LMFDB - Embedded newform 372.2.ba.a.55.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(43,372)] 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("372.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 0, 19])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.ba (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			55.3
Character	$\chi$	$=$	372.55
Dual form			372.2.ba.a.115.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32319 - 0.499154i) q^{2} +(0.978148 - 0.207912i) q^{3} +(1.50169 + 1.32096i) q^{4} +(-0.474253 + 0.821430i) q^{5} +(-1.39806 - 0.213139i) q^{6} +(-0.788705 + 1.77146i) q^{7} +(-1.32767 - 2.49746i) q^{8} +(0.913545 - 0.406737i) q^{9} +(1.03755 - 0.850186i) q^{10} +(0.536318 + 5.10272i) q^{11} +(1.74352 + 0.979872i) q^{12} +(0.659842 - 0.594124i) q^{13} +(1.92784 - 1.95030i) q^{14} +(-0.293104 + 0.902082i) q^{15} +(0.510143 + 3.96734i) q^{16} +(-5.73859 - 0.603150i) q^{17} +(-1.41182 + 0.0821915i) q^{18} +(5.46511 + 4.92081i) q^{19} +(-1.79725 + 0.607065i) q^{20} +(-0.403163 + 1.89673i) q^{21} +(1.83739 - 7.01960i) q^{22} +(-2.71056 - 1.96934i) q^{23} +(-1.81790 - 2.16685i) q^{24} +(2.05017 + 3.55100i) q^{25} +(-1.16966 + 0.456779i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.52441 + 1.61834i) q^{28} +(0.751196 - 0.244078i) q^{29} +(0.838112 - 1.04733i) q^{30} +(-5.47565 + 1.00861i) q^{31} +(1.30529 - 5.50420i) q^{32} +(1.58551 + 4.87971i) q^{33} +(7.29221 + 3.66253i) q^{34} +(-1.08108 - 1.48799i) q^{35} +(1.90914 + 0.595962i) q^{36} +(8.06562 - 4.65669i) q^{37} +(-4.77516 - 9.23912i) q^{38} +(0.521897 - 0.718330i) q^{39} +(2.68114 + 0.0938422i) q^{40} +(5.14864 + 1.09438i) q^{41} +(1.48022 - 2.30850i) q^{42} +(-3.50291 + 3.89037i) q^{43} +(-5.93510 + 8.37116i) q^{44} +(-0.0991458 + 0.943309i) q^{45} +(2.60360 + 3.95881i) q^{46} +(12.3543 + 4.01414i) q^{47} +(1.32385 + 3.77458i) q^{48} +(2.16790 + 2.40769i) q^{49} +(-0.940277 - 5.72201i) q^{50} +(-5.73859 + 0.603150i) q^{51} +(1.77569 - 0.0205672i) q^{52} +(1.56228 + 3.50893i) q^{53} +(-1.36388 + 0.373930i) q^{54} +(-4.44588 - 1.97943i) q^{55} +(5.47129 - 0.382150i) q^{56} +(6.36878 + 3.67701i) q^{57} +(-1.11581 - 0.0519996i) q^{58} +(-0.746806 - 3.51344i) q^{59} +(-1.63176 + 0.967469i) q^{60} -11.4924i q^{61} +(7.74880 + 1.39861i) q^{62} +1.93911i q^{63} +(-4.47461 + 6.63158i) q^{64} +(0.175099 + 0.823778i) q^{65} +(0.337785 - 7.24822i) q^{66} +(-10.9354 - 6.31358i) q^{67} +(-7.82085 - 8.48618i) q^{68} +(-3.06078 - 1.36275i) q^{69} +(0.687751 + 2.50852i) q^{70} +(-0.969294 - 2.17707i) q^{71} +(-2.22869 - 1.74153i) q^{72} +(-4.85149 + 0.509912i) q^{73} +(-12.9968 + 2.13572i) q^{74} +(2.74366 + 3.04714i) q^{75} +(1.70672 + 14.6087i) q^{76} +(-9.46227 - 3.07448i) q^{77} +(-1.04913 + 0.689983i) q^{78} +(0.620914 - 5.90761i) q^{79} +(-3.50082 - 1.46247i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-6.26639 - 4.01804i) q^{82} +(-5.77470 - 1.22745i) q^{83} +(-3.11093 + 2.31574i) q^{84} +(3.21699 - 4.42780i) q^{85} +(6.57693 - 3.39923i) q^{86} +(0.684034 - 0.394927i) q^{87} +(12.0318 - 8.11415i) q^{88} +(-1.40024 - 1.92727i) q^{89} +(0.602046 - 1.19869i) q^{90} +(0.532047 + 1.63747i) q^{91} +(-1.46901 - 6.53788i) q^{92} +(-5.14629 + 2.12502i) q^{93} +(-14.3434 - 11.4782i) q^{94} +(-6.63394 + 2.15550i) q^{95} +(0.132384 - 5.65530i) q^{96} +(6.37734 - 4.63341i) q^{97} +(-1.66674 - 4.26796i) q^{98} +(2.56542 + 4.44343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{3} + 2 q^{4} + 3 q^{6} - 6 q^{8} + 16 q^{9} - 2 q^{10} + 12 q^{11} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 10 q^{16} + 3 q^{18} + 18 q^{19} - 11 q^{20} - 10 q^{21} + 10 q^{22} + 48 q^{23} - 3 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) $ 128 * q - 16 * q^3 + 2 * q^4 + 3 * q^6 - 6 * q^8 + 16 * q^9 - 2 * q^10 + 12 * q^11 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 10 * q^16 + 3 * q^18 + 18 * q^19 - 11 * q^20 - 10 * q^21 + 10 * q^22 + 48 * q^23 - 3 * q^24 - 68 * q^25 - 20 * q^26 + 32 * q^27 + 21 * q^28 + 26 * q^30 + 30 * q^32 + 4 * q^33 - 20 * q^34 - q^36 - 6 * q^37 + 3 * q^38 + 10 * q^39 - 54 * q^40 - 5 * q^42 - 40 * q^43 - 51 * q^44 - 41 * q^46 + 15 * q^48 + 8 * q^49 - 37 * q^50 + 121 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^55 - 109 * q^56 + 18 * q^57 - 58 * q^58 - 62 * q^59 + 7 * q^60 - 3 * q^62 - 16 * q^64 + 25 * q^66 + 48 * q^67 - 111 * q^68 + 24 * q^69 - 133 * q^70 - 2 * q^72 + 18 * q^73 - 14 * q^74 - 22 * q^75 - 81 * q^76 - 75 * q^78 - 10 * q^79 - 5 * q^80 + 16 * q^81 + 16 * q^82 - 26 * q^83 - 15 * q^84 + 38 * q^86 + 85 * q^88 + 20 * q^89 - 2 * q^90 + 54 * q^91 - 56 * q^92 + 14 * q^93 - 28 * q^94 + 40 * q^95 - 38 * q^96 - 10 * q^97 - 9 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{30}\right)$

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 $

$2$	−1.32319	−	0.499154i	−0.935640	−	0.352956i
$2$	−1.32319	−	0.499154i	−0.935640	−	0.352956i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$4$	1.50169	+	1.32096i	0.750845	+	0.660479i
$5$	−0.474253	+	0.821430i	−0.212092	+	0.367355i	−0.952369	−	0.304948i	$-0.901361\pi$
$5$	−0.474253	+	0.821430i	−0.212092	+	0.367355i	0.740277	+	0.672302i	$0.234694\pi$
$6$	−1.39806	−	0.213139i	−0.570756	−	0.0870137i
$7$	−0.788705	+	1.77146i	−0.298103	+	0.669549i	−0.999046	−	0.0436675i	$-0.986096\pi$
$7$	−0.788705	+	1.77146i	−0.298103	+	0.669549i	0.700944	+	0.713217i	$0.252762\pi$
$8$	−1.32767	−	2.49746i	−0.469401	−	0.882985i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	1.03755	−	0.850186i	0.328102	−	0.268852i
$11$	0.536318	+	5.10272i	0.161706	+	1.53853i	0.711175	+	0.703015i	$0.248163\pi$
$11$	0.536318	+	5.10272i	0.161706	+	1.53853i	−0.549469	+	0.835514i	$0.685170\pi$
$12$	1.74352	+	0.979872i	0.503310	+	0.282865i
$13$	0.659842	−	0.594124i	0.183007	−	0.164780i	−0.572535	−	0.819880i	$-0.694040\pi$
$13$	0.659842	−	0.594124i	0.183007	−	0.164780i	0.755542	+	0.655100i	$0.227373\pi$
$14$	1.92784	−	1.95030i	0.515238	−	0.521240i
$15$	−0.293104	+	0.902082i	−0.0756792	+	0.232917i
$16$	0.510143	+	3.96734i	0.127536	+	0.991834i
$17$	−5.73859	−	0.603150i	−1.39181	−	0.146285i	−0.621232	−	0.783627i	$-0.713367\pi$
$17$	−5.73859	−	0.603150i	−1.39181	−	0.146285i	−0.770581	+	0.637342i	$0.780034\pi$
$18$	−1.41182	+	0.0821915i	−0.332770	+	0.0193727i
$19$	5.46511	+	4.92081i	1.25378	+	1.12891i	0.986232	+	0.165366i	$0.0528806\pi$
$19$	5.46511	+	4.92081i	1.25378	+	1.12891i	0.267550	+	0.963544i	$0.413786\pi$
$20$	−1.79725	+	0.607065i	−0.401878	+	0.135744i
$21$	−0.403163	+	1.89673i	−0.0879773	+	0.413901i
$22$	1.83739	−	7.01960i	0.391734	−	1.49658i
$23$	−2.71056	−	1.96934i	−0.565192	−	0.410636i	0.268164	−	0.963373i	$-0.413583\pi$
$23$	−2.71056	−	1.96934i	−0.565192	−	0.410636i	−0.833355	+	0.552738i	$0.813583\pi$
$24$	−1.81790	−	2.16685i	−0.371078	−	0.442306i
$25$	2.05017	+	3.55100i	0.410034	+	0.710199i
$26$	−1.16966	+	0.456779i	−0.229389	+	0.0895817i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−3.52441	+	1.61834i	−0.666052	+	0.305837i
$29$	0.751196	−	0.244078i	0.139494	−	0.0453242i	−0.238438	−	0.971158i	$-0.576635\pi$
$29$	0.751196	−	0.244078i	0.139494	−	0.0453242i	0.377932	+	0.925833i	$0.376635\pi$
$30$	0.838112	−	1.04733i	0.153018	−	0.191215i
$31$	−5.47565	+	1.00861i	−0.983455	+	0.181151i
$31$	−5.47565	+	1.00861i	−0.983455	+	0.181151i
$32$	1.30529	−	5.50420i	0.230746	−	0.973014i
$33$	1.58551	+	4.87971i	0.276003	+	0.849449i
$34$	7.29221	+	3.66253i	1.25060	+	0.628119i
$35$	−1.08108	−	1.48799i	−0.182737	−	0.251515i
$36$	1.90914	+	0.595962i	0.318191	+	0.0993271i
$37$	8.06562	−	4.65669i	1.32598	−	0.765555i	0.341304	−	0.939953i	$-0.389131\pi$
$37$	8.06562	−	4.65669i	1.32598	−	0.765555i	0.984675	+	0.174398i	$0.0557980\pi$
$38$	−4.77516	−	9.23912i	−0.774633	−	1.49878i
$39$	0.521897	−	0.718330i	0.0835704	−	0.115025i
$40$	2.68114	+	0.0938422i	0.423925	+	0.0148378i
$41$	5.14864	+	1.09438i	0.804083	+	0.170913i	0.591579	−	0.806247i	$-0.298505\pi$
$41$	5.14864	+	1.09438i	0.804083	+	0.170913i	0.212504	+	0.977160i	$0.431838\pi$
$42$	1.48022	−	2.30850i	0.228404	−	0.356210i
$43$	−3.50291	+	3.89037i	−0.534189	+	0.593277i	−0.948468	−	0.316873i	$-0.897367\pi$
$43$	−3.50291	+	3.89037i	−0.534189	+	0.593277i	0.414279	+	0.910150i	$0.364034\pi$
$44$	−5.93510	+	8.37116i	−0.894750	+	1.26200i
$45$	−0.0991458	+	0.943309i	−0.0147798	+	0.140620i
$46$	2.60360	+	3.95881i	0.383880	+	0.583695i
$47$	12.3543	+	4.01414i	1.80205	+	0.585523i	0.999932	−	0.0116383i	$-0.00370467\pi$
$47$	12.3543	+	4.01414i	1.80205	+	0.585523i	0.802121	+	0.597161i	$0.203705\pi$
$48$	1.32385	+	3.77458i	0.191081	+	0.544813i
$49$	2.16790	+	2.40769i	0.309700	+	0.343956i
$50$	−0.940277	−	5.72201i	−0.132975	−	0.809215i
$51$	−5.73859	+	0.603150i	−0.803564	+	0.0844579i
$52$	1.77569	−	0.0205672i	0.246244	−	0.00285216i
$53$	1.56228	+	3.50893i	0.214595	+	0.481988i	0.988483	−	0.151335i	$-0.0483571\pi$
$53$	1.56228	+	3.50893i	0.214595	+	0.481988i	−0.773888	+	0.633323i	$0.781690\pi$
$54$	−1.36388	+	0.373930i	−0.185601	+	0.0508854i
$55$	−4.44588	−	1.97943i	−0.599482	−	0.266907i
$56$	5.47129	−	0.382150i	0.731132	−	0.0510669i
$57$	6.36878	+	3.67701i	0.843565	+	0.487032i
$58$	−1.11581	−	0.0519996i	−0.146513	−	0.00682788i
$59$	−0.746806	−	3.51344i	−0.0972258	−	0.457411i	−0.999647	−	0.0265571i	$-0.991546\pi$
$59$	−0.746806	−	3.51344i	−0.0972258	−	0.457411i	0.902421	−	0.430854i	$-0.141788\pi$
$60$	−1.63176	+	0.967469i	−0.210660	+	0.124900i
$61$		−	11.4924i		−	1.47146i	−0.677277	−	0.735728i	$-0.736840\pi$
$61$		−	11.4924i		−	1.47146i	0.677277	−	0.735728i	$-0.263160\pi$
$62$	7.74880	+	1.39861i	0.984098	+	0.177624i
$63$			1.93911i			0.244304i
$64$	−4.47461	+	6.63158i	−0.559326	+	0.828948i
$65$	0.175099	+	0.823778i	0.0217184	+	0.102177i
$66$	0.337785	−	7.24822i	0.0415785	−	0.892195i
$67$	−10.9354	−	6.31358i	−1.33598	−	0.771327i	−0.349769	−	0.936836i	$-0.613740\pi$
$67$	−10.9354	−	6.31358i	−1.33598	−	0.771327i	−0.986208	+	0.165509i	$0.947073\pi$
$68$	−7.82085	−	8.48618i	−0.948417	−	1.02910i
$69$	−3.06078	−	1.36275i	−0.368475	−	0.164055i
$70$	0.687751	+	2.50852i	0.0822020	+	0.299826i
$71$	−0.969294	−	2.17707i	−0.115034	−	0.258371i	0.846848	−	0.531835i	$-0.178497\pi$
$71$	−0.969294	−	2.17707i	−0.115034	−	0.258371i	−0.961882	+	0.273464i	$0.911831\pi$
$72$	−2.22869	−	1.74153i	−0.262654	−	0.205242i
$73$	−4.85149	+	0.509912i	−0.567824	+	0.0596807i	−0.384090	−	0.923295i	$-0.625485\pi$
$73$	−4.85149	+	0.509912i	−0.567824	+	0.0596807i	−0.183733	+	0.982976i	$0.558818\pi$
$74$	−12.9968	+	2.13572i	−1.51085	+	0.248272i
$75$	2.74366	+	3.04714i	0.316811	+	0.351854i
$76$	1.70672	+	14.6087i	0.195774	+	1.67573i
$77$	−9.46227	−	3.07448i	−1.07833	−	0.350369i
$78$	−1.04913	+	0.689983i	−0.118790	+	0.0781252i
$79$	0.620914	−	5.90761i	0.0698583	−	0.664658i	−0.902424	−	0.430849i	$-0.858214\pi$
$79$	0.620914	−	5.90761i	0.0698583	−	0.664658i	0.972283	−	0.233809i	$-0.0751190\pi$
$80$	−3.50082	−	1.46247i	−0.391404	−	0.163509i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	−6.26639	−	4.01804i	−0.692007	−	0.443718i
$83$	−5.77470	−	1.22745i	−0.633856	−	0.134730i	−0.120232	−	0.992746i	$-0.538364\pi$
$83$	−5.77470	−	1.22745i	−0.633856	−	0.134730i	−0.513624	+	0.858016i	$0.671697\pi$
$84$	−3.11093	+	2.31574i	−0.339430	+	0.252668i
$85$	3.21699	−	4.42780i	0.348931	−	0.480263i
$86$	6.57693	−	3.39923i	0.709208	−	0.366548i
$87$	0.684034	−	0.394927i	0.0733362	−	0.0423406i
$88$	12.0318	−	8.11415i	1.28259	−	0.864971i
$89$	−1.40024	−	1.92727i	−0.148425	−	0.204290i	0.728330	−	0.685227i	$-0.240297\pi$
$89$	−1.40024	−	1.92727i	−0.148425	−	0.204290i	−0.876756	+	0.480936i	$0.840297\pi$
$90$	0.602046	−	1.19869i	0.0634612	−	0.126353i
$91$	0.532047	+	1.63747i	0.0557737	+	0.171654i
$92$	−1.46901	−	6.53788i	−0.153155	−	0.681621i
$93$	−5.14629	+	2.12502i	−0.533645	+	0.220354i
$94$	−14.3434	−	11.4782i	−1.47941	−	1.18388i
$95$	−6.63394	+	2.15550i	−0.680628	+	0.221149i
$96$	0.132384	−	5.65530i	0.0135113	−	0.577192i
$97$	6.37734	−	4.63341i	0.647520	−	0.470451i	−0.214905	−	0.976635i	$-0.568944\pi$
$97$	6.37734	−	4.63341i	0.647520	−	0.470451i	0.862426	+	0.506184i	$0.168944\pi$
$98$	−1.66674	−	4.26796i	−0.168366	−	0.431129i
$99$	2.56542	+	4.44343i	0.257834	+	0.446582i
$100$	−1.61200	+	8.04068i	−0.161200	+	0.804068i
$101$	−6.30977	−	4.58432i	−0.627845	−	0.456156i	0.227808	−	0.973706i	$-0.426844\pi$
$101$	−6.30977	−	4.58432i	−0.627845	−	0.456156i	−0.855653	+	0.517550i	$0.826844\pi$
$102$	7.89434	+	2.06636i	0.781656	+	0.204600i
$103$	2.62105	−	12.3311i	0.258260	−	1.21502i	−0.637490	−	0.770459i	$-0.720027\pi$
$103$	2.62105	−	12.3311i	0.258260	−	1.21502i	0.895750	−	0.444559i	$-0.146640\pi$
$104$	−2.35985	−	0.859129i	−0.231402	−	0.0842445i
$105$	−1.36683	−	1.23070i	−0.133389	−	0.120104i
$106$	−0.315698	−	5.42281i	−0.0306633	−	0.526710i
$107$	2.24367	+	0.235820i	0.216904	+	0.0227975i	0.212357	−	0.977192i	$-0.431886\pi$
$107$	2.24367	+	0.235820i	0.216904	+	0.0227975i	0.00454694	+	0.999990i	$0.498553\pi$
$108$	1.99133	+	0.186006i	0.191616	+	0.0178984i
$109$	2.38447	−	7.33865i	0.228391	−	0.702915i	−0.769539	−	0.638600i	$-0.779514\pi$
$109$	2.38447	−	7.33865i	0.228391	−	0.702915i	0.997930	−	0.0643149i	$-0.0204862\pi$
$110$	4.89472	+	4.83836i	0.466693	+	0.461319i
$111$	6.92119	−	6.23186i	0.656930	−	0.591502i
$112$	−7.43033	−	2.22536i	−0.702100	−	0.210277i
$113$	1.66443	+	15.8360i	0.156577	+	1.48973i	0.737267	+	0.675602i	$0.236116\pi$
$113$	1.66443	+	15.8360i	0.156577	+	1.48973i	−0.580690	+	0.814125i	$0.697217\pi$
$114$	−6.59173	−	8.04441i	−0.617372	−	0.753428i
$115$	2.90317	−	1.29257i	0.270722	−	0.120533i
$116$	1.45048	+	0.625768i	0.134674	+	0.0581011i
$117$	0.361143	−	0.811141i	0.0333877	−	0.0749900i
$118$	−0.765582	+	5.02174i	−0.0704775	+	0.462289i
$119$	5.59451	−	9.68998i	0.512848	−	0.888279i
$120$	2.64206	−	0.465648i	0.241186	−	0.0425077i
$121$	−14.9905	+	3.18634i	−1.36278	+	0.289667i
$122$	−5.73650	+	15.2067i	−0.519358	+	1.37675i
$123$	5.26366			0.474609
$124$	−9.55505	−	5.71848i	−0.858069	−	0.513535i
$125$	−8.63172			−0.772044
$126$	0.967913	−	2.56581i	0.0862285	−	0.228581i
$127$	−12.8083	+	2.72250i	−1.13656	+	0.241583i	−0.737502	−	0.675345i	$-0.763995\pi$
$127$	−12.8083	+	2.72250i	−1.13656	+	0.241583i	−0.399054	+	0.916927i	$0.630662\pi$
$128$	9.23096	−	6.54136i	0.815909	−	0.578180i
$129$	−2.61751	+	4.53366i	−0.230459	+	0.399166i
$130$	0.179502	−	1.17742i	0.0157434	−	0.103267i
$131$	−0.822947	+	1.84837i	−0.0719012	+	0.161493i	−0.945921	−	0.324398i	$-0.894838\pi$
$131$	−0.822947	+	1.84837i	−0.0719012	+	0.161493i	0.874019	+	0.485891i	$0.161505\pi$
$132$	−4.06494	+	9.42221i	−0.353808	+	0.820098i
$133$	−13.0274	+	5.80016i	−1.12962	+	0.502938i
$134$	11.3183	+	13.8126i	0.977750	+	1.19323i
$135$	0.0991458	+	0.943309i	0.00853311	+	0.0811871i
$136$	6.11259	+	15.1327i	0.524150	+	1.29762i
$137$	13.8714	−	12.4899i	1.18511	−	1.06708i	0.188738	−	0.982027i	$-0.439560\pi$
$137$	13.8714	−	12.4899i	1.18511	−	1.06708i	0.996376	−	0.0850545i	$-0.0271064\pi$
$138$	3.36979	+	3.33098i	0.286855	+	0.283552i
$139$	−3.37575	+	10.3895i	−0.286328	+	0.881226i	0.699670	+	0.714466i	$0.253330\pi$
$139$	−3.37575	+	10.3895i	−0.286328	+	0.881226i	−0.985998	+	0.166760i	$0.946670\pi$
$140$	0.342112	−	3.66256i	0.0289137	−	0.309543i
$141$	12.9189	+	1.35783i	1.08797	+	0.114350i
$142$	0.195871	+	3.36451i	0.0164371	+	0.282344i
$143$	3.38554	+	3.04835i	0.283113	+	0.254916i
$144$	2.07970	+	3.41685i	0.173308	+	0.284737i
$145$	−0.155764	+	0.732810i	−0.0129355	+	0.0608565i
$146$	6.67399	+	1.74693i	0.552343	+	0.144577i
$147$	2.62111	+	1.90435i	0.216186	+	0.157068i
$148$	18.2633	+	3.66144i	1.50124	+	0.300969i
$149$	−1.91822	−	3.32245i	−0.157146	−	0.272186i	0.776692	−	0.629880i	$-0.216896\pi$
$149$	−1.91822	−	3.32245i	−0.157146	−	0.272186i	−0.933839	+	0.357695i	$0.883563\pi$
$150$	−2.10940	−	5.40148i	−0.172232	−	0.441029i
$151$	2.93164	−	2.12996i	0.238574	−	0.173334i	−0.462074	−	0.886841i	$-0.652895\pi$
$151$	2.93164	−	2.12996i	0.238574	−	0.173334i	0.700648	+	0.713508i	$0.252895\pi$
$152$	5.03367	−	20.1821i	0.408285	−	1.63698i
$153$	−5.48779	+	1.78309i	−0.443661	+	0.144154i
$154$	10.9858	+	8.79127i	0.885260	+	0.708421i
$155$	1.76834	−	4.97619i	0.142037	−	0.399697i
$156$	1.73261	−	0.389304i	0.138720	−	0.0311693i
$157$	−3.60406	−	11.0921i	−0.287635	−	0.885250i	−0.985596	−	0.169114i	$-0.945909\pi$
$157$	−3.60406	−	11.0921i	−0.287635	−	0.885250i	0.697961	−	0.716135i	$-0.254091\pi$
$158$	−3.77040	+	7.50698i	−0.299957	+	0.597223i
$159$	2.25768	+	3.10743i	0.179046	+	0.246436i
$160$	3.90227	+	3.68259i	0.308502	+	0.291134i
$161$	5.62644	−	3.24843i	0.443426	−	0.256012i
$162$	−1.25633	+	0.649326i	−0.0987069	+	0.0510159i
$163$	6.06930	−	8.35367i	0.475384	−	0.654310i	−0.502226	−	0.864737i	$-0.667485\pi$
$163$	6.06930	−	8.35367i	0.475384	−	0.654310i	0.977610	+	0.210427i	$0.0674853\pi$
$164$	6.28603	+	8.44455i	0.490857	+	0.659409i
$165$	−4.76027	−	1.01183i	−0.370587	−	0.0787706i
$166$	7.02837	+	4.50662i	0.545507	+	0.349782i
$167$	0.837207	−	0.929813i	0.0647850	−	0.0719511i	−0.709881	−	0.704322i	$-0.751251\pi$
$167$	0.837207	−	0.929813i	0.0647850	−	0.0719511i	0.774666	+	0.632371i	$0.217918\pi$
$168$	5.27227	−	1.51134i	0.406765	−	0.116603i
$169$	−1.27646	+	12.1447i	−0.0981894	+	0.934210i
$170$	−6.46686	+	4.25307i	−0.495985	+	0.326196i
$171$	6.99410	+	2.27252i	0.534852	+	0.173784i
$172$	−10.3993	+	1.21494i	−0.792939	+	0.0926384i
$173$	6.29029	+	6.98608i	0.478242	+	0.531142i	0.933193	−	0.359375i	$-0.117010\pi$
$173$	6.29029	+	6.98608i	0.478242	+	0.531142i	−0.454951	+	0.890516i	$0.650343\pi$
$174$	−1.10224	+	0.181127i	−0.0835606	+	0.0137312i
$175$	−7.90743	+	0.831104i	−0.597746	+	0.0628256i
$176$	−19.9706	+	4.73087i	−1.50534	+	0.356603i
$177$	−1.46097	−	3.28140i	−0.109813	−	0.246645i
$178$	0.890790	+	3.24909i	0.0667675	+	0.243530i
$179$	16.7237	+	7.44586i	1.24999	+	0.556530i	0.921647	−	0.388030i	$-0.126844\pi$
$179$	16.7237	+	7.44586i	1.24999	+	0.556530i	0.328339	+	0.944560i	$0.393511\pi$
$180$	−1.39496	+	1.28559i	−0.103974	+	0.0958222i
$181$	2.55814	+	1.47694i	0.190145	+	0.109780i	0.592050	−	0.805901i	$-0.298319\pi$
$181$	2.55814	+	1.47694i	0.190145	+	0.109780i	−0.401905	+	0.915681i	$0.631652\pi$
$182$	0.113350	−	2.43227i	0.00840204	−	0.180292i
$183$	−2.38941	−	11.2413i	−0.176630	−	0.830981i
$184$	−1.31962	+	9.38415i	−0.0972838	+	0.691808i
$185$			8.83379i			0.649473i
$186$	7.87026	−	0.243017i	0.577075	−	0.0178188i
$187$		−	29.6059i		−	2.16500i
$188$	13.2497	+	22.3474i	0.966337	+	1.62985i
$189$	0.403163	+	1.89673i	0.0293258	+	0.137967i
$190$	9.85392	+	0.459217i	0.714878	+	0.0333151i
$191$	19.7315	+	11.3920i	1.42772	+	0.824296i	0.996941	−	0.0781608i	$-0.0249047\pi$
$191$	19.7315	+	11.3920i	1.42772	+	0.824296i	0.430781	+	0.902456i	$0.358238\pi$
$192$	−2.99804	+	7.41699i	−0.216365	+	0.535275i
$193$	8.67144	+	3.86077i	0.624184	+	0.277904i	0.694357	−	0.719630i	$-0.255689\pi$
$193$	8.67144	+	3.86077i	0.624184	+	0.277904i	−0.0701737	+	0.997535i	$0.522355\pi$
$194$	−10.7512	+	2.94762i	−0.771894	+	0.211627i
$195$	0.342546	+	0.769372i	0.0245302	+	0.0550958i
$196$	0.0750477	+	6.47931i	0.00536055	+	0.462808i
$197$	2.13589	−	0.224491i	0.152176	−	0.0159943i	−0.0281343	−	0.999604i	$-0.508957\pi$
$197$	2.13589	−	0.224491i	0.152176	−	0.0159943i	0.180310	+	0.983610i	$0.442290\pi$
$198$	−1.17659	−	7.16006i	−0.0836164	−	0.508844i
$199$	6.13853	+	6.81753i	0.435149	+	0.483282i	0.920336	−	0.391129i	$-0.127915\pi$
$199$	6.13853	+	6.81753i	0.435149	+	0.483282i	−0.485187	+	0.874410i	$0.661249\pi$
$200$	6.14653	−	9.83475i	0.434625	−	0.695422i
$201$	−12.0091	−	3.90201i	−0.847060	−	0.275227i
$202$	6.06077	+	9.21549i	0.426434	+	0.648400i
$203$	−0.160097	+	1.52322i	−0.0112366	+	0.106909i
$204$	−9.41432	−	6.67469i	−0.659134	−	0.467322i
$205$	−3.34071	+	3.71023i	−0.233325	+	0.259134i
$206$	−9.62328	+	15.0081i	−0.670486	+	1.04567i
$207$	−3.27723	−	0.696596i	−0.227783	−	0.0484168i
$208$	2.69370	+	2.31472i	0.186775	+	0.160497i
$209$	−22.1785	+	30.5261i	−1.53412	+	2.11153i
$210$	1.19427	+	2.31071i	0.0824127	+	0.159454i
$211$	8.82897	−	5.09741i	0.607812	−	0.350920i	−0.164297	−	0.986411i	$-0.552536\pi$
$211$	8.82897	−	5.09741i	0.607812	−	0.350920i	0.772108	+	0.635491i	$0.219202\pi$
$212$	−2.28909	+	7.33302i	−0.157216	+	0.503634i
$213$	−1.40075	−	1.92797i	−0.0959778	−	0.132102i
$214$	−2.85111	−	1.43197i	−0.194898	−	0.0978878i
$215$	−1.53441	−	4.72241i	−0.104646	−	0.322066i
$216$	−2.54207	−	1.24010i	−0.172966	−	0.0843784i
$217$	2.53197	−	10.4954i	0.171881	−	0.712473i
$218$	−6.81824	+	8.52024i	−0.461789	+	0.577064i
$219$	−4.63945	+	1.50745i	−0.313505	+	0.101864i
$220$	−4.06158	−	8.84531i	−0.273832	−	0.596351i
$221$	−4.14491	+	3.01145i	−0.278817	+	0.202572i
$222$	−12.2687	+	4.79123i	−0.823424	+	0.321566i
$223$	6.12406	+	10.6072i	0.410097	+	0.710310i	0.994900	−	0.100866i	$-0.0321614\pi$
$223$	6.12406	+	10.6072i	0.410097	+	0.710310i	−0.584803	+	0.811176i	$0.698828\pi$
$224$	8.72098	+	6.65347i	0.582695	+	0.444554i
$225$	3.31724	+	2.41012i	0.221150	+	0.160675i
$226$	5.70225	−	21.7849i	0.379308	−	1.44911i
$227$	4.06115	−	19.1062i	0.269548	−	1.26812i	−0.610033	−	0.792376i	$-0.708844\pi$
$227$	4.06115	−	19.1062i	0.269548	−	1.26812i	0.879581	−	0.475749i	$-0.157823\pi$
$228$	4.70674	+	13.9346i	0.311712	+	0.922842i
$229$	−11.5682	−	10.4161i	−0.764448	−	0.688312i	0.191616	−	0.981470i	$-0.438627\pi$
$229$	−11.5682	−	10.4161i	−0.764448	−	0.688312i	−0.956064	+	0.293158i	$0.905294\pi$
$230$	−4.48665	+	0.261197i	−0.295841	+	0.0172228i
$231$	−9.89472	−	1.03998i	−0.651025	−	0.0684254i
$232$	−1.60691	−	1.55203i	−0.105499	−	0.101896i
$233$	8.27872	−	25.4793i	0.542357	−	1.66920i	−0.184835	−	0.982770i	$-0.559175\pi$
$233$	8.27872	−	25.4793i	0.542357	−	1.66920i	0.727192	−	0.686434i	$-0.240825\pi$
$234$	−0.882748	+	0.893031i	−0.0577070	+	0.0583793i
$235$	−9.15637	+	8.24444i	−0.597296	+	0.537808i
$236$	3.51964	−	6.26260i	0.229109	−	0.407661i
$237$	−0.620914	−	5.90761i	−0.0403327	−	0.383740i
$238$	−12.2394	+	10.0292i	−0.793364	+	0.650097i
$239$	−17.0696	+	7.59988i	−1.10414	+	0.491595i	−0.876136	−	0.482065i	$-0.839887\pi$
$239$	−17.0696	+	7.59988i	−1.10414	+	0.491595i	−0.228005	+	0.973660i	$0.573220\pi$
$240$	−3.72839	−	0.702652i	−0.240666	−	0.0453560i
$241$	8.03765	−	18.0529i	0.517751	−	1.16289i	−0.445744	−	0.895160i	$-0.647061\pi$
$241$	8.03765	−	18.0529i	0.517751	−	1.16289i	0.963495	−	0.267727i	$-0.0862725\pi$
$242$	21.4259	+	3.26645i	1.37731	+	0.209975i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	15.1810	−	17.2581i	0.971865	−	1.10483i
$245$	−3.00588	+	0.638920i	−0.192039	+	0.0408191i
$246$	−6.96485	−	2.62738i	−0.444063	−	0.167516i
$247$	6.52967			0.415473
$248$	9.78878	+	12.3361i	0.621588	+	0.783344i
$249$	−5.90371			−0.374132
$250$	11.4214	+	4.30856i	0.722356	+	0.272497i
$251$	0.649952	−	0.138151i	0.0410246	−	0.00872005i	−0.187354	−	0.982293i	$-0.559991\pi$
$251$	0.649952	−	0.138151i	0.0410246	−	0.00872005i	0.228378	+	0.973572i	$0.426658\pi$
$252$	−2.56148	+	2.91193i	−0.161358	+	0.183435i
$253$	8.59527	−	14.8874i	0.540380	−	0.935966i
$254$	18.3069	+	2.79095i	1.14868	+	0.175120i
$255$	2.22610	−	4.99989i	0.139404	−	0.313106i
$256$	−15.4795	+	4.04782i	−0.967469	+	0.252989i
$257$	23.0752	−	10.2737i	1.43939	−	0.640859i	0.469178	−	0.883104i	$-0.344550\pi$
$257$	23.0752	−	10.2737i	1.43939	−	0.640859i	0.970215	+	0.242245i	$0.0778838\pi$
$258$	5.72647	−	4.69237i	0.356514	−	0.292134i
$259$	1.88774	+	17.9607i	0.117299	+	1.11602i
$260$	−0.825231	+	1.46836i	−0.0511787	+	0.0910637i
$261$	0.586976	−	0.528516i	0.0363329	−	0.0327143i
$262$	2.01154	−	2.03498i	0.124273	−	0.125721i
$263$	−3.62308	+	11.1507i	−0.223409	+	0.687581i	0.775040	+	0.631912i	$0.217729\pi$
$263$	−3.62308	+	11.1507i	−0.223409	+	0.687581i	−0.998449	+	0.0556698i	$0.982271\pi$
$264$	10.0818	−	10.4384i	0.620495	−	0.642438i
$265$	−3.62325	−	0.380819i	−0.222575	−	0.0233935i
$266$	20.1329	−	1.17207i	1.23443	−	0.0718643i
$267$	−1.77035	−	1.59403i	−0.108343	−	0.0975529i
$268$	−8.08167	−	23.9263i	−0.493667	−	1.46153i
$269$	1.48041	−	6.96476i	0.0902619	−	0.424649i	−0.909694	−	0.415279i	$-0.863684\pi$
$269$	1.48041	−	6.96476i	0.0902619	−	0.424649i	0.999956	−	0.00937014i	$-0.00298265\pi$
$270$	0.339668	−	1.29767i	0.0206715	−	0.0789737i
$271$	2.30663	+	1.67587i	0.140118	+	0.101802i	0.655636	−	0.755077i	$-0.272401\pi$
$271$	2.30663	+	1.67587i	0.140118	+	0.101802i	−0.515518	+	0.856879i	$0.672401\pi$
$272$	−0.534603	−	23.0746i	−0.0324151	−	1.39910i
$273$	0.860870	+	1.49107i	0.0521022	+	0.0902437i
$274$	−24.5890	+	9.60256i	−1.48547	+	0.580112i
$275$	−17.0202	+	12.3659i	−1.02636	+	0.745692i
$276$	−2.79621	−	6.08958i	−0.168312	−	0.366550i
$277$	−28.8658	+	9.37908i	−1.73438	+	0.563534i	−0.994071	−	0.108732i	$-0.965321\pi$
$277$	−28.8658	+	9.37908i	−1.73438	+	0.563534i	−0.740309	+	0.672266i	$0.765321\pi$
$278$	9.65274	−	12.0623i	0.578933	−	0.723449i
$279$	−4.59202	+	3.14855i	−0.274917	+	0.188499i
$280$	−2.28086	+	4.67551i	−0.136308	+	0.279415i
$281$	5.40411	+	16.6321i	0.322382	+	0.992190i	0.972608	+	0.232450i	$0.0746741\pi$
$281$	5.40411	+	16.6321i	0.322382	+	0.992190i	−0.650226	+	0.759741i	$0.725326\pi$
$282$	−16.4164	−	8.24519i	−0.977584	−	0.490994i
$283$	4.00094	+	5.50682i	0.237831	+	0.327347i	0.911203	−	0.411957i	$-0.135155\pi$
$283$	4.00094	+	5.50682i	0.237831	+	0.327347i	−0.673372	+	0.739304i	$0.735155\pi$
$284$	1.42024	−	4.54968i	0.0842756	−	0.269974i
$285$	−6.04082	+	3.48767i	−0.357827	+	0.206592i
$286$	−2.95813	−	5.72347i	−0.174918	−	0.338436i
$287$	−5.99941	+	8.25747i	−0.354134	+	0.487423i
$288$	−1.04631	−	5.55925i	−0.0616546	−	0.327582i
$289$	15.9391	+	3.38797i	0.937596	+	0.199292i
$290$	0.571891	−	0.891900i	0.0335826	−	0.0523742i
$291$	5.27464	−	5.85808i	0.309205	−	0.343407i
$292$	−7.95900	−	5.64288i	−0.465765	−	0.330224i
$293$	0.0398382	−	0.379035i	0.00232737	−	0.0221435i	−0.993297	−	0.115594i	$-0.963123\pi$
$293$	0.0398382	−	0.379035i	0.00232737	−	0.0221435i	0.995624	+	0.0934502i	$0.0297896\pi$
$294$	−2.51768	−	3.82816i	−0.146834	−	0.223263i
$295$	3.24022	+	1.05281i	0.188653	+	0.0612971i
$296$	−22.3383	−	13.9610i	−1.29839	−	0.811468i
$297$	3.43320	+	3.81295i	0.199214	+	0.221250i
$298$	0.879759	+	5.35373i	0.0509631	+	0.310133i
$299$	−2.95857	+	0.310959i	−0.171099	+	0.0179832i
$300$	0.0949794	+	8.20013i	0.00548364	+	0.473434i
$301$	−4.12888	−	9.27362i	−0.237985	−	0.534523i
$302$	−4.94231	+	1.35501i	−0.284398	+	0.0779723i
$303$	−7.12502	−	3.17226i	−0.409322	−	0.182242i
$304$	−16.7345	+	24.1922i	−0.959789	+	1.38752i
$305$	9.44023	+	5.45032i	0.540546	+	0.312084i
$306$	8.15145	+	0.379878i	0.465987	+	0.0217162i
$307$	−1.17333	−	5.52010i	−0.0669657	−	0.315049i	0.931897	−	0.362722i	$-0.118153\pi$
$307$	−1.17333	−	5.52010i	−0.0669657	−	0.315049i	−0.998863	+	0.0476734i	$0.984819\pi$
$308$	−10.1481	−	17.1162i	−0.578244	−	0.975284i
$309$		−	12.6066i		−	0.717163i
$310$	−4.82375	+	5.70180i	−0.273971	+	0.323840i
$311$		−	19.2442i		−	1.09124i	−0.838033	−	0.545619i	$-0.816294\pi$
$311$		−	19.2442i		−	1.09124i	0.838033	−	0.545619i	$-0.183706\pi$
$312$	−2.48690	−	0.349715i	−0.140793	−	0.0197987i
$313$	2.22096	+	10.4488i	0.125536	+	0.590601i	0.995276	+	0.0970898i	$0.0309534\pi$
$313$	2.22096	+	10.4488i	0.125536	+	0.590601i	−0.869740	+	0.493511i	$0.835713\pi$
$314$	−0.767825	+	16.4761i	−0.0433309	+	0.929798i
$315$	−1.59284	−	0.919626i	−0.0897463	−	0.0518150i
$316$	8.73612	−	8.05119i	0.491445	−	0.452915i
$317$	9.96216	+	4.43544i	0.559531	+	0.249119i	0.666960	−	0.745094i	$-0.267595\pi$
$317$	9.96216	+	4.43544i	0.559531	+	0.249119i	−0.107429	+	0.994213i	$0.534262\pi$
$318$	−1.43627	−	5.23868i	−0.0805418	−	0.293770i
$319$	1.64835	+	3.70224i	0.0922896	+	0.207286i
$320$	−3.32529	−	6.82062i	−0.185889	−	0.381284i
$321$	2.24367	−	0.235820i	0.125230	−	0.0131622i
$322$	−9.06635	+	1.48984i	−0.505248	+	0.0830255i
$323$	−28.3940	−	31.5348i	−1.57989	−	1.75464i
$324$	1.98649	−	0.232080i	0.110361	−	0.0128933i
$325$	3.46252	+	1.12504i	0.192066	+	0.0624060i
$326$	−12.2006	+	8.02402i	−0.675731	+	0.444409i
$327$	0.806574	−	7.67404i	0.0446037	−	0.424375i
$328$	−4.10251	−	14.3115i	−0.226523	−	0.790220i
$329$	−16.8548	+	18.7191i	−0.929233	+	1.03202i
$330$	5.79371	+	3.71496i	0.318933	+	0.204502i
$331$	9.21190	+	1.95805i	0.506332	+	0.107624i	0.453993	−	0.891005i	$-0.349999\pi$
$331$	9.21190	+	1.95805i	0.506332	+	0.107624i	0.0523389	+	0.998629i	$0.483332\pi$
$332$	−7.05040	−	9.47138i	−0.386941	−	0.519810i
$333$	5.47426	−	7.53468i	0.299988	−	0.412898i
$334$	−1.57191	+	0.812428i	−0.0860110	+	0.0444541i
$335$	10.3723	−	5.98847i	0.566701	−	0.327185i
$336$	−7.73064	−	0.631877i	−0.421741	−	0.0344717i
$337$	−1.76527	−	2.42969i	−0.0961604	−	0.132353i	0.758226	−	0.651992i	$-0.226067\pi$
$337$	−1.76527	−	2.42969i	−0.0961604	−	0.132353i	−0.854386	+	0.519639i	$0.826067\pi$
$338$	7.75110	−	15.4327i	0.421605	−	0.839428i
$339$	4.92055	+	15.1439i	0.267248	+	0.822504i
$340$	10.6799	−	2.39968i	0.579197	−	0.130141i
$341$	−8.08332	−	27.3998i	−0.437737	−	1.48378i
$342$	−8.12021	−	6.49812i	−0.439091	−	0.351378i
$343$	−18.8844	+	6.13590i	−1.01966	+	0.331307i
$344$	14.3667	+	3.58325i	0.774603	+	0.193196i
$345$	2.57098	−	1.86793i	0.138417	−	0.100566i
$346$	−4.83615	−	12.3838i	−0.259993	−	0.665756i
$347$	−1.30481	−	2.26000i	−0.0700459	−	0.121323i	0.828875	−	0.559433i	$-0.188981\pi$
$347$	−1.30481	−	2.26000i	−0.0700459	−	0.121323i	−0.898921	+	0.438110i	$0.855648\pi$
$348$	1.54889	+	0.310522i	0.0830292	+	0.0166457i
$349$	27.0892	+	19.6814i	1.45005	+	1.05352i	0.985820	+	0.167809i	$0.0536691\pi$
$349$	27.0892	+	19.6814i	1.45005	+	1.05352i	0.464231	+	0.885714i	$0.346331\pi$
$350$	10.8779	+	2.84732i	0.581449	+	0.152195i
$351$	0.184606	−	0.868502i	0.00985352	−	0.0463572i
$352$	28.7865	+	3.70856i	1.53432	+	0.197667i
$353$	26.1264	+	23.5243i	1.39057	+	1.25207i	0.931533	+	0.363657i	$0.118472\pi$
$353$	26.1264	+	23.5243i	1.39057	+	1.25207i	0.459037	+	0.888417i	$0.348195\pi$
$354$	0.295227	+	5.07118i	0.0156911	+	0.269530i
$355$	2.24800	+	0.236274i	0.119311	+	0.0125401i
$356$	0.443110	−	4.74382i	0.0234848	−	0.251422i
$357$	3.45760	−	10.6414i	0.182996	−	0.563202i
$358$	−18.4120	−	18.2000i	−0.973107	−	0.961901i
$359$	−18.2967	+	16.4744i	−0.965663	+	0.869487i	−0.991490	−	0.130179i	$-0.958445\pi$
$359$	−18.2967	+	16.4744i	−0.965663	+	0.869487i	0.0258273	+	0.999666i	$0.491778\pi$
$360$	2.48751	−	1.00479i	0.131103	−	0.0529569i
$361$	3.66704	+	34.8896i	0.193002	+	1.83629i
$362$	−2.64770	−	3.23119i	−0.139160	−	0.169828i
$363$	−14.0005	+	6.23341i	−0.734834	+	0.327169i
$364$	−1.36406	+	3.16179i	−0.0714963	+	0.165723i
$365$	1.88197	−	4.22698i	0.0985070	−	0.221250i
$366$	−2.44949	+	16.0671i	−0.128037	+	0.839841i
$367$	0.827518	−	1.43330i	0.0431961	−	0.0748178i	−0.843619	−	0.536942i	$-0.819579\pi$
$367$	0.827518	−	1.43330i	0.0431961	−	0.0748178i	0.886815	+	0.462124i	$0.152913\pi$
$368$	6.43026	−	11.7584i	0.335200	−	0.612947i
$369$	5.14864	−	1.09438i	0.268028	−	0.0569710i
$370$	4.40942	−	11.6888i	0.229235	−	0.607673i
$371$	−7.44810			−0.386686
$372$	−10.5352	−	3.60692i	−0.546224	−	0.187010i
$373$	−34.2077			−1.77121			−0.885604	−	0.464442i	$-0.846255\pi$
$373$	−34.2077			−1.77121			−0.885604	+	0.464442i	$0.846255\pi$
$374$	−14.7779	+	39.1744i	−0.764149	+	2.02566i
$375$	−8.44309	+	1.79464i	−0.436000	+	0.0926746i
$376$	−6.37717	−	36.1837i	−0.328878	−	1.86603i
$377$	0.350658	−	0.607357i	0.0180598	−	0.0312805i
$378$	0.413299	−	2.71099i	0.0212578	−	0.139438i
$379$	4.67578	−	10.5020i	0.240179	−	0.539450i	−0.752730	−	0.658329i	$-0.771263\pi$
$379$	4.67578	−	10.5020i	0.240179	−	0.539450i	0.992909	+	0.118879i	$0.0379301\pi$
$380$	−12.8094	−	5.52626i	−0.657110	−	0.283491i
$381$	−11.9624	+	5.32601i	−0.612853	+	0.272860i
$382$	−20.4223	−	24.9229i	−1.04489	−	1.27517i
$383$	−0.391515	−	3.72501i	−0.0200055	−	0.190339i	0.979955	−	0.199218i	$-0.0638403\pi$
$383$	−0.391515	−	3.72501i	−0.0200055	−	0.190339i	−0.999961	+	0.00887914i	$0.997174\pi$
$384$	7.66922	−	8.31764i	0.391368	−	0.424458i
$385$	7.01297	−	6.31451i	0.357414	−	0.321817i
$386$	−9.54688	−	9.43694i	−0.485923	−	0.480328i
$387$	−1.61771	+	4.97880i	−0.0822327	+	0.253086i
$388$	15.6973	+	1.46625i	0.796910	+	0.0744377i
$389$	15.6560	+	1.64551i	0.793790	+	0.0834307i	0.492739	−	0.870177i	$-0.335996\pi$
$389$	15.6560	+	1.64551i	0.793790	+	0.0834307i	0.301051	+	0.953608i	$0.402662\pi$
$390$	−0.0692202	−	1.18901i	−0.00350510	−	0.0602080i
$391$	14.3670	+	12.9361i	0.726571	+	0.654207i
$392$	3.13487	−	8.61085i	0.158335	−	0.434913i
$393$	−0.420666	+	1.97908i	−0.0212198	+	0.0998313i
$394$	−2.93825	−	0.769093i	−0.148027	−	0.0387463i
$395$	4.55821	+	3.31174i	0.229349	+	0.166631i
$396$	−2.01712	+	10.0615i	−0.101364	+	0.505607i
$397$	15.4459	+	26.7531i	0.775208	+	1.34270i	0.934678	+	0.355496i	$0.115688\pi$
$397$	15.4459	+	26.7531i	0.775208	+	1.34270i	−0.159470	+	0.987203i	$0.550978\pi$
$398$	−4.71947	−	12.0850i	−0.236566	−	0.605766i
$399$	−11.5368	+	8.38196i	−0.577561	+	0.419623i
$400$	−13.0421	+	9.94523i	−0.652106	+	0.497261i
$401$	−8.51996	+	2.76830i	−0.425467	+	0.138242i	−0.513921	−	0.857838i	$-0.671807\pi$
$401$	−8.51996	+	2.76830i	−0.425467	+	0.138242i	0.0884539	+	0.996080i	$0.471807\pi$
$402$	13.9427	+	11.1575i	0.695401	+	0.556488i
$403$	−3.01382	+	3.91873i	−0.150129	+	0.195206i
$404$	−3.41963	−	15.2192i	−0.170133	−	0.757181i
$405$	0.293104	+	0.902082i	0.0145645	+	0.0448248i
$406$	0.972162	−	1.93560i	0.0482476	−	0.0960625i
$407$	28.0875	+	38.6592i	1.39225	+	1.91626i
$408$	9.12528	+	13.5311i	0.451769	+	0.669890i
$409$	5.44940	−	3.14621i	0.269455	−	0.155570i	−0.359185	−	0.933266i	$-0.616945\pi$
$409$	5.44940	−	3.14621i	0.269455	−	0.155570i	0.628640	+	0.777696i	$0.283612\pi$
$410$	6.27239	−	3.24183i	0.309771	−	0.160103i
$411$	10.9715	−	15.1010i	0.541184	−	0.744876i
$412$	20.2248	−	15.0552i	0.996407	−	0.741715i
$413$	6.81294	+	1.44813i	0.335243	+	0.0712580i
$414$	3.98870	+	2.55757i	0.196034	+	0.125698i
$415$	3.74693	−	4.16139i	0.183930	−	0.204275i
$416$	−2.40889	−	4.40741i	−0.118106	−	0.216091i
$417$	−1.14189	+	10.8643i	−0.0559184	+	0.532028i
$418$	44.5837	−	29.3214i	2.18066	−	1.43416i
$419$	−15.9153	−	5.17119i	−0.777513	−	0.252629i	−0.106735	−	0.994288i	$-0.534040\pi$
$419$	−15.9153	−	5.17119i	−0.777513	−	0.252629i	−0.670778	+	0.741658i	$0.734040\pi$
$420$	−0.426853	−	3.65365i	−0.0208283	−	0.178280i
$421$	−8.19034	−	9.09629i	−0.399173	−	0.443326i	0.509730	−	0.860334i	$-0.329745\pi$
$421$	−8.19034	−	9.09629i	−0.399173	−	0.443326i	−0.908903	+	0.417008i	$0.863079\pi$
$422$	−14.2268	+	2.33785i	−0.692552	+	0.113805i
$423$	12.9189	−	1.35783i	0.628137	−	0.0660199i
$424$	6.68923	−	8.56041i	0.324858	−	0.415730i
$425$	−9.62330	−	21.6143i	−0.466798	−	1.04845i
$426$	0.891112	+	3.25027i	0.0431745	+	0.157476i
$427$	20.3584	+	9.06414i	0.985212	+	0.438645i
$428$	3.05779	+	3.31792i	0.147804	+	0.160378i
$429$	3.94534	+	2.27784i	0.190483	+	0.109975i
$430$	−0.326897	+	7.01458i	−0.0157644	+	0.338273i
$431$	4.22446	+	19.8745i	0.203485	+	0.957321i	0.954770	+	0.297344i	$0.0961008\pi$
$431$	4.22446	+	19.8745i	0.203485	+	0.957321i	−0.751285	+	0.659977i	$0.770566\pi$
$432$	2.74466	+	2.90979i	0.132052	+	0.139997i
$433$			38.8770i			1.86831i	0.356870	+	0.934154i	$0.383844\pi$
$433$			38.8770i			1.86831i	−0.356870	+	0.934154i	$0.616156\pi$
$434$	−8.58910	+	12.6236i	−0.412290	+	0.605952i
$435$			0.749181i			0.0359205i
$436$	13.2748	−	7.87059i	0.635747	−	0.376933i
$437$	−5.12278	−	24.1008i	−0.245056	−	1.15290i
$438$	6.89135	+	0.321154i	0.329282	+	0.0153453i
$439$	−20.4679	−	11.8172i	−0.976881	−	0.564002i	−0.0755538	−	0.997142i	$-0.524072\pi$
$439$	−20.4679	−	11.8172i	−0.976881	−	0.564002i	−0.901327	+	0.433139i	$0.857406\pi$
$440$	0.959090	+	13.7314i	0.0457228	+	0.654620i
$441$	2.95977	+	1.31777i	0.140941	+	0.0627512i
$442$	6.98770	−	1.91579i	0.332371	−	0.0911247i
$443$	−1.31582	−	2.95537i	−0.0625164	−	0.140414i	0.879586	−	0.475741i	$-0.157820\pi$
$443$	−1.31582	−	2.95537i	−0.0625164	−	0.140414i	−0.942102	+	0.335327i	$0.891153\pi$
$444$	18.6255	−	0.215733i	0.883927	−	0.0102382i
$445$	2.24719	−	0.236189i	0.106527	−	0.0111964i
$446$	−2.80870	−	17.0922i	−0.132996	−	0.809340i
$447$	−2.56707	−	2.85103i	−0.121418	−	0.134849i
$448$	−8.21845	−	13.1570i	−0.388285	−	0.621608i
$449$	9.17268	+	2.98039i	0.432886	+	0.140653i	0.517351	−	0.855773i	$-0.326918\pi$
$449$	9.17268	+	2.98039i	0.432886	+	0.140653i	−0.0844652	+	0.996426i	$0.526918\pi$
$450$	−3.18634	−	4.84487i	−0.150205	−	0.228389i
$451$	−2.82300	+	26.8590i	−0.132930	+	1.26474i
$452$	−18.4192	+	25.9794i	−0.866368	+	1.22197i
$453$	2.42473	−	2.69294i	0.113924	−	0.126525i
$454$	−14.9107	+	23.2541i	−0.699792	+	1.09137i
$455$	−1.59739	−	0.339536i	−0.0748869	−	0.0159177i
$456$	0.727585	−	20.7876i	0.0340723	−	0.973469i
$457$	−0.473592	+	0.651844i	−0.0221537	+	0.0304920i	−0.819950	−	0.572435i	$-0.805999\pi$
$457$	−0.473592	+	0.651844i	−0.0221537	+	0.0304920i	0.797796	+	0.602927i	$0.205999\pi$
$458$	10.1078	+	19.5568i	0.472305	+	0.913829i
$459$	−4.99714	+	2.88510i	−0.233247	+	0.134665i
$460$	6.06709	+	1.89392i	0.282879	+	0.0883043i
$461$	−4.55456	−	6.26881i	−0.212127	−	0.291968i	0.689673	−	0.724120i	$-0.257754\pi$
$461$	−4.55456	−	6.26881i	−0.212127	−	0.291968i	−0.901800	+	0.432153i	$0.857754\pi$
$462$	12.5735	+	6.31509i	0.584974	+	0.293804i
$463$	−9.27835	−	28.5558i	−0.431202	−	1.32710i	−0.896929	−	0.442174i	$-0.854207\pi$
$463$	−9.27835	−	28.5558i	−0.431202	−	1.32710i	0.465728	−	0.884928i	$-0.345793\pi$
$464$	1.35156	+	2.85573i	0.0627446	+	0.132574i
$465$	0.695090	−	5.23511i	0.0322340	−	0.242772i
$466$	−23.6725	+	29.5817i	−1.09661	+	1.37035i
$467$	−32.7148	+	10.6297i	−1.51386	+	0.491882i	−0.944024	−	0.329877i	$-0.892993\pi$
$467$	−32.7148	+	10.6297i	−1.51386	+	0.491882i	−0.569834	+	0.821759i	$0.692993\pi$
$468$	1.61381	−	0.741027i	0.0745983	−	0.0342540i
$469$	19.8091	−	14.3922i	0.914700	−	0.664568i
$470$	16.2309	−	6.33855i	0.748676	−	0.292376i
$471$	−5.83149	−	10.1004i	−0.268701	−	0.465403i
$472$	−7.78317	+	6.52980i	−0.358250	+	0.300558i
$473$	−21.7302	−	15.7879i	−0.999155	−	0.725928i
$474$	−2.12722	+	8.12685i	−0.0977063	+	0.373278i
$475$	−6.26937	+	29.4951i	−0.287658	+	1.35333i
$476$	21.2013	−	7.16123i	0.971759	−	0.328234i
$477$	2.85442	+	2.57013i	0.130695	+	0.117678i
$478$	26.3799	−	1.53575i	1.20659	−	0.0702435i
$479$	13.3979	+	1.40817i	0.612163	+	0.0643410i	0.405537	−	0.914079i	$-0.367085\pi$
$479$	13.3979	+	1.40817i	0.612163	+	0.0643410i	0.206627	+	0.978420i	$0.433751\pi$
$480$	4.58265	+	2.79079i	0.209168	+	0.127381i
$481$	2.55538	−	7.86465i	0.116515	−	0.358597i
$482$	−19.6466	+	19.8754i	−0.894876	+	0.905301i
$483$	4.82811	−	4.34725i	0.219686	−	0.197807i
$484$	−26.7201	−	15.0170i	−1.21455	−	0.682589i
$485$	0.781549	+	7.43594i	0.0354883	+	0.337649i
$486$	−1.09388	+	0.896343i	−0.0496193	+	0.0406590i
$487$	9.01790	−	4.01503i	0.408640	−	0.181938i	−0.192113	−	0.981373i	$-0.561534\pi$
$487$	9.01790	−	4.01503i	0.408640	−	0.181938i	0.600753	+	0.799434i	$0.294867\pi$
$488$	−28.7019	+	15.2581i	−1.29927	+	0.690702i
$489$	4.19984	−	9.43300i	0.189923	−	0.426575i
$490$	4.29629	+	0.654984i	0.194086	+	0.0295892i
$491$	15.3710	−	26.6233i	0.693682	−	1.20149i	−0.276942	−	0.960887i	$-0.589321\pi$
$491$	15.3710	−	26.6233i	0.693682	−	1.20149i	0.970623	−	0.240605i	$-0.0773458\pi$
$492$	7.90439	+	6.95308i	0.356357	+	0.313469i
$493$	−4.45802	+	0.947582i	−0.200779	+	0.0426770i
$494$	−8.64003	−	3.25932i	−0.388733	−	0.146644i
$495$	−4.86662			−0.218738
$496$	−6.79484	−	21.2092i	−0.305097	−	0.952321i
$497$	4.62108			0.207284
$498$	7.81176	+	2.94686i	0.350053	+	0.132052i
$499$	11.8657	−	2.52213i	0.531182	−	0.112906i	0.0654901	−	0.997853i	$-0.479139\pi$
$499$	11.8657	−	2.52213i	0.531182	−	0.112906i	0.465692	+	0.884947i	$0.345806\pi$
$500$	−12.9622	−	11.4021i	−0.579685	−	0.509919i
$501$	0.625593	−	1.08356i	0.0279494	−	0.0484099i
$502$	−0.928972	−	0.141625i	−0.0414620	−	0.00632103i
$503$	4.73910	−	10.6442i	0.211306	−	0.474601i	−0.776534	−	0.630076i	$-0.783024\pi$
$503$	4.73910	−	10.6442i	0.211306	−	0.474601i	0.987840	+	0.155474i	$0.0496906\pi$
$504$	4.84284	−	2.57448i	0.215717	−	0.114677i
$505$	6.75812	−	3.00891i	0.300732	−	0.133895i
$506$	−18.8044	+	15.4086i	−0.835956	+	0.684997i
$507$	1.27646	+	12.1447i	0.0566897	+	0.539366i
$508$	−22.8305	−	12.8309i	−1.01294	−	0.569280i
$509$	22.9140	−	20.6318i	1.01564	−	0.914489i	0.0192899	−	0.999814i	$-0.493859\pi$
$509$	22.9140	−	20.6318i	1.01564	−	0.914489i	0.996353	+	0.0853247i	$0.0271928\pi$
$510$	−5.44128	+	5.50467i	−0.240944	+	0.243751i
$511$	2.92310	−	8.99639i	0.129310	−	0.397977i
$512$	22.5029	+	2.37061i	0.994497	+	0.104767i
$513$	7.31374	+	0.768705i	0.322910	+	0.0339392i
$514$	−35.6612	+	2.07607i	−1.57295	+	0.0915717i
$515$	8.88608	+	8.00106i	0.391567	+	0.352569i
$516$	−9.91945	+	3.35053i	−0.436679	+	0.147499i
$517$	−13.8572	+	65.1932i	−0.609441	+	2.86719i
$518$	6.46730	−	24.7078i	0.284157	−	1.08560i
$519$	7.60532	+	5.52559i	0.333837	+	0.242547i
$520$	1.82488	−	1.53101i	0.0800262	−	0.0671391i
$521$	−13.4956	−	23.3750i	−0.591252	−	1.02408i	−0.994064	−	0.108796i	$-0.965300\pi$
$521$	−13.4956	−	23.3750i	−0.591252	−	1.02408i	0.402812	−	0.915283i	$-0.368033\pi$
$522$	−1.04050	+	0.406338i	−0.0455412	+	0.0177849i
$523$	−1.82101	+	1.32304i	−0.0796271	+	0.0578525i	−0.626887	−	0.779111i	$-0.715671\pi$
$523$	−1.82101	+	1.32304i	−0.0796271	+	0.0578525i	0.547260	+	0.836963i	$0.315671\pi$
$524$	−3.67743	+	1.68860i	−0.160649	+	0.0737668i
$525$	−7.56184	+	2.45699i	−0.330026	+	0.107232i
$526$	10.3600	−	12.9461i	0.451716	−	0.564475i
$527$	32.0308	−	2.48534i	1.39529	−	0.108263i
$528$	−18.5506	+	8.77962i	−0.807312	+	0.382084i
$529$	−3.63854	−	11.1983i	−0.158197	−	0.486881i
$530$	4.60418	+	2.31246i	0.199993	+	0.100447i
$531$	−2.11129	−	2.90594i	−0.0916221	−	0.126107i
$532$	−27.2248	−	8.49856i	−1.18035	−	0.368459i
$533$	4.04748	−	2.33682i	0.175316	−	0.101219i
$534$	1.54685	+	2.99288i	0.0669386	+	0.129515i
$535$	−1.25778	+	1.73118i	−0.0543784	+	0.0748455i
$536$	−1.24929	+	35.6932i	−0.0539613	+	1.54171i
$537$	17.9063	+	3.80610i	0.772714	+	0.164245i
$538$	−5.43536	+	8.47679i	−0.234335	+	0.365460i
$539$	−11.1231	+	12.3535i	−0.479106	+	0.532102i
$540$	−1.09719	+	1.54753i	−0.0472153	+	0.0665949i
$541$	−1.59844	+	15.2081i	−0.0687221	+	0.653847i	0.904891	+	0.425643i	$0.139952\pi$
$541$	−1.59844	+	15.2081i	−0.0687221	+	0.653847i	−0.973613	+	0.228204i	$0.926715\pi$
$542$	−2.21561	−	3.36887i	−0.0951686	−	0.144705i
$543$	2.80931	+	0.912801i	0.120559	+	0.0391720i
$544$	−10.8104	+	30.7991i	−0.463493	+	1.32050i
$545$	4.89734	+	5.43905i	0.209779	+	0.232983i
$546$	−0.394824	−	2.40268i	−0.0168969	−	0.102825i
$547$	5.27042	−	0.553944i	0.225347	−	0.0236849i	0.00881804	−	0.999961i	$-0.497193\pi$
$547$	5.27042	−	0.553944i	0.225347	−	0.0236849i	0.216529	+	0.976276i	$0.430526\pi$
$548$	37.3291	−	0.432371i	1.59462	−	0.0184700i
$549$	−4.67439	−	10.4989i	−0.199498	−	0.448080i
$550$	28.6936	−	7.86679i	1.22350	−	0.335441i
$551$	5.30643	+	2.36258i	0.226062	+	0.100649i
$552$	0.660289	+	9.45345i	0.0281038	+	0.402365i
$553$	9.97537	+	5.75928i	0.424196	+	0.244910i
$554$	42.8767	+	1.99816i	1.82166	+	0.0848938i
$555$	1.83665	+	8.64075i	0.0779613	+	0.366779i
$556$	−18.7934	+	11.1426i	−0.797018	+	0.472550i
$557$		−	14.5963i		−	0.618465i	−0.950987	−	0.309232i	$-0.899928\pi$
$557$		−	14.5963i		−	0.618465i	0.950987	−	0.309232i	$-0.100072\pi$
$558$	7.64775	−	1.87402i	0.323755	−	0.0793338i
$559$			4.64819i			0.196598i
$560$	5.35183	−	5.04811i	0.226156	−	0.213322i
$561$	−6.15542	−	28.9590i	−0.259882	−	1.22265i
$562$	1.15132	−	24.7050i	0.0485654	−	1.04212i
$563$	−30.0801	−	17.3668i	−1.26773	−	0.731922i	−0.293169	−	0.956061i	$-0.594710\pi$
$563$	−30.0801	−	17.3668i	−1.26773	−	0.731922i	−0.974557	+	0.224139i	$0.928043\pi$
$564$	17.6065	+	19.1043i	0.741368	+	0.804437i
$565$	−13.7975	−	6.14306i	−0.580466	−	0.258440i
$566$	−2.54527	−	9.28368i	−0.106986	−	0.390222i
$567$	0.788705	+	1.77146i	0.0331225	+	0.0743944i
$568$	−4.15024	+	5.31119i	−0.174140	+	0.222853i
$569$	−42.6646	+	4.48423i	−1.78859	+	0.187989i	−0.940027	−	0.341099i	$-0.889201\pi$
$569$	−42.6646	+	4.48423i	−1.78859	+	0.187989i	−0.848567	+	0.529088i	$0.822534\pi$
$570$	9.73406	−	1.59956i	0.407715	−	0.0669983i
$571$	−1.64158	−	1.82316i	−0.0686980	−	0.0762968i	0.707816	−	0.706397i	$-0.249681\pi$
$571$	−1.64158	−	1.82316i	−0.0686980	−	0.0762968i	−0.776514	+	0.630100i	$0.783014\pi$
$572$	1.05728	+	9.04982i	0.0442072	+	0.378392i
$573$	21.6689	+	7.04064i	0.905230	+	0.294127i
$574$	12.0601	−	7.93162i	0.503380	−	0.331059i
$575$	1.43601	−	13.6627i	0.0598856	−	0.569773i
$576$	−1.39045	+	7.87824i	−0.0579353	+	0.328260i
$577$	−7.79804	+	8.66060i	−0.324637	+	0.360546i	−0.883266	−	0.468872i	$-0.844661\pi$
$577$	−7.79804	+	8.66060i	−0.324637	+	0.360546i	0.558630	+	0.829417i	$0.311327\pi$
$578$	−19.3995	−	12.4390i	−0.806911	−	0.517395i
$579$	9.28464	+	1.97351i	0.385857	+	0.0820164i
$580$	−1.20192	+	0.894696i	−0.0499070	+	0.0371502i
$581$	6.72892	−	9.26156i	0.279162	−	0.384234i
$582$	−9.90346	+	5.11852i	−0.410512	+	0.212170i
$583$	−17.0672	+	9.85376i	−0.706852	+	0.408101i
$584$	7.71464	+	11.4394i	0.319234	+	0.473366i
$585$	0.495022	+	0.681340i	0.0204666	+	0.0281699i
$586$	−0.241911	+	0.481652i	−0.00999324	+	0.0198969i
$587$	−7.32804	−	22.5534i	−0.302461	−	0.930878i	−0.980613	−	0.195957i	$-0.937219\pi$
$587$	−7.32804	−	22.5534i	−0.302461	−	0.930878i	0.678152	−	0.734922i	$-0.262781\pi$
$588$	1.42053	+	6.32212i	0.0585817	+	0.260720i
$589$	−34.8882	−	21.4325i	−1.43754	−	0.883109i
$590$	−3.76193	−	3.01045i	−0.154876	−	0.123938i
$591$	2.04254	−	0.663661i	0.0840188	−	0.0272994i
$592$	22.5893	+	29.6234i	0.928413	+	1.21752i
$593$	−13.9564	+	10.1399i	−0.573119	+	0.416395i	−0.836237	−	0.548368i	$-0.815249\pi$
$593$	−13.9564	+	10.1399i	−0.573119	+	0.416395i	0.263118	+	0.964764i	$0.415249\pi$
$594$	−2.63954	−	6.75897i	−0.108301	−	0.277324i
$595$	5.30643	+	9.19100i	0.217542	+	0.376794i
$596$	1.50825	−	7.52317i	0.0617802	−	0.308161i
$597$	7.42183	+	5.39227i	0.303755	+	0.220691i
$598$	4.06999	+	1.06533i	0.166434	+	0.0435644i
$599$	−9.88524	+	46.5064i	−0.403900	+	1.90020i	0.0306088	+	0.999531i	$0.490255\pi$
$599$	−9.88524	+	46.5064i	−0.403900	+	1.90020i	−0.434509	+	0.900668i	$0.643078\pi$
$600$	3.96745	−	10.8978i	0.161971	−	0.444900i
$601$	−19.1525	−	17.2450i	−0.781249	−	0.703439i	0.178611	−	0.983920i	$-0.442840\pi$
$601$	−19.1525	−	17.2450i	−0.781249	−	0.703439i	−0.959860	+	0.280480i	$0.909506\pi$
$602$	0.834346	+	14.3318i	0.0340054	+	0.584119i
$603$	−12.5580	−	1.31990i	−0.511401	−	0.0537504i
$604$	7.21601	+	0.674032i	0.293615	+	0.0274260i
$605$	4.49195	−	13.8248i	0.182624	−	0.562058i
$606$	7.84434	+	7.75401i	0.318654	+	0.314985i
$607$	28.5818	−	25.7352i	1.16010	−	1.04456i	0.161768	−	0.986829i	$-0.448280\pi$
$607$	28.5818	−	25.7352i	1.16010	−	1.04456i	0.998332	−	0.0577300i	$-0.0183862\pi$
$608$	34.2187	−	23.6579i	1.38775	−	0.959456i
$609$	0.160097	+	1.52322i	0.00648746	+	0.0617240i
$610$	−9.77071	−	11.9240i	−0.395604	−	0.482787i
$611$	10.5368	−	4.69126i	0.426271	−	0.189788i
$612$	−10.5963	−	4.57149i	−0.428332	−	0.184791i
$613$	8.96685	−	20.1399i	0.362168	−	0.813442i	−0.636928	−	0.770923i	$-0.719795\pi$
$613$	8.96685	−	20.1399i	0.362168	−	0.813442i	0.999096	−	0.0425187i	$-0.0135382\pi$
$614$	−1.20283	+	7.88985i	−0.0485424	+	0.318408i
$615$	−2.49631	+	4.32373i	−0.100661	+	0.174350i
$616$	4.88435	+	27.7135i	0.196796	+	1.11661i
$617$	−12.0193	+	2.55478i	−0.483879	+	0.102852i	−0.443391	−	0.896328i	$-0.646225\pi$
$617$	−12.0193	+	2.55478i	−0.483879	+	0.102852i	−0.0404883	+	0.999180i	$0.512891\pi$
$618$	−6.29263	+	16.6809i	−0.253127	+	0.671006i
$619$	25.2589			1.01524			0.507620	−	0.861581i	$-0.330525\pi$
$619$	25.2589			1.01524			0.507620	+	0.861581i	$0.330525\pi$
$620$	9.22884	−	5.13679i	0.370639	−	0.206299i
$621$	−3.35044			−0.134449
$622$	−9.60583	+	25.4638i	−0.385159	+	1.02101i
$623$	4.51846	−	0.960429i	0.181028	−	0.0384788i
$624$	3.11610	+	1.70409i	0.124744	+	0.0682182i
$625$	−6.15723	+	10.6646i	−0.246289	+	0.426585i
$626$	2.27680	−	14.9344i	0.0909992	−	0.596898i
$627$	−15.3471	+	34.4701i	−0.612904	+	1.37661i
$628$	9.24008	−	21.4178i	0.368719	−	0.854662i
$629$	−49.0940	+	21.8580i	−1.95751	+	0.871537i
$630$	1.64860	+	2.01192i	0.0656818	+	0.0801567i
$631$	−2.14230	−	20.3826i	−0.0852836	−	0.811419i	−0.950647	−	0.310275i	$-0.899579\pi$
$631$	−2.14230	−	20.3826i	−0.0852836	−	0.811419i	0.865363	−	0.501145i	$-0.167088\pi$
$632$	−15.5784	+	6.29262i	−0.619674	+	0.250307i
$633$	7.57623	−	6.82167i	0.301128	−	0.271137i
$634$	−10.9679	−	10.8416i	−0.435591	−	0.430575i
$635$	3.83805	−	11.8123i	0.152308	−	0.468757i
$636$	−0.714449	+	7.64871i	−0.0283298	+	0.303291i
$637$	2.86094	+	0.300697i	0.113354	+	0.0119140i
$638$	−0.333090	−	5.72157i	−0.0131872	−	0.226519i
$639$	−1.77099	−	1.59460i	−0.0700592	−	0.0630816i
$640$	0.995460	+	10.6848i	0.0393490	+	0.422355i
$641$	−6.47904	+	30.4815i	−0.255907	+	1.20395i	0.643021	+	0.765849i	$0.277681\pi$
$641$	−6.47904	+	30.4815i	−0.255907	+	1.20395i	−0.898927	+	0.438098i	$0.855652\pi$
$642$	−3.08653	−	0.807904i	−0.121816	−	0.0318854i
$643$	−37.2144	−	27.0378i	−1.46759	−	1.06627i	−0.981303	−	0.192470i	$-0.938350\pi$
$643$	−37.2144	−	27.0378i	−1.46759	−	1.06627i	−0.486289	−	0.873798i	$-0.661650\pi$
$644$	12.7402	+	2.55416i	0.502034	+	0.100648i
$645$	−2.48272	−	4.30020i	−0.0977570	−	0.169320i
$646$	21.8301	+	55.8997i	0.858895	+	2.19934i
$647$	−15.6225	+	11.3504i	−0.614185	+	0.446231i	−0.850885	−	0.525351i	$-0.823934\pi$
$647$	−15.6225	+	11.3504i	−0.614185	+	0.446231i	0.236701	+	0.971583i	$0.423934\pi$
$648$	−2.74436	−	0.684478i	−0.107808	−	0.0268888i
$649$	17.5276	−	5.69507i	0.688019	−	0.223551i
$650$	−4.02002	−	3.21698i	−0.157678	−	0.126180i
$651$	0.294523	−	10.7925i	0.0115433	−	0.422990i
$652$	20.1490	−	4.52734i	0.789098	−	0.177304i
$653$	0.229743	+	0.707077i	0.00899055	+	0.0276701i	0.955451	−	0.295149i	$-0.0953694\pi$
$653$	0.229743	+	0.707077i	0.00899055	+	0.0276701i	−0.946461	+	0.322819i	$0.895369\pi$
$654$	−4.89779	+	9.75165i	−0.191519	+	0.381320i
$655$	−1.12802	−	1.55259i	−0.0440754	−	0.0606646i
$656$	−1.71522	+	20.9847i	−0.0669680	+	0.819314i
$657$	−4.22465	+	2.43911i	−0.164819	+	0.0951585i
$658$	31.6459	−	16.3559i	1.23368	−	0.637619i
$659$	7.08179	−	9.74725i	0.275867	−	0.379699i	−0.648492	−	0.761221i	$-0.724600\pi$
$659$	7.08179	−	9.74725i	0.275867	−	0.379699i	0.924360	+	0.381522i	$0.124600\pi$
$660$	−5.81187	−	7.80757i	−0.226227	−	0.303909i
$661$	35.9688	+	7.64540i	1.39902	+	0.297371i	0.844838	−	0.535022i	$-0.179697\pi$
$661$	35.9688	+	7.64540i	1.39902	+	0.297371i	0.554185	+	0.832394i	$0.313030\pi$
$662$	−11.2118	−	7.18905i	−0.435758	−	0.279410i
$663$	−3.42822	+	3.80742i	−0.133141	+	0.147868i
$664$	4.60137	+	16.0517i	0.178568	+	0.622928i
$665$	1.41384	−	13.4518i	0.0548265	−	0.521639i
$666$	−11.0045	+	7.23734i	−0.426415	+	0.280441i
$667$	−2.51684	−	0.817770i	−0.0974524	−	0.0316642i
$668$	2.48547	−	0.290375i	0.0961657	−	0.0112350i
$669$	8.19559	+	9.10213i	0.316860	+	0.351909i
$670$	−16.7138	+	2.74651i	−0.645710	+	0.106107i
$671$	58.6427	−	6.16360i	2.26388	−	0.237943i
$672$	9.91374	+	4.69488i	0.382431	+	0.181109i
$673$	18.1795	+	40.8318i	0.700768	+	1.57395i	0.814319	+	0.580418i	$0.197111\pi$
$673$	18.1795	+	40.8318i	0.700768	+	1.57395i	−0.113551	+	0.993532i	$0.536222\pi$
$674$	1.12301	+	4.09609i	0.0432567	+	0.157776i
$675$	3.74584	+	1.66776i	0.144178	+	0.0641920i
$676$	−17.9595	+	16.5515i	−0.690751	+	0.636595i
$677$	3.83184	+	2.21231i	0.147269	+	0.0850261i	0.571824	−	0.820376i	$-0.306236\pi$
$677$	3.83184	+	2.21231i	0.147269	+	0.0850261i	−0.424555	+	0.905402i	$0.639569\pi$
$678$	1.04830	−	22.4944i	0.0402596	−	0.863894i
$679$	3.17806	+	14.9516i	0.121963	+	0.573789i
$680$	−15.3293	−	2.15565i	−0.587854	−	0.0826654i
$681$		−	19.5331i		−	0.748509i
$682$	−2.98091	+	40.2901i	−0.114145	+	1.54279i
$683$		−	2.72035i		−	0.104091i	−0.998645	−	0.0520457i	$-0.983426\pi$
$683$		−	2.72035i		−	0.104091i	0.998645	−	0.0520457i	$-0.0165741\pi$
$684$	7.50106	+	12.6515i	0.286810	+	0.483743i
$685$	3.68100	+	17.3177i	0.140644	+	0.661677i
$686$	28.0504	+	1.30722i	1.07097	+	0.0499099i
$687$	−13.4810	−	7.78328i	−0.514333	−	0.296951i
$688$	−17.2214	−	11.9126i	−0.656560	−	0.454162i
$689$	3.11559	+	1.38715i	0.118695	+	0.0528463i
$690$	−4.33430	+	1.18832i	−0.165004	+	0.0452384i
$691$	8.51202	+	19.1183i	0.323813	+	0.727295i	0.999955	−	0.00947593i	$-0.00301633\pi$
$691$	8.51202	+	19.1183i	0.323813	+	0.727295i	−0.676143	+	0.736771i	$0.736350\pi$
$692$	0.217756	+	18.8001i	0.00827784	+	0.714674i
$693$	−9.89472	+	1.03998i	−0.375869	+	0.0395055i
$694$	0.598431	+	3.64172i	0.0227161	+	0.138238i
$695$	−6.93328	−	7.70019i	−0.262994	−	0.292085i
$696$	−1.89448	−	1.18402i	−0.0718102	−	0.0448800i
$697$	−28.8859	−	9.38559i	−1.09413	−	0.355505i
$698$	−26.0202	−	39.5641i	−0.984878	−	1.49752i
$699$	2.80037	−	26.6437i	0.105920	−	1.00776i
$700$	−12.9724	−	9.19732i	−0.490309	−	0.347626i
$701$	−8.63817	+	9.59366i	−0.326259	+	0.362347i	−0.883852	−	0.467767i	$-0.845058\pi$
$701$	−8.63817	+	9.59366i	−0.326259	+	0.362347i	0.557593	+	0.830115i	$0.311725\pi$
$702$	−0.677786	+	1.05705i	−0.0255814	+	0.0398958i
$703$	66.9941	+	14.2400i	2.52673	+	0.537073i
$704$	−36.2390	−	19.2760i	−1.36581	−	0.726493i
$705$	−7.24217	+	9.96799i	−0.272756	+	0.375416i
$706$	−22.8281	−	44.1684i	−0.859146	−	1.66230i
$707$	13.0975	−	7.56183i	0.492581	−	0.284392i
$708$	2.14066	−	6.85752i	0.0804509	−	0.257721i
$709$	−26.8866	−	37.0063i	−1.00975	−	1.38980i	−0.919148	−	0.393912i	$-0.871122\pi$
$709$	−26.8866	−	37.0063i	−1.00975	−	1.38980i	−0.0906000	−	0.995887i	$-0.528878\pi$
$710$	−2.85660	−	1.43474i	−0.107206	−	0.0538447i
$711$	−1.83561	−	5.64942i	−0.0688406	−	0.211870i
$712$	−2.95422	+	6.05582i	−0.110714	+	0.226951i
$713$	16.8284	+	8.04952i	0.630228	+	0.301457i
$714$	−9.88678	+	12.3548i	−0.370003	+	0.462366i
$715$	−4.10960	+	1.33529i	−0.153690	+	0.0499371i
$716$	15.2781	+	33.2726i	0.570970	+	1.24346i
$717$	−15.1165	+	10.9828i	−0.564536	+	0.410159i
$718$	32.4334	−	12.6660i	1.21040	−	0.472691i
$719$	−14.1029	−	24.4269i	−0.525949	−	0.910971i	−0.999543	−	0.0302275i	$-0.990377\pi$
$719$	−14.1029	−	24.4269i	−0.525949	−	0.910971i	0.473594	−	0.880743i	$-0.342957\pi$
$720$	−3.79300	+	0.0878781i	−0.141357	+	0.00327502i
$721$	19.7768	+	14.3687i	0.736526	+	0.535118i
$722$	12.5631	−	47.9961i	0.467549	−	1.78623i
$723$	4.10861	−	19.3295i	0.152801	−	0.718871i
$724$	1.89055	+	5.59710i	0.0702619	+	0.208015i
$725$	2.40680	+	2.16709i	0.0893864	+	0.0804838i
$726$	21.6368	−	1.25962i	0.803017	−	0.0467489i
$727$	5.44986	+	0.572804i	0.202124	+	0.0212441i	0.205049	−	0.978752i	$-0.434264\pi$
$727$	5.44986	+	0.572804i	0.202124	+	0.0212441i	−0.00292526	+	0.999996i	$0.500931\pi$
$728$	3.38314	−	3.50278i	0.125387	−	0.129822i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−4.60014	+	4.65373i	−0.170259	+	0.172242i
$731$	22.4482	−	20.2125i	0.830278	−	0.747586i
$732$	11.2611	−	20.0372i	0.416223	−	0.740598i
$733$	2.98183	+	28.3702i	0.110136	+	1.04788i	0.900386	+	0.435092i	$0.143284\pi$
$733$	2.98183	+	28.3702i	0.110136	+	1.04788i	−0.790250	+	0.612785i	$0.790049\pi$
$734$	−1.81041	+	1.48348i	−0.0668233	+	0.0547562i
$735$	−2.80736	+	1.24992i	−0.103551	+	0.0461038i
$736$	−14.3777	+	12.3489i	−0.529970	+	0.455187i
$737$	26.3516	−	59.1867i	0.970674	−	2.18017i
$738$	−7.35892	−	1.12189i	−0.270886	−	0.0412974i
$739$	18.6217	−	32.2536i	0.685009	−	1.18647i	−0.288426	−	0.957502i	$-0.593132\pi$
$739$	18.6217	−	32.2536i	0.685009	−	1.18647i	0.973434	−	0.228967i	$-0.0735349\pi$
$740$	−11.6691	+	13.2656i	−0.428963	+	0.487653i
$741$	6.38699	−	1.35760i	0.234632	−	0.0498725i
$742$	9.85529	+	3.71775i	0.361799	+	0.136483i
$743$	−35.6626			−1.30833			−0.654167	−	0.756350i	$-0.726981\pi$
$743$	−35.6626			−1.30833			−0.654167	+	0.756350i	$0.726981\pi$
$744$	12.1397	+	10.0313i	0.445063	+	0.367767i
$745$	3.63888			0.133318
$746$	45.2634	+	17.0749i	1.65721	+	0.625157i
$747$	−5.77470	+	1.22745i	−0.211285	+	0.0449101i
$748$	39.1082	−	44.4589i	1.42994	−	1.62558i
$749$	−2.18734	+	3.78859i	−0.0799237	+	0.138432i
$750$	12.0677	+	1.83976i	0.440649	+	0.0671784i
$751$	−13.2935	+	29.8577i	−0.485086	+	1.08952i	0.490806	+	0.871269i	$0.336702\pi$
$751$	−13.2935	+	29.8577i	−0.485086	+	1.08952i	−0.975892	+	0.218253i	$0.929964\pi$
$752$	−9.62301	+	51.0613i	−0.350915	+	1.86201i
$753$	0.607025	−	0.270265i	0.0221212	−	0.00984901i
$754$	−0.767153	+	0.628619i	−0.0279381	+	0.0228930i
$755$	0.359276	+	3.41828i	0.0130754	+	0.124404i
$756$	−1.90008	+	3.38086i	−0.0691051	+	0.122961i
$757$	35.0147	−	31.5274i	1.27263	−	1.14588i	0.290664	−	0.956825i	$-0.406124\pi$
$757$	35.0147	−	31.5274i	1.27263	−	1.14588i	0.981966	−	0.189056i	$-0.0605429\pi$
$758$	−11.4291	+	11.5622i	−0.415123	+	0.419959i
$759$	5.31217	−	16.3492i	0.192820	−	0.593438i
$760$	14.1909	+	13.7062i	0.514759	+	0.497176i
$761$	−11.2419	−	1.18157i	−0.407518	−	0.0428319i	−0.101448	−	0.994841i	$-0.532348\pi$
$761$	−11.2419	−	1.18157i	−0.407518	−	0.0428319i	−0.306070	+	0.952009i	$0.599014\pi$
$762$	18.4871	−	1.07626i	0.669717	−	0.0389886i
$763$	11.1195	+	10.0120i	0.402552	+	0.362460i
$764$	14.5823	+	43.1717i	0.527568	+	1.56190i
$765$	1.13791	−	5.35347i	0.0411414	−	0.193555i
$766$	−1.34131	+	5.12434i	−0.0484634	+	0.185150i
$767$	−2.58020	−	1.87462i	−0.0931654	−	0.0676887i
$768$	−14.2997	+	7.17773i	−0.515994	+	0.259004i
$769$	−22.6652	−	39.2572i	−0.817327	−	1.41565i	−0.907645	−	0.419739i	$-0.862122\pi$
$769$	−22.6652	−	39.2572i	−0.817327	−	1.41565i	0.0903176	−	0.995913i	$-0.471212\pi$
$770$	−12.4314	+	4.85477i	−0.447998	+	0.174954i
$771$	20.4349	−	14.8469i	0.735946	−	0.534696i
$772$	7.92189	+	17.2523i	0.285115	+	0.620923i
$773$	−34.6442	+	11.2566i	−1.24606	+	0.404871i	−0.856509	−	0.516132i	$-0.827371\pi$
$773$	−34.6442	+	11.2566i	−1.24606	+	0.404871i	−0.389555	+	0.921003i	$0.627371\pi$
$774$	4.62573	−	5.78043i	0.166268	−	0.207773i
$775$	−14.8076	−	17.3762i	−0.531903	−	0.624171i
$776$	−20.0387	−	9.77552i	−0.719348	−	0.350921i
$777$	5.58073	+	17.1757i	0.200207	+	0.616175i
$778$	−19.8946	−	9.99209i	−0.713254	−	0.358234i
$779$	22.7527	+	31.3163i	0.815199	+	1.12202i
$780$	−0.501909	+	1.60785i	−0.0179712	+	0.0575701i
$781$	10.5891	−	6.11364i	0.378909	−	0.218763i
$782$	−12.5532	−	24.2884i	−0.448903	−	0.868550i
$783$	0.464265	−	0.639006i	0.0165915	−	0.0228362i
$784$	−8.44619	+	9.82904i	−0.301650	+	0.351037i
$785$	10.8207	+	2.30000i	0.386206	+	0.0820906i
$786$	1.54449	−	2.40873i	0.0550901	−	0.0859165i
$787$	24.4534	−	27.1583i	0.871670	−	0.968088i	−0.128049	−	0.991768i	$-0.540872\pi$
$787$	24.4534	−	27.1583i	0.871670	−	0.968088i	0.999720	+	0.0236798i	$0.00753823\pi$
$788$	3.50398	+	2.48430i	0.124824	+	0.0884995i
$789$	−1.22555	+	11.6603i	−0.0436307	+	0.415118i
$790$	−4.37834	−	6.65732i	−0.155774	−	0.236857i
$791$	−29.3656	−	9.54147i	−1.04412	−	0.339256i
$792$	7.69127	−	12.3064i	0.273297	−	0.437289i
$793$	−6.82793	−	7.58319i	−0.242467	−	0.269287i
$794$	−7.08402	−	43.1094i	−0.251402	−	1.52990i
$795$	−3.62325	+	0.380819i	−0.128503	+	0.0135063i
$796$	0.212502	+	18.3465i	0.00753194	+	0.650276i
$797$	−16.2757	−	36.5558i	−0.576514	−	1.29487i	−0.932766	−	0.360483i	$-0.882612\pi$
$797$	−16.2757	−	36.5558i	−0.576514	−	1.29487i	0.356252	−	0.934390i	$-0.384055\pi$
$798$	19.4493	−	5.33233i	0.688497	−	0.188762i
$799$	−68.4749	−	30.4870i	−2.42247	−	1.07855i
$800$	22.2215	−	6.64944i	0.785647	−	0.235093i
$801$	−2.06308	−	1.19112i	−0.0728952	−	0.0420861i
$802$	12.6554	+	0.589772i	0.446877	+	0.0208256i
$803$	−5.20388	−	24.4823i	−0.183641	−	0.863962i
$804$	−12.8796	−	21.7232i	−0.454229	−	0.766118i
$805$			6.16230i			0.217193i
$806$	5.94393	−	3.68089i	0.209366	−	0.129654i
$807$		−	7.12036i		−	0.250648i
$808$	−3.07187	+	21.8448i	−0.108068	+	0.768498i
$809$	4.34666	+	20.4494i	0.152820	+	0.718964i	0.986106	+	0.166120i	$0.0531239\pi$
$809$	4.34666	+	20.4494i	0.152820	+	0.718964i	−0.833285	+	0.552843i	$0.813543\pi$
$810$	0.0624443	−	1.33993i	0.00219407	−	0.0470805i
$811$	10.0269	+	5.78901i	0.352091	+	0.203280i	0.665606	−	0.746303i	$-0.268173\pi$
$811$	10.0269	+	5.78901i	0.352091	+	0.203280i	−0.313515	+	0.949583i	$0.601507\pi$
$812$	−2.25253	+	2.07592i	−0.0790482	+	0.0728506i
$813$	2.60466	+	1.15967i	0.0913495	+	0.0406714i
$814$	−17.8684	−	65.1736i	−0.626286	−	2.28433i
$815$	3.98357	+	8.94725i	0.139538	+	0.313409i
$816$	−5.32040	−	22.4592i	−0.186251	−	0.786230i
$817$	−38.2875	+	4.02418i	−1.33951	+	0.140788i
$818$	−8.78106	+	1.44296i	−0.307023	+	0.0504519i
$819$	1.15207	+	1.27950i	0.0402565	+	0.0447094i
$820$	−9.91777	+	1.15868i	−0.346344	+	0.0404630i
$821$	−27.5078	−	8.93783i	−0.960029	−	0.311932i	−0.213245	−	0.976999i	$-0.568403\pi$
$821$	−27.5078	−	8.93783i	−0.960029	−	0.311932i	−0.746784	+	0.665067i	$0.768403\pi$
$822$	−22.0551	+	14.5051i	−0.769261	+	0.505922i
$823$	1.27137	−	12.0963i	0.0443171	−	0.421650i	−0.949761	−	0.312978i	$-0.898674\pi$
$823$	1.27137	−	12.0963i	0.0443171	−	0.421650i	0.994078	−	0.108672i	$-0.0346598\pi$
$824$	−34.2763	+	9.82559i	−1.19407	+	0.342291i
$825$	−14.0773	+	15.6344i	−0.490107	+	0.544319i
$826$	−8.29200	−	5.31687i	−0.288516	−	0.184998i
$827$	−23.5923	−	5.01469i	−0.820383	−	0.174378i	−0.221445	−	0.975173i	$-0.571077\pi$
$827$	−23.5923	−	5.01469i	−0.820383	−	0.174378i	−0.598938	+	0.800795i	$0.704411\pi$
$828$	−4.00120	−	5.37515i	−0.139051	−	0.186799i
$829$	−4.10009	+	5.64329i	−0.142402	+	0.195999i	−0.874260	−	0.485457i	$-0.838653\pi$
$829$	−4.10009	+	5.64329i	−0.142402	+	0.195999i	0.731859	+	0.681457i	$0.238653\pi$
$830$	−7.03510	+	3.63603i	−0.244192	+	0.126208i
$831$	−26.2850	+	15.1757i	−0.911818	+	0.526438i
$832$	0.987453	+	7.03427i	0.0342338	+	0.243869i
$833$	−10.9885	−	15.1243i	−0.380728	−	0.524027i
$834$	6.93391	−	13.8056i	0.240102	−	0.478050i
$835$	0.366728	+	1.12867i	0.0126911	+	0.0390593i
$836$	−73.6288	+	16.5438i	−2.54651	+	0.572180i
$837$	−3.83705	+	4.03448i	−0.132628	+	0.139452i
$838$	18.4778	+	14.7867i	0.638305	+	0.510797i
$839$	21.3655	−	6.94206i	0.737618	−	0.239667i	0.0839731	−	0.996468i	$-0.473239\pi$
$839$	21.3655	−	6.94206i	0.737618	−	0.239667i	0.653645	+	0.756801i	$0.273239\pi$
$840$	−1.25893	+	5.04756i	−0.0434371	+	0.174157i
$841$	−22.9568	+	16.6791i	−0.791613	+	0.575140i
$842$	6.29696	+	16.1244i	0.217008	+	0.555684i
$843$	8.74403	+	15.1451i	0.301160	+	0.521625i
$844$	19.9918	+	4.00797i	0.688147	+	0.137960i
$845$	−9.37067	−	6.80819i	−0.322361	−	0.234209i
$846$	−17.7720	−	4.65184i	−0.611012	−	0.159934i
$847$	6.17864	−	29.0682i	0.212301	−	0.998796i
$848$	−13.1241	+	7.98813i	−0.450684	+	0.274313i
$849$	5.05844	+	4.55464i	0.173605	+	0.156315i
$850$	1.94463	+	33.4034i	0.0667004	+	1.14573i
$851$	−31.0330	−	3.26170i	−1.06380	−	0.111810i
$852$	0.443271	−	4.74554i	0.0151862	−	0.162580i
$853$	−5.01611	+	15.4380i	−0.171748	+	0.528587i	−0.999470	−	0.0325516i	$-0.989637\pi$
$853$	−5.01611	+	15.4380i	−0.171748	+	0.528587i	0.827722	+	0.561139i	$0.189637\pi$
$854$	−22.4137	−	22.1556i	−0.766982	−	0.758149i
$855$	−5.18368	+	4.66741i	−0.177278	+	0.159622i
$856$	−2.38990	−	5.91657i	−0.0816851	−	0.202224i
$857$	2.57533	+	24.5026i	0.0879714	+	0.836992i	0.946169	+	0.323673i	$0.104918\pi$
$857$	2.57533	+	24.5026i	0.0879714	+	0.836992i	−0.858198	+	0.513319i	$0.828416\pi$
$858$	−4.08346	−	4.98337i	−0.139407	−	0.170129i
$859$	−12.6913	+	5.65051i	−0.433020	+	0.192793i	−0.611659	−	0.791122i	$-0.709497\pi$
$859$	−12.6913	+	5.65051i	−0.433020	+	0.192793i	0.178639	+	0.983915i	$0.442831\pi$
$860$	3.93391	−	9.11848i	0.134145	−	0.310938i
$861$	−4.15148	+	9.32437i	−0.141482	+	0.317774i
$862$	4.33067	−	28.4065i	0.147503	−	0.967529i
$863$	−18.8313	+	32.6167i	−0.641024	+	1.11029i	0.344181	+	0.938903i	$0.388157\pi$
$863$	−18.8313	+	32.6167i	−0.641024	+	1.11029i	−0.985205	+	0.171382i	$0.945177\pi$
$864$	−2.17928	−	5.22022i	−0.0741407	−	0.177596i
$865$	−8.72176	+	1.85387i	−0.296549	+	0.0630334i
$866$	19.4056	−	51.4418i	0.659430	−	1.74806i
$867$	16.2952			0.553415
$868$	17.6662	−	12.4162i	0.599629	−	0.421433i
$869$	30.4779			1.03389
$870$	0.373957	−	0.991313i	0.0126783	−	0.0336087i
$871$	−10.9667	+	2.33105i	−0.371593	+	0.0789845i
$872$	−21.4938	+	3.78816i	−0.727870	+	0.128283i
$873$	3.94141	−	6.82672i	0.133397	−	0.231050i
$874$	−5.25158	+	34.4471i	−0.177637	+	1.16519i
$875$	6.80788	−	15.2907i	0.230148	−	0.516922i
$876$	−8.95830	−	3.86480i	−0.302673	−	0.130579i
$877$	35.8560	−	15.9641i	1.21077	−	0.539070i	0.300779	−	0.953694i	$-0.402753\pi$
$877$	35.8560	−	15.9641i	1.21077	−	0.539070i	0.909993	+	0.414623i	$0.136087\pi$
$878$	21.1845	+	25.8531i	0.714941	+	0.872499i
$879$	−0.0398382	−	0.379035i	−0.00134371	−	0.0127845i
$880$	5.58504	−	18.6481i	0.188272	−	0.628627i
$881$	32.3941	−	29.1678i	1.09138	−	0.982687i	0.0914705	−	0.995808i	$-0.470843\pi$
$881$	32.3941	−	29.1678i	1.09138	−	0.982687i	0.999914	+	0.0131208i	$0.00417662\pi$
$882$	−3.25858	−	3.22105i	−0.109722	−	0.108459i
$883$	−8.50914	+	26.1884i	−0.286355	+	0.881311i	0.699634	+	0.714502i	$0.253347\pi$
$883$	−8.50914	+	26.1884i	−0.286355	+	0.881311i	−0.985989	+	0.166810i	$0.946653\pi$
$884$	−10.2024	−	0.952981i	−0.343143	−	0.0320522i
$885$	3.38831	+	0.356125i	0.113897	+	0.0119710i
$886$	0.265894	+	4.56733i	0.00893290	+	0.153443i
$887$	−13.4095	−	12.0740i	−0.450248	−	0.405405i	0.412565	−	0.910928i	$-0.364633\pi$
$887$	−13.4095	−	12.0740i	−0.450248	−	0.405405i	−0.862813	+	0.505523i	$0.831300\pi$
$888$	−24.7529	−	9.01155i	−0.830651	−	0.302408i
$889$	5.27921	−	24.8367i	0.177059	−	0.832997i
$890$	−3.09136	−	0.809169i	−0.103623	−	0.0271234i
$891$	4.15093	+	3.01583i	0.139061	+	0.101034i
$892$	−4.81520	+	24.0183i	−0.161225	+	0.804193i
$893$	47.7645	+	82.7306i	1.59838	+	2.76847i
$894$	1.97364	+	5.05383i	0.0660083	+	0.169025i
$895$	−14.0475	+	10.2061i	−0.469556	+	0.341152i
$896$	4.30726	+	21.5115i	0.143895	+	0.718648i
$897$	−2.82927	+	0.919286i	−0.0944666	+	0.0306941i
$898$	−10.6496	−	8.52222i	−0.355381	−	0.284390i
$899$	−3.86711	+	2.09415i	−0.128975	+	0.0698438i
$900$	1.79781	+	8.00119i	0.0599269	+	0.266706i
$901$	−6.84885	−	21.0786i	−0.228168	−	0.702230i
$902$	17.1422	−	34.1306i	0.570772	−	1.13643i
$903$	−5.96675	−	8.21253i	−0.198561	−	0.273296i
$904$	37.3400	−	25.1818i	1.24191	−	0.837534i
$905$	−2.42641	+	1.40089i	−0.0806566	+	0.0465671i
$906$	−4.55259	+	2.35297i	−0.151250	+	0.0781721i
$907$	5.99306	−	8.24874i	0.198996	−	0.273895i	−0.697844	−	0.716250i	$-0.745857\pi$
$907$	5.99306	−	8.24874i	0.198996	−	0.273895i	0.896840	+	0.442355i	$0.145857\pi$
$908$	31.3371	−	23.3270i	1.03996	−	0.774134i
$909$	−7.62887	−	1.62157i	−0.253034	−	0.0537840i
$910$	1.94418	+	1.24662i	0.0644490	+	0.0413250i
$911$	−8.52812	+	9.47144i	−0.282549	+	0.313803i	−0.867667	−	0.497145i	$-0.834382\pi$
$911$	−8.52812	+	9.47144i	−0.282549	+	0.313803i	0.585118	+	0.810948i	$0.301048\pi$
$912$	−11.3390	+	27.1429i	−0.375471	+	0.898790i
$913$	3.16627	−	30.1250i	0.104788	−	0.996992i
$914$	0.952026	−	0.626121i	0.0314902	−	0.0207102i
$915$	10.3671	+	3.36848i	0.342726	+	0.111359i
$916$	−3.61268	−	30.9228i	−0.119366	−	1.02172i
$917$	−2.62525	−	2.91564i	−0.0866935	−	0.0962828i
$918$	8.05230	−	1.32321i	0.265766	−	0.0436723i
$919$	−13.6678	+	1.43654i	−0.450859	+	0.0473872i	−0.327237	−	0.944942i	$-0.606118\pi$
$919$	−13.6678	+	1.43654i	−0.450859	+	0.0473872i	−0.123622	+	0.992329i	$0.539451\pi$
$920$	−7.08258	−	5.53443i	−0.233506	−	0.182465i
$921$	−2.29539	−	5.15553i	−0.0756356	−	0.169880i
$922$	2.89746	+	10.5683i	0.0954228	+	0.348048i
$923$	−1.93303	−	0.860640i	−0.0636264	−	0.0283283i
$924$	−13.4850	−	14.6322i	−0.443625	−	0.481365i
$925$	33.0718	+	19.0940i	1.08739	+	0.627807i
$926$	−1.97670	+	42.4163i	−0.0649585	+	1.39389i
$927$	−2.62105	−	12.3311i	−0.0860867	−	0.405006i
$928$	−0.362924	−	4.45333i	−0.0119136	−	0.146188i
$929$		−	11.0372i		−	0.362120i	−0.983472	−	0.181060i	$-0.942047\pi$
$929$		−	11.0372i		−	0.362120i	0.983472	−	0.181060i	$-0.0579528\pi$
$930$	−3.53287	+	6.58011i	−0.115847	+	0.215770i
$931$			23.8261i			0.780869i
$932$	46.0891	−	27.3261i	1.50970	−	0.895097i
$933$	−4.00110	−	18.8237i	−0.130990	−	0.616259i
$934$	48.5938	+	2.26459i	1.59004	+	0.0740998i
$935$	24.3192	+	14.0407i	0.795322	+	0.459180i
$936$	−2.50527	+	0.174984i	−0.0818873	+	0.00571953i
$937$	−24.4744	−	10.8967i	−0.799544	−	0.355980i	−0.0340475	−	0.999420i	$-0.510840\pi$
$937$	−24.4744	−	10.8967i	−0.799544	−	0.355980i	−0.765496	+	0.643440i	$0.777506\pi$
$938$	−33.3952	+	9.15583i	−1.09039	+	0.298948i
$939$	4.34485	+	9.75870i	0.141789	+	0.318463i
$940$	−24.6406	+	0.285404i	−0.803687	+	0.00930885i
$941$	23.3045	−	2.44940i	0.759704	−	0.0798481i	0.283248	−	0.959047i	$-0.408588\pi$
$941$	23.3045	−	2.44940i	0.759704	−	0.0798481i	0.476456	+	0.879198i	$0.341921\pi$
$942$	2.67452	+	16.2757i	0.0871405	+	0.530289i
$943$	−11.8005	−	13.1058i	−0.384278	−	0.426784i
$944$	13.5580	−	4.75519i	0.441276	−	0.154768i
$945$	−1.74923	−	0.568360i	−0.0569025	−	0.0184888i
$946$	20.8727	+	31.7372i	0.678629	+	1.03186i
$947$	1.76660	−	16.8081i	0.0574068	−	0.546189i	−0.927588	−	0.373605i	$-0.878122\pi$
$947$	1.76660	−	16.8081i	0.0574068	−	0.546189i	0.984995	−	0.172584i	$-0.0552117\pi$
$948$	6.87127	−	9.69159i	0.223169	−	0.314768i
$949$	−2.89826	+	3.21885i	−0.0940816	+	0.104488i
$950$	23.0182	−	35.8983i	0.746809	−	1.16470i
$951$	10.6666	+	2.26726i	0.345890	+	0.0735211i
$952$	−31.6280	−	1.10701i	−1.02507	−	0.0358783i
$953$	9.15092	−	12.5952i	0.296428	−	0.407997i	−0.634661	−	0.772791i	$-0.718860\pi$
$953$	9.15092	−	12.5952i	0.296428	−	0.407997i	0.931089	+	0.364793i	$0.118860\pi$
$954$	−2.49406	−	4.82558i	−0.0807482	−	0.156234i
$955$	−18.7154	+	10.8054i	−0.605617	+	0.349653i
$956$	−35.6724	−	11.1356i	−1.15373	−	0.360150i
$957$	2.38206	+	3.27863i	0.0770012	+	0.105983i
$958$	−17.0251	−	8.55088i	−0.550055	−	0.276266i
$959$	11.1849	+	34.4235i	0.361178	+	1.11159i
$960$	−4.67071	−	5.98021i	−0.150746	−	0.193010i
$961$	28.9654	−	11.0455i	0.934369	−	0.356308i
$962$	−7.30695	+	9.13094i	−0.235585	+	0.294393i
$963$	2.14561	−	0.697152i	0.0691414	−	0.0224654i
$964$	35.9171	−	16.4924i	1.15681	−	0.531185i
$965$	−7.28380	+	5.29199i	−0.234474	+	0.170355i
$966$	−8.55847	+	3.34228i	−0.275364	+	0.107536i
$967$	23.0031	+	39.8425i	0.739728	+	1.28125i	0.952618	+	0.304171i	$0.0983793\pi$
$967$	23.0031	+	39.8425i	0.739728	+	1.28125i	−0.212889	+	0.977076i	$0.568287\pi$
$968$	27.8602	+	33.2078i	0.895460	+	1.06734i
$969$	−34.3300	−	24.9422i	−1.10284	−	0.801259i
$970$	2.67754	−	10.2293i	0.0859707	−	0.328443i
$971$	4.24490	−	19.9707i	0.136225	−	0.640890i	−0.856056	−	0.516883i	$-0.827092\pi$
$971$	4.24490	−	19.9707i	0.136225	−	0.640890i	0.992281	−	0.124007i	$-0.0395745\pi$
$972$	1.89483	−	0.640023i	0.0607766	−	0.0205287i
$973$	−15.7421	−	14.1743i	−0.504669	−	0.454406i
$974$	−13.9366	+	0.811339i	−0.446556	+	0.0259970i
$975$	3.62076	+	0.380558i	0.115957	+	0.0121876i
$976$	45.5943	−	5.86279i	1.45944	−	0.187663i
$977$	−0.720295	+	2.21684i	−0.0230443	+	0.0709230i	−0.961917	−	0.273341i	$-0.911871\pi$
$977$	−0.720295	+	2.21684i	−0.0230443	+	0.0709230i	0.938873	+	0.344264i	$0.111871\pi$
$978$	−10.2657	+	10.3853i	−0.328262	+	0.332086i
$979$	9.08335	−	8.17868i	0.290305	−	0.261392i
$980$	−5.35789	−	3.01118i	−0.171151	−	0.0961887i
$981$	−0.806574	−	7.67404i	−0.0257519	−	0.245013i
$982$	−33.6279	+	27.5553i	−1.07311	+	0.879325i
$983$	20.5678	−	9.15740i	0.656012	−	0.292076i	−0.0516089	−	0.998667i	$-0.516435\pi$
$983$	20.5678	−	9.15740i	0.656012	−	0.292076i	0.707621	+	0.706592i	$0.249768\pi$
$984$	−6.98839	−	13.1458i	−0.222782	−	0.419072i
$985$	−0.828547	+	1.86095i	−0.0263997	+	0.0592947i
$986$	6.37183	+	0.971407i	0.202920	+	0.0309359i
$987$	−12.5945	+	21.8144i	−0.400888	+	0.694358i
$988$	9.80554	+	8.62542i	0.311956	+	0.274411i
$989$	17.1563	−	3.64669i	0.545539	−	0.115958i
$990$	6.43949	+	2.42920i	0.204660	+	0.0772049i
$991$	−19.0448			−0.604979			−0.302489	−	0.953153i	$-0.597818\pi$
$991$	−19.0448			−0.604979			−0.302489	+	0.953153i	$0.597818\pi$
$992$	−1.59577	+	31.4556i	−0.0506657	+	0.998716i
$993$	9.41770			0.298862
$994$	−6.11459	−	2.30663i	−0.193943	−	0.0731619i
$995$	−8.51133	+	1.80914i	−0.269827	+	0.0573536i
$996$	−8.86554	−	7.79855i	−0.280915	−	0.247107i
$997$	10.2066	−	17.6783i	0.323245	−	0.559876i	−0.657911	−	0.753096i	$-0.728560\pi$
$997$	10.2066	−	17.6783i	0.323245	−	0.559876i	0.981156	+	0.193219i	$0.0618929\pi$
$998$	−16.9596	−	2.58555i	−0.536846	−	0.0818440i
$999$	3.78809	−	8.50819i	0.119850	−	0.269187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.ba.a.55.3	✓	128
4.3	odd	2		372.2.ba.b.55.12	yes	128
31.22	odd	30		372.2.ba.b.115.12	yes	128
124.115	even	30	inner	372.2.ba.a.115.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.ba.a.55.3	✓	128	1.1	even	1	trivial
372.2.ba.a.115.3	yes	128	124.115	even	30	inner
372.2.ba.b.55.12	yes	128	4.3	odd	2
372.2.ba.b.115.12	yes	128	31.22	odd	30

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:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32319 - 0.499154i) q^{2} +(0.978148 - 0.207912i) q^{3} +(1.50169 + 1.32096i) q^{4} +(-0.474253 + 0.821430i) q^{5} +(-1.39806 - 0.213139i) q^{6} +(-0.788705 + 1.77146i) q^{7} +(-1.32767 - 2.49746i) q^{8} +(0.913545 - 0.406737i) q^{9} +(1.03755 - 0.850186i) q^{10} +(0.536318 + 5.10272i) q^{11} +(1.74352 + 0.979872i) q^{12} +(0.659842 - 0.594124i) q^{13} +(1.92784 - 1.95030i) q^{14} +(-0.293104 + 0.902082i) q^{15} +(0.510143 + 3.96734i) q^{16} +(-5.73859 - 0.603150i) q^{17} +(-1.41182 + 0.0821915i) q^{18} +(5.46511 + 4.92081i) q^{19} +(-1.79725 + 0.607065i) q^{20} +(-0.403163 + 1.89673i) q^{21} +(1.83739 - 7.01960i) q^{22} +(-2.71056 - 1.96934i) q^{23} +(-1.81790 - 2.16685i) q^{24} +(2.05017 + 3.55100i) q^{25} +(-1.16966 + 0.456779i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.52441 + 1.61834i) q^{28} +(0.751196 - 0.244078i) q^{29} +(0.838112 - 1.04733i) q^{30} +(-5.47565 + 1.00861i) q^{31} +(1.30529 - 5.50420i) q^{32} +(1.58551 + 4.87971i) q^{33} +(7.29221 + 3.66253i) q^{34} +(-1.08108 - 1.48799i) q^{35} +(1.90914 + 0.595962i) q^{36} +(8.06562 - 4.65669i) q^{37} +(-4.77516 - 9.23912i) q^{38} +(0.521897 - 0.718330i) q^{39} +(2.68114 + 0.0938422i) q^{40} +(5.14864 + 1.09438i) q^{41} +(1.48022 - 2.30850i) q^{42} +(-3.50291 + 3.89037i) q^{43} +(-5.93510 + 8.37116i) q^{44} +(-0.0991458 + 0.943309i) q^{45} +(2.60360 + 3.95881i) q^{46} +(12.3543 + 4.01414i) q^{47} +(1.32385 + 3.77458i) q^{48} +(2.16790 + 2.40769i) q^{49} +(-0.940277 - 5.72201i) q^{50} +(-5.73859 + 0.603150i) q^{51} +(1.77569 - 0.0205672i) q^{52} +(1.56228 + 3.50893i) q^{53} +(-1.36388 + 0.373930i) q^{54} +(-4.44588 - 1.97943i) q^{55} +(5.47129 - 0.382150i) q^{56} +(6.36878 + 3.67701i) q^{57} +(-1.11581 - 0.0519996i) q^{58} +(-0.746806 - 3.51344i) q^{59} +(-1.63176 + 0.967469i) q^{60} -11.4924i q^{61} +(7.74880 + 1.39861i) q^{62} +1.93911i q^{63} +(-4.47461 + 6.63158i) q^{64} +(0.175099 + 0.823778i) q^{65} +(0.337785 - 7.24822i) q^{66} +(-10.9354 - 6.31358i) q^{67} +(-7.82085 - 8.48618i) q^{68} +(-3.06078 - 1.36275i) q^{69} +(0.687751 + 2.50852i) q^{70} +(-0.969294 - 2.17707i) q^{71} +(-2.22869 - 1.74153i) q^{72} +(-4.85149 + 0.509912i) q^{73} +(-12.9968 + 2.13572i) q^{74} +(2.74366 + 3.04714i) q^{75} +(1.70672 + 14.6087i) q^{76} +(-9.46227 - 3.07448i) q^{77} +(-1.04913 + 0.689983i) q^{78} +(0.620914 - 5.90761i) q^{79} +(-3.50082 - 1.46247i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-6.26639 - 4.01804i) q^{82} +(-5.77470 - 1.22745i) q^{83} +(-3.11093 + 2.31574i) q^{84} +(3.21699 - 4.42780i) q^{85} +(6.57693 - 3.39923i) q^{86} +(0.684034 - 0.394927i) q^{87} +(12.0318 - 8.11415i) q^{88} +(-1.40024 - 1.92727i) q^{89} +(0.602046 - 1.19869i) q^{90} +(0.532047 + 1.63747i) q^{91} +(-1.46901 - 6.53788i) q^{92} +(-5.14629 + 2.12502i) q^{93} +(-14.3434 - 11.4782i) q^{94} +(-6.63394 + 2.15550i) q^{95} +(0.132384 - 5.65530i) q^{96} +(6.37734 - 4.63341i) q^{97} +(-1.66674 - 4.26796i) q^{98} +(2.56542 + 4.44343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} + 2 q^{4} + 3 q^{6} - 6 q^{8} + 16 q^{9} - 2 q^{10} + 12 q^{11} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 10 q^{16} + 3 q^{18} + 18 q^{19} - 11 q^{20} - 10 q^{21} + 10 q^{22} + 48 q^{23} - 3 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) \) 128 * q - 16 * q^3 + 2 * q^4 + 3 * q^6 - 6 * q^8 + 16 * q^9 - 2 * q^10 + 12 * q^11 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 10 * q^16 + 3 * q^18 + 18 * q^19 - 11 * q^20 - 10 * q^21 + 10 * q^22 + 48 * q^23 - 3 * q^24 - 68 * q^25 - 20 * q^26 + 32 * q^27 + 21 * q^28 + 26 * q^30 + 30 * q^32 + 4 * q^33 - 20 * q^34 - q^36 - 6 * q^37 + 3 * q^38 + 10 * q^39 - 54 * q^40 - 5 * q^42 - 40 * q^43 - 51 * q^44 - 41 * q^46 + 15 * q^48 + 8 * q^49 - 37 * q^50 + 121 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^55 - 109 * q^56 + 18 * q^57 - 58 * q^58 - 62 * q^59 + 7 * q^60 - 3 * q^62 - 16 * q^64 + 25 * q^66 + 48 * q^67 - 111 * q^68 + 24 * q^69 - 133 * q^70 - 2 * q^72 + 18 * q^73 - 14 * q^74 - 22 * q^75 - 81 * q^76 - 75 * q^78 - 10 * q^79 - 5 * q^80 + 16 * q^81 + 16 * q^82 - 26 * q^83 - 15 * q^84 + 38 * q^86 + 85 * q^88 + 20 * q^89 - 2 * q^90 + 54 * q^91 - 56 * q^92 + 14 * q^93 - 28 * q^94 + 40 * q^95 - 38 * q^96 - 10 * q^97 - 9 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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