07874			−0.539368	−	0.842070i	$-0.681337\pi$
$419$	−451.990			−1.07874			−0.539368	+	0.842070i	$0.681337\pi$
$420$		−	66.9335i		−	0.159366i
$421$	54.5548	+	54.5548i	0.129584	+	0.129584i	0.768924	−	0.639340i	$-0.220792\pi$
$421$	54.5548	+	54.5548i	0.129584	+	0.129584i	−0.639340	+	0.768924i	$0.720792\pi$
$422$	−35.8205	−	35.8205i	−0.0848827	−	0.0848827i
$423$	112.789	−	112.789i	0.266641	−	0.266641i
$424$	463.872	−	463.872i	1.09404	−	1.09404i
$425$	128.078			0.301360
$426$		−	69.9632i		−	0.164233i
$427$	361.859	−	361.859i	0.847446	−	0.847446i
$428$		−	512.612i		−	1.19769i
$429$	−111.208	−	299.557i	−0.259226	−	0.698268i
$430$	−91.3175			−0.212366
$431$	422.858	+	422.858i	0.981110	+	0.981110i	0.999825	−	0.0187153i	$-0.00595760\pi$
$431$	422.858	+	422.858i	0.981110	+	0.981110i	−0.0187153	+	0.999825i	$0.505958\pi$
$432$	−30.4297			−0.0704392
$433$			621.635i			1.43565i	0.696225	+	0.717824i	$0.254862\pi$
$433$			621.635i			1.43565i	−0.696225	+	0.717824i	$0.745138\pi$
$434$	−74.3445	−	74.3445i	−0.171301	−	0.171301i
$435$	22.5818	+	22.5818i	0.0519121	+	0.0519121i
$436$	−14.0793	+	14.0793i	−0.0322919	+	0.0322919i
$437$	269.425	−	269.425i	0.616534	−	0.616534i
$438$	25.7633			0.0588204
$439$		−	416.992i		−	0.949868i	−0.880021	−	0.474934i	$-0.842472\pi$
$439$		−	416.992i		−	0.949868i	0.880021	−	0.474934i	$-0.157528\pi$
$440$	151.970	−	151.970i	0.345387	−	0.345387i
$441$			52.7202i			0.119547i
$442$	27.7074	+	74.6345i	0.0626864	+	0.168856i
$443$	581.904			1.31355			0.656776	−	0.754086i	$-0.271920\pi$
$443$	581.904			1.31355			0.656776	+	0.754086i	$0.271920\pi$
$444$	199.046	+	199.046i	0.448302	+	0.448302i
$445$	−201.779			−0.453436
$446$		−	95.3060i		−	0.213690i
$447$	302.913	+	302.913i	0.677657	+	0.677657i
$448$	−31.1878	−	31.1878i	−0.0696157	−	0.0696157i
$449$	−66.7587	+	66.7587i	−0.148683	+	0.148683i	−0.777530	−	0.628846i	$-0.783527\pi$
$449$	−66.7587	+	66.7587i	−0.148683	+	0.148683i	0.628846	+	0.777530i	$0.283527\pi$
$450$	−40.5991	+	40.5991i	−0.0902202	+	0.0902202i
$451$	576.023			1.27721
$452$			187.415i			0.414636i
$453$	−66.0077	+	66.0077i	−0.145712	+	0.145712i
$454$			128.547i			0.283143i
$455$	−67.8762	+	148.029i	−0.149179	+	0.325339i
$456$	−128.420			−0.281623
$457$	−103.815	−	103.815i	−0.227167	−	0.227167i	0.584341	−	0.811508i	$-0.301353\pi$
$457$	−103.815	−	103.815i	−0.227167	−	0.227167i	−0.811508	+	0.584341i	$0.801353\pi$
$458$	−90.5071			−0.197614
$459$			33.2645i			0.0724716i
$460$	−169.773	−	169.773i	−0.369072	−	0.369072i
$461$	−203.938	−	203.938i	−0.442381	−	0.442381i	0.450430	−	0.892812i	$-0.351271\pi$
$461$	−203.938	−	203.938i	−0.442381	−	0.442381i	−0.892812	+	0.450430i	$0.851271\pi$
$462$	93.2054	−	93.2054i	0.201743	−	0.201743i
$463$	−481.370	+	481.370i	−1.03968	+	1.03968i	−0.0404953	+	0.999180i	$0.512894\pi$
$463$	−481.370	+	481.370i	−1.03968	+	1.03968i	−0.999180	+	0.0404953i	$0.987106\pi$
$464$	−48.3210			−0.104140
$465$			75.8812i			0.163185i
$466$	55.4127	−	55.4127i	0.118911	−	0.118911i
$467$			7.71730i			0.0165253i	0.999966	+	0.00826263i	$0.00263011\pi$
$467$			7.71730i			0.0165253i	−0.999966	+	0.00826263i	$0.997370\pi$
$468$	109.362	+	50.1462i	0.233680	+	0.107150i
$469$	−336.543			−0.717576
$470$	−80.3663	−	80.3663i	−0.170992	−	0.170992i
$471$	260.429			0.552928
$472$			363.201i			0.769494i
$473$	428.670	+	428.670i	0.906280	+	0.906280i
$474$	−119.539	−	119.539i	−0.252193	−	0.252193i
$475$	154.762	−	154.762i	0.325815	−	0.325815i
$476$	78.2841	−	78.2841i	0.164462	−	0.164462i
$477$	−290.380			−0.608763
$478$		−	6.92665i		−	0.0144909i
$479$	24.7867	−	24.7867i	0.0517467	−	0.0517467i	−0.680760	−	0.732507i	$-0.738350\pi$
$479$	24.7867	−	24.7867i	0.0517467	−	0.0517467i	0.732507	+	0.680760i	$0.238350\pi$
$480$			126.608i			0.263767i
$481$	−238.358	−	642.056i	−0.495546	−	1.33484i
$482$	205.907			0.427193
$483$	−239.136	−	239.136i	−0.495105	−	0.495105i
$484$	−247.976			−0.512346
$485$		−	185.508i		−	0.382491i
$486$	−10.5444	−	10.5444i	−0.0216963	−	0.0216963i
$487$	245.469	+	245.469i	0.504044	+	0.504044i	0.912692	−	0.408648i	$-0.134000\pi$
$487$	245.469	+	245.469i	0.504044	+	0.504044i	−0.408648	+	0.912692i	$0.634000\pi$
$488$	−437.481	+	437.481i	−0.896477	+	0.896477i
$489$	−290.194	+	290.194i	−0.593444	+	0.593444i
$490$	37.5650			0.0766632
$491$		−	25.3996i		−	0.0517304i	−0.999665	−	0.0258652i	$-0.991766\pi$
$491$		−	25.3996i		−	0.0517304i	0.999665	−	0.0258652i	$-0.00823406\pi$
$492$	−153.361	+	153.361i	−0.311709	+	0.311709i
$493$			52.8224i			0.107145i
$494$	123.664	+	56.7040i	0.250332	+	0.114785i
$495$	−95.1320			−0.192186
$496$	−81.1861	−	81.1861i	−0.163682	−	0.163682i
$497$	236.714			0.476285
$498$			199.819i			0.401242i
$499$	−328.094	−	328.094i	−0.657502	−	0.657502i	0.297286	−	0.954788i	$-0.403918\pi$
$499$	−328.094	−	328.094i	−0.657502	−	0.657502i	−0.954788	+	0.297286i	$0.903918\pi$
$500$	−219.380	−	219.380i	−0.438760	−	0.438760i
$501$	−58.4753	+	58.4753i	−0.116717	+	0.116717i
$502$	−150.083	+	150.083i	−0.298971	+	0.298971i
$503$	−399.152			−0.793543			−0.396771	−	0.917918i	$-0.629869\pi$
$503$	−399.152			−0.793543			−0.396771	+	0.917918i	$0.629869\pi$
$504$			113.982i			0.226156i
$505$	−205.608	+	205.608i	−0.407145	+	0.407145i
$506$		−	472.820i		−	0.934428i
$507$	−191.012	−	221.805i	−0.376749	−	0.437486i
$508$	401.674			0.790697
$509$	655.020	+	655.020i	1.28688	+	1.28688i	0.936674	+	0.350203i	$0.113887\pi$
$509$	655.020	+	655.020i	1.28688	+	1.28688i	0.350203	+	0.936674i	$0.386113\pi$
$510$	23.7021			0.0464747
$511$			87.1678i			0.170583i
$512$	−247.720	−	247.720i	−0.483829	−	0.483829i
$513$	40.1949	+	40.1949i	0.0783526	+	0.0783526i
$514$	−10.1709	+	10.1709i	−0.0197877	+	0.0197877i
$515$	−44.1185	+	44.1185i	−0.0856670	+	0.0856670i
$516$	−228.259			−0.442363
$517$			754.525i			1.45943i
$518$	199.772	−	199.772i	0.385660	−	0.385660i
$519$			260.206i			0.501361i
$520$	82.0610	−	178.964i	0.157810	−	0.344162i
$521$	287.758			0.552318			0.276159	−	0.961112i	$-0.410938\pi$
$521$	287.758			0.552318			0.276159	+	0.961112i	$0.410938\pi$
$522$	−16.7440	−	16.7440i	−0.0320767	−	0.0320767i
$523$	−148.325			−0.283604			−0.141802	−	0.989895i	$-0.545290\pi$
$523$	−148.325			−0.283604			−0.141802	+	0.989895i	$0.545290\pi$
$524$		−	418.099i		−	0.797898i
$525$	−137.363	−	137.363i	−0.261644	−	0.261644i
$526$	71.5139	+	71.5139i	0.135958	+	0.135958i
$527$	−88.7492	+	88.7492i	−0.168405	+	0.168405i
$528$	101.783	−	101.783i	0.192770	−	0.192770i
$529$	−684.108			−1.29321
$530$			206.906i			0.390389i
$531$	113.680	−	113.680i	0.214087	−	0.214087i
$532$		−	189.188i		−	0.355617i
$533$	494.692	−	183.650i	0.928127	−	0.344559i
$534$	149.616			0.280180
$535$	262.558	+	262.558i	0.490763	+	0.490763i
$536$	406.874			0.759094
$537$			427.999i			0.797019i
$538$	−114.140	−	114.140i	−0.212156	−	0.212156i
$539$	−176.341	−	176.341i	−0.327163	−	0.327163i
$540$	25.3280	−	25.3280i	0.0469037	−	0.0469037i
$541$	−378.819	+	378.819i	−0.700221	+	0.700221i	−0.964458	−	0.264237i	$-0.914880\pi$
$541$	−378.819	+	378.819i	−0.700221	+	0.700221i	0.264237	+	0.964458i	$0.414880\pi$
$542$	70.9958			0.130989
$543$		−	193.426i		−	0.356217i
$544$	−148.078	+	148.078i	−0.272202	+	0.272202i
$545$		−	14.4227i		−	0.0264637i
$546$	50.3291	−	109.761i	0.0921779	−	0.201028i
$547$	63.2197			0.115575			0.0577876	−	0.998329i	$-0.481595\pi$
$547$	63.2197			0.115575			0.0577876	+	0.998329i	$0.481595\pi$
$548$	−418.062	−	418.062i	−0.762888	−	0.762888i
$549$	273.859			0.498833
$550$		−	271.595i		−	0.493810i
$551$	63.8276	+	63.8276i	0.115839	+	0.115839i
$552$	289.110	+	289.110i	0.523750	+	0.523750i
$553$	404.450	−	404.450i	0.731374	−	0.731374i
$554$	103.505	−	103.505i	0.186832	−	0.186832i
$555$	−203.901			−0.367390
$556$			752.735i			1.35384i
$557$	599.495	−	599.495i	1.07629	−	1.07629i	0.0794543	−	0.996839i	$-0.474682\pi$
$557$	599.495	−	599.495i	1.07629	−	1.07629i	0.996839	−	0.0794543i	$-0.0253178\pi$
$558$		−	56.2647i		−	0.100833i
$559$	504.815	+	231.474i	0.903067	+	0.414086i
$560$	−73.3598			−0.131000
$561$	−111.264	−	111.264i	−0.198332	−	0.198332i
$562$	−51.2578			−0.0912060
$563$			79.3967i			0.141024i	0.997511	+	0.0705122i	$0.0224634\pi$
$563$			79.3967i			0.141024i	−0.997511	+	0.0705122i	$0.977537\pi$
$564$	−200.885	−	200.885i	−0.356180	−	0.356180i
$565$	−95.9937	−	95.9937i	−0.169900	−	0.169900i
$566$	−23.4870	+	23.4870i	−0.0414964	+	0.0414964i
$567$	35.6760	−	35.6760i	0.0629207	−	0.0629207i
$568$	−286.182			−0.503842
$569$		−	27.2834i		−	0.0479497i	−0.999713	−	0.0239748i	$-0.992368\pi$
$569$		−	27.2834i		−	0.0479497i	0.999713	−	0.0239748i	$-0.00763216\pi$
$570$	28.6403	−	28.6403i	0.0502461	−	0.0502461i
$571$			73.0650i			0.127960i	0.997951	+	0.0639799i	$0.0203793\pi$
$571$			73.0650i			0.127960i	−0.997951	+	0.0639799i	$0.979621\pi$
$572$	−533.531	+	198.069i	−0.932747	+	0.346274i
$573$	−112.062			−0.195571
$574$	153.920	+	153.920i	0.268154	+	0.268154i
$575$	−696.828			−1.21187
$576$		−	23.6033i		−	0.0409779i
$577$	172.432	+	172.432i	0.298841	+	0.298841i	0.840560	−	0.541719i	$-0.182226\pi$
$577$	172.432	+	172.432i	0.298841	+	0.298841i	−0.541719	+	0.840560i	$0.682226\pi$
$578$	−167.765	−	167.765i	−0.290251	−	0.290251i
$579$	168.180	−	168.180i	0.290466	−	0.290466i
$580$	40.2197	−	40.2197i	0.0693443	−	0.0693443i
$581$	−676.067			−1.16363
$582$			137.551i			0.236343i
$583$	971.276	−	971.276i	1.66600	−	1.66600i
$584$		−	105.384i		−	0.180452i
$585$	−81.6998	+	30.3303i	−0.139658	+	0.0518467i
$586$	−73.6854			−0.125743
$587$	766.322	+	766.322i	1.30549	+	1.30549i	0.924635	+	0.380854i	$0.124370\pi$
$587$	766.322	+	766.322i	1.30549	+	1.30549i	0.380854	+	0.924635i	$0.375630\pi$
$588$	93.8982			0.159691
$589$			214.479i			0.364141i
$590$	−81.0013	−	81.0013i	−0.137290	−	0.137290i
$591$	84.6496	+	84.6496i	0.143231	+	0.143231i
$592$	218.156	−	218.156i	0.368507	−	0.368507i
$593$	120.360	−	120.360i	0.202969	−	0.202969i	−0.598302	−	0.801271i	$-0.704158\pi$
$593$	120.360	−	120.360i	0.202969	−	0.202969i	0.801271	+	0.598302i	$0.204158\pi$
$594$	70.5388			0.118752
$595$			80.1938i			0.134779i
$596$	539.508	−	539.508i	0.905215	−	0.905215i
$597$		−	241.743i		−	0.404929i
$598$	−150.746	−	406.060i	−0.252084	−	0.679031i
$599$	323.635			0.540292			0.270146	−	0.962819i	$-0.412928\pi$
$599$	323.635			0.540292			0.270146	+	0.962819i	$0.412928\pi$
$600$	166.069	+	166.069i	0.276782	+	0.276782i
$601$	1108.97			1.84521			0.922607	−	0.385742i	$-0.126054\pi$
$601$	1108.97			1.84521			0.922607	+	0.385742i	$0.126054\pi$
$602$			229.092i			0.380551i
$603$	−127.350	−	127.350i	−0.211194	−	0.211194i
$604$	117.564	+	117.564i	0.194643	+	0.194643i
$605$	127.012	−	127.012i	0.209938	−	0.209938i
$606$	152.455	−	152.455i	0.251576	−	0.251576i
$607$	−196.769			−0.324167			−0.162084	−	0.986777i	$-0.551821\pi$
$607$	−196.769			−0.324167			−0.162084	+	0.986777i	$0.551821\pi$
$608$			357.858i			0.588583i
$609$	56.6518	−	56.6518i	0.0930243	−	0.0930243i
$610$		−	195.134i		−	0.319892i
$611$	240.561	+	647.990i	0.393716	+	1.06054i
$612$	59.2463			0.0968076
$613$	−702.697	−	702.697i	−1.14633	−	1.14633i	−0.987270	−	0.159055i	$-0.949155\pi$
$613$	−702.697	−	702.697i	−1.14633	−	1.14633i	−0.159055	−	0.987270i	$-0.550845\pi$
$614$	−302.206			−0.492193
$615$		−	157.102i		−	0.255450i
$616$	−381.254	−	381.254i	−0.618918	−	0.618918i
$617$	−305.273	−	305.273i	−0.494771	−	0.494771i	0.415035	−	0.909805i	$-0.363769\pi$
$617$	−305.273	−	305.273i	−0.494771	−	0.494771i	−0.909805	+	0.415035i	$0.863769\pi$
$618$	32.7132	−	32.7132i	0.0529339	−	0.0529339i
$619$	97.1707	−	97.1707i	0.156980	−	0.156980i	−0.624247	−	0.781227i	$-0.714594\pi$
$619$	97.1707	−	97.1707i	0.156980	−	0.156980i	0.781227	+	0.624247i	$0.214594\pi$
$620$	135.150			0.217983
$621$		−	180.980i		−	0.291434i
$622$	−349.359	+	349.359i	−0.561670	+	0.561670i
$623$			506.211i			0.812538i
$624$	54.9607	−	119.862i	0.0880781	−	0.192087i
$625$	−275.436			−0.440698
$626$	100.946	+	100.946i	0.161255	+	0.161255i
$627$	−268.891			−0.428854
$628$		−	463.842i		−	0.738601i
$629$	−238.479	−	238.479i	−0.379140	−	0.379140i
$630$	−25.4204	−	25.4204i	−0.0403499	−	0.0403499i
$631$	−368.719	+	368.719i	−0.584341	+	0.584341i	−0.936093	−	0.351752i	$-0.885586\pi$
$631$	−368.719	+	368.719i	−0.584341	+	0.584341i	0.351752	+	0.936093i	$0.385586\pi$
$632$	−488.972	+	488.972i	−0.773690	+	0.773690i
$633$	91.7219			0.144900
$634$			254.556i			0.401508i
$635$	−205.736	+	205.736i	−0.323994	+	0.323994i
$636$			517.187i			0.813186i
$637$	−207.664	−	95.2206i	−0.326003	−	0.149483i
$638$	112.012			0.175568
$639$	89.5738	+	89.5738i	0.140178	+	0.140178i
$640$	275.570			0.430579
$641$			779.737i			1.21644i	0.793769	+	0.608219i	$0.208116\pi$
$641$			779.737i			1.21644i	−0.793769	+	0.608219i	$0.791884\pi$
$642$	−194.683	−	194.683i	−0.303244	−	0.303244i
$643$	−719.483	−	719.483i	−1.11895	−	1.11895i	−0.991896	−	0.127051i	$-0.959449\pi$
$643$	−719.483	−	719.483i	−1.11895	−	1.11895i	−0.127051	−	0.991896i	$-0.540551\pi$
$644$	−425.917	+	425.917i	−0.661361	+	0.661361i
$645$	116.914	−	116.914i	0.181262	−	0.181262i
$646$	66.9942			0.103706
$647$		−	313.980i		−	0.485286i	−0.970116	−	0.242643i	$-0.921986\pi$
$647$		−	313.980i		−	0.485286i	0.970116	−	0.242643i	$-0.0780144\pi$
$648$	−43.1316	+	43.1316i	−0.0665611	+	0.0665611i
$649$			760.487i			1.17178i
$650$	−86.5910	−	233.247i	−0.133217	−	0.358842i
$651$	190.366			0.292421
$652$	516.856	+	516.856i	0.792724	+	0.792724i
$653$	−280.037			−0.428847			−0.214424	−	0.976741i	$-0.568787\pi$
$653$	−280.037			−0.428847			−0.214424	+	0.976741i	$0.568787\pi$
$654$			10.6942i			0.0163520i
$655$	214.149	+	214.149i	0.326945	+	0.326945i
$656$	168.085	+	168.085i	0.256227	+	0.256227i
$657$	−32.9848	+	32.9848i	−0.0502051	+	0.0502051i
$658$	−201.618	+	201.618i	−0.306411	+	0.306411i
$659$	−1021.28			−1.54974			−0.774871	−	0.632119i	$-0.782185\pi$
$659$	−1021.28			−1.54974			−0.774871	+	0.632119i	$0.782185\pi$
$660$			169.437i			0.256722i
$661$	638.747	−	638.747i	0.966334	−	0.966334i	−0.0331178	−	0.999451i	$-0.510544\pi$
$661$	638.747	−	638.747i	0.966334	−	0.966334i	0.999451	+	0.0331178i	$0.0105436\pi$
$662$			180.942i			0.273326i
$663$	−131.028	−	60.0807i	−0.197629	−	0.0906195i
$664$	817.352			1.23095
$665$	96.9016	+	96.9016i	0.145717	+	0.145717i
$666$	151.190			0.227012
$667$		−	287.388i		−	0.430867i
$668$	104.149	+	104.149i	0.155911	+	0.155911i
$669$	122.020	+	122.020i	0.182392	+	0.182392i
$670$	−90.7413	+	90.7413i	−0.135435	+	0.135435i
$671$	−916.016	+	916.016i	−1.36515	+	1.36515i
$672$	317.626			0.472658
$673$			236.547i			0.351482i	0.984436	+	0.175741i	$0.0562320\pi$
$673$			236.547i			0.351482i	−0.984436	+	0.175741i	$0.943768\pi$
$674$	−136.921	+	136.921i	−0.203147	+	0.203147i
$675$		−	103.958i		−	0.154012i
$676$	−395.050	+	340.205i	−0.584394	+	0.503261i
$677$	−788.423			−1.16458			−0.582292	−	0.812980i	$-0.697844\pi$
$677$	−788.423			−1.16458			−0.582292	+	0.812980i	$0.697844\pi$
$678$	71.1778	+	71.1778i	0.104982	+	0.104982i
$679$	−465.392			−0.685408
$680$		−	96.9527i		−	0.142578i
$681$	−164.579	−	164.579i	−0.241672	−	0.241672i
$682$	188.197	+	188.197i	0.275948	+	0.275948i
$683$	−278.551	+	278.551i	−0.407834	+	0.407834i	−0.880983	−	0.473149i	$-0.843117\pi$
$683$	−278.551	+	278.551i	−0.407834	+	0.407834i	0.473149	+	0.880983i	$0.343117\pi$
$684$	71.5898	−	71.5898i	0.104663	−	0.104663i
$685$	428.261			0.625198
$686$		−	357.013i		−	0.520427i
$687$	115.876	−	115.876i	0.168670	−	0.168670i
$688$			250.174i			0.363626i
$689$	524.471	−	1143.80i	0.761206	−	1.66009i
$690$	−128.955			−0.186891
$691$	−64.4993	−	64.4993i	−0.0933420	−	0.0933420i	0.658894	−	0.752236i	$-0.271025\pi$
$691$	−64.4993	−	64.4993i	−0.0933420	−	0.0933420i	−0.752236	+	0.658894i	$0.771025\pi$
$692$	463.445			0.669718
$693$			238.661i			0.344389i
$694$	−129.109	−	129.109i	−0.186037	−	0.186037i
$695$	−385.549	−	385.549i	−0.554746	−	0.554746i
$696$	−68.4909	+	68.4909i	−0.0984065	+	0.0984065i
$697$	183.743	−	183.743i	0.263620	−	0.263620i
$698$	638.590			0.914886
$699$			141.890i			0.202989i
$700$	−244.653	+	244.653i	−0.349504	+	0.349504i
$701$			136.339i			0.194493i	0.995260	+	0.0972463i	$0.0310035\pi$
$701$			136.339i			0.194493i	−0.995260	+	0.0972463i	$0.968997\pi$
$702$	60.5791	−	22.4895i	0.0862950	−	0.0320363i
$703$	−576.329			−0.819814
$704$	78.9493	+	78.9493i	0.112144	+	0.112144i
$705$	205.786			0.291895
$706$			403.824i			0.571989i
$707$	515.818	+	515.818i	0.729587	+	0.729587i
$708$	−202.473	−	202.473i	−0.285978	−	0.285978i
$709$	789.276	−	789.276i	1.11322	−	1.11322i	0.120513	−	0.992712i	$-0.461546\pi$
$709$	789.276	−	789.276i	1.11322	−	1.11322i	0.992712	−	0.120513i	$-0.0384540\pi$
$710$	63.8245	−	63.8245i	0.0898936	−	0.0898936i
$711$	306.092			0.430509
$712$		−	611.999i		−	0.859549i
$713$	482.854	−	482.854i	0.677214	−	0.677214i
$714$		−	59.4624i		−	0.0832807i
$715$	171.823	−	374.723i	0.240312	−	0.524089i
$716$	762.296			1.06466
$717$	8.86818	+	8.86818i	0.0123685	+	0.0123685i
$718$	116.834			0.162721
$719$		−	949.863i		−	1.32109i	−0.750787	−	0.660544i	$-0.770326\pi$
$719$		−	949.863i		−	1.32109i	0.750787	−	0.660544i	$-0.229674\pi$
$720$	−27.7598	−	27.7598i	−0.0385552	−	0.0385552i
$721$	110.682	+	110.682i	0.153512	+	0.153512i
$722$	−163.237	+	163.237i	−0.226091	+	0.226091i
$723$	−263.623	+	263.623i	−0.364623	+	0.364623i
$724$	−344.505			−0.475835
$725$		−	165.080i		−	0.227697i
$726$	−94.1777	+	94.1777i	−0.129721	+	0.129721i
$727$		−	195.690i		−	0.269175i	−0.990902	−	0.134588i	$-0.957029\pi$
$727$		−	195.690i		−	0.269175i	0.990902	−	0.134588i	$-0.0429710\pi$
$728$	−448.975	−	205.870i	−0.616724	−	0.282788i
$729$	27.0000			0.0370370
$730$	23.5028	+	23.5028i	0.0321956	+	0.0321956i
$731$	273.480			0.374117
$732$		−	487.762i		−	0.666341i
$733$	−373.535	−	373.535i	−0.509597	−	0.509597i	0.404806	−	0.914403i	$-0.367339\pi$
$733$	−373.535	−	373.535i	−0.509597	−	0.509597i	−0.914403	+	0.404806i	$0.867339\pi$
$734$	36.6588	+	36.6588i	0.0499439	+	0.0499439i
$735$	−48.0944	+	48.0944i	−0.0654345	+	0.0654345i
$736$	805.642	−	805.642i	1.09462	−	1.09462i
$737$	851.931			1.15594
$738$			116.489i			0.157844i
$739$	−868.098	+	868.098i	−1.17469	+	1.17469i	−0.193615	+	0.981078i	$0.562021\pi$
$739$	−868.098	+	868.098i	−1.17469	+	1.17469i	−0.981078	+	0.193615i	$0.937979\pi$
$740$			363.162i			0.490760i
$741$	−230.925	+	85.7289i	−0.311640	+	0.115694i
$742$	519.073			0.699560
$743$	−744.696	−	744.696i	−1.00228	−	1.00228i	−0.999997	−	0.00228459i	$-0.999273\pi$
$743$	−744.696	−	744.696i	−1.00228	−	1.00228i	−0.00228459	−	0.999997i	$-0.500727\pi$
$744$	−230.149			−0.309340
$745$			552.669i			0.741837i
$746$	12.1325	+	12.1325i	0.0162633	+	0.0162633i
$747$	−255.828	−	255.828i	−0.342473	−	0.342473i
$748$	−198.170	+	198.170i	−0.264933	+	0.264933i
$749$	658.690	−	658.690i	0.879426	−	0.879426i
$750$	−166.635			−0.222180
$751$			267.175i			0.355760i	0.984052	+	0.177880i	$0.0569238\pi$
$751$			267.175i			0.355760i	−0.984052	+	0.177880i	$0.943076\pi$
$752$	−220.172	+	220.172i	−0.292783	+	0.292783i
$753$		−	384.303i		−	0.510362i
$754$	96.1967	−	35.7122i	0.127582	−	0.0473636i
$755$	−120.432			−0.159513
$756$	−63.5414	−	63.5414i	−0.0840495	−	0.0840495i
$757$	−421.716			−0.557088			−0.278544	−	0.960423i	$-0.589852\pi$
$757$	−421.716			−0.557088			−0.278544	+	0.960423i	$0.589852\pi$
$758$			380.915i			0.502527i
$759$	605.351	+	605.351i	0.797565	+	0.797565i
$760$	−117.152	−	117.152i	−0.154148	−	0.154148i
$761$	937.965	−	937.965i	1.23254	−	1.23254i	0.269558	−	0.962984i	$-0.413122\pi$
$761$	937.965	−	937.965i	1.23254	−	1.23254i	0.962984	−	0.269558i	$-0.0868776\pi$
$762$	152.550	−	152.550i	0.200197	−	0.200197i
$763$	−36.1828			−0.0474218
$764$			199.590i			0.261244i
$765$	−30.3458	+	30.3458i	−0.0396677	+	0.0396677i
$766$			331.214i			0.432395i
$767$	242.461	+	653.109i	0.316116	+	0.851512i
$768$	−258.840			−0.337032
$769$	749.082	+	749.082i	0.974098	+	0.974098i	0.999673	−	0.0255747i	$-0.00814156\pi$
$769$	749.082	+	749.082i	0.974098	+	0.974098i	−0.0255747	+	0.999673i	$0.508142\pi$
$770$	170.055			0.220850
$771$		−	26.0436i		−	0.0337789i
$772$	−299.539	−	299.539i	−0.388004	−	0.388004i
$773$	292.773	+	292.773i	0.378749	+	0.378749i	0.870651	−	0.491902i	$-0.163698\pi$
$773$	292.773	+	292.773i	0.378749	+	0.378749i	−0.491902	+	0.870651i	$0.663698\pi$
$774$	−86.6896	+	86.6896i	−0.112002	+	0.112002i
$775$	277.358	−	277.358i	0.357882	−	0.357882i
$776$	562.650			0.725064
$777$			511.536i			0.658347i
$778$	393.855	−	393.855i	0.506241	−	0.506241i
$779$		−	444.050i		−	0.570025i
$780$	54.0204	+	145.513i	0.0692569	+	0.186555i
$781$	−599.221			−0.767248
$782$	−150.823	−	150.823i	−0.192868	−	0.192868i
$783$	42.8747			0.0547570
$784$		−	102.913i		−	0.131267i
$785$	237.578	+	237.578i	0.302648	+	0.302648i
$786$	−158.788	−	158.788i	−0.202020	−	0.202020i
$787$	−992.205	+	992.205i	−1.26074	+	1.26074i	−0.310010	+	0.950733i	$0.600332\pi$
$787$	−992.205	+	992.205i	−1.26074	+	1.26074i	−0.950733	+	0.310010i	$0.899668\pi$
$788$	150.767	−	150.767i	0.191328	−	0.191328i
$789$	−183.118			−0.232089
$790$		−	218.101i		−	0.276078i
$791$	−240.823	+	240.823i	−0.304454	+	0.304454i
$792$		−	288.537i		−	0.364314i
$793$	−494.631	+	1078.73i	−0.623747	+	1.36031i
$794$	−503.341			−0.633931
$795$	−264.902	−	264.902i	−0.333209	−	0.333209i
$796$	−430.560			−0.540905
$797$		−	96.6901i		−	0.121318i	−0.998159	−	0.0606588i	$-0.980680\pi$
$797$		−	96.6901i		−	0.121318i	0.998159	−	0.0606588i	$-0.0193202\pi$
$798$	−71.8510	−	71.8510i	−0.0900388	−	0.0900388i
$799$	240.683	+	240.683i	0.301230	+	0.301230i
$800$	462.773	−	462.773i	0.578466	−	0.578466i
$801$	−191.553	+	191.553i	−0.239142	+	0.239142i
$802$	514.423			0.641425
$803$		−	220.658i		−	0.274792i
$804$	−226.819	+	226.819i	−0.282113	+	0.282113i
$805$		−	436.307i		−	0.541996i
$806$	221.626	+	101.623i	0.274970	+	0.126083i
$807$	292.266			0.362163
$808$	−623.614	−	623.614i	−0.771799	−	0.771799i
$809$	−800.289			−0.989233			−0.494616	−	0.869111i	$-0.664691\pi$
$809$	−800.289			−0.989233			−0.494616	+	0.869111i	$0.664691\pi$
$810$		−	19.2384i		−	0.0237512i
$811$	1015.91	+	1015.91i	1.25267	+	1.25267i	0.954520	+	0.298147i	$0.0963686\pi$
$811$	1015.91	+	1015.91i	1.25267	+	1.25267i	0.298147	+	0.954520i	$0.403631\pi$
$812$	−100.901	−	100.901i	−0.124262	−	0.124262i
$813$	−90.8958	+	90.8958i	−0.111803	+	0.111803i
$814$	−505.706	+	505.706i	−0.621260	+	0.621260i
$815$	−529.464			−0.649649
$816$		−	64.9345i		−	0.0795766i
$817$	330.457	−	330.457i	0.404476	−	0.404476i
$818$		−	79.2532i		−	0.0968866i
$819$	76.0909	+	204.964i	0.0929071	+	0.250261i
$820$	−279.809			−0.341231
$821$	−515.901	−	515.901i	−0.628381	−	0.628381i	0.319280	−	0.947661i	$-0.396559\pi$
$821$	−515.901	−	515.901i	−0.628381	−	0.628381i	−0.947661	+	0.319280i	$0.896559\pi$
$822$	−317.548			−0.386312
$823$			563.080i			0.684179i	0.939667	+	0.342090i	$0.111135\pi$
$823$			563.080i			0.684179i	−0.939667	+	0.342090i	$0.888865\pi$
$824$	−133.812	−	133.812i	−0.162393	−	0.162393i
$825$	347.723	+	347.723i	0.421483	+	0.421483i
$826$	−203.211	+	203.211i	−0.246018	+	0.246018i
$827$	−129.875	+	129.875i	−0.157044	+	0.157044i	−0.781255	−	0.624212i	$-0.785420\pi$
$827$	−129.875	+	129.875i	−0.157044	+	0.157044i	0.624212	+	0.781255i	$0.285420\pi$
$828$	−322.338			−0.389298
$829$		−	1140.27i		−	1.37548i	−0.725957	−	0.687740i	$-0.758603\pi$
$829$		−	1140.27i		−	1.37548i	0.725957	−	0.687740i	$-0.241397\pi$
$830$	−182.286	+	182.286i	−0.219622	+	0.219622i
$831$			265.035i			0.318935i
$832$	92.9730	+	42.6311i	0.111746	+	0.0512394i
$833$	−112.500			−0.135055
$834$	285.878	+	285.878i	0.342779	+	0.342779i
$835$	−106.689			−0.127771
$836$			478.913i			0.572863i
$837$	72.0356	+	72.0356i	0.0860641	+	0.0860641i
$838$	305.737	+	305.737i	0.364841	+	0.364841i
$839$	373.307	−	373.307i	0.444942	−	0.444942i	−0.448727	−	0.893669i	$-0.648122\pi$
$839$	373.307	−	373.307i	0.444942	−	0.444942i	0.893669	+	0.448727i	$0.148122\pi$
$840$	−103.981	+	103.981i	−0.123787	+	0.123787i
$841$	−772.917			−0.919045
$842$		−	73.8044i		−	0.0876537i
$843$	65.6252	−	65.6252i	0.0778473	−	0.0778473i
$844$		−	163.363i		−	0.193558i
$845$	28.0916	−	376.595i	0.0332445	−	0.445675i
$846$	−152.587			−0.180363
$847$	−318.641	−	318.641i	−0.376200	−	0.376200i
$848$	566.842			0.668446
$849$		−	60.1406i		−	0.0708370i
$850$	−86.6351	−	86.6351i	−0.101924	−	0.101924i
$851$	1297.48	+	1297.48i	1.52466	+	1.52466i
$852$	159.537	−	159.537i	0.187250	−	0.187250i
$853$	−65.1164	+	65.1164i	−0.0763381	+	0.0763381i	−0.744245	−	0.667907i	$-0.767190\pi$
$853$	−65.1164	+	65.1164i	−0.0763381	+	0.0763381i	0.667907	+	0.744245i	$0.267190\pi$
$854$	−489.541			−0.573233
$855$			73.3362i			0.0857733i
$856$	−796.344	+	796.344i	−0.930308	+	0.930308i
$857$		−	98.7570i		−	0.115236i	−0.998339	−	0.0576178i	$-0.981650\pi$
$857$		−	98.7570i		−	0.115236i	0.998339	−	0.0576178i	$-0.0183505\pi$
$858$	−127.404	+	277.851i	−0.148489	+	0.323836i
$859$	959.271			1.11673			0.558365	−	0.829595i	$-0.311429\pi$
$859$	959.271			1.11673			0.558365	+	0.829595i	$0.311429\pi$
$860$	−208.231	−	208.231i	−0.242129	−	0.242129i
$861$	−394.128			−0.457756
$862$		−	572.063i		−	0.663647i
$863$	−30.4807	−	30.4807i	−0.0353194	−	0.0353194i	0.689227	−	0.724546i	$-0.257950\pi$
$863$	−30.4807	−	30.4807i	−0.0353194	−	0.0353194i	−0.724546	+	0.689227i	$0.757950\pi$
$864$	120.192	+	120.192i	0.139111	+	0.139111i
$865$	−237.375	+	237.375i	−0.274422	+	0.274422i
$866$	420.489	−	420.489i	0.485554	−	0.485554i
$867$	429.579			0.495478
$868$		−	339.055i		−	0.390617i
$869$	−1023.83	+	1023.83i	−1.17817	+	1.17817i
$870$		−	30.5497i		−	0.0351146i
$871$	731.642	−	271.616i	0.840003	−	0.311844i
$872$	43.7443			0.0501655
$873$	−176.107	−	176.107i	−0.201726	−	0.201726i
$874$	−364.492			−0.417039
$875$		−	563.793i		−	0.644334i
$876$	58.7481	+	58.7481i	0.0670640	+	0.0670640i
$877$	66.1101	+	66.1101i	0.0753821	+	0.0753821i	0.743793	−	0.668410i	$-0.233025\pi$
$877$	66.1101	+	66.1101i	0.0753821	+	0.0753821i	−0.668410	+	0.743793i	$0.733025\pi$
$878$	−282.064	+	282.064i	−0.321257	+	0.321257i
$879$	94.3393	−	94.3393i	0.107326	−	0.107326i
$880$	185.704			0.211027
$881$			825.315i			0.936794i	0.883518	+	0.468397i	$0.155168\pi$
$881$			825.315i			0.936794i	−0.883518	+	0.468397i	$0.844832\pi$
$882$	35.6612	−	35.6612i	0.0404322	−	0.0404322i
$883$		−	1501.16i		−	1.70007i	−0.526724	−	0.850037i	$-0.676580\pi$
$883$		−	1501.16i		−	1.70007i	0.526724	−	0.850037i	$-0.323420\pi$
$884$	−107.008	+	233.370i	−0.121050	+	0.263993i
$885$	207.412			0.234363
$886$	−393.614	−	393.614i	−0.444260	−	0.444260i
$887$	−122.414			−0.138009			−0.0690045	−	0.997616i	$-0.521982\pi$
$887$	−122.414			−0.138009			−0.0690045	+	0.997616i	$0.521982\pi$
$888$		−	618.437i		−	0.696438i
$889$	516.139	+	516.139i	0.580584	+	0.580584i
$890$	136.488	+	136.488i	0.153358	+	0.153358i
$891$	−90.3108	+	90.3108i	−0.101359	+	0.101359i
$892$	217.326	−	217.326i	0.243639	−	0.243639i
$893$	581.655			0.651349
$894$		−	409.795i		−	0.458384i
$895$	−390.446	+	390.446i	−0.436252	+	0.436252i
$896$		−	691.334i		−	0.771578i
$897$	712.879	+	326.878i	0.794737	+	0.364413i
$898$	90.3144			0.100573
$899$	114.389	+	114.389i	0.127240	+	0.127240i
$900$	−185.156			−0.205729
$901$		−	619.647i		−	0.687732i
$902$	−389.636	−	389.636i	−0.431969	−	0.431969i
$903$	−293.306	−	293.306i	−0.324813	−	0.324813i
$904$	291.150	−	291.150i	0.322069	−	0.322069i
$905$	176.454	−	176.454i	0.194977	−	0.194977i
$906$	89.2984			0.0985633
$907$		−	976.517i		−	1.07665i	−0.842739	−	0.538323i	$-0.819058\pi$
$907$		−	976.517i		−	1.07665i	0.842739	−	0.538323i	$-0.180942\pi$
$908$	−293.126	+	293.126i	−0.322825	+	0.322825i
$909$			390.377i			0.429457i
$910$	146.044	−	54.2174i	0.160488	−	0.0595796i
$911$	−1291.48			−1.41765			−0.708825	−	0.705384i	$-0.750775\pi$
$911$	−1291.48			−1.41765			−0.708825	+	0.705384i	$0.750775\pi$
$912$	−78.4632	−	78.4632i	−0.0860342	−	0.0860342i
$913$	1711.41			1.87449
$914$			140.446i			0.153661i
$915$	249.830	+	249.830i	0.273038	+	0.273038i
$916$	−206.383	−	206.383i	−0.225309	−	0.225309i
$917$	537.244	−	537.244i	0.585871	−	0.585871i
$918$	22.5009	−	22.5009i	0.0245108	−	0.0245108i
$919$	1651.58			1.79715			0.898575	−	0.438819i	$-0.144603\pi$
$919$	1651.58			1.79715			0.898575	+	0.438819i	$0.144603\pi$
$920$			527.486i			0.573355i
$921$	386.914	−	386.914i	0.420103	−	0.420103i
$922$			275.897i			0.299238i
$923$	−514.614	+	191.046i	−0.557544	+	0.206983i
$924$	425.072			0.460035
$925$	745.293	+	745.293i	0.805723	+	0.805723i
$926$	651.220			0.703262
$927$			83.7652i			0.0903616i
$928$	190.858	+	190.858i	0.205666	+	0.205666i
$929$	644.310	+	644.310i	0.693552	+	0.693552i	0.963012	−	0.269460i	$-0.0868451\pi$
$929$	644.310	+	644.310i	0.693552	+	0.693552i	−0.269460	+	0.963012i	$0.586845\pi$
$930$	51.3279	−	51.3279i	0.0551913	−	0.0551913i
$931$	−135.939	+	135.939i	−0.146014	+	0.146014i
$932$	252.715			0.271153
$933$		−	894.567i		−	0.958807i
$934$	5.22017	−	5.22017i	0.00558905	−	0.00558905i
$935$		−	203.004i		−	0.217116i
$936$	−91.9924	−	247.797i	−0.0982825	−	0.264740i
$937$	−939.846			−1.00304			−0.501519	−	0.865147i	$-0.667225\pi$
$937$	−939.846			−1.00304			−0.501519	+	0.865147i	$0.667225\pi$
$938$	227.646	+	227.646i	0.242693	+	0.242693i
$939$	−258.482			−0.275273
$940$		−	366.519i		−	0.389913i
$941$	−767.549	−	767.549i	−0.815674	−	0.815674i	0.169804	−	0.985478i	$-0.445687\pi$
$941$	−767.549	−	767.549i	−0.815674	−	0.815674i	−0.985478	+	0.169804i	$0.945687\pi$
$942$	−176.160	−	176.160i	−0.187007	−	0.187007i
$943$	−999.684	+	999.684i	−1.06011	+	1.06011i
$944$	−221.912	+	221.912i	−0.235076	+	0.235076i
$945$	65.0914			0.0688798
$946$		−	579.926i		−	0.613030i
$947$	−518.599	+	518.599i	−0.547623	+	0.547623i	−0.925753	−	0.378130i	$-0.876567\pi$
$947$	−518.599	+	518.599i	−0.547623	+	0.547623i	0.378130	+	0.925753i	$0.376567\pi$
$948$		−	545.171i		−	0.575075i
$949$	−70.3509	−	189.502i	−0.0741316	−	0.199686i
$950$	−209.370			−0.220389
$951$	−325.908	−	325.908i	−0.342700	−	0.342700i
$952$	−243.229			−0.255493
$953$			1429.04i			1.49952i	0.661709	+	0.749761i	$0.269831\pi$
$953$			1429.04i			1.49952i	−0.661709	+	0.749761i	$0.730169\pi$
$954$	196.420	+	196.420i	0.205891	+	0.205891i
$955$	−102.230	−	102.230i	−0.107047	−	0.107047i
$956$	15.7948	−	15.7948i	0.0165218	−	0.0165218i
$957$	−143.409	+	143.409i	−0.149853	+	0.149853i
$958$	−33.5326			−0.0350027
$959$		−	1074.39i		−	1.12033i
$960$	21.5323	−	21.5323i	0.0224295	−	0.0224295i
$961$		−	576.620i		−	0.600020i
$962$	−273.072	+	595.534i	−0.283858	+	0.619058i
$963$	498.504			0.517657
$964$	469.530	+	469.530i	0.487064	+	0.487064i
$965$	306.847			0.317976
$966$			323.514i			0.334901i
$967$	507.433	+	507.433i	0.524749	+	0.524749i	0.919002	−	0.394253i	$-0.128997\pi$
$967$	507.433	+	507.433i	0.524749	+	0.524749i	−0.394253	+	0.919002i	$0.628997\pi$
$968$	385.231	+	385.231i	0.397966	+	0.397966i
$969$	−85.7725	+	85.7725i	−0.0885165	+	0.0885165i
$970$	−125.482	+	125.482i	−0.129363	+	0.129363i
$971$	832.781			0.857652			0.428826	−	0.903387i	$-0.358927\pi$
$971$	832.781			0.857652			0.428826	+	0.903387i	$0.358927\pi$
$972$		−	48.0888i		−	0.0494741i
$973$	−967.241	+	967.241i	−0.994081	+	0.994081i
$974$		−	332.083i		−	0.340947i
$975$	409.489	+	187.764i	0.419988	+	0.192578i
$976$	−534.592			−0.547738
$977$	−562.185	−	562.185i	−0.575419	−	0.575419i	0.358219	−	0.933638i	$-0.383384\pi$
$977$	−562.185	−	562.185i	−0.575419	−	0.575419i	−0.933638	+	0.358219i	$0.883384\pi$
$978$	392.589			0.401420
$979$		−	1281.43i		−	1.30892i
$980$	85.6593	+	85.6593i	0.0874075	+	0.0874075i
$981$	−13.6918	−	13.6918i	−0.0139570	−	0.0139570i
$982$	−17.1809	+	17.1809i	−0.0174958	+	0.0174958i
$983$	351.787	−	351.787i	0.357870	−	0.357870i	−0.505157	−	0.863027i	$-0.668565\pi$
$983$	351.787	−	351.787i	0.357870	−	0.357870i	0.863027	+	0.505157i	$0.168565\pi$
$984$	476.493			0.484241
$985$			154.445i			0.156797i
$986$	35.7304	−	35.7304i	0.0362377	−	0.0362377i
$987$		−	516.263i		−	0.523063i
$988$	152.689	+	411.293i	0.154543	+	0.416289i
$989$	−1487.91			−1.50446
$990$	64.3496	+	64.3496i	0.0649996	+	0.0649996i
$991$	96.6030			0.0974803			0.0487401	−	0.998811i	$-0.484479\pi$
$991$	96.6030			0.0974803			0.0487401	+	0.998811i	$0.484479\pi$
$992$			641.339i			0.646511i
$993$	−231.659	−	231.659i	−0.233292	−	0.233292i
$994$	−160.119	−	160.119i	−0.161085	−	0.161085i
$995$	220.532	−	220.532i	0.221640	−	0.221640i
$996$	−455.646	+	455.646i	−0.457476	+	0.457476i
$997$	−1290.54			−1.29443			−0.647213	−	0.762309i	$-0.724065\pi$
$997$	−1290.54			−1.29443			−0.647213	+	0.762309i	$0.724065\pi$
$998$			443.861i			0.444751i
$999$	−193.568	+	193.568i	−0.193762	+	0.193762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.3.g.a.34.2	yes	8
3.2	odd	2		117.3.j.b.73.3		8
4.3	odd	2		624.3.ba.b.385.2		8
13.5	odd	4	inner	39.3.g.a.31.2	✓	8
39.5	even	4		117.3.j.b.109.3		8
52.31	even	4		624.3.ba.b.577.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.g.a.31.2	✓	8	13.5	odd	4	inner
39.3.g.a.34.2	yes	8	1.1	even	1	trivial
117.3.j.b.73.3		8	3.2	odd	2
117.3.j.b.109.3		8	39.5	even	4
624.3.ba.b.385.2		8	4.3	odd	2
624.3.ba.b.577.2		8	52.31	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	39.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.676424 - 0.676424i) q^{2} +1.73205 q^{3} -3.08490i q^{4} +(1.58008 + 1.58008i) q^{5} +(-1.17160 - 1.17160i) q^{6} +(3.96400 - 3.96400i) q^{7} +(-4.79240 + 4.79240i) q^{8} +3.00000 q^{9} -2.13761i q^{10} +(-10.0345 + 10.0345i) q^{11} -5.34320i q^{12} +(-5.41846 + 11.8170i) q^{13} -5.36270 q^{14} +(2.73677 + 2.73677i) q^{15} -5.85621 q^{16} +6.40175i q^{17} +(-2.02927 - 2.02927i) q^{18} +(7.73551 + 7.73551i) q^{19} +(4.87438 - 4.87438i) q^{20} +(6.86585 - 6.86585i) q^{21} +13.5752 q^{22} -34.8297i q^{23} +(-8.30068 + 8.30068i) q^{24} -20.0067i q^{25} +(11.6585 - 4.32810i) q^{26} +5.19615 q^{27} +(-12.2285 - 12.2285i) q^{28} +8.25124 q^{29} -3.70244i q^{30} +(13.8633 + 13.8633i) q^{31} +(23.1309 + 23.1309i) q^{32} +(-17.3803 + 17.3803i) q^{33} +(4.33030 - 4.33030i) q^{34} +12.5269 q^{35} -9.25470i q^{36} +(-37.2522 + 37.2522i) q^{37} -10.4650i q^{38} +(-9.38504 + 20.4676i) q^{39} -15.1447 q^{40} +(-28.7020 - 28.7020i) q^{41} -9.28846 q^{42} -42.7195i q^{43} +(30.9555 + 30.9555i) q^{44} +(4.74023 + 4.74023i) q^{45} +(-23.5597 + 23.5597i) q^{46} +(37.5964 - 37.5964i) q^{47} -10.1432 q^{48} +17.5734i q^{49} +(-13.5330 + 13.5330i) q^{50} +11.0882i q^{51} +(36.4541 + 16.7154i) q^{52} -96.7934 q^{53} +(-3.51480 - 3.51480i) q^{54} -31.7107 q^{55} +37.9942i q^{56} +(13.3983 + 13.3983i) q^{57} +(-5.58134 - 5.58134i) q^{58} +(37.8935 - 37.8935i) q^{59} +(8.44267 - 8.44267i) q^{60} +91.2864 q^{61} -18.7549i q^{62} +(11.8920 - 11.8920i) q^{63} -7.86776i q^{64} +(-27.2333 + 10.1101i) q^{65} +23.5129 q^{66} +(-42.4500 - 42.4500i) q^{67} +19.7488 q^{68} -60.3268i q^{69} +(-8.47347 - 8.47347i) q^{70} +(29.8579 + 29.8579i) q^{71} +(-14.3772 + 14.3772i) q^{72} +(-10.9949 + 10.9949i) q^{73} +50.3966 q^{74} -34.6526i q^{75} +(23.8633 - 23.8633i) q^{76} +79.5538i q^{77} +(20.1930 - 7.49649i) q^{78} +102.031 q^{79} +(-9.25326 - 9.25326i) q^{80} +9.00000 q^{81} +38.8295i q^{82} +(-85.2758 - 85.2758i) q^{83} +(-21.1805 - 21.1805i) q^{84} +(-10.1153 + 10.1153i) q^{85} +(-28.8965 + 28.8965i) q^{86} +14.2916 q^{87} -96.1790i q^{88} +(-63.8510 + 63.8510i) q^{89} -6.41282i q^{90} +(25.3636 + 68.3212i) q^{91} -107.446 q^{92} +(24.0119 + 24.0119i) q^{93} -50.8623 q^{94} +24.4454i q^{95} +(40.0639 + 40.0639i) q^{96} +(-58.7023 - 58.7023i) q^{97} +(11.8871 - 11.8871i) q^{98} +(-30.1036 + 30.1036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 20 q^{5} + 8 q^{7} - 24 q^{8} + 24 q^{9} - 20 q^{11} + 8 q^{13} - 16 q^{14} + 12 q^{15} + 56 q^{16} + 12 q^{18} - 40 q^{19} + 44 q^{20} - 48 q^{21} - 128 q^{22} + 36 q^{24} - 32 q^{26} + 32 q^{28}+ \cdots - 60 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 20 * q^5 + 8 * q^7 - 24 * q^8 + 24 * q^9 - 20 * q^11 + 8 * q^13 - 16 * q^14 + 12 * q^15 + 56 * q^16 + 12 * q^18 - 40 * q^19 + 44 * q^20 - 48 * q^21 - 128 * q^22 + 36 * q^24 - 32 * q^26 + 32 * q^28 + 56 * q^29 + 32 * q^31 + 148 * q^32 - 36 * q^33 + 96 * q^34 + 104 * q^35 - 16 * q^37 + 24 * q^39 + 48 * q^40 - 116 * q^41 - 216 * q^42 - 92 * q^44 - 60 * q^45 - 264 * q^46 + 100 * q^47 + 20 * q^50 + 72 * q^52 - 232 * q^53 - 176 * q^55 + 120 * q^57 - 104 * q^58 + 316 * q^59 + 12 * q^60 + 160 * q^61 + 24 * q^63 - 92 * q^65 + 312 * q^66 + 176 * q^67 + 168 * q^68 + 184 * q^70 + 4 * q^71 - 72 * q^72 - 64 * q^73 - 64 * q^74 + 112 * q^76 + 180 * q^78 + 208 * q^79 - 332 * q^80 + 72 * q^81 - 212 * q^83 - 240 * q^84 - 168 * q^85 - 24 * q^87 - 452 * q^89 - 400 * q^91 - 720 * q^92 - 24 * q^93 + 16 * q^94 + 24 * q^96 + 128 * q^97 + 724 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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