LMFDB - Embedded newform 945.2.cl.a.194.124

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(164,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1, 9, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("945.164");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cl (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			194.124
Character	$\chi$	$=$	945.194
Dual form			945.2.cl.a.794.124

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.403021 + 2.28564i) q^{2} +(-1.37484 - 1.05348i) q^{3} +(-3.18236 + 1.15828i) q^{4} +(-1.21624 + 1.87637i) q^{5} +(1.85379 - 3.56696i) q^{6} +(-0.890305 - 2.49146i) q^{7} +(-1.60908 - 2.78700i) q^{8} +(0.780360 + 2.89673i) q^{9} +O(q^{10})$	\(q+(0.403021 + 2.28564i) q^{2} +(-1.37484 - 1.05348i) q^{3} +(-3.18236 + 1.15828i) q^{4} +(-1.21624 + 1.87637i) q^{5} +(1.85379 - 3.56696i) q^{6} +(-0.890305 - 2.49146i) q^{7} +(-1.60908 - 2.78700i) q^{8} +(0.780360 + 2.89673i) q^{9} +(-4.77888 - 2.02367i) q^{10} +(-4.66187 + 0.822013i) q^{11} +(5.59545 + 1.76010i) q^{12} +(2.46136 + 2.06532i) q^{13} +(5.33577 - 3.03903i) q^{14} +(3.64885 - 1.29842i) q^{15} +(0.533037 - 0.447271i) q^{16} -2.91569i q^{17} +(-6.30639 + 2.95107i) q^{18} -7.21834i q^{19} +(1.69713 - 7.38003i) q^{20} +(-1.40068 + 4.36327i) q^{21} +(-3.75766 - 10.3241i) q^{22} +(-0.947193 - 0.794789i) q^{23} +(-0.723831 + 5.52680i) q^{24} +(-2.04153 - 4.56422i) q^{25} +(-3.72862 + 6.45816i) q^{26} +(1.97878 - 4.80463i) q^{27} +(5.71908 + 6.89748i) q^{28} +(4.21789 + 5.02668i) q^{29} +(4.43830 + 7.81668i) q^{30} +(0.00194275 + 0.00533765i) q^{31} +(-3.69337 - 3.09910i) q^{32} +(7.27529 + 3.78105i) q^{33} +(6.66423 - 1.17508i) q^{34} +(5.75772 + 1.35966i) q^{35} +(-5.83862 - 8.31455i) q^{36} +(10.3008 - 5.94717i) q^{37} +(16.4986 - 2.90914i) q^{38} +(-1.20819 - 5.43248i) q^{39} +(7.18646 + 0.370432i) q^{40} +(3.67394 + 3.08281i) q^{41} +(-10.5374 - 1.44296i) q^{42} +(0.149570 - 0.410940i) q^{43} +(13.8836 - 8.01570i) q^{44} +(-6.38444 - 2.05887i) q^{45} +(1.43487 - 2.48526i) q^{46} +(1.17383 - 3.22508i) q^{47} +(-1.20403 + 0.0533816i) q^{48} +(-5.41472 + 4.43631i) q^{49} +(9.60941 - 6.50569i) q^{50} +(-3.07162 + 4.00860i) q^{51} +(-10.2252 - 3.72165i) q^{52} +(-2.37616 - 4.11562i) q^{53} +(11.7792 + 2.58642i) q^{54} +(4.12754 - 9.74715i) q^{55} +(-5.51112 + 6.49022i) q^{56} +(-7.60438 + 9.92405i) q^{57} +(-9.78931 + 11.6664i) q^{58} +(8.84429 + 7.42124i) q^{59} +(-10.1080 + 8.35845i) q^{60} +(2.21853 - 6.09537i) q^{61} +(-0.0114170 + 0.00659161i) q^{62} +(6.52232 - 4.52320i) q^{63} +(6.29077 - 10.8959i) q^{64} +(-6.86891 + 2.10649i) q^{65} +(-5.71004 + 18.1526i) q^{66} +(-11.6956 - 2.06225i) q^{67} +(3.37720 + 9.27877i) q^{68} +(0.464942 + 2.09056i) q^{69} +(-0.787223 + 13.7081i) q^{70} +(-7.50774 - 4.33460i) q^{71} +(6.81753 - 6.83592i) q^{72} +(0.125380 - 0.217164i) q^{73} +(17.7445 + 21.1471i) q^{74} +(-2.00154 + 8.42578i) q^{75} +(8.36088 + 22.9713i) q^{76} +(6.19849 + 10.8830i) q^{77} +(11.9298 - 4.95090i) q^{78} +(-1.92114 - 10.8953i) q^{79} +(0.190947 + 1.54416i) q^{80} +(-7.78208 + 4.52098i) q^{81} +(-5.56552 + 9.63976i) q^{82} +(-7.10287 - 8.46487i) q^{83} +(-0.596451 - 15.5079i) q^{84} +(5.47092 + 3.54617i) q^{85} +(0.999541 + 0.176246i) q^{86} +(-0.503403 - 11.3543i) q^{87} +(9.79224 + 11.6699i) q^{88} -8.45076 q^{89} +(2.13277 - 15.4223i) q^{90} +(2.95431 - 7.97114i) q^{91} +(3.93490 + 1.43219i) q^{92} +(0.00295215 - 0.00938505i) q^{93} +(7.84446 + 1.38319i) q^{94} +(13.5443 + 8.77922i) q^{95} +(1.81294 + 8.15165i) q^{96} +(4.55306 + 1.65718i) q^{97} +(-12.3221 - 10.5882i) q^{98} +(-6.01908 - 12.8627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 6 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) $ 840 * q - 6 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	$ 840 q - 6 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 12 q^{11} - 6 q^{14} - 18 q^{16} - 18 q^{20} - 30 q^{21} - 18 q^{24} - 3 q^{25} - 42 q^{29} - 21 q^{30} - 18 q^{31} + 36 q^{34} + 18 q^{35} - 42 q^{36} + 72 q^{39} + 36 q^{40} - 18 q^{44} - 9 q^{45} + 6 q^{46} + 6 q^{49} - 48 q^{50} + 66 q^{51} - 144 q^{54} + 12 q^{56} - 18 q^{59} - 87 q^{60} - 18 q^{61} - 348 q^{64} - 9 q^{65} - 18 q^{66} - 60 q^{70} - 36 q^{71} - 30 q^{74} - 54 q^{75} + 72 q^{76} + 12 q^{79} - 72 q^{80} + 72 q^{81} - 264 q^{84} + 3 q^{85} - 174 q^{86} - 36 q^{89} + 81 q^{90} - 6 q^{91} - 18 q^{94} + 69 q^{95} + 126 q^{96} - 60 q^{99}+O(q^{100}) $ 840 * q - 6 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 12 * q^11 - 6 * q^14 - 18 * q^16 - 18 * q^20 - 30 * q^21 - 18 * q^24 - 3 * q^25 - 42 * q^29 - 21 * q^30 - 18 * q^31 + 36 * q^34 + 18 * q^35 - 42 * q^36 + 72 * q^39 + 36 * q^40 - 18 * q^44 - 9 * q^45 + 6 * q^46 + 6 * q^49 - 48 * q^50 + 66 * q^51 - 144 * q^54 + 12 * q^56 - 18 * q^59 - 87 * q^60 - 18 * q^61 - 348 * q^64 - 9 * q^65 - 18 * q^66 - 60 * q^70 - 36 * q^71 - 30 * q^74 - 54 * q^75 + 72 * q^76 + 12 * q^79 - 72 * q^80 + 72 * q^81 - 264 * q^84 + 3 * q^85 - 174 * q^86 - 36 * q^89 + 81 * q^90 - 6 * q^91 - 18 * q^94 + 69 * q^95 + 126 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	0.403021	+	2.28564i	0.284979	+	1.61619i	0.705362	+	0.708848i	$0.250785\pi$
$2$	0.403021	+	2.28564i	0.284979	+	1.61619i	−0.420383	+	0.907347i	$0.638104\pi$
$3$	−1.37484	−	1.05348i	−0.793763	−	0.608227i
$3$	−1.37484	−	1.05348i	−0.793763	−	0.608227i
$4$	−3.18236	+	1.15828i	−1.59118	+	0.579142i
$5$	−1.21624	+	1.87637i	−0.543918	+	0.839138i
$5$	−1.21624	+	1.87637i	−0.543918	+	0.839138i
$6$	1.85379	−	3.56696i	0.756807	−	1.45621i
$7$	−0.890305	−	2.49146i	−0.336503	−	0.941682i
$7$	−0.890305	−	2.49146i	−0.336503	−	0.941682i
$8$	−1.60908	−	2.78700i	−0.568894	−	0.985353i
$9$	0.780360	+	2.89673i	0.260120	+	0.965576i
$10$	−4.77888	−	2.02367i	−1.51122	−	0.639940i
$11$	−4.66187	+	0.822013i	−1.40561	+	0.247846i	−0.824445	−	0.565942i	$-0.808512\pi$
$11$	−4.66187	+	0.822013i	−1.40561	+	0.247846i	−0.581161	+	0.813789i	$0.697401\pi$
$12$	5.59545	+	1.76010i	1.61527	+	0.508096i
$13$	2.46136	+	2.06532i	0.682658	+	0.572818i	0.916782	−	0.399389i	$-0.130778\pi$
$13$	2.46136	+	2.06532i	0.682658	+	0.572818i	−0.234124	+	0.972207i	$0.575222\pi$
$14$	5.33577	−	3.03903i	1.42605	−	0.812214i
$15$	3.64885	−	1.29842i	0.942129	−	0.335252i
$16$	0.533037	−	0.447271i	0.133259	−	0.111818i
$17$		−	2.91569i		−	0.707159i	−0.935404	−	0.353580i	$-0.884964\pi$
$17$		−	2.91569i		−	0.707159i	0.935404	−	0.353580i	$-0.115036\pi$
$18$	−6.30639	+	2.95107i	−1.48643	+	0.695573i
$19$		−	7.21834i		−	1.65600i	−0.560727	−	0.828001i	$-0.689478\pi$
$19$		−	7.21834i		−	1.65600i	0.560727	−	0.828001i	$-0.310522\pi$
$20$	1.69713	−	7.38003i	0.379491	−	1.65022i
$21$	−1.40068	+	4.36327i	−0.305652	+	0.952143i
$22$	−3.75766	−	10.3241i	−0.801135	−	2.20110i
$23$	−0.947193	−	0.794789i	−0.197503	−	0.165725i	0.538673	−	0.842515i	$-0.318926\pi$
$23$	−0.947193	−	0.794789i	−0.197503	−	0.165725i	−0.736176	+	0.676790i	$0.763370\pi$
$24$	−0.723831	+	5.52680i	−0.147751	+	1.12815i
$25$	−2.04153	−	4.56422i	−0.408307	−	0.912845i
$26$	−3.72862	+	6.45816i	−0.731242	+	1.26655i
$27$	1.97878	−	4.80463i	0.380816	−	0.924651i
$28$	5.71908	+	6.89748i	1.08080	+	1.30350i
$29$	4.21789	+	5.02668i	0.783242	+	0.933431i	0.999075	−	0.0429989i	$-0.0136912\pi$
$29$	4.21789	+	5.02668i	0.783242	+	0.933431i	−0.215833	+	0.976430i	$0.569247\pi$
$30$	4.43830	+	7.81668i	0.810318	+	1.42712i
$31$	0.00194275	+	0.00533765i	0.000348927	+	0.000958670i	0.939867	−	0.341541i	$-0.110949\pi$
$31$	0.00194275	+	0.00533765i	0.000348927	+	0.000958670i	−0.939518	+	0.342499i	$0.888727\pi$
$32$	−3.69337	−	3.09910i	−0.652901	−	0.547849i
$33$	7.27529	+	3.78105i	1.26646	+	0.658196i
$34$	6.66423	−	1.17508i	1.14291	−	0.201525i
$35$	5.75772	+	1.35966i	0.973232	+	0.229825i
$36$	−5.83862	−	8.31455i	−0.973103	−	1.38576i
$37$	10.3008	−	5.94717i	1.69344	−	0.977708i	0.741737	−	0.670691i	$-0.234002\pi$
$37$	10.3008	−	5.94717i	1.69344	−	0.977708i	0.951704	−	0.307017i	$-0.0993309\pi$
$38$	16.4986	−	2.90914i	2.67642	−	0.471925i
$39$	−1.20819	−	5.43248i	−0.193465	−	0.869893i
$40$	7.18646	+	0.370432i	1.13628	+	0.0585705i
$41$	3.67394	+	3.08281i	0.573774	+	0.481453i	0.882896	−	0.469569i	$-0.155591\pi$
$41$	3.67394	+	3.08281i	0.573774	+	0.481453i	−0.309122	+	0.951022i	$0.600035\pi$
$42$	−10.5374	−	1.44296i	−1.62595	−	0.222653i
$43$	0.149570	−	0.410940i	0.0228092	−	0.0626677i	−0.927765	−	0.373164i	$-0.878273\pi$
$43$	0.149570	−	0.410940i	0.0228092	−	0.0626677i	0.950575	+	0.310496i	$0.100495\pi$
$44$	13.8836	−	8.01570i	2.09303	−	1.20841i
$45$	−6.38444	−	2.05887i	−0.951736	−	0.306918i
$46$	1.43487	−	2.48526i	0.211560	−	0.366432i
$47$	1.17383	−	3.22508i	0.171221	−	0.470426i	−0.824168	−	0.566345i	$-0.808357\pi$
$47$	1.17383	−	3.22508i	0.171221	−	0.470426i	0.995389	+	0.0959192i	$0.0305790\pi$
$48$	−1.20403	+	0.0533816i	−0.173787	+	0.00770497i
$49$	−5.41472	+	4.43631i	−0.773531	+	0.633759i
$50$	9.60941	−	6.50569i	1.35898	−	0.920044i
$51$	−3.07162	+	4.00860i	−0.430113	+	0.561317i
$52$	−10.2252	−	3.72165i	−1.41797	−	0.516100i
$53$	−2.37616	−	4.11562i	−0.326390	−	0.565325i	0.655402	−	0.755280i	$-0.272499\pi$
$53$	−2.37616	−	4.11562i	−0.326390	−	0.565325i	−0.981793	+	0.189955i	$0.939166\pi$
$54$	11.7792	+	2.58642i	1.60294	+	0.351967i
$55$	4.12754	−	9.74715i	0.556557	−	1.31431i
$56$	−5.51112	+	6.49022i	−0.736455	+	0.867292i
$57$	−7.60438	+	9.92405i	−1.00722	+	1.31447i
$58$	−9.78931	+	11.6664i	−1.28540	+	1.53188i
$59$	8.84429	+	7.42124i	1.15143	+	0.966163i	0.999752	−	0.0222672i	$-0.00708847\pi$
$59$	8.84429	+	7.42124i	1.15143	+	0.966163i	0.151676	+	0.988430i	$0.451533\pi$
$60$	−10.1080	+	8.35845i	−1.30494	+	1.07907i
$61$	2.21853	−	6.09537i	0.284054	−	0.780433i	−0.712814	−	0.701353i	$-0.752580\pi$
$61$	2.21853	−	6.09537i	0.284054	−	0.780433i	0.996868	−	0.0790795i	$-0.0251981\pi$
$62$	−0.0114170	+	0.00659161i	−0.00144996	+	0.000837135i
$63$	6.52232	−	4.52320i	0.821735	−	0.569870i
$64$	6.29077	−	10.8959i	0.786346	−	1.36199i
$65$	−6.86891	+	2.10649i	−0.851983	+	0.261279i
$66$	−5.71004	+	18.1526i	−0.702857	+	2.23442i
$67$	−11.6956	−	2.06225i	−1.42885	−	0.251945i	−0.594906	−	0.803796i	$-0.702811\pi$
$67$	−11.6956	−	2.06225i	−1.42885	−	0.251945i	−0.833943	+	0.551851i	$0.813922\pi$
$68$	3.37720	+	9.27877i	0.409545	+	1.12522i
$69$	0.464942	+	2.09056i	0.0559725	+	0.251673i
$70$	−0.787223	+	13.7081i	−0.0940912	+	1.63843i
$71$	−7.50774	−	4.33460i	−0.891005	−	0.514422i	−0.0167341	−	0.999860i	$-0.505327\pi$
$71$	−7.50774	−	4.33460i	−0.891005	−	0.514422i	−0.874271	+	0.485438i	$0.838660\pi$
$72$	6.81753	−	6.83592i	0.803453	−	0.805621i
$73$	0.125380	−	0.217164i	0.0146746	−	0.0254171i	−0.858595	−	0.512655i	$-0.828662\pi$
$73$	0.125380	−	0.217164i	0.0146746	−	0.0254171i	0.873269	+	0.487238i	$0.161995\pi$
$74$	17.7445	+	21.1471i	2.06276	+	2.45830i
$75$	−2.00154	+	8.42578i	−0.231118	+	0.972926i
$76$	8.36088	+	22.9713i	0.959059	+	2.63499i
$77$	6.19849	+	10.8830i	0.706384	+	1.24023i
$78$	11.9298	−	4.95090i	1.35078	−	0.560578i
$79$	−1.92114	−	10.8953i	−0.216145	−	1.22582i	−0.878908	−	0.476991i	$-0.841727\pi$
$79$	−1.92114	−	10.8953i	−0.216145	−	1.22582i	0.662763	−	0.748830i	$-0.269384\pi$
$80$	0.190947	+	1.54416i	0.0213485	+	0.172643i
$81$	−7.78208	+	4.52098i	−0.864675	+	0.502331i
$82$	−5.56552	+	9.63976i	−0.614609	+	1.06453i
$83$	−7.10287	−	8.46487i	−0.779641	−	0.929140i	0.219276	−	0.975663i	$-0.429631\pi$
$83$	−7.10287	−	8.46487i	−0.779641	−	0.929140i	−0.998917	+	0.0465225i	$0.985186\pi$
$84$	−0.596451	−	15.5079i	−0.0650781	−	1.69205i
$85$	5.47092	+	3.54617i	0.593404	+	0.384636i
$86$	0.999541	+	0.176246i	0.107783	+	0.0190051i
$87$	−0.503403	−	11.3543i	−0.0539704	−	1.21731i
$88$	9.79224	+	11.6699i	1.04386	+	1.24402i
$89$	−8.45076			−0.895779			−0.447890	−	0.894089i	$-0.647824\pi$
$89$	−8.45076			−0.895779			−0.447890	+	0.894089i	$0.647824\pi$
$90$	2.13277	−	15.4223i	0.224814	−	1.62566i
$91$	2.95431	−	7.97114i	0.309696	−	0.835602i
$92$	3.93490	+	1.43219i	0.410241	+	0.149316i
$93$	0.00295215	−	0.00938505i	0.000306123	−	0.000973184i
$94$	7.84446	+	1.38319i	0.809095	+	0.142665i
$95$	13.5443	+	8.77922i	1.38961	+	0.900729i
$96$	1.81294	+	8.15165i	0.185032	+	0.831974i
$97$	4.55306	+	1.65718i	0.462293	+	0.168261i	0.562658	−	0.826690i	$-0.309779\pi$
$97$	4.55306	+	1.65718i	0.462293	+	0.168261i	−0.100365	+	0.994951i	$0.532001\pi$
$98$	−12.3221	−	10.5882i	−1.24472	−	1.06957i
$99$	−6.01908	−	12.8627i	−0.604940	−	1.29275i
$100$	11.7836	+	12.1603i	1.17836	+	1.21603i
$101$	8.47234	−	7.10914i	0.843029	−	0.707386i	−0.115214	−	0.993341i	$-0.536755\pi$
$101$	8.47234	−	7.10914i	0.843029	−	0.707386i	0.958243	+	0.285955i	$0.0923108\pi$
$102$	−10.4002	−	5.40509i	−1.02977	−	0.535183i
$103$	0.300913	−	1.70656i	0.0296498	−	0.168152i	−0.966387	−	0.257090i	$-0.917236\pi$
$103$	0.300913	−	1.70656i	0.0296498	−	0.168152i	0.996037	+	0.0889380i	$0.0283473\pi$
$104$	1.79555	−	10.1831i	0.176068	−	0.998532i
$105$	−6.48355	−	7.93496i	−0.632730	−	0.774372i
$106$	8.44921	−	7.08973i	0.820660	−	0.688616i
$107$	−0.100836	+	0.174653i	−0.00974817	+	0.0168843i	−0.870858	−	0.491534i	$-0.836436\pi$
$107$	−0.100836	+	0.174653i	−0.00974817	+	0.0168843i	0.861110	+	0.508418i	$0.169770\pi$
$108$	−0.732059	+	17.5820i	−0.0704424	+	1.69183i
$109$	−0.705525	−	1.22201i	−0.0675771	−	0.117047i	0.830257	−	0.557380i	$-0.188194\pi$
$109$	−0.705525	−	1.22201i	−0.0675771	−	0.117047i	−0.897834	+	0.440334i	$0.854860\pi$
$110$	23.9420	+	5.50577i	2.28278	+	0.524955i
$111$	−20.4272	−	2.67529i	−1.93886	−	0.253927i
$112$	−1.58892	−	0.929831i	−0.150139	−	0.0878608i
$113$	−6.50995	+	2.36943i	−0.612405	+	0.222897i	−0.629555	−	0.776956i	$-0.716763\pi$
$113$	−6.50995	+	2.36943i	−0.612405	+	0.222897i	0.0171504	+	0.999853i	$0.494541\pi$
$114$	−25.7476	−	13.3813i	−2.41148	−	1.25327i
$115$	2.64333	−	0.810633i	0.246492	−	0.0755919i
$116$	−19.2451	−	11.1112i	−1.78687	−	1.03165i
$117$	−4.06194	+	8.74158i	−0.375527	+	0.808160i
$118$	−13.3979	+	23.2058i	−1.23337	+	2.13627i
$119$	−7.26432	+	2.59585i	−0.665919	+	0.237961i
$120$	−9.48998	−	8.08008i	−0.866313	−	0.737607i
$121$	10.7207	−	3.90201i	0.974607	−	0.354728i
$122$	14.8260	+	2.61422i	1.34228	+	0.236680i
$123$	−1.80341	−	8.10879i	−0.162608	−	0.731145i
$124$	−0.0123650	−	0.0147361i	−0.00111041	−	0.00132334i
$125$	11.0472	+	1.72051i	0.988088	+	0.153887i
$126$	12.9671	+	13.0848i	1.15520	+	1.16568i
$127$	−16.9236	+	9.77086i	−1.50173	+	0.867024i	−0.501731	+	0.865024i	$0.667303\pi$
$127$	−16.9236	+	9.77086i	−1.50173	+	0.867024i	−0.999998	+	0.00199967i	$0.999363\pi$
$128$	18.3784	+	6.68918i	1.62443	+	0.591246i
$129$	−0.638551	+	0.407407i	−0.0562213	+	0.0358702i
$130$	−7.58301	−	14.8509i	−0.665074	−	1.30251i
$131$	−1.20027	−	1.00715i	−0.104868	−	0.0879947i	0.588846	−	0.808245i	$-0.299582\pi$
$131$	−1.20027	−	1.00715i	−0.104868	−	0.0879947i	−0.693714	+	0.720250i	$0.744027\pi$
$132$	−27.5321	−	3.60581i	−2.39636	−	0.313845i
$133$	−17.9842	+	6.42652i	−1.55943	+	0.557250i
$134$		−	27.5632i		−	2.38110i
$135$	6.60860	+	9.55649i	0.568777	+	0.822491i
$136$	−8.12603	+	4.69157i	−0.696802	+	0.402299i
$137$	2.99227	+	1.08910i	0.255647	+	0.0930478i	0.466664	−	0.884434i	$-0.345456\pi$
$137$	2.99227	+	1.08910i	0.255647	+	0.0930478i	−0.211018	+	0.977482i	$0.567678\pi$
$138$	−4.59088	+	1.90523i	−0.390802	+	0.162184i
$139$	5.94607	+	1.04845i	0.504339	+	0.0889285i	0.420028	−	0.907511i	$-0.362020\pi$
$139$	5.94607	+	1.04845i	0.504339	+	0.0889285i	0.0843104	+	0.996440i	$0.473131\pi$
$140$	−19.8980	+	2.34214i	−1.68169	+	0.197947i
$141$	−5.01139	+	3.19735i	−0.422035	+	0.269266i
$142$	6.88157	−	18.9070i	0.577489	−	1.58664i
$143$	−13.1722	−	7.60500i	−1.10152	−	0.635962i
$144$	1.71158	+	1.19503i	0.142632	+	0.0995859i
$145$	−14.5619	+	1.80068i	−1.20930	+	0.149538i
$146$	0.546890	+	0.199052i	0.0452609	+	0.0164736i
$147$	12.1179	−	0.394915i	0.999469	−	0.0325720i
$148$	−25.8923	+	30.8573i	−2.12833	+	2.53645i
$149$	−6.34691	−	17.4380i	−0.519959	−	1.42858i	−0.870565	−	0.492053i	$-0.836247\pi$
$149$	−6.34691	−	17.4380i	−0.519959	−	1.42858i	0.350606	−	0.936523i	$-0.385976\pi$
$150$	−20.0650	−	1.17905i	−1.63830	−	0.0962686i
$151$	1.62123	+	9.19443i	0.131933	+	0.748232i	0.976946	+	0.213486i	$0.0684817\pi$
$151$	1.62123	+	9.19443i	0.131933	+	0.748232i	−0.845013	+	0.534746i	$0.820407\pi$
$152$	−20.1175	+	11.6149i	−1.63175	+	0.942089i
$153$	8.44597	−	2.27529i	0.682816	−	0.183946i
$154$	−22.3765	+	18.5536i	−1.80315	+	1.49509i
$155$	−0.0123782	−	0.00284654i	−0.000994245	−	0.000228639i
$156$	10.1372	+	15.8887i	0.811629	+	1.27211i
$157$	−14.8619	−	12.4707i	−1.18611	−	0.995267i	−0.999919	−	0.0127535i	$-0.995940\pi$
$157$	−14.8619	−	12.4707i	−1.18611	−	0.995267i	−0.186194	−	0.982513i	$-0.559615\pi$
$158$	24.1286	−	8.78209i	1.91957	−	0.698666i
$159$	−1.06890	+	8.16155i	−0.0847691	+	0.647253i
$160$	10.3071	−	3.16088i	0.814846	−	0.249889i
$161$	−1.13689	+	3.06750i	−0.0895997	+	0.241752i
$162$	−13.4697	−	15.9650i	−1.05828	−	1.25433i
$163$	−13.8267	−	7.98283i	−1.08299	−	0.625264i	−0.151287	−	0.988490i	$-0.548342\pi$
$163$	−13.8267	−	7.98283i	−1.08299	−	0.625264i	−0.931701	+	0.363226i	$0.881675\pi$
$164$	−15.2626	−	5.55512i	−1.19181	−	0.433782i
$165$	−15.9431	+	9.05248i	−1.24117	+	0.704735i
$166$	16.4851	−	19.6462i	1.27949	−	1.52484i
$167$	−3.35249	−	9.21090i	−0.259424	−	0.712761i	−0.999203	−	0.0399116i	$-0.987292\pi$
$167$	−3.35249	−	9.21090i	−0.259424	−	0.712761i	0.739779	−	0.672850i	$-0.234930\pi$
$168$	14.4142	−	3.11714i	1.11208	−	0.240493i
$169$	−0.464709	−	2.63549i	−0.0357468	−	0.202730i
$170$	−5.90040	+	13.9338i	−0.452540	+	1.06867i
$171$	20.9096	−	5.63290i	1.59900	−	0.430759i
$172$			1.48100i			0.112925i
$173$	2.18826	+	2.60787i	0.166370	+	0.198272i	0.842788	−	0.538246i	$-0.180913\pi$
$173$	2.18826	+	2.60787i	0.166370	+	0.198272i	−0.676417	+	0.736518i	$0.736468\pi$
$174$	25.7491	−	5.72663i	1.95203	−	0.434135i
$175$	−9.55398	+	9.14994i	−0.722213	+	0.691671i
$176$	−2.11728	+	2.52328i	−0.159596	+	0.190199i
$177$	−4.34134	−	19.5203i	−0.326315	−	1.46723i
$178$	−3.40583	−	19.3154i	−0.255278	−	1.44775i
$179$		−	9.84462i		−	0.735822i	−0.929861	−	0.367911i	$-0.880073\pi$
$179$		−	9.84462i		−	0.735822i	0.929861	−	0.367911i	$-0.119927\pi$
$180$	22.7023	−	0.842943i	1.69213	−	0.0628293i
$181$	10.1144	−	5.83954i	0.751796	−	0.434049i	−0.0745467	−	0.997218i	$-0.523751\pi$
$181$	10.1144	−	5.83954i	0.751796	−	0.434049i	0.826342	+	0.563168i	$0.190418\pi$
$182$	19.4098	+	3.53997i	1.43875	+	0.262400i
$183$	−9.47148	+	6.04297i	−0.700152	+	0.446709i
$184$	−0.690973	+	3.91870i	−0.0509392	+	0.288891i
$185$	−1.36912	+	26.5613i	−0.100660	+	1.95282i
$186$	0.0226407	+	0.00296519i	0.00166009	+	0.000217418i
$187$	2.39674	+	13.5926i	0.175267	+	0.993987i
$188$			11.6230i			0.847694i
$189$	−13.7322	−	0.652458i	−0.998873	−	0.0474594i
$190$	−14.6075	+	34.4956i	−1.05974	+	2.50258i
$191$	−1.13714	+	0.200508i	−0.0822805	+	0.0145083i	−0.214637	−	0.976694i	$-0.568857\pi$
$191$	−1.13714	+	0.200508i	−0.0822805	+	0.0145083i	0.132356	+	0.991202i	$0.457746\pi$
$192$	−20.1274	+	8.35295i	−1.45257	+	0.602822i
$193$	5.37618	+	14.7709i	0.386986	+	1.06324i	0.968351	+	0.249592i	$0.0802966\pi$
$193$	5.37618	+	14.7709i	0.386986	+	1.06324i	−0.581365	+	0.813643i	$0.697481\pi$
$194$	−1.95274	+	11.0746i	−0.140199	+	0.795107i
$195$	11.6628	+	4.34017i	0.835190	+	0.310806i
$196$	12.0931	−	20.3897i	0.863790	−	1.45641i
$197$	−11.3786	−	19.7083i	−0.810690	−	1.40416i	−0.912382	−	0.409340i	$-0.865759\pi$
$197$	−11.3786	−	19.7083i	−0.810690	−	1.40416i	0.101692	−	0.994816i	$-0.467574\pi$
$198$	26.9737	−	18.9414i	1.91694	−	1.34611i
$199$			8.90234i			0.631070i	0.948914	+	0.315535i	$0.102184\pi$
$199$			8.90234i			0.631070i	−0.948914	+	0.315535i	$0.897816\pi$
$200$	−9.43551	+	13.0339i	−0.667192	+	0.921638i
$201$	13.9071	+	15.1564i	0.980928	+	1.06905i
$202$	19.6635	+	16.4996i	1.38352	+	1.16091i
$203$	8.76856	−	14.9840i	0.615432	−	1.05167i
$204$	5.13190	−	16.3146i	0.359305	−	1.14225i
$205$	−10.2529	+	3.14426i	−0.716092	+	0.219605i
$206$	4.02186			0.280216
$207$	1.56314	−	3.36398i	0.108646	−	0.233813i
$208$	2.23575			0.155022
$209$	5.93357	+	33.6509i	0.410434	+	2.32768i
$210$	15.5235	−	18.0170i	1.07122	−	1.24329i
$211$	−12.9032	+	4.69640i	−0.888296	+	0.323313i	−0.745553	−	0.666446i	$-0.767814\pi$
$211$	−12.9032	+	4.69640i	−0.888296	+	0.323313i	−0.142743	+	0.989760i	$0.545592\pi$
$212$	12.3288	+	10.3451i	0.846748	+	0.710506i
$213$	5.75552	+	13.8686i	0.394362	+	0.950263i
$214$	−0.439833	−	0.160086i	−0.0300664	−	0.0109433i
$215$	0.589163	+	0.780449i	0.0401806	+	0.0532261i
$216$	−16.5745	+	2.21615i	−1.12775	+	0.150790i
$217$	0.0115689	−	0.00959240i	0.000785347	−	0.000651175i
$218$	2.50873	−	2.10507i	0.169913	−	0.142574i
$219$	−0.401154	+	0.166480i	−0.0271075	+	0.0112497i
$220$	−1.84533	+	35.7998i	−0.124412	+	2.41362i
$221$	6.02185	−	7.17656i	0.405073	−	0.482748i
$222$	−2.11780	−	47.7674i	−0.142138	−	3.20594i
$223$	−1.35036	−	7.65828i	−0.0904269	−	0.512836i	−0.996053	−	0.0887594i	$-0.971710\pi$
$223$	−1.35036	−	7.65828i	−0.0904269	−	0.512836i	0.905626	−	0.424077i	$-0.139401\pi$
$224$	−4.43306	+	11.9610i	−0.296196	+	0.799178i
$225$	11.6282	−	9.47551i	0.775213	−	0.631700i
$226$	−8.03931	−	13.9245i	−0.534767	−	0.926244i
$227$	27.3242	−	4.81800i	1.81357	−	0.319782i	0.839047	−	0.544058i	$-0.183113\pi$
$227$	27.3242	−	4.81800i	1.81357	−	0.319782i	0.974526	+	0.224276i	$0.0720018\pi$
$228$	12.7050	−	40.3899i	0.841408	−	2.67489i
$229$	4.90147	+	13.4667i	0.323898	+	0.889904i	0.989621	+	0.143704i	$0.0459013\pi$
$229$	4.90147	+	13.4667i	0.323898	+	0.889904i	−0.665722	+	0.746200i	$0.731876\pi$
$230$	2.91813	+	5.71501i	0.192416	+	0.376837i
$231$	2.94310	−	21.4923i	0.193642	−	1.41409i
$232$	7.22247	−	19.8436i	0.474178	−	1.30279i
$233$	−3.76717	−	6.52492i	−0.246795	−	0.427462i	0.715840	−	0.698265i	$-0.246044\pi$
$233$	−3.76717	−	6.52492i	−0.246795	−	0.427462i	−0.962635	+	0.270803i	$0.912711\pi$
$234$	−21.6172	−	5.76111i	−1.41316	−	0.376616i
$235$	4.62379	+	6.12501i	0.301623	+	0.399552i
$236$	−36.7416	−	13.3728i	−2.39167	−	0.870498i
$237$	−8.83676	+	17.0032i	−0.574009	+	1.10448i
$238$	−8.86087	−	15.5575i	−0.574365	−	1.00844i
$239$	15.3398	+	2.70483i	0.992252	+	0.174961i	0.646129	−	0.763228i	$-0.276387\pi$
$239$	15.3398	+	2.70483i	0.992252	+	0.174961i	0.346123	+	0.938189i	$0.387498\pi$
$240$	1.36422	−	2.32413i	0.0880602	−	0.150022i
$241$	−0.273758	+	0.752145i	−0.0176343	+	0.0484499i	−0.948197	−	0.317682i	$-0.897096\pi$
$241$	−0.273758	+	0.752145i	−0.0176343	+	0.0484499i	0.930563	+	0.366131i	$0.119318\pi$
$242$	13.2393	+	22.9311i	0.851051	+	1.47406i
$243$	15.4619	+	1.98265i	0.991879	+	0.127187i
$244$			21.9673i			1.40632i
$245$	−1.73858	−	15.5556i	−0.111074	−	0.993812i
$246$	17.8070	−	7.38995i	1.13533	−	0.471166i
$247$	14.9082	−	17.7669i	0.948587	−	1.13048i
$248$	0.0117500	−	0.0140031i	0.000746126	−	0.000889198i
$249$	0.847724	+	19.1206i	0.0537223	+	1.21172i
$250$	0.519769	+	25.9433i	0.0328731	+	1.64080i
$251$	6.01802	+	10.4235i	0.379854	+	0.657927i	0.991041	−	0.133560i	$-0.0426408\pi$
$251$	6.01802	+	10.4235i	0.379854	+	0.657927i	−0.611187	+	0.791487i	$0.709308\pi$
$252$	−15.5172	+	21.9491i	−0.977491	+	1.38267i
$253$	5.06901	+	2.92660i	0.318686	+	0.183994i
$254$	−29.1533	−	34.7435i	−1.82924	−	2.18000i
$255$	−3.78580	−	10.6389i	−0.237076	−	0.666235i
$256$	−3.51270	+	19.9215i	−0.219543	+	1.24509i
$257$	−8.44111	−	23.1918i	−0.526542	−	1.44666i	−0.863116	−	0.505006i	$-0.831490\pi$
$257$	−8.44111	−	23.1918i	−0.526542	−	1.44666i	0.336574	−	0.941657i	$-0.390732\pi$
$258$	−1.18854	−	1.29531i	−0.0739950	−	0.0806423i
$259$	−23.9880	−	20.3692i	−1.49054	−	1.26568i
$260$	19.4194	−	14.6598i	1.20434	−	0.909160i
$261$	−11.2695	+	16.1407i	−0.697562	+	0.999084i
$262$	1.81824	−	3.14929i	0.112331	−	0.194564i
$263$	−20.8266	+	17.4756i	−1.28422	+	1.07759i	−0.291575	+	0.956548i	$0.594179\pi$
$263$	−20.8266	+	17.4756i	−1.28422	+	1.07759i	−0.992647	+	0.121043i	$0.961376\pi$
$264$	−1.16870	−	26.3602i	−0.0719285	−	1.62236i
$265$	10.6124	+	0.547025i	0.651915	+	0.0336035i
$266$	−21.9367	−	38.5154i	−1.34503	−	2.36153i
$267$	11.6184	+	8.90271i	0.711037	+	0.544837i
$268$	39.6083	−	6.98402i	2.41946	−	0.426617i
$269$	−13.5428	−	23.4568i	−0.825718	−	1.43019i	−0.901369	−	0.433052i	$-0.857437\pi$
$269$	−13.5428	−	23.4568i	−0.825718	−	1.43019i	0.0756510	−	0.997134i	$-0.475897\pi$
$270$	−19.1793	+	18.9564i	−1.16722	+	1.15365i
$271$	−12.9669	−	7.48642i	−0.787681	−	0.454768i	0.0514646	−	0.998675i	$-0.483611\pi$
$271$	−12.9669	−	7.48642i	−0.787681	−	0.454768i	−0.839145	+	0.543907i	$0.816944\pi$
$272$	−1.30410	−	1.55417i	−0.0790729	−	0.0942355i
$273$	−12.4591	+	7.84672i	−0.754061	+	0.474905i
$274$	−1.28334	+	7.27819i	−0.0775295	+	0.439691i
$275$	13.2692	+	19.5996i	0.800163	+	1.18190i
$276$	−3.90107	−	6.11436i	−0.234817	−	0.368041i
$277$	9.77890	+	11.6540i	0.587557	+	0.700223i	0.975134	−	0.221614i	$-0.0711325\pi$
$277$	9.77890	+	11.6540i	0.587557	+	0.700223i	−0.387577	+	0.921837i	$0.626688\pi$
$278$			14.0131i			0.840452i
$279$	−0.0139457	+	0.00979289i	−0.000834906	+	0.000586285i
$280$	−5.47522	−	18.2346i	−0.327207	−	1.08972i
$281$	−1.53763	+	4.22459i	−0.0917270	+	0.252018i	−0.977069	−	0.212922i	$-0.931702\pi$
$281$	−1.53763	+	4.22459i	−0.0917270	+	0.252018i	0.885342	+	0.464940i	$0.153924\pi$
$282$	−9.32770	−	10.1656i	−0.555457	−	0.605356i
$283$	−0.307687	+	1.74498i	−0.0182901	+	0.103728i	−0.992586	−	0.121543i	$-0.961216\pi$
$283$	−0.307687	+	1.74498i	−0.0182901	+	0.103728i	0.974296	+	0.225271i	$0.0723269\pi$
$284$	28.9130	+	5.09814i	1.71567	+	0.302519i
$285$	−9.37247	−	26.3386i	−0.555177	−	1.56017i
$286$	12.0736	−	33.1720i	0.713929	−	1.96150i
$287$	4.40975	−	11.8981i	0.260299	−	0.702323i
$288$	6.09510	−	13.1171i	0.359157	−	0.772932i
$289$	8.49874			0.499926
$290$	−9.98445	−	32.5575i	−0.586307	−	1.91184i
$291$	−4.51392	−	7.07491i	−0.264611	−	0.414739i
$292$	−0.147465	+	0.836318i	−0.00862976	+	0.0489418i
$293$	−16.8867	−	2.97758i	−0.986531	−	0.173952i	−0.342970	−	0.939346i	$-0.611433\pi$
$293$	−16.8867	−	2.97758i	−0.986531	−	0.173952i	−0.643562	+	0.765394i	$0.722544\pi$
$294$	5.78641	+	27.5381i	0.337470	+	1.60605i
$295$	−24.6817	+	7.56917i	−1.43703	+	0.440694i
$296$	−33.1495	−	19.1389i	−1.92678	−	1.11242i
$297$	−5.27533	+	24.0251i	−0.306106	+	1.39408i
$298$	37.2991	−	21.5347i	2.16068	−	1.24747i
$299$	−0.689883	−	3.91252i	−0.0398970	−	0.226267i
$300$	−3.38983	−	29.1322i	−0.195712	−	1.68195i
$301$	−1.15700	−	0.00678528i	−0.0666884	−	0.000391097i
$302$	−20.3618	+	7.41109i	−1.17169	+	0.426460i
$303$	−19.1374	+	0.848472i	−1.09942	+	0.0487435i
$304$	−3.22856	−	3.84764i	−0.185170	−	0.220677i
$305$	8.73891	+	11.5762i	0.500389	+	0.662852i
$306$	8.60440	+	18.3875i	0.491881	+	1.05114i
$307$	2.39703	−	4.15178i	0.136806	−	0.236955i	−0.789480	−	0.613776i	$-0.789650\pi$
$307$	2.39703	−	4.15178i	0.136806	−	0.236955i	0.926286	+	0.376822i	$0.122983\pi$
$308$	−32.3314	−	27.4540i	−1.84225	−	1.56434i
$309$	−2.21153	+	2.02924i	−0.125810	+	0.115439i
$310$	0.00151748	−	0.0294395i	8.61872e−5	−	0.00167205i
$311$	−4.75410	+	26.9618i	−0.269580	+	1.52887i	0.486087	+	0.873910i	$0.338424\pi$
$311$	−4.75410	+	26.9618i	−0.269580	+	1.52887i	−0.755668	+	0.654955i	$0.772687\pi$
$312$	−13.1962	+	12.1085i	−0.747091	+	0.685509i
$313$	−9.92408	+	8.32730i	−0.560942	+	0.470687i	−0.878626	−	0.477510i	$-0.841539\pi$
$313$	−9.92408	+	8.32730i	−0.560942	+	0.470687i	0.317684	+	0.948197i	$0.397095\pi$
$314$	22.5138	−	38.9950i	1.27053	−	2.20062i
$315$	0.554520	+	17.7396i	0.0312436	+	0.999512i
$316$	18.7336	+	32.4476i	1.05385	+	1.82532i
$317$	11.9655	+	4.35509i	0.672050	+	0.244606i	0.655430	−	0.755256i	$-0.272487\pi$
$317$	11.9655	+	4.35509i	0.672050	+	0.244606i	0.0166198	+	0.999862i	$0.494710\pi$
$318$	−19.0852	+	0.846156i	−1.07024	+	0.0474501i
$319$	−23.7952	−	19.9666i	−1.33228	−	1.11791i
$320$	12.7937	+	25.0559i	0.715192	+	1.40067i
$321$	0.322626	−	0.133891i	0.0180072	−	0.00747306i
$322$	−7.46939	−	1.36227i	−0.416253	−	0.0759163i
$323$	−21.0465			−1.17106
$324$	19.5288	−	23.4012i	1.08493	−	1.30007i
$325$	4.40166	−	15.4506i	0.244160	−	0.857046i
$326$	12.6735	−	34.8201i	0.701919	−	1.92851i
$327$	−0.317376	+	2.42332i	−0.0175509	+	0.134010i
$328$	2.68013	−	15.1998i	0.147985	−	0.839266i
$329$	−9.08022	−	0.0532513i	−0.500609	−	0.00293584i
$330$	−27.1162	−	32.7920i	−1.49270	−	1.80514i
$331$	22.1597	+	8.06547i	1.21801	+	0.443318i	0.869474	−	0.493979i	$-0.164458\pi$
$331$	22.1597	+	8.06547i	1.21801	+	0.443318i	0.348532	+	0.937297i	$0.386680\pi$
$332$	32.4086	+	18.7111i	1.77865	+	1.02691i
$333$	25.2657	+	25.1977i	1.38455	+	1.38082i
$334$	19.7017	−	11.3748i	1.07803	−	0.622401i
$335$	18.0942	−	19.4371i	0.988592	−	1.06196i
$336$	1.20495	+	2.95226i	0.0657355	+	0.161059i
$337$	14.7048	−	17.5244i	0.801019	−	0.954617i	−0.198657	−	0.980069i	$-0.563658\pi$
$337$	14.7048	−	17.5244i	0.801019	−	0.954617i	0.999676	+	0.0254520i	$0.00810250\pi$
$338$	5.83651	−	2.12432i	0.317464	−	0.115548i
$339$	11.4463	+	3.60052i	0.621676	+	0.195554i
$340$	−21.5179	−	4.94832i	−1.16697	−	0.268360i
$341$	−0.0134444	−	0.0232864i	−0.000728057	−	0.00126103i
$342$	21.3018	+	45.5217i	1.15187	+	2.46153i
$343$	15.8736	+	9.54086i	0.857095	+	0.515158i
$344$	−1.38596	+	0.244382i	−0.0747258	+	0.0131762i
$345$	−4.48814	−	1.67021i	−0.241633	−	0.0899209i
$346$	−5.07874	+	6.05261i	−0.273035	+	0.325390i
$347$	−17.5353	+	6.38231i	−0.941342	+	0.342621i	−0.766696	−	0.642011i	$-0.778100\pi$
$347$	−17.5353	+	6.38231i	−0.941342	+	0.342621i	−0.174646	+	0.984631i	$0.555878\pi$
$348$	14.7535	+	35.5505i	0.790873	+	1.90570i
$349$	−13.8348	−	16.4877i	−0.740559	−	0.882564i	0.255894	−	0.966705i	$-0.417630\pi$
$349$	−13.8348	−	16.4877i	−0.740559	−	0.882564i	−0.996454	+	0.0841404i	$0.973186\pi$
$350$	−24.7640	−	18.1494i	−1.32369	−	0.970125i
$351$	14.7936	−	7.73909i	0.789624	−	0.413082i
$352$	19.7655	+	11.4116i	1.05350	+	0.608241i
$353$	−0.738426	+	2.02881i	−0.0393024	+	0.107983i	−0.957791	−	0.287464i	$-0.907188\pi$
$353$	−0.738426	+	2.02881i	−0.0393024	+	0.107983i	0.918489	+	0.395446i	$0.129410\pi$
$354$	42.8668	−	17.7898i	2.27834	−	0.945519i
$355$	17.2645	−	8.81541i	0.916305	−	0.467873i
$356$	26.8933	−	9.78838i	1.42534	−	0.518783i
$357$	12.7219	+	4.08394i	0.673317	+	0.216145i
$358$	22.5013	−	3.96759i	1.18923	−	0.209693i
$359$			16.7984i			0.886587i	0.896377	+	0.443293i	$0.146190\pi$
$359$			16.7984i			0.886587i	−0.896377	+	0.443293i	$0.853810\pi$
$360$	4.53498	+	21.1063i	0.239015	+	1.11240i
$361$	−33.1045			−1.74234
$362$	17.4234	+	20.7644i	0.915754	+	1.09135i
$363$	−18.8499	−	5.92939i	−0.989362	−	0.311212i
$364$	−0.168834	+	28.7889i	−0.00884930	+	1.50895i
$365$	0.254988	+	0.499381i	0.0133467	+	0.0261388i
$366$	−17.6293	−	19.2130i	−0.921497	−	1.00428i
$367$	−1.32892	−	7.53668i	−0.0693691	−	0.393412i	−0.999647	−	0.0265569i	$-0.991546\pi$
$367$	−1.32892	−	7.53668i	−0.0693691	−	0.393412i	0.930278	−	0.366855i	$-0.119565\pi$
$368$	−0.860375			−0.0448501
$369$	−6.06305	+	13.0481i	−0.315630	+	0.679258i
$370$	−61.2614	+	7.57542i	−3.18483	+	0.393827i
$371$	−8.13840	+	9.58425i	−0.422525	+	0.497590i
$372$	0.00147576	+	0.0332860i	7.65146e−5	+	0.00172580i
$373$	−11.1910	−	1.97328i	−0.579450	−	0.102173i	−0.123761	−	0.992312i	$-0.539496\pi$
$373$	−11.1910	−	1.97328i	−0.579450	−	0.102173i	−0.455688	+	0.890139i	$0.650607\pi$
$374$	−30.1018	+	10.9562i	−1.55653	+	0.566530i
$375$	−13.3755	−	14.0034i	−0.690710	−	0.723132i
$376$	−10.8771	+	1.91792i	−0.560943	+	0.0989094i
$377$			21.0838i			1.08587i
$378$	−4.04309	−	31.6500i	−0.207954	−	1.62790i
$379$	22.7732			1.16978			0.584890	−	0.811113i	$-0.301138\pi$
$379$	22.7732			1.16978			0.584890	+	0.811113i	$0.301138\pi$
$380$	−53.2716	−	12.2505i	−2.73277	−	0.628437i
$381$	33.5606	+	4.39535i	1.71936	+	0.225181i
$382$	−0.916581	−	2.51828i	−0.0468964	−	0.128847i
$383$	13.9011	+	2.45115i	0.710315	+	0.125248i	0.517120	−	0.855913i	$-0.327004\pi$
$383$	13.9011	+	2.45115i	0.710315	+	0.125248i	0.193195	+	0.981160i	$0.438115\pi$
$384$	−18.2204	−	28.5578i	−0.929804	−	1.45733i
$385$	−27.9594	−	1.60564i	−1.42494	−	0.0818312i
$386$	−31.5944	+	18.2410i	−1.60811	+	0.928444i
$387$	1.30710	+	0.112582i	0.0664436	+	0.00572289i
$388$	−16.4090			−0.833039
$389$	28.8726	−	5.09102i	1.46390	−	0.258125i	0.615774	−	0.787923i	$-0.288843\pi$
$389$	28.8726	−	5.09102i	1.46390	−	0.258125i	0.848124	+	0.529798i	$0.177732\pi$
$390$	−5.21974	+	28.4062i	−0.264312	+	1.43840i
$391$	−2.31736	+	2.76172i	−0.117194	+	0.139666i
$392$	21.0767	+	7.95246i	1.06453	+	0.401660i
$393$	0.589168	+	2.64912i	0.0297196	+	0.133630i
$394$	40.4603	−	33.9502i	2.03836	−	1.71039i
$395$	22.7802	+	9.64654i	1.14620	+	0.485370i
$396$	34.0535	+	33.9619i	1.71125	+	1.70665i
$397$	22.8428			1.14645			0.573225	−	0.819398i	$-0.305692\pi$
$397$	22.8428			1.14645			0.573225	+	0.819398i	$0.305692\pi$
$398$	−20.3476	+	3.58783i	−1.01993	+	0.179841i
$399$	31.4956	+	10.1106i	1.57675	+	0.506161i
$400$	−3.12966	−	1.51978i	−0.156483	−	0.0759891i
$401$	−11.0156	+	13.1278i	−0.550091	+	0.655573i	−0.967418	−	0.253183i	$-0.918522\pi$
$401$	−11.0156	+	13.1278i	−0.550091	+	0.655573i	0.417327	+	0.908756i	$0.362967\pi$
$402$	−29.0372	+	37.8949i	−1.44825	+	1.89003i
$403$	−0.00624219	+	0.0171503i	−0.000310945	+	0.000854316i
$404$	−18.7276	+	32.4372i	−0.931734	+	1.61381i
$405$	0.981817	−	20.1006i	0.0487869	−	0.998809i
$406$	37.7819	+	14.0030i	1.87508	+	0.694955i
$407$	−43.1323	+	36.1923i	−2.13799	+	1.79399i
$408$	16.1145	+	2.11047i	0.797784	+	0.104484i
$409$	−7.28305	−	20.0100i	−0.360123	−	0.989431i	−0.978985	−	0.203931i	$-0.934628\pi$
$409$	−7.28305	−	20.0100i	−0.360123	−	0.989431i	0.618862	−	0.785500i	$-0.287594\pi$
$410$	−11.3188	−	22.1672i	−0.558994	−	1.09476i
$411$	−2.96654	−	4.64963i	−0.146329	−	0.229349i
$412$	1.01907	+	5.77943i	0.0502059	+	0.284732i
$413$	10.6156	−	28.6423i	0.522359	−	1.40940i
$414$	8.31884	+	2.21702i	0.408849	+	0.108961i
$415$	24.5220	−	3.03232i	1.20374	−	0.148851i
$416$	−2.69004	−	15.2560i	−0.131890	−	0.747987i
$417$	−7.07035	−	7.70551i	−0.346237	−	0.377341i
$418$	−74.5227	+	27.1241i	−3.64503	+	1.32668i
$419$	−7.13616	−	5.98795i	−0.348624	−	0.292530i	0.451613	−	0.892214i	$-0.350849\pi$
$419$	−7.13616	−	5.98795i	−0.348624	−	0.292530i	−0.800237	+	0.599684i	$0.795293\pi$
$420$	29.8239	+	17.7421i	1.45526	+	0.865724i
$421$	6.58807	+	2.39786i	0.321083	+	0.116865i	0.497533	−	0.867445i	$-0.334239\pi$
$421$	6.58807	+	2.39786i	0.321083	+	0.116865i	−0.176450	+	0.984310i	$0.556461\pi$
$422$	−15.9346	−	27.5995i	−0.775682	−	1.34352i
$423$	10.2582	+	0.883554i	0.498770	+	0.0429599i
$424$	−7.64683	+	13.2447i	−0.371363	+	0.643220i
$425$	−13.3079	+	5.95248i	−0.645526	+	0.288738i
$426$	−29.3792	+	18.7444i	−1.42342	+	0.908170i
$427$	−17.1615	−	0.100645i	−0.830505	−	0.00487053i
$428$	0.118598	−	0.672604i	0.00573266	−	0.0325116i
$429$	10.0980	+	24.3323i	0.487536	+	1.17478i
$430$	−1.54638	+	1.66115i	−0.0745732	+	0.0801079i
$431$	−23.8672	+	13.7798i	−1.14964	+	0.663747i	−0.948800	−	0.315876i	$-0.897702\pi$
$431$	−23.8672	+	13.7798i	−1.14964	+	0.663747i	−0.200844	+	0.979623i	$0.564368\pi$
$432$	−1.09421	−	3.44609i	−0.0526452	−	0.165800i
$433$	−1.37621			−0.0661367			−0.0330683	−	0.999453i	$-0.510528\pi$
$433$	−1.37621			−0.0661367			−0.0330683	+	0.999453i	$0.510528\pi$
$434$	0.0265873	+	0.0225764i	0.00127623	+	0.00108370i
$435$	21.9172	+	12.8650i	1.05085	+	0.616829i
$436$	3.66066	+	3.07166i	0.175314	+	0.147106i
$437$	−5.73706	+	6.83716i	−0.274441	+	0.327066i
$438$	−0.542188	−	0.849801i	−0.0259067	−	0.0406051i
$439$	1.11588	−	3.06584i	0.0532578	−	0.146325i	−0.910211	−	0.414144i	$-0.864081\pi$
$439$	1.11588	−	3.06584i	0.0532578	−	0.146325i	0.963469	+	0.267820i	$0.0863031\pi$
$440$	−33.8068	+	4.18046i	−1.61168	+	0.199296i
$441$	−17.0762	−	12.2230i	−0.813153	−	0.582050i
$442$	18.8300	+	10.8715i	0.895651	+	0.517105i
$443$	−7.61552	+	6.39018i	−0.361824	+	0.303607i	−0.805517	−	0.592572i	$-0.798112\pi$
$443$	−7.61552	+	6.39018i	−0.361824	+	0.303607i	0.443693	+	0.896179i	$0.353668\pi$
$444$	68.1052	−	15.1467i	3.23213	−	0.718830i
$445$	10.2781	−	15.8568i	0.487230	−	0.751683i
$446$	16.9599	−	6.17289i	0.803073	−	0.292295i
$447$	−9.64460	+	30.6608i	−0.456174	+	1.45020i
$448$	−32.7475	−	5.97248i	−1.54717	−	0.282173i
$449$	18.1130	+	10.4576i	0.854807	+	0.493523i	0.862270	−	0.506449i	$-0.169042\pi$
$449$	18.1130	+	10.4576i	0.854807	+	0.493523i	−0.00746259	+	0.999972i	$0.502375\pi$
$450$	26.3440	+	22.7591i	1.24187	+	1.07287i
$451$	−19.6615	−	11.3516i	−0.925826	−	0.534526i
$452$	17.9725	−	15.0807i	0.845356	−	0.709338i
$453$	7.45722	−	14.3488i	0.350371	−	0.674164i
$454$	22.0245	+	60.5117i	1.03366	+	2.83996i
$455$	11.3637	+	15.2382i	0.532737	+	0.714377i
$456$	39.8944	+	5.22486i	1.86822	+	0.244676i
$457$	−3.49313	+	0.615934i	−0.163402	+	0.0288122i	−0.254751	−	0.967007i	$-0.581993\pi$
$457$	−3.49313	+	0.615934i	−0.163402	+	0.0288122i	0.0913486	+	0.995819i	$0.470882\pi$
$458$	−28.8047	+	16.6304i	−1.34595	+	0.777086i
$459$	−14.0088	−	5.76951i	−0.653875	−	0.269297i
$460$	−7.47308	+	5.64145i	−0.348434	+	0.263034i
$461$	−6.60502	+	5.54227i	−0.307626	+	0.258129i	−0.783510	−	0.621379i	$-0.786573\pi$
$461$	−6.60502	+	5.54227i	−0.307626	+	0.258129i	0.475884	+	0.879508i	$0.342128\pi$
$462$	50.3100	−	1.93498i	2.34063	−	0.0900235i
$463$	24.6708	+	4.35014i	1.14655	+	0.202168i	0.714470	−	0.699666i	$-0.246668\pi$
$463$	24.6708	+	4.35014i	1.14655	+	0.202168i	0.432082	+	0.901834i	$0.357779\pi$
$464$	4.49658	+	0.792868i	0.208748	+	0.0368080i
$465$	0.0140193	+	0.0169538i	0.000650130	+	0.000786212i
$466$	13.3954	−	11.2401i	0.620530	−	0.520687i
$467$			20.8894i			0.966646i	0.875442	+	0.483323i	$0.160570\pi$
$467$			20.8894i			0.966646i	−0.875442	+	0.483323i	$0.839430\pi$
$468$	2.80132	−	32.5237i	0.129491	−	1.50341i
$469$	5.27465	+	30.9752i	0.243561	+	1.43030i
$470$	−12.1361	+	13.0368i	−0.559797	+	0.601344i
$471$	7.29519	+	32.8019i	0.336144	+	1.51143i
$472$	6.45187	−	36.5904i	0.296971	−	1.68421i
$473$	−0.359477	+	2.03869i	−0.0165288	+	0.0937393i
$474$	−42.4247	−	13.3450i	−1.94863	−	0.612958i
$475$	−32.9461	+	14.7365i	−1.51167	+	0.676156i
$476$	20.1109	−	16.6751i	0.921783	−	0.764301i
$477$	10.0676	−	10.0948i	0.460963	−	0.462207i
$478$			36.1515i			1.65353i
$479$	15.8286	−	13.2818i	0.723229	−	0.606861i	−0.205047	−	0.978752i	$-0.565735\pi$
$479$	15.8286	−	13.2818i	0.723229	−	0.606861i	0.928277	+	0.371891i	$0.121290\pi$
$480$	−17.5005	−	6.51260i	−0.798784	−	0.297258i
$481$	37.6368	+	6.63638i	1.71609	+	0.302593i
$482$	−1.82947	−	0.322584i	−0.0833299	−	0.0146933i
$483$	4.79459	−	3.01962i	0.218161	−	0.137397i
$484$	−29.5974	+	24.8352i	−1.34534	+	1.12887i
$485$	−8.64709	+	6.52771i	−0.392644	+	0.296408i
$486$	1.69983	+	36.1394i	0.0771058	+	1.63931i
$487$	23.2776	−	13.4393i	1.05481	−	0.608993i	0.130816	−	0.991407i	$-0.458240\pi$
$487$	23.2776	−	13.4393i	1.05481	−	0.608993i	0.923991	+	0.382414i	$0.124907\pi$
$488$	−20.5576	+	3.62486i	−0.930599	+	0.164090i
$489$	10.5997	+	25.5412i	0.479334	+	1.15501i
$490$	34.8539	−	10.2430i	1.57454	−	0.462732i
$491$	9.80755	+	26.9460i	0.442609	+	1.21606i	0.937770	+	0.347257i	$0.112887\pi$
$491$	9.80755	+	26.9460i	0.442609	+	1.21606i	−0.495161	+	0.868801i	$0.664891\pi$
$492$	15.1314	+	23.7162i	0.682174	+	1.06921i
$493$	14.6563	−	12.2981i	0.660084	−	0.553877i
$494$	46.6172	+	26.9144i	2.09741	+	1.21094i
$495$	31.4558	+	4.35007i	1.41383	+	0.195521i
$496$	0.00342293	+	0.00197623i	0.000153694	+	8.87353e-5i
$497$	−4.11529	+	22.5643i	−0.184596	+	1.01215i
$498$	−43.3611	+	9.64358i	−1.94306	+	0.432139i
$499$	25.7894	−	9.38657i	1.15449	−	0.420200i	0.307365	−	0.951592i	$-0.400553\pi$
$499$	25.7894	−	9.38657i	1.15449	−	0.420200i	0.847126	+	0.531391i	$0.178331\pi$
$500$	−37.1489	+	7.32048i	−1.66135	+	0.327382i
$501$	−5.09437	+	16.1953i	−0.227599	+	0.723552i
$502$	−21.3991	+	17.9559i	−0.955087	+	0.801413i
$503$	10.2556	+	5.92109i	0.457276	+	0.264008i	0.710898	−	0.703295i	$-0.248289\pi$
$503$	10.2556	+	5.92109i	0.457276	+	0.264008i	−0.253622	+	0.967303i	$0.581622\pi$
$504$	−23.1011	−	10.8995i	−1.02900	−	0.485503i
$505$	3.03500	+	24.5437i	0.135056	+	1.09218i
$506$	−4.64624	+	12.7654i	−0.206551	+	0.567493i
$507$	−2.13754	+	4.11294i	−0.0949315	+	0.182662i
$508$	42.5396	−	50.6967i	1.88739	−	2.24930i
$509$	−19.3764	−	16.2587i	−0.858843	−	0.720655i	0.102875	−	0.994694i	$-0.467196\pi$
$509$	−19.3764	−	16.2587i	−0.858843	−	0.720655i	−0.961719	+	0.274039i	$0.911640\pi$
$510$	22.7910	−	12.9407i	1.00920	−	0.573024i
$511$	−0.652680	−	0.119036i	−0.0288729	−	0.00526584i
$512$	−7.83341			−0.346191
$513$	−34.6814	−	14.2835i	−1.53122	−	0.630632i
$514$	49.6062	−	28.6401i	2.18803	−	1.26326i
$515$	2.83616	+	2.64021i	0.124976	+	0.116341i
$516$	1.56020	−	2.03614i	0.0686842	−	0.0896359i
$517$	−2.82120	+	15.9998i	−0.124076	+	0.703670i
$518$	36.8891	−	63.0371i	1.62081	−	2.76969i
$519$	−0.261168	−	5.89068i	−0.0114640	−	0.258572i
$520$	16.9234	+	15.7541i	0.742140	+	0.690865i
$521$	18.1142	−	31.3747i	0.793598	−	1.37455i	−0.130127	−	0.991497i	$-0.541539\pi$
$521$	18.1142	−	31.3747i	0.793598	−	1.37455i	0.923725	−	0.383055i	$-0.125128\pi$
$522$	−41.4337	−	19.2530i	−1.81350	−	0.842679i
$523$	−10.0536	−	17.4133i	−0.439613	−	0.761432i	0.558046	−	0.829810i	$-0.311551\pi$
$523$	−10.0536	−	17.4133i	−0.439613	−	0.761432i	−0.997660	+	0.0683774i	$0.978218\pi$
$524$	4.98624	+	1.81484i	0.217825	+	0.0792819i
$525$	22.7745	−	2.51476i	0.993959	−	0.109753i
$526$	−48.3365	−	40.5591i	−2.10757	−	1.76846i
$527$	0.0155629	−	0.00566445i	0.000677932	−	0.000246747i
$528$	5.56915	−	1.23859i	0.242366	−	0.0539026i
$529$	−3.72842	−	21.1449i	−0.162105	−	0.919345i
$530$	3.02671	+	24.4766i	0.131472	+	1.06320i
$531$	−14.5956	+	31.4107i	−0.633395	+	1.36311i
$532$	49.7884	−	41.2823i	2.15860	−	1.78981i
$533$	2.67590	+	15.1758i	0.115906	+	0.657336i
$534$	−15.6660	+	30.1436i	−0.677932	+	1.30444i
$535$	−0.205073	−	0.401625i	−0.00886608	−	0.0173638i
$536$	13.0716	+	35.9140i	0.564609	+	1.55125i
$537$	−10.3711	+	13.5348i	−0.447547	+	0.584068i
$538$	48.1559	−	40.4076i	2.07615	−	1.74209i
$539$	21.5960	−	25.1325i	0.930205	−	1.08253i
$540$	−32.1000	−	22.7575i	−1.38137	−	0.979328i
$541$	−20.6733	+	35.8071i	−0.888813	+	1.53947i	−0.0475322	+	0.998870i	$0.515136\pi$
$541$	−20.6733	+	35.8071i	−0.888813	+	1.53947i	−0.841280	+	0.540599i	$0.818198\pi$
$542$	11.8854	−	32.6548i	0.510521	−	1.40264i
$543$	−20.0575	−	2.62687i	−0.860748	−	0.112730i
$544$	−9.03602	+	10.7687i	−0.387416	+	0.461705i
$545$	3.15102	+	0.162422i	0.134975	+	0.00695740i
$546$	−22.9561	−	25.3147i	−0.982430	−	1.08337i
$547$	−30.9558	+	5.45834i	−1.32357	+	0.233382i	−0.790383	−	0.612613i	$-0.790119\pi$
$547$	−30.9558	+	5.45834i	−1.32357	+	0.233382i	−0.533191	+	0.845995i	$0.679007\pi$
$548$	−10.7839			−0.460667
$549$	19.3879	+	1.66991i	0.827455	+	0.0712700i
$550$	−39.4500	+	38.2277i	−1.68215	+	1.63004i
$551$	36.2843	−	30.4461i	1.54576	−	1.29705i
$552$	5.07825	−	4.65966i	0.216145	−	0.198328i
$553$	−25.4349	+	14.4866i	−1.08160	+	0.616033i
$554$	−22.6959	+	27.0479i	−0.964256	+	1.14916i
$555$	29.8641	−	35.0751i	1.26766	−	1.48886i
$556$	−20.1369	+	3.55068i	−0.853995	+	0.150582i
$557$	16.5671			0.701971			0.350985	−	0.936381i	$-0.385847\pi$
$557$	16.5671			0.701971			0.350985	+	0.936381i	$0.385847\pi$
$558$	−0.0280035	−	0.0279281i	−0.00118548	−	0.00118229i
$559$	1.21687	−	0.702559i	0.0514681	−	0.0297151i
$560$	3.67721	−	1.85051i	0.155391	−	0.0781984i
$561$	11.0244	−	21.2125i	0.465449	−	0.895592i
$562$	−10.2756	−	1.81187i	−0.433450	−	0.0764290i
$563$	−11.3202	−	31.1020i	−0.477089	−	1.31079i	−0.911952	−	0.410296i	$-0.865425\pi$
$563$	−11.3202	−	31.1020i	−0.477089	−	1.31079i	0.434863	−	0.900497i	$-0.356797\pi$
$564$	12.2446	−	15.9797i	0.515590	−	0.672868i
$565$	3.47172	−	15.0969i	0.146056	−	0.635130i
$566$	−4.11241			−0.172858
$567$	18.1922	+	15.3637i	0.764003	+	0.645213i
$568$			27.8988i			1.17061i
$569$	−15.0329	+	2.65070i	−0.630211	+	0.111123i	−0.479625	−	0.877474i	$-0.659227\pi$
$569$	−15.0329	+	2.65070i	−0.630211	+	0.111123i	−0.150586	+	0.988597i	$0.548116\pi$
$570$	56.4234	−	32.0371i	2.36332	−	1.34189i
$571$	42.6373	−	15.5187i	1.78431	−	0.649437i	0.784753	−	0.619808i	$-0.212790\pi$
$571$	42.6373	−	15.5187i	1.78431	−	0.649437i	0.999561	−	0.0296289i	$-0.00943256\pi$
$572$	50.7275	+	8.94463i	2.12102	+	0.373994i
$573$	1.77461	+	0.922286i	0.0741355	+	0.0385291i
$574$	28.9721	+	5.28393i	1.20927	+	0.220547i
$575$	−1.69387	+	5.94579i	−0.0706393	+	0.247957i
$576$	36.4716	+	9.71991i	1.51965	+	0.404996i
$577$	−11.6902			−0.486668			−0.243334	−	0.969943i	$-0.578241\pi$
$577$	−11.6902			−0.486668			−0.243334	+	0.969943i	$0.578241\pi$
$578$	3.42517	+	19.4251i	0.142468	+	0.807978i
$579$	8.16951	−	25.9713i	0.339513	−	1.07933i
$580$	44.2554	−	22.5972i	1.83760	−	0.938297i
$581$	−14.7661	+	25.2328i	−0.612603	+	1.04683i
$582$	14.3515	−	13.1685i	0.594890	−	0.545854i
$583$	14.4604	+	17.2333i	0.598890	+	0.713729i
$584$	−0.806981			−0.0333931
$585$	−11.4622	−	18.2535i	−0.473902	−	0.754691i
$586$		−	39.7970i		−	1.64400i
$587$	−1.87813	+	0.331165i	−0.0775187	+	0.0136686i	−0.212273	−	0.977210i	$-0.568087\pi$
$587$	−1.87813	+	0.331165i	−0.0775187	+	0.0136686i	0.134754	+	0.990879i	$0.456975\pi$
$588$	−38.1061	+	15.2927i	−1.57147	+	0.630662i
$589$	0.0385290	−	0.0140234i	0.00158756	−	0.000577824i
$590$	−27.2477	−	53.3632i	−1.12177	−	2.19693i
$591$	−5.11857	+	39.0828i	−0.210550	+	1.60765i
$592$	2.83071	−	7.77731i	0.116341	−	0.319645i
$593$	−6.28615	−	3.62931i	−0.258141	−	0.149038i	0.365345	−	0.930872i	$-0.380951\pi$
$593$	−6.28615	−	3.62931i	−0.258141	−	0.149038i	−0.623486	+	0.781834i	$0.714284\pi$
$594$	−57.0389	−	2.37492i	−2.34034	−	0.0974440i
$595$	3.96435	−	16.7877i	0.162523	−	0.688230i
$596$	40.3963	+	48.1424i	1.65470	+	1.97199i
$597$	9.37843	−	12.2393i	0.383834	−	0.500920i
$598$	8.66460	−	3.15365i	0.354322	−	0.128963i
$599$	−27.8290	+	33.1654i	−1.13706	+	1.35510i	−0.211110	+	0.977462i	$0.567708\pi$
$599$	−27.8290	+	33.1654i	−1.13706	+	1.35510i	−0.925954	+	0.377637i	$0.876737\pi$
$600$	26.7033	−	7.97943i	1.09016	−	0.325759i
$601$	−40.5055	+	7.14221i	−1.65225	+	0.291337i	−0.920648	−	0.390393i	$-0.872339\pi$
$601$	−40.5055	+	7.14221i	−1.65225	+	0.291337i	−0.731604	+	0.681730i	$0.761228\pi$
$602$	−0.450787	−	2.64723i	−0.0183727	−	0.107893i
$603$	−3.15300	−	35.4884i	−0.128400	−	1.44520i
$604$	−15.8091	−	27.3821i	−0.643262	−	1.11416i
$605$	−5.71728	+	24.8617i	−0.232440	+	1.01077i
$606$	−9.65209	−	43.3994i	−0.392089	−	1.76298i
$607$	19.0031	−	6.91656i	0.771312	−	0.280735i	0.0737670	−	0.997276i	$-0.476498\pi$
$607$	19.0031	−	6.91656i	0.771312	−	0.280735i	0.697545	+	0.716541i	$0.254276\pi$
$608$	−22.3704	+	26.6600i	−0.907239	+	1.08120i
$609$	−27.8406	+	11.3630i	−1.12816	+	0.460453i
$610$	−22.9371	+	24.6395i	−0.928698	+	0.997624i
$611$	9.55006	−	5.51373i	0.386354	−	0.223062i
$612$	−24.2427	+	17.0236i	−0.979951	+	0.688138i
$613$	−5.85940	−	3.38293i	−0.236659	−	0.136635i	0.376981	−	0.926221i	$-0.376962\pi$
$613$	−5.85940	−	3.38293i	−0.236659	−	0.136635i	−0.613640	+	0.789586i	$0.710295\pi$
$614$	10.4556	+	3.80551i	0.421952	+	0.153578i
$615$	17.4085	+	6.47835i	0.701977	+	0.261232i
$616$	20.3571	−	34.7868i	0.820210	−	1.40160i
$617$	−2.01623	+	11.4346i	−0.0811702	+	0.460339i	0.916947	+	0.399008i	$0.130646\pi$
$617$	−2.01623	+	11.4346i	−0.0811702	+	0.460339i	−0.998118	+	0.0613307i	$0.980466\pi$
$618$	−5.52941	−	4.23695i	−0.222425	−	0.170435i
$619$	6.53489	−	17.9545i	0.262660	−	0.721651i	−0.736326	−	0.676627i	$-0.763441\pi$
$619$	6.53489	−	17.9545i	0.262660	−	0.721651i	0.998986	−	0.0450246i	$-0.0143366\pi$
$620$	0.0426891	−	0.00527882i	0.00171444	−	0.000212002i
$621$	−5.69295	+	2.97820i	−0.228450	+	0.119511i
$622$	−63.5412			−2.54777
$623$	7.52375	+	21.0547i	0.301433	+	0.843539i
$624$	−3.07380	−	2.35532i	−0.123051	−	0.0942884i
$625$	−16.6643	+	18.6360i	−0.666571	+	0.745441i
$626$	−23.0328	−	19.3268i	−0.920578	−	0.772456i
$627$	27.2929	−	52.5155i	1.08997	−	2.09727i
$628$	61.7406	+	22.4717i	2.46372	+	0.896720i
$629$	−17.3401	−	30.0339i	−0.691395	−	1.19753i
$630$	−40.3229	+	8.41685i	−1.60650	+	0.335335i
$631$	1.51428	−	2.62280i	0.0602824	−	0.104412i	−0.834309	−	0.551297i	$-0.814133\pi$
$631$	1.51428	−	2.62280i	0.0602824	−	0.104412i	0.894592	+	0.446885i	$0.147467\pi$
$632$	−27.2740	+	22.8856i	−1.08490	+	0.910342i
$633$	22.6874	+	7.13652i	0.901744	+	0.283651i
$634$	−5.13184	+	29.1041i	−0.203811	+	1.15587i
$635$	2.24939	−	43.6387i	0.0892644	−	1.73175i
$636$	−6.05178	−	27.2111i	−0.239969	−	1.07899i
$637$	−22.4900	−	0.263796i	−0.891085	−	0.0104520i
$638$	36.0465	−	62.4343i	1.42709	−	2.47180i
$639$	6.69741	−	25.1304i	0.264946	−	0.994145i
$640$	−34.9038	+	26.3490i	−1.37970	+	1.04154i
$641$	−27.5006	−	32.7740i	−1.08621	−	1.29449i	−0.952855	−	0.303425i	$-0.901870\pi$
$641$	−27.5006	−	32.7740i	−1.08621	−	1.29449i	−0.133354	−	0.991068i	$-0.542575\pi$
$642$	0.436052	+	0.683448i	0.0172096	+	0.0269735i
$643$	−2.68049	+	0.975620i	−0.105708	+	0.0384747i	−0.394333	−	0.918968i	$-0.629024\pi$
$643$	−2.68049	+	0.975620i	−0.105708	+	0.0384747i	0.288625	+	0.957442i	$0.406802\pi$
$644$	0.0649716	−	11.0787i	0.00256024	−	0.436562i
$645$	0.0121836	−	1.69366i	0.000479729	−	0.0666879i
$646$	−8.48216	−	48.1047i	−0.333726	−	1.89265i
$647$	7.22516	−	4.17145i	0.284050	−	0.163996i	−0.351205	−	0.936298i	$-0.614228\pi$
$647$	7.22516	−	4.17145i	0.284050	−	0.163996i	0.635256	+	0.772302i	$0.280895\pi$
$648$	25.1219	+	14.4141i	0.986882	+	0.566237i
$649$	−47.3312	−	27.3267i	−1.85791	−	1.07267i
$650$	37.0886	+	3.83371i	1.45473	+	0.150370i
$651$	−0.0260107	+	0.00100040i	−0.00101944	+	3.92090e-5i
$652$	53.2478	+	9.38902i	2.08534	+	0.367702i
$653$	−4.53113	+	25.6973i	−0.177317	+	1.00561i	0.758119	+	0.652117i	$0.226119\pi$
$653$	−4.53113	+	25.6973i	−0.177317	+	1.00561i	−0.935436	+	0.353497i	$0.884992\pi$
$654$	−5.66675	+	0.251240i	−0.221587	+	0.00982424i
$655$	3.34959	−	1.02722i	0.130879	−	0.0401369i
$656$	3.33720			0.130296
$657$	0.726906	+	0.193725i	0.0283593	+	0.00755792i
$658$	−3.53780	−	20.7756i	−0.137918	−	0.809917i
$659$	2.19670	−	6.03539i	0.0855714	−	0.235105i	−0.889525	−	0.456886i	$-0.848965\pi$
$659$	2.19670	−	6.03539i	0.0855714	−	0.235105i	0.975097	+	0.221781i	$0.0711869\pi$
$660$	40.2514	−	47.2749i	1.56678	−	1.84017i
$661$	−47.0450	−	8.29529i	−1.82984	−	0.322650i	−0.850669	−	0.525702i	$-0.823803\pi$
$661$	−47.0450	−	8.29529i	−1.82984	−	0.322650i	−0.979168	+	0.203052i	$0.934914\pi$
$662$	−9.50397	+	53.8997i	−0.369382	+	2.09487i
$663$	−15.8394	+	3.52271i	−0.615153	+	0.136811i
$664$	−12.1625	+	33.4163i	−0.471998	+	1.29680i
$665$	9.81450	−	41.5612i	0.380590	−	1.61167i
$666$	−47.4104	+	67.9035i	−1.83711	+	2.63121i
$667$		−	8.11357i		−	0.314159i
$668$	21.3377	+	25.4292i	0.825579	+	0.983887i
$669$	−6.21131	+	11.9515i	−0.240143	+	0.462071i
$670$	51.7187	+	33.5234i	1.99807	+	1.29512i
$671$	−5.33204	+	30.2395i	−0.205841	+	1.16738i
$672$	18.6954	−	11.7743i	0.721191	−	0.454204i
$673$	14.2424	+	16.9734i	0.549004	+	0.654277i	0.967181	−	0.254088i	$-0.0817754\pi$
$673$	14.2424	+	16.9734i	0.549004	+	0.654277i	−0.418177	+	0.908365i	$0.637331\pi$
$674$	45.9809	+	26.5471i	1.77112	+	1.02256i
$675$	−25.9691	+	0.777220i	−0.999552	+	0.0299152i
$676$	4.53152	+	7.84882i	0.174289	+	0.301878i
$677$	34.6006	−	6.10102i	1.32981	−	0.234481i	0.536810	−	0.843703i	$-0.319629\pi$
$677$	34.6006	−	6.10102i	1.32981	−	0.234481i	0.793000	+	0.609222i	$0.208518\pi$
$678$	−3.61643	+	27.6132i	−0.138888	+	1.06048i
$679$	0.0751785	−	12.8192i	0.00288508	−	0.491954i
$680$	1.08007	−	20.9535i	0.0414186	−	0.803530i
$681$	−42.6421	−	22.1616i	−1.63405	−	0.849233i
$682$	0.0478061	−	0.0401141i	0.00183059	−	0.00153605i
$683$	0.124737	−	0.216051i	0.00477294	−	0.00826698i	−0.863629	−	0.504128i	$-0.831814\pi$
$683$	0.124737	−	0.216051i	0.00477294	−	0.00826698i	0.868402	+	0.495861i	$0.165147\pi$
$684$	−60.0173	+	42.1451i	−2.29482	+	1.61146i
$685$	−5.68286	+	4.29000i	−0.217131	+	0.163913i
$686$	−15.4096	+	40.1266i	−0.588342	+	1.53204i
$687$	7.44815	−	23.6781i	0.284165	−	0.903376i
$688$	−0.104075	−	0.285944i	−0.00396783	−	0.0109015i
$689$	2.65153	−	15.0376i	0.101015	−	0.572885i
$690$	2.00869	−	10.9314i	0.0764694	−	0.416152i
$691$	12.0669	+	14.3807i	0.459045	+	0.547069i	0.945066	−	0.326878i	$-0.105997\pi$
$691$	12.0669	+	14.3807i	0.459045	+	0.547069i	−0.486021	+	0.873947i	$0.661552\pi$
$692$	−9.98447	−	5.76454i	−0.379553	−	0.219135i
$693$	−26.6880	+	26.4480i	−1.01379	+	1.00468i
$694$	−21.6548	−	37.5072i	−0.822004	−	1.42375i
$695$	−9.19911	+	9.88186i	−0.348942	+	0.374840i
$696$	−30.8345	+	19.6730i	−1.16878	+	0.745702i
$697$	8.98851	−	10.7121i	0.340464	−	0.405749i
$698$	32.1092	−	38.2663i	1.21535	−	1.44840i
$699$	−1.69463	+	12.9393i	−0.0640969	+	0.489411i
$700$	19.8060	−	40.1846i	0.748595	−	1.51884i
$701$			1.49711i			0.0565452i	0.999600	+	0.0282726i	$0.00900064\pi$
$701$			1.49711i			0.0565452i	−0.999600	+	0.0282726i	$0.990999\pi$
$702$	23.6509	+	30.6939i	0.892647	+	1.15847i
$703$	−42.9287	−	74.3547i	−1.61909	−	2.80434i
$704$	−20.3701	+	55.9665i	−0.767728	+	2.10932i
$705$	0.0956177	−	13.2920i	0.00360117	−	0.500604i
$706$	−4.93473	−	0.870127i	−0.185721	−	0.0327476i
$707$	−25.2551	−	14.7792i	−0.949815	−	0.555828i
$708$	36.4257	+	57.0920i	1.36896	+	2.14565i
$709$	−24.8649	−	9.05008i	−0.933820	−	0.339883i	−0.170098	−	0.985427i	$-0.554408\pi$
$709$	−24.8649	−	9.05008i	−0.933820	−	0.339883i	−0.763723	+	0.645544i	$0.776630\pi$
$710$	27.1068	+	35.9077i	1.01730	+	1.34759i
$711$	30.0616	−	14.0673i	1.12740	−	0.527565i
$712$	13.5979	+	23.5523i	0.509603	+	0.882659i
$713$	0.00240215	−	0.00659986i	8.99613e−5	−	0.000247167i
$714$	−4.20722	+	30.7237i	−0.157451	+	1.14981i
$715$	30.2904	−	15.4665i	1.13280	−	0.578415i
$716$	11.4029	+	31.3291i	0.426145	+	1.17082i
$717$	−18.2403	−	19.8789i	−0.681197	−	0.742392i
$718$	−38.3952	+	6.77011i	−1.43290	+	0.252658i
$719$	1.28741	+	2.22986i	0.0480123	+	0.0831597i	0.889033	−	0.457844i	$-0.151378\pi$
$719$	1.28741	+	2.22986i	0.0480123	+	0.0831597i	−0.841021	+	0.541003i	$0.818045\pi$
$720$	−4.32401	+	1.75812i	−0.161146	+	0.0655214i
$721$	−4.51972	+	0.769647i	−0.168323	+	0.0286632i
$722$	−13.3418	−	75.6650i	−0.496530	−	2.81596i
$723$	1.16874	−	0.745678i	0.0434660	−	0.0277321i
$724$	−25.4237	+	30.2988i	−0.944865	+	1.12605i
$725$	14.3319	−	29.5135i	0.532275	−	1.09610i
$726$	5.95558	−	45.4738i	0.221032	−	1.68769i
$727$	26.5542	−	22.2816i	0.984840	−	0.826379i	2.71941e−5	−	1.00000i	$-0.499991\pi$
$727$	26.5542	−	22.2816i	0.984840	−	0.826379i	0.984812	+	0.173621i	$0.0555469\pi$
$728$	−26.9693	+	4.59250i	−0.999547	+	0.170209i
$729$	−19.1689	−	19.0146i	−0.709958	−	0.704244i
$730$	−1.03864	+	0.784074i	−0.0384419	+	0.0290199i
$731$	−1.19817	−	0.436099i	−0.0443160	−	0.0161297i
$732$	23.1422	−	30.2015i	0.855359	−	1.11628i
$733$	−32.6775	−	27.4197i	−1.20697	−	1.01277i	−0.999403	−	0.0345481i	$-0.989001\pi$
$733$	−32.6775	−	27.4197i	−1.20697	−	1.01277i	−0.207568	−	0.978221i	$-0.566555\pi$
$734$	16.6906	−	6.07488i	0.616061	−	0.224228i
$735$	−13.9973	+	23.2180i	−0.516297	+	0.856410i
$736$	1.03520	+	5.87090i	0.0381579	+	0.216404i
$737$	56.2187			2.07084
$738$	−32.2669	−	8.59932i	−1.18776	−	0.316545i
$739$	32.7329			1.20410			0.602050	−	0.798458i	$-0.294351\pi$
$739$	32.7329			1.20410			0.602050	+	0.798458i	$0.294351\pi$
$740$	−26.4084	−	86.1133i	−0.970794	−	3.16559i
$741$	−39.2135	+	8.72113i	−1.44054	+	0.320379i
$742$	−25.1861	−	14.7388i	−0.924612	−	0.541079i
$743$	10.8226	+	9.08125i	0.397043	+	0.333159i	0.819349	−	0.573294i	$-0.194335\pi$
$743$	10.8226	+	9.08125i	0.397043	+	0.333159i	−0.422306	+	0.906453i	$0.638779\pi$
$744$	−0.0309064	+	0.00687362i	−0.00113308	+	0.000251999i
$745$	40.4395	+	9.29959i	1.48159	+	0.340710i
$746$		−	26.3740i		−	0.965620i
$747$	18.9776	−	27.1807i	0.694356	−	0.994491i
$748$	−23.3713	−	40.4803i	−0.854540	−	1.48011i
$749$	0.524915	+	0.0957340i	0.0191800	+	0.00349804i
$750$	26.6161	−	36.2154i	0.971884	−	1.32240i
$751$	2.94320	−	16.6917i	0.107399	−	0.609089i	−0.882836	−	0.469681i	$-0.844369\pi$
$751$	2.94320	−	16.6917i	0.107399	−	0.609089i	0.990235	−	0.139408i	$-0.0445200\pi$
$752$	−0.816789	−	2.24411i	−0.0297852	−	0.0818342i
$753$	2.70716	−	20.6705i	0.0986545	−	0.753276i
$754$	−48.1900	+	8.49720i	−1.75498	+	0.309450i
$755$	−19.2240	−	8.14059i	−0.699631	−	0.296266i
$756$	44.4566	−	13.8295i	1.61687	−	0.502973i
$757$		−	22.3006i		−	0.810531i	−0.914199	−	0.405265i	$-0.867179\pi$
$757$		−	22.3006i		−	0.810531i	0.914199	−	0.405265i	$-0.132821\pi$
$758$	9.17806	+	52.0514i	0.333362	+	1.89059i
$759$	−3.88596	−	9.36370i	−0.141052	−	0.339881i
$760$	2.67391	−	51.8743i	0.0969928	−	1.88168i
$761$	2.46290	−	13.9678i	0.0892800	−	0.506332i	−0.907071	−	0.420978i	$-0.861687\pi$
$761$	2.46290	−	13.9678i	0.0892800	−	0.506332i	0.996351	−	0.0853536i	$-0.0272020\pi$
$762$	3.47943	+	78.4791i	0.126046	+	2.84300i
$763$	−2.41644	+	2.84574i	−0.0874811	+	0.103023i
$764$	3.38654	−	1.95522i	0.122521	−	0.0707373i
$765$	−6.00302	+	18.6151i	−0.217040	+	0.673029i
$766$			32.7609i			1.18370i
$767$	6.44169	+	36.5327i	0.232596	+	1.31912i
$768$	25.8163	−	23.6883i	0.931565	−	0.854777i
$769$	0.150947	−	0.179892i	0.00544330	−	0.00648708i	−0.763316	−	0.646025i	$-0.776430\pi$
$769$	0.150947	−	0.179892i	0.00544330	−	0.00648708i	0.768759	+	0.639538i	$0.220874\pi$
$770$	−7.59828	−	64.5523i	−0.273823	−	2.32630i
$771$	−12.8269	+	40.7775i	−0.461950	+	1.46856i
$772$	−34.2179	−	40.7793i	−1.23153	−	1.46768i
$773$		−	32.6777i		−	1.17533i	−0.809103	−	0.587667i	$-0.800046\pi$
$773$		−	32.6777i		−	1.17533i	0.809103	−	0.587667i	$-0.199954\pi$
$774$	0.269465	+	3.03294i	0.00968571	+	0.109017i
$775$	0.0203960	−	0.0197641i	0.000732648	−	0.000709948i
$776$	−2.70766	−	15.3559i	−0.0971994	−	0.551245i
$777$	11.5210	+	53.2752i	0.413314	+	1.91124i
$778$	23.2725	+	63.9407i	0.834360	+	2.29238i
$779$	22.2527	−	26.5198i	0.797287	−	0.950170i
$780$	−42.1423	−	0.303157i	−1.50894	−	0.0108548i
$781$	38.5632	+	14.0359i	1.37990	+	0.502242i
$782$	−7.24626	−	4.18363i	−0.259126	−	0.149606i
$783$	32.4976	−	10.3187i	1.16137	−	0.368760i
$784$	−0.902010	+	4.78656i	−0.0322146	+	0.170949i
$785$	41.4752	−	12.7192i	1.48031	−	0.453969i
$786$	−5.81750	+	2.41428i	−0.207503	+	0.0861145i
$787$	7.96526	−	2.89912i	0.283931	−	0.103342i	−0.196129	−	0.980578i	$-0.562837\pi$
$787$	7.96526	−	2.89912i	0.283931	−	0.103342i	0.480060	+	0.877236i	$0.340615\pi$
$788$	59.0384	+	49.5391i	2.10316	+	1.76476i
$789$	47.0434	−	2.08570i	1.67479	−	0.0742530i
$790$	−12.8676	+	55.9553i	−0.457810	+	1.99080i
$791$	11.6992	+	14.1097i	0.415975	+	0.501685i
$792$	−26.1632	+	37.4722i	−0.929668	+	1.33152i
$793$	18.0495	−	10.4209i	0.640958	−	0.370057i
$794$	9.20614	+	52.2106i	0.326714	+	1.85288i
$795$	−14.0141	−	11.9320i	−0.497028	−	0.423186i
$796$	−10.3114	−	28.3304i	−0.365479	−	1.00414i
$797$	18.0610	−	21.5243i	0.639754	−	0.762429i	−0.344577	−	0.938758i	$-0.611978\pi$
$797$	18.0610	−	21.5243i	0.639754	−	0.762429i	0.984331	+	0.176329i	$0.0564223\pi$
$798$	−10.4158	+	76.0624i	−0.368714	+	2.69258i
$799$	−9.40334	−	3.42254i	−0.332666	−	0.121081i
$800$	−6.60487	+	23.1843i	−0.233517	+	0.819688i
$801$	−6.59464	−	24.4796i	−0.233010	−	0.864943i
$802$	−34.4451	−	19.8869i	−1.21630	−	0.702230i
$803$	−0.405991	+	1.11545i	−0.0143271	+	0.0393634i
$804$	−61.8126	−	32.1247i	−2.17996	−	1.13295i
$805$	−4.37303	−	5.86403i	−0.154129	−	0.206680i
$806$	−0.0417151	−	0.00735550i	−0.00146935	−	0.000259087i
$807$	−6.09212	+	46.5163i	−0.214453	+	1.63745i
$808$	−33.4458	−	12.1733i	−1.17662	−	0.428254i
$809$	−18.4329	+	10.6422i	−0.648065	+	0.374161i	−0.787715	−	0.616040i	$-0.788736\pi$
$809$	−18.4329	+	10.6422i	−0.648065	+	0.374161i	0.139649	+	0.990201i	$0.455402\pi$
$810$	46.3386	−	5.85689i	1.62817	−	0.205790i
$811$			35.7637i			1.25583i	0.778280	+	0.627917i	$0.216092\pi$
$811$			35.7637i			1.25583i	−0.778280	+	0.627917i	$0.783908\pi$
$812$	−10.5490	+	57.8408i	−0.370198	+	2.02981i
$813$	9.94054	+	23.9529i	0.348630	+	0.840067i
$814$	−100.106	−	83.9988i	−3.50871	−	2.94416i
$815$	31.7953	−	16.2349i	1.11374	−	0.568685i
$816$	0.155644	+	3.51058i	0.00544864	+	0.122895i
$817$	−2.96630	−	1.07965i	−0.103778	−	0.0377720i
$818$	42.8005	−	24.7109i	1.49649	−	0.863996i
$819$	25.3956	+	2.33748i	0.887396	+	0.0816781i
$820$	28.9864	−	21.8819i	1.01225	−	0.764149i
$821$	8.47119	+	10.0956i	0.295647	+	0.352338i	0.893336	−	0.449390i	$-0.148359\pi$
$821$	8.47119	+	10.0956i	0.295647	+	0.352338i	−0.597689	+	0.801728i	$0.703914\pi$
$822$	9.43181	−	8.65436i	0.328972	−	0.301855i
$823$	5.03439	+	0.887700i	0.175488	+	0.0309433i	0.260702	−	0.965419i	$-0.416046\pi$
$823$	5.03439	+	0.887700i	0.175488	+	0.0309433i	−0.0852136	+	0.996363i	$0.527157\pi$
$824$	−5.24037	+	1.90734i	−0.182557	+	0.0664453i
$825$	2.40482	−	40.9252i	0.0837249	−	1.42483i
$826$	69.7445	+	12.7200i	2.42672	+	0.442586i
$827$	−9.78948	+	16.9559i	−0.340414	+	0.589614i	−0.984510	−	0.175331i	$-0.943900\pi$
$827$	−9.78948	+	16.9559i	−0.340414	+	0.589614i	0.644096	+	0.764945i	$0.277234\pi$
$828$	−1.07802	+	12.5160i	−0.0374637	+	0.434959i
$829$	−1.40797	−	0.812890i	−0.0489007	−	0.0282328i	0.475350	−	0.879797i	$-0.342321\pi$
$829$	−1.40797	−	0.812890i	−0.0489007	−	0.0282328i	−0.524251	+	0.851564i	$0.675655\pi$
$830$	16.8137	+	54.8265i	0.583612	+	1.90306i
$831$	−1.16711	−	26.3243i	−0.0404865	−	0.913179i
$832$	37.9875	−	13.8263i	1.31698	−	0.479341i
$833$	12.9349	+	15.7876i	0.448168	+	0.547009i
$834$	14.7626	−	19.2658i	0.511186	−	0.667120i
$835$	21.3605	+	4.91212i	0.739211	+	0.169991i
$836$	−57.8601	−	100.217i	−2.00113	−	3.46606i
$837$	0.0294897	+	0.00122785i	0.00101931	+	4.24409e-5i
$838$	10.8103	−	18.7240i	0.373435	−	0.646809i
$839$	−4.27500	+	3.58715i	−0.147589	+	0.123842i	−0.713593	−	0.700561i	$-0.752933\pi$
$839$	−4.27500	+	3.58715i	−0.147589	+	0.123842i	0.566003	+	0.824403i	$0.308489\pi$
$840$	−11.6822	+	30.8376i	−0.403074	+	1.06400i
$841$	−2.44116	+	13.8445i	−0.0841780	+	0.477397i
$842$	−2.82553	+	16.0244i	−0.0973742	+	0.552236i
$843$	6.56451	−	4.18827i	0.226094	−	0.144252i
$844$	35.6230	−	29.8912i	1.22619	−	1.02890i
$845$	5.51036	+	2.33342i	0.189562	+	0.0802721i
$846$	2.11478	+	23.8027i	0.0727075	+	0.818353i
$847$	−19.2663	−	23.2361i	−0.662000	−	0.798403i
$848$	−3.10738	−	1.13099i	−0.106708	−	0.0388385i
$849$	2.26132	−	2.07492i	0.0776084	−	0.0712112i
$850$	−18.9686	−	28.0181i	−0.650618	−	0.961012i
$851$	−14.4836	−	2.55385i	−0.496491	−	0.0875448i
$852$	−34.3799	−	37.4684i	−1.17784	−	1.28365i
$853$	−9.96952	−	3.62861i	−0.341350	−	0.124241i	0.165656	−	0.986184i	$-0.447026\pi$
$853$	−9.96952	−	3.62861i	−0.341350	−	0.124241i	−0.507006	+	0.861942i	$0.669248\pi$
$854$	−6.68641	−	39.2657i	−0.228804	−	1.34364i
$855$	−14.8616	+	46.0851i	−0.508256	+	1.57608i
$856$	0.649010			0.0221827
$857$	−10.7457	−	12.8062i	−0.367067	−	0.437453i	0.550621	−	0.834755i	$-0.314391\pi$
$857$	−10.7457	−	12.8062i	−0.367067	−	0.437453i	−0.917688	+	0.397302i	$0.869946\pi$
$858$	−51.5454	+	32.8868i	−1.75973	+	1.12274i
$859$	4.94622	+	0.872152i	0.168763	+	0.0297574i	0.257391	−	0.966307i	$-0.417137\pi$
$859$	4.94622	+	0.872152i	0.168763	+	0.0297574i	−0.0886282	+	0.996065i	$0.528248\pi$
$860$	−2.77891	−	1.80125i	−0.0947599	−	0.0614221i
$861$	−18.5971	+	11.7124i	−0.633788	+	0.399157i
$862$	−41.1146	−	48.9985i	−1.40037	−	1.66889i
$863$	−15.4606	+	26.7785i	−0.526285	+	0.911552i	0.473246	+	0.880930i	$0.343082\pi$
$863$	−15.4606	+	26.7785i	−0.526285	+	0.911552i	−0.999531	+	0.0306219i	$0.990251\pi$
$864$	−22.1984	+	11.6128i	−0.755204	+	0.395076i
$865$	−7.55477	+	0.934201i	−0.256870	+	0.0317638i
$866$	−0.554643	−	3.14554i	−0.0188475	−	0.106890i
$867$	−11.6844	−	8.95326i	−0.396823	−	0.304069i
$868$	−0.0257056	+	0.0439265i	−0.000872506	+	0.00149096i
$869$	17.9122	+	49.2134i	0.607630	+	1.66945i
$870$	−20.5717	+	55.2798i	−0.697446	+	1.87416i
$871$	−24.5279	−	29.2312i	−0.831096	−	0.990462i
$872$	−2.27049	+	3.93260i	−0.0768884	+	0.133175i
$873$	−1.24737	+	14.4822i	−0.0422172	+	0.490148i
$874$	−17.9395	−	10.3574i	−0.606812	−	0.350343i
$875$	−5.54877	−	29.0553i	−0.187583	−	0.982249i
$876$	1.08378	−	0.994450i	0.0366177	−	0.0335993i
$877$	2.85139	+	7.83414i	0.0962847	+	0.264540i	0.978479	−	0.206345i	$-0.0661569\pi$
$877$	2.85139	+	7.83414i	0.0962847	+	0.264540i	−0.882195	+	0.470885i	$0.843935\pi$
$878$	7.45714	+	1.31490i	0.251666	+	0.0443756i
$879$	20.0797	+	21.8835i	0.677270	+	0.738112i
$880$	−2.15949	−	7.04172i	−0.0727964	−	0.237376i
$881$	5.05615	−	8.75751i	0.170346	−	0.295048i	−0.768195	−	0.640216i	$-0.778845\pi$
$881$	5.05615	−	8.75751i	0.170346	−	0.295048i	0.938541	+	0.345168i	$0.112178\pi$
$882$	21.0555	−	43.9563i	0.708974	−	1.48009i
$883$	5.68611	−	3.28288i	0.191353	−	0.110478i	−0.401263	−	0.915963i	$-0.631429\pi$
$883$	5.68611	−	3.28288i	0.191353	−	0.110478i	0.592616	+	0.805485i	$0.298095\pi$
$884$	−10.8512	+	29.8134i	−0.364965	+	1.00273i
$885$	41.9074	+	15.5953i	1.40870	+	0.524232i
$886$	−17.6749	−	14.8310i	−0.593799	−	0.498257i
$887$	−3.35112	+	3.99371i	−0.112520	+	0.134096i	−0.819364	−	0.573273i	$-0.805673\pi$
$887$	−3.35112	+	3.99371i	−0.112520	+	0.134096i	0.706845	+	0.707369i	$0.250118\pi$
$888$	25.4128	+	61.2352i	0.852797	+	2.05492i
$889$	39.4109	+	33.4654i	1.32180	+	1.12239i
$890$	40.3852	+	17.1016i	1.35372	+	0.573245i
$891$	32.5627	−	27.4732i	1.09089	−	0.920386i
$892$	13.1678	+	22.8073i	0.440890	+	0.763644i
$893$	−23.2797	−	8.47313i	−0.779026	−	0.283542i
$894$	−73.9666	−	9.68721i	−2.47381	−	0.323989i
$895$	18.4722	+	11.9734i	0.617456	+	0.400227i
$896$	0.303457	−	51.7443i	0.0101378	−	1.72866i
$897$	−3.17329	+	6.10586i	−0.105953	+	0.203869i
$898$	−16.6024	+	45.6146i	−0.554028	+	1.52218i
$899$	−0.0186364	+	0.0322792i	−0.000621558	+	0.00107657i
$900$	−26.0297	+	43.6232i	−0.867658	+	1.45411i
$901$	−11.9999	+	6.92814i	−0.399774	+	0.230810i
$902$	18.0217	−	49.5142i	0.600057	−	1.64864i
$903$	1.58354	+	1.22821i	0.0526969	+	0.0408721i
$904$	17.0786	+	14.3306i	0.568026	+	0.476630i
$905$	−1.34435	+	26.0806i	−0.0446876	+	0.866948i
$906$	35.8016	+	11.2617i	1.18943	+	0.374145i
$907$	−24.9615	+	4.40138i	−0.828832	+	0.146146i	−0.571941	−	0.820295i	$-0.693809\pi$
$907$	−24.9615	+	4.40138i	−0.828832	+	0.146146i	−0.256891	+	0.966440i	$0.582698\pi$
$908$	−81.3749	+	46.9818i	−2.70052	+	1.55915i
$909$	27.2047	+	18.9944i	0.902324	+	0.630004i
$910$	−30.2492	+	32.1146i	−1.00275	+	1.06459i
$911$	13.0656	−	2.30382i	0.432882	−	0.0763288i	0.0470388	−	0.998893i	$-0.485022\pi$
$911$	13.0656	−	2.30382i	0.432882	−	0.0763288i	0.385844	+	0.922564i	$0.373910\pi$
$912$	0.385327	+	8.69110i	0.0127594	+	0.287791i
$913$	40.0709	+	33.6235i	1.32615	+	1.11277i
$914$	−2.81561	−	7.73583i	−0.0931321	−	0.255878i
$915$	0.180717	−	25.1217i	0.00597431	−	0.830497i
$916$	−31.1965	−	37.1785i	−1.03076	−	1.22841i
$917$	−1.44065	+	3.88708i	−0.0475746	+	0.128363i
$918$	7.54119	−	34.3444i	0.248897	−	1.13353i
$919$	−9.36009	+	16.2122i	−0.308761	+	0.534790i	−0.978092	−	0.208175i	$-0.933248\pi$
$919$	−9.36009	+	16.2122i	−0.308761	+	0.534790i	0.669331	+	0.742965i	$0.266581\pi$
$920$	−6.51255	−	6.06259i	−0.214712	−	0.199878i
$921$	−7.66935	+	3.18280i	−0.252714	+	0.104877i
$922$	−15.3296	−	12.8631i	−0.504854	−	0.423622i
$923$	−9.52689	−	26.1749i	−0.313582	−	0.861558i
$924$	15.5282	+	71.8053i	0.510841	+	2.36222i
$925$	−48.1736	−	34.8738i	−1.58394	−	1.14664i
$926$			58.1420i			1.91066i
$927$	5.17826	−	0.460069i	0.170076	−	0.0151106i
$928$		−	31.6370i		−	1.03854i
$929$	−16.0235	+	13.4453i	−0.525713	+	0.441126i	−0.866618	−	0.498972i	$-0.833711\pi$
$929$	−16.0235	+	13.4453i	−0.525713	+	0.441126i	0.340905	+	0.940098i	$0.389267\pi$
$930$	−0.0331002	+	0.0388759i	−0.00108540	+	0.00127479i
$931$	32.0228	+	39.0853i	1.04951	+	1.28097i
$932$	19.5462	+	16.4012i	0.640256	+	0.537239i
$933$	34.9399	−	32.0598i	1.14388	−	1.04959i
$934$	−47.7457	+	8.41886i	−1.56229	+	0.275473i
$935$	−28.4197	−	12.0346i	−0.929423	−	0.393574i
$936$	30.8988	−	2.74524i	1.00996	−	0.0897308i
$937$	12.2889	+	21.2850i	0.401460	+	0.695349i	0.993902	−	0.110264i	$-0.0351695\pi$
$937$	12.2889	+	21.2850i	0.401460	+	0.695349i	−0.592442	+	0.805613i	$0.701836\pi$
$938$	−68.6725	+	24.5396i	−2.24224	+	0.801247i
$939$	22.4166	−	0.993859i	0.731540	−	0.0324334i
$940$	−21.8090	−	14.1363i	−0.711332	−	0.461076i
$941$	−23.9426	+	8.71438i	−0.780505	+	0.284081i	−0.701383	−	0.712784i	$-0.747434\pi$
$941$	−23.9426	+	8.71438i	−0.780505	+	0.284081i	−0.0791220	+	0.996865i	$0.525212\pi$
$942$	−72.0333	+	29.8940i	−2.34697	+	0.974000i
$943$	−1.02975	−	5.84002i	−0.0335334	−	0.190177i
$944$	8.03364			0.261473
$945$	17.9259	−	24.9732i	0.583130	−	0.812379i
$946$	−4.80461			−0.156211
$947$	−5.69981	−	32.3252i	−0.185219	−	1.05043i	−0.925674	−	0.378323i	$-0.876501\pi$
$947$	−5.69981	−	32.3252i	−0.185219	−	1.05043i	0.740455	−	0.672106i	$-0.234610\pi$
$948$	8.42719	−	64.3457i	0.273703	−	2.08985i
$949$	0.757118	−	0.275568i	0.0245771	−	0.00894532i
$950$	−46.9603	−	69.3640i	−1.52359	−	2.25047i
$951$	−11.8626	−	18.5930i	−0.384673	−	0.602918i
$952$	18.9235	+	16.0687i	0.613314	+	0.520791i
$953$	−10.6122	−	18.3808i	−0.343762	−	0.595413i	0.641366	−	0.767235i	$-0.278368\pi$
$953$	−10.6122	−	18.3808i	−0.343762	−	0.595413i	−0.985128	+	0.171822i	$0.945035\pi$
$954$	27.1305	+	18.9425i	0.878381	+	0.613287i
$955$	1.00680	−	2.37756i	0.0325794	−	0.0769360i
$956$	−51.9498	+	9.16015i	−1.68018	+	0.296260i
$957$	11.6802	+	52.5186i	0.377567	+	1.69768i
$958$	36.7368	+	30.8258i	1.18691	+	0.995936i
$959$	0.0494072	−	8.42473i	0.00159544	−	0.272049i
$960$	8.80653	−	47.9257i	0.284229	−	1.54680i
$961$	23.7474	−	19.9264i	0.766044	−	0.642787i
$962$			88.6989i			2.85977i
$963$	−0.584610	−	0.155802i	−0.0188388	−	0.00502065i
$964$		−	2.71068i		−	0.0873052i
$965$	−34.2545	−	7.87726i	−1.10269	−	0.253578i
$966$	8.83408	+	9.74176i	0.284232	+	0.313436i
$967$	3.59244	+	9.87013i	0.115525	+	0.317402i	0.983957	−	0.178406i	$-0.0570941\pi$
$967$	3.59244	+	9.87013i	0.115525	+	0.317402i	−0.868432	+	0.495808i	$0.834872\pi$
$968$	−28.1253	−	23.5999i	−0.903980	−	0.758530i
$969$	28.9355	+	22.1720i	0.929541	+	0.712268i
$970$	−18.4050	−	17.1334i	−0.590948	−	0.550119i
$971$	−0.699752	+	1.21201i	−0.0224561	+	0.0388951i	−0.877035	−	0.480426i	$-0.840482\pi$
$971$	−0.699752	+	1.21201i	−0.0224561	+	0.0388951i	0.854579	+	0.519321i	$0.173815\pi$
$972$	−51.5016	+	11.5997i	−1.65192	+	0.372061i
$973$	−2.68164	−	15.7478i	−0.0859693	−	0.504852i
$974$	40.0988	+	47.7879i	1.28485	+	1.53122i
$975$	−22.3285	+	16.6050i	−0.715084	+	0.531787i
$976$	−1.54372	−	4.24134i	−0.0494134	−	0.135762i
$977$	−44.1438	−	37.0411i	−1.41229	−	1.18505i	−0.955323	−	0.295563i	$-0.904493\pi$
$977$	−44.1438	−	37.0411i	−1.41229	−	1.18505i	−0.456962	−	0.889486i	$-0.651063\pi$
$978$	−54.1063	+	34.5207i	−1.73013	+	1.10385i
$979$	39.3963	−	6.94664i	1.25911	−	0.222015i
$980$	23.5506	+	47.4898i	0.752297	+	1.51701i
$981$	2.98926	−	2.99732i	0.0954396	−	0.0956971i
$982$	−57.6364	+	33.2764i	−1.83925	+	1.06189i
$983$	−20.1881	+	3.55970i	−0.643899	+	0.113537i	−0.486056	−	0.873928i	$-0.661565\pi$
$983$	−20.1881	+	3.55970i	−0.643899	+	0.113537i	−0.157843	+	0.987464i	$0.550454\pi$
$984$	−19.6974	+	18.0737i	−0.627929	+	0.576170i
$985$	50.8191	+	2.61951i	1.61923	+	0.0834646i
$986$	34.0157	+	28.5426i	1.08328	+	0.908982i
$987$	12.4277	+	9.63904i	0.395579	+	0.306814i
$988$	−26.8641	+	73.8086i	−0.854662	+	2.34817i
$989$	−0.468282	+	0.270363i	−0.0148905	+	0.00859703i
$990$	2.73464	+	73.6500i	0.0869126	+	2.34075i
$991$	16.8793	−	29.2358i	0.536189	−	0.928707i	−0.462916	−	0.886402i	$-0.653197\pi$
$991$	16.8793	−	29.2358i	0.536189	−	0.928707i	0.999105	−	0.0423043i	$-0.0134699\pi$
$992$	0.00936665	−	0.0257347i	0.000297391	−	0.000817076i
$993$	−21.9692	−	34.4335i	−0.697171	−	1.09271i
$994$	−53.2326	−	0.312185i	−1.68843	−	0.00990190i
$995$	−16.7041	−	10.8274i	−0.529555	−	0.343250i
$996$	−24.8448	−	59.8666i	−0.787237	−	1.89694i
$997$	7.46228	+	2.71605i	0.236333	+	0.0860181i	0.457472	−	0.889224i	$-0.348755\pi$
$997$	7.46228	+	2.71605i	0.236333	+	0.0860181i	−0.221139	+	0.975242i	$0.570977\pi$
$998$	31.8480	+	55.1624i	1.00813	+	1.74613i
$999$	−8.19093	−	61.2596i	−0.259150	−	1.93817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cl.a.194.124	yes	840
5.4	even	2	inner	945.2.cl.a.194.17	✓	840
7.3	odd	6		945.2.cq.a.59.17	yes	840
27.11	odd	18		945.2.cq.a.929.124	yes	840
35.24	odd	6		945.2.cq.a.59.124	yes	840
135.119	odd	18		945.2.cq.a.929.17	yes	840
189.38	even	18	inner	945.2.cl.a.794.17	yes	840
945.794	even	18	inner	945.2.cl.a.794.124	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cl.a.194.17	✓	840	5.4	even	2	inner
945.2.cl.a.194.124	yes	840	1.1	even	1	trivial
945.2.cl.a.794.17	yes	840	189.38	even	18	inner
945.2.cl.a.794.124	yes	840	945.794	even	18	inner
945.2.cq.a.59.17	yes	840	7.3	odd	6
945.2.cq.a.59.124	yes	840	35.24	odd	6
945.2.cq.a.929.17	yes	840	135.119	odd	18
945.2.cq.a.929.124	yes	840	27.11	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cl (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.403021 + 2.28564i) q^{2} +(-1.37484 - 1.05348i) q^{3} +(-3.18236 + 1.15828i) q^{4} +(-1.21624 + 1.87637i) q^{5} +(1.85379 - 3.56696i) q^{6} +(-0.890305 - 2.49146i) q^{7} +(-1.60908 - 2.78700i) q^{8} +(0.780360 + 2.89673i) q^{9} +O(q^{10})\)	\(q+(0.403021 + 2.28564i) q^{2} +(-1.37484 - 1.05348i) q^{3} +(-3.18236 + 1.15828i) q^{4} +(-1.21624 + 1.87637i) q^{5} +(1.85379 - 3.56696i) q^{6} +(-0.890305 - 2.49146i) q^{7} +(-1.60908 - 2.78700i) q^{8} +(0.780360 + 2.89673i) q^{9} +(-4.77888 - 2.02367i) q^{10} +(-4.66187 + 0.822013i) q^{11} +(5.59545 + 1.76010i) q^{12} +(2.46136 + 2.06532i) q^{13} +(5.33577 - 3.03903i) q^{14} +(3.64885 - 1.29842i) q^{15} +(0.533037 - 0.447271i) q^{16} -2.91569i q^{17} +(-6.30639 + 2.95107i) q^{18} -7.21834i q^{19} +(1.69713 - 7.38003i) q^{20} +(-1.40068 + 4.36327i) q^{21} +(-3.75766 - 10.3241i) q^{22} +(-0.947193 - 0.794789i) q^{23} +(-0.723831 + 5.52680i) q^{24} +(-2.04153 - 4.56422i) q^{25} +(-3.72862 + 6.45816i) q^{26} +(1.97878 - 4.80463i) q^{27} +(5.71908 + 6.89748i) q^{28} +(4.21789 + 5.02668i) q^{29} +(4.43830 + 7.81668i) q^{30} +(0.00194275 + 0.00533765i) q^{31} +(-3.69337 - 3.09910i) q^{32} +(7.27529 + 3.78105i) q^{33} +(6.66423 - 1.17508i) q^{34} +(5.75772 + 1.35966i) q^{35} +(-5.83862 - 8.31455i) q^{36} +(10.3008 - 5.94717i) q^{37} +(16.4986 - 2.90914i) q^{38} +(-1.20819 - 5.43248i) q^{39} +(7.18646 + 0.370432i) q^{40} +(3.67394 + 3.08281i) q^{41} +(-10.5374 - 1.44296i) q^{42} +(0.149570 - 0.410940i) q^{43} +(13.8836 - 8.01570i) q^{44} +(-6.38444 - 2.05887i) q^{45} +(1.43487 - 2.48526i) q^{46} +(1.17383 - 3.22508i) q^{47} +(-1.20403 + 0.0533816i) q^{48} +(-5.41472 + 4.43631i) q^{49} +(9.60941 - 6.50569i) q^{50} +(-3.07162 + 4.00860i) q^{51} +(-10.2252 - 3.72165i) q^{52} +(-2.37616 - 4.11562i) q^{53} +(11.7792 + 2.58642i) q^{54} +(4.12754 - 9.74715i) q^{55} +(-5.51112 + 6.49022i) q^{56} +(-7.60438 + 9.92405i) q^{57} +(-9.78931 + 11.6664i) q^{58} +(8.84429 + 7.42124i) q^{59} +(-10.1080 + 8.35845i) q^{60} +(2.21853 - 6.09537i) q^{61} +(-0.0114170 + 0.00659161i) q^{62} +(6.52232 - 4.52320i) q^{63} +(6.29077 - 10.8959i) q^{64} +(-6.86891 + 2.10649i) q^{65} +(-5.71004 + 18.1526i) q^{66} +(-11.6956 - 2.06225i) q^{67} +(3.37720 + 9.27877i) q^{68} +(0.464942 + 2.09056i) q^{69} +(-0.787223 + 13.7081i) q^{70} +(-7.50774 - 4.33460i) q^{71} +(6.81753 - 6.83592i) q^{72} +(0.125380 - 0.217164i) q^{73} +(17.7445 + 21.1471i) q^{74} +(-2.00154 + 8.42578i) q^{75} +(8.36088 + 22.9713i) q^{76} +(6.19849 + 10.8830i) q^{77} +(11.9298 - 4.95090i) q^{78} +(-1.92114 - 10.8953i) q^{79} +(0.190947 + 1.54416i) q^{80} +(-7.78208 + 4.52098i) q^{81} +(-5.56552 + 9.63976i) q^{82} +(-7.10287 - 8.46487i) q^{83} +(-0.596451 - 15.5079i) q^{84} +(5.47092 + 3.54617i) q^{85} +(0.999541 + 0.176246i) q^{86} +(-0.503403 - 11.3543i) q^{87} +(9.79224 + 11.6699i) q^{88} -8.45076 q^{89} +(2.13277 - 15.4223i) q^{90} +(2.95431 - 7.97114i) q^{91} +(3.93490 + 1.43219i) q^{92} +(0.00295215 - 0.00938505i) q^{93} +(7.84446 + 1.38319i) q^{94} +(13.5443 + 8.77922i) q^{95} +(1.81294 + 8.15165i) q^{96} +(4.55306 + 1.65718i) q^{97} +(-12.3221 - 10.5882i) q^{98} +(-6.01908 - 12.8627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 6 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) \) 840 * q - 6 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	\( 840 q - 6 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 12 q^{11} - 6 q^{14} - 18 q^{16} - 18 q^{20} - 30 q^{21} - 18 q^{24} - 3 q^{25} - 42 q^{29} - 21 q^{30} - 18 q^{31} + 36 q^{34} + 18 q^{35} - 42 q^{36} + 72 q^{39} + 36 q^{40} - 18 q^{44} - 9 q^{45} + 6 q^{46} + 6 q^{49} - 48 q^{50} + 66 q^{51} - 144 q^{54} + 12 q^{56} - 18 q^{59} - 87 q^{60} - 18 q^{61} - 348 q^{64} - 9 q^{65} - 18 q^{66} - 60 q^{70} - 36 q^{71} - 30 q^{74} - 54 q^{75} + 72 q^{76} + 12 q^{79} - 72 q^{80} + 72 q^{81} - 264 q^{84} + 3 q^{85} - 174 q^{86} - 36 q^{89} + 81 q^{90} - 6 q^{91} - 18 q^{94} + 69 q^{95} + 126 q^{96} - 60 q^{99}+O(q^{100}) \) 840 * q - 6 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 12 * q^11 - 6 * q^14 - 18 * q^16 - 18 * q^20 - 30 * q^21 - 18 * q^24 - 3 * q^25 - 42 * q^29 - 21 * q^30 - 18 * q^31 + 36 * q^34 + 18 * q^35 - 42 * q^36 + 72 * q^39 + 36 * q^40 - 18 * q^44 - 9 * q^45 + 6 * q^46 + 6 * q^49 - 48 * q^50 + 66 * q^51 - 144 * q^54 + 12 * q^56 - 18 * q^59 - 87 * q^60 - 18 * q^61 - 348 * q^64 - 9 * q^65 - 18 * q^66 - 60 * q^70 - 36 * q^71 - 30 * q^74 - 54 * q^75 + 72 * q^76 + 12 * q^79 - 72 * q^80 + 72 * q^81 - 264 * q^84 + 3 * q^85 - 174 * q^86 - 36 * q^89 + 81 * q^90 - 6 * q^91 - 18 * q^94 + 69 * q^95 + 126 * q^96 - 60 * q^99

Introduction

L-functions

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