LMFDB - Embedded newform 117.3.n.a.38.12

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			38.12
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.12

$q$-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} +(-12.6433 + 3.02429i) 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} +(38.6722 + 5.04584i) 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} +(-33.5995 - 35.4655i) 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} +(-24.2099 - 25.5544i) 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} +(-11.6615 + 15.2340i) 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	−0.920942	−	0.389700i	$-0.872579\pi$
$2$	−0.245962	+	0.426018i	−0.122981	+	0.213009i	0.797961	+	0.602709i	$0.205912\pi$
$3$	−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	0.969062	−	0.246817i	$-0.0793846\pi$
$5$	1.35391	+	2.34503i	0.270781	+	0.469007i	−0.698281	+	0.715824i	$0.746051\pi$
$6$	1.14504	−	0.931009i	0.190840	−	0.155168i
$7$	−8.51494	−	4.91611i	−1.21642	−	0.702301i	−0.252270	−	0.967657i	$-0.581177\pi$
$7$	−8.51494	−	4.91611i	−1.21642	−	0.702301i	−0.964150	+	0.265356i	$0.914510\pi$
$8$	−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	$0.416370\pi$
$11$	−7.77093	+	13.4596i	−0.706448	+	1.22360i	−0.966166	+	0.257920i	$0.916963\pi$
$12$	−1.78576	−	11.1317i	−0.148813	−	0.927642i
$13$	−12.6433	+	3.02429i	−0.972564	+	0.232637i
$13$	−12.6433	+	3.02429i	−0.972564	+	0.232637i
$14$	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	$-0.910491\pi$
$19$		−	10.5454i		−	0.555020i	0.960723	−	0.277510i	$-0.0895091\pi$
$20$	−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	0.136687	−	0.990614i	$-0.456354\pi$
$31$	32.9508	−	19.0241i	1.06293	−	0.613682i	0.926241	+	0.376933i	$0.123021\pi$
$32$	−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	$0.0447912\pi$
$37$			10.3786i			0.280504i	−0.990116	+	0.140252i	$0.955209\pi$
$38$	4.49252	+	2.59376i	0.118224	+	0.0682568i
$39$	38.6722	+	5.04584i	0.991595	+	0.129380i
$40$	−5.16698	−	8.94947i	−0.129174	−	0.223737i
$41$	36.5879	+	63.3720i	0.892387	+	1.54566i	0.837006	+	0.547194i	$0.184304\pi$
$41$	36.5879	+	63.3720i	0.892387	+	1.54566i	0.0553805	+	0.998465i	$0.482363\pi$
$42$	−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	−0.683000	−	0.730418i	$-0.739325\pi$
$47$	13.6798	−	23.6942i	0.291060	−	0.504132i	0.974061	+	0.226287i	$0.0726586\pi$
$48$	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
$52$	−33.5995	−	35.4655i	−0.646145	−	0.682028i
$53$		−	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	$0.0218373\pi$
$59$	32.9332	+	57.0420i	0.558190	+	0.966814i	−0.439458	+	0.898263i	$0.644829\pi$
$60$	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
$65$	−24.2099	−	25.5544i	−0.372461	−	0.393145i
$66$	3.63301	+	22.6467i	0.0550455	+	0.343131i
$67$	−56.2009	+	32.4476i	−0.838819	+	0.484293i	−0.856863	−	0.515545i	$-0.827590\pi$
$67$	−56.2009	+	32.4476i	−0.838819	+	0.484293i	0.0180434	+	0.999837i	$0.494256\pi$
$68$	−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	$-0.566814\pi$
$71$	−29.5878			−0.416730			−0.208365	+	0.978051i	$0.566814\pi$
$72$	−25.6160	−	22.8811i	−0.355778	−	0.317794i
$73$			28.3208i			0.387956i	0.981006	+	0.193978i	$0.0621390\pi$
$73$			28.3208i			0.387956i	−0.981006	+	0.193978i	$0.937861\pi$
$74$	−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
$78$	−11.6615	+	15.2340i	−0.149506	+	0.195308i
$79$	−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	$-0.499565\pi$
$83$	71.9367	−	124.598i	0.866708	−	1.50118i	0.865342	−	0.501182i	$-0.167101\pi$
$84$	−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	$-0.649547\pi$
$89$	−80.5846			−0.905445			−0.452722	+	0.891652i	$0.649547\pi$
$90$	−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	0.910384	−	0.413765i	$-0.135787\pi$
$97$	97.7027	+	56.4087i	1.00724	+	0.581533i	0.0968606	+	0.995298i	$0.469120\pi$
$98$	−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	$0.799555\pi$
$104$	48.2513	−	11.5417i	0.463955	−	0.110978i
$105$	−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	$0.180463\pi$
$109$			117.078i			1.07411i	−0.843548	+	0.537055i	$0.819537\pi$
$110$	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
$117$	−102.996	−	55.5043i	−0.880312	−	0.474395i
$118$	−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
$130$	16.8414	−	4.02846i	0.129549	−	0.0309882i
$131$	−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	−0.709559	−	0.704646i	$-0.751106\pi$
$137$	34.9983	−	60.6188i	0.255462	−	0.442473i	0.965021	+	0.262173i	$0.0844391\pi$
$138$	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	0.915400	−	0.402544i	$-0.131874\pi$
$149$	16.2539	+	28.1526i	0.109087	+	0.188944i	−0.806314	+	0.591488i	$0.798541\pi$
$150$	−4.12994	−	25.7444i	−0.0275330	−	0.171629i
$151$	−29.5608	−	17.0670i	−0.195767	−	0.113026i	0.398912	−	0.916989i	$-0.369388\pi$
$151$	−29.5608	−	17.0670i	−0.195767	−	0.113026i	−0.594680	+	0.803963i	$0.702721\pi$
$152$			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
$156$	56.2434	+	135.341i	0.360535	+	0.867571i
$157$	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	$-0.958314\pi$
$163$		−	42.5714i		−	0.261174i	0.991437	−	0.130587i	$-0.0416862\pi$
$164$	−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	$0.0472667\pi$
$167$	103.978	+	180.096i	0.622624	+	1.07842i	−0.366371	+	0.930469i	$0.619400\pi$
$168$	−71.0159	−	87.3420i	−0.422713	−	0.519893i
$169$	150.707	−	76.4741i	0.891760	−	0.452509i
$170$		−	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	$0.347393\pi$
$182$	−45.6453	+	43.2438i	−0.250799	+	0.237603i
$183$	−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	−0.391646	−	0.920116i	$-0.628094\pi$
$193$	40.4093	−	23.3303i	0.209375	−	0.120883i	0.601021	+	0.799233i	$0.294761\pi$
$194$	−48.0623	+	27.7488i	−0.247744	+	0.143035i
$195$	40.5259	+	97.5193i	0.207825	+	0.500099i
$196$	−89.5766	+	155.151i	−0.457024	+	0.791588i
$197$	−194.423			−0.986919			−0.493460	−	0.869769i	$-0.664268\pi$
$197$	−194.423			−0.986919			−0.493460	+	0.869769i	$0.664268\pi$
$198$	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
$221$	−67.9555	−	284.095i	−0.307491	−	1.28550i
$222$	9.66260	+	11.8840i	0.0435252	+	0.0535314i
$223$	198.753	+	114.750i	0.891271	+	0.514575i	0.874358	−	0.485282i	$-0.161283\pi$
$223$	198.753	+	114.750i	0.891271	+	0.514575i	0.0169128	+	0.999857i	$0.494616\pi$
$224$			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	$0.351629\pi$
$227$	−124.606	+	215.824i	−0.548925	+	0.950766i	−0.998349	+	0.0574473i	$0.981704\pi$
$228$	−117.388	+	18.8315i	−0.514860	+	0.0825944i
$229$	−46.3299	+	26.7486i	−0.202314	+	0.116806i	−0.597734	−	0.801694i	$-0.703932\pi$
$229$	−46.3299	+	26.7486i	−0.202314	+	0.116806i	0.395420	+	0.918500i	$0.370599\pi$
$230$	−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	$-0.0768602\pi$
$234$	48.9790	−	30.2265i	0.209312	−	0.129173i
$235$	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	0.999960	−	0.00896368i	$-0.00285327\pi$
$239$	117.640	+	203.758i	0.492217	+	0.852545i	−0.507743	+	0.861509i	$0.669520\pi$
$240$	99.8395	+	38.0974i	0.415998	+	0.158739i
$241$	−220.705	−	127.424i	−0.915787	−	0.528730i	−0.0334983	−	0.999439i	$-0.510665\pi$
$241$	−220.705	−	127.424i	−0.915787	−	0.528730i	−0.882289	+	0.470709i	$0.843998\pi$
$242$	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
$247$	31.8922	+	133.329i	0.129118	+	0.539792i
$248$	−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	$-0.548112\pi$
$271$		−	535.820i		−	1.97720i	0.150574	−	0.988599i	$-0.451888\pi$
$272$	−255.984	−	147.792i	−0.941118	−	0.543355i
$273$	−304.486	−	233.082i	−1.11533	−	0.853779i
$274$	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	−0.793514	−	0.608553i	$-0.791750\pi$
$281$	36.6045	−	63.4009i	0.130265	−	0.225626i	0.923779	+	0.382927i	$0.125084\pi$
$282$	−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
$286$	68.3559	+	72.1520i	0.239006	+	0.252280i
$287$		−	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	0.827744	−	0.561105i	$-0.189624\pi$
$293$	−21.1134	−	36.5695i	−0.0720594	−	0.124810i	−0.899804	+	0.436295i	$0.856290\pi$
$294$	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
$299$	−23.8259	+	22.5724i	−0.0796853	+	0.0754928i
$300$	−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	$0.0713385\pi$
$307$			136.458i			0.444490i	−0.974991	+	0.222245i	$0.928662\pi$
$308$	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	$0.164274\pi$
$312$	−147.587	−	19.2567i	−0.473034	−	0.0617201i
$313$	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	−0.923624	−	0.383299i	$-0.874788\pi$
$317$	−41.1674	+	71.3040i	−0.129866	+	0.224934i	0.793759	+	0.608233i	$0.208121\pi$
$318$	−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	0.289644	−	0.957135i	$-0.406463\pi$
$331$	−130.559	−	75.3781i	−0.394437	−	0.227728i	−0.684081	+	0.729406i	$0.739797\pi$
$332$	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	$0.716758\pi$
$338$	−4.48889	+	83.0138i	−0.0132807	+	0.245603i
$339$	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	0.877019	−	0.480456i	$-0.159529\pi$
$349$	313.905	+	181.233i	0.899442	+	0.519293i	0.0224227	+	0.999749i	$0.492862\pi$
$350$		−	85.4535i		−	0.244153i
$351$	229.322	+	265.730i	0.653339	+	0.757066i
$352$	337.826			0.959732
$353$	31.9628	−	55.3612i	0.0905462	−	0.156831i	−0.817195	−	0.576361i	$-0.804472\pi$
$353$	31.9628	−	55.3612i	0.0905462	−	0.156831i	0.907741	+	0.419531i	$0.137805\pi$
$354$	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	$-0.667143\pi$
$359$	−359.930			−1.00259			−0.501295	+	0.865276i	$0.667143\pi$
$360$	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
$364$	111.746	+	467.165i	0.306995	+	1.28342i
$365$	−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	$0.145034\pi$
$379$			333.547i			0.880071i	−0.897980	+	0.440036i	$0.854966\pi$
$380$	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	$-0.964813\pi$
$383$	−226.922	−	393.041i	−0.592486	−	1.02622i	0.401410	−	0.915898i	$-0.368520\pi$
$384$	−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	$0.830569\pi$
$390$	−51.5128	−	6.72124i	−0.132084	−	0.0172340i
$391$	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	$-0.953894\pi$
$397$		−	114.607i		−	0.288682i	0.989528	−	0.144341i	$-0.0461062\pi$
$398$	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	0.575832	−	0.817568i	$-0.304678\pi$
$401$	−168.468	−	291.795i	−0.420119	−	0.727667i	−0.995951	+	0.0899009i	$0.971345\pi$
$402$	−34.1434	+	89.4774i	−0.0849338	+	0.222581i
$403$	−359.073	+	340.181i	−0.891000	+	0.844121i
$404$		−	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	0.331395	−	0.943492i	$-0.392481\pi$
$409$	537.500	−	310.326i	1.31418	−	0.758742i	0.982786	+	0.184750i	$0.0591475\pi$
$410$	−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
$416$	194.341	+	205.134i	0.467166	+	0.493110i
$417$	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	$0.0109896\pi$
$421$	643.709	+	371.645i	1.52900	+	0.882768i	0.529595	+	0.848250i	$0.322344\pi$
$422$	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
$429$	−368.434	+	481.303i	−0.858821	+	1.12192i
$430$	30.5880	−	52.9799i	0.0711348	−	0.123209i
$431$	649.249			1.50638			0.753189	−	0.657804i	$-0.228515\pi$
$431$	649.249			1.50638			0.753189	+	0.657804i	$0.228515\pi$
$432$	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	$-0.544955\pi$
$449$	−126.404			−0.281523			−0.140762	+	0.990044i	$0.544955\pi$
$450$	−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
$455$	80.5180	+	336.613i	0.176963	+	0.739809i
$456$	43.0434	−	112.801i	0.0943934	−	0.247371i
$457$	−574.817	−	331.871i	−1.25781	−	0.726194i	−0.285158	−	0.958481i	$-0.592046\pi$
$457$	−574.817	−	331.871i	−1.25781	−	0.726194i	−0.972647	+	0.232286i	$0.925379\pi$
$458$		−	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	−0.848584	−	0.529061i	$-0.822544\pi$
$461$	15.6227	−	27.0593i	0.0338887	−	0.0586969i	0.882472	+	0.470364i	$0.155877\pi$
$462$	80.3986	−	210.695i	0.174023	−	0.456051i
$463$	558.193	−	322.273i	1.20560	−	0.696053i	0.243805	−	0.969824i	$-0.421604\pi$
$463$	558.193	−	322.273i	1.20560	−	0.696053i	0.961795	+	0.273771i	$0.0882710\pi$
$464$	−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	$0.780166\pi$
$468$	−12.8905	−	439.498i	−0.0275439	−	0.939099i
$469$	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	−0.831303	−	0.555820i	$-0.812405\pi$
$479$	31.4715	−	54.5102i	0.0657025	−	0.113800i	0.897005	+	0.442020i	$0.145738\pi$
$480$	−137.004	+	111.395i	−0.285424	+	0.232072i
$481$	−31.3880	−	131.220i	−0.0652556	−	0.272808i
$482$	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	$0.0470516\pi$
$487$			143.450i			0.294558i	−0.989095	+	0.147279i	$0.952948\pi$
$488$	−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	−0.442477	−	0.896780i	$-0.645900\pi$
$499$	56.3465	−	32.5317i	0.112919	−	0.0651937i	0.555396	+	0.831586i	$0.312567\pi$
$500$	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
$507$	−504.205	+	53.1597i	−0.994488	+	0.104851i
$508$	133.196	+	230.702i	0.262196	+	0.454137i
$509$	−288.131	−	499.058i	−0.566073	−	0.980468i	−0.996949	−	0.0780566i	$-0.975129\pi$
$509$	−288.131	−	499.058i	−0.566073	−	0.980468i	0.430875	−	0.902411i	$-0.358205\pi$
$510$	−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
$520$	92.3936	+	97.5246i	0.177680	+	0.187547i
$521$		−	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
$533$	−654.247	−	690.581i	−1.22748	−	1.29565i
$534$	−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	$0.0216469\pi$
$541$			73.5254i			0.135906i	−0.997689	+	0.0679532i	$0.978353\pi$
$542$	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
$546$	174.189	−	72.3873i	0.319027	−	0.132578i
$547$	−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	$-0.640425\pi$
$557$	−475.662			−0.853972			−0.426986	+	0.904258i	$0.640425\pi$
$558$	−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	$0.552919\pi$
$572$	738.452	−	176.638i	1.29100	−	0.308808i
$573$	−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	$-0.831143\pi$
$577$		−	583.864i		−	1.01190i	0.862564	−	0.505948i	$-0.168857\pi$
$578$	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
$585$	−9.28820	−	316.678i	−0.0158773	−	0.541330i
$586$	20.7724			0.0354477
$587$	−375.099	+	649.690i	−0.639010	+	1.10680i	0.346640	+	0.937998i	$0.387322\pi$
$587$	−375.099	+	649.690i	−0.639010	+	1.10680i	−0.985650	+	0.168800i	$0.946011\pi$
$588$	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	$-0.862567\pi$
$593$	−1077.16			−1.81646			−0.908231	+	0.418469i	$0.862567\pi$
$594$	−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
$598$	−3.75597	−	15.7022i	−0.00628089	−	0.0262579i
$599$	−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	$-0.765819\pi$
$613$		−	822.777i		−	1.34221i	0.741360	−	0.671107i	$-0.234181\pi$
$614$	−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	0.998206	−	0.0598711i	$-0.0190690\pi$
$617$	275.955	+	477.968i	0.447253	+	0.774665i	−0.550953	+	0.834536i	$0.685736\pi$
$618$	30.0841	+	11.4797i	0.0486797	+	0.0185755i
$619$	−350.084	−	202.121i	−0.565564	−	0.326529i	0.189812	−	0.981821i	$-0.439212\pi$
$619$	−350.084	−	202.121i	−0.565564	−	0.326529i	−0.755376	+	0.655292i	$0.772546\pi$
$620$			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
$624$	−311.844	+	407.377i	−0.499750	+	0.652848i
$625$	−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	$0.114349\pi$
$631$			443.670i			0.703123i	−0.936165	+	0.351561i	$0.885651\pi$
$632$	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
$637$	−426.228	−	449.898i	−0.669117	−	0.706277i
$638$		−	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	−0.896961	−	0.442110i	$-0.854230\pi$
$643$	−618.928	+	357.338i	−0.962563	+	0.555736i	−0.0656022	+	0.997846i	$0.520897\pi$
$644$	−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
$650$	−77.7059	−	82.0213i	−0.119548	−	0.126187i
$651$	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	−0.444222	−	0.895917i	$-0.646520\pi$
$661$	72.4148	−	41.8087i	0.109553	−	0.0632507i	0.553776	+	0.832666i	$0.313187\pi$
$662$	64.2249	−	37.0803i	0.0970165	−	0.0560125i
$663$	−113.380	+	868.961i	−0.171010	+	1.31065i
$664$	−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	$-0.748230\pi$
$683$	−960.521			−1.40633			−0.703163	+	0.711029i	$0.748230\pi$
$684$	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
$689$	0.111908	+	0.467841i	0.000162421	+	0.000679015i
$690$	9.96143	−	1.59802i	0.0144369	−	0.00231598i
$691$	−398.707	−	230.194i	−0.577000	−	0.333131i	0.182940	−	0.983124i	$-0.441438\pi$
$691$	−398.707	−	230.194i	−0.577000	−	0.333131i	−0.759940	+	0.649993i	$0.774772\pi$
$692$			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	$-0.167476\pi$
$702$	−169.610	+	32.3359i	−0.241610	+	0.0460626i
$703$	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	$0.0555026\pi$
$709$	1153.90	+	666.202i	1.62750	+	0.939636i	0.642660	+	0.766151i	$0.277831\pi$
$710$	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
$715$	532.087	−	127.275i	0.744178	−	0.178008i
$716$	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	0.245108	−	0.969496i	$-0.421177\pi$
$733$	884.929	−	510.914i	1.20727	−	0.697018i	0.962162	+	0.272478i	$0.0878432\pi$
$734$	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	$0.179912\pi$
$739$			791.607i			1.07119i	−0.844476	+	0.535593i	$0.820088\pi$
$740$	−91.4634	−	52.8064i	−0.123599	−	0.0713600i
$741$	53.2103	−	407.813i	0.0718087	−	0.550355i
$742$	−0.0894862	−	0.154995i	−0.000120601	−	0.000208888i
$743$	−186.552	−	323.118i	−0.251080	−	0.434883i	0.712743	−	0.701425i	$-0.247452\pi$
$743$	−186.552	−	323.118i	−0.251080	−	0.434883i	−0.963823	+	0.266542i	$0.914119\pi$
$744$	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
$754$	11.4024	−	10.8025i	0.0151226	−	0.0143269i
$755$		−	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	0.547971	−	0.836497i	$-0.315400\pi$
$761$	−342.786	−	593.723i	−0.450442	−	0.780189i	−0.998413	+	0.0563086i	$0.982067\pi$
$762$	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
$767$	−588.897	−	621.601i	−0.767792	−	0.810432i
$768$	54.5458	+	340.016i	0.0710232	+	0.442729i
$769$	907.453	−	523.918i	1.18004	−	0.681298i	0.224019	−	0.974585i	$-0.428082\pi$
$769$	907.453	−	523.918i	1.18004	−	0.681298i	0.956025	+	0.293287i	$0.0947490\pi$
$770$	−176.279	+	101.775i	−0.228934	+	0.132175i
$771$	−697.650	+	111.918i

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} +(-12.6433 + 3.02429i) 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} +(38.6722 + 5.04584i) 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} +(-33.5995 - 35.4655i) 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} +(-24.2099 - 25.5544i) 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} +(-11.6615 + 15.2340i) 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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