LMFDB - Embedded newform 48.7.l.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	48.19
Dual form			48.7.l.a.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75499 - 7.06400i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-35.8001 + 53.0505i) q^{4} +(107.837 - 107.837i) q^{5} +(119.254 + 36.4742i) q^{6} +5.36994 q^{7} +(509.177 + 53.6875i) q^{8} -243.000i q^{9} +O(q^{10})$	\(q+(-3.75499 - 7.06400i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-35.8001 + 53.0505i) q^{4} +(107.837 - 107.837i) q^{5} +(119.254 + 36.4742i) q^{6} +5.36994 q^{7} +(509.177 + 53.6875i) q^{8} -243.000i q^{9} +(-1166.68 - 356.832i) q^{10} +(-48.9517 - 48.9517i) q^{11} +(-190.146 - 979.373i) q^{12} +(-2118.46 - 2118.46i) q^{13} +(-20.1641 - 37.9332i) q^{14} +2377.30i q^{15} +(-1532.71 - 3798.42i) q^{16} -3884.97 q^{17} +(-1716.55 + 912.463i) q^{18} +(-5877.62 + 5877.62i) q^{19} +(1860.23 + 9581.35i) q^{20} +(-59.1913 + 59.1913i) q^{21} +(-161.981 + 529.608i) q^{22} -3237.03 q^{23} +(-6204.29 + 5020.73i) q^{24} -7632.48i q^{25} +(-7010.00 + 22919.6i) q^{26} +(2678.52 + 2678.52i) q^{27} +(-192.244 + 284.878i) q^{28} +(-30583.8 - 30583.8i) q^{29} +(16793.3 - 8926.75i) q^{30} -54018.7i q^{31} +(-21076.7 + 25090.1i) q^{32} +1079.16 q^{33} +(14588.0 + 27443.4i) q^{34} +(579.076 - 579.076i) q^{35} +(12891.3 + 8699.42i) q^{36} +(33650.8 - 33650.8i) q^{37} +(63589.9 + 19449.1i) q^{38} +46702.3 q^{39} +(60697.5 - 49118.5i) q^{40} +29052.0i q^{41} +(640.390 + 195.864i) q^{42} +(-24548.9 - 24548.9i) q^{43} +(4349.38 - 844.436i) q^{44} +(-26204.3 - 26204.3i) q^{45} +(12155.0 + 22866.4i) q^{46} +58193.1i q^{47} +(58763.5 + 24974.3i) q^{48} -117620. q^{49} +(-53915.8 + 28659.9i) q^{50} +(42822.9 - 42822.9i) q^{51} +(188226. - 36544.3i) q^{52} +(27071.8 - 27071.8i) q^{53} +(8863.23 - 28978.8i) q^{54} -10557.6 q^{55} +(2734.25 + 288.299i) q^{56} -129575. i q^{57} +(-101202. + 330885. i) q^{58} +(225328. + 225328. i) q^{59} +(-126117. - 85107.6i) q^{60} +(-1789.71 - 1789.71i) q^{61} +(-381588. + 202840. i) q^{62} -1304.90i q^{63} +(256379. + 54672.9i) q^{64} -456895. q^{65} +(-4052.24 - 7623.18i) q^{66} +(122582. - 122582. i) q^{67} +(139082. - 206100. i) q^{68} +(35680.9 - 35680.9i) q^{69} +(-6265.02 - 1916.17i) q^{70} -213921. q^{71} +(13046.1 - 123730. i) q^{72} -337380. i q^{73} +(-364067. - 111351. i) q^{74} +(84130.6 + 84130.6i) q^{75} +(-101391. - 522230. i) q^{76} +(-262.868 - 262.868i) q^{77} +(-175367. - 329905. i) q^{78} +715537. i q^{79} +(-574891. - 244327. i) q^{80} -59049.0 q^{81} +(205223. - 109090. i) q^{82} +(338143. - 338143. i) q^{83} +(-1021.07 - 5259.18i) q^{84} +(-418942. + 418942. i) q^{85} +(-81232.4 + 265594. i) q^{86} +674232. q^{87} +(-22297.0 - 27553.2i) q^{88} +527375. i q^{89} +(-86710.2 + 283504. i) q^{90} +(-11376.0 - 11376.0i) q^{91} +(115886. - 171726. i) q^{92} +(595432. + 595432. i) q^{93} +(411076. - 218515. i) q^{94} +1.26765e6i q^{95} +(-44238.0 - 508883. i) q^{96} -1.55143e6 q^{97} +(441663. + 830868. i) q^{98} +(-11895.3 + 11895.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) $ 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−3.75499	−	7.06400i	−0.469374	−	0.883000i
$2$	−3.75499	−	7.06400i	−0.469374	−	0.883000i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$4$	−35.8001	+	53.0505i	−0.559376	+	0.828914i
$5$	107.837	−	107.837i	0.862693	−	0.862693i	−0.128957	−	0.991650i	$-0.541163\pi$
$5$	107.837	−	107.837i	0.862693	−	0.862693i	0.991650	+	0.128957i	$0.0411629\pi$
$6$	119.254	+	36.4742i	0.552104	+	0.168862i
$7$	5.36994			0.0156558			0.00782790	−	0.999969i	$-0.497508\pi$
$7$	5.36994			0.0156558			0.00782790	+	0.999969i	$0.497508\pi$
$8$	509.177	+	53.6875i	0.994487	+	0.104858i
$9$		−	243.000i		−	0.333333i
$10$	−1166.68	−	356.832i	−1.16668	−	0.356832i
$11$	−48.9517	−	48.9517i	−0.0367781	−	0.0367781i	0.688479	−	0.725257i	$-0.258279\pi$
$11$	−48.9517	−	48.9517i	−0.0367781	−	0.0367781i	−0.725257	+	0.688479i	$0.758279\pi$
$12$	−190.146	−	979.373i	−0.110038	−	0.566767i
$13$	−2118.46	−	2118.46i	−0.964252	−	0.964252i	0.0351311	−	0.999383i	$-0.488815\pi$
$13$	−2118.46	−	2118.46i	−0.964252	−	0.964252i	−0.999383	+	0.0351311i	$0.988815\pi$
$14$	−20.1641	−	37.9332i	−0.00734843	−	0.0138241i
$15$			2377.30i			0.704386i
$16$	−1532.71	−	3798.42i	−0.374196	−	0.927349i
$17$	−3884.97			−0.790753			−0.395377	−	0.918519i	$-0.629386\pi$
$17$	−3884.97			−0.790753			−0.395377	+	0.918519i	$0.629386\pi$
$18$	−1716.55	+	912.463i	−0.294333	+	0.156458i
$19$	−5877.62	+	5877.62i	−0.856921	+	0.856921i	−0.990974	−	0.134053i	$-0.957201\pi$
$19$	−5877.62	+	5877.62i	−0.856921	+	0.856921i	0.134053	+	0.990974i	$0.457201\pi$
$20$	1860.23	+	9581.35i	0.232528	+	1.19767i
$21$	−59.1913	+	59.1913i	−0.00639146	+	0.00639146i
$22$	−161.981	+	529.608i	−0.0152124	+	0.0497377i
$23$	−3237.03			−0.266050			−0.133025	−	0.991113i	$-0.542469\pi$
$23$	−3237.03			−0.266050			−0.133025	+	0.991113i	$0.542469\pi$
$24$	−6204.29	+	5020.73i	−0.448806	+	0.363189i
$25$		−	7632.48i		−	0.488479i
$26$	−7010.00	+	22919.6i	−0.398839	+	1.30403i
$27$	2678.52	+	2678.52i	0.136083	+	0.136083i
$28$	−192.244	+	284.878i	−0.00875749	+	0.0129773i
$29$	−30583.8	−	30583.8i	−1.25400	−	1.25400i	−0.953912	−	0.300087i	$-0.902984\pi$
$29$	−30583.8	−	30583.8i	−1.25400	−	1.25400i	−0.300087	−	0.953912i	$-0.597016\pi$
$30$	16793.3	−	8926.75i	0.621973	−	0.330620i
$31$		−	54018.7i		−	1.81326i	−0.421932	−	0.906628i	$-0.638648\pi$
$31$		−	54018.7i		−	1.81326i	0.421932	−	0.906628i	$-0.361352\pi$
$32$	−21076.7	+	25090.1i	−0.643211	+	0.765689i
$33$	1079.16			0.0300292
$34$	14588.0	+	27443.4i	0.371159	+	0.698235i
$35$	579.076	−	579.076i	0.0135062	−	0.0135062i
$36$	12891.3	+	8699.42i	0.276305	+	0.186459i
$37$	33650.8	−	33650.8i	0.664339	−	0.664339i	−0.292060	−	0.956400i	$-0.594341\pi$
$37$	33650.8	−	33650.8i	0.664339	−	0.664339i	0.956400	+	0.292060i	$0.0943408\pi$
$38$	63589.9	+	19449.1i	1.15888	+	0.354444i
$39$	46702.3			0.787308
$40$	60697.5	−	49118.5i	0.948398	−	0.767477i
$41$			29052.0i			0.421526i	0.977537	+	0.210763i	$0.0675949\pi$
$41$			29052.0i			0.421526i	−0.977537	+	0.210763i	$0.932405\pi$
$42$	640.390	+	195.864i	0.00864363	+	0.00264367i
$43$	−24548.9	−	24548.9i	−0.308764	−	0.308764i	0.535666	−	0.844430i	$-0.320061\pi$
$43$	−24548.9	−	24548.9i	−0.308764	−	0.308764i	−0.844430	+	0.535666i	$0.820061\pi$
$44$	4349.38	−	844.436i	0.0510587	−	0.00991309i
$45$	−26204.3	−	26204.3i	−0.287564	−	0.287564i
$46$	12155.0	+	22866.4i	0.124877	+	0.234922i
$47$			58193.1i			0.560503i	0.959927	+	0.280251i	$0.0904178\pi$
$47$			58193.1i			0.560503i	−0.959927	+	0.280251i	$0.909582\pi$
$48$	58763.5	+	24974.3i	0.531354	+	0.225824i
$49$	−117620.			−0.999755
$50$	−53915.8	+	28659.9i	−0.431327	+	0.229279i
$51$	42822.9	−	42822.9i	0.322824	−	0.322824i
$52$	188226.	−	36544.3i	1.33866	−	0.259902i
$53$	27071.8	−	27071.8i	0.181840	−	0.181840i	−0.610317	−	0.792157i	$-0.708958\pi$
$53$	27071.8	−	27071.8i	0.181840	−	0.181840i	0.792157	+	0.610317i	$0.208958\pi$
$54$	8863.23	−	28978.8i	0.0562873	−	0.184035i
$55$	−10557.6			−0.0634565
$56$	2734.25	+	288.299i	0.0155695	+	0.00164164i
$57$		−	129575.i		−	0.699673i
$58$	−101202.	+	330885.i	−0.518686	+	1.69587i
$59$	225328.	+	225328.i	1.09713	+	1.09713i	0.994745	+	0.102387i	$0.0326481\pi$
$59$	225328.	+	225328.i	1.09713	+	1.09713i	0.102387	+	0.994745i	$0.467352\pi$
$60$	−126117.	−	85107.6i	−0.583875	−	0.394017i
$61$	−1789.71	−	1789.71i	−0.00788485	−	0.00788485i	0.703153	−	0.711038i	$-0.251775\pi$
$61$	−1789.71	−	1789.71i	−0.00788485	−	0.00788485i	−0.711038	+	0.703153i	$0.751775\pi$
$62$	−381588.	+	202840.i	−1.60110	+	0.851095i
$63$		−	1304.90i		−	0.00521860i
$64$	256379.	+	54672.9i	0.978009	+	0.208561i
$65$	−456895.			−1.66371
$66$	−4052.24	−	7623.18i	−0.0140949	−	0.0265158i
$67$	122582.	−	122582.i	0.407571	−	0.407571i	−0.473320	−	0.880891i	$-0.656944\pi$
$67$	122582.	−	122582.i	0.407571	−	0.407571i	0.880891	+	0.473320i	$0.156944\pi$
$68$	139082.	−	206100.i	0.442329	−	0.655466i
$69$	35680.9	−	35680.9i	0.108615	−	0.108615i
$70$	−6265.02	−	1916.17i	−0.0182654	−	0.00558649i
$71$	−213921.			−0.597692			−0.298846	−	0.954301i	$-0.596602\pi$
$71$	−213921.			−0.597692			−0.298846	+	0.954301i	$0.596602\pi$
$72$	13046.1	−	123730.i	0.0349528	−	0.331496i
$73$		−	337380.i		−	0.867263i	−0.901090	−	0.433631i	$-0.857232\pi$
$73$		−	337380.i		−	0.867263i	0.901090	−	0.433631i	$-0.142768\pi$
$74$	−364067.	−	111351.i	−0.898435	−	0.274788i
$75$	84130.6	+	84130.6i	0.199421	+	0.199421i
$76$	−101391.	−	522230.i	−0.230972	−	1.18965i
$77$	−262.868	−	262.868i	−0.000575791	−	0.000575791i
$78$	−175367.	−	329905.i	−0.369542	−	0.695193i
$79$			715537.i			1.45128i	0.688075	+	0.725639i	$0.258456\pi$
$79$			715537.i			1.45128i	−0.688075	+	0.725639i	$0.741544\pi$
$80$	−574891.	−	244327.i	−1.12283	−	0.477201i
$81$	−59049.0			−0.111111
$82$	205223.	−	109090.i	0.372207	−	0.197853i
$83$	338143.	−	338143.i	0.591380	−	0.591380i	−0.346624	−	0.938004i	$-0.612672\pi$
$83$	338143.	−	338143.i	0.591380	−	0.591380i	0.938004	+	0.346624i	$0.112672\pi$
$84$	−1021.07	−	5259.18i	−0.00172274	−	0.00887319i
$85$	−418942.	+	418942.i	−0.682177	+	0.682177i
$86$	−81232.4	+	265594.i	−0.127713	+	0.417564i
$87$	674232.			1.02389
$88$	−22297.0	−	27553.2i	−0.0327189	−	0.0404319i
$89$			527375.i			0.748083i	0.927412	+	0.374041i	$0.122028\pi$
$89$			527375.i			0.748083i	−0.927412	+	0.374041i	$0.877972\pi$
$90$	−86710.2	+	283504.i	−0.118944	+	0.388894i
$91$	−11376.0	−	11376.0i	−0.0150961	−	0.0150961i
$92$	115886.	−	171726.i	0.148822	−	0.220533i
$93$	595432.	+	595432.i	0.740258	+	0.740258i
$94$	411076.	−	218515.i	0.494924	−	0.263085i
$95$			1.26765e6i			1.47852i
$96$	−44238.0	−	508883.i	−0.0500013	−	0.575181i
$97$	−1.55143e6			−1.69987			−0.849937	−	0.526884i	$-0.823360\pi$
$97$	−1.55143e6			−1.69987			−0.849937	+	0.526884i	$0.823360\pi$
$98$	441663.	+	830868.i	0.469259	+	0.882783i
$99$	−11895.3	+	11895.3i	−0.0122594	+	0.0122594i
$100$	404907.	+	273244.i	0.404907	+	0.273244i
$101$	1.16299e6	−	1.16299e6i	1.12879	−	1.12879i	0.138413	−	0.990375i	$-0.455800\pi$
$101$	1.16299e6	−	1.16299e6i	1.12879	−	1.12879i	0.990375	−	0.138413i	$-0.0442002\pi$
$102$	−463300.	−	141701.i	−0.436578	−	0.133528i
$103$	1.22358e6			1.11975			0.559873	−	0.828578i	$-0.310850\pi$
$103$	1.22358e6			1.11975			0.559873	+	0.828578i	$0.310850\pi$
$104$	−964938.	−	1.19241e6i	−0.857826	−	1.06005i
$105$			12766.0i			0.0110277i
$106$	−292889.	−	89580.7i	−0.245916	−	0.0752137i
$107$	421967.	+	421967.i	0.344450	+	0.344450i	0.858038	−	0.513587i	$-0.171684\pi$
$107$	421967.	+	421967.i	0.344450	+	0.344450i	−0.513587	+	0.858038i	$0.671684\pi$
$108$	−237988.	+	46205.5i	−0.188922	+	0.0366794i
$109$	−966244.	−	966244.i	−0.746118	−	0.746118i	0.227630	−	0.973748i	$-0.426902\pi$
$109$	−966244.	−	966244.i	−0.746118	−	0.746118i	−0.973748	+	0.227630i	$0.926902\pi$
$110$	39643.6	+	74578.6i	0.0297848	+	0.0560320i
$111$			741845.i			0.542431i
$112$	−8230.55	−	20397.3i	−0.00585835	−	0.0145184i
$113$	1.34165e6			0.929833			0.464916	−	0.885355i	$-0.346084\pi$
$113$	1.34165e6			0.929833			0.464916	+	0.885355i	$0.346084\pi$
$114$	−915314.	+	486551.i	−0.617811	+	0.328408i
$115$	−349071.	+	349071.i	−0.229520	+	0.229520i
$116$	2.71739e6	−	527583.i	1.74091	−	0.338000i
$117$	−514786.	+	514786.i	−0.321417	+	0.321417i
$118$	745611.	−	2.43782e6i	0.453802	−	1.48373i
$119$	−20862.1			−0.0123799
$120$	−127631.	+	1.21047e6i	−0.0738608	+	0.700503i
$121$		−	1.76677e6i		−	0.997295i
$122$	−5922.16	+	19362.9i	−0.00326138	+	0.0106633i
$123$	−320232.	−	320232.i	−0.172087	−	0.172087i
$124$	2.86572e6	+	1.93387e6i	1.50303	+	1.01429i
$125$	861886.	+	861886.i	0.441286	+	0.441286i
$126$	−9217.78	+	4899.87i	−0.00460802	+	0.00244948i
$127$			512988.i			0.250435i	0.992129	+	0.125218i	$0.0399629\pi$
$127$			512988.i			0.250435i	−0.992129	+	0.125218i	$0.960037\pi$
$128$	−576493.	−	2.01636e6i	−0.274893	−	0.961475i
$129$	541191.			0.252105
$130$	1.71564e6	+	3.22751e6i	0.780900	+	1.46905i
$131$	1.55668e6	−	1.55668e6i	0.692444	−	0.692444i	−0.270325	−	0.962769i	$-0.587131\pi$
$131$	1.55668e6	−	1.55668e6i	0.692444	−	0.692444i	0.962769	+	0.270325i	$0.0871312\pi$
$132$	−38634.0	+	57249.9i	−0.0167976	+	0.0248916i
$133$	−31562.5	+	31562.5i	−0.0134158	+	0.0134158i
$134$	−1.32622e6	−	405626.i	−0.551188	−	0.168582i
$135$	577685.			0.234795
$136$	−1.97814e6	−	208574.i	−0.786394	−	0.0829171i
$137$			24036.2i			0.00934768i	0.999989	+	0.00467384i	$0.00148773\pi$
$137$			24036.2i			0.00934768i	−0.999989	+	0.00467384i	$0.998512\pi$
$138$	−386031.	−	118068.i	−0.146887	−	0.0449258i
$139$	−3.76939e6	−	3.76939e6i	−1.40355	−	1.40355i	−0.788460	−	0.615086i	$-0.789121\pi$
$139$	−3.76939e6	−	3.76939e6i	−1.40355	−	1.40355i	−0.615086	−	0.788460i	$-0.710879\pi$
$140$	9989.30	+	51451.3i	0.00364042	+	0.0187505i
$141$	−641445.	−	641445.i	−0.228824	−	0.228824i
$142$	803270.	+	1.51113e6i	0.280541	+	0.527762i
$143$			207404.i			0.0709267i
$144$	−923017.	+	372448.i	−0.309116	+	0.124732i
$145$	−6.59610e6			−2.16363
$146$	−2.38325e6	+	1.26686e6i	−0.765793	+	0.407071i
$147$	1.29649e6	−	1.29649e6i	0.408148	−	0.408148i
$148$	580490.	+	2.98989e6i	0.179064	+	0.922296i
$149$	2.54711e6	−	2.54711e6i	0.769998	−	0.769998i	−0.208108	−	0.978106i	$-0.566731\pi$
$149$	2.54711e6	−	2.54711e6i	0.769998	−	0.769998i	0.978106	+	0.208108i	$0.0667306\pi$
$150$	278389.	−	910208.i	0.0824855	−	0.269691i
$151$	−4.85437e6			−1.40995			−0.704973	−	0.709235i	$-0.749041\pi$
$151$	−4.85437e6			−1.40995			−0.704973	+	0.709235i	$0.749041\pi$
$152$	−3.30831e6	+	2.67720e6i	−0.942052	+	0.762341i
$153$			944048.i			0.263584i
$154$	−869.830	+	2843.96i	−0.000238162	+	0.000778684i
$155$	−5.82519e6	−	5.82519e6i	−1.56428	−	1.56428i
$156$	−1.67195e6	+	2.47758e6i	−0.440401	+	0.652611i
$157$	4.73206e6	+	4.73206e6i	1.22279	+	1.22279i	0.966637	+	0.256151i	$0.0824544\pi$
$157$	4.73206e6	+	4.73206e6i	1.22279	+	1.22279i	0.256151	+	0.966637i	$0.417546\pi$
$158$	5.05455e6	−	2.68683e6i	1.28148	−	0.681192i
$159$			596809.i			0.148472i
$160$	432786.	+	4.97848e6i	0.105661	+	1.21545i
$161$	−17382.7			−0.00416523
$162$	221728.	+	417122.i	0.0521527	+	0.0981111i
$163$	2.25527e6	−	2.25527e6i	0.520758	−	0.520758i	−0.397042	−	0.917800i	$-0.629963\pi$
$163$	2.25527e6	−	2.25527e6i	0.520758	−	0.520758i	0.917800	+	0.397042i	$0.129963\pi$
$164$	−1.54122e6	−	1.04006e6i	−0.349409	−	0.235792i
$165$	116373.	−	116373.i	0.0259060	−	0.0259060i
$166$	−3.65837e6	−	1.11892e6i	−0.799767	−	0.244610i
$167$	−5.96746e6			−1.28127			−0.640634	−	0.767846i	$-0.721329\pi$
$167$	−5.96746e6			−1.28127			−0.640634	+	0.767846i	$0.721329\pi$
$168$	−33316.7	+	26961.0i	−0.00702642	+	0.00568602i
$169$			4.14894e6i			0.859562i
$170$	4.53253e6	+	1.38628e6i	0.922559	+	0.282166i
$171$	1.42826e6	+	1.42826e6i	0.285640	+	0.285640i
$172$	2.18118e6	−	423479.i	0.428654	−	0.0832235i
$173$	6.11242e6	+	6.11242e6i	1.18052	+	1.18052i	0.979609	+	0.200916i	$0.0643917\pi$
$173$	6.11242e6	+	6.11242e6i	1.18052	+	1.18052i	0.200916	+	0.979609i	$0.435608\pi$
$174$	−2.53173e6	−	4.76277e6i	−0.480585	−	0.904091i
$175$		−	40986.0i		−	0.00764753i
$176$	−110911.	+	260968.i	−0.0203439	+	0.0478684i
$177$	−4.96744e6			−0.895804
$178$	3.72538e6	−	1.98029e6i	0.660557	−	0.351130i
$179$	−328581.	+	328581.i	−0.0572906	+	0.0572906i	−0.735172	−	0.677881i	$-0.762898\pi$
$179$	−328581.	+	328581.i	−0.0572906	+	0.0572906i	0.677881	+	0.735172i	$0.262898\pi$
$180$	2.32827e6	−	452035.i	0.399223	−	0.0775094i
$181$	1.85271e6	−	1.85271e6i	0.312444	−	0.312444i	−0.533412	−	0.845856i	$-0.679090\pi$
$181$	1.85271e6	−	1.85271e6i	0.312444	−	0.312444i	0.845856	+	0.533412i	$0.179090\pi$
$182$	−37643.3	+	123077.i	−0.00624415	+	0.0204156i
$183$	39454.9			0.00643795
$184$	−1.64822e6	−	173788.i	−0.264584	−	0.0278976i
$185$		−	7.25758e6i		−	1.14624i
$186$	1.97029e6	−	6.44197e6i	0.306190	−	1.00111i
$187$	190176.	+	190176.i	0.0290824	+	0.0290824i
$188$	−3.08717e6	−	2.08332e6i	−0.464609	−	0.313532i
$189$	14383.5	+	14383.5i	0.00213049	+	0.00213049i
$190$	8.95464e6	−	4.76000e6i	1.30553	−	0.693979i
$191$			8.50584e6i			1.22072i	0.792123	+	0.610361i	$0.208976\pi$
$191$			8.50584e6i			1.22072i	−0.792123	+	0.610361i	$0.791024\pi$
$192$	−3.42864e6	+	2.22335e6i	−0.484415	+	0.314126i
$193$	4.58702e6			0.638056			0.319028	−	0.947745i	$-0.396644\pi$
$193$	4.58702e6			0.638056			0.319028	+	0.947745i	$0.396644\pi$
$194$	5.82561e6	+	1.09593e7i	0.797877	+	1.50099i
$195$	5.03622e6	−	5.03622e6i	0.679205	−	0.679205i
$196$	4.21081e6	−	6.23981e6i	0.559239	−	0.828711i
$197$	5.84236e6	−	5.84236e6i	0.764169	−	0.764169i	−0.212904	−	0.977073i	$-0.568292\pi$
$197$	5.84236e6	−	5.84236e6i	0.764169	−	0.764169i	0.977073	+	0.212904i	$0.0682922\pi$
$198$	128695.	+	39361.5i	0.0165792	+	0.00507079i
$199$	2.72449e6			0.345721			0.172861	−	0.984946i	$-0.444699\pi$
$199$	2.72449e6			0.345721			0.172861	+	0.984946i	$0.444699\pi$
$200$	409769.	−	3.88629e6i	0.0512211	−	0.485786i
$201$			2.70238e6i			0.332780i
$202$	−1.25824e7	−	3.84834e6i	−1.52654	−	0.466896i
$203$	−164233.	−	164233.i	−0.0196324	−	0.0196324i
$204$	738712.	+	3.80484e6i	0.0870131	+	0.448173i
$205$	3.13287e6	+	3.13287e6i	0.363648	+	0.363648i
$206$	−4.59452e6	−	8.64334e6i	−0.525580	−	0.988735i
$207$			786599.i			0.0886834i
$208$	−4.79983e6	+	1.12938e7i	−0.533379	+	1.25502i
$209$	575439.			0.0630319
$210$	90178.8	−	47936.1i	0.00973748	−	0.00517613i
$211$	4.15605e6	−	4.15605e6i	0.442419	−	0.442419i	−0.450405	−	0.892824i	$-0.648720\pi$
$211$	4.15605e6	−	4.15605e6i	0.442419	−	0.442419i	0.892824	+	0.450405i	$0.148720\pi$
$212$	466999.	+	2.40534e6i	0.0490127	+	0.252447i
$213$	2.35798e6	−	2.35798e6i	0.244007	−	0.244007i
$214$	1.39629e6	−	4.56525e6i	0.142474	−	0.465826i
$215$	−5.29454e6			−0.532737
$216$	1.22004e6	+	1.50764e6i	0.121063	+	0.149602i
$217$		−	290077.i		−	0.0283880i
$218$	−3.19731e6	+	1.04538e7i	−0.308613	+	1.00903i
$219$	3.71884e6	+	3.71884e6i	0.354059	+	0.354059i
$220$	377962.	−	560084.i	0.0354960	−	0.0525999i
$221$	8.23016e6	+	8.23016e6i	0.762485	+	0.762485i
$222$	5.24039e6	−	2.78562e6i	0.478966	−	0.254603i
$223$			2.24265e6i			0.202230i	0.994875	+	0.101115i	$0.0322411\pi$
$223$			2.24265e6i			0.202230i	−0.994875	+	0.101115i	$0.967759\pi$
$224$	−113181.	+	134732.i	−0.0100700	+	0.0119875i
$225$	−1.85469e6			−0.162826
$226$	−5.03789e6	−	9.47743e6i	−0.436439	−	0.821042i
$227$	−1.51072e7	+	1.51072e7i	−1.29154	+	1.29154i	−0.357700	+	0.933837i	$0.616439\pi$
$227$	−1.51072e7	+	1.51072e7i	−1.29154	+	1.29154i	−0.933837	+	0.357700i	$0.883561\pi$
$228$	6.87399e6	+	4.63878e6i	0.579969	+	0.391380i
$229$	4.67653e6	−	4.67653e6i	0.389419	−	0.389419i	−0.485061	−	0.874480i	$-0.661203\pi$
$229$	4.67653e6	−	4.67653e6i	0.389419	−	0.389419i	0.874480	+	0.485061i	$0.161203\pi$
$230$	3.77659e6	+	1.15508e6i	0.310396	+	0.0949352i
$231$	5795.02			0.000470131
$232$	−1.39306e7	−	1.72145e7i	−1.11559	−	1.37858i
$233$			1.98032e7i			1.56555i	0.622304	+	0.782776i	$0.286197\pi$
$233$			1.98032e7i			1.56555i	−0.622304	+	0.782776i	$0.713803\pi$
$234$	5.56946e6	+	1.70343e6i	0.434676	+	0.132946i
$235$	6.27535e6	+	6.27535e6i	0.483542	+	0.483542i
$236$	−2.00205e7	+	3.88700e6i	−1.52314	+	0.295718i
$237$	−7.88715e6	−	7.88715e6i	−0.592482	−	0.592482i
$238$	78336.9	+	147370.i	0.00581079	+	0.0109314i
$239$			3.78826e6i			0.277489i	0.990328	+	0.138745i	$0.0443067\pi$
$239$			3.78826e6i			0.277489i	−0.990328	+	0.138745i	$0.955693\pi$
$240$	9.03000e6	−	3.64371e6i	0.653212	−	0.263579i
$241$	−1.52426e7			−1.08895			−0.544475	−	0.838777i	$-0.683271\pi$
$241$	−1.52426e7			−1.08895			−0.544475	+	0.838777i	$0.683271\pi$
$242$	−1.24804e7	+	6.63420e6i	−0.880611	+	0.468104i
$243$	650880.	−	650880.i	0.0453609	−	0.0453609i
$244$	159017.	−	30873.2i	0.0109465	−	0.00212526i
$245$	−1.26838e7	+	1.26838e7i	−0.862482	+	0.862482i
$246$	−1.05965e6	+	3.46458e6i	−0.0711797	+	0.232726i
$247$	2.49030e7			1.65257
$248$	2.90013e6	−	2.75051e7i	0.190135	−	1.80326i
$249$			7.45451e6i			0.482860i
$250$	2.85199e6	−	9.32474e6i	0.182527	−	0.596783i
$251$	−1.55084e7	−	1.55084e7i	−0.980720	−	0.980720i	0.0190975	−	0.999818i	$-0.493921\pi$
$251$	−1.55084e7	−	1.55084e7i	−0.980720	−	0.980720i	−0.999818	+	0.0190975i	$0.993921\pi$
$252$	69225.4	+	46715.4i	0.00432577	+	0.00291916i
$253$	158458.	+	158458.i	0.00978483	+	0.00978483i
$254$	3.62374e6	−	1.92626e6i	0.221134	−	0.117548i
$255$		−	9.23575e6i		−	0.556996i
$256$	−1.20788e7	+	1.16438e7i	−0.719954	+	0.694022i
$257$	2.30378e7			1.35720			0.678598	−	0.734510i	$-0.262588\pi$
$257$	2.30378e7			1.35720			0.678598	+	0.734510i	$0.262588\pi$
$258$	−2.03217e6	−	3.82297e6i	−0.118331	−	0.222608i
$259$	180703.	−	180703.i	0.0104008	−	0.0104008i
$260$	1.63569e7	−	2.42385e7i	0.930638	−	1.37907i
$261$	−7.43186e6	+	7.43186e6i	−0.418000	+	0.418000i
$262$	−1.68417e7	−	5.15105e6i	−0.936443	−	0.286413i
$263$	−1.14678e7			−0.630395			−0.315198	−	0.949026i	$-0.602071\pi$
$263$	−1.14678e7			−0.630395			−0.315198	+	0.949026i	$0.602071\pi$
$264$	549484.	+	57937.4i	0.0298637	+	0.00314882i
$265$		−	5.83866e6i		−	0.313744i
$266$	341474.	+	104440.i	0.0181432	+	0.00554911i
$267$	−5.81310e6	−	5.81310e6i	−0.305403	−	0.305403i
$268$	2.11460e6	+	1.08915e7i	0.109856	+	0.565827i
$269$	−1.81452e7	−	1.81452e7i	−0.932191	−	0.932191i	0.0656520	−	0.997843i	$-0.479087\pi$
$269$	−1.81452e7	−	1.81452e7i	−0.932191	−	0.932191i	−0.997843	+	0.0656520i	$0.979087\pi$
$270$	−2.16920e6	−	4.08076e6i	−0.110207	−	0.207324i
$271$		−	1.68065e7i		−	0.844441i	−0.906493	−	0.422221i	$-0.861251\pi$
$271$		−	1.68065e7i		−	0.844441i	0.906493	−	0.422221i	$-0.138749\pi$
$272$	5.95453e6	+	1.47568e7i	0.295897	+	0.733305i
$273$	250789.			0.0123259
$274$	169791.	−	90255.6i	0.00825399	−	0.00438756i
$275$	−373623.	+	373623.i	−0.0179653	+	0.0179653i
$276$	615509.	+	3.17026e6i	0.0292757	+	0.150789i
$277$	−1.32183e7	+	1.32183e7i	−0.621922	+	0.621922i	−0.946022	−	0.324101i	$-0.894938\pi$
$277$	−1.32183e7	+	1.32183e7i	−0.621922	+	0.621922i	0.324101	+	0.946022i	$0.394938\pi$
$278$	−1.24729e7	+	4.07810e7i	−0.580543	+	1.89812i
$279$	−1.31265e7			−0.604418
$280$	325942.	−	263763.i	0.0148479	−	0.0120155i
$281$		−	3.78604e7i		−	1.70634i	−0.521632	−	0.853170i	$-0.674677\pi$
$281$		−	3.78604e7i		−	1.70634i	0.521632	−	0.853170i	$-0.325323\pi$
$282$	−2.12255e6	+	6.93979e6i	−0.0946476	+	0.309456i
$283$	2.50461e7	+	2.50461e7i	1.10505	+	1.10505i	0.993792	+	0.111254i	$0.0354866\pi$
$283$	2.50461e7	+	2.50461e7i	1.10505	+	1.10505i	0.111254	+	0.993792i	$0.464513\pi$
$284$	7.65838e6	−	1.13486e7i	0.334335	−	0.495436i
$285$	−1.39729e7	−	1.39729e7i	−0.603603	−	0.603603i
$286$	1.46510e6	−	778802.i	0.0626283	−	0.0332912i
$287$			156008.i			0.00659933i
$288$	6.09689e6	+	5.12165e6i	0.255230	+	0.214404i
$289$	−9.04457e6			−0.374709
$290$	2.47683e7	+	4.65948e7i	1.01555	+	1.91049i
$291$	1.71010e7	−	1.71010e7i	0.693971	−	0.693971i
$292$	1.78982e7	+	1.20782e7i	0.718886	+	0.485126i
$293$	2.24773e7	−	2.24773e7i	0.893596	−	0.893596i	−0.101263	−	0.994860i	$-0.532289\pi$
$293$	2.24773e7	−	2.24773e7i	0.893596	−	0.893596i	0.994860	+	0.101263i	$0.0322885\pi$
$294$	−1.40267e7	−	4.29010e6i	−0.551969	−	0.168821i
$295$	4.85972e7			1.89298
$296$	1.89408e7	−	1.53276e7i	0.730339	−	0.591015i
$297$		−	262236.i		−	0.0100097i
$298$	−2.75572e7	−	8.42841e6i	−1.04132	−	0.318491i
$299$	6.85753e6	+	6.85753e6i	0.256539	+	0.256539i
$300$	−7.47505e6	+	1.45129e6i	−0.276854	+	0.0537514i
$301$	−131826.	−	131826.i	−0.00483395	−	0.00483395i
$302$	1.82281e7	+	3.42913e7i	0.661791	+	1.24498i
$303$			2.56386e7i			0.921651i
$304$	3.13344e7	+	1.33170e7i	1.11532	+	0.474008i
$305$	−385993.			−0.0136044
$306$	6.66875e6	−	3.54489e6i	0.232745	−	0.123720i
$307$	−2.44973e7	+	2.44973e7i	−0.846650	+	0.846650i	−0.989714	−	0.143063i	$-0.954305\pi$
$307$	−2.44973e7	+	2.44973e7i	−0.846650	+	0.846650i	0.143063	+	0.989714i	$0.454305\pi$
$308$	23355.9	−	4534.57i	0.000799365	−	0.000155197i
$309$	−1.34871e7	+	1.34871e7i	−0.457134	+	0.457134i
$310$	−1.92756e7	+	6.30227e7i	−0.647027	+	2.11549i
$311$	−2.12390e7			−0.706078			−0.353039	−	0.935609i	$-0.614852\pi$
$311$	−2.12390e7			−0.706078			−0.353039	+	0.935609i	$0.614852\pi$
$312$	2.37798e7	+	2.50733e6i	0.782968	+	0.0825559i
$313$		−	3.85664e7i		−	1.25770i	−0.777527	−	0.628849i	$-0.783526\pi$
$313$		−	3.85664e7i		−	1.25770i	0.777527	−	0.628849i	$-0.216474\pi$
$314$	1.56584e7	−	5.11961e7i	0.505776	−	1.65367i
$315$	−140716.	−	140716.i	−0.00450205	−	0.00450205i
$316$	−3.79596e7	−	2.56163e7i	−1.20298	−	0.811811i
$317$	−2.55878e7	−	2.55878e7i	−0.803257	−	0.803257i	0.180346	−	0.983603i	$-0.442278\pi$
$317$	−2.55878e7	−	2.55878e7i	−0.803257	−	0.803257i	−0.983603	+	0.180346i	$0.942278\pi$
$318$	4.21585e6	−	2.24101e6i	0.131100	−	0.0696888i
$319$			2.99425e6i			0.0922394i
$320$	3.35428e7	−	2.17513e7i	1.02365	−	0.663798i
$321$	−9.30243e6			−0.281243
$322$	65271.8	+	122791.i	0.00195505	+	0.00367790i
$323$	2.28344e7	−	2.28344e7i	0.677613	−	0.677613i
$324$	2.11396e6	−	3.13258e6i	0.0621529	−	0.0921015i
$325$	−1.61691e7	+	1.61691e7i	−0.471017	+	0.471017i
$326$	−2.43998e7	−	7.46270e6i	−0.704259	−	0.215399i
$327$	2.13012e7			0.609203
$328$	−1.55973e6	+	1.47926e7i	−0.0442006	+	0.419202i
$329$			312493.i			0.00877512i
$330$	−1.25904e6	−	385079.i	−0.0350346	−	0.0107154i
$331$	4.02071e6	+	4.02071e6i	0.110871	+	0.110871i	0.760366	−	0.649495i	$-0.225020\pi$
$331$	4.02071e6	+	4.02071e6i	0.110871	+	0.110871i	−0.649495	+	0.760366i	$0.725020\pi$
$332$	5.83311e6	+	3.00442e7i	0.159399	+	0.821007i
$333$	−8.17714e6	−	8.17714e6i	−0.221446	−	0.221446i
$334$	2.24078e7	+	4.21541e7i	0.601394	+	1.13136i
$335$		−	2.64377e7i		−	0.703218i
$336$	315556.	+	134111.i	0.00831877	+	0.00353545i
$337$	1.58536e7			0.414226			0.207113	−	0.978317i	$-0.433593\pi$
$337$	1.58536e7			0.414226			0.207113	+	0.978317i	$0.433593\pi$
$338$	2.93081e7	−	1.55792e7i	0.758993	−	0.403456i
$339$	−1.47886e7	+	1.47886e7i	−0.379603	+	0.379603i
$340$	−7.22692e6	−	3.72233e7i	−0.183872	−	0.947060i
$341$	−2.64431e6	+	2.64431e6i	−0.0666881	+	0.0666881i
$342$	4.72612e6	−	1.54523e7i	0.118148	−	0.386292i
$343$	−1.26338e6			−0.0313078
$344$	−1.11818e7	−	1.38177e7i	−0.274685	−	0.339438i
$345$		−	7.69541e6i		−	0.187402i
$346$	2.02260e7	−	6.61302e7i	0.488295	−	1.59651i
$347$	3.19130e7	+	3.19130e7i	0.763798	+	0.763798i	0.977007	−	0.213208i	$-0.0683913\pi$
$347$	3.19130e7	+	3.19130e7i	0.763798	+	0.763798i	−0.213208	+	0.977007i	$0.568391\pi$
$348$	−2.41376e7	+	3.57683e7i	−0.572737	+	0.848713i
$349$	2.14408e7	+	2.14408e7i	0.504388	+	0.504388i	0.912798	−	0.408411i	$-0.133917\pi$
$349$	2.14408e7	+	2.14408e7i	0.504388	+	0.504388i	−0.408411	+	0.912798i	$0.633917\pi$
$350$	−289525.	+	153902.i	−0.00675277	+	0.00358955i
$351$		−	1.13487e7i		−	0.262436i
$352$	2.25994e6	−	196460.i	0.0518167	−	0.00450450i
$353$	4.67083e7			1.06187			0.530933	−	0.847414i	$-0.321841\pi$
$353$	4.67083e7			1.06187			0.530933	+	0.847414i	$0.321841\pi$
$354$	1.86527e7	+	3.50900e7i	0.420467	+	0.790995i
$355$	−2.30685e7	+	2.30685e7i	−0.515625	+	0.515625i
$356$	−2.79775e7	−	1.88801e7i	−0.620096	−	0.418460i
$357$	229956.	−	229956.i	0.00505406	−	0.00505406i
$358$	3.55491e6	+	1.08728e6i	0.0774783	+	0.0236969i
$359$	−2.17927e7			−0.471006			−0.235503	−	0.971874i	$-0.575674\pi$
$359$	−2.17927e7			−0.471006			−0.235503	+	0.971874i	$0.575674\pi$
$360$	−1.19358e7	−	1.47495e7i	−0.255826	−	0.316133i
$361$		−	2.20470e7i		−	0.468627i
$362$	−2.00445e7	−	6.13063e6i	−0.422541	−	0.129235i
$363$	1.94746e7	+	1.94746e7i	0.407144	+	0.407144i
$364$	1.01076e6	−	196241.i	0.0209578	−	0.00406898i
$365$	−3.63819e7	−	3.63819e7i	−0.748182	−	0.748182i
$366$	−148153.	−	278709.i	−0.00302181	−	0.00568471i
$367$		−	8.36110e7i		−	1.69147i	−0.533600	−	0.845737i	$-0.679161\pi$
$367$		−	8.36110e7i		−	1.69147i	0.533600	−	0.845737i	$-0.320839\pi$
$368$	4.96143e6	+	1.22956e7i	0.0995551	+	0.246722i
$369$	7.05964e6			0.140509
$370$	−5.12675e7	+	2.72521e7i	−1.01213	+	0.538016i
$371$	145374.	−	145374.i	0.00284685	−	0.00284685i
$372$	−5.29045e7	+	1.02714e7i	−1.02769	+	0.199527i
$373$	−3.88117e7	+	3.88117e7i	−0.747887	+	0.747887i	−0.974082	−	0.226195i	$-0.927371\pi$
$373$	−3.88117e7	+	3.88117e7i	−0.747887	+	0.747887i	0.226195	+	0.974082i	$0.427371\pi$
$374$	629293.	−	2.05751e6i	0.0120292	−	0.0393303i
$375$	−1.90006e7			−0.360308
$376$	−3.12424e6	+	2.96306e7i	−0.0587734	+	0.557413i
$377$			1.29581e8i			2.41834i
$378$	47595.0	−	155615.i	0.000881223	−	0.00288121i
$379$	−5.20448e7	−	5.20448e7i	−0.956004	−	0.956004i	0.0430678	−	0.999072i	$-0.486287\pi$
$379$	−5.20448e7	−	5.20448e7i	−0.956004	−	0.956004i	−0.999072	+	0.0430678i	$0.986287\pi$
$380$	−6.72492e7	−	4.53818e7i	−1.22557	−	0.827049i
$381$	−5.65451e6	−	5.65451e6i	−0.102240	−	0.102240i
$382$	6.00852e7	−	3.19393e7i	1.07790	−	0.572975i
$383$			1.32415e7i			0.235691i	0.993032	+	0.117845i	$0.0375987\pi$
$383$			1.32415e7i			0.235691i	−0.993032	+	0.117845i	$0.962401\pi$
$384$	2.85802e7	+	1.58712e7i	0.504745	+	0.280296i
$385$	−56693.5			−0.000993462
$386$	−1.72242e7	−	3.24027e7i	−0.299487	−	0.563403i
$387$	−5.96538e6	+	5.96538e6i	−0.102921	+	0.102921i
$388$	5.55413e7	−	8.23041e7i	0.950870	−	1.40905i
$389$	−2.91185e6	+	2.91185e6i	−0.0494675	+	0.0494675i	−0.731408	−	0.681940i	$-0.761136\pi$
$389$	−2.91185e6	+	2.91185e6i	−0.0494675	+	0.0494675i	0.681940	+	0.731408i	$0.261136\pi$
$390$	−5.44868e7	−	1.66649e7i	−0.918539	−	0.280937i
$391$	1.25758e7			0.210380
$392$	−5.98895e7	−	6.31473e6i	−0.994243	−	0.104833i
$393$			3.43176e7i			0.565378i
$394$	−6.32084e7	−	1.93324e7i	−1.03344	−	0.316080i
$395$	7.71611e7	+	7.71611e7i	1.25201	+	1.25201i
$396$	−205198.	−	1.05690e6i	−0.00330436	−	0.0170196i
$397$	1.15219e7	+	1.15219e7i	0.184142	+	0.184142i	0.793158	−	0.609016i	$-0.208435\pi$
$397$	1.15219e7	+	1.15219e7i	0.184142	+	0.184142i	−0.609016	+	0.793158i	$0.708435\pi$
$398$	−1.02304e7	−	1.92458e7i	−0.162273	−	0.305272i
$399$		−	695808.i		−	0.0109539i
$400$	−2.89914e7	+	1.16984e7i	−0.452991	+	0.182787i
$401$	7.10441e7			1.10178			0.550890	−	0.834578i	$-0.314288\pi$
$401$	7.10441e7			1.10178			0.550890	+	0.834578i	$0.314288\pi$
$402$	1.90896e7	−	1.01474e7i	0.293845	−	0.156198i
$403$	−1.14436e8	+	1.14436e8i	−1.74843	+	1.74843i
$404$	2.00621e7	+	1.03332e8i	0.304251	+	1.56708i
$405$	−6.36765e6	+	6.36765e6i	−0.0958548	+	0.0958548i
$406$	−543448.	+	1.77684e6i	−0.00812045	+	0.0265503i
$407$	−3.29452e6			−0.0488663
$408$	2.41035e7	−	1.95054e7i	0.354895	−	0.287193i
$409$			1.89990e7i			0.277691i	0.990314	+	0.138845i	$0.0443391\pi$
$409$			1.89990e7i			0.277691i	−0.990314	+	0.138845i	$0.955661\pi$
$410$	1.03667e7	−	3.38945e7i	0.150414	−	0.491788i
$411$	−264944.	−	264944.i	−0.00381617	−	0.00381617i
$412$	−4.38042e7	+	6.49113e7i	−0.626359	+	0.928173i
$413$	1.21000e6	+	1.21000e6i	0.0171765	+	0.0171765i
$414$	5.55653e6	−	2.95367e6i	0.0783074	−	0.0416257i
$415$		−	7.29285e7i		−	1.02036i
$416$	9.78026e7	−	8.50213e6i	1.35853	−	0.118099i
$417$	8.30977e7			1.14599
$418$	−2.16077e6	−	4.06490e6i	−0.0295855	−	0.0556571i
$419$	−3.56420e7	+	3.56420e7i	−0.484529	+	0.484529i	−0.906575	−	0.422045i	$-0.861312\pi$
$419$	−3.56420e7	+	3.56420e7i	−0.484529	+	0.484529i	0.422045	+	0.906575i	$0.361312\pi$
$420$	−677241.	−	457023.i	−0.00914104	−	0.00616865i
$421$	4.15849e7	−	4.15849e7i	0.557301	−	0.557301i	−0.371237	−	0.928538i	$-0.621066\pi$
$421$	4.15849e7	−	4.15849e7i	0.557301	−	0.557301i	0.928538	+	0.371237i	$0.121066\pi$
$422$	−4.49643e7	−	1.37524e7i	−0.598316	−	0.182996i
$423$	1.41409e7			0.186834
$424$	1.52378e7	−	1.23309e7i	0.199905	−	0.161770i
$425$			2.96520e7i			0.386266i
$426$	−2.55110e7	−	7.80258e6i	−0.329988	−	0.100927i
$427$	−9610.64	−	9610.64i	−0.000123444	−	0.000123444i
$428$	−3.74920e7	+	7.27910e6i	−0.478197	+	0.0928424i
$429$	−2.28616e6	−	2.28616e6i	−0.0289557	−	0.0289557i
$430$	1.98810e7	+	3.74006e7i	0.250053	+	0.470407i
$431$		−	6.32371e7i		−	0.789842i	−0.918715	−	0.394921i	$-0.870772\pi$
$431$		−	6.32371e7i		−	0.789842i	0.918715	−	0.394921i	$-0.129228\pi$
$432$	6.06876e6	−	1.42795e7i	0.0752746	−	0.177118i
$433$	4.88658e6			0.0601924			0.0300962	−	0.999547i	$-0.490419\pi$
$433$	4.88658e6			0.0601924			0.0300962	+	0.999547i	$0.490419\pi$
$434$	−2.04910e6	+	1.08924e6i	−0.0250666	+	0.0133246i
$435$	7.27069e7	−	7.27069e7i	0.883299	−	0.883299i
$436$	8.58513e7	−	1.66681e7i	1.03583	−	0.201107i
$437$	1.90261e7	−	1.90261e7i	0.227984	−	0.227984i
$438$	1.23057e7	−	4.02341e7i	0.146448	−	0.478819i
$439$	1.89631e7			0.224138			0.112069	−	0.993700i	$-0.464252\pi$
$439$	1.89631e7			0.224138			0.112069	+	0.993700i	$0.464252\pi$
$440$	−5.37568e6	−	566810.i	−0.0631066	−	0.00665394i
$441$			2.85817e7i			0.333252i
$442$	2.72336e7	−	8.90420e7i	0.315383	−	1.03116i
$443$	−7.56690e7	−	7.56690e7i	−0.870376	−	0.870376i	0.122137	−	0.992513i	$-0.461025\pi$
$443$	−7.56690e7	−	7.56690e7i	−0.870376	−	0.870376i	−0.992513	+	0.122137i	$0.961025\pi$
$444$	−3.93553e7	−	2.65581e7i	−0.449628	−	0.303423i
$445$	5.68704e7	+	5.68704e7i	0.645366	+	0.645366i
$446$	1.58420e7	−	8.42112e6i	0.178569	−	0.0949216i
$447$			5.61522e7i			0.628701i
$448$	1.37674e6	+	293590.i	0.0153115	+	0.00326519i
$449$	−3.34359e7			−0.369381			−0.184690	−	0.982797i	$-0.559128\pi$
$449$	−3.34359e7			−0.369381			−0.184690	+	0.982797i	$0.559128\pi$
$450$	6.96436e6	+	1.31015e7i	0.0764264	+	0.143776i
$451$	1.42214e6	−	1.42214e6i	0.0155029	−	0.0155029i
$452$	−4.80313e7	+	7.11753e7i	−0.520126	+	0.770751i
$453$	5.35083e7	−	5.35083e7i	0.575608	−	0.575608i
$454$	1.63445e8	+	4.99898e7i	1.74664	+	0.534213i
$455$	−2.45350e6			−0.0260467
$456$	6.95653e6	−	6.59764e7i	0.0733666	−	0.695816i
$457$		−	5.54209e7i		−	0.580664i	−0.956926	−	0.290332i	$-0.906234\pi$
$457$		−	5.54209e7i		−	0.580664i	0.956926	−	0.290332i	$-0.0937657\pi$
$458$	−5.05953e7	−	1.54746e7i	−0.526640	−	0.161074i
$459$	−1.04060e7	−	1.04060e7i	−0.107608	−	0.107608i
$460$	−6.02161e6	−	3.10151e7i	−0.0618642	−	0.318640i
$461$	2.76199e7	+	2.76199e7i	0.281916	+	0.281916i	0.833873	−	0.551957i	$-0.186119\pi$
$461$	2.76199e7	+	2.76199e7i	0.281916	+	0.281916i	−0.551957	+	0.833873i	$0.686119\pi$
$462$	−21760.3	−	40936.0i	−0.000220667	−	0.000415126i
$463$		−	6.48037e7i		−	0.652915i	−0.945212	−	0.326457i	$-0.894145\pi$
$463$		−	6.48037e7i		−	0.652915i	0.945212	−	0.326457i	$-0.105855\pi$
$464$	−6.92941e7	+	1.63046e8i	−0.693653	+	1.63214i
$465$	1.28419e8			1.27723
$466$	1.39890e8	−	7.43608e7i	1.38238	−	0.734829i
$467$	1.01369e8	−	1.01369e8i	0.995297	−	0.995297i	−0.00469233	−	0.999989i	$-0.501494\pi$
$467$	1.01369e8	−	1.01369e8i	0.995297	−	0.995297i	0.999989	+	0.00469233i	$0.00149362\pi$
$468$	−8.88027e6	−	4.57390e7i	−0.0866340	−	0.446220i
$469$	658260.	−	658260.i	0.00638085	−	0.00638085i
$470$	2.07652e7	−	6.78929e7i	0.200005	−	0.653929i
$471$	−1.04320e8			−0.998402
$472$	1.02635e8	+	1.26829e8i	0.976040	+	1.20613i
$473$			2.40342e6i			0.0227115i
$474$	−2.60986e7	+	8.53310e7i	−0.245066	+	0.801257i
$475$	4.48608e7	+	4.48608e7i	0.418588	+	0.418588i
$476$	746864.	−	1.10674e6i	0.00692501	−	0.0102619i
$477$	−6.57845e6	−	6.57845e6i	−0.0606133	−	0.0606133i
$478$	2.67603e7	−	1.42249e7i	0.245023	−	0.130246i
$479$			5.97214e7i			0.543404i	0.962381	+	0.271702i	$0.0875866\pi$
$479$			5.97214e7i			0.543404i	−0.962381	+	0.271702i	$0.912413\pi$
$480$	−5.96467e7	−	5.01058e7i	−0.539341	−	0.453069i
$481$	−1.42576e8			−1.28118
$482$	5.72358e7	+	1.07674e8i	0.511124	+	0.961542i
$483$	191604.	−	191604.i	0.00170045	−	0.00170045i
$484$	9.37279e7	+	6.32505e7i	0.826671	+	0.557863i
$485$	−1.67301e8	+	1.67301e8i	−1.46647	+	1.46647i
$486$	−7.04186e6	−	2.15376e6i	−0.0613449	−	0.0187624i
$487$	−8.93709e7			−0.773765			−0.386882	−	0.922129i	$-0.626448\pi$
$487$	−8.93709e7			−0.773765			−0.386882	+	0.922129i	$0.626448\pi$
$488$	−815195.	−	1.00737e6i	−0.00701459	−	0.00866818i
$489$			4.97184e7i			0.425197i
$490$	1.37225e8	+	4.19706e7i	1.16640	+	0.356745i
$491$	−5.33343e7	−	5.33343e7i	−0.450570	−	0.450570i	0.444974	−	0.895544i	$-0.353213\pi$
$491$	−5.33343e7	−	5.33343e7i	−0.450570	−	0.450570i	−0.895544	+	0.444974i	$0.853213\pi$
$492$	2.84528e7	−	5.52413e6i	0.238907	−	0.0463840i
$493$	1.18817e8	+	1.18817e8i	0.991604	+	0.991604i
$494$	−9.35106e7	−	1.75915e8i	−0.775675	−	1.45922i
$495$			2.56549e6i			0.0211522i
$496$	−2.05186e8	+	8.27949e7i	−1.68152	+	0.678514i
$497$	−1.14874e6			−0.00935736
$498$	5.26586e7	−	2.79916e7i	0.426365	−	0.226642i
$499$	−1.13240e8	+	1.13240e8i	−0.911379	+	0.911379i	−0.996381	−	0.0850014i	$-0.972911\pi$
$499$	−1.13240e8	+	1.13240e8i	−0.911379	+	0.911379i	0.0850014	+	0.996381i	$0.472911\pi$
$500$	−7.65791e7	+	1.48679e7i	−0.612633	+	0.118943i
$501$	6.57776e7	−	6.57776e7i	0.523076	−	0.523076i
$502$	−5.13173e7	+	1.67785e8i	−0.405651	+	1.32630i
$503$	−4.14356e7			−0.325589			−0.162794	−	0.986660i	$-0.552051\pi$
$503$	−4.14356e7			−0.325589			−0.162794	+	0.986660i	$0.552051\pi$
$504$	70056.6	−	664423.i	0.000547214	−	0.00518983i
$505$		−	2.50826e8i		−	1.94760i
$506$	524339.	−	1.71436e6i	0.00404726	−	0.0132327i
$507$	−4.57326e7	−	4.57326e7i	−0.350915	−	0.350915i
$508$	−2.72142e7	−	1.83650e7i	−0.207589	−	0.140088i
$509$	−7.15789e7	−	7.15789e7i	−0.542790	−	0.542790i	0.381556	−	0.924346i	$-0.375388\pi$
$509$	−7.15789e7	−	7.15789e7i	−0.542790	−	0.542790i	−0.924346	+	0.381556i	$0.875388\pi$
$510$	−6.52413e7	+	3.46802e7i	−0.491827	+	0.261439i
$511$		−	1.81171e6i		−	0.0135777i
$512$	1.27607e8	+	4.16026e7i	0.950748	+	0.309963i
$513$	−3.14866e7			−0.233224
$514$	−8.65069e7	−	1.62739e8i	−0.637032	−	1.19840i
$515$	1.31946e8	−	1.31946e8i	0.965997	−	0.965997i
$516$	−1.93747e7	+	2.87104e7i	−0.141021	+	0.208973i
$517$	2.84865e6	−	2.84865e6i	0.0206142	−	0.0206142i
$518$	−1.95502e6	−	597946.i	−0.0140657	−	0.00430202i
$519$	−1.34751e8			−0.963894
$520$	−2.32641e8	−	2.45296e7i	−1.65453	−	0.174454i
$521$		−	7.24342e7i		−	0.512189i	−0.966652	−	0.256095i	$-0.917564\pi$
$521$		−	7.24342e7i		−	0.512189i	0.966652	−	0.256095i	$-0.0824358\pi$
$522$	8.04052e7	+	2.45921e7i	0.565292	+	0.172895i
$523$	−1.89689e8	−	1.89689e8i	−1.32598	−	1.32598i	−0.908845	−	0.417135i	$-0.863034\pi$
$523$	−1.89689e8	−	1.89689e8i	−1.32598	−	1.32598i	−0.417135	−	0.908845i	$-0.636966\pi$
$524$	2.68533e7	+	1.38312e8i	0.186640	+	0.961313i
$525$	451776.	+	451776.i	0.00312209	+	0.00312209i
$526$	4.30615e7	+	8.10085e7i	0.295891	+	0.556639i
$527$			2.09861e8i			1.43384i
$528$	−1.65404e6	−	4.09911e6i	−0.0112368	−	0.0278476i
$529$	−1.37558e8			−0.929217
$530$	−4.12443e7	+	2.19241e7i	−0.277036	+	0.147263i
$531$	5.47547e7	−	5.47547e7i	0.365711	−	0.365711i
$532$	−544466.	−	2.80434e6i	−0.00361606	−	0.0186250i
$533$	6.15455e7	−	6.15455e7i	0.406457	−	0.406457i
$534$	−1.92356e7	+	6.28918e7i	−0.126323	+	0.413019i
$535$	9.10069e7			0.594310
$536$	6.89973e7	−	5.58350e7i	0.448062	−	0.362587i
$537$		−	7.24370e6i		−	0.0467776i
$538$	−6.00425e7	+	1.96313e8i	−0.385578	+	1.26067i
$539$	5.75770e6	+	5.75770e6i	0.0367691	+	0.0367691i
$540$	−2.06812e7	+	3.06464e7i	−0.131339	+	0.194625i
$541$	−1.36734e8	−	1.36734e8i	−0.863545	−	0.863545i	0.128203	−	0.991748i	$-0.459079\pi$
$541$	−1.36734e8	−	1.36734e8i	−0.863545	−	0.863545i	−0.991748	+	0.128203i	$0.959079\pi$
$542$	−1.18721e8	+	6.31083e7i	−0.745641	+	0.396359i
$543$			4.08438e7i			0.255110i
$544$	8.18825e7	−	9.74743e7i	0.508621	−	0.605471i
$545$	−2.08393e8			−1.28734
$546$	−941710.	−	1.77157e6i	−0.00578548	−	0.0108838i
$547$	5.12718e7	−	5.12718e7i	0.313269	−	0.313269i	−0.532906	−	0.846175i	$-0.678900\pi$
$547$	5.12718e7	−	5.12718e7i	0.313269	−	0.313269i	0.846175	+	0.532906i	$0.178900\pi$
$548$	−1.27513e6	−	860497.i	−0.00774842	−	0.00522887i
$549$	−434900.	+	434900.i	−0.00262828	+	0.00262828i
$550$	4.04222e6	+	1.23632e6i	0.0242958	+	0.00743092i
$551$	3.59520e8			2.14916
$552$	2.00835e7	−	1.62523e7i	0.119405	−	0.0966266i
$553$			3.84239e6i			0.0227209i
$554$	1.43008e8	+	4.37393e7i	0.841070	+	0.257243i
$555$	7.99981e7	+	7.99981e7i	0.467951	+	0.467951i
$556$	3.34912e8	−	6.50235e7i	1.94853	−	0.378308i
$557$	5.82264e7	+	5.82264e7i	0.336941	+	0.336941i	0.855215	−	0.518274i	$-0.173425\pi$
$557$	5.82264e7	+	5.82264e7i	0.336941	+	0.336941i	−0.518274	+	0.855215i	$0.673425\pi$
$558$	4.92901e7	+	9.27258e7i	0.283698	+	0.533701i
$559$			1.04012e8i			0.595452i
$560$	−3.08713e6	−	1.31202e6i	−0.0175789	−	0.00747097i
$561$	−4.19250e6			−0.0237457
$562$	−2.67445e8	+	1.42165e8i	−1.50670	+	0.800912i
$563$	8.25505e6	−	8.25505e6i	0.0462588	−	0.0462588i	−0.683599	−	0.729858i	$-0.739586\pi$
$563$	8.25505e6	−	8.25505e6i	0.0462588	−	0.0462588i	0.729858	+	0.683599i	$0.239586\pi$
$564$	5.69928e7	−	1.10652e7i	0.317675	−	0.0616768i
$565$	1.44679e8	−	1.44679e8i	0.802160	−	0.802160i
$566$	8.28776e7	−	2.70973e8i	0.457075	−	1.49443i
$567$	−317090.			−0.00173953
$568$	−1.08924e8	−	1.14849e7i	−0.594397	−	0.0626731i
$569$		−	8.93722e7i		−	0.485138i	−0.970134	−	0.242569i	$-0.922010\pi$
$569$		−	8.93722e7i		−	0.485138i	0.970134	−	0.242569i	$-0.0779902\pi$
$570$	−4.62363e7	+	1.51172e8i	−0.249666	+	0.816297i
$571$	−3.04844e7	−	3.04844e7i	−0.163746	−	0.163746i	0.620478	−	0.784224i	$-0.286939\pi$
$571$	−3.04844e7	−	3.04844e7i	−0.163746	−	0.163746i	−0.784224	+	0.620478i	$0.786939\pi$
$572$	−1.10029e7	−	7.42509e6i	−0.0587921	−	0.0396747i
$573$	−9.37573e7	−	9.37573e7i	−0.498358	−	0.498358i
$574$	1.10204e6	−	585807.i	0.00582721	−	0.00309755i
$575$			2.47066e7i			0.129960i
$576$	1.32855e7	−	6.23002e7i	0.0695202	−	0.326003i
$577$	−5.99952e7			−0.312312			−0.156156	−	0.987732i	$-0.549910\pi$
$577$	−5.99952e7			−0.312312			−0.156156	+	0.987732i	$0.549910\pi$
$578$	3.39623e7	+	6.38908e7i	0.175879	+	0.330868i
$579$	−5.05613e7	+	5.05613e7i	−0.260485	+	0.260485i
$580$	2.36141e8	−	3.49927e8i	1.21028	−	1.79346i
$581$	1.81581e6	−	1.81581e6i	0.00925853	−	0.00925853i
$582$	−1.85015e8	−	5.65871e7i	−0.938508	−	0.287044i
$583$	−2.65042e6			−0.0133755
$584$	1.81131e7	−	1.71786e8i	0.0909398	−	0.862482i
$585$			1.11026e8i			0.554569i
$586$	−2.43182e8	−	7.43775e7i	−1.20848	−	0.369614i
$587$	9.99854e7	+	9.99854e7i	0.494336	+	0.494336i	0.909669	−	0.415333i	$-0.136335\pi$
$587$	9.99854e7	+	9.99854e7i	0.494336	+	0.494336i	−0.415333	+	0.909669i	$0.636335\pi$
$588$	2.23650e7	+	1.15194e8i	0.110011	+	0.566628i
$589$	3.17501e8	+	3.17501e8i	1.55382	+	1.55382i
$590$	−1.82482e8	−	3.43290e8i	−0.888514	−	1.67150i
$591$			1.28797e8i			0.623941i
$592$	−1.79397e8	−	7.62431e7i	−0.864668	−	0.367481i
$593$	−1.00872e8			−0.483734			−0.241867	−	0.970309i	$-0.577760\pi$
$593$	−1.00872e8			−0.483734			−0.241867	+	0.970309i	$0.577760\pi$
$594$	−1.85243e6	+	984693.i	−0.00883859	+	0.00469831i
$595$	−2.24970e6	+	2.24970e6i	−0.0106800	+	0.0106800i
$596$	4.39387e7	+	2.26312e8i	0.207543	+	1.06898i
$597$	−3.00313e7	+	3.00313e7i	−0.141140	+	0.141140i
$598$	2.26916e7	−	7.41915e7i	0.106111	−	0.346937i
$599$	3.34581e7			0.155676			0.0778379	−	0.996966i	$-0.475198\pi$
$599$	3.34581e7			0.155676			0.0778379	+	0.996966i	$0.475198\pi$
$600$	3.83206e7	+	4.73542e7i	0.177410	+	0.219232i
$601$			1.30304e8i			0.600251i	0.953900	+	0.300126i	$0.0970286\pi$
$601$			1.30304e8i			0.600251i	−0.953900	+	0.300126i	$0.902971\pi$
$602$	−436213.	+	1.42623e6i	−0.00199945	+	0.00653730i
$603$	−2.97875e7	−	2.97875e7i	−0.135857	−	0.135857i
$604$	1.73787e8	−	2.57527e8i	0.788690	−	1.16872i
$605$	−1.90522e8	−	1.90522e8i	−0.860359	−	0.860359i
$606$	1.81111e8	−	9.62728e7i	0.813818	−	0.432599i
$607$			3.04854e8i			1.36309i	0.731775	+	0.681546i	$0.238692\pi$
$607$			3.04854e8i			1.36309i	−0.731775	+	0.681546i	$0.761308\pi$
$608$	−2.35890e7	−	2.71351e8i	−0.104954	−	1.20732i
$609$	3.62058e6			0.0160298
$610$	1.44940e6	+	2.72665e6i	0.00638556	+	0.0120127i
$611$	1.23280e8	−	1.23280e8i	0.540466	−	0.540466i
$612$	−5.00822e7	−	3.37970e7i	−0.218489	−	0.147443i
$613$	−6.47373e7	+	6.47373e7i	−0.281043	+	0.281043i	−0.833525	−	0.552482i	$-0.813681\pi$
$613$	−6.47373e7	+	6.47373e7i	−0.281043	+	0.281043i	0.552482	+	0.833525i	$0.313681\pi$
$614$	2.65037e8	+	8.10618e7i	1.14499	+	0.350196i
$615$	−6.90654e7			−0.296917
$616$	−119734.	−	147959.i	−0.000512240	−	0.000632993i
$617$			1.34382e8i			0.572117i	0.958212	+	0.286059i	$0.0923452\pi$
$617$			1.34382e8i			0.572117i	−0.958212	+	0.286059i	$0.907655\pi$
$618$	1.45917e8	+	4.46290e7i	0.618216	+	0.189083i
$619$	1.65022e8	+	1.65022e8i	0.695776	+	0.695776i	0.963497	−	0.267720i	$-0.0862703\pi$
$619$	1.65022e8	+	1.65022e8i	0.695776	+	0.695776i	−0.267720	+	0.963497i	$0.586270\pi$
$620$	5.17572e8	−	1.00487e8i	2.17168	−	0.421633i
$621$	−8.67045e6	−	8.67045e6i	−0.0362049	−	0.0362049i
$622$	7.97523e7	+	1.50032e8i	0.331415	+	0.623467i
$623$			2.83197e6i			0.0117118i
$624$	−7.15811e7	−	1.77395e8i	−0.294608	−	0.730110i
$625$	3.05143e8			1.24987
$626$	−2.72433e8	+	1.44817e8i	−1.11055	+	0.590331i
$627$	−6.34289e6	+	6.34289e6i	−0.0257327	+	0.0257327i
$628$	−4.20446e8	+	8.16299e7i	−1.69758	+	0.329587i
$629$	−1.30732e8	+	1.30732e8i	−0.525329	+	0.525329i
$630$	−465628.	+	1.52240e6i	−0.00186216	+	0.00608846i
$631$	3.33511e8			1.32746			0.663731	−	0.747971i	$-0.268972\pi$
$631$	3.33511e8			1.32746			0.663731	+	0.747971i	$0.268972\pi$
$632$	−3.84154e7	+	3.64335e8i	−0.152179	+	1.44328i
$633$			9.16219e7i			0.361234i
$634$	−8.46700e7	+	2.76834e8i	−0.332248	+	1.08630i
$635$	5.53189e7	+	5.53189e7i	0.216049	+	0.216049i
$636$	−3.16610e7	−	2.13658e7i	−0.123070	−	0.0830516i
$637$	2.49174e8	+	2.49174e8i	0.964015	+	0.964015i
$638$	2.11514e7	−	1.12434e7i	0.0814474	−	0.0432948i
$639$			5.19827e7i			0.199231i
$640$	−2.79604e8	−	1.55270e8i	−1.06661	−	0.592309i
$641$	−2.80056e8			−1.06334			−0.531669	−	0.846952i	$-0.678435\pi$
$641$	−2.80056e8			−1.06334			−0.531669	+	0.846952i	$0.678435\pi$
$642$	3.49305e7	+	6.57123e7i	0.132008	+	0.248337i
$643$	−3.76599e7	+	3.76599e7i	−0.141660	+	0.141660i	−0.774380	−	0.632721i	$-0.781938\pi$
$643$	−3.76599e7	+	3.76599e7i	−0.141660	+	0.141660i	0.632721	+	0.774380i	$0.281938\pi$
$644$	622301.	−	922160.i	0.00232993	−	0.00345262i
$645$	5.83602e7	−	5.83602e7i	0.217489	−	0.217489i
$646$	−2.47045e8	−	7.55591e7i	−0.916386	−	0.280278i
$647$	2.17484e8			0.802999			0.401500	−	0.915859i	$-0.368489\pi$
$647$	2.17484e8			0.802999			0.401500	+	0.915859i	$0.368489\pi$
$648$	−3.00664e7	−	3.17019e6i	−0.110499	−	0.0116509i
$649$		−	2.20604e7i		−	0.0807009i
$650$	1.74933e8	+	5.35037e7i	0.636990	+	0.194825i
$651$	3.19743e6	+	3.19743e6i	0.0115893	+	0.0115893i
$652$	3.89043e7	+	2.00382e8i	0.140364	+	0.722963i
$653$	−1.83718e7	−	1.83718e7i	−0.0659800	−	0.0659800i	0.673347	−	0.739327i	$-0.264856\pi$
$653$	−1.83718e7	−	1.83718e7i	−0.0659800	−	0.0659800i	−0.739327	+	0.673347i	$0.764856\pi$
$654$	−7.99860e7	−	1.50472e8i	−0.285944	−	0.537926i
$655$		−	3.35734e8i		−	1.19473i
$656$	1.10352e8	−	4.45283e7i	0.390902	−	0.157734i
$657$	−8.19833e7			−0.289088
$658$	2.20745e6	−	1.17341e6i	0.00774843	−	0.00411881i
$659$	2.77669e8	−	2.77669e8i	0.970221	−	0.970221i	−0.0293478	−	0.999569i	$-0.509343\pi$
$659$	2.77669e8	−	2.77669e8i	0.970221	−	0.970221i	0.999569	+	0.0293478i	$0.00934305\pi$
$660$	2.00748e6	+	1.03398e7i	0.00698264	+	0.0359650i
$661$	9.11648e7	−	9.11648e7i	0.315662	−	0.315662i	−0.531436	−	0.847098i	$-0.678347\pi$
$661$	9.11648e7	−	9.11648e7i	0.315662	−	0.315662i	0.847098	+	0.531436i	$0.178347\pi$
$662$	1.33046e7	−	4.35000e7i	0.0458592	−	0.149939i
$663$	−1.81437e8			−0.622567
$664$	1.90329e8	−	1.54021e8i	0.650131	−	0.526109i
$665$			6.80718e6i			0.0231474i
$666$	−2.70582e7	+	8.84684e7i	−0.0915959	+	0.299478i
$667$	9.90007e7	+	9.90007e7i	0.333627	+	0.333627i
$668$	2.13636e8	−	3.16577e8i	0.716711	−	1.06206i
$669$	−2.47200e7	−	2.47200e7i	−0.0825602	−	0.0825602i
$670$	−1.86756e8	+	9.92735e7i	−0.620941	+	0.330072i
$671$			175219.i			0.000579980i
$672$	−237555.	−	2.73267e6i	−0.000782811	−	0.00900492i
$673$	−5.24674e8			−1.72125			−0.860626	−	0.509238i	$-0.829927\pi$
$673$	−5.24674e8			−1.72125			−0.860626	+	0.509238i	$0.829927\pi$
$674$	−5.95300e7	−	1.11990e8i	−0.194427	−	0.365761i
$675$	2.04437e7	−	2.04437e7i	0.0664736	−	0.0664736i
$676$	−2.20103e8	−	1.48533e8i	−0.712503	−	0.480819i
$677$	4.13584e8	−	4.13584e8i	1.33290	−	1.33290i	0.430136	−	0.902764i	$-0.358466\pi$
$677$	4.13584e8	−	4.13584e8i	1.33290	−	1.33290i	0.902764	−	0.430136i	$-0.141534\pi$
$678$	1.59998e8	+	4.89357e7i	0.513364	+	0.157013i
$679$	−8.33109e6			−0.0266129
$680$	−2.35808e8	+	1.90824e8i	−0.749949	+	0.606885i
$681$		−	3.33045e8i		−	1.05454i
$682$	2.86087e7	+	8.75002e6i	0.0901872	+	0.0275839i
$683$	−1.09574e8	−	1.09574e8i	−0.343911	−	0.343911i	0.513924	−	0.857836i	$-0.328191\pi$
$683$	−1.09574e8	−	1.09574e8i	−0.343911	−	0.343911i	−0.857836	+	0.513924i	$0.828191\pi$
$684$	−1.26902e8	+	2.46381e7i	−0.396552	+	0.0769908i
$685$	2.59198e6	+	2.59198e6i	0.00806418	+	0.00806418i
$686$	4.74399e6	+	8.92452e6i	0.0146951	+	0.0276447i
$687$			1.03096e8i			0.317959i
$688$	−5.56208e7	+	1.30873e8i	−0.170794	+	0.401871i
$689$	−1.14701e8			−0.350679
$690$	−5.43603e7	+	2.88962e7i	−0.165476	+	0.0879616i
$691$	−2.60873e8	+	2.60873e8i	−0.790669	+	0.790669i	−0.981603	−	0.190934i	$-0.938848\pi$
$691$	−2.60873e8	+	2.60873e8i	−0.790669	+	0.790669i	0.190934	+	0.981603i	$0.438848\pi$
$692$	−5.43092e8	+	1.05442e8i	−1.63891	+	0.318196i
$693$	−63876.8	+	63876.8i	−0.000191930	+	0.000191930i
$694$	1.05600e8	−	3.45266e8i	0.315927	−	1.03294i
$695$	−8.12957e8			−2.42166
$696$	3.43304e8	+	3.61978e7i	1.01824	+	0.107363i
$697$		−	1.12866e8i		−	0.333323i
$698$	7.09477e7	−	2.31968e8i	0.208628	−	0.682120i
$699$	−2.18285e8	−	2.18285e8i	−0.639134	−	0.639134i
$700$	2.17433e6	+	1.46730e6i	0.00633914	+	0.00427785i
$701$	−5.66448e7	−	5.66448e7i	−0.164439	−	0.164439i	0.620091	−	0.784530i	$-0.287096\pi$
$701$	−5.66448e7	−	5.66448e7i	−0.164439	−	0.164439i	−0.784530	+	0.620091i	$0.787096\pi$
$702$	−8.01669e7	+	4.26141e7i	−0.231731	+	0.123181i
$703$			3.95573e8i			1.13857i
$704$	−9.87386e6	−	1.52265e7i	−0.0282989	−	0.0436398i
$705$	−1.38343e8			−0.394810
$706$	−1.75389e8	−	3.29947e8i	−0.498412	−	0.937628i
$707$	6.24519e6	−	6.24519e6i	0.0176721	−	0.0176721i
$708$	1.77835e8	−	2.63525e8i	0.501092	−	0.742545i
$709$	2.04815e8	−	2.04815e8i	0.574676	−	0.574676i	−0.358755	−	0.933432i	$-0.616799\pi$
$709$	2.04815e8	−	2.04815e8i	0.574676	−	0.574676i	0.933432	+	0.358755i	$0.116799\pi$
$710$	2.49578e8	+	7.63337e7i	0.697318	+	0.213276i
$711$	1.73875e8			0.483760
$712$	−2.83135e7	+	2.68527e8i	−0.0784428	+	0.743959i
$713$			1.74860e8i			0.482417i
$714$	−2.48790e6	−	760927.i	−0.00683498	−	0.00209049i
$715$	2.23658e7	+	2.23658e7i	0.0611880	+	0.0611880i
$716$	−5.66816e6	−	2.91946e7i	−0.0154420	−	0.0795360i
$717$	−4.17569e7	−	4.17569e7i	−0.113285	−	0.113285i
$718$	8.18312e7	+	1.53943e8i	0.221078	+	0.415898i
$719$			6.77714e8i			1.82331i	0.410959	+	0.911654i	$0.365194\pi$
$719$			6.77714e8i			1.82331i	−0.410959	+	0.911654i	$0.634806\pi$
$720$	−5.93715e7	+	1.39699e8i	−0.159067	+	0.374278i
$721$	6.57054e6			0.0175305
$722$	−1.55740e8	+	8.27861e7i	−0.413797	+	0.219961i
$723$	1.68015e8	−	1.68015e8i	0.444562	−	0.444562i
$724$	3.19600e7	+	1.64615e8i	0.0842154	+	0.433763i
$725$	−2.33430e8	+	2.33430e8i	−0.612552	+	0.612552i
$726$	6.44414e7	−	2.10695e8i	0.168405	−	0.550611i
$727$	3.48046e8			0.905802			0.452901	−	0.891561i	$-0.350389\pi$
$727$	3.48046e8			0.905802			0.452901	+	0.891561i	$0.350389\pi$
$728$	−5.18166e6	−	6.40316e6i	−0.0134300	−	0.0165959i
$729$			1.43489e7i			0.0370370i
$730$	−1.20388e8	+	3.93616e8i	−0.309467	+	1.01182i
$731$	9.53718e7	+	9.53718e7i	0.244156	+	0.244156i
$732$	−1.41249e6	+	2.09310e6i	−0.00360124	+	0.00533651i
$733$	1.36324e7	+	1.36324e7i	0.0346146	+	0.0346146i	0.724202	−	0.689588i	$-0.242208\pi$
$733$	1.36324e7	+	1.36324e7i	0.0346146	+	0.0346146i	−0.689588	+	0.724202i	$0.742208\pi$
$734$	−5.90628e8	+	3.13959e8i	−1.49357	+	0.793934i
$735$		−	2.79619e8i		−	0.704213i
$736$	6.82261e7	−	8.12175e7i	0.171126	−	0.203712i
$737$	−1.20012e7			−0.0299794
$738$	−2.65089e7	−	4.98692e7i	−0.0659511	−	0.124069i
$739$	2.89963e8	−	2.89963e8i	0.718470	−	0.718470i	−0.249821	−	0.968292i	$-0.580372\pi$
$739$	2.89963e8	−	2.89963e8i	0.718470	−	0.718470i	0.968292	+	0.249821i	$0.0803719\pi$
$740$	3.85018e8	+	2.59822e8i	0.950136	+	0.641181i
$741$	−2.74499e8	+	2.74499e8i	−0.674661	+	0.674661i
$742$	−1.57280e6	−	481043.i	−0.00385001	−	0.00117753i
$743$	−5.94522e8			−1.44944			−0.724722	−	0.689041i	$-0.758032\pi$
$743$	−5.94522e8			−1.44944			−0.724722	+	0.689041i	$0.758032\pi$
$744$	2.71213e8	+	3.35148e8i	0.658555	+	0.813800i
$745$		−	5.49344e8i		−	1.32854i
$746$	4.19903e8	+	1.28428e8i	1.01142	+	0.309345i
$747$	−8.21689e7	−	8.21689e7i	−0.197127	−	0.197127i
$748$	−1.68972e7	+	3.28061e6i	−0.0403748	+	0.00783881i
$749$	2.26594e6	+	2.26594e6i	0.00539265	+	0.00539265i
$750$	7.13472e7	+	1.34220e8i	0.169119	+	0.318152i
$751$		−	5.29349e8i		−	1.24975i	−0.780726	−	0.624874i	$-0.785150\pi$
$751$		−	5.29349e8i		−	1.24975i	0.780726	−	0.624874i	$-0.214850\pi$
$752$	2.21042e8	−	8.91930e7i	0.519782	−	0.209738i
$753$	3.41888e8			0.800755
$754$	9.15360e8	−	4.86576e8i	2.13539	−	1.13511i
$755$	−5.23479e8	+	5.23479e8i	−1.21635	+	1.21635i
$756$	−1.27798e6	+	248121.i	−0.00295773	+	0.000574246i
$757$	−2.90978e8	+	2.90978e8i	−0.670768	+	0.670768i	−0.957893	−	0.287125i	$-0.907300\pi$
$757$	−2.90978e8	+	2.90978e8i	−0.670768	+	0.670768i	0.287125	+	0.957893i	$0.407300\pi$
$758$	−1.72217e8	+	5.63072e8i	−0.395428	+	1.29287i
$759$	−3.49328e6			−0.00798928
$760$	−6.80567e7	+	6.45457e8i	−0.155035	+	1.47037i
$761$			1.25159e8i			0.283994i	0.989867	+	0.141997i	$0.0453524\pi$
$761$			1.25159e8i			0.283994i	−0.989867	+	0.141997i	$0.954648\pi$
$762$	−1.87108e7	+	6.11761e7i	−0.0422890	+	0.138266i
$763$	−5.18867e6	−	5.18867e6i	−0.0116811	−	0.0116811i
$764$	−4.51239e8	−	3.04510e8i	−1.01187	−	0.682843i
$765$	1.01803e8	+	1.01803e8i	0.227392	+	0.227392i
$766$	9.35382e7	−	4.97219e7i	0.208115	−	0.110627i
$767$		−	9.54696e8i		−	2.11582i
$768$	4.79569e6	−	2.61487e8i	0.0105869	−	0.577253i
$769$	2.33480e8			0.513418			0.256709	−	0.966489i	$-0.417362\pi$
$769$	2.33480e8			0.513418			0.256709	+	0.966489i	$0.417362\pi$
$770$	212884.	+	400483.i	0.000466305	+	0.000877226i
$771$	−2.53939e8	+	2.53939e8i	−0.554073	+	0.554073i
$772$	−1.64216e8	+	2.43344e8i	−0.356913	+	0.528893i
$773$	1.82416e8	−	1.82416e8i	0.394934	−	0.394934i	−0.481507	−	0.876442i	$-0.659911\pi$
$773$	1.82416e8	−	1.82416e8i	0.394934	−	0.394934i	0.876442	+	0.481507i	$0.159911\pi$
$774$	6.45394e7	+	1.97395e7i	0.139188	+	0.0425709i
$775$	−4.12297e8			−0.885737
$776$	−7.89953e8	−	8.32924e7i	−1.69050	−	0.178246i
$777$			3.98367e6i			0.00849219i
$778$	3.15033e7	+	9.63532e6i	0.0668986	+	0.0204610i
$779$	−1.70757e8	−	1.70757e8i	−0.361215	−	0.361215i
$780$	8.68769e7	+	4.47471e8i	0.183071	+	0.942934i
$781$	1.04718e7	+	1.04718e7i	0.0219820	+	0.0219820i
$782$	−4.72220e7	−	8.88353e7i	−0.0987469	−	0.185766i
$783$		−	1.63838e8i		−	0.341295i
$784$	1.80277e8	+	4.46771e8i	0.374105	+	0.927122i
$785$	1.02058e9			2.10978
$786$	2.42419e8	−	1.28862e8i	0.499229	−	0.265374i
$787$	5.04645e8	−	5.04645e8i	1.03529	−	1.03529i	0.0359348	−	0.999354i	$-0.488559\pi$
$787$	5.04645e8	−	5.04645e8i	1.03529	−	1.03529i	0.999354	−	0.0359348i	$-0.0114409\pi$
$788$	1.00783e8	+	5.19097e8i	0.205972	+	1.06089i
$789$	1.26406e8	−	1.26406e8i	0.257358	−	0.257358i
$790$	2.55326e8	−	8.34805e8i	0.517863	−	1.69318i
$791$	7.20460e6			0.0145573
$792$	−6.69542e6	+	5.41817e6i	−0.0134773	+	0.0109063i
$793$			7.58287e6i			0.0152060i
$794$	3.81261e7	−	1.24656e8i	0.0761660	−	0.249029i
$795$	6.43578e7	+	6.43578e7i	0.128086	+	0.128086i
$796$	−9.75370e7	+	1.44536e8i	−0.193388	+	0.286573i
$797$	1.49530e8	+	1.49530e8i	0.295362	+	0.295362i	0.839194	−	0.543832i	$-0.183027\pi$
$797$	1.49530e8	+	1.49530e8i	0.295362	+	0.295362i	−0.543832	+	0.839194i	$0.683027\pi$
$798$	−4.91518e6	+	2.61275e6i	−0.00967233	+	0.00514150i
$799$		−	2.26078e8i		−	0.443219i
$800$	1.91500e8	+	1.60868e8i	0.374023	+	0.314195i
$801$	1.28152e8			0.249361
$802$	−2.66770e8	−	5.01855e8i	−0.517147	−	0.972872i
$803$	−1.65153e7	+	1.65153e7i	−0.0318963	+	0.0318963i
$804$	−1.43362e8	−	9.67453e7i	−0.275846	−	0.186150i
$805$	−1.87449e6	+	1.87449e6i	−0.00359332	+	0.00359332i
$806$	1.23809e9	+	3.78671e8i	2.36454	+	0.723197i
$807$	4.00018e8			0.761130
$808$	6.54607e8	−	5.29731e8i	1.24093	−	1.00420i
$809$			6.79235e8i			1.28285i	0.767187	+	0.641423i	$0.221656\pi$
$809$			6.79235e8i			1.28285i	−0.767187	+	0.641423i	$0.778344\pi$
$810$	6.88915e7	+	2.10706e7i	0.129631	+	0.0396480i
$811$	−6.71312e8	−	6.71312e8i	−1.25852	−	1.25852i	−0.951798	−	0.306727i	$-0.900766\pi$
$811$	−6.71312e8	−	6.71312e8i	−1.25852	−	1.25852i	−0.306727	−	0.951798i	$-0.599234\pi$
$812$	1.45922e7	−	2.83309e6i	0.0272554	−	0.00529166i
$813$	1.85253e8	+	1.85253e8i	0.344742	+	0.344742i
$814$	1.23709e7	+	2.32725e7i	0.0229366	+	0.0431489i
$815$		−	4.86402e8i		−	0.898509i
$816$	−2.28294e8	−	9.70245e7i	−0.420170	−	0.178571i
$817$	2.88578e8			0.529173
$818$	1.34209e8	−	7.13412e7i	0.245201	−	0.130341i
$819$	−2.76437e6	+	2.76437e6i	−0.00503204	+	0.00503204i
$820$	−2.78357e8	+	5.40433e7i	−0.504849	+	0.0980167i
$821$	−1.13933e8	+	1.13933e8i	−0.205882	+	0.205882i	−0.802515	−	0.596632i	$-0.796505\pi$
$821$	−1.13933e8	+	1.13933e8i	−0.205882	+	0.205882i	0.596632	+	0.802515i	$0.296505\pi$
$822$	−876700.	+	2.86642e6i	−0.00157847	+	0.00516089i
$823$	3.09924e8			0.555975			0.277987	−	0.960585i	$-0.410333\pi$
$823$	3.09924e8			0.555975			0.277987	+	0.960585i	$0.410333\pi$
$824$	6.23018e8	+	6.56908e7i	1.11357	+	0.117415i
$825$		−	8.23667e6i		−	0.0146686i
$826$	4.00389e6	−	1.30909e7i	0.00710463	−	0.0232290i
$827$	−2.49487e8	−	2.49487e8i	−0.441095	−	0.441095i	0.451285	−	0.892380i	$-0.350966\pi$
$827$	−2.49487e8	−	2.49487e8i	−0.441095	−	0.441095i	−0.892380	+	0.451285i	$0.850966\pi$
$828$	−4.17295e7	−	2.81603e7i	−0.0735109	−	0.0496074i
$829$	−6.63974e8	−	6.63974e8i	−1.16543	−	1.16543i	−0.983268	−	0.182165i	$-0.941690\pi$
$829$	−6.63974e8	−	6.63974e8i	−1.16543	−	1.16543i	−0.182165	−	0.983268i	$-0.558310\pi$
$830$	−5.15167e8	+	2.73846e8i	−0.900977	+	0.478930i
$831$		−	2.91402e8i		−	0.507797i
$832$	−4.27307e8	−	6.58952e8i	−0.741942	−	1.14415i
$833$	4.56951e8			0.790560
$834$	−3.12031e8	−	5.87002e8i	−0.537898	−	1.01191i
$835$	−6.43511e8	+	6.43511e8i	−1.10534	+	1.10534i
$836$	−2.06008e7	+	3.05273e7i	−0.0352585	+	0.0522480i
$837$	1.44690e8	−	1.44690e8i	0.246753	−	0.246753i
$838$	3.85610e8	+	1.17940e8i	0.655265	+	0.200414i
$839$	4.18417e7			0.0708473			0.0354237	−	0.999372i	$-0.488722\pi$
$839$	4.18417e7			0.0708473			0.0354237	+	0.999372i	$0.488722\pi$
$840$	−685373.	+	6.50015e6i	−0.00115635	+	0.0109669i
$841$			1.27591e9i			2.14503i
$842$	−4.49907e8	−	1.37605e8i	−0.753679	−	0.230514i
$843$	4.17324e8	+	4.17324e8i	0.696611	+	0.696611i
$844$	7.16936e7	+	3.69268e8i	0.119249	+	0.614206i
$845$	4.47408e8	+	4.47408e8i	0.741539	+	0.741539i
$846$	−5.30990e7	−	9.98914e7i	−0.0876951	−	0.164975i
$847$		−	9.48744e6i		−	0.0156135i
$848$	−1.44323e8	−	6.13370e7i	−0.236673	−	0.100585i
$849$	−5.52151e8			−0.902266
$850$	2.09461e8	−	1.11343e8i	0.341073	−	0.181303i
$851$	−1.08929e8	+	1.08929e8i	−0.176748	+	0.176748i
$852$	4.06762e7	+	2.09508e8i	0.0657690	+	0.338752i
$853$	−6.18731e8	+	6.18731e8i	−0.996908	+	0.996908i	−0.999995	−	0.00308725i	$-0.999017\pi$
$853$	−6.18731e8	+	6.18731e8i	−0.996908	+	0.996908i	0.00308725	+	0.999995i	$0.499017\pi$
$854$	−31801.7	+	103977.i	−5.10595e−5	+	0.000166942i
$855$	3.08038e8			0.492840
$856$	1.92202e8	+	2.37510e8i	0.306433	+	0.378670i
$857$		−	9.35284e8i		−	1.48594i	−0.669325	−	0.742970i	$-0.733417\pi$
$857$		−	9.35284e8i		−	1.48594i	0.669325	−	0.742970i	$-0.266583\pi$
$858$	−7.56491e6	+	2.47339e7i	−0.0119768	+	0.0391589i
$859$	3.05653e8	+	3.05653e8i	0.482225	+	0.482225i	0.905841	−	0.423617i	$-0.139240\pi$
$859$	3.05653e8	+	3.05653e8i	0.482225	+	0.482225i	−0.423617	+	0.905841i	$0.639240\pi$
$860$	1.89545e8	−	2.80878e8i	0.298001	−	0.441593i
$861$	−1.71963e6	−	1.71963e6i	−0.00269417	−	0.00269417i
$862$	−4.46707e8	+	2.37455e8i	−0.697430	+	0.370731i
$863$			1.52011e8i			0.236506i	0.992984	+	0.118253i	$0.0377293\pi$
$863$			1.52011e8i			0.236506i	−0.992984	+	0.118253i	$0.962271\pi$
$864$	−1.23659e8	+	1.07498e7i	−0.191727	+	0.0166671i
$865$	1.31829e9			2.03686
$866$	−1.83491e7	−	3.45188e7i	−0.0282527	−	0.0531498i
$867$	9.96956e7	−	9.96956e7i	0.152974	−	0.152974i
$868$	1.53887e7	+	1.03848e7i	0.0235312	+	0.0158796i
$869$	3.50267e7	−	3.50267e7i	0.0533753	−	0.0533753i
$870$	−7.86615e8	−	2.40587e8i	−1.19455	−	0.365355i
$871$	−5.19372e8			−0.786002
$872$	−4.40114e8	−	5.43865e8i	−0.663768	−	0.820241i
$873$			3.76997e8i			0.566625i
$874$	−2.05843e8	−	6.29573e7i	−0.308320	−	0.0943000i
$875$	4.62828e6	+	4.62828e6i	0.00690868	+	0.00690868i
$876$	−3.30421e8	+	6.41515e7i	−0.491536	+	0.0954321i
$877$	−6.76555e8	−	6.76555e8i	−1.00301	−	1.00301i	−0.999995	−	0.00301200i	$-0.999041\pi$
$877$	−6.76555e8	−	6.76555e8i	−1.00301	−	1.00301i	−0.00301200	−	0.999995i	$-0.500959\pi$
$878$	−7.12062e7	−	1.33955e8i	−0.105204	−	0.197914i
$879$			4.95521e8i			0.729618i
$880$	1.61817e7	+	4.01021e7i	0.0237452	+	0.0588463i
$881$	5.67082e8			0.829313			0.414656	−	0.909978i	$-0.363902\pi$
$881$	5.67082e8			0.829313			0.414656	+	0.909978i	$0.363902\pi$
$882$	2.01901e8	−	1.07324e8i	0.294261	−	0.156420i
$883$	−2.70776e8	+	2.70776e8i	−0.393303	+	0.393303i	−0.875863	−	0.482560i	$-0.839707\pi$
$883$	−2.70776e8	+	2.70776e8i	−0.393303	+	0.393303i	0.482560	+	0.875863i	$0.339707\pi$
$884$	−7.31254e8	+	1.41974e8i	−1.05855	+	0.205518i
$885$	−5.35673e8	+	5.35673e8i	−0.772804	+	0.772804i
$886$	−2.50389e8	+	8.18662e8i	−0.360010	+	1.17707i
$887$	8.61154e8			1.23399			0.616993	−	0.786969i	$-0.288351\pi$
$887$	8.61154e8			1.23399			0.616993	+	0.786969i	$0.288351\pi$
$888$	−3.98278e7	+	3.77731e8i	−0.0568784	+	0.539441i
$889$			2.75471e6i			0.00392077i
$890$	1.88184e8	−	6.15280e8i	0.266940	−	0.872775i
$891$	2.89055e6	+	2.89055e6i	0.00408646	+	0.00408646i
$892$	−1.18974e8	−	8.02869e7i	−0.167632	−	0.113123i
$893$	−3.42037e8	−	3.42037e8i	−0.480307	−	0.480307i
$894$	3.96659e8	−	2.10851e8i	0.555142	−	0.295096i
$895$			7.08661e7i			0.0988484i
$896$	−3.09573e6	−	1.08277e7i	−0.00430367	−	0.0150527i
$897$	−1.51177e8			−0.209464
$898$	1.25552e8	+	2.36191e8i	0.173378	+	0.326163i
$899$	−1.65210e9	+	1.65210e9i	−2.27382	+	2.27382i
$900$	6.63982e7	−	9.83924e7i	0.0910812	−	0.134969i
$901$	−1.05173e8	+	1.05173e8i	−0.143791	+	0.143791i
$902$	−1.53862e7	−	4.70588e6i	−0.0209658	−	0.00641241i
$903$	2.90616e6			0.00394690
$904$	6.83139e8	+	7.20300e7i	0.924707	+	0.0975008i
$905$		−	3.99581e8i		−	0.539087i
$906$	−5.78906e8	−	1.77059e8i	−0.778437	−	0.238086i
$907$	4.01148e8	+	4.01148e8i	0.537629	+	0.537629i	0.922832	−	0.385203i	$-0.125868\pi$
$907$	4.01148e8	+	4.01148e8i	0.537629	+	0.537629i	−0.385203	+	0.922832i	$0.625868\pi$
$908$	−2.60606e8	−	1.34228e9i	−0.348118	−	1.79303i
$909$	−2.82607e8	−	2.82607e8i	−0.376263	−	0.376263i
$910$	9.21288e6	+	1.73315e7i	0.0122256	+	0.0229992i
$911$		−	9.73411e7i		−	0.128748i	−0.997926	−	0.0643741i	$-0.979495\pi$
$911$		−	9.73411e7i		−	0.128748i	0.997926	−	0.0643741i	$-0.0205051\pi$
$912$	−4.92179e8	+	1.98600e8i	−0.648841	+	0.261815i
$913$	−3.31054e7			−0.0434997
$914$	−3.91493e8	+	2.08105e8i	−0.512726	+	0.272549i
$915$	4.25469e6	−	4.25469e6i	0.00555398	−	0.00555398i
$916$	8.06720e7	+	4.15512e8i	0.104963	+	0.540626i
$917$	8.35927e6	−	8.35927e6i	0.0108408	−	0.0108408i
$918$	−3.44334e7	+	1.12582e8i	−0.0445094	+	0.145526i
$919$	−7.96503e8			−1.02622			−0.513110	−	0.858323i	$-0.671507\pi$
$919$	−7.96503e8			−1.02622			−0.513110	+	0.858323i	$0.671507\pi$
$920$	−1.96480e8	+	1.58998e8i	−0.252322	+	0.204187i
$921$		−	5.40054e8i		−	0.691287i
$922$	9.13944e7	−	2.98819e8i	0.116608	−	0.381256i
$923$	4.53183e8	+	4.53183e8i	0.576326	+	0.576326i
$924$	−207462.	+	307429.i	−0.000262980	+	0.000389698i
$925$	−2.56839e8	−	2.56839e8i	−0.324516	−	0.324516i
$926$	−4.57773e8	+	2.43337e8i	−0.576524	+	0.306461i
$927$		−	2.97329e8i		−	0.373249i
$928$	1.41196e9	−	1.22743e8i	1.76676	−	0.153587i
$929$	7.73176e7			0.0964342			0.0482171	−	0.998837i	$-0.484646\pi$
$929$	7.73176e7			0.0964342			0.0482171	+	0.998837i	$0.484646\pi$
$930$	−4.82211e8	−	9.07150e8i	−0.599499	−	1.12779i
$931$	6.91327e8	−	6.91327e8i	0.856711	−	0.856711i
$932$	−1.05057e9	−	7.08956e8i	−1.29771	−	0.875733i
$933$	2.34111e8	−	2.34111e8i	0.288255	−	0.288255i
$934$	−1.09670e9	−	3.35429e8i	−1.34601	−	0.411680i
$935$	4.10159e7			0.0501784
$936$	−2.89755e8	+	2.34480e8i	−0.353349	+	0.285942i
$937$			1.24173e9i			1.50941i	0.656063	+	0.754706i	$0.272220\pi$
$937$			1.24173e9i			1.50941i	−0.656063	+	0.754706i	$0.727780\pi$
$938$	−7.12171e6	−	2.17819e6i	−0.00862930	−	0.00263928i
$939$	4.25106e8	+	4.25106e8i	0.513453	+	0.513453i
$940$	−5.57568e8	+	1.08252e8i	−0.671297	+	0.130333i
$941$	6.89816e8	+	6.89816e8i	0.827874	+	0.827874i	0.987222	−	0.159349i	$-0.0509394\pi$
$941$	6.89816e8	+	6.89816e8i	0.827874	+	0.827874i	−0.159349	+	0.987222i	$0.550939\pi$
$942$	3.91721e8	+	7.36917e8i	0.468624	+	0.881588i
$943$		−	9.40423e7i		−	0.112147i
$944$	5.10529e8	−	1.20125e9i	0.606882	−	1.42797i
$945$	3.10213e6			0.00367591
$946$	1.69777e7	−	9.02482e6i	0.0200543	−	0.0106602i
$947$	5.78686e8	−	5.78686e8i	0.681386	−	0.681386i	−0.278926	−	0.960313i	$-0.589979\pi$
$947$	5.78686e8	−	5.78686e8i	0.681386	−	0.681386i	0.960313	+	0.278926i	$0.0899785\pi$
$948$	7.00778e8	−	1.36057e8i	0.822537	−	0.159696i
$949$	−7.14726e8	+	7.14726e8i	−0.836260	+	0.836260i
$950$	1.48445e8	−	4.85349e8i	0.173139	−	0.566087i
$951$	5.64093e8			0.655857
$952$	−1.06225e7	−	1.12003e6i	−0.0123116	−	0.00129813i
$953$		−	1.10265e9i		−	1.27397i	−0.770875	−	0.636986i	$-0.780181\pi$
$953$		−	1.10265e9i		−	1.27397i	0.770875	−	0.636986i	$-0.219819\pi$
$954$	−2.17681e7	+	7.11721e7i	−0.0250712	+	0.0819719i
$955$	9.17241e8	+	9.17241e8i	1.05311	+	1.05311i
$956$	−2.00969e8	−	1.35620e8i	−0.230015	−	0.155221i
$957$	−3.30048e7	−	3.30048e7i	−0.0376566	−	0.0376566i
$958$	4.21871e8	−	2.24253e8i	0.479826	−	0.255060i
$959$			129073.i			0.000146345i
$960$	−1.29974e8	+	6.09491e8i	−0.146907	+	0.688896i
$961$	−2.03052e9			−2.28790
$962$	5.35371e8	+	1.00715e9i	0.601353	+	1.13128i
$963$	1.02538e8	−	1.02538e8i	0.114817	−	0.114817i
$964$	5.45686e8	−	8.08627e8i	0.609132	−	0.902645i
$965$	4.94649e8	−	4.94649e8i	0.550446	−	0.550446i
$966$	−2.07296e6	−	634019.i	−0.00229964	−	0.000703349i
$967$	−7.32629e8			−0.810223			−0.405111	−	0.914267i	$-0.632767\pi$
$967$	−7.32629e8			−0.810223			−0.405111	+	0.914267i	$0.632767\pi$
$968$	9.48534e7	−	8.99599e8i	0.104575	−	0.991797i
$969$			5.03393e8i			0.553269i
$970$	1.81003e9	+	5.53600e8i	1.98322	+	0.606570i
$971$	6.01418e8	+	6.01418e8i	0.656930	+	0.656930i	0.954652	−	0.297723i	$-0.0962270\pi$
$971$	6.01418e8	+	6.01418e8i	0.656930	+	0.656930i	−0.297723	+	0.954652i	$0.596227\pi$
$972$	1.12279e7	+	5.78310e7i	0.0122265	+	0.0629741i
$973$	−2.02414e7	−	2.02414e7i	−0.0219736	−	0.0219736i
$974$	3.35587e8	+	6.31315e8i	0.363185	+	0.683234i
$975$		−	3.56455e8i		−	0.384583i
$976$	−4.05498e6	+	9.54119e6i	−0.00436153	+	0.0102625i
$977$	6.27375e8			0.672734			0.336367	−	0.941731i	$-0.390802\pi$
$977$	6.27375e8			0.672734			0.336367	+	0.941731i	$0.390802\pi$
$978$	3.51210e8	−	1.86692e8i	0.375449	−	0.199576i
$979$	2.58159e7	−	2.58159e7i	0.0275131	−	0.0275131i
$980$	−2.18800e8	−	1.12696e9i	−0.232471	−	1.19737i
$981$	−2.34797e8	+	2.34797e8i	−0.248706	+	0.248706i
$982$	−1.76484e8	+	5.77023e8i	−0.186367	+	0.609339i
$983$	7.60602e8			0.800750			0.400375	−	0.916351i	$-0.368880\pi$
$983$	7.60602e8			0.800750			0.400375	+	0.916351i	$0.368880\pi$
$984$	−1.45862e8	−	1.80247e8i	−0.153094	−	0.189183i
$985$		−	1.26004e9i		−	1.31849i
$986$	3.93166e8	−	1.28548e9i	0.410153	−	1.34102i
$987$	−3.44452e6	−	3.44452e6i	−0.00358243	−	0.00358243i
$988$	−8.91530e8	+	1.32112e9i	−0.924411	+	1.36984i
$989$	7.94656e7	+	7.94656e7i	0.0821468	+	0.0821468i
$990$	1.81226e7	−	9.63339e6i	0.0186773	−	0.00992827i
$991$			1.26374e8i			0.129848i	0.997890	+	0.0649240i	$0.0206805\pi$
$991$			1.26374e8i			0.129848i	−0.997890	+	0.0649240i	$0.979319\pi$
$992$	1.35533e9	+	1.13854e9i	1.38839	+	1.16631i
$993$	−8.86382e7			−0.0905260
$994$	4.31351e6	+	8.11471e6i	0.00439210	+	0.00826254i
$995$	2.93800e8	−	2.93800e8i	0.298251	−	0.298251i
$996$	−3.95465e8	−	2.66872e8i	−0.400249	−	0.270100i
$997$	1.36158e9	−	1.36158e9i	1.37391	−	1.37391i	0.519348	−	0.854563i	$-0.326175\pi$
$997$	1.36158e9	−	1.36158e9i	1.37391	−	1.37391i	0.854563	−	0.519348i	$-0.173825\pi$
$998$	1.22514e9	+	3.74713e8i	1.23253	+	0.376970i
$999$	1.80268e8			0.180810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.19.8	✓	48
4.3	odd	2		192.7.l.a.175.23		48
8.3	odd	2		384.7.l.a.223.2		48
8.5	even	2		384.7.l.b.223.23		48
16.3	odd	4		384.7.l.b.31.23		48
16.5	even	4		192.7.l.a.79.23		48
16.11	odd	4	inner	48.7.l.a.43.8	yes	48
16.13	even	4		384.7.l.a.31.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.8	✓	48	1.1	even	1	trivial
48.7.l.a.43.8	yes	48	16.11	odd	4	inner
192.7.l.a.79.23		48	16.5	even	4
192.7.l.a.175.23		48	4.3	odd	2
384.7.l.a.31.2		48	16.13	even	4
384.7.l.a.223.2		48	8.3	odd	2
384.7.l.b.31.23		48	16.3	odd	4
384.7.l.b.223.23		48	8.5	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.75499 - 7.06400i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-35.8001 + 53.0505i) q^{4} +(107.837 - 107.837i) q^{5} +(119.254 + 36.4742i) q^{6} +5.36994 q^{7} +(509.177 + 53.6875i) q^{8} -243.000i q^{9} +O(q^{10})\)	\(q+(-3.75499 - 7.06400i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-35.8001 + 53.0505i) q^{4} +(107.837 - 107.837i) q^{5} +(119.254 + 36.4742i) q^{6} +5.36994 q^{7} +(509.177 + 53.6875i) q^{8} -243.000i q^{9} +(-1166.68 - 356.832i) q^{10} +(-48.9517 - 48.9517i) q^{11} +(-190.146 - 979.373i) q^{12} +(-2118.46 - 2118.46i) q^{13} +(-20.1641 - 37.9332i) q^{14} +2377.30i q^{15} +(-1532.71 - 3798.42i) q^{16} -3884.97 q^{17} +(-1716.55 + 912.463i) q^{18} +(-5877.62 + 5877.62i) q^{19} +(1860.23 + 9581.35i) q^{20} +(-59.1913 + 59.1913i) q^{21} +(-161.981 + 529.608i) q^{22} -3237.03 q^{23} +(-6204.29 + 5020.73i) q^{24} -7632.48i q^{25} +(-7010.00 + 22919.6i) q^{26} +(2678.52 + 2678.52i) q^{27} +(-192.244 + 284.878i) q^{28} +(-30583.8 - 30583.8i) q^{29} +(16793.3 - 8926.75i) q^{30} -54018.7i q^{31} +(-21076.7 + 25090.1i) q^{32} +1079.16 q^{33} +(14588.0 + 27443.4i) q^{34} +(579.076 - 579.076i) q^{35} +(12891.3 + 8699.42i) q^{36} +(33650.8 - 33650.8i) q^{37} +(63589.9 + 19449.1i) q^{38} +46702.3 q^{39} +(60697.5 - 49118.5i) q^{40} +29052.0i q^{41} +(640.390 + 195.864i) q^{42} +(-24548.9 - 24548.9i) q^{43} +(4349.38 - 844.436i) q^{44} +(-26204.3 - 26204.3i) q^{45} +(12155.0 + 22866.4i) q^{46} +58193.1i q^{47} +(58763.5 + 24974.3i) q^{48} -117620. q^{49} +(-53915.8 + 28659.9i) q^{50} +(42822.9 - 42822.9i) q^{51} +(188226. - 36544.3i) q^{52} +(27071.8 - 27071.8i) q^{53} +(8863.23 - 28978.8i) q^{54} -10557.6 q^{55} +(2734.25 + 288.299i) q^{56} -129575. i q^{57} +(-101202. + 330885. i) q^{58} +(225328. + 225328. i) q^{59} +(-126117. - 85107.6i) q^{60} +(-1789.71 - 1789.71i) q^{61} +(-381588. + 202840. i) q^{62} -1304.90i q^{63} +(256379. + 54672.9i) q^{64} -456895. q^{65} +(-4052.24 - 7623.18i) q^{66} +(122582. - 122582. i) q^{67} +(139082. - 206100. i) q^{68} +(35680.9 - 35680.9i) q^{69} +(-6265.02 - 1916.17i) q^{70} -213921. q^{71} +(13046.1 - 123730. i) q^{72} -337380. i q^{73} +(-364067. - 111351. i) q^{74} +(84130.6 + 84130.6i) q^{75} +(-101391. - 522230. i) q^{76} +(-262.868 - 262.868i) q^{77} +(-175367. - 329905. i) q^{78} +715537. i q^{79} +(-574891. - 244327. i) q^{80} -59049.0 q^{81} +(205223. - 109090. i) q^{82} +(338143. - 338143. i) q^{83} +(-1021.07 - 5259.18i) q^{84} +(-418942. + 418942. i) q^{85} +(-81232.4 + 265594. i) q^{86} +674232. q^{87} +(-22297.0 - 27553.2i) q^{88} +527375. i q^{89} +(-86710.2 + 283504. i) q^{90} +(-11376.0 - 11376.0i) q^{91} +(115886. - 171726. i) q^{92} +(595432. + 595432. i) q^{93} +(411076. - 218515. i) q^{94} +1.26765e6i q^{95} +(-44238.0 - 508883. i) q^{96} -1.55143e6 q^{97} +(441663. + 830868. i) q^{98} +(-11895.3 + 11895.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Introduction

L-functions

Modular forms

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