LMFDB - Embedded newform 522.2.q.b.223.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [522,2,Mod(7,522)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(522, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([28, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("522.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 522 = 2 \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	522.q (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [180,15] 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:	$4.16819098551$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			223.3
Character	$\chi$	$=$	522.223
Dual form			522.2.q.b.103.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0747301 - 0.997204i) q^{2} +(-1.51947 + 0.831387i) q^{3} +(-0.988831 - 0.149042i) q^{4} +(-3.10490 - 2.11689i) q^{5} +(0.715512 + 1.57735i) q^{6} +(1.34451 - 0.202652i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(1.61759 - 2.52654i) q^{9} +(-2.34300 + 2.93802i) q^{10} +(-0.998912 - 0.308124i) q^{11} +(1.62641 - 0.595636i) q^{12} +(-1.51983 + 1.41019i) q^{13} +(-0.101610 - 1.35589i) q^{14} +(6.47776 + 0.635174i) q^{15} +(0.955573 + 0.294755i) q^{16} +2.33360 q^{17} +(-2.39859 - 1.80188i) q^{18} +(-5.34325 + 6.70023i) q^{19} +(2.75472 + 2.55600i) q^{20} +(-1.87446 + 1.42573i) q^{21} +(-0.381911 + 0.973093i) q^{22} +(0.347405 + 4.63580i) q^{23} +(-0.472428 - 1.66638i) q^{24} +(3.33250 + 8.49108i) q^{25} +(1.29267 + 1.62096i) q^{26} +(-0.357351 + 5.18385i) q^{27} -1.35969 q^{28} +(0.988774 - 5.29361i) q^{29} +(1.11748 - 6.41218i) q^{30} +(8.31316 + 5.66782i) q^{31} +(0.365341 - 0.930874i) q^{32} +(1.77399 - 0.362298i) q^{33} +(0.174390 - 2.32708i) q^{34} +(-4.60356 - 2.21696i) q^{35} +(-1.97608 + 2.25723i) q^{36} +(-0.0929923 + 0.407426i) q^{37} +(6.28219 + 5.82902i) q^{38} +(1.13692 - 3.40632i) q^{39} +(2.75472 - 2.55600i) q^{40} +(3.48663 + 6.03902i) q^{41} +(1.28167 + 1.97576i) q^{42} +(1.38560 - 0.944686i) q^{43} +(0.941832 + 0.453562i) q^{44} +(-10.3709 + 4.42040i) q^{45} +4.64880 q^{46} +(-9.65124 - 2.97701i) q^{47} +(-1.69702 + 0.346579i) q^{48} +(-4.92238 + 1.51835i) q^{49} +(8.71638 - 2.68865i) q^{50} +(-3.54584 + 1.94013i) q^{51} +(1.71303 - 1.16793i) q^{52} +(-8.96829 + 4.31890i) q^{53} +(5.14265 + 0.743742i) q^{54} +(2.44926 + 3.07128i) q^{55} +(-0.101610 + 1.35589i) q^{56} +(2.54844 - 14.6231i) q^{57} +(-5.20492 - 1.38160i) q^{58} +(4.02281 + 6.96770i) q^{59} +(-6.31075 - 1.59354i) q^{60} +(-4.42329 + 0.666704i) q^{61} +(6.27321 - 7.86636i) q^{62} +(1.66286 - 3.72476i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(7.70414 - 1.16121i) q^{65} +(-0.228714 - 1.79610i) q^{66} +(8.03299 - 2.47785i) q^{67} +(-2.30754 - 0.347805i) q^{68} +(-4.38202 - 6.75514i) q^{69} +(-2.55478 + 4.42501i) q^{70} +(-3.54249 - 15.5207i) q^{71} +(2.10325 + 2.13924i) q^{72} +(-4.72154 - 2.27377i) q^{73} +(0.399337 + 0.123179i) q^{74} +(-12.1230 - 10.1314i) q^{75} +(6.28219 - 5.82902i) q^{76} +(-1.40549 - 0.211843i) q^{77} +(-3.31183 - 1.38829i) q^{78} +(3.96967 + 3.68332i) q^{79} +(-2.34300 - 2.93802i) q^{80} +(-3.76680 - 8.17381i) q^{81} +(6.28269 - 3.02558i) q^{82} +(0.0269485 + 0.0686638i) q^{83} +(2.06602 - 1.13043i) q^{84} +(-7.24561 - 4.93997i) q^{85} +(-0.838498 - 1.45232i) q^{86} +(2.89863 + 8.86555i) q^{87} +(0.522677 - 0.905304i) q^{88} +(-4.74290 + 2.28406i) q^{89} +(3.63303 + 10.6722i) q^{90} +(-1.75764 + 2.20401i) q^{91} +(0.347405 - 4.63580i) q^{92} +(-17.3438 - 1.70063i) q^{93} +(-3.68993 + 9.40178i) q^{94} +(30.7739 - 9.49249i) q^{95} +(0.218791 + 1.71818i) q^{96} +(2.36834 + 6.03443i) q^{97} +(1.14626 + 5.02208i) q^{98} +(-2.39432 + 2.02537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q + 15 q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} + 10 q^{6} + 5 q^{7} - 30 q^{8} - 6 q^{9} - 4 q^{10} - 4 q^{11} + 2 q^{12} - 2 q^{14} - q^{15} + 15 q^{16} + 12 q^{17} + 6 q^{18} - 6 q^{19} + 2 q^{20} - 13 q^{21}+ \cdots - 172 q^{99}+O(q^{100}) $ 180 * q + 15 * q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 + 10 * q^6 + 5 * q^7 - 30 * q^8 - 6 * q^9 - 4 * q^10 - 4 * q^11 + 2 * q^12 - 2 * q^14 - q^15 + 15 * q^16 + 12 * q^17 + 6 * q^18 - 6 * q^19 + 2 * q^20 - 13 * q^21 - 4 * q^22 + 30 * q^23 - 5 * q^24 + 15 * q^25 + 11 * q^27 + 4 * q^28 + 3 * q^29 - 60 * q^30 + 2 * q^31 + 15 * q^32 + 66 * q^33 - 6 * q^34 - 32 * q^35 + 14 * q^36 - 90 * q^37 + 3 * q^38 + 21 * q^39 + 2 * q^40 + 22 * q^41 + 2 * q^42 + 14 * q^43 - 20 * q^44 - 26 * q^45 + 24 * q^46 - 10 * q^47 - 4 * q^48 + 50 * q^49 + 15 * q^50 - 7 * q^51 + 56 * q^53 - 31 * q^54 - 56 * q^55 - 2 * q^56 + 70 * q^57 - 25 * q^58 - 40 * q^59 + 5 * q^60 - 6 * q^61 - 4 * q^62 + 114 * q^63 - 30 * q^64 + 47 * q^65 - 20 * q^66 - 6 * q^68 - 17 * q^69 - 12 * q^70 - 22 * q^71 + 22 * q^72 - 40 * q^73 + 45 * q^74 - 30 * q^75 + 3 * q^76 - 66 * q^77 - 37 * q^78 - 22 * q^79 - 4 * q^80 - 162 * q^81 + 40 * q^82 + 4 * q^83 - 10 * q^84 + 52 * q^85 - 56 * q^86 + 10 * q^87 - 4 * q^88 - 76 * q^89 - 65 * q^90 - 100 * q^91 + 30 * q^92 - 86 * q^93 + 46 * q^94 - 56 * q^95 + 2 * q^96 - 18 * q^97 - 100 * q^98 - 172 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/522\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.0747301	−	0.997204i	0.0528422	−	0.705130i
$2$	0.0747301	−	0.997204i	0.0528422	−	0.705130i
$3$	−1.51947	+	0.831387i	−0.877268	+	0.480002i
$3$	−1.51947	+	0.831387i	−0.877268	+	0.480002i
$4$	−0.988831	−	0.149042i	−0.494415	−	0.0745211i
$5$	−3.10490	−	2.11689i	−1.38855	−	0.946700i	−0.999677	−	0.0254108i	$-0.991911\pi$
$5$	−3.10490	−	2.11689i	−1.38855	−	0.946700i	−0.388877	−	0.921290i	$-0.627137\pi$
$6$	0.715512	+	1.57735i	0.292107	+	0.643952i
$7$	1.34451	−	0.202652i	0.508176	−	0.0765952i	0.110050	−	0.993926i	$-0.464899\pi$
$7$	1.34451	−	0.202652i	0.508176	−	0.0765952i	0.398126	+	0.917331i	$0.369661\pi$
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	1.61759	−	2.52654i	0.539197	−	0.842180i
$10$	−2.34300	+	2.93802i	−0.740921	+	0.929085i
$11$	−0.998912	−	0.308124i	−0.301183	−	0.0929028i	0.140480	−	0.990083i	$-0.455135\pi$
$11$	−0.998912	−	0.308124i	−0.301183	−	0.0929028i	−0.441664	+	0.897181i	$0.645612\pi$
$12$	1.62641	−	0.595636i	0.469505	−	0.171945i
$13$	−1.51983	+	1.41019i	−0.421524	+	0.391118i	−0.862216	−	0.506541i	$-0.830924\pi$
$13$	−1.51983	+	1.41019i	−0.421524	+	0.391118i	0.440691	+	0.897659i	$0.354733\pi$
$14$	−0.101610	−	1.35589i	−0.0271564	−	0.362378i
$15$	6.47776	+	0.635174i	1.67255	+	0.164001i
$16$	0.955573	+	0.294755i	0.238893	+	0.0736888i
$17$	2.33360			0.565982			0.282991	−	0.959123i	$-0.408673\pi$
$17$	2.33360			0.565982			0.282991	+	0.959123i	$0.408673\pi$
$18$	−2.39859	−	1.80188i	−0.565354	−	0.424706i
$19$	−5.34325	+	6.70023i	−1.22583	+	1.53714i	−0.469516	+	0.882924i	$0.655571\pi$
$19$	−5.34325	+	6.70023i	−1.22583	+	1.53714i	−0.756310	+	0.654213i	$0.773000\pi$
$20$	2.75472	+	2.55600i	0.615974	+	0.571540i
$21$	−1.87446	+	1.42573i	−0.409041	+	0.311120i
$22$	−0.381911	+	0.973093i	−0.0814237	+	0.207464i
$23$	0.347405	+	4.63580i	0.0724390	+	0.966631i	0.908470	+	0.417950i	$0.137251\pi$
$23$	0.347405	+	4.63580i	0.0724390	+	0.966631i	−0.836031	+	0.548682i	$0.815130\pi$
$24$	−0.472428	−	1.66638i	−0.0964340	−	0.340148i
$25$	3.33250	+	8.49108i	0.666501	+	1.69822i
$26$	1.29267	+	1.62096i	0.253514	+	0.317897i
$27$	−0.357351	+	5.18385i	−0.0687723	+	0.997632i
$28$	−1.35969			−0.256958
$29$	0.988774	−	5.29361i	0.183611	−	0.982999i
$29$	0.988774	−	5.29361i	0.183611	−	0.982999i
$30$	1.11748	−	6.41218i	0.204023	−	1.17070i
$31$	8.31316	+	5.66782i	1.49309	+	1.01797i	0.987923	+	0.154948i	$0.0495210\pi$
$31$	8.31316	+	5.66782i	1.49309	+	1.01797i	0.505166	+	0.863022i	$0.331431\pi$
$32$	0.365341	−	0.930874i	0.0645838	−	0.164557i
$33$	1.77399	−	0.362298i	0.308812	−	0.0630679i
$34$	0.174390	−	2.32708i	0.0299077	−	0.399091i
$35$	−4.60356	−	2.21696i	−0.778143	−	0.374734i
$36$	−1.97608	+	2.25723i	−0.329347	+	0.376205i
$37$	−0.0929923	+	0.407426i	−0.0152878	+	0.0669804i	−0.981996	−	0.188899i	$-0.939508\pi$
$37$	−0.0929923	+	0.407426i	−0.0152878	+	0.0669804i	0.966709	+	0.255880i	$0.0823651\pi$
$38$	6.28219	+	5.82902i	1.01911	+	0.945592i
$39$	1.13692	−	3.40632i	0.182053	−	0.545447i
$40$	2.75472	−	2.55600i	0.435559	−	0.404140i
$41$	3.48663	+	6.03902i	0.544520	+	0.943136i	0.998637	+	0.0521940i	$0.0166214\pi$
$41$	3.48663	+	6.03902i	0.544520	+	0.943136i	−0.454117	+	0.890942i	$0.650045\pi$
$42$	1.28167	+	1.97576i	0.197765	+	0.304867i
$43$	1.38560	−	0.944686i	0.211302	−	0.144063i	−0.453045	−	0.891488i	$-0.649662\pi$
$43$	1.38560	−	0.944686i	0.211302	−	0.144063i	0.664347	+	0.747425i	$0.268710\pi$
$44$	0.941832	+	0.453562i	0.141987	+	0.0683771i
$45$	−10.3709	+	4.42040i	−1.54600	+	0.658955i
$46$	4.64880			0.685428
$47$	−9.65124	−	2.97701i	−1.40778	−	0.434242i	−0.504543	−	0.863387i	$-0.668339\pi$
$47$	−9.65124	−	2.97701i	−1.40778	−	0.434242i	−0.903236	+	0.429144i	$0.858815\pi$
$48$	−1.69702	+	0.346579i	−0.244944	+	0.0500243i
$49$	−4.92238	+	1.51835i	−0.703197	+	0.216907i
$50$	8.71638	−	2.68865i	1.23268	−	0.380232i
$51$	−3.54584	+	1.94013i	−0.496518	+	0.271672i
$52$	1.71303	−	1.16793i	0.237555	−	0.161962i
$53$	−8.96829	+	4.31890i	−1.23189	+	0.593247i	−0.932599	−	0.360915i	$-0.882464\pi$
$53$	−8.96829	+	4.31890i	−1.23189	+	0.593247i	−0.299291	+	0.954162i	$0.596750\pi$
$54$	5.14265	+	0.743742i	0.699826	+	0.101210i
$55$	2.44926	+	3.07128i	0.330258	+	0.414131i
$56$	−0.101610	+	1.35589i	−0.0135782	+	0.181189i
$57$	2.54844	−	14.6231i	0.337549	−	1.93688i
$58$	−5.20492	−	1.38160i	−0.683439	−	0.181413i
$59$	4.02281	+	6.96770i	0.523725	+	0.907118i	0.999619	+	0.0276151i	$0.00879128\pi$
$59$	4.02281	+	6.96770i	0.523725	+	0.907118i	−0.475894	+	0.879503i	$0.657875\pi$
$60$	−6.31075	−	1.59354i	−0.814714	−	0.205725i
$61$	−4.42329	+	0.666704i	−0.566344	+	0.0853627i	−0.425972	−	0.904736i	$-0.640068\pi$
$61$	−4.42329	+	0.666704i	−0.566344	+	0.0853627i	−0.140372	+	0.990099i	$0.544830\pi$
$62$	6.27321	−	7.86636i	0.796699	−	0.999029i
$63$	1.66286	−	3.72476i	0.209500	−	0.469276i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	7.70414	−	1.16121i	0.955581	−	0.144031i
$66$	−0.228714	−	1.79610i	−0.0281528	−	0.221085i
$67$	8.03299	−	2.47785i	0.981386	−	0.302718i	0.237768	−	0.971322i	$-0.423584\pi$
$67$	8.03299	−	2.47785i	0.981386	−	0.302718i	0.743618	+	0.668604i	$0.233108\pi$
$68$	−2.30754	−	0.347805i	−0.279830	−	0.0421776i
$69$	−4.38202	−	6.75514i	−0.527533	−	0.813224i
$70$	−2.55478	+	4.42501i	−0.305355	+	0.528890i
$71$	−3.54249	−	15.5207i	−0.420417	−	1.84197i	−0.530013	−	0.847989i	$-0.677813\pi$
$71$	−3.54249	−	15.5207i	−0.420417	−	1.84197i	0.109597	−	0.993976i	$-0.465044\pi$
$72$	2.10325	+	2.13924i	0.247870	+	0.252112i
$73$	−4.72154	−	2.27377i	−0.552615	−	0.266125i	0.136669	−	0.990617i	$-0.456360\pi$
$73$	−4.72154	−	2.27377i	−0.552615	−	0.266125i	−0.689284	+	0.724492i	$0.742075\pi$
$74$	0.399337	+	0.123179i	0.0464220	+	0.0143193i
$75$	−12.1230	−	10.1314i	−1.39985	−	1.16987i
$76$	6.28219	−	5.82902i	0.720616	−	0.668634i
$77$	−1.40549	−	0.211843i	−0.160170	−	0.0241418i
$78$	−3.31183	−	1.38829i	−0.374991	−	0.157193i
$79$	3.96967	+	3.68332i	0.446623	+	0.414406i	0.871156	−	0.491007i	$-0.163371\pi$
$79$	3.96967	+	3.68332i	0.446623	+	0.414406i	−0.424532	+	0.905413i	$0.639561\pi$
$80$	−2.34300	−	2.93802i	−0.261955	−	0.328481i
$81$	−3.76680	−	8.17381i	−0.418533	−	0.908201i
$82$	6.28269	−	3.02558i	0.693807	−	0.334120i
$83$	0.0269485	+	0.0686638i	0.00295799	+	0.00753683i	0.932345	−	0.361570i	$-0.117759\pi$
$83$	0.0269485	+	0.0686638i	0.00295799	+	0.00753683i	−0.929387	+	0.369106i	$0.879664\pi$
$84$	2.06602	−	1.13043i	0.225421	−	0.123340i
$85$	−7.24561	−	4.93997i	−0.785897	−	0.535815i
$86$	−0.838498	−	1.45232i	−0.0904176	−	0.156608i
$87$	2.89863	+	8.86555i	0.310765	+	0.950487i
$88$	0.522677	−	0.905304i	0.0557176	−	0.0965057i
$89$	−4.74290	+	2.28406i	−0.502747	+	0.242110i	−0.668028	−	0.744136i	$-0.732861\pi$
$89$	−4.74290	+	2.28406i	−0.502747	+	0.242110i	0.165281	+	0.986247i	$0.447147\pi$
$90$	3.63303	+	10.6722i	0.382955	+	1.12495i
$91$	−1.75764	+	2.20401i	−0.184251	+	0.231043i
$92$	0.347405	−	4.63580i	0.0362195	−	0.483316i
$93$	−17.3438	−	1.70063i	−1.79847	−	0.176348i
$94$	−3.68993	+	9.40178i	−0.380587	+	0.969720i
$95$	30.7739	−	9.49249i	3.15733	−	0.973909i
$96$	0.218791	+	1.71818i	0.0223303	+	0.175361i
$97$	2.36834	+	6.03443i	0.240469	+	0.612704i	0.999253	−	0.0386376i	$-0.0123018\pi$
$97$	2.36834	+	6.03443i	0.240469	+	0.612704i	−0.758785	+	0.651341i	$0.774207\pi$
$98$	1.14626	+	5.02208i	0.115789	+	0.507307i
$99$	−2.39432	+	2.02537i	−0.240638	+	0.203558i
$100$	−2.02975	−	8.89293i	−0.202975	−	0.889293i
$101$	8.04853	−	5.48739i	0.800858	−	0.546016i	−0.0923143	−	0.995730i	$-0.529426\pi$
$101$	8.04853	−	5.48739i	0.800858	−	0.546016i	0.893173	+	0.449714i	$0.148474\pi$
$102$	1.66972	+	3.68092i	0.165327	+	0.364465i
$103$	−5.42122	+	5.03016i	−0.534169	+	0.495637i	−0.900505	−	0.434846i	$-0.856803\pi$
$103$	−5.42122	+	5.03016i	−0.534169	+	0.495637i	0.366336	+	0.930483i	$0.380612\pi$
$104$	−1.03664	−	1.79552i	−0.101651	−	0.176065i
$105$	8.83812	−	0.458735i	0.862513	−	0.0447680i
$106$	3.63662	+	9.26597i	0.353220	+	0.899990i
$107$	−1.48645	+	6.51257i	−0.143701	+	0.629593i	0.850856	+	0.525399i	$0.176084\pi$
$107$	−1.48645	+	6.51257i	−0.143701	+	0.629593i	−0.994557	+	0.104195i	$0.966773\pi$
$108$	1.12597	−	5.07269i	0.108347	−	0.488120i
$109$	−3.51350	−	4.40579i	−0.336532	−	0.421998i	0.584555	−	0.811354i	$-0.301269\pi$
$109$	−3.51350	−	4.40579i	−0.336532	−	0.421998i	−0.921087	+	0.389356i	$0.872698\pi$
$110$	3.24572	−	2.21290i	0.309468	−	0.210991i
$111$	−0.197429	−	0.696385i	−0.0187392	−	0.0660979i
$112$	1.34451	+	0.202652i	0.127044	+	0.0191488i
$113$	−4.89013	+	12.4598i	−0.460024	+	1.17212i	0.493215	+	0.869907i	$0.335822\pi$
$113$	−4.89013	+	12.4598i	−0.460024	+	1.17212i	−0.953240	+	0.302216i	$0.902274\pi$
$114$	−14.3918	−	3.63410i	−1.34791	−	0.340365i
$115$	8.73481	−	15.1291i	0.814525	−	1.41080i
$116$	−1.76670	+	5.08712i	−0.164034	+	0.472327i
$117$	1.10445	+	6.12102i	0.102107	+	0.565889i
$118$	7.24885	−	3.49086i	0.667310	−	0.321360i
$119$	3.13755	−	0.472909i	0.287619	−	0.0433515i
$120$	−2.06069	+	6.17401i	−0.188114	+	0.563608i
$121$	−8.18574	−	5.58094i	−0.744158	−	0.507359i
$122$	0.334287	+	4.46075i	0.0302649	+	0.403857i
$123$	−10.3186	−	6.27738i	−0.930396	−	0.566012i
$124$	−7.37557	−	6.84353i	−0.662346	−	0.614567i
$125$	3.44653	−	15.1002i	0.308267	−	1.35060i
$126$	−3.59008	−	1.93656i	−0.319830	−	0.172522i
$127$	3.76057	+	16.4761i	0.333696	+	1.46202i	0.811914	+	0.583778i	$0.198426\pi$
$127$	3.76057	+	16.4761i	0.333696	+	1.46202i	−0.478217	+	0.878242i	$0.658717\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.31998	+	2.58739i	−0.116218	+	0.227807i
$130$	−0.582234	−	7.76937i	−0.0510653	−	0.681419i
$131$	0.477920	+	6.37739i	0.0417560	+	0.557195i	0.978374	+	0.206843i	$0.0663190\pi$
$131$	0.477920	+	6.37739i	0.0417560	+	0.557195i	−0.936618	+	0.350352i	$0.886062\pi$
$132$	−1.80817	+	0.0938517i	−0.157381	+	0.00816874i
$133$	−5.82623	+	10.0913i	−0.505198	+	0.875029i
$134$	−1.87062	−	8.19570i	−0.161597	−	0.708001i
$135$	12.0832	−	15.3389i	1.03995	−	1.32016i
$136$	−0.519276	+	2.27509i	−0.0445275	+	0.195088i
$137$	−2.27858	−	2.11422i	−0.194672	−	0.180630i	0.576814	−	0.816876i	$-0.304296\pi$
$137$	−2.27858	−	2.11422i	−0.194672	−	0.180630i	−0.771486	+	0.636246i	$0.780486\pi$
$138$	−7.06372	+	3.86495i	−0.601304	+	0.329007i
$139$	−1.19918	−	16.0020i	−0.101714	−	1.35727i	−0.781520	−	0.623881i	$-0.785555\pi$
$139$	−1.19918	−	16.0020i	−0.101714	−	1.35727i	0.679806	−	0.733392i	$-0.262064\pi$
$140$	4.22172	+	2.87832i	0.356800	+	0.243262i
$141$	17.1398	−	3.50043i	1.44344	−	0.294789i
$142$	−15.7420	+	2.37273i	−1.32104	+	0.199115i
$143$	1.95269	−	0.940366i	0.163292	−	0.0786373i
$144$	2.29044	−	1.93750i	0.190870	−	0.161458i
$145$	−14.2760	+	14.3430i	−1.18556	+	1.19112i
$146$	−2.62026	+	4.53842i	−0.216854	+	0.375602i
$147$	6.21707	−	6.39949i	0.512776	−	0.527821i
$148$	0.152677	−	0.389015i	0.0125500	−	0.0319769i
$149$	−2.12843	−	0.320810i	−0.174368	−	0.0262818i	0.0612778	−	0.998121i	$-0.480482\pi$
$149$	−2.12843	−	0.320810i	−0.174368	−	0.0262818i	−0.235646	+	0.971839i	$0.575721\pi$
$150$	−11.0090	+	11.3320i	−0.898880	+	0.925254i
$151$	−6.11604	+	4.16984i	−0.497716	+	0.339337i	−0.786019	−	0.618202i	$-0.787861\pi$
$151$	−6.11604	+	4.16984i	−0.497716	+	0.339337i	0.288303	+	0.957539i	$0.406909\pi$
$152$	−5.34325	−	6.70023i	−0.433395	−	0.543460i
$153$	3.77481	−	5.89594i	0.305176	−	0.476658i
$154$	−0.316283	+	1.38573i	−0.0254868	+	0.111665i
$155$	−13.8134	−	35.1960i	−1.10952	−	2.82701i
$156$	−1.63191	+	3.19882i	−0.130657	+	0.256111i
$157$	4.25037	+	7.36185i	0.339216	+	0.587540i	0.984286	−	0.176584i	$-0.0565048\pi$
$157$	4.25037	+	7.36185i	0.339216	+	0.587540i	−0.645069	+	0.764124i	$0.723171\pi$
$158$	3.96967	−	3.68332i	0.315810	−	0.293029i
$159$	10.0364	−	14.0186i	0.795937	−	1.11175i
$160$	−3.10490	+	2.11689i	−0.245464	+	0.167355i
$161$	1.40654	+	6.16247i	0.110851	+	0.485671i
$162$	−8.43245	+	3.14544i	−0.662516	+	0.247129i
$163$	1.12941	+	4.94828i	0.0884625	+	0.387579i	0.999705	−	0.0242910i	$-0.00773281\pi$
$163$	1.12941	+	4.94828i	0.0884625	+	0.387579i	−0.911242	+	0.411870i	$0.864876\pi$
$164$	−2.54762	−	6.49122i	−0.198935	−	0.506879i
$165$	−6.27501	−	2.63044i	−0.488509	−	0.204779i
$166$	0.0704856	−	0.0217419i	0.00547075	−	0.00168750i
$167$	−4.12047	+	10.4988i	−0.318852	+	0.812421i	0.678141	+	0.734932i	$0.262786\pi$
$167$	−4.12047	+	10.4988i	−0.318852	+	0.812421i	−0.996993	+	0.0774898i	$0.975309\pi$
$168$	−0.972878	−	2.14472i	−0.0750592	−	0.165469i
$169$	−0.650262	+	8.67714i	−0.0500202	+	0.667473i
$170$	−5.46762	+	6.85618i	−0.419348	+	0.525845i
$171$	8.28519	+	24.3382i	0.633584	+	1.86119i
$172$	−1.51092	+	0.727622i	−0.115207	+	0.0554806i
$173$	−11.6343	+	20.1512i	−0.884540	+	1.53207i	−0.0383010	+	0.999266i	$0.512195\pi$
$173$	−11.6343	+	20.1512i	−0.884540	+	1.53207i	−0.846239	+	0.532803i	$0.821139\pi$
$174$	9.05737	−	2.22800i	0.686638	−	0.168904i
$175$	6.20131	+	10.7410i	0.468775	+	0.811942i
$176$	−0.863712	−	0.588869i	−0.0651048	−	0.0443877i
$177$	−11.9054	−	7.24272i	−0.894865	−	0.544396i
$178$	1.92324	+	4.90033i	0.144153	+	0.367295i
$179$	−6.13402	+	2.95399i	−0.458478	+	0.220792i	−0.648844	−	0.760922i	$-0.724747\pi$
$179$	−6.13402	+	2.95399i	−0.458478	+	0.220792i	0.190365	+	0.981713i	$0.439033\pi$
$180$	10.9138	−	2.82533i	0.813470	−	0.210588i
$181$	2.75314	+	3.45233i	0.204639	+	0.256609i	0.873551	−	0.486732i	$-0.161811\pi$
$181$	2.75314	+	3.45233i	0.204639	+	0.256609i	−0.668912	+	0.743341i	$0.733240\pi$
$182$	2.06650	+	1.91743i	0.153179	+	0.142130i
$183$	6.16678	−	4.69051i	0.455861	−	0.346732i
$184$	−4.59688	−	0.692868i	−0.338886	−	0.0510789i
$185$	1.15121	−	1.06816i	0.0846383	−	0.0785329i
$186$	−2.99198	+	17.1682i	−0.219383	+	1.25883i
$187$	−2.33107	−	0.719038i	−0.170464	−	0.0525813i
$188$	9.09975	+	4.38221i	0.663667	+	0.319605i
$189$	0.570056	+	7.04215i	0.0414655	+	0.512241i
$190$	−7.16621	−	31.3972i	−0.519891	−	2.27779i
$191$	5.17027	−	8.95518i	0.374108	−	0.647974i	−0.616085	−	0.787680i	$-0.711282\pi$
$191$	5.17027	−	8.95518i	0.374108	−	0.647974i	0.990193	+	0.139706i	$0.0446156\pi$
$192$	1.72972	−	0.0897798i	0.124832	−	0.00647930i
$193$	−22.8638	−	3.44616i	−1.64577	−	0.248060i	−0.740241	−	0.672342i	$-0.765289\pi$
$193$	−22.8638	−	3.44616i	−1.64577	−	0.248060i	−0.905530	+	0.424282i	$0.860527\pi$
$194$	6.19455	−	1.91076i	0.444742	−	0.137185i
$195$	−10.7408	+	8.16955i	−0.769165	+	0.585034i
$196$	5.09370	−	0.767751i	0.363835	−	0.0548394i
$197$	1.29320	+	0.622772i	0.0921366	+	0.0443707i	0.479384	−	0.877605i	$-0.340860\pi$
$197$	1.29320	+	0.622772i	0.0921366	+	0.0443707i	−0.387248	+	0.921976i	$0.626574\pi$
$198$	1.84078	+	2.53898i	0.130819	+	0.180437i
$199$	9.90956	−	12.4262i	0.702470	−	0.880869i	−0.294735	−	0.955579i	$-0.595232\pi$
$199$	9.90956	−	12.4262i	0.702470	−	0.880869i	0.997205	+	0.0747095i	$0.0238030\pi$
$200$	−9.01974	+	1.35951i	−0.637792	+	0.0961317i
$201$	−10.1459	+	10.4436i	−0.715633	+	0.736631i
$202$	−4.87058	−	8.43610i	−0.342693	−	0.593562i
$203$	0.256653	−	7.31768i	0.0180135	−	0.513600i
$204$	3.79540	−	1.38998i	0.265731	−	0.0973179i
$205$	1.95827	−	26.1313i	0.136772	−	1.82509i
$206$	4.61097	+	5.78197i	0.321261	+	0.402849i
$207$	12.2745	+	6.62110i	0.853136	+	0.460198i
$208$	−1.86797	+	0.899566i	−0.129520	+	0.0623737i
$209$	7.40194	−	5.04656i	0.512003	−	0.349078i
$210$	0.203021	−	8.84769i	0.0140098	−	0.610549i
$211$	5.09724	−	1.57229i	0.350908	−	0.108241i	−0.114290	−	0.993447i	$-0.536459\pi$
$211$	5.09724	−	1.57229i	0.350908	−	0.108241i	0.465198	+	0.885207i	$0.345983\pi$
$212$	9.51182	−	2.93401i	0.653275	−	0.201509i
$213$	18.2864	+	20.6380i	1.25296	+	1.41410i
$214$	6.38327	+	1.96898i	0.436352	+	0.134597i
$215$	−6.30194			−0.429789
$216$	−4.97436	−	1.50191i	−0.338462	−	0.102192i
$217$	12.3257	+	5.93575i	0.836724	+	0.402945i
$218$	−4.65603	+	3.17443i	−0.315346	+	0.214999i
$219$	9.06464	−	0.470492i	0.612531	−	0.0317929i
$220$	−1.96416	−	3.40202i	−0.132423	−	0.229364i
$221$	−3.54668	+	3.29083i	−0.238575	+	0.221365i
$222$	−0.709191	+	0.144836i	−0.0475978	+	0.00972079i
$223$	2.29068	+	2.12544i	0.153396	+	0.142330i	0.753137	−	0.657863i	$-0.228540\pi$
$223$	2.29068	+	2.12544i	0.153396	+	0.142330i	−0.599742	+	0.800194i	$0.704730\pi$
$224$	0.302561	−	1.32560i	0.0202157	−	0.0885707i
$225$	26.8437	+	5.31539i	1.78958	+	0.354359i
$226$	12.0596	+	5.80758i	0.802190	+	0.386314i
$227$	−1.61007	+	21.4848i	−0.106864	+	1.42600i	0.643739	+	0.765245i	$0.277382\pi$
$227$	−1.61007	+	21.4848i	−0.106864	+	1.42600i	−0.750603	+	0.660754i	$0.770237\pi$
$228$	−4.69944	+	14.0800i	−0.311228	+	0.932468i
$229$	6.47658	−	16.5021i	0.427984	−	1.09049i	−0.540485	−	0.841354i	$-0.681759\pi$
$229$	6.47658	−	16.5021i	0.427984	−	1.09049i	0.968469	−	0.249133i	$-0.0801456\pi$
$230$	−14.4341	−	9.84098i	−0.951754	−	0.648895i
$231$	2.31172	−	0.846615i	0.152100	−	0.0557032i
$232$	4.94087	+	2.14192i	0.324384	+	0.140624i
$233$	0.190672			0.0124914			0.00624568	−	0.999980i	$-0.498012\pi$
$233$	0.190672			0.0124914			0.00624568	+	0.999980i	$0.498012\pi$
$234$	6.18644	−	0.643939i	0.404420	−	0.0420956i
$235$	23.6642	+	29.6739i	1.54368	+	1.93571i
$236$	−2.93939	−	7.48945i	−0.191338	−	0.487522i
$237$	−9.09407	−	2.29636i	−0.590724	−	0.149165i
$238$	−0.237118	−	3.16412i	−0.0153701	−	0.205099i
$239$	−1.63625	+	4.16909i	−0.105840	+	0.269676i	−0.973976	−	0.226650i	$-0.927223\pi$
$239$	−1.63625	+	4.16909i	−0.105840	+	0.269676i	0.868136	+	0.496326i	$0.165318\pi$
$240$	6.00275	+	2.51631i	0.387476	+	0.162427i
$241$	−9.92671	−	9.21064i	−0.639436	−	0.593309i	0.292353	−	0.956310i	$-0.405562\pi$
$241$	−9.92671	−	9.21064i	−0.639436	−	0.593309i	−0.931789	+	0.363001i	$0.881752\pi$
$242$	−6.17706	+	7.74579i	−0.397076	+	0.497918i
$243$	12.5192	+	9.28821i	0.803104	+	0.595839i
$244$	4.47325			0.286371
$245$	18.4977	+	5.70578i	1.18177	+	0.364529i
$246$	−7.03094	+	9.82063i	−0.448276	+	0.626141i
$247$	−1.32780	−	17.7182i	−0.0844857	−	1.12738i
$248$	−7.37557	+	6.84353i	−0.468349	+	0.434564i
$249$	−0.0980337	−	0.0819280i	−0.00621263	−	0.00519198i
$250$	−14.8004	−	4.56533i	−0.936062	−	0.288737i
$251$	−6.47125	+	8.11469i	−0.408462	+	0.512195i	−0.942929	−	0.332994i	$-0.891941\pi$
$251$	−6.47125	+	8.11469i	−0.408462	+	0.512195i	0.534467	+	0.845189i	$0.320512\pi$
$252$	−2.19943	+	3.43532i	−0.138551	+	0.216405i
$253$	1.08137	−	4.73780i	0.0679853	−	0.297863i
$254$	16.7111	−	2.51879i	1.04855	−	0.158043i
$255$	15.1165	+	1.48224i	0.946634	+	0.0928217i
$256$	0.826239	+	0.563320i	0.0516399	+	0.0352075i
$257$	0.330161	+	0.0497637i	0.0205949	+	0.00310417i	0.159332	−	0.987225i	$-0.449066\pi$
$257$	0.330161	+	0.0497637i	0.0205949	+	0.00310417i	−0.138737	+	0.990329i	$0.544304\pi$
$258$	2.48152	+	1.50965i	0.154492	+	0.0939864i
$259$	−0.0424632	+	0.566632i	−0.00263854	+	0.0352088i
$260$	−7.79116			−0.483187
$261$	−11.7751	−	11.0611i	−0.728860	−	0.684663i
$262$	6.39528			0.395101
$263$	1.61245	−	21.5166i	0.0994278	−	1.32677i	−0.694823	−	0.719181i	$-0.744517\pi$
$263$	1.61245	−	21.5166i	0.0994278	−	1.32677i	0.794251	−	0.607590i	$-0.207864\pi$
$264$	−0.0415357	+	1.81013i	−0.00255634	+	0.111406i
$265$	36.9883	+	5.57509i	2.27217	+	0.342475i
$266$	9.62771	+	6.56406i	0.590313	+	0.402469i
$267$	5.30777	−	7.41376i	0.324830	−	0.453715i
$268$	−8.31258	+	1.25292i	−0.507771	+	0.0765342i
$269$	−4.65722	+	20.4046i	−0.283956	+	1.24409i	0.608717	+	0.793387i	$0.291684\pi$
$269$	−4.65722	+	20.4046i	−0.283956	+	1.24409i	−0.892673	+	0.450705i	$0.851173\pi$
$270$	−14.3930	−	13.1957i	−0.875931	−	0.803062i
$271$	17.3906	−	21.8071i	1.05640	−	1.32469i	0.112795	−	0.993618i	$-0.464020\pi$
$271$	17.3906	−	21.8071i	1.05640	−	1.32469i	0.943607	−	0.331068i	$-0.107409\pi$
$272$	2.22993	+	0.687842i	0.135209	+	0.0417065i
$273$	0.838299	−	4.81022i	0.0507362	−	0.291128i
$274$	−2.27858	+	2.11422i	−0.137654	+	0.127724i
$275$	−0.712576	−	9.50867i	−0.0429700	−	0.573394i
$276$	3.32627	+	7.33280i	0.200218	+	0.441383i
$277$	3.52830	+	1.08834i	0.211995	+	0.0653919i	0.398934	−	0.916980i	$-0.369380\pi$
$277$	3.52830	+	1.08834i	0.211995	+	0.0653919i	−0.186939	+	0.982372i	$0.559857\pi$
$278$	−16.0469			−0.962428
$279$	27.7673	−	11.8353i	1.66238	−	0.708562i
$280$	3.18576	−	3.99482i	0.190386	−	0.238736i
$281$	5.12249	+	4.75298i	0.305582	+	0.283539i	0.818025	−	0.575182i	$-0.195069\pi$
$281$	5.12249	+	4.75298i	0.305582	+	0.283539i	−0.512443	+	0.858721i	$0.671259\pi$
$282$	−2.20978	−	17.3535i	−0.131591	−	1.03339i
$283$	2.80802	−	7.15471i	0.166919	−	0.425303i	−0.822799	−	0.568332i	$-0.807589\pi$
$283$	2.80802	−	7.15471i	0.166919	−	0.425303i	0.989719	+	0.143029i	$0.0456841\pi$
$284$	1.18969	+	15.8753i	0.0705951	+	0.942026i
$285$	−38.8681	+	40.0086i	−2.30235	+	2.36990i
$286$	−0.791812	−	2.01750i	−0.0468208	−	0.119297i
$287$	5.91162	+	7.41293i	0.348952	+	0.437572i
$288$	−1.76092	−	2.42882i	−0.103763	−	0.143120i
$289$	−11.5543			−0.679664
$290$	13.2361	+	15.3080i	0.777249	+	0.898914i
$291$	−8.61558	−	7.20014i	−0.505054	−	0.422080i
$292$	4.32992	+	2.95209i	0.253389	+	0.172758i
$293$	1.66736	−	4.24837i	0.0974084	−	0.248193i	−0.873861	−	0.486176i	$-0.838391\pi$
$293$	1.66736	−	4.24837i	0.0974084	−	0.248193i	0.971269	+	0.237984i	$0.0764865\pi$
$294$	−5.91700	−	6.67792i	−0.345086	−	0.389464i
$295$	2.25942	−	30.1499i	0.131549	−	1.75539i
$296$	−0.376518	−	0.181322i	−0.0218847	−	0.0105391i
$297$	1.95423	−	5.06810i	0.113396	−	0.294081i
$298$	−0.478971	+	2.09851i	−0.0277460	+	0.121563i
$299$	−7.06538	−	6.55571i	−0.408601	−	0.379127i
$300$	10.4776	+	11.8250i	0.604926	+	0.682719i
$301$	1.67151	−	1.55093i	0.0963441	−	0.0893943i
$302$	3.70113	+	6.41055i	0.212976	+	0.368886i
$303$	−7.66736	+	15.0294i	−0.440479	+	0.863415i
$304$	−7.08079	+	4.82760i	−0.406111	+	0.276882i
$305$	15.1452	+	7.29356i	0.867213	+	0.417628i
$306$	−5.59736	−	4.20486i	−0.319980	−	0.240376i
$307$	12.7887			0.729892			0.364946	−	0.931029i	$-0.381087\pi$
$307$	12.7887			0.729892			0.364946	+	0.931029i	$0.381087\pi$
$308$	1.35822	+	0.418954i	0.0773915	+	0.0238721i
$309$	4.05539	−	12.1503i	0.230703	−	0.691208i
$310$	−36.1299	+	11.1446i	−2.05204	+	0.632971i
$311$	−23.2541	+	7.17295i	−1.31862	+	0.406740i	−0.872667	−	0.488316i	$-0.837611\pi$
$311$	−23.2541	+	7.17295i	−1.31862	+	0.406740i	−0.445953	+	0.895056i	$0.647135\pi$
$312$	3.06792	+	1.86639i	0.173687	+	0.105664i
$313$	−8.96674	+	6.11342i	−0.506830	+	0.345551i	−0.789585	−	0.613641i	$-0.789704\pi$
$313$	−8.96674	+	6.11342i	−0.506830	+	0.345551i	0.282755	+	0.959192i	$0.408752\pi$
$314$	7.65890	−	3.68833i	0.432217	−	0.208145i
$315$	−13.0479	+	8.04494i	−0.735166	+	0.453281i
$316$	−3.37637	−	4.23383i	−0.189935	−	0.238172i
$317$	0.599479	−	7.99949i	0.0336701	−	0.449296i	−0.954735	−	0.297457i	$-0.903861\pi$
$317$	0.599479	−	7.99949i	0.0336701	−	0.449296i	0.988405	−	0.151839i	$-0.0485195\pi$
$318$	−13.2294	−	11.0559i	−0.741865	−	0.619986i
$319$	−2.61879	+	4.98319i	−0.146624	+	0.279005i
$320$	1.87894	+	3.25442i	0.105036	+	0.181927i
$321$	−3.15584	−	11.1315i	−0.176142	−	0.621298i
$322$	6.25035	−	0.942089i	0.348318	−	0.0525005i
$323$	−12.4690	+	15.6357i	−0.693795	+	0.869992i
$324$	2.50649	+	8.64393i	0.139249	+	0.480218i
$325$	−17.0389	−	8.20550i	−0.945148	−	0.455160i
$326$	5.01885	−	0.756469i	0.277968	−	0.0418970i
$327$	9.00158	+	3.77339i	0.497788	+	0.208669i
$328$	−6.66345	+	2.05540i	−0.367928	+	0.113491i
$329$	−13.5795	−	2.04678i	−0.748661	−	0.112842i
$330$	−3.09201	+	6.06089i	−0.170210	+	0.333641i
$331$	−8.12747	+	14.0772i	−0.446726	+	0.773753i	−0.998171	−	0.0604590i	$-0.980744\pi$
$331$	−8.12747	+	14.0772i	−0.446726	+	0.773753i	0.551444	+	0.834212i	$0.314077\pi$
$332$	−0.0164137	−	0.0719133i	−0.000900821	−	0.00394676i
$333$	0.878954	+	0.893997i	0.0481664	+	0.0489907i
$334$	10.1615	+	4.89353i	0.556013	+	0.267762i
$335$	−30.1870	−	9.31145i	−1.64929	−	0.508739i
$336$	−2.21142	+	0.809883i	−0.120643	+	0.0441827i
$337$	6.03789	−	5.60234i	0.328905	−	0.305179i	−0.498384	−	0.866957i	$-0.666073\pi$
$337$	6.03789	−	5.60234i	0.328905	−	0.305179i	0.827288	+	0.561778i	$0.189882\pi$
$338$	8.60429	+	1.29689i	0.468011	+	0.0705414i
$339$	−2.92854	−	22.9980i	−0.159056	−	1.24908i
$340$	6.42842	+	5.96470i	0.348630	+	0.323481i
$341$	−6.55773	−	8.22314i	−0.355121	−	0.445308i
$342$	24.8893	−	6.44323i	1.34586	−	0.348410i
$343$	−14.8858	+	7.16861i	−0.803756	+	0.387069i
$344$	0.612676	+	1.56107i	0.0330333	+	0.0841674i
$345$	−0.694130	+	30.2503i	−0.0373707	+	1.62862i
$346$	19.2254	+	13.1077i	1.03357	+	0.704673i
$347$	6.80510	+	11.7868i	0.365317	+	0.632748i	0.988827	−	0.149068i	$-0.0476273\pi$
$347$	6.80510	+	11.7868i	0.365317	+	0.632748i	−0.623510	+	0.781815i	$0.714294\pi$
$348$	−1.54491	−	9.19855i	−0.0828159	−	0.493094i
$349$	11.9845	−	20.7578i	0.641516	−	1.11114i	−0.343579	−	0.939124i	$-0.611639\pi$
$349$	11.9845	−	20.7578i	0.641516	−	1.11114i	0.985095	−	0.172014i	$-0.0550274\pi$
$350$	11.1744	−	5.38130i	0.597296	−	0.287642i
$351$	−6.76712	−	8.38250i	−0.361202	−	0.447424i
$352$	−0.651768	+	0.817291i	−0.0347393	+	0.0435618i
$353$	−1.09109	+	14.5596i	−0.0580729	+	0.774929i	0.889814	+	0.456323i	$0.150834\pi$
$353$	−1.09109	+	14.5596i	−0.0580729	+	0.774929i	−0.947887	+	0.318606i	$0.896785\pi$
$354$	−8.11216	+	11.3309i	−0.431157	+	0.602229i
$355$	−21.8564	+	55.6892i	−1.16002	+	2.95568i
$356$	5.03035	−	1.55166i	0.266608	−	0.0822377i
$357$	−4.37425	+	3.32709i	−0.231510	+	0.176088i
$358$	2.48733	+	6.33762i	0.131460	+	0.334954i
$359$	0.964611	+	4.22624i	0.0509102	+	0.223052i	0.993983	−	0.109534i	$-0.0349359\pi$
$359$	0.964611	+	4.22624i	0.0509102	+	0.223052i	−0.943073	+	0.332586i	$0.892079\pi$
$360$	−2.00184	−	11.0945i	−0.105506	−	0.584730i
$361$	−12.1148	−	53.0784i	−0.637620	−	2.79360i
$362$	3.64842	−	2.48745i	0.191756	−	0.130737i
$363$	17.0779	+	1.67457i	0.896359	+	0.0878920i
$364$	2.06650	−	1.91743i	0.108314	−	0.100501i
$365$	9.84660	+	17.0548i	0.515395	+	0.892690i
$366$	−4.21655	−	6.50006i	−0.220402	−	0.339763i
$367$	5.98176	+	15.2413i	0.312245	+	0.795588i	0.997720	+	0.0674912i	$0.0214995\pi$
$367$	5.98176	+	15.2413i	0.312245	+	0.795588i	−0.685475	+	0.728096i	$0.740405\pi$
$368$	−1.03446	+	4.53225i	−0.0539247	+	0.236260i
$369$	20.8977	+	0.959554i	1.08789	+	0.0499524i
$370$	−0.979146	−	1.22781i	−0.0509034	−	0.0638308i
$371$	−11.1827	+	7.62424i	−0.580577	+	0.395831i
$372$	16.8966	+	4.26659i	0.876047	+	0.221213i
$373$	28.7629	+	4.33531i	1.48929	+	0.224474i	0.842708	−	0.538372i	$-0.180960\pi$
$373$	28.7629	+	4.33531i	1.48929	+	0.224474i	0.646581	+	0.762846i	$0.276198\pi$
$374$	−0.891228	+	2.27081i	−0.0460843	+	0.117421i
$375$	7.31723	+	25.8098i	0.377860	+	1.33281i
$376$	5.04998	−	8.74682i	0.260433	−	0.451083i
$377$	5.96226	+	9.43974i	0.307072	+	0.486171i
$378$	7.06505	−	0.0422017i	0.363387	−	0.00217062i
$379$	2.58694	−	1.24581i	0.132882	−	0.0639927i	−0.366261	−	0.930512i	$-0.619362\pi$
$379$	2.58694	−	1.24581i	0.132882	−	0.0639927i	0.499144	+	0.866519i	$0.333648\pi$
$380$	−31.8450	+	4.79985i	−1.63361	+	0.246227i
$381$	−19.4121	−	21.9085i	−0.994513	−	1.12241i
$382$	−8.54376	−	5.82504i	−0.437137	−	0.298035i
$383$	−2.20349	−	29.4035i	−0.112593	−	1.50245i	−0.712100	−	0.702078i	$-0.752256\pi$
$383$	−2.20349	−	29.4035i	−0.112593	−	1.50245i	0.599507	−	0.800370i	$-0.295363\pi$
$384$	0.0397336	−	1.73159i	0.00202765	−	0.0883651i
$385$	3.91545	+	3.63301i	0.199550	+	0.185155i
$386$	−5.14514	+	22.5423i	−0.261881	+	1.14737i
$387$	−0.145453	−	5.02889i	−0.00739379	−	0.255633i
$388$	−1.44250	−	6.32002i	−0.0732320	−	0.320850i
$389$	19.1341	−	33.1412i	0.970138	−	1.68033i	0.275011	−	0.961441i	$-0.411319\pi$
$389$	19.1341	−	33.1412i	0.970138	−	1.68033i	0.695127	−	0.718887i	$-0.255348\pi$
$390$	7.34405	+	11.3213i	0.371880	+	0.573275i
$391$	0.810706	+	10.8181i	0.0409992	+	0.547096i
$392$	−0.384952	−	5.13683i	−0.0194430	−	0.259449i
$393$	−6.02827	−	9.29294i	−0.304086	−	0.468767i
$394$	0.717671	−	1.24304i	0.0361558	−	0.0626236i
$395$	−4.52828	−	19.8397i	−0.227843	−	0.998243i
$396$	2.66944	−	1.64590i	0.134144	−	0.0827094i
$397$	−3.88148	+	17.0059i	−0.194806	+	0.853501i	0.779163	+	0.626821i	$0.215644\pi$
$397$	−3.88148	+	17.0059i	−0.194806	+	0.853501i	−0.973969	+	0.226680i	$0.927213\pi$
$398$	−11.6509	−	10.8105i	−0.584007	−	0.541879i
$399$	0.462994	−	20.1773i	0.0231787	−	1.01013i
$400$	0.681660	+	9.09612i	0.0340830	+	0.454806i
$401$	−20.3335	−	13.8631i	−1.01540	−	0.692291i	−0.0632779	−	0.997996i	$-0.520155\pi$
$401$	−20.3335	−	13.8631i	−1.01540	−	0.692291i	−0.952126	+	0.305705i	$0.901108\pi$
$402$	9.65615	+	10.8979i	0.481605	+	0.543539i
$403$	−20.6273	+	3.10907i	−1.02752	+	0.154874i
$404$	−8.77649	+	4.22653i	−0.436646	+	0.210278i
$405$	−5.60748	+	33.3528i	−0.278638	+	1.65731i
$406$	−7.27804	−	0.802786i	−0.361203	−	0.0398416i
$407$	0.218429	−	0.378330i	0.0108271	−	0.0187531i
$408$	−1.10246	−	3.88866i	−0.0545799	−	0.192517i
$409$	5.58119	−	14.2206i	0.275972	−	0.703165i	−0.723939	−	0.689864i	$-0.757671\pi$
$409$	5.58119	−	14.2206i	0.275972	−	0.703165i	0.999912	−	0.0133019i	$-0.00423424\pi$
$410$	−25.9119	−	3.90560i	−1.27970	−	0.192884i
$411$	5.21997	+	1.31811i	0.257482	+	0.0650174i
$412$	6.11038	−	4.16599i	0.301037	−	0.205243i
$413$	6.82071	+	8.55290i	0.335625	+	0.420861i
$414$	7.51986	−	11.7454i	0.369581	−	0.577254i
$415$	0.0616808	−	0.270241i	0.00302779	−	0.0132656i
$416$	0.757457	+	1.92997i	0.0371374	+	0.0946246i
$417$	15.1260	+	23.3176i	0.740723	+	1.14187i
$418$	−4.47930	−	7.75837i	−0.219090	−	0.379474i
$419$	−24.6938	+	22.9125i	−1.20637	+	1.11935i	−0.216661	+	0.976247i	$0.569517\pi$
$419$	−24.6938	+	22.9125i	−1.20637	+	1.11935i	−0.989708	+	0.143100i	$0.954293\pi$
$420$	−8.80778	−	0.863642i	−0.429776	−	0.0421414i
$421$	30.5232	−	20.8103i	1.48761	−	1.01423i	0.498525	−	0.866876i	$-0.333875\pi$
$421$	30.5232	−	20.8103i	1.48761	−	1.01423i	0.989083	−	0.147358i	$-0.0470770\pi$
$422$	−1.18698	−	5.20048i	−0.0577811	−	0.253155i
$423$	−23.1333	+	19.5687i	−1.12478	+	0.951461i
$424$	−2.21498	−	9.70448i	−0.107569	−	0.471291i
$425$	7.77674	+	19.8148i	0.377227	+	0.961160i
$426$	21.9469	−	16.6930i	1.06333	−	0.808778i
$427$	−5.81204	+	1.79278i	−0.281264	+	0.0867586i
$428$	2.44050	−	6.21828i	0.117966	−	0.300572i
$429$	−2.18525	+	3.05230i	−0.105505	+	0.147366i
$430$	−0.470945	+	6.28432i	−0.0227110	+	0.303057i
$431$	−18.2989	+	22.9461i	−0.881428	+	1.10528i	0.112324	+	0.993672i	$0.464170\pi$
$431$	−18.2989	+	22.9461i	−0.881428	+	1.10528i	−0.993753	+	0.111605i	$0.964401\pi$
$432$	−1.86944	+	4.84821i	−0.0899436	+	0.233260i
$433$	−18.3218	+	8.82330i	−0.880488	+	0.424021i	−0.818803	−	0.574075i	$-0.805362\pi$
$433$	−18.3218	+	8.82330i	−0.880488	+	0.424021i	−0.0616852	+	0.998096i	$0.519647\pi$
$434$	6.84025	−	11.8477i	0.328343	−	0.568706i
$435$	9.76741	−	33.6627i	0.468311	−	1.61400i
$436$	2.81761	+	4.88024i	0.134939	+	0.233721i
$437$	−32.9172	−	22.4426i	−1.57464	−	1.07357i
$438$	0.208224	−	9.07445i	0.00994935	−	0.433594i
$439$	1.57966	+	4.02490i	0.0753930	+	0.192098i	0.963602	−	0.267342i	$-0.0861453\pi$
$439$	1.57966	+	4.02490i	0.0753930	+	0.192098i	−0.888209	+	0.459440i	$0.848050\pi$
$440$	−3.53929	+	1.70443i	−0.168729	+	0.0812555i
$441$	−4.12621	+	14.8926i	−0.196486	+	0.709174i
$442$	3.01659	+	3.78268i	0.143484	+	0.179924i
$443$	12.8992	+	11.9687i	0.612860	+	0.568651i	0.924325	−	0.381607i	$-0.124629\pi$
$443$	12.8992	+	11.9687i	0.612860	+	0.568651i	−0.311465	+	0.950258i	$0.600820\pi$
$444$	0.0914335	+	0.718032i	0.00433924	+	0.0340763i
$445$	19.5614	+	2.94840i	0.927297	+	0.139768i
$446$	2.29068	−	2.12544i	0.108467	−	0.100643i
$447$	3.50081	−	1.28209i	0.165583	−	0.0606408i
$448$	−1.29929	−	0.400777i	−0.0613855	−	0.0189349i
$449$	10.4894	+	5.05142i	0.495025	+	0.238391i	0.664702	−	0.747108i	$-0.268558\pi$
$449$	10.4894	+	5.05142i	0.495025	+	0.238391i	−0.169678	+	0.985500i	$0.554273\pi$
$450$	7.30656	−	26.3714i	0.344434	−	1.24316i
$451$	−1.62207	−	7.10676i	−0.0763804	−	0.334644i
$452$	6.69255	−	11.5918i	0.314791	−	0.545234i
$453$	5.82639	−	11.4208i	0.273748	−	0.536594i
$454$	21.3045	+	3.21113i	0.999867	+	0.150706i
$455$	10.1230	−	3.12252i	0.474571	−	0.146386i
$456$	13.6894	+	5.73849i	0.641065	+	0.268730i
$457$	22.9762	−	3.46311i	1.07478	−	0.161997i	0.412280	−	0.911057i	$-0.364732\pi$
$457$	22.9762	−	3.46311i	1.07478	−	0.161997i	0.662503	+	0.749060i	$0.269494\pi$
$458$	−15.9719	−	7.69167i	−0.746319	−	0.359408i
$459$	−0.833916	+	12.0970i	−0.0389239	+	0.564642i
$460$	−10.8921	+	13.6583i	−0.507848	+	0.636821i
$461$	−29.8568	+	4.50018i	−1.39057	+	0.209594i	−0.801261	−	0.598315i	$-0.795837\pi$
$461$	−29.8568	+	4.50018i	−1.39057	+	0.209594i	−0.589307	+	0.807909i	$0.700599\pi$
$462$	−0.671492	−	2.36853i	−0.0312406	−	0.110194i
$463$	21.0368	+	36.4367i	0.977661	+	1.69336i	0.670858	+	0.741586i	$0.265926\pi$
$463$	21.0368	+	36.4367i	0.977661	+	1.69336i	0.306803	+	0.951773i	$0.400741\pi$
$464$	2.50516	−	4.76699i	0.116299	−	0.221302i
$465$	50.2507	+	41.9951i	2.33032	+	1.94748i
$466$	0.0142490	−	0.190139i	0.000660070	−	0.00880803i
$467$	−22.4739	−	28.1814i	−1.03997	−	1.30408i	−0.951383	−	0.308011i	$-0.900337\pi$
$467$	−22.4739	−	28.1814i	−1.03997	−	1.30408i	−0.0885863	−	0.996069i	$-0.528235\pi$
$468$	−0.179825	−	6.21727i	−0.00831241	−	0.287393i
$469$	10.2983	−	4.95939i	0.475530	−	0.229003i
$470$	31.3594	−	21.3805i	1.44650	−	0.986207i
$471$	−12.5789	−	7.65243i	−0.579604	−	0.352605i
$472$	−7.68817	+	2.37149i	−0.353877	+	0.109156i
$473$	−1.67517	+	0.516722i	−0.0770245	+	0.0237589i
$474$	−2.96954	+	8.89704i	−0.136396	+	0.408654i
$475$	−74.6986	−	23.0415i	−3.42740	−	1.05721i
$476$	−3.17299			−0.145434
$477$	−3.59515	+	29.6450i	−0.164611	+	1.35735i
$478$	4.03515	+	1.94323i	0.184564	+	0.0888811i
$479$	−2.15009	+	1.46591i	−0.0982401	+	0.0669790i	−0.611444	−	0.791288i	$-0.709411\pi$
$479$	−2.15009	+	1.46591i	−0.0982401	+	0.0669790i	0.513204	+	0.858267i	$0.328459\pi$
$480$	2.95786	−	5.79793i	0.135007	−	0.264638i
$481$	−0.433217	−	0.750354i	−0.0197530	−	0.0342132i
$482$	−9.92671	+	9.21064i	−0.452149	+	0.419533i
$483$	−7.26060	−	8.19432i	−0.330369	−	0.372854i
$484$	7.26252	+	6.73863i	0.330114	+	0.306301i
$485$	5.42074	−	23.7498i	0.246143	−	1.07842i
$486$	10.1978	−	11.7900i	0.462581	−	0.534807i
$487$	−37.9767	−	18.2886i	−1.72089	−	0.828735i	−0.989108	−	0.147193i	$-0.952976\pi$
$487$	−37.9767	−	18.2886i	−1.72089	−	0.828735i	−0.731779	−	0.681543i	$-0.761309\pi$
$488$	0.334287	−	4.46075i	0.0151324	−	0.201928i
$489$	−5.83005	−	6.57980i	−0.263644	−	0.297549i
$490$	7.07215	−	18.0196i	0.319487	−	0.814041i
$491$	−22.9241	−	15.6294i	−1.03455	−	0.705345i	−0.0780134	−	0.996952i	$-0.524858\pi$
$491$	−22.9241	−	15.6294i	−1.03455	−	0.705345i	−0.956538	+	0.291607i	$0.905810\pi$
$492$	9.26775	+	7.74517i	0.417822	+	0.349179i
$493$	2.30741	−	12.3532i	0.103920	−	0.556360i
$494$	−17.7679			−0.799415
$495$	11.7216	−	1.22009i	0.526847	−	0.0548389i
$496$	6.27321	+	7.86636i	0.281676	+	0.353210i
$497$	−7.90821	−	20.1498i	−0.354731	−	0.903841i
$498$	−0.0890250	+	0.0916371i	−0.00398930	+	0.00410636i
$499$	0.122720	+	1.63758i	0.00549370	+	0.0733084i	0.999277	−	0.0380254i	$-0.0121068\pi$
$499$	0.122720	+	1.63758i	0.00549370	+	0.0733084i	−0.993783	+	0.111334i	$0.964488\pi$
$500$	−5.65860	+	14.4179i	−0.253060	+	0.644787i
$501$	−2.46762	−	19.3783i	−0.110245	−	0.865760i
$502$	7.60841	+	7.05957i	0.339580	+	0.315084i
$503$	14.4791	−	18.1562i	0.645590	−	0.809544i	−0.346099	−	0.938198i	$-0.612494\pi$
$503$	14.4791	−	18.1562i	0.645590	−	0.809544i	0.991690	+	0.128653i	$0.0410655\pi$
$504$	3.26135	+	2.45000i	0.145272	+	0.109132i
$505$	−36.6061			−1.62895
$506$	−4.64374	−	1.43241i	−0.206440	−	0.0636782i
$507$	−6.22601	−	13.7253i	−0.276507	−	0.609562i
$508$	−1.26293	−	16.8526i	−0.0560333	−	0.747712i
$509$	15.4926	−	14.3750i	0.686698	−	0.637163i	−0.257601	−	0.966251i	$-0.582932\pi$
$509$	15.4926	−	14.3750i	0.686698	−	0.637163i	0.944299	+	0.329089i	$0.106742\pi$
$510$	2.60776	−	14.9635i	0.115473	−	0.662595i
$511$	−6.80894	−	2.10028i	−0.301210	−	0.0929108i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	−32.8235	−	30.0929i	−1.44919	−	1.32864i
$514$	0.0742975	−	0.325519i	0.00327712	−	0.0143580i
$515$	27.4807	−	4.14204i	1.21094	−	0.182520i
$516$	1.69087	−	2.36176i	0.0744363	−	0.103971i
$517$	8.72346	+	5.94755i	0.383657	+	0.261573i
$518$	0.561875	+	0.0846890i	0.0246874	+	0.00372102i
$519$	0.924546	−	40.2918i	0.0405830	−	1.76862i
$520$	−0.582234	+	7.76937i	−0.0255327	+	0.340710i
$521$	2.97381			0.130285			0.0651424	−	0.997876i	$-0.479250\pi$
$521$	2.97381			0.130285			0.0651424	+	0.997876i	$0.479250\pi$
$522$	−11.9101	+	10.9156i	−0.521291	+	0.477761i
$523$	−26.0140			−1.13751			−0.568757	−	0.822506i	$-0.692576\pi$
$523$	−26.0140			−1.13751			−0.568757	+	0.822506i	$0.692576\pi$
$524$	0.477920	−	6.37739i	0.0208780	−	0.278598i
$525$	−18.3526	−	11.1649i	−0.800975	−	0.487278i
$526$	−21.3359	−	3.21588i	−0.930292	−	0.140219i
$527$	19.3996	+	13.2264i	0.845061	+	0.576153i
$528$	1.80197	+	0.176691i	0.0784205	+	0.00768948i
$529$	1.37314	−	0.206968i	0.0597019	−	0.00899861i
$530$	8.32364	−	36.4682i	0.361556	−	1.58408i
$531$	24.1114	+	1.10712i	1.04635	+	0.0480447i
$532$	7.26519	−	9.11026i	0.314986	−	0.394980i
$533$	−13.8153	−	4.26144i	−0.598405	−	0.184584i
$534$	−6.99638	−	5.84696i	−0.302763	−	0.253023i
$535$	18.4016	−	17.0742i	0.795572	−	0.738183i
$536$	0.628216	+	8.38296i	0.0271348	+	0.362089i
$537$	6.86457	−	9.58825i	0.296228	−	0.413764i
$538$	19.9995	+	6.16904i	0.862241	+	0.265966i
$539$	5.38486			0.231942
$540$	−14.2343	+	13.3666i	−0.612549	+	0.575209i
$541$	4.87601	−	6.11432i	0.209636	−	0.262875i	−0.665886	−	0.746054i	$-0.731946\pi$
$541$	4.87601	−	6.11432i	0.209636	−	0.262875i	0.875522	+	0.483178i	$0.160518\pi$
$542$	−20.4465	−	18.9716i	−0.878253	−	0.814899i
$543$	−7.05354	−	2.95679i	−0.302696	−	0.126888i
$544$	0.852561	−	2.17229i	0.0365532	−	0.0931362i
$545$	1.58252	+	21.1172i	0.0677875	+	0.904562i
$546$	−4.73412	−	1.19542i	−0.202602	−	0.0511594i
$547$	−8.04677	−	20.5028i	−0.344055	−	0.876638i	−0.993248	−	0.116014i	$-0.962988\pi$
$547$	−8.04677	−	20.5028i	−0.344055	−	0.876638i	0.649192	−	0.760624i	$-0.275107\pi$
$548$	1.93803	+	2.43021i	0.0827883	+	0.103813i
$549$	−5.47062	+	12.2541i	−0.233480	+	0.522991i
$550$	−9.53533			−0.406588
$551$	30.1851	+	34.9101i	1.28593	+	1.48722i
$552$	7.56087	−	2.76899i	0.321812	−	0.117856i
$553$	6.08369	+	4.14779i	0.258705	+	0.176382i
$554$	1.34896	−	3.43711i	0.0573120	−	0.146029i
$555$	−0.861168	+	2.58014i	−0.0365546	+	0.109521i
$556$	−1.19918	+	16.0020i	−0.0508568	+	0.678636i
$557$	−15.6276	−	7.52586i	−0.662163	−	0.318881i	0.0724454	−	0.997372i	$-0.476920\pi$
$557$	−15.6276	−	7.52586i	−0.662163	−	0.318881i	−0.734608	+	0.678492i	$0.762634\pi$
$558$	−9.72718	−	28.5741i	−0.411784	−	1.20964i
$559$	−0.773683	+	3.38973i	−0.0327233	+	0.143370i
$560$	−3.74557	−	3.47538i	−0.158279	−	0.146862i
$561$	4.13979	−	0.845459i	0.174782	−	0.0356953i
$562$	5.12249	−	4.75298i	0.216079	−	0.200492i
$563$	19.7582	+	34.2223i	0.832710	+	1.44230i	0.895881	+	0.444294i	$0.146545\pi$
$563$	19.7582	+	34.2223i	0.832710	+	1.44230i	−0.0631710	+	0.998003i	$0.520121\pi$
$564$	−17.4701	+	0.906772i	−0.735625	+	0.0381820i
$565$	41.5594	−	28.3347i	1.74842	−	1.19205i
$566$	−6.92486	−	3.33484i	−0.291074	−	0.140174i
$567$	−6.72093	−	10.2264i	−0.282253	−	0.429469i
$568$	15.9198			0.667981
$569$	1.44330	+	0.445198i	0.0605061	+	0.0186637i	0.324860	−	0.945762i	$-0.394683\pi$
$569$	1.44330	+	0.445198i	0.0605061	+	0.0186637i	−0.264354	+	0.964426i	$0.585159\pi$
$570$	36.9921	+	41.7493i	1.54943	+	1.74869i
$571$	6.24878	−	1.92749i	0.261503	−	0.0806631i	−0.161231	−	0.986917i	$-0.551546\pi$
$571$	6.24878	−	1.92749i	0.261503	−	0.0806631i	0.422735	+	0.906254i	$0.361070\pi$
$572$	−2.07103	+	0.638829i	−0.0865943	+	0.0267108i
$573$	−0.410867	+	17.9056i	−0.0171642	+	0.748019i
$574$	7.83398	−	5.34112i	0.326984	−	0.222934i
$575$	−38.2052	+	18.3987i	−1.59327	+	0.767278i
$576$	−2.55362	+	1.57449i	−0.106401	+	0.0656036i
$577$	−20.0753	−	25.1736i	−0.835744	−	1.04799i	−0.998122	−	0.0612611i	$-0.980488\pi$
$577$	−20.0753	−	25.1736i	−0.835744	−	1.04799i	0.162378	−	0.986729i	$-0.448084\pi$
$578$	−0.863454	+	11.5220i	−0.0359149	+	0.479252i
$579$	37.6060	−	13.7723i	1.56285	−	0.572358i
$580$	16.2543	−	12.0551i	0.674922	−	0.500561i
$581$	0.0501474	+	0.0868578i	0.00208046	+	0.00360347i
$582$	−7.82385	+	8.05342i	−0.324309	+	0.333825i
$583$	10.2893	−	1.55086i	0.426139	−	0.0642301i
$584$	3.26741	−	4.09720i	0.135206	−	0.169543i
$585$	9.52829	−	21.3432i	0.393946	−	0.882432i
$586$	−4.11189	−	1.98018i	−0.169861	−	0.0818006i
$587$	−11.6046	+	1.74911i	−0.478974	+	0.0721937i	−0.384092	−	0.923295i	$-0.625485\pi$
$587$	−11.6046	+	1.74911i	−0.478974	+	0.0721937i	−0.0948818	+	0.995489i	$0.530247\pi$
$588$	−7.10143	+	5.40141i	−0.292858	+	0.222750i
$589$	−82.3950	+	25.4155i	−3.39503	+	1.04723i
$590$	−29.8967	−	4.50620i	−1.23083	−	0.185517i
$591$	−2.48274	+	0.128865i	−0.102126	+	0.00530079i
$592$	−0.208952	+	0.361915i	−0.00858786	+	0.0148746i
$593$	−5.08687	−	22.2870i	−0.208893	−	0.915219i	−0.965305	−	0.261124i	$-0.915907\pi$
$593$	−5.08687	−	22.2870i	−0.208893	−	0.915219i	0.756412	−	0.654095i	$-0.226950\pi$
$594$	−4.90789	−	2.32750i	−0.201373	−	0.0954987i
$595$	−10.7429	−	5.17350i	−0.440415	−	0.212093i
$596$	2.05685	+	0.634453i	0.0842517	+	0.0259882i
$597$	−4.72632	+	27.1199i	−0.193435	+	1.10994i
$598$	−7.06538	+	6.55571i	−0.288925	+	0.268083i
$599$	36.9565	+	5.57029i	1.51000	+	0.227596i	0.851248	−	0.524764i	$-0.175846\pi$
$599$	36.9565	+	5.57029i	1.51000	+	0.227596i	0.658753	+	0.752360i	$0.271084\pi$
$600$	12.5750	−	9.56463i	0.513371	−	0.390475i
$601$	17.6264	+	16.3549i	0.718994	+	0.667129i	0.952262	−	0.305283i	$-0.0987512\pi$
$601$	17.6264	+	16.3549i	0.718994	+	0.667129i	−0.233267	+	0.972413i	$0.574942\pi$
$602$	−1.42168	−	1.78274i	−0.0579435	−	0.0726589i
$603$	6.73371	−	24.3038i	0.274218	−	0.989728i
$604$	6.66921	−	3.21172i	0.271366	−	0.130683i
$605$	13.6017	+	34.6566i	0.552988	+	1.40899i
$606$	14.4144	+	8.76907i	0.585544	+	0.356219i
$607$	6.19465	+	4.22344i	0.251433	+	0.171424i	0.682478	−	0.730906i	$-0.260902\pi$
$607$	6.19465	+	4.22344i	0.251433	+	0.171424i	−0.431044	+	0.902331i	$0.641855\pi$
$608$	4.28496	+	7.42176i	0.173778	+	0.300992i
$609$	5.69385	+	11.3324i	0.230726	+	0.459212i
$610$	8.40497	−	14.5578i	0.340307	−	0.589429i
$611$	18.8664	−	9.08558i	0.763253	−	0.367563i
$612$	−4.61140	+	5.26748i	−0.186405	+	0.212925i
$613$	6.34715	−	7.95908i	0.256359	−	0.321464i	−0.636952	−	0.770904i	$-0.719805\pi$
$613$	6.34715	−	7.95908i	0.256359	−	0.321464i	0.893311	+	0.449440i	$0.148376\pi$
$614$	0.955704	−	12.7530i	0.0385691	−	0.514668i
$615$	18.7497	+	41.3339i	0.756062	+	1.66675i
$616$	0.519282	−	1.32311i	0.0209225	−	0.0533096i
$617$	21.0585	−	6.49568i	0.847783	−	0.261506i	0.159724	−	0.987162i	$-0.448939\pi$
$617$	21.0585	−	6.49568i	0.847783	−	0.261506i	0.688058	+	0.725655i	$0.258463\pi$
$618$	−11.8133	−	4.95204i	−0.475200	−	0.199200i
$619$	6.42091	+	16.3602i	0.258078	+	0.657573i	0.999915	−	0.0130073i	$-0.00414047\pi$
$619$	6.42091	+	16.3602i	0.258078	+	0.657573i	−0.741837	+	0.670580i	$0.766045\pi$
$620$	8.41345	+	36.8617i	0.337892	+	1.48040i
$621$	−24.1554	+	0.144288i	−0.969325	+	0.00579007i
$622$	5.41511	+	23.7251i	0.217126	+	0.951291i
$623$	−5.91400	+	4.03210i	−0.236940	+	0.161543i
$624$	2.09044	−	2.91987i	0.0836845	−	0.116888i
$625$	−9.23345	+	8.56739i	−0.369338	+	0.342696i
$626$	5.42624	+	9.39853i	0.216876	+	0.375641i
$627$	−7.05140	+	13.8220i	−0.281606	+	0.551997i
$628$	−3.10567	−	7.91311i	−0.123930	−	0.315768i
$629$	−0.217007	+	0.950770i	−0.00865264	+	0.0379097i
$630$	7.04737	+	13.6126i	0.280774	+	0.542339i
$631$	18.5473	+	23.2576i	0.738357	+	0.925871i	0.999219	−	0.0395052i	$-0.0125782\pi$
$631$	18.5473	+	23.2576i	0.738357	+	0.925871i	−0.260862	+	0.965376i	$0.584007\pi$
$632$	−4.47431	+	3.05053i	−0.177978	+	0.121344i
$633$	−6.43793	+	6.62683i	−0.255885	+	0.263393i
$634$	−7.93232	−	1.19561i	−0.315033	−	0.0474836i
$635$	23.2019	−	59.1174i	0.920739	−	2.34600i
$636$	−12.0136	+	12.3662i	−0.476372	+	0.490350i
$637$	5.33999	−	9.24914i	0.211578	−	0.366464i
$638$	4.77355	+	2.98386i	0.188987	+	0.118132i
$639$	−44.9439	−	16.1559i	−1.77795	−	0.639116i
$640$	3.38573	−	1.63048i	0.133833	−	0.0644504i
$641$	40.9427	−	6.17113i	1.61714	−	0.243745i	0.722776	−	0.691082i	$-0.242866\pi$
$641$	40.9427	−	6.17113i	1.61714	−	0.243745i	0.894365	+	0.447338i	$0.147628\pi$
$642$	−11.3362	+	2.31516i	−0.447404	+	0.0913722i
$643$	14.6068	+	9.95875i	0.576036	+	0.392735i	0.816004	−	0.578046i	$-0.196185\pi$
$643$	14.6068	+	9.95875i	0.576036	+	0.392735i	−0.239968	+	0.970781i	$0.577137\pi$
$644$	−0.472365	−	6.30327i	−0.0186138	−	0.248384i
$645$	9.57563	−	5.23936i	0.377040	−	0.206299i
$646$	14.6601	+	13.6026i	0.576795	+	0.535188i
$647$	−0.685720	+	3.00434i	−0.0269585	+	0.118113i	−0.986617	−	0.163056i	$-0.947865\pi$
$647$	−0.685720	+	3.00434i	−0.0269585	+	0.118113i	0.959658	+	0.281169i	$0.0907220\pi$
$648$	8.80707	−	1.85352i	0.345974	−	0.0728130i
$649$	−1.87152	−	8.19965i	−0.0734634	−	0.321864i
$650$	−9.45588	+	16.3781i	−0.370890	+	0.642401i
$651$	−23.6635	+	1.22823i	−0.927445	+	0.0481382i
$652$	−0.379295	−	5.06134i	−0.0148544	−	0.198218i
$653$	2.06739	+	27.5874i	0.0809033	+	1.07958i	0.878928	+	0.476955i	$0.158259\pi$
$653$	2.06739	+	27.5874i	0.0809033	+	1.07958i	−0.798025	+	0.602625i	$0.794122\pi$
$654$	4.43553	−	8.69442i	0.173443	−	0.339979i
$655$	12.0163	−	20.8129i	0.469517	−	0.813227i
$656$	1.55170	+	6.79842i	0.0605835	+	0.265434i
$657$	−13.3823	+	8.25112i	−0.522093	+	0.321907i
$658$	−3.05585	+	13.3885i	−0.119129	+	0.521940i
$659$	18.1871	+	16.8751i	0.708468	+	0.657362i	0.949720	−	0.313100i	$-0.101368\pi$
$659$	18.1871	+	16.8751i	0.708468	+	0.657362i	−0.241252	+	0.970462i	$0.577558\pi$
$660$	5.81287	+	3.53630i	0.226266	+	0.137650i
$661$	−2.75907	−	36.8173i	−0.107316	−	1.43203i	−0.747733	−	0.664000i	$-0.768858\pi$
$661$	−2.75907	−	36.8173i	−0.107316	−	1.43203i	0.640417	−	0.768027i	$-0.278761\pi$
$662$	13.4305	+	9.15674i	0.521990	+	0.355887i
$663$	2.65312	−	7.94899i	0.103039	−	0.308713i
$664$	−0.0729388	+	0.0109938i	−0.00283058	+	0.000426641i
$665$	39.4521	−	18.9991i	1.52989	−	0.736754i
$666$	0.957181	−	0.809688i	0.0370900	−	0.0313748i
$667$	24.8836	+	2.74473i	0.963498	+	0.106276i
$668$	5.63922	−	9.76741i	0.218188	−	0.377912i
$669$	−5.24770	−	1.32511i	−0.202888	−	0.0512316i
$670$	−11.5413	+	29.4067i	−0.445879	+	1.13608i
$671$	4.62391	+	0.696942i	0.178504	+	0.0269051i
$672$	0.642358	+	2.26576i	0.0247795	+	0.0874037i
$673$	−37.4760	+	25.5507i	−1.44459	+	0.984907i	−0.448766	+	0.893649i	$0.648136\pi$
$673$	−37.4760	+	25.5507i	−1.44459	+	0.984907i	−0.995827	+	0.0912581i	$0.970911\pi$
$674$	−5.13546	−	6.43967i	−0.197811	−	0.248047i
$675$	−45.2074	+	14.2409i	−1.74003	+	0.548133i
$676$	1.93626	−	8.48331i	0.0744715	−	0.326281i
$677$	−4.84347	−	12.3410i	−0.186150	−	0.474301i	0.807084	−	0.590437i	$-0.201045\pi$
$677$	−4.84347	−	12.3410i	−0.186150	−	0.474301i	−0.993233	+	0.116136i	$0.962949\pi$
$678$	−23.1525	+	1.20171i	−0.889167	+	0.0461515i
$679$	4.40714	+	7.63339i	0.169131	+	0.292943i
$680$	6.42842	−	5.96470i	0.246519	−	0.228736i
$681$	−15.4158	−	33.9842i	−0.590734	−	1.30228i
$682$	−8.69020	+	5.92488i	−0.332765	+	0.226875i
$683$	6.72643	+	29.4704i	0.257380	+	1.12765i	0.924041	+	0.382294i	$0.124866\pi$
$683$	6.72643	+	29.4704i	0.257380	+	1.12765i	−0.666661	+	0.745361i	$0.732277\pi$
$684$	−4.56524	−	25.3012i	−0.174556	−	0.967414i
$685$	2.59922	+	11.3879i	0.0993111	+	0.435111i
$686$	6.03615	+	15.3799i	0.230461	+	0.587206i
$687$	3.87862	+	30.4590i	0.147978	+	1.16208i
$688$	1.60249	−	0.494304i	0.0610945	−	0.0188451i
$689$	7.53977	−	19.2110i	0.287242	−	0.731882i
$690$	30.1138	+	2.95280i	1.14641	+	0.112411i
$691$	−0.286171	+	3.81869i	−0.0108865	+	0.145270i	−0.999998	−	0.00189665i	$-0.999396\pi$
$691$	−0.286171	+	3.81869i	−0.0108865	+	0.145270i	0.989112	+	0.147167i	$0.0470153\pi$
$692$	14.5078	−	18.1921i	0.551502	−	0.691562i
$693$	−2.80873	+	3.20834i	−0.106695	+	0.121875i
$694$	12.2624	−	5.90525i	0.465473	−	0.224160i
$695$	−30.1511	+	52.2232i	−1.14370	+	1.98094i
$696$	−9.28828	+	0.853183i	−0.352071	+	0.0323398i
$697$	8.13641	+	14.0927i	0.308188	+	0.533798i
$698$	−19.8041	−	13.5022i	−0.749597	−	0.511067i
$699$	−0.289721	+	0.158523i	−0.0109583	+	0.00599587i
$700$	−4.53119	−	11.5453i	−0.171263	−	0.436370i
$701$	12.5419	−	6.03987i	0.473702	−	0.228123i	−0.181772	−	0.983341i	$-0.558183\pi$
$701$	12.5419	−	6.03987i	0.473702	−	0.228123i	0.655474	+	0.755218i	$0.272469\pi$
$702$	−8.86476	+	6.12178i	−0.334579	+	0.231052i
$703$	−2.23296	−	2.80005i	−0.0842178	−	0.105606i
$704$	0.766299	+	0.711022i	0.0288810	+	0.0267976i
$705$	−60.6276	−	25.4146i	−2.28337	−	0.957170i
$706$	14.4373	+	2.17608i	0.543357	+	0.0818978i
$707$	9.70928	−	9.00889i	0.365155	−	0.338814i
$708$	10.6930	+	8.93623i	0.401866	+	0.335844i
$709$	−47.4847	−	14.6471i	−1.78333	−	0.550083i	−0.785679	−	0.618635i	$-0.787686\pi$
$709$	−47.4847	−	14.6471i	−1.78333	−	0.550083i	−0.997648	+	0.0685517i	$0.978162\pi$
$710$	53.9002	+	25.9570i	2.02284	+	0.974147i
$711$	15.7274	−	4.07144i	0.589822	−	0.152691i
$712$	−1.17140	−	5.13224i	−0.0439001	−	0.192339i
$713$	−23.3868	+	40.5072i	−0.875844	+	1.51701i
$714$	2.99090	+	4.61065i	0.111932	+	0.172549i
$715$	−8.05356	−	1.21388i	−0.301186	−	0.0453965i
$716$	6.50578	−	2.00677i	0.243132	−	0.0749964i
$717$	−0.979895	−	7.69516i	−0.0365949	−	0.287381i
$718$	4.28651	−	0.646087i	0.159971	−	0.0241117i
$719$	28.8161	+	13.8771i	1.07466	+	0.517528i	0.885605	−	0.464439i	$-0.153744\pi$
$719$	28.8161	+	13.8771i	1.07466	+	0.517528i	0.189053	+	0.981967i	$0.439458\pi$
$720$	−11.2130	+	1.16715i	−0.417886	+	0.0434972i
$721$	−6.26951	+	7.86171i	−0.233489	+	0.292786i
$722$	−53.8353	+	8.11436i	−2.00354	+	0.301985i
$723$	22.7410	+	5.74237i	0.845746	+	0.213561i
$724$	−2.20785	−	3.82410i	−0.0820539	−	0.142122i
$725$	48.2436	−	9.24522i	1.79172	−	0.343359i
$726$	2.94612	−	16.9050i	0.109341	−	0.627405i
$727$	0.452996	−	6.04481i	0.0168007	−	0.224189i	−0.982483	−	0.186351i	$-0.940334\pi$
$727$	0.452996	−	6.04481i	0.0168007	−	0.224189i	0.999284	−	0.0378383i	$-0.0120472\pi$
$728$	−1.75764	−	2.20401i	−0.0651426	−	0.0816862i
$729$	−26.7446	−	3.70491i	−0.990541	−	0.137219i
$730$	17.7430	−	8.54456i	0.656697	−	0.316248i
$731$	3.23344	−	2.20452i	0.119593	−	0.0815372i
$732$	−6.79699	+	3.71901i	−0.251224	+	0.137458i
$733$	−8.79316	+	2.71233i	−0.324783	+	0.100182i	−0.452859	−	0.891582i	$-0.649596\pi$
$733$	−8.79316	+	2.71233i	−0.324783	+	0.100182i	0.128076	+	0.991764i	$0.459120\pi$
$734$	15.6457	−	4.82605i	0.577492	−	0.178133i
$735$	−32.8504	+	6.70896i	−1.21171	+	0.247464i
$736$	4.44227	+	1.37026i	0.163744	+	0.0505084i
$737$	−8.78774			−0.323701
$738$	2.51856	−	20.7676i	0.0927095	−	0.764466i
$739$	30.1841	+	14.5359i	1.11034	+	0.534712i	0.896895	−	0.442243i	$-0.145817\pi$
$739$	30.1841	+	14.5359i	1.11034	+	0.534712i	0.213446	+	0.976955i	$0.431531\pi$
$740$	−1.29755	+	0.884654i	−0.0476989	+	0.0325205i
$741$	16.7482	+	25.8184i	0.615262	+	0.948463i
$742$	6.76724	+	11.7212i	0.248433	+	0.430299i
$743$	21.7253	−	20.1581i	0.797023	−	0.739529i	−0.172373	−	0.985032i	$-0.555143\pi$
$743$	21.7253	−	20.1581i	0.797023	−	0.739529i	0.969396	+	0.245502i	$0.0789529\pi$
$744$	5.51735	−	16.5305i	0.202276	−	0.606038i
$745$	5.92946	+	5.50174i	0.217239	+	0.201568i
$746$	6.47265	−	28.3585i	0.236980	−	1.03828i
$747$	0.217073	+	0.0429833i	0.00794230	+	0.00157268i
$748$	2.19786	+	1.05843i	0.0803618	+	0.0387002i
$749$	−0.678760	+	9.05743i	−0.0248014	+	0.330951i
$750$	26.2844	−	5.36800i	0.959771	−	0.196012i
$751$	7.84403	−	19.9863i	0.286233	−	0.729309i	−0.713361	−	0.700797i	$-0.752828\pi$
$751$	7.84403	−	19.9863i	0.286233	−	0.729309i	0.999593	−	0.0285121i	$-0.00907690\pi$
$752$	−8.34498	−	5.68951i	−0.304310	−	0.207475i
$753$	3.08643	−	17.7102i	0.112476	−	0.645394i
$754$	9.85891	−	5.24015i	0.359040	−	0.190835i
$755$	27.8168			1.01236
$756$	0.485888	−	7.04845i	0.0176716	−	0.256350i
$757$	1.52487	+	1.91212i	0.0554222	+	0.0694972i	0.808770	−	0.588125i	$-0.200134\pi$
$757$	1.52487	+	1.91212i	0.0554222	+	0.0694972i	−0.753348	+	0.657622i	$0.771562\pi$
$758$	−1.04900	−	2.67281i	−0.0381014	−	0.0970807i
$759$	2.29583	+	8.09800i	0.0833335	+	0.293939i
$760$	2.40666	+	32.1146i	0.0872986	+	1.16492i
$761$	−7.37146	+	18.7822i	−0.267215	+	0.680853i	0.732785	+	0.680461i	$0.238220\pi$
$761$	−7.37146	+	18.7822i	−0.267215	+	0.680853i	−1.00000		0.000392737i	$0.999875\pi$
$762$	−23.2979	+	17.7206i	−0.843995	+	0.641950i
$763$	−5.61677	−	5.21160i	−0.203341	−	0.188673i
$764$	−6.44723	+	8.08457i	−0.233252	+	0.292489i
$765$	−24.2015	+	10.3155i	−0.875006	+	0.372956i
$766$	−29.4859			−1.06537
$767$	−15.9398	−	4.91677i	−0.575552	−	0.177534i
$768$	−1.72378	−	0.169025i	−0.0622017	−	0.00609915i
$769$	0.973663	+	12.9926i	0.0351112	+	0.468526i	0.986852	+	0.161624i	$0.0516733\pi$
$769$	0.973663	+	12.9926i	0.0351112	+	0.468526i	−0.951741	+	0.306902i	$0.900708\pi$
$770$	3.91545	−	3.63301i	0.141103	−	0.130925i
$771$	−0.543043	+	0.198877i	−0.0195572	+	0.00716237i
$772$	22.0948	+	6.81534i	0.795209	+	0.245289i
$773$	−0.432540	+	0.542388i	−0.0155574	+	0.0195083i	−0.789549	−	0.613687i	$-0.789686\pi$
$773$	−0.432540	+	0.542388i	−0.0155574	+	0.0195083i	0.773992	+	0.633195i	$0.218257\pi$
$774$	−5.02570	−	0.230763i	−0.180645	−	0.00829460i
$775$	−20.4223	+	89.4758i	−0.733589	+	3.21406i
$776$	−6.41014	+	0.966174i	−0.230111	+	0.0346836i
$777$	−0.406569	−	0.896285i	−0.0145856	−	0.0321541i
$778$	−31.6187	−	21.5573i	−1.13358	−	0.772865i
$779$	−59.0927	−	8.90679i	−2.11722	−	0.319119i
$780$	11.8384	−	6.47747i	0.423884	−	0.231931i
$781$	−1.24365	+	16.5953i	−0.0445012	+	0.593827i
$782$	10.8485			0.387940
$783$	27.0880	+	7.01733i	0.968044	+	0.250779i
$784$	−5.15123			−0.183973
$785$	2.38723	−	31.8554i	0.0852039	−	1.13697i
$786$	−9.71744	+	5.31695i	−0.346610	+	0.189649i
$787$	−54.2233	−	8.17284i	−1.93285	−	0.291330i	−0.934877	−	0.354971i	$-0.884491\pi$
$787$	−54.2233	−	8.17284i	−1.93285	−	0.291330i	−0.997973	+	0.0636404i	$0.979729\pi$
$788$	−1.18594	−	0.808557i	−0.0422472	−	0.0288037i
$789$	15.4386	+	34.0345i	0.549628	+	1.21166i
$790$	−20.1226	+	3.03300i	−0.715931	+	0.107909i
$791$	−4.04980	+	17.7433i	−0.143994	+	0.630881i
$792$	−1.44181	−	2.78498i	−0.0512324	−	0.0989598i
$793$	5.78246	−	7.25098i	0.205341	−	0.257490i
$794$	16.6683	+	5.14148i	0.591535	+	0.182464i
$795$	−60.8377	+	22.2804i	−2.15769	+	0.790204i
$796$	−11.6509	+	10.8105i	−0.412955	+	0.383167i
$797$	2.88800	+	38.5377i	0.102298	+	1.36508i	0.778169	+	0.628055i	$0.216149\pi$
$797$	2.88800	+	38.5377i	0.102298	+	1.36508i	−0.675870	+	0.737021i	$0.736232\pi$
$798$	−20.0863	−	1.96955i	−0.711048	−	0.0697215i
$799$	−22.5222	−	6.94717i	−0.796777	−	0.245773i
$800$	9.12162			0.322498
$801$	−1.90130	+	15.6778i	−0.0671793	+	0.553948i
$802$	−15.3439	+	19.2406i	−0.541811	+	0.679409i
$803$	4.01580	+	3.72612i	0.141715	+	0.131492i
$804$	11.5891	−	8.81474i	0.408715	−	0.310872i
$805$	8.67807	−	22.1114i	0.305862	−	0.779323i
$806$	1.55889	+	20.8020i	0.0549096	+	0.732718i
$807$	−9.88763	−	34.8762i	−0.348061	−	1.22770i
$808$	3.55885	+	9.06779i	0.125200	+	0.319004i
$809$	23.2833	+	29.1963i	0.818596	+	1.02649i	0.999079	+	0.0429086i	$0.0136624\pi$
$809$	23.2833	+	29.1963i	0.818596	+	1.02649i	−0.180483	+	0.983578i	$0.557766\pi$
$810$	32.8405	+	8.08426i	1.15390	+	0.284052i
$811$	−4.10167			−0.144029			−0.0720145	−	0.997404i	$-0.522943\pi$
$811$	−4.10167			−0.144029			−0.0720145	+	0.997404i	$0.522943\pi$
$812$	−1.34443	+	7.19770i	−0.0471802	+	0.252590i
$813$	−8.29435	+	47.5935i	−0.290896	+	1.66918i
$814$	−0.360948	−	0.246090i	−0.0126512	−	0.00862547i
$815$	6.96823	−	17.7548i	0.244087	−	0.621922i
$816$	−3.96018	+	0.808777i	−0.138634	+	0.0283129i
$817$	−1.07400	+	14.3315i	−0.0375745	+	0.501397i
$818$	−13.7638	−	6.62829i	−0.481240	−	0.231753i
$819$	2.72538	+	8.00594i	0.0952325	+	0.279750i
$820$	−5.83108	+	25.5476i	−0.203630	+	0.892162i
$821$	−7.12824	−	6.61404i	−0.248777	−	0.230832i	0.545920	−	0.837837i	$-0.316180\pi$
$821$	−7.12824	−	6.61404i	−0.248777	−	0.230832i	−0.794698	+	0.607005i	$0.792371\pi$
$822$	1.70451	−	5.10688i	0.0594516	−	0.178123i
$823$	3.40177	−	3.15638i	0.118578	−	0.110025i	−0.618655	−	0.785663i	$-0.712322\pi$
$823$	3.40177	−	3.15638i	0.118578	−	0.110025i	0.737234	+	0.675638i	$0.236132\pi$
$824$	−3.69771	−	6.40462i	−0.128816	−	0.223115i
$825$	8.98813	+	13.8557i	0.312926	+	0.482395i
$826$	9.03870	−	6.16248i	0.314497	−	0.214420i
$827$	−38.3475	−	18.4672i	−1.33347	−	0.642167i	−0.374914	−	0.927060i	$-0.622328\pi$
$827$	−38.3475	−	18.4672i	−1.33347	−	0.642167i	−0.958559	+	0.284893i	$0.908042\pi$
$828$	−11.1506	−	8.37656i	−0.387509	−	0.291106i
$829$	33.0377			1.14745			0.573723	−	0.819049i	$-0.305498\pi$
$829$	33.0377			1.14745			0.573723	+	0.819049i	$0.305498\pi$
$830$	−0.264876	−	0.0817035i	−0.00919399	−	0.00283597i
$831$	−6.26599	+	1.27969i	−0.217365	+	0.0443919i
$832$	1.98118	−	0.611113i	0.0686850	−	0.0211865i
$833$	−11.4869	+	3.54323i	−0.397997	+	0.122766i
$834$	24.3828	−	13.3412i	0.844307	−	0.461967i
$835$	35.0184	−	23.8752i	1.21186	−	0.826234i
$836$	−8.07141	+	3.88699i	−0.279156	+	0.134434i
$837$	−32.3518	+	41.0688i	−1.11824	+	1.41955i
$838$	21.0030	+	26.3370i	0.725537	+	0.909795i
$839$	−0.860546	+	11.4832i	−0.0297093	+	0.396444i	0.962450	+	0.271461i	$0.0875067\pi$
$839$	−0.860546	+	11.4832i	−0.0297093	+	0.396444i	−0.992159	+	0.124983i	$0.960112\pi$
$840$	−1.51943	+	8.71861i	−0.0524254	+	0.300821i
$841$	−27.0447	−	10.4684i	−0.932574	−	0.360978i
$842$	−18.4711	−	31.9930i	−0.636558	−	1.10255i
$843$	−11.7351	−	2.96324i	−0.404177	−	0.102060i
$844$	−5.27464	+	0.795024i	−0.181561	+	0.0273659i
$845$	20.3875	−	25.5651i	0.701352	−	0.879468i
$846$	17.7852	+	24.5310i	0.611467	+	0.843393i
$847$	−12.1368	−	5.84477i	−0.417025	−	0.200829i
$848$	−9.84287	+	1.48357i	−0.338006	+	0.0509462i
$849$	1.68163	+	13.2059i	0.0577134	+	0.453226i
$850$	20.3406	−	6.27423i	0.697676	−	0.215204i
$851$	−1.92105	−	0.289552i	−0.0658528	−	0.00992571i
$852$	−15.0062	−	23.1330i	−0.514105	−	0.792523i
$853$	−3.46360	+	5.99912i	−0.118591	+	0.205406i	−0.919210	−	0.393769i	$-0.871171\pi$
$853$	−3.46360	+	5.99912i	−0.118591	+	0.205406i	0.800618	+	0.599175i	$0.204504\pi$
$854$	1.35343	+	5.92976i	0.0463134	+	0.202912i
$855$	25.7964	−	93.1064i	0.882219	−	3.18417i
$856$	−6.01852	−	2.89836i	−0.205709	−	0.0990641i
$857$	−14.5896	−	4.50031i	−0.498372	−	0.153727i	0.0353707	−	0.999374i	$-0.488739\pi$
$857$	−14.5896	−	4.50031i	−0.498372	−	0.153727i	−0.533743	+	0.845647i	$0.679215\pi$
$858$	2.88046	+	2.40724i	0.0983373	+	0.0821817i
$859$	11.5097	−	10.6794i	0.392705	−	0.364377i	−0.458966	−	0.888454i	$-0.651780\pi$
$859$	11.5097	−	10.6794i	0.392705	−	0.364377i	0.851671	+	0.524077i	$0.175589\pi$
$860$	6.23156	+	0.939256i	0.212494	+	0.0320284i
$861$	−15.1456	−	6.34890i	−0.516159	−	0.216370i
$862$	21.5145	+	19.9625i	0.732786	+	0.679926i
$863$	5.46527	+	6.85324i	0.186040	+	0.233287i	0.866101	−	0.499868i	$-0.166618\pi$
$863$	5.46527	+	6.85324i	0.186040	+	0.233287i	−0.680061	+	0.733155i	$0.738047\pi$
$864$	4.69495	+	2.22652i	0.159726	+	0.0757478i
$865$	78.7812	−	37.9391i	2.67864	−	1.28997i
$866$	7.42944	+	18.9299i	0.252463	+	0.643264i
$867$	17.5564	−	9.60609i	0.596248	−	0.326240i
$868$	−11.3034	−	7.70650i	−0.383661	−	0.261576i
$869$	−2.83044	−	4.90246i	−0.0960161	−	0.166305i
$870$	−32.8387	−	12.2557i	−1.11334	−	0.415508i
$871$	−8.71452	+	15.0940i	−0.295280	+	0.511440i
$872$	5.07715	−	2.44503i	0.171934	−	0.0827991i
$873$	19.0772	+	3.77754i	0.645667	+	0.127850i
$874$	−24.8397	+	31.1480i	−0.840216	+	1.05360i
$875$	1.57379	−	21.0008i	0.0532039	−	0.709957i
$876$	−9.03352	−	0.885777i	−0.305214	−	0.0299276i
$877$	12.9550	−	33.0088i	0.437459	−	1.11463i	−0.526876	−	0.849942i	$-0.676637\pi$
$877$	12.9550	−	33.0088i	0.437459	−	1.11463i	0.964335	−	0.264685i	$-0.0852679\pi$
$878$	4.13170	−	1.27446i	0.139438	−	0.0430109i
$879$	0.998530	+	7.84151i	0.0336796	+	0.264487i
$880$	1.43517	+	3.65676i	0.0483797	+	0.123269i
$881$	−2.04314	−	8.95157i	−0.0688351	−	0.301586i	0.928778	−	0.370636i	$-0.120860\pi$
$881$	−2.04314	−	8.95157i	−0.0688351	−	0.301586i	−0.997613	+	0.0690500i	$0.978003\pi$
$882$	14.5427	+	5.22760i	0.489677	+	0.176023i
$883$	2.25650	+	9.88636i	0.0759371	+	0.332702i	0.998599	−	0.0529066i	$-0.0168485\pi$
$883$	2.25650	+	9.88636i	0.0759371	+	0.332702i	−0.922662	+	0.385609i	$0.873991\pi$
$884$	3.99754	−	2.72547i	0.134452	−	0.0916676i
$885$	21.6331	+	47.6903i	0.727188	+	1.60309i
$886$	12.8992	−	11.9687i	0.433357	−	0.402097i
$887$	−7.74820	−	13.4203i	−0.260159	−	0.450609i	0.706125	−	0.708087i	$-0.250442\pi$
$887$	−7.74820	−	13.4203i	−0.260159	−	0.450609i	−0.966284	+	0.257478i	$0.917108\pi$
$888$	0.722857	−	0.0375193i	0.0242575	−	0.00125906i
$889$	8.39503	+	21.3902i	0.281560	+	0.717404i
$890$	4.40198	−	19.2863i	0.147555	−	0.646479i
$891$	1.24416	+	9.32556i	0.0416809	+	0.312418i
$892$	−1.94832	−	2.44311i	−0.0652345	−	0.0818015i
$893$	71.5157	−	48.7586i	2.39318	−	1.63164i
$894$	−1.01689	−	3.58684i	−0.0340099	−	0.119962i
$895$	25.2988	+	3.81318i	0.845646	+	0.127461i
$896$	−0.496752	+	1.26570i	−0.0165953	+	0.0422842i
$897$	16.1860	+	4.08716i	0.540434	+	0.136466i
$898$	5.82117	−	10.0826i	0.194255	−	0.336460i
$899$	38.2231	−	38.4025i	1.27481	−	1.28079i
$900$	−25.7516	−	9.25686i	−0.858388	−	0.308562i
$901$	−20.9284	+	10.0786i	−0.697227	+	0.335767i
$902$	−7.20811	+	1.08645i	−0.240004	+	0.0361747i
$903$	−1.25038	+	3.74627i	−0.0416102	+	0.124668i
$904$	−11.0593	−	7.54010i	−0.367826	−	0.250780i
$905$	−1.24004	−	16.5472i	−0.0412204	−	0.550048i
$906$	−10.9534	−	6.66358i	−0.363903	−	0.221383i
$907$	26.8231	+	24.8882i	0.890645	+	0.826398i	0.985602	−	0.169084i	$-0.0540808\pi$
$907$	26.8231	+	24.8882i	0.890645	+	0.826398i	−0.0949568	+	0.995481i	$0.530271\pi$
$908$	4.79423	−	21.0049i	0.159102	−	0.697072i
$909$	−0.844892	−	29.2113i	−0.0280233	−	0.968877i
$910$	−2.35730	−	10.3280i	−0.0781436	−	0.342370i
$911$	6.86820	−	11.8961i	0.227554	−	0.394135i	−0.729529	−	0.683950i	$-0.760261\pi$
$911$	6.86820	−	11.8961i	0.227554	−	0.394135i	0.957083	+	0.289815i	$0.0935939\pi$
$912$	6.74546	−	13.2223i	0.223364	−	0.437834i
$913$	−0.00576230	−	0.0768926i	−0.000190704	−	0.00254477i
$914$	−1.73641	−	23.1708i	−0.0574354	−	0.766422i
$915$	−29.0765	+	1.50919i	−0.961240	+	0.0498924i
$916$	−8.86375	+	15.3525i	−0.292866	+	0.507259i
$917$	1.93496	+	8.47761i	0.0638979	+	0.279955i
$918$	12.0009	+	1.73560i	0.396089	+	0.0572833i
$919$	−4.44746	+	19.4856i	−0.146708	+	0.642771i	0.847078	+	0.531468i	$0.178360\pi$
$919$	−4.44746	+	19.4856i	−0.146708	+	0.642771i	−0.993787	+	0.111303i	$0.964498\pi$
$920$	12.8061	+	11.8824i	0.422206	+	0.391750i
$921$	−19.4321	+	10.6324i	−0.640311	+	0.350349i
$922$	2.25640	+	30.1096i	0.0743106	+	0.991606i
$923$	27.2711	+	18.5932i	0.897641	+	0.612001i
$924$	−2.41208	+	0.492614i	−0.0793517	+	0.0162058i
$925$	−3.76938	+	0.568143i	−0.123937	+	0.0186804i
$926$	37.9069	−	18.2550i	1.24570	−	0.599897i
$927$	3.93958	+	21.8337i	0.129393	+	0.717112i
$928$	−4.56644	−	2.85440i	−0.149901	−	0.0937002i
$929$	18.3532	−	31.7887i	0.602150	−	1.04295i	−0.390345	−	0.920669i	$-0.627644\pi$
$929$	18.3532	−	31.7887i	0.602150	−	1.04295i	0.992495	−	0.122286i	$-0.0390224\pi$
$930$	45.6329	−	46.9719i	1.49636	−	1.54027i
$931$	16.1282	−	41.0940i	0.528580	−	1.34680i
$932$	−0.188543	−	0.0284182i	−0.00617592	−	0.000930870i
$933$	29.3705	−	30.2323i	0.961547	−	0.989760i
$934$	−29.7821	+	20.3051i	−0.974499	+	0.664403i
$935$	5.71561	+	7.16714i	0.186920	+	0.234391i
$936$	−6.21332	−	0.285295i	−0.203089	−	0.00932515i
$937$	1.44121	−	6.31437i	0.0470824	−	0.206281i	−0.945916	−	0.324413i	$-0.894833\pi$
$937$	1.44121	−	6.31437i	0.0470824	−	0.206281i	0.992998	+	0.118131i	$0.0376904\pi$
$938$	−4.17593	−	10.6401i	−0.136349	−	0.347412i
$939$	8.54209	−	16.7440i	0.278761	−	0.546420i
$940$	−18.9772	−	32.8695i	−0.618968	−	1.07208i
$941$	−11.0532	+	10.2559i	−0.360325	+	0.334333i	−0.839473	−	0.543401i	$-0.817136\pi$
$941$	−11.0532	+	10.2559i	−0.360325	+	0.334333i	0.479148	+	0.877734i	$0.340946\pi$
$942$	−8.57105	+	11.9718i	−0.279260	+	0.390063i
$943$	−26.7844	+	18.2613i	−0.872220	+	0.594670i
$944$	1.79032	+	7.84389i	0.0582699	+	0.255297i
$945$	13.1375	−	23.0719i	0.427361	−	0.750529i
$946$	0.390092	+	1.70910i	0.0126830	+	0.0555678i
$947$	−10.8149	−	27.5559i	−0.351437	−	0.895447i	−0.991849	−	0.127416i	$-0.959332\pi$
$947$	−10.8149	−	27.5559i	−0.351437	−	0.895447i	0.640412	−	0.768031i	$-0.278764\pi$
$948$	8.65025	+	3.62612i	0.280947	+	0.117771i
$949$	10.3824	−	3.20255i	0.337027	−	0.103959i
$950$	−28.5593	+	72.7678i	−0.926585	+	2.36090i
$951$	5.73978	+	12.6534i	0.186125	+	0.410315i
$952$	−0.237118	+	3.16412i	−0.00768503	+	0.102550i
$953$	2.37023	−	2.97217i	0.0767792	−	0.0962781i	−0.741958	−	0.670446i	$-0.766103\pi$
$953$	2.37023	−	2.97217i	0.0767792	−	0.0962781i	0.818738	+	0.574168i	$0.194674\pi$
$954$	29.2934	+	5.80047i	0.948409	+	0.187797i
$955$	−35.0103	+	16.8601i	−1.13291	+	0.545579i
$956$	2.23934	−	3.87865i	0.0724254	−	0.125445i
$957$	−0.163789	−	9.74904i	−0.00529456	−	0.315142i
$958$	1.30113	+	2.25363i	0.0420377	+	0.0728113i
$959$	−3.49202	−	2.38082i	−0.112763	−	0.0768807i
$960$	−5.56067	−	3.38287i	−0.179470	−	0.109182i
$961$	25.6589	+	65.3779i	0.827708	+	2.10897i
$962$	−0.780631	+	0.375932i	−0.0251685	+	0.0121205i
$963$	14.0498	+	14.2902i	0.452748	+	0.460497i
$964$	8.44306	+	10.5873i	0.271933	+	0.340993i
$965$	63.6947	+	59.1000i	2.05040	+	1.90250i
$966$	−8.71399	+	6.62794i	−0.280368	+	0.213250i
$967$	−24.5790	−	3.70468i	−0.790406	−	0.119135i	−0.258582	−	0.965989i	$-0.583255\pi$
$967$	−24.5790	−	3.70468i	−0.790406	−	0.119135i	−0.531824	+	0.846855i	$0.678493\pi$
$968$	7.26252	−	6.73863i	0.233426	−	0.216588i
$969$	5.94705	−	34.1246i	0.191047	−	1.09624i
$970$	−23.2783	−	7.18041i	−0.747422	−	0.230549i
$971$	−49.2630	−	23.7238i	−1.58092	−	0.761333i	−0.582260	−	0.813003i	$-0.697831\pi$
$971$	−49.2630	−	23.7238i	−1.58092	−	0.761333i	−0.998664	+	0.0516698i	$0.983546\pi$
$972$	−10.9950	−	11.0503i	−0.352664	−	0.354440i
$973$	−4.85515	−	21.2718i	−0.155649	−	0.681943i
$974$	−21.0755	+	36.5038i	−0.675301	+	1.16966i
$975$	32.7121	−	1.69789i	1.04763	−	0.0543761i
$976$	−4.42329	−	0.666704i	−0.141586	−	0.0213407i
$977$	34.6712	−	10.6946i	1.10923	−	0.342152i	0.314586	−	0.949229i	$-0.398134\pi$
$977$	34.6712	−	10.6946i	1.10923	−	0.342152i	0.794643	+	0.607077i	$0.207658\pi$
$978$	−6.99708	+	5.32204i	−0.223742	+	0.170180i
$979$	5.44152	−	0.820177i	0.173912	−	0.0262130i
$980$	−17.4407	−	8.39898i	−0.557122	−	0.268296i
$981$	−16.8148	+	1.75023i	−0.536855	+	0.0558806i
$982$	−17.2988	+	21.6920i	−0.552028	+	0.692221i
$983$	−25.5376	+	3.84917i	−0.814523	+	0.122770i	−0.543076	−	0.839684i	$-0.682740\pi$
$983$	−25.5376	+	3.84917i	−0.814523	+	0.122770i	−0.271447	+	0.962453i	$0.587502\pi$
$984$	8.41610	−	8.66304i	0.268295	−	0.276168i
$985$	−2.69692	−	4.67120i	−0.0859310	−	0.148837i
$986$	−12.1462	−	3.22411i	−0.386814	−	0.102677i
$987$	22.3353	−	8.17978i	0.710940	−	0.260365i
$988$	−1.32780	+	17.7182i	−0.0422428	+	0.563691i
$989$	4.86074	+	6.09518i	0.154563	+	0.193815i
$990$	−0.340719	−	11.7800i	−0.0108288	−	0.374393i
$991$	3.72823	−	1.79542i	0.118431	−	0.0570334i	−0.373730	−	0.927538i	$-0.621921\pi$
$991$	3.72823	−	1.79542i	0.118431	−	0.0570334i	0.492161	+	0.870504i	$0.336207\pi$
$992$	8.31316	−	5.66782i	0.263943	−	0.179953i
$993$	0.645867	−	28.1470i	0.0204960	−	0.893217i
$994$	−20.6844	+	6.38030i	−0.656070	+	0.202371i
$995$	−57.0730	+	17.6047i	−1.80934	+	0.558107i
$996$	0.0847280	+	0.0956241i	0.00268471	+	0.00302997i
$997$	51.8030	+	15.9791i	1.64062	+	0.506063i	0.971489	−	0.237085i	$-0.0761919\pi$
$997$	51.8030	+	15.9791i	1.64062	+	0.506063i	0.669127	+	0.743148i	$0.266668\pi$
$998$	1.64218			0.0519822
$999$	−2.07880	−	0.627652i	−0.0657704	−	0.0198580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	522.2.q.b.223.3	yes	180
9.4	even	3	inner	522.2.q.b.49.11	✓	180
29.16	even	7	inner	522.2.q.b.277.11	yes	180
261.103	even	21	inner	522.2.q.b.103.3	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
522.2.q.b.49.11	✓	180	9.4	even	3	inner
522.2.q.b.103.3	yes	180	261.103	even	21	inner
522.2.q.b.223.3	yes	180	1.1	even	1	trivial
522.2.q.b.277.11	yes	180	29.16	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0747301 - 0.997204i) q^{2} +(-1.51947 + 0.831387i) q^{3} +(-0.988831 - 0.149042i) q^{4} +(-3.10490 - 2.11689i) q^{5} +(0.715512 + 1.57735i) q^{6} +(1.34451 - 0.202652i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(1.61759 - 2.52654i) q^{9} +(-2.34300 + 2.93802i) q^{10} +(-0.998912 - 0.308124i) q^{11} +(1.62641 - 0.595636i) q^{12} +(-1.51983 + 1.41019i) q^{13} +(-0.101610 - 1.35589i) q^{14} +(6.47776 + 0.635174i) q^{15} +(0.955573 + 0.294755i) q^{16} +2.33360 q^{17} +(-2.39859 - 1.80188i) q^{18} +(-5.34325 + 6.70023i) q^{19} +(2.75472 + 2.55600i) q^{20} +(-1.87446 + 1.42573i) q^{21} +(-0.381911 + 0.973093i) q^{22} +(0.347405 + 4.63580i) q^{23} +(-0.472428 - 1.66638i) q^{24} +(3.33250 + 8.49108i) q^{25} +(1.29267 + 1.62096i) q^{26} +(-0.357351 + 5.18385i) q^{27} -1.35969 q^{28} +(0.988774 - 5.29361i) q^{29} +(1.11748 - 6.41218i) q^{30} +(8.31316 + 5.66782i) q^{31} +(0.365341 - 0.930874i) q^{32} +(1.77399 - 0.362298i) q^{33} +(0.174390 - 2.32708i) q^{34} +(-4.60356 - 2.21696i) q^{35} +(-1.97608 + 2.25723i) q^{36} +(-0.0929923 + 0.407426i) q^{37} +(6.28219 + 5.82902i) q^{38} +(1.13692 - 3.40632i) q^{39} +(2.75472 - 2.55600i) q^{40} +(3.48663 + 6.03902i) q^{41} +(1.28167 + 1.97576i) q^{42} +(1.38560 - 0.944686i) q^{43} +(0.941832 + 0.453562i) q^{44} +(-10.3709 + 4.42040i) q^{45} +4.64880 q^{46} +(-9.65124 - 2.97701i) q^{47} +(-1.69702 + 0.346579i) q^{48} +(-4.92238 + 1.51835i) q^{49} +(8.71638 - 2.68865i) q^{50} +(-3.54584 + 1.94013i) q^{51} +(1.71303 - 1.16793i) q^{52} +(-8.96829 + 4.31890i) q^{53} +(5.14265 + 0.743742i) q^{54} +(2.44926 + 3.07128i) q^{55} +(-0.101610 + 1.35589i) q^{56} +(2.54844 - 14.6231i) q^{57} +(-5.20492 - 1.38160i) q^{58} +(4.02281 + 6.96770i) q^{59} +(-6.31075 - 1.59354i) q^{60} +(-4.42329 + 0.666704i) q^{61} +(6.27321 - 7.86636i) q^{62} +(1.66286 - 3.72476i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(7.70414 - 1.16121i) q^{65} +(-0.228714 - 1.79610i) q^{66} +(8.03299 - 2.47785i) q^{67} +(-2.30754 - 0.347805i) q^{68} +(-4.38202 - 6.75514i) q^{69} +(-2.55478 + 4.42501i) q^{70} +(-3.54249 - 15.5207i) q^{71} +(2.10325 + 2.13924i) q^{72} +(-4.72154 - 2.27377i) q^{73} +(0.399337 + 0.123179i) q^{74} +(-12.1230 - 10.1314i) q^{75} +(6.28219 - 5.82902i) q^{76} +(-1.40549 - 0.211843i) q^{77} +(-3.31183 - 1.38829i) q^{78} +(3.96967 + 3.68332i) q^{79} +(-2.34300 - 2.93802i) q^{80} +(-3.76680 - 8.17381i) q^{81} +(6.28269 - 3.02558i) q^{82} +(0.0269485 + 0.0686638i) q^{83} +(2.06602 - 1.13043i) q^{84} +(-7.24561 - 4.93997i) q^{85} +(-0.838498 - 1.45232i) q^{86} +(2.89863 + 8.86555i) q^{87} +(0.522677 - 0.905304i) q^{88} +(-4.74290 + 2.28406i) q^{89} +(3.63303 + 10.6722i) q^{90} +(-1.75764 + 2.20401i) q^{91} +(0.347405 - 4.63580i) q^{92} +(-17.3438 - 1.70063i) q^{93} +(-3.68993 + 9.40178i) q^{94} +(30.7739 - 9.49249i) q^{95} +(0.218791 + 1.71818i) q^{96} +(2.36834 + 6.03443i) q^{97} +(1.14626 + 5.02208i) q^{98} +(-2.39432 + 2.02537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q + 15 q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} + 10 q^{6} + 5 q^{7} - 30 q^{8} - 6 q^{9} - 4 q^{10} - 4 q^{11} + 2 q^{12} - 2 q^{14} - q^{15} + 15 q^{16} + 12 q^{17} + 6 q^{18} - 6 q^{19} + 2 q^{20} - 13 q^{21}+ \cdots - 172 q^{99}+O(q^{100}) \) 180 * q + 15 * q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 + 10 * q^6 + 5 * q^7 - 30 * q^8 - 6 * q^9 - 4 * q^10 - 4 * q^11 + 2 * q^12 - 2 * q^14 - q^15 + 15 * q^16 + 12 * q^17 + 6 * q^18 - 6 * q^19 + 2 * q^20 - 13 * q^21 - 4 * q^22 + 30 * q^23 - 5 * q^24 + 15 * q^25 + 11 * q^27 + 4 * q^28 + 3 * q^29 - 60 * q^30 + 2 * q^31 + 15 * q^32 + 66 * q^33 - 6 * q^34 - 32 * q^35 + 14 * q^36 - 90 * q^37 + 3 * q^38 + 21 * q^39 + 2 * q^40 + 22 * q^41 + 2 * q^42 + 14 * q^43 - 20 * q^44 - 26 * q^45 + 24 * q^46 - 10 * q^47 - 4 * q^48 + 50 * q^49 + 15 * q^50 - 7 * q^51 + 56 * q^53 - 31 * q^54 - 56 * q^55 - 2 * q^56 + 70 * q^57 - 25 * q^58 - 40 * q^59 + 5 * q^60 - 6 * q^61 - 4 * q^62 + 114 * q^63 - 30 * q^64 + 47 * q^65 - 20 * q^66 - 6 * q^68 - 17 * q^69 - 12 * q^70 - 22 * q^71 + 22 * q^72 - 40 * q^73 + 45 * q^74 - 30 * q^75 + 3 * q^76 - 66 * q^77 - 37 * q^78 - 22 * q^79 - 4 * q^80 - 162 * q^81 + 40 * q^82 + 4 * q^83 - 10 * q^84 + 52 * q^85 - 56 * q^86 + 10 * q^87 - 4 * q^88 - 76 * q^89 - 65 * q^90 - 100 * q^91 + 30 * q^92 - 86 * q^93 + 46 * q^94 - 56 * q^95 + 2 * q^96 - 18 * q^97 - 100 * q^98 - 172 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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