LMFDB - Embedded newform 531.2.i.b.307.3

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			307.3
Character	$\chi$	$=$	531.307
Dual form			531.2.i.b.64.3

$q$-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 $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{26}{29}\right)$

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	−0.592594	−	0.805501i	$-0.701896\pi$
$2$	−0.815839	+	0.274888i	−0.576885	+	0.194375i	0.0157086	+	0.999877i	$0.495000\pi$
$3$		0			0
$3$		0			0
$4$	−1.00216	+	0.761819i	−0.501078	+	0.380910i
$5$	−1.45570	−	3.65354i	−0.651010	−	1.63391i	−0.767750	−	0.640749i	$-0.778624\pi$
$5$	−1.45570	−	3.65354i	−0.651010	−	1.63391i	0.116740	−	0.993162i	$-0.462755\pi$
$6$		0			0
$7$	0.847760	+	0.392216i	0.320423	+	0.148244i	0.573507	−	0.819201i	$-0.305583\pi$
$7$	0.847760	+	0.392216i	0.320423	+	0.148244i	−0.253083	+	0.967444i	$0.581445\pi$
$8$	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	0.849764	+	0.527164i	$0.176745\pi$
$11$	1.30482	+	4.69955i	0.393419	+	1.41697i	−0.456345	+	0.889803i	$0.650842\pi$
$12$		0			0
$13$	−1.78293	−	3.36297i	−0.494496	−	0.932719i	−0.997650	−	0.0685218i	$-0.978172\pi$
$13$	−1.78293	−	3.36297i	−0.494496	−	0.932719i	0.503153	−	0.864197i	$-0.332173\pi$
$14$	−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	−0.880614	−	0.473834i	$-0.842870\pi$
$17$	−4.49242	+	2.07842i	−1.08957	+	0.504090i	−0.208959	+	0.977924i	$0.567007\pi$
$18$		0			0
$19$	−1.47865	−	0.325475i	−0.339225	−	0.0746691i	0.0420909	−	0.999114i	$-0.486598\pi$
$19$	−1.47865	−	0.325475i	−0.339225	−	0.0746691i	−0.381316	+	0.924445i	$0.624529\pi$
$20$	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	0.986649	+	0.162860i	$0.0520718\pi$
$23$	0.497085	+	3.03208i	0.103649	+	0.632233i	−0.883000	+	0.469373i	$0.844480\pi$
$24$		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	−0.651914	−	0.758293i	$-0.726034\pi$
$29$	−8.77673	−	2.95723i	−1.62980	−	0.549143i	−0.977884	+	0.209150i	$0.932930\pi$
$30$		0			0
$31$	−7.13289	+	1.57007i	−1.28110	+	0.281992i	−0.802825	−	0.596215i	$-0.796670\pi$
$31$	−7.13289	+	1.57007i	−1.28110	+	0.281992i	−0.478280	+	0.878208i	$0.658739\pi$
$32$	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	0.974281	−	0.225338i	$-0.0723488\pi$
$37$	2.45943	+	3.62739i	0.404328	+	0.596339i	−0.569953	+	0.821678i	$0.693038\pi$
$38$	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	−0.438427	−	0.898767i	$-0.644464\pi$
$41$	1.69060	−	10.3122i	0.264027	−	1.61050i	0.702454	−	0.711729i	$-0.252088\pi$
$42$		0			0
$43$	−0.416141	+	1.49880i	−0.0634609	+	0.228565i	−0.988479	−	0.151357i	$-0.951636\pi$
$43$	−0.416141	+	1.49880i	−0.0634609	+	0.228565i	0.925018	+	0.379923i	$0.124049\pi$
$44$	−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	0.615421	+	0.788199i	$0.288986\pi$
$47$	−2.56001	+	6.42514i	−0.373416	+	0.937202i	−0.988837	+	0.149004i	$0.952393\pi$
$48$		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	−0.722908	−	0.690944i	$-0.757195\pi$
$53$	0.552469	−	0.650416i	0.0758874	−	0.0893416i	0.798796	+	0.601603i	$0.205471\pi$
$54$		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	−0.473398	−	0.880849i	$-0.656973\pi$
$61$	−2.47741	+	0.834738i	−0.317200	+	0.106877i	0.156198	+	0.987726i	$0.450076\pi$
$62$	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	−0.997496	−	0.0707238i	$-0.977469\pi$
$67$	−4.60495	+	6.79179i	−0.562584	+	0.829749i	0.434912	+	0.900473i	$0.356779\pi$
$68$	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	−0.966573	−	0.256390i	$-0.917467\pi$
$71$	−0.745934	+	1.87215i	−0.0885261	+	0.222184i	0.878047	+	0.478574i	$0.158846\pi$
$72$		0			0
$73$	−10.4550	−	1.13705i	−1.22367	−	0.133082i	−0.526617	−	0.850102i	$-0.676540\pi$
$73$	−10.4550	−	1.13705i	−1.22367	−	0.133082i	−0.697052	+	0.717020i	$0.745505\pi$
$74$	−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	0.684604	−	0.728915i	$-0.259975\pi$
$79$	3.21106	+	1.93203i	0.361273	+	0.217371i	−0.323331	+	0.946286i	$0.604803\pi$
$80$	−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	−0.983007	−	0.183568i	$-0.941235\pi$
$83$	0.128318	−	2.36669i	0.0140848	−	0.259778i	0.997092	−	0.0762102i	$-0.0242820\pi$
$84$		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	0.0740534	−	0.997254i	$-0.476406\pi$
$89$	−4.43874	−	1.49559i	−0.470506	−	0.158532i	−0.544559	+	0.838722i	$0.683303\pi$
$90$		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	−0.480287	−	0.877112i	$-0.659467\pi$
$97$	−7.49293	+	0.814905i	−0.760791	+	0.0827411i	−0.280505	+	0.959853i	$0.590502\pi$
$98$	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	−0.0364579	−	0.999335i	$-0.511607\pi$
$101$	7.05094	−	3.26211i	0.701595	−	0.324592i	0.738053	+	0.674743i	$0.235745\pi$
$102$		0			0
$103$	14.5612	+	11.0691i	1.43475	+	1.09067i	0.979760	+	0.200177i	$0.0641516\pi$
$103$	14.5612	+	11.0691i	1.43475	+	1.09067i	0.454994	+	0.890495i	$0.349641\pi$
$104$	−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	−0.890043	−	0.455876i	$-0.849326\pi$
$107$	−3.74902	−	13.5028i	−0.362432	−	1.30536i	0.527611	−	0.849486i	$-0.323088\pi$
$108$		0			0
$109$	3.08301	−	5.81517i	0.295299	−	0.556992i	−0.690822	−	0.723025i	$-0.742751\pi$
$109$	3.08301	−	5.81517i	0.295299	−	0.556992i	0.986120	+	0.166033i	$0.0530958\pi$
$110$	−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	0.999811	−	0.0194234i	$-0.00618306\pi$
$113$	2.77017	+	6.95259i	0.260595	+	0.654045i	−0.739216	+	0.673468i	$0.764804\pi$
$114$		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	−0.608909	−	0.793240i	$-0.708393\pi$
$127$	4.38785	−	8.27636i	0.389359	−	0.734408i	0.998268	+	0.0588315i	$0.0187375\pi$
$128$	−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	0.863030	−	0.505153i	$-0.168564\pi$
$131$	−0.450959	−	0.850600i	−0.0394005	−	0.0743172i	−0.902431	+	0.430835i	$0.858219\pi$
$132$		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	−0.0292236	−	0.999573i	$-0.509303\pi$
$137$	−5.56507	−	1.22496i	−0.475456	−	0.104656i	−0.446232	+	0.894917i	$0.647235\pi$
$138$		0			0
$139$	2.38178	−	0.259034i	0.202020	−	0.0219710i	−0.00654964	−	0.999979i	$-0.502085\pi$
$139$	2.38178	−	0.259034i	0.202020	−	0.0219710i	0.208569	+	0.978008i	$0.433119\pi$
$140$	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	0.227589	−	0.973757i	$-0.426916\pi$
$149$	10.2903	−	2.26506i	0.843012	−	0.185561i	0.615424	+	0.788196i	$0.288985\pi$
$150$		0			0
$151$	−9.90209	−	9.37975i	−0.805820	−	0.763313i	0.169164	−	0.985588i	$-0.445893\pi$
$151$	−9.90209	−	9.37975i	−0.805820	−	0.763313i	−0.974984	+	0.222274i	$0.928652\pi$
$152$	−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	0.567577	−	0.823320i	$-0.307881\pi$
$157$	1.32846	+	0.799306i	0.106022	+	0.0637915i	−0.461555	+	0.887112i	$0.652708\pi$
$158$	−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	−0.491829	−	0.870692i	$-0.663672\pi$
$163$	−14.8014	−	1.60975i	−1.15933	−	0.126085i	−0.667504	+	0.744607i	$0.732637\pi$
$164$	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	0.370756	−	0.928730i	$-0.379099\pi$
$167$	−7.82764	−	9.21542i	−0.605721	−	0.713110i	−0.976477	+	0.215620i	$0.930823\pi$
$168$		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	0.317818	−	0.948152i	$-0.397050\pi$
$173$	17.3150	−	13.1625i	1.31644	−	1.00073i	0.998617	−	0.0525764i	$-0.0167433\pi$
$174$		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	−0.480898	−	0.876777i	$-0.659689\pi$
$179$	−4.45704	+	1.50175i	−0.333135	+	0.112246i	0.147763	+	0.989023i	$0.452793\pi$
$180$		0			0
$181$	19.5700	−	14.8767i	1.45462	−	1.10578i	0.481242	−	0.876588i	$-0.340186\pi$
$181$	19.5700	−	14.8767i	1.45462	−	1.10578i	0.973382	−	0.229189i	$-0.0736073\pi$
$182$	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	−0.571530	−	0.820581i	$-0.693650\pi$
$191$	−18.0506	−	1.96313i	−1.30610	−	0.142047i	−0.734568	+	0.678535i	$0.762615\pi$
$192$		0			0
$193$	3.19213	−	11.4970i	0.229775	−	0.827573i	−0.755290	−	0.655390i	$-0.772504\pi$
$193$	3.19213	−	11.4970i	0.229775	−	0.827573i	0.985065	−	0.172183i	$-0.0550820\pi$
$194$	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	0.528752	−	0.848776i	$-0.322660\pi$
$197$	0.372221	+	0.223958i	0.0265196	+	0.0159563i	−0.502232	+	0.864733i	$0.667488\pi$
$198$		0			0
$199$	1.20428	+	1.77618i	0.0853692	+	0.125910i	0.867976	−	0.496606i	$-0.165421\pi$
$199$	1.20428	+	1.77618i	0.0853692	+	0.125910i	−0.782607	+	0.622516i	$0.786110\pi$
$200$	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	−0.780965	−	0.624575i	$-0.785272\pi$
$211$	−2.89916	+	2.74623i	−0.199586	+	0.189058i	0.581379	+	0.813633i	$0.302514\pi$
$212$	−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	−0.990110	−	0.140294i	$-0.955195\pi$
$223$	−8.22210	−	15.5085i	−0.550593	−	1.03853i	0.439517	−	0.898234i	$-0.355150\pi$
$224$	−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	−0.994283	−	0.106780i	$-0.965946\pi$
$227$	−5.24199	+	9.88745i	−0.347923	+	0.656253i	0.646359	+	0.763033i	$0.276291\pi$
$228$		0			0
$229$	14.8892	+	6.88847i	0.983905	+	0.455203i	0.844804	−	0.535075i	$-0.179717\pi$
$229$	14.8892	+	6.88847i	0.983905	+	0.455203i	0.139101	+	0.990278i	$0.455579\pi$
$230$	−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	−0.292850	−	0.956159i	$-0.594603\pi$
$233$	6.33096	−	3.80921i	0.414755	−	0.249550i	0.707604	+	0.706609i	$0.249776\pi$
$234$		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	−0.836965	−	0.547257i	$-0.815672\pi$
$239$	−11.5251	+	6.93444i	−0.745499	+	0.448552i	0.0914663	+	0.995808i	$0.470845\pi$
$240$		0			0
$241$	1.99880	+	5.01661i	0.128754	+	0.323149i	0.979195	−	0.202922i	$-0.0650439\pi$
$241$	1.99880	+	5.01661i	0.128754	+	0.323149i	−0.850441	+	0.526071i	$0.823665\pi$
$242$	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	0.359742	−	0.933052i	$-0.382865\pi$
$251$	−7.01937	−	5.33599i	−0.443059	−	0.336805i	−0.802801	+	0.596247i	$0.796658\pi$
$252$		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	−0.978744	−	0.205088i	$-0.934252\pi$
$257$	−30.3073	+	3.29612i	−1.89052	+	0.205606i	−0.911773	+	0.410694i	$0.865287\pi$
$258$		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	0.971987	+	0.235034i	$0.0755201\pi$
$263$	0.504510	+	9.30515i	0.0311094	+	0.573780i	−0.940878	+	0.338746i	$0.889997\pi$
$264$		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	0.201477	−	0.979493i	$-0.435426\pi$
$269$	−12.5579	−	11.8955i	−0.765672	−	0.725283i	−0.967149	+	0.254210i	$0.918184\pi$
$270$		0			0
$271$	1.01650	−	18.7482i	0.0617479	−	1.13887i	−0.789376	−	0.613909i	$-0.789596\pi$
$271$	1.01650	−	18.7482i	0.0617479	−	1.13887i	0.851124	−	0.524964i	$-0.175921\pi$
$272$	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	0.538666	+	0.842519i	$0.318929\pi$
$277$	−4.00805	+	24.4480i	−0.240820	+	1.46894i	−0.779486	+	0.626419i	$0.784520\pi$
$278$	−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	−0.332049	−	0.943262i	$-0.607740\pi$
$281$	−14.4013	−	1.56624i	−0.859109	−	0.0934337i	−0.527060	+	0.849828i	$0.676706\pi$
$282$		0			0
$283$	−9.83311	+	24.6792i	−0.584518	+	1.46703i	0.277789	+	0.960642i	$0.410398\pi$
$283$	−9.83311	+	24.6792i	−0.584518	+	1.46703i	−0.862306	+	0.506387i	$0.830981\pi$
$284$	−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	0.445015	−	0.895523i	$-0.353198\pi$
$293$	22.9583	−	7.73554i	1.34124	−	0.451915i	0.896221	+	0.443608i	$0.146302\pi$
$294$		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	0.640234	+	0.768180i	$0.278837\pi$
$307$	−6.18243	+	15.5167i	−0.352850	+	0.885586i	−0.993084	+	0.117406i	$0.962542\pi$
$308$	−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	−0.430009	−	0.902825i	$-0.641490\pi$
$311$	7.12289	−	25.6543i	0.403902	−	1.45472i	0.833911	−	0.551899i	$-0.186097\pi$
$312$		0			0
$313$	0.351118	−	2.14173i	0.0198464	−	0.121058i	−0.975045	−	0.222006i	$-0.928739\pi$
$313$	0.351118	−	2.14173i	0.0198464	−	0.121058i	0.994892	+	0.100949i	$0.0321878\pi$
$314$	−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	0.887122	−	0.461535i	$-0.152701\pi$
$317$	2.31476	+	3.41401i	0.130010	+	0.191750i	−0.757113	+	0.653284i	$0.773391\pi$
$318$		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	−0.905328	−	0.424714i	$-0.860375\pi$
$331$	−3.32944	−	20.3087i	−0.183003	−	1.11627i	0.722325	−	0.691554i	$-0.243074\pi$
$332$	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	−0.632847	−	0.774277i	$-0.718114\pi$
$337$	−8.30529	+	3.84244i	−0.452418	+	0.209311i	0.180428	+	0.983588i	$0.442252\pi$
$338$	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	0.141296	−	0.989967i	$-0.454873\pi$
$347$	−9.71905	−	4.49651i	−0.521746	−	0.241385i	−0.663042	+	0.748582i	$0.730735\pi$
$348$		0			0
$349$	4.14086	+	10.3928i	0.221655	+	0.556312i	0.997184	−	0.0750004i	$-0.0238958\pi$
$349$	4.14086	+	10.3928i	0.221655	+	0.556312i	−0.775528	+	0.631313i	$0.782516\pi$
$350$	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	0.888297	+	0.459270i	$0.151889\pi$
$359$	10.5960	+	26.5940i	0.559237	+	1.40358i	−0.329060	+	0.944309i	$0.606732\pi$
$360$		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	0.869734	−	0.493521i	$-0.164291\pi$
$367$	−0.514026	−	0.969555i	−0.0268319	−	0.0506104i	−0.896566	+	0.442911i	$0.853946\pi$
$368$	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	0.466629	−	0.884453i	$-0.345468\pi$
$373$	10.0189	+	2.20532i	0.518758	+	0.114187i	0.0521288	+	0.998640i	$0.483399\pi$
$374$	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	−0.863410	−	0.504502i	$-0.831676\pi$
$379$	−7.91161	+	7.49428i	−0.406392	+	0.384955i	0.457018	+	0.889457i	$0.348917\pi$
$380$	−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	0.767959	−	0.640499i	$-0.221273\pi$
$383$	19.4082	+	6.53938i	0.991712	+	0.334147i	0.223753	+	0.974646i	$0.428169\pi$
$384$		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	0.761326	+	0.648370i	$0.224549\pi$
$389$	−1.29459	+	23.8773i	−0.0656382	+	1.21063i	−0.826964	+	0.562255i	$0.809934\pi$
$390$		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	0.251395	+	0.967885i	$0.419111\pi$
$397$	−9.22544	+	33.2270i	−0.463011	+	1.66762i	−0.714406	+	0.699731i	$0.753303\pi$
$398$	−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	−0.715410	−	0.698705i	$-0.753760\pi$
$401$	5.69657	−	14.2973i	0.284473	−	0.713974i	0.999883	−	0.0152691i	$-0.00486050\pi$
$402$		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	0.221039	−	0.975265i	$-0.429055\pi$
$409$	24.6708	−	18.7542i	1.21989	−	0.927336i	0.998851	+	0.0479285i	$0.0152620\pi$
$410$	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	−0.117358	−	0.993090i	$-0.537442\pi$
$419$	18.0466	−	21.2461i	0.881636	−	1.03794i	0.998994	−	0.0448523i	$-0.0142817\pi$
$420$		0			0
$421$	19.5363	−	28.8138i	0.952139	−	1.40430i	0.0378290	−	0.999284i	$-0.487956\pi$
$421$	19.5363	−	28.8138i	0.952139	−	1.40430i	0.914310	−	0.405016i	$-0.132734\pi$
$422$	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	0.308126	+	0.951345i	$0.400298\pi$
$431$	−5.97149	+	36.4245i	−0.287637	+	1.75451i	−0.595763	+	0.803160i	$0.703150\pi$
$432$		0			0
$433$	−19.1067	−	11.4961i	−0.918210	−	0.552469i	−0.0238002	−	0.999717i	$-0.507577\pi$
$433$	−19.1067	−	11.4961i	−0.918210	−	0.552469i	−0.894410	+	0.447248i	$0.852404\pi$
$434$	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	0.982630	−	0.185577i	$-0.0594155\pi$
$439$	17.8204	+	16.8804i	0.850523	+	0.805658i	−0.132107	+	0.991236i	$0.542174\pi$
$440$	−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	0.135491	−	0.990779i	$-0.456739\pi$
$443$	−7.49796	−	2.52636i	−0.356239	−	0.120031i	−0.491730	+	0.870748i	$0.663635\pi$
$444$		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	0.998340	−	0.0576025i	$-0.0183456\pi$
$449$	0.717636	+	4.37739i	0.0338674	+	0.206582i	−0.964472	+	0.264184i	$0.914897\pi$
$450$		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	0.976017	−	0.217694i	$-0.0698536\pi$
$457$	21.9627	+	16.6956i	1.02737	+	0.780986i	0.0513529	+	0.998681i	$0.483647\pi$
$458$	−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	0.860833	+	0.508888i	$0.169943\pi$
$461$	8.27878	+	29.8175i	0.385581	+	1.38874i	−0.475252	+	0.879850i	$0.657643\pi$
$462$		0			0
$463$	−3.53517	+	6.66804i	−0.164293	+	0.309890i	−0.951966	−	0.306204i	$-0.900941\pi$
$463$	−3.53517	+	6.66804i	−0.164293	+	0.309890i	0.787673	+	0.616094i	$0.211286\pi$
$464$	−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	0.965398	−	0.260782i	$-0.0839803\pi$
$467$	1.84084	+	4.62016i	0.0851838	+	0.213795i	−0.880214	+	0.474577i	$0.842601\pi$
$468$		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	−0.235687	−	0.971829i	$-0.575734\pi$
$479$	−24.7085	−	11.4313i	−1.12896	−	0.522312i	−0.893272	+	0.449517i	$0.851596\pi$
$480$		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	0.0893724	−	0.995998i	$-0.471514\pi$
$487$	−18.6787	−	14.1992i	−0.846412	−	0.643426i	−0.935784	+	0.352573i	$0.885307\pi$
$488$	−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	0.247354	−	0.968925i	$-0.420439\pi$
$491$	1.44042	+	0.317060i	0.0650052	+	0.0143087i	−0.182349	+	0.983234i	$0.558370\pi$
$492$		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	−0.847023	−	0.531556i	$-0.821608\pi$
$499$	−1.39473	−	25.7242i	−0.0624366	−	1.15158i	0.784587	−	0.620019i	$-0.212875\pi$
$500$	−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	−0.382550	−	0.923935i	$-0.624954\pi$
$503$	−7.66561	+	1.68733i	−0.341792	+	0.0752342i	0.0407574	+	0.999169i	$0.487023\pi$
$504$		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	−0.988514	−	0.151130i	$-0.951709\pi$
$509$	−17.2146	−	25.3896i	−0.763024	−	1.12538i	0.225490	−	0.974245i	$-0.427602\pi$
$510$		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	0.908792	−	0.417250i	$-0.137006\pi$
$521$	7.98919	+	9.40560i	0.350013	+	0.412067i	−0.558779	+	0.829317i	$0.688730\pi$
$522$		0			0
$523$	−10.5802	+	15.6047i	−0.462641	+	0.682345i	−0.985423	−	0.170122i	$-0.945584\pi$
$523$	−10.5802	+	15.6047i	−0.462641	+	0.682345i	0.522782	+	0.852467i	$0.324894\pi$
$524$	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	0.662664	−	0.748916i	$-0.269426\pi$
$541$	−4.27027	−	5.02736i	−0.183593	−	0.216143i	−0.846258	+	0.532774i	$0.821150\pi$
$542$	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	0.634553	+	0.772880i	$0.281184\pi$
$547$	−7.19485	+	25.9135i	−0.307629	+	1.10798i	−0.942182	+	0.335102i	$0.891229\pi$
$548$	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	0.880441	−	0.474155i	$-0.157246\pi$
$557$	10.7301	+	10.1641i	0.454647	+	0.430665i	−0.425794	+	0.904820i	$0.640005\pi$
$558$		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	−0.876523	−	0.481360i	$-0.840143\pi$
$563$	−1.35680	−	25.0247i	−0.0571823	−	1.05467i	0.819341	−	0.573307i	$-0.194340\pi$
$564$		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	−0.0554789	−	0.998460i	$-0.517669\pi$
$569$	2.50413	−	0.272340i	0.104979	−	0.0114171i	0.160457	+	0.987043i	$0.448703\pi$
$570$		0			0
$571$	18.9840	+	4.17870i	0.794456	+	0.174873i	0.593613	−	0.804750i	$-0.297701\pi$
$571$	18.9840	+	4.17870i	0.794456	+	0.174873i	0.200843	+	0.979623i	$0.435632\pi$
$572$	−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	0.614447	−	0.788958i	$-0.289379\pi$
$577$	−9.20921	−	17.3704i	−0.383384	−	0.723139i	−0.997832	+	0.0658184i	$0.979034\pi$
$578$	−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	−0.461419	−	0.887182i	$-0.652659\pi$
$587$	2.57509	−	1.54938i	0.106285	−	0.0639497i	0.567704	+	0.823233i	$0.307832\pi$
$588$		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	−0.213637	−	0.976913i	$-0.568531\pi$
$593$	13.3789	−	8.04984i	0.549407	−	0.330567i	0.763045	+	0.646346i	$0.223704\pi$
$594$		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	−0.831961	−	0.554834i	$-0.812782\pi$
$599$	2.30439	−	4.34655i	0.0941550	−	0.177595i	0.926116	+	0.377239i	$0.123127\pi$
$600$		0			0
$601$	−5.26560	−	18.9650i	−0.214788	−	0.773598i	−0.989899	−	0.141773i	$-0.954720\pi$
$601$	−5.26560	−	18.9650i	−0.214788	−	0.773598i	0.775111	−	0.631825i	$-0.217694\pi$
$602$	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	−0.175495	−	0.984480i	$-0.556153\pi$
$607$	11.3634	−	5.25726i	0.461225	−	0.213386i	0.636720	+	0.771095i	$0.280291\pi$
$608$	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	0.952807	−	0.303575i	$-0.0981804\pi$
$613$	−1.16504	−	7.10644i	−0.0470556	−	0.287026i	−0.999863	+	0.0165488i	$0.994732\pi$
$614$	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	0.819870	+	0.572550i	$0.194046\pi$
$617$	1.65703	+	30.5622i	0.0667097	+	1.23039i	−0.753160	+	0.657838i	$0.771471\pi$
$618$		0			0
$619$	−19.9157	−	6.71040i	−0.800481	−	0.269714i	−0.110815	−	0.993841i	$-0.535346\pi$
$619$	−19.9157	−	6.71040i	−0.800481	−	0.269714i	−0.689666	+	0.724127i	$0.742243\pi$
$620$	−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	0.714955	+	0.699171i	$0.246447\pi$
$631$	−4.66776	+	28.4721i	−0.185821	+	1.13346i	−0.900775	+	0.434285i	$0.857001\pi$
$632$	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	0.190786	+	0.981632i	$0.438896\pi$
$641$	−20.0454	+	29.5647i	−0.791744	+	1.16774i	−0.982530	+	0.186104i	$0.940414\pi$
$642$		0			0
$643$	15.0536	−	17.7225i	0.593658	−	0.698908i	−0.380499	−	0.924781i	$-0.624248\pi$
$643$	15.0536	−	17.7225i	0.593658	−	0.698908i	0.974157	+	0.225873i	$0.0725236\pi$
$644$	−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	0.216856	−	0.976204i	$-0.430420\pi$
$647$	24.9343	−	8.40133i	0.980267	−	0.330290i	0.763411	+	0.645913i	$0.223523\pi$
$648$		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	−0.853753	−	0.520679i	$-0.825679\pi$
$653$	−14.8329	+	11.2757i	−0.580456	+	0.441251i	0.273297	+	0.961930i	$0.411886\pi$
$654$		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	0.938318	−	0.345774i	$-0.112384\pi$
$659$	11.4312	+	13.4578i	0.445296	+	0.524243i	−0.493022	+	0.870017i	$0.664108\pi$
$660$		0			0
$661$	6.54181	−	16.4187i	0.254447	−	0.638614i	−0.745153	−	0.666893i	$-0.767624\pi$
$661$	6.54181	−	16.4187i	0.254447	−	0.638614i	0.999600	+	0.0282798i	$0.00900293\pi$
$662$	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	−0.997327	−	0.0730723i	$-0.976720\pi$
$673$	0.0532889	−	0.982856i	0.00205414	−	0.0378863i	0.999381	+	0.0351860i	$0.0112024\pi$
$674$	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	−0.0279859	−	0.999608i	$-0.508909\pi$
$677$	9.53187	−	2.09812i	0.366339	−	0.0806374i	0.394325	+	0.918971i	$0.370978\pi$
$678$		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	−0.940411	−	0.340040i	$-0.889560\pi$
$683$	−17.0339	+	16.1353i	−0.651783	+	0.617402i	0.288628	+	0.957441i	$0.406801\pi$
$684$		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	−0.154114	−	0.988053i	$-0.549252\pi$
$691$	13.1217	−	6.07073i	0.499172	−	0.230941i	0.653286	+	0.757112i	$0.273390\pi$
$692$	−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	0.138215	−	0.990402i	$-0.455863\pi$
$701$	−13.9571	−	6.45725i	−0.527153	−	0.243887i	−0.665368	+	0.746515i	$0.731725\pi$
$702$		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	0.981345	+	0.192255i	$0.0615801\pi$
$719$	6.42442	+	23.1387i	0.239590	+	0.862927i	−0.741755	+	0.670671i	$0.766006\pi$
$720$		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	−0.806870	−	0.590729i	$-0.798840\pi$
$727$	−48.1883	−	10.6071i	−1.78721	−	0.393394i	−0.980336	+	0.197335i	$0.936771\pi$
$728$	−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	−0.513228	−	0.858252i	$-0.671551\pi$
$733$	8.55482	−	8.10355i	0.315979	−	0.299312i	0.829208	+	0.558941i	$0.188792\pi$
$734$	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	−0.849950	−	0.526863i	$-0.823368\pi$
$739$	−38.0617	+	8.37800i	−1.40012	+	0.308190i	−0.550170	+	0.835052i	$0.685437\pi$
$740$	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	0.941161	+	0.337958i	$0.109736\pi$
$743$	−0.845612	+	15.5964i	−0.0310225	+	0.572176i	−0.972184	+	0.234219i	$0.924747\pi$
$744$		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	0.691581	+	0.722299i	$0.256914\pi$
$751$	−7.49205	+	26.9839i	−0.273389	+	0.984658i	−0.964970	+	0.262359i	$0.915499\pi$
$752$	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	0.924269	−	0.381742i	$-0.124676\pi$
$757$	10.9511	+	12.8927i	0.398026	+	0.468592i	−0.526243	+	0.850334i	$0.676400\pi$
$758$	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	−0.730838	−	0.682551i	$-0.760871\pi$
$761$	1.68160	−	1.97973i	0.0609578	−	0.0717650i	0.791796	+	0.610786i	$0.209146\pi$
$762$		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	−0.581711	−	0.813395i	$-0.697617\pi$
$769$	−15.3230	+	5.16292i	−0.552561	+	0.186180i	0.0291497	+	0.999575i	$0.490720\pi$
$770$	−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	−0.865710	−	0.500546i	$-0.833133\pi$
$773$	−6.44197	+	7.58408i	−0.231702	+	0.272780i	0.634008	+	0.773326i	$0.281408\pi$
$774$		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	0.792347	−	0.610071i	$-0.208859\pi$
$787$	17.5190	+	10.5408i	0.624484	+	0.375740i	−0.167863	+	0.985810i	$0.553687\pi$
$788$	−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	−0.217938	−	0.975963i	$-0.569933\pi$
$797$	−27.7248	−	9.34158i	−0.982064	−	0.330896i	−0.764126	+	0.645067i	$0.776830\pi$
$798$		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	−0.306097	−	0.952000i	$-0.599023\pi$
$809$	6.29495	−	2.91235i	0.221319	−	0.102393i	0.527416	+	0.849607i	$0.323161\pi$
$810$		0			0
$811$	2.57537	+	1.95774i	0.0904334	+	0.0687457i	0.649414	−	0.760435i	$-0.275014\pi$
$811$	2.57537	+	1.95774i	0.0904334	+	0.0687457i	−0.558981	+	0.829181i	$0.688807\pi$
$812$	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	−0.838002	−	0.545667i	$-0.816276\pi$
$821$	−17.3314	−	43.4986i	−0.604871	−	1.51811i	0.233131	−	0.972445i	$-0.425103\pi$
$822$		0			0
$823$	−17.8352	+	10.7311i	−0.621695	+	0.374061i	−0.791280	−	0.611454i	$-0.790585\pi$
$823$	−17.8352	+	10.7311i	−0.621695	+	0.374061i	0.169585	+	0.985516i	$0.445757\pi$
$824$	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	−0.801917	−	0.597435i	$-0.796187\pi$
$829$	−18.7064	+	11.2553i	−0.649701	+	0.390912i	0.152216	+	0.988347i	$0.451359\pi$
$830$	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	0.862979	−	0.505240i	$-0.168596\pi$
$839$	−1.14401	−	2.15783i	−0.0394956	−	0.0744966i	−0.902474	+	0.430744i	$0.858251\pi$
$840$		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	0.549825	+	0.835280i	$0.314694\pi$
$853$	2.73173	+	50.3838i	0.0935327	+	1.72511i	−0.456292	+	0.889830i	$0.650823\pi$
$854$	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	−0.874451	−	0.485114i	$-0.838778\pi$
$857$	−42.8693	+	9.43625i	−1.46439	+	0.322336i	−0.589936	+	0.807450i	$0.700847\pi$
$858$		0			0
$859$	40.5723	+	38.4322i	1.38431	+	1.31129i	0.899667	+	0.436577i	$0.143809\pi$
$859$	40.5723	+	38.4322i	1.38431	+	1.31129i	0.484643	+	0.874712i	$0.338949\pi$
$860$	−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	0.743002	−	0.669289i	$-0.233401\pi$
$863$	−4.51714	−	6.66228i	−0.153765	−	0.226787i	−0.896767	+	0.442502i	$0.854091\pi$
$864$		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	−0.541470	−	0.840720i	$-0.682132\pi$
$877$	13.0290	−	19.2163i	0.439958	−	0.648889i	0.981428	+	0.191831i	$0.0614425\pi$
$878$	−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	−0.820749	−	0.571290i	$-0.806443\pi$
$881$	−14.5397	+	11.0528i	−0.489856	+	0.372379i	0.330893	+	0.943668i	$0.392650\pi$
$882$		0			0
$883$	−21.5958	+	7.27646i	−0.726755	+	0.244872i	−0.658272	−	0.752780i	$-0.728712\pi$
$883$	−21.5958	+	7.27646i	−0.726755	+	0.244872i	−0.0684829	+	0.997652i	$0.521816\pi$
$884$	−23.7181			−0.797725
$885$		0			0
$886$	6.81159			0.228840
$887$	−22.3149	+	7.51876i	−0.749261	+	0.252455i	−0.667922	−	0.744231i	$-0.732816\pi$
$887$	−22.3149	+	7.51876i	−0.749261	+	0.252455i	−0.0813386	+	0.996687i	$0.525920\pi$
$888$		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	0.999955	+	0.00950243i	$0.00302476\pi$
$907$	19.2342	+	28.3683i	0.638661	+	0.941954i	−0.361294	+	0.932452i	$0.617665\pi$
$908$	−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	0.573950	−	0.818891i	$-0.305410\pi$
$911$	−6.41888	−	6.08028i	−0.212667	−	0.201449i	−0.786617	+	0.617442i	$0.788169\pi$
$912$		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	−0.378442	−	0.925625i	$-0.623540\pi$
$919$	15.9256	−	15.0855i	0.525338	−	0.497626i	0.903779	+	0.427999i	$0.140781\pi$
$920$	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	0.914767	−	0.403981i	$-0.132374\pi$
$929$	23.4765	+	17.8463i	0.770238	+	0.585520i	−0.144530	+	0.989500i	$0.546167\pi$
$930$		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	−0.0530418	−	0.998592i	$-0.516892\pi$
$937$	−25.9720	−	12.0159i	−0.848469	−	0.392544i	−0.795428	+	0.606049i	$0.792754\pi$
$938$	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	0.0135832	−	0.999908i	$-0.495676\pi$
$941$	27.7117	−	16.6736i	0.903376	−	0.543543i	0.889793	+	0.456364i	$0.150849\pi$
$942$		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	0.768161	−	0.640257i	$-0.221172\pi$
$947$	52.1193	−	31.3591i	1.69365	−	1.01903i	0.925488	−	0.378778i	$-0.123655\pi$
$948$		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	−0.935531	−	0.353246i	$-0.885078\pi$
$953$	−3.64723	+	6.87940i	−0.118145	+	0.222846i	0.817385	+	0.576091i	$0.195423\pi$
$954$		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	0.959300	+	0.282388i	$0.0911265\pi$
$967$	4.36544	+	26.6280i	0.140383	+	0.856300i	−0.818917	+	0.573912i	$0.805425\pi$
$968$	−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	0.812505	+	0.582954i	$0.198103\pi$
$971$	2.11244	+	38.9616i	0.0677913	+	1.25034i	−0.744714	+	0.667384i	$0.767414\pi$
$972$		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	0.833336	−	0.552767i	$-0.186428\pi$
$977$	10.2053	+	9.66694i	0.326495	+	0.309273i	−0.506841	+	0.862040i	$0.669187\pi$
$978$		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	0.298982	−	0.954259i	$-0.403353\pi$
$983$	−12.6688	−	7.62255i	−0.404071	−	0.243122i	−0.703053	+	0.711137i	$0.748180\pi$
$984$		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	−0.0911522	−	0.995837i	$-0.529055\pi$
$991$	20.7725	−	52.1351i	0.659860	−	1.65612i	0.751013	−	0.660288i	$-0.229566\pi$
$992$	−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	−0.989693	−	0.143209i	$-0.954258\pi$
$997$	−21.7319	+	25.5848i	−0.688256	+	0.810278i	0.301436	+	0.953486i	$0.402534\pi$
$998$	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.307.3		140
3.2	odd	2		177.2.e.b.130.3	yes	140
59.5	even	29	inner	531.2.i.b.64.3		140
177.5	odd	58		177.2.e.b.64.3	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.b.64.3	✓	140	177.5	odd	58
177.2.e.b.130.3	yes	140	3.2	odd	2
531.2.i.b.64.3		140	59.5	even	29	inner
531.2.i.b.307.3		140	1.1	even	1	trivial

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

Fields

Representations

Groups

Database

Properties

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