LMFDB - Embedded newform 43.7.d.a.37.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.15
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.95456i q^{2} +(-14.3583 - 8.28978i) q^{3} +15.6341 q^{4} +(9.86801 + 5.69730i) q^{5} +(57.6517 - 99.8557i) q^{6} +(-310.875 + 179.484i) q^{7} +553.820i q^{8} +(-227.059 - 393.278i) q^{9} +O(q^{10})$	\(q+6.95456i q^{2} +(-14.3583 - 8.28978i) q^{3} +15.6341 q^{4} +(9.86801 + 5.69730i) q^{5} +(57.6517 - 99.8557i) q^{6} +(-310.875 + 179.484i) q^{7} +553.820i q^{8} +(-227.059 - 393.278i) q^{9} +(-39.6222 + 68.6277i) q^{10} -1005.14 q^{11} +(-224.480 - 129.604i) q^{12} +(-901.804 - 1561.97i) q^{13} +(-1248.23 - 2162.00i) q^{14} +(-94.4587 - 163.607i) q^{15} -2850.99 q^{16} +(-1332.58 - 2308.09i) q^{17} +(2735.07 - 1579.10i) q^{18} +(-2771.47 - 1600.11i) q^{19} +(154.278 + 89.0724i) q^{20} +5951.53 q^{21} -6990.29i q^{22} +(-516.012 + 893.760i) q^{23} +(4591.05 - 7951.92i) q^{24} +(-7747.58 - 13419.2i) q^{25} +(10862.8 - 6271.65i) q^{26} +19615.6i q^{27} +(-4860.27 + 2806.08i) q^{28} +(-27655.6 + 15967.0i) q^{29} +(1137.82 - 656.918i) q^{30} +(-12598.6 + 21821.3i) q^{31} +15617.1i q^{32} +(14432.1 + 8332.38i) q^{33} +(16051.8 - 9267.49i) q^{34} -4090.30 q^{35} +(-3549.87 - 6148.56i) q^{36} +(13186.5 + 7613.22i) q^{37} +(11128.1 - 19274.4i) q^{38} +29903.0i q^{39} +(-3155.28 + 5465.10i) q^{40} +34456.6 q^{41} +41390.3i q^{42} +(60437.9 + 51658.8i) q^{43} -15714.5 q^{44} -5174.50i q^{45} +(-6215.70 - 3588.64i) q^{46} +101043. q^{47} +(40935.4 + 23634.1i) q^{48} +(5604.54 - 9707.34i) q^{49} +(93324.6 - 53881.0i) q^{50} +44187.1i q^{51} +(-14098.9 - 24420.1i) q^{52} +(41465.7 - 71820.7i) q^{53} -136418. q^{54} +(-9918.72 - 5726.58i) q^{55} +(-99401.9 - 172169. i) q^{56} +(26529.1 + 45949.8i) q^{57} +(-111043. - 192333. i) q^{58} +122696. q^{59} +(-1476.78 - 2557.86i) q^{60} +(-342276. + 197613. i) q^{61} +(-151758. - 87617.4i) q^{62} +(141174. + 81507.0i) q^{63} -291073. q^{64} -20551.4i q^{65} +(-57948.0 + 100369. i) q^{66} +(77054.5 - 133462. i) q^{67} +(-20833.7 - 36085.0i) q^{68} +(14818.1 - 8555.26i) q^{69} -28446.2i q^{70} +(-172204. + 99422.2i) q^{71} +(217805. - 125750. i) q^{72} +(-21379.0 + 12343.2i) q^{73} +(-52946.5 + 91706.1i) q^{74} +256903. i q^{75} +(-43329.6 - 25016.4i) q^{76} +(312473. - 180406. i) q^{77} -207962. q^{78} +(-306288. - 530507. i) q^{79} +(-28133.6 - 16242.9i) q^{80} +(-2917.37 + 5053.04i) q^{81} +239630. i q^{82} +(214087. - 370810. i) q^{83} +93047.1 q^{84} -30368.4i q^{85} +(-359264. + 420319. i) q^{86} +529451. q^{87} -556666. i q^{88} +(902697. + 521172. i) q^{89} +35986.3 q^{90} +(560698. + 323719. i) q^{91} +(-8067.41 + 13973.2i) q^{92} +(361788. - 208878. i) q^{93} +702711. i q^{94} +(-18232.6 - 31579.8i) q^{95} +(129463. - 224236. i) q^{96} -1.53601e6 q^{97} +(67510.3 + 38977.1i) q^{98} +(228226. + 395299. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			6.95456i			0.869320i	0.900595	+	0.434660i	$0.143131\pi$
$2$			6.95456i			0.869320i	−0.900595	+	0.434660i	$0.856869\pi$
$3$	−14.3583	−	8.28978i	−0.531789	−	0.307029i	0.209955	−	0.977711i	$-0.432668\pi$
$3$	−14.3583	−	8.28978i	−0.531789	−	0.307029i	−0.741745	+	0.670682i	$0.766001\pi$
$4$	15.6341			0.244283
$5$	9.86801	+	5.69730i	0.0789441	+	0.0455784i	0.538952	−	0.842336i	$-0.318820\pi$
$5$	9.86801	+	5.69730i	0.0789441	+	0.0455784i	−0.460008	+	0.887915i	$0.652154\pi$
$6$	57.6517	−	99.8557i	0.266906	−	0.462295i
$7$	−310.875	+	179.484i	−0.906342	+	0.523277i	−0.879253	−	0.476356i	$-0.841957\pi$
$7$	−310.875	+	179.484i	−0.906342	+	0.523277i	−0.0270899	+	0.999633i	$0.508624\pi$
$8$			553.820i			1.08168i
$9$	−227.059	−	393.278i	−0.311467	−	0.539476i
$10$	−39.6222	+	68.6277i	−0.0396222	+	0.0686277i
$11$	−1005.14			−0.755176			−0.377588	−	0.925974i	$-0.623246\pi$
$11$	−1005.14			−0.755176			−0.377588	+	0.925974i	$0.623246\pi$
$12$	−224.480	−	129.604i	−0.129907	−	0.0750021i
$13$	−901.804	−	1561.97i	−0.410471	−	0.710956i	0.584471	−	0.811415i	$-0.301302\pi$
$13$	−901.804	−	1561.97i	−0.410471	−	0.710956i	−0.994941	+	0.100459i	$0.967969\pi$
$14$	−1248.23	−	2162.00i	−0.454895	−	0.787901i
$15$	−94.4587	−	163.607i	−0.0279878	−	0.0484762i
$16$	−2850.99			−0.696042
$17$	−1332.58	−	2308.09i	−0.271235	−	0.469793i	0.697943	−	0.716153i	$-0.254099\pi$
$17$	−1332.58	−	2308.09i	−0.271235	−	0.469793i	−0.969178	+	0.246360i	$0.920765\pi$
$18$	2735.07	−	1579.10i	0.468977	−	0.270764i
$19$	−2771.47	−	1600.11i	−0.404064	−	0.233286i	0.284172	−	0.958773i	$-0.408281\pi$
$19$	−2771.47	−	1600.11i	−0.404064	−	0.233286i	−0.688236	+	0.725487i	$0.741615\pi$
$20$	154.278	+	89.0724i	0.0192847	+	0.0111340i
$21$	5951.53			0.642645
$22$		−	6990.29i		−	0.656489i
$23$	−516.012	+	893.760i	−0.0424108	+	0.0734577i	−0.886452	−	0.462821i	$-0.846837\pi$
$23$	−516.012	+	893.760i	−0.0424108	+	0.0734577i	0.844041	+	0.536279i	$0.180170\pi$
$24$	4591.05	−	7951.92i	0.332107	−	0.575226i
$25$	−7747.58	−	13419.2i	−0.495845	−	0.858829i
$26$	10862.8	−	6271.65i	0.618048	−	0.356830i
$27$			19615.6i			0.996575i
$28$	−4860.27	+	2806.08i	−0.221404	+	0.127828i
$29$	−27655.6	+	15967.0i	−1.13394	+	0.654680i	−0.944923	−	0.327294i	$-0.893863\pi$
$29$	−27655.6	+	15967.0i	−1.13394	+	0.654680i	−0.189017	+	0.981974i	$0.560530\pi$
$30$	1137.82	−	656.918i	0.0421413	−	0.0243303i
$31$	−12598.6	+	21821.3i	−0.422898	+	0.732481i	−0.996222	−	0.0868483i	$-0.972320\pi$
$31$	−12598.6	+	21821.3i	−0.422898	+	0.732481i	0.573324	+	0.819329i	$0.305654\pi$
$32$			15617.1i			0.476597i
$33$	14432.1	+	8332.38i	0.401594	+	0.231861i
$34$	16051.8	−	9267.49i	0.408400	−	0.235790i
$35$	−4090.30			−0.0954005
$36$	−3549.87	−	6148.56i	−0.0760861	−	0.131785i
$37$	13186.5	+	7613.22i	0.260330	+	0.150301i	0.624485	−	0.781037i	$-0.285309\pi$
$37$	13186.5	+	7613.22i	0.260330	+	0.150301i	−0.364155	+	0.931338i	$0.618642\pi$
$38$	11128.1	−	19274.4i	0.202800	−	0.351261i
$39$			29903.0i			0.504105i
$40$	−3155.28	+	5465.10i	−0.0493012	+	0.0853923i
$41$	34456.6			0.499943			0.249972	−	0.968253i	$-0.419579\pi$
$41$	34456.6			0.499943			0.249972	+	0.968253i	$0.419579\pi$
$42$			41390.3i			0.558663i
$43$	60437.9	+	51658.8i	0.760158	+	0.649738i
$43$	60437.9	+	51658.8i	0.760158	+	0.649738i
$44$	−15714.5			−0.184477
$45$		−	5174.50i		−	0.0567846i
$46$	−6215.70	−	3588.64i	−0.0638582	−	0.0368685i
$47$	101043.			0.973226			0.486613	−	0.873618i	$-0.338232\pi$
$47$	101043.			0.973226			0.486613	+	0.873618i	$0.338232\pi$
$48$	40935.4	+	23634.1i	0.370148	+	0.213705i
$49$	5604.54	−	9707.34i	0.0476378	−	0.0825111i
$50$	93324.6	−	53881.0i	0.746597	−	0.431048i
$51$			44187.1i			0.333108i
$52$	−14098.9	−	24420.1i	−0.100271	−	0.173675i
$53$	41465.7	−	71820.7i	0.278523	−	0.482417i	−0.692495	−	0.721423i	$-0.743488\pi$
$53$	41465.7	−	71820.7i	0.278523	−	0.482417i	0.971018	+	0.239006i	$0.0768217\pi$
$54$	−136418.			−0.866342
$55$	−9918.72	−	5726.58i	−0.0596167	−	0.0344197i
$56$	−99401.9	−	172169.i	−0.566018	−	0.980373i
$57$	26529.1	+	45949.8i	0.143251	+	0.248119i
$58$	−111043.	−	192333.i	−0.569126	−	0.985756i
$59$	122696.			0.597413			0.298707	−	0.954345i	$-0.403445\pi$
$59$	122696.			0.597413			0.298707	+	0.954345i	$0.403445\pi$
$60$	−1476.78	−	2557.86i	−0.00683695	−	0.0118419i
$61$	−342276.	+	197613.i	−1.50795	+	0.870616i	−0.507995	+	0.861360i	$0.669613\pi$
$61$	−342276.	+	197613.i	−1.50795	+	0.870616i	−0.999957	+	0.00925632i	$0.997054\pi$
$62$	−151758.	−	87617.4i	−0.636760	−	0.367633i
$63$	141174.	+	81507.0i	0.564591	+	0.325967i
$64$	−291073.			−1.11036
$65$		−	20551.4i		−	0.0748344i
$66$	−57948.0	+	100369.i	−0.201561	+	0.349114i
$67$	77054.5	−	133462.i	0.256197	−	0.443746i	−0.709023	−	0.705185i	$-0.750864\pi$
$67$	77054.5	−	133462.i	0.256197	−	0.443746i	0.965220	+	0.261440i	$0.0841972\pi$
$68$	−20833.7	−	36085.0i	−0.0662582	−	0.114763i
$69$	14818.1	−	8555.26i	0.0451072	−	0.0260427i
$70$		−	28446.2i		−	0.0829335i
$71$	−172204.	+	99422.2i	−0.481137	+	0.277785i	−0.720890	−	0.693049i	$-0.756267\pi$
$71$	−172204.	+	99422.2i	−0.481137	+	0.277785i	0.239753	+	0.970834i	$0.422933\pi$
$72$	217805.	−	125750.i	0.583540	−	0.336907i
$73$	−21379.0	+	12343.2i	−0.0549565	+	0.0317292i	−0.527227	−	0.849725i	$-0.676768\pi$
$73$	−21379.0	+	12343.2i	−0.0549565	+	0.0317292i	0.472270	+	0.881454i	$0.343435\pi$
$74$	−52946.5	+	91706.1i	−0.130660	+	0.226310i
$75$			256903.i			0.608955i
$76$	−43329.6	−	25016.4i	−0.0987061	−	0.0569880i
$77$	312473.	−	180406.i	0.684448	−	0.395166i
$78$	−207962.			−0.438229
$79$	−306288.	−	530507.i	−0.621225	−	1.07599i	−0.989258	−	0.146180i	$-0.953302\pi$
$79$	−306288.	−	530507.i	−0.621225	−	1.07599i	0.368033	−	0.929813i	$-0.380031\pi$
$80$	−28133.6	−	16242.9i	−0.0549484	−	0.0317245i
$81$	−2917.37	+	5053.04i	−0.00548955	+	0.00950818i
$82$			239630.i			0.434611i
$83$	214087.	−	370810.i	0.374418	−	0.648511i	−0.615822	−	0.787886i	$-0.711176\pi$
$83$	214087.	−	370810.i	0.374418	−	0.648511i	0.990240	+	0.139374i	$0.0445091\pi$
$84$	93047.1			0.156987
$85$		−	30368.4i		−	0.0494498i
$86$	−359264.	+	420319.i	−0.564830	+	0.660820i
$87$	529451.			0.804023
$88$		−	556666.i		−	0.816858i
$89$	902697.	+	521172.i	1.28048	+	0.739284i	0.976936	−	0.213534i	$-0.0684974\pi$
$89$	902697.	+	521172.i	1.28048	+	0.739284i	0.303542	+	0.952818i	$0.401831\pi$
$90$	35986.3			0.0493640
$91$	560698.	+	323719.i	0.744054	+	0.429580i
$92$	−8067.41	+	13973.2i	−0.0103603	+	0.0179445i
$93$	361788.	−	208878.i	0.449785	−	0.259684i
$94$			702711.i			0.846044i
$95$	−18232.6	−	31579.8i	−0.0212656	−	0.0368332i
$96$	129463.	−	224236.i	0.146329	−	0.253449i
$97$	−1.53601e6			−1.68298			−0.841488	−	0.540276i	$-0.818320\pi$
$97$	−1.53601e6			−1.68298			−0.841488	+	0.540276i	$0.818320\pi$
$98$	67510.3	+	38977.1i	0.0717285	+	0.0414125i
$99$	228226.	+	395299.i	0.235212	+	0.407399i
$100$	−121127.	−	209798.i	−0.121127	−	0.209798i
$101$	−298522.	−	517055.i	−0.289742	−	0.501848i	0.684006	−	0.729476i	$-0.260236\pi$
$101$	−298522.	−	517055.i	−0.289742	−	0.501848i	−0.973748	+	0.227628i	$0.926903\pi$
$102$	−307302.			−0.289577
$103$	850263.	+	1.47270e6i	0.778111	+	1.34773i	0.933029	+	0.359800i	$0.117155\pi$
$103$	850263.	+	1.47270e6i	0.778111	+	1.34773i	−0.154918	+	0.987927i	$0.549511\pi$
$104$	865051.	−	499437.i	0.769027	−	0.443998i
$105$	58729.8	+	33907.7i	0.0507330	+	0.0292907i
$106$	499481.	+	288376.i	0.419374	+	0.242126i
$107$	307656.			0.251139			0.125570	−	0.992085i	$-0.459924\pi$
$107$	307656.			0.251139			0.125570	+	0.992085i	$0.459924\pi$
$108$			306673.i			0.243447i
$109$	−418448.	+	724773.i	−0.323119	+	0.559658i	−0.981130	−	0.193350i	$-0.938065\pi$
$109$	−418448.	+	724773.i	−0.323119	+	0.559658i	0.658011	+	0.753008i	$0.271398\pi$
$110$	39825.8	−	68980.3i	0.0299217	−	0.0518259i
$111$	−126224.	−	218626.i	−0.0922937	−	0.159857i
$112$	886302.	−	511707.i	0.630853	−	0.364223i
$113$			550895.i			0.381798i	0.981610	+	0.190899i	$0.0611402\pi$
$113$			550895.i			0.381798i	−0.981610	+	0.190899i	$0.938860\pi$
$114$	−319561.	+	184498.i	−0.215694	+	0.124531i
$115$	−10184.0	+	5879.75i	−0.00669617	+	0.00386603i
$116$	−432372.	+	249630.i	−0.277003	+	0.159928i
$117$	−409526.	+	709319.i	−0.255696	+	0.442878i
$118$			853297.i			0.519343i
$119$	828531.	+	478353.i	0.491664	+	0.283862i
$120$	90609.0	−	52313.1i	0.0524358	−	0.0302738i
$121$	−761257.			−0.429710
$122$	−1.37431e6	−	2.38038e6i	−0.756844	−	1.31089i
$123$	−494739.	−	285638.i	−0.265865	−	0.153497i
$124$	−196968.	+	341158.i	−0.103307	+	0.178933i
$125$		−	354602.i		−	0.181556i
$126$	−566845.	+	981804.i	−0.283369	+	0.490810i
$127$	−2.75996e6			−1.34738			−0.673692	−	0.739013i	$-0.735292\pi$
$127$	−2.75996e6			−1.34738			−0.673692	+	0.739013i	$0.735292\pi$
$128$		−	1.02479e6i		−	0.488658i
$129$	−439546.	−	1.24275e6i	−0.204756	−	0.578914i
$130$	142926.			0.0650550
$131$		−	3.02421e6i		−	1.34523i	−0.739991	−	0.672617i	$-0.765170\pi$
$131$		−	3.02421e6i		−	1.34523i	0.739991	−	0.672617i	$-0.234830\pi$
$132$	225633.	+	130270.i	0.0981029	+	0.0566397i
$133$	1.14878e6			0.488294
$134$	928171.	+	535880.i	0.385757	+	0.222717i
$135$	−111756.	+	193567.i	−0.0454223	+	0.0786737i
$136$	1.27827e6	−	738008.i	0.508165	−	0.293389i
$137$		−	4.66521e6i		−	1.81430i	−0.420806	−	0.907151i	$-0.638253\pi$
$137$		−	4.66521e6i		−	1.81430i	0.420806	−	0.907151i	$-0.361747\pi$
$138$	59498.0	+	103054.i	0.0226394	+	0.0392126i
$139$	−577643.	+	1.00051e6i	−0.215087	+	0.372542i	−0.953300	−	0.302026i	$-0.902337\pi$
$139$	−577643.	+	1.00051e6i	−0.215087	+	0.372542i	0.738212	+	0.674568i	$0.235670\pi$
$140$	−63948.3			−0.0233048
$141$	−1.45081e6	−	837626.i	−0.517551	−	0.298808i
$142$	−691437.	−	1.19760e6i	−0.241484	−	0.418262i
$143$	906438.	+	1.57000e6i	0.309977	+	0.536897i
$144$	647343.	+	1.12123e6i	0.216794	+	0.375498i
$145$	−363875.			−0.119357
$146$	−85841.4	−	148682.i	−0.0275828	−	0.0477748i
$147$	−160943.	+	92920.7i	−0.0506665	+	0.0292523i
$148$	206159.	+	119026.i	0.0635942	+	0.0367161i
$149$	−977471.	−	564343.i	−0.295492	−	0.170602i	0.344924	−	0.938631i	$-0.387905\pi$
$149$	−977471.	−	564343.i	−0.295492	−	0.170602i	−0.640416	+	0.768028i	$0.721238\pi$
$150$	−1.78665e6			−0.529377
$151$			462133.i			0.134226i	0.997745	+	0.0671129i	$0.0213788\pi$
$151$			462133.i			0.134226i	−0.997745	+	0.0671129i	$0.978621\pi$
$152$	886174.	−	1.53490e6i	0.252341	−	0.437068i
$153$	−605148.	+	1.04815e6i	−0.168961	+	0.292650i
$154$	1.25465e6	+	2.17311e6i	0.343526	+	0.595004i
$155$	−248645.	+	143555.i	−0.0667706	+	0.0385500i
$156$			467508.i			0.123145i
$157$	−871134.	+	502950.i	−0.225106	+	0.129965i	−0.608312	−	0.793698i	$-0.708153\pi$
$157$	−871134.	+	502950.i	−0.225106	+	0.129965i	0.383207	+	0.923663i	$0.374820\pi$
$158$	3.68944e6	−	2.13010e6i	0.935382	−	0.540043i
$159$	−1.19076e6	+	687483.i	−0.296232	+	0.171029i
$160$	−88975.5	+	154110.i	−0.0217225	+	0.0376245i
$161$		−	370464.i		−	0.0887704i
$162$	−35141.6	−	20289.0i	−0.00826565	−	0.00477217i
$163$	459244.	−	265145.i	0.106043	−	0.0612238i	−0.446041	−	0.895013i	$-0.647166\pi$
$163$	459244.	−	265145.i	0.106043	−	0.0612238i	0.552083	+	0.833789i	$0.313833\pi$
$164$	538699.			0.122128
$165$	94944.1	+	164448.i	0.0211357	+	0.0366081i
$166$	2.57882e6	+	1.48888e6i	0.563764	+	0.325489i
$167$	−30644.6	+	53078.1i	−0.00657969	+	0.0113964i	−0.869297	−	0.494291i	$-0.835428\pi$
$167$	−30644.6	+	53078.1i	−0.00657969	+	0.0113964i	0.862717	+	0.505687i	$0.168761\pi$
$168$			3.29608e6i			0.695136i
$169$	786903.	−	1.36296e6i	0.163028	−	0.282372i
$170$	211199.			0.0429877
$171$			1.45328e6i			0.290644i
$172$	944894.	+	807640.i	0.185694	+	0.158720i
$173$	−5.53281e6			−1.06858			−0.534291	−	0.845301i	$-0.679421\pi$
$173$	−5.53281e6			−1.06858			−0.534291	+	0.845301i	$0.679421\pi$
$174$			3.68210e6i			0.698953i
$175$	4.81707e6	+	2.78113e6i	0.898811	+	0.518929i
$176$	2.86564e6			0.525634
$177$	−1.76171e6	−	1.01712e6i	−0.317698	−	0.183423i
$178$	−3.62452e6	+	6.27786e6i	−0.642674	+	1.11314i
$179$	−1.49410e6	+	862621.i	−0.260508	+	0.150405i	−0.624566	−	0.780972i	$-0.714724\pi$
$179$	−1.49410e6	+	862621.i	−0.260508	+	0.150405i	0.364058	+	0.931376i	$0.381391\pi$
$180$		−	80898.8i		−	0.0138715i
$181$	−300028.	−	519664.i	−0.0505972	−	0.0876368i	0.839618	−	0.543178i	$-0.182779\pi$
$181$	−300028.	−	519664.i	−0.0505972	−	0.0876368i	−0.890215	+	0.455541i	$0.849446\pi$
$182$	−2.25132e6	+	3.89940e6i	−0.373442	+	0.646821i
$183$	6.55268e6			1.06922
$184$	−494982.	−	285778.i	−0.0794577	−	0.0458749i
$185$	86749.5	+	150255.i	0.0137010	+	0.0237308i
$186$	1.45266e6	+	2.51608e6i	0.225748	+	0.391007i
$187$	1.33943e6	+	2.31995e6i	0.204830	+	0.354776i
$188$	1.57972e6			0.237743
$189$	−3.52068e6	−	6.09800e6i	−0.521485	−	0.903238i
$190$	219624.	−	126800.i	0.0320198	−	0.0184866i
$191$	−5.26297e6	−	3.03858e6i	−0.755319	−	0.436084i	0.0722935	−	0.997383i	$-0.476968\pi$
$191$	−5.26297e6	−	3.03858e6i	−0.755319	−	0.436084i	−0.827613	+	0.561300i	$0.810302\pi$
$192$	4.17932e6	+	2.41293e6i	0.590476	+	0.340912i
$193$	8.80070e6			1.22418			0.612090	−	0.790788i	$-0.290329\pi$
$193$	8.80070e6			1.22418			0.612090	+	0.790788i	$0.290329\pi$
$194$		−	1.06822e7i		−	1.46304i
$195$	−170366.	+	295083.i	−0.0229763	+	0.0397961i
$196$	87622.1	−	151766.i	0.0116371	−	0.0201561i
$197$	−2.47651e6	−	4.28944e6i	−0.323923	−	0.561051i	0.657371	−	0.753567i	$-0.271668\pi$
$197$	−2.47651e6	−	4.28944e6i	−0.323923	−	0.561051i	−0.981294	+	0.192516i	$0.938335\pi$
$198$	−2.74913e6	+	1.58721e6i	−0.354160	+	0.204474i
$199$			3.02183e6i			0.383452i	0.981448	+	0.191726i	$0.0614086\pi$
$199$			3.02183e6i			0.383452i	−0.981448	+	0.191726i	$0.938591\pi$
$200$	7.43183e6	−	4.29077e6i	0.928978	−	0.536346i
$201$	−2.21274e6	+	1.27753e6i	−0.272485	+	0.157319i
$202$	3.59589e6	−	2.07609e6i	0.436266	−	0.251879i
$203$	5.73164e6	−	9.92749e6i	0.685158	−	1.18673i
$204$			690827.i			0.0813727i
$205$	340018.	+	196310.i	0.0394676	+	0.0227866i
$206$	−1.02420e7	+	5.91320e6i	−1.17161	+	0.676427i
$207$	468661.			0.0528382
$208$	2.57103e6	+	4.45316e6i	0.285705	+	0.494855i
$209$	2.78572e6	+	1.60833e6i	0.305139	+	0.176172i
$210$	−235813.	+	408440.i	−0.0254630	+	0.0441032i
$211$		−	1.18294e6i		−	0.125926i	−0.998016	−	0.0629629i	$-0.979945\pi$
$211$		−	1.18294e6i		−	0.125926i	0.998016	−	0.0629629i	$-0.0200550\pi$
$212$	648281.	−	1.12286e6i	0.0680387	−	0.117846i
$213$	3.29675e6			0.341151
$214$			2.13961e6i			0.218320i
$215$	302086.	+	854102.i	0.0303959	+	0.0859398i
$216$	−1.08635e7			−1.07797
$217$		−	9.04496e6i		−	0.885171i
$218$	−5.04048e6	−	2.91012e6i	−0.486522	−	0.280893i
$219$	409289.			0.0389671
$220$	−155071.	−	89530.1i	−0.0145634	−	0.00840816i
$221$	−2.40345e6	+	4.16289e6i	−0.222668	+	0.385672i
$222$	1.52045e6	−	877830.i	0.138967	−	0.0802327i
$223$			3.37747e6i			0.304563i	0.988337	+	0.152282i	$0.0486621\pi$
$223$			3.37747e6i			0.304563i	−0.988337	+	0.152282i	$0.951338\pi$
$224$	−2.80302e6	−	4.85498e6i	−0.249392	−	0.431960i
$225$	−3.51832e6	+	6.09391e6i	−0.308878	+	0.534993i
$226$	−3.83123e6			−0.331904
$227$	−3.57950e6	−	2.06662e6i	−0.306016	−	0.176678i	0.339126	−	0.940741i	$-0.389869\pi$
$227$	−3.57950e6	−	2.06662e6i	−0.306016	−	0.176678i	−0.645142	+	0.764062i	$0.723202\pi$
$228$	414760.	+	718386.i	0.0349939	+	0.0606112i
$229$	−6.43178e6	−	1.11402e7i	−0.535580	−	0.927652i	−0.999135	−	0.0415840i	$-0.986760\pi$
$229$	−6.43178e6	−	1.11402e7i	−0.535580	−	0.927652i	0.463555	−	0.886068i	$-0.346574\pi$
$230$	−40891.1	−	70825.4i	−0.00336082	−	0.00582111i
$231$	−5.98211e6			−0.485310
$232$	−8.84284e6	−	1.53163e7i	−0.708154	−	1.22656i
$233$	1.26156e7	−	7.28360e6i	0.997331	−	0.575809i	0.0898732	−	0.995953i	$-0.471354\pi$
$233$	1.26156e7	−	7.28360e6i	0.997331	−	0.575809i	0.907457	+	0.420144i	$0.138020\pi$
$234$	−4.93300e6	−	2.84807e6i	−0.385003	−	0.222281i
$235$	997096.	+	575674.i	0.0768305	+	0.0443581i
$236$	1.91825e6			0.145938
$237$			1.01562e7i			0.762936i
$238$	−3.32673e6	+	5.76207e6i	−0.246767	+	0.427413i
$239$	−7.19423e6	+	1.24608e7i	−0.526975	+	0.912748i	0.472530	+	0.881314i	$0.343341\pi$
$239$	−7.19423e6	+	1.24608e7i	−0.526975	+	0.912748i	−0.999506	+	0.0314339i	$0.989993\pi$
$240$	269301.	+	466442.i	0.0194807	+	0.0337415i
$241$	−1.56084e7	+	9.01150e6i	−1.11508	+	0.643793i	−0.940141	−	0.340786i	$-0.889307\pi$
$241$	−1.56084e7	+	9.01150e6i	−1.11508	+	0.643793i	−0.174941	+	0.984579i	$0.555973\pi$
$242$		−	5.29420e6i		−	0.373555i
$243$	1.24677e7	−	7.19825e6i	0.868897	−	0.501658i
$244$	−5.35120e6	+	3.08952e6i	−0.368368	+	0.212677i
$245$	110611.	−	63861.5i	0.00752144	−	0.00434251i
$246$	1.98648e6	−	3.44069e6i	0.133438	−	0.231121i
$247$			5.77195e6i			0.383029i
$248$	−1.20851e7	−	6.97733e6i	−0.792310	−	0.457440i
$249$	−6.14787e6	+	3.54947e6i	−0.398223	+	0.229914i
$250$	2.46610e6			0.157830
$251$	9.64978e6	+	1.67139e7i	0.610234	+	1.05696i	0.991201	+	0.132367i	$0.0422579\pi$
$251$	9.64978e6	+	1.67139e7i	0.610234	+	1.05696i	−0.380967	+	0.924589i	$0.624409\pi$
$252$	2.20714e6	+	1.27429e6i	0.137920	+	0.0796283i
$253$	518664.	−	898352.i	0.0320276	−	0.0554735i
$254$		−	1.91943e7i		−	1.17131i
$255$	−251747.	+	436039.i	−0.0151825	+	0.0262969i
$256$	−1.15017e7			−0.685557
$257$		−	4.81023e6i		−	0.283378i	−0.989911	−	0.141689i	$-0.954747\pi$
$257$		−	4.81023e6i		−	0.283378i	0.989911	−	0.141689i	$-0.0452534\pi$
$258$	8.64277e6	−	3.05685e6i	0.503262	−	0.177998i
$259$	−5.46580e6			−0.314597
$260$		−	321303.i		−	0.0182808i
$261$	1.25589e7	+	7.25091e6i	0.706369	+	0.407822i
$262$	2.10320e7			1.16944
$263$	2.73098e7	+	1.57673e7i	1.50124	+	0.866743i	0.999999	+	0.00143725i	$0.000457492\pi$
$263$	2.73098e7	+	1.57673e7i	1.50124	+	0.866743i	0.501244	+	0.865306i	$0.332876\pi$
$264$	−4.61464e6	+	7.99279e6i	−0.250799	+	0.434397i
$265$	818369.	−	472485.i	0.0439756	−	0.0253893i
$266$			7.98924e6i			0.424483i
$267$	−8.64081e6	−	1.49663e7i	−0.453963	−	0.786287i
$268$	1.20468e6	−	2.08657e6i	0.0625846	−	0.108400i
$269$	3.20131e7			1.64464			0.822319	−	0.569026i	$-0.192680\pi$
$269$	3.20131e7			1.64464			0.822319	+	0.569026i	$0.192680\pi$
$270$	−1.34617e6	−	777212.i	−0.0683926	−	0.0394865i
$271$	−9.54153e6	−	1.65264e7i	−0.479413	−	0.830368i	0.520308	−	0.853979i	$-0.325817\pi$
$271$	−9.54153e6	−	1.65264e7i	−0.479413	−	0.830368i	−0.999721	+	0.0236106i	$0.992484\pi$
$272$	3.79916e6	+	6.58034e6i	0.188791	+	0.326996i
$273$	−5.36712e6	−	9.29612e6i	−0.263787	−	0.456892i
$274$	3.24445e7			1.57721
$275$	7.78739e6	+	1.34882e7i	0.374450	+	0.648567i
$276$	231669.	−	133754.i	0.0110190	−	0.00636180i
$277$	−8.89203e6	−	5.13382e6i	−0.418371	−	0.241547i	0.276009	−	0.961155i	$-0.410988\pi$
$277$	−8.89203e6	−	5.13382e6i	−0.418371	−	0.241547i	−0.694380	+	0.719608i	$0.744321\pi$
$278$	−6.95808e6	−	4.01725e6i	−0.323858	−	0.186980i
$279$	1.14425e7			0.526874
$280$		−	2.26529e6i		−	0.103193i
$281$	−1.59716e7	+	2.76636e7i	−0.719828	+	1.24678i	0.241240	+	0.970465i	$0.422446\pi$
$281$	−1.59716e7	+	2.76636e7i	−0.719828	+	1.24678i	−0.961068	+	0.276313i	$0.910887\pi$
$282$	5.82532e6	−	1.00897e7i	0.259760	−	0.449918i
$283$	1.83564e7	+	3.17943e7i	0.809896	+	1.40278i	0.912936	+	0.408103i	$0.133810\pi$
$283$	1.83564e7	+	3.17943e7i	0.809896	+	1.40278i	−0.103040	+	0.994677i	$0.532857\pi$
$284$	−2.69227e6	+	1.55438e6i	−0.117534	+	0.0678582i
$285$			604578.i			0.0261167i
$286$	−1.09186e7	+	6.30388e6i	−0.466735	+	0.269469i
$287$	−1.07117e7	+	6.18441e6i	−0.453120	+	0.261609i
$288$	6.14187e6	−	3.54601e6i	0.257113	−	0.148444i
$289$	8.51726e6	−	1.47523e7i	0.352863	−	0.611177i
$290$		−	2.53059e6i		−	0.103759i
$291$	2.20545e7	+	1.27332e7i	0.894989	+	0.516722i
$292$	−334243.	+	192975.i	−0.0134250	+	0.00775091i
$293$	−1.12332e7			−0.446581			−0.223290	−	0.974752i	$-0.571680\pi$
$293$	−1.12332e7			−0.446581			−0.223290	+	0.974752i	$0.571680\pi$
$294$	−646223.	−	1.11929e6i	−0.0254296	−	0.0440454i
$295$	1.21077e6	+	699037.i	0.0471623	+	0.0272291i
$296$	−4.21635e6	+	7.30294e6i	−0.162578	+	0.281593i
$297$		−	1.97164e7i		−	0.752589i
$298$	3.92476e6	−	6.79788e6i	0.148308	−	0.256877i
$299$	1.86137e6			0.0696336
$300$			4.01646e6i			0.148758i
$301$	−2.80606e7	−	5.21181e6i	−1.02896	−	0.191112i
$302$	−3.21393e6			−0.116685
$303$			9.89871e6i			0.355837i
$304$	7.90144e6	+	4.56190e6i	0.281246	+	0.162377i
$305$	−4.50345e6			−0.158725
$306$	−7.28940e6	−	4.20854e6i	−0.254406	−	0.146881i
$307$	−1.80163e7	+	3.12051e7i	−0.622658	+	1.07848i	0.366330	+	0.930485i	$0.380614\pi$
$307$	−1.80163e7	+	3.12051e7i	−0.622658	+	1.07848i	−0.988989	+	0.147991i	$0.952719\pi$
$308$	4.88525e6	−	2.82050e6i	0.167199	−	0.0965325i
$309$		−	2.81940e7i		−	0.955610i
$310$	−998365.	−	1.72922e6i	−0.0335123	−	0.0580450i
$311$	−1.69354e7	+	2.93330e7i	−0.563008	+	0.975158i	0.434224	+	0.900805i	$0.357023\pi$
$311$	−1.69354e7	+	2.93330e7i	−0.563008	+	0.975158i	−0.997232	+	0.0743532i	$0.976311\pi$
$312$	−1.65609e7			−0.545281
$313$	−2.65877e7	−	1.53504e7i	−0.867056	−	0.500595i	−0.000687505	−	1.00000i	$-0.500219\pi$
$313$	−2.65877e7	−	1.53504e7i	−0.867056	−	0.500595i	−0.866369	+	0.499404i	$0.833552\pi$
$314$	−3.49779e6	−	6.05835e6i	−0.112981	−	0.195689i
$315$	928740.	+	1.60862e6i	0.0297141	+	0.0514663i
$316$	−4.78855e6	−	8.29401e6i	−0.151755	−	0.262847i
$317$	1.69993e7			0.533647			0.266824	−	0.963745i	$-0.414026\pi$
$317$	1.69993e7			0.533647			0.266824	+	0.963745i	$0.414026\pi$
$318$	−4.78114e6	−	8.28118e6i	−0.148679	−	0.257520i
$319$	2.77978e7	−	1.60490e7i	0.856323	−	0.494399i
$320$	−2.87232e6	−	1.65833e6i	−0.0876561	−	0.0506083i
$321$	−4.41742e6	−	2.55040e6i	−0.133553	−	0.0771069i
$322$	2.57641e6			0.0771699
$323$			8.52909e6i			0.253102i
$324$	−45610.6	+	78999.9i	−0.00134101	+	0.00232269i
$325$	−1.39736e7	+	2.42030e7i	−0.407060	+	0.705048i
$326$	1.84397e6	+	3.19384e6i	0.0532231	+	0.0921851i
$327$	1.20164e7	−	6.93768e6i	0.343662	−	0.198414i
$328$			1.90828e7i			0.540779i
$329$	−3.14119e7	+	1.81357e7i	−0.882076	+	0.509267i
$330$	−1.14366e6	+	660294.i	−0.0318241	+	0.0183737i
$331$	2.19377e7	−	1.26657e7i	0.604933	−	0.349258i	−0.166047	−	0.986118i	$-0.553100\pi$
$331$	2.19377e7	−	1.26657e7i	0.604933	−	0.349258i	0.770980	+	0.636860i	$0.219767\pi$
$332$	3.34707e6	−	5.79730e6i	0.0914641	−	0.158421i
$333$		−	6.91460e6i		−	0.187255i
$334$	−369135.	−	213120.i	−0.00990707	−	0.00571985i
$335$	1.52075e6	−	878005.i	0.0404504	−	0.0233541i
$336$	−1.69677e7			−0.447308
$337$	−2.72649e7	−	4.72241e7i	−0.712383	−	1.23388i	−0.963960	−	0.266046i	$-0.914283\pi$
$337$	−2.72649e7	−	4.72241e7i	−0.712383	−	1.23388i	0.251577	−	0.967837i	$-0.419051\pi$
$338$	9.47876e6	+	5.47256e6i	0.245472	+	0.141723i
$339$	4.56679e6	−	7.90992e6i	0.117223	−	0.203036i
$340$		−	474783.i		−	0.0120798i
$341$	1.26633e7	−	2.19335e7i	0.319362	−	0.553152i
$342$	−1.01069e7			−0.252662
$343$		−	3.82085e7i		−	0.946843i
$344$	−2.86097e7	+	3.34717e7i	−0.702809	+	0.822248i
$345$	194967.			0.00474793
$346$		−	3.84783e7i		−	0.928939i
$347$	6.50146e7	+	3.75362e7i	1.55605	+	0.898384i	0.997629	+	0.0688243i	$0.0219248\pi$
$347$	6.50146e7	+	3.75362e7i	1.55605	+	0.898384i	0.558418	+	0.829560i	$0.311409\pi$
$348$	8.27752e6			0.196409
$349$	−7.03612e6	−	4.06230e6i	−0.165522	−	0.0955644i	0.414950	−	0.909844i	$-0.363799\pi$
$349$	−7.03612e6	−	4.06230e6i	−0.165522	−	0.0955644i	−0.580473	+	0.814280i	$0.697132\pi$
$350$	−1.93416e7	+	3.35006e7i	−0.451115	+	0.781354i
$351$	3.06390e7	−	1.76894e7i	0.708521	−	0.409065i
$352$		−	1.56974e7i		−	0.359914i
$353$	−2.44682e7	−	4.23801e7i	−0.556259	−	0.963469i	−0.997804	−	0.0662301i	$-0.978903\pi$
$353$	−2.44682e7	−	4.23801e7i	−0.556259	−	0.963469i	0.441545	−	0.897239i	$-0.354430\pi$
$354$	7.07365e6	−	1.22519e7i	0.159453	−	0.276181i
$355$	−2.26575e6			−0.0506439
$356$	1.41129e7	+	8.14808e6i	0.312799	+	0.180595i
$357$	−7.93088e6	−	1.37367e7i	−0.174308	−	0.301910i
$358$	−5.99915e6	−	1.03908e7i	−0.130750	−	0.226465i
$359$	−4.19885e7	−	7.27262e7i	−0.907501	−	1.57184i	−0.817525	−	0.575894i	$-0.804654\pi$
$359$	−4.19885e7	−	7.27262e7i	−0.907501	−	1.57184i	−0.0899761	−	0.995944i	$-0.528679\pi$
$360$	2.86574e6			0.0614228
$361$	−1.84022e7	−	3.18736e7i	−0.391155	−	0.677500i
$362$	3.61403e6	−	2.08656e6i	0.0761844	−	0.0439851i
$363$	1.09304e7	+	6.31065e6i	0.228515	+	0.131933i
$364$	8.76602e6	+	5.06107e6i	0.181760	+	0.104939i
$365$	−281291.			−0.00578466
$366$			4.55710e7i			0.929492i
$367$	−8.49001e6	+	1.47051e7i	−0.171755	+	0.297489i	−0.939034	−	0.343825i	$-0.888277\pi$
$367$	−8.49001e6	+	1.47051e7i	−0.171755	+	0.297489i	0.767278	+	0.641314i	$0.221611\pi$
$368$	1.47115e6	−	2.54810e6i	0.0295197	−	0.0511296i
$369$	−7.82369e6	−	1.35510e7i	−0.155716	−	0.269708i
$370$	−1.04495e6	+	603305.i	−0.0206297	+	0.0119105i
$371$			2.97697e7i			0.582980i
$372$	5.65624e6	−	3.26563e6i	0.109875	−	0.0634364i
$373$	−5.45539e7	+	3.14967e7i	−1.05123	+	0.606930i	−0.922995	−	0.384813i	$-0.874266\pi$
$373$	−5.45539e7	+	3.14967e7i	−1.05123	+	0.606930i	−0.128240	+	0.991743i	$0.540933\pi$
$374$	−1.61342e7	+	9.31511e6i	−0.308414	+	0.178063i
$375$	−2.93957e6	+	5.09148e6i	−0.0557430	+	0.0965496i
$376$			5.59598e7i			1.05272i
$377$	4.98800e7	+	2.87982e7i	0.930898	+	0.537454i
$378$	4.24089e7	−	2.44848e7i	0.785202	−	0.453337i
$379$	5.48520e6			0.100757			0.0503785	−	0.998730i	$-0.483957\pi$
$379$	5.48520e6			0.100757			0.0503785	+	0.998730i	$0.483957\pi$
$380$	−285051.	−	493724.i	−0.00519484	−	0.00899773i
$381$	3.96283e7	+	2.28794e7i	0.716524	+	0.413685i
$382$	2.11319e7	−	3.66016e7i	0.379096	−	0.656614i
$383$			5.34591e7i			0.951536i	0.879571	+	0.475768i	$0.157830\pi$
$383$			5.34591e7i			0.951536i	−0.879571	+	0.475768i	$0.842170\pi$
$384$	−8.49529e6	+	1.47143e7i	−0.150032	+	0.259863i
$385$	4.11132e6			0.0720442
$386$			6.12049e7i			1.06420i
$387$	6.59328e6	−	3.54985e7i	0.113754	−	0.612459i
$388$	−2.40141e7			−0.411123
$389$		−	9.24506e7i		−	1.57058i	−0.619126	−	0.785292i	$-0.712513\pi$
$389$		−	9.24506e7i		−	1.57058i	0.619126	−	0.785292i	$-0.287487\pi$
$390$	−2.05217e6	−	1.18482e6i	−0.0345956	−	0.0199738i
$391$	2.75051e6			0.0460132
$392$	5.37612e6	+	3.10391e6i	0.0892506	+	0.0515288i
$393$	−2.50700e7	+	4.34226e7i	−0.413026	+	0.715381i
$394$	2.98312e7	−	1.72230e7i	0.487732	−	0.281592i
$395$		−	6.98006e6i		−	0.113258i
$396$	3.56812e6	+	6.18016e6i	0.0574584	+	0.0995209i
$397$	2.39879e6	−	4.15483e6i	0.0383373	−	0.0664021i	−0.846220	−	0.532833i	$-0.821127\pi$
$397$	2.39879e6	−	4.15483e6i	0.0383373	−	0.0664021i	0.884557	+	0.466431i	$0.154461\pi$
$398$	−2.10155e7			−0.333343
$399$	−1.64945e7	−	9.52311e6i	−0.259669	−	0.149920i
$400$	2.20883e7	+	3.82580e7i	0.345129	+	0.597781i
$401$	4.03538e7	+	6.98949e7i	0.625823	+	1.08396i	0.988381	+	0.151996i	$0.0485701\pi$
$401$	4.03538e7	+	6.98949e7i	0.625823	+	1.08396i	−0.362558	+	0.931961i	$0.618097\pi$
$402$	−8.88465e6	−	1.53887e7i	−0.136761	−	0.236877i
$403$	4.54457e7			0.694349
$404$	−4.66713e6	−	8.08370e6i	−0.0707792	−	0.122593i
$405$	−57577.3	+	33242.3i	−0.000866735	+	0.000500410i
$406$	6.90413e7	+	3.98610e7i	1.03165	+	0.595621i
$407$	−1.32542e7	−	7.65234e6i	−0.196595	−	0.113504i
$408$	−2.44717e7			−0.360316
$409$			1.24867e7i			0.182507i	0.995828	+	0.0912534i	$0.0290873\pi$
$409$			1.24867e7i			0.182507i	−0.995828	+	0.0912534i	$0.970913\pi$
$410$	−1.36525e6	+	2.36468e6i	−0.0198089	+	0.0343099i
$411$	−3.86735e7	+	6.69845e7i	−0.557043	+	0.964826i
$412$	1.32931e7	+	2.30244e7i	0.190080	+	0.329228i
$413$	−3.81432e7	+	2.20220e7i	−0.541461	+	0.312613i
$414$			3.25933e6i			0.0459333i
$415$	4.22523e6	−	2.43944e6i	0.0591162	−	0.0341308i
$416$	2.43935e7	−	1.40836e7i	0.338839	−	0.195629i
$417$	1.65879e7	−	9.57706e6i	0.228762	−	0.132076i
$418$	−1.11853e7	+	1.93734e7i	−0.153150	+	0.265263i
$419$			1.31295e8i			1.78487i	0.451174	+	0.892436i	$0.351005\pi$
$419$			1.31295e8i			1.78487i	−0.451174	+	0.892436i	$0.648995\pi$
$420$	918190.	+	530117.i	0.0123932	+	0.00715523i
$421$	3.68617e7	−	2.12821e7i	0.494002	−	0.285212i	−0.232231	−	0.972661i	$-0.574603\pi$
$421$	3.68617e7	−	2.12821e7i	0.494002	−	0.285212i	0.726233	+	0.687448i	$0.241269\pi$
$422$	8.22681e6			0.109470
$423$	−2.29428e7	−	3.97381e7i	−0.303127	−	0.525032i
$424$	3.97758e7	+	2.29646e7i	0.521820	+	0.301273i
$425$	−2.06485e7	+	3.57643e7i	−0.268981	+	0.465889i
$426$			2.29274e7i			0.296570i
$427$	7.09369e7	−	1.22866e8i	0.911147	−	1.57815i
$428$	4.80994e6			0.0613491
$429$		−	3.00567e7i		−	0.380688i
$430$	−5.93990e6	+	2.10088e6i	−0.0747091	+	0.0264238i
$431$	−1.33016e8			−1.66139			−0.830693	−	0.556731i	$-0.812056\pi$
$431$	−1.33016e8			−1.66139			−0.830693	+	0.556731i	$0.812056\pi$
$432$		−	5.59238e7i		−	0.693658i
$433$	6.92501e7	+	3.99816e7i	0.853016	+	0.492489i	0.861667	−	0.507474i	$-0.169421\pi$
$433$	6.92501e7	+	3.99816e7i	0.853016	+	0.492489i	−0.00865163	+	0.999963i	$0.502754\pi$
$434$	6.29037e7			0.769497
$435$	5.22463e6	+	3.01644e6i	0.0634728	+	0.0366461i
$436$	−6.54208e6	+	1.13312e7i	−0.0789326	+	0.136715i
$437$	2.86023e6	−	1.65135e6i	0.0342734	−	0.0197877i
$438$			2.84642e6i			0.0338748i
$439$	−6.16179e7	−	1.06725e8i	−0.728305	−	1.26146i	−0.957599	−	0.288104i	$-0.906975\pi$
$439$	−6.16179e7	−	1.06725e8i	−0.728305	−	1.26146i	0.229294	−	0.973357i	$-0.426358\pi$
$440$	3.17149e6	−	5.49319e6i	0.0372311	−	0.0644862i
$441$	−5.09025e6			−0.0593503
$442$	−2.89511e7	−	1.67149e7i	−0.335273	−	0.193570i
$443$	−3.71413e7	−	6.43307e7i	−0.427215	−	0.739958i	0.569410	−	0.822054i	$-0.307172\pi$
$443$	−3.71413e7	−	6.43307e7i	−0.427215	−	0.739958i	−0.996624	+	0.0820962i	$0.973839\pi$
$444$	−1.97340e6	−	3.41803e6i	−0.0225458	−	0.0390505i
$445$	5.93855e6	+	1.02859e7i	0.0673908	+	0.116724i
$446$	−2.34888e7			−0.264763
$447$	9.35656e6	+	1.62060e7i	0.104760	+	0.181449i
$448$	9.04876e7	−	5.22430e7i	1.00636	−	0.581024i
$449$	−1.06016e8	−	6.12081e7i	−1.17120	−	0.676192i	−0.217237	−	0.976119i	$-0.569704\pi$
$449$	−1.06016e8	−	6.12081e7i	−1.17120	−	0.676192i	−0.953962	+	0.299927i	$0.903038\pi$
$450$	−4.23804e7	−	2.44683e7i	−0.465080	−	0.268514i
$451$	−3.46337e7			−0.377545
$452$			8.61276e6i			0.0932668i
$453$	3.83098e6	−	6.63545e6i	0.0412112	−	0.0713798i
$454$	1.43724e7	−	2.48938e7i	0.153590	−	0.266026i
$455$	3.68865e6	+	6.38892e6i	0.0391591	+	0.0678256i
$456$	−2.54479e7	+	1.46924e7i	−0.268385	+	0.154952i
$457$		−	1.34681e8i		−	1.41110i	−0.708659	−	0.705551i	$-0.750700\pi$
$457$		−	1.34681e8i		−	1.41110i	0.708659	−	0.705551i	$-0.249300\pi$
$458$	7.74749e7	−	4.47302e7i	0.806426	−	0.465590i
$459$	4.52746e7	−	2.61393e7i	0.468184	−	0.270306i
$460$	−159219.	+	91924.9i	−0.00163576	+	0.000944408i
$461$	−6.90013e7	+	1.19514e8i	−0.704295	+	1.21987i	0.262651	+	0.964891i	$0.415403\pi$
$461$	−6.90013e7	+	1.19514e8i	−0.704295	+	1.21987i	−0.966945	+	0.254983i	$0.917930\pi$
$462$		−	4.16030e7i		−	0.421889i
$463$	−9.24446e7	−	5.33729e7i	−0.931405	−	0.537747i	−0.0441497	−	0.999025i	$-0.514058\pi$
$463$	−9.24446e7	−	5.33729e7i	−0.931405	−	0.537747i	−0.887256	+	0.461278i	$0.847391\pi$
$464$	7.88459e7	−	4.55217e7i	0.789270	−	0.455685i
$465$	4.76017e6			0.0473439
$466$	5.06542e7	+	8.77357e7i	0.500562	+	0.866999i
$467$	4.10901e7	+	2.37234e7i	0.403447	+	0.232930i	0.687970	−	0.725739i	$-0.258502\pi$
$467$	4.10901e7	+	2.37234e7i	0.403447	+	0.232930i	−0.284523	+	0.958669i	$0.591835\pi$
$468$	−6.40258e6	+	1.10896e7i	−0.0624623	+	0.108188i
$469$			5.53202e7i			0.536247i
$470$	−4.00356e6	+	6.93436e6i	−0.0385614	+	0.0667902i
$471$	1.66774e7			0.159612
$472$			6.79516e7i			0.646210i
$473$	−6.07484e7	−	5.19242e7i	−0.574053	−	0.490667i
$474$	−7.06322e7			−0.663235
$475$			4.95880e7i			0.462696i
$476$	1.29534e7	+	7.47863e6i	0.120105	+	0.0693428i
$477$	−3.76607e7			−0.347003
$478$	−8.66591e7	−	5.00327e7i	−0.793470	−	0.458110i
$479$	−3.85960e7	+	6.68502e7i	−0.351185	+	0.608270i	−0.986457	−	0.164018i	$-0.947554\pi$
$479$	−3.85960e7	+	6.68502e7i	−0.351185	+	0.608270i	0.635272	+	0.772288i	$0.280888\pi$
$480$	2.55508e6	−	1.47517e6i	0.0231036	−	0.0133389i
$481$		−	2.74625e7i		−	0.246777i
$482$	−6.26710e7	−	1.08549e8i	−0.559661	−	0.969362i
$483$	−3.07106e6	+	5.31924e6i	−0.0272551	+	0.0472072i
$484$	−1.19016e7			−0.104971
$485$	−1.51573e7	−	8.75109e6i	−0.132861	−	0.0767074i
$486$	5.00606e7	+	8.67075e7i	0.436101	+	0.755350i
$487$	8.64250e7	+	1.49693e8i	0.748260	+	1.29602i	0.948656	+	0.316310i	$0.102444\pi$
$487$	8.64250e7	+	1.49693e8i	0.748260	+	1.29602i	−0.200396	+	0.979715i	$0.564223\pi$
$488$	−1.09442e8	−	1.89560e8i	−0.941728	−	1.63112i
$489$	−8.79197e6			−0.0751899
$490$	444128.	+	769253.i	0.00377503	+	0.00653854i
$491$	2.98407e7	−	1.72285e7i	0.252095	−	0.145547i	−0.368628	−	0.929577i	$-0.620172\pi$
$491$	2.98407e7	−	1.72285e7i	0.252095	−	0.145547i	0.620723	+	0.784030i	$0.286839\pi$
$492$	−7.73482e6	−	4.46570e6i	−0.0649463	−	0.0374968i
$493$	7.37066e7	+	4.25545e7i	0.615128	+	0.355144i
$494$	−4.01413e7			−0.332975
$495$			5.20109e6i			0.0428823i
$496$	3.59183e7	−	6.22124e7i	0.294355	−	0.509837i
$497$	3.56894e7	−	6.18158e7i	0.290717	−	0.503536i
$498$	−2.46850e7	−	4.27557e7i	−0.199869	−	0.346183i
$499$	5.13234e7	−	2.96316e7i	0.413061	−	0.238481i	−0.279043	−	0.960279i	$-0.590017\pi$
$499$	5.13234e7	−	2.96316e7i	0.413061	−	0.238481i	0.692104	+	0.721798i	$0.256684\pi$
$500$		−	5.54389e6i		−	0.0443512i
$501$	880011.	−	508075.i	0.00699802	−	0.00404031i
$502$	−1.16238e8	+	6.71100e7i	−0.918833	+	0.530488i
$503$	4.13481e7	−	2.38723e7i	0.324901	−	0.187582i	−0.328674	−	0.944443i	$-0.606602\pi$
$503$	4.13481e7	−	2.38723e7i	0.324901	−	0.187582i	0.653575	+	0.756862i	$0.273268\pi$
$504$	−4.51402e7	+	7.81851e7i	−0.352592	+	0.610707i
$505$		−	6.80307e6i		−	0.0528239i
$506$	6.24764e6	+	3.60708e6i	0.0482242	+	0.0278422i
$507$	−2.25972e7	+	1.30465e7i	−0.173393	+	0.100108i
$508$	−4.31495e7			−0.329143
$509$	1.13553e8	+	1.96680e8i	0.861083	+	1.49144i	0.870884	+	0.491488i	$0.163547\pi$
$509$	1.13553e8	+	1.96680e8i	0.861083	+	1.49144i	−0.00980085	+	0.999952i	$0.503120\pi$
$510$	−3.03246e6	−	1.75079e6i	−0.0228604	−	0.0131985i
$511$	4.43081e6	−	7.67439e6i	0.0332063	−	0.0575150i
$512$		−	1.45576e8i		−	1.08463i
$513$	3.13871e7	−	5.43641e7i	0.232487	−	0.402680i
$514$	3.34530e7			0.246346
$515$			1.93768e7i			0.141860i
$516$	−6.87193e6	−	1.94293e7i	−0.0500184	−	0.141419i
$517$	−1.01562e8			−0.734957
$518$		−	3.80122e7i		−	0.273485i
$519$	7.94419e7	+	4.58658e7i	0.568260	+	0.328085i
$520$	1.13818e7			0.0809469
$521$	7.64489e7	+	4.41378e7i	0.540578	+	0.312103i	0.745313	−	0.666715i	$-0.232300\pi$
$521$	7.64489e7	+	4.41378e7i	0.540578	+	0.312103i	−0.204735	+	0.978817i	$0.565633\pi$
$522$	−5.04268e7	+	8.73418e7i	−0.354528	+	0.614060i
$523$	−2.31602e8	+	1.33715e8i	−1.61896	+	0.934709i	−0.631776	+	0.775151i	$0.717674\pi$
$523$	−2.31602e8	+	1.33715e8i	−1.61896	+	0.934709i	−0.987189	+	0.159558i	$0.948993\pi$
$524$		−	4.72809e7i		−	0.328618i
$525$	−4.61100e7	−	7.98648e7i	−0.318652	−	0.551922i
$526$	−1.09655e8	+	1.89927e8i	−0.753477	+	1.30506i
$527$	6.71542e7			0.458819
$528$	−4.11458e7	−	2.37555e7i	−0.279527	−	0.161385i
$529$	7.34854e7	+	1.27280e8i	0.496403	+	0.859795i
$530$	3.28593e6	+	5.69139e6i	0.0220714	+	0.0382288i
$531$	−2.78593e7	−	4.82537e7i	−0.186074	−	0.322290i
$532$	1.79602e7			0.119282
$533$	−3.10731e7	−	5.38202e7i	−0.205212	−	0.355438i
$534$	1.04084e8	−	6.00930e7i	0.683535	−	0.394639i
$535$	3.03595e6	+	1.75281e6i	0.0198259	+	0.0114465i
$536$	7.39141e7	+	4.26743e7i	0.479991	+	0.277123i
$537$	2.86037e7			0.184714
$538$			2.22637e8i			1.42972i
$539$	−5.63334e6	+	9.75723e6i	−0.0359749	+	0.0623103i
$540$	−1.74721e6	+	3.02625e6i	−0.0110959	+	0.0192187i
$541$	4.69570e7	+	8.13319e7i	0.296557	+	0.513652i	0.975346	−	0.220681i	$-0.0708281\pi$
$541$	4.69570e7	+	8.13319e7i	0.296557	+	0.513652i	−0.678789	+	0.734334i	$0.737495\pi$
$542$	1.14934e8	−	6.63571e7i	0.721855	−	0.416763i
$543$			9.94866e6i			0.0621391i
$544$	3.60458e7	−	2.08110e7i	0.223902	−	0.129270i
$545$	−8.25850e6	+	4.76805e6i	−0.0510166	+	0.0294545i
$546$	6.46504e7	−	3.73259e7i	0.397185	−	0.229315i
$547$	1.47952e8	−	2.56261e8i	0.903981	−	1.56574i	0.0817025	−	0.996657i	$-0.473964\pi$
$547$	1.47952e8	−	2.56261e8i	0.903981	−	1.56574i	0.822279	−	0.569085i	$-0.192702\pi$
$548$		−	7.29365e7i		−	0.443204i
$549$	1.55434e8	+	8.97399e7i	0.939353	+	0.542336i
$550$	−9.38042e7	+	5.41579e7i	−0.563812	+	0.325517i
$551$	1.02196e8			0.610912
$552$	4.73807e6	+	8.20658e6i	0.0281698	+	0.0487916i
$553$	1.90435e8	+	1.09948e8i	1.12609	+	0.650146i
$554$	3.57034e7	−	6.18402e7i	0.209981	−	0.363698i
$555$		−	2.87654e6i		−	0.0168264i
$556$	−9.03094e6	+	1.56421e7i	−0.0525423	+	0.0910059i
$557$	2.99466e8			1.73293			0.866466	−	0.499236i	$-0.166386\pi$
$557$	2.99466e8			1.73293			0.866466	+	0.499236i	$0.166386\pi$
$558$			7.95773e7i			0.458022i
$559$	2.61863e7	−	1.40988e8i	0.149913	−	0.807137i
$560$	1.16614e7			0.0664028
$561$		−	4.44142e7i		−	0.251555i
$562$	−1.92388e8	−	1.11075e8i	−1.08385	−	0.625760i
$563$	−4.46590e7			−0.250256			−0.125128	−	0.992141i	$-0.539934\pi$
$563$	−4.46590e7			−0.250256			−0.125128	+	0.992141i	$0.539934\pi$
$564$	−2.26822e7	−	1.30956e7i	−0.126429	−	0.0729940i
$565$	−3.13861e6	+	5.43624e6i	−0.0174017	+	0.0301407i
$566$	−2.21115e8	+	1.27661e8i	−1.21946	+	0.704058i
$567$		−	2.09449e6i		−	0.0114902i
$568$	−5.50620e7	−	9.53702e7i	−0.300474	−	0.520436i
$569$	4.25234e7	−	7.36526e7i	0.230829	−	0.399808i	−0.727223	−	0.686401i	$-0.759189\pi$
$569$	4.25234e7	−	7.36526e7i	0.230829	−	0.399808i	0.958052	+	0.286593i	$0.0925228\pi$
$570$	−4.20457e6			−0.0227037
$571$	−7.11166e7	−	4.10592e7i	−0.381999	−	0.220547i	0.296688	−	0.954974i	$-0.404118\pi$
$571$	−7.11166e7	−	4.10592e7i	−0.381999	−	0.220547i	−0.678688	+	0.734427i	$0.737451\pi$
$572$	1.41714e7	+	2.45456e7i	0.0757224	+	0.131155i
$573$	5.03782e7	+	8.72576e7i	0.267781	+	0.463809i
$574$	−4.30098e7	−	7.44952e7i	−0.227422	−	0.393906i
$575$	1.59914e7			0.0841168
$576$	6.60909e7	+	1.14473e8i	0.345839	+	0.599011i
$577$	1.46768e8	−	8.47368e7i	0.764021	−	0.441108i	−0.0667165	−	0.997772i	$-0.521252\pi$
$577$	1.46768e8	−	8.47368e7i	0.764021	−	0.441108i	0.830738	+	0.556664i	$0.187919\pi$
$578$	1.02596e8	+	5.92338e7i	0.531308	+	0.306751i
$579$	−1.26363e8	−	7.29558e7i	−0.651006	−	0.375858i
$580$	−5.68887e6			−0.0291570
$581$			1.53701e8i			0.783698i
$582$	−8.85535e7	+	1.53379e8i	−0.449197	+	0.778032i
$583$	−4.16788e7	+	7.21898e7i	−0.210334	+	0.364309i
$584$	−6.83591e6	−	1.18401e7i	−0.0343208	−	0.0594454i
$585$	−8.08241e6	+	4.66638e6i	−0.0403714	+	0.0233084i
$586$		−	7.81218e7i		−	0.388221i
$587$	−4.39769e7	+	2.53901e7i	−0.217426	+	0.125531i	−0.604758	−	0.796410i	$-0.706730\pi$
$587$	−4.39769e7	+	2.53901e7i	−0.217426	+	0.125531i	0.387332	+	0.921940i	$0.373397\pi$
$588$	−2.51621e6	+	1.45274e6i	−0.0123770	+	0.00714586i
$589$	6.98331e7	−	4.03182e7i	0.341756	−	0.197313i
$590$	−4.86149e6	+	8.42035e6i	−0.0236708	+	0.0409991i
$591$			8.21189e7i			0.397815i
$592$	−3.75945e7	−	2.17052e7i	−0.181200	−	0.104616i
$593$	6.93171e7	−	4.00202e7i	0.332412	−	0.191918i	−0.324500	−	0.945886i	$-0.605196\pi$
$593$	6.93171e7	−	4.00202e7i	0.332412	−	0.191918i	0.656911	+	0.753968i	$0.271863\pi$
$594$	1.37119e8			0.654240
$595$	5.45064e6	+	9.44078e6i	0.0258760	+	0.0448185i
$596$	−1.52819e7	−	8.82302e6i	−0.0721837	−	0.0416753i
$597$	2.50503e7	−	4.33885e7i	0.117731	−	0.203916i
$598$			1.29450e7i			0.0605338i
$599$	−8.15823e7	+	1.41305e8i	−0.379591	+	0.657470i	−0.991003	−	0.133842i	$-0.957268\pi$
$599$	−8.15823e7	+	1.41305e8i	−0.379591	+	0.657470i	0.611412	+	0.791312i	$0.290602\pi$
$600$	−1.42278e8			−0.658694
$601$			2.94599e8i			1.35709i	0.734559	+	0.678545i	$0.237389\pi$
$601$			2.94599e8i			1.35709i	−0.734559	+	0.678545i	$0.762611\pi$
$602$	3.62458e7	−	1.95149e8i	0.166138	−	0.894492i
$603$	−6.99837e7			−0.319187
$604$			7.22504e6i			0.0327891i
$605$	−7.51209e6	−	4.33711e6i	−0.0339230	−	0.0195855i
$606$	−6.88412e7			−0.309336
$607$	−2.31940e8	−	1.33911e8i	−1.03707	−	0.598755i	−0.118071	−	0.993005i	$-0.537671\pi$
$607$	−2.31940e8	−	1.33911e8i	−1.03707	−	0.598755i	−0.919003	+	0.394250i	$0.871004\pi$
$608$	2.49891e7	−	4.32825e7i	0.111184	−	0.192576i
$609$	−1.64593e8	+	9.50281e7i	−0.728720	+	0.420727i
$610$		−	3.13195e7i		−	0.137983i
$611$	−9.11212e7	−	1.57827e8i	−0.399481	−	0.691921i
$612$	−9.46097e6	+	1.63869e7i	−0.0412744	+	0.0714894i
$613$	6.93307e7			0.300985			0.150492	−	0.988611i	$-0.451914\pi$
$613$	6.93307e7			0.300985			0.150492	+	0.988611i	$0.451914\pi$
$614$	−2.17018e8	−	1.25295e8i	−0.937540	−	0.541289i
$615$	−3.25473e6	−	5.63735e6i	−0.0139923	−	0.0242354i
$616$	9.99127e7	+	1.73054e8i	0.427443	+	0.740353i
$617$	−9.97575e7	−	1.72785e8i	−0.424708	−	0.735615i	0.571685	−	0.820473i	$-0.306290\pi$
$617$	−9.97575e7	−	1.72785e8i	−0.424708	−	0.735615i	−0.996393	+	0.0848577i	$0.972956\pi$
$618$	1.96076e8			0.830730
$619$	−1.28419e8	−	2.22428e8i	−0.541449	−	0.937817i	−0.998821	−	0.0485418i	$-0.984543\pi$
$619$	−1.28419e8	−	2.22428e8i	−0.541449	−	0.937817i	0.457372	−	0.889275i	$-0.348791\pi$
$620$	−3.88736e6	+	2.24437e6i	−0.0163110	+	0.00941713i
$621$	−1.75316e7	−	1.01219e7i	−0.0732061	−	0.0422655i
$622$	−2.03998e8	−	1.17778e8i	−0.847724	−	0.489434i
$623$	−3.74168e8			−1.54740
$624$		−	8.52532e7i		−	0.350879i
$625$	−1.19036e8	+	2.06176e8i	−0.487570	+	0.844496i
$626$	1.06755e8	−	1.84906e8i	0.435177	−	0.753749i
$627$	−2.66655e7	−	4.61859e7i	−0.108180	−	0.187373i
$628$	−1.36194e7	+	7.86319e6i	−0.0549896	+	0.0317482i
$629$		−	4.05808e7i		−	0.163068i
$630$	−1.11873e7	+	6.45897e6i	−0.0447407	+	0.0258310i
$631$	−1.55185e8	+	8.95964e7i	−0.617679	+	0.356617i	−0.775965	−	0.630776i	$-0.782737\pi$
$631$	−1.55185e8	+	8.95964e7i	−0.617679	+	0.356617i	0.158286	+	0.987393i	$0.449403\pi$
$632$	2.93805e8	−	1.69629e8i	1.16388	−	0.671967i
$633$	−9.80630e6	+	1.69850e7i	−0.0386629	+	0.0669660i
$634$			1.18223e8i			0.463910i
$635$	−2.72353e7	−	1.57243e7i	−0.106368	−	0.0614116i
$636$	−1.86164e7	+	1.07482e7i	−0.0723645	+	0.0417797i
$637$	−2.02168e7			−0.0782157
$638$	1.11614e8	+	1.93321e8i	0.429790	+	0.744419i
$639$	7.82011e7	+	4.51494e7i	0.299716	+	0.173041i
$640$	5.83854e6	−	1.01126e7i	0.0222723	−	0.0385767i
$641$		−	2.48622e8i		−	0.943986i	−0.881602	−	0.471993i	$-0.843535\pi$
$641$		−	2.48622e8i		−	0.943986i	0.881602	−	0.471993i	$-0.156465\pi$
$642$	1.77369e7	−	3.07212e7i	0.0670305	−	0.116100i
$643$	1.71652e8			0.645678			0.322839	−	0.946454i	$-0.395363\pi$
$643$	1.71652e8			0.645678			0.322839	+	0.946454i	$0.395363\pi$
$644$		−	5.79188e6i		−	0.0216851i
$645$	2.74286e6	−	1.47677e7i	0.0102217	−	0.0550343i
$646$	−5.93160e7			−0.220026
$647$		−	1.59674e8i		−	0.589550i	−0.955567	−	0.294775i	$-0.904755\pi$
$647$		−	1.59674e8i		−	0.589550i	0.955567	−	0.294775i	$-0.0952447\pi$
$648$	−2.79847e6	−	1.61570e6i	−0.0102848	−	0.00593794i
$649$	−1.23327e8			−0.451152
$650$	−1.68321e8	−	9.71802e7i	−0.612912	−	0.353865i
$651$	−7.49807e7	+	1.29870e8i	−0.271773	+	0.470725i
$652$	7.17989e6	−	4.14531e6i	0.0259045	−	0.0149560i
$653$			3.54086e8i			1.27165i	0.771832	+	0.635826i	$0.219341\pi$
$653$			3.54086e8i			1.27165i	−0.771832	+	0.635826i	$0.780659\pi$
$654$	4.82485e7	+	8.35689e7i	0.172485	+	0.298752i
$655$	1.72298e7	−	2.98429e7i	0.0613136	−	0.106198i
$656$	−9.82354e7			−0.347982
$657$	9.70861e6	+	5.60527e6i	0.0342343	+	0.0197652i
$658$	−1.26125e8	−	2.18456e8i	−0.442716	−	0.766806i
$659$	−1.66857e8	−	2.89004e8i	−0.583025	−	1.00983i	−0.995118	−	0.0986874i	$-0.968536\pi$
$659$	−1.66857e8	−	2.89004e8i	−0.583025	−	1.00983i	0.412093	−	0.911142i	$-0.364798\pi$
$660$	1.48437e6	+	2.57100e6i	0.00516310	+	0.00894274i
$661$	4.20052e8			1.45445			0.727224	−	0.686400i	$-0.240810\pi$
$661$	4.20052e8			1.45445			0.727224	+	0.686400i	$0.240810\pi$
$662$	8.80846e7	+	1.52567e8i	0.303617	+	0.525880i
$663$	6.90189e7	−	3.98481e7i	0.236825	−	0.136731i
$664$	2.05362e8	+	1.18566e8i	0.701482	+	0.405001i
$665$	1.13362e7	+	6.54493e6i	0.0385479	+	0.0222556i
$666$	4.80880e7			0.162785
$667$		−	3.29567e7i		−	0.111062i
$668$	−479103.	+	829830.i	−0.00160731	+	0.00278394i
$669$	2.79985e7	−	4.84948e7i	0.0935097	−	0.161964i
$670$	6.10613e6	+	1.05761e7i	0.0203021	+	0.0351643i
$671$	3.44035e8	−	1.98629e8i	1.13877	−	0.657468i
$672$			9.29458e7i			0.306282i
$673$	−4.87619e8	+	2.81527e8i	−1.59969	+	0.923580i	−0.608141	+	0.793829i	$0.708085\pi$
$673$	−4.87619e8	+	2.81527e8i	−1.59969	+	0.923580i	−0.991547	+	0.129751i	$0.958582\pi$
$674$	3.28423e8	−	1.89615e8i	1.07264	−	0.619289i
$675$	2.63225e8	−	1.51973e8i	0.855887	−	0.494147i
$676$	1.23026e7	−	2.13086e7i	0.0398249	−	0.0689788i
$677$			2.57725e7i			0.0830596i	0.999137	+	0.0415298i	$0.0132231\pi$
$677$			2.57725e7i			0.0830596i	−0.999137	+	0.0415298i	$0.986777\pi$
$678$	5.50100e7	+	3.17600e7i	0.176503	+	0.101904i
$679$	4.77507e8	−	2.75689e8i	1.52535	−	0.880663i
$680$	1.68186e7			0.0534889
$681$	3.42637e7	+	5.93464e7i	0.108491	+	0.187912i
$682$	1.52538e8	+	8.80676e7i	0.480866	+	0.277628i
$683$	1.29490e7	−	2.24283e7i	0.0406419	−	0.0703938i	−0.844989	−	0.534784i	$-0.820393\pi$
$683$	1.29490e7	−	2.24283e7i	0.0406419	−	0.0703938i	0.885631	+	0.464390i	$0.153726\pi$
$684$			2.27208e7i			0.0709994i
$685$	2.65791e7	−	4.60363e7i	0.0826929	−	0.143228i
$686$	2.65723e8			0.823109
$687$			2.13272e8i			0.657754i
$688$	−1.72308e8	−	1.47279e8i	−0.529102	−	0.452245i
$689$	−1.49576e8			−0.457303
$690$			1.35591e6i			0.00412747i
$691$	−4.16121e8	−	2.40248e8i	−1.26120	−	0.728157i	−0.287897	−	0.957661i	$-0.592956\pi$
$691$	−4.16121e8	−	2.40248e8i	−1.26120	−	0.728157i	−0.973308	+	0.229504i	$0.926289\pi$
$692$	−8.65008e7			−0.261037
$693$	−1.41900e8	−	8.19258e7i	−0.426365	−	0.246162i
$694$	−2.61048e8	+	4.52148e8i	−0.780983	+	1.35270i
$695$	−1.14004e7	+	6.58201e6i	−0.0339597	+	0.0196067i
$696$			2.93221e8i			0.869695i
$697$	−4.59161e7	−	7.95290e7i	−0.135602	−	0.234870i
$698$	2.82515e7	−	4.89331e7i	0.0830760	−	0.143892i
$699$	−2.41518e8			−0.707160
$700$	7.53107e7	+	4.34806e7i	0.219565	+	0.126766i
$701$	2.03859e8	+	3.53093e8i	0.591800	+	1.02503i	0.993990	+	0.109471i	$0.0349158\pi$
$701$	2.03859e8	+	3.53093e8i	0.591800	+	1.02503i	−0.402190	+	0.915556i	$0.631751\pi$
$702$	1.23022e8	+	2.13080e8i	0.355608	+	0.615931i
$703$	−2.43640e7	−	4.21997e7i	−0.0701265	−	0.121463i
$704$	2.92569e8			0.838515
$705$	−9.54441e6	−	1.65314e7i	−0.0272384	−	0.0471783i
$706$	2.94735e8	−	1.70165e8i	0.837563	−	0.483567i
$707$	1.85606e8	+	1.07160e8i	0.525211	+	0.303231i
$708$	−2.75428e7	−	1.59019e7i	−0.0776084	−	0.0448072i
$709$	−2.29705e8			−0.644514			−0.322257	−	0.946652i	$-0.604442\pi$
$709$	−2.29705e8			−0.644514			−0.322257	+	0.946652i	$0.604442\pi$
$710$		−	1.57573e7i		−	0.0440257i
$711$	−1.39091e8	+	2.40913e8i	−0.386982	+	0.670272i
$712$	−2.88636e8	+	4.99932e8i	−0.799669	+	1.38507i
$713$	−1.30020e7	−	2.25202e7i	−0.0358709	−	0.0621302i
$714$	9.55325e7	−	5.51557e7i	0.262456	−	0.151529i
$715$			2.06570e7i			0.0565131i
$716$	−2.33590e7	+	1.34863e7i	−0.0636379	+	0.0367413i
$717$	2.06594e8	−	1.19277e8i	0.560480	−	0.323593i
$718$	5.05779e8	−	2.92011e8i	1.36643	−	0.788908i
$719$	−1.90521e8	+	3.29993e8i	−0.512575	+	0.887805i	0.487319	+	0.873224i	$0.337975\pi$
$719$	−1.90521e8	+	3.29993e8i	−0.512575	+	0.887805i	−0.999894	+	0.0145813i	$0.995358\pi$
$720$			1.47524e7i			0.0395245i
$721$	−5.28652e8	−	3.05217e8i	−1.41047	−	0.814335i
$722$	2.21667e8	−	1.27979e8i	0.588964	−	0.340039i
$723$	2.98813e8			0.790651
$724$	−4.69068e6	−	8.12450e6i	−0.0123600	−	0.0214082i
$725$	4.28529e8	+	2.47411e8i	1.12452	+	0.649240i
$726$	−4.38878e7	+	7.60159e7i	−0.114692	+	0.198653i
$727$			3.00705e8i			0.782595i	0.920264	+	0.391297i	$0.127974\pi$
$727$			3.00705e8i			0.782595i	−0.920264	+	0.391297i	$0.872026\pi$
$728$	−1.79282e8	+	3.10526e8i	−0.464668	+	0.804828i
$729$	−2.34434e8			−0.605115
$730$		−	1.95626e6i		−	0.00502872i
$731$	3.86950e7	−	2.08335e8i	0.0990610	−	0.533348i
$732$	1.02446e8			0.261192
$733$			1.57657e8i			0.400314i	0.979764	+	0.200157i	$0.0641452\pi$
$733$			1.57657e8i			0.400314i	−0.979764	+	0.200157i	$0.935855\pi$
$734$	−1.02268e8	−	5.90443e7i	−0.258613	−	0.149310i
$735$	−2.11759e6			−0.00533310
$736$	−1.39580e7	−	8.05863e6i	−0.0350097	−	0.0202129i
$737$	−7.74504e7	+	1.34148e8i	−0.193473	+	0.335106i
$738$	9.42414e7	−	5.44103e7i	0.234462	−	0.135367i
$739$			5.04892e8i			1.25102i	0.780215	+	0.625512i	$0.215110\pi$
$739$			5.04892e8i			1.25102i	−0.780215	+	0.625512i	$0.784890\pi$
$740$	1.35625e6	+	2.34910e6i	0.00334693	+	0.00579704i
$741$	4.78482e7	−	8.28755e7i	0.117601	−	0.203691i
$742$	−2.07035e8			−0.506796
$743$	−3.37302e8	−	1.94741e8i	−0.822342	−	0.474779i	0.0288817	−	0.999583i	$-0.490805\pi$
$743$	−3.37302e8	−	1.94741e8i	−0.822342	−	0.474779i	−0.851223	+	0.524804i	$0.824139\pi$
$744$	1.15681e8	+	2.00365e8i	0.280895	+	0.486524i
$745$	−6.43046e6	−	1.11379e7i	−0.0155515	−	0.0269361i
$746$	−2.19046e8	−	3.79398e8i	−0.527617	−	0.913859i
$747$	−1.94442e8			−0.466475
$748$	2.09408e7	+	3.62705e7i	0.0500366	+	0.0866659i
$749$	−9.56427e7	+	5.52194e7i	−0.227618	+	0.131415i
$750$	−3.54090e7	−	2.04434e7i	−0.0839325	−	0.0484584i
$751$	2.99909e8	+	1.73153e8i	0.708060	+	0.408799i	0.810342	−	0.585957i	$-0.199281\pi$
$751$	2.99909e8	+	1.73153e8i	0.708060	+	0.408799i	−0.102282	+	0.994755i	$0.532615\pi$
$752$	−2.88073e8			−0.677406
$753$		−	3.19978e8i		−	0.749437i
$754$	−2.00279e8	+	3.46893e8i	−0.467219	+	0.809248i
$755$	−2.63291e6	+	4.56033e6i	−0.00611779	+	0.0105963i
$756$	−5.50428e7	−	9.53370e7i	−0.127390	−	0.220646i
$757$	7.16024e8	−	4.13397e8i	1.65059	−	0.952970i	0.673765	−	0.738946i	$-0.264676\pi$
$757$	7.16024e8	−	4.13397e8i	1.65059	−	0.952970i	0.976828	−	0.214024i	$-0.0686572\pi$
$758$			3.81472e7i			0.0875900i
$759$	−1.48943e7	+	8.59922e6i	−0.0340639	+	0.0196668i
$760$	1.74896e7	−	1.00976e7i	0.0398417	−	0.0230026i
$761$	−3.85298e8	+	2.22452e8i	−0.874264	+	0.504756i	−0.868763	−	0.495229i	$-0.835084\pi$
$761$	−3.85298e8	+	2.22452e8i	−0.874264	+	0.504756i	−0.00550085	+	0.999985i	$0.501751\pi$
$762$	−1.59116e8	+	2.75597e8i	−0.359625	+	0.622888i
$763$		−	3.00419e8i		−	0.676323i
$764$	−8.22820e7	−	4.75055e7i	−0.184512	−	0.106528i
$765$	−1.19432e7	+	6.89542e6i	−0.0266770	+	0.0154020i
$766$	−3.71784e8			−0.827189
$767$	−1.10648e8	−	1.91648e8i	−0.245221	−	0.424735i
$768$	1.65146e8	+	9.53468e7i	0.364572	+	0.210486i
$769$	4.05504e8	−	7.02354e8i	0.891695	−	1.54446i	0.0538534	−	0.998549i	$-0.482850\pi$
$769$	4.05504e8	−	7.02354e8i	0.891695	−	1.54446i	0.837842	−	0.545913i	$-0.183817\pi$
$770$			2.85924e7i			0.0626294i
$771$	−3.98758e7	+	6.90669e7i	−0.0870054	+	0.150698i
$772$	1.37591e8			0.299047
$773$			3.04151e8i			0.658493i	0.944244	+	0.329246i	$0.106795\pi$
$773$			3.04151e8i			0.658493i	−0.944244	+	0.329246i	$0.893205\pi$
$774$	2.46876e8	+	4.58533e7i	0.532422	+	0.0988890i
$775$	3.90433e8			0.838768
$776$		−	8.50672e8i		−	1.82044i
$777$	7.84797e7	+	4.53103e7i	0.167299	+	0.0965903i
$778$	6.42953e8			1.36534
$779$	−9.54956e7	−	5.51344e7i	−0.202009	−	0.116630i
$780$	−2.66353e6	+	4.61338e6i	−0.00561273	+	0.00972154i
$781$	1.73089e8	−	9.99331e7i	0.363343	−	0.209776i
$782$			1.91285e7i			0.0400002i
$783$	−3.13202e8	−	5.42481e8i	−0.652438	−	1.13006i
$784$	−1.59785e7	+	2.76755e7i	−0.0331579	+	0.0574312i
$785$	−1.14618e7			−0.0236943
$786$	−3.01985e8	−	1.74351e8i	−0.621895	−	0.359051i
$787$	2.83509e8	+	4.91052e8i	0.581624	+	1.00740i	0.995287	+	0.0969721i	$0.0309158\pi$
$787$	2.83509e8	+	4.91052e8i	0.581624	+	1.00740i	−0.413663	+	0.910430i	$0.635751\pi$
$788$	−3.87181e7	−	6.70617e7i	−0.0791290	−	0.137055i
$789$	−2.61415e8	−	4.52784e8i	−0.532230	−	0.921850i
$790$	4.85432e7			0.0984572
$791$	−9.88768e7	−	1.71260e8i	−0.199786	−	0.346039i
$792$	−2.18925e8	+	1.26396e8i	−0.440676	+	0.254424i
$793$	6.17333e8	+	3.56417e8i	1.23794	+	0.714725i
$794$	2.88950e7	+	1.66825e7i	0.0577246	+	0.0333273i
$795$	−1.56672e7			−0.0311810
$796$			4.72438e7i			0.0936711i
$797$	−3.64591e8	+	6.31490e8i	−0.720163	+	1.24736i	0.240771	+	0.970582i	$0.422600\pi$
$797$	−3.64591e8	+	6.31490e8i	−0.720163	+	1.24736i	−0.960934	+	0.276777i	$0.910734\pi$
$798$	6.62290e7	−	1.14712e8i	0.130329	−	0.225736i
$799$	−1.34648e8	−	2.33217e8i	−0.263973	−	0.457215i
$800$	2.09569e8	−	1.20995e8i	0.409315	−	0.236318i
$801$		−	4.73348e8i		−	0.921049i
$802$	−4.86088e8	+	2.80643e8i	−0.942305	+	0.544040i
$803$	2.14889e7	−	1.24066e7i	0.0415018	−	0.0239611i
$804$	−3.45944e7	+	1.99731e7i	−0.0665637	+	0.0384305i
$805$	2.11064e6	−	3.65574e6i	0.00404601	−	0.00700790i
$806$			3.16055e8i			0.603611i
$807$	−4.59654e8	−	2.65381e8i	−0.874602	−	0.504951i
$808$	2.86355e8	−	1.65327e8i	0.542839	−	0.313408i
$809$	−7.45882e6			−0.0140872			−0.00704360	−	0.999975i	$-0.502242\pi$
$809$	−7.45882e6			−0.0140872			−0.00704360	+	0.999975i	$0.502242\pi$
$810$	−231185.	−	400425.i	−0.000435016	−	0.000753470i
$811$	−2.62898e8	−	1.51784e8i	−0.492861	−	0.284553i	0.232900	−	0.972501i	$-0.425179\pi$
$811$	−2.62898e8	−	1.51784e8i	−0.492861	−	0.284553i	−0.725761	+	0.687947i	$0.758512\pi$
$812$	8.96093e7	−	1.55208e8i	0.167373	−	0.289898i
$813$			3.16389e8i			0.588775i
$814$	5.32186e7	−	9.21774e7i	0.0986712	−	0.170904i
$815$	6.04244e6			0.0111619
$816$		−	1.25977e8i		−	0.231857i
$817$	−8.48422e7	−	2.39878e8i	−0.155577	−	0.439870i
$818$	−8.68398e7			−0.158657
$819$		−	2.94013e8i		−	0.535199i
$820$	5.31589e6	+	3.06913e6i	0.00964128	+	0.00556639i
$821$	9.63350e7			0.174082			0.0870411	−	0.996205i	$-0.472259\pi$
$821$	9.63350e7			0.174082			0.0870411	+	0.996205i	$0.472259\pi$
$822$	−4.65848e8	−	2.68957e8i	−0.838742	−	0.484248i
$823$	4.27919e8	−	7.41177e8i	0.767647	−	1.32960i	−0.171188	−	0.985238i	$-0.554761\pi$
$823$	4.27919e8	−	7.41177e8i	0.767647	−	1.32960i	0.938835	−	0.344366i	$-0.111906\pi$
$824$	−8.15610e8	+	4.70893e8i	−1.45781	+	0.841667i
$825$		−	2.58223e8i		−	0.459868i
$826$	−1.53153e8	−	2.65269e8i	−0.271760	−	0.470703i
$827$	−3.56939e8	+	6.18236e8i	−0.631069	+	1.09304i	0.356264	+	0.934385i	$0.384050\pi$
$827$	−3.56939e8	+	6.18236e8i	−0.631069	+	1.09304i	−0.987334	+	0.158659i	$0.949283\pi$
$828$	7.32712e6			0.0129075
$829$	−5.02175e8	−	2.89931e8i	−0.881437	−	0.508898i	−0.0103052	−	0.999947i	$-0.503280\pi$
$829$	−5.02175e8	−	2.89931e8i	−0.881437	−	0.508898i	−0.871132	+	0.491049i	$0.836614\pi$
$830$	1.69652e7	+	2.93846e7i	0.0296705	+	0.0513909i
$831$	8.51164e7	+	1.47426e8i	0.148324	+	0.256904i
$832$	2.62491e8	+	4.54648e8i	0.455769	+	0.789415i
$833$	−2.98739e7			−0.0516841
$834$	6.66042e7	+	1.15362e8i	0.114816	+	0.198868i
$835$	−604804.	+	349184.i	−0.00103885	+	0.000599783i
$836$	4.35523e7	+	2.51449e7i	0.0745405	+	0.0430360i
$837$	−4.28038e8	−	2.47128e8i	−0.729972	−	0.421449i
$838$	−9.13101e8			−1.55162
$839$		−	2.04314e8i		−	0.345949i	−0.984926	−	0.172974i	$-0.944662\pi$
$839$		−	2.04314e8i		−	0.345949i	0.984926	−	0.172974i	$-0.0553378\pi$
$840$	−1.87787e7	+	3.25257e7i	−0.0316832	+	0.0548769i
$841$	2.12478e8	−	3.68023e8i	0.357212	−	0.618710i
$842$	1.48008e8	+	2.56357e8i	0.247941	+	0.429446i
$843$	4.58650e8	−	2.64801e8i	0.765594	−	0.442016i
$844$		−	1.84942e7i		−	0.0307616i
$845$	1.55303e7	−	8.96645e6i	0.0257401	−	0.0148611i
$846$	2.76361e8	−	1.59557e8i	0.456421	−	0.263515i
$847$	2.36656e8	−	1.36633e8i	0.389464	−	0.224857i
$848$	−1.18218e8	+	2.04760e8i	−0.193864	+	0.335782i
$849$		−	6.08683e8i		−	0.994645i
$850$	−2.48725e8	−	1.43601e8i	−0.405006	−	0.233831i
$851$	−1.36088e7	+	7.85703e6i	−0.0220816	+	0.0127488i
$852$	5.15419e7			0.0833377
$853$	3.30208e8	+	5.71937e8i	0.532036	+	0.921513i	0.999301	+	0.0373956i	$0.0119062\pi$
$853$	3.30208e8	+	5.71937e8i	0.532036	+	0.921513i	−0.467265	+	0.884117i	$0.654761\pi$
$854$	8.54481e8	+	4.93335e8i	1.37192	+	0.792078i
$855$	−8.27977e6	+	1.43410e7i	−0.0132471	+	0.0229446i
$856$			1.70386e8i			0.271652i
$857$	−3.40887e8	+	5.90434e8i	−0.541587	+	0.938056i	0.457226	+	0.889350i	$0.348843\pi$
$857$	−3.40887e8	+	5.90434e8i	−0.541587	+	0.938056i	−0.998813	+	0.0487056i	$0.984490\pi$
$858$	2.09031e8			0.330940
$859$			1.03103e9i			1.62664i	0.581816	+	0.813321i	$0.302342\pi$
$859$			1.03103e9i			1.62664i	−0.581816	+	0.813321i	$0.697658\pi$
$860$	4.72286e6	+	1.33531e7i	0.00742523	+	0.0209937i
$861$	2.05070e8			0.321286
$862$		−	9.25064e8i		−	1.44428i
$863$	6.22214e8	+	3.59235e8i	0.968072	+	0.558916i	0.898648	−	0.438671i	$-0.144551\pi$
$863$	6.22214e8	+	3.59235e8i	0.968072	+	0.558916i	0.0694237	+	0.997587i	$0.477884\pi$
$864$	−3.06339e8			−0.474964
$865$	−5.45979e7	−	3.15221e7i	−0.0843582	−	0.0487042i
$866$	−2.78054e8	+	4.81604e8i	−0.428130	+	0.741543i
$867$	−2.44587e8	+	1.41212e8i	−0.375298	+	0.216678i
$868$		−	1.41410e8i		−	0.216233i
$869$	3.07862e8	+	5.33233e8i	0.469134	+	0.812564i
$870$	−2.09780e7	+	3.63350e7i	−0.0318571	+	0.0551782i
$871$	−2.77952e8			−0.420645
$872$	−4.01394e8	−	2.31745e8i	−0.605371	−	0.349511i
$873$	3.48764e8	+	6.04078e8i	0.524191	+	0.907925i
$874$	1.14844e7	+	1.98916e7i	0.0172019	+	0.0297945i
$875$	6.36454e7	+	1.10237e8i	0.0950042	+	0.164552i
$876$	6.39888e6			0.00951901
$877$	5.13232e8	+	8.88944e8i	0.760878	+	1.31788i	0.942399	+	0.334492i	$0.108565\pi$
$877$	5.13232e8	+	8.88944e8i	0.760878	+	1.31788i	−0.181521	+	0.983387i	$0.558102\pi$
$878$	7.42228e8	−	4.28525e8i	1.09661	−	0.633130i
$879$	1.61290e8	+	9.31206e7i	0.237487	+	0.137113i
$880$	2.82782e7	+	1.63264e7i	0.0414957	+	0.0239576i
$881$	−1.06738e9			−1.56095			−0.780477	−	0.625184i	$-0.785024\pi$
$881$	−1.06738e9			−1.56095			−0.780477	+	0.625184i	$0.785024\pi$
$882$		−	3.54004e7i		−	0.0515944i
$883$	−4.65939e8	+	8.07030e8i	−0.676779	+	1.17222i	0.299167	+	0.954201i	$0.403291\pi$
$883$	−4.65939e8	+	8.07030e8i	−0.676779	+	1.17222i	−0.975946	+	0.218015i	$0.930042\pi$
$884$	−3.75758e7	+	6.50833e7i	−0.0543941	+	0.0942134i
$885$	−1.15897e7	−	2.00740e7i	−0.0167203	−	0.0289603i
$886$	4.47391e8	−	2.58301e8i	0.643260	−	0.371386i
$887$			7.01148e8i			1.00471i	0.864663	+	0.502353i	$0.167532\pi$
$887$			7.01148e8i			1.00471i	−0.864663	+	0.502353i	$0.832468\pi$
$888$	1.21079e8	−	6.99052e7i	0.172915	−	0.0998322i
$889$	8.58003e8	−	4.95368e8i	1.22119	−	0.705055i
$890$	−7.15337e7	+	4.13000e7i	−0.101471	+	0.0585841i
$891$	2.93236e6	−	5.07900e6i	0.00414558	−	0.00718035i
$892$			5.28039e7i			0.0743998i
$893$	−2.80039e8	−	1.61680e8i	−0.393246	−	0.227040i
$894$	−1.12706e8	+	6.50707e7i	−0.157737	+	0.0910695i
$895$	−1.96584e7			−0.0274208
$896$	1.83934e8	+	3.18582e8i	0.255704	+	0.442892i
$897$	−2.67261e7	−	1.54303e7i	−0.0370304	−	0.0213795i
$898$	4.25675e8	−	7.37291e8i	0.587827	−	1.01815i
$899$		−	8.04644e8i		−	1.10745i
$900$	−5.50059e7	+	9.52730e7i	−0.0754539	+	0.130690i
$901$	−2.21025e8			−0.302181
$902$		−	2.40862e8i		−	0.328207i
$903$	3.59698e8	+	3.07449e8i	0.488511	+	0.417551i
$904$	−3.05097e8			−0.412983
$905$		−	6.83740e6i		−	0.00922455i
$906$	4.61466e7	+	2.66427e7i	0.0620519	+	0.0358257i
$907$	9.50602e8			1.27402			0.637011	−	0.770855i	$-0.280171\pi$
$907$	9.50602e8			1.27402			0.637011	+	0.770855i	$0.280171\pi$
$908$	−5.59623e7	−	3.23099e7i	−0.0747547	−	0.0431596i
$909$	−1.35564e8	+	2.34804e8i	−0.180490	+	0.312618i
$910$	−4.44321e7	+	2.56529e7i	−0.0589621	+	0.0340418i
$911$			2.30820e8i			0.305294i	0.988281	+	0.152647i	$0.0487798\pi$
$911$			2.30820e8i			0.305294i	−0.988281	+	0.152647i	$0.951220\pi$
$912$	−7.56343e7	−	1.31002e8i	−0.0997089	−	0.172701i
$913$	−2.15188e8	+	3.72716e8i	−0.282751	+	0.489740i
$914$	9.36648e8			1.22670
$915$	6.46620e7	+	3.73326e7i	0.0844084	+	0.0487332i
$916$	−1.00555e8	−	1.74167e8i	−0.130833	−	0.226610i
$917$	5.42797e8	+	9.40152e8i	0.703930	+	1.21924i
$918$	1.81787e8	+	3.14864e8i	0.234982	+	0.407001i
$919$	−1.65676e8			−0.213459			−0.106729	−	0.994288i	$-0.534038\pi$
$919$	−1.65676e8			−0.213459			−0.106729	+	0.994288i	$0.534038\pi$
$920$	−3.25633e6	−	5.64012e6i	−0.00418181	−	0.00724311i
$921$	5.17367e8	−	2.98702e8i	0.662246	−	0.382348i
$922$	−8.31165e8	−	4.79873e8i	−1.06046	−	0.612257i
$923$	3.10589e8	+	1.79319e8i	0.394985	+	0.228045i
$924$	−9.35252e7			−0.118553
$925$		−	2.35936e8i		−	0.298105i
$926$	3.71185e8	−	6.42912e8i	0.467474	−	0.809689i
$927$	3.86120e8	−	6.68779e8i	0.484711	−	0.839544i
$928$	−2.49359e8	−	4.31902e8i	−0.312019	−	0.540432i
$929$	4.46077e8	−	2.57543e8i	0.556369	−	0.321220i	−0.195318	−	0.980740i	$-0.562574\pi$
$929$	4.46077e8	−	2.57543e8i	0.556369	−	0.321220i	0.751687	+	0.659520i	$0.229241\pi$
$930$			3.31049e7i			0.0411570i
$931$	−3.10657e7	+	1.79358e7i	−0.0384974	+	0.0222265i
$932$	1.97234e8	−	1.13873e8i	0.243631	−	0.140661i
$933$	4.86328e8	−	2.80781e8i	0.598803	−	0.345719i
$934$	−1.64986e8	+	2.85764e8i	−0.202491	+	0.350725i
$935$			3.05244e7i			0.0373433i
$936$	−3.92835e8	−	2.26804e8i	−0.479052	−	0.276581i
$937$	−1.99755e8	+	1.15329e8i	−0.242817	+	0.140191i	−0.616471	−	0.787378i	$-0.711438\pi$
$937$	−1.99755e8	+	1.15329e8i	−0.242817	+	0.140191i	0.373654	+	0.927568i	$0.378105\pi$
$938$	−3.84727e8			−0.466170
$939$	2.54503e8	+	4.40812e8i	0.307394	+	0.532423i
$940$	1.55887e7	+	9.00016e6i	0.0187684	+	0.0108359i
$941$	9.54695e7	−	1.65358e8i	0.114577	−	0.198452i	−0.803034	−	0.595933i	$-0.796782\pi$
$941$	9.54695e7	−	1.65358e8i	0.114577	−	0.198452i	0.917610	+	0.397481i	$0.130116\pi$
$942$			1.15984e8i			0.138754i
$943$	−1.77800e7	+	3.07959e7i	−0.0212030	+	0.0367247i
$944$	−3.49805e8			−0.415825
$945$		−	8.02335e7i		−	0.0950737i
$946$	3.61110e8	−	4.22479e8i	0.426546	−	0.499035i
$947$	−5.39270e8			−0.634974			−0.317487	−	0.948263i	$-0.602839\pi$
$947$	−5.39270e8			−0.634974			−0.317487	+	0.948263i	$0.602839\pi$
$948$			1.58784e8i			0.186373i
$949$	3.85594e7	+	2.22623e7i	0.0451161	+	0.0260478i
$950$	−3.44862e8			−0.402231
$951$	−2.44082e8	−	1.40921e8i	−0.283788	−	0.163845i
$952$	−2.64921e8	+	4.58857e8i	−0.307048	+	0.531823i
$953$	−7.28893e8	+	4.20827e8i	−0.842142	+	0.486211i	−0.857992	−	0.513664i	$-0.828288\pi$
$953$	−7.28893e8	+	4.20827e8i	−0.842142	+	0.486211i	0.0158500	+	0.999874i	$0.494955\pi$
$954$		−	2.61913e8i		−	0.301656i
$955$	−3.46233e7	−	5.99694e7i	−0.0397520	−	0.0688525i
$956$	−1.12476e8	+	1.94813e8i	−0.128731	+	0.222969i
$957$	−5.32172e8			−0.607178
$958$	−4.64914e8	−	2.68418e8i	−0.528781	−	0.305292i
$959$	8.37331e8	+	1.45030e9i	0.949382	+	1.64438i
$960$	2.74944e7	+	4.76217e7i	0.0310764	+	0.0538259i
$961$	1.26305e8	+	2.18766e8i	0.142315	+	0.246496i
$962$	1.90990e8			0.214528
$963$	−6.98561e7	−	1.20994e8i	−0.0782214	−	0.135483i
$964$	−2.44024e8	+	1.40887e8i	−0.272396	+	0.157268i
$965$	8.68454e7	+	5.01402e7i	0.0966417	+	0.0557961i
$966$	−3.69929e7	−	2.13579e7i	−0.0410381	−	0.0236934i
$967$	−7.57221e8			−0.837420			−0.418710	−	0.908120i	$-0.637518\pi$
$967$	−7.57221e8			−0.837420			−0.418710	+	0.908120i	$0.637518\pi$
$968$		−	4.21599e8i		−	0.464808i
$969$	7.07043e7	−	1.22463e8i	0.0777095	−	0.134597i
$970$	6.08600e7	−	1.05413e8i	0.0666832	−	0.115499i
$971$	−7.49298e8	−	1.29782e9i	−0.818459	−	1.41761i	−0.906817	−	0.421524i	$-0.861495\pi$
$971$	−7.49298e8	−	1.29782e9i	−0.818459	−	1.41761i	0.0883586	−	0.996089i	$-0.471838\pi$
$972$	1.94922e8	−	1.12538e8i	0.212257	−	0.122547i
$973$		−	4.14710e8i		−	0.450201i
$974$	−1.04105e9	+	6.01048e8i	−1.12666	+	0.650477i
$975$	4.01275e8	−	2.31676e8i	0.432940	−	0.249958i
$976$	9.75826e8	−	5.63394e8i	1.04960	−	0.605986i
$977$	3.42447e8	−	5.93136e8i	0.367206	−	0.636019i	−0.621922	−	0.783079i	$-0.713648\pi$
$977$	3.42447e8	−	5.93136e8i	0.367206	−	0.636019i	0.989128	+	0.147060i	$0.0469811\pi$
$978$		−	6.11443e7i		−	0.0653641i
$979$	−9.07336e8	−	5.23851e8i	−0.966986	−	0.558289i
$980$	1.72931e6	−	998419.i	0.00183736	−	0.00106080i
$981$	3.80050e8			0.402563
$982$	1.19817e8	+	2.07529e8i	0.126527	+	0.219151i
$983$	8.16104e8	+	4.71178e8i	0.859182	+	0.496049i	0.863738	−	0.503941i	$-0.168117\pi$
$983$	8.16104e8	+	4.71178e8i	0.859182	+	0.496049i	−0.00455655	+	0.999990i	$0.501450\pi$
$984$	1.58192e8	−	2.73996e8i	0.166035	−	0.287581i
$985$		−	5.64377e7i		−	0.0590555i
$986$	−2.95948e8	+	5.12597e8i	−0.308734	+	0.534743i
$987$	6.01362e8			0.625438
$988$			9.02394e7i			0.0935676i
$989$	−7.73572e7	+	2.73604e7i	−0.0799672	+	0.0282835i
$990$	−3.61713e7			−0.0372785
$991$		−	1.18617e9i		−	1.21879i	−0.792868	−	0.609393i	$-0.791413\pi$
$991$		−	1.18617e9i		−	1.21879i	0.792868	−	0.609393i	$-0.208587\pi$
$992$	−3.40787e8	−	1.96753e8i	−0.349098	−	0.201552i
$993$	−4.19985e8			−0.428929
$994$	4.29902e8	+	2.48204e8i	0.437734	+	0.252726i
$995$	−1.72163e7	+	2.98195e7i	−0.0174771	+	0.0302713i
$996$	−9.61167e7	+	5.54930e7i	−0.0972793	+	0.0561643i
$997$			9.11144e8i			0.919394i	0.888076	+	0.459697i	$0.152042\pi$
$997$			9.11144e8i			0.919394i	−0.888076	+	0.459697i	$0.847958\pi$
$998$	2.06075e8	+	3.56932e8i	0.207316	+	0.359082i
$999$	−1.49338e8	+	2.58660e8i	−0.149787	+	0.259438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.15	yes	42
43.7	odd	6	inner	43.7.d.a.7.7	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.7	✓	42	43.7	odd	6	inner
43.7.d.a.37.15	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+6.95456i q^{2} +(-14.3583 - 8.28978i) q^{3} +15.6341 q^{4} +(9.86801 + 5.69730i) q^{5} +(57.6517 - 99.8557i) q^{6} +(-310.875 + 179.484i) q^{7} +553.820i q^{8} +(-227.059 - 393.278i) q^{9} +O(q^{10})\)	\(q+6.95456i q^{2} +(-14.3583 - 8.28978i) q^{3} +15.6341 q^{4} +(9.86801 + 5.69730i) q^{5} +(57.6517 - 99.8557i) q^{6} +(-310.875 + 179.484i) q^{7} +553.820i q^{8} +(-227.059 - 393.278i) q^{9} +(-39.6222 + 68.6277i) q^{10} -1005.14 q^{11} +(-224.480 - 129.604i) q^{12} +(-901.804 - 1561.97i) q^{13} +(-1248.23 - 2162.00i) q^{14} +(-94.4587 - 163.607i) q^{15} -2850.99 q^{16} +(-1332.58 - 2308.09i) q^{17} +(2735.07 - 1579.10i) q^{18} +(-2771.47 - 1600.11i) q^{19} +(154.278 + 89.0724i) q^{20} +5951.53 q^{21} -6990.29i q^{22} +(-516.012 + 893.760i) q^{23} +(4591.05 - 7951.92i) q^{24} +(-7747.58 - 13419.2i) q^{25} +(10862.8 - 6271.65i) q^{26} +19615.6i q^{27} +(-4860.27 + 2806.08i) q^{28} +(-27655.6 + 15967.0i) q^{29} +(1137.82 - 656.918i) q^{30} +(-12598.6 + 21821.3i) q^{31} +15617.1i q^{32} +(14432.1 + 8332.38i) q^{33} +(16051.8 - 9267.49i) q^{34} -4090.30 q^{35} +(-3549.87 - 6148.56i) q^{36} +(13186.5 + 7613.22i) q^{37} +(11128.1 - 19274.4i) q^{38} +29903.0i q^{39} +(-3155.28 + 5465.10i) q^{40} +34456.6 q^{41} +41390.3i q^{42} +(60437.9 + 51658.8i) q^{43} -15714.5 q^{44} -5174.50i q^{45} +(-6215.70 - 3588.64i) q^{46} +101043. q^{47} +(40935.4 + 23634.1i) q^{48} +(5604.54 - 9707.34i) q^{49} +(93324.6 - 53881.0i) q^{50} +44187.1i q^{51} +(-14098.9 - 24420.1i) q^{52} +(41465.7 - 71820.7i) q^{53} -136418. q^{54} +(-9918.72 - 5726.58i) q^{55} +(-99401.9 - 172169. i) q^{56} +(26529.1 + 45949.8i) q^{57} +(-111043. - 192333. i) q^{58} +122696. q^{59} +(-1476.78 - 2557.86i) q^{60} +(-342276. + 197613. i) q^{61} +(-151758. - 87617.4i) q^{62} +(141174. + 81507.0i) q^{63} -291073. q^{64} -20551.4i q^{65} +(-57948.0 + 100369. i) q^{66} +(77054.5 - 133462. i) q^{67} +(-20833.7 - 36085.0i) q^{68} +(14818.1 - 8555.26i) q^{69} -28446.2i q^{70} +(-172204. + 99422.2i) q^{71} +(217805. - 125750. i) q^{72} +(-21379.0 + 12343.2i) q^{73} +(-52946.5 + 91706.1i) q^{74} +256903. i q^{75} +(-43329.6 - 25016.4i) q^{76} +(312473. - 180406. i) q^{77} -207962. q^{78} +(-306288. - 530507. i) q^{79} +(-28133.6 - 16242.9i) q^{80} +(-2917.37 + 5053.04i) q^{81} +239630. i q^{82} +(214087. - 370810. i) q^{83} +93047.1 q^{84} -30368.4i q^{85} +(-359264. + 420319. i) q^{86} +529451. q^{87} -556666. i q^{88} +(902697. + 521172. i) q^{89} +35986.3 q^{90} +(560698. + 323719. i) q^{91} +(-8067.41 + 13973.2i) q^{92} +(361788. - 208878. i) q^{93} +702711. i q^{94} +(-18232.6 - 31579.8i) q^{95} +(129463. - 224236. i) q^{96} -1.53601e6 q^{97} +(67510.3 + 38977.1i) q^{98} +(228226. + 395299. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

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