LMFDB - Embedded newform 72.7.p.b.43.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(43,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("72.43");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.16
Character	$\chi$	$=$	72.43
Dual form			72.7.p.b.67.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.00254 + 5.28862i) q^{2} +(26.0855 + 6.96739i) q^{3} +(8.06090 - 63.4903i) q^{4} +(17.5470 - 10.1308i) q^{5} +(-193.427 + 96.1346i) q^{6} +(-225.997 - 130.480i) q^{7} +(287.391 + 423.734i) q^{8} +(631.911 + 363.496i) q^{9} +O(q^{10})$	\(q+(-6.00254 + 5.28862i) q^{2} +(26.0855 + 6.96739i) q^{3} +(8.06090 - 63.4903i) q^{4} +(17.5470 - 10.1308i) q^{5} +(-193.427 + 96.1346i) q^{6} +(-225.997 - 130.480i) q^{7} +(287.391 + 423.734i) q^{8} +(631.911 + 363.496i) q^{9} +(-51.7487 + 153.610i) q^{10} +(-680.854 + 1179.27i) q^{11} +(652.635 - 1600.02i) q^{12} +(3334.63 - 1925.25i) q^{13} +(2046.62 - 412.006i) q^{14} +(528.308 - 142.010i) q^{15} +(-3966.04 - 1023.58i) q^{16} +1287.63 q^{17} +(-5715.46 + 1160.04i) q^{18} +7365.34 q^{19} +(-501.761 - 1195.73i) q^{20} +(-4986.16 - 4978.24i) q^{21} +(-2149.89 - 10679.4i) q^{22} +(13248.9 - 7649.26i) q^{23} +(4544.42 + 13055.7i) q^{24} +(-7607.24 + 13176.1i) q^{25} +(-9834.31 + 29192.0i) q^{26} +(13951.1 + 13884.8i) q^{27} +(-10105.9 + 13296.9i) q^{28} +(40952.4 + 23643.9i) q^{29} +(-2420.15 + 3646.44i) q^{30} +(-26406.2 + 15245.6i) q^{31} +(29219.6 - 14830.8i) q^{32} +(-25976.9 + 26018.2i) q^{33} +(-7729.02 + 6809.77i) q^{34} -5287.43 q^{35} +(28172.3 - 37190.1i) q^{36} +18515.0i q^{37} +(-44210.7 + 38952.5i) q^{38} +(100400. - 26987.5i) q^{39} +(9335.59 + 4523.77i) q^{40} +(30907.1 + 53532.7i) q^{41} +(56257.7 + 3512.16i) q^{42} +(10318.3 - 17871.8i) q^{43} +(69384.2 + 52733.7i) q^{44} +(14770.6 - 23.4700i) q^{45} +(-39073.0 + 115983. i) q^{46} +(-26889.3 - 15524.5i) q^{47} +(-96324.7 - 54333.6i) q^{48} +(-24774.6 - 42910.9i) q^{49} +(-24020.8 - 119322. i) q^{50} +(33588.4 + 8971.39i) q^{51} +(-95354.5 - 227236. i) q^{52} -129402. i q^{53} +(-157173. - 9561.64i) q^{54} +27590.3i q^{55} +(-9660.85 - 133261. i) q^{56} +(192129. + 51317.2i) q^{57} +(-370861. + 74658.5i) q^{58} +(85314.3 + 147769. i) q^{59} +(-4757.60 - 34687.2i) q^{60} +(-265445. - 153254. i) q^{61} +(77875.9 - 231165. i) q^{62} +(-95381.3 - 164601. i) q^{63} +(-96957.2 + 243554. i) q^{64} +(39008.5 - 67564.6i) q^{65} +(18326.8 - 293557. i) q^{66} +(-5333.78 - 9238.38i) q^{67} +(10379.4 - 81751.7i) q^{68} +(398900. - 107225. i) q^{69} +(31738.0 - 27963.2i) q^{70} -76570.2i q^{71} +(27579.4 + 372228. i) q^{72} +489158. q^{73} +(-97919.1 - 111137. i) q^{74} +(-290242. + 290704. i) q^{75} +(59371.3 - 467628. i) q^{76} +(307742. - 177675. i) q^{77} +(-459925. + 692969. i) q^{78} +(-120367. - 69494.1i) q^{79} +(-79961.8 + 22218.3i) q^{80} +(267182. + 459395. i) q^{81} +(-468636. - 157876. i) q^{82} +(17734.7 - 30717.4i) q^{83} +(-356263. + 276444. i) q^{84} +(22593.9 - 13044.6i) q^{85} +(32581.4 + 161846. i) q^{86} +(903528. + 902094. i) q^{87} +(-695370. + 50411.2i) q^{88} +965126. q^{89} +(-88537.1 + 78257.2i) q^{90} -1.00482e6 q^{91} +(-378856. - 902837. i) q^{92} +(-795043. + 213708. i) q^{93} +(243507. - 49020.7i) q^{94} +(129240. - 74616.5i) q^{95} +(865543. - 183286. i) q^{96} +(788121. - 1.36507e6i) q^{97} +(375650. + 126551. i) q^{98} +(-858901. + 497708. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) $ 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.00254	+	5.28862i	−0.750317	+	0.661078i
$2$	−6.00254	+	5.28862i	−0.750317	+	0.661078i
$3$	26.0855	+	6.96739i	0.966131	+	0.258052i
$3$	26.0855	+	6.96739i	0.966131	+	0.258052i
$4$	8.06090	−	63.4903i	0.125952	−	0.992036i
$5$	17.5470	−	10.1308i	0.140376	−	0.0810461i	−0.428167	−	0.903700i	$-0.640841\pi$
$5$	17.5470	−	10.1308i	0.140376	−	0.0810461i	0.568543	+	0.822653i	$0.307507\pi$
$6$	−193.427	+	96.1346i	−0.895497	+	0.445068i
$7$	−225.997	−	130.480i	−0.658884	−	0.380407i	0.132967	−	0.991120i	$-0.457549\pi$
$7$	−225.997	−	130.480i	−0.658884	−	0.380407i	−0.791852	+	0.610713i	$0.790883\pi$
$8$	287.391	+	423.734i	0.561310	+	0.827606i
$9$	631.911	+	363.496i	0.866819	+	0.498623i
$10$	−51.7487	+	153.610i	−0.0517487	+	0.153610i
$11$	−680.854	+	1179.27i	−0.511536	+	0.886006i	0.488375	+	0.872634i	$0.337590\pi$
$11$	−680.854	+	1179.27i	−0.511536	+	0.886006i	−0.999911	+	0.0133720i	$0.995743\pi$
$12$	652.635	−	1600.02i	0.377682	−	0.925935i
$13$	3334.63	−	1925.25i	1.51781	−	0.876308i	0.518029	−	0.855363i	$-0.326666\pi$
$13$	3334.63	−	1925.25i	1.51781	−	0.876308i	0.999781	−	0.0209445i	$-0.00666732\pi$
$14$	2046.62	−	412.006i	0.745851	−	0.150148i
$15$	528.308	−	142.010i	0.156536	−	0.0420769i
$16$	−3966.04	−	1023.58i	−0.968272	−	0.249897i
$17$	1287.63			0.262085			0.131043	−	0.991377i	$-0.458168\pi$
$17$	1287.63			0.262085			0.131043	+	0.991377i	$0.458168\pi$
$18$	−5715.46	+	1160.04i	−0.980018	+	0.198909i
$19$	7365.34			1.07382			0.536911	−	0.843639i	$-0.319591\pi$
$19$	7365.34			1.07382			0.536911	+	0.843639i	$0.319591\pi$
$20$	−501.761	−	1195.73i	−0.0627201	−	0.149466i
$21$	−4986.16	−	4978.24i	−0.538404	−	0.537549i
$22$	−2149.89	−	10679.4i	−0.201905	−	1.00295i
$23$	13248.9	−	7649.26i	1.08892	−	0.628689i	0.155632	−	0.987815i	$-0.450259\pi$
$23$	13248.9	−	7649.26i	1.08892	−	0.628689i	0.933289	+	0.359126i	$0.116925\pi$
$24$	4544.42	+	13055.7i	0.328734	+	0.944423i
$25$	−7607.24	+	13176.1i	−0.486863	+	0.843272i
$26$	−9834.31	+	29192.0i	−0.559531	+	1.66090i
$27$	13951.1	+	13884.8i	0.708790	+	0.705419i
$28$	−10105.9	+	13296.9i	−0.460365	+	0.605724i
$29$	40952.4	+	23643.9i	1.67913	+	0.969447i	0.962216	+	0.272288i	$0.0877803\pi$
$29$	40952.4	+	23643.9i	1.67913	+	0.969447i	0.716916	+	0.697159i	$0.245553\pi$
$30$	−2420.15	+	3646.44i	−0.0896353	+	0.135053i
$31$	−26406.2	+	15245.6i	−0.886382	+	0.511753i	−0.872757	−	0.488154i	$-0.837670\pi$
$31$	−26406.2	+	15245.6i	−0.886382	+	0.511753i	−0.0136249	+	0.999907i	$0.504337\pi$
$32$	29219.6	−	14830.8i	0.891713	−	0.452602i
$33$	−25976.9	+	26018.2i	−0.722846	+	0.723995i
$34$	−7729.02	+	6809.77i	−0.196647	+	0.173259i
$35$	−5287.43			−0.123322
$36$	28172.3	−	37190.1i	0.603830	−	0.797113i
$37$			18515.0i			0.365527i	0.983157	+	0.182764i	$0.0585043\pi$
$37$			18515.0i			0.365527i	−0.983157	+	0.182764i	$0.941496\pi$
$38$	−44210.7	+	38952.5i	−0.805707	+	0.709880i
$39$	100400.	−	26987.5i	1.69254	−	0.454955i
$40$	9335.59	+	4523.77i	0.145869	+	0.0706840i
$41$	30907.1	+	53532.7i	0.448443	+	0.776726i	0.998285	−	0.0585429i	$-0.0186454\pi$
$41$	30907.1	+	53532.7i	0.448443	+	0.776726i	−0.549842	+	0.835269i	$0.685312\pi$
$42$	56257.7	+	3512.16i	0.759336	+	0.0474053i
$43$	10318.3	−	17871.8i	0.129779	−	0.224783i	−0.793812	−	0.608163i	$-0.791907\pi$
$43$	10318.3	−	17871.8i	0.129779	−	0.224783i	0.923591	+	0.383380i	$0.125240\pi$
$44$	69384.2	+	52733.7i	0.814521	+	0.619056i
$45$	14770.6	−	23.4700i	0.162092	−	0.000257558i
$46$	−39073.0	+	115983.i	−0.401424	+	1.19158i
$47$	−26889.3	−	15524.5i	−0.258992	−	0.149529i	0.364883	−	0.931053i	$-0.381109\pi$
$47$	−26889.3	−	15524.5i	−0.258992	−	0.149529i	−0.623874	+	0.781525i	$0.714442\pi$
$48$	−96324.7	−	54333.6i	−0.870992	−	0.491298i
$49$	−24774.6	−	42910.9i	−0.210581	−	0.364737i
$50$	−24020.8	−	119322.i	−0.192167	−	0.954576i
$51$	33588.4	+	8971.39i	0.253209	+	0.0676315i
$52$	−95354.5	−	227236.i	−0.678159	−	1.61609i
$53$		−	129402.i		−	0.869186i	−0.900627	−	0.434593i	$-0.856892\pi$
$53$		−	129402.i		−	0.869186i	0.900627	−	0.434593i	$-0.143108\pi$
$54$	−157173.	−	9561.64i	−0.998155	−	0.0607227i
$55$			27590.3i			0.165832i
$56$	−9660.85	−	133261.i	−0.0550112	−	0.758823i
$57$	192129.	+	51317.2i	1.03745	+	0.277101i
$58$	−370861.	+	74658.5i	−1.90076	+	0.382644i
$59$	85314.3	+	147769.i	0.415399	+	0.719493i	0.995470	−	0.0950731i	$-0.0303085\pi$
$59$	85314.3	+	147769.i	0.415399	+	0.719493i	−0.580071	+	0.814566i	$0.696975\pi$
$60$	−4757.60	−	34687.2i	−0.0220259	−	0.160589i
$61$	−265445.	−	153254.i	−1.16946	−	0.675186i	−0.215905	−	0.976414i	$-0.569270\pi$
$61$	−265445.	−	153254.i	−1.16946	−	0.675186i	−0.953552	+	0.301228i	$0.902603\pi$
$62$	77875.9	−	231165.i	0.326759	−	0.969945i
$63$	−95381.3	−	164601.i	−0.381454	−	0.658279i
$64$	−96957.2	+	243554.i	−0.369863	+	0.929086i
$65$	39008.5	−	67564.6i	0.142043	−	0.246025i
$66$	18326.8	−	293557.i	0.0637462	−	1.02108i
$67$	−5333.78	−	9238.38i	−0.0177342	−	0.0307165i	0.857022	−	0.515280i	$-0.172312\pi$
$67$	−5333.78	−	9238.38i	−0.0177342	−	0.0307165i	−0.874756	+	0.484563i	$0.838979\pi$
$68$	10379.4	−	81751.7i	0.0330101	−	0.259998i
$69$	398900.	−	107225.i	1.21428	−	0.326398i
$70$	31738.0	−	27963.2i	0.0925306	−	0.0815255i
$71$		−	76570.2i		−	0.213936i	−0.994262	−	0.106968i	$-0.965886\pi$
$71$		−	76570.2i		−	0.213936i	0.994262	−	0.106968i	$-0.0341143\pi$
$72$	27579.4	+	372228.i	0.0738904	+	0.997266i
$73$	489158.			1.25742			0.628711	−	0.777639i	$-0.283583\pi$
$73$	489158.			1.25742			0.628711	+	0.777639i	$0.283583\pi$
$74$	−97919.1	−	111137.i	−0.241642	−	0.274261i
$75$	−290242.	+	290704.i	−0.687981	+	0.689075i
$76$	59371.3	−	467628.i	0.135250	−	1.06527i
$77$	307742.	−	177675.i	0.674086	−	0.389184i
$78$	−459925.	+	692969.i	−0.969178	+	1.46026i
$79$	−120367.	−	69494.1i	−0.244134	−	0.140951i	0.372942	−	0.927855i	$-0.378349\pi$
$79$	−120367.	−	69494.1i	−0.244134	−	0.140951i	−0.617075	+	0.786904i	$0.711683\pi$
$80$	−79961.8	+	22218.3i	−0.156175	+	0.0433951i
$81$	267182.	+	459395.i	0.502750	+	0.864432i
$82$	−468636.	−	157876.i	−0.849951	−	0.286335i
$83$	17734.7	−	30717.4i	0.0310163	−	0.0537217i	−0.850101	−	0.526620i	$-0.823459\pi$
$83$	17734.7	−	30717.4i	0.0310163	−	0.0537217i	0.881117	+	0.472899i	$0.156792\pi$
$84$	−356263.	+	276444.i	−0.601081	+	0.466411i
$85$	22593.9	−	13044.6i	0.0367905	−	0.0212410i
$86$	32581.4	+	161846.i	0.0512241	+	0.254453i
$87$	903528.	+	902094.i	1.37209	+	1.36992i
$88$	−695370.	+	50411.2i	−1.02039	+	0.0739739i
$89$	965126.			1.36903			0.684517	−	0.728997i	$-0.260013\pi$
$89$	965126.			1.36903			0.684517	+	0.728997i	$0.260013\pi$
$90$	−88537.1	+	78257.2i	−0.121450	+	0.107349i
$91$	−1.00482e6			−1.33341
$92$	−378856.	−	902837.i	−0.486531	−	1.15943i
$93$	−795043.	+	213708.i	−0.988420	+	0.265688i
$94$	243507.	−	49020.7i	0.293176	−	0.0590196i
$95$	129240.	−	74616.5i	0.150739	−	0.0870291i
$96$	865543.	−	183286.i	0.978306	−	0.207165i
$97$	788121.	−	1.36507e6i	0.863530	−	1.49568i	−0.00496885	−	0.999988i	$-0.501582\pi$
$97$	788121.	−	1.36507e6i	0.863530	−	1.49568i	0.868499	−	0.495691i	$-0.165085\pi$
$98$	375650.	+	126551.i	0.399122	+	0.134458i
$99$	−858901.	+	497708.i	−0.885192	+	0.512943i
$100$	775235.	+	589197.i	0.775235	+	0.589197i
$101$	−978014.	−	564657.i	−0.949251	−	0.548050i	−0.0564025	−	0.998408i	$-0.517963\pi$
$101$	−978014.	−	564657.i	−0.949251	−	0.548050i	−0.892848	+	0.450358i	$0.851296\pi$
$102$	−249062.	+	123785.i	−0.234697	+	0.116646i
$103$	−522164.	+	301471.i	−0.477854	+	0.275889i	−0.719522	−	0.694470i	$-0.755639\pi$
$103$	−522164.	+	301471.i	−0.477854	+	0.275889i	0.241668	+	0.970359i	$0.422306\pi$
$104$	1.77413e6	+	859697.i	1.57720	+	0.764268i
$105$	−137926.	−	36839.6i	−0.119145	−	0.0318234i
$106$	684358.	+	776740.i	0.574600	+	0.652166i
$107$	−2.38957e6			−1.95060			−0.975301	−	0.220878i	$-0.929108\pi$
$107$	−2.38957e6			−1.95060			−0.975301	+	0.220878i	$0.929108\pi$
$108$	994007.	−	773837.i	0.789075	−	0.614297i
$109$			171535.i			0.132457i	0.997804	+	0.0662283i	$0.0210966\pi$
$109$			171535.i			0.132457i	−0.997804	+	0.0662283i	$0.978903\pi$
$110$	−145915.	−	165612.i	−0.109628	−	0.124427i
$111$	−129002.	+	482975.i	−0.0943248	+	0.353147i
$112$	762759.	+	748814.i	0.542917	+	0.532991i
$113$	−102066.	−	176784.i	−0.0707369	−	0.122520i	0.828488	−	0.560007i	$-0.189202\pi$
$113$	−102066.	−	176784.i	−0.0707369	−	0.122520i	−0.899224	+	0.437488i	$0.855868\pi$
$114$	−1.42466e6	+	708064.i	−0.961604	+	0.477923i
$115$	154986.	−	268443.i	0.101906	−	0.176506i
$116$	1.83127e6	−	2.40949e6i	1.17322	−	1.54366i
$117$	2.80701e6	−	4460.23i	1.75261	−	0.00278483i
$118$	−1.29360e6	−	435792.i	−0.787322	−	0.265236i
$119$	−291000.	−	168009.i	−0.172684	−	0.0996991i
$120$	212005.	+	183050.i	0.122688	+	0.105932i
$121$	−41344.3	−	71610.5i	−0.0233378	−	0.0404223i
$122$	2.40385e6	−	483921.i	1.32381	−	0.266499i
$123$	433246.	+	1.61177e6i	0.232819	+	0.866140i
$124$	755093.	+	1.79943e6i	0.396036	+	0.943780i
$125$			624855.i			0.319926i
$126$	1.44304e6	+	483586.i	0.721385	+	0.241748i
$127$			566080.i			0.276355i	0.990408	+	0.138177i	$0.0441244\pi$
$127$			566080.i			0.276355i	−0.990408	+	0.138177i	$0.955876\pi$
$128$	−706079.	−	1.97472e6i	−0.336684	−	0.941618i
$129$	393679.	−	394305.i	0.183389	−	0.183681i
$130$	123174.	+	611860.i	0.0560647	+	0.278498i
$131$	−1.17630e6	−	2.03742e6i	−0.523245	−	0.906287i	−0.999634	−	0.0270524i	$-0.991388\pi$
$131$	−1.17630e6	−	2.03742e6i	−0.523245	−	0.906287i	0.476389	−	0.879235i	$-0.341945\pi$
$132$	1.44251e6	+	1.85901e6i	0.627186	+	0.808278i
$133$	−1.66455e6	−	961027.i	−0.707524	−	0.408489i
$134$	80874.5	+	27245.3i	0.0336122	+	0.0113234i
$135$	385463.	+	102301.i	0.156669	+	0.0415793i
$136$	370051.	+	545611.i	0.147111	+	0.216903i
$137$	−241639.	+	418531.i	−0.0939736	+	0.162767i	−0.909180	−	0.416404i	$-0.863290\pi$
$137$	−241639.	+	418531.i	−0.0939736	+	0.162767i	0.815206	+	0.579171i	$0.196624\pi$
$138$	−1.82734e6	+	2.75325e6i	−0.695317	+	1.04763i
$139$	−1.50607e6	−	2.60859e6i	−0.560791	−	0.971318i	−0.997428	−	0.0716805i	$-0.977164\pi$
$139$	−1.50607e6	−	2.60859e6i	−0.560791	−	0.971318i	0.436637	−	0.899638i	$-0.356170\pi$
$140$	−42621.5	+	335701.i	−0.0155326	+	0.122340i
$141$	−593256.	−	592314.i	−0.211634	−	0.211298i
$142$	404951.	+	459615.i	0.141429	+	0.160520i
$143$			5.24325e6i			1.79305i
$144$	−2.13412e6	−	2.08845e6i	−0.714712	−	0.699419i
$145$	958121.			0.314280
$146$	−2.93619e6	+	2.58697e6i	−0.943465	+	0.831254i
$147$	−347283.	−	1.29197e6i	−0.109328	−	0.406724i
$148$	1.17553e6	+	149248.i	0.362616	+	0.0460387i
$149$	−809915.	+	467605.i	−0.244839	+	0.141358i	−0.617399	−	0.786650i	$-0.711814\pi$
$149$	−809915.	+	467605.i	−0.244839	+	0.141358i	0.372560	+	0.928008i	$0.378480\pi$
$150$	204766.	−	3.27994e6i	0.0606716	−	0.971834i
$151$	−3.33229e6	−	1.92390e6i	−0.967859	−	0.558793i	−0.0692759	−	0.997598i	$-0.522069\pi$
$151$	−3.33229e6	−	1.92390e6i	−0.967859	−	0.558793i	−0.898583	+	0.438804i	$0.855402\pi$
$152$	2.11673e6	+	3.12095e6i	0.602747	+	0.888701i
$153$	813664.	+	468047.i	0.227180	+	0.130682i
$154$	−907578.	+	2.69404e6i	−0.248497	+	0.737635i
$155$	−308900.	+	535030.i	−0.0829512	+	0.143676i
$156$	−904133.	−	6.59194e6i	−0.238154	−	1.73636i
$157$	−3.98816e6	+	2.30257e6i	−1.03056	+	0.594995i	−0.917145	−	0.398553i	$-0.869513\pi$
$157$	−3.98816e6	+	2.30257e6i	−1.03056	+	0.594995i	−0.113416	+	0.993548i	$0.536179\pi$
$158$	1.09004e6	−	219437.i	0.276357	−	0.0556337i
$159$	901594.	−	3.37552e6i	0.224295	−	0.839748i
$160$	362469.	−	556254.i	0.0884935	−	0.135804i
$161$	−3.99229e6			−0.956631
$162$	−4.03333e6	−	1.34451e6i	−0.948679	−	0.316241i
$163$	1.26191e6			0.291385			0.145692	−	0.989330i	$-0.453459\pi$
$163$	1.26191e6			0.291385			0.145692	+	0.989330i	$0.453459\pi$
$164$	3.64795e6	−	1.53078e6i	0.827022	−	0.347042i
$165$	−192232.	+	719708.i	−0.0427932	+	0.160215i
$166$	55999.6	+	278174.i	0.0122422	+	0.0608125i
$167$	−1.77120e6	+	1.02260e6i	−0.380294	+	0.219563i	−0.677946	−	0.735112i	$-0.737130\pi$
$167$	−1.77120e6	+	1.02260e6i	−0.380294	+	0.219563i	0.297652	+	0.954674i	$0.403796\pi$
$168$	676476.	−	3.54351e6i	0.142667	−	0.747318i
$169$	4.99975e6	−	8.65983e6i	1.03583	−	1.79411i
$170$	−66632.9	+	197792.i	−0.0135626	+	0.0402589i
$171$	4.65424e6	+	2.67728e6i	0.930809	+	0.535432i
$172$	−1.05151e6	−	799176.i	−0.206647	−	0.157057i
$173$	3.65312e6	+	2.10913e6i	0.705547	+	0.407348i	0.809410	−	0.587244i	$-0.199787\pi$
$173$	3.65312e6	+	2.10913e6i	0.705547	+	0.407348i	−0.103863	+	0.994592i	$0.533120\pi$
$174$	−1.01943e7	−	636429.i	−1.93513	−	0.120810i
$175$	3.43843e6	−	1.98518e6i	0.641573	−	0.370412i
$176$	3.90738e6	−	3.98014e6i	0.716716	−	0.730064i
$177$	1.19591e6	+	4.44905e6i	0.215664	+	0.802319i
$178$	−5.79321e6	+	5.10419e6i	−1.02721	+	0.905038i
$179$	−6.29380e6			−1.09737			−0.548686	−	0.836028i	$-0.684872\pi$
$179$	−6.29380e6			−1.09737			−0.548686	+	0.836028i	$0.684872\pi$
$180$	117575.	−	937981.i	0.0201602	−	0.160834i
$181$		−	1.06981e7i		−	1.80415i	−0.431584	−	0.902073i	$-0.642045\pi$
$181$		−	1.06981e7i		−	1.80415i	0.431584	−	0.902073i	$-0.357955\pi$
$182$	6.03148e6	−	5.31413e6i	1.00048	−	0.881491i
$183$	−5.85648e6	−	5.84718e6i	−0.955616	−	0.954099i
$184$	7.04886e6	+	3.41569e6i	1.13153	+	0.548308i
$185$	187571.	+	324883.i	0.0296245	+	0.0513112i
$186$	3.64205e6	−	5.48747e6i	0.565988	−	0.852773i
$187$	−876685.	+	1.51846e6i	−0.134066	+	0.232209i
$188$	−1.20241e6	+	1.58207e6i	−0.180959	+	0.238096i
$189$	−1.34124e6	−	4.95826e6i	−0.198664	−	0.734419i
$190$	−381147.	+	1.13139e6i	−0.0555689	+	0.164949i
$191$	1.76482e6	+	1.01892e6i	0.253279	+	0.146231i	0.621265	−	0.783601i	$-0.286619\pi$
$191$	1.76482e6	+	1.01892e6i	0.253279	+	0.146231i	−0.367986	+	0.929831i	$0.619952\pi$
$192$	−4.22612e6	+	5.67771e6i	−0.597088	+	0.802176i
$193$	367384.	+	636328.i	0.0511033	+	0.0885134i	0.890445	−	0.455090i	$-0.150393\pi$
$193$	367384.	+	636328.i	0.0511033	+	0.0885134i	−0.839342	+	0.543603i	$0.817060\pi$
$194$	2.48859e6	+	1.23619e7i	0.340839	+	1.69309i
$195$	1.48831e6	−	1.49067e6i	0.200719	−	0.201038i
$196$	−2.92413e6	+	1.22705e6i	−0.388355	+	0.162965i
$197$			1.33337e7i			1.74403i	0.489483	+	0.872013i	$0.337186\pi$
$197$			1.33337e7i			1.74403i	−0.489483	+	0.872013i	$0.662814\pi$
$198$	2.52339e6	−	7.52992e6i	0.325079	−	0.970051i
$199$			8.92824e6i			1.13294i	0.824083	+	0.566469i	$0.191691\pi$
$199$			8.92824e6i			1.13294i	−0.824083	+	0.566469i	$0.808309\pi$
$200$	−7.76942e6	+	563248.i	−0.971177	+	0.0704060i
$201$	−74767.1	−	278151.i	−0.00920709	−	0.0342525i
$202$	8.85682e6	−	1.78298e6i	1.07454	−	0.216317i
$203$	−6.17008e6	−	1.06869e7i	−0.737569	−	1.27751i
$204$	840349.	−	2.06022e6i	0.0989850	−	0.242674i
$205$	1.08465e6	+	626226.i	0.125901	+	0.0726891i
$206$	1.53994e6	−	4.57112e6i	0.176158	−	0.522903i
$207$	1.11526e7	−	17721.1i	1.25738	−	0.00199792i
$208$	−1.51959e7	+	4.22236e6i	−1.68864	+	0.469208i
$209$	−5.01472e6	+	8.68576e6i	−0.549298	+	0.951412i
$210$	1.02273e6	−	508305.i	0.110435	−	0.0548866i
$211$	7.06212e6	+	1.22319e7i	0.751775	+	1.30211i	0.946962	+	0.321346i	$0.104135\pi$
$211$	7.06212e6	+	1.22319e7i	0.751775	+	1.30211i	−0.195187	+	0.980766i	$0.562531\pi$
$212$	−8.21577e6	−	1.04310e6i	−0.862265	−	0.109475i
$213$	533494.	−	1.99737e6i	0.0552066	−	0.206691i
$214$	1.43435e7	−	1.26376e7i	1.46357	−	1.28950i
$215$		−	418130.i		−	0.0420722i
$216$	−1.87403e6	+	9.90192e6i	−0.185958	+	0.982558i
$217$	7.95698e6			0.778698
$218$	−907185.	−	1.02965e6i	−0.0875642	−	0.0993845i
$219$	1.27600e7	+	3.40816e6i	1.21483	+	0.324480i
$220$	1.75172e6	+	222403.i	0.164511	+	0.0208868i
$221$	4.29375e6	−	2.47900e6i	0.397796	−	0.229667i
$222$	−1.77994e6	−	3.58132e6i	−0.162684	−	0.327328i
$223$	−5.86393e6	−	3.38554e6i	−0.528779	−	0.305291i	0.211740	−	0.977326i	$-0.432087\pi$
$223$	−5.86393e6	−	3.38554e6i	−0.528779	−	0.305291i	−0.740519	+	0.672035i	$0.765420\pi$
$224$	−8.53869e6	−	460837.i	−0.759708	−	0.0410018i
$225$	−9.59657e6	+	5.56093e6i	−0.842497	+	0.488202i
$226$	1.54760e6	+	521361.i	0.134070	+	0.0451662i
$227$	−4.69747e6	+	8.13626e6i	−0.401593	+	0.695580i	−0.993918	−	0.110119i	$-0.964877\pi$
$227$	−4.69747e6	+	8.13626e6i	−0.401593	+	0.695580i	0.592325	+	0.805699i	$0.298210\pi$
$228$	4.80688e6	−	1.17847e7i	0.405563	−	0.994289i
$229$	1.48063e7	−	8.54843e6i	1.23294	−	0.711836i	0.265295	−	0.964167i	$-0.414531\pi$
$229$	1.48063e7	−	8.54843e6i	1.23294	−	0.711836i	0.967641	+	0.252331i	$0.0811973\pi$
$230$	489387.	+	2.43100e6i	0.0402225	+	0.199803i
$231$	9.26556e6	−	2.49059e6i	0.751685	−	0.202054i
$232$	1.75062e6	+	2.41479e7i	0.140193	+	1.93382i
$233$	817479.			0.0646263			0.0323131	−	0.999478i	$-0.489713\pi$
$233$	817479.			0.0646263			0.0323131	+	0.999478i	$0.489713\pi$
$234$	−1.68256e7	+	1.48720e7i	−1.31317	+	1.16070i
$235$	−629102.			−0.0484749
$236$	1.00696e7	−	4.22548e6i	0.766083	−	0.321470i
$237$	−2.65565e6	−	2.65144e6i	−0.199492	−	0.199176i
$238$	2.63527e6	−	530510.i	0.195477	−	0.0393516i
$239$	−1.25935e7	+	7.27089e6i	−0.922474	+	0.532591i	−0.884424	−	0.466685i	$-0.845448\pi$
$239$	−1.25935e7	+	7.27089e6i	−0.922474	+	0.532591i	−0.0380506	+	0.999276i	$0.512115\pi$
$240$	−2.24065e6	+	22451.7i	−0.162084	+	0.00162411i
$241$	1.93833e6	−	3.35728e6i	0.138476	−	0.239848i	−0.788444	−	0.615107i	$-0.789113\pi$
$241$	1.93833e6	−	3.35728e6i	0.138476	−	0.239848i	0.926920	+	0.375259i	$0.122446\pi$
$242$	626892.	+	211190.i	0.0442330	+	0.0149014i
$243$	3.76880e6	+	1.38451e7i	0.262654	+	0.964890i
$244$	−1.18699e7	+	1.56178e7i	−0.817104	+	1.07510i
$245$	−869441.	−	501972.i	−0.0591210	−	0.0341335i
$246$	−1.11246e7	−	7.38345e6i	−0.747275	−	0.495968i
$247$	2.45607e7	−	1.41801e7i	1.62986	−	0.940998i
$248$	−1.40490e7	−	6.80776e6i	−0.921065	−	0.446323i
$249$	676639.	−	677715.i	0.0438287	−	0.0438984i
$250$	−3.30462e6	−	3.75071e6i	−0.211496	−	0.240046i
$251$	1.21937e7			0.771104			0.385552	−	0.922686i	$-0.374011\pi$
$251$	1.21937e7			0.771104			0.385552	+	0.922686i	$0.374011\pi$
$252$	−1.12194e7	+	4.72896e6i	−0.701081	+	0.295504i
$253$			2.08321e7i			1.28639i
$254$	−2.99378e6	−	3.39792e6i	−0.182692	−	0.207354i
$255$	680262.	−	182855.i	0.0410257	−	0.0110277i
$256$	1.46818e7	+	8.11912e6i	0.875103	+	0.483937i
$257$	6.95845e6	+	1.20524e7i	0.409933	+	0.710025i	0.994882	−	0.101045i	$-0.0322187\pi$
$257$	6.95845e6	+	1.20524e7i	0.409933	+	0.710025i	−0.584949	+	0.811070i	$0.698885\pi$
$258$	−277742.	+	4.44885e6i	−0.0161727	+	0.259053i
$259$	2.41584e6	−	4.18435e6i	0.139049	−	0.240840i
$260$	−3.97526e6	−	3.02129e6i	−0.226175	−	0.171899i
$261$	1.72838e7	+	2.98268e7i	0.972114	+	1.67759i
$262$	1.78359e7	+	6.00864e6i	0.991726	+	0.334097i
$263$	6.63380e6	+	3.83002e6i	0.364666	+	0.210540i	0.671126	−	0.741344i	$-0.265811\pi$
$263$	6.63380e6	+	3.83002e6i	0.364666	+	0.210540i	−0.306460	+	0.951884i	$0.599144\pi$
$264$	−1.84903e7	−	3.52991e6i	−1.00492	−	0.191846i
$265$	−1.31094e6	−	2.27061e6i	−0.0704442	−	0.122013i
$266$	1.50740e7	−	3.03457e6i	0.800911	−	0.161232i
$267$	2.51758e7	+	6.72441e6i	1.32267	+	0.353281i
$268$	−629543.	+	264174.i	−0.0327055	+	0.0137241i
$269$		−	2.65894e7i		−	1.36600i	−0.730417	−	0.683002i	$-0.760674\pi$
$269$		−	2.65894e7i		−	1.36600i	0.730417	−	0.683002i	$-0.239326\pi$
$270$	−2.85479e6	+	1.42451e6i	−0.145038	+	0.0723725i
$271$		−	1.68485e7i		−	0.846553i	−0.906001	−	0.423276i	$-0.860880\pi$
$271$		−	1.68485e7i		−	0.846553i	0.906001	−	0.423276i	$-0.139120\pi$
$272$	−5.10678e6	−	1.31799e6i	−0.253770	−	0.0654944i
$273$	−2.62113e7	−	7.00099e6i	−1.28825	−	0.344090i
$274$	−763007.	−	3.79019e6i	−0.0370917	−	0.184251i
$275$	−1.03588e7	−	1.79420e7i	−0.498096	−	0.862727i
$276$	−3.59224e6	−	2.61906e7i	−0.170859	−	1.24572i
$277$	−3.60679e7	−	2.08238e7i	−1.69700	−	0.979764i	−0.948579	−	0.316540i	$-0.897479\pi$
$277$	−3.60679e7	−	2.08238e7i	−1.69700	−	0.979764i	−0.748421	−	0.663224i	$-0.769188\pi$
$278$	2.28361e7	+	7.69312e6i	1.06289	+	0.358070i
$279$	−2.22281e7	+	35319.6i	−1.02350	+	0.00162631i
$280$	−1.51956e6	−	2.24047e6i	−0.0692219	−	0.102062i
$281$	−1.07290e7	+	1.85831e7i	−0.483547	+	0.837529i	−0.999821	−	0.0188949i	$-0.993985\pi$
$281$	−1.07290e7	+	1.85831e7i	−0.483547	+	0.837529i	0.516274	+	0.856423i	$0.327319\pi$
$282$	6.69357e6	+	417879.i	0.298477	+	0.0186339i
$283$	4.06037e6	+	7.03277e6i	0.179146	+	0.310290i	0.941588	−	0.336766i	$-0.109333\pi$
$283$	4.06037e6	+	7.03277e6i	0.179146	+	0.310290i	−0.762442	+	0.647056i	$0.776000\pi$
$284$	−4.86146e6	−	617225.i	−0.212233	−	0.0269456i
$285$	3.89117e6	−	1.04595e6i	0.168091	−	0.0451831i
$286$	−2.77296e7	−	3.14728e7i	−1.18535	−	1.34536i
$287$		−	1.61310e7i		−	0.682363i
$288$	2.38552e7	+	1.24946e6i	0.998631	+	0.0523053i
$289$	−2.24796e7			−0.931311
$290$	−5.75116e6	+	5.06714e6i	−0.235809	+	0.207763i
$291$	3.00695e7	−	3.01173e7i	1.22025	−	1.22219i
$292$	3.94306e6	−	3.10568e7i	0.158374	−	1.24741i
$293$	−1.63909e7	+	9.46330e6i	−0.651629	+	0.376218i	−0.789080	−	0.614290i	$-0.789442\pi$
$293$	−1.63909e7	+	9.46330e6i	−0.651629	+	0.376218i	0.137451	+	0.990509i	$0.456109\pi$
$294$	8.91732e6	+	5.91845e6i	0.350907	+	0.232898i
$295$	2.99402e6	+	1.72860e6i	0.116624	+	0.0673330i
$296$	−7.84545e6	+	5.32105e6i	−0.302512	+	0.205174i
$297$	−2.58726e7	+	6.99868e6i	−0.987577	+	0.267145i
$298$	2.38856e6	−	7.09015e6i	0.0902584	−	0.267921i
$299$	2.94534e7	−	5.10149e7i	1.10185	−	1.90846i
$300$	1.61173e7	+	2.07709e7i	0.596935	+	0.769292i
$301$	−4.66382e6	+	2.69266e6i	−0.171018	+	0.0987375i
$302$	3.01770e7	−	6.07496e6i	1.09561	−	0.220558i
$303$	−2.15778e7	−	2.15436e7i	−0.775675	−	0.774444i
$304$	−2.92113e7	−	7.53901e6i	−1.03975	−	0.268345i
$305$	−6.21034e6			−0.218885
$306$	−7.35938e6	+	1.49370e6i	−0.256848	+	0.0521312i
$307$	−1.97037e7			−0.680978			−0.340489	−	0.940249i	$-0.610593\pi$
$307$	−1.97037e7			−0.680978			−0.340489	+	0.940249i	$0.610593\pi$
$308$	−8.79997e6	−	2.09709e7i	−0.301182	−	0.717736i
$309$	−1.57214e7	+	4.22592e6i	−0.532863	+	0.143234i
$310$	−975391.	−	4.84519e6i	−0.0327411	−	0.162640i
$311$	−1.81956e7	+	1.05053e7i	−0.604904	+	0.349241i	−0.770968	−	0.636873i	$-0.780227\pi$
$311$	−1.81956e7	+	1.05053e7i	−0.604904	+	0.349241i	0.166064	+	0.986115i	$0.446894\pi$
$312$	4.02894e7	+	3.47868e7i	1.32656	+	1.14538i
$313$	2.60211e7	−	4.50699e7i	0.848581	−	1.46979i	−0.0338937	−	0.999425i	$-0.510791\pi$
$313$	2.60211e7	−	4.50699e7i	0.848581	−	1.46979i	0.882475	−	0.470360i	$-0.155876\pi$
$314$	1.17617e7	−	3.49131e7i	0.379910	−	1.12772i
$315$	−3.34119e6	−	1.92196e6i	−0.106898	−	0.0614912i
$316$	−5.38247e6	+	7.08198e6i	−0.170577	+	0.224436i
$317$	3.94491e7	+	2.27759e7i	1.23839	+	0.714987i	0.968766	−	0.247977i	$-0.0797658\pi$
$317$	3.94491e7	+	2.27759e7i	1.23839	+	0.714987i	0.269628	+	0.962964i	$0.413099\pi$
$318$	1.24400e7	+	2.50299e7i	0.386847	+	0.778354i
$319$	−5.57652e7	+	3.21960e7i	−1.71787	+	0.991814i
$320$	766084.	+	5.25590e6i	0.0233790	+	0.160397i
$321$	−6.23333e7	−	1.66491e7i	−1.88454	−	0.503356i
$322$	2.39639e7	−	2.11137e7i	0.717777	−	0.632408i
$323$	9.48380e6			0.281433
$324$	3.13208e7	−	1.32603e7i	0.920870	−	0.389869i
$325$			5.85833e7i			1.70657i
$326$	−7.57469e6	+	6.67379e6i	−0.218631	+	0.192628i
$327$	−1.19515e6	+	4.47459e6i	−0.0341806	+	0.127970i
$328$	−1.38012e7	+	2.84812e7i	−0.391107	+	0.807118i
$329$	4.05127e6	+	7.01701e6i	0.113764	+	0.197044i
$330$	−2.65238e6	−	5.33672e6i	−0.0738064	−	0.148502i
$331$	−2.33733e7	+	4.04837e7i	−0.644519	+	1.11634i	0.339894	+	0.940464i	$0.389609\pi$
$331$	−2.33733e7	+	4.04837e7i	−0.644519	+	1.11634i	−0.984412	+	0.175875i	$0.943725\pi$
$332$	−1.80730e6	−	1.37359e6i	−0.0493874	−	0.0375356i
$333$	−6.73015e6	+	1.16999e7i	−0.182260	+	0.316846i
$334$	5.22354e6	−	1.55055e7i	0.140193	−	0.416145i
$335$	−187184.	−	108071.i	−0.00497890	−	0.00287457i
$336$	1.46797e7	+	2.48477e7i	0.386990	+	0.655040i
$337$	−1.90122e7	−	3.29300e7i	−0.496754	−	0.860404i	0.503239	−	0.864148i	$-0.332142\pi$
$337$	−1.90122e7	−	3.29300e7i	−0.496754	−	0.860404i	−0.999993	+	0.00374357i	$0.998808\pi$
$338$	1.57874e7	+	7.84228e7i	0.408846	+	2.03092i
$339$	−1.43073e6	−	5.32263e6i	−0.0367247	−	0.136624i
$340$	−646080.	−	1.53965e6i	−0.0164380	−	0.0391728i
$341$		−	4.15202e7i		−	1.04712i
$342$	−4.20964e7	+	8.54408e6i	−1.05236	+	0.213593i
$343$			4.36319e7i			1.08124i
$344$	1.05383e7	−	763979.i	0.258878	−	0.0187675i
$345$	5.91323e6	−	5.92264e6i	0.144002	−	0.144231i
$346$	−3.30824e7	+	6.65986e6i	−0.798673	+	0.160782i
$347$	−1.07957e7	−	1.86988e7i	−0.258383	−	0.447533i	0.707426	−	0.706788i	$-0.249856\pi$
$347$	−1.07957e7	−	1.86988e7i	−0.258383	−	0.447533i	−0.965809	+	0.259255i	$0.916523\pi$
$348$	6.45575e7	−	5.00936e7i	1.53182	−	1.18862i
$349$	−1.46124e7	−	8.43645e6i	−0.343751	−	0.198465i	0.318178	−	0.948031i	$-0.396929\pi$
$349$	−1.46124e7	−	8.43645e6i	−0.343751	−	0.198465i	−0.661930	+	0.749566i	$0.730262\pi$
$350$	−1.01404e7	+	3.01007e7i	−0.236512	+	0.702056i
$351$	7.32534e7	+	1.94412e7i	1.69397	+	0.449574i
$352$	−2.40469e6	+	4.45556e7i	−0.0551354	+	1.02158i
$353$	−1.99054e7	+	3.44772e7i	−0.452530	+	0.783805i	−0.998542	−	0.0539724i	$-0.982812\pi$
$353$	−1.99054e7	+	3.44772e7i	−0.452530	+	0.783805i	0.546013	+	0.837777i	$0.316145\pi$
$354$	−3.07078e7	−	2.03809e7i	−0.692212	−	0.459423i
$355$	−775714.	−	1.34358e6i	−0.0173387	−	0.0300315i
$356$	7.77979e6	−	6.12762e7i	0.172432	−	1.35813i
$357$	−6.42030e6	−	6.41011e6i	−0.141108	−	0.140884i
$358$	3.77788e7	−	3.32856e7i	0.823378	−	0.725449i
$359$		−	6.86187e7i		−	1.48306i	−0.670918	−	0.741531i	$-0.734100\pi$
$359$		−	6.86187e7i		−	1.48306i	0.670918	−	0.741531i	$-0.265900\pi$
$360$	4.25489e6	+	6.25208e6i	0.0911970	+	0.134004i
$361$	7.20239e6			0.153093
$362$	5.65783e7	+	6.42158e7i	1.19268	+	1.35368i
$363$	−579551.	−	2.15606e6i	−0.0121164	−	0.0450756i
$364$	−8.09978e6	+	6.37965e7i	−0.167946	+	1.32280i
$365$	8.58326e6	−	4.95555e6i	0.176512	−	0.101909i
$366$	6.60773e7	+	4.12520e6i	1.34775	+	0.0841399i
$367$	5.39804e7	+	3.11656e7i	1.09204	+	0.630489i	0.934119	−	0.356963i	$-0.116188\pi$
$367$	5.39804e7	+	3.11656e7i	1.09204	+	0.630489i	0.157920	+	0.987452i	$0.449521\pi$
$368$	−6.03754e7	+	1.67760e7i	−1.21148	+	0.336624i
$369$	71602.6	+	4.50625e7i	0.00142511	+	0.896885i
$370$	−2.84409e6	−	958129.i	−0.0561485	−	0.0189155i
$371$	−1.68843e7	+	2.92445e7i	−0.330645	+	0.572693i
$372$	7.15964e6	+	5.22002e7i	0.139079	+	1.01401i
$373$	5.83377e6	−	3.36813e6i	0.112415	−	0.0649026i	−0.442739	−	0.896651i	$-0.645993\pi$
$373$	5.83377e6	−	3.36813e6i	0.112415	−	0.0649026i	0.555153	+	0.831748i	$0.312660\pi$
$374$	−2.76825e6	−	1.37511e7i	−0.0529163	−	0.262859i
$375$	−4.35361e6	+	1.62997e7i	−0.0825573	+	0.309090i
$376$	−1.14945e6	−	1.58555e7i	−0.0216236	−	0.298275i
$377$	1.82081e8			3.39814
$378$	3.42732e7	+	2.26688e7i	0.634569	+	0.419714i
$379$	−7.04541e7			−1.29416			−0.647081	−	0.762421i	$-0.724010\pi$
$379$	−7.04541e7			−1.29416			−0.647081	+	0.762421i	$0.724010\pi$
$380$	−3.69564e6	−	8.80694e6i	−0.0673502	−	0.160500i
$381$	−3.94410e6	+	1.47665e7i	−0.0713137	+	0.266995i
$382$	−1.59820e7	+	3.21736e6i	−0.286710	+	0.0577178i
$383$	7.76177e6	−	4.48126e6i	0.138154	−	0.0797635i	−0.429330	−	0.903148i	$-0.641250\pi$
$383$	7.76177e6	−	4.48126e6i	0.138154	−	0.0797635i	0.567484	+	0.823384i	$0.307917\pi$
$384$	−4.65983e6	−	5.64310e7i	−0.0822955	−	0.996608i
$385$	3.59997e6	−	6.23533e6i	0.0630836	−	0.109264i
$386$	−5.57054e6	−	1.87663e6i	−0.0968579	−	0.0326299i
$387$	1.30166e7	−	7.54274e6i	0.224577	−	0.130136i
$388$	−8.03155e7	−	6.10417e7i	−1.37500	−	1.04504i
$389$	−3.83765e6	−	2.21567e6i	−0.0651953	−	0.0376405i	0.467048	−	0.884232i	$-0.345318\pi$
$389$	−3.83765e6	−	2.21567e6i	−0.0651953	−	0.0376405i	−0.532243	+	0.846591i	$0.678651\pi$
$390$	−1.05000e6	+	1.68189e7i	−0.0177010	+	0.283533i
$391$	1.70596e7	−	9.84938e6i	0.285390	−	0.164770i
$392$	1.10628e7	−	2.28301e7i	0.183657	−	0.379008i
$393$	−1.64890e7	−	6.13429e7i	−0.271655	−	1.01062i
$394$	−7.05171e7	−	8.00362e7i	−1.15294	−	1.30857i
$395$	−2.81611e6			−0.0456940
$396$	2.46761e7	+	5.85439e7i	0.397367	+	0.942749i
$397$		−	1.01128e8i		−	1.61622i	−0.589034	−	0.808108i	$-0.700492\pi$
$397$		−	1.01128e8i		−	1.61622i	0.589034	−	0.808108i	$-0.299508\pi$
$398$	−4.72181e7	−	5.35921e7i	−0.748961	−	0.850063i
$399$	−3.67248e7	−	3.66665e7i	−0.578150	−	0.577232i
$400$	4.36574e7	−	4.44705e7i	0.682147	−	0.694851i
$401$	3.27748e7	+	5.67676e7i	0.508284	+	0.880374i	0.999954	+	0.00959237i	$0.00305339\pi$
$401$	3.27748e7	+	5.67676e7i	0.508284	+	0.880374i	−0.491670	+	0.870782i	$0.663613\pi$
$402$	1.91983e6	+	1.27419e6i	0.0295518	+	0.0196136i
$403$	−5.87033e7	+	1.01677e8i	−0.896906	+	1.55349i
$404$	−4.37339e7	+	5.75428e7i	−0.663245	+	0.872663i
$405$	9.34225e6	+	5.35424e6i	0.140633	+	0.0805996i
$406$	9.35551e7	+	3.15172e7i	1.39794	+	0.470945i
$407$	−2.18343e7	−	1.26060e7i	−0.323859	−	0.186980i
$408$	5.85151e6	+	1.68108e7i	0.0861563	+	0.247519i
$409$	2.66047e7	+	4.60807e7i	0.388855	+	0.673517i	0.992296	−	0.123891i	$-0.0395372\pi$
$409$	2.66047e7	+	4.60807e7i	0.388855	+	0.673517i	−0.603440	+	0.797408i	$0.706204\pi$
$410$	−9.82255e6	+	1.97739e6i	−0.142519	+	0.0286906i
$411$	−9.21936e6	+	9.23402e6i	−0.132793	+	0.133004i
$412$	1.49314e7	+	3.55825e7i	0.213505	+	0.508797i
$413$		−	4.45271e7i		−	0.632083i
$414$	−6.68502e7	+	5.90883e7i	−0.942110	+	0.832723i
$415$		−	718664.i		−	0.0100550i
$416$	6.88836e7	−	1.05710e8i	0.956832	−	1.46838i
$417$	−2.11116e7	−	7.85399e7i	−0.291147	−	1.08313i
$418$	−1.58346e7	−	7.86576e7i	−0.216810	−	1.07699i
$419$	−5.50909e7	−	9.54203e7i	−0.748925	−	1.29718i	−0.948339	−	0.317260i	$-0.897237\pi$
$419$	−5.50909e7	−	9.54203e7i	−0.748925	−	1.29718i	0.199414	−	0.979915i	$-0.436096\pi$
$420$	−3.45076e6	+	8.45998e6i	−0.0465765	+	0.114188i
$421$	3.66891e7	+	2.11824e7i	0.491689	+	0.283877i	0.725275	−	0.688459i	$-0.241713\pi$
$421$	3.66891e7	+	2.11824e7i	0.491689	+	0.283877i	−0.233586	+	0.972336i	$0.575046\pi$
$422$	−1.07081e8	−	3.60738e7i	−1.42487	−	0.480015i
$423$	−1.13485e7	−	1.95843e7i	−0.149940	−	0.258754i
$424$	5.48320e7	−	3.71889e7i	0.719344	−	0.487883i
$425$	−9.79527e6	+	1.69659e7i	−0.127600	+	0.221009i
$426$	7.36104e6	+	1.48108e7i	0.0952161	+	0.191579i
$427$	3.99932e7	+	6.92702e7i	0.513691	+	0.889740i
$428$	−1.92621e7	+	1.51715e8i	−0.245682	+	1.93507i
$429$	−3.65318e7	+	1.36773e8i	−0.462700	+	1.73232i
$430$	2.21133e6	+	2.50984e6i	0.0278130	+	0.0315675i
$431$			1.22070e8i			1.52467i	0.647181	+	0.762337i	$0.275948\pi$
$431$			1.22070e8i			1.52467i	−0.647181	+	0.762337i	$0.724052\pi$
$432$	−4.11186e7	−	6.93477e7i	−0.510020	−	0.860163i
$433$	9.28584e7			1.14382			0.571910	−	0.820316i	$-0.306203\pi$
$433$	9.28584e7			1.14382			0.571910	+	0.820316i	$0.306203\pi$
$434$	−4.77621e7	+	4.20815e7i	−0.584270	+	0.514780i
$435$	2.49931e7	+	6.67560e6i	0.303635	+	0.0811004i
$436$	1.08908e7	+	1.38273e6i	0.131402	+	0.0166831i
$437$	9.75827e7	−	5.63394e7i	1.16931	−	0.675100i
$438$	−9.46166e7	+	4.70250e7i	−1.12602	+	0.559638i
$439$	7.01503e7	+	4.05013e7i	0.829156	+	0.478713i	0.853563	−	0.520989i	$-0.174437\pi$
$439$	7.01503e7	+	4.05013e7i	0.829156	+	0.478713i	−0.0244079	+	0.999702i	$0.507770\pi$
$440$	−1.16909e7	+	7.92919e6i	−0.137243	+	0.0930831i
$441$	−57395.4	−	3.61214e7i	−0.000669209	−	0.421161i
$442$	−1.26629e7	+	3.75883e7i	−0.146645	+	0.435297i
$443$	−9.65570e6	+	1.67242e7i	−0.111064	+	0.192368i	−0.916199	−	0.400723i	$-0.868759\pi$
$443$	−9.65570e6	+	1.67242e7i	−0.111064	+	0.192368i	0.805136	+	0.593091i	$0.202092\pi$
$444$	2.96244e7	+	1.20836e7i	0.338454	+	0.138053i
$445$	1.69351e7	−	9.77746e6i	0.192179	−	0.110955i
$446$	5.31033e7	−	1.06903e7i	0.598573	−	0.120499i
$447$	−2.43851e7	+	6.55473e6i	−0.273024	+	0.0733892i
$448$	5.36910e7	−	4.23917e7i	0.597128	−	0.471462i
$449$	8.24873e7			0.911272			0.455636	−	0.890166i	$-0.349412\pi$
$449$	8.24873e7			0.911272			0.455636	+	0.890166i	$0.349412\pi$
$450$	2.81941e7	−	8.41323e7i	0.309400	−	0.923263i
$451$	−8.41730e7			−0.917578
$452$	−1.20468e7	+	5.05517e6i	−0.130454	+	0.0547420i
$453$	−7.35200e7	−	7.34033e7i	−0.790881	−	0.789625i
$454$	−1.48329e7	−	7.36814e7i	−0.158510	−	0.787390i
$455$	−1.76316e7	+	1.01796e7i	−0.187179	+	0.108068i
$456$	3.34712e7	+	9.61597e7i	0.353002	+	1.01414i
$457$	2.82687e7	−	4.89628e7i	0.296181	−	0.513001i	−0.679078	−	0.734066i	$-0.737620\pi$
$457$	2.82687e7	−	4.89628e7i	0.296181	−	0.513001i	0.975259	+	0.221065i	$0.0709535\pi$
$458$	−4.36660e7	+	1.29617e8i	−0.454514	+	1.34917i
$459$	1.79638e7	+	1.78784e7i	0.185763	+	0.184880i
$460$	−1.57942e7	−	1.20040e7i	−0.162265	−	0.123325i
$461$	−7.04608e7	−	4.06806e7i	−0.719192	−	0.415226i	0.0952630	−	0.995452i	$-0.469631\pi$
$461$	−7.04608e7	−	4.06806e7i	−0.719192	−	0.415226i	−0.814455	+	0.580226i	$0.802964\pi$
$462$	−4.24451e7	+	6.39519e7i	−0.430429	+	0.648527i
$463$	1.43439e8	−	8.28145e7i	1.44519	−	0.834379i	0.446998	−	0.894535i	$-0.352493\pi$
$463$	1.43439e8	−	8.28145e7i	1.44519	−	0.834379i	0.998189	+	0.0601561i	$0.0191599\pi$
$464$	−1.38217e8	−	1.35691e8i	−1.38360	−	1.35830i
$465$	−1.17856e7	+	1.18043e7i	−0.117217	+	0.117404i
$466$	−4.90695e6	+	4.32334e6i	−0.0484902	+	0.0427230i
$467$	2.77934e7			0.272892			0.136446	−	0.990647i	$-0.456432\pi$
$467$	2.77934e7			0.272892			0.136446	+	0.990647i	$0.456432\pi$
$468$	2.23438e7	−	1.78254e8i	0.217982	−	1.73901i
$469$			2.78380e6i			0.0269848i
$470$	3.77621e6	−	3.32708e6i	0.0363716	−	0.0320457i
$471$	−1.20076e8	+	3.22766e7i	−1.14920	+	0.308905i
$472$	−3.80961e7	+	7.86179e7i	−0.362289	+	0.747645i
$473$	1.40505e7	+	2.43362e7i	0.132773	+	0.229969i
$474$	2.99631e7	+	1.87060e6i	0.281353	+	0.0175649i
$475$	−5.60299e7	+	9.70466e7i	−0.522804	+	0.905523i
$476$	−1.30127e7	+	1.71214e7i	−0.120655	+	0.158751i
$477$	4.70371e7	−	8.17705e7i	0.433397	−	0.753427i
$478$	3.71402e7	−	1.10246e8i	0.340064	−	1.00944i
$479$	−3.95717e7	−	2.28468e7i	−0.360063	−	0.207883i	0.309045	−	0.951047i	$-0.399991\pi$
$479$	−3.95717e7	−	2.28468e7i	−0.360063	−	0.207883i	−0.669108	+	0.743165i	$0.733324\pi$
$480$	1.33308e7	−	1.19847e7i	0.120541	−	0.108369i
$481$	3.56460e7	+	6.17408e7i	0.320314	+	0.554800i
$482$	6.12051e6	+	3.04033e7i	0.0546571	+	0.271506i
$483$	−1.04141e8	−	2.78158e7i	−0.924231	−	0.246860i
$484$	−4.87985e6	+	2.04772e6i	−0.0430398	+	0.0180607i
$485$		−	3.19371e7i		−	0.279943i
$486$	−9.58440e7	−	6.31741e7i	−0.834941	−	0.550339i
$487$			5.77726e7i			0.500190i	0.968221	+	0.250095i	$0.0804619\pi$
$487$			5.77726e7i			0.500190i	−0.968221	+	0.250095i	$0.919538\pi$
$488$	−1.13471e7	−	1.56522e8i	−0.0976397	−	1.34684i
$489$	3.29177e7	+	8.79225e6i	0.281516	+	0.0751923i
$490$	7.87359e6	−	1.58504e6i	0.0669244	−	0.0134726i
$491$	−2.03599e7	−	3.52644e7i	−0.172001	−	0.297914i	0.767118	−	0.641506i	$-0.221690\pi$
$491$	−2.03599e7	−	3.52644e7i	−0.172001	−	0.297914i	−0.939119	+	0.343591i	$0.888357\pi$
$492$	1.05824e8	−	1.45146e7i	0.888567	−	0.121873i
$493$	5.27313e7	+	3.04444e7i	0.440076	+	0.254078i
$494$	−7.24331e7	+	2.15009e8i	−0.600836	+	1.78351i
$495$	−1.00290e7	+	1.74346e7i	−0.0826877	+	0.143746i
$496$	1.20333e8	−	3.34360e7i	0.986145	−	0.274012i
$497$	−9.99084e6	+	1.73047e7i	−0.0813829	+	0.140959i
$498$	−477371.	+	7.64650e6i	−0.00386516	+	0.0619120i
$499$	−1.99001e7	−	3.44680e7i	−0.160160	−	0.277405i	0.774766	−	0.632248i	$-0.217868\pi$
$499$	−1.99001e7	−	3.44680e7i	−0.160160	−	0.277405i	−0.934926	+	0.354843i	$0.884534\pi$
$500$	3.96722e7	+	5.03689e6i	0.317378	+	0.0402951i
$501$	−5.33277e7	+	1.43345e7i	−0.424072	+	0.113991i
$502$	−7.31929e7	+	6.44877e7i	−0.578572	+	0.509760i
$503$		−	1.81502e8i		−	1.42619i	−0.701067	−	0.713096i	$-0.747292\pi$
$503$		−	1.81502e8i		−	1.42619i	0.701067	−	0.713096i	$-0.252708\pi$
$504$	4.23352e7	−	8.77210e7i	0.330682	−	0.685192i
$505$	−2.28816e7			−0.177669
$506$	−1.10173e8	−	1.25046e8i	−0.850403	−	0.965199i
$507$	1.90758e8	−	1.91061e8i	1.46372	−	1.46605i
$508$	3.59406e7	+	4.56312e6i	0.274154	+	0.0348073i
$509$	−1.67252e8	+	9.65629e7i	−1.26829	+	0.732246i	−0.974664	−	0.223675i	$-0.928195\pi$
$509$	−1.67252e8	+	9.65629e7i	−1.26829	+	0.732246i	−0.293624	+	0.955921i	$0.594861\pi$
$510$	−3.11625e6	+	4.69525e6i	−0.0234921	+	0.0353955i
$511$	−1.10548e8	−	6.38252e7i	−0.828495	−	0.478332i
$512$	−1.31067e8	+	2.89112e7i	−0.976525	+	0.215405i
$513$	1.02755e8	+	1.02266e8i	0.761114	+	0.757495i
$514$	−1.05509e8	−	3.55443e7i	−0.776962	−	0.261746i
$515$	−6.10827e6	+	1.05798e7i	−0.0447195	+	0.0774564i
$516$	−2.18611e7	−	2.81733e7i	−0.159120	−	0.205063i
$517$	3.66154e7	−	2.11399e7i	0.264967	−	0.152979i
$518$	7.62831e6	+	3.78932e7i	0.0548832	+	0.272629i
$519$	8.05986e7	+	8.04706e7i	0.576534	+	0.575619i
$520$	3.98401e7	−	2.88823e6i	0.283342	−	0.0205410i
$521$	−1.03916e8			−0.734797			−0.367399	−	0.930064i	$-0.619751\pi$
$521$	−1.03916e8			−0.734797			−0.367399	+	0.930064i	$0.619751\pi$
$522$	−2.61489e8	−	8.76293e7i	−1.83841	−	0.616081i
$523$	2.49124e8			1.74145			0.870725	−	0.491771i	$-0.163650\pi$
$523$	2.49124e8			1.74145			0.870725	+	0.491771i	$0.163650\pi$
$524$	−1.38838e8	+	5.82604e7i	−0.964973	+	0.404930i
$525$	1.03525e8	−	2.78276e7i	0.715429	−	0.192308i
$526$	−6.00752e7	+	1.20938e7i	−0.412798	+	0.0831009i
$527$	−3.40013e7	+	1.96307e7i	−0.232308	+	0.134123i
$528$	1.29657e8	−	7.66000e7i	0.880836	−	0.520388i
$529$	4.30044e7	−	7.44858e7i	0.290500	−	0.503160i
$530$	1.98774e7	+	6.69638e6i	0.133516	+	0.0449793i
$531$	197648.	+	1.24388e8i	0.00132010	+	0.830798i
$532$	−7.44337e7	+	9.79359e7i	−0.494350	+	0.650440i
$533$	2.06128e8	+	1.19008e8i	1.36130	+	0.785948i
$534$	−1.86682e8	+	9.27820e7i	−1.22597	+	0.609312i
$535$	−4.19298e7	+	2.42082e7i	−0.273818	+	0.158089i
$536$	2.38174e6	−	4.91513e6i	0.0154668	−	0.0319183i
$537$	−1.64177e8	−	4.38514e7i	−1.06021	−	0.283179i
$538$	1.40621e8	+	1.59604e8i	0.903035	+	1.02494i
$539$	6.74717e7			0.430879
$540$	9.60228e6	−	2.36486e7i	0.0609808	−	0.150184i
$541$		−	6.77348e6i		−	0.0427780i	−0.999771	−	0.0213890i	$-0.993191\pi$
$541$		−	6.77348e6i		−	0.0427780i	0.999771	−	0.0213890i	$-0.00680885\pi$
$542$	8.91055e7	+	1.01134e8i	0.559638	+	0.635183i
$543$	7.45380e7	−	2.79066e8i	0.465563	−	1.74304i
$544$	3.76240e7	−	1.90966e7i	0.233705	−	0.118620i
$545$	1.73778e6	+	3.00993e6i	0.0107351	+	0.0185937i
$546$	1.94360e8	−	9.65982e7i	1.19407	−	0.593460i
$547$	−1.11840e8	+	1.93712e8i	−0.683336	+	1.18357i	0.290620	+	0.956838i	$0.406138\pi$
$547$	−1.11840e8	+	1.93712e8i	−0.683336	+	1.18357i	−0.973957	+	0.226735i	$0.927195\pi$
$548$	2.46249e7	+	1.87155e7i	0.149635	+	0.113726i
$549$	−1.12030e8	−	1.93331e8i	−0.677044	−	1.16838i
$550$	1.57068e8	+	5.29137e7i	0.944060	+	0.318039i
$551$	3.01628e8	+	1.74145e8i	1.80309	+	1.04101i
$552$	1.60075e8	+	1.38212e8i	0.951714	+	0.821730i
$553$	1.81351e7	+	3.14110e7i	0.107237	+	0.185740i
$554$	3.26629e8	−	6.57539e7i	1.92099	−	0.386716i
$555$	2.62931e6	+	9.78164e6i	0.0153803	+	0.0572180i
$556$	−1.77761e8	+	7.45933e7i	−1.03422	+	0.433986i
$557$			8.23747e7i			0.476681i	0.971182	+	0.238341i	$0.0766035\pi$
$557$			8.23747e7i			0.476681i	−0.971182	+	0.238341i	$0.923397\pi$
$558$	1.33238e8	−	1.17768e8i	0.766878	−	0.677837i
$559$		−	7.94613e7i		−	0.454904i
$560$	2.09702e7	+	5.41210e6i	0.119409	+	0.0308178i
$561$	−3.34485e7	+	3.35017e7i	−0.189447	+	0.189749i
$562$	−3.38781e7	−	1.68287e8i	−0.190858	−	0.948075i
$563$	−8.00260e7	−	1.38609e8i	−0.448442	−	0.776724i	0.549843	−	0.835268i	$-0.314687\pi$
$563$	−8.00260e7	−	1.38609e8i	−0.448442	−	0.776724i	−0.998285	+	0.0585442i	$0.981354\pi$
$564$	−4.23884e7	+	3.28914e7i	−0.236271	+	0.183335i
$565$	−3.58190e6	−	2.06801e6i	−0.0198595	−	0.0114659i
$566$	−6.15662e7	−	2.07407e7i	−0.339542	−	0.114386i
$567$	−440727.	−	1.38684e8i	−0.00241780	−	0.760810i
$568$	3.24454e7	−	2.20055e7i	0.177055	−	0.120085i
$569$	−6.19990e7	+	1.07385e8i	−0.336549	+	0.582919i	−0.983781	−	0.179373i	$-0.942593\pi$
$569$	−6.19990e7	+	1.07385e8i	−0.336549	+	0.582919i	0.647232	+	0.762293i	$0.275926\pi$
$570$	−1.78252e7	+	2.68573e7i	−0.0962523	+	0.145023i
$571$	−1.35049e8	−	2.33911e8i	−0.725407	−	1.25644i	−0.958806	−	0.284060i	$-0.908318\pi$
$571$	−1.35049e8	−	2.33911e8i	−0.725407	−	1.25644i	0.233400	−	0.972381i	$-0.425015\pi$
$572$	3.32896e8	+	4.22654e7i	1.77877	+	0.225838i
$573$	3.89370e7	+	3.88752e7i	0.206966	+	0.206637i
$574$	8.53108e7	+	9.68269e7i	0.451095	+	0.511989i
$575$			2.32759e8i			1.22434i
$576$	−1.49800e8	+	1.18661e8i	−0.783868	+	0.620928i
$577$	−1.19041e8			−0.619681			−0.309840	−	0.950789i	$-0.600276\pi$
$577$	−1.19041e8			−0.619681			−0.309840	+	0.950789i	$0.600276\pi$
$578$	1.34935e8	−	1.18886e8i	0.698779	−	0.615669i
$579$	5.14987e6	+	1.91587e7i	0.0265314	+	0.0987029i
$580$	7.72332e6	−	6.08314e7i	0.0395840	−	0.311777i
$581$	−8.01599e6	+	4.62803e6i	−0.0408722	+	0.0235976i
$582$	−2.12141e7	+	3.39807e8i	−0.107611	+	1.72370i
$583$	1.52600e8	+	8.81038e7i	0.770104	+	0.444620i
$584$	1.40580e8	+	2.07273e8i	0.705803	+	1.04065i
$585$	4.92094e7	−	2.85154e7i	0.245799	−	0.142433i
$586$	4.83392e7	−	1.43489e8i	0.240219	−	0.713060i
$587$	−1.12621e8	+	1.95066e8i	−0.556809	+	0.964421i	0.440952	+	0.897531i	$0.354641\pi$
$587$	−1.12621e8	+	1.95066e8i	−0.556809	+	0.964421i	−0.997760	+	0.0668902i	$0.978692\pi$
$588$	−8.48270e7	+	1.16346e7i	−0.417255	+	0.0572296i
$589$	−1.94491e8	+	1.12289e8i	−0.951817	+	0.549532i
$590$	−2.71136e7	+	5.45827e6i	−0.132017	+	0.0265766i
$591$	−9.29013e7	+	3.47818e8i	−0.450049	+	1.68496i
$592$	1.89516e7	−	7.34315e7i	0.0913442	−	0.353930i
$593$	−9.79025e7			−0.469493			−0.234747	−	0.972057i	$-0.575426\pi$
$593$	−9.79025e7			−0.469493			−0.234747	+	0.972057i	$0.575426\pi$
$594$	1.18288e8	−	1.78840e8i	0.564393	−	0.853309i
$595$	−6.80823e6			−0.0323209
$596$	2.31597e7	+	5.51911e7i	0.109394	+	0.260694i
$597$	−6.22065e7	+	2.32898e8i	−0.292357	+	1.09457i
$598$	9.30030e7	+	4.61987e8i	0.434904	+	2.16036i
$599$	−2.52042e8	+	1.45517e8i	−1.17272	+	0.677068i	−0.954318	−	0.298792i	$-0.903416\pi$
$599$	−2.52042e8	+	1.45517e8i	−1.17272	+	0.677068i	−0.218398	+	0.975860i	$0.570083\pi$
$600$	−2.06594e8	−	3.94400e7i	−0.956453	−	0.182592i
$601$	2.46887e7	−	4.27621e7i	0.113730	−	0.196986i	−0.803541	−	0.595249i	$-0.797053\pi$
$601$	2.46887e7	−	4.27621e7i	0.113730	−	0.196986i	0.917271	+	0.398263i	$0.130387\pi$
$602$	1.37543e7	−	4.08280e7i	0.0630448	−	0.187141i
$603$	−12356.8	−	7.77664e6i	−5.63577e−5	−	0.0354683i
$604$	−1.49010e8	+	1.96060e8i	−0.676247	+	0.889770i
$605$	−1.45094e6	−	837699.i	−0.00655213	−	0.00378288i
$606$	2.43458e8	+	1.51990e7i	1.09397	+	0.0682965i
$607$	−3.16369e8	+	1.82656e8i	−1.41458	+	0.816709i	−0.995816	−	0.0913860i	$-0.970870\pi$
$607$	−3.16369e8	+	1.82656e8i	−1.41458	+	0.816709i	−0.418765	+	0.908095i	$0.637537\pi$
$608$	2.15213e8	−	1.09234e8i	0.957541	−	0.486013i
$609$	−8.64901e7	−	3.21763e8i	−0.382926	−	1.42457i
$610$	3.72778e7	−	3.28441e7i	0.164233	−	0.144700i
$611$	−1.19554e8			−0.524133
$612$	3.62753e7	−	4.78869e7i	0.158255	−	0.208912i
$613$		−	2.35066e7i		−	0.102049i	−0.998697	−	0.0510244i	$-0.983751\pi$
$613$		−	2.35066e7i		−	0.102049i	0.998697	−	0.0510244i	$-0.0162486\pi$
$614$	1.18272e8	−	1.04206e8i	0.510949	−	0.450180i
$615$	2.39306e7	+	2.38926e7i	0.102880	+	0.102716i
$616$	1.63729e8	+	7.93388e7i	0.700462	+	0.339425i
$617$	−1.81112e8	−	3.13696e8i	−0.771068	−	1.33553i	−0.936978	−	0.349388i	$-0.886390\pi$
$617$	−1.81112e8	−	3.13696e8i	−0.771068	−	1.33553i	0.165911	−	0.986141i	$-0.446944\pi$
$618$	7.20189e7	−	1.08511e8i	0.305127	−	0.459735i
$619$	2.22576e8	−	3.85513e8i	0.938440	−	1.62543i	0.170058	−	0.985434i	$-0.445604\pi$
$619$	2.22576e8	−	3.85513e8i	0.938440	−	1.62543i	0.768382	−	0.639992i	$-0.221062\pi$
$620$	3.14792e7	+	2.39250e7i	0.132084	+	0.100387i
$621$	2.91045e8	+	7.72423e7i	1.21531	+	0.322538i
$622$	5.36617e7	−	1.59288e8i	0.222994	−	0.661931i
$623$	−2.18116e8	−	1.25929e8i	−0.902035	−	0.520790i
$624$	−4.25813e8	+	4.26671e6i	−1.75253	+	0.0175606i
$625$	−1.12533e8	−	1.94913e8i	−0.460934	−	0.798362i
$626$	8.21651e7	+	4.08150e8i	0.334938	+	1.66378i
$627$	−1.91329e8	+	1.91633e8i	−0.776208	+	0.777442i
$628$	1.14043e8	+	2.71771e8i	0.460456	+	1.09729i
$629$			2.38404e7i			0.0957993i
$630$	3.02201e7	−	6.13363e6i	0.120858	−	0.0245299i
$631$		−	4.22360e8i		−	1.68110i	−0.541732	−	0.840551i	$-0.682231\pi$
$631$		−	4.22360e8i		−	1.68110i	0.541732	−	0.840551i	$-0.317769\pi$
$632$	−5.14542e6	−	7.09757e7i	−0.0203831	−	0.281163i
$633$	9.89944e7	+	3.68282e8i	0.390301	+	1.45201i
$634$	−3.57248e8	+	7.19179e7i	−1.40185	+	0.282208i
$635$	5.73482e6	+	9.93300e6i	0.0223975	+	0.0387935i
$636$	−2.07045e8	−	8.44522e7i	−0.804810	−	0.328276i
$637$	−1.65228e8	−	9.53946e7i	−0.639243	−	0.369067i
$638$	1.64460e8	−	4.88179e8i	0.633283	−	1.87982i
$639$	2.78330e7	−	4.83855e7i	0.106674	−	0.185444i
$640$	−3.23949e7	−	2.74972e7i	−0.123577	−	0.104893i
$641$	6.16641e7	−	1.06805e8i	0.234131	−	0.405526i	−0.724889	−	0.688866i	$-0.758109\pi$
$641$	6.16641e7	−	1.06805e8i	0.234131	−	0.405526i	0.959020	+	0.283339i	$0.0914423\pi$
$642$	4.62209e8	−	2.29721e8i	1.74676	−	0.868150i
$643$	−1.52014e8	−	2.63296e8i	−0.571808	−	0.990400i	−0.996380	−	0.0850065i	$-0.972909\pi$
$643$	−1.52014e8	−	2.63296e8i	−0.571808	−	0.990400i	0.424572	−	0.905394i	$-0.360424\pi$
$644$	−3.21815e7	+	2.53472e8i	−0.120489	+	0.949013i
$645$	2.91327e6	−	1.09071e7i	0.0108568	−	0.0406473i
$646$	−5.69269e7	+	5.01563e7i	−0.211164	+	0.186049i
$647$		−	1.41001e8i		−	0.520605i	−0.965527	−	0.260303i	$-0.916178\pi$
$647$		−	1.41001e8i		−	0.520605i	0.965527	−	0.260303i	$-0.0838223\pi$
$648$	−1.17876e8	+	2.45240e8i	−0.433211	+	0.901293i
$649$	−2.32346e8			−0.849967
$650$	−3.09825e8	−	3.51648e8i	−1.12817	−	1.28047i
$651$	2.07562e8	+	5.54394e7i	0.752324	+	0.200944i
$652$	1.01722e7	−	8.01194e7i	0.0367004	−	0.289064i
$653$	−8.02763e6	+	4.63476e6i	−0.0288302	+	0.0166451i	−0.514346	−	0.857583i	$-0.671965\pi$
$653$	−8.02763e6	+	4.63476e6i	−0.0288302	+	0.0166451i	0.485516	+	0.874228i	$0.338632\pi$
$654$	−1.64905e7	−	3.31796e7i	−0.0589522	−	0.118615i
$655$	−4.12811e7	−	2.38337e7i	−0.146902	−	0.0848139i
$656$	−6.77841e7	−	2.43949e8i	−0.240113	−	0.864147i
$657$	3.09104e8	+	1.77807e8i	1.08996	+	0.626980i
$658$	−6.14282e7	−	2.06942e7i	−0.215621	−	0.0726392i
$659$	−9.84627e6	+	1.70542e7i	−0.0344045	+	0.0595903i	−0.882715	−	0.469909i	$-0.844287\pi$
$659$	−9.84627e6	+	1.70542e7i	−0.0344045	+	0.0595903i	0.848310	+	0.529499i	$0.177620\pi$
$660$	4.41449e7	+	1.80064e7i	0.153550	+	0.0626318i
$661$	−1.65567e8	+	9.55899e7i	−0.573282	+	0.330984i	−0.758459	−	0.651721i	$-0.774047\pi$
$661$	−1.65567e8	+	9.55899e7i	−0.573282	+	0.330984i	0.185177	+	0.982705i	$0.440714\pi$
$662$	−7.38041e7	−	3.66617e8i	−0.254394	−	1.26369i
$663$	1.29277e8	−	3.47498e7i	0.443589	−	0.119237i
$664$	1.81128e7	−	1.31309e6i	0.0618701	−	0.00448530i
$665$	−3.89437e7			−0.132426
$666$	−2.14782e7	−	1.05822e8i	−0.0727067	−	0.358223i
$667$	7.23432e8			2.43792
$668$	5.06480e7	+	1.20697e8i	0.169916	+	0.404919i
$669$	−1.29375e8	−	1.29170e8i	−0.432089	−	0.431403i
$670$	1.69512e6	−	341247.i	0.00563607	−	0.00113460i
$671$	3.61458e8	−	2.08688e8i	1.19644	−	0.690764i
$672$	−2.19525e8	−	7.15136e7i	−0.723397	−	0.235657i
$673$	−9.35030e7	+	1.61952e8i	−0.306747	+	0.531301i	−0.977649	−	0.210245i	$-0.932574\pi$
$673$	−9.35030e7	+	1.61952e8i	−0.306747	+	0.531301i	0.670902	+	0.741546i	$0.265907\pi$
$674$	2.88276e8	+	9.71155e7i	0.941518	+	0.317182i
$675$	−2.89077e8	+	7.81968e7i	−0.939944	+	0.254260i
$676$	−5.09513e8	−	3.87242e8i	−1.64936	−	1.25355i
$677$	−1.11866e8	−	6.45861e7i	−0.360523	−	0.208148i	0.308787	−	0.951131i	$-0.400077\pi$
$677$	−1.11866e8	−	6.45861e7i	−0.360523	−	0.208148i	−0.669310	+	0.742983i	$0.733410\pi$
$678$	3.67374e7	+	2.43827e7i	0.117874	+	0.0782335i
$679$	−3.56226e8	+	2.05667e8i	−1.13793	+	0.656986i
$680$	1.20207e7	+	5.82493e6i	0.0382300	+	0.0185252i
$681$	−1.79225e8	+	1.79510e8i	−0.567488	+	0.568390i
$682$	2.19585e8	+	2.49227e8i	0.692228	+	0.785672i
$683$	5.50734e8			1.72854			0.864271	−	0.503026i	$-0.167780\pi$
$683$	5.50734e8			1.72854			0.864271	+	0.503026i	$0.167780\pi$
$684$	2.07498e8	−	2.73918e8i	0.648405	−	0.855958i
$685$			9.79196e6i			0.0304648i
$686$	−2.30753e8	−	2.61902e8i	−0.714784	−	0.811273i
$687$	4.45791e8	−	1.19829e8i	1.37487	−	0.369566i
$688$	−5.92161e7	+	6.03189e7i	−0.181834	+	0.185220i
$689$	−2.49131e8	−	4.31507e8i	−0.761675	−	1.31926i
$690$	−4.17180e6	+	6.68237e7i	−0.0126992	+	0.203415i
$691$	1.16311e8	−	2.01456e8i	0.352521	−	0.610585i	−0.634169	−	0.773194i	$-0.718658\pi$
$691$	1.16311e8	−	2.01456e8i	0.352521	−	0.610585i	0.986690	+	0.162610i	$0.0519911\pi$
$692$	1.63357e8	−	2.14937e8i	0.492969	−	0.648622i
$693$	2.59050e8	−	411620.i	0.778366	−	0.00123679i
$694$	1.63693e8	+	5.51455e7i	0.489723	+	0.164980i
$695$	−5.28540e7	−	3.05153e7i	−0.157443	−	0.0908998i
$696$	−1.22582e8	+	6.42109e8i	−0.363580	+	1.90450i
$697$	3.97968e7	+	6.89301e7i	0.117530	+	0.203568i
$698$	1.32329e8	−	2.66392e7i	0.389123	−	0.0783348i
$699$	2.13244e7	+	5.69570e6i	0.0624375	+	0.0166769i
$700$	−9.83228e7	−	2.34309e8i	−0.286655	−	0.683118i
$701$		−	2.36475e8i		−	0.686486i	−0.939247	−	0.343243i	$-0.888475\pi$
$701$		−	2.36475e8i		−	0.686486i	0.939247	−	0.343243i	$-0.111525\pi$
$702$	−5.42523e8	+	2.70713e8i	−1.56822	+	0.782525i
$703$			1.36370e8i			0.392511i
$704$	−2.21204e8	−	2.80164e8i	−0.633978	−	0.802961i
$705$	−1.64105e7	−	4.38320e6i	−0.0468331	−	0.0125090i
$706$	−6.28539e7	−	3.12223e8i	−0.178615	−	0.887260i
$707$	1.47352e8	+	2.55222e8i	0.416964	+	0.722203i
$708$	2.92111e8	−	4.00652e7i	0.823093	−	0.112893i
$709$	1.04496e8	+	6.03309e7i	0.293198	+	0.169278i	0.639383	−	0.768888i	$-0.279190\pi$
$709$	1.04496e8	+	6.03309e7i	0.293198	+	0.169278i	−0.346185	+	0.938166i	$0.612523\pi$
$710$	1.17619e7	+	3.96240e6i	0.0328627	+	0.0110709i
$711$	−5.08006e7	−	8.76672e7i	−0.141338	−	0.243909i
$712$	2.77368e8	+	4.08957e8i	0.768452	+	1.13302i
$713$	−2.33236e8	+	4.03976e8i	−0.643467	+	1.11452i
$714$	7.24388e7	+	4.52235e6i	0.199011	+	0.0124242i
$715$	5.31181e7	+	9.20033e7i	0.145320	+	0.251701i
$716$	−5.07337e7	+	3.99596e8i	−0.138216	+	1.08863i
$717$	−3.79168e8	+	1.01921e8i	−1.02867	+	0.276507i
$718$	3.62899e8	+	4.11887e8i	0.980420	+	1.11277i
$719$		−	6.10386e8i		−	1.64217i	−0.570806	−	0.821085i	$-0.693369\pi$
$719$		−	6.10386e8i		−	1.64217i	0.570806	−	0.821085i	$-0.306631\pi$
$720$	−5.86050e7	−	1.50258e7i	−0.157014	−	0.0402569i
$721$	1.57343e8			0.419800
$722$	−4.32326e7	+	3.80907e7i	−0.114868	+	0.101206i
$723$	7.39537e7	−	7.40713e7i	0.195679	−	0.195991i
$724$	−6.79227e8	−	8.62365e7i	−1.78978	−	0.227235i
$725$	−6.23068e8	+	3.59729e8i	−1.63501	+	0.943976i
$726$	1.48814e7	+	9.87681e6i	0.0388896	+	0.0258111i
$727$	−2.25784e8	−	1.30356e8i	−0.587611	−	0.339257i	0.176541	−	0.984293i	$-0.443509\pi$
$727$	−2.25784e8	−	1.30356e8i	−0.587611	−	0.339257i	−0.764152	+	0.645036i	$0.776842\pi$
$728$	−2.88777e8	−	4.25778e8i	−0.748459	−	1.10354i
$729$	1.84678e6	+	3.87416e8i	0.00476686	+	0.999989i
$730$	−2.53133e7	+	7.51395e7i	−0.0650699	+	0.193152i
$731$	1.32861e7	−	2.30122e7i	0.0340131	−	0.0589124i
$732$	−4.18448e8	+	3.24696e8i	−1.06686	+	0.827836i
$733$	4.07340e8	−	2.35178e8i	1.03430	−	0.597151i	0.116084	−	0.993239i	$-0.462966\pi$
$733$	4.07340e8	−	2.35178e8i	1.03430	−	0.597151i	0.918212	+	0.396088i	$0.129633\pi$
$734$	−4.88843e8	+	9.84094e7i	−1.23618	+	0.248856i
$735$	−1.91824e7	−	1.91519e7i	−0.0483104	−	0.0482337i
$736$	2.73683e8	−	4.20001e8i	0.686460	−	1.05346i
$737$	1.45261e7			0.0362866
$738$	−2.38749e8	−	2.70111e8i	−0.593980	−	0.672006i
$739$	1.60827e8			0.398497			0.199249	−	0.979949i	$-0.436150\pi$
$739$	1.60827e8			0.398497			0.199249	+	0.979949i	$0.436150\pi$
$740$	2.21389e7	−	9.29012e6i	0.0546338	−	0.0229259i
$741$	7.39477e8	−	1.98772e8i	1.81748	−	0.488541i
$742$	−5.33144e7	−	2.64836e8i	−0.130507	−	0.648284i
$743$	−2.95162e8	+	1.70412e8i	−0.719605	+	0.415464i	−0.814607	−	0.580013i	$-0.803047\pi$
$743$	−2.95162e8	+	1.70412e8i	−0.719605	+	0.415464i	0.0950025	+	0.995477i	$0.469714\pi$
$744$	−3.19043e8	−	2.75469e8i	−0.774695	−	0.668889i
$745$	−9.47439e6	+	1.64101e7i	−0.0229130	+	0.0396865i
$746$	−1.72046e7	+	5.10699e7i	−0.0414409	+	0.123012i
$747$	2.23724e7	−	1.29642e7i	0.0536724	−	0.0311016i
$748$	8.93408e7	+	6.79012e7i	0.213474	+	0.162245i
$749$	5.40037e8	+	3.11791e8i	1.28522	+	0.742023i
$750$	−6.00702e7	−	1.20864e8i	−0.142389	−	0.286492i
$751$	3.01470e8	−	1.74054e8i	0.711744	−	0.410926i	−0.0999622	−	0.994991i	$-0.531872\pi$
$751$	3.01470e8	−	1.74054e8i	0.711744	−	0.410926i	0.811707	+	0.584065i	$0.198539\pi$
$752$	9.07535e7	+	8.90943e7i	0.213408	+	0.209506i
$753$	3.18078e8	+	8.49580e7i	0.744987	+	0.198985i
$754$	−1.09295e9	+	9.62959e8i	−2.54968	+	2.24643i
$755$	−7.79622e7			−0.181152
$756$	−3.25613e8	+	4.51874e7i	−0.753592	+	0.104581i
$757$		−	1.88339e8i		−	0.434163i	−0.976153	−	0.217082i	$-0.930346\pi$
$757$		−	1.88339e8i		−	0.434163i	0.976153	−	0.217082i	$-0.0696538\pi$
$758$	4.22903e8	−	3.72605e8i	0.971032	−	0.855542i
$759$	−1.45146e8	+	5.43417e8i	−0.331954	+	1.24282i
$760$	6.87598e7	+	3.33191e7i	0.156637	+	0.0759020i
$761$	−1.49571e8	−	2.59064e8i	−0.339385	−	0.587833i	0.644932	−	0.764240i	$-0.276886\pi$
$761$	−1.49571e8	−	2.59064e8i	−0.339385	−	0.587833i	−0.984317	+	0.176407i	$0.943552\pi$
$762$	−5.44199e7	−	1.09495e8i	−0.122996	−	0.247475i
$763$	2.23818e7	−	3.87665e7i	0.0503874	−	0.0872736i
$764$	7.89174e7	−	1.03835e8i	0.176967	−	0.232844i
$765$	1.90190e7	−	30220.5i	0.0424819	−	6.75021e-5i
$766$	−2.28906e7	+	6.79481e7i	−0.0509297	+	0.151179i
$767$	5.68983e8	+	3.28502e8i	1.26099	+	0.728035i
$768$	3.26413e8	+	3.14085e8i	0.720583	+	0.693368i
$769$	1.49172e8	+	2.58374e8i	0.328026	+	0.568158i	0.982120	−	0.188255i	$-0.0602833\pi$
$769$	1.49172e8	+	2.58374e8i	0.328026	+	0.568158i	−0.654094	+	0.756413i	$0.726950\pi$
$770$	1.13674e7	+	5.64667e7i	0.0248993	+	0.123686i
$771$	9.75412e7	+	3.62875e8i	0.212826	+	0.791761i
$772$	4.33621e7	−	1.81960e7i	0.0942451	−	0.0395479i
$773$			2.07252e8i			0.448704i	0.974508	+	0.224352i	$0.0720265\pi$
$773$			2.07252e8i			0.448704i	−0.974508	+	0.224352i	$0.927973\pi$
$774$	−3.82419e7	+	1.14116e8i	−0.0824740	+	0.246106i
$775$		−	4.63909e8i		−	0.996615i
$776$	8.04923e8	−	5.83533e7i	1.72254	−	0.124876i
$777$	9.21724e7	−	9.23190e7i	0.196489	−	0.196801i
$778$	3.47535e7	−	6.99626e6i	0.0738005	−	0.0148569i
$779$	2.27642e8	+	3.94287e8i	0.481548	+	0.834065i
$780$	−8.26462e7	−	1.06509e8i	−0.174156	−	0.224442i
$781$	9.02972e7	+	5.21331e7i	0.189549	+	0.109436i
$782$	−5.03114e7	+	1.49343e8i	−0.105207	+	0.312295i
$783$	2.43042e8	+	8.98472e8i	0.506285	+	1.87163i
$784$	5.43346e7	+	1.95545e8i	0.112753	+	0.405788i
$785$	−4.66535e7	+	8.08062e7i	−0.0964440	+	0.167046i
$786$	4.23395e8	+	2.81009e8i	0.871923	+	0.578698i
$787$	−2.77108e8	−	4.79964e8i	−0.568492	−	0.984657i	−0.996715	−	0.0809838i	$-0.974194\pi$
$787$	−2.77108e8	−	4.79964e8i	−0.568492	−	0.984657i	0.428224	−	0.903673i	$-0.359140\pi$
$788$	8.46563e8	+	1.07482e8i	1.73014	+	0.219663i
$789$	1.46361e8	+	1.46129e8i	0.297985	+	0.297512i
$790$	1.69038e7	−	1.48934e7i	0.0342850	−	0.0302073i
$791$			5.32702e7i			0.107635i
$792$	−4.57736e8	−	2.20909e8i	−0.921382	−	0.444670i
$793$	−1.18021e9			−2.36668
$794$	5.34827e8	+	6.07024e8i	1.06844	+	1.21267i
$795$	−1.83763e7	−	6.83640e7i	−0.0365727	−	0.136059i
$796$	5.66857e8	+	7.19696e7i	1.12392	+	0.142695i
$797$	2.89311e8	−	1.67034e8i	0.571465	−	0.329935i	−0.186270	−	0.982499i	$-0.559640\pi$
$797$	2.89311e8	−	1.67034e8i	0.571465	−	0.329935i	0.757734	+	0.652563i	$0.226306\pi$
$798$	4.14357e8	+	2.58683e7i	0.815391	+	0.0509048i
$799$	−3.46233e7	−	1.99898e7i	−0.0678779	−	0.0391893i
$800$	−2.68678e7	+	4.97823e8i	−0.0524761	+	0.972311i
$801$	6.09874e8	+	3.50820e8i	1.18670	+	0.682632i
$802$	−4.96954e8	−	1.67416e8i	−0.963370	−	0.324544i
$803$	−3.33046e8	+	5.76852e8i	−0.643216	+	1.11408i
$804$	−1.82626e7	+	2.50484e6i	−0.0351393	+	0.00481962i
$805$	−7.00527e7	+	4.04449e7i	−0.134288	+	0.0775312i
$806$	−1.85363e8	−	9.20780e8i	−0.354012	−	1.75853i
$807$	1.85259e8	−	6.93599e8i	0.352499	−	1.31974i
$808$	−4.18078e7	−	5.76695e8i	−0.0792543	−	1.09323i
$809$	−3.36902e8			−0.636294			−0.318147	−	0.948041i	$-0.603061\pi$
$809$	−3.36902e8			−0.636294			−0.318147	+	0.948041i	$0.603061\pi$
$810$	−8.43938e7	+	1.72686e7i	−0.158802	+	0.0324940i
$811$	5.95159e8			1.11576			0.557880	−	0.829922i	$-0.311615\pi$
$811$	5.95159e8			1.11576			0.557880	+	0.829922i	$0.311615\pi$
$812$	−7.28251e8	+	3.05594e8i	−1.36023	+	0.570791i
$813$	1.17390e8	−	4.39503e8i	0.218454	−	0.817881i
$814$	1.97730e8	−	3.98052e7i	0.366606	−	0.0738018i
$815$	2.21428e7	−	1.27842e7i	0.0409034	−	0.0236156i
$816$	−1.24030e8	−	6.99613e7i	−0.228274	−	0.128762i
$817$	7.59979e7	−	1.31632e8i	0.139359	−	0.241377i
$818$	−4.03399e8	−	1.35899e8i	−0.737012	−	0.248288i
$819$	−6.34958e8	−	3.65249e8i	−1.15583	−	0.664872i
$820$	4.85026e7	−	6.38171e7i	0.0879677	−	0.115743i
$821$	−5.54509e8	−	3.20146e8i	−1.00203	−	0.578520i	−0.0931786	−	0.995649i	$-0.529703\pi$
$821$	−5.54509e8	−	3.20146e8i	−1.00203	−	0.578520i	−0.908847	+	0.417130i	$0.863036\pi$
$822$	6.50428e6	−	1.04185e8i	0.0117107	−	0.187582i
$823$	9.95156e7	−	5.74554e7i	0.178522	−	0.103070i	−0.408076	−	0.912948i	$-0.633800\pi$
$823$	9.95156e7	−	5.74554e7i	0.178522	−	0.103070i	0.586598	+	0.809878i	$0.300467\pi$
$824$	−2.77809e8	−	1.34619e8i	−0.496551	−	0.240615i
$825$	−1.45207e8	−	5.40202e8i	−0.258598	−	0.962042i
$826$	2.35487e8	+	2.67276e8i	0.417857	+	0.474263i
$827$	3.08175e8			0.544855			0.272428	−	0.962176i	$-0.412173\pi$
$827$	3.08175e8			0.544855			0.272428	+	0.962176i	$0.412173\pi$
$828$	8.87750e7	−	7.08225e8i	0.156387	−	1.24761i
$829$			9.01988e8i			1.58321i	0.611036	+	0.791603i	$0.290753\pi$
$829$			9.01988e8i			1.58321i	−0.611036	+	0.791603i	$0.709247\pi$
$830$	3.80074e6	+	4.31381e6i	0.00664713	+	0.00754443i
$831$	−7.95764e8	−	7.94500e8i	−1.38670	−	1.38449i
$832$	1.45586e8	+	9.98830e8i	0.252785	+	1.73429i
$833$	−3.19004e7	−	5.52532e7i	−0.0551902	−	0.0955922i
$834$	5.42091e8	+	3.59787e8i	0.934489	+	0.620223i
$835$	−2.07195e7	+	3.58873e7i	−0.0355894	+	0.0616426i
$836$	5.11038e8	+	3.88402e8i	0.874651	+	0.664756i
$837$	−5.80078e8	−	1.53951e8i	−0.989260	−	0.262546i
$838$	8.35328e8	+	2.81409e8i	1.41947	+	0.478195i
$839$	6.89956e8	+	3.98346e8i	1.16825	+	0.674489i	0.953267	−	0.302129i	$-0.0976972\pi$
$839$	6.89956e8	+	3.98346e8i	1.16825	+	0.674489i	0.214983	+	0.976618i	$0.431031\pi$
$840$	−2.40283e7	−	6.90311e7i	−0.0405401	−	0.116468i
$841$	8.20652e8	+	1.42141e9i	1.37966	+	2.38963i
$842$	−3.32253e8	+	6.68863e7i	−0.556587	+	0.112047i
$843$	−4.09347e8	+	4.09998e8i	−0.683296	+	0.684382i
$844$	8.33538e8	−	3.49776e8i	1.38643	−	0.581785i
$845$		−	2.02605e8i		−	0.335800i
$846$	1.71694e8	+	5.75373e7i	0.283559	+	0.0950251i
$847$			2.15784e7i			0.0355115i
$848$	−1.32453e8	+	5.13213e8i	−0.217207	+	0.841609i
$849$	5.69169e7	+	2.11744e8i	0.0930076	+	0.346009i
$850$	−3.09298e7	−	1.53642e8i	−0.0503640	−	0.250180i
$851$	1.41626e8	+	2.45304e8i	0.229803	+	0.398030i
$852$	−1.22513e8	−	4.99724e7i	−0.198091	−	0.0808000i
$853$	−8.71216e7	−	5.02997e7i	−0.140371	−	0.0810435i	0.428170	−	0.903698i	$-0.359159\pi$
$853$	−8.71216e7	−	5.02997e7i	−0.140371	−	0.0810435i	−0.568541	+	0.822655i	$0.692492\pi$
$854$	−6.06405e8	−	2.04288e8i	−0.973619	−	0.327997i
$855$	1.08791e8	−	172864.i	0.174058	−	0.000276571i
$856$	−6.86741e8	−	1.01254e9i	−1.09489	−	1.61433i
$857$	5.71436e8	−	9.89756e8i	0.907873	−	1.57248i	0.0908591	−	0.995864i	$-0.471039\pi$
$857$	5.71436e8	−	9.89756e8i	0.907873	−	1.57248i	0.817014	−	0.576618i	$-0.195628\pi$
$858$	−5.04058e8	−	1.01419e9i	−0.798029	−	1.60567i
$859$	−2.92297e8	−	5.06273e8i	−0.461152	−	0.798739i	0.537866	−	0.843030i	$-0.319231\pi$
$859$	−2.92297e8	−	5.06273e8i	−0.461152	−	0.798739i	−0.999019	+	0.0442908i	$0.985897\pi$
$860$	−2.65472e7	−	3.37050e6i	−0.0417372	−	0.00529906i
$861$	1.12391e8	−	4.20786e8i	0.176085	−	0.659252i
$862$	−6.45582e8	−	7.32729e8i	−1.00793	−	1.14399i
$863$			9.04810e8i			1.40775i	0.710324	+	0.703874i	$0.248548\pi$
$863$			9.04810e8i			1.40775i	−0.710324	+	0.703874i	$0.751452\pi$
$864$	6.13570e8	+	1.98801e8i	0.951311	+	0.308232i
$865$	8.54685e7			0.132056
$866$	−5.57386e8	+	4.91093e8i	−0.858228	+	0.756154i
$867$	−5.86392e8	−	1.56624e8i	−0.899769	−	0.240326i
$868$	6.41404e7	−	5.05191e8i	0.0980783	−	0.772497i
$869$	1.63905e8	−	9.46307e7i	0.249766	−	0.144203i
$870$	−1.85327e8	+	9.21086e7i	−0.281437	+	0.139876i
$871$	−3.55723e7	−	2.05377e7i	−0.0538342	−	0.0310812i
$872$	−7.26853e7	+	4.92976e7i	−0.109622	+	0.0743492i
$873$	9.94218e8	−	5.76121e8i	1.49430	−	0.865906i
$874$	−2.87786e8	+	8.54258e8i	−0.431058	+	1.27954i
$875$	8.15308e7	−	1.41215e8i	0.121702	−	0.210794i
$876$	3.19242e8	−	7.82661e8i	0.474906	−	1.16429i
$877$	2.14001e7	−	1.23553e7i	0.0317261	−	0.0183171i	−0.484053	−	0.875039i	$-0.660836\pi$
$877$	2.14001e7	−	1.23553e7i	0.0317261	−	0.0183171i	0.515779	+	0.856722i	$0.327503\pi$
$878$	−6.35276e8	+	1.27888e8i	−0.938596	+	0.188950i
$879$	−4.93500e8	+	1.32653e8i	−0.726643	+	0.195322i
$880$	2.82408e7	−	1.09424e8i	0.0414409	−	0.160570i
$881$	5.19484e8			0.759705			0.379852	−	0.925047i	$-0.375975\pi$
$881$	5.19484e8			0.759705			0.379852	+	0.925047i	$0.375975\pi$
$882$	1.91377e8	+	2.16516e8i	0.278923	+	0.315562i
$883$	−2.26257e8			−0.328639			−0.164319	−	0.986407i	$-0.552543\pi$
$883$	−2.26257e8			−0.328639			−0.164319	+	0.986407i	$0.552543\pi$
$884$	−1.22781e8	−	2.92595e8i	−0.177735	−	0.423555i
$885$	6.60568e7	+	6.59519e7i	0.0952989	+	0.0951476i
$886$	−3.04891e7	−	1.51453e8i	−0.0438373	−	0.217759i
$887$	3.29161e8	−	1.90041e8i	0.471669	−	0.272318i	−0.245269	−	0.969455i	$-0.578876\pi$
$887$	3.29161e8	−	1.90041e8i	0.471669	−	0.272318i	0.716938	+	0.697137i	$0.245543\pi$
$888$	−2.41727e8	+	8.41401e7i	−0.345212	+	0.120161i
$889$	7.38619e7	−	1.27933e8i	0.105127	−	0.182086i
$890$	−4.99440e7	+	1.48253e8i	−0.0708457	+	0.210297i
$891$	−7.23664e8	+	2.29975e6i	−1.02307	+	0.00325123i
$892$	−2.62218e8	+	3.45012e8i	−0.369460	+	0.486116i
$893$	−1.98049e8	−	1.14344e8i	−0.278111	−	0.160567i
$894$	1.11707e8	−	1.68308e8i	0.156339	−	0.235556i
$895$	−1.10437e8	+	6.37610e7i	−0.154045	+	0.0889378i
$896$	−9.80882e7	+	5.38409e8i	−0.136362	+	0.748494i
$897$	1.12375e9	−	1.12554e9i	1.55701	−	1.55949i
$898$	−4.95133e8	+	4.36245e8i	−0.683743	+	0.602422i
$899$	−1.44186e9			−1.98447
$900$	2.75708e8	+	6.54115e8i	0.378201	+	0.897277i
$901$		−	1.66621e8i		−	0.227801i
$902$	5.05252e8	−	4.45159e8i	0.688475	−	0.606591i
$903$	−1.40419e8	+	3.77448e7i	−0.190705	+	0.0512618i
$904$	4.55764e7	−	9.40548e7i	0.0616928	−	0.127314i
$905$	−1.08380e8	−	1.87720e8i	−0.146219	−	0.253259i
$906$	8.29509e8	+	5.17862e7i	1.11542	+	0.0696353i
$907$	−3.45582e8	+	5.98565e8i	−0.463158	+	0.802212i	−0.999116	−	0.0420318i	$-0.986617\pi$
$907$	−3.45582e8	+	5.98565e8i	−0.463158	+	0.802212i	0.535959	+	0.844244i	$0.319950\pi$
$908$	4.78708e8	+	3.63830e8i	0.639460	+	0.486005i
$909$	−4.12767e8	−	7.12317e8i	−0.549558	−	0.948378i
$910$	5.19982e7	−	1.54351e8i	0.0690025	−	0.204825i
$911$	−1.26125e9	−	7.28186e8i	−1.66820	−	0.963135i	−0.968609	−	0.248590i	$-0.920033\pi$
$911$	−1.26125e9	−	7.28186e8i	−1.66820	−	0.963135i	−0.699590	−	0.714545i	$-0.746634\pi$
$912$	−7.09465e8	−	4.00185e8i	−0.935290	−	0.527566i
$913$	2.41495e7	+	4.18281e7i	0.0317319	+	0.0549612i
$914$	8.92621e7	+	4.43404e8i	0.116904	+	0.580712i
$915$	−1.62000e8	−	4.32699e7i	−0.211472	−	0.0564836i
$916$	−4.23390e8	−	1.00897e9i	−0.550877	−	1.31277i
$917$			6.13934e8i			0.796184i
$918$	−2.02380e8	−	1.23118e7i	−0.261602	−	0.0159145i
$919$			8.77218e8i			1.13022i	0.825017	+	0.565108i	$0.191165\pi$
$919$			8.77218e8i			1.13022i	−0.825017	+	0.565108i	$0.808835\pi$
$920$	1.58290e8	−	1.14753e7i	0.203278	−	0.0147367i
$921$	−5.13982e8	−	1.37284e8i	−0.657914	−	0.175727i
$922$	6.38088e8	−	1.28454e8i	0.814119	−	0.163891i
$923$	−1.47417e8	−	2.55333e8i	−0.187474	−	0.324715i
$924$	−8.34397e7	−	6.08350e8i	−0.105769	−	0.771148i
$925$	−2.43956e8	−	1.40848e8i	−0.308239	−	0.177962i
$926$	−4.23023e8	+	1.25569e9i	−0.532759	+	1.58143i
$927$	−4.39545e8	+	698419.i	−0.551777	+	0.000876752i
$928$	1.54727e9	+	8.35070e7i	1.93608	+	0.104491i
$929$	1.88301e8	−	3.26147e8i	0.234858	−	0.406787i	−0.724373	−	0.689408i	$-0.757871\pi$
$929$	1.88301e8	−	3.26147e8i	0.234858	−	0.406787i	0.959232	+	0.282621i	$0.0912040\pi$
$930$	8.31476e6	−	1.33185e8i	0.0103372	−	0.165580i
$931$	−1.82474e8	−	3.16054e8i	−0.226126	−	0.391662i
$932$	6.58962e6	−	5.19020e7i	0.00813978	−	0.0641116i
$933$	−5.47838e8	+	1.47259e8i	−0.674539	+	0.181317i
$934$	−1.66831e8	+	1.46989e8i	−0.204756	+	0.180403i
$935$			3.55259e7i			0.0434621i
$936$	8.08598e8	+	1.18814e9i	0.986064	+	1.44891i
$937$	−1.76012e8			−0.213955			−0.106978	−	0.994261i	$-0.534117\pi$
$937$	−1.76012e8			−0.213955			−0.106978	+	0.994261i	$0.534117\pi$
$938$	−1.47225e7	−	1.67099e7i	−0.0178391	−	0.0202472i
$939$	9.92795e8	−	9.94374e8i	1.19912	−	1.20103i
$940$	−5.07113e6	+	3.99419e7i	−0.00610550	+	0.0480889i
$941$	−5.52511e8	+	3.18992e8i	−0.663089	+	0.382835i	−0.793453	−	0.608631i	$-0.791719\pi$
$941$	−5.52511e8	+	3.18992e8i	−0.663089	+	0.382835i	0.130364	+	0.991466i	$0.458385\pi$
$942$	5.50063e8	−	8.28780e8i	0.658052	−	0.991486i
$943$	8.18971e8	+	4.72833e8i	0.976638	+	0.563862i
$944$	−1.87107e8	−	6.73383e8i	−0.222421	−	0.800472i
$945$	−7.37656e7	−	7.34148e7i	−0.0874094	−	0.0869938i
$946$	−2.13044e8	−	7.17712e7i	−0.251650	−	0.0847767i
$947$	−5.62243e8	+	9.73833e8i	−0.662025	+	1.14666i	0.318058	+	0.948071i	$0.396969\pi$
$947$	−5.62243e8	+	9.73833e8i	−0.662025	+	1.14666i	−0.980083	+	0.198589i	$0.936364\pi$
$948$	−1.89748e8	+	1.47235e8i	−0.222716	+	0.172817i
$949$	1.63116e9	−	9.41751e8i	1.90853	−	1.10189i
$950$	−1.76922e8	−	8.78847e8i	−0.206353	−	1.02504i
$951$	8.70361e8	+	8.68979e8i	1.01195	+	1.01034i
$952$	−1.24395e7	−	1.71591e8i	−0.0144176	−	0.198876i
$953$	1.35637e8			0.156710			0.0783552	−	0.996926i	$-0.475033\pi$
$953$	1.35637e8			0.156710			0.0783552	+	0.996926i	$0.475033\pi$
$954$	1.50111e8	+	7.39592e8i	0.172889	+	0.851818i
$955$	4.12896e7			0.0474057
$956$	3.60116e8	+	8.58178e8i	0.412162	+	0.982209i
$957$	−1.67899e9	+	4.51313e8i	−1.91563	+	0.514923i
$958$	3.58359e8	−	7.21416e7i	0.407588	−	0.0820520i
$959$	1.09220e8	−	6.30580e7i	0.123835	−	0.0714964i
$960$	−1.66362e7	+	1.42441e8i	−0.0188036	+	0.160998i
$961$	2.11070e7	−	3.65584e7i	0.0237824	−	0.0411924i
$962$	−5.40490e8	−	1.82083e8i	−0.607104	−	0.204524i
$963$	−1.51000e9	−	8.68601e8i	−1.69082	−	0.972616i
$964$	−1.97530e8	−	1.50128e8i	−0.220497	−	0.167583i
$965$	1.28930e7	+	7.44376e6i	0.0143473	+	0.00828344i
$966$	7.72218e8	−	3.83797e8i	0.856660	−	0.425765i
$967$	−3.22501e8	+	1.86196e8i	−0.356658	+	0.205917i	−0.667614	−	0.744508i	$-0.732684\pi$
$967$	−3.22501e8	+	1.86196e8i	−0.356658	+	0.205917i	0.310956	+	0.950424i	$0.399351\pi$
$968$	1.84618e7	−	3.80992e7i	0.0203540	−	0.0420039i
$969$	2.47390e8	+	6.60774e7i	0.271901	+	0.0726242i
$970$	1.68903e8	+	1.91703e8i	0.185064	+	0.210046i
$971$	1.36810e9			1.49438			0.747190	−	0.664610i	$-0.231402\pi$
$971$	1.36810e9			1.49438			0.747190	+	0.664610i	$0.231402\pi$
$972$	9.09411e8	−	1.27678e8i	0.990288	−	0.139033i
$973$			7.86046e8i			0.853315i
$974$	−3.05538e8	−	3.46782e8i	−0.330665	−	0.375301i
$975$	−4.08173e8	+	1.52818e9i	−0.440382	+	1.64877i
$976$	8.95897e8	+	8.79517e8i	0.963626	+	0.946008i
$977$	−4.89788e7	−	8.48337e7i	−0.0525199	−	0.0909672i	0.838570	−	0.544794i	$-0.183392\pi$
$977$	−4.89788e7	−	8.48337e7i	−0.0525199	−	0.0909672i	−0.891090	+	0.453826i	$0.850059\pi$
$978$	−2.44089e8	+	1.21314e8i	−0.260934	+	0.129686i
$979$	−6.57110e8	+	1.13815e9i	−0.700310	+	1.21297i
$980$	−3.88788e7	+	5.11547e7i	−0.0413081	+	0.0543510i
$981$	−6.23524e7	+	1.08395e8i	−0.0660460	+	0.114816i
$982$	3.08711e8	+	1.04000e8i	0.326000	+	0.109824i
$983$	−3.56895e8	−	2.06053e8i	−0.375733	−	0.216930i	0.300227	−	0.953868i	$-0.402938\pi$
$983$	−3.56895e8	−	2.06053e8i	−0.375733	−	0.216930i	−0.675960	+	0.736938i	$0.736271\pi$
$984$	−5.58452e8	+	6.46789e8i	−0.586139	+	0.678856i
$985$	1.35081e8	+	2.33967e8i	0.141347	+	0.244819i
$986$	−4.77531e8	+	9.61322e7i	−0.498162	+	0.100285i
$987$	5.67894e7	+	2.11269e8i	0.0590630	+	0.219728i
$988$	−7.02319e8	−	1.67367e9i	−0.728221	−	1.73540i
$989$		−	3.15710e8i		−	0.326362i
$990$	−3.20058e7	−	1.57691e8i	−0.0329855	−	0.162518i
$991$		−	7.57478e8i		−	0.778303i	−0.921174	−	0.389152i	$-0.872768\pi$
$991$		−	7.57478e8i		−	0.778303i	0.921174	−	0.389152i	$-0.127232\pi$
$992$	−5.45475e8	+	8.37099e8i	−0.558778	+	0.857515i
$993$	−8.91770e8	+	8.93188e8i	−0.910762	+	0.912211i
$994$	−3.15474e7	−	1.56710e8i	−0.0321221	−	0.159565i
$995$	9.04498e7	+	1.56664e8i	0.0918203	+	0.159037i
$996$	−3.75740e7	−	4.84230e7i	−0.0380286	−	0.0490088i
$997$	−1.32422e8	−	7.64538e7i	−0.133621	−	0.0771460i	0.431699	−	0.902017i	$-0.357914\pi$
$997$	−1.32422e8	−	7.64538e7i	−0.133621	−	0.0771460i	−0.565320	+	0.824871i	$0.691247\pi$
$998$	3.01739e8	+	1.01651e8i	0.303557	+	0.102264i
$999$	−2.57077e8	+	2.58305e8i	−0.257850	+	0.259082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.p.b.43.16	✓	136
8.3	odd	2	inner	72.7.p.b.43.32	yes	136
9.4	even	3	inner	72.7.p.b.67.32	yes	136
72.67	odd	6	inner	72.7.p.b.67.16	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.p.b.43.16	✓	136	1.1	even	1	trivial
72.7.p.b.43.32	yes	136	8.3	odd	2	inner
72.7.p.b.67.16	yes	136	72.67	odd	6	inner
72.7.p.b.67.32	yes	136	9.4	even	3	inner

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.00254 + 5.28862i) q^{2} +(26.0855 + 6.96739i) q^{3} +(8.06090 - 63.4903i) q^{4} +(17.5470 - 10.1308i) q^{5} +(-193.427 + 96.1346i) q^{6} +(-225.997 - 130.480i) q^{7} +(287.391 + 423.734i) q^{8} +(631.911 + 363.496i) q^{9} +O(q^{10})\)	\(q+(-6.00254 + 5.28862i) q^{2} +(26.0855 + 6.96739i) q^{3} +(8.06090 - 63.4903i) q^{4} +(17.5470 - 10.1308i) q^{5} +(-193.427 + 96.1346i) q^{6} +(-225.997 - 130.480i) q^{7} +(287.391 + 423.734i) q^{8} +(631.911 + 363.496i) q^{9} +(-51.7487 + 153.610i) q^{10} +(-680.854 + 1179.27i) q^{11} +(652.635 - 1600.02i) q^{12} +(3334.63 - 1925.25i) q^{13} +(2046.62 - 412.006i) q^{14} +(528.308 - 142.010i) q^{15} +(-3966.04 - 1023.58i) q^{16} +1287.63 q^{17} +(-5715.46 + 1160.04i) q^{18} +7365.34 q^{19} +(-501.761 - 1195.73i) q^{20} +(-4986.16 - 4978.24i) q^{21} +(-2149.89 - 10679.4i) q^{22} +(13248.9 - 7649.26i) q^{23} +(4544.42 + 13055.7i) q^{24} +(-7607.24 + 13176.1i) q^{25} +(-9834.31 + 29192.0i) q^{26} +(13951.1 + 13884.8i) q^{27} +(-10105.9 + 13296.9i) q^{28} +(40952.4 + 23643.9i) q^{29} +(-2420.15 + 3646.44i) q^{30} +(-26406.2 + 15245.6i) q^{31} +(29219.6 - 14830.8i) q^{32} +(-25976.9 + 26018.2i) q^{33} +(-7729.02 + 6809.77i) q^{34} -5287.43 q^{35} +(28172.3 - 37190.1i) q^{36} +18515.0i q^{37} +(-44210.7 + 38952.5i) q^{38} +(100400. - 26987.5i) q^{39} +(9335.59 + 4523.77i) q^{40} +(30907.1 + 53532.7i) q^{41} +(56257.7 + 3512.16i) q^{42} +(10318.3 - 17871.8i) q^{43} +(69384.2 + 52733.7i) q^{44} +(14770.6 - 23.4700i) q^{45} +(-39073.0 + 115983. i) q^{46} +(-26889.3 - 15524.5i) q^{47} +(-96324.7 - 54333.6i) q^{48} +(-24774.6 - 42910.9i) q^{49} +(-24020.8 - 119322. i) q^{50} +(33588.4 + 8971.39i) q^{51} +(-95354.5 - 227236. i) q^{52} -129402. i q^{53} +(-157173. - 9561.64i) q^{54} +27590.3i q^{55} +(-9660.85 - 133261. i) q^{56} +(192129. + 51317.2i) q^{57} +(-370861. + 74658.5i) q^{58} +(85314.3 + 147769. i) q^{59} +(-4757.60 - 34687.2i) q^{60} +(-265445. - 153254. i) q^{61} +(77875.9 - 231165. i) q^{62} +(-95381.3 - 164601. i) q^{63} +(-96957.2 + 243554. i) q^{64} +(39008.5 - 67564.6i) q^{65} +(18326.8 - 293557. i) q^{66} +(-5333.78 - 9238.38i) q^{67} +(10379.4 - 81751.7i) q^{68} +(398900. - 107225. i) q^{69} +(31738.0 - 27963.2i) q^{70} -76570.2i q^{71} +(27579.4 + 372228. i) q^{72} +489158. q^{73} +(-97919.1 - 111137. i) q^{74} +(-290242. + 290704. i) q^{75} +(59371.3 - 467628. i) q^{76} +(307742. - 177675. i) q^{77} +(-459925. + 692969. i) q^{78} +(-120367. - 69494.1i) q^{79} +(-79961.8 + 22218.3i) q^{80} +(267182. + 459395. i) q^{81} +(-468636. - 157876. i) q^{82} +(17734.7 - 30717.4i) q^{83} +(-356263. + 276444. i) q^{84} +(22593.9 - 13044.6i) q^{85} +(32581.4 + 161846. i) q^{86} +(903528. + 902094. i) q^{87} +(-695370. + 50411.2i) q^{88} +965126. q^{89} +(-88537.1 + 78257.2i) q^{90} -1.00482e6 q^{91} +(-378856. - 902837. i) q^{92} +(-795043. + 213708. i) q^{93} +(243507. - 49020.7i) q^{94} +(129240. - 74616.5i) q^{95} +(865543. - 183286. i) q^{96} +(788121. - 1.36507e6i) q^{97} +(375650. + 126551. i) q^{98} +(-858901. + 497708. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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