LMFDB - Embedded newform 28.6.f.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,6,Mod(3,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("28.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	28.f (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:	$4.49074695476$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	28.19
Dual form			28.6.f.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.40397 - 5.12064i) q^{2} +(4.28235 + 7.41724i) q^{3} +(-20.4419 + 24.6197i) q^{4} +(47.5979 + 27.4807i) q^{5} +(27.6864 - 39.7592i) q^{6} +(-6.17988 + 129.494i) q^{7} +(175.210 + 45.4904i) q^{8} +(84.8230 - 146.918i) q^{9} +O(q^{10})$	\(q+(-2.40397 - 5.12064i) q^{2} +(4.28235 + 7.41724i) q^{3} +(-20.4419 + 24.6197i) q^{4} +(47.5979 + 27.4807i) q^{5} +(27.6864 - 39.7592i) q^{6} +(-6.17988 + 129.494i) q^{7} +(175.210 + 45.4904i) q^{8} +(84.8230 - 146.918i) q^{9} +(26.2947 - 309.794i) q^{10} +(455.168 - 262.791i) q^{11} +(-270.149 - 46.1922i) q^{12} +1005.77i q^{13} +(677.950 - 279.656i) q^{14} +470.727i q^{15} +(-188.260 - 1006.55i) q^{16} +(-1162.96 + 671.435i) q^{17} +(-956.225 - 81.1623i) q^{18} +(23.5393 - 40.7713i) q^{19} +(-1649.56 + 610.090i) q^{20} +(-986.956 + 508.702i) q^{21} +(-2439.87 - 1699.01i) q^{22} +(691.417 + 399.190i) q^{23} +(412.897 + 1494.38i) q^{24} +(-52.1274 - 90.2873i) q^{25} +(5150.20 - 2417.84i) q^{26} +3534.19 q^{27} +(-3061.79 - 2799.26i) q^{28} -600.350 q^{29} +(2410.42 - 1131.61i) q^{30} +(-2619.28 - 4536.73i) q^{31} +(-4701.59 + 3383.71i) q^{32} +(3898.37 + 2250.73i) q^{33} +(6233.89 + 4340.99i) q^{34} +(-3852.74 + 5993.83i) q^{35} +(1883.13 + 5091.59i) q^{36} +(6609.88 - 11448.6i) q^{37} +(-265.363 - 22.5234i) q^{38} +(-7460.05 + 4307.06i) q^{39} +(7089.53 + 6980.14i) q^{40} -3464.72i q^{41} +(4977.49 + 3830.94i) q^{42} -11552.1i q^{43} +(-2834.64 + 16578.0i) q^{44} +(8074.79 - 4661.98i) q^{45} +(381.962 - 4500.13i) q^{46} +(-1794.83 + 3108.74i) q^{47} +(6659.60 - 5706.74i) q^{48} +(-16730.6 - 1600.52i) q^{49} +(-337.016 + 483.973i) q^{50} +(-9960.39 - 5750.63i) q^{51} +(-24761.8 - 20559.9i) q^{52} +(1345.08 + 2329.75i) q^{53} +(-8496.07 - 18097.3i) q^{54} +28886.7 q^{55} +(-6973.54 + 22407.6i) q^{56} +403.214 q^{57} +(1443.22 + 3074.17i) q^{58} +(-4131.27 - 7155.58i) q^{59} +(-11589.2 - 9622.53i) q^{60} +(-11256.3 - 6498.83i) q^{61} +(-16934.3 + 24318.6i) q^{62} +(18500.8 + 11892.0i) q^{63} +(28629.2 + 15940.8i) q^{64} +(-27639.3 + 47872.6i) q^{65} +(2153.59 - 25372.8i) q^{66} +(-48300.6 + 27886.4i) q^{67} +(7242.54 - 42357.1i) q^{68} +6837.87i q^{69} +(39954.1 + 5319.51i) q^{70} -37357.0i q^{71} +(21545.2 - 21882.9i) q^{72} +(42602.5 - 24596.6i) q^{73} +(-74514.3 - 6324.62i) q^{74} +(446.455 - 773.283i) q^{75} +(522.589 + 1412.97i) q^{76} +(31217.1 + 60565.7i) q^{77} +(39988.7 + 27846.2i) q^{78} +(94085.5 + 54320.3i) q^{79} +(18699.8 - 53082.9i) q^{80} +(-5477.39 - 9487.12i) q^{81} +(-17741.6 + 8329.08i) q^{82} +71003.7 q^{83} +(7651.12 - 34697.4i) q^{84} -73805.9 q^{85} +(-59154.1 + 27770.9i) q^{86} +(-2570.90 - 4452.94i) q^{87} +(91704.5 - 25337.9i) q^{88} +(60615.8 + 34996.5i) q^{89} +(-43283.9 - 30140.8i) q^{90} +(-130242. - 6215.56i) q^{91} +(-23961.8 + 8862.29i) q^{92} +(22433.3 - 38855.7i) q^{93} +(20233.5 + 1717.37i) q^{94} +(2240.84 - 1293.75i) q^{95} +(-45231.6 - 20382.6i) q^{96} -110504. i q^{97} +(32024.2 + 89519.0i) q^{98} -89163.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4} - 6 q^{5} - 72 q^{8} - 1136 q^{9}+O(q^{10}) $ 36 * q - 12 * q^4 - 6 * q^5 - 72 * q^8 - 1136 * q^9	$ 36 q - 12 q^{4} - 6 q^{5} - 72 q^{8} - 1136 q^{9} - 804 q^{10} + 1632 q^{12} + 1024 q^{14} + 664 q^{16} - 6 q^{17} - 1780 q^{18} - 4586 q^{21} + 13768 q^{22} + 564 q^{24} + 7612 q^{25} - 8892 q^{26} - 5928 q^{28} + 176 q^{29} - 5836 q^{30} + 1160 q^{32} - 14154 q^{33} - 27920 q^{36} + 11722 q^{37} - 5652 q^{38} + 35052 q^{40} + 23140 q^{42} + 9096 q^{44} + 19152 q^{45} - 1040 q^{46} + 43900 q^{49} - 51168 q^{50} - 61776 q^{52} - 33486 q^{53} - 30996 q^{54} + 19952 q^{56} - 1668 q^{57} - 48436 q^{58} + 14312 q^{60} + 18846 q^{61} + 44544 q^{64} + 15356 q^{65} + 221808 q^{66} + 25020 q^{68} + 81192 q^{70} + 148064 q^{72} - 236562 q^{73} + 17152 q^{74} - 140010 q^{77} + 127704 q^{78} - 277224 q^{80} + 160402 q^{81} - 391836 q^{82} - 379540 q^{84} + 71212 q^{85} - 252496 q^{86} + 55268 q^{88} - 23706 q^{89} - 190176 q^{92} - 165162 q^{93} + 359988 q^{94} + 1061736 q^{96} + 418676 q^{98}+O(q^{100}) $ 36 * q - 12 * q^4 - 6 * q^5 - 72 * q^8 - 1136 * q^9 - 804 * q^10 + 1632 * q^12 + 1024 * q^14 + 664 * q^16 - 6 * q^17 - 1780 * q^18 - 4586 * q^21 + 13768 * q^22 + 564 * q^24 + 7612 * q^25 - 8892 * q^26 - 5928 * q^28 + 176 * q^29 - 5836 * q^30 + 1160 * q^32 - 14154 * q^33 - 27920 * q^36 + 11722 * q^37 - 5652 * q^38 + 35052 * q^40 + 23140 * q^42 + 9096 * q^44 + 19152 * q^45 - 1040 * q^46 + 43900 * q^49 - 51168 * q^50 - 61776 * q^52 - 33486 * q^53 - 30996 * q^54 + 19952 * q^56 - 1668 * q^57 - 48436 * q^58 + 14312 * q^60 + 18846 * q^61 + 44544 * q^64 + 15356 * q^65 + 221808 * q^66 + 25020 * q^68 + 81192 * q^70 + 148064 * q^72 - 236562 * q^73 + 17152 * q^74 - 140010 * q^77 + 127704 * q^78 - 277224 * q^80 + 160402 * q^81 - 391836 * q^82 - 379540 * q^84 + 71212 * q^85 - 252496 * q^86 + 55268 * q^88 - 23706 * q^89 - 190176 * q^92 - 165162 * q^93 + 359988 * q^94 + 1061736 * q^96 + 418676 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.40397	−	5.12064i	−0.424966	−	0.905210i
$2$	−2.40397	−	5.12064i	−0.424966	−	0.905210i
$3$	4.28235	+	7.41724i	0.274713	+	0.475816i	0.970063	−	0.242855i	$-0.0780840\pi$
$3$	4.28235	+	7.41724i	0.274713	+	0.475816i	−0.695350	+	0.718671i	$0.744751\pi$
$4$	−20.4419	+	24.6197i	−0.638809	+	0.769366i
$5$	47.5979	+	27.4807i	0.851457	+	0.491589i	0.861142	−	0.508364i	$-0.169750\pi$
$5$	47.5979	+	27.4807i	0.851457	+	0.491589i	−0.00968526	+	0.999953i	$0.503083\pi$
$6$	27.6864	−	39.7592i	0.313970	−	0.450878i
$7$	−6.17988	+	129.494i	−0.0476689	+	0.998863i
$7$	−6.17988	+	129.494i	−0.0476689	+	0.998863i
$8$	175.210	+	45.4904i	0.967909	+	0.251302i
$9$	84.8230	−	146.918i	0.349066	−	0.604600i
$10$	26.2947	−	309.794i	0.0831510	−	0.979655i
$11$	455.168	−	262.791i	1.13420	−	0.654831i	0.189212	−	0.981936i	$-0.439407\pi$
$11$	455.168	−	262.791i	1.13420	−	0.654831i	0.944988	+	0.327105i	$0.106073\pi$
$12$	−270.149	−	46.1922i	−0.541565	−	0.0926010i
$13$			1005.77i			1.65060i	0.564696	+	0.825299i	$0.308993\pi$
$13$			1005.77i			1.65060i	−0.564696	+	0.825299i	$0.691007\pi$
$14$	677.950	−	279.656i	0.924438	−	0.381332i
$15$			470.727i			0.540183i
$16$	−188.260	−	1006.55i	−0.183847	−	0.982955i
$17$	−1162.96	+	671.435i	−0.975983	+	0.563484i	−0.901055	−	0.433705i	$-0.857206\pi$
$17$	−1162.96	+	671.435i	−0.975983	+	0.563484i	−0.0749282	+	0.997189i	$0.523873\pi$
$18$	−956.225	−	81.1623i	−0.695631	−	0.0590437i
$19$	23.5393	−	40.7713i	0.0149592	−	0.0259102i	−0.858449	−	0.512899i	$-0.828571\pi$
$19$	23.5393	−	40.7713i	0.0149592	−	0.0259102i	0.873408	+	0.486989i	$0.161905\pi$
$20$	−1649.56	+	610.090i	−0.922130	+	0.341051i
$21$	−986.956	+	508.702i	−0.488371	+	0.251719i
$22$	−2439.87	−	1699.01i	−1.07476	−	0.748408i
$23$	691.417	+	399.190i	0.272534	+	0.157347i	0.630039	−	0.776564i	$-0.283039\pi$
$23$	691.417	+	399.190i	0.272534	+	0.157347i	−0.357505	+	0.933911i	$0.616372\pi$
$24$	412.897	+	1494.38i	0.146323	+	0.529582i
$25$	−52.1274	−	90.2873i	−0.0166808	−	0.0288919i
$26$	5150.20	−	2417.84i	1.49414	−	0.701447i
$27$	3534.19			0.932996
$28$	−3061.79	−	2799.26i	−0.738040	−	0.674757i
$29$	−600.350			−0.132559			−0.0662795	−	0.997801i	$-0.521113\pi$
$29$	−600.350			−0.132559			−0.0662795	+	0.997801i	$0.521113\pi$
$30$	2410.42	−	1131.61i	0.488978	−	0.229559i
$31$	−2619.28	−	4536.73i	−0.489529	−	0.847888i	0.510399	−	0.859938i	$-0.329498\pi$
$31$	−2619.28	−	4536.73i	−0.489529	−	0.847888i	−0.999927	+	0.0120494i	$0.996164\pi$
$32$	−4701.59	+	3383.71i	−0.811651	+	0.584142i
$33$	3898.37	+	2250.73i	0.623158	+	0.359781i
$34$	6233.89	+	4340.99i	0.924831	+	0.644008i
$35$	−3852.74	+	5993.83i	−0.531618	+	0.827055i
$36$	1883.13	+	5091.59i	0.242172	+	0.654783i
$37$	6609.88	−	11448.6i	0.793760	−	1.37483i	−0.129864	−	0.991532i	$-0.541454\pi$
$37$	6609.88	−	11448.6i	0.793760	−	1.37483i	0.923624	−	0.383301i	$-0.125213\pi$
$38$	−265.363	−	22.5234i	−0.0298113	−	0.00253032i
$39$	−7460.05	+	4307.06i	−0.785381	+	0.453440i
$40$	7089.53	+	6980.14i	0.700596	+	0.689786i
$41$		−	3464.72i		−	0.321891i	−0.986963	−	0.160946i	$-0.948546\pi$
$41$		−	3464.72i		−	0.321891i	0.986963	−	0.160946i	$-0.0514543\pi$
$42$	4977.49	+	3830.94i	0.435399	+	0.335106i
$43$		−	11552.1i		−	0.952773i	−0.879236	−	0.476387i	$-0.841946\pi$
$43$		−	11552.1i		−	0.952773i	0.879236	−	0.476387i	$-0.158054\pi$
$44$	−2834.64	+	16578.0i	−0.220732	+	1.29093i
$45$	8074.79	−	4661.98i	0.594429	−	0.343194i
$46$	381.962	−	4500.13i	0.0266149	−	0.313567i
$47$	−1794.83	+	3108.74i	−0.118517	+	0.205277i	−0.919180	−	0.393838i	$-0.871147\pi$
$47$	−1794.83	+	3108.74i	−0.118517	+	0.205277i	0.800663	+	0.599114i	$0.204481\pi$
$48$	6659.60	−	5706.74i	0.417201	−	0.357508i
$49$	−16730.6	−	1600.52i	−0.995455	−	0.0952294i
$50$	−337.016	+	483.973i	−0.0190645	+	0.0273777i
$51$	−9960.39	−	5750.63i	−0.536230	−	0.309592i
$52$	−24761.8	−	20559.9i	−1.26991	−	1.05442i
$53$	1345.08	+	2329.75i	0.0657748	+	0.113925i	0.897037	−	0.441955i	$-0.145715\pi$
$53$	1345.08	+	2329.75i	0.0657748	+	0.113925i	−0.831263	+	0.555880i	$0.812381\pi$
$54$	−8496.07	−	18097.3i	−0.396491	−	0.844557i
$55$	28886.7			1.28763
$56$	−6973.54	+	22407.6i	−0.297155	+	0.954829i
$57$	403.214			0.0164380
$58$	1443.22	+	3074.17i	0.0563330	+	0.119994i
$59$	−4131.27	−	7155.58i	−0.154509	−	0.267618i	0.778371	−	0.627804i	$-0.216046\pi$
$59$	−4131.27	−	7155.58i	−0.154509	−	0.267618i	−0.932880	+	0.360187i	$0.882713\pi$
$60$	−11589.2	−	9622.53i	−0.415598	−	0.345073i
$61$	−11256.3	−	6498.83i	−0.387321	−	0.223620i	0.293678	−	0.955905i	$-0.405121\pi$
$61$	−11256.3	−	6498.83i	−0.387321	−	0.223620i	−0.680999	+	0.732284i	$0.738454\pi$
$62$	−16934.3	+	24318.6i	−0.559484	+	0.803449i
$63$	18500.8	+	11892.0i	0.587273	+	0.377490i
$64$	28629.2	+	15940.8i	0.873695	+	0.486474i
$65$	−27639.3	+	47872.6i	−0.811416	+	1.40541i
$66$	2153.59	−	25372.8i	0.0608560	−	0.716983i
$67$	−48300.6	+	27886.4i	−1.31451	+	0.758936i	−0.982840	−	0.184458i	$-0.940947\pi$
$67$	−48300.6	+	27886.4i	−1.31451	+	0.758936i	−0.331675	+	0.943394i	$0.607614\pi$
$68$	7242.54	−	42357.1i	0.189941	−	1.11085i
$69$			6837.87i			0.172901i
$70$	39954.1	+	5319.51i	0.974578	+	0.129756i
$71$		−	37357.0i		−	0.879480i	−0.898125	−	0.439740i	$-0.855071\pi$
$71$		−	37357.0i		−	0.879480i	0.898125	−	0.439740i	$-0.144929\pi$
$72$	21545.2	−	21882.9i	0.489801	−	0.497477i
$73$	42602.5	−	24596.6i	0.935681	−	0.540216i	0.0470771	−	0.998891i	$-0.485009\pi$
$73$	42602.5	−	24596.6i	0.935681	−	0.540216i	0.888604	+	0.458676i	$0.151676\pi$
$74$	−74514.3	−	6324.62i	−1.58183	−	0.134263i
$75$	446.455	−	773.283i	0.00916483	−	0.0158740i
$76$	522.589	+	1412.97i	0.0103783	+	0.0280608i
$77$	31217.1	+	60565.7i	0.600020	+	1.16413i
$78$	39988.7	+	27846.2i	0.744218	+	0.518238i
$79$	94085.5	+	54320.3i	1.69611	+	0.979252i	0.949380	+	0.314130i	$0.101713\pi$
$79$	94085.5	+	54320.3i	1.69611	+	0.979252i	0.746735	+	0.665122i	$0.231621\pi$
$80$	18699.8	−	53082.9i	0.326672	−	0.927321i
$81$	−5477.39	−	9487.12i	−0.0927601	−	0.160665i
$82$	−17741.6	+	8329.08i	−0.291379	+	0.136793i
$83$	71003.7			1.13132			0.565661	−	0.824638i	$-0.308621\pi$
$83$	71003.7			1.13132			0.565661	+	0.824638i	$0.308621\pi$
$84$	7651.12	−	34697.4i	0.118312	−	0.536536i
$85$	−73805.9			−1.10801
$86$	−59154.1	+	27770.9i	−0.862459	+	0.404896i
$87$	−2570.90	−	4452.94i	−0.0364156	−	0.0630737i
$88$	91704.5	−	25337.9i	1.26236	−	0.348790i
$89$	60615.8	+	34996.5i	0.811167	+	0.468328i	0.847361	−	0.531017i	$-0.178190\pi$
$89$	60615.8	+	34996.5i	0.811167	+	0.468328i	−0.0361937	+	0.999345i	$0.511523\pi$
$90$	−43283.9	−	30140.8i	−0.563274	−	0.392237i
$91$	−130242.	−	6215.56i	−1.64872	−	0.0786822i
$92$	−23961.8	+	8862.29i	−0.295155	+	0.109163i
$93$	22433.3	−	38855.7i	0.268959	−	0.465851i
$94$	20233.5	+	1717.37i	0.236184	+	0.0200468i
$95$	2240.84	−	1293.75i	0.0254743	−	0.0147076i
$96$	−45231.6	−	20382.6i	−0.500915	−	0.225726i
$97$		−	110504.i		−	1.19247i	−0.802809	−	0.596236i	$-0.796662\pi$
$97$		−	110504.i		−	1.19247i	0.802809	−	0.596236i	$-0.203338\pi$
$98$	32024.2	+	89519.0i	0.336832	+	0.941565i
$99$		−	89163.0i		−	0.914317i
$100$	3288.43	+	562.280i	0.0328843	+	0.00562280i
$101$	−48103.9	+	27772.8i	−0.469220	+	0.270904i	−0.715913	−	0.698189i	$-0.753989\pi$
$101$	−48103.9	+	27772.8i	−0.469220	+	0.270904i	0.246693	+	0.969094i	$0.420656\pi$
$102$	−5502.45	+	64827.9i	−0.0523668	+	0.616966i
$103$	−58825.8	+	101889.i	−0.546355	+	0.946315i	0.452165	+	0.891934i	$0.350652\pi$
$103$	−58825.8	+	101889.i	−0.546355	+	0.946315i	−0.998520	+	0.0543805i	$0.982682\pi$
$104$	−45753.0	+	176222.i	−0.414798	+	1.59763i
$105$	−60956.5	−	2909.04i	−0.539569	−	0.0257499i
$106$	8696.29	−	12488.3i	0.0751743	−	0.107954i
$107$	−130422.	−	75298.9i	−1.10126	−	0.635813i	−0.164709	−	0.986342i	$-0.552668\pi$
$107$	−130422.	−	75298.9i	−1.10126	−	0.635813i	−0.936552	+	0.350529i	$0.886002\pi$
$108$	−72245.4	+	87010.6i	−0.596006	+	0.717816i
$109$	−29130.8	−	50456.0i	−0.234847	−	0.406768i	0.724381	−	0.689400i	$-0.242126\pi$
$109$	−29130.8	−	50456.0i	−0.234847	−	0.406768i	−0.959228	+	0.282632i	$0.908792\pi$
$110$	−69442.7	−	147918.i	−0.547199	−	1.16558i
$111$	113223.			0.872223
$112$	131505.	−	18158.2i	0.990601	−	0.136782i
$113$	−60945.6			−0.449000			−0.224500	−	0.974474i	$-0.572075\pi$
$113$	−60945.6			−0.449000			−0.224500	+	0.974474i	$0.572075\pi$
$114$	−969.313	−	2064.71i	−0.00698557	−	0.0148798i
$115$	21940.0	+	38001.2i	0.154701	+	0.267949i
$116$	12272.3	−	14780.4i	0.0846798	−	0.101986i
$117$	147766.	+	85312.7i	0.997952	+	0.576168i
$118$	−26709.7	+	38356.5i	−0.176589	+	0.253591i
$119$	−79760.2	−	154746.i	−0.516320	−	1.00173i
$120$	−21413.6	+	82476.1i	−0.135749	+	0.522848i
$121$	57593.0	−	99753.9i	0.357607	−	0.619393i
$122$	−6218.36	+	73262.5i	−0.0378248	+	0.445638i
$123$	25698.7	−	14837.1i	0.153161	−	0.0884275i
$124$	165236.	+	28253.3i	0.965051	+	0.165012i
$125$		−	177484.i		−	1.01598i
$126$	16419.4	−	123324.i	0.0921365	−	0.692025i
$127$		−	49258.1i		−	0.270999i	−0.990777	−	0.135500i	$-0.956736\pi$
$127$		−	49258.1i		−	0.270999i	0.990777	−	0.135500i	$-0.0432639\pi$
$128$	12803.2	−	184921.i	0.0690706	−	0.997612i
$129$	85684.6	−	49470.1i	0.453345	−	0.261739i
$130$	311582.	+	26446.5i	1.61702	+	0.137249i
$131$	−74225.7	+	128563.i	−0.377899	+	0.654541i	−0.990756	−	0.135653i	$-0.956687\pi$
$131$	−74225.7	+	128563.i	−0.377899	+	0.654541i	0.612857	+	0.790194i	$0.290020\pi$
$132$	−135102.	+	49967.7i	−0.674882	+	0.249606i
$133$	5134.18	+	3300.17i	0.0251676	+	0.0161774i
$134$	258909.	+	180292.i	1.24562	+	0.867390i
$135$	168220.	+	97121.7i	0.794406	+	0.458651i
$136$	−234306.	+	64738.7i	−1.08627	+	0.300135i
$137$	133953.	+	232013.i	0.609747	+	1.05611i	0.991282	+	0.131758i	$0.0420622\pi$
$137$	133953.	+	232013.i	0.609747	+	1.05611i	−0.381535	+	0.924354i	$0.624604\pi$
$138$	35014.3	−	16438.0i	0.156512	−	0.0734771i
$139$	−181033.			−0.794732			−0.397366	−	0.917660i	$-0.630076\pi$
$139$	−181033.			−0.794732			−0.397366	+	0.917660i	$0.630076\pi$
$140$	−68809.2	−	217379.i	−0.296706	−	0.937339i
$141$	−30744.4			−0.130232
$142$	−191292.	+	89805.0i	−0.796114	+	0.373749i
$143$	264308.	+	457795.i	1.08086	+	1.87211i
$144$	−163848.	−	57719.6i	−0.658469	−	0.231962i
$145$	−28575.4	−	16498.0i	−0.112868	−	0.0651645i
$146$	−228365.	−	159023.i	−0.886640	−	0.617414i
$147$	−59774.8	−	130949.i	−0.228152	−	0.499814i
$148$	146744.	+	396765.i	0.550688	+	1.48895i
$149$	−33057.5	+	57257.2i	−0.121984	+	0.211283i	−0.920550	−	0.390624i	$-0.872259\pi$
$149$	−33057.5	+	57257.2i	−0.121984	+	0.211283i	0.798566	+	0.601908i	$0.205592\pi$
$150$	−5032.96	−	427.187i	−0.0182640	−	0.00155021i
$151$	144778.	−	83587.7i	0.516727	−	0.298332i	−0.218868	−	0.975755i	$-0.570236\pi$
$151$	144778.	−	83587.7i	0.516727	−	0.298332i	0.735594	+	0.677422i	$0.236903\pi$
$152$	5979.03	−	6072.73i	0.0209905	−	0.0213194i
$153$			227813.i			0.786773i
$154$	235090.	−	305450.i	0.798790	−	1.03786i
$155$		−	287918.i		−	0.962587i
$156$	46458.8	−	271709.i	0.152847	−	0.893907i
$157$	−336141.	+	194071.i	−1.08836	+	0.628365i	−0.933139	−	0.359515i	$-0.882942\pi$
$157$	−336141.	+	194071.i	−1.08836	+	0.628365i	−0.155220	+	0.987880i	$0.549609\pi$
$158$	51976.0	−	612362.i	0.165638	−	1.95149i
$159$	−11520.2	+	19953.6i	−0.0361383	+	0.0625935i
$160$	−316772.	+	31855.0i	−0.978244	+	0.0983733i
$161$	−55965.7	+	87067.7i	−0.170160	+	0.264723i
$162$	−35412.6	+	50854.5i	−0.106016	+	0.152244i
$163$	−251621.	−	145273.i	−0.741783	−	0.428269i	0.0809340	−	0.996719i	$-0.474210\pi$
$163$	−251621.	−	145273.i	−0.741783	−	0.428269i	−0.822717	+	0.568451i	$0.807543\pi$
$164$	85300.5	+	70825.4i	0.247652	+	0.205627i
$165$	123703.	+	214260.i	0.353728	+	0.612675i
$166$	−170691.	−	363584.i	−0.480772	−	1.02408i
$167$	556102.			1.54299			0.771496	−	0.636234i	$-0.219509\pi$
$167$	556102.			1.54299			0.771496	+	0.636234i	$0.219509\pi$
$168$	−196066.	+	44232.8i	−0.535955	+	0.120912i
$169$	−640285.			−1.72447
$170$	177427.	+	377933.i	0.470866	+	1.00298i
$171$	−3993.35	−	6916.69i	−0.0104435	−	0.0180887i
$172$	284409.	+	236146.i	0.733031	+	0.608640i
$173$	−40646.5	−	23467.3i	−0.103254	−	0.0596139i	0.447484	−	0.894292i	$-0.352320\pi$
$173$	−40646.5	−	23467.3i	−0.103254	−	0.0596139i	−0.550738	+	0.834678i	$0.685654\pi$
$174$	−16621.5	+	23869.4i	−0.0416195	+	0.0597679i
$175$	12013.8	−	6192.24i	0.0296542	−	0.0152846i
$176$	−350201.	−	408674.i	−0.852189	−	0.994479i
$177$	35383.1	−	61285.3i	0.0848912	−	0.147036i
$178$	33486.2	−	394522.i	0.0792165	−	0.933300i
$179$	−27816.7	+	16060.0i	−0.0648892	+	0.0374638i	−0.532094	−	0.846686i	$-0.678595\pi$
$179$	−27816.7	+	16060.0i	−0.0648892	+	0.0374638i	0.467204	+	0.884149i	$0.345261\pi$
$180$	−50287.2	+	294099.i	−0.115685	+	0.676569i
$181$		−	512222.i		−	1.16215i	−0.813851	−	0.581074i	$-0.802633\pi$
$181$		−	512222.i		−	1.16215i	0.813851	−	0.581074i	$-0.197367\pi$
$182$	281270.	+	681864.i	0.629426	+	1.52588i
$183$		−	111321.i		−	0.245725i
$184$	102984.	+	101395.i	0.224246	+	0.220786i
$185$	629232.	−	363288.i	1.35170	−	0.780407i
$186$	−252895.	−	21465.2i	−0.535991	−	0.0454938i
$187$	−352895.	+	611231.i	−0.737974	+	1.27821i
$188$	−39846.6	−	107737.i	−0.0822236	−	0.222315i
$189$	−21840.9	+	457657.i	−0.0444749	+	0.931936i
$190$	−12011.7	−	8364.41i	−0.0241392	−	0.0168094i
$191$	−3654.81	−	2110.11i	−0.00724905	−	0.00418524i	0.496371	−	0.868110i	$-0.334666\pi$
$191$	−3654.81	−	2110.11i	−0.00724905	−	0.00418524i	−0.503620	+	0.863925i	$0.667999\pi$
$192$	4363.69	+	280614.i	0.00854282	+	0.549359i
$193$	−8567.98	−	14840.2i	−0.0165571	−	0.0286778i	0.857628	−	0.514270i	$-0.171937\pi$
$193$	−8567.98	−	14840.2i	−0.0165571	−	0.0286778i	−0.874185	+	0.485593i	$0.838604\pi$
$194$	−565851.	+	265648.i	−1.07944	+	0.506760i
$195$	−473444.			−0.891624
$196$	381410.	−	379185.i	0.709172	−	0.705036i
$197$	958831.			1.76026			0.880129	−	0.474734i	$-0.157456\pi$
$197$	958831.			1.76026			0.880129	+	0.474734i	$0.157456\pi$
$198$	−456571.	+	214345.i	−0.827648	+	0.388553i
$199$	−28509.3	−	49379.5i	−0.0510332	−	0.0883922i	0.839380	−	0.543545i	$-0.182918\pi$
$199$	−28509.3	−	49379.5i	−0.0510332	−	0.0883922i	−0.890414	+	0.455152i	$0.849585\pi$
$200$	−5026.04	−	18190.6i	−0.00888487	−	0.0321567i
$201$	−413680.	−	238838.i	−0.722228	−	0.416978i
$202$	257855.	+	179558.i	0.444628	+	0.309617i
$203$	3710.09	−	77741.9i	0.00631894	−	0.132408i
$204$	345188.	−	127668.i	0.580738	−	0.214787i
$205$	95212.9	−	164914.i	0.158238	−	0.274076i
$206$	663154.	+	56287.1i	1.08880	+	0.0924146i
$207$	117296.	−	67721.0i	0.190265	−	0.109849i
$208$	1.01236e6	−	189346.i	1.62246	−	0.303458i
$209$		−	24743.7i		−	0.0391831i
$210$	131641.	+	319129.i	0.205989	+	0.499365i
$211$			96012.1i			0.148464i	0.997241	+	0.0742318i	$0.0236505\pi$
$211$			96012.1i			0.148464i	−0.997241	+	0.0742318i	$0.976350\pi$
$212$	−84853.9	−	14509.0i	−0.129668	−	0.0221716i
$213$	277086.	−	159976.i	0.418471	−	0.241604i
$214$	−72049.3	+	848858.i	−0.107546	+	1.26707i
$215$	317459.	−	549855.i	0.468373	−	0.811245i
$216$	619226.	+	160772.i	0.903056	+	0.234463i
$217$	603668.	−	311146.i	0.870260	−	0.448554i
$218$	−188337.	+	270463.i	−0.268408	+	0.385448i
$219$	364877.	+	210662.i	0.514087	+	0.296808i
$220$	−590498.	+	711182.i	−0.822549	+	0.990659i
$221$	−675311.	−	1.16967e6i	−0.930086	−	1.61096i
$222$	−272185.	−	579775.i	−0.370665	−	0.789545i
$223$	−618991.			−0.833532			−0.416766	−	0.909014i	$-0.636837\pi$
$223$	−618991.			−0.833532			−0.416766	+	0.909014i	$0.636837\pi$
$224$	−409117.	−	629740.i	−0.544788	−	0.838574i
$225$	−17686.4			−0.0232907
$226$	146511.	+	312080.i	0.190809	+	0.406439i
$227$	−658750.	−	1.14099e6i	−0.848508	−	1.46966i	−0.882539	−	0.470239i	$-0.844168\pi$
$227$	−658750.	−	1.14099e6i	−0.848508	−	1.46966i	0.0340308	−	0.999421i	$-0.489166\pi$
$228$	−8242.45	+	9927.01i	−0.0105007	+	0.0126468i
$229$	−28630.5	−	16529.8i	−0.0360778	−	0.0208296i	0.481853	−	0.876252i	$-0.339964\pi$
$229$	−28630.5	−	16529.8i	−0.0360778	−	0.0208296i	−0.517930	+	0.855423i	$0.673297\pi$
$230$	141847.	−	203700.i	0.176808	−	0.253906i
$231$	−315548.	+	490908.i	−0.389077	+	0.605299i
$232$	−105187.	−	27310.2i	−0.128305	−	0.0333123i
$233$	−381435.	+	660664.i	−0.460289	+	0.797244i	−0.998975	−	0.0452628i	$-0.985587\pi$
$233$	−381435.	+	660664.i	−0.460289	+	0.797244i	0.538686	+	0.842506i	$0.318921\pi$
$234$	81630.8	−	961744.i	0.0974573	−	1.14821i
$235$	−170861.	+	98646.4i	−0.201824	+	0.116523i
$236$	260619.	+	44562.6i	0.304597	+	0.0520824i
$237$			930473.i			1.07605i
$238$	−600658.	+	780428.i	−0.687362	+	0.893080i
$239$			1.17736e6i			1.33326i	0.745387	+	0.666632i	$0.232265\pi$
$239$			1.17736e6i			1.33326i	−0.745387	+	0.666632i	$0.767735\pi$
$240$	473808.	−	88618.9i	0.530975	−	0.0993112i
$241$	−1.11276e6	+	642453.i	−1.23412	+	0.712522i	−0.967887	−	0.251385i	$-0.919114\pi$
$241$	−1.11276e6	+	642453.i	−1.23412	+	0.712522i	−0.266238	+	0.963907i	$0.585781\pi$
$242$	−649255.	−	55107.4i	−0.712651	−	0.0604883i
$243$	476316.	−	825003.i	0.517463	−	0.896272i
$244$	390099.	−	144279.i	0.419470	−	0.155141i
$245$	−752359.	−	535950.i	−0.800774	−	0.570439i
$246$	−137754.	−	95925.6i	−0.145134	−	0.101064i
$247$	41006.6	+	23675.2i	0.0427673	+	0.0246917i
$248$	−252547.	−	914034.i	−0.260743	−	0.943698i
$249$	304062.	+	526652.i	0.310788	+	0.538301i
$250$	−908832.	+	426666.i	−0.919673	+	0.431756i
$251$	1.48159e6			1.48437			0.742186	−	0.670194i	$-0.233789\pi$
$251$	1.48159e6			1.48437			0.742186	+	0.670194i	$0.233789\pi$
$252$	−670970.	+	212390.i	−0.665583	+	0.210684i
$253$	419614.			0.412144
$254$	−252233.	+	118415.i	−0.245311	+	0.115165i
$255$	−316062.	−	547436.i	−0.304384	−	0.527209i
$256$	−977693.	+	378984.i	−0.932400	+	0.361427i
$257$	965433.	+	557393.i	0.911778	+	0.526415i	0.881003	−	0.473111i	$-0.156869\pi$
$257$	965433.	+	557393.i	0.911778	+	0.526415i	0.0307754	+	0.999526i	$0.490202\pi$
$258$	−459301.	−	319836.i	−0.429584	−	0.299142i
$259$	1.44169e6	+	926694.i	1.33543	+	0.858394i
$260$	−613612.	−	1.65908e6i	−0.562937	−	1.52207i
$261$	−50923.5	+	88202.0i	−0.0462718	+	0.0801452i
$262$	836760.	+	71022.4i	0.753091	+	0.0639208i
$263$	−1.39056e6	+	802838.i	−1.23965	+	0.715713i	−0.969023	−	0.246971i	$-0.920565\pi$
$263$	−1.39056e6	+	802838.i	−1.23965	+	0.715713i	−0.270628	+	0.962684i	$0.587231\pi$
$264$	580648.	+	571689.i	0.512747	+	0.504835i
$265$			147855.i			0.129337i
$266$	4556.57	−	34223.8i	0.00394852	−	0.0296568i
$267$			599469.i			0.514622i
$268$	300801.	−	1.75920e6i	0.255824	−	1.49616i
$269$	−703306.	+	406054.i	−0.592602	+	0.342139i	−0.766126	−	0.642691i	$-0.777818\pi$
$269$	−703306.	+	406054.i	−0.592602	+	0.342139i	0.173523	+	0.984830i	$0.444485\pi$
$270$	92930.3	−	1.09487e6i	0.0775796	−	0.914015i
$271$	922903.	−	1.59851e6i	0.763366	−	1.32219i	−0.177740	−	0.984077i	$-0.556879\pi$
$271$	922903.	−	1.59851e6i	0.763366	−	1.32219i	0.941106	−	0.338111i	$-0.109788\pi$
$272$	894769.	+	1.04417e6i	0.733311	+	0.855752i
$273$	−511639.	−	992653.i	−0.415486	−	0.806103i
$274$	866035.	−	1.24367e6i	0.696882	−	1.00076i
$275$	−47453.4	−	27397.2i	−0.0378387	−	0.0218462i
$276$	−168346.	−	139779.i	−0.133024	−	0.110451i
$277$	235194.	+	407368.i	0.184173	+	0.318997i	0.943298	−	0.331948i	$-0.107706\pi$
$277$	235194.	+	407368.i	0.184173	+	0.318997i	−0.759124	+	0.650946i	$0.774373\pi$
$278$	435197.	+	927004.i	0.337734	+	0.719399i
$279$	−888702.			−0.683511
$280$	−947702.	+	874918.i	−0.722398	+	0.666918i
$281$	115672.			0.0873901			0.0436950	−	0.999045i	$-0.486087\pi$
$281$	115672.			0.0873901			0.0436950	+	0.999045i	$0.486087\pi$
$282$	73908.5	+	157431.i	0.0553442	+	0.117887i
$283$	596666.	+	1.03346e6i	0.442859	+	0.767054i	0.997900	−	0.0647689i	$-0.0206310\pi$
$283$	596666.	+	1.03346e6i	0.442859	+	0.767054i	−0.555042	+	0.831823i	$0.687298\pi$
$284$	919718.	+	763647.i	0.676642	+	0.561819i
$285$	19192.1	+	11080.6i	0.0139962	+	0.00808073i
$286$	1.70881e6	−	2.45395e6i	1.23532	−	1.77399i
$287$	448662.	+	21411.6i	0.321525	+	0.0153442i
$288$	98325.0	+	977764.i	0.0698526	+	0.694629i
$289$	191722.	−	332072.i	0.135029	−	0.233877i
$290$	−15786.0	+	185985.i	−0.0110224	+	0.129862i
$291$	819634.	−	473216.i	0.567398	−	0.327587i
$292$	−265315.	+	1.55166e6i	−0.182098	+	1.06498i
$293$			2.48950e6i			1.69411i	0.531503	+	0.847056i	$0.321627\pi$
$293$			2.48950e6i			1.69411i	−0.531503	+	0.847056i	$0.678373\pi$
$294$	−526846.	+	620883.i	−0.355480	+	0.418930i
$295$		−	454120.i		−	0.303820i
$296$	1.67892e6	−	1.70523e6i	1.11378	−	1.13124i
$297$	1.60865e6	−	928753.i	1.05820	−	0.610955i
$298$	372663.	+	31630.8i	0.243095	+	0.0206334i
$299$	−401494.	+	695408.i	−0.259717	+	0.449844i
$300$	9911.62	+	26798.9i	0.00635830	+	0.0171915i
$301$	1.49593e6	+	71390.6i	0.951690	+	0.0454177i
$302$	−776065.	−	540414.i	−0.489644	−	0.340965i
$303$	−411995.	−	237865.i	−0.257801	−	0.148842i
$304$	−45469.7	−	16017.8i	−0.0282188	−	0.00994075i
$305$	−357184.	−	618662.i	−0.219858	−	0.380806i
$306$	1.16655e6	−	547654.i	0.712194	−	0.334351i
$307$	−1.47151e6			−0.891079			−0.445540	−	0.895262i	$-0.646988\pi$
$307$	−1.47151e6			−0.891079			−0.445540	+	0.895262i	$0.646988\pi$
$308$	−2.12925e6	−	469520.i	−1.27894	−	0.282019i
$309$	−1.00765e6			−0.600362
$310$	−1.47433e6	+	692147.i	−0.871343	+	0.409066i
$311$	−575342.	−	996521.i	−0.337307	−	0.584232i	0.646619	−	0.762814i	$-0.276183\pi$
$311$	−575342.	−	996521.i	−0.337307	−	0.584232i	−0.983925	+	0.178581i	$0.942849\pi$
$312$	−1.50301e6	+	415281.i	−0.874128	+	0.241521i
$313$	−1.11634e6	−	644520.i	−0.644074	−	0.371856i	0.142108	−	0.989851i	$-0.454612\pi$
$313$	−1.11634e6	−	644520.i	−0.644074	−	0.371856i	−0.786182	+	0.617995i	$0.787945\pi$
$314$	1.80184e6	+	1.25472e6i	1.03132	+	0.718160i
$315$	553800.	+	1.07445e6i	0.314468	+	0.610113i
$316$	−3.26063e6	+	1.20595e6i	−1.83690	+	0.679378i
$317$	133339.	−	230951.i	0.0745265	−	0.129084i	−0.826354	−	0.563151i	$-0.809589\pi$
$317$	133339.	−	230951.i	0.0745265	−	0.129084i	0.900880	+	0.434068i	$0.142922\pi$
$318$	129870.	+	11023.0i	0.0720177	+	0.00611271i
$319$	−273260.	+	157767.i	−0.150348	+	0.0868037i
$320$	924628.	+	1.54550e6i	0.504768	+	0.843710i
$321$		−	1.28982e6i		−	0.698663i
$322$	580382.	+	77272.2i	0.311942	+	0.0415321i
$323$			63220.5i			0.0337172i
$324$	345538.	+	59082.7i	0.182866	+	0.0312679i
$325$	90808.4	−	52428.3i	0.0476890	−	0.0275332i
$326$	−139004.	+	1.63769e6i	−0.0724406	+	0.853469i
$327$	249496.	−	432140.i	0.129031	−	0.223488i
$328$	157612.	−	607055.i	0.0808917	−	0.311561i
$329$	−391473.	−	251633.i	−0.199394	−	0.128167i
$330$	799768.	−	1.14851e6i	0.404277	−	0.580564i
$331$	−76872.3	−	44382.3i	−0.0385656	−	0.0222659i	0.480593	−	0.876944i	$-0.340421\pi$
$331$	−76872.3	−	44382.3i	−0.0385656	−	0.0222659i	−0.519159	+	0.854678i	$0.673755\pi$
$332$	−1.45145e6	+	1.74809e6i	−0.722697	+	0.870400i
$333$	−1.12134e6	−	1.94222e6i	−0.554149	−	0.959814i
$334$	−1.33685e6	−	2.84760e6i	−0.655718	−	1.39673i
$335$	−3.06534e6			−1.49234
$336$	697836.	+	897648.i	0.337214	+	0.433768i
$337$	2.73985e6			1.31417			0.657086	−	0.753816i	$-0.271789\pi$
$337$	2.73985e6			1.31417			0.657086	+	0.753816i	$0.271789\pi$
$338$	1.53922e6	+	3.27867e6i	0.732842	+	1.56101i
$339$	−260990.	−	452048.i	−0.123346	−	0.213641i
$340$	1.50873e6	−	1.81708e6i	0.707806	−	0.852465i
$341$	−2.38443e6	−	1.37665e6i	−1.11045	−	0.641117i
$342$	−25818.0	+	37076.0i	−0.0119359	+	0.0171407i
$343$	310652.	−	2.15663e6i	0.142573	−	0.989784i
$344$	525510.	−	2.02404e6i	0.239433	−	0.922198i
$345$	−187909.	+	325468.i	−0.0849964	+	0.147218i
$346$	−22454.5	+	264551.i	−0.0100835	+	0.118801i
$347$	1.69876e6	−	980779.i	0.757370	−	0.437268i	−0.0709805	−	0.997478i	$-0.522613\pi$
$347$	1.69876e6	−	980779.i	0.757370	−	0.437268i	0.828351	+	0.560210i	$0.189279\pi$
$348$	162184.	+	27731.5i	0.0717894	+	0.0122751i
$349$		−	16825.6i		−	0.00739446i	−0.999993	−	0.00369723i	$-0.998823\pi$
$349$		−	16825.6i		−	0.00739446i	0.999993	−	0.00369723i	$-0.00117687\pi$
$350$	−60589.1	−	46632.6i	−0.0264378	−	0.0203479i
$351$			3.55459e6i			1.54000i
$352$	−1.25080e6	+	2.77569e6i	−0.538061	+	1.19403i
$353$	−1.74597e6	+	1.00804e6i	−0.745764	+	0.430567i	−0.824161	−	0.566355i	$-0.808353\pi$
$353$	−1.74597e6	+	1.00804e6i	−0.745764	+	0.430567i	0.0783976	+	0.996922i	$0.475020\pi$
$354$	−398880.	−	33856.1i	−0.169174	−	0.0143591i
$355$	1.02659e6	−	1.77811e6i	0.432343	−	0.748839i
$356$	−2.10070e6	+	776948.i	−0.878496	+	0.324913i
$357$	806229.	−	1.25428e6i	0.334802	−	0.520862i
$358$	149108.	+	103831.i	0.0614882	+	0.0428175i
$359$	−762917.	−	440470.i	−0.312422	−	0.180377i	0.335588	−	0.942009i	$-0.391065\pi$
$359$	−762917.	−	440470.i	−0.312422	−	0.180377i	−0.648010	+	0.761632i	$0.724398\pi$
$360$	1.62686e6	−	449501.i	0.661599	−	0.182799i
$361$	1.23694e6	+	2.14245e6i	0.499552	+	0.865250i
$362$	−2.62290e6	+	1.23136e6i	−1.05199	+	0.493873i
$363$	986532.			0.392957
$364$	2.81541e6	−	3.07946e6i	1.11375	−	1.21821i
$365$	2.70372e6			1.06226
$366$	−570035.	+	267612.i	−0.222433	+	0.104425i
$367$	−838276.	−	1.45194e6i	−0.324879	−	0.562707i	0.656609	−	0.754231i	$-0.271990\pi$
$367$	−838276.	−	1.45194e6i	−0.324879	−	0.562707i	−0.981488	+	0.191524i	$0.938657\pi$
$368$	271637.	−	771094.i	0.104561	−	0.296816i
$369$	−509030.	−	293888.i	−0.194615	−	0.112361i
$370$	−3.37292e6	−	2.34874e6i	−1.28086	−	0.891930i
$371$	−310003.	+	159783.i	−0.116931	+	0.0602694i
$372$	498036.	+	1.34659e6i	0.186596	+	0.504518i
$373$	83254.1	−	144200.i	0.0309837	−	0.0536654i	−0.850118	−	0.526593i	$-0.823469\pi$
$373$	83254.1	−	144200.i	0.0309837	−	0.0536654i	0.881101	+	0.472927i	$0.156803\pi$
$374$	3.97824e6	+	337665.i	1.47066	+	0.124826i
$375$	1.31644e6	−	760048.i	0.483419	−	0.279102i
$376$	−455891.	+	463036.i	−0.166300	+	0.168906i
$377$		−	603815.i		−	0.218802i
$378$	2.39600e6	−	988355.i	0.862497	−	0.355782i
$379$			2.67656e6i			0.957147i	0.878047	+	0.478574i	$0.158846\pi$
$379$			2.67656e6i			0.957147i	−0.878047	+	0.478574i	$0.841154\pi$
$380$	−13955.3	+	81615.6i	−0.00495768	+	0.0289944i
$381$	365359.	−	210940.i	0.128946	−	0.0744469i
$382$	−2019.04	+	23787.6i	−0.000707924	+	0.00834050i
$383$	−2.24211e6	+	3.88344e6i	−0.781015	+	1.35276i	0.150336	+	0.988635i	$0.451965\pi$
$383$	−2.24211e6	+	3.88344e6i	−0.781015	+	1.35276i	−0.931351	+	0.364123i	$0.881369\pi$
$384$	1.42643e6	−	696932.i	0.493654	−	0.241192i
$385$	−178516.	+	3.74067e6i	−0.0613799	+	1.28617i
$386$	−55394.0	+	79548.8i	−0.0189232	+	0.0271747i
$387$	−1.69721e6	−	979883.i	−0.576047	−	0.332581i
$388$	2.72057e6	+	2.25891e6i	0.917447	+	0.761762i
$389$	1.13870e6	+	1.97229e6i	0.381536	+	0.660841i	0.991282	−	0.131757i	$-0.0420617\pi$
$389$	1.13870e6	+	1.97229e6i	0.381536	+	0.660841i	−0.609746	+	0.792597i	$0.708728\pi$
$390$	1.13814e6	+	2.42433e6i	0.378910	+	0.807107i
$391$	−1.07212e6			−0.354651
$392$	−2.85857e6	−	1.04151e6i	−0.939579	−	0.342333i
$393$	−1.27144e6			−0.415255
$394$	−2.30500e6	−	4.90983e6i	−0.748049	−	1.59340i
$395$	2.98552e6	+	5.17106e6i	0.962779	+	1.66758i
$396$	2.19517e6	+	1.82266e6i	0.703444	+	0.584073i
$397$	565098.	+	326260.i	0.179948	+	0.103893i	0.587268	−	0.809392i	$-0.300203\pi$
$397$	565098.	+	326260.i	0.179948	+	0.103893i	−0.407320	+	0.913285i	$0.633537\pi$
$398$	−184319.	+	264692.i	−0.0583261	+	0.0837594i
$399$	−2491.82	+	52214.0i	−0.000783580	+	0.0164193i
$400$	−81064.8	+	69466.1i	−0.0253327	+	0.0217081i
$401$	149897.	−	259629.i	0.0465513	−	0.0806292i	−0.841811	−	0.539773i	$-0.818510\pi$
$401$	149897.	−	259629.i	0.0465513	−	0.0806292i	0.888362	+	0.459143i	$0.151844\pi$
$402$	−228531.	+	2.69246e6i	−0.0705309	+	0.830969i
$403$	4.56292e6	−	2.63440e6i	1.39952	−	0.808015i
$404$	299575.	−	1.75203e6i	0.0913173	−	0.534058i
$405$		−	602089.i		−	0.182399i
$406$	−407007.	+	167891.i	−0.122543	+	0.0505490i
$407$		−	6.94807e6i		−	2.07911i
$408$	−1.48356e6	−	1.46067e6i	−0.441221	−	0.434413i
$409$	−1.21651e6	+	702354.i	−0.359591	+	0.207610i	−0.668901	−	0.743351i	$-0.733235\pi$
$409$	−1.21651e6	+	702354.i	−0.359591	+	0.207610i	0.309310	+	0.950961i	$0.399902\pi$
$410$	−1.07335e6	−	91103.8i	−0.315342	−	0.0267656i
$411$	−1.14726e6	+	1.98712e6i	−0.335010	+	0.580255i
$412$	−1.30597e6	−	3.53108e6i	−0.379046	−	1.02486i
$413$	952138.	−	490756.i	0.274679	−	0.141576i
$414$	−628751.	−	437832.i	−0.180292	−	0.125547i
$415$	3.37963e6	+	1.95123e6i	0.963271	+	0.556145i
$416$	−3.40325e6	−	4.72873e6i	−0.964184	−	1.33971i
$417$	−775246.	−	1.34276e6i	−0.218323	−	0.378146i
$418$	−126704.	+	59483.1i	−0.0354689	+	0.0166515i
$419$	2.63281e6			0.732630			0.366315	−	0.930491i	$-0.380619\pi$
$419$	2.63281e6			0.732630			0.366315	+	0.930491i	$0.380619\pi$
$420$	1.31768e6	−	1.44126e6i	0.364492	−	0.398676i
$421$	−2.29645e6			−0.631469			−0.315735	−	0.948848i	$-0.602251\pi$
$421$	−2.29645e6			−0.631469			−0.315735	+	0.948848i	$0.602251\pi$
$422$	491643.	−	230810.i	0.134391	−	0.0630919i
$423$	304486.	+	527386.i	0.0827403	+	0.143310i
$424$	129691.	+	469385.i	0.0350344	+	0.126799i
$425$	121244.	+	70000.3i	0.0325603	+	0.0187987i
$426$	−1.48528e6	−	1.03428e6i	−0.396538	−	0.276130i
$427$	911125.	−	1.41747e6i	0.241829	−	0.376221i
$428$	4.51990e6	−	1.67169e6i	1.19267	−	0.441109i
$429$	−2.26372e6	+	3.92087e6i	−0.593853	+	1.02858i
$430$	−3.57877e6	−	303758.i	−0.933389	−	0.0792241i
$431$	−2.19080e6	+	1.26486e6i	−0.568079	+	0.327981i	−0.756382	−	0.654130i	$-0.773035\pi$
$431$	−2.19080e6	+	1.26486e6i	−0.568079	+	0.327981i	0.188303	+	0.982111i	$0.439701\pi$
$432$	−665345.	−	3.55732e6i	−0.171529	−	0.917093i
$433$			506501.i			0.129826i	0.997891	+	0.0649128i	$0.0206769\pi$
$433$			506501.i			0.129826i	−0.997891	+	0.0649128i	$0.979323\pi$
$434$	−3.04447e6	−	2.34318e6i	−0.775866	−	0.597147i
$435$		−	282600.i		−	0.0716061i
$436$	1.83770e6	+	314224.i	0.462975	+	0.0791631i
$437$	32551.0	−	18793.3i	0.00815380	−	0.00470760i
$438$	201570.	−	2.37483e6i	0.0502043	−	0.591489i
$439$	247642.	−	428928.i	0.0613285	−	0.106224i	−0.833731	−	0.552171i	$-0.813800\pi$
$439$	247642.	−	428928.i	0.0613285	−	0.106224i	0.895059	+	0.445947i	$0.147133\pi$
$440$	5.06124e6	+	1.31407e6i	1.24631	+	0.323584i
$441$	−1.65429e6	+	2.32226e6i	−0.405055	+	0.568611i
$442$	−4.36605e6	+	6.26988e6i	−1.06300	+	1.52652i
$443$	216689.	+	125105.i	0.0524599	+	0.0302877i	0.526001	−	0.850484i	$-0.323691\pi$
$443$	216689.	+	125105.i	0.0524599	+	0.0302877i	−0.473541	+	0.880772i	$0.657024\pi$
$444$	−2.31449e6	+	2.78752e6i	−0.557184	+	0.671059i
$445$	1.92345e6	+	3.33152e6i	0.460449	+	0.797522i
$446$	1.48804e6	+	3.16963e6i	0.354222	+	0.754521i
$447$	−566254.			−0.134043
$448$	−2.24117e6	+	3.60881e6i	−0.527569	+	0.849512i
$449$	−5.81736e6			−1.36179			−0.680894	−	0.732382i	$-0.738409\pi$
$449$	−5.81736e6			−1.36179			−0.680894	+	0.732382i	$0.738409\pi$
$450$	42517.6	+	90565.7i	0.00989777	+	0.0210830i
$451$	−910499.	−	1.57703e6i	−0.210784	−	0.365089i
$452$	1.24584e6	−	1.50046e6i	0.286825	−	0.345445i
$453$	1.23998e6	+	715903.i	0.283903	+	0.163911i
$454$	−4.25898e6	+	6.11612e6i	−0.969763	+	1.39263i
$455$	−6.02843e6	−	3.87498e6i	−1.36514	−	0.877488i
$456$	70647.2	+	18342.4i	0.0159105	+	0.00413089i
$457$	2.62103e6	−	4.53976e6i	0.587059	−	1.01682i	−0.407556	−	0.913180i	$-0.633619\pi$
$457$	2.62103e6	−	4.53976e6i	0.587059	−	1.01682i	0.994615	−	0.103636i	$-0.0330478\pi$
$458$	−15816.5	+	186344.i	−0.00352327	+	0.0415099i
$459$	−4.11012e6	+	2.37298e6i	−0.910589	+	0.525729i
$460$	−1.38407e6	−	236659.i	−0.304975	−	0.0521469i
$461$		−	2.57206e6i		−	0.563674i	−0.959462	−	0.281837i	$-0.909056\pi$
$461$		−	2.57206e6i		−	0.563674i	0.959462	−	0.281837i	$-0.0909438\pi$
$462$	3.27233e6	+	435679.i	0.713267	+	0.0949646i
$463$			1.72459e6i			0.373881i	0.982371	+	0.186940i	$0.0598571\pi$
$463$			1.72459e6i			0.373881i	−0.982371	+	0.186940i	$0.940143\pi$
$464$	113022.	+	604279.i	0.0243706	+	0.130299i
$465$	2.13556e6	−	1.23297e6i	0.458015	−	0.264435i
$466$	4.29998e6	+	364973.i	0.917279	+	0.0778567i
$467$	479153.	−	829918.i	0.101667	−	0.176093i	−0.810704	−	0.585456i	$-0.800916\pi$
$467$	479153.	−	829918.i	0.101667	−	0.176093i	0.912372	+	0.409363i	$0.134249\pi$
$468$	−5.12098e6	+	1.89400e6i	−1.08078	+	0.399729i
$469$	−3.31264e6	−	6.42699e6i	−0.695411	−	1.34920i
$470$	915876.	+	637772.i	0.191246	+	0.133174i
$471$	−2.87894e6	−	1.66216e6i	−0.597972	−	0.345239i
$472$	−398331.	−	1.44166e6i	−0.0822980	−	0.297858i
$473$	−3.03579e6	−	5.25814e6i	−0.623905	−	1.08064i
$474$	4.76462e6	−	2.23683e6i	0.974052	−	0.457285i
$475$	−4908.17			−0.000998127
$476$	5.44025e6	+	1.19963e6i	1.10053	+	0.242678i
$477$	456376.			0.0918390
$478$	6.02886e6	−	2.83035e6i	1.20688	−	0.566591i
$479$	4.58381e6	+	7.93939e6i	0.912825	+	1.58106i	0.810055	+	0.586354i	$0.199437\pi$
$479$	4.58381e6	+	7.93939e6i	0.912825	+	1.58106i	0.102770	+	0.994705i	$0.467229\pi$
$480$	−1.59280e6	−	2.21316e6i	−0.315544	−	0.438440i
$481$	1.15147e7	+	6.64803e6i	2.26930	+	1.31018i
$482$	5.96481e6	+	4.15361e6i	1.16944	+	0.814344i
$483$	−885466.	−	42257.3i	−0.172705	−	0.00824202i
$484$	1.27860e6	+	3.45708e6i	0.248098	+	0.670804i
$485$	3.03672e6	−	5.25975e6i	0.586206	−	1.01534i
$486$	−5.36959e6	−	455759.i	−1.03122	−	0.0875276i
$487$	−3.32863e6	+	1.92178e6i	−0.635979	+	0.367183i	−0.783064	−	0.621941i	$-0.786344\pi$
$487$	−3.32863e6	+	1.92178e6i	−0.635979	+	0.367183i	0.147085	+	0.989124i	$0.453011\pi$
$488$	−1.67659e6	−	1.65072e6i	−0.318696	−	0.313778i
$489$		−	2.48844e6i		−	0.470603i
$490$	−935758.	+	5.14096e6i	−0.176065	+	0.967285i
$491$		−	8.08747e6i		−	1.51394i	−0.653449	−	0.756971i	$-0.726678\pi$
$491$		−	8.08747e6i		−	1.51394i	0.653449	−	0.756971i	$-0.273322\pi$
$492$	−160043.	+	935993.i	−0.0298074	+	0.174325i
$493$	698182.	−	403096.i	0.129375	−	0.0746949i
$494$	22653.4	−	266895.i	0.00417654	−	0.0492065i
$495$	2.45026e6	−	4.24397e6i	0.449468	−	0.778501i
$496$	−4.07332e6	+	3.49051e6i	−0.743437	+	0.637067i
$497$	4.83752e6	+	230862.i	0.878480	+	0.0419239i
$498$	1.96584e6	−	2.82305e6i	0.355201	−	0.510088i
$499$	−1.39207e6	−	803713.i	−0.250271	−	0.144494i	0.369617	−	0.929184i	$-0.379489\pi$
$499$	−1.39207e6	−	803713.i	−0.250271	−	0.144494i	−0.619888	+	0.784690i	$0.712822\pi$
$500$	4.36961e6	+	3.62811e6i	0.781659	+	0.649015i
$501$	2.38142e6	+	4.12475e6i	0.423879	+	0.734180i
$502$	−3.56169e6	−	7.58667e6i	−0.630807	−	1.34367i
$503$	9.86993e6			1.73938			0.869689	−	0.493600i	$-0.164319\pi$
$503$	9.86993e6			1.73938			0.869689	+	0.493600i	$0.164319\pi$
$504$	2.70056e6	+	2.92522e6i	0.473563	+	0.512958i
$505$	−3.05286e6			−0.532694
$506$	−1.00874e6	−	2.14869e6i	−0.175147	−	0.373077i
$507$	−2.74192e6	−	4.74915e6i	−0.473735	−	0.820532i
$508$	1.21272e6	+	1.00693e6i	0.208497	+	0.173117i
$509$	−4.49202e6	−	2.59347e6i	−0.768505	−	0.443697i	0.0638357	−	0.997960i	$-0.479667\pi$
$509$	−4.49202e6	−	2.59347e6i	−0.768505	−	0.443697i	−0.832341	+	0.554264i	$0.813000\pi$
$510$	−2.04342e6	+	2.93446e6i	−0.347882	+	0.499577i
$511$	2.92184e6	+	5.66879e6i	0.494999	+	0.960369i
$512$	4.29098e6	+	4.09534e6i	0.723405	+	0.690423i
$513$	83192.3	−	144093.i	0.0139569	−	0.0241741i
$514$	533338.	−	6.28359e6i	0.0890419	−	1.04906i
$515$	−5.59997e6	+	3.23314e6i	−0.930395	+	0.537164i
$516$	−533616.	+	3.12079e6i	−0.0882277	+	0.515989i
$517$			1.88667e6i			0.310433i
$518$	1.27949e6	−	9.61010e6i	0.209514	−	1.57363i
$519$		−	401980.i		−	0.0655067i
$520$	−7.02043e6	+	7.13045e6i	−1.13856	+	1.15640i
$521$	2.69810e6	−	1.55775e6i	0.435475	−	0.251422i	−0.266201	−	0.963917i	$-0.585769\pi$
$521$	2.69810e6	−	1.55775e6i	0.435475	−	0.251422i	0.701676	+	0.712496i	$0.252435\pi$
$522$	574069.	+	48725.8i	0.0922121	+	0.00782677i
$523$	−4.98484e6	+	8.63399e6i	−0.796887	+	1.38025i	0.124747	+	0.992189i	$0.460188\pi$
$523$	−4.98484e6	+	8.63399e6i	−0.796887	+	1.38025i	−0.921634	+	0.388060i	$0.873145\pi$
$524$	−1.64786e6	−	4.45548e6i	−0.262176	−	0.708869i
$525$	97376.8	+	62592.2i	0.0154190	+	0.00991111i
$526$	7.45390e6	+	5.19054e6i	1.17468	+	0.817990i
$527$	6.09224e6	+	3.51736e6i	0.955543	+	0.551683i
$528$	1.53155e6	−	4.34761e6i	0.239082	−	0.678681i
$529$	−2.89947e6	−	5.02202e6i	−0.450484	−	0.780260i
$530$	757113.	−	355439.i	0.117077	−	0.0549636i
$531$	−1.40171e6			−0.215735
$532$	−186202.	+	58940.4i	−0.0285236	+	0.00902888i
$533$	3.48472e6			0.531313
$534$	3.06966e6	−	1.44110e6i	0.465841	−	0.218697i
$535$	−4.13853e6	−	7.16814e6i	−0.625117	−	1.08273i
$536$	−9.73132e6	+	2.68876e6i	−1.46305	+	0.404241i
$537$	−238241.	−	137549.i	−0.0356517	−	0.0205835i
$538$	3.76998e6	+	2.62523e6i	0.561543	+	0.391032i
$539$	−8.03584e6	+	3.66815e6i	−1.19140	+	0.543846i
$540$	−5.82984e6	+	2.15617e6i	−0.860344	+	0.318199i
$541$	−4.55739e6	+	7.89364e6i	−0.669458	+	1.15954i	0.308598	+	0.951193i	$0.400140\pi$
$541$	−4.55739e6	+	7.89364e6i	−0.669458	+	1.15954i	−0.978056	+	0.208343i	$0.933193\pi$
$542$	−1.04040e7	−	883073.i	−1.52126	−	0.129121i
$543$	3.79927e6	−	2.19351e6i	0.552969	−	0.319257i
$544$	3.19581e6	−	7.09193e6i	0.463003	−	1.02747i
$545$		−	3.20213e6i		−	0.461793i
$546$	−3.85305e6	+	5.00622e6i	−0.553125	+	0.718668i
$547$		−	7.96828e6i		−	1.13867i	−0.822107	−	0.569333i	$-0.807201\pi$
$547$		−	7.96828e6i		−	1.13867i	0.822107	−	0.569333i	$-0.192799\pi$
$548$	−8.45032e6	−	1.44490e6i	−1.20205	−	0.205535i
$549$	−1.90959e6	+	1.10250e6i	−0.270401	+	0.156116i
$550$	−26214.9	+	308854.i	−0.00369522	+	0.0435358i
$551$	−14131.8	+	24477.0i	−0.00198298	+	0.00343463i
$552$	−311058.	+	1.19807e6i	−0.0434504	+	0.167353i
$553$	−7.61562e6	+	1.18479e7i	−1.05899	+	1.64751i
$554$	1.52058e6	−	2.18364e6i	0.210492	−	0.302278i
$555$	5.38918e6	+	3.11145e6i	0.742661	+	0.428775i
$556$	3.70065e6	−	4.45698e6i	0.507682	−	0.611440i
$557$	−377435.	−	653737.i	−0.0515471	−	0.0892822i	0.839101	−	0.543976i	$-0.183082\pi$
$557$	−377435.	−	653737.i	−0.0515471	−	0.0892822i	−0.890648	+	0.454694i	$0.849749\pi$
$558$	2.13641e6	+	4.55072e6i	0.290469	+	0.618721i
$559$	1.16188e7			1.57265
$560$	6.75838e6	+	2.74956e6i	0.910695	+	0.370505i
$561$	−6.04487e6			−0.810923
$562$	−278072.	−	592314.i	−0.0371378	−	0.0791063i
$563$	−2.91545e6	−	5.04970e6i	−0.387645	−	0.671420i	0.604488	−	0.796615i	$-0.293378\pi$
$563$	−2.91545e6	−	5.04970e6i	−0.387645	−	0.671420i	−0.992132	+	0.125194i	$0.960045\pi$
$564$	628473.	−	756918.i	0.0831934	−	0.100196i
$565$	−2.90088e6	−	1.67482e6i	−0.382304	−	0.220723i
$566$	3.85759e6	−	5.53971e6i	0.506145	−	0.726851i
$567$	1.26238e6	−	650662.i	0.164904	−	0.0849959i
$568$	1.69939e6	−	6.54533e6i	0.221015	−	0.851256i
$569$	−3.66247e6	+	6.34359e6i	−0.474235	+	0.821399i	−0.999565	−	0.0294995i	$-0.990609\pi$
$569$	−3.66247e6	+	6.34359e6i	−0.474235	+	0.821399i	0.525330	+	0.850899i	$0.323942\pi$
$570$	10602.4	−	124913.i	0.00136683	−	0.0161035i
$571$	−5.61585e6	+	3.24232e6i	−0.720818	+	0.416164i	−0.815054	−	0.579385i	$-0.803293\pi$
$571$	−5.61585e6	+	3.24232e6i	−0.720818	+	0.416164i	0.0942357	+	0.995550i	$0.469959\pi$
$572$	−1.66737e7	−	2.85100e6i	−2.13080	−	0.364340i
$573$		−	36144.8i		−	0.00459896i
$574$	−968929.	−	2.34891e6i	−0.122747	−	0.297568i
$575$		−	83234.9i		−	0.0104987i
$576$	4.77040e6	−	2.85400e6i	0.599099	−	0.358424i
$577$	1.80740e6	−	1.04350e6i	0.226004	−	0.130483i	−0.382723	−	0.923863i	$-0.625014\pi$
$577$	1.80740e6	−	1.04350e6i	0.226004	−	0.130483i	0.608727	+	0.793380i	$0.291680\pi$
$578$	−2.16131e6	−	183448.i	−0.269090	−	0.0228398i
$579$	73382.1	−	127101.i	0.00909690	−	0.0157563i
$580$	990310.	−	366267.i	0.122237	−	0.0452093i
$581$	−438795.	+	9.19459e6i	−0.0539288	+	1.13003i
$582$	−4.39354e6	−	3.05945e6i	−0.537660	−	0.374400i
$583$	1.22448e6	+	706952.i	0.149204	+	0.0861428i
$584$	8.58330e6	−	2.37156e6i	1.04141	−	0.287741i
$585$	4.68890e6	+	8.12140e6i	0.566475	+	0.981164i
$586$	1.27478e7	−	5.98467e6i	1.53353	−	0.719940i
$587$	8.74889e6			1.04799			0.523996	−	0.851721i	$-0.324441\pi$
$587$	8.74889e6			1.04799			0.523996	+	0.851721i	$0.324441\pi$
$588$	4.44584e6	+	1.20520e6i	0.530286	+	0.143753i
$589$	−246624.			−0.0292919
$590$	−2.32539e6	+	1.09169e6i	−0.275020	+	0.129113i
$591$	4.10605e6	+	7.11188e6i	0.483565	+	0.837560i
$592$	−1.27680e7	−	4.49783e6i	−1.49733	−	0.527471i
$593$	3.16430e6	+	1.82691e6i	0.369523	+	0.213344i	0.673250	−	0.739415i	$-0.264898\pi$
$593$	3.16430e6	+	1.82691e6i	0.369523	+	0.213344i	−0.303727	+	0.952759i	$0.598231\pi$
$594$	−8.62295e6	−	6.00461e6i	−1.00274	−	0.698262i
$595$	456112.	−	9.55745e6i	0.0528176	−	1.10675i
$596$	−733899.	−	1.98431e6i	−0.0846293	−	0.228820i
$597$	244173.	−	422920.i	0.0280390	−	0.0485649i
$598$	4.52611e6	+	384167.i	0.517574	+	0.0439306i
$599$	6.06782e6	−	3.50326e6i	0.690981	−	0.398938i	−0.112999	−	0.993595i	$-0.536046\pi$
$599$	6.06782e6	−	3.50326e6i	0.690981	−	0.398938i	0.803979	+	0.594657i	$0.202712\pi$
$600$	113400.	−	115178.i	0.0128599	−	0.0130614i
$601$		−	1.24584e7i		−	1.40694i	−0.710723	−	0.703472i	$-0.751632\pi$
$601$		−	1.24584e7i		−	1.40694i	0.710723	−	0.703472i	$-0.248368\pi$
$602$	−3.23061e6	−	7.83175e6i	−0.363323	−	0.880780i
$603$			9.46162e6i			1.05967i
$604$	−901632.	+	5.27309e6i	−0.100563	+	0.588129i
$605$	5.48261e6	−	3.16538e6i	0.608974	−	0.351591i
$606$	−227600.	+	2.68150e6i	−0.0251762	+	0.296617i
$607$	−4.10484e6	+	7.10979e6i	−0.452194	+	0.783222i	−0.998522	−	0.0543487i	$-0.982692\pi$
$607$	−4.10484e6	+	7.10979e6i	−0.452194	+	0.783222i	0.546328	+	0.837571i	$0.316025\pi$
$608$	27286.3	+	271340.i	0.00299354	+	0.0297684i
$609$	592518.	−	305399.i	0.0647379	−	0.0333676i
$610$	−2.30928e6	+	3.31625e6i	−0.251277	+	0.360847i
$611$	−3.12669e6	−	1.80519e6i	−0.338830	−	0.195623i
$612$	−5.60868e6	−	4.65692e6i	−0.605316	−	0.502597i
$613$	−5.65213e6	−	9.78977e6i	−0.607520	−	1.05226i	−0.991648	−	0.128976i	$-0.958831\pi$
$613$	−5.65213e6	−	9.78977e6i	−0.607520	−	1.05226i	0.384128	−	0.923280i	$-0.374502\pi$
$614$	3.53746e6	+	7.53506e6i	0.378678	+	0.806614i
$615$	1.63094e6			0.173880
$616$	2.71440e6	+	1.20318e7i	0.288218	+	1.27755i
$617$	8.66997e6			0.916864			0.458432	−	0.888729i	$-0.348411\pi$
$617$	8.66997e6			0.916864			0.458432	+	0.888729i	$0.348411\pi$
$618$	2.42236e6	+	5.15981e6i	0.255133	+	0.543454i
$619$	−595862.	−	1.03206e6i	−0.0625056	−	0.108263i	0.833079	−	0.553154i	$-0.186576\pi$
$619$	−595862.	−	1.03206e6i	−0.0625056	−	0.108263i	−0.895585	+	0.444891i	$0.853242\pi$
$620$	7.08846e6	+	5.88559e6i	0.740582	+	0.614909i
$621$	2.44360e6	+	1.41081e6i	0.254273	+	0.146805i
$622$	−3.71972e6	+	5.34172e6i	−0.385509	+	0.553612i
$623$	−4.90645e6	+	7.63313e6i	−0.506463	+	0.787921i
$624$	5.73969e6	+	6.69804e6i	0.590101	+	0.688630i
$625$	4.71448e6	−	8.16572e6i	0.482763	−	0.836170i
$626$	−616704.	+	7.26578e6i	−0.0628986	+	0.741048i
$627$	183530.	−	105961.i	0.0186440	−	0.0107641i
$628$	2.09338e6	−	1.22429e7i	0.211811	−	1.23875i
$629$			1.77524e7i			1.78908i
$630$	4.17056e6	−	5.41876e6i	0.418642	−	0.543936i
$631$			351151.i			0.0351092i	0.999846	+	0.0175546i	$0.00558809\pi$
$631$			351151.i			0.0351092i	−0.999846	+	0.0175546i	$0.994412\pi$
$632$	1.40137e7	+	1.37975e7i	1.39560	+	1.37406i
$633$	−712145.	+	411157.i	−0.0706414	+	0.0407848i
$634$	−1.50316e6	−	127585.i	−0.148519	−	0.0126060i
$635$	1.35364e6	−	2.34458e6i	0.133220	−	0.230744i
$636$	−255757.	−	691514.i	−0.0250718	−	0.0677888i
$637$	1.60976e6	−	1.68272e7i	0.157186	−	1.64310i
$638$	1.46477e6	+	1.02000e6i	0.142468	+	0.0992083i
$639$	−5.48841e6	−	3.16873e6i	−0.531734	−	0.306997i
$640$	5.69116e6	−	8.45001e6i	0.549225	−	0.815469i
$641$	5.22118e6	+	9.04335e6i	0.501908	+	0.869329i	0.999998	+	0.00220408i	$0.000701581\pi$
$641$	5.22118e6	+	9.04335e6i	0.501908	+	0.869329i	−0.498090	+	0.867125i	$0.665965\pi$
$642$	−6.60472e6	+	3.10070e6i	−0.632437	+	0.296908i
$643$	−2.01326e7			−1.92032			−0.960159	−	0.279456i	$-0.909846\pi$
$643$	−2.01326e7			−1.92032			−0.960159	+	0.279456i	$0.909846\pi$
$644$	−999537.	−	3.15769e6i	−0.0949695	−	0.300023i
$645$	5.43788e6			0.514671
$646$	323729.	−	151980.i	0.0305211	−	0.0143287i
$647$	1.45870e6	+	2.52655e6i	0.136995	+	0.237283i	0.926358	−	0.376644i	$-0.122922\pi$
$647$	1.45870e6	+	2.52655e6i	0.136995	+	0.237283i	−0.789363	+	0.613927i	$0.789589\pi$
$648$	−528122.	−	1.91141e6i	−0.0494079	−	0.178820i
$649$	−3.76084e6	−	2.17132e6i	−0.350488	−	0.202355i
$650$	−486767.	−	338961.i	−0.0451895	−	0.0314678i
$651$	4.89296e6	+	3.14512e6i	0.452501	+	0.290860i
$652$	8.72018e6	−	3.22517e6i	0.803353	−	0.297121i
$653$	903298.	−	1.56456e6i	0.0828987	−	0.143585i	−0.821595	−	0.570071i	$-0.806916\pi$
$653$	903298.	−	1.56456e6i	0.0828987	−	0.143585i	0.904494	+	0.426487i	$0.140249\pi$
$654$	−2.81261e6	−	238728.i	−0.257137	−	0.0218253i
$655$	−7.06598e6	+	4.07954e6i	−0.643530	+	0.371542i
$656$	−3.48740e6	+	652268.i	−0.316404	+	0.0591788i
$657$		−	8.34542e6i		−	0.754283i
$658$	−347431.	+	2.60951e6i	−0.0312827	+	0.234960i
$659$		−	1.63666e7i		−	1.46807i	−0.679113	−	0.734034i	$-0.737635\pi$
$659$		−	1.63666e7i		−	1.46807i	0.679113	−	0.734034i	$-0.262365\pi$
$660$	−7.80372e6	−	1.33434e6i	−0.697336	−	0.119236i
$661$	−1.01749e6	+	587448.i	−0.0905788	+	0.0522957i	−0.544605	−	0.838693i	$-0.683321\pi$
$661$	−1.01749e6	+	587448.i	−0.0905788	+	0.0522957i	0.454026	+	0.890988i	$0.349987\pi$
$662$	−42466.8	+	500329.i	−0.00376621	+	0.0443722i
$663$	5.78383e6	−	1.00179e7i	0.511013	−	0.885100i
$664$	1.24406e7	+	3.22999e6i	1.09502	+	0.284303i
$665$	153685.	+	298172.i	0.0134765	+	0.0261464i
$666$	−7.24973e6	+	1.04110e7i	−0.633339	+	0.909509i
$667$	−415092.	−	239653.i	−0.0361268	−	0.0208578i
$668$	−1.13678e7	+	1.36911e7i	−0.985676	+	1.18713i
$669$	−2.65073e6	−	4.59121e6i	−0.228982	−	0.396608i
$670$	7.36899e6	+	1.56965e7i	0.634192	+	1.35088i
$671$	−6.83135e6			−0.585733
$672$	2.91895e6	−	5.73128e6i	0.249347	−	0.489586i
$673$	−1.58661e7			−1.35031			−0.675154	−	0.737677i	$-0.735923\pi$
$673$	−1.58661e7			−1.35031			−0.675154	+	0.737677i	$0.735923\pi$
$674$	−6.58651e6	−	1.40298e7i	−0.558478	−	1.18960i
$675$	−184228.	−	319092.i	−0.0155631	−	0.0269561i
$676$	1.30886e7	−	1.57636e7i	1.10161	−	1.32675i
$677$	−1.53216e7	−	8.84592e6i	−1.28479	−	0.741773i	−0.307069	−	0.951687i	$-0.599348\pi$
$677$	−1.53216e7	−	8.84592e6i	−1.28479	−	0.741773i	−0.977720	+	0.209914i	$0.932682\pi$
$678$	−1.68736e6	+	2.42314e6i	−0.140972	+	0.202444i
$679$	1.43096e7	+	682901.i	1.19112	+	0.0568439i
$680$	−1.29315e7	−	3.35746e6i	−1.07245	−	0.278445i
$681$	5.64199e6	−	9.77222e6i	0.466192	−	0.807468i
$682$	−1.31724e6	+	1.55192e7i	−0.108443	+	1.27764i
$683$	2.76226e6	−	1.59479e6i	0.226575	−	0.130813i	−0.382416	−	0.923990i	$-0.624908\pi$
$683$	2.76226e6	−	1.59479e6i	0.226575	−	0.130813i	0.608991	+	0.793177i	$0.291574\pi$
$684$	251918.	+	43074.9i	0.0205883	+	0.00352034i
$685$			1.47244e7i			1.19898i
$686$	−1.17901e7	+	3.59374e6i	−0.956551	+	0.291565i
$687$		−	283146.i		−	0.0228886i
$688$	−1.16277e7	+	2.17479e6i	−0.936533	+	0.175165i
$689$	−2.34320e6	+	1.35285e6i	−0.188045	+	0.108568i
$690$	2.11833e6	+	179800.i	0.169384	+	0.0143769i
$691$	1.18606e6	−	2.05431e6i	0.0944954	−	0.163671i	−0.814902	−	0.579598i	$-0.803210\pi$
$691$	1.18606e6	−	2.05431e6i	0.0944954	−	0.163671i	0.909398	+	0.415927i	$0.136543\pi$
$692$	1.40865e6	−	520990.i	0.111825	−	0.0413584i
$693$	1.15461e7	+	551017.i	0.913277	+	0.0435845i
$694$	−9.10598e6	−	6.34097e6i	−0.717675	−	0.499755i
$695$	−8.61679e6	−	4.97490e6i	−0.676680	−	0.390681i
$696$	−247883.	−	897152.i	−0.0193965	−	0.0702009i
$697$	2.32634e6	+	4.02933e6i	0.181381	+	0.314160i
$698$	−86157.8	+	40448.2i	−0.00669354	+	0.00314239i
$699$	−6.53374e6			−0.505789
$700$	−93134.3	+	422358.i	−0.00718397	+	0.0325789i
$701$	1.76418e6			0.135597			0.0677983	−	0.997699i	$-0.478403\pi$
$701$	1.76418e6			0.135597			0.0677983	+	0.997699i	$0.478403\pi$
$702$	1.82018e7	−	8.54511e6i	1.39402	−	0.654448i
$703$	−311184.	−	538986.i	−0.0237481	−	0.0411329i
$704$	1.72202e7	−	267783.i	1.30950	−	0.0203635i
$705$	−1.46337e6	−	844876.i	−0.110887	−	0.0640206i
$706$	9.35907e6	+	6.51721e6i	0.706677	+	0.492096i
$707$	−3.29914e6	−	6.40082e6i	−0.248229	−	0.481600i
$708$	785529.	+	2.12391e6i	0.0588951	+	0.159240i
$709$	6.30354e6	−	1.09181e7i	0.470944	−	0.815699i	−0.528504	−	0.848931i	$-0.677247\pi$
$709$	6.30354e6	−	1.09181e7i	0.470944	−	0.815699i	0.999448	+	0.0332322i	$0.0105801\pi$
$710$	−1.15730e7	−	982290.i	−0.861587	−	0.0731297i
$711$	1.59612e7	−	9.21523e6i	1.18411	−	0.683647i
$712$	9.02849e6	+	8.88919e6i	0.667445	+	0.657146i
$713$		−	4.18236e6i		−	0.308104i
$714$	−8.36085e6	−	1.11317e6i	−0.613769	−	0.0817174i
$715$			2.90534e7i			2.12536i
$716$	173233.	−	1.01313e6i	0.0126284	−	0.0738557i
$717$	−8.73279e6	+	5.04188e6i	−0.634388	+	0.366264i
$718$	−421461.	+	4.96550e6i	−0.0305103	+	0.359461i
$719$	−5.24339e6	+	9.08182e6i	−0.378260	+	0.655165i	−0.990809	−	0.135267i	$-0.956811\pi$
$719$	−5.24339e6	+	9.08182e6i	−0.378260	+	0.655165i	0.612549	+	0.790432i	$0.290144\pi$
$720$	−6.21266e6	−	7.24999e6i	−0.446628	−	0.521202i
$721$	−1.28306e7	−	8.24728e6i	−0.919195	−	0.590844i
$722$	7.99712e6	−	1.14843e7i	0.570940	−	0.819901i
$723$	−9.53045e6	−	5.50241e6i	−0.678059	−	0.391478i
$724$	1.26107e7	+	1.04708e7i	0.894117	+	0.742390i
$725$	31294.7	+	54203.9i	0.00221119	+	0.00382988i
$726$	−2.37159e6	−	5.05167e6i	−0.166993	−	0.355708i
$727$	−1.88450e7			−1.32239			−0.661196	−	0.750213i	$-0.729951\pi$
$727$	−1.88450e7			−1.32239			−0.661196	+	0.750213i	$0.729951\pi$
$728$	−2.25370e7	−	7.01379e6i	−1.57604	−	0.490484i
$729$	5.49698e6			0.383094
$730$	−6.49965e6	−	1.38448e7i	−0.451422	−	0.961564i
$731$	7.75648e6	+	1.34346e7i	0.536873	+	0.929891i
$732$	2.74069e6	+	2.27561e6i	0.189052	+	0.156971i
$733$	1.19812e7	+	6.91737e6i	0.823648	+	0.475533i	0.851673	−	0.524074i	$-0.175589\pi$
$733$	1.19812e7	+	6.91737e6i	0.823648	+	0.475533i	−0.0280252	+	0.999607i	$0.508922\pi$
$734$	−5.41965e6	+	7.78292e6i	−0.371305	+	0.533215i
$735$	753408.	−	7.87555e6i	0.0514413	−	0.537728i
$736$	−4.60150e6	+	462732.i	−0.313116	+	0.0314873i
$737$	−1.46566e7	+	2.53859e7i	−0.993949	+	1.72157i
$738$	−281205.	+	3.31305e6i	−0.0190056	+	0.223917i
$739$	7.66001e6	−	4.42251e6i	0.515963	−	0.297891i	−0.219319	−	0.975653i	$-0.570383\pi$
$739$	7.66001e6	−	4.42251e6i	0.515963	−	0.297891i	0.735281	+	0.677762i	$0.237050\pi$
$740$	−3.91866e6	+	2.29178e7i	−0.263062	+	1.53849i
$741$			405541.i			0.0271325i
$742$	1.56343e6	+	1.20330e6i	0.104248	+	0.0802349i
$743$			1.25478e7i			0.833865i	0.908937	+	0.416933i	$0.136895\pi$
$743$			1.25478e7i			0.833865i	−0.908937	+	0.416933i	$0.863105\pi$
$744$	5.69811e6	−	5.78741e6i	0.377397	−	0.383312i
$745$	−3.14693e6	+	1.81688e6i	−0.207729	+	0.119932i
$746$	−938538.	−	79661.1i	−0.0617454	−	0.00524082i
$747$	6.02275e6	−	1.04317e7i	0.394906	−	0.683997i
$748$	−7.83451e6	−	2.11829e7i	−0.511986	−	1.38430i
$749$	1.05568e7	−	1.64235e7i	0.687586	−	1.06970i
$750$	−7.05662e6	−	4.91389e6i	−0.458082	−	0.318987i
$751$	1.71827e7	+	9.92042e6i	1.11171	+	0.641845i	0.939271	−	0.343176i	$-0.111503\pi$
$751$	1.71827e7	+	9.92042e6i	1.11171	+	0.641845i	0.172437	+	0.985021i	$0.444836\pi$
$752$	3.46699e6	+	1.22133e6i	0.223567	+	0.0787569i
$753$	6.34466e6	+	1.09893e7i	0.407776	+	0.706288i
$754$	−3.09192e6	+	1.45155e6i	−0.198061	+	0.0929831i
$755$	9.18818e6			0.586627
$756$	−1.08209e7	−	9.89309e6i	−0.688589	−	0.629546i
$757$	2.81038e7			1.78248			0.891241	−	0.453530i	$-0.149835\pi$
$757$	2.81038e7			1.78248			0.891241	+	0.453530i	$0.149835\pi$
$758$	1.37057e7	−	6.43436e6i	0.866419	−	0.406755i
$759$	1.79693e6	+	3.11238e6i	0.113221	+	0.196105i
$760$	451472.	−	124742.i	0.0283529	−	0.00783388i
$761$	1.63240e7	+	9.42465e6i	1.02180	+	0.589934i	0.914624	−	0.404307i	$-0.132487\pi$
$761$	1.63240e7	+	9.42465e6i	1.02180	+	0.589934i	0.107172	+	0.994240i	$0.465820\pi$
$762$	−1.95846e6	−	1.36378e6i	−0.122188	−	0.0850856i
$763$	6.71379e6	−	3.46046e6i	0.417500	−	0.215190i
$764$	126661.	−	46845.8i	0.00785074	−	0.00290361i
$765$	−6.26044e6	+	1.08434e7i	−0.386769	+	0.669903i
$766$	2.52757e7	+	2.14534e6i	1.55643	+	0.132107i
$767$	7.19688e6	−	4.15512e6i	0.441729	−	0.255032i
$768$	−6.99783e6	−	5.62884e6i	−0.428115	−	0.344363i
$769$			1.42553e6i			0.0869279i	0.999055	+	0.0434639i	$0.0138394\pi$
$769$			1.42553e6i			0.0869279i	−0.999055	+	0.0434639i	$0.986161\pi$
$770$	1.95837e7	−	8.07833e6i	1.19033	−	0.491015i
$771$			9.54780e6i			0.578452i
$772$	540506.	+	92419.8i	0.0326405	+	0.00558113i
$773$	−2.09617e7	+	1.21023e7i	−1.26177	+	0.728480i	−0.973416	−	0.229045i	$-0.926440\pi$
$773$	−2.09617e7	+	1.21023e7i	−1.26177	+	0.728480i	−0.288349	+	0.957525i	$0.593106\pi$
$774$	−937595.	+	1.10464e7i	−0.0562552	+	0.662778i
$775$	−273073.	+	472976.i	−0.0163314	+	0.0282868i
$776$	5.02687e6	−	1.93614e7i	0.299670	−	1.15420i
$777$	−699706.	+	1.46618e7i	−0.0415779	+	0.871232i
$778$	7.36198e6	−	1.05722e7i	0.436059	−	0.626205i
$779$	−141261.	−	81557.2i	−0.00834025	−	0.00481525i
$780$	9.67808e6	−	1.16560e7i	0.569577	−	0.685985i
$781$	−9.81709e6	−	1.70037e7i	−0.575911	−	0.997506i
$782$	2.57734e6	+	5.48994e6i	0.150715	+	0.321034i
$783$	−2.12175e6			−0.123677
$784$	1.53870e6	+	1.71414e7i	0.0894056	+	0.995995i
$785$	−2.13328e7			−1.23559
$786$	3.05650e6	+	6.51059e6i	0.176469	+	0.375893i
$787$	20697.4	+	35848.9i	0.00119118	+	0.00206319i	0.866620	−	0.498968i	$-0.166288\pi$
$787$	20697.4	+	35848.9i	0.00119118	+	0.00206319i	−0.865429	+	0.501031i	$0.832954\pi$
$788$	−1.96003e7	+	2.36061e7i	−1.12447	+	1.35428i
$789$	−1.19097e7	−	6.87606e6i	−0.681095	−	0.393231i
$790$	1.93021e7	−	2.77188e7i	1.10036	−	1.58018i
$791$	376637.	−	7.89211e6i	0.0214033	−	0.448489i
$792$	4.05606e6	−	1.56223e7i	0.229769	−	0.884975i
$793$	6.53635e6	−	1.13213e7i	0.369107	−	0.639312i
$794$	312179.	−	3.67798e6i	0.0175733	−	0.207042i
$795$	−1.09668e6	+	633167.i	−0.0615405	+	0.0355304i
$796$	1.79849e6	+	307520.i	0.100606	+	0.0172024i
$797$			1.28311e7i			0.715512i	0.933815	+	0.357756i	$0.116458\pi$
$797$			1.28311e7i			0.715512i	−0.933815	+	0.357756i	$0.883542\pi$
$798$	273359.	−	112761.i	0.0151959	−	0.00626833i
$799$		−	4.82046e6i		−	0.267129i
$800$	550588.	+	248109.i	0.0304160	+	0.0137062i
$801$	1.02832e7	−	5.93702e6i	0.566302	−	0.326955i
$802$	−1.68981e6	−	143428.i	−0.0927690	−	0.00787404i
$803$	1.29275e7	−	2.23911e7i	0.707500	−	1.22543i
$804$	1.43365e7	−	5.30237e6i	0.782174	−	0.289288i
$805$	−5.05653e6	+	2.60626e6i	−0.275019	+	0.141752i
$806$	−2.44589e7	−	1.70320e7i	−1.32617	−	0.923483i
$807$	−6.02360e6	−	3.47772e6i	−0.325591	−	0.187980i
$808$	−9.69169e6	+	2.67781e6i	−0.522241	+	0.144295i
$809$	1.51749e6	+	2.62837e6i	0.0815182	+	0.141194i	0.903902	−	0.427739i	$-0.140690\pi$
$809$	1.51749e6	+	2.62837e6i	0.0815182	+	0.141194i	−0.822384	+	0.568933i	$0.807356\pi$
$810$	−3.08308e6	+	1.44740e6i	−0.165110	+	0.0775134i
$811$	−2.07140e7			−1.10589			−0.552945	−	0.833218i	$-0.686496\pi$
$811$	−2.07140e7			−1.10589			−0.552945	+	0.833218i	$0.686496\pi$
$812$	1.83814e6	+	1.68053e6i	0.0978338	+	0.0894451i
$813$	1.58088e7			0.838825
$814$	−3.55786e7	+	1.67029e7i	−1.88203	+	0.883552i
$815$	−7.98441e6	−	1.38294e7i	−0.421064	−	0.729305i
$816$	−3.91314e6	+	1.11082e7i	−0.205731	+	0.584007i
$817$	−470994.	−	271928.i	−0.0246865	−	0.0142528i
$818$	6.52096e6	+	4.54089e6i	0.340744	+	0.237278i
$819$	−1.19607e7	+	1.86076e7i	−0.623084	+	0.969352i
$820$	2.11379e6	+	5.71525e6i	0.109781	+	0.296825i
$821$	−1.63626e6	+	2.83409e6i	−0.0847217	+	0.146742i	−0.905273	−	0.424831i	$-0.860333\pi$
$821$	−1.63626e6	+	2.83409e6i	−0.0847217	+	0.146742i	0.820551	+	0.571573i	$0.193667\pi$
$822$	1.29333e7	+	1.09775e6i	0.667620	+	0.0566662i
$823$	−1.48775e6	+	858951.i	−0.0765648	+	0.0442047i	−0.537794	−	0.843076i	$-0.680742\pi$
$823$	−1.48775e6	+	858951.i	−0.0765648	+	0.0442047i	0.461229	+	0.887281i	$0.347409\pi$
$824$	−1.49419e7	+	1.51760e7i	−0.766632	+	0.778646i
$825$		−	469298.i		−	0.0240057i
$826$	−4.80189e6	−	3.69579e6i	−0.244885	−	0.188477i
$827$			2.41034e7i			1.22550i	0.790275	+	0.612752i	$0.209937\pi$
$827$			2.41034e7i			1.22550i	−0.790275	+	0.612752i	$0.790063\pi$
$828$	−730483.	+	4.27214e6i	−0.0370283	+	0.216556i
$829$	−1.00011e7	+	5.77411e6i	−0.505428	+	0.291809i	−0.730952	−	0.682429i	$-0.760924\pi$
$829$	−1.00011e7	+	5.77411e6i	−0.505428	+	0.291809i	0.225524	+	0.974238i	$0.427590\pi$
$830$	1.86702e6	−	2.19965e7i	0.0940705	−	1.10830i
$831$	−2.01436e6	+	3.48898e6i	−0.101189	+	0.175265i
$832$	−1.60328e7	+	2.87945e7i	−0.802973	+	1.44212i
$833$	2.05317e7	−	9.37218e6i	1.02521	−	0.467981i
$834$	−5.01215e6	+	7.19772e6i	−0.249522	+	0.358327i
$835$	2.64693e7	+	1.52821e7i	1.31379	+	0.758518i
$836$	609183.	+	505808.i	0.0301461	+	0.0250305i
$837$	−9.25703e6	−	1.60336e7i	−0.456728	−	0.791077i
$838$	−6.32920e6	−	1.34817e7i	−0.311343	−	0.663184i
$839$	−1.35657e7			−0.665332			−0.332666	−	0.943045i	$-0.607948\pi$
$839$	−1.35657e7			−0.665332			−0.332666	+	0.943045i	$0.607948\pi$
$840$	−1.05479e7	−	3.28263e6i	−0.515782	−	0.160518i
$841$	−2.01507e7			−0.982428
$842$	5.52060e6	+	1.17593e7i	0.268353	+	0.571612i
$843$	495347.	+	857966.i	0.0240071	+	0.0415816i
$844$	−2.36379e6	−	1.96267e6i	−0.114223	−	0.0948398i
$845$	−3.04762e7	−	1.75954e7i	−1.46831	−	0.847732i
$846$	1.96858e6	−	2.82698e6i	0.0945641	−	0.135799i
$847$	1.25617e7	+	8.07444e6i	0.601643	+	0.386726i
$848$	2.09178e6	−	1.79249e6i	0.0998909	−	0.0855986i
$849$	−5.11026e6	+	8.85123e6i	−0.243318	+	0.421439i
$850$	66979.3	−	789126.i	0.00317975	−	0.0374627i
$851$	9.14036e6	−	5.27719e6i	0.432653	−	0.249792i
$852$	−1.72560e6	+	1.00920e7i	−0.0814407	+	0.476296i
$853$			1.43938e7i			0.677335i	0.940906	+	0.338668i	$0.109976\pi$
$853$			1.43938e7i			0.677335i	−0.940906	+	0.338668i	$0.890024\pi$
$854$	−9.44866e6	−	1.25800e6i	−0.443328	−	0.0590249i
$855$		−	438960.i		−	0.0205357i
$856$	−1.94258e7	−	1.91261e7i	−0.906139	−	0.892158i
$857$	2.14796e7	−	1.24012e7i	0.999018	−	0.576784i	0.0910607	−	0.995845i	$-0.470974\pi$
$857$	2.14796e7	−	1.24012e7i	0.999018	−	0.576784i	0.907958	+	0.419062i	$0.137641\pi$
$858$	2.55193e7	+	2.16602e6i	1.18345	+	0.100449i
$859$	4.68067e6	−	8.10716e6i	0.216434	−	0.374874i	−0.737281	−	0.675586i	$-0.763891\pi$
$859$	4.68067e6	−	8.10716e6i	0.216434	−	0.374874i	0.953715	+	0.300711i	$0.0972241\pi$
$860$	7.04782e6	+	1.90558e7i	0.324944	+	0.878580i
$861$	1.76251e6	+	3.41953e6i	0.0810260	+	0.157202i
$862$	1.17435e7	+	8.17760e6i	0.538305	+	0.374850i
$863$	−2.89287e7	−	1.67020e7i	−1.32221	−	0.763380i	−0.338131	−	0.941099i	$-0.609795\pi$
$863$	−2.89287e7	−	1.67020e7i	−1.32221	−	0.763380i	−0.984081	+	0.177719i	$0.943128\pi$
$864$	−1.66163e7	+	1.19587e7i	−0.757268	+	0.545003i
$865$	−1.28979e6	−	2.23398e6i	−0.0586110	−	0.101517i
$866$	2.59361e6	−	1.21761e6i	0.117519	−	0.0551714i
$867$	3.28408e6			0.148377
$868$	−4.67978e6	+	2.12225e7i	−0.210827	+	0.956088i
$869$	5.70996e7			2.56498
$870$	−1.44709e6	+	679363.i	−0.0648185	+	0.0304301i
$871$	−2.80473e7	−	4.85794e7i	−1.25270	−	2.16974i
$872$	−2.80874e6	−	1.01656e7i	−0.125089	−	0.452731i
$873$	−1.62350e7	−	9.37328e6i	−0.720969	−	0.416252i
$874$	−174485.	−	121503.i	−0.00772645	−	0.00538033i
$875$	2.29832e7	+	1.09683e6i	1.01482	+	0.0484306i
$876$	−1.26452e7	+	4.67684e6i	−0.556757	+	0.205917i
$877$	−8.72555e6	+	1.51131e7i	−0.383084	+	0.663520i	−0.991501	−	0.130097i	$-0.958471\pi$
$877$	−8.72555e6	+	1.51131e7i	−0.383084	+	0.663520i	0.608418	+	0.793617i	$0.291805\pi$
$878$	−2.79171e6	−	236954.i	−0.122218	−	0.0103736i
$879$	−1.84652e7	+	1.06609e7i	−0.806086	+	0.465394i
$880$	−5.43820e6	−	2.90758e7i	−0.236727	−	1.26568i
$881$		−	3.98953e7i		−	1.73174i	−0.500271	−	0.865869i	$-0.666766\pi$
$881$		−	3.98953e7i		−	1.73174i	0.500271	−	0.865869i	$-0.333234\pi$
$882$	1.58683e7	+	2.88835e6i	0.686847	+	0.125020i
$883$		−	1.52150e7i		−	0.656706i	−0.944555	−	0.328353i	$-0.893506\pi$
$883$		−	1.52150e7i		−	0.656706i	0.944555	−	0.328353i	$-0.106494\pi$
$884$	4.26016e7	+	7.28435e6i	1.83356	+	0.313516i
$885$	3.36832e6	−	1.94470e6i	0.144562	−	0.0834631i
$886$	119706.	−	1.41034e6i	0.00512310	−	0.0603584i
$887$	−1.23399e7	+	2.13734e7i	−0.526627	+	0.912146i	0.472891	+	0.881121i	$0.343210\pi$
$887$	−1.23399e7	+	2.13734e7i	−0.526627	+	0.912146i	−0.999519	+	0.0310247i	$0.990123\pi$
$888$	1.98378e7	+	5.15057e6i	0.844233	+	0.219191i
$889$	6.37864e6	+	304409.i	0.270691	+	0.0129182i
$890$	1.24356e7	−	1.78582e7i	0.526249	−	0.755722i
$891$	−4.98626e6	−	2.87882e6i	−0.210417	−	0.121484i
$892$	1.26533e7	−	1.52394e7i	0.532467	−	0.641291i
$893$	84498.3	+	146355.i	0.00354584	+	0.00614158i
$894$	1.36126e6	+	2.89958e6i	0.0569635	+	0.121337i
$895$	−1.76535e6			−0.0736671
$896$	2.38671e7	+	2.80073e6i	0.993185	+	0.116547i
$897$	−6.87734e6			−0.285391
$898$	1.39847e7	+	2.97886e7i	0.578713	+	1.23270i
$899$	1.57248e6	+	2.72362e6i	0.0648914	+	0.112395i
$900$	361543.	−	435434.i	0.0148783	−	0.0179191i
$901$	−3.12856e6	−	1.80627e6i	−0.128390	−	0.0741262i
$902$	−5.88659e6	+	8.45347e6i	−0.240906	+	0.345954i
$903$	5.87658e6	+	1.14014e7i	0.239831	+	0.465306i
$904$	−1.06783e7	−	2.77244e6i	−0.434591	−	0.112834i
$905$	1.40762e7	−	2.43807e7i	0.571299	−	0.989519i
$906$	685007.	−	8.07050e6i	0.0277252	−	0.326648i
$907$	−5.47609e6	+	3.16162e6i	−0.221030	+	0.127612i	−0.606427	−	0.795139i	$-0.707398\pi$
$907$	−5.47609e6	+	3.16162e6i	−0.221030	+	0.127612i	0.385397	+	0.922751i	$0.374065\pi$
$908$	4.15569e7	+	7.10571e6i	1.67274	+	0.286018i
$909$			9.42309e6i			0.378254i
$910$	−5.35021e6	+	4.01848e7i	−0.214174	+	1.60864i
$911$		−	2.11360e6i		−	0.0843774i	−0.999110	−	0.0421887i	$-0.986567\pi$
$911$		−	2.11360e6i		−	0.0843774i	0.999110	−	0.0421887i	$-0.0134331\pi$
$912$	−75908.9	−	405853.i	−0.00302208	−	0.0161578i
$913$	3.23186e7	−	1.86592e7i	1.28314	−	0.740824i
$914$	−2.95474e7	−	2.50792e6i	−1.16991	−	0.0992996i
$915$	3.05917e6	−	5.29864e6i	0.120796	−	0.209224i
$916$	992221.	−	366974.i	0.0390724	−	0.0144510i
$917$	−1.61895e7	−	1.04063e7i	−0.635783	−	0.408671i
$918$	2.20317e7	+	1.53419e7i	0.862864	+	0.600857i
$919$	−9.98589e6	−	5.76536e6i	−0.390030	−	0.225184i	0.292143	−	0.956375i	$-0.405632\pi$
$919$	−9.98589e6	−	5.76536e6i	−0.390030	−	0.225184i	−0.682173	+	0.731191i	$0.738965\pi$
$920$	2.11542e6	+	7.65625e6i	0.0823999	+	0.298227i
$921$	−6.30150e6	−	1.09145e7i	−0.244791	−	0.423990i
$922$	−1.31706e7	+	6.18314e6i	−0.510243	+	0.239542i
$923$	3.75726e7			1.45167
$924$	−5.63562e6	−	1.78038e7i	−0.217151	−	0.686013i
$925$	−1.37822e6			−0.0529621
$926$	8.83100e6	−	4.14586e6i	0.338441	−	0.158887i
$927$	9.97957e6	+	1.72851e7i	0.381428	+	0.660652i
$928$	2.82259e6	−	2.03141e6i	0.107592	−	0.0774333i
$929$	2.84500e7	+	1.64256e7i	1.08154	+	0.624429i	0.931312	−	0.364222i	$-0.118665\pi$
$929$	2.84500e7	+	1.64256e7i	1.08154	+	0.624429i	0.150231	+	0.988651i	$0.451998\pi$
$930$	−1.14474e7	−	7.97142e6i	−0.434009	−	0.302223i
$931$	−459083.	+	644454.i	−0.0173587	+	0.0243679i
$932$	−8.46812e6	−	2.28960e7i	−0.319336	−	0.863416i
$933$	4.92762e6	−	8.53490e6i	0.185325	−	0.320992i
$934$	−5.40158e6	−	458474.i	−0.202606	−	0.0171968i
$935$	−3.35941e7	+	1.93955e7i	−1.25671	+	0.725559i
$936$	2.20092e7	+	2.16696e7i	0.821134	+	0.808464i
$937$			4.13580e7i			1.53890i	0.638707	+	0.769450i	$0.279469\pi$
$937$			4.13580e7i			1.53890i	−0.638707	+	0.769450i	$0.720531\pi$
$938$	−2.49468e7	+	3.24131e7i	−0.925781	+	1.20286i
$939$		−	1.10402e7i		−	0.408615i
$940$	1.06406e6	−	6.22305e6i	0.0392779	−	0.229712i
$941$	−7.11791e6	+	4.10953e6i	−0.262047	+	0.151293i	−0.625268	−	0.780410i	$-0.715010\pi$
$941$	−7.11791e6	+	4.10953e6i	−0.262047	+	0.151293i	0.363221	+	0.931703i	$0.381677\pi$
$942$	−1.59043e6	+	1.87378e7i	−0.0583964	+	0.688005i
$943$	1.38308e6	−	2.39557e6i	0.0506487	−	0.0877262i
$944$	−6.42466e6	+	5.50542e6i	−0.234650	+	0.201076i
$945$	−1.36163e7	+	2.11833e7i	−0.495998	+	0.771640i
$946$	−1.96271e7	+	2.81856e7i	−0.713063	+	1.02400i
$947$	3.09169e7	+	1.78499e7i	1.12026	+	0.646785i	0.941468	−	0.337101i	$-0.109446\pi$
$947$	3.09169e7	+	1.78499e7i	1.12026	+	0.646785i	0.178796	+	0.983886i	$0.442780\pi$
$948$	−2.29080e7	−	1.90206e7i	−0.827877	−	0.687391i
$949$	2.47385e7	+	4.28484e7i	0.891679	+	1.54443i
$950$	11799.1	+	25133.0i	0.000424170	+	0.000903514i
$951$	2.28402e6			0.0818935
$952$	−6.93532e6	−	3.07414e7i	−0.248013	−	1.09934i
$953$	−4.96767e7			−1.77182			−0.885912	−	0.463853i	$-0.846466\pi$
$953$	−4.96767e7			−1.77182			−0.885912	+	0.463853i	$0.846466\pi$
$954$	−1.09711e6	−	2.33694e6i	−0.0390284	−	0.0831335i
$955$	−115974.	−	200873.i	−0.00411484	−	0.00712711i
$956$	−2.89864e7	−	2.40675e7i	−1.02577	−	0.851700i
$957$	−2.34039e6	−	1.35122e6i	−0.0826052	−	0.0476921i
$958$	2.96354e7	−	4.25581e7i	1.04327	−	1.49819i
$959$	−3.08722e7	+	1.59123e7i	−1.08398	+	0.558710i
$960$	−7.50375e6	+	1.34765e7i	−0.262785	+	0.471955i
$961$	593298.	−	1.02762e6i	0.0207235	−	0.0358942i
$962$	6.36112e6	−	7.49444e7i	0.221613	−	2.61097i
$963$	−2.21255e7	+	1.27742e7i	−0.768825	+	0.443881i
$964$	6.92992e6	−	4.05288e7i	0.240179	−	1.40466i
$965$		−	941814.i		−	0.0325572i
$966$	1.91225e6	+	4.63574e6i	0.0659328	+	0.159837i
$967$		−	2.53358e7i		−	0.871303i	−0.900115	−	0.435651i	$-0.856518\pi$
$967$		−	2.53358e7i		−	0.871303i	0.900115	−	0.435651i	$-0.143482\pi$
$968$	1.46287e7	−	1.48580e7i	0.501785	−	0.509649i
$969$	−468922.	+	270732.i	−0.0160432	+	0.00926254i
$970$	−3.42335e7	−	2.90566e6i	−1.16821	−	0.0991553i
$971$	9.34288e6	−	1.61823e7i	0.318004	−	0.550799i	−0.662067	−	0.749444i	$-0.730321\pi$
$971$	9.34288e6	−	1.61823e7i	0.318004	−	0.550799i	0.980072	+	0.198645i	$0.0636541\pi$
$972$	1.05745e7	+	2.85914e7i	0.359001	+	0.970665i
$973$	1.11876e6	−	2.34428e7i	0.0378840	−	0.793828i
$974$	1.78427e7	+	1.24248e7i	0.602646	+	0.419654i
$975$	777746.	+	449032.i	0.0262015	+	0.0151275i
$976$	−4.42226e6	+	1.25535e7i	−0.148600	+	0.421831i
$977$	−2.90767e6	−	5.03623e6i	−0.0974561	−	0.168799i	0.813175	−	0.582019i	$-0.197737\pi$
$977$	−2.90767e6	−	5.03623e6i	−0.0974561	−	0.168799i	−0.910631	+	0.413220i	$0.864404\pi$
$978$	−1.27424e7	+	5.98213e6i	−0.425995	+	0.199990i
$979$	3.67871e7			1.22670
$980$	2.85745e7	−	7.56703e6i	0.950417	−	0.251687i
$981$	−9.88384e6			−0.327909
$982$	−4.14130e7	+	1.94420e7i	−1.37043	+	0.643373i
$983$	1.45631e7	+	2.52241e7i	0.480696	+	0.832590i	0.999755	−	0.0221485i	$-0.00705066\pi$
$983$	1.45631e7	+	2.52241e7i	0.480696	+	0.832590i	−0.519059	+	0.854739i	$0.673717\pi$
$984$	5.17762e6	−	1.43057e6i	0.170468	−	0.0471002i
$985$	4.56383e7	+	2.63493e7i	1.49878	+	0.865324i
$986$	−3.74252e6	−	2.60611e6i	−0.122595	−	0.0853690i
$987$	189997.	−	3.98123e6i	0.00620802	−	0.130084i
$988$	−1.42113e6	+	525606.i	−0.0463171	+	0.0171304i
$989$	4.61148e6	−	7.98731e6i	0.149916	−	0.259663i
$990$	−2.76222e7	−	2.34451e6i	−0.895715	−	0.0760264i
$991$	3.22692e7	−	1.86306e7i	1.04377	−	0.602619i	0.122869	−	0.992423i	$-0.460790\pi$
$991$	3.22692e7	−	1.86306e7i	1.04377	−	0.602619i	0.920898	+	0.389803i	$0.127457\pi$
$992$	2.76658e7	+	1.24669e7i	0.892614	+	0.402235i
$993$		−	760241.i		−	0.0244668i
$994$	−1.04471e7	−	2.53262e7i	−0.335374	−	0.813025i
$995$		−	3.13381e6i		−	0.100350i
$996$	−1.91816e7	−	3.27982e6i	−0.612684	−	0.104761i
$997$	−4.11055e7	+	2.37323e7i	−1.30967	+	0.756139i	−0.982041	−	0.188667i	$-0.939583\pi$
$997$	−4.11055e7	+	2.37323e7i	−1.30967	+	0.756139i	−0.327631	+	0.944806i	$0.606250\pi$
$998$	−769027.	+	9.06040e6i	−0.0244408	+	0.287953i
$999$	2.33605e7	−	4.04616e7i	0.740575	−	1.28271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.6.f.a.19.7	yes	36
4.3	odd	2	inner	28.6.f.a.19.17	yes	36
7.2	even	3		196.6.d.b.195.11		36
7.3	odd	6	inner	28.6.f.a.3.17	yes	36
7.5	odd	6		196.6.d.b.195.12		36
28.3	even	6	inner	28.6.f.a.3.7	✓	36
28.19	even	6		196.6.d.b.195.9		36
28.23	odd	6		196.6.d.b.195.10		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.f.a.3.7	✓	36	28.3	even	6	inner
28.6.f.a.3.17	yes	36	7.3	odd	6	inner
28.6.f.a.19.7	yes	36	1.1	even	1	trivial
28.6.f.a.19.17	yes	36	4.3	odd	2	inner
196.6.d.b.195.9		36	28.19	even	6
196.6.d.b.195.10		36	28.23	odd	6
196.6.d.b.195.11		36	7.2	even	3
196.6.d.b.195.12		36	7.5	odd	6

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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	28.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.40397 - 5.12064i) q^{2} +(4.28235 + 7.41724i) q^{3} +(-20.4419 + 24.6197i) q^{4} +(47.5979 + 27.4807i) q^{5} +(27.6864 - 39.7592i) q^{6} +(-6.17988 + 129.494i) q^{7} +(175.210 + 45.4904i) q^{8} +(84.8230 - 146.918i) q^{9} +O(q^{10})\)	\(q+(-2.40397 - 5.12064i) q^{2} +(4.28235 + 7.41724i) q^{3} +(-20.4419 + 24.6197i) q^{4} +(47.5979 + 27.4807i) q^{5} +(27.6864 - 39.7592i) q^{6} +(-6.17988 + 129.494i) q^{7} +(175.210 + 45.4904i) q^{8} +(84.8230 - 146.918i) q^{9} +(26.2947 - 309.794i) q^{10} +(455.168 - 262.791i) q^{11} +(-270.149 - 46.1922i) q^{12} +1005.77i q^{13} +(677.950 - 279.656i) q^{14} +470.727i q^{15} +(-188.260 - 1006.55i) q^{16} +(-1162.96 + 671.435i) q^{17} +(-956.225 - 81.1623i) q^{18} +(23.5393 - 40.7713i) q^{19} +(-1649.56 + 610.090i) q^{20} +(-986.956 + 508.702i) q^{21} +(-2439.87 - 1699.01i) q^{22} +(691.417 + 399.190i) q^{23} +(412.897 + 1494.38i) q^{24} +(-52.1274 - 90.2873i) q^{25} +(5150.20 - 2417.84i) q^{26} +3534.19 q^{27} +(-3061.79 - 2799.26i) q^{28} -600.350 q^{29} +(2410.42 - 1131.61i) q^{30} +(-2619.28 - 4536.73i) q^{31} +(-4701.59 + 3383.71i) q^{32} +(3898.37 + 2250.73i) q^{33} +(6233.89 + 4340.99i) q^{34} +(-3852.74 + 5993.83i) q^{35} +(1883.13 + 5091.59i) q^{36} +(6609.88 - 11448.6i) q^{37} +(-265.363 - 22.5234i) q^{38} +(-7460.05 + 4307.06i) q^{39} +(7089.53 + 6980.14i) q^{40} -3464.72i q^{41} +(4977.49 + 3830.94i) q^{42} -11552.1i q^{43} +(-2834.64 + 16578.0i) q^{44} +(8074.79 - 4661.98i) q^{45} +(381.962 - 4500.13i) q^{46} +(-1794.83 + 3108.74i) q^{47} +(6659.60 - 5706.74i) q^{48} +(-16730.6 - 1600.52i) q^{49} +(-337.016 + 483.973i) q^{50} +(-9960.39 - 5750.63i) q^{51} +(-24761.8 - 20559.9i) q^{52} +(1345.08 + 2329.75i) q^{53} +(-8496.07 - 18097.3i) q^{54} +28886.7 q^{55} +(-6973.54 + 22407.6i) q^{56} +403.214 q^{57} +(1443.22 + 3074.17i) q^{58} +(-4131.27 - 7155.58i) q^{59} +(-11589.2 - 9622.53i) q^{60} +(-11256.3 - 6498.83i) q^{61} +(-16934.3 + 24318.6i) q^{62} +(18500.8 + 11892.0i) q^{63} +(28629.2 + 15940.8i) q^{64} +(-27639.3 + 47872.6i) q^{65} +(2153.59 - 25372.8i) q^{66} +(-48300.6 + 27886.4i) q^{67} +(7242.54 - 42357.1i) q^{68} +6837.87i q^{69} +(39954.1 + 5319.51i) q^{70} -37357.0i q^{71} +(21545.2 - 21882.9i) q^{72} +(42602.5 - 24596.6i) q^{73} +(-74514.3 - 6324.62i) q^{74} +(446.455 - 773.283i) q^{75} +(522.589 + 1412.97i) q^{76} +(31217.1 + 60565.7i) q^{77} +(39988.7 + 27846.2i) q^{78} +(94085.5 + 54320.3i) q^{79} +(18699.8 - 53082.9i) q^{80} +(-5477.39 - 9487.12i) q^{81} +(-17741.6 + 8329.08i) q^{82} +71003.7 q^{83} +(7651.12 - 34697.4i) q^{84} -73805.9 q^{85} +(-59154.1 + 27770.9i) q^{86} +(-2570.90 - 4452.94i) q^{87} +(91704.5 - 25337.9i) q^{88} +(60615.8 + 34996.5i) q^{89} +(-43283.9 - 30140.8i) q^{90} +(-130242. - 6215.56i) q^{91} +(-23961.8 + 8862.29i) q^{92} +(22433.3 - 38855.7i) q^{93} +(20233.5 + 1717.37i) q^{94} +(2240.84 - 1293.75i) q^{95} +(-45231.6 - 20382.6i) q^{96} -110504. i q^{97} +(32024.2 + 89519.0i) q^{98} -89163.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4} - 6 q^{5} - 72 q^{8} - 1136 q^{9}+O(q^{10}) \) 36 * q - 12 * q^4 - 6 * q^5 - 72 * q^8 - 1136 * q^9	\( 36 q - 12 q^{4} - 6 q^{5} - 72 q^{8} - 1136 q^{9} - 804 q^{10} + 1632 q^{12} + 1024 q^{14} + 664 q^{16} - 6 q^{17} - 1780 q^{18} - 4586 q^{21} + 13768 q^{22} + 564 q^{24} + 7612 q^{25} - 8892 q^{26} - 5928 q^{28} + 176 q^{29} - 5836 q^{30} + 1160 q^{32} - 14154 q^{33} - 27920 q^{36} + 11722 q^{37} - 5652 q^{38} + 35052 q^{40} + 23140 q^{42} + 9096 q^{44} + 19152 q^{45} - 1040 q^{46} + 43900 q^{49} - 51168 q^{50} - 61776 q^{52} - 33486 q^{53} - 30996 q^{54} + 19952 q^{56} - 1668 q^{57} - 48436 q^{58} + 14312 q^{60} + 18846 q^{61} + 44544 q^{64} + 15356 q^{65} + 221808 q^{66} + 25020 q^{68} + 81192 q^{70} + 148064 q^{72} - 236562 q^{73} + 17152 q^{74} - 140010 q^{77} + 127704 q^{78} - 277224 q^{80} + 160402 q^{81} - 391836 q^{82} - 379540 q^{84} + 71212 q^{85} - 252496 q^{86} + 55268 q^{88} - 23706 q^{89} - 190176 q^{92} - 165162 q^{93} + 359988 q^{94} + 1061736 q^{96} + 418676 q^{98}+O(q^{100}) \) 36 * q - 12 * q^4 - 6 * q^5 - 72 * q^8 - 1136 * q^9 - 804 * q^10 + 1632 * q^12 + 1024 * q^14 + 664 * q^16 - 6 * q^17 - 1780 * q^18 - 4586 * q^21 + 13768 * q^22 + 564 * q^24 + 7612 * q^25 - 8892 * q^26 - 5928 * q^28 + 176 * q^29 - 5836 * q^30 + 1160 * q^32 - 14154 * q^33 - 27920 * q^36 + 11722 * q^37 - 5652 * q^38 + 35052 * q^40 + 23140 * q^42 + 9096 * q^44 + 19152 * q^45 - 1040 * q^46 + 43900 * q^49 - 51168 * q^50 - 61776 * q^52 - 33486 * q^53 - 30996 * q^54 + 19952 * q^56 - 1668 * q^57 - 48436 * q^58 + 14312 * q^60 + 18846 * q^61 + 44544 * q^64 + 15356 * q^65 + 221808 * q^66 + 25020 * q^68 + 81192 * q^70 + 148064 * q^72 - 236562 * q^73 + 17152 * q^74 - 140010 * q^77 + 127704 * q^78 - 277224 * q^80 + 160402 * q^81 - 391836 * q^82 - 379540 * q^84 + 71212 * q^85 - 252496 * q^86 + 55268 * q^88 - 23706 * q^89 - 190176 * q^92 - 165162 * q^93 + 359988 * q^94 + 1061736 * q^96 + 418676 * q^98

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