LMFDB - Embedded newform 60.7.c.a.31.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.18
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.21792 + 6.06410i) q^{2} +15.5885i q^{3} +(-9.54653 + 63.2840i) q^{4} +55.9017 q^{5} +(-94.5299 + 81.3394i) q^{6} +234.050i q^{7} +(-433.573 + 272.320i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(5.21792 + 6.06410i) q^{2} +15.5885i q^{3} +(-9.54653 + 63.2840i) q^{4} +55.9017 q^{5} +(-94.5299 + 81.3394i) q^{6} +234.050i q^{7} +(-433.573 + 272.320i) q^{8} -243.000 q^{9} +(291.691 + 338.993i) q^{10} +611.126i q^{11} +(-986.500 - 148.816i) q^{12} +446.025 q^{13} +(-1419.30 + 1221.26i) q^{14} +871.421i q^{15} +(-3913.73 - 1208.29i) q^{16} -4753.29 q^{17} +(-1267.96 - 1473.58i) q^{18} -4220.36i q^{19} +(-533.667 + 3537.68i) q^{20} -3648.49 q^{21} +(-3705.93 + 3188.81i) q^{22} +3897.71i q^{23} +(-4245.05 - 6758.74i) q^{24} +3125.00 q^{25} +(2327.33 + 2704.74i) q^{26} -3788.00i q^{27} +(-14811.6 - 2234.37i) q^{28} +15226.1 q^{29} +(-5284.38 + 4547.01i) q^{30} +25735.3i q^{31} +(-13094.4 - 30038.0i) q^{32} -9526.51 q^{33} +(-24802.3 - 28824.4i) q^{34} +13083.8i q^{35} +(2319.81 - 15378.0i) q^{36} -12963.9 q^{37} +(25592.7 - 22021.5i) q^{38} +6952.85i q^{39} +(-24237.5 + 15223.2i) q^{40} +71144.7 q^{41} +(-19037.5 - 22124.8i) q^{42} +101623. i q^{43} +(-38674.5 - 5834.13i) q^{44} -13584.1 q^{45} +(-23636.1 + 20338.0i) q^{46} +132654. i q^{47} +(18835.3 - 61009.0i) q^{48} +62869.4 q^{49} +(16306.0 + 18950.3i) q^{50} -74096.4i q^{51} +(-4257.99 + 28226.3i) q^{52} +283151. q^{53} +(22970.8 - 19765.5i) q^{54} +34163.0i q^{55} +(-63736.6 - 101478. i) q^{56} +65788.9 q^{57} +(79448.8 + 92332.7i) q^{58} -176836. i q^{59} +(-55147.0 - 8319.05i) q^{60} +219488. q^{61} +(-156061. + 134285. i) q^{62} -56874.3i q^{63} +(113828. - 236141. i) q^{64} +24933.6 q^{65} +(-49708.6 - 57769.7i) q^{66} +420905. i q^{67} +(45377.4 - 300807. i) q^{68} -60759.3 q^{69} +(-79341.5 + 68270.4i) q^{70} -427721. i q^{71} +(105358. - 66173.8i) q^{72} +276028. q^{73} +(-67644.4 - 78614.1i) q^{74} +48713.9i q^{75} +(267081. + 40289.8i) q^{76} -143034. q^{77} +(-42162.7 + 36279.4i) q^{78} +616843. i q^{79} +(-218784. - 67545.2i) q^{80} +59049.0 q^{81} +(371228. + 431429. i) q^{82} -632235. i q^{83} +(34830.4 - 230891. i) q^{84} -265717. q^{85} +(-616250. + 530260. i) q^{86} +237352. i q^{87} +(-166422. - 264968. i) q^{88} -1.04325e6 q^{89} +(-70880.9 - 82375.4i) q^{90} +104392. i q^{91} +(-246663. - 37209.6i) q^{92} -401174. q^{93} +(-804429. + 692181. i) q^{94} -235925. i q^{95} +(468245. - 204121. i) q^{96} -1.31029e6 q^{97} +(328048. + 381246. i) q^{98} -148504. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) $ 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	5.21792	+	6.06410i	0.652241	+	0.758012i
$2$	5.21792	+	6.06410i	0.652241	+	0.758012i
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	−9.54653	+	63.2840i	−0.149165	+	0.988812i
$5$	55.9017			0.447214
$5$	55.9017			0.447214
$6$	−94.5299	+	81.3394i	−0.437638	+	0.376571i
$7$			234.050i			0.682363i	0.939997	+	0.341181i	$0.110827\pi$
$7$			234.050i			0.682363i	−0.939997	+	0.341181i	$0.889173\pi$
$8$	−433.573	+	272.320i	−0.846823	+	0.531875i
$9$	−243.000			−0.333333
$10$	291.691	+	338.993i	0.291691	+	0.338993i
$11$			611.126i			0.459148i	0.973291	+	0.229574i	$0.0737333\pi$
$11$			611.126i			0.459148i	−0.973291	+	0.229574i	$0.926267\pi$
$12$	−986.500	−	148.816i	−0.570891	−	0.0861202i
$13$	446.025			0.203016			0.101508	−	0.994835i	$-0.467633\pi$
$13$	446.025			0.203016			0.101508	+	0.994835i	$0.467633\pi$
$14$	−1419.30	+	1221.26i	−0.517239	+	0.445065i
$15$			871.421i			0.258199i
$16$	−3913.73	−	1208.29i	−0.955500	−	0.294991i
$17$	−4753.29			−0.967491			−0.483746	−	0.875209i	$-0.660724\pi$
$17$	−4753.29			−0.967491			−0.483746	+	0.875209i	$0.660724\pi$
$18$	−1267.96	−	1473.58i	−0.217414	−	0.252671i
$19$		−	4220.36i		−	0.615302i	−0.951499	−	0.307651i	$-0.900457\pi$
$19$		−	4220.36i		−	0.615302i	0.951499	−	0.307651i	$-0.0995430\pi$
$20$	−533.667	+	3537.68i	−0.0667084	+	0.442210i
$21$	−3648.49			−0.393962
$22$	−3705.93	+	3188.81i	−0.348040	+	0.299475i
$23$			3897.71i			0.320351i	0.987089	+	0.160176i	$0.0512061\pi$
$23$			3897.71i			0.320351i	−0.987089	+	0.160176i	$0.948794\pi$
$24$	−4245.05	−	6758.74i	−0.307078	−	0.488913i
$25$	3125.00			0.200000
$26$	2327.33	+	2704.74i	0.132415	+	0.153888i
$27$		−	3788.00i		−	0.192450i
$28$	−14811.6	−	2234.37i	−0.674729	−	0.101784i
$29$	15226.1			0.624303			0.312152	−	0.950032i	$-0.398950\pi$
$29$	15226.1			0.624303			0.312152	+	0.950032i	$0.398950\pi$
$30$	−5284.38	+	4547.01i	−0.195718	+	0.168408i
$31$			25735.3i			0.863862i	0.901907	+	0.431931i	$0.142168\pi$
$31$			25735.3i			0.863862i	−0.901907	+	0.431931i	$0.857832\pi$
$32$	−13094.4	−	30038.0i	−0.399609	−	0.916686i
$33$	−9526.51			−0.265089
$34$	−24802.3	−	28824.4i	−0.631037	−	0.733370i
$35$			13083.8i			0.305162i
$36$	2319.81	−	15378.0i	0.0497215	−	0.329604i
$37$	−12963.9			−0.255935			−0.127967	−	0.991778i	$-0.540845\pi$
$37$	−12963.9			−0.255935			−0.127967	+	0.991778i	$0.540845\pi$
$38$	25592.7	−	22021.5i	0.466407	−	0.401325i
$39$			6952.85i			0.117211i
$40$	−24237.5	+	15223.2i	−0.378711	+	0.237862i
$41$	71144.7			1.03227			0.516133	−	0.856509i	$-0.327371\pi$
$41$	71144.7			1.03227			0.516133	+	0.856509i	$0.327371\pi$
$42$	−19037.5	−	22124.8i	−0.256958	−	0.298628i
$43$			101623.i			1.27816i	0.769140	+	0.639080i	$0.220685\pi$
$43$			101623.i			1.27816i	−0.769140	+	0.639080i	$0.779315\pi$
$44$	−38674.5	−	5834.13i	−0.454011	−	0.0684886i
$45$	−13584.1			−0.149071
$46$	−23636.1	+	20338.0i	−0.242830	+	0.208946i
$47$			132654.i			1.27770i	0.769332	+	0.638849i	$0.220589\pi$
$47$			132654.i			1.27770i	−0.769332	+	0.638849i	$0.779411\pi$
$48$	18835.3	−	61009.0i	0.170313	−	0.551658i
$49$	62869.4			0.534381
$50$	16306.0	+	18950.3i	0.130448	+	0.151602i
$51$		−	74096.4i		−	0.558581i
$52$	−4257.99	+	28226.3i	−0.0302827	+	0.200744i
$53$	283151.			1.90192			0.950958	−	0.309321i	$-0.100102\pi$
$53$	283151.			1.90192			0.950958	+	0.309321i	$0.100102\pi$
$54$	22970.8	−	19765.5i	0.145879	−	0.125524i
$55$			34163.0i			0.205337i
$56$	−63736.6	−	101478.i	−0.362932	−	0.577840i
$57$	65788.9			0.355245
$58$	79448.8	+	92332.7i	0.407196	+	0.473229i
$59$		−	176836.i		−	0.861022i	−0.902585	−	0.430511i	$-0.858333\pi$
$59$		−	176836.i		−	0.861022i	0.902585	−	0.430511i	$-0.141667\pi$
$60$	−55147.0	−	8319.05i	−0.255310	−	0.0385141i
$61$	219488.			0.966986			0.483493	−	0.875348i	$-0.339368\pi$
$61$	219488.			0.966986			0.483493	+	0.875348i	$0.339368\pi$
$62$	−156061.	+	134285.i	−0.654817	+	0.563446i
$63$		−	56874.3i		−	0.227454i
$64$	113828.	−	236141.i	0.434218	−	0.900808i
$65$	24933.6			0.0907913
$66$	−49708.6	−	57769.7i	−0.172902	−	0.200941i
$67$			420905.i			1.39946i	0.714408	+	0.699729i	$0.246696\pi$
$67$			420905.i			1.39946i	−0.714408	+	0.699729i	$0.753304\pi$
$68$	45377.4	−	300807.i	0.144315	−	0.956668i
$69$	−60759.3			−0.184955
$70$	−79341.5	+	68270.4i	−0.231316	+	0.199039i
$71$		−	427721.i		−	1.19505i	−0.801851	−	0.597524i	$-0.796151\pi$
$71$		−	427721.i		−	1.19505i	0.801851	−	0.597524i	$-0.203849\pi$
$72$	105358.	−	66173.8i	0.282274	−	0.177292i
$73$	276028.			0.709553			0.354777	−	0.934951i	$-0.384557\pi$
$73$	276028.			0.709553			0.354777	+	0.934951i	$0.384557\pi$
$74$	−67644.4	−	78614.1i	−0.166931	−	0.194002i
$75$			48713.9i			0.115470i
$76$	267081.	+	40289.8i	0.608419	+	0.0917813i
$77$	−143034.			−0.313305
$78$	−42162.7	+	36279.4i	−0.0888474	+	0.0764498i
$79$			616843.i			1.25110i	0.780182	+	0.625552i	$0.215126\pi$
$79$			616843.i			1.25110i	−0.780182	+	0.625552i	$0.784874\pi$
$80$	−218784.	−	67545.2i	−0.427313	−	0.131924i
$81$	59049.0			0.111111
$82$	371228.	+	431429.i	0.673285	+	0.782469i
$83$		−	632235.i		−	1.10572i	−0.833275	−	0.552859i	$-0.813537\pi$
$83$		−	632235.i		−	1.10572i	0.833275	−	0.552859i	$-0.186463\pi$
$84$	34830.4	−	230891.i	0.0587652	−	0.389555i
$85$	−265717.			−0.432675
$86$	−616250.	+	530260.i	−0.968861	+	0.833668i
$87$			237352.i			0.360442i
$88$	−166422.	−	264968.i	−0.244209	−	0.388817i
$89$	−1.04325e6			−1.47985			−0.739926	−	0.672689i	$-0.765139\pi$
$89$	−1.04325e6			−1.47985			−0.739926	+	0.672689i	$0.765139\pi$
$90$	−70880.9	−	82375.4i	−0.0972303	−	0.112998i
$91$			104392.i			0.138530i
$92$	−246663.	−	37209.6i	−0.316767	−	0.0477850i
$93$	−401174.			−0.498751
$94$	−804429.	+	692181.i	−0.968510	+	0.833366i
$95$		−	235925.i		−	0.275172i
$96$	468245.	−	204121.i	0.529249	−	0.230714i
$97$	−1.31029e6			−1.43566			−0.717832	−	0.696216i	$-0.754866\pi$
$97$	−1.31029e6			−1.43566			−0.717832	+	0.696216i	$0.754866\pi$
$98$	328048.	+	381246.i	0.348545	+	0.405067i
$99$		−	148504.i		−	0.153049i
$100$	−29832.9	+	197762.i	−0.0298329	+	0.197762i
$101$	−591531.			−0.574134			−0.287067	−	0.957911i	$-0.592680\pi$
$101$	−591531.			−0.574134			−0.287067	+	0.957911i	$0.592680\pi$
$102$	449328.	−	386629.i	0.423411	−	0.364329i
$103$			369642.i			0.338275i	0.985592	+	0.169138i	$0.0540982\pi$
$103$			369642.i			0.338275i	−0.985592	+	0.169138i	$0.945902\pi$
$104$	−193385.	+	121462.i	−0.171918	+	0.107979i
$105$	−203957.			−0.176185
$106$	1.47746e6	+	1.71706e6i	1.24051	+	1.44167i
$107$		−	829937.i		−	0.677476i	−0.940881	−	0.338738i	$-0.890000\pi$
$107$		−	829937.i		−	0.677476i	0.940881	−	0.338738i	$-0.110000\pi$
$108$	239719.	+	36162.2i	0.190297	+	0.0287067i
$109$	−2.19532e6			−1.69519			−0.847594	−	0.530646i	$-0.821949\pi$
$109$	−2.19532e6			−1.69519			−0.847594	+	0.530646i	$0.821949\pi$
$110$	−207168.	+	178260.i	−0.155648	+	0.133929i
$111$		−	202087.i		−	0.147764i
$112$	282800.	−	916010.i	0.201291	−	0.651998i
$113$	2.57865e6			1.78713			0.893565	−	0.448933i	$-0.148196\pi$
$113$	2.57865e6			1.78713			0.893565	+	0.448933i	$0.148196\pi$
$114$	343281.	+	398950.i	0.231705	+	0.269280i
$115$			217889.i			0.143265i
$116$	−145357.	+	963571.i	−0.0931239	+	0.617319i
$117$	−108384.			−0.0676719
$118$	1.07235e6	−	922716.i	0.652665	−	0.561593i
$119$		−	1.11251e6i		−	0.660180i
$120$	−237305.	−	377825.i	−0.137330	−	0.218649i
$121$	1.39809e6			0.789183
$122$	1.14527e6	+	1.33099e6i	0.630708	+	0.732987i
$123$			1.10904e6i			0.595979i
$124$	−1.62863e6	−	245683.i	−0.854197	−	0.128858i
$125$	174693.			0.0894427
$126$	344891.	−	296766.i	0.172413	−	0.148355i
$127$		−	3.88504e6i		−	1.89664i	−0.317320	−	0.948319i	$-0.602783\pi$
$127$		−	3.88504e6i		−	1.89664i	0.317320	−	0.948319i	$-0.397217\pi$
$128$	2.02593e6	−	541906.i	0.966038	−	0.258401i
$129$	−1.58414e6			−0.737946
$130$	130101.	+	151200.i	0.0592178	+	0.0688209i
$131$		−	2.17769e6i		−	0.968685i	−0.874878	−	0.484343i	$-0.839059\pi$
$131$		−	2.17769e6i		−	0.968685i	0.874878	−	0.484343i	$-0.160941\pi$
$132$	90945.1	−	602876.i	0.0395419	−	0.262123i
$133$	987777.			0.419859
$134$	−2.55241e6	+	2.19625e6i	−1.06081	+	0.912784i
$135$		−	211755.i		−	0.0860663i
$136$	2.06090e6	−	1.29441e6i	0.819294	−	0.514585i
$137$	4.01481e6			1.56136			0.780681	−	0.624929i	$-0.214872\pi$
$137$	4.01481e6			1.56136			0.780681	+	0.624929i	$0.214872\pi$
$138$	−317038.	−	368451.i	−0.120635	−	0.140198i
$139$			278268.i			0.103614i	0.998657	+	0.0518070i	$0.0164981\pi$
$139$			278268.i			0.103614i	−0.998657	+	0.0518070i	$0.983502\pi$
$140$	−827996.	−	124905.i	−0.301748	−	0.0455193i
$141$	−2.06788e6			−0.737679
$142$	2.59374e6	−	2.23181e6i	0.905861	−	0.779459i
$143$			272578.i			0.0932142i
$144$	951036.	+	293613.i	0.318500	+	0.0983305i
$145$	851167.			0.279197
$146$	1.44030e6	+	1.67386e6i	0.462800	+	0.537850i
$147$			980037.i			0.308525i
$148$	123760.	−	820405.i	0.0381764	−	0.253071i
$149$	991141.			0.299624			0.149812	−	0.988715i	$-0.452133\pi$
$149$	991141.			0.299624			0.149812	+	0.988715i	$0.452133\pi$
$150$	−295406.	+	254186.i	−0.0875277	+	0.0753143i
$151$			29572.7i			0.00858936i	0.999991	+	0.00429468i	$0.00136704\pi$
$151$			29572.7i			0.00858936i	−0.999991	+	0.00429468i	$0.998633\pi$
$152$	1.14929e6	+	1.82984e6i	0.327264	+	0.521052i
$153$	1.15505e6			0.322497
$154$	−746342.	−	867374.i	−0.204351	−	0.237489i
$155$			1.43865e6i			0.386331i
$156$	−440004.	−	66375.5i	−0.115900	−	0.0174837i
$157$	−2.86209e6			−0.739580			−0.369790	−	0.929115i	$-0.620570\pi$
$157$	−2.86209e6			−0.739580			−0.369790	+	0.929115i	$0.620570\pi$
$158$	−3.74060e6	+	3.21864e6i	−0.948352	+	0.816021i
$159$			4.41389e6i			1.09807i
$160$	−731998.	−	1.67917e6i	−0.178710	−	0.409954i
$161$	−912262.			−0.218596
$162$	308113.	+	358079.i	0.0724712	+	0.0842236i
$163$			5.86822e6i			1.35501i	0.735517	+	0.677506i	$0.236939\pi$
$163$			5.86822e6i			1.35501i	−0.735517	+	0.677506i	$0.763061\pi$
$164$	−679185.	+	4.50232e6i	−0.153977	+	1.02072i
$165$	−532548.			−0.118551
$166$	3.83393e6	−	3.29895e6i	0.838147	−	0.721194i
$167$			635821.i			0.136517i	0.997668	+	0.0682583i	$0.0217442\pi$
$167$			635821.i			0.136517i	−0.997668	+	0.0682583i	$0.978256\pi$
$168$	1.58189e6	−	993556.i	0.333616	−	0.209539i
$169$	−4.62787e6			−0.958785
$170$	−1.38649e6	−	1.61133e6i	−0.282208	−	0.327973i
$171$			1.02555e6i			0.205101i
$172$	−6.43109e6	−	970144.i	−1.26386	−	0.190656i
$173$	7.53757e6			1.45577			0.727886	−	0.685698i	$-0.240503\pi$
$173$	7.53757e6			1.45577			0.727886	+	0.685698i	$0.240503\pi$
$174$	−1.43932e6	+	1.23848e6i	−0.273219	+	0.235095i
$175$			731408.i			0.136473i
$176$	738414.	−	2.39178e6i	0.135445	−	0.438716i
$177$	2.75660e6			0.497111
$178$	−5.44360e6	−	6.32636e6i	−0.965219	−	1.12175i
$179$			878241.i			0.153128i	0.997065	+	0.0765640i	$0.0243949\pi$
$179$			878241.i			0.153128i	−0.997065	+	0.0765640i	$0.975605\pi$
$180$	129681.	−	859657.i	0.0222361	−	0.147403i
$181$	−4.23487e6			−0.714174			−0.357087	−	0.934071i	$-0.616230\pi$
$181$	−4.23487e6			−0.714174			−0.357087	+	0.934071i	$0.616230\pi$
$182$	−633046.	+	544712.i	−0.105008	+	0.0903551i
$183$			3.42147e6i			0.558290i
$184$	−1.06143e6	−	1.68994e6i	−0.170387	−	0.271281i
$185$	−724702.			−0.114457
$186$	−2.09329e6	−	2.43276e6i	−0.325305	−	0.378059i
$187$		−	2.90486e6i		−	0.444222i
$188$	−8.39490e6	−	1.26639e6i	−1.26340	−	0.190587i
$189$	886582.			0.131321
$190$	1.43067e6	−	1.23104e6i	0.208583	−	0.179478i
$191$		−	8.58674e6i		−	1.23233i	−0.787616	−	0.616167i	$-0.788685\pi$
$191$		−	8.58674e6i		−	1.23233i	0.787616	−	0.616167i	$-0.211315\pi$
$192$	3.68108e6	+	1.77440e6i	0.520082	+	0.250696i
$193$	9.47926e6			1.31857			0.659284	−	0.751894i	$-0.270859\pi$
$193$	9.47926e6			1.31857			0.659284	+	0.751894i	$0.270859\pi$
$194$	−6.83701e6	−	7.94574e6i	−0.936399	−	1.08825i
$195$			388676.i			0.0524184i
$196$	−600185.	+	3.97863e6i	−0.0797107	+	0.528403i
$197$	−152893.			−0.0199981			−0.00999903	−	0.999950i	$-0.503183\pi$
$197$	−152893.			−0.0199981			−0.00999903	+	0.999950i	$0.503183\pi$
$198$	900540.	−	774880.i	0.116013	−	0.0998250i
$199$		−	4.24007e6i		−	0.538038i	−0.963135	−	0.269019i	$-0.913300\pi$
$199$		−	4.24007e6i		−	0.538038i	0.963135	−	0.269019i	$-0.0866995\pi$
$200$	−1.35492e6	+	851000.i	−0.169365	+	0.106375i
$201$	−6.56126e6			−0.807978
$202$	−3.08656e6	−	3.58710e6i	−0.374473	−	0.435200i
$203$			3.56368e6i			0.426001i
$204$	4.68912e6	+	707363.i	0.552332	+	0.0833205i
$205$	3.97711e6			0.461643
$206$	−2.24155e6	+	1.92877e6i	−0.256417	+	0.220637i
$207$		−	947144.i		−	0.106784i
$208$	−1.74562e6	−	538926.i	−0.193981	−	0.0598879i
$209$	2.57917e6			0.282515
$210$	−1.06423e6	−	1.23681e6i	−0.114915	−	0.133551i
$211$			7.09394e6i			0.755162i	0.925977	+	0.377581i	$0.123244\pi$
$211$			7.09394e6i			0.755162i	−0.925977	+	0.377581i	$0.876756\pi$
$212$	−2.70311e6	+	1.79190e7i	−0.283698	+	1.88064i
$213$	6.66751e6			0.689961
$214$	5.03282e6	−	4.33055e6i	0.513535	−	0.441877i
$215$			5.68088e6i			0.571611i
$216$	1.03155e6	+	1.64237e6i	0.102359	+	0.162971i
$217$	−6.02336e6			−0.589467
$218$	−1.14550e7	−	1.33126e7i	−1.10567	−	1.28497i
$219$			4.30286e6i			0.409661i
$220$	−2.16197e6	−	326138.i	−0.203040	−	0.0306290i
$221$	−2.12009e6			−0.196416
$222$	1.22547e6	−	1.05447e6i	0.112007	−	0.0963776i
$223$		−	1.19865e6i		−	0.108088i	−0.998539	−	0.0540442i	$-0.982789\pi$
$223$		−	1.19865e6i		−	0.108088i	0.998539	−	0.0540442i	$-0.0172112\pi$
$224$	7.03040e6	−	3.06474e6i	0.625512	−	0.272678i
$225$	−759375.			−0.0666667
$226$	1.34552e7	+	1.56372e7i	1.16564	+	1.35467i
$227$			5.84907e6i			0.500045i	0.968240	+	0.250023i	$0.0804380\pi$
$227$			5.84907e6i			0.500045i	−0.968240	+	0.250023i	$0.919562\pi$
$228$	−628056.	+	4.16338e6i	−0.0529900	+	0.351271i
$229$	1.27570e7			1.06228			0.531142	−	0.847283i	$-0.321763\pi$
$229$	1.27570e7			1.06228			0.531142	+	0.847283i	$0.321763\pi$
$230$	−1.32130e6	+	1.13693e6i	−0.108597	+	0.0934435i
$231$		−	2.22968e6i		−	0.180887i
$232$	−6.60164e6	+	4.14638e6i	−0.528674	+	0.332051i
$233$	−6.04654e6			−0.478012			−0.239006	−	0.971018i	$-0.576822\pi$
$233$	−6.04654e6			−0.478012			−0.239006	+	0.971018i	$0.576822\pi$
$234$	−565540.	−	657252.i	−0.0441383	−	0.0512961i
$235$			7.41561e6i			0.571404i
$236$	1.11909e7	+	1.68817e6i	0.851389	+	0.128434i
$237$	−9.61564e6			−0.722326
$238$	6.74636e6	−	5.80499e6i	0.500425	−	0.430596i
$239$		−	2.45629e7i		−	1.79923i	−0.436685	−	0.899614i	$-0.643848\pi$
$239$		−	2.45629e7i		−	1.79923i	0.436685	−	0.899614i	$-0.356152\pi$
$240$	1.05293e6	−	3.41051e6i	0.0761665	−	0.246709i
$241$	−5.34775e6			−0.382050			−0.191025	−	0.981585i	$-0.561181\pi$
$241$	−5.34775e6			−0.382050			−0.191025	+	0.981585i	$0.561181\pi$
$242$	7.29511e6	+	8.47813e6i	0.514737	+	0.598210i
$243$			920483.i			0.0641500i
$244$	−2.09534e6	+	1.38900e7i	−0.144240	+	0.956168i
$245$	3.51451e6			0.238982
$246$	−6.72531e6	+	5.78687e6i	−0.451759	+	0.388721i
$247$		−	1.88239e6i		−	0.124916i
$248$	−7.00824e6	−	1.11581e7i	−0.459466	−	0.731538i
$249$	9.85557e6			0.638386
$250$	911534.	+	1.05935e6i	0.0583382	+	0.0677987i
$251$		−	1.62600e6i		−	0.102825i	−0.998677	−	0.0514126i	$-0.983628\pi$
$251$		−	1.62600e6i		−	0.102825i	0.998677	−	0.0514126i	$-0.0163724\pi$
$252$	3.59923e6	+	542952.i	0.224910	+	0.0339281i
$253$	−2.38199e6			−0.147089
$254$	2.35593e7	−	2.02718e7i	1.43767	−	1.23706i
$255$		−	4.14211e6i		−	0.249805i
$256$	1.38573e7	+	9.45780e6i	0.825960	+	0.563729i
$257$	−5.96301e6			−0.351290			−0.175645	−	0.984454i	$-0.556201\pi$
$257$	−5.96301e6			−0.351290			−0.175645	+	0.984454i	$0.556201\pi$
$258$	−8.26593e6	−	9.60639e6i	−0.481319	−	0.559372i
$259$		−	3.03420e6i		−	0.174640i
$260$	−238029.	+	1.57790e6i	−0.0135428	+	0.0897756i
$261$	−3.69995e6			−0.208101
$262$	1.32057e7	−	1.13630e7i	0.734275	−	0.631816i
$263$			5.56063e6i			0.305673i	0.988252	+	0.152836i	$0.0488407\pi$
$263$			5.56063e6i			0.305673i	−0.988252	+	0.152836i	$0.951159\pi$
$264$	4.13044e6	−	2.59426e6i	0.224484	−	0.140994i
$265$	1.58286e7			0.850562
$266$	5.15415e6	+	5.98997e6i	0.273849	+	0.318259i
$267$		−	1.62626e7i		−	0.854393i
$268$	−2.66366e7	−	4.01818e6i	−1.38380	−	0.208750i
$269$	8.71314e6			0.447629			0.223814	−	0.974632i	$-0.428149\pi$
$269$	8.71314e6			0.447629			0.223814	+	0.974632i	$0.428149\pi$
$270$	1.28410e6	−	1.10492e6i	0.0652393	−	0.0561359i
$271$		−	2.16067e7i		−	1.08563i	−0.839853	−	0.542815i	$-0.817359\pi$
$271$		−	2.16067e7i		−	1.08563i	0.839853	−	0.542815i	$-0.182641\pi$
$272$	1.86031e7	+	5.74332e6i	0.924438	+	0.285402i
$273$	−1.62732e6			−0.0799805
$274$	2.09490e7	+	2.43462e7i	1.01838	+	1.18353i
$275$			1.90977e6i			0.0918296i
$276$	580041.	−	3.84509e6i	0.0275887	−	0.182886i
$277$	−1.96628e7			−0.925138			−0.462569	−	0.886583i	$-0.653072\pi$
$277$	−1.96628e7			−0.925138			−0.462569	+	0.886583i	$0.653072\pi$
$278$	−1.68744e6	+	1.45198e6i	−0.0785407	+	0.0675813i
$279$		−	6.25368e6i		−	0.287954i
$280$	−3.56299e6	−	5.67279e6i	−0.162308	−	0.258418i
$281$	−4.23673e7			−1.90946			−0.954732	−	0.297467i	$-0.903858\pi$
$281$	−4.23673e7			−1.90946			−0.954732	+	0.297467i	$0.903858\pi$
$282$	−1.07900e7	−	1.25398e7i	−0.481144	−	0.559170i
$283$			3.51305e7i			1.54998i	0.631975	+	0.774989i	$0.282245\pi$
$283$			3.51305e7i			1.54998i	−0.631975	+	0.774989i	$0.717755\pi$
$284$	2.70679e7	+	4.08325e6i	1.18168	+	0.178259i
$285$	3.67771e6			0.158870
$286$	−1.65294e6	+	1.42229e6i	−0.0706575	+	0.0607981i
$287$			1.66515e7i			0.704379i
$288$	3.18193e6	+	7.29922e6i	0.133203	+	0.305562i
$289$	−1.54385e6			−0.0639603
$290$	4.44132e6	+	5.16156e6i	0.182104	+	0.211635i
$291$		−	2.04254e7i		−	0.828882i
$292$	−2.63511e6	+	1.74682e7i	−0.105840	+	0.701615i
$293$	1.11354e7			0.442695			0.221348	−	0.975195i	$-0.428954\pi$
$293$	1.11354e7			0.442695			0.221348	+	0.975195i	$0.428954\pi$
$294$	−5.94304e6	+	5.11376e6i	−0.233866	+	0.201233i
$295$		−	9.88542e6i		−	0.385061i
$296$	5.62078e6	−	3.53032e6i	0.216731	−	0.136125i
$297$	2.31494e6			0.0883631
$298$	5.17170e6	+	6.01037e6i	0.195427	+	0.227119i
$299$			1.73848e6i			0.0650363i
$300$	−3.08281e6	−	465049.i	−0.114178	−	0.0172240i
$301$	−2.37848e7			−0.872169
$302$	−179332.	+	154308.i	−0.00651084	+	0.00560233i
$303$		−	9.22105e6i		−	0.331476i
$304$	−5.09940e6	+	1.65173e7i	−0.181509	+	0.587921i
$305$	1.22697e7			0.432450
$306$	6.02696e6	+	7.00432e6i	0.210346	+	0.244457i
$307$		−	1.40533e7i		−	0.485695i	−0.970064	−	0.242847i	$-0.921919\pi$
$307$		−	1.40533e7i		−	0.485695i	0.970064	−	0.242847i	$-0.0780814\pi$
$308$	1.36548e6	−	9.05178e6i	0.0467341	−	0.309800i
$309$	−5.76215e6			−0.195303
$310$	−8.72409e6	+	7.50675e6i	−0.292843	+	0.251981i
$311$		−	4.02124e7i		−	1.33684i	−0.743785	−	0.668419i	$-0.766971\pi$
$311$		−	4.02124e7i		−	1.33684i	0.743785	−	0.668419i	$-0.233029\pi$
$312$	−1.89340e6	−	3.01457e6i	−0.0623417	−	0.0992570i
$313$	−2.19464e7			−0.715699			−0.357850	−	0.933779i	$-0.616490\pi$
$313$	−2.19464e7			−0.715699			−0.357850	+	0.933779i	$0.616490\pi$
$314$	−1.49342e7	−	1.73560e7i	−0.482384	−	0.560610i
$315$		−	3.17937e6i		−	0.101721i
$316$	−3.90363e7	−	5.88871e6i	−1.23711	−	0.186620i
$317$	−2.87330e7			−0.901992			−0.450996	−	0.892526i	$-0.648931\pi$
$317$	−2.87330e7			−0.901992			−0.450996	+	0.892526i	$0.648931\pi$
$318$	−2.67663e7	+	2.30314e7i	−0.832351	+	0.716207i
$319$			9.30508e6i			0.286648i
$320$	6.36316e6	−	1.32007e7i	0.194188	−	0.402854i
$321$	1.29374e7			0.391141
$322$	−4.76011e6	−	5.53204e6i	−0.142577	−	0.165698i
$323$			2.00606e7i			0.595300i
$324$	−563713.	+	3.73686e6i	−0.0165738	+	0.109868i
$325$	1.39383e6			0.0406031
$326$	−3.55854e7	+	3.06199e7i	−1.02712	+	0.883794i
$327$		−	3.42216e7i		−	0.978717i
$328$	−3.08465e7	+	1.93741e7i	−0.874146	+	0.549036i
$329$	−3.10478e7			−0.871853
$330$	−2.77880e6	−	3.22942e6i	−0.0773241	−	0.0898635i
$331$		−	6.61370e6i		−	0.182373i	−0.995834	−	0.0911865i	$-0.970934\pi$
$331$		−	6.61370e6i		−	0.182373i	0.995834	−	0.0911865i	$-0.0290660\pi$
$332$	4.00104e7	+	6.03565e6i	1.09335	+	0.164934i
$333$	3.15022e6			0.0853116
$334$	−3.85568e6	+	3.31767e6i	−0.103481	+	0.0890417i
$335$			2.35293e7i			0.625857i
$336$	1.42792e7	+	4.40841e6i	0.376431	+	0.116216i
$337$	2.36992e7			0.619219			0.309610	−	0.950864i	$-0.399802\pi$
$337$	2.36992e7			0.619219			0.309610	+	0.950864i	$0.399802\pi$
$338$	−2.41479e7	−	2.80639e7i	−0.625358	−	0.726770i
$339$			4.01971e7i			1.03180i
$340$	2.53667e6	−	1.68156e7i	0.0645398	−	0.427835i
$341$	−1.57275e7			−0.396640
$342$	−6.21902e6	+	5.35123e6i	−0.155469	+	0.133775i
$343$			4.22504e7i			1.04700i
$344$	−2.76739e7	−	4.40609e7i	−0.679822	−	1.08238i
$345$	−3.39655e6			−0.0827143
$346$	3.93305e7	+	4.57086e7i	0.949513	+	1.10349i
$347$			7.87037e7i			1.88368i	0.336065	+	0.941839i	$0.390904\pi$
$347$			7.87037e7i			1.88368i	−0.336065	+	0.941839i	$0.609096\pi$
$348$	−1.50206e7	−	2.26589e6i	−0.356409	−	0.0537651i
$349$	5.84311e7			1.37457			0.687286	−	0.726387i	$-0.258802\pi$
$349$	5.84311e7			1.37457			0.687286	+	0.726387i	$0.258802\pi$
$350$	−4.43533e6	+	3.81643e6i	−0.103448	+	0.0890129i
$351$		−	1.68954e6i		−	0.0390704i
$352$	1.83570e7	−	8.00231e6i	0.420894	−	0.183479i
$353$	2.20704e6			0.0501749			0.0250875	−	0.999685i	$-0.492014\pi$
$353$	2.20704e6			0.0501749			0.0250875	+	0.999685i	$0.492014\pi$
$354$	1.43837e7	+	1.67163e7i	0.324236	+	0.376816i
$355$		−	2.39103e7i		−	0.534442i
$356$	9.95941e6	−	6.60210e7i	0.220741	−	1.46330i
$357$	1.73423e7			0.381155
$358$	−5.32574e6	+	4.58259e6i	−0.116073	+	0.0998763i
$359$			1.20278e7i			0.259957i	0.991517	+	0.129979i	$0.0414909\pi$
$359$			1.20278e7i			0.259957i	−0.991517	+	0.129979i	$0.958509\pi$
$360$	5.88971e6	−	3.69923e6i	0.126237	−	0.0792872i
$361$	2.92344e7			0.621403
$362$	−2.20972e7	−	2.56806e7i	−0.465813	−	0.541352i
$363$			2.17940e7i			0.455635i
$364$	−6.60637e6	−	996585.i	−0.136980	−	0.0206638i
$365$	1.54305e7			0.317322
$366$	−2.07481e7	+	1.78530e7i	−0.423190	+	0.364139i
$367$		−	7.63147e7i		−	1.54387i	−0.635703	−	0.771934i	$-0.719290\pi$
$367$		−	7.63147e7i		−	1.54387i	0.635703	−	0.771934i	$-0.280710\pi$
$368$	4.70955e6	−	1.52546e7i	0.0945009	−	0.306096i
$369$	−1.72882e7			−0.344088
$370$	−3.78144e6	−	4.39466e6i	−0.0746538	−	0.0867601i
$371$			6.62717e7i			1.29780i
$372$	3.82982e6	−	2.53879e7i	0.0743959	−	0.493171i
$373$	5.43943e7			1.04816			0.524079	−	0.851669i	$-0.324410\pi$
$373$	5.43943e7			1.04816			0.524079	+	0.851669i	$0.324410\pi$
$374$	1.76153e7	−	1.51573e7i	0.336725	−	0.289739i
$375$			2.72319e6i			0.0516398i
$376$	−3.61244e7	−	5.75154e7i	−0.679575	−	1.08198i
$377$	6.79124e6			0.126743
$378$	4.62612e6	+	5.37632e6i	0.0856527	+	0.0995427i
$379$			1.26362e7i			0.232113i	0.993243	+	0.116057i	$0.0370254\pi$
$379$			1.26362e7i			0.232113i	−0.993243	+	0.116057i	$0.962975\pi$
$380$	1.49303e7	+	2.25227e6i	0.272093	+	0.0410458i
$381$	6.05618e7			1.09502
$382$	5.20708e7	−	4.48050e7i	0.934124	−	0.803778i
$383$		−	6.10284e7i		−	1.08627i	−0.839647	−	0.543133i	$-0.817238\pi$
$383$		−	6.10284e7i		−	1.08627i	0.839647	−	0.543133i	$-0.182762\pi$
$384$	8.44748e6	+	3.15811e7i	0.149188	+	0.557742i
$385$	−7.99586e6			−0.140114
$386$	4.94621e7	+	5.74832e7i	0.860024	+	0.999491i
$387$		−	2.46943e7i		−	0.426054i
$388$	1.25087e7	−	8.29205e7i	0.214150	−	1.41960i
$389$	−6.42261e7			−1.09110			−0.545548	−	0.838080i	$-0.683678\pi$
$389$	−6.42261e7			−1.09110			−0.545548	+	0.838080i	$0.683678\pi$
$390$	−2.35697e6	+	2.02808e6i	−0.0397338	+	0.0341894i
$391$		−	1.85269e7i		−	0.309937i
$392$	−2.72585e7	+	1.71206e7i	−0.452526	+	0.284224i
$393$	3.39469e7			0.559271
$394$	−797782.	−	927156.i	−0.0130435	−	0.0151588i
$395$			3.44826e7i			0.559511i
$396$	9.39790e6	+	1.41769e6i	0.151337	+	0.0228295i
$397$	5.76615e7			0.921540			0.460770	−	0.887520i	$-0.347573\pi$
$397$	5.76615e7			0.921540			0.460770	+	0.887520i	$0.347573\pi$
$398$	2.57122e7	−	2.21243e7i	0.407840	−	0.350931i
$399$			1.53979e7i			0.242406i
$400$	−1.22304e7	−	3.77589e6i	−0.191100	−	0.0589983i
$401$	6.22427e7			0.965285			0.482643	−	0.875817i	$-0.339677\pi$
$401$	6.22427e7			0.965285			0.482643	+	0.875817i	$0.339677\pi$
$402$	−3.42362e7	−	3.97881e7i	−0.526996	−	0.612457i
$403$			1.14786e7i			0.175377i
$404$	5.64706e6	−	3.74344e7i	0.0856404	−	0.567711i
$405$	3.30094e6			0.0496904
$406$	−2.16105e7	+	1.85950e7i	−0.322914	+	0.277855i
$407$		−	7.92255e6i		−	0.117512i
$408$	2.01779e7	+	3.21262e7i	0.297096	+	0.473020i
$409$	6.41818e7			0.938084			0.469042	−	0.883176i	$-0.344599\pi$
$409$	6.41818e7			0.938084			0.469042	+	0.883176i	$0.344599\pi$
$410$	2.07523e7	+	2.41176e7i	0.301102	+	0.349931i
$411$			6.25848e7i			0.901453i
$412$	−2.33924e7	−	3.52880e6i	−0.334491	−	0.0504587i
$413$	4.13885e7			0.587529
$414$	5.74358e6	−	4.94213e6i	0.0809434	−	0.0696487i
$415$		−	3.53430e7i		−	0.494492i
$416$	−5.84042e6	−	1.33977e7i	−0.0811268	−	0.186102i
$417$	−4.33777e6			−0.0598216
$418$	1.34579e7	+	1.56403e7i	0.184268	+	0.214150i
$419$		−	7.52734e6i		−	0.102329i	−0.998690	−	0.0511646i	$-0.983707\pi$
$419$		−	7.52734e6i		−	0.102329i	0.998690	−	0.0511646i	$-0.0162933\pi$
$420$	1.94708e6	−	1.29072e7i	0.0262806	−	0.174214i
$421$	−9.54679e7			−1.27941			−0.639707	−	0.768619i	$-0.720944\pi$
$421$	−9.54679e7			−1.27941			−0.639707	+	0.768619i	$0.720944\pi$
$422$	−4.30183e7	+	3.70156e7i	−0.572422	+	0.492547i
$423$		−	3.22350e7i		−	0.425899i
$424$	−1.22767e8	+	7.71078e7i	−1.61059	+	1.01158i
$425$	−1.48540e7			−0.193498
$426$	3.47905e7	+	4.04324e7i	0.450021	+	0.522999i
$427$			5.13712e7i			0.659836i
$428$	5.25217e7	+	7.92302e6i	0.669897	+	0.101055i
$429$	−4.24906e6			−0.0538172
$430$	−3.44494e7	+	2.96424e7i	−0.433288	+	0.372828i
$431$			6.05446e7i			0.756212i	0.925762	+	0.378106i	$0.123424\pi$
$431$			6.05446e7i			0.756212i	−0.925762	+	0.378106i	$0.876576\pi$
$432$	−4.57698e6	+	1.48252e7i	−0.0567711	+	0.183886i
$433$	−4.68934e7			−0.577628			−0.288814	−	0.957385i	$-0.593261\pi$
$433$	−4.68934e7			−0.577628			−0.288814	+	0.957385i	$0.593261\pi$
$434$	−3.14294e7	−	3.65262e7i	−0.384474	−	0.446823i
$435$			1.32684e7i			0.161194i
$436$	2.09577e7	−	1.38928e8i	0.252862	−	1.67622i
$437$	1.64498e7			0.197113
$438$	−2.60929e7	+	2.24520e7i	−0.310528	+	0.267197i
$439$		−	7.62674e7i		−	0.901457i	−0.892661	−	0.450729i	$-0.851164\pi$
$439$		−	7.62674e7i		−	0.901457i	0.892661	−	0.450729i	$-0.148836\pi$
$440$	−9.30326e6	−	1.48122e7i	−0.109214	−	0.173884i
$441$	−1.52773e7			−0.178127
$442$	−1.10624e7	−	1.28564e7i	−0.128110	−	0.148886i
$443$		−	4.11703e7i		−	0.473558i	−0.971564	−	0.236779i	$-0.923908\pi$
$443$		−	4.11703e7i		−	0.473558i	0.971564	−	0.236779i	$-0.0760917\pi$
$444$	1.27888e7	+	1.92923e6i	0.146111	+	0.0220411i
$445$	−5.83194e7			−0.661810
$446$	7.26874e6	−	6.25448e6i	0.0819322	−	0.0704996i
$447$			1.54504e7i			0.172988i
$448$	5.52690e7	+	2.66414e7i	0.614678	+	0.296294i
$449$	−2.74161e7			−0.302877			−0.151439	−	0.988467i	$-0.548391\pi$
$449$	−2.74161e7			−0.302877			−0.151439	+	0.988467i	$0.548391\pi$
$450$	−3.96236e6	−	4.60492e6i	−0.0434827	−	0.0505341i
$451$			4.34784e7i			0.473962i
$452$	−2.46171e7	+	1.63187e8i	−0.266577	+	1.76714i
$453$	−460994.			−0.00495907
$454$	−3.54693e7	+	3.05200e7i	−0.379040	+	0.326150i
$455$			5.83571e6i			0.0619526i
$456$	−2.85243e7	+	1.79156e7i	−0.300830	+	0.188946i
$457$	−3.51153e7			−0.367915			−0.183957	−	0.982934i	$-0.558891\pi$
$457$	−3.51153e7			−0.367915			−0.183957	+	0.982934i	$0.558891\pi$
$458$	6.65649e7	+	7.73595e7i	0.692865	+	0.805225i
$459$			1.80054e7i			0.186194i
$460$	−1.37889e7	−	2.08008e6i	−0.141663	−	0.0213701i
$461$	7.39800e7			0.755112			0.377556	−	0.925987i	$-0.376765\pi$
$461$	7.39800e7			0.755112			0.377556	+	0.925987i	$0.376765\pi$
$462$	1.35210e7	−	1.16343e7i	0.137115	−	0.117982i
$463$		−	1.00507e8i		−	1.01263i	−0.862348	−	0.506316i	$-0.831007\pi$
$463$		−	1.00507e8i		−	1.01263i	0.862348	−	0.506316i	$-0.168993\pi$
$464$	−5.95909e7	−	1.83975e7i	−0.596522	−	0.184164i
$465$	−2.24263e7			−0.223048
$466$	−3.15504e7	−	3.66668e7i	−0.311779	−	0.362339i
$467$			1.62350e8i			1.59405i	0.603945	+	0.797026i	$0.293595\pi$
$467$			1.62350e8i			1.59405i	−0.603945	+	0.797026i	$0.706405\pi$
$468$	1.03469e6	−	6.85898e6i	0.0100942	−	0.0669148i
$469$	−9.85131e7			−0.954938
$470$	−4.49689e7	+	3.86941e7i	−0.433131	+	0.372693i
$471$		−	4.46156e7i		−	0.426997i
$472$	4.81559e7	+	7.66713e7i	0.457956	+	0.729133i
$473$	−6.21043e7			−0.586865
$474$	−5.01737e7	−	5.83102e7i	−0.471130	−	0.547532i
$475$		−	1.31886e7i		−	0.123060i
$476$	7.04040e7	+	1.06206e7i	0.652794	+	0.0984755i
$477$	−6.88058e7			−0.633972
$478$	1.48952e8	−	1.28167e8i	1.36384	−	1.17353i
$479$		−	1.59054e8i		−	1.44723i	−0.690202	−	0.723617i	$-0.742478\pi$
$479$		−	1.59054e8i		−	1.44723i	0.690202	−	0.723617i	$-0.257522\pi$
$480$	2.61757e7	−	1.14107e7i	0.236687	−	0.103179i
$481$	−5.78221e6			−0.0519587
$482$	−2.79042e7	−	3.24293e7i	−0.249188	−	0.289598i
$483$		−	1.42208e7i		−	0.126206i
$484$	−1.33469e7	+	8.84765e7i	−0.117718	+	0.780354i
$485$	−7.32476e7			−0.642049
$486$	−5.58190e6	+	4.80301e6i	−0.0486265	+	0.0418413i
$487$		−	1.46667e7i		−	0.126983i	−0.997982	−	0.0634914i	$-0.979776\pi$
$487$		−	1.46667e7i		−	0.126983i	0.997982	−	0.0634914i	$-0.0202236\pi$
$488$	−9.51639e7	+	5.97709e7i	−0.818866	+	0.514316i
$489$	−9.14765e7			−0.782317
$490$	1.83384e7	+	2.13123e7i	0.155874	+	0.181152i
$491$		−	1.18752e8i		−	1.00322i	−0.865094	−	0.501610i	$-0.832741\pi$
$491$		−	1.18752e8i		−	1.00322i	0.865094	−	0.501610i	$-0.167259\pi$
$492$	−7.01843e7	−	1.05875e7i	−0.589311	−	0.0888989i
$493$	−7.23742e7			−0.604008
$494$	1.14150e7	−	9.82215e6i	0.0946878	−	0.0814753i
$495$		−	8.30160e6i		−	0.0684457i
$496$	3.10956e7	−	1.00721e8i	0.254832	−	0.825420i
$497$	1.00108e8			0.815456
$498$	5.14256e7	+	5.97651e7i	0.416382	+	0.483905i
$499$		−	2.10310e7i		−	0.169261i	−0.996412	−	0.0846307i	$-0.973029\pi$
$499$		−	2.10310e7i		−	0.169261i	0.996412	−	0.0846307i	$-0.0269711\pi$
$500$	−1.66771e6	+	1.10553e7i	−0.0133417	+	0.0884421i
$501$	−9.91147e6			−0.0788179
$502$	9.86023e6	−	8.48435e6i	0.0779428	−	0.0670668i
$503$		−	1.30335e8i		−	1.02414i	−0.858944	−	0.512069i	$-0.828879\pi$
$503$		−	1.30335e8i		−	1.02414i	0.858944	−	0.512069i	$-0.171121\pi$
$504$	1.54880e7	+	2.46592e7i	0.120977	+	0.192613i
$505$	−3.30676e7			−0.256760
$506$	−1.24291e7	−	1.44446e7i	−0.0959372	−	0.111495i
$507$		−	7.21414e7i		−	0.553555i
$508$	2.45861e8	+	3.70886e7i	1.87542	+	0.282911i
$509$	−9.12352e7			−0.691846			−0.345923	−	0.938263i	$-0.612434\pi$
$509$	−9.12352e7			−0.691846			−0.345923	+	0.938263i	$0.612434\pi$
$510$	2.51182e7	−	2.16132e7i	0.189355	−	0.162933i
$511$			6.46046e7i			0.484173i
$512$	1.49534e7	+	1.33382e8i	0.111412	+	0.993774i
$513$	−1.59867e7			−0.118415
$514$	−3.11145e7	−	3.61603e7i	−0.229126	−	0.266282i
$515$			2.06636e7i			0.151281i
$516$	1.51231e7	−	1.00251e8i	0.110075	−	0.729691i
$517$	−8.10685e7			−0.586652
$518$	1.83997e7	−	1.58322e7i	0.132379	−	0.113907i
$519$			1.17499e8i			0.840490i
$520$	−1.08105e7	+	6.78991e6i	−0.0768842	+	0.0482896i
$521$	1.57984e8			1.11712			0.558560	−	0.829464i	$-0.311354\pi$
$521$	1.57984e8			1.11712			0.558560	+	0.829464i	$0.311354\pi$
$522$	−1.93061e7	−	2.24369e7i	−0.135732	−	0.157743i
$523$			1.17971e8i			0.824653i	0.911036	+	0.412327i	$0.135284\pi$
$523$			1.17971e8i			0.824653i	−0.911036	+	0.412327i	$0.864716\pi$
$524$	1.37813e8	+	2.07894e7i	0.957848	+	0.144494i
$525$	−1.14015e7			−0.0787925
$526$	−3.37202e7	+	2.90149e7i	−0.231704	+	0.199372i
$527$		−	1.22327e8i		−	0.835779i
$528$	3.72842e7	+	1.15107e7i	0.253293	+	0.0781990i
$529$	1.32844e8			0.897375
$530$	8.25927e7	+	9.59864e7i	0.554771	+	0.644736i
$531$			4.29711e7i			0.287007i
$532$	−9.42984e6	+	6.25105e7i	−0.0626281	+	0.415162i
$533$	3.17324e7			0.209566
$534$	9.86183e7	−	8.48573e7i	0.647640	−	0.557269i
$535$		−	4.63949e7i		−	0.302976i
$536$	−1.14621e8	−	1.82493e8i	−0.744337	−	1.18509i
$537$	−1.36904e7			−0.0884085
$538$	4.54645e7	+	5.28373e7i	0.291962	+	0.339308i
$539$			3.84211e7i			0.245360i
$540$	1.34007e7	+	2.02153e6i	0.0851034	+	0.0128380i
$541$	−2.37184e7			−0.149794			−0.0748969	−	0.997191i	$-0.523863\pi$
$541$	−2.37184e7			−0.149794			−0.0748969	+	0.997191i	$0.523863\pi$
$542$	1.31025e8	−	1.12742e8i	0.822920	−	0.708091i
$543$		−	6.60150e7i		−	0.412328i
$544$	6.22413e7	+	1.42779e8i	0.386618	+	0.886886i
$545$	−1.22722e8			−0.758111
$546$	−8.49121e6	−	9.86820e6i	−0.0521665	−	0.0606262i
$547$			1.30769e8i			0.798992i	0.916735	+	0.399496i	$0.130815\pi$
$547$			1.30769e8i			0.798992i	−0.916735	+	0.399496i	$0.869185\pi$
$548$	−3.83275e7	+	2.54073e8i	−0.232900	+	1.54389i
$549$	−5.33355e7			−0.322329
$550$	−1.15810e7	+	9.96503e6i	−0.0696079	+	0.0598950i
$551$		−	6.42598e7i		−	0.384135i
$552$	2.63436e7	−	1.65460e7i	0.156624	−	0.0983729i
$553$	−1.44372e8			−0.853707
$554$	−1.02599e8	−	1.19237e8i	−0.603412	−	0.701266i
$555$		−	1.12970e7i		−	0.0660821i
$556$	−1.76099e7	−	2.65649e6i	−0.102455	−	0.0154555i
$557$	8.04273e7			0.465412			0.232706	−	0.972547i	$-0.425242\pi$
$557$	8.04273e7			0.465412			0.232706	+	0.972547i	$0.425242\pi$
$558$	3.79229e7	−	3.26312e7i	0.218272	−	0.187815i
$559$			4.53263e7i			0.259487i
$560$	1.58090e7	−	5.12065e7i	0.0900202	−	0.291582i
$561$	4.52822e7			0.256472
$562$	−2.21069e8	−	2.56919e8i	−1.24543	−	1.44740i
$563$		−	2.79719e8i		−	1.56746i	−0.621101	−	0.783730i	$-0.713314\pi$
$563$		−	2.79719e8i		−	1.56746i	0.621101	−	0.783730i	$-0.286686\pi$
$564$	1.97411e7	−	1.30864e8i	0.110036	−	0.729426i
$565$	1.44151e8			0.799229
$566$	−2.13035e8	+	1.83308e8i	−1.17490	+	1.01096i
$567$			1.38204e7i			0.0758181i
$568$	1.16477e8	+	1.85448e8i	0.635616	+	1.01199i
$569$	8.01186e7			0.434907			0.217454	−	0.976071i	$-0.430225\pi$
$569$	8.01186e7			0.434907			0.217454	+	0.976071i	$0.430225\pi$
$570$	1.91900e7	+	2.23020e7i	0.103622	+	0.120426i
$571$			2.60254e8i			1.39794i	0.715149	+	0.698972i	$0.246359\pi$
$571$			2.60254e8i			1.39794i	−0.715149	+	0.698972i	$0.753641\pi$
$572$	−1.72498e7	−	2.60217e6i	−0.0921713	−	0.0139042i
$573$	1.33854e8			0.711488
$574$	−1.00976e8	+	8.68861e7i	−0.533928	+	0.459425i
$575$			1.21804e7i			0.0640703i
$576$	−2.76601e7	+	5.73824e7i	−0.144739	+	0.300269i
$577$	2.08528e8			1.08552			0.542760	−	0.839888i	$-0.317379\pi$
$577$	2.08528e8			1.08552			0.542760	+	0.839888i	$0.317379\pi$
$578$	−8.05567e6	−	9.36203e6i	−0.0417175	−	0.0484827i
$579$			1.47767e8i			0.761276i
$580$	−8.12569e6	+	5.38652e7i	−0.0416463	+	0.276073i
$581$	1.47975e8			0.754501
$582$	1.23862e8	−	1.06578e8i	0.628302	−	0.540630i
$583$			1.73041e8i			0.873260i
$584$	−1.19679e8	+	7.51680e7i	−0.600866	+	0.377394i
$585$	−6.05886e6			−0.0302638
$586$	5.81039e7	+	6.75264e7i	0.288744	+	0.335568i
$587$		−	2.03436e8i		−	1.00580i	−0.864343	−	0.502902i	$-0.832266\pi$
$587$		−	2.03436e8i		−	1.00580i	0.864343	−	0.502902i	$-0.167734\pi$
$588$	−6.20206e7	−	9.35595e6i	−0.305073	−	0.0460210i
$589$	1.08612e8			0.531536
$590$	5.99461e7	−	5.15814e7i	0.291881	−	0.251152i
$591$		−	2.38336e6i		−	0.0115459i
$592$	5.07370e7	+	1.56640e7i	0.244546	+	0.0754985i
$593$	−2.65879e7			−0.127503			−0.0637513	−	0.997966i	$-0.520306\pi$
$593$	−2.65879e7			−0.127503			−0.0637513	+	0.997966i	$0.520306\pi$
$594$	1.20792e7	+	1.40380e7i	0.0576340	+	0.0669803i
$595$		−	6.21911e7i		−	0.295242i
$596$	−9.46195e6	+	6.27233e7i	−0.0446933	+	0.296272i
$597$	6.60961e7			0.310637
$598$	−1.05423e7	+	9.07125e6i	−0.0492983	+	0.0424193i
$599$			1.00479e8i			0.467516i	0.972295	+	0.233758i	$0.0751023\pi$
$599$			1.00479e8i			0.467516i	−0.972295	+	0.233758i	$0.924898\pi$
$600$	−1.32658e7	−	2.11211e7i	−0.0614156	−	0.0977827i
$601$	3.21498e8			1.48100			0.740500	−	0.672056i	$-0.234589\pi$
$601$	3.21498e8			1.48100			0.740500	+	0.672056i	$0.234589\pi$
$602$	−1.24108e8	−	1.44234e8i	−0.568864	−	0.661115i
$603$		−	1.02280e8i		−	0.466486i
$604$	−1.87148e6	−	282317.i	−0.00849327	−	0.00128123i
$605$	7.81554e7			0.352933
$606$	5.59173e7	−	4.81147e7i	0.251263	−	0.216202i
$607$			1.80290e8i			0.806130i	0.915171	+	0.403065i	$0.132055\pi$
$607$			1.80290e8i			0.806130i	−0.915171	+	0.403065i	$0.867945\pi$
$608$	−1.26771e8	+	5.52630e7i	−0.564039	+	0.245880i
$609$	−5.55523e7			−0.245952
$610$	6.40225e7	+	7.44048e7i	0.282061	+	0.327802i
$611$			5.91672e7i			0.259393i
$612$	−1.10267e7	+	7.30961e7i	−0.0481051	+	0.318889i
$613$	−4.52010e8			−1.96230			−0.981152	−	0.193237i	$-0.938101\pi$
$613$	−4.52010e8			−1.96230			−0.981152	+	0.193237i	$0.938101\pi$
$614$	8.52206e7	−	7.33291e7i	0.368163	−	0.316790i
$615$			6.19970e7i			0.266530i
$616$	6.20158e7	−	3.89511e7i	0.265314	−	0.166639i
$617$	5.84022e6			0.0248641			0.0124321	−	0.999923i	$-0.496043\pi$
$617$	5.84022e6			0.0248641			0.0124321	+	0.999923i	$0.496043\pi$
$618$	−3.00665e7	−	3.49423e7i	−0.127385	−	0.148042i
$619$		−	2.69398e8i		−	1.13586i	−0.823078	−	0.567928i	$-0.807745\pi$
$619$		−	2.69398e8i		−	1.13586i	0.823078	−	0.567928i	$-0.192255\pi$
$620$	−9.10433e7	−	1.37341e7i	−0.382009	−	0.0576268i
$621$	1.47645e7			0.0616516
$622$	2.43852e8	−	2.09825e8i	1.01334	−	0.871940i
$623$		−	2.44173e8i		−	1.00980i
$624$	8.40102e6	−	2.72115e7i	0.0345763	−	0.111995i
$625$	9.76562e6			0.0400000
$626$	−1.14515e8	−	1.33085e8i	−0.466808	−	0.542509i
$627$			4.02053e7i			0.163110i
$628$	2.73231e7	−	1.81125e8i	0.110319	−	0.731306i
$629$	6.16209e7			0.247615
$630$	1.92800e7	−	1.65897e7i	0.0771055	−	0.0663463i
$631$			2.83825e8i			1.12970i	0.825195	+	0.564848i	$0.191065\pi$
$631$			2.83825e8i			1.12970i	−0.825195	+	0.564848i	$0.808935\pi$
$632$	−1.67979e8	−	2.67447e8i	−0.665431	−	1.05946i
$633$	−1.10584e8			−0.435993
$634$	−1.49926e8	−	1.74240e8i	−0.588316	−	0.683721i
$635$		−	2.17180e8i		−	0.848202i
$636$	−2.79329e8	−	4.21374e7i	−1.08579	−	0.163793i
$637$	2.80413e7			0.108488
$638$	−5.64269e7	+	4.85532e7i	−0.217282	+	0.186963i
$639$			1.03936e8i			0.398349i
$640$	1.13253e8	−	3.02935e7i	0.432025	−	0.115560i
$641$	8.05312e7			0.305767			0.152883	−	0.988244i	$-0.451144\pi$
$641$	8.05312e7			0.305767			0.152883	+	0.988244i	$0.451144\pi$
$642$	6.75066e7	+	7.84539e7i	0.255118	+	0.296490i
$643$			1.70629e8i			0.641829i	0.947108	+	0.320915i	$0.103990\pi$
$643$			1.70629e8i			0.641829i	−0.947108	+	0.320915i	$0.896010\pi$
$644$	8.70893e6	−	5.77316e7i	0.0326067	−	0.216150i
$645$	−8.85562e7			−0.330020
$646$	−1.21649e8	+	1.04675e8i	−0.451244	+	0.388279i
$647$			1.72635e8i			0.637404i	0.947855	+	0.318702i	$0.103247\pi$
$647$			1.72635e8i			0.637404i	−0.947855	+	0.318702i	$0.896753\pi$
$648$	−2.56021e7	+	1.60802e7i	−0.0940914	+	0.0590972i
$649$	1.08069e8			0.395336
$650$	7.27289e6	+	8.45231e6i	0.0264830	+	0.0307777i
$651$		−	9.38949e7i		−	0.340329i
$652$	−3.71364e8	−	5.60211e7i	−1.33985	−	0.202120i
$653$	−9.10476e7			−0.326986			−0.163493	−	0.986545i	$-0.552276\pi$
$653$	−9.10476e7			−0.326986			−0.163493	+	0.986545i	$0.552276\pi$
$654$	2.07523e8	−	1.78566e8i	0.741879	−	0.638359i
$655$		−	1.21737e8i		−	0.433209i
$656$	−2.78441e8	−	8.59631e7i	−0.986329	−	0.304509i
$657$	−6.70749e7			−0.236518
$658$	−1.62005e8	−	1.88277e8i	−0.568658	−	0.660875i
$659$			4.48502e8i			1.56714i	0.621302	+	0.783571i	$0.286604\pi$
$659$			4.48502e8i			1.56714i	−0.621302	+	0.783571i	$0.713396\pi$
$660$	5.08399e6	−	3.37018e7i	0.0176837	−	0.117225i
$661$	−1.10377e8			−0.382186			−0.191093	−	0.981572i	$-0.561203\pi$
$661$	−1.10377e8			−0.382186			−0.191093	+	0.981572i	$0.561203\pi$
$662$	4.01061e7	−	3.45098e7i	0.138241	−	0.118951i
$663$		−	3.30489e7i		−	0.113401i
$664$	1.72170e8	+	2.74120e8i	0.588104	+	0.936347i
$665$	5.52184e7			0.187767
$666$	1.64376e7	+	1.91032e7i	0.0556437	+	0.0646672i
$667$			5.93471e7i			0.199996i
$668$	−4.02373e7	−	6.06989e6i	−0.134989	−	0.0203634i
$669$	1.86851e7			0.0624048
$670$	−1.42684e8	+	1.22774e8i	−0.474407	+	0.408209i
$671$			1.34135e8i			0.443990i
$672$	4.77746e7	+	1.09593e8i	0.157431	+	0.361140i
$673$	−3.09349e8			−1.01485			−0.507427	−	0.861695i	$-0.669403\pi$
$673$	−3.09349e8			−1.01485			−0.507427	+	0.861695i	$0.669403\pi$
$674$	1.23661e8	+	1.43714e8i	0.403880	+	0.469376i
$675$		−	1.18375e7i		−	0.0384900i
$676$	4.41801e7	−	2.92870e8i	0.143017	−	0.948058i
$677$	1.46692e8			0.472761			0.236381	−	0.971661i	$-0.424039\pi$
$677$	1.46692e8			0.472761			0.236381	+	0.971661i	$0.424039\pi$
$678$	−2.43759e8	+	2.09745e8i	−0.782117	+	0.672982i
$679$		−	3.06675e8i		−	0.979644i
$680$	1.15208e8	−	7.23600e7i	0.366399	−	0.230129i
$681$	−9.11780e7			−0.288701
$682$	−8.20649e7	−	9.53731e7i	−0.258705	−	0.300658i
$683$			4.83173e8i			1.51649i	0.651968	+	0.758247i	$0.273944\pi$
$683$			4.83173e8i			1.51649i	−0.651968	+	0.758247i	$0.726056\pi$
$684$	−6.49007e7	−	9.79042e6i	−0.202806	−	0.0305938i
$685$	2.24435e8			0.698263
$686$	−2.56211e8	+	2.20459e8i	−0.793642	+	0.682899i
$687$			1.98861e8i			0.613310i
$688$	1.22789e8	−	3.97724e8i	0.377047	−	1.22128i
$689$	1.26293e8			0.386118
$690$	−1.77229e7	−	2.05970e7i	−0.0539496	−	0.0626985i
$691$			1.33819e8i			0.405586i	0.979222	+	0.202793i	$0.0650019\pi$
$691$			1.33819e8i			0.405586i	−0.979222	+	0.202793i	$0.934998\pi$
$692$	−7.19577e7	+	4.77008e8i	−0.217149	+	1.43948i
$693$	3.47573e7			0.104435
$694$	−4.77267e8	+	4.10670e8i	−1.42785	+	1.22861i
$695$			1.55556e7i			0.0463376i
$696$	−6.46357e7	−	1.02909e8i	−0.191710	−	0.305230i
$697$	−3.38171e8			−0.998708
$698$	3.04889e8	+	3.54332e8i	0.896552	+	1.04194i
$699$		−	9.42562e7i		−	0.275980i
$700$	−4.62864e7	−	6.98240e6i	−0.134946	−	0.0203569i
$701$	−2.21186e8			−0.642101			−0.321050	−	0.947062i	$-0.604036\pi$
$701$	−2.21186e8			−0.642101			−0.321050	+	0.947062i	$0.604036\pi$
$702$	1.02455e7	−	8.81590e6i	0.0296158	−	0.0254833i
$703$			5.47121e7i			0.157477i
$704$	1.44312e8	+	6.95630e7i	0.413604	+	0.199370i
$705$	−1.15598e8			−0.329900
$706$	1.15162e7	+	1.33837e7i	0.0327261	+	0.0380332i
$707$		−	1.38448e8i		−	0.391768i
$708$	−2.63159e7	+	1.74448e8i	−0.0741513	+	0.491550i
$709$	4.32781e8			1.21431			0.607155	−	0.794583i	$-0.292311\pi$
$709$	4.32781e8			1.21431			0.607155	+	0.794583i	$0.292311\pi$
$710$	1.44994e8	−	1.24762e8i	0.405113	−	0.348584i
$711$		−	1.49893e8i		−	0.417035i
$712$	4.52325e8	−	2.84098e8i	1.25317	−	0.787096i
$713$	−1.00309e8			−0.276739
$714$	9.04908e7	+	1.05165e8i	0.248605	+	0.288920i
$715$			1.52375e7i			0.0416866i
$716$	−5.55786e7	−	8.38415e6i	−0.151415	−	0.0228413i
$717$	3.82898e8			1.03879
$718$	−7.29376e7	+	6.27601e7i	−0.197051	+	0.169555i
$719$			5.42829e8i			1.46042i	0.683225	+	0.730208i	$0.260577\pi$
$719$			5.42829e8i			1.46042i	−0.683225	+	0.730208i	$0.739423\pi$
$720$	5.31645e7	+	1.64135e7i	0.142438	+	0.0439747i
$721$	−8.65150e7			−0.230826
$722$	1.52543e8	+	1.77280e8i	0.405304	+	0.471031i
$723$		−	8.33632e7i		−	0.220577i
$724$	4.04283e7	−	2.67999e8i	0.106529	−	0.706184i
$725$	4.75817e7			0.124861
$726$	−1.32161e8	+	1.13719e8i	−0.345377	+	0.297184i
$727$		−	1.71836e8i		−	0.447210i	−0.974680	−	0.223605i	$-0.928217\pi$
$727$		−	1.71836e8i		−	0.447210i	0.974680	−	0.223605i	$-0.0717826\pi$
$728$	−2.84281e7	−	4.52618e7i	−0.0736808	−	0.117311i
$729$	−1.43489e7			−0.0370370
$730$	8.05149e7	+	9.35718e7i	0.206970	+	0.240534i
$731$		−	4.83042e8i		−	1.23661i
$732$	−2.16524e8	−	3.26632e7i	−0.552044	−	0.0832770i
$733$	−3.55710e8			−0.903200			−0.451600	−	0.892221i	$-0.649147\pi$
$733$	−3.55710e8			−0.903200			−0.451600	+	0.892221i	$0.649147\pi$
$734$	4.62780e8	−	3.98204e8i	1.17027	−	1.00697i
$735$			5.47857e7i			0.137977i
$736$	1.17079e8	−	5.10381e7i	0.293661	−	0.128015i
$737$	−2.57226e8			−0.642558
$738$	−9.02084e7	−	1.04837e8i	−0.224428	−	0.260823i
$739$		−	6.71490e8i		−	1.66382i	−0.554912	−	0.831909i	$-0.687248\pi$
$739$		−	6.71490e8i		−	1.66382i	0.554912	−	0.831909i	$-0.312752\pi$
$740$	6.91839e6	−	4.58620e7i	0.0170730	−	0.113177i
$741$	2.93435e7			0.0721203
$742$	−4.01878e8	+	3.45801e8i	−0.983745	+	0.846475i
$743$		−	2.37075e8i		−	0.577988i	−0.957331	−	0.288994i	$-0.906679\pi$
$743$		−	2.37075e8i		−	0.577988i	0.957331	−	0.288994i	$-0.0933208\pi$
$744$	1.73938e8	−	1.09248e8i	0.422354	−	0.265273i
$745$	5.54064e7			0.133996
$746$	2.83825e8	+	3.29852e8i	0.683652	+	0.794517i
$747$			1.53633e8i			0.368573i
$748$	1.83831e8	+	2.77313e7i	0.439252	+	0.0662621i
$749$	1.94247e8			0.462284
$750$	−1.65137e7	+	1.42094e7i	−0.0391436	+	0.0336816i
$751$		−	5.41645e8i		−	1.27878i	−0.768884	−	0.639389i	$-0.779187\pi$
$751$		−	5.41645e8i		−	1.27878i	0.768884	−	0.639389i	$-0.220813\pi$
$752$	1.60284e8	−	5.19173e8i	0.376910	−	1.22084i
$753$	2.53469e7			0.0593662
$754$	3.54362e7	+	4.11827e7i	0.0826671	+	0.0960729i
$755$			1.65317e6i			0.00384128i
$756$	−8.46378e6	+	5.61064e7i	−0.0195884	+	0.129852i
$757$	−5.37604e8			−1.23930			−0.619648	−	0.784880i	$-0.712725\pi$
$757$	−5.37604e8			−1.23930			−0.619648	+	0.784880i	$0.712725\pi$
$758$	−7.66273e7	+	6.59349e7i	−0.175945	+	0.151394i
$759$		−	3.71316e7i		−	0.0849217i
$760$	6.42472e7	+	1.02291e8i	0.146357	+	0.233022i
$761$	−4.02108e8			−0.912407			−0.456204	−	0.889875i	$-0.650791\pi$
$761$	−4.02108e8			−0.912407			−0.456204	+	0.889875i	$0.650791\pi$
$762$	3.16007e8	+	3.67252e8i	0.714219	+	0.830041i
$763$		−	5.13815e8i		−	1.15673i
$764$	5.43403e8	+	8.19736e7i	1.21855	+	0.183820i
$765$	6.45692e7			0.144225
$766$	3.70082e8	−	3.18442e8i	0.823402	−	0.708506i
$767$		−	7.88732e7i		−	0.174801i
$768$	−1.47432e8	+	2.16014e8i	−0.325469	+	0.476868i
$769$	7.17215e8			1.57714			0.788570	−	0.614945i	$-0.210822\pi$
$769$	7.17215e8			1.57714			0.788570	+	0.614945i	$0.210822\pi$
$770$	−4.17218e7	−	4.84877e7i	−0.0913883	−	0.106208i
$771$		−	9.29541e7i		−	0.202817i
$772$	−9.04941e7	+	5.99886e8i	−0.196684	+	1.30382i
$773$	7.16120e8			1.55041			0.775207	−	0.631708i	$-0.217646\pi$
$773$	7.16120e8			1.55041			0.775207	+	0.631708i	$0.217646\pi$
$774$	1.49749e8	−	1.28853e8i	0.322954	−	0.277889i
$775$			8.04228e7i			0.172772i
$776$	5.68108e8	−	3.56819e8i	1.21575	−	0.763594i
$777$	4.72984e7			0.100829
$778$	−3.35127e8	−	3.89473e8i	−0.711657	−	0.827064i
$779$		−	3.00256e8i		−	0.635155i
$780$	−2.45970e7	−	3.71051e6i	−0.0518320	−	0.00781897i
$781$	2.61391e8			0.548704
$782$	1.12349e8	−	9.66722e7i	0.234936	−	0.202154i
$783$		−	5.76765e7i		−	0.120147i
$784$	−2.46054e8	−	7.59641e7i	−0.510601	−	0.157638i
$785$	−1.59996e8			−0.330750
$786$	1.77132e8	+	2.05857e8i	0.364779	+	0.423934i
$787$		−	4.14567e8i		−	0.850493i	−0.905077	−	0.425247i	$-0.860187\pi$
$787$		−	4.14567e8i		−	0.850493i	0.905077	−	0.425247i	$-0.139813\pi$
$788$	1.45959e6	−	9.67566e6i	0.00298300	−	0.0197743i
$789$	−8.66816e7			−0.176480
$790$	−2.09106e8	+	1.79928e8i	−0.424116	+	0.364936i
$791$			6.03533e8i			1.21947i
$792$	4.04405e7	+	6.43872e7i	0.0814031	+	0.129606i
$793$	9.78970e7			0.196313
$794$	3.00873e8	+	3.49665e8i	0.601066	+	0.698538i
$795$			2.46744e8i			0.491072i
$796$	2.68328e8	+	4.04779e7i	0.532019	+	0.0802563i
$797$	−8.17450e7			−0.161468			−0.0807339	−	0.996736i	$-0.525726\pi$
$797$	−8.17450e7			−0.161468			−0.0807339	+	0.996736i	$0.525726\pi$
$798$	−9.33745e7	+	8.03452e7i	−0.183747	+	0.158107i
$799$		−	6.30544e8i		−	1.23616i
$800$	−4.09199e7	−	9.38686e7i	−0.0799217	−	0.183337i
$801$	2.53510e8			0.493284
$802$	3.24778e8	+	3.77446e8i	0.629598	+	0.731698i
$803$			1.68688e8i			0.325790i
$804$	6.26373e7	−	4.15223e8i	0.120522	−	0.798938i
$805$	−5.09970e7			−0.0977590
$806$	−6.96073e7	+	5.98944e7i	−0.132938	+	0.114388i
$807$			1.35824e8i			0.258439i
$808$	2.56472e8	−	1.61086e8i	0.486190	−	0.305367i
$809$	−9.14566e8			−1.72731			−0.863653	−	0.504086i	$-0.831829\pi$
$809$	−9.14566e8			−1.72731			−0.863653	+	0.504086i	$0.831829\pi$
$810$	1.72241e7	+	2.00172e7i	0.0324101	+	0.0376659i
$811$			2.18494e8i			0.409617i	0.978802	+	0.204808i	$0.0656572\pi$
$811$			2.18494e8i			0.409617i	−0.978802	+	0.204808i	$0.934343\pi$
$812$	−2.25524e8	−	3.40208e7i	−0.421235	−	0.0635443i
$813$	3.36816e8			0.626788
$814$	4.80431e7	−	4.13393e7i	0.0890754	−	0.0766460i
$815$			3.28043e8i			0.605980i
$816$	−8.95296e7	+	2.89993e8i	−0.164777	+	0.533725i
$817$	4.28884e8			0.786455
$818$	3.34896e8	+	3.89204e8i	0.611857	+	0.711079i
$819$		−	2.53674e7i		−	0.0461768i
$820$	−3.79676e7	+	2.51688e8i	−0.0688608	+	0.456478i
$821$	−8.45664e8			−1.52816			−0.764079	−	0.645123i	$-0.776806\pi$
$821$	−8.45664e8			−1.52816			−0.764079	+	0.645123i	$0.776806\pi$
$822$	−3.79520e8	+	3.26563e8i	−0.683312	+	0.587964i
$823$			7.93523e8i			1.42351i	0.702429	+	0.711754i	$0.252099\pi$
$823$			7.93523e8i			1.42351i	−0.702429	+	0.711754i	$0.747901\pi$
$824$	−1.00661e8	−	1.60267e8i	−0.179920	−	0.286459i
$825$	−2.97703e7			−0.0530178
$826$	2.15962e8	+	2.50984e8i	0.383210	+	0.445354i
$827$		−	2.55103e8i		−	0.451023i	−0.974240	−	0.225512i	$-0.927595\pi$
$827$		−	2.55103e8i		−	0.451023i	0.974240	−	0.225512i	$-0.0724053\pi$
$828$	5.99391e7	+	9.04194e6i	0.105589	+	0.0159283i
$829$	−6.38970e8			−1.12155			−0.560773	−	0.827970i	$-0.689496\pi$
$829$	−6.38970e8			−1.12155			−0.560773	+	0.827970i	$0.689496\pi$
$830$	2.14323e8	−	1.84417e8i	0.374831	−	0.322528i
$831$		−	3.06513e8i		−	0.534129i
$832$	5.07700e7	−	1.05325e8i	0.0881530	−	0.182878i
$833$	−2.98836e8			−0.517009
$834$	−2.26341e7	−	2.63046e7i	−0.0390181	−	0.0453455i
$835$			3.55435e7i			0.0610521i
$836$	−2.46221e7	+	1.63220e8i	−0.0421412	+	0.279354i
$837$	9.74852e7			0.166250
$838$	4.56465e7	−	3.92771e7i	0.0775668	−	0.0667433i
$839$			8.37669e8i			1.41836i	0.705028	+	0.709180i	$0.250935\pi$
$839$			8.37669e8i			1.41836i	−0.705028	+	0.709180i	$0.749065\pi$
$840$	8.84301e7	−	5.55414e7i	0.149198	−	0.0937086i
$841$	−3.62988e8			−0.610245
$842$	−4.98144e8	−	5.78927e8i	−0.834486	−	0.969812i
$843$		−	6.60440e8i		−	1.10243i
$844$	−4.48933e8	−	6.77225e7i	−0.746713	−	0.112643i
$845$	−2.58706e8			−0.428782
$846$	1.95476e8	−	1.68200e8i	0.322837	−	0.277789i
$847$			3.27223e8i			0.538509i
$848$	−1.10818e9	−	3.42128e8i	−1.81728	−	0.561049i
$849$	−5.47631e8			−0.894880
$850$	−7.75071e7	−	9.00762e7i	−0.126207	−	0.146674i
$851$		−	5.05294e7i		−	0.0819890i
$852$	−6.36515e7	+	4.21946e8i	−0.102918	+	0.682242i
$853$	6.48236e8			1.04445			0.522223	−	0.852809i	$-0.325103\pi$
$853$	6.48236e8			1.04445			0.522223	+	0.852809i	$0.325103\pi$
$854$	−3.11520e8	+	2.68051e8i	−0.500163	+	0.430372i
$855$			5.73298e7i			0.0917239i
$856$	2.26009e8	+	3.59839e8i	0.360333	+	0.573702i
$857$	−7.42707e8			−1.17998			−0.589991	−	0.807410i	$-0.700869\pi$
$857$	−7.42707e8			−1.17998			−0.589991	+	0.807410i	$0.700869\pi$
$858$	−2.21713e7	−	2.57667e7i	−0.0351018	−	0.0407941i
$859$		−	1.14216e9i		−	1.80197i	−0.433848	−	0.900986i	$-0.642845\pi$
$859$		−	1.14216e9i		−	1.80197i	0.433848	−	0.900986i	$-0.357155\pi$
$860$	−3.59509e8	−	5.42327e7i	−0.565216	−	0.0852641i
$861$	−2.59571e8			−0.406674
$862$	−3.67148e8	+	3.15917e8i	−0.573218	+	0.493232i
$863$			7.21139e8i			1.12198i	0.827822	+	0.560992i	$0.189580\pi$
$863$			7.21139e8i			1.12198i	−0.827822	+	0.560992i	$0.810420\pi$
$864$	−1.13784e8	+	4.96014e7i	−0.176416	+	0.0769047i
$865$	4.21363e8			0.651041
$866$	−2.44686e8	−	2.84366e8i	−0.376752	−	0.437849i
$867$		−	2.40662e7i		−	0.0369275i
$868$	5.75022e7	−	3.81182e8i	0.0879276	−	0.582872i
$869$	−3.76969e8			−0.574442
$870$	−8.04607e7	+	6.92334e7i	−0.122187	+	0.105138i
$871$			1.87734e8i			0.284112i
$872$	9.51831e8	−	5.97829e8i	1.43552	−	0.901628i
$873$	3.18401e8			0.478555
$874$	8.58336e7	+	9.97529e7i	0.128565	+	0.149414i
$875$			4.08869e7i			0.0610324i
$876$	−2.72302e8	−	4.10773e7i	−0.405078	−	0.0611069i
$877$	−6.88487e8			−1.02070			−0.510349	−	0.859967i	$-0.670484\pi$
$877$	−6.88487e8			−1.02070			−0.510349	+	0.859967i	$0.670484\pi$
$878$	4.62493e8	−	3.97957e8i	0.683315	−	0.587967i
$879$			1.73584e8i			0.255590i
$880$	4.12786e7	−	1.33705e8i	0.0605727	−	0.196200i
$881$	4.33117e8			0.633399			0.316700	−	0.948526i	$-0.397425\pi$
$881$	4.33117e8			0.633399			0.316700	+	0.948526i	$0.397425\pi$
$882$	−7.97156e7	−	9.26428e7i	−0.116182	−	0.135022i
$883$			1.05024e9i			1.52548i	0.646705	+	0.762740i	$0.276147\pi$
$883$			1.05024e9i			1.52548i	−0.646705	+	0.762740i	$0.723853\pi$
$884$	2.02395e7	−	1.34167e8i	0.0292983	−	0.194218i
$885$	1.54098e8			0.222315
$886$	2.49661e8	−	2.14824e8i	0.358963	−	0.308874i
$887$		−	7.88286e8i		−	1.12957i	−0.825238	−	0.564785i	$-0.808959\pi$
$887$		−	7.88286e8i		−	1.12957i	0.825238	−	0.564785i	$-0.191041\pi$
$888$	5.50322e7	+	8.76193e7i	0.0785920	+	0.125130i
$889$	9.09295e8			1.29419
$890$	−3.04306e8	−	3.53655e8i	−0.431659	−	0.501660i
$891$			3.60864e7i			0.0510164i
$892$	7.58555e7	+	1.14430e7i	0.106879	+	0.0161229i
$893$	5.59849e8			0.786170
$894$	−9.36924e7	+	8.06188e7i	−0.131127	+	0.112830i
$895$			4.90952e7i			0.0684809i
$896$	1.26833e8	+	4.74169e8i	0.176323	+	0.659188i
$897$	−2.71002e7			−0.0375487
$898$	−1.43055e8	−	1.66254e8i	−0.197549	−	0.229584i
$899$			3.91849e8i			0.539312i
$900$	7.24940e6	−	4.80563e7i	0.00994430	−	0.0659208i
$901$	−1.34590e9			−1.84009
$902$	−2.63657e8	+	2.26867e8i	−0.359269	+	0.309137i
$903$		−	3.70769e8i		−	0.503547i
$904$	−1.11803e9	+	7.02217e8i	−1.51338	+	0.950530i
$905$	−2.36736e8			−0.319388
$906$	−2.40543e6	−	2.79551e6i	−0.00323451	−	0.00375903i
$907$		−	2.31644e7i		−	0.0310455i	−0.999880	−	0.0155227i	$-0.995059\pi$
$907$		−	2.31644e7i		−	0.0310455i	0.999880	−	0.0155227i	$-0.00494124\pi$
$908$	−3.70152e8	−	5.58383e7i	−0.494451	−	0.0745890i
$909$	1.43742e8			0.191378
$910$	−3.53883e7	+	3.04503e7i	−0.0469608	+	0.0404080i
$911$		−	5.38656e8i		−	0.712454i	−0.934399	−	0.356227i	$-0.884063\pi$
$911$		−	5.38656e8i		−	0.712454i	0.934399	−	0.356227i	$-0.115937\pi$
$912$	−2.57480e8	−	7.94917e7i	−0.339437	−	0.104794i
$913$	3.86375e8			0.507688
$914$	−1.83229e8	−	2.12942e8i	−0.239969	−	0.278884i
$915$			1.91266e8i			0.249675i
$916$	−1.21785e8	+	8.07312e8i	−0.158455	+	1.05040i
$917$	5.09690e8			0.660995
$918$	−1.09187e8	+	9.39509e7i	−0.141137	+	0.121443i
$919$			1.29910e9i			1.67377i	0.547377	+	0.836886i	$0.315626\pi$
$919$			1.29910e9i			1.67377i	−0.547377	+	0.836886i	$0.684374\pi$
$920$	−5.93355e7	−	9.44708e7i	−0.0761993	−	0.121320i
$921$	2.19069e8			0.280416
$922$	3.86022e8	+	4.48622e8i	0.492515	+	0.572384i
$923$		−	1.90774e8i		−	0.242613i
$924$	1.41103e8	+	2.12857e7i	0.178863	+	0.0269819i
$925$	−4.05121e7			−0.0511869
$926$	6.09482e8	−	5.24436e8i	0.767588	−	0.660480i
$927$		−	8.98231e7i		−	0.112758i
$928$	−1.99377e8	−	4.57362e8i	−0.249477	−	0.572290i
$929$	−4.24439e8			−0.529381			−0.264691	−	0.964333i	$-0.585270\pi$
$929$	−4.24439e8			−0.529381			−0.264691	+	0.964333i	$0.585270\pi$
$930$	−1.17019e8	−	1.35995e8i	−0.145481	−	0.169073i
$931$		−	2.65331e8i		−	0.328806i
$932$	5.77234e7	−	3.82649e8i	0.0713024	−	0.472664i
$933$	6.26849e8			0.771823
$934$	−9.84508e8	+	8.47132e8i	−1.20831	+	1.03971i
$935$		−	1.62386e8i		−	0.198662i
$936$	4.69925e7	−	2.95152e7i	0.0573061	−	0.0359930i
$937$	1.45041e9			1.76308			0.881539	−	0.472111i	$-0.156508\pi$
$937$	1.45041e9			1.76308			0.881539	+	0.472111i	$0.156508\pi$
$938$	−5.14034e8	−	5.97393e8i	−0.622849	−	0.723855i
$939$		−	3.42111e8i		−	0.413209i
$940$	−4.69289e8	−	7.07933e7i	−0.565011	−	0.0852332i
$941$	1.06912e9			1.28309			0.641544	−	0.767086i	$-0.278294\pi$
$941$	1.06912e9			1.28309			0.641544	+	0.767086i	$0.278294\pi$
$942$	2.70554e8	−	2.32801e8i	0.323669	−	0.278504i
$943$			2.77302e8i			0.330687i
$944$	−2.13668e8	+	6.92087e8i	−0.253994	+	0.822706i
$945$	4.95614e7			0.0587284
$946$	−3.24055e8	−	3.76606e8i	−0.382777	−	0.444851i
$947$		−	2.62002e8i		−	0.308499i	−0.988032	−	0.154250i	$-0.950704\pi$
$947$		−	2.62002e8i		−	0.308499i	0.988032	−	0.154250i	$-0.0492960\pi$
$948$	9.17960e7	−	6.08516e8i	0.107745	−	0.714245i
$949$	1.23116e8			0.144050
$950$	7.99771e7	−	6.88172e7i	0.0932813	−	0.0802650i
$951$		−	4.47903e8i		−	0.520765i
$952$	3.02958e8	+	4.82354e8i	0.351133	+	0.559056i
$953$	9.09209e8			1.05047			0.525237	−	0.850956i	$-0.323977\pi$
$953$	9.09209e8			1.05047			0.525237	+	0.850956i	$0.323977\pi$
$954$	−3.59023e8	−	4.17245e8i	−0.413502	−	0.480558i
$955$		−	4.80013e8i		−	0.551116i
$956$	1.55444e9	+	2.34491e8i	1.77910	+	0.268381i
$957$	−1.45052e8			−0.165496
$958$	9.64521e8	−	8.29933e8i	1.09702	−	0.943945i
$959$			9.39669e8i			1.06542i
$960$	2.05779e8	+	9.91918e7i	0.232588	+	0.112115i
$961$	2.25198e8			0.253743
$962$	−3.01711e7	−	3.50639e7i	−0.0338896	−	0.0393853i
$963$			2.01675e8i			0.225825i
$964$	5.10525e7	−	3.38427e8i	0.0569883	−	0.377776i
$965$	5.29907e8			0.589682
$966$	8.62360e7	−	7.42028e7i	0.0956659	−	0.0823169i
$967$			1.49745e9i			1.65605i	0.560691	+	0.828025i	$0.310536\pi$
$967$			1.49745e9i			1.65605i	−0.560691	+	0.828025i	$0.689464\pi$
$968$	−6.06173e8	+	3.80727e8i	−0.668298	+	0.419747i
$969$	−3.12713e8			−0.343697
$970$	−3.82200e8	−	4.44180e8i	−0.418770	−	0.486681i
$971$		−	4.91944e8i		−	0.537351i	−0.963231	−	0.268676i	$-0.913414\pi$
$971$		−	4.91944e8i		−	0.537351i	0.963231	−	0.268676i	$-0.0865860\pi$
$972$	−5.82518e7	−	8.78742e6i	−0.0634323	−	0.00956891i
$973$	−6.51287e7			−0.0707024
$974$	8.89402e7	−	7.65297e7i	0.0962546	−	0.0828234i
$975$			2.17276e7i			0.0234422i
$976$	−8.59015e8	−	2.65204e8i	−0.923955	−	0.285253i
$977$	7.44362e8			0.798180			0.399090	−	0.916912i	$-0.369326\pi$
$977$	7.44362e8			0.798180			0.399090	+	0.916912i	$0.369326\pi$
$978$	−4.77317e8	−	5.54722e8i	−0.510259	−	0.593006i
$979$		−	6.37557e8i		−	0.679471i
$980$	−3.35513e7	+	2.22412e8i	−0.0356477	+	0.236309i
$981$	5.33462e8			0.565062
$982$	7.20124e8	−	6.19639e8i	0.760453	−	0.654341i
$983$			1.04089e9i			1.09584i	0.836532	+	0.547918i	$0.184580\pi$
$983$			1.04089e9i			1.09584i	−0.836532	+	0.547918i	$0.815420\pi$
$984$	−3.02013e8	−	4.80849e8i	−0.316986	−	0.504688i
$985$	−8.54696e6			−0.00894341
$986$	−3.77643e8	−	4.38884e8i	−0.393959	−	0.457845i
$987$		−	4.83988e8i		−	0.503365i
$988$	1.19125e8	+	1.79703e7i	0.123518	+	0.0186330i
$989$	−3.96096e8			−0.409460
$990$	5.03417e7	−	4.33171e7i	0.0518827	−	0.0446431i
$991$			3.31402e8i			0.340513i	0.985400	+	0.170257i	$0.0544597\pi$
$991$			3.31402e8i			0.340513i	−0.985400	+	0.170257i	$0.945540\pi$
$992$	7.73036e8	−	3.36988e8i	0.791890	−	0.345207i
$993$	1.03097e8			0.105293
$994$	5.22357e8	+	6.07066e8i	0.531874	+	0.618126i
$995$		−	2.37027e8i		−	0.240618i
$996$	−9.40865e7	+	6.23700e8i	−0.0952246	+	0.631244i
$997$	−3.43230e7			−0.0346338			−0.0173169	−	0.999850i	$-0.505512\pi$
$997$	−3.43230e7			−0.0346338			−0.0173169	+	0.999850i	$0.505512\pi$
$998$	1.27534e8	−	1.09738e8i	0.128302	−	0.110399i
$999$			4.91070e7i			0.0492547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.18	yes	24
3.2	odd	2		180.7.c.b.91.7		24
4.3	odd	2	inner	60.7.c.a.31.17	✓	24
12.11	even	2		180.7.c.b.91.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.17	✓	24	4.3	odd	2	inner
60.7.c.a.31.18	yes	24	1.1	even	1	trivial
180.7.c.b.91.7		24	3.2	odd	2
180.7.c.b.91.8		24	12.11	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(5.21792 + 6.06410i) q^{2} +15.5885i q^{3} +(-9.54653 + 63.2840i) q^{4} +55.9017 q^{5} +(-94.5299 + 81.3394i) q^{6} +234.050i q^{7} +(-433.573 + 272.320i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(5.21792 + 6.06410i) q^{2} +15.5885i q^{3} +(-9.54653 + 63.2840i) q^{4} +55.9017 q^{5} +(-94.5299 + 81.3394i) q^{6} +234.050i q^{7} +(-433.573 + 272.320i) q^{8} -243.000 q^{9} +(291.691 + 338.993i) q^{10} +611.126i q^{11} +(-986.500 - 148.816i) q^{12} +446.025 q^{13} +(-1419.30 + 1221.26i) q^{14} +871.421i q^{15} +(-3913.73 - 1208.29i) q^{16} -4753.29 q^{17} +(-1267.96 - 1473.58i) q^{18} -4220.36i q^{19} +(-533.667 + 3537.68i) q^{20} -3648.49 q^{21} +(-3705.93 + 3188.81i) q^{22} +3897.71i q^{23} +(-4245.05 - 6758.74i) q^{24} +3125.00 q^{25} +(2327.33 + 2704.74i) q^{26} -3788.00i q^{27} +(-14811.6 - 2234.37i) q^{28} +15226.1 q^{29} +(-5284.38 + 4547.01i) q^{30} +25735.3i q^{31} +(-13094.4 - 30038.0i) q^{32} -9526.51 q^{33} +(-24802.3 - 28824.4i) q^{34} +13083.8i q^{35} +(2319.81 - 15378.0i) q^{36} -12963.9 q^{37} +(25592.7 - 22021.5i) q^{38} +6952.85i q^{39} +(-24237.5 + 15223.2i) q^{40} +71144.7 q^{41} +(-19037.5 - 22124.8i) q^{42} +101623. i q^{43} +(-38674.5 - 5834.13i) q^{44} -13584.1 q^{45} +(-23636.1 + 20338.0i) q^{46} +132654. i q^{47} +(18835.3 - 61009.0i) q^{48} +62869.4 q^{49} +(16306.0 + 18950.3i) q^{50} -74096.4i q^{51} +(-4257.99 + 28226.3i) q^{52} +283151. q^{53} +(22970.8 - 19765.5i) q^{54} +34163.0i q^{55} +(-63736.6 - 101478. i) q^{56} +65788.9 q^{57} +(79448.8 + 92332.7i) q^{58} -176836. i q^{59} +(-55147.0 - 8319.05i) q^{60} +219488. q^{61} +(-156061. + 134285. i) q^{62} -56874.3i q^{63} +(113828. - 236141. i) q^{64} +24933.6 q^{65} +(-49708.6 - 57769.7i) q^{66} +420905. i q^{67} +(45377.4 - 300807. i) q^{68} -60759.3 q^{69} +(-79341.5 + 68270.4i) q^{70} -427721. i q^{71} +(105358. - 66173.8i) q^{72} +276028. q^{73} +(-67644.4 - 78614.1i) q^{74} +48713.9i q^{75} +(267081. + 40289.8i) q^{76} -143034. q^{77} +(-42162.7 + 36279.4i) q^{78} +616843. i q^{79} +(-218784. - 67545.2i) q^{80} +59049.0 q^{81} +(371228. + 431429. i) q^{82} -632235. i q^{83} +(34830.4 - 230891. i) q^{84} -265717. q^{85} +(-616250. + 530260. i) q^{86} +237352. i q^{87} +(-166422. - 264968. i) q^{88} -1.04325e6 q^{89} +(-70880.9 - 82375.4i) q^{90} +104392. i q^{91} +(-246663. - 37209.6i) q^{92} -401174. q^{93} +(-804429. + 692181. i) q^{94} -235925. i q^{95} +(468245. - 204121. i) q^{96} -1.31029e6 q^{97} +(328048. + 381246. i) q^{98} -148504. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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