LMFDB - Embedded newform 531.2.i.b.64.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [531,2,Mod(19,531)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("531.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(531, base_ring=CyclotomicField(58)) chi = DirichletCharacter(H, H._module([0, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, minimal)

Newform invariants

comment:select newform

sage:traces = [140,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			64.3
Character	$\chi$	$=$	531.64
Dual form			531.2.i.b.307.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.815839 - 0.274888i) q^{2} +(-1.00216 - 0.761819i) q^{4} +(-1.45570 + 3.65354i) q^{5} +(0.847760 - 0.392216i) q^{7} +(1.57444 + 2.32213i) q^{8} +(2.19193 - 2.58054i) q^{10} +(1.30482 - 4.69955i) q^{11} +(-1.78293 + 3.36297i) q^{13} +(-0.799452 + 0.0869456i) q^{14} +(0.0273873 + 0.0986401i) q^{16} +(-4.49242 - 2.07842i) q^{17} +(-1.47865 + 0.325475i) q^{19} +(4.24218 - 2.55243i) q^{20} +(-2.35638 + 3.47539i) q^{22} +(0.497085 - 3.03208i) q^{23} +(-7.59929 - 7.19843i) q^{25} +(2.37903 - 2.25353i) q^{26} +(-1.14839 - 0.252779i) q^{28} +(-8.77673 + 2.95723i) q^{29} +(-7.13289 - 1.57007i) q^{31} +(0.308551 - 5.69088i) q^{32} +(3.09376 + 2.93057i) q^{34} +(0.198888 + 3.66827i) q^{35} +(2.45943 - 3.62739i) q^{37} +(1.29581 + 0.140928i) q^{38} +(-10.7759 + 2.37195i) q^{40} +(1.69060 + 10.3122i) q^{41} +(-0.416141 - 1.49880i) q^{43} +(-4.88784 + 3.71564i) q^{44} +(-1.23903 + 2.33705i) q^{46} +(-2.56001 - 6.42514i) q^{47} +(-3.96684 + 4.67012i) q^{49} +(4.22103 + 7.96172i) q^{50} +(4.34875 - 2.01195i) q^{52} +(0.552469 + 0.650416i) q^{53} +(15.2705 + 11.6084i) q^{55} +(2.24552 + 1.35109i) q^{56} +7.97331 q^{58} +(4.84647 - 5.95917i) q^{59} +(-2.47741 - 0.834738i) q^{61} +(5.38770 + 3.24167i) q^{62} +(-1.74030 + 4.36782i) q^{64} +(-9.69131 - 11.4095i) q^{65} +(-4.60495 - 6.79179i) q^{67} +(2.91873 + 5.50531i) q^{68} +(0.846105 - 3.04739i) q^{70} +(-0.745934 - 1.87215i) q^{71} +(-10.4550 + 1.13705i) q^{73} +(-3.00363 + 2.28330i) q^{74} +(1.72979 + 0.800286i) q^{76} +(-0.737059 - 4.49586i) q^{77} +(3.21106 - 1.93203i) q^{79} +(-0.400253 - 0.0435301i) q^{80} +(1.45545 - 8.87783i) q^{82} +(0.128318 + 2.36669i) q^{83} +(14.1332 - 13.3877i) q^{85} +(-0.0724995 + 1.33718i) q^{86} +(12.9673 - 4.36919i) q^{88} +(-4.43874 + 1.49559i) q^{89} +(-0.192491 + 3.55028i) q^{91} +(-2.80806 + 2.65993i) q^{92} +(0.322361 + 5.94559i) q^{94} +(0.963337 - 5.87610i) q^{95} +(-7.49293 - 0.814905i) q^{97} +(4.52007 - 2.71963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} - 116 q^{10} - 2 q^{11} + 4 q^{13} + 43 q^{14} + 7 q^{16} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 6 q^{23} - 57 q^{25} - 12 q^{26} - 10 q^{28} + 4 q^{29}+ \cdots + 143 q^{98}+O(q^{100}) $ 140 * q - q^2 - q^4 - 2 * q^5 - 2 * q^7 + 3 * q^8 - 116 * q^10 - 2 * q^11 + 4 * q^13 + 43 * q^14 + 7 * q^16 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 6 * q^23 - 57 * q^25 - 12 * q^26 - 10 * q^28 + 4 * q^29 - 12 * q^31 + 150 * q^32 - 2 * q^34 - 6 * q^35 + 12 * q^37 + 12 * q^38 - 66 * q^40 + 4 * q^41 - 60 * q^43 - 20 * q^44 + 76 * q^46 + 25 * q^47 + 31 * q^49 - 137 * q^50 + 118 * q^52 - 48 * q^53 + 93 * q^55 - 228 * q^56 - 120 * q^58 - 57 * q^59 + 72 * q^61 + 179 * q^62 + 249 * q^64 + 39 * q^65 + 40 * q^67 - 94 * q^68 + 94 * q^70 - 30 * q^71 - 205 * q^73 - 66 * q^74 - 216 * q^76 + 46 * q^77 + 4 * q^79 + 356 * q^80 - 28 * q^82 - 4 * q^83 + 50 * q^85 + 18 * q^86 - 162 * q^88 - 26 * q^89 - 198 * q^91 - 10 * q^92 - 4 * q^94 + 326 * q^95 - 20 * q^97 + 143 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{3}{29}\right)$

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 $

$2$	−0.815839	−	0.274888i	−0.576885	−	0.194375i	0.0157086	−	0.999877i	$-0.495000\pi$
$2$	−0.815839	−	0.274888i	−0.576885	−	0.194375i	−0.592594	+	0.805501i	$0.701896\pi$
$3$		0			0
$3$		0			0
$4$	−1.00216	−	0.761819i	−0.501078	−	0.380910i
$5$	−1.45570	+	3.65354i	−0.651010	+	1.63391i	0.116740	+	0.993162i	$0.462755\pi$
$5$	−1.45570	+	3.65354i	−0.651010	+	1.63391i	−0.767750	+	0.640749i	$0.778624\pi$
$6$		0			0
$7$	0.847760	−	0.392216i	0.320423	−	0.148244i	−0.253083	−	0.967444i	$-0.581445\pi$
$7$	0.847760	−	0.392216i	0.320423	−	0.148244i	0.573507	+	0.819201i	$0.305583\pi$
$8$	1.57444	+	2.32213i	0.556649	+	0.820995i
$9$		0			0
$10$	2.19193	−	2.58054i	0.693150	−	0.816040i
$11$	1.30482	−	4.69955i	0.393419	−	1.41697i	−0.456345	−	0.889803i	$-0.650842\pi$
$11$	1.30482	−	4.69955i	0.393419	−	1.41697i	0.849764	−	0.527164i	$-0.176745\pi$
$12$		0			0
$13$	−1.78293	+	3.36297i	−0.494496	+	0.932719i	0.503153	+	0.864197i	$0.332173\pi$
$13$	−1.78293	+	3.36297i	−0.494496	+	0.932719i	−0.997650	+	0.0685218i	$0.978172\pi$
$14$	−0.799452	+	0.0869456i	−0.213662	+	0.0232372i
$15$		0			0
$16$	0.0273873	+	0.0986401i	0.00684682	+	0.0246600i
$17$	−4.49242	−	2.07842i	−1.08957	−	0.504090i	−0.208959	−	0.977924i	$-0.567007\pi$
$17$	−4.49242	−	2.07842i	−1.08957	−	0.504090i	−0.880614	+	0.473834i	$0.842870\pi$
$18$		0			0
$19$	−1.47865	+	0.325475i	−0.339225	+	0.0746691i	−0.381316	−	0.924445i	$-0.624529\pi$
$19$	−1.47865	+	0.325475i	−0.339225	+	0.0746691i	0.0420909	+	0.999114i	$0.486598\pi$
$20$	4.24218	−	2.55243i	0.948580	−	0.570741i
$21$		0			0
$22$	−2.35638	+	3.47539i	−0.502381	+	0.740957i
$23$	0.497085	−	3.03208i	0.103649	−	0.632233i	−0.883000	−	0.469373i	$-0.844480\pi$
$23$	0.497085	−	3.03208i	0.103649	−	0.632233i	0.986649	−	0.162860i	$-0.0520718\pi$
$24$		0			0
$25$	−7.59929	−	7.19843i	−1.51986	−	1.43969i
$26$	2.37903	−	2.25353i	0.466565	−	0.441954i
$27$		0			0
$28$	−1.14839	−	0.252779i	−0.217025	−	0.0477707i
$29$	−8.77673	+	2.95723i	−1.62980	+	0.549143i	−0.977884	−	0.209150i	$-0.932930\pi$
$29$	−8.77673	+	2.95723i	−1.62980	+	0.549143i	−0.651914	+	0.758293i	$0.726034\pi$
$30$		0			0
$31$	−7.13289	−	1.57007i	−1.28110	−	0.281992i	−0.478280	−	0.878208i	$-0.658739\pi$
$31$	−7.13289	−	1.57007i	−1.28110	−	0.281992i	−0.802825	+	0.596215i	$0.796670\pi$
$32$	0.308551	−	5.69088i	0.0545446	−	1.00602i
$33$		0			0
$34$	3.09376	+	2.93057i	0.530576	+	0.502588i
$35$	0.198888	+	3.66827i	0.0336182	+	0.620051i
$36$		0			0
$37$	2.45943	−	3.62739i	0.404328	−	0.596339i	−0.569953	−	0.821678i	$-0.693038\pi$
$37$	2.45943	−	3.62739i	0.404328	−	0.596339i	0.974281	+	0.225338i	$0.0723488\pi$
$38$	1.29581	+	0.140928i	0.210208	+	0.0228615i
$39$		0			0
$40$	−10.7759	+	2.37195i	−1.70382	+	0.375039i
$41$	1.69060	+	10.3122i	0.264027	+	1.61050i	0.702454	+	0.711729i	$0.252088\pi$
$41$	1.69060	+	10.3122i	0.264027	+	1.61050i	−0.438427	+	0.898767i	$0.644464\pi$
$42$		0			0
$43$	−0.416141	−	1.49880i	−0.0634609	−	0.228565i	0.925018	−	0.379923i	$-0.124049\pi$
$43$	−0.416141	−	1.49880i	−0.0634609	−	0.228565i	−0.988479	+	0.151357i	$0.951636\pi$
$44$	−4.88784	+	3.71564i	−0.736870	+	0.560154i
$45$		0			0
$46$	−1.23903	+	2.33705i	−0.182684	+	0.344579i
$47$	−2.56001	−	6.42514i	−0.373416	−	0.937202i	−0.988837	−	0.149004i	$-0.952393\pi$
$47$	−2.56001	−	6.42514i	−0.373416	−	0.937202i	0.615421	−	0.788199i	$-0.288986\pi$
$48$		0			0
$49$	−3.96684	+	4.67012i	−0.566691	+	0.667161i
$50$	4.22103	+	7.96172i	0.596944	+	1.12596i
$51$		0			0
$52$	4.34875	−	2.01195i	0.603063	−	0.279007i
$53$	0.552469	+	0.650416i	0.0758874	+	0.0893416i	0.798796	−	0.601603i	$-0.205471\pi$
$53$	0.552469	+	0.650416i	0.0758874	+	0.0893416i	−0.722908	+	0.690944i	$0.757195\pi$
$54$		0			0
$55$	15.2705	+	11.6084i	2.05908	+	1.56527i
$56$	2.24552	+	1.35109i	0.300071	+	0.180546i
$57$		0			0
$58$	7.97331			1.04695
$59$	4.84647	−	5.95917i	0.630956	−	0.775818i
$59$	4.84647	−	5.95917i	0.630956	−	0.775818i
$60$		0			0
$61$	−2.47741	−	0.834738i	−0.317200	−	0.106877i	0.156198	−	0.987726i	$-0.450076\pi$
$61$	−2.47741	−	0.834738i	−0.317200	−	0.106877i	−0.473398	+	0.880849i	$0.656973\pi$
$62$	5.38770	+	3.24167i	0.684238	+	0.411692i
$63$		0			0
$64$	−1.74030	+	4.36782i	−0.217538	+	0.545978i
$65$	−9.69131	−	11.4095i	−1.20206	−	1.41517i
$66$		0			0
$67$	−4.60495	−	6.79179i	−0.562584	−	0.829749i	0.434912	−	0.900473i	$-0.356779\pi$
$67$	−4.60495	−	6.79179i	−0.562584	−	0.829749i	−0.997496	+	0.0707238i	$0.977469\pi$
$68$	2.91873	+	5.50531i	0.353948	+	0.667617i
$69$		0			0
$70$	0.846105	−	3.04739i	0.101129	−	0.364233i
$71$	−0.745934	−	1.87215i	−0.0885261	−	0.222184i	0.878047	−	0.478574i	$-0.158846\pi$
$71$	−0.745934	−	1.87215i	−0.0885261	−	0.222184i	−0.966573	+	0.256390i	$0.917467\pi$
$72$		0			0
$73$	−10.4550	+	1.13705i	−1.22367	+	0.133082i	−0.697052	−	0.717020i	$-0.745505\pi$
$73$	−10.4550	+	1.13705i	−1.22367	+	0.133082i	−0.526617	+	0.850102i	$0.676540\pi$
$74$	−3.00363	+	2.28330i	−0.349165	+	0.265428i
$75$		0			0
$76$	1.72979	+	0.800286i	0.198421	+	0.0917991i
$77$	−0.737059	−	4.49586i	−0.0839957	−	0.512351i
$78$		0			0
$79$	3.21106	−	1.93203i	0.361273	−	0.217371i	−0.323331	−	0.946286i	$-0.604803\pi$
$79$	3.21106	−	1.93203i	0.361273	−	0.217371i	0.684604	+	0.728915i	$0.259975\pi$
$80$	−0.400253	−	0.0435301i	−0.0447497	−	0.00486682i
$81$		0			0
$82$	1.45545	−	8.87783i	0.160727	−	0.980392i
$83$	0.128318	+	2.36669i	0.0140848	+	0.259778i	0.997092	+	0.0762102i	$0.0242820\pi$
$83$	0.128318	+	2.36669i	0.0140848	+	0.259778i	−0.983007	+	0.183568i	$0.941235\pi$
$84$		0			0
$85$	14.1332	−	13.3877i	1.53296	−	1.45210i
$86$	−0.0724995	+	1.33718i	−0.00781783	+	0.144191i
$87$		0			0
$88$	12.9673	−	4.36919i	1.38232	−	0.465758i
$89$	−4.43874	+	1.49559i	−0.470506	+	0.158532i	−0.544559	−	0.838722i	$-0.683303\pi$
$89$	−4.43874	+	1.49559i	−0.470506	+	0.158532i	0.0740534	+	0.997254i	$0.476406\pi$
$90$		0			0
$91$	−0.192491	+	3.55028i	−0.0201785	+	0.372171i
$92$	−2.80806	+	2.65993i	−0.292760	+	0.277317i
$93$		0			0
$94$	0.322361	+	5.94559i	0.0332490	+	0.613241i
$95$	0.963337	−	5.87610i	0.0988363	−	0.602875i
$96$		0			0
$97$	−7.49293	−	0.814905i	−0.760791	−	0.0827411i	−0.280505	−	0.959853i	$-0.590502\pi$
$97$	−7.49293	−	0.814905i	−0.760791	−	0.0827411i	−0.480287	+	0.877112i	$0.659467\pi$
$98$	4.52007	−	2.71963i	0.456596	−	0.274724i
$99$		0			0
$100$	2.13177	+	13.0032i	0.213177	+	1.30032i
$101$	7.05094	+	3.26211i	0.701595	+	0.324592i	0.738053	−	0.674743i	$-0.235745\pi$
$101$	7.05094	+	3.26211i	0.701595	+	0.324592i	−0.0364579	+	0.999335i	$0.511607\pi$
$102$		0			0
$103$	14.5612	−	11.0691i	1.43475	−	1.09067i	0.454994	−	0.890495i	$-0.349641\pi$
$103$	14.5612	−	11.0691i	1.43475	−	1.09067i	0.979760	−	0.200177i	$-0.0641516\pi$
$104$	−10.6163	+	1.15460i	−1.04102	+	0.113218i
$105$		0			0
$106$	−0.271934	−	0.682502i	−0.0264125	−	0.0662905i
$107$	−3.74902	+	13.5028i	−0.362432	+	1.30536i	0.527611	+	0.849486i	$0.323088\pi$
$107$	−3.74902	+	13.5028i	−0.362432	+	1.30536i	−0.890043	+	0.455876i	$0.849326\pi$
$108$		0			0
$109$	3.08301	+	5.81517i	0.295299	+	0.556992i	0.986120	−	0.166033i	$-0.0530958\pi$
$109$	3.08301	+	5.81517i	0.295299	+	0.556992i	−0.690822	+	0.723025i	$0.742751\pi$
$110$	−9.26730	−	13.6682i	−0.883603	−	1.30322i
$111$		0			0
$112$	0.0619061	+	0.0728815i	0.00584957	+	0.00688665i
$113$	2.77017	−	6.95259i	0.260595	−	0.654045i	−0.739216	−	0.673468i	$-0.764804\pi$
$113$	2.77017	−	6.95259i	0.260595	−	0.654045i	0.999811	+	0.0194234i	$0.00618306\pi$
$114$		0			0
$115$	10.3542	+	6.22993i	0.965536	+	0.580944i
$116$	11.0485	+	3.72268i	1.02583	+	0.345642i
$117$		0			0
$118$	−5.59204	+	3.52949i	−0.514789	+	0.324916i
$119$	−4.62369			−0.423853
$120$		0			0
$121$	−10.9578	−	6.59306i	−0.996159	−	0.599369i
$122$	1.79171	+	1.36202i	0.162214	+	0.123312i
$123$		0			0
$124$	5.95216	+	7.00742i	0.534520	+	0.629285i
$125$	19.5152	−	9.02869i	1.74549	−	0.807551i
$126$		0			0
$127$	4.38785	+	8.27636i	0.389359	+	0.734408i	0.998268	−	0.0588315i	$-0.0187375\pi$
$127$	4.38785	+	8.27636i	0.389359	+	0.734408i	−0.608909	+	0.793240i	$0.708393\pi$
$128$	−4.75875	+	5.60243i	−0.420618	+	0.495190i
$129$		0			0
$130$	4.77021	+	11.9723i	0.418375	+	1.05004i
$131$	−0.450959	+	0.850600i	−0.0394005	+	0.0743172i	−0.902431	−	0.430835i	$-0.858219\pi$
$131$	−0.450959	+	0.850600i	−0.0394005	+	0.0743172i	0.863030	+	0.505153i	$0.168564\pi$
$132$		0			0
$133$	−1.12588	+	0.855874i	−0.0976265	+	0.0742137i
$134$	1.88991	+	6.80685i	0.163264	+	0.588023i
$135$		0			0
$136$	−2.24671	−	13.7043i	−0.192654	−	1.17514i
$137$	−5.56507	+	1.22496i	−0.475456	+	0.104656i	−0.446232	−	0.894917i	$-0.647235\pi$
$137$	−5.56507	+	1.22496i	−0.475456	+	0.104656i	−0.0292236	+	0.999573i	$0.509303\pi$
$138$		0			0
$139$	2.38178	+	0.259034i	0.202020	+	0.0219710i	0.208569	−	0.978008i	$-0.433119\pi$
$139$	2.38178	+	0.259034i	0.202020	+	0.0219710i	−0.00654964	+	0.999979i	$0.502085\pi$
$140$	2.59525	−	3.82770i	0.219338	−	0.323500i
$141$		0			0
$142$	0.0939293	+	1.73242i	0.00788237	+	0.145382i
$143$	13.4780	+	12.7670i	1.12709	+	1.06763i
$144$		0			0
$145$	1.97198	−	36.3710i	0.163764	−	3.02044i
$146$	8.84219	+	1.94631i	0.731785	+	0.161078i
$147$		0			0
$148$	−5.22815	+	1.76157i	−0.429751	+	0.144800i
$149$	10.2903	+	2.26506i	0.843012	+	0.185561i	0.615424	−	0.788196i	$-0.288985\pi$
$149$	10.2903	+	2.26506i	0.843012	+	0.185561i	0.227589	+	0.973757i	$0.426916\pi$
$150$		0			0
$151$	−9.90209	+	9.37975i	−0.805820	+	0.763313i	−0.974984	−	0.222274i	$-0.928652\pi$
$151$	−9.90209	+	9.37975i	−0.805820	+	0.763313i	0.169164	+	0.985588i	$0.445893\pi$
$152$	−3.08384	−	2.92117i	−0.250132	−	0.236938i
$153$		0			0
$154$	−0.634538	+	3.87051i	−0.0511325	+	0.311895i
$155$	16.1197	−	23.7747i	1.29476	−	1.90963i
$156$		0			0
$157$	1.32846	−	0.799306i	0.106022	−	0.0637915i	−0.461555	−	0.887112i	$-0.652708\pi$
$157$	1.32846	−	0.799306i	0.106022	−	0.0637915i	0.567577	+	0.823320i	$0.307881\pi$
$158$	−3.15080	+	0.693544i	−0.250664	+	0.0551754i
$159$		0			0
$160$	20.3427	+	9.41153i	1.60823	+	0.744047i
$161$	−0.767822	−	2.76544i	−0.0605128	−	0.217948i
$162$		0			0
$163$	−14.8014	+	1.60975i	−1.15933	+	0.126085i	−0.667504	−	0.744607i	$-0.732637\pi$
$163$	−14.8014	+	1.60975i	−1.15933	+	0.126085i	−0.491829	+	0.870692i	$0.663672\pi$
$164$	6.16179	−	11.6224i	0.481155	−	0.907555i
$165$		0			0
$166$	0.545889	−	1.96611i	0.0423692	−	0.152600i
$167$	−7.82764	+	9.21542i	−0.605721	+	0.713110i	−0.976477	−	0.215620i	$-0.930823\pi$
$167$	−7.82764	+	9.21542i	−0.605721	+	0.713110i	0.370756	+	0.928730i	$0.379099\pi$
$168$		0			0
$169$	−0.835263	−	1.23192i	−0.0642510	−	0.0947632i
$170$	−15.2105	+	7.03715i	−1.16660	+	0.539724i
$171$		0			0
$172$	−0.724780	+	1.81906i	−0.0552639	+	0.138702i
$173$	17.3150	+	13.1625i	1.31644	+	1.00073i	0.998617	+	0.0525764i	$0.0167433\pi$
$173$	17.3150	+	13.1625i	1.31644	+	1.00073i	0.317818	+	0.948152i	$0.397050\pi$
$174$		0			0
$175$	−9.26572	−	3.12198i	−0.700422	−	0.236000i
$176$	0.499299			0.0376361
$177$		0			0
$178$	4.03242			0.302243
$179$	−4.45704	−	1.50175i	−0.333135	−	0.112246i	0.147763	−	0.989023i	$-0.452793\pi$
$179$	−4.45704	−	1.50175i	−0.333135	−	0.112246i	−0.480898	+	0.876777i	$0.659689\pi$
$180$		0			0
$181$	19.5700	+	14.8767i	1.45462	+	1.10578i	0.973382	+	0.229189i	$0.0736073\pi$
$181$	19.5700	+	14.8767i	1.45462	+	1.10578i	0.481242	+	0.876588i	$0.340186\pi$
$182$	1.13297	−	2.84355i	0.0839815	−	0.210778i
$183$		0			0
$184$	7.82351	−	3.61954i	0.576757	−	0.266836i
$185$	9.67261	+	14.2660i	0.711144	+	1.04886i
$186$		0			0
$187$	−15.6294	+	18.4004i	−1.14294	+	1.34557i
$188$	−2.32926	+	8.38925i	−0.169879	+	0.611849i
$189$		0			0
$190$	−2.40120	+	4.52914i	−0.174201	+	0.328578i
$191$	−18.0506	+	1.96313i	−1.30610	+	0.142047i	−0.734568	−	0.678535i	$-0.762615\pi$
$191$	−18.0506	+	1.96313i	−1.30610	+	0.142047i	−0.571530	+	0.820581i	$0.693650\pi$
$192$		0			0
$193$	3.19213	+	11.4970i	0.229775	+	0.827573i	0.985065	+	0.172183i	$0.0550820\pi$
$193$	3.19213	+	11.4970i	0.229775	+	0.827573i	−0.755290	+	0.655390i	$0.772504\pi$
$194$	5.88901	+	2.72455i	0.422807	+	0.195611i
$195$		0			0
$196$	7.53318	−	1.65818i	0.538085	−	0.118441i
$197$	0.372221	−	0.223958i	0.0265196	−	0.0159563i	−0.502232	−	0.864733i	$-0.667488\pi$
$197$	0.372221	−	0.223958i	0.0265196	−	0.0159563i	0.528752	+	0.848776i	$0.322660\pi$
$198$		0			0
$199$	1.20428	−	1.77618i	0.0853692	−	0.125910i	−0.782607	−	0.622516i	$-0.786110\pi$
$199$	1.20428	−	1.77618i	0.0853692	−	0.125910i	0.867976	+	0.496606i	$0.165421\pi$
$200$	4.75103	−	28.9800i	0.335949	−	2.04920i
$201$		0			0
$202$	−4.85572	−	4.59958i	−0.341647	−	0.323625i
$203$	−6.28070	+	5.94939i	−0.440818	+	0.417565i
$204$		0			0
$205$	−40.1370	−	8.83483i	−2.80329	−	0.617051i
$206$	−14.9223	+	5.02792i	−1.03969	+	0.350312i
$207$		0			0
$208$	−0.380553	−	0.0837660i	−0.0263866	−	0.00580813i
$209$	−0.399789	+	7.37367i	−0.0276540	+	0.510047i
$210$		0			0
$211$	−2.89916	−	2.74623i	−0.199586	−	0.189058i	0.581379	−	0.813633i	$-0.302514\pi$
$211$	−2.89916	−	2.74623i	−0.199586	−	0.189058i	−0.780965	+	0.624575i	$0.785272\pi$
$212$	−0.0581601	−	1.07270i	−0.00399445	−	0.0736733i
$213$		0			0
$214$	6.77035	−	9.98552i	0.462812	−	0.682596i
$215$	6.08171	+	0.661426i	0.414769	+	0.0451089i
$216$		0			0
$217$	−6.66278	+	1.46659i	−0.452299	+	0.0995586i
$218$	−0.916717	−	5.59173i	−0.0620879	−	0.378720i
$219$		0			0
$220$	−6.45999	−	23.2668i	−0.435532	−	1.56865i
$221$	14.9993	−	11.4022i	1.00896	−	0.766995i
$222$		0			0
$223$	−8.22210	+	15.5085i	−0.550593	+	1.03853i	0.439517	+	0.898234i	$0.355150\pi$
$223$	−8.22210	+	15.5085i	−0.550593	+	1.03853i	−0.990110	+	0.140294i	$0.955195\pi$
$224$	−1.97048	−	4.94552i	−0.131658	−	0.330437i
$225$		0			0
$226$	−4.17120	+	4.91071i	−0.277464	+	0.326656i
$227$	−5.24199	−	9.88745i	−0.347923	−	0.656253i	0.646359	−	0.763033i	$-0.276291\pi$
$227$	−5.24199	−	9.88745i	−0.347923	−	0.656253i	−0.994283	+	0.106780i	$0.965946\pi$
$228$		0			0
$229$	14.8892	−	6.88847i	0.983905	−	0.455203i	0.139101	−	0.990278i	$-0.455579\pi$
$229$	14.8892	−	6.88847i	0.983905	−	0.455203i	0.844804	+	0.535075i	$0.179717\pi$
$230$	−6.73485	−	7.92887i	−0.444083	−	0.522814i
$231$		0			0
$232$	−20.6855	−	15.7247i	−1.35807	−	1.03238i
$233$	6.33096	+	3.80921i	0.414755	+	0.249550i	0.707604	−	0.706609i	$-0.249776\pi$
$233$	6.33096	+	3.80921i	0.414755	+	0.249550i	−0.292850	+	0.956159i	$0.594603\pi$
$234$		0			0
$235$	27.2011			1.77440
$236$	−9.39673	+	2.27989i	−0.611675	+	0.148408i
$237$		0			0
$238$	3.77219	+	1.27100i	0.244514	+	0.0823865i
$239$	−11.5251	−	6.93444i	−0.745499	−	0.448552i	0.0914663	−	0.995808i	$-0.470845\pi$
$239$	−11.5251	−	6.93444i	−0.745499	−	0.448552i	−0.836965	+	0.547257i	$0.815672\pi$
$240$		0			0
$241$	1.99880	−	5.01661i	0.128754	−	0.323149i	−0.850441	−	0.526071i	$-0.823665\pi$
$241$	1.99880	−	5.01661i	0.128754	−	0.323149i	0.979195	+	0.202922i	$0.0650439\pi$
$242$	7.12741	+	8.39104i	0.458167	+	0.539396i
$243$		0			0
$244$	1.84684	+	2.72388i	0.118232	+	0.174378i
$245$	−11.2879	−	21.2913i	−0.721160	−	1.36025i
$246$		0			0
$247$	1.54177	−	5.55295i	0.0981004	−	0.353326i
$248$	−7.58441	−	19.0354i	−0.481611	−	1.20875i
$249$		0			0
$250$	−18.4031	+	2.00146i	−1.16392	+	0.126584i
$251$	−7.01937	+	5.33599i	−0.443059	+	0.336805i	−0.802801	−	0.596247i	$-0.796658\pi$
$251$	−7.01937	+	5.33599i	−0.443059	+	0.336805i	0.359742	+	0.933052i	$0.382865\pi$
$252$		0			0
$253$	−13.6008	−	6.29240i	−0.855076	−	0.395600i
$254$	−1.30471	−	7.95835i	−0.0818645	−	0.499351i
$255$		0			0
$256$	13.4799	−	8.11058i	0.842493	−	0.506911i
$257$	−30.3073	−	3.29612i	−1.89052	−	0.205606i	−0.911773	−	0.410694i	$-0.865287\pi$
$257$	−30.3073	−	3.29612i	−1.89052	−	0.205606i	−0.978744	+	0.205088i	$0.934252\pi$
$258$		0			0
$259$	0.662289	−	4.03979i	0.0411527	−	0.251020i
$260$	1.02023	+	18.8171i	0.0632722	+	1.16699i
$261$		0			0
$262$	0.601730	−	0.569989i	0.0371750	−	0.0352140i
$263$	0.504510	−	9.30515i	0.0311094	−	0.573780i	−0.940878	−	0.338746i	$-0.889997\pi$
$263$	0.504510	−	9.30515i	0.0311094	−	0.573780i	0.971987	−	0.235034i	$-0.0755201\pi$
$264$		0			0
$265$	−3.18055	+	1.07165i	−0.195380	+	0.0658311i
$266$	1.15381	−	0.388764i	0.0707446	−	0.0238366i
$267$		0			0
$268$	−0.559240	+	10.3146i	−0.0341610	+	0.630063i
$269$	−12.5579	+	11.8955i	−0.765672	+	0.725283i	−0.967149	−	0.254210i	$-0.918184\pi$
$269$	−12.5579	+	11.8955i	−0.765672	+	0.725283i	0.201477	+	0.979493i	$0.435426\pi$
$270$		0			0
$271$	1.01650	+	18.7482i	0.0617479	+	1.13887i	0.851124	+	0.524964i	$0.175921\pi$
$271$	1.01650	+	18.7482i	0.0617479	+	1.13887i	−0.789376	+	0.613909i	$0.789596\pi$
$272$	0.0819799	−	0.500055i	0.00497076	−	0.0303203i
$273$		0			0
$274$	4.87693	+	0.530398i	0.294626	+	0.0320425i
$275$	−43.7451	+	26.3205i	−2.63793	+	1.58719i
$276$		0			0
$277$	−4.00805	−	24.4480i	−0.240820	−	1.46894i	−0.779486	−	0.626419i	$-0.784520\pi$
$277$	−4.00805	−	24.4480i	−0.240820	−	1.46894i	0.538666	−	0.842519i	$-0.318929\pi$
$278$	−1.87194	−	0.866052i	−0.112272	−	0.0519424i
$279$		0			0
$280$	−8.20506	+	6.23732i	−0.490346	+	0.372751i
$281$	−14.4013	+	1.56624i	−0.859109	+	0.0934337i	−0.527060	−	0.849828i	$-0.676706\pi$
$281$	−14.4013	+	1.56624i	−0.859109	+	0.0934337i	−0.332049	+	0.943262i	$0.607740\pi$
$282$		0			0
$283$	−9.83311	−	24.6792i	−0.584518	−	1.46703i	−0.862306	−	0.506387i	$-0.830981\pi$
$283$	−9.83311	−	24.6792i	−0.584518	−	1.46703i	0.277789	−	0.960642i	$-0.410398\pi$
$284$	−0.678700	+	2.44446i	−0.0402734	+	0.145052i
$285$		0			0
$286$	−7.48638	−	14.1208i	−0.442679	−	0.834981i
$287$	5.47783	+	8.07920i	0.323346	+	0.476900i
$288$		0			0
$289$	4.85649	+	5.71750i	0.285676	+	0.336324i
$290$	−11.6068	+	29.1308i	−0.681573	+	1.71062i
$291$		0			0
$292$	11.3438	+	6.82534i	0.663846	+	0.399423i
$293$	22.9583	+	7.73554i	1.34124	+	0.451915i	0.896221	−	0.443608i	$-0.146302\pi$
$293$	22.9583	+	7.73554i	1.34124	+	0.451915i	0.445015	+	0.895523i	$0.353198\pi$
$294$		0			0
$295$	14.7171	+	26.3815i	0.856860	+	1.53599i
$296$	12.2955			0.714661
$297$		0			0
$298$	−7.77257	−	4.67660i	−0.450253	−	0.270908i
$299$	9.31052	+	7.07768i	0.538441	+	0.409313i
$300$		0			0
$301$	−0.940642	−	1.10741i	−0.0542177	−	0.0638300i
$302$	10.6569	−	4.93040i	0.613235	−	0.283713i
$303$		0			0
$304$	−0.0726011	−	0.136940i	−0.00416396	−	0.00785406i
$305$	6.65612	−	7.83619i	0.381128	−	0.448699i
$306$		0			0
$307$	−6.18243	−	15.5167i	−0.352850	−	0.885586i	−0.993084	−	0.117406i	$-0.962542\pi$
$307$	−6.18243	−	15.5167i	−0.352850	−	0.885586i	0.640234	−	0.768180i	$-0.278837\pi$
$308$	−2.68639	+	5.06706i	−0.153071	+	0.288723i
$309$		0			0
$310$	−19.6864	+	14.9652i	−1.11811	+	0.849969i
$311$	7.12289	+	25.6543i	0.403902	+	1.45472i	0.833911	+	0.551899i	$0.186097\pi$
$311$	7.12289	+	25.6543i	0.403902	+	1.45472i	−0.430009	+	0.902825i	$0.641490\pi$
$312$		0			0
$313$	0.351118	+	2.14173i	0.0198464	+	0.121058i	0.994892	−	0.100949i	$-0.0321878\pi$
$313$	0.351118	+	2.14173i	0.0198464	+	0.121058i	−0.975045	+	0.222006i	$0.928739\pi$
$314$	−1.30353	+	0.286928i	−0.0735622	+	0.0161923i
$315$		0			0
$316$	−4.68984	−	0.510051i	−0.263824	−	0.0286926i
$317$	2.31476	−	3.41401i	0.130010	−	0.191750i	−0.757113	−	0.653284i	$-0.773391\pi$
$317$	2.31476	−	3.41401i	0.130010	−	0.191750i	0.887122	+	0.461535i	$0.152701\pi$
$318$		0			0
$319$	2.44554	+	45.1053i	0.136924	+	2.52541i
$320$	−13.4247	−	12.7165i	−0.750461	−	0.710874i
$321$		0			0
$322$	−0.133769	+	2.46722i	−0.00745465	+	0.137493i
$323$	7.31919	+	1.61108i	0.407251	+	0.0896427i
$324$		0			0
$325$	37.7571	−	12.7218i	2.09439	−	0.705681i
$326$	12.5180	+	2.75543i	0.693310	+	0.152609i
$327$		0			0
$328$	−21.2845	+	20.1617i	−1.17524	+	1.11325i
$329$	−4.69031	−	4.44290i	−0.258585	−	0.244945i
$330$		0			0
$331$	−3.32944	+	20.3087i	−0.183003	+	1.11627i	0.722325	+	0.691554i	$0.243074\pi$
$331$	−3.32944	+	20.3087i	−0.183003	+	1.11627i	−0.905328	+	0.424714i	$0.860375\pi$
$332$	1.67440	−	2.46955i	0.0918945	−	0.135534i
$333$		0			0
$334$	8.91931	−	5.36657i	0.488043	−	0.293646i
$335$	31.5175	−	6.93752i	1.72198	−	0.379037i
$336$		0			0
$337$	−8.30529	−	3.84244i	−0.452418	−	0.209311i	0.180428	−	0.983588i	$-0.442252\pi$
$337$	−8.30529	−	3.84244i	−0.452418	−	0.209311i	−0.632847	+	0.774277i	$0.718114\pi$
$338$	0.342800	+	1.23465i	0.0186459	+	0.0671563i
$339$		0			0
$340$	−24.3627	+	2.64960i	−1.32125	+	0.143695i
$341$	−16.6858	+	31.4727i	−0.903584	+	1.70434i
$342$		0			0
$343$	−3.28051	+	11.8153i	−0.177131	+	0.637968i
$344$	2.82522	−	3.32611i	0.152326	−	0.179332i
$345$		0			0
$346$	−10.5080	−	15.4982i	−0.564915	−	0.833188i
$347$	−9.71905	+	4.49651i	−0.521746	+	0.241385i	−0.663042	−	0.748582i	$-0.730735\pi$
$347$	−9.71905	+	4.49651i	−0.521746	+	0.241385i	0.141296	+	0.989967i	$0.454873\pi$
$348$		0			0
$349$	4.14086	−	10.3928i	0.221655	−	0.556312i	−0.775528	−	0.631313i	$-0.782516\pi$
$349$	4.14086	−	10.3928i	0.221655	−	0.556312i	0.997184	+	0.0750004i	$0.0238958\pi$
$350$	6.70114	+	5.09407i	0.358191	+	0.272290i
$351$		0			0
$352$	−26.3420	−	8.87564i	−1.40403	−	0.473073i
$353$	−12.7467			−0.678437			−0.339219	−	0.940708i	$-0.610163\pi$
$353$	−12.7467			−0.678437			−0.339219	+	0.940708i	$0.610163\pi$
$354$		0			0
$355$	7.92584			0.420660
$356$	5.58768	+	1.88271i	0.296146	+	0.0997834i
$357$		0			0
$358$	3.22341	+	2.45037i	0.170363	+	0.129506i
$359$	10.5960	−	26.5940i	0.559237	−	1.40358i	−0.329060	−	0.944309i	$-0.606732\pi$
$359$	10.5960	−	26.5940i	0.559237	−	1.40358i	0.888297	−	0.459270i	$-0.151889\pi$
$360$		0			0
$361$	−15.1635	+	7.01537i	−0.798077	+	0.369230i
$362$	−11.8765	−	17.5165i	−0.624216	−	0.920649i
$363$		0			0
$364$	2.89758	−	3.41130i	0.151874	−	0.178800i
$365$	11.0652	−	39.8531i	0.579177	−	2.08601i
$366$		0			0
$367$	−0.514026	+	0.969555i	−0.0268319	+	0.0506104i	−0.896566	−	0.442911i	$-0.853946\pi$
$367$	−0.514026	+	0.969555i	−0.0268319	+	0.0506104i	0.869734	+	0.493521i	$0.164291\pi$
$368$	0.312699	−	0.0340080i	0.0163006	−	0.00177279i
$369$		0			0
$370$	−3.96973	−	14.2977i	−0.206376	−	0.743300i
$371$	0.723465	+	0.334710i	0.0375604	+	0.0173773i
$372$		0			0
$373$	10.0189	−	2.20532i	0.518758	−	0.114187i	0.0521288	−	0.998640i	$-0.483399\pi$
$373$	10.0189	−	2.20532i	0.518758	−	0.114187i	0.466629	+	0.884453i	$0.345468\pi$
$374$	17.8092	−	10.7154i	0.920890	−	0.554081i
$375$		0			0
$376$	10.8894	−	16.0607i	0.561578	−	0.828265i
$377$	5.70327	−	34.7884i	0.293733	−	1.79169i
$378$		0			0
$379$	−7.91161	−	7.49428i	−0.406392	−	0.384955i	0.457018	−	0.889457i	$-0.348917\pi$
$379$	−7.91161	−	7.49428i	−0.406392	−	0.384955i	−0.863410	+	0.504502i	$0.831676\pi$
$380$	−5.44194	+	5.15488i	−0.279165	+	0.264440i
$381$		0			0
$382$	15.2661	+	3.36031i	0.781079	+	0.171929i
$383$	19.4082	−	6.53938i	0.991712	−	0.334147i	0.223753	−	0.974646i	$-0.428169\pi$
$383$	19.4082	−	6.53938i	0.991712	−	0.334147i	0.767959	+	0.640499i	$0.221273\pi$
$384$		0			0
$385$	17.4987	+	3.85176i	0.891818	+	0.196304i
$386$	0.556129	−	10.2572i	0.0283062	−	0.522077i
$387$		0			0
$388$	6.88827	+	6.52492i	0.349699	+	0.331253i
$389$	−1.29459	−	23.8773i	−0.0656382	−	1.21063i	−0.826964	−	0.562255i	$-0.809934\pi$
$389$	−1.29459	−	23.8773i	−0.0656382	−	1.21063i	0.761326	−	0.648370i	$-0.224549\pi$
$390$		0			0
$391$	−8.53505	+	12.5883i	−0.431636	+	0.636615i
$392$	−17.0902	−	1.85867i	−0.863184	−	0.0938769i
$393$		0			0
$394$	−0.365236	+	0.0803944i	−0.0184003	+	0.00405021i
$395$	2.38440	+	14.5442i	0.119972	+	0.731798i
$396$		0			0
$397$	−9.22544	−	33.2270i	−0.463011	−	1.66762i	−0.714406	−	0.699731i	$-0.753303\pi$
$397$	−9.22544	−	33.2270i	−0.463011	−	1.66762i	0.251395	−	0.967885i	$-0.419111\pi$
$398$	−1.47075	+	1.11804i	−0.0737220	+	0.0560420i
$399$		0			0
$400$	0.501930	−	0.946740i	0.0250965	−	0.0473370i
$401$	5.69657	+	14.2973i	0.284473	+	0.713974i	0.999883	+	0.0152691i	$0.00486050\pi$
$401$	5.69657	+	14.2973i	0.284473	+	0.713974i	−0.715410	+	0.698705i	$0.753760\pi$
$402$		0			0
$403$	17.9975	−	21.1883i	0.896521	−	1.05547i
$404$	−4.58101	−	8.64069i	−0.227914	−	0.429891i
$405$		0			0
$406$	6.75945	−	3.12726i	0.335466	−	0.155203i
$407$	−13.8380	−	16.2913i	−0.685923	−	0.807531i
$408$		0			0
$409$	24.6708	+	18.7542i	1.21989	+	0.927336i	0.998851	−	0.0479285i	$-0.0152620\pi$
$409$	24.6708	+	18.7542i	1.21989	+	0.927336i	0.221039	+	0.975265i	$0.429055\pi$
$410$	30.3168	+	18.2410i	1.49724	+	0.900859i
$411$		0			0
$412$	−23.0252			−1.13437
$413$	1.77136	−	6.95281i	0.0871630	−	0.342126i
$414$		0			0
$415$	−8.83359	−	2.97638i	−0.433624	−	0.146105i
$416$	18.5881	+	11.1841i	0.911357	+	0.548345i
$417$		0			0
$418$	2.35310	−	5.90583i	0.115094	−	0.288864i
$419$	18.0466	+	21.2461i	0.881636	+	1.03794i	0.998994	+	0.0448523i	$0.0142817\pi$
$419$	18.0466	+	21.2461i	0.881636	+	1.03794i	−0.117358	+	0.993090i	$0.537442\pi$
$420$		0			0
$421$	19.5363	+	28.8138i	0.952139	+	1.40430i	0.914310	+	0.405016i	$0.132734\pi$
$421$	19.5363	+	28.8138i	0.952139	+	1.40430i	0.0378290	+	0.999284i	$0.487956\pi$
$422$	1.61034	+	3.03742i	0.0783901	+	0.147859i
$423$		0			0
$424$	−0.640520	+	2.30694i	−0.0311064	+	0.112035i
$425$	19.1779	+	48.1329i	0.930265	+	2.33479i
$426$		0			0
$427$	−2.42765	+	0.264023i	−0.117482	+	0.0127770i
$428$	14.0438	−	10.6758i	0.678832	−	0.516034i
$429$		0			0
$430$	−4.77988	−	2.21141i	−0.230506	−	0.106644i
$431$	−5.97149	−	36.4245i	−0.287637	−	1.75451i	−0.595763	−	0.803160i	$-0.703150\pi$
$431$	−5.97149	−	36.4245i	−0.287637	−	1.75451i	0.308126	−	0.951345i	$-0.400298\pi$
$432$		0			0
$433$	−19.1067	+	11.4961i	−0.918210	+	0.552469i	−0.894410	−	0.447248i	$-0.852404\pi$
$433$	−19.1067	+	11.4961i	−0.918210	+	0.552469i	−0.0238002	+	0.999717i	$0.507577\pi$
$434$	5.83891	+	0.635020i	0.280277	+	0.0304819i
$435$		0			0
$436$	1.34045	−	8.17641i	0.0641961	−	0.391579i
$437$	0.251854	+	4.64518i	0.0120478	+	0.222209i
$438$		0			0
$439$	17.8204	−	16.8804i	0.850523	−	0.805658i	−0.132107	−	0.991236i	$-0.542174\pi$
$439$	17.8204	−	16.8804i	0.850523	−	0.805658i	0.982630	+	0.185577i	$0.0594155\pi$
$440$	−2.91352	+	53.7368i	−0.138897	+	2.56180i
$441$		0			0
$442$	−15.3714	+	5.17922i	−0.731142	+	0.246350i
$443$	−7.49796	+	2.52636i	−0.356239	+	0.120031i	−0.491730	−	0.870748i	$-0.663635\pi$
$443$	−7.49796	+	2.52636i	−0.356239	+	0.120031i	0.135491	+	0.990779i	$0.456739\pi$
$444$		0			0
$445$	0.997307	−	18.3942i	0.0472769	−	0.871971i
$446$	10.9710	−	10.3923i	0.519493	−	0.492090i
$447$		0			0
$448$	0.237772	+	4.38544i	0.0112337	+	0.207193i
$449$	0.717636	−	4.37739i	0.0338674	−	0.206582i	−0.964472	−	0.264184i	$-0.914897\pi$
$449$	0.717636	−	4.37739i	0.0338674	−	0.206582i	0.998340	+	0.0576025i	$0.0183456\pi$
$450$		0			0
$451$	50.6686	+	5.51055i	2.38589	+	0.259481i
$452$	−8.07276	+	4.85722i	−0.379711	+	0.228464i
$453$		0			0
$454$	1.55868	+	9.50753i	0.0731525	+	0.446210i
$455$	−12.6909	−	5.87143i	−0.594958	−	0.275257i
$456$		0			0
$457$	21.9627	−	16.6956i	1.02737	−	0.780986i	0.0513529	−	0.998681i	$-0.483647\pi$
$457$	21.9627	−	16.6956i	1.02737	−	0.780986i	0.976017	+	0.217694i	$0.0698536\pi$
$458$	−14.0407	+	1.52702i	−0.656081	+	0.0713531i
$459$		0			0
$460$	−5.63047	−	14.1314i	−0.262522	−	0.658880i
$461$	8.27878	−	29.8175i	0.385581	−	1.38874i	−0.475252	−	0.879850i	$-0.657643\pi$
$461$	8.27878	−	29.8175i	0.385581	−	1.38874i	0.860833	−	0.508888i	$-0.169943\pi$
$462$		0			0
$463$	−3.53517	−	6.66804i	−0.164293	−	0.309890i	0.787673	−	0.616094i	$-0.211286\pi$
$463$	−3.53517	−	6.66804i	−0.164293	−	0.309890i	−0.951966	+	0.306204i	$0.900941\pi$
$464$	−0.532072	−	0.784747i	−0.0247008	−	0.0364310i
$465$		0			0
$466$	−4.11794	−	4.84801i	−0.190760	−	0.224580i
$467$	1.84084	−	4.62016i	0.0851838	−	0.213795i	−0.880214	−	0.474577i	$-0.842601\pi$
$467$	1.84084	−	4.62016i	0.0851838	−	0.213795i	0.965398	+	0.260782i	$0.0839803\pi$
$468$		0			0
$469$	−6.56774	−	3.95168i	−0.303270	−	0.182472i
$470$	−22.1917	−	7.47726i	−1.02363	−	0.344900i
$471$		0			0
$472$	21.4684	+	1.87174i	0.988164	+	0.0861539i
$473$	−7.58669			−0.348836
$474$		0			0
$475$	13.5796	+	8.17057i	0.623075	+	0.374891i
$476$	4.63366	+	3.52241i	0.212383	+	0.161450i
$477$		0			0
$478$	7.49646	+	8.82551i	0.342880	+	0.403669i
$479$	−24.7085	+	11.4313i	−1.12896	+	0.522312i	−0.893272	−	0.449517i	$-0.851596\pi$
$479$	−24.7085	+	11.4313i	−1.12896	+	0.522312i	−0.235687	+	0.971829i	$0.575734\pi$
$480$		0			0
$481$	7.81379	+	14.7384i	0.356278	+	0.672012i
$482$	−3.00971	+	3.54330i	−0.137088	+	0.161393i
$483$		0			0
$484$	5.95866	+	14.9551i	0.270848	+	0.679778i
$485$	13.8848	−	26.1894i	0.630474	−	1.18920i
$486$		0			0
$487$	−18.6787	+	14.1992i	−0.846412	+	0.643426i	−0.935784	−	0.352573i	$-0.885307\pi$
$487$	−18.6787	+	14.1992i	−0.846412	+	0.643426i	0.0893724	+	0.995998i	$0.471514\pi$
$488$	−1.96217	−	7.06711i	−0.0888234	−	0.319913i
$489$		0			0
$490$	3.35641	+	20.4732i	0.151627	+	0.924885i
$491$	1.44042	−	0.317060i	0.0650052	−	0.0143087i	−0.182349	−	0.983234i	$-0.558370\pi$
$491$	1.44042	−	0.317060i	0.0650052	−	0.0143087i	0.247354	+	0.968925i	$0.420439\pi$
$492$		0			0
$493$	45.5751	+	4.95660i	2.05260	+	0.223234i
$494$	−2.78427	+	4.10650i	−0.125270	+	0.184760i
$495$		0			0
$496$	−0.0404789	−	0.746589i	−0.00181755	−	0.0335228i
$497$	−1.36666	−	1.29457i	−0.0613031	−	0.0580694i
$498$		0			0
$499$	−1.39473	+	25.7242i	−0.0624366	+	1.15158i	0.784587	+	0.620019i	$0.212875\pi$
$499$	−1.39473	+	25.7242i	−0.0624366	+	1.15158i	−0.847023	+	0.531556i	$0.821608\pi$
$500$	−26.4355	−	5.81889i	−1.18223	−	0.260229i
$501$		0			0
$502$	7.19348	−	2.42376i	0.321061	−	0.108178i
$503$	−7.66561	−	1.68733i	−0.341792	−	0.0752342i	0.0407574	−	0.999169i	$-0.487023\pi$
$503$	−7.66561	−	1.68733i	−0.341792	−	0.0752342i	−0.382550	+	0.923935i	$0.624954\pi$
$504$		0			0
$505$	−22.1823	+	21.0122i	−0.987101	+	0.935032i
$506$	9.36636	+	8.87229i	0.416386	+	0.394421i
$507$		0			0
$508$	1.90778	−	11.6370i	0.0846442	−	0.516306i
$509$	−17.2146	+	25.3896i	−0.763024	+	1.12538i	0.225490	+	0.974245i	$0.427602\pi$
$509$	−17.2146	+	25.3896i	−0.763024	+	1.12538i	−0.988514	+	0.151130i	$0.951709\pi$
$510$		0			0
$511$	−8.41740	+	5.06458i	−0.372364	+	0.224044i
$512$	1.13079	−	0.248905i	0.0499742	−	0.0110002i
$513$		0			0
$514$	23.8198	+	11.0202i	1.05065	+	0.486081i
$515$	19.2447	+	69.3131i	0.848022	+	3.05430i
$516$		0			0
$517$	−33.5356	+	3.64722i	−1.47489	+	0.160404i
$518$	−1.65081	+	3.11376i	−0.0725325	+	0.136811i
$519$		0			0
$520$	11.2359	−	40.4680i	0.492726	−	1.77464i
$521$	7.98919	−	9.40560i	0.350013	−	0.412067i	−0.558779	−	0.829317i	$-0.688730\pi$
$521$	7.98919	−	9.40560i	0.350013	−	0.412067i	0.908792	+	0.417250i	$0.137006\pi$
$522$		0			0
$523$	−10.5802	−	15.6047i	−0.462641	−	0.682345i	0.522782	−	0.852467i	$-0.324894\pi$
$523$	−10.5802	−	15.6047i	−0.462641	−	0.682345i	−0.985423	+	0.170122i	$0.945584\pi$
$524$	1.09993	−	0.508884i	0.0480509	−	0.0222307i
$525$		0			0
$526$	−2.96947	+	7.45282i	−0.129475	+	0.324958i
$527$	28.7807	+	21.8785i	1.25371	+	0.953043i
$528$		0			0
$529$	12.8496	+	4.32953i	0.558678	+	0.188240i
$530$	2.88940			0.125508
$531$		0			0
$532$	1.78033			0.0771872
$533$	−37.6938	−	12.7005i	−1.63270	−	0.550121i
$534$		0			0
$535$	−43.8754	−	33.3532i	−1.89690	−	1.44199i
$536$	8.52117	−	21.3865i	0.368059	−	0.923758i
$537$		0			0
$538$	13.5152	−	6.25280i	0.582682	−	0.269577i
$539$	16.7714	+	24.7360i	0.722397	+	1.06546i
$540$		0			0
$541$	−4.27027	+	5.02736i	−0.183593	+	0.216143i	−0.846258	−	0.532774i	$-0.821150\pi$
$541$	−4.27027	+	5.02736i	−0.183593	+	0.216143i	0.662664	+	0.748916i	$0.269426\pi$
$542$	4.32437	−	15.5750i	0.185747	−	0.669002i
$543$		0			0
$544$	−13.2142	+	24.9246i	−0.566553	+	1.06863i
$545$	−25.7339	+	2.79873i	−1.10232	+	0.119884i
$546$		0			0
$547$	−7.19485	−	25.9135i	−0.307629	−	1.10798i	−0.942182	−	0.335102i	$-0.891229\pi$
$547$	−7.19485	−	25.9135i	−0.307629	−	1.10798i	0.634553	−	0.772880i	$-0.281184\pi$
$548$	6.51027	+	3.01197i	0.278105	+	0.128665i
$549$		0			0
$550$	42.9242	−	9.44832i	1.83029	−	0.402878i
$551$	12.0152	−	7.22931i	0.511865	−	0.307979i
$552$		0			0
$553$	1.96444	−	2.89733i	0.0835364	−	0.123207i
$554$	−3.45055	+	21.0474i	−0.146600	+	0.894219i
$555$		0			0
$556$	−2.18958	−	2.07408i	−0.0928587	−	0.0879604i
$557$	10.7301	−	10.1641i	0.454647	−	0.430665i	−0.425794	−	0.904820i	$-0.640005\pi$
$557$	10.7301	−	10.1641i	0.454647	−	0.430665i	0.880441	+	0.474155i	$0.157246\pi$
$558$		0			0
$559$	5.78238	+	1.27280i	0.244569	+	0.0538336i
$560$	−0.356392	+	0.120082i	−0.0150603	+	0.00507441i
$561$		0			0
$562$	12.1797	+	2.68095i	0.513769	+	0.113089i
$563$	−1.35680	+	25.0247i	−0.0571823	+	1.05467i	0.819341	+	0.573307i	$0.194340\pi$
$563$	−1.35680	+	25.0247i	−0.0571823	+	1.05467i	−0.876523	+	0.481360i	$0.840143\pi$
$564$		0			0
$565$	21.3690	+	20.2418i	0.899002	+	0.851580i
$566$	1.23820	+	22.8373i	0.0520455	+	0.959923i
$567$		0			0
$568$	3.17295	−	4.67975i	0.133134	−	0.196358i
$569$	2.50413	+	0.272340i	0.104979	+	0.0114171i	0.160457	−	0.987043i	$-0.448703\pi$
$569$	2.50413	+	0.272340i	0.104979	+	0.0114171i	−0.0554789	+	0.998460i	$0.517669\pi$
$570$		0			0
$571$	18.9840	−	4.17870i	0.794456	−	0.174873i	0.200843	−	0.979623i	$-0.435632\pi$
$571$	18.9840	−	4.17870i	0.794456	−	0.174873i	0.593613	+	0.804750i	$0.297701\pi$
$572$	−3.78089	−	23.0624i	−0.158087	−	0.964287i
$573$		0			0
$574$	−2.24815	−	8.09712i	−0.0938361	−	0.337967i
$575$	−25.6037	+	19.4634i	−1.06775	+	0.811682i
$576$		0			0
$577$	−9.20921	+	17.3704i	−0.383384	+	0.723139i	−0.997832	−	0.0658184i	$-0.979034\pi$
$577$	−9.20921	+	17.3704i	−0.383384	+	0.723139i	0.614447	+	0.788958i	$0.289379\pi$
$578$	−2.39044	−	5.99956i	−0.0994293	−	0.249549i
$579$		0			0
$580$	−29.6843	+	34.9471i	−1.23257	+	1.45110i
$581$	1.03704	+	1.95606i	0.0430236	+	0.0811510i
$582$		0			0
$583$	3.77754	−	1.74767i	0.156450	−	0.0723813i
$584$	−19.1012	−	22.4877i	−0.790414	−	0.930547i
$585$		0			0
$586$	−16.6038	−	12.6219i	−0.685899	−	0.521407i
$587$	2.57509	+	1.54938i	0.106285	+	0.0639497i	0.567704	−	0.823233i	$-0.307832\pi$
$587$	2.57509	+	1.54938i	0.106285	+	0.0639497i	−0.461419	+	0.887182i	$0.652659\pi$
$588$		0			0
$589$	11.0581			0.455639
$590$	−4.75477	−	25.5686i	−0.195751	−	1.05264i
$591$		0			0
$592$	0.425163	+	0.143254i	0.0174741	+	0.00588771i
$593$	13.3789	+	8.04984i	0.549407	+	0.330567i	0.763045	−	0.646346i	$-0.223704\pi$
$593$	13.3789	+	8.04984i	0.549407	+	0.330567i	−0.213637	+	0.976913i	$0.568531\pi$
$594$		0			0
$595$	6.73071	−	16.8928i	0.275932	−	0.692538i
$596$	−8.58690	−	10.1093i	−0.351733	−	0.414092i
$597$		0			0
$598$	−5.65032	−	8.33360i	−0.231059	−	0.340786i
$599$	2.30439	+	4.34655i	0.0941550	+	0.177595i	0.926116	−	0.377239i	$-0.123127\pi$
$599$	2.30439	+	4.34655i	0.0941550	+	0.177595i	−0.831961	+	0.554834i	$0.812782\pi$
$600$		0			0
$601$	−5.26560	+	18.9650i	−0.214788	+	0.773598i	0.775111	+	0.631825i	$0.217694\pi$
$601$	−5.26560	+	18.9650i	−0.214788	+	0.773598i	−0.989899	+	0.141773i	$0.954720\pi$
$602$	0.462999	+	1.16204i	0.0188704	+	0.0473612i
$603$		0			0
$604$	17.0691	−	1.85638i	0.694532	−	0.0755349i
$605$	40.0392	−	30.4370i	1.62783	−	1.23744i
$606$		0			0
$607$	11.3634	+	5.25726i	0.461225	+	0.213386i	0.636720	−	0.771095i	$-0.280291\pi$
$607$	11.3634	+	5.25726i	0.461225	+	0.213386i	−0.175495	+	0.984480i	$0.556153\pi$
$608$	1.39600	+	8.51524i	0.0566154	+	0.345339i
$609$		0			0
$610$	−7.58440	+	4.56338i	−0.307083	+	0.184766i
$611$	26.1718	+	2.84636i	1.05880	+	0.115151i
$612$		0			0
$613$	−1.16504	+	7.10644i	−0.0470556	+	0.287026i	−0.999863	−	0.0165488i	$-0.994732\pi$
$613$	−1.16504	+	7.10644i	−0.0470556	+	0.287026i	0.952807	+	0.303575i	$0.0981804\pi$
$614$	0.778502	+	14.3586i	0.0314178	+	0.579467i
$615$		0			0
$616$	9.27950	−	8.79001i	0.373882	−	0.354160i
$617$	1.65703	−	30.5622i	0.0667097	−	1.23039i	−0.753160	−	0.657838i	$-0.771471\pi$
$617$	1.65703	−	30.5622i	0.0667097	−	1.23039i	0.819870	−	0.572550i	$-0.194046\pi$
$618$		0			0
$619$	−19.9157	+	6.71040i	−0.800481	+	0.269714i	−0.689666	−	0.724127i	$-0.742243\pi$
$619$	−19.9157	+	6.71040i	−0.800481	+	0.269714i	−0.110815	+	0.993841i	$0.535346\pi$
$620$	−34.2665	+	11.5457i	−1.37617	+	0.463687i
$621$		0			0
$622$	1.24094	−	22.8878i	0.0497572	−	0.917717i
$623$	−3.17640	+	3.00884i	−0.127260	+	0.120547i
$624$		0			0
$625$	1.74487	+	32.1823i	0.0697950	+	1.28729i
$626$	0.302279	−	1.84382i	0.0120815	−	0.0736940i
$627$		0			0
$628$	−1.94025	−	0.211015i	−0.0774243	−	0.00842040i
$629$	−18.5880	+	11.1841i	−0.741154	+	0.445937i
$630$		0			0
$631$	−4.66776	−	28.4721i	−0.185821	−	1.13346i	−0.900775	−	0.434285i	$-0.857001\pi$
$631$	−4.66776	−	28.4721i	−0.185821	−	1.13346i	0.714955	−	0.699171i	$-0.246447\pi$
$632$	9.54205	+	4.41462i	0.379562	+	0.175604i
$633$		0			0
$634$	−2.82694	+	2.14898i	−0.112272	+	0.0853470i
$635$	−36.6254	+	3.98325i	−1.45344	+	0.158071i
$636$		0			0
$637$	−8.63287	−	21.6669i	−0.342047	−	0.858472i
$638$	10.4038	−	37.4709i	0.411889	−	1.48349i
$639$		0			0
$640$	−13.5414	−	25.5417i	−0.535270	−	1.00963i
$641$	−20.0454	−	29.5647i	−0.791744	−	1.16774i	−0.982530	−	0.186104i	$-0.940414\pi$
$641$	−20.0454	−	29.5647i	−0.791744	−	1.16774i	0.190786	−	0.981632i	$-0.438896\pi$
$642$		0			0
$643$	15.0536	+	17.7225i	0.593658	+	0.698908i	0.974157	−	0.225873i	$-0.0725236\pi$
$643$	15.0536	+	17.7225i	0.593658	+	0.698908i	−0.380499	+	0.924781i	$0.624248\pi$
$644$	−1.33729	+	3.35635i	−0.0526967	+	0.132259i
$645$		0			0
$646$	−5.52842	−	3.32634i	−0.217513	−	0.130873i
$647$	24.9343	+	8.40133i	0.980267	+	0.330290i	0.763411	−	0.645913i	$-0.223523\pi$
$647$	24.9343	+	8.40133i	0.980267	+	0.330290i	0.216856	+	0.976204i	$0.430420\pi$
$648$		0			0
$649$	−21.6816	−	30.5519i	−0.851079	−	1.19927i
$650$	−34.3008			−1.34539
$651$		0			0
$652$	16.0596	+	9.66275i	0.628943	+	0.378423i
$653$	−14.8329	−	11.2757i	−0.580456	−	0.441251i	0.273297	−	0.961930i	$-0.411886\pi$
$653$	−14.8329	−	11.2757i	−0.580456	−	0.441251i	−0.853753	+	0.520679i	$0.825679\pi$
$654$		0			0
$655$	−2.45123	−	2.88582i	−0.0957777	−	0.112758i
$656$	−0.970896	+	0.449184i	−0.0379071	+	0.0175377i
$657$		0			0
$658$	2.60524	+	4.91400i	0.101563	+	0.191568i
$659$	11.4312	−	13.4578i	0.445296	−	0.524243i	−0.493022	−	0.870017i	$-0.664108\pi$
$659$	11.4312	−	13.4578i	0.445296	−	0.524243i	0.938318	+	0.345774i	$0.112384\pi$
$660$		0			0
$661$	6.54181	+	16.4187i	0.254447	+	0.638614i	0.999600	−	0.0282798i	$-0.00900293\pi$
$661$	6.54181	+	16.4187i	0.254447	+	0.638614i	−0.745153	+	0.666893i	$0.767624\pi$
$662$	8.29892	−	15.6534i	0.322547	−	0.608387i
$663$		0			0
$664$	−5.29373	+	4.02419i	−0.205436	+	0.156169i
$665$	−1.48802	−	5.35936i	−0.0577029	−	0.207827i
$666$		0			0
$667$	4.60377	+	28.0818i	0.178259	+	1.08733i
$668$	14.8650	−	3.27203i	0.575144	−	0.126599i
$669$		0			0
$670$	−27.6202	−	3.00388i	−1.06706	−	0.116050i
$671$	−7.15547	+	10.5535i	−0.276234	+	0.407415i
$672$		0			0
$673$	0.0532889	+	0.982856i	0.00205414	+	0.0378863i	0.999381	−	0.0351860i	$-0.0112024\pi$
$673$	0.0532889	+	0.982856i	0.00205414	+	0.0378863i	−0.997327	+	0.0730723i	$0.976720\pi$
$674$	5.71954	+	5.41784i	0.220309	+	0.208687i
$675$		0			0
$676$	−0.101437	+	1.87090i	−0.00390143	+	0.0719576i
$677$	9.53187	+	2.09812i	0.366339	+	0.0806374i	0.394325	−	0.918971i	$-0.370978\pi$
$677$	9.53187	+	2.09812i	0.366339	+	0.0806374i	−0.0279859	+	0.999608i	$0.508909\pi$
$678$		0			0
$679$	−6.67183	+	2.24800i	−0.256041	+	0.0862703i
$680$	53.3398	+	11.7410i	2.04549	+	0.450246i
$681$		0			0
$682$	22.2644	−	21.0899i	0.852547	−	0.807575i
$683$	−17.0339	−	16.1353i	−0.651783	−	0.617402i	0.288628	−	0.957441i	$-0.406801\pi$
$683$	−17.0339	−	16.1353i	−0.651783	−	0.617402i	−0.940411	+	0.340040i	$0.889560\pi$
$684$		0			0
$685$	3.62563	−	22.1154i	0.138528	−	0.844985i
$686$	5.92426	−	8.73763i	0.226189	−	0.333604i
$687$		0			0
$688$	0.136445	−	0.0820964i	0.00520193	−	0.00312989i
$689$	−3.17234	+	0.698285i	−0.120857	+	0.0266026i
$690$		0			0
$691$	13.1217	+	6.07073i	0.499172	+	0.230941i	0.653286	−	0.757112i	$-0.273390\pi$
$691$	13.1217	+	6.07073i	0.499172	+	0.230941i	−0.154114	+	0.988053i	$0.549252\pi$
$692$	−7.32487	−	26.3818i	−0.278450	−	1.00289i
$693$		0			0
$694$	9.16522	−	0.996777i	0.347907	−	0.0378372i
$695$	−4.41355	+	8.32483i	−0.167415	+	0.315779i
$696$		0			0
$697$	13.8382	−	49.8406i	0.524158	−	1.88785i
$698$	−6.23512	+	7.34056i	−0.236003	+	0.277844i
$699$		0			0
$700$	6.90731	+	10.1875i	0.261072	+	0.385052i
$701$	−13.9571	+	6.45725i	−0.527153	+	0.243887i	−0.665368	−	0.746515i	$-0.731725\pi$
$701$	−13.9571	+	6.45725i	−0.527153	+	0.243887i	0.138215	+	0.990402i	$0.455863\pi$
$702$		0			0
$703$	−2.45601	+	6.16412i	−0.0926302	+	0.232484i
$704$	18.2560	+	13.8779i	0.688049	+	0.523042i
$705$		0			0
$706$	10.3992	+	3.50391i	0.391381	+	0.131871i
$707$	7.25696			0.272926
$708$		0			0
$709$	−23.0178			−0.864452			−0.432226	−	0.901765i	$-0.642272\pi$
$709$	−23.0178			−0.864452			−0.432226	+	0.901765i	$0.642272\pi$
$710$	−6.46621	−	2.17872i	−0.242673	−	0.0817659i
$711$		0			0
$712$	−10.4615	−	7.95261i	−0.392060	−	0.298037i
$713$	−8.30622	+	20.8470i	−0.311070	+	0.780728i
$714$		0			0
$715$	−66.2649	+	30.6574i	−2.47817	+	1.14652i
$716$	3.32258	+	4.90044i	0.124171	+	0.183138i
$717$		0			0
$718$	−15.9550	+	18.7837i	−0.595437	+	0.701002i
$719$	6.42442	−	23.1387i	0.239590	−	0.862927i	−0.741755	−	0.670671i	$-0.766006\pi$
$719$	6.42442	−	23.1387i	0.239590	−	0.862927i	0.981345	−	0.192255i	$-0.0615801\pi$
$720$		0			0
$721$	8.00290	−	15.0951i	0.298043	−	0.562170i
$722$	14.2994	−	1.55515i	0.532168	−	0.0578768i
$723$		0			0
$724$	−8.27880	−	29.8176i	−0.307679	−	1.10816i
$725$	87.9843	+	40.7059i	3.26766	+	1.51178i
$726$		0			0
$727$	−48.1883	+	10.6071i	−1.78721	+	0.393394i	−0.980336	−	0.197335i	$-0.936771\pi$
$727$	−48.1883	+	10.6071i	−1.78721	+	0.393394i	−0.806870	+	0.590729i	$0.798840\pi$
$728$	−8.54727	+	5.14272i	−0.316783	+	0.190602i
$729$		0			0
$730$	−19.9825	+	29.4720i	−0.739587	+	1.09081i
$731$	−1.24566	+	7.59818i	−0.0460723	+	0.281029i
$732$		0			0
$733$	8.55482	+	8.10355i	0.315979	+	0.299312i	0.829208	−	0.558941i	$-0.188792\pi$
$733$	8.55482	+	8.10355i	0.315979	+	0.299312i	−0.513228	+	0.858252i	$0.671551\pi$
$734$	0.685882	−	0.649701i	0.0253163	−	0.0239809i
$735$		0			0
$736$	−17.1018	−	3.76440i	−0.630382	−	0.138758i
$737$	−37.9270	+	12.7791i	−1.39706	+	0.470724i
$738$		0			0
$739$	−38.0617	−	8.37800i	−1.40012	−	0.308190i	−0.550170	−	0.835052i	$-0.685437\pi$
$739$	−38.0617	−	8.37800i	−1.40012	−	0.308190i	−0.849950	+	0.526863i	$0.823368\pi$
$740$	1.17467	−	21.6656i	0.0431818	−	0.796442i
$741$		0			0
$742$	−0.498223	−	0.471942i	−0.0182903	−	0.0173255i
$743$	−0.845612	−	15.5964i	−0.0310225	−	0.572176i	−0.972184	−	0.234219i	$-0.924747\pi$
$743$	−0.845612	−	15.5964i	−0.0310225	−	0.572176i	0.941161	−	0.337958i	$-0.109736\pi$
$744$		0			0
$745$	−23.2551	+	34.2987i	−0.852000	+	1.25661i
$746$	−8.78001	−	0.954884i	−0.321459	−	0.0349608i
$747$		0			0
$748$	29.6809	−	6.53326i	1.08524	−	0.238880i
$749$	2.11772	+	12.9175i	0.0773799	+	0.471997i
$750$		0			0
$751$	−7.49205	−	26.9839i	−0.273389	−	0.984658i	−0.964970	−	0.262359i	$-0.915499\pi$
$751$	−7.49205	−	26.9839i	−0.273389	−	0.984658i	0.691581	−	0.722299i	$-0.256914\pi$
$752$	0.563664	−	0.428487i	0.0205547	−	0.0156253i
$753$		0			0
$754$	−14.2159	+	26.8140i	−0.517711	+	0.976507i
$755$	−19.8548	−	49.8318i	−0.722590	−	1.81356i
$756$		0			0
$757$	10.9511	−	12.8927i	0.398026	−	0.468592i	−0.526243	−	0.850334i	$-0.676400\pi$
$757$	10.9511	−	12.8927i	0.398026	−	0.468592i	0.924269	+	0.381742i	$0.124676\pi$
$758$	4.39451	+	8.28893i	0.159616	+	0.301068i
$759$		0			0
$760$	15.1617	−	7.01457i	0.549974	−	0.254445i
$761$	1.68160	+	1.97973i	0.0609578	+	0.0717650i	0.791796	−	0.610786i	$-0.209146\pi$
$761$	1.68160	+	1.97973i	0.0609578	+	0.0717650i	−0.730838	+	0.682551i	$0.760871\pi$
$762$		0			0
$763$	4.89446	+	3.72067i	0.177191	+	0.134697i
$764$	19.5851	+	11.7840i	0.708564	+	0.426329i
$765$		0			0
$766$	−17.6316			−0.637054
$767$	11.3996	+	26.9233i	0.411615	+	0.972144i
$768$		0			0
$769$	−15.3230	−	5.16292i	−0.552561	−	0.186180i	0.0291497	−	0.999575i	$-0.490720\pi$
$769$	−15.3230	−	5.16292i	−0.552561	−	0.186180i	−0.581711	+	0.813395i	$0.697617\pi$
$770$	−13.2174	−	7.95262i	−0.476320	−	0.286592i
$771$		0			0
$772$	5.55963	−	13.9536i	0.200096	−	0.502202i
$773$	−6.44197	−	7.58408i	−0.231702	−	0.272780i	0.634008	−	0.773326i	$-0.281408\pi$
$773$	−6.44197	−	7.58408i	−0.231702	−	0.272780i	−0.865710	+	0.500546i	$0.833133\pi$
$774$		0			0
$775$	42.9029	+	63.2770i	1.54112	+	2.27298i
$776$	−9.90485	−	18.6825i	−0.355564	−	0.670664i
$777$		0			0
$778$	−5.50740	+	19.8359i	−0.197450	+	0.711150i
$779$	−5.85617	−	14.6979i	−0.209819	−	0.526606i
$780$		0			0
$781$	−9.77158	+	1.06272i	−0.349655	+	0.0380272i
$782$	10.4236	−	7.92381i	0.372747	−	0.283355i
$783$		0			0
$784$	−0.569303	−	0.263387i	−0.0203322	−	0.00940669i
$785$	0.986456	+	6.01712i	0.0352081	+	0.214760i
$786$		0			0
$787$	17.5190	−	10.5408i	0.624484	−	0.375740i	−0.167863	−	0.985810i	$-0.553687\pi$
$787$	17.5190	−	10.5408i	0.624484	−	0.375740i	0.792347	+	0.610071i	$0.208859\pi$
$788$	−0.543639	−	0.0591243i	−0.0193663	−	0.00210621i
$789$		0			0
$790$	2.05274	−	12.5212i	0.0730333	−	0.445483i
$791$	−0.378479	−	6.98064i	−0.0134572	−	0.248203i
$792$		0			0
$793$	7.22425	−	6.84318i	0.256541	−	0.243008i
$794$	−1.60724	+	29.6439i	−0.0570389	+	1.05202i
$795$		0			0
$796$	−2.56001	+	0.862566i	−0.0907370	+	0.0305729i
$797$	−27.7248	+	9.34158i	−0.982064	+	0.330896i	−0.764126	−	0.645067i	$-0.776830\pi$
$797$	−27.7248	+	9.34158i	−0.982064	+	0.330896i	−0.217938	+	0.975963i	$0.569933\pi$
$798$		0			0
$799$	−1.85347	+	34.1852i	−0.0655710	+	1.20939i
$800$	−43.3102	+	41.0256i	−1.53125	+	1.45047i
$801$		0			0
$802$	−0.717322	−	13.2302i	−0.0253295	−	0.467176i
$803$	−8.29833	+	50.6176i	−0.292842	+	1.78626i
$804$		0			0
$805$	11.2214	+	1.22040i	0.395502	+	0.0430134i
$806$	−20.5075	+	12.3390i	−0.722346	+	0.434621i
$807$		0			0
$808$	3.52625	+	21.5092i	0.124053	+	0.756690i
$809$	6.29495	+	2.91235i	0.221319	+	0.102393i	0.527416	−	0.849607i	$-0.323161\pi$
$809$	6.29495	+	2.91235i	0.221319	+	0.102393i	−0.306097	+	0.952000i	$0.599023\pi$
$810$		0			0
$811$	2.57537	−	1.95774i	0.0904334	−	0.0687457i	−0.558981	−	0.829181i	$-0.688807\pi$
$811$	2.57537	−	1.95774i	0.0904334	−	0.0687457i	0.649414	+	0.760435i	$0.275014\pi$
$812$	10.8266	−	1.17746i	0.379939	−	0.0413209i
$813$		0			0
$814$	6.81127	+	17.0950i	0.238735	+	0.599179i
$815$	15.6651	−	56.4207i	0.548725	−	1.97633i
$816$		0			0
$817$	1.10315	+	2.08076i	0.0385943	+	0.0727966i
$818$	−14.9721	−	22.0821i	−0.523485	−	0.772083i
$819$		0			0
$820$	33.4930	+	39.4310i	1.16963	+	1.37699i
$821$	−17.3314	+	43.4986i	−0.604871	+	1.51811i	0.233131	+	0.972445i	$0.425103\pi$
$821$	−17.3314	+	43.4986i	−0.604871	+	1.51811i	−0.838002	+	0.545667i	$0.816276\pi$
$822$		0			0
$823$	−17.8352	−	10.7311i	−0.621695	−	0.374061i	0.169585	−	0.985516i	$-0.445757\pi$
$823$	−17.8352	−	10.7311i	−0.621695	−	0.374061i	−0.791280	+	0.611454i	$0.790585\pi$
$824$	48.6295	+	16.3852i	1.69409	+	0.570805i
$825$		0			0
$826$	−3.35639	+	5.18545i	−0.116784	+	0.180425i
$827$	32.9263			1.14496			0.572479	−	0.819919i	$-0.305982\pi$
$827$	32.9263			1.14496			0.572479	+	0.819919i	$0.305982\pi$
$828$		0			0
$829$	−18.7064	−	11.2553i	−0.649701	−	0.390912i	0.152216	−	0.988347i	$-0.451359\pi$
$829$	−18.7064	−	11.2553i	−0.649701	−	0.390912i	−0.801917	+	0.597435i	$0.796187\pi$
$830$	6.38862	+	4.85650i	0.221752	+	0.168572i
$831$		0			0
$832$	−11.5860	−	13.6401i	−0.401673	−	0.472886i
$833$	27.5272	−	12.7354i	0.953761	−	0.441257i
$834$		0			0
$835$	−22.2741	−	42.0135i	−0.770829	−	1.45394i
$836$	6.01805	−	7.08500i	0.208139	−	0.245040i
$837$		0			0
$838$	−8.88284	−	22.2942i	−0.306853	−	0.770142i
$839$	−1.14401	+	2.15783i	−0.0394956	+	0.0744966i	−0.902474	−	0.430744i	$-0.858251\pi$
$839$	−1.14401	+	2.15783i	−0.0394956	+	0.0744966i	0.862979	+	0.505240i	$0.168596\pi$
$840$		0			0
$841$	45.1991	−	34.3595i	1.55859	−	1.18481i
$842$	−8.01786	−	28.8777i	−0.276314	−	0.995192i
$843$		0			0
$844$	0.813279	+	4.96078i	0.0279942	+	0.170757i
$845$	5.71677	−	1.25836i	0.196663	−	0.0432887i
$846$		0			0
$847$	−11.8755	−	1.29153i	−0.408045	−	0.0443776i
$848$	−0.0490265	+	0.0723087i	−0.00168358	+	0.00248309i
$849$		0			0
$850$	−2.41491	−	44.5405i	−0.0828309	−	1.52773i
$851$	−9.77600	−	9.26032i	−0.335117	−	0.317440i
$852$		0			0
$853$	2.73173	−	50.3838i	0.0935327	−	1.72511i	−0.456292	−	0.889830i	$-0.650823\pi$
$853$	2.73173	−	50.3838i	0.0935327	−	1.72511i	0.549825	−	0.835280i	$-0.314694\pi$
$854$	2.05315	+	0.451932i	0.0702573	+	0.0154648i
$855$		0			0
$856$	−37.2577	+	12.5536i	−1.27344	+	0.429073i
$857$	−42.8693	−	9.43625i	−1.46439	−	0.322336i	−0.589936	−	0.807450i	$-0.700847\pi$
$857$	−42.8693	−	9.43625i	−1.46439	−	0.322336i	−0.874451	+	0.485114i	$0.838778\pi$
$858$		0			0
$859$	40.5723	−	38.4322i	1.38431	−	1.31129i	0.484643	−	0.874712i	$-0.338949\pi$
$859$	40.5723	−	38.4322i	1.38431	−	1.31129i	0.899667	−	0.436577i	$-0.143809\pi$
$860$	−5.59094	−	5.29602i	−0.190649	−	0.180593i
$861$		0			0
$862$	−5.14089	+	31.3580i	−0.175099	+	1.06806i
$863$	−4.51714	+	6.66228i	−0.153765	+	0.226787i	−0.896767	−	0.442502i	$-0.854091\pi$
$863$	−4.51714	+	6.66228i	−0.153765	+	0.226787i	0.743002	+	0.669289i	$0.233401\pi$
$864$		0			0
$865$	−73.2953	+	44.1003i	−2.49211	+	1.49946i
$866$	18.7482	−	4.12678i	0.637088	−	0.140234i
$867$		0			0
$868$	7.79443	+	3.60609i	0.264560	+	0.122399i
$869$	−4.88981	−	17.6115i	−0.165875	−	0.597429i
$870$		0			0
$871$	31.0509	−	3.37698i	1.05212	−	0.114425i
$872$	−8.64955	+	16.3148i	−0.292911	+	0.552488i
$873$		0			0
$874$	1.07143	−	3.85895i	0.0362417	−	0.130531i
$875$	13.0030	−	15.3083i	0.439582	−	0.517516i
$876$		0			0
$877$	13.0290	+	19.2163i	0.439958	+	0.648889i	0.981428	−	0.191831i	$-0.0614425\pi$
$877$	13.0290	+	19.2163i	0.439958	+	0.648889i	−0.541470	+	0.840720i	$0.682132\pi$
$878$	−19.1788	+	8.87307i	−0.647254	+	0.299452i
$879$		0			0
$880$	−0.726831	+	1.82421i	−0.0245015	+	0.0614941i
$881$	−14.5397	−	11.0528i	−0.489856	−	0.372379i	0.330893	−	0.943668i	$-0.392650\pi$
$881$	−14.5397	−	11.0528i	−0.489856	−	0.372379i	−0.820749	+	0.571290i	$0.806443\pi$
$882$		0			0
$883$	−21.5958	−	7.27646i	−0.726755	−	0.244872i	−0.0684829	−	0.997652i	$-0.521816\pi$
$883$	−21.5958	−	7.27646i	−0.726755	−	0.244872i	−0.658272	+	0.752780i	$0.728712\pi$
$884$	−23.7181			−0.797725
$885$		0			0
$886$	6.81159			0.228840
$887$	−22.3149	−	7.51876i	−0.749261	−	0.252455i	−0.0813386	−	0.996687i	$-0.525920\pi$
$887$	−22.3149	−	7.51876i	−0.749261	−	0.252455i	−0.667922	+	0.744231i	$0.732816\pi$
$888$		0			0
$889$	6.96597	+	5.29539i	0.233631	+	0.177602i
$890$	−5.87000	+	14.7326i	−0.196763	+	0.493838i
$891$		0			0
$892$	20.0545	−	9.27822i	0.671475	−	0.310658i
$893$	5.87658	+	8.66730i	0.196652	+	0.290040i
$894$		0			0
$895$	11.9748	−	14.0978i	0.400274	−	0.471239i
$896$	−1.83692	+	6.61598i	−0.0613671	+	0.221024i
$897$		0			0
$898$	−1.78877	+	3.37397i	−0.0596920	+	0.112591i
$899$	67.2465	−	7.31349i	2.24280	−	0.243919i
$900$		0			0
$901$	−1.13009	−	4.07021i	−0.0376487	−	0.135598i
$902$	−39.8227	−	18.4239i	−1.32595	−	0.613450i
$903$		0			0
$904$	20.5063	−	4.51377i	0.682028	−	0.150126i
$905$	−82.8406	+	49.8436i	−2.75372	+	1.65686i
$906$		0			0
$907$	19.2342	−	28.3683i	0.638661	−	0.941954i	−0.361294	−	0.932452i	$-0.617665\pi$
$907$	19.2342	−	28.3683i	0.638661	−	0.941954i	0.999955	−	0.00950243i	$-0.00302476\pi$
$908$	−2.27915	+	13.9022i	−0.0756363	+	0.461361i
$909$		0			0
$910$	8.73973	+	8.27872i	0.289719	+	0.274437i
$911$	−6.41888	+	6.08028i	−0.212667	+	0.201449i	−0.786617	−	0.617442i	$-0.788169\pi$
$911$	−6.41888	+	6.08028i	−0.212667	+	0.201449i	0.573950	+	0.818891i	$0.305410\pi$
$912$		0			0
$913$	11.2898	+	2.48508i	0.373638	+	0.0822440i
$914$	−22.5074	+	7.58363i	−0.744479	+	0.250844i
$915$		0			0
$916$	−20.1691	−	4.43955i	−0.666405	−	0.146687i
$917$	−0.0486870	+	0.897978i	−0.00160778	+	0.0296538i
$918$		0			0
$919$	15.9256	+	15.0855i	0.525338	+	0.497626i	0.903779	−	0.427999i	$-0.140781\pi$
$919$	15.9256	+	15.0855i	0.525338	+	0.497626i	−0.378442	+	0.925625i	$0.623540\pi$
$920$	1.83543	+	33.8525i	0.0605122	+	1.11608i
$921$		0			0
$922$	−14.9506	+	22.0505i	−0.492372	+	0.726195i
$923$	7.62594	+	0.829371i	0.251011	+	0.0272991i
$924$		0			0
$925$	−44.8014	+	9.86154i	−1.47306	+	0.324246i
$926$	1.05116	+	6.41182i	0.0345434	+	0.210706i
$927$		0			0
$928$	14.1211	+	50.8598i	0.463549	+	1.66955i
$929$	23.4765	−	17.8463i	0.770238	−	0.585520i	−0.144530	−	0.989500i	$-0.546167\pi$
$929$	23.4765	−	17.8463i	0.770238	−	0.585520i	0.914767	+	0.403981i	$0.132374\pi$
$930$		0			0
$931$	4.34555	−	8.19658i	0.142420	−	0.268632i
$932$	−3.44268	−	8.64047i	−0.112769	−	0.283028i
$933$		0			0
$934$	−2.77185	+	3.26328i	−0.0906978	+	0.106778i
$935$	−44.4747	−	83.8882i	−1.45448	−	2.74344i
$936$		0			0
$937$	−25.9720	+	12.0159i	−0.848469	+	0.392544i	−0.795428	−	0.606049i	$-0.792754\pi$
$937$	−25.9720	+	12.0159i	−0.848469	+	0.392544i	−0.0530418	+	0.998592i	$0.516892\pi$
$938$	4.27195	+	5.02933i	0.139484	+	0.164213i
$939$		0			0
$940$	−27.2597	−	20.7223i	−0.889115	−	0.675887i
$941$	27.7117	+	16.6736i	0.903376	+	0.543543i	0.889793	−	0.456364i	$-0.150849\pi$
$941$	27.7117	+	16.6736i	0.903376	+	0.543543i	0.0135832	+	0.999908i	$0.495676\pi$
$942$		0			0
$943$	32.1078			1.04557
$944$	0.720545	+	0.314850i	0.0234517	+	0.0102475i
$945$		0			0
$946$	6.18952	+	2.08549i	0.201239	+	0.0678052i
$947$	52.1193	+	31.3591i	1.69365	+	1.01903i	0.925488	+	0.378778i	$0.123655\pi$
$947$	52.1193	+	31.3591i	1.69365	+	1.01903i	0.768161	+	0.640257i	$0.221172\pi$
$948$		0			0
$949$	14.8167	−	37.1872i	0.480972	−	1.20715i
$950$	−8.83277	−	10.3987i	−0.286573	−	0.337380i
$951$		0			0
$952$	−7.27972	−	10.7368i	−0.235937	−	0.347981i
$953$	−3.64723	−	6.87940i	−0.118145	−	0.222846i	0.817385	−	0.576091i	$-0.195423\pi$
$953$	−3.64723	−	6.87940i	−0.118145	−	0.222846i	−0.935531	+	0.353246i	$0.885078\pi$
$954$		0			0
$955$	19.1040	−	68.8064i	0.618191	−	2.22652i
$956$	6.26719	+	15.7295i	0.202695	+	0.508727i
$957$		0			0
$958$	23.3005	−	2.53408i	0.752804	−	0.0818724i
$959$	−4.23740	+	3.22118i	−0.136833	+	0.104017i
$960$		0			0
$961$	20.2781	+	9.38166i	0.654133	+	0.302634i
$962$	−2.32339	−	14.1721i	−0.0749092	−	0.456926i
$963$		0			0
$964$	−5.82486	+	3.50470i	−0.187606	+	0.112879i
$965$	−46.6516	−	5.07366i	−1.50177	−	0.163327i
$966$		0			0
$967$	4.36544	−	26.6280i	0.140383	−	0.856300i	−0.818917	−	0.573912i	$-0.805425\pi$
$967$	4.36544	−	26.6280i	0.140383	−	0.856300i	0.959300	−	0.282388i	$-0.0911265\pi$
$968$	−1.94241	−	35.8257i	−0.0624315	−	1.15148i
$969$		0			0
$970$	−18.5269	+	17.5496i	−0.594863	+	0.563484i
$971$	2.11244	−	38.9616i	0.0677913	−	1.25034i	−0.744714	−	0.667384i	$-0.767414\pi$
$971$	2.11244	−	38.9616i	0.0677913	−	1.25034i	0.812505	−	0.582954i	$-0.198103\pi$
$972$		0			0
$973$	2.12077	−	0.714572i	0.0679889	−	0.0229081i
$974$	19.1420	−	6.44969i	0.613349	−	0.206661i
$975$		0			0
$976$	0.0144890	−	0.267233i	0.000463781	−	0.00855393i
$977$	10.2053	−	9.66694i	0.326495	−	0.309273i	−0.506841	−	0.862040i	$-0.669187\pi$
$977$	10.2053	−	9.66694i	0.326495	−	0.309273i	0.833336	+	0.552767i	$0.186428\pi$
$978$		0			0
$979$	1.23681	+	22.8116i	0.0395285	+	0.729061i
$980$	−4.90785	+	29.9366i	−0.156776	+	0.956289i
$981$		0			0
$982$	−1.26231	−	0.137284i	−0.0402818	−	0.00438091i
$983$	−12.6688	+	7.62255i	−0.404071	+	0.243122i	−0.703053	−	0.711137i	$-0.748180\pi$
$983$	−12.6688	+	7.62255i	−0.404071	+	0.243122i	0.298982	+	0.954259i	$0.403353\pi$
$984$		0			0
$985$	0.276396	+	1.68594i	0.00880669	+	0.0537185i
$986$	−35.8195	−	16.5719i	−1.14072	−	0.527755i
$987$		0			0
$988$	−5.77543	+	4.39037i	−0.183741	+	0.139676i
$989$	−4.75136	+	0.516741i	−0.151084	+	0.0164314i
$990$		0			0
$991$	20.7725	+	52.1351i	0.659860	+	1.65612i	0.751013	+	0.660288i	$0.229566\pi$
$991$	20.7725	+	52.1351i	0.659860	+	1.65612i	−0.0911522	+	0.995837i	$0.529055\pi$
$992$	−11.1359	+	40.1080i	−0.353566	+	1.27343i
$993$		0			0
$994$	0.759114	+	1.43184i	0.0240776	+	0.0454152i
$995$	4.73627	+	6.98547i	0.150150	+	0.221454i
$996$		0			0
$997$	−21.7319	−	25.5848i	−0.688256	−	0.810278i	0.301436	−	0.953486i	$-0.402534\pi$
$997$	−21.7319	−	25.5848i	−0.688256	−	0.810278i	−0.989693	+	0.143209i	$0.954258\pi$
$998$	8.20916	−	20.6034i	0.259857	−	0.652191i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.b.64.3		140
3.2	odd	2		177.2.e.b.64.3	✓	140
59.12	even	29	inner	531.2.i.b.307.3		140
177.71	odd	58		177.2.e.b.130.3	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.b.64.3	✓	140	3.2	odd	2
177.2.e.b.130.3	yes	140	177.71	odd	58
531.2.i.b.64.3		140	1.1	even	1	trivial
531.2.i.b.307.3		140	59.12	even	29	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.815839 - 0.274888i) q^{2} +(-1.00216 - 0.761819i) q^{4} +(-1.45570 + 3.65354i) q^{5} +(0.847760 - 0.392216i) q^{7} +(1.57444 + 2.32213i) q^{8} +(2.19193 - 2.58054i) q^{10} +(1.30482 - 4.69955i) q^{11} +(-1.78293 + 3.36297i) q^{13} +(-0.799452 + 0.0869456i) q^{14} +(0.0273873 + 0.0986401i) q^{16} +(-4.49242 - 2.07842i) q^{17} +(-1.47865 + 0.325475i) q^{19} +(4.24218 - 2.55243i) q^{20} +(-2.35638 + 3.47539i) q^{22} +(0.497085 - 3.03208i) q^{23} +(-7.59929 - 7.19843i) q^{25} +(2.37903 - 2.25353i) q^{26} +(-1.14839 - 0.252779i) q^{28} +(-8.77673 + 2.95723i) q^{29} +(-7.13289 - 1.57007i) q^{31} +(0.308551 - 5.69088i) q^{32} +(3.09376 + 2.93057i) q^{34} +(0.198888 + 3.66827i) q^{35} +(2.45943 - 3.62739i) q^{37} +(1.29581 + 0.140928i) q^{38} +(-10.7759 + 2.37195i) q^{40} +(1.69060 + 10.3122i) q^{41} +(-0.416141 - 1.49880i) q^{43} +(-4.88784 + 3.71564i) q^{44} +(-1.23903 + 2.33705i) q^{46} +(-2.56001 - 6.42514i) q^{47} +(-3.96684 + 4.67012i) q^{49} +(4.22103 + 7.96172i) q^{50} +(4.34875 - 2.01195i) q^{52} +(0.552469 + 0.650416i) q^{53} +(15.2705 + 11.6084i) q^{55} +(2.24552 + 1.35109i) q^{56} +7.97331 q^{58} +(4.84647 - 5.95917i) q^{59} +(-2.47741 - 0.834738i) q^{61} +(5.38770 + 3.24167i) q^{62} +(-1.74030 + 4.36782i) q^{64} +(-9.69131 - 11.4095i) q^{65} +(-4.60495 - 6.79179i) q^{67} +(2.91873 + 5.50531i) q^{68} +(0.846105 - 3.04739i) q^{70} +(-0.745934 - 1.87215i) q^{71} +(-10.4550 + 1.13705i) q^{73} +(-3.00363 + 2.28330i) q^{74} +(1.72979 + 0.800286i) q^{76} +(-0.737059 - 4.49586i) q^{77} +(3.21106 - 1.93203i) q^{79} +(-0.400253 - 0.0435301i) q^{80} +(1.45545 - 8.87783i) q^{82} +(0.128318 + 2.36669i) q^{83} +(14.1332 - 13.3877i) q^{85} +(-0.0724995 + 1.33718i) q^{86} +(12.9673 - 4.36919i) q^{88} +(-4.43874 + 1.49559i) q^{89} +(-0.192491 + 3.55028i) q^{91} +(-2.80806 + 2.65993i) q^{92} +(0.322361 + 5.94559i) q^{94} +(0.963337 - 5.87610i) q^{95} +(-7.49293 - 0.814905i) q^{97} +(4.52007 - 2.71963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} - 116 q^{10} - 2 q^{11} + 4 q^{13} + 43 q^{14} + 7 q^{16} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 6 q^{23} - 57 q^{25} - 12 q^{26} - 10 q^{28} + 4 q^{29}+ \cdots + 143 q^{98}+O(q^{100}) \) 140 * q - q^2 - q^4 - 2 * q^5 - 2 * q^7 + 3 * q^8 - 116 * q^10 - 2 * q^11 + 4 * q^13 + 43 * q^14 + 7 * q^16 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 6 * q^23 - 57 * q^25 - 12 * q^26 - 10 * q^28 + 4 * q^29 - 12 * q^31 + 150 * q^32 - 2 * q^34 - 6 * q^35 + 12 * q^37 + 12 * q^38 - 66 * q^40 + 4 * q^41 - 60 * q^43 - 20 * q^44 + 76 * q^46 + 25 * q^47 + 31 * q^49 - 137 * q^50 + 118 * q^52 - 48 * q^53 + 93 * q^55 - 228 * q^56 - 120 * q^58 - 57 * q^59 + 72 * q^61 + 179 * q^62 + 249 * q^64 + 39 * q^65 + 40 * q^67 - 94 * q^68 + 94 * q^70 - 30 * q^71 - 205 * q^73 - 66 * q^74 - 216 * q^76 + 46 * q^77 + 4 * q^79 + 356 * q^80 - 28 * q^82 - 4 * q^83 + 50 * q^85 + 18 * q^86 - 162 * q^88 - 26 * q^89 - 198 * q^91 - 10 * q^92 - 4 * q^94 + 326 * q^95 - 20 * q^97 + 143 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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