LMFDB - Embedded newform 117.3.n.a.38.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.15
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.245962 - 0.426018i) q^{2} +(-2.80287 - 1.06954i) q^{3} +(1.87901 + 3.25453i) q^{4} +(-1.35391 - 2.34503i) q^{5} +(-1.14504 + 0.931009i) q^{6} +(8.51494 + 4.91611i) q^{7} +3.81635 q^{8} +(6.71217 + 5.99556i) q^{9} -1.33204 q^{10} +(7.77093 - 13.4596i) q^{11} +(-1.78576 - 11.1317i) q^{12} +(8.94077 - 9.43730i) q^{13} +(4.18870 - 2.41835i) q^{14} +(1.28672 + 8.02089i) q^{15} +(-6.57735 + 11.3923i) q^{16} +22.4699i q^{17} +(4.20516 - 1.38483i) q^{18} +10.5454i q^{19} +(5.08800 - 8.81267i) q^{20} +(-18.6083 - 22.8863i) q^{21} +(-3.82270 - 6.62112i) q^{22} +(2.18641 - 1.26233i) q^{23} +(-10.6967 - 4.08173i) q^{24} +(8.83387 - 15.3007i) q^{25} +(-1.82137 - 6.13015i) q^{26} +(-12.4009 - 23.9837i) q^{27} +36.9496i q^{28} +(2.12707 + 1.22806i) q^{29} +(3.73353 + 1.42467i) q^{30} +(-32.9508 + 19.0241i) q^{31} +(10.8683 + 18.8244i) q^{32} +(-36.1765 + 29.4143i) q^{33} +(9.57260 + 5.52674i) q^{34} -26.6238i q^{35} +(-6.90053 + 33.1107i) q^{36} -10.3786i q^{37} +(4.49252 + 2.59376i) q^{38} +(-35.1534 + 16.8890i) q^{39} +(-5.16698 - 8.94947i) q^{40} +(-36.5879 - 63.3720i) q^{41} +(-14.3269 + 2.29834i) q^{42} +(-22.9633 + 39.7736i) q^{43} +58.4065 q^{44} +(4.97214 - 23.8577i) q^{45} -1.24194i q^{46} +(-13.6798 + 23.6942i) q^{47} +(30.6200 - 24.8964i) q^{48} +(23.8362 + 41.2855i) q^{49} +(-4.34559 - 7.52679i) q^{50} +(24.0324 - 62.9803i) q^{51} +(47.5138 + 11.3653i) q^{52} -0.0370030i q^{53} +(-13.2676 - 0.616076i) q^{54} -42.0844 q^{55} +(32.4960 + 18.7616i) q^{56} +(11.2787 - 29.5573i) q^{57} +(1.04636 - 0.604114i) q^{58} +(-32.9332 - 57.0420i) q^{59} +(-23.6865 + 19.2590i) q^{60} +(40.6820 - 70.4633i) q^{61} +18.7168i q^{62} +(27.6790 + 84.0496i) q^{63} -41.9261 q^{64} +(-34.2358 - 8.18920i) q^{65} +(3.63301 + 22.6467i) q^{66} +(56.2009 - 32.4476i) q^{67} +(-73.1291 + 42.2211i) q^{68} +(-7.47835 + 1.19968i) q^{69} +(-11.3422 - 6.54843i) q^{70} +29.5878 q^{71} +(25.6160 + 22.8811i) q^{72} -28.3208i q^{73} +(-4.42149 - 2.55275i) q^{74} +(-41.1249 + 33.4378i) q^{75} +(-34.3203 + 19.8148i) q^{76} +(132.338 - 76.4054i) q^{77} +(-1.45136 + 19.1300i) q^{78} +(-36.3943 + 63.0368i) q^{79} +35.6204 q^{80} +(9.10655 + 80.4865i) q^{81} -35.9969 q^{82} +(-71.9367 + 124.598i) q^{83} +(39.5190 - 103.565i) q^{84} +(52.6927 - 30.4222i) q^{85} +(11.2962 + 19.5656i) q^{86} +(-4.64844 - 5.71709i) q^{87} +(29.6566 - 51.3667i) q^{88} +80.5846 q^{89} +(-8.94086 - 7.98631i) q^{90} +(122.525 - 36.4043i) q^{91} +(8.21657 + 4.74384i) q^{92} +(112.704 - 18.0801i) q^{93} +(6.72944 + 11.6557i) q^{94} +(24.7293 - 14.2775i) q^{95} +(-10.3289 - 64.3863i) q^{96} +(-97.7027 - 56.4087i) q^{97} +23.4512 q^{98} +(132.858 - 43.7524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.245962	−	0.426018i	0.122981	−	0.213009i	−0.797961	−	0.602709i	$-0.794088\pi$
$2$	0.245962	−	0.426018i	0.122981	−	0.213009i	0.920942	+	0.389700i	$0.127421\pi$
$3$	−2.80287	−	1.06954i	−0.934290	−	0.356513i
$3$	−2.80287	−	1.06954i	−0.934290	−	0.356513i
$4$	1.87901	+	3.25453i	0.469751	+	0.813633i
$5$	−1.35391	−	2.34503i	−0.270781	−	0.469007i	0.698281	−	0.715824i	$-0.253949\pi$
$5$	−1.35391	−	2.34503i	−0.270781	−	0.469007i	−0.969062	+	0.246817i	$0.920615\pi$
$6$	−1.14504	+	0.931009i	−0.190840	+	0.155168i
$7$	8.51494	+	4.91611i	1.21642	+	0.702301i	0.964150	−	0.265356i	$-0.0854895\pi$
$7$	8.51494	+	4.91611i	1.21642	+	0.702301i	0.252270	+	0.967657i	$0.418823\pi$
$8$	3.81635			0.477044
$9$	6.71217	+	5.99556i	0.745797	+	0.666173i
$10$	−1.33204			−0.133204
$11$	7.77093	−	13.4596i	0.706448	−	1.22360i	−0.259718	−	0.965684i	$-0.583630\pi$
$11$	7.77093	−	13.4596i	0.706448	−	1.22360i	0.966166	−	0.257920i	$-0.0830370\pi$
$12$	−1.78576	−	11.1317i	−0.148813	−	0.927642i
$13$	8.94077	−	9.43730i	0.687752	−	0.725946i
$13$	8.94077	−	9.43730i	0.687752	−	0.725946i
$14$	4.18870	−	2.41835i	0.299193	−	0.172739i
$15$	1.28672	+	8.02089i	0.0857813	+	0.534726i
$16$	−6.57735	+	11.3923i	−0.411084	+	0.712019i
$17$			22.4699i			1.32176i	0.750492	+	0.660880i	$0.229817\pi$
$17$			22.4699i			1.32176i	−0.750492	+	0.660880i	$0.770183\pi$
$18$	4.20516	−	1.38483i	0.233620	−	0.0769350i
$19$			10.5454i			0.555020i	0.960723	+	0.277510i	$0.0895091\pi$
$19$			10.5454i			0.555020i	−0.960723	+	0.277510i	$0.910491\pi$
$20$	5.08800	−	8.81267i	0.254400	−	0.440633i
$21$	−18.6083	−	22.8863i	−0.886111	−	1.08982i
$22$	−3.82270	−	6.62112i	−0.173759	−	0.300960i
$23$	2.18641	−	1.26233i	0.0950615	−	0.0548838i	−0.451716	−	0.892162i	$-0.649188\pi$
$23$	2.18641	−	1.26233i	0.0950615	−	0.0548838i	0.546777	+	0.837278i	$0.315854\pi$
$24$	−10.6967	−	4.08173i	−0.445697	−	0.170072i
$25$	8.83387	−	15.3007i	0.353355	−	0.612029i
$26$	−1.82137	−	6.13015i	−0.0700528	−	0.235775i
$27$	−12.4009	−	23.9837i	−0.459292	−	0.888286i
$28$			36.9496i			1.31963i
$29$	2.12707	+	1.22806i	0.0733472	+	0.0423470i	0.536225	−	0.844075i	$-0.319850\pi$
$29$	2.12707	+	1.22806i	0.0733472	+	0.0423470i	−0.462878	+	0.886422i	$0.653183\pi$
$30$	3.73353	+	1.42467i	0.124451	+	0.0474888i
$31$	−32.9508	+	19.0241i	−1.06293	+	0.613682i	−0.926241	−	0.376933i	$-0.876979\pi$
$31$	−32.9508	+	19.0241i	−1.06293	+	0.613682i	−0.136687	+	0.990614i	$0.543646\pi$
$32$	10.8683	+	18.8244i	0.339633	+	0.588261i
$33$	−36.1765	+	29.4143i	−1.09626	+	0.891344i
$34$	9.57260	+	5.52674i	0.281547	+	0.162551i
$35$		−	26.6238i		−	0.760680i
$36$	−6.90053	+	33.1107i	−0.191681	+	0.919741i
$37$		−	10.3786i		−	0.280504i	−0.990116	−	0.140252i	$-0.955209\pi$
$37$		−	10.3786i		−	0.280504i	0.990116	−	0.140252i	$-0.0447912\pi$
$38$	4.49252	+	2.59376i	0.118224	+	0.0682568i
$39$	−35.1534	+	16.8890i	−0.901369	+	0.433052i
$40$	−5.16698	−	8.94947i	−0.129174	−	0.223737i
$41$	−36.5879	−	63.3720i	−0.892387	−	1.54566i	−0.837006	−	0.547194i	$-0.815696\pi$
$41$	−36.5879	−	63.3720i	−0.892387	−	1.54566i	−0.0553805	−	0.998465i	$-0.517637\pi$
$42$	−14.3269	+	2.29834i	−0.341117	+	0.0547224i
$43$	−22.9633	+	39.7736i	−0.534030	+	0.924967i	0.465180	+	0.885216i	$0.345990\pi$
$43$	−22.9633	+	39.7736i	−0.534030	+	0.924967i	−0.999210	+	0.0397508i	$0.987344\pi$
$44$	58.4065			1.32742
$45$	4.97214	−	23.8577i	0.110492	−	0.530171i
$46$		−	1.24194i		−	0.0269986i
$47$	−13.6798	+	23.6942i	−0.291060	+	0.504132i	−0.974061	−	0.226287i	$-0.927341\pi$
$47$	−13.6798	+	23.6942i	−0.291060	+	0.504132i	0.683000	+	0.730418i	$0.260675\pi$
$48$	30.6200	−	24.8964i	0.637916	−	0.518675i
$49$	23.8362	+	41.2855i	0.486453	+	0.842561i
$50$	−4.34559	−	7.52679i	−0.0869118	−	0.150536i
$51$	24.0324	−	62.9803i	0.471224	−	1.23491i
$52$	47.5138	+	11.3653i	0.913726	+	0.218564i
$53$		−	0.0370030i		−	0.000698170i	−1.00000		0.000349085i	$-0.999889\pi$
$53$		−	0.0370030i		−	0.000698170i	1.00000		0.000349085i	$-0.000111117\pi$
$54$	−13.2676	−	0.616076i	−0.245697	−	0.0114088i
$55$	−42.0844			−0.765172
$56$	32.4960	+	18.7616i	0.580286	+	0.335028i
$57$	11.2787	−	29.5573i	0.197872	−	0.518550i
$58$	1.04636	−	0.604114i	0.0180406	−	0.0104158i
$59$	−32.9332	−	57.0420i	−0.558190	−	0.966814i	−0.997648	−	0.0685502i	$-0.978163\pi$
$59$	−32.9332	−	57.0420i	−0.558190	−	0.966814i	0.439458	−	0.898263i	$-0.355171\pi$
$60$	−23.6865	+	19.2590i	−0.394775	+	0.320983i
$61$	40.6820	−	70.4633i	0.666918	−	1.15514i	−0.311843	−	0.950134i	$-0.600946\pi$
$61$	40.6820	−	70.4633i	0.666918	−	1.15514i	0.978761	−	0.205003i	$-0.0657204\pi$
$62$			18.7168i			0.301885i
$63$	27.6790	+	84.0496i	0.439349	+	1.33412i
$64$	−41.9261			−0.655095
$65$	−34.2358	−	8.18920i	−0.526704	−	0.125988i
$66$	3.63301	+	22.6467i	0.0550455	+	0.343131i
$67$	56.2009	−	32.4476i	0.838819	−	0.484293i	−0.0180434	−	0.999837i	$-0.505744\pi$
$67$	56.2009	−	32.4476i	0.838819	−	0.484293i	0.856863	+	0.515545i	$0.172410\pi$
$68$	−73.1291	+	42.2211i	−1.07543	+	0.620899i
$69$	−7.47835	+	1.19968i	−0.108382	+	0.0173867i
$70$	−11.3422	−	6.54843i	−0.162032	−	0.0935491i
$71$	29.5878			0.416730			0.208365	−	0.978051i	$-0.433186\pi$
$71$	29.5878			0.416730			0.208365	+	0.978051i	$0.433186\pi$
$72$	25.6160	+	22.8811i	0.355778	+	0.317794i
$73$		−	28.3208i		−	0.387956i	−0.981006	−	0.193978i	$-0.937861\pi$
$73$		−	28.3208i		−	0.387956i	0.981006	−	0.193978i	$-0.0621390\pi$
$74$	−4.42149	−	2.55275i	−0.0597498	−	0.0344966i
$75$	−41.1249	+	33.4378i	−0.548332	+	0.445837i
$76$	−34.3203	+	19.8148i	−0.451583	+	0.260721i
$77$	132.338	−	76.4054i	1.71868	−	0.992278i
$78$	−1.45136	+	19.1300i	−0.0186071	+	0.245257i
$79$	−36.3943	+	63.0368i	−0.460688	+	0.797935i	−0.998995	−	0.0448138i	$-0.985731\pi$
$79$	−36.3943	+	63.0368i	−0.460688	+	0.797935i	0.538308	+	0.842748i	$0.319064\pi$
$80$	35.6204			0.445256
$81$	9.10655	+	80.4865i	0.112427	+	0.993660i
$82$	−35.9969			−0.438986
$83$	−71.9367	+	124.598i	−0.866708	+	1.50118i	−0.00136586	+	0.999999i	$0.500435\pi$
$83$	−71.9367	+	124.598i	−0.866708	+	1.50118i	−0.865342	+	0.501182i	$0.832899\pi$
$84$	39.5190	−	103.565i	0.470464	−	1.23291i
$85$	52.6927	−	30.4222i	0.619915	−	0.357908i
$86$	11.2962	+	19.5656i	0.131351	+	0.227507i
$87$	−4.64844	−	5.71709i	−0.0534304	−	0.0657137i
$88$	29.6566	−	51.3667i	0.337007	−	0.583713i
$89$	80.5846			0.905445			0.452722	−	0.891652i	$-0.350453\pi$
$89$	80.5846			0.905445			0.452722	+	0.891652i	$0.350453\pi$
$90$	−8.94086	−	7.98631i	−0.0993429	−	0.0887367i
$91$	122.525	−	36.4043i	1.34643	−	0.400047i
$92$	8.21657	+	4.74384i	0.0893105	+	0.0515635i
$93$	112.704	−	18.0801i	1.21187	−	0.194409i
$94$	6.72944	+	11.6557i	0.0715898	+	0.123997i
$95$	24.7293	−	14.2775i	0.260308	−	0.150289i
$96$	−10.3289	−	64.3863i	−0.107593	−	0.670690i
$97$	−97.7027	−	56.4087i	−1.00724	−	0.581533i	−0.0968606	−	0.995298i	$-0.530880\pi$
$97$	−97.7027	−	56.4087i	−1.00724	−	0.581533i	−0.910384	+	0.413765i	$0.864213\pi$
$98$	23.4512			0.239298
$99$	132.858	−	43.7524i	1.34200	−	0.441944i
$100$	66.3956			0.663956
$101$	−171.233	−	98.8613i	−1.69538	−	0.978825i	−0.950036	−	0.312139i	$-0.898954\pi$
$101$	−171.233	−	98.8613i	−1.69538	−	0.978825i	−0.745339	−	0.666686i	$-0.767712\pi$
$102$	−20.9197	−	25.7290i	−0.205095	−	0.252245i
$103$	10.9095	+	18.8959i	0.105918	+	0.183455i	0.914113	−	0.405460i	$-0.132889\pi$
$103$	10.9095	+	18.8959i	0.105918	+	0.183455i	−0.808195	+	0.588915i	$0.799555\pi$
$104$	34.1211	−	36.0160i	0.328088	−	0.346308i
$105$	−28.4752	+	74.6230i	−0.271192	+	0.710696i
$106$	−0.0157640	−	0.00910133i	−0.000148717	−	8.58616e-5i
$107$			180.007i			1.68231i	0.540796	+	0.841154i	$0.318123\pi$
$107$			180.007i			1.68231i	−0.540796	+	0.841154i	$0.681877\pi$
$108$	54.7545	−	85.4246i	0.506986	−	0.790968i
$109$		−	117.078i		−	1.07411i	−0.843548	−	0.537055i	$-0.819537\pi$
$109$		−	117.078i		−	1.07411i	0.843548	−	0.537055i	$-0.180463\pi$
$110$	−10.3512	+	17.9287i	−0.0941015	+	0.162989i
$111$	−11.1003	+	29.0900i	−0.100003	+	0.262072i
$112$	−112.011	+	64.6699i	−1.00010	+	0.577409i
$113$	−59.6664	+	34.4484i	−0.528021	+	0.304853i	−0.740210	−	0.672375i	$-0.765274\pi$
$113$	−59.6664	+	34.4484i	−0.528021	+	0.304853i	0.212189	+	0.977229i	$0.431941\pi$
$114$	−9.81784	−	12.0749i	−0.0861214	−	0.105920i
$115$	−5.92040	−	3.41815i	−0.0514818	−	0.0297230i
$116$			9.23016i			0.0795703i
$117$	116.594	−	9.73985i	0.996529	−	0.0832466i
$118$	−32.4013			−0.274587
$119$	−110.464	+	191.330i	−0.928273	+	1.60782i
$120$	4.91057	+	30.6105i	0.0409214	+	0.255087i
$121$	−60.2747	−	104.399i	−0.498138	−	0.862801i
$122$	−20.0124	−	34.6626i	−0.164036	−	0.284119i
$123$	34.7722	+	216.756i	0.282701	+	1.76224i
$124$	−123.829	−	71.4929i	−0.998624	−	0.576556i
$125$	−115.536			−0.924290
$126$	42.6146	+	8.88124i	0.338211	+	0.0704860i
$127$	70.8862			0.558159			0.279080	−	0.960268i	$-0.409971\pi$
$127$	70.8862			0.558159			0.279080	+	0.960268i	$0.409971\pi$
$128$	−53.7852	+	93.1587i	−0.420197	+	0.727803i
$129$	106.903	−	86.9201i	0.828702	−	0.673799i
$130$	−11.9094	+	12.5708i	−0.0916111	+	0.0966987i
$131$	−127.088	+	73.3745i	−0.970140	+	0.560111i	−0.899279	−	0.437376i	$-0.855908\pi$
$131$	−127.088	+	73.3745i	−0.970140	+	0.560111i	−0.0708610	+	0.997486i	$0.522575\pi$
$132$	−163.706	−	62.4680i	−1.24020	−	0.473242i
$133$	−51.8422	+	89.7933i	−0.389791	+	0.675137i
$134$		−	31.9235i		−	0.238235i
$135$	−39.4530	+	61.5522i	−0.292244	+	0.455942i
$136$			85.7531i			0.630537i
$137$	−34.9983	+	60.6188i	−0.255462	+	0.442473i	−0.965021	−	0.262173i	$-0.915561\pi$
$137$	−34.9983	+	60.6188i	−0.255462	+	0.442473i	0.709559	+	0.704646i	$0.248894\pi$
$138$	−1.32830	+	3.48099i	−0.00962536	+	0.0252246i
$139$	−76.5741	−	132.630i	−0.550892	−	0.954174i	−0.998210	−	0.0597988i	$-0.980954\pi$
$139$	−76.5741	−	132.630i	−0.550892	−	0.954174i	0.447318	−	0.894375i	$-0.352379\pi$
$140$	86.6480	−	50.0262i	0.618914	−	0.357330i
$141$	63.6847	−	51.7806i	0.451664	−	0.367238i
$142$	7.27747	−	12.6049i	0.0512498	−	0.0887672i
$143$	−57.5446	−	193.676i	−0.402410	−	1.35438i
$144$	−112.451	+	37.0322i	−0.780913	+	0.257168i
$145$		−	6.65074i		−	0.0458672i
$146$	−12.0652	−	6.96583i	−0.0826382	−	0.0477112i
$147$	−22.6533	−	141.212i	−0.154104	−	0.960623i
$148$	33.7776	−	19.5015i	0.228227	−	0.131767i
$149$	−16.2539	−	28.1526i	−0.109087	−	0.188944i	0.806314	−	0.591488i	$-0.201459\pi$
$149$	−16.2539	−	28.1526i	−0.109087	−	0.188944i	−0.915400	+	0.402544i	$0.868126\pi$
$150$	4.12994	+	25.7444i	0.0275330	+	0.171629i
$151$	29.5608	+	17.0670i	0.195767	+	0.113026i	0.594680	−	0.803963i	$-0.297279\pi$
$151$	29.5608	+	17.0670i	0.195767	+	0.113026i	−0.398912	+	0.916989i	$0.630612\pi$
$152$			40.2448i			0.264769i
$153$	−134.720	+	150.822i	−0.880521	+	0.985765i
$154$		−	75.1713i		−	0.488125i
$155$	89.2245	+	51.5138i	0.575642	+	0.332347i
$156$	−121.019	−	82.6733i	−0.775765	−	0.529957i
$157$	110.354	+	191.138i	0.702889	+	1.21744i	0.967448	+	0.253070i	$0.0814401\pi$
$157$	110.354	+	191.138i	0.702889	+	1.21744i	−0.264559	+	0.964369i	$0.585227\pi$
$158$	17.9032	+	31.0093i	0.113312	+	0.196261i
$159$	−0.0395762	+	0.103715i	−0.000248907	+	0.000652294i
$160$	29.4292	−	50.9728i	0.183932	−	0.318580i
$161$	24.8229			0.154180
$162$	36.5286	+	15.9170i	0.225485	+	0.0982533i
$163$			42.5714i			0.261174i	0.991437	+	0.130587i	$0.0416862\pi$
$163$			42.5714i			0.261174i	−0.991437	+	0.130587i	$0.958314\pi$
$164$	137.498	−	238.153i	0.838400	−	1.45215i
$165$	117.957	+	45.0110i	0.714893	+	0.272794i
$166$	35.3874	+	61.2927i	0.213177	+	0.369233i
$167$	−103.978	−	180.096i	−0.622624	−	1.07842i	−0.988995	−	0.147948i	$-0.952733\pi$
$167$	−103.978	−	180.096i	−0.622624	−	1.07842i	0.366371	−	0.930469i	$-0.380600\pi$
$168$	−71.0159	−	87.3420i	−0.422713	−	0.519893i
$169$	−9.12517	−	168.753i	−0.0539951	−	0.998541i
$170$		−	29.9308i		−	0.176063i
$171$	−63.2254	+	70.7824i	−0.369739	+	0.413932i
$172$	−172.593			−1.00345
$173$	47.0331	+	27.1546i	0.271867	+	0.156963i	0.629736	−	0.776809i	$-0.283163\pi$
$173$	47.0331	+	27.1546i	0.271867	+	0.156963i	−0.357869	+	0.933772i	$0.616496\pi$
$174$	−3.57892	+	0.574135i	−0.0205685	+	0.00329963i
$175$	150.440	−	86.8565i	0.859657	−	0.496323i
$176$	102.224	+	177.058i	0.580819	+	1.00601i
$177$	31.2989	+	195.105i	0.176830	+	1.10229i
$178$	19.8207	−	34.3305i	0.111352	−	0.192868i
$179$		−	82.5470i		−	0.461156i	−0.973054	−	0.230578i	$-0.925938\pi$
$179$		−	82.5470i		−	0.461156i	0.973054	−	0.230578i	$-0.0740617\pi$
$180$	86.9884	−	28.6468i	0.483269	−	0.159149i
$181$	166.981			0.922544			0.461272	−	0.887259i	$-0.347393\pi$
$181$	166.981			0.922544			0.461272	+	0.887259i	$0.347393\pi$
$182$	14.6276	−	61.1519i	0.0803712	−	0.336000i
$183$	−189.390	+	153.989i	−1.03492	+	0.841468i
$184$	8.34412	−	4.81748i	0.0453485	−	0.0261820i
$185$	−24.3383	+	14.0517i	−0.131558	+	0.0759551i
$186$	20.0184	−	52.4609i	0.107626	−	0.282048i
$187$	302.437	+	174.612i	1.61731	+	0.933755i
$188$	−102.818			−0.546904
$189$	12.3137	−	265.184i	0.0651517	−	1.40309i
$190$		−	14.0468i		−	0.0739307i
$191$	61.1253	+	35.2907i	0.320028	+	0.184768i	0.651405	−	0.758730i	$-0.274180\pi$
$191$	61.1253	+	35.2907i	0.320028	+	0.184768i	−0.331377	+	0.943498i	$0.607513\pi$
$192$	117.513	+	44.8416i	0.612049	+	0.233550i
$193$	−40.4093	+	23.3303i	−0.209375	+	0.120883i	−0.601021	−	0.799233i	$-0.705239\pi$
$193$	−40.4093	+	23.3303i	−0.209375	+	0.120883i	0.391646	+	0.920116i	$0.371906\pi$
$194$	−48.0623	+	27.7488i	−0.247744	+	0.143035i
$195$	87.1998	+	59.5698i	0.447178	+	0.305486i
$196$	−89.5766	+	155.151i	−0.457024	+	0.791588i
$197$	194.423			0.986919			0.493460	−	0.869769i	$-0.335732\pi$
$197$	194.423			0.986919			0.493460	+	0.869769i	$0.335732\pi$
$198$	14.0386	−	67.3613i	0.0709023	−	0.340209i
$199$	−22.2689			−0.111904			−0.0559520	−	0.998433i	$-0.517819\pi$
$199$	−22.2689			−0.111904			−0.0559520	+	0.998433i	$0.517819\pi$
$200$	33.7131	−	58.3929i	0.168566	−	0.291964i
$201$	−192.228	+	30.8374i	−0.956357	+	0.153420i
$202$	−84.2335	+	48.6322i	−0.416998	+	0.240754i
$203$	12.0746	+	20.9138i	0.0594807	+	0.103024i
$204$	250.129	−	40.1259i	1.22612	−	0.196696i
$205$	−99.0731	+	171.600i	−0.483283	+	0.837071i
$206$	10.7333			0.0521034
$207$	22.2440	+	4.63582i	0.107459	+	0.0223953i
$208$	48.7059	+	163.928i	0.234163	+	0.788117i
$209$	141.937	+	81.9474i	0.679125	+	0.392093i
$210$	24.7870	+	30.4854i	0.118033	+	0.145168i
$211$	−96.7627	−	167.598i	−0.458591	−	0.794303i	0.540296	−	0.841475i	$-0.318312\pi$
$211$	−96.7627	−	167.598i	−0.458591	−	0.794303i	−0.998887	+	0.0471724i	$0.984979\pi$
$212$	0.120428	−	0.0695289i	0.000568054	−	0.000327966i
$213$	−82.9308	−	31.6453i	−0.389347	−	0.148570i
$214$	76.6863	+	44.2748i	0.358347	+	0.206892i
$215$	124.361			0.578421
$216$	−47.3261	−	91.5302i	−0.219102	−	0.423751i
$217$	−374.099			−1.72396
$218$	−49.8773	−	28.7967i	−0.228795	−	0.132095i
$219$	−30.2902	+	79.3795i	−0.138311	+	0.362464i
$220$	−79.0769	−	136.965i	−0.359441	−	0.622569i
$221$	212.055	+	200.898i	0.959526	+	0.909043i
$222$	9.66260	+	11.8840i	0.0435252	+	0.0535314i
$223$	−198.753	−	114.750i	−0.891271	−	0.514575i	−0.0169128	−	0.999857i	$-0.505384\pi$
$223$	−198.753	−	114.750i	−0.891271	−	0.514575i	−0.874358	+	0.485282i	$0.838717\pi$
$224$			213.718i			0.954097i
$225$	151.031	−	49.7371i	0.671248	−	0.221054i
$226$			33.8920i			0.149964i
$227$	124.606	−	215.824i	0.548925	−	0.950766i	−0.449423	−	0.893319i	$-0.648371\pi$
$227$	124.606	−	215.824i	0.548925	−	0.950766i	0.998349	−	0.0574473i	$-0.0182961\pi$
$228$	117.388	−	18.8315i	0.514860	−	0.0825944i
$229$	46.3299	−	26.7486i	0.202314	−	0.116806i	−0.395420	−	0.918500i	$-0.629401\pi$
$229$	46.3299	−	26.7486i	0.202314	−	0.116806i	0.597734	+	0.801694i	$0.296068\pi$
$230$	−2.91239	+	1.68147i	−0.0126625	+	0.00731072i
$231$	−452.645	+	72.6139i	−1.95950	+	0.314346i
$232$	8.11764	+	4.68672i	0.0349898	+	0.0202014i
$233$		−	111.432i		−	0.478248i	−0.970989	−	0.239124i	$-0.923140\pi$
$233$		−	111.432i		−	0.478248i	0.970989	−	0.239124i	$-0.0768602\pi$
$234$	24.5283	−	52.0668i	0.104822	−	0.222508i
$235$	74.0849			0.315255
$236$	123.763	−	214.364i	0.524421	−	0.908324i
$237$	169.429	−	137.759i	0.714890	−	0.581262i
$238$	54.3401	+	94.1198i	0.228320	+	0.395461i
$239$	−117.640	−	203.758i	−0.492217	−	0.852545i	0.507743	−	0.861509i	$-0.330480\pi$
$239$	−117.640	−	203.758i	−0.492217	−	0.852545i	−0.999960	+	0.00896368i	$0.997147\pi$
$240$	−99.8395	−	38.0974i	−0.415998	−	0.158739i
$241$	220.705	+	127.424i	0.915787	+	0.528730i	0.882289	−	0.470709i	$-0.156002\pi$
$241$	220.705	+	127.424i	0.915787	+	0.528730i	0.0334983	+	0.999439i	$0.489335\pi$
$242$	−59.3011			−0.245046
$243$	60.5589	−	235.333i	0.249214	−	0.968449i
$244$	305.767			1.25314
$245$	64.5439	−	111.793i	0.263445	−	0.456299i
$246$	100.895	+	38.5000i	0.410140	+	0.156504i
$247$	99.5198	+	94.2838i	0.402914	+	0.381716i
$248$	−125.752	+	72.6027i	−0.507063	+	0.292753i
$249$	334.892	−	272.293i	1.34495	−	1.09355i
$250$	−28.4175	+	49.2206i	−0.113670	+	0.196882i
$251$			222.888i			0.888002i	0.896026	+	0.444001i	$0.146441\pi$
$251$			222.888i			0.888002i	−0.896026	+	0.444001i	$0.853559\pi$
$252$	−221.533	+	248.012i	−0.879100	+	0.984174i
$253$		−	39.2378i		−	0.155090i
$254$	17.4353	−	30.1988i	0.0686429	−	0.118893i
$255$	−180.229	+	28.9125i	−0.706779	+	0.113382i
$256$	−57.3939	−	99.4092i	−0.224195	−	0.388317i
$257$	203.969	−	117.762i	0.793654	−	0.458217i	−0.0475931	−	0.998867i	$-0.515155\pi$
$257$	203.969	−	117.762i	0.793654	−	0.458217i	0.841247	+	0.540650i	$0.181822\pi$
$258$	−10.7356	−	66.9215i	−0.0416109	−	0.259386i
$259$	51.0224	−	88.3735i	0.196998	−	0.341210i
$260$	−37.6771	−	126.809i	−0.144912	−	0.487727i
$261$	6.91433	+	20.9960i	0.0264917	+	0.0804443i
$262$			72.1893i			0.275532i
$263$	−45.2489	−	26.1244i	−0.172049	−	0.0993325i	0.411503	−	0.911409i	$-0.365004\pi$
$263$	−45.2489	−	26.1244i	−0.172049	−	0.0993325i	−0.583552	+	0.812076i	$0.698337\pi$
$264$	−138.062	+	112.255i	−0.522963	+	0.425210i
$265$	−0.0867734	+	0.0500986i	−0.000327447	+	0.000189051i
$266$	25.5024	+	44.1714i	0.0958737	+	0.166058i
$267$	−225.868	−	86.1883i	−0.845948	−	0.322803i
$268$	211.204	+	121.938i	0.788073	+	0.454994i
$269$			435.342i			1.61837i	0.587553	+	0.809186i	$0.300091\pi$
$269$			435.342i			1.61837i	−0.587553	+	0.809186i	$0.699909\pi$
$270$	16.5184	+	31.9472i	0.0611794	+	0.118323i
$271$			535.820i			1.97720i	0.150574	+	0.988599i	$0.451888\pi$
$271$			535.820i			1.97720i	−0.150574	+	0.988599i	$0.548112\pi$
$272$	−255.984	−	147.792i	−0.941118	−	0.543355i
$273$	−382.357	−	29.0086i	−1.40058	−	0.106259i
$274$	17.2165	+	29.8198i	0.0628339	+	0.108832i
$275$	−137.295	−	237.802i	−0.499254	−	0.864733i
$276$	−17.9563	−	22.0843i	−0.0650589	−	0.0800156i
$277$	13.4558	−	23.3061i	0.0485769	−	0.0841376i	−0.840715	−	0.541479i	$-0.817865\pi$
$277$	13.4558	−	23.3061i	0.0485769	−	0.0841376i	0.889291	+	0.457341i	$0.151198\pi$
$278$	−75.3372			−0.270997
$279$	−335.232	−	69.8650i	−1.20155	−	0.250412i
$280$		−	101.606i		−	0.362877i
$281$	−36.6045	+	63.4009i	−0.130265	+	0.225626i	−0.923779	−	0.382927i	$-0.874916\pi$
$281$	−36.6045	+	63.4009i	−0.130265	+	0.225626i	0.793514	+	0.608553i	$0.208250\pi$
$282$	−6.39549	−	39.8669i	−0.0226791	−	0.141372i
$283$	127.130	+	220.196i	0.449223	+	0.778077i	0.998336	−	0.0576712i	$-0.0183675\pi$
$283$	127.130	+	220.196i	0.449223	+	0.778077i	−0.549113	+	0.835748i	$0.685034\pi$
$284$	55.5957	+	96.2945i	0.195759	+	0.339065i
$285$	−84.5833	+	13.5689i	−0.296783	+	0.0476103i
$286$	−96.6634	−	23.1219i	−0.337984	−	0.0808458i
$287$		−	719.479i		−	2.50690i
$288$	−39.9130	+	191.514i	−0.138587	+	0.664978i
$289$	−215.897			−0.747049
$290$	−2.83334	−	1.63583i	−0.00977012	−	0.00564078i
$291$	213.517	+	262.603i	0.733735	+	0.902416i
$292$	92.1709	−	53.2149i	0.315654	−	0.182243i
$293$	21.1134	+	36.5695i	0.0720594	+	0.124810i	0.899804	−	0.436295i	$-0.143710\pi$
$293$	21.1134	+	36.5695i	0.0720594	+	0.124810i	−0.827744	+	0.561105i	$0.810376\pi$
$294$	−65.7306	−	25.0819i	−0.223573	−	0.0853127i
$295$	−89.1770	+	154.459i	−0.302295	+	0.523590i
$296$		−	39.6085i		−	0.133812i
$297$	−419.179	−	19.4643i	−1.41138	−	0.0655365i
$298$	−15.9914			−0.0536623
$299$	7.63528	−	31.9200i	0.0255361	−	0.106756i
$300$	−186.098	−	71.0127i	−0.620328	−	0.236709i
$301$	−391.062	+	225.780i	−1.29921	+	0.750099i
$302$	14.5417	−	8.39564i	0.0481512	−	0.0278001i
$303$	374.208	+	460.236i	1.23501	+	1.51893i
$304$	−120.136	−	69.3606i	−0.395184	−	0.228160i
$305$	−220.319			−0.722356
$306$	31.1170	+	94.4895i	0.101690	+	0.308789i
$307$		−	136.458i		−	0.444490i	−0.974991	−	0.222245i	$-0.928662\pi$
$307$		−	136.458i		−	0.444490i	0.974991	−	0.222245i	$-0.0713385\pi$
$308$	497.328	+	287.132i	1.61470	+	0.932248i
$309$	−10.3681	−	64.6308i	−0.0335539	−	0.209161i
$310$	43.8916	−	25.3409i	0.141586	−	0.0817447i
$311$	272.833	−	157.520i	0.877277	−	0.506496i	0.00751707	−	0.999972i	$-0.497607\pi$
$311$	272.833	−	157.520i	0.877277	−	0.506496i	0.869759	+	0.493476i	$0.164274\pi$
$312$	−134.158	+	64.4544i	−0.429992	+	0.206585i
$313$	261.082	−	452.207i	0.834127	−	1.44475i	−0.0606123	−	0.998161i	$-0.519305\pi$
$313$	261.082	−	452.207i	0.834127	−	1.44475i	0.894739	−	0.446589i	$-0.147361\pi$
$314$	108.571			0.345768
$315$	159.624	−	178.703i	0.506744	−	0.567313i
$316$	−273.541			−0.865635
$317$	41.1674	−	71.3040i	0.129866	−	0.224934i	−0.793759	−	0.608233i	$-0.791879\pi$
$317$	41.1674	−	71.3040i	0.129866	−	0.224934i	0.923624	+	0.383299i	$0.125212\pi$
$318$	0.0344501	+	0.0423700i	0.000108334	+	0.000133239i
$319$	33.0586	−	19.0864i	0.103632	−	0.0598320i
$320$	56.7640	+	98.3181i	0.177387	+	0.307244i
$321$	192.524	−	504.536i	0.599765	−	1.57176i
$322$	6.10549	−	10.5750i	0.0189612	−	0.0328417i
$323$	−236.954			−0.733603
$324$	−244.835	+	180.872i	−0.755662	+	0.558247i
$325$	−65.4158	−	220.168i	−0.201279	−	0.677440i
$326$	18.1362	+	10.4709i	0.0556325	+	0.0321194i
$327$	−125.219	+	328.154i	−0.382934	+	1.00353i
$328$	−139.632	−	241.850i	−0.425707	−	0.737347i
$329$	−232.966	+	134.503i	−0.708104	+	0.408824i
$330$	48.1885	−	39.1810i	0.146026	−	0.118730i
$331$	130.559	+	75.3781i	0.394437	+	0.227728i	0.684081	−	0.729406i	$-0.260203\pi$
$331$	130.559	+	75.3781i	0.394437	+	0.227728i	−0.289644	+	0.957135i	$0.593537\pi$
$332$	−540.678			−1.62855
$333$	62.2257	−	69.6632i	0.186864	−	0.209199i
$334$	−102.299			−0.306283
$335$	−152.182	−	87.8620i	−0.454273	−	0.262275i
$336$	383.121	−	61.4607i	1.14024	−	0.182919i
$337$	120.680	+	209.024i	0.358100	+	0.620248i	0.987643	−	0.156718i	$-0.0500912\pi$
$337$	120.680	+	209.024i	0.358100	+	0.620248i	−0.629543	+	0.776966i	$0.716758\pi$
$338$	−74.1365	−	37.6194i	−0.219339	−	0.111300i
$339$	204.081	−	32.7389i	0.602009	−	0.0965750i
$340$	198.020	+	114.327i	0.582411	+	0.336255i
$341$			591.341i			1.73414i
$342$	14.6036	+	44.3450i	0.0427005	+	0.129664i
$343$		−	13.0537i		−	0.0380573i
$344$	−87.6359	+	151.790i	−0.254756	+	0.441250i
$345$	12.9383	+	15.9127i	0.0375023	+	0.0461238i
$346$	23.1367	−	13.3580i	0.0668690	−	0.0386068i
$347$	−449.622	+	259.590i	−1.29574	+	0.748097i	−0.979666	−	0.200637i	$-0.935699\pi$
$347$	−449.622	+	259.590i	−1.29574	+	0.748097i	−0.316076	+	0.948734i	$0.602366\pi$
$348$	9.87201	−	25.8709i	0.0283679	−	0.0743418i
$349$	−313.905	−	181.233i	−0.899442	−	0.519293i	−0.0224227	−	0.999749i	$-0.507138\pi$
$349$	−313.905	−	181.233i	−0.899442	−	0.519293i	−0.877019	+	0.480456i	$0.840471\pi$
$350$		−	85.4535i		−	0.244153i
$351$	−337.215	−	97.4021i	−0.960726	−	0.277499i
$352$	337.826			0.959732
$353$	−31.9628	+	55.3612i	−0.0905462	+	0.156831i	−0.907741	−	0.419531i	$-0.862195\pi$
$353$	−31.9628	+	55.3612i	−0.0905462	+	0.156831i	0.817195	+	0.576361i	$0.195528\pi$
$354$	90.8165	+	34.6544i	0.256544	+	0.0978938i
$355$	−40.0591	−	69.3844i	−0.112843	−	0.195449i
$356$	151.419	+	262.265i	0.425334	+	0.736700i
$357$	514.253	−	418.128i	1.44048	−	1.17123i
$358$	−35.1665	−	20.3034i	−0.0982305	−	0.0567134i
$359$	359.930			1.00259			0.501295	−	0.865276i	$-0.332857\pi$
$359$	359.930			1.00259			0.501295	+	0.865276i	$0.332857\pi$
$360$	18.9754	−	91.0493i	0.0527095	−	0.252915i
$361$	249.795			0.691953
$362$	41.0708	−	71.1368i	0.113455	−	0.196510i
$363$	57.2836	+	357.083i	0.157806	+	0.983699i
$364$	348.704	+	330.358i	0.957978	+	0.907576i
$365$	−66.4132	+	38.3437i	−0.181954	+	0.105051i
$366$	19.0193	+	118.559i	0.0519654	+	0.323931i
$367$	73.7089	−	127.668i	0.200842	−	0.347868i	−0.747958	−	0.663746i	$-0.768966\pi$
$367$	73.7089	−	127.668i	0.200842	−	0.347868i	0.948800	+	0.315878i	$0.102299\pi$
$368$			33.2110i			0.0902474i
$369$	134.367	−	644.729i	0.364137	−	1.74723i
$370$			13.8247i			0.0373641i
$371$	0.181911	−	0.315079i	0.000490325	−	0.000849268i
$372$	270.613	+	332.826i	0.727455	+	0.894693i
$373$	−285.025	−	493.678i	−0.764143	−	1.32353i	−0.940699	−	0.339243i	$-0.889829\pi$
$373$	−285.025	−	493.678i	−0.764143	−	1.32353i	0.176556	−	0.984291i	$-0.443504\pi$
$374$	148.776	−	85.8959i	0.397797	−	0.229668i
$375$	323.833	+	123.571i	0.863555	+	0.329521i
$376$	−52.2071	+	90.4253i	−0.138849	+	0.240493i
$377$	30.6073	−	9.09395i	0.0811864	−	0.0241219i
$378$	−109.945	−	70.4710i	−0.290859	−	0.186431i
$379$		−	333.547i		−	0.880071i	−0.897980	−	0.440036i	$-0.854966\pi$
$379$		−	333.547i		−	0.880071i	0.897980	−	0.440036i	$-0.145034\pi$
$380$	92.9329	+	53.6548i	0.244560	+	0.141197i
$381$	−198.685	−	75.8155i	−0.521483	−	0.198991i
$382$	30.0690	−	17.3603i	0.0787146	−	0.0454459i
$383$	226.922	+	393.041i	0.592486	+	1.02622i	0.993896	+	0.110318i	$0.0351868\pi$
$383$	226.922	+	393.041i	0.592486	+	1.02622i	−0.401410	+	0.915898i	$0.631480\pi$
$384$	250.390	−	203.587i	0.652057	−	0.530173i
$385$	−358.347	−	206.892i	−0.930771	−	0.537381i
$386$			22.9535i			0.0594650i
$387$	−392.598	+	129.289i	−1.01447	+	0.334081i
$388$		−	423.969i		−	1.09270i
$389$	−331.803	−	191.567i	−0.852965	−	0.492460i	0.00868524	−	0.999962i	$-0.497235\pi$
$389$	−331.803	−	191.567i	−0.852965	−	0.492460i	−0.861650	+	0.507503i	$0.830569\pi$
$390$	46.8256	−	22.4968i	0.120066	−	0.0576841i
$391$	28.3644	+	49.1286i	0.0725432	+	0.125648i
$392$	90.9672	+	157.560i	0.232059	+	0.401938i
$393$	434.689	−	69.7333i	1.10608	−	0.177438i
$394$	47.8206	−	82.8278i	0.121372	−	0.210223i
$395$	197.098			0.498983
$396$	392.034	+	350.180i	0.989986	+	0.884292i
$397$			114.607i			0.288682i	0.989528	+	0.144341i	$0.0461062\pi$
$397$			114.607i			0.288682i	−0.989528	+	0.144341i	$0.953894\pi$
$398$	−5.47730	+	9.48696i	−0.0137621	+	0.0238366i
$399$	241.344	−	196.232i	0.604873	−	0.491809i
$400$	116.207	+	201.276i	0.290517	+	0.503191i
$401$	168.468	+	291.795i	0.420119	+	0.727667i	0.995951	−	0.0899009i	$-0.0286550\pi$
$401$	168.468	+	291.795i	0.420119	+	0.727667i	−0.575832	+	0.817568i	$0.695322\pi$
$402$	−34.1434	+	89.4774i	−0.0849338	+	0.222581i
$403$	−115.069	+	481.057i	−0.285531	+	1.19369i
$404$		−	743.044i		−	1.83922i
$405$	176.414	−	130.326i	0.435590	−	0.321793i
$406$	11.8795			0.0292600
$407$	−139.693	−	80.6516i	−0.343225	−	0.198161i
$408$	91.7162	−	240.355i	0.224795	−	0.589105i
$409$	−537.500	+	310.326i	−1.31418	+	0.758742i	−0.982786	−	0.184750i	$-0.940852\pi$
$409$	−537.500	+	310.326i	−1.31418	+	0.758742i	−0.331395	+	0.943492i	$0.607519\pi$
$410$	48.7364	+	84.4139i	0.118869	+	0.205888i
$411$	162.930	−	132.475i	0.396423	−	0.322323i
$412$	−40.9981	+	71.0108i	−0.0995100	+	0.172356i
$413$		−	647.613i		−	1.56807i
$414$	7.44611	−	8.33610i	0.0179858	−	0.0201355i
$415$	389.582			0.938753
$416$	274.822	+	65.7374i	0.660629	+	0.158023i
$417$	72.7741	+	453.644i	0.174518	+	1.08788i
$418$	69.8222	−	40.3119i	0.167039	−	0.0964398i
$419$	217.694	−	125.686i	0.519557	−	0.299966i	−0.217196	−	0.976128i	$-0.569691\pi$
$419$	217.694	−	125.686i	0.519557	−	0.299966i	0.736753	+	0.676162i	$0.236358\pi$
$420$	−296.368	+	47.5437i	−0.705638	+	0.113199i
$421$	−643.709	−	371.645i	−1.52900	−	0.882768i	−0.999404	−	0.0345179i	$-0.989010\pi$
$421$	−643.709	−	371.645i	−1.52900	−	0.882768i	−0.529595	−	0.848250i	$-0.677656\pi$
$422$	−95.1997			−0.225592
$423$	−233.881	+	77.0212i	−0.552911	+	0.182083i
$424$		−	0.141216i		−	0.000333058i
$425$	343.806	+	198.496i	0.808955	+	0.467050i
$426$	−33.8793	+	27.5465i	−0.0795289	+	0.0646632i
$427$	692.810	−	399.994i	1.62251	−	0.936755i
$428$	−585.839	+	338.234i	−1.36878	+	0.790267i
$429$	−45.8542	+	604.396i	−0.106886	+	1.40885i
$430$	30.5880	−	52.9799i	0.0711348	−	0.123209i
$431$	−649.249			−1.50638			−0.753189	−	0.657804i	$-0.771485\pi$
$431$	−649.249			−1.50638			−0.753189	+	0.657804i	$0.771485\pi$
$432$	354.794	+	16.4747i	0.821283	+	0.0381358i
$433$	245.607			0.567222			0.283611	−	0.958939i	$-0.408468\pi$
$433$	245.607			0.567222			0.283611	+	0.958939i	$0.408468\pi$
$434$	−92.0140	+	159.373i	−0.212014	+	0.367219i
$435$	−7.11322	+	18.6412i	−0.0163522	+	0.0428532i
$436$	381.034	−	219.990i	0.873931	−	0.504564i
$437$	13.3117	+	23.0566i	0.0304616	+	0.0527610i
$438$	26.3669	+	32.4285i	0.0601984	+	0.0740377i
$439$	15.0625	−	26.0889i	0.0343108	−	0.0594281i	−0.848360	−	0.529420i	$-0.822410\pi$
$439$	15.0625	−	26.0889i	0.0343108	−	0.0594281i	0.882671	+	0.469992i	$0.155743\pi$
$440$	−160.609			−0.365020
$441$	−87.5369	+	420.026i	−0.198496	+	0.952441i
$442$	137.744	−	40.9261i	0.311638	−	0.0925930i
$443$	152.079	+	87.8030i	0.343294	+	0.198201i	0.661728	−	0.749744i	$-0.269824\pi$
$443$	152.079	+	87.8030i	0.343294	+	0.198201i	−0.318434	+	0.947945i	$0.603157\pi$
$444$	−115.532	+	18.5338i	−0.260207	+	0.0417427i
$445$	−109.104	−	188.974i	−0.245178	−	0.424660i
$446$	−97.7715	+	56.4484i	−0.219219	+	0.126566i
$447$	15.4473	+	96.2922i	0.0345577	+	0.215419i
$448$	−356.998	−	206.113i	−0.796871	−	0.460074i
$449$	126.404			0.281523			0.140762	−	0.990044i	$-0.455045\pi$
$449$	126.404			0.281523			0.140762	+	0.990044i	$0.455045\pi$
$450$	15.9589	−	76.5753i	0.0354643	−	0.170167i
$451$	−1137.29			−2.52170
$452$	−224.227	−	129.458i	−0.496077	−	0.286410i
$453$	−64.6014	−	79.4529i	−0.142608	−	0.175393i
$454$	−61.2966	−	106.169i	−0.135015	−	0.233852i
$455$	−251.257	−	238.037i	−0.552212	−	0.523159i
$456$	43.0434	−	112.801i	0.0943934	−	0.247371i
$457$	574.817	+	331.871i	1.25781	+	0.726194i	0.972647	−	0.232286i	$-0.0746207\pi$
$457$	574.817	+	331.871i	1.25781	+	0.726194i	0.285158	+	0.958481i	$0.407954\pi$
$458$		−	26.3165i		−	0.0574597i
$459$	538.912	−	278.647i	1.17410	−	0.607073i
$460$		−	25.6909i		−	0.0558497i
$461$	−15.6227	+	27.0593i	−0.0338887	+	0.0586969i	−0.882472	−	0.470364i	$-0.844123\pi$
$461$	−15.6227	+	27.0593i	−0.0338887	+	0.0586969i	0.848584	+	0.529061i	$0.177456\pi$
$462$	−80.3986	+	210.695i	−0.174023	+	0.456051i
$463$	−558.193	+	322.273i	−1.20560	+	0.696053i	−0.961795	−	0.273771i	$-0.911729\pi$
$463$	−558.193	+	322.273i	−1.20560	+	0.696053i	−0.243805	+	0.969824i	$0.578396\pi$
$464$	−27.9810	+	16.1548i	−0.0603038	+	0.0348164i
$465$	−194.989	−	239.816i	−0.419331	−	0.515732i
$466$	−47.4720	−	27.4080i	−0.101871	−	0.0588154i
$467$			594.979i			1.27405i	0.770845	+	0.637023i	$0.219834\pi$
$467$			594.979i			1.27405i	−0.770845	+	0.637023i	$0.780166\pi$
$468$	250.779	+	361.157i	0.535853	+	0.771704i
$469$	638.063			1.36048
$470$	18.2221	−	31.5615i	0.0387703	−	0.0671522i
$471$	−104.877	−	653.762i	−0.222669	−	1.38803i
$472$	−125.685	−	217.692i	−0.266281	−	0.461212i
$473$	356.892	+	618.156i	0.754529	+	1.30688i
$474$	−17.0148	−	106.063i	−0.0358962	−	0.223762i
$475$	161.352	+	93.1565i	0.339688	+	0.196119i
$476$	−830.254			−1.74423
$477$	0.221854	−	0.248371i	0.000465102	−	0.000520693i
$478$	−115.740			−0.242133
$479$	−31.4715	+	54.5102i	−0.0657025	+	0.113800i	−0.897005	−	0.442020i	$-0.854262\pi$
$479$	−31.4715	+	54.5102i	−0.0657025	+	0.113800i	0.831303	+	0.555820i	$0.187595\pi$
$480$	−137.004	+	111.395i	−0.285424	+	0.232072i
$481$	−97.9462	−	92.7930i	−0.203630	−	0.192917i
$482$	108.570	−	62.6828i	0.225249	−	0.130047i
$483$	−69.5755	−	26.5491i	−0.144049	−	0.0549671i
$484$	226.513	−	392.332i	0.468002	−	0.810604i
$485$			305.488i			0.629873i
$486$	−85.3610	−	83.6821i	−0.175640	−	0.172185i
$487$		−	143.450i		−	0.294558i	−0.989095	−	0.147279i	$-0.952948\pi$
$487$		−	143.450i		−	0.294558i	0.989095	−	0.147279i	$-0.0470516\pi$
$488$	155.257	−	268.913i	0.318149	−	0.551051i
$489$	45.5317	−	119.322i	0.0931119	−	0.244012i
$490$	−31.7507	−	54.9938i	−0.0647973	−	0.112232i
$491$	824.274	−	475.895i	1.67877	−	0.969236i	0.716316	−	0.697776i	$-0.245827\pi$
$491$	824.274	−	475.895i	1.67877	−	0.969236i	0.962450	−	0.271460i	$-0.0875063\pi$
$492$	−640.102	+	520.452i	−1.30102	+	1.05783i
$493$	−27.5945	+	47.7951i	−0.0559726	+	0.0969474i
$494$	64.6447	−	19.2071i	0.130860	−	0.0388807i
$495$	−282.478	−	252.320i	−0.570663	−	0.509737i
$496$		−	500.513i		−	1.00910i
$497$	251.939	+	145.457i	0.506919	+	0.292670i
$498$	−33.6313	−	209.644i	−0.0675327	−	0.420971i
$499$	−56.3465	+	32.5317i	−0.112919	+	0.0651937i	−0.555396	−	0.831586i	$-0.687433\pi$
$499$	−56.3465	+	32.5317i	−0.112919	+	0.0651937i	0.442477	+	0.896780i	$0.354100\pi$
$500$	−217.093	−	376.017i	−0.434187	−	0.752033i
$501$	98.8184	+	615.993i	0.197242	+	1.22953i
$502$	94.9546	+	54.8221i	0.189153	+	0.109207i
$503$			493.047i			0.980213i	0.871662	+	0.490107i	$0.163042\pi$
$503$			493.047i			0.980213i	−0.871662	+	0.490107i	$0.836958\pi$
$504$	105.633	+	320.763i	0.209589	+	0.636434i
$505$			535.396i			1.06019i
$506$	−16.7160	−	9.65101i	−0.0330356	−	0.0190731i
$507$	−154.912	+	482.754i	−0.305546	+	0.952177i
$508$	133.196	+	230.702i	0.262196	+	0.454137i
$509$	288.131	+	499.058i	0.566073	+	0.980468i	0.996949	+	0.0780566i	$0.0248715\pi$
$509$	288.131	+	499.058i	0.566073	+	0.980468i	−0.430875	+	0.902411i	$0.641795\pi$
$510$	−32.0121	+	83.8921i	−0.0627689	+	0.164494i
$511$	139.228	−	241.150i	0.272462	−	0.471918i
$512$	−486.749			−0.950681
$513$	252.917	−	130.772i	0.493016	−	0.254916i
$514$		−	115.859i		−	0.225408i
$515$	29.5410	−	51.1664i	0.0573611	−	0.0993523i
$516$	483.755	+	184.594i	0.937509	+	0.357741i
$517$	212.610	+	368.252i	0.411238	+	0.712286i
$518$	−25.0991	−	43.4730i	−0.0484540	−	0.0839247i
$519$	−102.785	−	126.414i	−0.198044	−	0.243573i
$520$	−130.656	−	31.2529i	−0.251261	−	0.0601017i
$521$		−	501.004i		−	0.961620i	−0.876825	−	0.480810i	$-0.840343\pi$
$521$		−	501.004i		−	0.961620i	0.876825	−	0.480810i	$-0.159657\pi$
$522$	10.6453	+	2.21857i	0.0203933	+	0.00425014i
$523$	−400.933			−0.766602			−0.383301	−	0.923624i	$-0.625213\pi$
$523$	−400.933			−0.766602			−0.383301	+	0.923624i	$0.625213\pi$
$524$	−477.599	−	275.742i	−0.911449	−	0.526225i
$525$	−514.560	+	82.5463i	−0.980114	+	0.157231i
$526$	−22.2590	+	12.8512i	−0.0423175	+	0.0244320i
$527$	−427.471	−	740.401i	−0.811140	−	1.40494i
$528$	−97.1514	−	605.602i	−0.183999	−	1.14697i
$529$	−261.313	+	452.607i	−0.493976	+	0.855591i
$530$			0.0492894i			9.29988e-5i
$531$	120.945	−	580.329i	0.227769	−	1.09290i
$532$	−389.647			−0.732419
$533$	−925.184	−	221.304i	−1.73581	−	0.415205i
$534$	−92.2728	+	75.0250i	−0.172795	+	0.140496i
$535$	422.123	−	243.713i	0.789014	−	0.455538i
$536$	214.482	−	123.831i	0.400153	−	0.231029i
$537$	−88.2872	+	231.369i	−0.164408	+	0.430854i
$538$	185.464	+	107.077i	0.344728	+	0.199029i
$539$	740.917			1.37461
$540$	−274.456	−	12.7442i	−0.508252	−	0.0236004i
$541$		−	73.5254i		−	0.135906i	−0.997689	−	0.0679532i	$-0.978353\pi$
$541$		−	73.5254i		−	0.135906i	0.997689	−	0.0679532i	$-0.0216469\pi$
$542$	228.269	+	131.791i	0.421161	+	0.243158i
$543$	−468.025	−	178.592i	−0.861924	−	0.328899i
$544$	−422.982	+	244.209i	−0.777540	+	0.448913i
$545$	−274.552	+	158.513i	−0.503765	+	0.290849i
$546$	−106.404	+	155.756i	−0.194878	+	0.285268i
$547$	−20.0152	+	34.6674i	−0.0365909	+	0.0633774i	−0.883741	−	0.467976i	$-0.844983\pi$
$547$	−20.0152	+	34.6674i	−0.0365909	+	0.0633774i	0.847150	+	0.531354i	$0.178317\pi$
$548$	−263.048			−0.480015
$549$	695.532	−	229.051i	1.26691	−	0.417214i
$550$	−135.077			−0.245595
$551$	−12.9504	+	22.4308i	−0.0235034	+	0.0407092i
$552$	−28.5400	+	4.57842i	−0.0517029	+	0.00829423i
$553$	−619.791	+	357.837i	−1.12078	+	0.647083i
$554$	−6.61922	−	11.4648i	−0.0119481	−	0.0206946i
$555$	83.2458	−	13.3544i	0.149992	−	0.0240620i
$556$	287.766	−	498.426i	0.517565	−	0.896449i
$557$	475.662			0.853972			0.426986	−	0.904258i	$-0.359575\pi$
$557$	475.662			0.853972			0.426986	+	0.904258i	$0.359575\pi$
$558$	−112.218	+	125.631i	−0.201107	+	0.225145i
$559$	170.046	+	572.318i	0.304196	+	1.02382i
$560$	303.306	+	175.114i	0.541618	+	0.312703i
$561$	−660.938	−	812.884i	−1.17814	−	1.44899i
$562$	18.0066	+	31.1884i	0.0320403	+	0.0554954i
$563$	494.852	−	285.703i	0.878955	−	0.507465i	0.00864136	−	0.999963i	$-0.497249\pi$
$563$	494.852	−	285.703i	0.878955	−	0.507465i	0.870314	+	0.492498i	$0.163916\pi$
$564$	288.186	+	109.968i	0.510967	+	0.194978i
$565$	161.565	+	93.2798i	0.285957	+	0.165097i
$566$	125.077			0.220983
$567$	−318.138	+	730.106i	−0.561090	+	1.28767i
$568$	112.917			0.198798
$569$	−334.478	−	193.111i	−0.587835	−	0.339387i	0.176406	−	0.984318i	$-0.443553\pi$
$569$	−334.478	−	193.111i	−0.587835	−	0.339387i	−0.764241	+	0.644931i	$0.776886\pi$
$570$	−15.0236	+	39.3715i	−0.0263572	+	0.0690727i
$571$	440.436	+	762.858i	0.771342	+	1.33600i	0.936828	+	0.349791i	$0.113748\pi$
$571$	440.436	+	762.858i	0.771342	+	1.33600i	−0.165486	+	0.986212i	$0.552919\pi$
$572$	522.199	−	551.199i	0.912935	−	0.963635i
$573$	−133.582	−	164.291i	−0.233127	−	0.286721i
$574$	−306.511	−	176.964i	−0.533992	−	0.308300i
$575$		−	44.6050i		−	0.0775738i
$576$	−281.415	−	251.370i	−0.488568	−	0.436407i
$577$			583.864i			1.01190i	0.862564	+	0.505948i	$0.168857\pi$
$577$			583.864i			1.01190i	−0.862564	+	0.505948i	$0.831143\pi$
$578$	−53.1025	+	91.9762i	−0.0918728	+	0.159128i
$579$	138.215	−	22.1726i	0.238713	−	0.0382946i
$580$	21.6450	−	12.4968i	0.0373190	−	0.0215462i
$581$	−1225.07	+	707.297i	−2.10856	+	1.21738i
$582$	164.391	−	26.3717i	0.282458	−	0.0453123i
$583$	−0.498047	−	0.287548i	−0.000854284	−	0.000493221i
$584$		−	108.082i		−	0.185072i
$585$	−180.698	−	260.230i	−0.308885	−	0.444837i
$586$	20.7724			0.0354477
$587$	375.099	−	649.690i	0.639010	−	1.10680i	−0.346640	−	0.937998i	$-0.612678\pi$
$587$	375.099	−	649.690i	0.639010	−	1.10680i	0.985650	−	0.168800i	$-0.0539892\pi$
$588$	417.012	−	339.063i	0.709204	−	0.576638i
$589$	−200.617	−	347.478i	−0.340605	−	0.589946i
$590$	43.8683	+	75.9821i	0.0743530	+	0.128783i
$591$	−544.943	−	207.943i	−0.922069	−	0.351849i
$592$	118.236	+	68.2639i	0.199724	+	0.115311i
$593$	1077.16			1.81646			0.908231	−	0.418469i	$-0.137433\pi$
$593$	1077.16			1.81646			0.908231	+	0.418469i	$0.137433\pi$
$594$	−111.394	+	173.790i	−0.187532	+	0.292576i
$595$	598.234			1.00544
$596$	61.0823	−	105.798i	0.102487	−	0.177513i
$597$	62.4169	+	23.8175i	0.104551	+	0.0398952i
$598$	−11.7205	−	11.1039i	−0.0195995	−	0.0185684i
$599$	−245.190	+	141.561i	−0.409333	+	0.236329i	−0.690503	−	0.723329i	$-0.742611\pi$
$599$	−245.190	+	141.561i	−0.409333	+	0.236329i	0.281170	+	0.959658i	$0.409277\pi$
$600$	−156.947	+	127.610i	−0.261578	+	0.212684i
$601$	66.0237	−	114.356i	0.109856	−	0.190277i	−0.805856	−	0.592112i	$-0.798294\pi$
$601$	66.0237	−	114.356i	0.109856	−	0.190277i	0.915712	+	0.401835i	$0.131628\pi$
$602$			222.133i			0.368992i
$603$	571.772	+	119.162i	0.948212	+	0.197615i
$604$			128.276i			0.212377i
$605$	−163.213	+	282.693i	−0.269773	+	0.467260i
$606$	288.110	−	46.2189i	0.475429	−	0.0762688i
$607$	−120.206	−	208.203i	−0.198033	−	0.343003i	0.749858	−	0.661599i	$-0.230122\pi$
$607$	−120.206	−	208.203i	−0.198033	−	0.343003i	−0.947891	+	0.318596i	$0.896789\pi$
$608$	−198.510	+	114.610i	−0.326497	+	0.188503i
$609$	−11.4754	−	71.5329i	−0.0188430	−	0.117460i
$610$	−54.1900	+	93.8598i	−0.0888360	+	0.153868i
$611$	101.301	+	340.945i	0.165795	+	0.558012i
$612$	−743.994	−	155.054i	−1.21568	−	0.253357i
$613$			822.777i			1.34221i	0.741360	+	0.671107i	$0.234181\pi$
$613$			822.777i			1.34221i	−0.741360	+	0.671107i	$0.765819\pi$
$614$	−58.1338	−	33.5636i	−0.0946804	−	0.0546638i
$615$	461.221	−	375.009i	0.749953	−	0.609771i
$616$	505.048	−	291.590i	0.819884	−	0.473360i
$617$	−275.955	−	477.968i	−0.447253	−	0.774665i	0.550953	−	0.834536i	$-0.314264\pi$
$617$	−275.955	−	477.968i	−0.447253	−	0.774665i	−0.998206	+	0.0598711i	$0.980931\pi$
$618$	−30.0841	−	11.4797i	−0.0486797	−	0.0185755i
$619$	350.084	+	202.121i	0.565564	+	0.326529i	0.755376	−	0.655292i	$-0.227454\pi$
$619$	350.084	+	202.121i	0.565564	+	0.326529i	−0.189812	+	0.981821i	$0.560788\pi$
$620$			387.179i			0.624482i
$621$	−57.3887	−	36.7844i	−0.0924134	−	0.0592341i
$622$		−	154.976i		−	0.249157i
$623$	686.173	+	396.162i	1.10140	+	0.635895i
$624$	38.8112	−	511.563i	0.0621974	−	0.819812i
$625$	−64.4216	−	111.581i	−0.103074	−	0.178530i
$626$	−128.432	−	222.451i	−0.205163	−	0.355353i
$627$	−310.185	−	381.495i	−0.494713	−	0.608445i
$628$	−414.710	+	718.298i	−0.660366	+	1.14379i
$629$	233.207			0.370758
$630$	−36.8694	−	111.957i	−0.0585229	−	0.177710i
$631$		−	443.670i		−	0.703123i	−0.936165	−	0.351561i	$-0.885651\pi$
$631$		−	443.670i		−	0.703123i	0.936165	−	0.351561i	$-0.114349\pi$
$632$	−138.893	+	240.571i	−0.219768	+	0.380650i
$633$	91.9609	+	573.247i	0.145278	+	0.905603i
$634$	−20.2512	−	35.0761i	−0.0319420	−	0.0553251i
$635$	−95.9733	−	166.231i	−0.151139	−	0.261780i
$636$	−0.411907	+	0.0660785i	−0.000647652	+	0.000103897i
$637$	602.737	+	144.175i	0.946212	+	0.226334i
$638$		−	18.7781i		−	0.0294328i
$639$	198.599	+	177.395i	0.310796	+	0.277614i
$640$	291.281			0.455126
$641$	543.758	+	313.939i	0.848297	+	0.489764i	0.860076	−	0.510166i	$-0.170416\pi$
$641$	543.758	+	313.939i	0.848297	+	0.489764i	−0.0117791	+	0.999931i	$0.503749\pi$
$642$	−167.588	−	206.116i	−0.261041	−	0.321052i
$643$	618.928	−	357.338i	0.962563	−	0.555736i	0.0656022	−	0.997846i	$-0.479103\pi$
$643$	618.928	−	357.338i	0.962563	−	0.555736i	0.896961	+	0.442110i	$0.145770\pi$
$644$	46.6424	+	80.7870i	0.0724261	+	0.125446i
$645$	−348.567	−	133.008i	−0.540413	−	0.206215i
$646$	−58.2816	+	100.947i	−0.0902192	+	0.156264i
$647$		−	50.9073i		−	0.0786820i	−0.999226	−	0.0393410i	$-0.987474\pi$
$647$		−	50.9073i		−	0.0786820i	0.999226	−	0.0393410i	$-0.0125259\pi$
$648$	34.7538	+	307.164i	0.0536324	+	0.474019i
$649$	−1023.69			−1.57733
$650$	−109.885	−	26.2846i	−0.169055	−	0.0404379i
$651$	1048.55	+	400.113i	1.61068	+	0.614613i
$652$	−138.550	+	79.9918i	−0.212500	+	0.122687i
$653$	370.592	−	213.962i	0.567523	−	0.327659i	−0.188637	−	0.982047i	$-0.560407\pi$
$653$	370.592	−	213.962i	0.567523	−	0.327659i	0.756159	+	0.654388i	$0.227074\pi$
$654$	109.001	+	134.059i	0.166668	+	0.204983i
$655$	344.131	+	198.684i	0.525391	+	0.303335i
$656$	962.604			1.46738
$657$	169.799	−	190.094i	0.258446	−	0.289336i
$658$			132.331i			0.201110i
$659$	472.394	+	272.737i	0.716835	+	0.413865i	0.813587	−	0.581444i	$-0.197512\pi$
$659$	472.394	+	272.737i	0.716835	+	0.413865i	−0.0967518	+	0.995309i	$0.530845\pi$
$660$	75.1528	+	468.472i	0.113868	+	0.709806i
$661$	−72.4148	+	41.8087i	−0.109553	+	0.0632507i	−0.553776	−	0.832666i	$-0.686813\pi$
$661$	−72.4148	+	41.8087i	−0.109553	+	0.0632507i	0.444222	+	0.895917i	$0.353480\pi$
$662$	64.2249	−	37.0803i	0.0970165	−	0.0560125i
$663$	−379.495	−	789.894i	−0.572391	−	1.19139i
$664$	−274.536	+	475.510i	−0.413457	+	0.716129i
$665$	280.758			0.422192
$666$	−14.3726	−	43.6438i	−0.0215806	−	0.0655312i
$667$	6.20088			0.00929667
$668$	390.751	−	676.801i	0.584957	−	1.01318i
$669$	434.350	+	534.205i	0.649253	+	0.798512i
$670$	−74.8617	+	43.2214i	−0.111734	+	0.0645096i
$671$	−632.274	−	1095.13i	−0.942287	−	1.63209i
$672$	228.580	−	599.024i	0.340148	−	0.891404i
$673$	−65.7751	+	113.926i	−0.0977341	+	0.169280i	−0.910746	−	0.412966i	$-0.864493\pi$
$673$	−65.7751	+	113.926i	−0.0977341	+	0.169280i	0.813012	+	0.582247i	$0.197826\pi$
$674$	118.730			0.176158
$675$	−476.516	−	22.1268i	−0.705949	−	0.0327804i
$676$	532.067	−	346.787i	0.787082	−	0.512998i
$677$	151.765	+	87.6217i	0.224173	+	0.129426i	0.607881	−	0.794028i	$-0.292020\pi$
$677$	151.765	+	87.6217i	0.224173	+	0.129426i	−0.383708	+	0.923454i	$0.625353\pi$
$678$	36.2488	−	94.9948i	0.0534643	−	0.140110i
$679$	−554.622	−	960.633i	−0.816822	−	1.41478i
$680$	201.094	−	116.102i	0.295726	−	0.170738i
$681$	−580.087	+	471.656i	−0.851816	+	0.692593i
$682$	251.922	+	145.447i	0.369387	+	0.213266i
$683$	960.521			1.40633			0.703163	−	0.711029i	$-0.251770\pi$
$683$	960.521			1.40633			0.703163	+	0.711029i	$0.251770\pi$
$684$	−349.165	−	72.7687i	−0.510474	−	0.106387i
$685$	189.538			0.276697
$686$	−5.56110	−	3.21070i	−0.00810656	−	0.00468032i
$687$	−158.466	+	25.4212i	−0.230663	+	0.0370032i
$688$	−302.075	−	523.209i	−0.439063	−	0.760479i
$689$	−0.349208	−	0.330836i	−0.000506834	−	0.000480168i
$690$	9.96143	−	1.59802i	0.0144369	−	0.00231598i
$691$	398.707	+	230.194i	0.577000	+	0.333131i	0.759940	−	0.649993i	$-0.225228\pi$
$691$	398.707	+	230.194i	0.577000	+	0.333131i	−0.182940	+	0.983124i	$0.558562\pi$
$692$			204.094i			0.294934i
$693$	1346.37	+	280.594i	1.94281	+	0.404898i
$694$			255.397i			0.368007i
$695$	−207.348	+	359.138i	−0.298343	+	0.516745i
$696$	−17.7401	−	21.8184i	−0.0254886	−	0.0313483i
$697$	1423.96	−	822.126i	2.04299	−	1.17952i
$698$	−154.417	+	89.1529i	−0.221228	+	0.127726i
$699$	−119.181	+	312.329i	−0.170502	+	0.446822i
$700$	565.355	+	326.408i	0.807650	+	0.466297i
$701$		−	704.086i		−	1.00440i	−0.864751	−	0.502201i	$-0.832524\pi$
$701$		−	704.086i		−	1.00440i	0.864751	−	0.502201i	$-0.167476\pi$
$702$	−124.437	+	119.702i	−0.177261	+	0.170516i
$703$	109.447			0.155685
$704$	−325.805	+	564.310i	−0.462791	+	0.801577i
$705$	−207.650	−	79.2367i	−0.294540	−	0.112392i
$706$	15.7233	+	27.2335i	0.0222709	+	0.0385743i
$707$	−972.026	−	1683.60i	−1.37486	−	2.38133i
$708$	−576.164	+	468.466i	−0.813791	+	0.661676i
$709$	−1153.90	−	666.202i	−1.62750	−	0.939636i	−0.984837	−	0.173484i	$-0.944497\pi$
$709$	−1153.90	−	666.202i	−1.62750	−	0.939636i	−0.642660	−	0.766151i	$-0.722169\pi$
$710$	−39.4121			−0.0555099
$711$	−622.226	+	204.910i	−0.875142	+	0.288199i
$712$	307.539			0.431937
$713$	−48.0294	+	83.1893i	−0.0673624	+	0.116675i
$714$	−51.6435	−	321.924i	−0.0723298	−	0.450875i
$715$	−376.267	+	397.163i	−0.526248	+	0.555473i
$716$	268.652	−	155.106i	0.375212	−	0.216629i
$717$	111.802	+	696.929i	0.155930	+	0.972006i
$718$	88.5290	−	153.337i	0.123299	−	0.213561i
$719$			761.577i			1.05922i	0.848242	+	0.529608i	$0.177661\pi$
$719$			761.577i			1.05922i	−0.848242	+	0.529608i	$0.822339\pi$
$720$	239.091	+	213.564i	0.332070	+	0.296617i
$721$			214.529i			0.297544i
$722$	61.4400	−	106.417i	0.0850970	−	0.147392i
$723$	−482.322	−	593.205i	−0.667112	−	0.820477i
$724$	313.757	+	543.444i	0.433367	+	0.750613i
$725$	37.5805	−	21.6971i	0.0518352	−	0.0299271i
$726$	166.213	+	63.4248i	0.228944	+	0.0873620i
$727$	−482.133	+	835.078i	−0.663181	+	1.14866i	0.316594	+	0.948561i	$0.397461\pi$
$727$	−482.133	+	835.078i	−0.663181	+	1.14866i	−0.979775	+	0.200102i	$0.935873\pi$
$728$	467.598	−	138.931i	0.642305	−	0.190840i
$729$	−421.437	+	594.838i	−0.578102	+	0.815964i
$730$			37.7243i			0.0516772i
$731$	−893.709	−	515.983i	−1.22258	−	0.705859i
$732$	−857.025	−	327.030i	−1.17080	−	0.446762i
$733$	−884.929	+	510.914i	−1.20727	+	0.697018i	−0.962162	−	0.272478i	$-0.912157\pi$
$733$	−884.929	+	510.914i	−1.20727	+	0.697018i	−0.245108	+	0.969496i	$0.578823\pi$
$734$	−36.2591	−	62.8027i	−0.0493994	−	0.0855622i
$735$	−300.476	+	244.310i	−0.408810	+	0.332395i
$736$	47.5250	+	27.4386i	0.0645720	+	0.0372807i
$737$		−	1008.59i		−	1.36851i
$738$	−241.617	−	215.821i	−0.327395	−	0.292441i
$739$		−	791.607i		−	1.07119i	−0.844476	−	0.535593i	$-0.820088\pi$
$739$		−	791.607i		−	1.07119i	0.844476	−	0.535593i	$-0.179912\pi$
$740$	−91.4634	−	52.8064i	−0.123599	−	0.0713600i
$741$	−178.101	−	370.706i	−0.240352	−	0.500278i
$742$	−0.0894862	−	0.154995i	−0.000120601	−	0.000208888i
$743$	186.552	+	323.118i	0.251080	+	0.434883i	0.963823	−	0.266542i	$-0.0858809\pi$
$743$	186.552	+	323.118i	0.251080	+	0.434883i	−0.712743	+	0.701425i	$0.752548\pi$
$744$	430.117	−	68.9999i	0.578114	−	0.0927418i
$745$	−44.0125	+	76.2319i	−0.0590772	+	0.102325i
$746$	−280.421			−0.375900
$747$	−1229.89	+	405.023i	−1.64643	+	0.542199i
$748$			1312.39i			1.75453i
$749$	−884.933	+	1532.75i	−1.18149	+	2.04639i
$750$	132.294	−	107.565i	0.176392	−	0.143420i
$751$	446.787	+	773.858i	0.594923	+	1.03044i	0.993558	+	0.113327i	$0.0361507\pi$
$751$	446.787	+	773.858i	0.594923	+	1.03044i	−0.398635	+	0.917110i	$0.630516\pi$
$752$	−179.954	−	311.690i	−0.239301	−	0.414481i
$753$	238.388	−	624.728i	0.316584	−	0.829652i
$754$	3.65403	−	15.2760i	0.00484619	−	0.0202600i
$755$		−	92.4282i		−	0.122421i
$756$	886.187	−	458.207i	1.17221	−	0.606094i
$757$	−121.247			−0.160168			−0.0800839	−	0.996788i	$-0.525519\pi$
$757$	−121.247			−0.160168			−0.0800839	+	0.996788i	$0.525519\pi$
$758$	−142.097	−	82.0398i	−0.187463	−	0.108232i
$759$	−41.9664	+	109.979i	−0.0552917	+	0.144899i
$760$	94.3755	−	54.4877i	0.124178	−	0.0716944i
$761$	342.786	+	593.723i	0.450442	+	0.780189i	0.998413	−	0.0563086i	$-0.0179331\pi$
$761$	342.786	+	593.723i	0.450442	+	0.780189i	−0.547971	+	0.836497i	$0.684600\pi$
$762$	−81.1677	+	65.9957i	−0.106519	+	0.0866085i
$763$	575.567	−	996.912i	0.754348	−	1.30657i
$764$			265.246i			0.347180i
$765$	536.081	+	111.724i	0.700759	+	0.146044i
$766$	223.257			0.291458
$767$	−832.771	−	199.199i	−1.08575	−	0.259712i
$768$	54.5458	+	340.016i	0.0710232	+	0.442729i
$769$	−907.453	+	523.918i	−1.18004	+	0.681298i	−0.956025	−	0.293287i	$-0.905251\pi$
$769$	−907.453	+	523.918i	−1.18004	+	0.681298i	−0.224019	+	0.974585i	$0.571918\pi$
$770$	−176.279	+	101.775i	−0.228934	+	0.132175i
$771$	−697.650	+

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.245962 - 0.426018i) q^{2} +(-2.80287 - 1.06954i) q^{3} +(1.87901 + 3.25453i) q^{4} +(-1.35391 - 2.34503i) q^{5} +(-1.14504 + 0.931009i) q^{6} +(8.51494 + 4.91611i) q^{7} +3.81635 q^{8} +(6.71217 + 5.99556i) q^{9} -1.33204 q^{10} +(7.77093 - 13.4596i) q^{11} +(-1.78576 - 11.1317i) q^{12} +(8.94077 - 9.43730i) q^{13} +(4.18870 - 2.41835i) q^{14} +(1.28672 + 8.02089i) q^{15} +(-6.57735 + 11.3923i) q^{16} +22.4699i q^{17} +(4.20516 - 1.38483i) q^{18} +10.5454i q^{19} +(5.08800 - 8.81267i) q^{20} +(-18.6083 - 22.8863i) q^{21} +(-3.82270 - 6.62112i) q^{22} +(2.18641 - 1.26233i) q^{23} +(-10.6967 - 4.08173i) q^{24} +(8.83387 - 15.3007i) q^{25} +(-1.82137 - 6.13015i) q^{26} +(-12.4009 - 23.9837i) q^{27} +36.9496i q^{28} +(2.12707 + 1.22806i) q^{29} +(3.73353 + 1.42467i) q^{30} +(-32.9508 + 19.0241i) q^{31} +(10.8683 + 18.8244i) q^{32} +(-36.1765 + 29.4143i) q^{33} +(9.57260 + 5.52674i) q^{34} -26.6238i q^{35} +(-6.90053 + 33.1107i) q^{36} -10.3786i q^{37} +(4.49252 + 2.59376i) q^{38} +(-35.1534 + 16.8890i) q^{39} +(-5.16698 - 8.94947i) q^{40} +(-36.5879 - 63.3720i) q^{41} +(-14.3269 + 2.29834i) q^{42} +(-22.9633 + 39.7736i) q^{43} +58.4065 q^{44} +(4.97214 - 23.8577i) q^{45} -1.24194i q^{46} +(-13.6798 + 23.6942i) q^{47} +(30.6200 - 24.8964i) q^{48} +(23.8362 + 41.2855i) q^{49} +(-4.34559 - 7.52679i) q^{50} +(24.0324 - 62.9803i) q^{51} +(47.5138 + 11.3653i) q^{52} -0.0370030i q^{53} +(-13.2676 - 0.616076i) q^{54} -42.0844 q^{55} +(32.4960 + 18.7616i) q^{56} +(11.2787 - 29.5573i) q^{57} +(1.04636 - 0.604114i) q^{58} +(-32.9332 - 57.0420i) q^{59} +(-23.6865 + 19.2590i) q^{60} +(40.6820 - 70.4633i) q^{61} +18.7168i q^{62} +(27.6790 + 84.0496i) q^{63} -41.9261 q^{64} +(-34.2358 - 8.18920i) q^{65} +(3.63301 + 22.6467i) q^{66} +(56.2009 - 32.4476i) q^{67} +(-73.1291 + 42.2211i) q^{68} +(-7.47835 + 1.19968i) q^{69} +(-11.3422 - 6.54843i) q^{70} +29.5878 q^{71} +(25.6160 + 22.8811i) q^{72} -28.3208i q^{73} +(-4.42149 - 2.55275i) q^{74} +(-41.1249 + 33.4378i) q^{75} +(-34.3203 + 19.8148i) q^{76} +(132.338 - 76.4054i) q^{77} +(-1.45136 + 19.1300i) q^{78} +(-36.3943 + 63.0368i) q^{79} +35.6204 q^{80} +(9.10655 + 80.4865i) q^{81} -35.9969 q^{82} +(-71.9367 + 124.598i) q^{83} +(39.5190 - 103.565i) q^{84} +(52.6927 - 30.4222i) q^{85} +(11.2962 + 19.5656i) q^{86} +(-4.64844 - 5.71709i) q^{87} +(29.6566 - 51.3667i) q^{88} +80.5846 q^{89} +(-8.94086 - 7.98631i) q^{90} +(122.525 - 36.4043i) q^{91} +(8.21657 + 4.74384i) q^{92} +(112.704 - 18.0801i) q^{93} +(6.72944 + 11.6557i) q^{94} +(24.7293 - 14.2775i) q^{95} +(-10.3289 - 64.3863i) q^{96} +(-97.7027 - 56.4087i) q^{97} +23.4512 q^{98} +(132.858 - 43.7524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

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