LMFDB - Embedded newform 72.8.l.b.11.55

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,8,Mod(11,72)]

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, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("72.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	72.l (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:	$22.4917218349$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.55
Character	$\chi$	$=$	72.11
Dual form			72.8.l.b.59.55

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.97385 - 9.60797i) q^{2} +(-10.7297 - 45.5178i) q^{3} +(-56.6262 - 114.793i) q^{4} +(90.9504 + 157.531i) q^{5} +(-501.432 - 168.826i) q^{6} +(-631.205 - 364.426i) q^{7} +(-1441.21 - 141.694i) q^{8} +(-1956.75 + 976.785i) q^{9} +O(q^{10})$	\(q+(5.97385 - 9.60797i) q^{2} +(-10.7297 - 45.5178i) q^{3} +(-56.6262 - 114.793i) q^{4} +(90.9504 + 157.531i) q^{5} +(-501.432 - 168.826i) q^{6} +(-631.205 - 364.426i) q^{7} +(-1441.21 - 141.694i) q^{8} +(-1956.75 + 976.785i) q^{9} +(2056.87 + 67.2160i) q^{10} +(4969.22 + 2868.98i) q^{11} +(-4617.55 + 3809.20i) q^{12} +(-10351.5 + 5976.45i) q^{13} +(-7272.12 + 3887.57i) q^{14} +(6194.59 - 5830.12i) q^{15} +(-9970.94 + 13000.6i) q^{16} -20155.9i q^{17} +(-2304.39 + 24635.5i) q^{18} -37949.6 q^{19} +(12933.3 - 19360.8i) q^{20} +(-9815.27 + 32641.3i) q^{21} +(57250.4 - 30605.2i) q^{22} +(44422.2 + 76941.5i) q^{23} +(9014.10 + 67120.9i) q^{24} +(22518.6 - 39003.3i) q^{25} +(-4416.83 + 135159. i) q^{26} +(65456.4 + 78586.3i) q^{27} +(-6090.90 + 93094.1i) q^{28} +(102316. - 177217. i) q^{29} +(-19010.1 - 94345.7i) q^{30} +(-126819. + 73218.7i) q^{31} +(65344.6 + 173464. i) q^{32} +(77271.5 - 256971. i) q^{33} +(-193657. - 120408. i) q^{34} -132579. i q^{35} +(222931. + 169310. i) q^{36} +279848. i q^{37} +(-226705. + 364619. i) q^{38} +(383104. + 407053. i) q^{39} +(-108757. - 239921. i) q^{40} +(-581277. + 335600. i) q^{41} +(254982. + 289299. i) q^{42} +(216217. - 374499. i) q^{43} +(47951.1 - 732891. i) q^{44} +(-331840. - 219409. i) q^{45} +(1.00462e6 + 32829.8i) q^{46} +(-162993. + 282312. i) q^{47} +(698745. + 314363. i) q^{48} +(-146158. - 253154. i) q^{49} +(-240220. - 449358. i) q^{50} +(-917452. + 216266. i) q^{51} +(1.27222e6 + 849859. i) q^{52} -386950. q^{53} +(1.14608e6 - 159441. i) q^{54} +1.04374e6i q^{55} +(858060. + 614651. i) q^{56} +(407188. + 1.72738e6i) q^{57} +(-1.09147e6 - 2.04172e6i) q^{58} +(-1.71965e6 + 992841. i) q^{59} +(-1.02003e6 - 380958. i) q^{60} +(-659668. - 380859. i) q^{61} +(-54111.6 + 1.65587e6i) q^{62} +(1.59108e6 + 96538.8i) q^{63} +(2.05700e6 + 408420. i) q^{64} +(-1.88295e6 - 1.08712e6i) q^{65} +(-2.00736e6 - 2.27753e6i) q^{66} +(-1.02078e6 - 1.76804e6i) q^{67} +(-2.31376e6 + 1.14135e6i) q^{68} +(3.02557e6 - 2.84756e6i) q^{69} +(-1.27381e6 - 792006. i) q^{70} -2.16625e6 q^{71} +(2.95848e6 - 1.13049e6i) q^{72} -6.07704e6 q^{73} +(2.68877e6 + 1.67177e6i) q^{74} +(-2.01696e6 - 606503. i) q^{75} +(2.14894e6 + 4.35635e6i) q^{76} +(-2.09106e6 - 3.62183e6i) q^{77} +(6.19956e6 - 1.24917e6i) q^{78} +(1.38089e6 + 797260. i) q^{79} +(-2.95485e6 - 388319. i) q^{80} +(2.87475e6 - 3.82264e6i) q^{81} +(-248022. + 7.58972e6i) q^{82} +(-1.91684e6 - 1.10669e6i) q^{83} +(4.30280e6 - 721627. i) q^{84} +(3.17517e6 - 1.83318e6i) q^{85} +(-2.30653e6 - 4.31461e6i) q^{86} +(-9.16436e6 - 2.75573e6i) q^{87} +(-6.75515e6 - 4.83890e6i) q^{88} -1.18845e6i q^{89} +(-4.09044e6 + 1.87760e6i) q^{90} +8.71190e6 q^{91} +(6.31690e6 - 9.45627e6i) q^{92} +(4.69348e6 + 4.98689e6i) q^{93} +(1.73875e6 + 3.25252e6i) q^{94} +(-3.45153e6 - 5.97822e6i) q^{95} +(7.19459e6 - 4.83556e6i) q^{96} +(4.45411e6 - 7.71475e6i) q^{97} +(-3.30542e6 - 108017. i) q^{98} +(-1.25259e7 - 760010. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9}+O(q^{10}) $ 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9} + 252 q^{10} - 26448 q^{11} - 27234 q^{12} - 43488 q^{14} + 32767 q^{16} + 21762 q^{18} - 119452 q^{19} + 130806 q^{20} - 6049 q^{22} - 83379 q^{24} - 1312502 q^{25} - 94428 q^{27} - 32772 q^{28} + 735060 q^{30} + 308907 q^{32} - 1249812 q^{33} - 188203 q^{34} - 1410345 q^{36} + 353415 q^{38} - 477876 q^{40} - 1612476 q^{41} - 39360 q^{42} + 220508 q^{43} + 1082496 q^{46} - 3515619 q^{48} + 9882514 q^{49} - 136947 q^{50} - 2358786 q^{51} + 1089018 q^{52} - 8083005 q^{54} - 1285266 q^{56} - 2070294 q^{57} + 1295022 q^{58} - 8748744 q^{59} - 3070044 q^{60} + 16058050 q^{64} - 6 q^{65} - 19546374 q^{66} + 3851300 q^{67} + 10545975 q^{68} + 979920 q^{70} + 12593427 q^{72} - 9731236 q^{73} + 13246572 q^{74} + 8347746 q^{75} - 4009903 q^{76} - 9123732 q^{78} - 6855198 q^{81} + 21020522 q^{82} - 14348826 q^{83} + 44644836 q^{84} + 80099985 q^{86} + 10463891 q^{88} + 7437678 q^{90} - 3294180 q^{91} - 57890184 q^{92} - 1609122 q^{94} + 69780834 q^{96} + 9938888 q^{97} - 16049670 q^{99}+O(q^{100}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9 + 252 * q^10 - 26448 * q^11 - 27234 * q^12 - 43488 * q^14 + 32767 * q^16 + 21762 * q^18 - 119452 * q^19 + 130806 * q^20 - 6049 * q^22 - 83379 * q^24 - 1312502 * q^25 - 94428 * q^27 - 32772 * q^28 + 735060 * q^30 + 308907 * q^32 - 1249812 * q^33 - 188203 * q^34 - 1410345 * q^36 + 353415 * q^38 - 477876 * q^40 - 1612476 * q^41 - 39360 * q^42 + 220508 * q^43 + 1082496 * q^46 - 3515619 * q^48 + 9882514 * q^49 - 136947 * q^50 - 2358786 * q^51 + 1089018 * q^52 - 8083005 * q^54 - 1285266 * q^56 - 2070294 * q^57 + 1295022 * q^58 - 8748744 * q^59 - 3070044 * q^60 + 16058050 * q^64 - 6 * q^65 - 19546374 * q^66 + 3851300 * q^67 + 10545975 * q^68 + 979920 * q^70 + 12593427 * q^72 - 9731236 * q^73 + 13246572 * q^74 + 8347746 * q^75 - 4009903 * q^76 - 9123732 * q^78 - 6855198 * q^81 + 21020522 * q^82 - 14348826 * q^83 + 44644836 * q^84 + 80099985 * q^86 + 10463891 * q^88 + 7437678 * q^90 - 3294180 * q^91 - 57890184 * q^92 - 1609122 * q^94 + 69780834 * q^96 + 9938888 * q^97 - 16049670 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	5.97385	−	9.60797i	0.528019	−	0.849233i
$2$	5.97385	−	9.60797i	0.528019	−	0.849233i
$3$	−10.7297	−	45.5178i	−0.229437	−	0.973324i
$3$	−10.7297	−	45.5178i	−0.229437	−	0.973324i
$4$	−56.6262	−	114.793i	−0.442392	−	0.896822i
$5$	90.9504	+	157.531i	0.325394	+	0.563599i	0.981592	−	0.190990i	$-0.0611698\pi$
$5$	90.9504	+	157.531i	0.325394	+	0.563599i	−0.656198	+	0.754589i	$0.727836\pi$
$6$	−501.432	−	168.826i	−0.947725	−	0.319088i
$7$	−631.205	−	364.426i	−0.695548	−	0.401575i	0.110139	−	0.993916i	$-0.464870\pi$
$7$	−631.205	−	364.426i	−0.695548	−	0.401575i	−0.805687	+	0.592341i	$0.798204\pi$
$8$	−1441.21	−	141.694i	−0.995202	−	0.0978444i
$9$	−1956.75	+	976.785i	−0.894718	+	0.446632i
$10$	2056.87	+	67.2160i	0.650441	+	0.0212556i
$11$	4969.22	+	2868.98i	1.12568	+	0.649909i	0.942844	−	0.333235i	$-0.108140\pi$
$11$	4969.22	+	2868.98i	1.12568	+	0.649909i	0.182832	+	0.983144i	$0.441474\pi$
$12$	−4617.55	+	3809.20i	−0.771397	+	0.636355i
$13$	−10351.5	+	5976.45i	−1.30678	+	0.754469i	−0.981557	−	0.191169i	$-0.938772\pi$
$13$	−10351.5	+	5976.45i	−1.30678	+	0.754469i	−0.325221	+	0.945638i	$0.605439\pi$
$14$	−7272.12	+	3887.57i	−0.708293	+	0.378643i
$15$	6194.59	−	5830.12i	0.473907	−	0.446024i
$16$	−9970.94	+	13000.6i	−0.608578	+	0.793494i
$17$		−	20155.9i		−	0.995017i	−0.867459	−	0.497508i	$-0.834248\pi$
$17$		−	20155.9i		−	0.995017i	0.867459	−	0.497508i	$-0.165752\pi$
$18$	−2304.39	+	24635.5i	−0.0931328	+	0.995654i
$19$	−37949.6			−1.26932			−0.634658	−	0.772793i	$-0.718859\pi$
$19$	−37949.6			−1.26932			−0.634658	+	0.772793i	$0.718859\pi$
$20$	12933.3	−	19360.8i	0.361496	−	0.541152i
$21$	−9815.27	+	32641.3i	−0.231278	+	0.769130i
$22$	57250.4	−	30605.2i	1.14630	−	0.612797i
$23$	44422.2	+	76941.5i	0.761295	+	1.31860i	0.942184	+	0.335097i	$0.108769\pi$
$23$	44422.2	+	76941.5i	0.761295	+	1.31860i	−0.180889	+	0.983504i	$0.557897\pi$
$24$	9014.10	+	67120.9i	0.133102	+	0.991102i
$25$	22518.6	−	39003.3i	0.288238	−	0.499242i
$26$	−4416.83	+	135159.i	−0.0492838	+	1.50813i
$27$	65456.4	+	78586.3i	0.639999	+	0.768376i
$28$	−6090.90	+	93094.1i	−0.0524358	+	0.801437i
$29$	102316.	−	177217.i	0.779026	−	1.34931i	−0.153477	−	0.988152i	$-0.549047\pi$
$29$	102316.	−	177217.i	0.779026	−	1.34931i	0.932504	−	0.361161i	$-0.117619\pi$
$30$	−19010.1	−	94345.7i	−0.128546	−	0.637966i
$31$	−126819.	+	73218.7i	−0.764569	+	0.441424i	−0.830934	−	0.556371i	$-0.812193\pi$
$31$	−126819.	+	73218.7i	−0.764569	+	0.441424i	0.0663647	+	0.997795i	$0.478860\pi$
$32$	65344.6	+	173464.i	0.352521	+	0.935804i
$33$	77271.5	−	256971.i	0.374301	−	1.24476i
$34$	−193657.	−	120408.i	−0.845001	−	0.525387i
$35$		−	132579.i		−	0.522680i
$36$	222931.	+	169310.i	0.796366	+	0.604815i
$37$			279848.i			0.908272i	0.890932	+	0.454136i	$0.150052\pi$
$37$			279848.i			0.908272i	−0.890932	+	0.454136i	$0.849948\pi$
$38$	−226705.	+	364619.i	−0.670222	+	1.07794i
$39$	383104.	+	407053.i	1.03417	+	1.09882i
$40$	−108757.	−	239921.i	−0.268688	−	0.592732i
$41$	−581277.	+	335600.i	−1.31716	+	0.760464i	−0.983271	−	0.182147i	$-0.941695\pi$
$41$	−581277.	+	335600.i	−1.31716	+	0.760464i	−0.333892	+	0.942611i	$0.608362\pi$
$42$	254982.	+	289299.i	0.531051	+	0.602524i
$43$	216217.	−	374499.i	0.414716	−	0.718309i	−0.580682	−	0.814130i	$-0.697214\pi$
$43$	216217.	−	374499.i	0.414716	−	0.718309i	0.995399	+	0.0958207i	$0.0305475\pi$
$44$	47951.1	−	732891.i	0.0848622	−	1.29705i
$45$	−331840.	−	219409.i	−0.542857	−	0.358930i
$46$	1.00462e6	+	32829.8i	1.52178	+	0.0497297i
$47$	−162993.	+	282312.i	−0.228995	+	0.396631i	−0.957511	−	0.288398i	$-0.906877\pi$
$47$	−162993.	+	282312.i	−0.228995	+	0.396631i	0.728515	+	0.685029i	$0.240211\pi$
$48$	698745.	+	314363.i	0.911957	+	0.410286i
$49$	−146158.	−	253154.i	−0.177475	−	0.307396i
$50$	−240220.	−	449358.i	−0.271778	−	0.508390i
$51$	−917452.	+	216266.i	−0.968473	+	0.228293i
$52$	1.27222e6	+	849859.i	1.25473	+	0.838176i
$53$	−386950.			−0.357017			−0.178509	−	0.983938i	$-0.557127\pi$
$53$	−386950.			−0.357017			−0.178509	+	0.983938i	$0.557127\pi$
$54$	1.14608e6	−	159441.i	0.990461	−	0.137791i
$55$			1.04374e6i			0.845906i
$56$	858060.	+	614651.i	0.652919	+	0.467704i
$57$	407188.	+	1.72738e6i	0.291228	+	1.23545i
$58$	−1.09147e6	−	2.04172e6i	−0.734540	−	1.37404i
$59$	−1.71965e6	+	992841.i	−1.09008	+	0.629358i	−0.933598	−	0.358323i	$-0.883349\pi$
$59$	−1.71965e6	+	992841.i	−1.09008	+	0.629358i	−0.156482	+	0.987681i	$0.550015\pi$
$60$	−1.02003e6	−	380958.i	−0.609657	−	0.227692i
$61$	−659668.	−	380859.i	−0.372110	−	0.214838i	0.302270	−	0.953222i	$-0.402256\pi$
$61$	−659668.	−	380859.i	−0.372110	−	0.214838i	−0.674380	+	0.738385i	$0.735589\pi$
$62$	−54111.6	+	1.65587e6i	−0.0288349	+	0.882377i
$63$	1.59108e6	+	96538.8i	0.801676	+	0.0486418i
$64$	2.05700e6	+	408420.i	0.980853	+	0.194750i
$65$	−1.88295e6	−	1.08712e6i	−0.850436	−	0.490999i
$66$	−2.00736e6	−	2.27753e6i	−0.859453	−	0.975125i
$67$	−1.02078e6	−	1.76804e6i	−0.414638	−	0.718173i	0.580753	−	0.814080i	$-0.302758\pi$
$67$	−1.02078e6	−	1.76804e6i	−0.414638	−	0.718173i	−0.995390	+	0.0959067i	$0.969425\pi$
$68$	−2.31376e6	+	1.14135e6i	−0.892352	+	0.440188i
$69$	3.02557e6	−	2.84756e6i	1.10876	−	1.04352i
$70$	−1.27381e6	−	792006.i	−0.443877	−	0.275985i
$71$	−2.16625e6			−0.718296			−0.359148	−	0.933281i	$-0.616933\pi$
$71$	−2.16625e6			−0.718296			−0.359148	+	0.933281i	$0.616933\pi$
$72$	2.95848e6	−	1.13049e6i	0.934125	−	0.356946i
$73$	−6.07704e6			−1.82836			−0.914181	−	0.405306i	$-0.867165\pi$
$73$	−6.07704e6			−1.82836			−0.914181	+	0.405306i	$0.867165\pi$
$74$	2.68877e6	+	1.67177e6i	0.771334	+	0.479585i
$75$	−2.01696e6	−	606503.i	−0.552056	−	0.166004i
$76$	2.14894e6	+	4.35635e6i	0.561536	+	1.13835i
$77$	−2.09106e6	−	3.62183e6i	−0.521975	−	0.904087i
$78$	6.19956e6	−	1.24917e6i	1.47921	−	0.298052i
$79$	1.38089e6	+	797260.i	0.315113	+	0.181930i	0.649212	−	0.760608i	$-0.275099\pi$
$79$	1.38089e6	+	797260.i	0.315113	+	0.181930i	−0.334099	+	0.942538i	$0.608432\pi$
$80$	−2.95485e6	−	388319.i	−0.645240	−	0.0847956i
$81$	2.87475e6	−	3.82264e6i	0.601039	−	0.799220i
$82$	−248022.	+	7.58972e6i	−0.0496755	+	1.52012i
$83$	−1.91684e6	−	1.10669e6i	−0.367969	−	0.212447i	0.304602	−	0.952480i	$-0.401477\pi$
$83$	−1.91684e6	−	1.10669e6i	−0.367969	−	0.212447i	−0.672571	+	0.740033i	$0.734810\pi$
$84$	4.30280e6	−	721627.i	0.792088	−	0.132842i
$85$	3.17517e6	−	1.83318e6i	0.560790	−	0.323772i
$86$	−2.30653e6	−	4.31461e6i	−0.391034	−	0.731471i
$87$	−9.16436e6	−	2.75573e6i	−1.49206	−	0.448663i
$88$	−6.75515e6	−	4.83890e6i	−1.05668	−	0.756932i
$89$		−	1.18845e6i		−	0.178697i	−0.996000	−	0.0893485i	$-0.971522\pi$
$89$		−	1.18845e6i		−	0.178697i	0.996000	−	0.0893485i	$-0.0284785\pi$
$90$	−4.09044e6	+	1.87760e6i	−0.591454	+	0.271490i
$91$	8.71190e6			1.21190
$92$	6.31690e6	−	9.45627e6i	0.845759	−	1.26608i
$93$	4.69348e6	+	4.98689e6i	0.605069	+	0.642894i
$94$	1.73875e6	+	3.25252e6i	0.215918	+	0.403899i
$95$	−3.45153e6	−	5.97822e6i	−0.413027	−	0.715385i
$96$	7.19459e6	−	4.83556e6i	0.829959	−	0.557825i
$97$	4.45411e6	−	7.71475e6i	0.495519	−	0.858264i	−0.504468	−	0.863431i	$-0.668311\pi$
$97$	4.45411e6	−	7.71475e6i	0.495519	−	0.858264i	0.999987	+	0.00516654i	$0.00164457\pi$
$98$	−3.30542e6	−	108017.i	−0.354761	−	0.0115931i
$99$	−1.25259e7	−	760010.i	−1.29743	−	0.0787220i
$100$	−5.75245e6	−	376367.i	−0.575245	−	0.0376367i
$101$	−912628.	+	1.58072e6i	−0.0881392	+	0.152662i	−0.906725	−	0.421723i	$-0.861425\pi$
$101$	−912628.	+	1.58072e6i	−0.0881392	+	0.152662i	0.818585	+	0.574385i	$0.194759\pi$
$102$	−3.40284e6	+	1.01068e7i	−0.317498	+	0.943002i
$103$	−1.14583e7	+	6.61546e6i	−1.03321	+	0.596527i	−0.917904	−	0.396803i	$-0.870120\pi$
$103$	−1.14583e7	+	6.61546e6i	−1.03321	+	0.596527i	−0.115311	+	0.993329i	$0.536786\pi$
$104$	1.57655e7	−	7.14655e6i	1.37433	−	0.622988i
$105$	−6.03470e6	+	1.42253e6i	−0.508737	+	0.119922i
$106$	−2.31158e6	+	3.71780e6i	−0.188512	+	0.303191i
$107$		−	1.28592e7i		−	1.01478i	−0.861718	−	0.507388i	$-0.830611\pi$
$107$		−	1.28592e7i		−	1.01478i	0.861718	−	0.507388i	$-0.169389\pi$
$108$	5.31462e6	−	1.19640e7i	0.405965	−	0.913888i
$109$			9.02382e6i			0.667418i	0.942676	+	0.333709i	$0.108300\pi$
$109$			9.02382e6i			0.667418i	−0.942676	+	0.333709i	$0.891700\pi$
$110$	1.00282e7	+	6.23514e6i	0.718371	+	0.446654i
$111$	1.27381e7	−	3.00268e6i	0.884042	−	0.208391i
$112$	1.10315e7	−	4.57238e6i	0.741943	−	0.307524i
$113$	−1.23650e7	+	7.13892e6i	−0.806155	+	0.465434i	−0.845619	−	0.533787i	$-0.820768\pi$
$113$	−1.23650e7	+	7.13892e6i	−0.806155	+	0.465434i	0.0394638	+	0.999221i	$0.487435\pi$
$114$	1.90291e7	+	6.40688e6i	1.20296	+	0.405023i
$115$	−8.08043e6	+	1.39957e7i	−0.495441	+	0.858129i
$116$	−2.61371e7	−	1.71008e6i	−1.55473	−	0.101722i
$117$	1.44176e7	−	2.18056e7i	0.832227	−	1.25869i
$118$	−733749.	+	2.24534e7i	−0.0411112	+	1.25804i
$119$	−7.34533e6	+	1.27225e7i	−0.399574	+	0.692082i
$120$	−9.75377e6	+	7.52467e6i	−0.515274	+	0.397515i
$121$	6.71848e6	+	1.16367e7i	0.344764	+	0.597149i
$122$	−7.60004e6	+	4.06287e6i	−0.378928	+	0.202569i
$123$	2.15127e7	+	2.28576e7i	1.04238	+	1.10755i
$124$	1.55863e7	+	1.04118e7i	0.734118	+	0.490399i
$125$	2.24033e7			1.02595
$126$	1.04324e7	−	1.47103e7i	0.464608	−	0.655126i
$127$			2.66402e7i			1.15405i	0.816727	+	0.577025i	$0.195786\pi$
$127$			2.66402e7i			1.15405i	−0.816727	+	0.577025i	$0.804214\pi$
$128$	1.62123e7	−	1.73237e7i	0.683297	−	0.730141i
$129$	−1.93664e7	−	5.82348e6i	−0.794299	−	0.238846i
$130$	−2.16935e7	+	1.15970e7i	−0.866019	+	0.462961i
$131$	6.39040e6	−	3.68950e6i	0.248358	−	0.143390i	−0.370654	−	0.928771i	$-0.620866\pi$
$131$	6.39040e6	−	3.68950e6i	0.248358	−	0.143390i	0.619012	+	0.785381i	$0.287533\pi$
$132$	−3.38741e7	+	5.68107e6i	−1.28192	+	0.214992i
$133$	2.39540e7	+	1.38298e7i	0.882870	+	0.509725i
$134$	−2.30852e7	−	754394.i	−0.828833	−	0.0270852i
$135$	−6.42646e6	+	1.74588e7i	−0.224804	+	0.610727i
$136$	−2.85596e6	+	2.90488e7i	−0.0973568	+	0.990242i
$137$	2.40919e7	+	1.39095e7i	0.800477	+	0.462155i	0.843638	−	0.536913i	$-0.180410\pi$
$137$	2.40919e7	+	1.39095e7i	0.800477	+	0.462155i	−0.0431611	+	0.999068i	$0.513743\pi$
$138$	−9.28496e6	−	4.60805e7i	−0.300748	−	1.49259i
$139$	−1.32254e6	−	2.29070e6i	−0.0417692	−	0.0723463i	0.844385	−	0.535737i	$-0.179966\pi$
$139$	−1.32254e6	−	2.29070e6i	−0.0417692	−	0.0723463i	−0.886154	+	0.463390i	$0.846633\pi$
$140$	−1.52191e7	+	7.50744e6i	−0.468751	+	0.231230i
$141$	1.45991e7	+	4.38996e6i	0.438590	+	0.131885i
$142$	−1.29408e7	+	2.08132e7i	−0.379274	+	0.610001i
$143$	−6.85852e7			−1.96135
$144$	6.81181e6	−	3.51784e7i	0.190105	−	0.981764i
$145$	3.72228e7			1.01396
$146$	−3.63033e7	+	5.83880e7i	−0.965409	+	1.55270i
$147$	−9.95477e6	+	9.36907e6i	−0.258476	+	0.243268i
$148$	3.21246e7	−	1.58467e7i	0.814558	−	0.401813i
$149$	−3.44682e7	−	5.97007e7i	−0.853625	−	1.47852i	−0.877915	−	0.478817i	$-0.841066\pi$
$149$	−3.44682e7	−	5.97007e7i	−0.853625	−	1.47852i	0.0242901	−	0.999705i	$-0.492267\pi$
$150$	−1.78763e7	+	1.57558e7i	−0.432472	+	0.381171i
$151$	−4.02026e6	−	2.32110e6i	−0.0950242	−	0.0548623i	0.451735	−	0.892152i	$-0.350805\pi$
$151$	−4.02026e6	−	2.32110e6i	−0.0950242	−	0.0548623i	−0.546759	+	0.837290i	$0.684139\pi$
$152$	5.46932e7	+	5.37723e6i	1.26322	+	0.124195i
$153$	1.96880e7	+	3.94399e7i	0.444407	+	0.890259i
$154$	−4.72901e7	−	1.54538e6i	−1.04339	−	0.0340967i
$155$	−2.30684e7	−	1.33185e7i	−0.497572	−	0.287273i
$156$	2.50332e7	−	6.70275e7i	0.527934	−	1.41357i
$157$	−7.72628e6	+	4.46077e6i	−0.159339	+	0.0919943i	−0.577549	−	0.816356i	$-0.695991\pi$
$157$	−7.72628e6	+	4.46077e6i	−0.159339	+	0.0919943i	0.418210	+	0.908350i	$0.362657\pi$
$158$	1.59093e7	−	8.50488e6i	0.320887	−	0.171541i
$159$	4.15185e6	+	1.76131e7i	0.0819129	+	0.347493i
$160$	−2.13828e7	+	2.60704e7i	−0.412710	+	0.503185i
$161$		−	6.47545e7i		−	1.22287i
$162$	−1.95545e7	−	5.04564e7i	−0.361364	−	0.932425i
$163$	8.74584e7			1.58178			0.790888	−	0.611961i	$-0.209619\pi$
$163$	8.74584e7			1.58178			0.790888	+	0.611961i	$0.209619\pi$
$164$	7.14401e7	+	4.77228e7i	1.26470	+	0.844836i
$165$	4.75087e7	−	1.11990e7i	0.823340	−	0.194082i
$166$	−2.20839e7	+	1.18057e7i	−0.374712	+	0.200315i
$167$	4.15790e7	+	7.20169e7i	0.690822	+	1.19654i	0.971569	+	0.236757i	$0.0760846\pi$
$167$	4.15790e7	+	7.20169e7i	0.690822	+	1.19654i	−0.280747	+	0.959782i	$0.590582\pi$
$168$	1.87709e7	−	4.56520e7i	0.305423	−	0.742810i
$169$	4.00616e7	−	6.93887e7i	0.638447	−	1.10582i
$170$	1.35480e6	−	4.14581e7i	0.0211496	−	0.647199i
$171$	7.42578e7	−	3.70686e7i	1.13568	−	0.566917i
$172$	−5.52336e7	−	3.61378e6i	−0.827663	−	0.0541517i
$173$	4.18219e7	−	7.24377e7i	0.614105	−	1.06366i	−0.376435	−	0.926443i	$-0.622850\pi$
$173$	4.18219e7	−	7.24377e7i	0.614105	−	1.06366i	0.990541	−	0.137219i	$-0.0438163\pi$
$174$	−8.12235e7	+	7.15886e7i	−1.16885	+	1.03020i
$175$	−2.84277e7	+	1.64127e7i	−0.400966	+	0.231498i
$176$	−8.68462e7	+	3.59964e7i	−1.20076	+	0.497697i
$177$	6.36433e7	+	6.76219e7i	0.862673	+	0.916602i
$178$	−1.14186e7	−	7.09965e6i	−0.151755	−	0.0943554i
$179$			1.82229e7i			0.237482i	0.992925	+	0.118741i	$0.0378858\pi$
$179$			1.82229e7i			0.237482i	−0.992925	+	0.118741i	$0.962114\pi$
$180$	−6.39575e6	+	5.05173e7i	−0.0817405	+	0.645634i
$181$		−	1.20380e8i		−	1.50897i	−0.656318	−	0.754485i	$-0.727887\pi$
$181$		−	1.20380e8i		−	1.50897i	0.656318	−	0.754485i	$-0.272113\pi$
$182$	5.20436e7	−	8.37037e7i	0.639908	−	1.02919i
$183$	−1.02579e7	+	3.41132e7i	−0.123731	+	0.411475i
$184$	−5.31194e7	−	1.17183e8i	−0.628624	−	1.38676i
$185$	−4.40846e7	+	2.54523e7i	−0.511901	+	0.295546i
$186$	7.59521e7	−	1.53039e7i	0.865454	−	0.174384i
$187$	5.78267e7	−	1.00159e8i	0.646671	−	1.12007i
$188$	4.16372e7	+	2.72421e6i	0.457013	+	0.0299011i
$189$	−1.26775e7	−	7.34581e7i	−0.136590	−	0.791450i
$190$	−7.80575e7	−	2.55082e6i	−0.825614	−	0.0269800i
$191$	−1.49097e6	+	2.58244e6i	−0.0154829	+	0.0268172i	−0.873663	−	0.486531i	$-0.838262\pi$
$191$	−1.49097e6	+	2.58244e6i	−0.0154829	+	0.0268172i	0.858180	+	0.513349i	$0.171595\pi$
$192$	−3.48055e6	−	9.80123e7i	−0.0354890	−	0.999370i
$193$	2.24845e7	+	3.89444e7i	0.225130	+	0.389937i	0.956358	−	0.292196i	$-0.0943860\pi$
$193$	2.24845e7	+	3.89444e7i	0.225130	+	0.389937i	−0.731228	+	0.682133i	$0.761053\pi$
$194$	−4.75149e7	−	8.88818e7i	−0.467223	−	0.873990i
$195$	−2.92799e7	+	9.73722e7i	−0.282780	+	0.940402i
$196$	−2.07839e7	+	3.11131e7i	−0.197165	+	0.295153i
$197$	−2.81122e6			−0.0261977			−0.0130988	−	0.999914i	$-0.504170\pi$
$197$	−2.81122e6			−0.0261977			−0.0130988	+	0.999914i	$0.504170\pi$
$198$	−8.21298e7	+	1.15808e8i	−0.751922	+	1.06026i
$199$		−	1.09869e7i		−	0.0988298i	−0.998778	−	0.0494149i	$-0.984264\pi$
$199$		−	1.09869e7i		−	0.0988298i	0.998778	−	0.0494149i	$-0.0157357\pi$
$200$	−3.79804e7	+	5.30210e7i	−0.335703	+	0.468644i
$201$	−6.95246e7	+	6.54340e7i	−0.603882	+	0.568352i
$202$	9.73559e6	+	1.82115e7i	0.0831060	+	0.155459i
$203$	−1.29165e8	+	7.45736e7i	−1.08370	+	0.625675i
$204$	7.67777e7	+	9.30708e7i	0.633184	+	0.767552i
$205$	−1.05735e8	−	6.10459e7i	−0.857194	−	0.494901i
$206$	−4.88909e6	+	1.49611e8i	−0.0389666	+	1.19242i
$207$	−1.62078e8	−	1.07164e8i	−1.27007	−	0.839757i
$208$	2.55168e7	−	1.94167e8i	0.196610	−	1.49607i
$209$	−1.88580e8	−	1.08877e8i	−1.42884	−	0.824940i
$210$	−2.23828e7	+	6.64792e7i	−0.166781	+	0.495357i
$211$	−3.40097e7	−	5.89066e7i	−0.249238	−	0.431693i	0.714076	−	0.700068i	$-0.246847\pi$
$211$	−3.40097e7	−	5.89066e7i	−0.249238	−	0.431693i	−0.963315	+	0.268374i	$0.913514\pi$
$212$	2.19115e7	+	4.44192e7i	0.157942	+	0.320181i
$213$	2.32432e7	+	9.86029e7i	0.164804	+	0.699135i
$214$	−1.23551e8	−	7.68189e7i	−0.861782	−	0.535821i
$215$	7.86602e7			0.539784
$216$	−8.32010e7	−	1.22534e8i	−0.561747	−	0.827309i
$217$	1.06731e8			0.709060
$218$	8.67006e7	+	5.39069e7i	0.566793	+	0.352409i
$219$	6.52048e7	+	2.76614e8i	0.419493	+	1.77959i
$220$	1.19814e8	−	5.91030e7i	0.758627	−	0.374223i
$221$	1.20460e8	+	2.08644e8i	0.750709	+	1.30027i
$222$	4.72456e7	−	1.40325e8i	0.289819	−	0.860792i
$223$	−1.67624e7	−	9.67775e6i	−0.101220	−	0.0584396i	0.448535	−	0.893765i	$-0.351946\pi$
$223$	−1.67624e7	−	9.67775e6i	−0.101220	−	0.0584396i	−0.549756	+	0.835326i	$0.685279\pi$
$224$	2.19691e7	−	1.33305e8i	0.130600	−	0.792461i
$225$	−5.96531e6	+	9.83154e7i	−0.0349135	+	0.575417i
$226$	−5.27595e6	+	1.61449e8i	−0.0304033	+	0.930371i
$227$	−7.97911e7	−	4.60674e7i	−0.452756	−	0.261399i	0.256238	−	0.966614i	$-0.417517\pi$
$227$	−7.97911e7	−	4.60674e7i	−0.452756	−	0.261399i	−0.708993	+	0.705215i	$0.750850\pi$
$228$	1.75234e8	−	1.44558e8i	0.979145	−	0.807735i
$229$	1.31194e8	−	7.57448e7i	0.721920	−	0.416801i	−0.0935387	−	0.995616i	$-0.529818\pi$
$229$	1.31194e8	−	7.57448e7i	0.721920	−	0.416801i	0.815459	+	0.578815i	$0.196485\pi$
$230$	8.61992e7	+	1.61245e8i	0.467149	+	0.873853i
$231$	−1.42421e8	+	1.34042e8i	−0.760209	+	0.715481i
$232$	−1.72570e8	+	2.40909e8i	−0.907311	+	1.26662i
$233$		−	1.95412e8i		−	1.01206i	−0.862517	−	0.506028i	$-0.831113\pi$
$233$		−	1.95412e8i		−	1.01206i	0.862517	−	0.506028i	$-0.168887\pi$
$234$	−1.23379e8	−	2.68787e8i	−0.629486	−	1.37136i
$235$	−5.92971e7			−0.298054
$236$	2.11349e8	+	1.41183e8i	1.04666	+	0.699184i
$237$	2.14730e7	−	7.14097e7i	0.104779	−	0.348448i
$238$	7.83574e7	+	1.46576e8i	0.376756	+	0.704764i
$239$	3.89249e7	+	6.74200e7i	0.184432	+	0.319445i	0.943385	−	0.331700i	$-0.107622\pi$
$239$	3.89249e7	+	6.74200e7i	0.184432	+	0.319445i	−0.758953	+	0.651145i	$0.774289\pi$
$240$	1.40293e7	+	1.38665e8i	0.0655082	+	0.647482i
$241$	3.73653e7	−	6.47186e7i	0.171953	−	0.297831i	−0.767150	−	0.641468i	$-0.778326\pi$
$241$	3.73653e7	−	6.47186e7i	0.171953	−	0.297831i	0.939102	+	0.343637i	$0.111659\pi$
$242$	1.51941e8	+	4.96523e6i	0.689161	+	0.0225209i
$243$	−2.04844e8	−	8.98367e7i	−0.915800	−	0.401635i
$244$	−6.36555e6	+	9.72920e7i	−0.0280525	+	0.428759i
$245$	2.65863e7	−	4.60488e7i	0.115499	−	0.200049i
$246$	3.48129e8	−	7.01459e7i	1.49096	−	0.300420i
$247$	3.92836e8	−	2.26804e8i	1.65871	−	0.957659i
$248$	1.93146e8	−	8.75538e7i	0.804091	−	0.364497i
$249$	−2.98069e7	+	9.91246e7i	−0.122354	+	0.406896i
$250$	1.33834e8	−	2.15250e8i	0.541721	−	0.871271i
$251$		−	2.22620e8i		−	0.888601i	−0.895878	−	0.444300i	$-0.853452\pi$
$251$		−	2.22620e8i		−	0.888601i	0.895878	−	0.444300i	$-0.146548\pi$
$252$	−7.90146e7	−	1.88111e8i	−0.311032	−	0.740479i
$253$			5.09785e8i			1.97909i
$254$	2.55958e8	+	1.59145e8i	0.980056	+	0.609360i
$255$	−1.17511e8	−	1.24857e8i	−0.443801	−	0.471545i
$256$	−6.95962e7	−	2.59257e8i	−0.259266	−	0.965806i
$257$	−2.23977e8	+	1.29313e8i	−0.823071	+	0.475200i	−0.851474	−	0.524396i	$-0.824291\pi$
$257$	−2.23977e8	+	1.29313e8i	−0.823071	+	0.475200i	0.0284031	+	0.999597i	$0.490958\pi$
$258$	−1.71644e8	+	1.51283e8i	−0.622241	+	0.548429i
$259$	1.01984e8	−	1.76641e8i	0.364739	−	0.631747i
$260$	−1.81697e7	+	2.77709e8i	−0.0641124	+	0.979903i
$261$	−2.71042e7	+	4.46710e8i	−0.0943616	+	1.55519i
$262$	2.72669e6	−	8.34392e7i	0.00936657	−	0.286626i
$263$	−2.48391e8	+	4.30226e8i	−0.841959	+	1.45832i	0.0462767	+	0.998929i	$0.485264\pi$
$263$	−2.48391e8	+	4.30226e8i	−0.841959	+	1.45832i	−0.888236	+	0.459388i	$0.848069\pi$
$264$	−1.47775e8	+	3.59400e8i	−0.494298	+	1.20216i
$265$	−3.51932e7	−	6.09565e7i	−0.116171	−	0.201214i
$266$	2.75974e8	−	1.47532e8i	0.899047	−	0.480618i
$267$	−5.40959e7	+	1.27517e7i	−0.173930	+	0.0409997i
$268$	−1.45156e8	+	2.17295e8i	−0.460641	+	0.689570i
$269$	9.91365e6			0.0310528			0.0155264	−	0.999879i	$-0.495058\pi$
$269$	9.91365e6			0.0310528			0.0155264	+	0.999879i	$0.495058\pi$
$270$	1.29353e8	+	1.66042e8i	0.399949	+	0.513386i
$271$		−	3.11196e8i		−	0.949819i	−0.880035	−	0.474910i	$-0.842481\pi$
$271$		−	3.11196e8i		−	0.949819i	0.880035	−	0.474910i	$-0.157519\pi$
$272$	2.62039e8	+	2.00973e8i	0.789540	+	0.605545i
$273$	−9.34760e7	−	3.96547e8i	−0.278055	−	1.17957i
$274$	2.77563e8	−	1.48381e8i	0.815144	−	0.435764i
$275$	2.23799e8	−	1.29211e8i	0.648924	−	0.374657i
$276$	−4.98208e8	−	1.86069e8i	−1.42636	−	0.532711i
$277$	−4.31892e8	−	2.49353e8i	−1.22094	−	0.704913i	−0.255825	−	0.966723i	$-0.582347\pi$
$277$	−4.31892e8	−	2.49353e8i	−1.22094	−	0.704913i	−0.965119	+	0.261810i	$0.915681\pi$
$278$	−2.99096e7	−	977407.i	−0.0834937	−	0.00272847i
$279$	1.76633e8	−	2.67145e8i	0.486919	−	0.736431i
$280$	−1.87856e7	+	1.91073e8i	−0.0511414	+	0.520172i
$281$	4.01637e7	+	2.31885e7i	0.107985	+	0.0623450i	0.553020	−	0.833168i	$-0.313475\pi$
$281$	4.01637e7	+	2.31885e7i	0.107985	+	0.0623450i	−0.445035	+	0.895513i	$0.646809\pi$
$282$	1.29391e8	−	1.14043e8i	0.343585	−	0.302828i
$283$	7.10500e7	+	1.23062e8i	0.186342	+	0.322754i	0.944028	−	0.329865i	$-0.107003\pi$
$283$	7.10500e7	+	1.23062e8i	0.186342	+	0.322754i	−0.757686	+	0.652620i	$0.773670\pi$
$284$	1.22666e8	+	2.48670e8i	0.317769	+	0.644184i
$285$	−2.35082e8	+	2.21251e8i	−0.601537	+	0.566145i
$286$	−4.09718e8	+	6.58964e8i	−1.03563	+	1.66564i
$287$	4.89207e8			1.22153
$288$	−2.97300e8	−	2.75598e8i	−0.733367	−	0.679833i
$289$	4.07961e6			0.00994205
$290$	2.22364e8	−	3.57636e8i	0.535391	−	0.861089i
$291$	−3.98950e8	−	1.19965e8i	−0.949059	−	0.285383i
$292$	3.44120e8	+	6.97603e8i	0.808854	+	1.63971i
$293$	−1.86245e8	−	3.22586e8i	−0.432562	−	0.749220i	0.564531	−	0.825412i	$-0.309057\pi$
$293$	−1.86245e8	−	3.22586e8i	−0.432562	−	0.749220i	−0.997093	+	0.0761921i	$0.975724\pi$
$294$	3.05494e7	+	1.51615e8i	0.0701112	+	0.347957i
$295$	−3.12806e8	−	1.80598e8i	−0.709410	−	0.409578i
$296$	3.96527e7	−	4.03318e8i	0.0888693	−	0.903914i
$297$	9.98048e7	+	5.78305e8i	0.221057	+	1.28088i
$298$	−7.79511e8	−	2.54734e7i	−1.70634	−	0.0557609i
$299$	−9.19674e8	−	5.30974e8i	−1.98969	−	1.14875i
$300$	4.45906e7	+	2.65878e8i	0.0953497	+	0.568535i
$301$	−2.72955e8	+	1.57591e8i	−0.576910	+	0.333079i
$302$	−4.63174e7	+	2.47606e7i	−0.0967654	+	0.0517294i
$303$	8.17431e7	+	2.45802e7i	0.168811	+	0.0507618i
$304$	3.78393e8	−	4.93368e8i	0.772477	−	1.00719i
$305$		−	1.38557e8i		−	0.279627i
$306$	4.96551e8	+	4.64470e7i	0.990692	+	0.0926687i
$307$	6.59295e8			1.30045			0.650227	−	0.759740i	$-0.274674\pi$
$307$	6.59295e8			1.30045			0.650227	+	0.759740i	$0.274674\pi$
$308$	−2.97352e8	+	4.45130e8i	−0.579887	+	0.868079i
$309$	4.24066e8	+	4.50576e8i	0.817671	+	0.868787i
$310$	−2.65771e8	+	1.42077e8i	−0.506690	+	0.270869i
$311$	−5.02772e7	−	8.70827e7i	−0.0947785	−	0.164161i	0.814738	−	0.579830i	$-0.196881\pi$
$311$	−5.02772e7	−	8.70827e7i	−0.0947785	−	0.164161i	−0.909516	+	0.415669i	$0.863548\pi$
$312$	−4.94454e8	−	6.40931e8i	−0.921690	−	1.19473i
$313$	−2.67947e7	+	4.64097e7i	−0.0493904	+	0.0855468i	−0.889664	−	0.456616i	$-0.849061\pi$
$313$	−2.67947e7	+	4.64097e7i	−0.0493904	+	0.0855468i	0.840273	+	0.542163i	$0.182395\pi$
$314$	−3.29669e6	+	1.00882e8i	−0.00600930	+	0.183890i
$315$	1.29501e8	+	2.59423e8i	0.233446	+	0.467651i
$316$	1.33251e7	−	2.03663e8i	0.0237556	−	0.363084i
$317$	2.38638e8	−	4.13334e8i	0.420758	−	0.728775i	−0.575255	−	0.817974i	$-0.695097\pi$
$317$	2.38638e8	−	4.13334e8i	0.420758	−	0.728775i	0.996014	+	0.0891989i	$0.0284307\pi$
$318$	1.94029e8	+	6.53272e7i	0.338354	+	0.113920i
$319$	1.01686e9	−	5.87087e8i	1.75386	−	1.01259i
$320$	1.22746e8	+	3.61186e8i	0.209403	+	0.616178i
$321$	−5.85323e8	+	1.37975e8i	−0.987706	+	0.232827i
$322$	−6.22159e8	−	3.86834e8i	−1.03850	−	0.645697i
$323$			7.64907e8i			1.26299i
$324$	−6.01600e8	−	1.13540e8i	−0.982653	−	0.185456i
$325$			5.38324e8i			0.869865i
$326$	5.22463e8	−	8.40297e8i	0.835207	−	1.34330i
$327$	4.10745e8	−	9.68228e7i	0.649613	−	0.153130i
$328$	8.85292e8	−	4.01306e8i	1.38525	−	0.627938i
$329$	2.05764e8	−	1.18798e8i	0.318554	−	0.183917i
$330$	1.76210e8	−	5.23363e8i	0.269918	−	0.801687i
$331$	−4.45926e8	+	7.72366e8i	−0.675872	+	1.17064i	0.300341	+	0.953832i	$0.402899\pi$
$331$	−4.45926e8	+	7.72366e8i	−0.675872	+	1.17064i	−0.976213	+	0.216813i	$0.930434\pi$
$332$	−1.84968e7	+	2.82707e8i	−0.0277404	+	0.423988i
$333$	−2.73351e8	−	5.47591e8i	−0.405664	−	0.812647i
$334$	9.40323e8	+	3.07285e7i	1.38091	+	0.0451263i
$335$	1.85680e8	−	3.21607e8i	0.269841	−	0.467378i
$336$	−3.26489e8	−	4.53069e8i	−0.469549	−	0.651593i
$337$	−2.27350e8	−	3.93782e8i	−0.323587	−	0.560468i	0.657639	−	0.753334i	$-0.271555\pi$
$337$	−2.27350e8	−	3.93782e8i	−0.323587	−	0.560468i	−0.981225	+	0.192865i	$0.938222\pi$
$338$	−4.27363e8	−	7.99428e8i	−0.601989	−	1.12608i
$339$	4.57621e8	+	4.86228e8i	0.637979	+	0.677862i
$340$	−3.90235e8	−	2.60681e8i	−0.538455	−	0.359694i
$341$	−8.40251e8			−1.14754
$342$	8.74508e7	−	9.34909e8i	0.118215	−	1.26380i
$343$			8.13297e8i			1.08823i
$344$	−3.64678e8	+	5.09094e8i	−0.483009	+	0.674285i
$345$	7.23755e8	+	2.17634e8i	0.948910	+	0.285338i
$346$	−4.46142e8	−	8.34556e8i	−0.579037	−	1.08315i
$347$	9.31728e8	−	5.37933e8i	1.19712	−	0.691155i	0.237204	−	0.971460i	$-0.423769\pi$
$347$	9.31728e8	−	5.37933e8i	1.19712	−	0.691155i	0.959911	+	0.280305i	$0.0904356\pi$
$348$	2.02604e8	+	1.20805e9i	0.257704	+	1.53659i
$349$	−1.09296e9	−	6.31018e8i	−1.37630	−	0.794608i	−0.384590	−	0.923088i	$-0.625657\pi$
$349$	−1.09296e9	−	6.31018e8i	−1.37630	−	0.794608i	−0.991712	+	0.128480i	$0.958990\pi$
$350$	−1.21297e7	+	3.71179e8i	−0.0151220	+	0.462749i
$351$	−1.14724e9	−	4.22290e8i	−1.41605	−	0.521238i
$352$	−1.72954e8	+	1.04945e9i	−0.211364	+	1.28252i
$353$	−1.57120e8	−	9.07134e7i	−0.190117	−	0.109764i	0.401920	−	0.915675i	$-0.368343\pi$
$353$	−1.57120e8	−	9.07134e7i	−0.190117	−	0.109764i	−0.592037	+	0.805911i	$0.701676\pi$
$354$	1.02990e9	−	2.07520e8i	1.23392	−	0.248627i
$355$	−1.97021e8	−	3.41250e8i	−0.233729	−	0.404831i
$356$	−1.36426e8	+	6.72977e7i	−0.160259	+	0.0790542i
$357$	6.57913e8	+	1.97835e8i	0.765297	+	0.230126i
$358$	1.75085e8	+	1.08861e8i	0.201678	+	0.125395i
$359$	−1.63644e8			−0.186668			−0.0933338	−	0.995635i	$-0.529752\pi$
$359$	−1.63644e8			−0.186668			−0.0933338	+	0.995635i	$0.529752\pi$
$360$	4.47162e8	+	3.63233e8i	0.505133	+	0.410324i
$361$	5.46300e8			0.611161
$362$	−1.15661e9	−	7.19134e8i	−1.28147	−	0.796764i
$363$	4.57592e8	−	4.30669e8i	0.502118	−	0.472575i
$364$	−4.93322e8	−	1.00007e9i	−0.536137	−	1.08686i
$365$	−5.52709e8	−	9.57320e8i	−0.594938	−	1.03046i
$366$	2.66479e8	+	3.02344e8i	0.284106	+	0.322343i
$367$	1.05323e9	+	6.08083e8i	1.11222	+	0.642143i	0.939405	−	0.342810i	$-0.111379\pi$
$367$	1.05323e9	+	6.08083e8i	1.11222	+	0.642143i	0.172820	+	0.984953i	$0.444712\pi$
$368$	−1.44322e9	−	1.89664e8i	−1.50961	−	0.198388i
$369$	8.09602e8	−	1.22447e9i	0.838841	−	1.26869i
$370$	−1.88102e7	+	5.75612e8i	−0.0193058	+	0.590777i
$371$	2.44245e8	+	1.41015e8i	0.248323	+	0.143369i
$372$	3.06687e8	−	8.21168e8i	0.308884	−	0.827050i
$373$	−1.54932e9	+	8.94503e8i	−1.54583	+	0.892485i	−0.547376	+	0.836887i	$0.684373\pi$
$373$	−1.54932e9	+	8.94503e8i	−1.54583	+	0.892485i	−0.998453	+	0.0555982i	$0.982293\pi$
$374$	−6.16875e8	−	1.15393e9i	−0.609743	−	1.14059i
$375$	−2.40380e8	−	1.01975e9i	−0.235391	−	0.998582i
$376$	2.74908e8	−	3.83775e8i	0.266704	−	0.372322i
$377$			2.44595e9i			2.35100i
$378$	−7.81517e8	−	3.17023e8i	−0.744247	−	0.301904i
$379$	−5.31195e7			−0.0501206			−0.0250603	−	0.999686i	$-0.507978\pi$
$379$	−5.31195e7			−0.0501206			−0.0250603	+	0.999686i	$0.507978\pi$
$380$	−4.90812e8	+	7.34736e8i	−0.458852	+	0.686893i
$381$	1.21260e9	−	2.85841e8i	1.12326	−	0.264781i
$382$	1.59052e7	+	2.97523e7i	0.0145988	+	0.0273086i
$383$	6.47627e8	+	1.12172e9i	0.589018	+	1.02021i	0.994361	+	0.106045i	$0.0338188\pi$
$383$	6.47627e8	+	1.12172e9i	0.589018	+	1.02021i	−0.405343	+	0.914165i	$0.632848\pi$
$384$	−9.62492e8	−	5.52070e8i	−0.867437	−	0.497548i
$385$	3.80366e8	−	6.58813e8i	0.339695	−	0.588369i
$386$	5.08496e8	+	1.66170e7i	0.450020	+	0.0147061i
$387$	−5.72773e7	+	9.43999e8i	−0.0502336	+	0.827910i
$388$	−1.13782e9	−	7.44445e7i	−0.988924	−	0.0647026i
$389$	−3.35601e8	+	5.81279e8i	−0.289068	+	0.500681i	−0.973588	−	0.228314i	$-0.926679\pi$
$389$	−3.35601e8	+	5.81279e8i	−0.289068	+	0.500681i	0.684519	+	0.728995i	$0.260012\pi$
$390$	7.60635e8	+	8.63007e8i	0.649307	+	0.736696i
$391$	1.55082e9	−	8.95368e8i	1.31203	−	0.757501i
$392$	1.74774e8	+	3.85556e8i	0.146546	+	0.323286i
$393$	−2.36505e8	−	2.51290e8i	−0.196547	−	0.208834i
$394$	−1.67938e7	+	2.70101e7i	−0.0138329	+	0.0222479i
$395$			2.90044e8i			0.236796i
$396$	6.22049e8	+	1.48092e9i	0.503375	+	1.19839i
$397$			1.67730e9i			1.34538i	0.739924	+	0.672690i	$0.234861\pi$
$397$			1.67730e9i			1.34538i	−0.739924	+	0.672690i	$0.765139\pi$
$398$	−1.05561e8	−	6.56339e7i	−0.0839295	−	0.0521840i
$399$	3.72485e8	−	1.23872e9i	0.293565	−	0.976268i
$400$	2.82535e8	+	6.81654e8i	0.220731	+	0.532543i
$401$	1.06602e9	−	6.15467e8i	0.825581	−	0.476650i	−0.0267559	−	0.999642i	$-0.508518\pi$
$401$	1.06602e9	−	6.15467e8i	0.825581	−	0.476650i	0.852337	+	0.522992i	$0.175184\pi$
$402$	2.13359e8	+	1.05888e9i	0.163802	+	0.812937i
$403$	8.75176e8	−	1.51585e9i	0.666082	−	1.15369i
$404$	2.33134e8	+	1.52533e7i	0.175902	+	0.0115088i
$405$	8.63643e8	+	1.05191e8i	0.646014	+	0.0786837i
$406$	−5.51129e7	+	1.68651e9i	−0.0408707	+	1.25068i
$407$	−8.02877e8	+	1.39062e9i	−0.590294	+	1.02242i
$408$	1.35288e9	−	1.81687e8i	0.986163	−	0.132438i
$409$	1.00310e9	+	1.73743e9i	0.724961	+	1.25567i	0.958990	+	0.283440i	$0.0914756\pi$
$409$	1.00310e9	+	1.73743e9i	0.724961	+	1.25567i	−0.234029	+	0.972230i	$0.575191\pi$
$410$	−1.21817e9	+	6.51216e8i	−0.872900	+	0.466640i
$411$	3.74630e8	−	1.24585e9i	0.266168	−	0.885158i
$412$	1.40825e9	+	9.40728e8i	0.992064	+	0.662710i
$413$	1.44727e9			1.01094
$414$	−1.99786e9	+	9.17062e8i	−1.38377	+	0.635181i
$415$		−	4.02614e8i		−	0.276516i
$416$	−1.71311e9	−	1.40509e9i	−1.16670	−	0.956923i
$417$	−9.00773e7	+	8.47775e7i	−0.0608330	+	0.0572538i
$418$	−2.17263e9	+	1.16146e9i	−1.45502	+	0.777832i
$419$	−3.44954e8	+	1.99159e8i	−0.229093	+	0.132267i	−0.610154	−	0.792283i	$-0.708892\pi$
$419$	−3.44954e8	+	1.99159e8i	−0.229093	+	0.132267i	0.381060	+	0.924550i	$0.375559\pi$
$420$	5.05019e8	+	6.12190e8i	0.332610	+	0.403194i
$421$	1.14817e9	+	6.62895e8i	0.749925	+	0.432969i	0.825667	−	0.564158i	$-0.190799\pi$
$421$	1.14817e9	+	6.62895e8i	0.749925	+	0.432969i	−0.0757419	+	0.997127i	$0.524132\pi$
$422$	−7.69142e8	−	2.51346e7i	−0.498211	−	0.0162809i
$423$	4.31778e7	−	7.11622e8i	0.0277376	−	0.457150i
$424$	5.57674e8	+	5.48284e7i	0.355304	+	0.0349321i
$425$	−7.86145e8	−	4.53881e8i	−0.496754	−	0.286801i
$426$	1.08622e9	+	3.65719e8i	0.680747	+	0.229200i
$427$	2.77591e8	+	4.80801e8i	0.172547	+	0.298860i
$428$	−1.47615e9	+	7.28168e8i	−0.910074	+	0.448930i
$429$	7.35898e8	+	3.12185e9i	0.450005	+	1.90902i
$430$	4.69904e8	−	7.55765e8i	0.285016	−	0.458403i
$431$	−2.36608e9			−1.42351			−0.711753	−	0.702430i	$-0.752099\pi$
$431$	−2.36608e9			−1.42351			−0.711753	+	0.702430i	$0.752099\pi$
$432$	−1.67433e9	+	6.73943e7i	−0.999191	+	0.0402189i
$433$	−1.59221e9			−0.942525			−0.471263	−	0.881993i	$-0.656202\pi$
$433$	−1.59221e9			−0.942525			−0.471263	+	0.881993i	$0.656202\pi$
$434$	6.37597e8	−	1.02547e9i	0.374397	−	0.602157i
$435$	−3.99390e8	−	1.69430e9i	−0.232640	−	0.986913i
$436$	1.03587e9	−	5.10985e8i	0.598554	−	0.295260i
$437$	−1.68580e9	−	2.91990e9i	−0.966323	−	1.67372i
$438$	3.04722e9	+	1.02596e9i	1.73278	+	0.583408i
$439$	−2.69361e8	−	1.55516e8i	−0.151953	−	0.0877300i	0.422096	−	0.906551i	$-0.361295\pi$
$439$	−2.69361e8	−	1.55516e8i	−0.151953	−	0.0877300i	−0.574049	+	0.818821i	$0.694628\pi$
$440$	1.47891e8	−	1.50424e9i	0.0827672	−	0.841847i
$441$	5.33271e8	+	3.52592e8i	0.296083	+	0.195766i
$442$	2.72426e9	+	8.90251e7i	1.50062	+	0.0490382i
$443$	1.95244e9	+	1.12724e9i	1.06700	+	0.616034i	0.927361	−	0.374168i	$-0.122072\pi$
$443$	1.95244e9	+	1.12724e9i	1.06700	+	0.616034i	0.139641	+	0.990202i	$0.455405\pi$
$444$	−1.06600e9	−	1.29221e9i	−0.577983	−	0.700638i
$445$	1.87218e8	−	1.08090e8i	0.100713	−	0.0581469i
$446$	−1.93119e8	+	1.03239e8i	−0.103075	+	0.0551025i
$447$	−2.34761e9	+	2.20949e9i	−1.24323	+	1.17008i
$448$	−1.14955e9	−	1.00742e9i	−0.604024	−	0.529344i
$449$		−	2.00521e9i		−	1.04544i	−0.852505	−	0.522719i	$-0.824918\pi$
$449$		−	2.00521e9i		−	1.04544i	0.852505	−	0.522719i	$-0.175082\pi$
$450$	9.08976e8	+	6.44636e8i	0.470228	+	0.333481i
$451$	−3.85132e9			−1.97693
$452$	1.51968e9	+	1.01516e9i	0.774048	+	0.517073i
$453$	−6.25152e7	+	2.07898e8i	−0.0315967	+	0.105077i
$454$	−9.19275e8	+	4.91431e8i	−0.461052	+	0.246472i
$455$	7.92351e8	+	1.37239e9i	0.394346	+	0.683027i
$456$	−3.42081e8	−	2.54721e9i	−0.168948	−	1.25802i
$457$	−1.84296e9	+	3.19210e9i	−0.903253	+	1.56448i	−0.0800085	+	0.996794i	$0.525495\pi$
$457$	−1.84296e9	+	3.19210e9i	−0.903253	+	1.56448i	−0.823245	+	0.567686i	$0.807839\pi$
$458$	5.59785e7	−	1.71299e9i	0.0272265	−	0.833157i
$459$	1.58398e9	−	1.31933e9i	0.764547	−	0.636809i
$460$	2.06418e9	+	1.35053e8i	0.988768	+	0.0646924i
$461$	1.52766e9	−	2.64598e9i	0.726226	−	1.25786i	−0.232241	−	0.972658i	$-0.574606\pi$
$461$	1.52766e9	−	2.64598e9i	0.726226	−	1.25786i	0.958467	−	0.285203i	$-0.0920609\pi$
$462$	4.37066e8	+	2.16912e9i	0.206205	+	1.02338i
$463$	−1.43181e9	+	8.26657e8i	−0.670428	+	0.387072i	−0.796239	−	0.604982i	$-0.793180\pi$
$463$	−1.43181e9	+	8.26657e8i	−0.670428	+	0.387072i	0.125811	+	0.992054i	$0.459847\pi$
$464$	1.28374e9	+	3.09720e9i	0.596574	+	1.43931i
$465$	−3.58714e8	+	1.19293e9i	−0.165449	+	0.550210i
$466$	−1.87751e9	−	1.16736e9i	−0.859472	−	0.534385i
$467$			3.82199e9i			1.73652i	0.496105	+	0.868262i	$0.334763\pi$
$467$			3.82199e9i			1.73652i	−0.496105	+	0.868262i	$0.665237\pi$
$468$	−3.31955e9	−	4.20271e8i	−1.49699	−	0.189526i
$469$			1.48799e9i			0.666032i
$470$	−3.54232e8	+	5.69724e8i	−0.157378	+	0.253118i
$471$	2.85945e8	+	3.03821e8i	0.126098	+	0.133981i
$472$	2.61905e9	−	1.18722e9i	1.14643	−	0.519680i
$473$	2.14886e9	−	1.24065e9i	0.933672	−	0.539056i
$474$	−5.57826e8	−	6.32902e8i	−0.240588	−	0.272969i
$475$	−8.54570e8	+	1.48016e9i	−0.365864	+	0.633696i
$476$	1.87639e9	+	1.22767e8i	0.797443	+	0.0521745i
$477$	7.57163e8	−	3.77967e8i	0.319430	−	0.159455i
$478$	8.80301e8	+	2.87671e7i	0.368666	+	0.0120475i
$479$	−4.38915e8	+	7.60223e8i	−0.182476	+	0.316058i	−0.942723	−	0.333576i	$-0.891745\pi$
$479$	−4.38915e8	+	7.60223e8i	−0.182476	+	0.316058i	0.760247	+	0.649634i	$0.225078\pi$
$480$	1.41610e9	+	6.93572e8i	0.584453	+	0.286251i
$481$	−1.67250e9	−	2.89685e9i	−0.685263	−	1.18691i
$482$	−3.98600e8	−	7.45624e8i	−0.162133	−	0.303288i
$483$	−2.94749e9	+	6.94796e8i	−1.19025	+	0.280571i
$484$	9.55377e8	−	1.43018e9i	0.383015	−	0.573366i
$485$	1.62041e9			0.644955
$486$	−2.08685e9	+	1.43146e9i	−0.824641	+	0.565656i
$487$		−	4.01672e9i		−	1.57587i	−0.615759	−	0.787935i	$-0.711150\pi$
$487$		−	4.01672e9i		−	1.57587i	0.615759	−	0.787935i	$-0.288850\pi$
$488$	8.96752e8	+	6.42368e8i	0.349304	+	0.250216i
$489$	−9.38401e8	−	3.98092e9i	−0.362917	−	1.53958i
$490$	−2.83613e8	−	5.30529e8i	−0.108903	−	0.203715i
$491$	1.85007e9	−	1.06814e9i	0.705347	−	0.407232i	−0.103989	−	0.994578i	$-0.533161\pi$
$491$	1.85007e9	−	1.06814e9i	0.705347	−	0.407232i	0.809336	+	0.587346i	$0.199827\pi$
$492$	1.40571e9	−	3.76385e9i	0.532130	−	1.42480i
$493$	−3.57196e9	−	2.06227e9i	−1.34259	−	0.775144i
$494$	1.67617e8	−	5.12925e9i	0.0625567	−	1.91430i
$495$	−1.01951e9	−	2.04233e9i	−0.377809	−	0.756847i
$496$	3.12612e8	−	2.37878e9i	0.115032	−	0.875322i
$497$	1.36735e9	+	7.89437e8i	0.499610	+	0.288450i
$498$	7.74325e8	+	8.78539e8i	0.280944	+	0.318756i
$499$	6.41059e8	+	1.11035e9i	0.230965	+	0.400043i	0.958092	−	0.286459i	$-0.0924783\pi$
$499$	6.41059e8	+	1.11035e9i	0.230965	+	0.400043i	−0.727127	+	0.686503i	$0.759145\pi$
$500$	−1.26861e9	−	2.57174e9i	−0.453873	−	0.920095i
$501$	2.83193e9	−	2.66531e9i	1.00612	−	0.946924i
$502$	−2.13893e9	−	1.32990e9i	−0.754629	−	0.469198i
$503$	4.98040e8			0.174492			0.0872462	−	0.996187i	$-0.472193\pi$
$503$	4.98040e8			0.174492			0.0872462	+	0.996187i	$0.472193\pi$
$504$	−2.27939e9	−	3.64578e8i	−0.793070	−	0.126848i
$505$	−3.32015e8			−0.114720
$506$	4.89800e9	+	3.04538e9i	1.68071	+	1.04500i
$507$	−3.58827e9	−	1.07900e9i	−1.22281	−	0.367699i
$508$	3.05811e9	−	1.50853e9i	1.03498	−	0.510543i
$509$	1.74386e8	+	3.02045e8i	0.0586136	+	0.101522i	0.893843	−	0.448380i	$-0.147999\pi$
$509$	1.74386e8	+	3.02045e8i	0.0586136	+	0.101522i	−0.835230	+	0.549901i	$0.814665\pi$
$510$	−1.90162e9	+	3.83165e8i	−0.634787	+	0.127906i
$511$	3.83586e9	+	2.21463e9i	1.27171	+	0.734225i
$512$	−2.90669e9	−	8.80082e8i	−0.957091	−	0.289786i
$513$	−2.48405e9	−	2.98232e9i	−0.812360	−	0.975311i
$514$	−9.55676e7	+	2.92446e9i	−0.0310413	+	0.949894i
$515$	−2.08428e9	−	1.20336e9i	−0.672403	−	0.388212i
$516$	4.28148e8	+	2.55289e9i	0.137189	+	0.818008i
$517$	−1.61989e9	+	9.35246e8i	−0.515549	+	0.297652i
$518$	−1.08793e9	−	2.03509e9i	−0.343911	−	0.643323i
$519$	−3.74595e9	−	1.12641e9i	−1.17619	−	0.353680i
$520$	2.55968e9	+	1.83357e9i	0.798313	+	0.571854i
$521$			3.31978e9i			1.02844i	0.857659	+	0.514218i	$0.171918\pi$
$521$			3.31978e9i			1.02844i	−0.857659	+	0.514218i	$0.828082\pi$
$522$	4.13006e9	+	2.92900e9i	1.27090	+	0.901306i
$523$	−6.64834e8			−0.203216			−0.101608	−	0.994825i	$-0.532399\pi$
$523$	−6.64834e8			−0.203216			−0.101608	+	0.994825i	$0.532399\pi$
$524$	−7.85393e8	−	5.24651e8i	−0.238467	−	0.159298i
$525$	1.05209e9	+	1.11786e9i	0.317319	+	0.337156i
$526$	2.64975e9	+	4.95664e9i	0.793880	+	1.48504i
$527$	1.47579e9	+	2.55614e9i	0.439224	+	0.760759i
$528$	2.57031e9	+	3.56682e9i	0.759919	+	1.05454i
$529$	−2.24425e9	+	3.88716e9i	−0.659139	+	1.14166i
$530$	−7.95907e8	−	2.60092e7i	−0.232218	−	0.00758860i
$531$	2.39513e9	−	3.62247e9i	0.694222	−	1.04996i
$532$	2.31147e8	−	3.53288e9i	0.0665576	−	1.01728i
$533$	4.01140e9	−	6.94794e9i	1.14749	−	1.98752i
$534$	−2.00642e8	+	5.95928e8i	−0.0570201	+	0.169356i
$535$	2.02572e9	−	1.16955e9i	0.571927	−	0.330202i
$536$	1.22063e9	+	2.69274e9i	0.342379	+	0.755297i
$537$	8.29465e8	−	1.95526e8i	0.231147	−	0.0544871i
$538$	5.92226e7	−	9.52501e7i	0.0163965	−	0.0263710i
$539$		−	1.67730e9i		−	0.461371i
$540$	2.36806e9	−	2.50915e8i	0.647165	−	0.0685722i
$541$		−	4.00506e9i		−	1.08747i	−0.839256	−	0.543737i	$-0.817009\pi$
$541$		−	4.00506e9i		−	1.08747i	0.839256	−	0.543737i	$-0.182991\pi$
$542$	−2.98996e9	−	1.85904e9i	−0.806617	−	0.501522i
$543$	−5.47945e9	+	1.29164e9i	−1.46872	+	0.346213i
$544$	3.49632e9	−	1.31708e9i	0.931140	−	0.350764i
$545$	−1.42153e9	+	8.20720e8i	−0.376156	+	0.217174i
$546$	−4.36842e9	−	1.47080e9i	−1.14855	−	0.386704i
$547$	−2.20258e9	+	3.81497e9i	−0.575407	+	0.996635i	0.420590	+	0.907251i	$0.361823\pi$
$547$	−2.20258e9	+	3.81497e9i	−0.575407	+	0.996635i	−0.995997	+	0.0893838i	$0.971510\pi$
$548$	2.32478e8	−	3.55322e9i	0.0603461	−	0.922339i
$549$	1.66282e9	+	1.00892e8i	0.428886	+	0.0260228i
$550$	9.54918e7	−	2.92214e9i	0.0244735	−	0.748913i
$551$	−3.88286e9	+	6.72532e9i	−0.988830	+	1.71270i
$552$	−4.76396e9	+	3.67522e9i	−1.20554	+	0.930029i
$553$	−5.81085e8	−	1.00647e9i	−0.146117	−	0.253083i
$554$	−4.97584e9	+	2.66001e9i	−1.24332	+	0.664659i
$555$	1.63155e9	+	1.73354e9i	0.405111	+	0.430436i
$556$	−1.88066e8	+	2.81532e8i	−0.0464034	+	0.0694649i
$557$	−2.89077e9			−0.708795			−0.354397	−	0.935095i	$-0.615314\pi$
$557$	−2.89077e9			−0.708795			−0.354397	+	0.935095i	$0.615314\pi$
$558$	−1.51154e9	−	3.29297e9i	−0.368299	−	0.802357i
$559$			5.16885e9i			1.25156i
$560$	1.72361e9	+	1.32194e9i	0.414744	+	0.318092i
$561$	−5.17948e9	−	1.55747e9i	−1.23856	−	0.372435i
$562$	4.62727e8	−	2.47367e8i	0.109963	−	0.0587848i
$563$	2.74069e9	−	1.58234e9i	0.647262	−	0.373697i	−0.140144	−	0.990131i	$-0.544757\pi$
$563$	2.74069e9	−	1.58234e9i	0.647262	−	0.373697i	0.787406	+	0.616434i	$0.211423\pi$
$564$	−3.22754e8	−	1.92446e9i	−0.0757521	−	0.451682i
$565$	−2.24920e9	−	1.29857e9i	−0.524636	−	0.302899i
$566$	1.60682e9	+	5.25088e7i	0.372486	+	0.0121724i
$567$	−3.20763e9	+	1.36524e9i	−0.738998	+	0.314534i
$568$	3.12201e9	+	3.06944e8i	0.714850	+	0.0702813i
$569$	−1.17064e9	−	6.75871e8i	−0.266398	−	0.153805i	0.360851	−	0.932623i	$-0.382486\pi$
$569$	−1.17064e9	−	6.75871e8i	−0.266398	−	0.153805i	−0.627250	+	0.778818i	$0.715819\pi$
$570$	7.21426e8	+	3.58038e9i	0.163166	+	0.809780i
$571$	−2.72288e9	−	4.71616e9i	−0.612071	−	1.06014i	−0.990891	−	0.134667i	$-0.957003\pi$
$571$	−2.72288e9	−	4.71616e9i	−0.612071	−	1.06014i	0.378820	−	0.925470i	$-0.376330\pi$
$572$	3.88372e9	+	7.87311e9i	0.867684	+	1.75898i
$573$	1.33545e8	+	4.01571e7i	0.0296542	+	0.00891704i
$574$	2.92245e9	−	4.70028e9i	0.644993	−	1.03737i
$575$	4.00130e9			0.877735
$576$	−4.42396e9	+	1.21007e9i	−0.964568	+	0.263834i
$577$	2.55344e9			0.553363			0.276682	−	0.960962i	$-0.410765\pi$
$577$	2.55344e9			0.553363			0.276682	+	0.960962i	$0.410765\pi$
$578$	2.43710e7	−	3.91968e7i	0.00524959	−	0.00844312i
$579$	1.53141e9	−	1.44131e9i	0.327881	−	0.308590i
$580$	−2.10779e9	−	4.27293e9i	−0.448569	−	0.909343i
$581$	8.06611e8	+	1.39709e9i	0.170627	+	0.295535i
$582$	−3.53589e9	+	3.11645e9i	−0.743477	+	0.655284i
$583$	−1.92284e9	−	1.11015e9i	−0.401886	−	0.232029i
$584$	8.75827e9	+	8.61080e8i	1.81959	+	0.178895i
$585$	4.74633e9	+	2.87985e8i	0.980196	+	0.0594736i
$586$	−4.21200e9	−	1.37643e8i	−0.864663	−	0.0282561i
$587$	7.29134e8	+	4.20966e8i	0.148790	+	0.0859041i	0.572547	−	0.819872i	$-0.305955\pi$
$587$	7.29134e8	+	4.20966e8i	0.148790	+	0.0859041i	−0.423757	+	0.905776i	$0.639289\pi$
$588$	1.63921e9	+	6.12204e8i	0.332516	+	0.124187i
$589$	4.81271e9	−	2.77862e9i	0.970479	−	0.560306i
$590$	−3.60384e9	+	1.92656e9i	−0.722409	+	0.386190i
$591$	3.01635e7	+	1.27960e8i	0.00601070	+	0.0254988i
$592$	−3.63819e9	−	2.79035e9i	−0.720708	−	0.552754i
$593$			7.05193e9i			1.38873i	0.719625	+	0.694363i	$0.244314\pi$
$593$			7.05193e9i			1.38873i	−0.719625	+	0.694363i	$0.755686\pi$
$594$	6.15256e9	+	2.49579e9i	1.20449	+	0.488602i
$595$	−2.67224e9			−0.520076
$596$	−4.90143e9	+	7.33734e9i	−0.948333	+	1.41964i
$597$	−5.00098e8	+	1.17886e8i	−0.0961934	+	0.0226752i
$598$	−1.05956e10	+	5.66424e9i	−2.02614	+	1.08315i
$599$	1.98431e9	+	3.43692e9i	0.377238	+	0.653395i	0.990659	−	0.136361i	$-0.0435406\pi$
$599$	1.98431e9	+	3.43692e9i	0.377238	+	0.653395i	−0.613421	+	0.789756i	$0.710207\pi$
$600$	2.82092e9	+	1.15989e9i	0.533165	+	0.219223i
$601$	4.27775e9	−	7.40929e9i	0.803813	−	1.39225i	−0.113276	−	0.993564i	$-0.536134\pi$
$601$	4.27775e9	−	7.40929e9i	0.803813	−	1.39225i	0.917089	−	0.398682i	$-0.130532\pi$
$602$	−1.16466e8	+	3.56397e9i	−0.0217576	+	0.665803i
$603$	3.72439e9	+	2.46252e9i	0.691743	+	0.457372i
$604$	−3.87940e7	+	5.92933e8i	−0.00716366	+	0.109490i
$605$	−1.22210e9	+	2.11673e9i	−0.224368	+	0.388617i
$606$	7.24487e8	−	6.38547e8i	0.132244	−	0.116557i
$607$	3.93811e9	−	2.27367e9i	0.714706	−	0.412636i	−0.0980952	−	0.995177i	$-0.531275\pi$
$607$	3.93811e9	−	2.27367e9i	0.714706	−	0.412636i	0.812801	+	0.582541i	$0.197942\pi$
$608$	−2.47980e9	−	6.58290e9i	−0.447460	−	1.18783i
$609$	4.78033e9	+	5.07917e9i	0.857625	+	0.911239i
$610$	−1.33125e9	−	8.27720e8i	−0.237469	−	0.147649i
$611$		−	3.89647e9i		−	0.691079i
$612$	3.41258e9	−	4.49338e9i	0.601801	−	0.792397i
$613$			7.13790e8i			0.125158i	0.998040	+	0.0625790i	$0.0199325\pi$
$613$			7.13790e8i			0.125158i	−0.998040	+	0.0625790i	$0.980067\pi$
$614$	3.93853e9	−	6.33448e9i	0.686664	−	1.10439i
$615$	−1.64418e9	+	5.46782e9i	−0.285027	+	0.947875i
$616$	2.50046e9	+	5.51609e9i	0.431010	+	0.950821i
$617$	6.16093e9	−	3.55702e9i	1.05596	−	0.609660i	0.131650	−	0.991296i	$-0.457973\pi$
$617$	6.16093e9	−	3.55702e9i	1.05596	−	0.609660i	0.924313	+	0.381636i	$0.124639\pi$
$618$	6.86243e9	−	1.38274e9i	1.16955	−	0.235657i
$619$	2.44550e9	−	4.23572e9i	0.414429	−	0.717811i	−0.580940	−	0.813947i	$-0.697315\pi$
$619$	2.44550e9	−	4.23572e9i	0.414429	−	0.717811i	0.995368	+	0.0961353i	$0.0306482\pi$
$620$	−2.22601e8	+	3.40227e9i	−0.0375108	+	0.573321i
$621$	−3.13883e9	+	8.52730e9i	−0.525953	+	1.42886i
$622$	−1.13704e9	−	3.71569e7i	−0.189456	−	0.00619117i
$623$	−4.33104e8	+	7.50158e8i	−0.0717603	+	0.124292i
$624$	−9.11184e9	+	9.21879e8i	−1.50127	+	0.151889i
$625$	2.78324e8	+	4.82071e8i	0.0456006	+	0.0789825i
$626$	2.85836e8	+	5.34687e8i	0.0465700	+	0.0871143i
$627$	−2.93242e9	+	9.75195e9i	−0.475106	+	1.57999i
$628$	9.49576e8	+	6.34327e8i	0.152993	+	0.102201i
$629$	5.64058e9			0.903745
$630$	3.26615e9	+	3.05514e8i	0.520409	+	0.0486787i
$631$		−	9.88391e9i		−	1.56612i	−0.621944	−	0.783062i	$-0.713657\pi$
$631$		−	9.88391e9i		−	1.56612i	0.621944	−	0.783062i	$-0.286343\pi$
$632$	−1.87719e9	−	1.34468e9i	−0.295800	−	0.211889i
$633$	−2.31639e9	+	2.18010e9i	−0.362993	+	0.341636i
$634$	−2.54571e9	−	4.76202e9i	−0.396731	−	0.742129i
$635$	−4.19665e9	+	2.42294e9i	−0.650421	+	0.375521i
$636$	1.78676e9	−	1.47397e9i	0.275402	−	0.227190i
$637$	3.02592e9	+	1.74701e9i	0.463841	+	0.267799i
$638$	4.33881e8	−	1.32772e10i	0.0661451	−	2.02410i
$639$	4.23880e9	−	2.11596e9i	0.642672	−	0.320814i
$640$	4.20353e9	+	9.78332e8i	0.633847	+	0.147522i
$641$	−4.27623e9	−	2.46888e9i	−0.641295	−	0.370252i	0.143818	−	0.989604i	$-0.454062\pi$
$641$	−4.27623e9	−	2.46888e9i	−0.641295	−	0.370252i	−0.785113	+	0.619352i	$0.787395\pi$
$642$	−2.17097e9	+	6.44801e9i	−0.323803	+	0.961729i
$643$	5.27674e9	+	9.13958e9i	0.782758	+	1.35578i	0.930329	+	0.366725i	$0.119521\pi$
$643$	5.27674e9	+	9.13958e9i	0.782758	+	1.35578i	−0.147572	+	0.989051i	$0.547146\pi$
$644$	−7.43337e9	+	3.66680e9i	−1.09669	+	0.540987i
$645$	−8.44000e8	−	3.58044e9i	−0.123846	−	0.525385i
$646$	7.34921e9	+	4.56944e9i	1.07257	+	0.666882i
$647$	−5.72454e8			−0.0830951			−0.0415476	−	0.999137i	$-0.513229\pi$
$647$	−5.72454e8			−0.0830951			−0.0415476	+	0.999137i	$0.513229\pi$
$648$	−4.68475e9	+	5.10188e9i	−0.676354	+	0.736576i
$649$	−1.13938e10			−1.63610
$650$	5.17220e9	+	3.21587e9i	0.738718	+	0.459305i
$651$	−1.14519e9	−	4.85818e9i	−0.162684	−	0.690145i
$652$	−4.95244e9	−	1.00396e10i	−0.699765	−	1.41857i
$653$	−3.18867e8	−	5.52295e8i	−0.0448140	−	0.0776202i	0.842748	−	0.538308i	$-0.180936\pi$
$653$	−3.18867e8	−	5.52295e8i	−0.0448140	−	0.0776202i	−0.887562	+	0.460688i	$0.847603\pi$
$654$	1.52346e9	−	4.52483e9i	0.212965	−	0.632528i
$655$	1.16242e9	+	6.71122e8i	0.161628	+	0.0933162i
$656$	1.43287e9	−	1.09032e10i	0.198172	−	1.50796i
$657$	1.18912e10	−	5.93596e9i	1.63587	−	0.816606i
$658$	8.77964e7	−	2.68665e9i	0.0120140	−	0.367639i
$659$	1.02918e9	+	5.94200e8i	0.140086	+	0.0808786i	0.568405	−	0.822749i	$-0.307561\pi$
$659$	1.02918e9	+	5.94200e8i	0.140086	+	0.0808786i	−0.428319	+	0.903628i	$0.640894\pi$
$660$	−3.97581e9	−	4.81952e9i	−0.538296	−	0.652529i
$661$	−1.14702e10	+	6.62232e9i	−1.54478	+	0.891878i	−0.546250	+	0.837622i	$0.683945\pi$
$661$	−1.14702e10	+	6.62232e9i	−1.54478	+	0.891878i	−0.998527	+	0.0542558i	$0.982721\pi$
$662$	4.75698e9	+	8.89844e9i	0.637277	+	1.19210i
$663$	8.20451e9	−	7.72178e9i	1.09334	−	1.02901i
$664$	2.60574e9	+	1.86657e9i	0.345417	+	0.247431i
$665$			5.03131e9i			0.663446i
$666$	−6.89420e9	−	6.44879e8i	−0.904324	−	0.0845899i
$667$	1.81805e10			2.37227
$668$	5.91259e9	−	8.85103e9i	0.767468	−	1.14888i
$669$	−2.60655e8	+	8.66826e8i	−0.0336570	+	0.111928i
$670$	−1.98077e9	−	3.70524e9i	−0.254432	−	0.475942i
$671$	−2.18535e9	−	3.78515e9i	−0.279250	−	0.483675i
$672$	−6.30347e9	+	4.30333e8i	−0.801285	+	0.0547032i
$673$	1.30729e9	−	2.26429e9i	0.165317	−	0.286338i	−0.771451	−	0.636289i	$-0.780469\pi$
$673$	1.30729e9	−	2.26429e9i	0.165317	−	0.286338i	0.936768	+	0.349951i	$0.113802\pi$
$674$	−5.14160e9	−	1.68021e8i	−0.646828	−	0.0211375i
$675$	4.53911e9	−	7.83366e8i	0.568077	−	0.0980396i
$676$	−1.02339e10	−	6.69575e8i	−1.27417	−	0.0833654i
$677$	−9.63461e8	+	1.66876e9i	−0.119337	+	0.206697i	−0.919505	−	0.393078i	$-0.871410\pi$
$677$	−9.63461e8	+	1.66876e9i	−0.119337	+	0.206697i	0.800168	+	0.599775i	$0.204743\pi$
$678$	7.40542e9	−	1.49215e9i	0.912528	−	0.183869i
$679$	−5.62292e9	+	3.24639e9i	−0.689315	+	0.397976i
$680$	−4.83582e9	+	2.19209e9i	−0.589779	+	0.267349i
$681$	−1.24076e9	+	4.12621e9i	−0.150547	+	0.500652i
$682$	−5.01954e9	+	8.07311e9i	−0.605924	+	0.974531i
$683$			9.77654e9i			1.17412i	0.809543	+	0.587060i	$0.199715\pi$
$683$			9.77654e9i			1.17412i	−0.809543	+	0.587060i	$0.800285\pi$
$684$	−8.46016e9	−	6.42523e9i	−1.01084	−	0.767701i
$685$			5.06028e9i			0.601530i
$686$	7.81414e9	+	4.85852e9i	0.924159	+	0.574605i
$687$	−4.85541e9	−	5.15894e9i	−0.571317	−	0.607033i
$688$	2.71283e9	+	6.54507e9i	0.317587	+	0.766222i
$689$	4.00552e9	−	2.31259e9i	0.466542	−	0.269358i
$690$	6.41463e9	−	5.65371e9i	0.743361	−	0.655181i
$691$	−7.88844e7	+	1.36632e8i	−0.00909531	+	0.0157535i	−0.870537	−	0.492103i	$-0.836229\pi$
$691$	−7.88844e7	+	1.36632e8i	−0.00909531	+	0.0157535i	0.861442	+	0.507856i	$0.169562\pi$
$692$	−1.06836e10	−	6.98997e8i	−1.22559	−	0.0801870i
$693$	7.62943e9	+	5.04448e9i	0.870814	+	0.575772i
$694$	3.97554e8	−	1.21655e10i	0.0451480	−	1.38157i
$695$	2.40570e8	−	4.16680e8i	0.0271829	−	0.0470821i
$696$	1.28173e10	+	5.27011e9i	1.44100	+	0.592499i
$697$	6.76432e9	+	1.17161e10i	0.756675	+	1.31060i
$698$	−1.25920e10	+	6.73148e9i	−1.40152	+	0.749232i
$699$	−8.89472e9	+	2.09671e9i	−0.985059	+	0.232203i
$700$	3.49382e9	+	2.33391e9i	0.384997	+	0.257182i
$701$	−6.33475e8			−0.0694571			−0.0347286	−	0.999397i	$-0.511057\pi$
$701$	−6.33475e8			−0.0694571			−0.0347286	+	0.999397i	$0.511057\pi$
$702$	−1.09108e10	+	8.49995e9i	−1.19035	+	0.927335i
$703$		−	1.06201e10i		−	1.15288i
$704$	9.04992e9	+	7.93101e9i	0.977553	+	0.856691i
$705$	6.36239e8	+	2.69907e9i	0.0683846	+	0.290103i
$706$	−1.81019e9	+	9.67699e8i	−0.193601	+	0.103496i
$707$	1.15211e9	−	6.65172e8i	0.122610	−	0.0707890i
$708$	4.15865e9	−	1.11350e10i	0.440389	−	1.17916i
$709$	1.80462e9	+	1.04190e9i	0.190162	+	0.109790i	0.592058	−	0.805895i	$-0.298315\pi$
$709$	1.80462e9	+	1.04190e9i	0.190162	+	0.109790i	−0.401896	+	0.915685i	$0.631649\pi$
$710$	−4.45570e9	−	1.45606e8i	−0.467209	−	0.0152678i
$711$	−3.48081e9	−	2.11199e8i	−0.363193	−	0.0220368i
$712$	−1.68397e8	+	1.71281e9i	−0.0174845	+	0.177840i
$713$	−1.12671e10	−	6.50507e9i	−1.16412	−	0.672108i
$714$	5.83107e9	−	5.13937e9i	0.599521	−	0.528404i
$715$	−6.23785e9	−	1.08043e10i	−0.638210	−	1.10541i
$716$	2.09186e9	−	1.03189e9i	0.212979	−	0.105060i
$717$	2.65116e9	−	2.49517e9i	0.268608	−	0.252804i
$718$	−9.77584e8	+	1.57228e9i	−0.0985640	+	0.158524i
$719$	−1.68854e9			−0.169418			−0.0847092	−	0.996406i	$-0.526996\pi$
$719$	−1.68854e9			−0.169418			−0.0847092	+	0.996406i	$0.526996\pi$
$720$	6.16121e9	−	2.12642e9i	0.615180	−	0.212317i
$721$	9.64340e9			0.958201
$722$	3.26351e9	−	5.24883e9i	0.322705	−	0.519018i
$723$	−3.34677e9	−	1.00638e9i	−0.329338	−	0.0990322i
$724$	−1.38188e10	+	6.81668e9i	−1.35328	+	0.667557i
$725$	−4.60803e9	−	7.98135e9i	−0.449089	−	0.777845i
$726$	−1.40427e9	−	6.96929e9i	−0.136199	−	0.675943i
$727$	1.30820e10	+	7.55291e9i	1.26271	+	0.729027i	0.973598	−	0.228268i	$-0.0733061\pi$
$727$	1.30820e10	+	7.55291e9i	1.26271	+	0.729027i	0.289114	+	0.957295i	$0.406639\pi$
$728$	−1.25556e10	−	1.23442e9i	−1.20609	−	0.118578i
$729$	−1.89126e9	+	1.02880e10i	−0.180803	+	0.983519i
$730$	−1.24997e10	−	4.08474e8i	−1.18924	−	0.0388629i
$731$	−7.54836e9	−	4.35805e9i	−0.714730	−	0.412649i
$732$	4.49682e9	−	7.54167e8i	0.423757	−	0.0710688i
$733$	1.08599e9	−	6.26994e8i	0.101850	−	0.0588030i	−0.448210	−	0.893928i	$-0.647938\pi$
$733$	1.08599e9	−	6.26994e8i	0.101850	−	0.0588030i	0.550060	+	0.835125i	$0.314605\pi$
$734$	1.21343e10	−	6.48682e9i	1.13260	−	0.605474i
$735$	−2.38131e9	−	7.16061e8i	−0.221212	−	0.0665188i
$736$	−1.04438e10	+	1.27334e10i	−0.965580	+	1.17726i
$737$		−	1.17143e10i		−	1.07791i
$738$	−6.92820e9	−	1.50934e10i	−0.634488	−	1.38226i
$739$	−2.99067e9			−0.272592			−0.136296	−	0.990668i	$-0.543520\pi$
$739$	−2.99067e9			−0.272592			−0.136296	+	0.990668i	$0.543520\pi$
$740$	5.41809e9	+	3.61935e9i	0.491513	+	0.328336i
$741$	−1.45386e10	−	1.54475e10i	−1.31268	−	1.39474i
$742$	2.81395e9	−	1.50430e9i	0.252873	−	0.135182i
$743$	−1.01067e10	−	1.75053e10i	−0.903958	−	1.56570i	−0.822309	−	0.569041i	$-0.807315\pi$
$743$	−1.01067e10	−	1.75053e10i	−0.903958	−	1.56570i	−0.0816491	−	0.996661i	$-0.526019\pi$
$744$	−6.05766e9	−	7.85217e9i	−0.539262	−	0.699012i
$745$	6.26980e9	−	1.08596e10i	0.555529	−	0.962204i
$746$	−6.61074e8	+	2.02295e10i	−0.0582994	+	1.78402i
$747$	4.83176e9	+	2.93168e8i	0.424114	+	0.0257332i
$748$	−1.47721e10	−	9.66496e8i	−1.29058	−	0.0844393i
$749$	−4.68623e9	+	8.11679e9i	−0.407509	+	0.705826i
$750$	−1.12337e10	−	3.78226e9i	−0.972319	−	0.327369i
$751$	−8.09198e9	+	4.67191e9i	−0.697132	+	0.402489i	−0.806278	−	0.591536i	$-0.798522\pi$
$751$	−8.09198e9	+	4.67191e9i	−0.697132	+	0.402489i	0.109146	+	0.994026i	$0.465188\pi$
$752$	−2.04504e9	−	4.93392e9i	−0.175363	−	0.423087i
$753$	−1.01332e10	+	2.38865e9i	−0.864896	+	0.203878i
$754$	2.35006e10	+	1.46118e10i	1.99655	+	1.24137i
$755$		−	8.44418e8i		−	0.0714074i
$756$	−7.71461e9	+	5.61495e9i	−0.649363	+	0.472628i
$757$			1.50501e10i			1.26096i	0.776204	+	0.630482i	$0.217143\pi$
$757$			1.50501e10i			1.26096i	−0.776204	+	0.630482i	$0.782857\pi$
$758$	−3.17328e8	+	5.10370e8i	−0.0264646	+	0.0425641i
$759$	2.32043e10	−	5.46984e9i	1.92629	−	0.454076i
$760$	4.12729e9	+	9.10491e9i	0.341049	+	0.752364i
$761$	−1.41713e9	+	8.18183e8i	−0.116564	+	0.0672983i	−0.557148	−	0.830413i	$-0.688105\pi$
$761$	−1.41713e9	+	8.18183e8i	−0.116564	+	0.0672983i	0.440584	+	0.897711i	$0.354771\pi$
$762$	4.49756e9	−	1.33582e10i	0.368243	−	1.09372i
$763$	3.28852e9	−	5.69588e9i	0.268018	−	0.464221i
$764$	3.80875e8	+	2.49196e7i	0.0308998	+	0.00202169i
$765$	−4.42237e9	+	6.68853e9i	−0.357142	+	0.540152i
$766$	1.46463e10	+	4.78622e8i	1.17741	+	0.0384762i
$767$	1.18673e10	−	2.05548e10i	0.949662	−	1.64486i
$768$	−1.10541e10	+	5.94961e9i	−0.880557	+	0.473941i
$769$	3.26519e9	+	5.65548e9i	0.258921	+	0.448464i	0.965953	−	0.258717i	$-0.0832999\pi$
$769$	3.26519e9	+	5.65548e9i	0.258921	+	0.448464i	−0.707032	+	0.707181i	$0.749967\pi$
$770$	−4.05761e9	−	7.59019e9i	−0.320297	−	0.599150i
$771$	8.28926e9	+	8.80746e9i	0.651367	+	0.692086i
$772$	3.19733e9	−	4.78634e9i	0.250108	−	0.374406i
$773$	−2.27913e10			−1.77476			−0.887381	−	0.461036i	$-0.847478\pi$
$773$	−2.27913e10			−1.77476			−0.887381	+	0.461036i	$0.847478\pi$
$774$	8.72775e9	+	6.18963e9i	0.676564	+	0.479812i
$775$			6.59512e9i			0.508940i
$776$	−7.51243e9	+	1.04874e10i	−0.577118	+	0.805662i
$777$	−9.13459e9	−	2.74678e9i	−0.698579	−	0.210063i
$778$	3.58008e9	+	6.69692e9i	0.272561	+	0.509855i
$779$	2.20592e10	−	1.27359e10i	1.67190	−	0.965269i
$780$	1.28357e10	−	2.15269e9i	0.968473	−	0.162424i
$781$	−1.07645e10	−	6.21491e9i	−0.808569	−	0.466827i
$782$	6.61713e8	−	2.02491e10i	0.0494819	−	1.51419i
$783$	2.06241e10	−	3.55934e9i	1.53536	−	0.264974i
$784$	4.74848e9	+	6.24032e8i	0.351924	+	0.0462488i
$785$	−1.40542e9	−	8.11417e8i	−0.103696	−	0.0598688i
$786$	−3.82723e9	+	7.71165e8i	−0.281129	+	0.0566459i
$787$	−2.53508e9	−	4.39089e9i	−0.185388	−	0.321101i	0.758319	−	0.651883i	$-0.226021\pi$
$787$	−2.53508e9	−	4.39089e9i	−0.185388	−	0.321101i	−0.943707	+	0.330782i	$0.892687\pi$
$788$	1.59189e8	+	3.22708e8i	0.0115896	+	0.0234946i
$789$	2.22481e10	+	6.69004e9i	1.61259	+	0.484907i
$790$	2.78674e9	+	1.73268e9i	0.201095	+	0.125033i
$791$	1.04064e10			0.747626
$792$	1.79447e10	+	2.87017e9i	1.28350	+	0.205291i
$793$	9.10475e9			0.648353
$794$	1.61155e10	+	1.00200e10i	1.14254	+	0.710386i
$795$	−2.39699e9	+	2.25596e9i	−0.169193	+	0.159238i
$796$	−1.26122e9	+	6.22145e8i	−0.0886327	+	0.0437215i
$797$	3.44786e9	+	5.97187e9i	0.241238	+	0.417836i	0.961067	−	0.276315i	$-0.0891133\pi$
$797$	3.44786e9	+	5.97187e9i	0.241238	+	0.417836i	−0.719829	+	0.694151i	$0.755780\pi$
$798$	−9.67645e9	−	1.09788e10i	−0.674071	−	0.764793i
$799$	5.69024e9	+	3.28526e9i	0.394655	+	0.227854i
$800$	8.23714e9	+	1.35751e9i	0.568803	+	0.0937407i
$801$	1.16086e9	+	2.32550e9i	0.0798119	+	0.159883i
$802$	4.54855e8	−	1.39190e10i	0.0311360	−	0.952791i
$803$	−3.01981e10	−	1.74349e10i	−2.05814	−	1.18827i
$804$	1.14483e10	+	4.27566e9i	0.776863	+	0.290140i
$805$	1.02008e10	−	5.88945e9i	0.689207	−	0.397914i
$806$	−9.33606e9	−	1.74641e10i	−0.628045	−	1.17483i
$807$	−1.06370e8	−	4.51248e8i	−0.00712465	−	0.0302244i
$808$	1.53926e9	−	2.14883e9i	0.102653	−	0.143305i
$809$		−	1.36597e9i		−	0.0907028i	−0.998971	−	0.0453514i	$-0.985559\pi$
$809$		−	1.36597e9i		−	0.0907028i	0.998971	−	0.0453514i	$-0.0144408\pi$
$810$	6.16994e9	−	7.66946e9i	0.407928	−	0.507070i
$811$	4.21572e9			0.277523			0.138762	−	0.990326i	$-0.455688\pi$
$811$	4.21572e9			0.277523			0.138762	+	0.990326i	$0.455688\pi$
$812$	1.58747e10	+	1.06045e10i	1.04054	+	0.695092i
$813$	−1.41650e10	+	3.33903e9i	−0.924481	+	0.217923i
$814$	8.56481e9	+	1.60214e10i	0.556586	+	1.04115i
$815$	7.95437e9	+	1.37774e10i	0.514700	+	0.891487i
$816$	6.33626e9	−	1.40838e10i	0.408242	−	0.907412i
$817$	−8.20536e9	+	1.42121e10i	−0.526406	+	0.911761i
$818$	2.26856e10	+	7.41335e8i	1.44915	+	0.0473563i
$819$	−1.70470e10	+	8.50965e9i	−1.08431	+	0.541275i
$820$	−1.02030e9	+	1.55944e10i	−0.0646219	+	0.987690i
$821$	−1.35757e10	+	2.35137e10i	−0.856169	+	1.48293i	0.0193869	+	0.999812i	$0.493829\pi$
$821$	−1.35757e10	+	2.35137e10i	−0.856169	+	1.48293i	−0.875556	+	0.483116i	$0.839505\pi$
$822$	−9.73215e9	−	1.10420e10i	−0.611164	−	0.693419i
$823$	−2.52858e10	+	1.45988e10i	−1.58117	+	0.912888i	−0.586479	+	0.809964i	$0.699486\pi$
$823$	−2.52858e10	+	1.45988e10i	−1.58117	+	0.912888i	−0.994689	+	0.102924i	$0.967180\pi$
$824$	1.74512e10	−	7.91067e9i	1.08662	−	0.492570i
$825$	−8.28268e9	−	8.80046e9i	−0.513549	−	0.545653i
$826$	8.64577e9	−	1.39053e10i	0.533794	−	0.858521i
$827$			9.24804e9i			0.568565i	0.958740	+	0.284283i	$0.0917554\pi$
$827$			9.24804e9i			0.568565i	−0.958740	+	0.284283i	$0.908245\pi$
$828$	−3.12383e9	+	2.46738e10i	−0.191241	+	1.51053i
$829$		−	2.12867e10i		−	1.29768i	−0.760926	−	0.648839i	$-0.775255\pi$
$829$		−	2.12867e10i		−	1.29768i	0.760926	−	0.648839i	$-0.224745\pi$
$830$	−3.86830e9	−	2.40515e9i	−0.234826	−	0.146006i
$831$	−6.71594e9	+	2.23343e10i	−0.405979	+	1.35011i
$832$	−2.37339e10	+	8.06577e9i	−1.42869	+	0.485528i
$833$	−5.10253e9	+	2.94595e9i	−0.305864	+	0.176591i
$834$	2.76431e8	+	1.37191e9i	0.0165008	+	0.0818924i
$835$	−7.56325e9	+	1.30999e10i	−0.449579	+	0.778693i
$836$	−1.81972e9	+	2.78129e10i	−0.107717	+	1.64636i
$837$	−1.40551e10	−	5.17356e9i	−0.828503	−	0.304965i
$838$	−1.47187e8	+	4.50406e9i	−0.00864002	+	0.264393i
$839$	2.27085e9	−	3.93323e9i	0.132746	−	0.229923i	−0.791988	−	0.610537i	$-0.790954\pi$
$839$	2.27085e9	−	3.93323e9i	0.132746	−	0.229923i	0.924734	+	0.380613i	$0.124287\pi$
$840$	8.89882e9	−	1.19508e9i	0.518030	−	0.0695695i
$841$	−1.23123e10	−	2.13256e10i	−0.713763	−	1.23627i
$842$	1.32281e10	−	7.07152e9i	0.763666	−	0.408245i
$843$	6.24548e8	−	2.07697e9i	0.0359062	−	0.119408i
$844$	−4.83623e9	+	7.23975e9i	−0.276891	+	0.414500i
$845$	1.45745e10			0.830987
$846$	−6.57931e9	−	4.66598e9i	−0.373580	−	0.264939i
$847$		−	9.79357e9i		−	0.553795i
$848$	3.85825e9	−	5.03058e9i	0.217273	−	0.283291i
$849$	4.83918e9	−	4.55446e9i	0.271391	−	0.255423i
$850$	−9.05719e9	+	4.84184e9i	−0.505856	+	0.270424i
$851$	−2.15319e10	+	1.24315e10i	−1.19765	+	0.691462i
$852$	1.00028e10	−	8.25166e9i	0.554091	−	0.457091i
$853$	1.44878e10	+	8.36455e9i	0.799248	+	0.461446i	0.843208	−	0.537587i	$-0.180664\pi$
$853$	1.44878e10	+	8.36455e9i	0.799248	+	0.461446i	−0.0439599	+	0.999033i	$0.513997\pi$
$854$	6.27781e9	+	2.05151e8i	0.344910	+	0.0112712i
$855$	1.25932e10	+	8.32647e9i	0.689057	+	0.455596i
$856$	−1.82207e9	+	1.85327e10i	−0.0992903	+	1.00991i
$857$	−2.62128e10	−	1.51340e10i	−1.42259	−	0.821334i	−0.426073	−	0.904689i	$-0.640103\pi$
$857$	−2.62128e10	−	1.51340e10i	−1.42259	−	0.821334i	−0.996520	+	0.0833543i	$0.973437\pi$
$858$	3.43908e10	+	1.15790e10i	1.85882	+	0.625842i
$859$	4.61744e9	+	7.99764e9i	0.248557	+	0.430513i	0.963126	−	0.269052i	$-0.0867105\pi$
$859$	4.61744e9	+	7.99764e9i	0.248557	+	0.430513i	−0.714569	+	0.699565i	$0.753377\pi$
$860$	−4.45423e9	−	9.02965e9i	−0.238797	−	0.484090i
$861$	−5.24904e9	−	2.22676e10i	−0.280265	−	1.18895i
$862$	−1.41346e10	+	2.27333e10i	−0.751638	+	1.20889i
$863$	−3.07806e10			−1.63019			−0.815097	−	0.579324i	$-0.803316\pi$
$863$	−3.07806e10			−1.63019			−0.815097	+	0.579324i	$0.803316\pi$
$864$	−9.35469e9	+	1.64895e10i	−0.493436	+	0.869782i
$865$	1.52149e10			0.799305
$866$	−9.51163e9	+	1.52979e10i	−0.497671	+	0.800423i
$867$	−4.37730e7	−	1.85695e8i	−0.00228107	−	0.00967684i
$868$	−6.04379e9	−	1.22520e10i	−0.313683	−	0.635900i
$869$	4.57464e9	+	7.92351e9i	0.236476	+	0.409589i
$870$	−1.86647e10	−	6.28419e9i	−0.960957	−	0.323543i
$871$	2.11331e10	+	1.22012e10i	1.08368	+	0.625662i
$872$	1.27862e9	−	1.30052e10i	0.0653031	−	0.664215i
$873$	−1.17992e9	+	1.94465e10i	−0.0600210	+	0.989219i
$874$	−3.81251e10	−	1.24588e9i	−1.93161	−	0.0631227i
$875$	−1.41411e10	−	8.16435e9i	−0.713598	−	0.411996i
$876$	2.80611e10	−	2.31487e10i	1.41039	−	1.16349i
$877$	−2.26157e9	+	1.30572e9i	−0.113217	+	0.0653659i	−0.555539	−	0.831490i	$-0.687488\pi$
$877$	−2.26157e9	+	1.30572e9i	−0.113217	+	0.0653659i	0.442322	+	0.896856i	$0.354155\pi$
$878$	−3.10331e9	+	1.65899e9i	−0.154737	+	0.0827203i
$879$	−1.26851e10	+	1.19387e10i	−0.629988	+	0.592922i
$880$	−1.35692e10	−	1.04071e10i	−0.671222	−	0.514800i
$881$			2.74403e10i			1.35199i	0.736908	+	0.675993i	$0.236285\pi$
$881$			2.74403e10i			1.35199i	−0.736908	+	0.675993i	$0.763715\pi$
$882$	6.57338e9	−	3.01732e9i	0.322588	−	0.148075i
$883$	−1.41822e10			−0.693237			−0.346618	−	0.938006i	$-0.612670\pi$
$883$	−1.41822e10			−0.693237			−0.346618	+	0.938006i	$0.612670\pi$
$884$	1.71296e10	−	2.56427e10i	0.833999	−	1.24848i
$885$	−4.86414e9	+	1.61760e10i	−0.235887	+	0.784458i
$886$	2.24941e10	−	1.20250e10i	1.08655	−	0.580856i
$887$	−1.73696e9	−	3.00850e9i	−0.0835711	−	0.144749i	0.821210	−	0.570626i	$-0.193299\pi$
$887$	−1.73696e9	−	3.00850e9i	−0.0835711	−	0.144749i	−0.904781	+	0.425876i	$0.859966\pi$
$888$	−1.87836e10	+	2.52258e9i	−0.900190	+	0.120892i
$889$	9.70839e9	−	1.68154e10i	0.463437	−	0.802697i
$890$	7.98831e7	−	2.44450e9i	0.00379830	−	0.116232i
$891$	2.52523e10	−	1.07479e10i	1.19600	−	0.509041i
$892$	−1.61751e8	+	2.47222e9i	−0.00763078	+	0.116630i
$893$	6.18551e9	−	1.07136e10i	0.290667	−	0.503450i
$894$	7.20442e9	+	3.57550e10i	0.337223	+	1.67361i
$895$	−2.87066e9	+	1.65738e9i	−0.133845	+	0.0772752i
$896$	−1.65465e10	+	5.02664e9i	−0.768472	+	0.233453i
$897$	−1.43010e10	+	4.75588e10i	−0.661594	+	2.20017i
$898$	−1.92660e10	−	1.19788e10i	−0.887820	−	0.552011i
$899$			2.99659e10i			1.37552i
$900$	1.16237e10	−	4.88245e9i	0.531492	−	0.223249i
$901$			7.79931e9i			0.355238i
$902$	−2.30072e10	+	3.70034e10i	−1.04386	+	1.67887i
$903$	1.01019e10	+	1.07334e10i	0.456558	+	0.485100i
$904$	1.88320e10	−	8.53661e9i	0.847827	−	0.384323i
$905$	1.89636e10	−	1.09486e10i	0.850453	−	0.491009i
$906$	1.62402e9	+	1.84260e9i	0.0725510	+	0.0823154i
$907$	2.18411e10	−	3.78300e10i	0.971963	−	1.68349i	0.282351	−	0.959311i	$-0.408886\pi$
$907$	2.18411e10	−	3.78300e10i	0.971963	−	1.68349i	0.689612	−	0.724179i	$-0.257781\pi$
$908$	−7.69955e8	+	1.17681e10i	−0.0341322	+	0.521682i
$909$	2.41761e8	−	3.98451e9i	0.0106761	−	0.175955i
$910$	1.79193e10	+	5.85579e8i	0.788271	+	0.0257597i
$911$	7.00550e9	−	1.21339e10i	0.306990	−	0.531723i	−0.670712	−	0.741718i	$-0.734011\pi$
$911$	7.00550e9	−	1.21339e10i	0.306990	−	0.531723i	0.977703	+	0.209995i	$0.0673447\pi$
$912$	−2.65171e10	−	1.19300e10i	−1.15756	−	0.520783i
$913$	−6.35011e9	−	1.09987e10i	−0.276143	−	0.478293i
$914$	1.96601e10	+	3.67763e10i	0.851673	+	1.59315i
$915$	−6.30683e9	+	1.48668e9i	−0.272168	+	0.0641568i
$916$	−1.61240e10	−	1.07710e10i	−0.693168	−	0.463044i
$917$	−5.37820e9			−0.230327
$918$	−3.21367e9	−	2.31003e10i	−0.137104	−	0.985525i
$919$		−	1.67421e10i		−	0.711552i	−0.934571	−	0.355776i	$-0.884217\pi$
$919$		−	1.67421e10i		−	0.711552i	0.934571	−	0.355776i	$-0.115783\pi$
$920$	1.36287e10	−	1.90258e10i	0.577027	−	0.805536i
$921$	−7.07403e9	−	3.00097e10i	−0.298372	−	1.26576i
$922$	−1.62965e10	−	3.04843e10i	−0.684756	−	1.28091i
$923$	2.24239e10	−	1.29465e10i	0.938654	−	0.541932i
$924$	2.34519e10	+	8.75871e9i	0.977969	+	0.365248i
$925$	1.09150e10	+	6.30177e9i	0.453448	+	0.261798i
$926$	−6.10933e8	+	1.86951e10i	−0.0252845	+	0.773731i
$927$	1.59591e10	−	2.41371e10i	0.658007	−	0.995190i
$928$	3.74266e10	+	6.16804e9i	1.53732	+	0.253355i
$929$	−7.98801e9	−	4.61188e9i	−0.326877	−	0.188722i	0.327577	−	0.944824i	$-0.393768\pi$
$929$	−7.98801e9	−	4.61188e9i	−0.326877	−	0.188722i	−0.654454	+	0.756102i	$0.727101\pi$
$930$	9.31870e9	+	1.05729e10i	0.379896	+	0.431026i
$931$	5.54665e9	+	9.60707e9i	0.225272	+	0.390182i
$932$	−2.24319e10	+	1.10654e10i	−0.907635	+	0.447726i
$933$	−3.42436e9	+	3.22288e9i	−0.138036	+	0.129915i
$934$	3.67216e10	+	2.28320e10i	1.47471	+	0.916918i
$935$	2.10375e10			0.841691
$936$	−2.38684e10	+	2.93835e10i	−0.951390	+	1.17122i
$937$	−1.79900e10			−0.714400			−0.357200	−	0.934028i	$-0.616269\pi$
$937$	−1.79900e10			−0.714400			−0.357200	+	0.934028i	$0.616269\pi$
$938$	1.42966e10	+	8.88904e9i	0.565617	+	0.351678i
$939$	2.39997e9	+	7.21673e8i	0.0945967	+	0.0284453i
$940$	3.35777e9	+	6.80690e9i	0.131857	+	0.267302i
$941$	2.25896e10	+	3.91264e10i	0.883782	+	1.53076i	0.847103	+	0.531428i	$0.178344\pi$
$941$	2.25896e10	+	3.91264e10i	0.883782	+	1.53076i	0.0366787	+	0.999327i	$0.488322\pi$
$942$	4.62730e9	−	9.32373e8i	0.180364	−	0.0363422i
$943$	−5.16432e10	−	2.98162e10i	−2.00550	−	1.15787i
$944$	4.23900e9	−	3.22561e10i	0.164007	−	1.24798i
$945$	1.04189e10	−	8.67814e9i	0.401615	−	0.334515i
$946$	9.16887e8	−	2.80576e10i	0.0352125	−	1.07754i
$947$	−5.54383e9	−	3.20073e9i	−0.212121	−	0.122468i	0.390175	−	0.920741i	$-0.372414\pi$
$947$	−5.54383e9	−	3.20073e9i	−0.212121	−	0.122468i	−0.602297	+	0.798272i	$0.705748\pi$
$948$	−9.41328e9	+	1.57871e9i	−0.358849	+	0.0601830i
$949$	6.29066e10	−	3.63191e10i	2.38926	−	1.37944i
$950$	9.11625e9	+	1.70529e10i	0.344972	+	0.645307i
$951$	−2.13746e10	−	6.42736e9i	−0.805871	−	0.242326i
$952$	1.23888e10	−	1.72949e10i	0.465373	−	0.649665i
$953$		−	1.05932e10i		−	0.396461i	−0.980155	−	0.198231i	$-0.936481\pi$
$953$		−	1.05932e10i		−	0.396461i	0.980155	−	0.198231i	$-0.0635195\pi$
$954$	8.91684e8	−	9.53272e9i	0.0332500	−	0.355465i
$955$	−5.42418e8			−0.0201522
$956$	5.53518e9	−	8.28606e9i	0.204894	−	0.306722i
$957$	−3.76336e10	−	3.99862e10i	−1.38798	−	1.47475i
$958$	4.68219e9	+	8.75854e9i	0.172056	+	0.321849i
$959$	−1.01379e10	−	1.75594e10i	−0.371180	−	0.642903i
$960$	1.51234e10	−	9.46255e9i	0.551696	−	0.345191i
$961$	−3.03435e9	+	5.25565e9i	−0.110289	+	0.191027i
$962$	−3.78241e10	−	1.23604e9i	−1.36979	−	0.0447631i
$963$	1.25607e10	+	2.51622e10i	0.453232	+	0.907939i
$964$	−9.54511e9	−	6.24510e8i	−0.343171	−	0.0224528i
$965$	−4.08995e9	+	7.08401e9i	−0.146512	+	0.253766i
$966$	−1.09323e10	+	3.24700e10i	−0.390202	+	1.15894i
$967$	−3.28579e10	+	1.89705e10i	−1.16855	+	0.674663i	−0.953338	−	0.301904i	$-0.902378\pi$
$967$	−3.28579e10	+	1.89705e10i	−1.16855	+	0.674663i	−0.215212	+	0.976567i	$0.569044\pi$
$968$	−8.03386e9	−	1.77229e10i	−0.284682	−	0.628017i
$969$	3.48169e10	−	8.20722e9i	1.22930	−	0.289776i
$970$	9.68011e9	−	1.55689e10i	0.340549	−	0.547717i
$971$		−	4.79317e10i		−	1.68018i	−0.542448	−	0.840089i	$-0.682503\pi$
$971$		−	4.79317e10i		−	1.68018i	0.542448	−	0.840089i	$-0.317497\pi$
$972$	1.28689e9	+	2.86018e10i	0.0449478	+	0.998989i
$973$			1.92787e9i			0.0670938i
$974$	−3.85925e10	−	2.39953e10i	−1.33828	−	0.832088i
$975$	2.45033e10	−	5.77605e9i	0.846660	−	0.199579i
$976$	1.15289e10	−	4.77856e9i	0.396930	−	0.164521i
$977$	1.09208e10	−	6.30514e9i	0.374649	−	0.216304i	−0.300839	−	0.953675i	$-0.597267\pi$
$977$	1.09208e10	−	6.30514e9i	0.374649	−	0.216304i	0.675487	+	0.737371i	$0.263933\pi$
$978$	−4.38544e10	−	1.47653e10i	−1.49909	−	0.504725i
$979$	3.40965e9	−	5.90568e9i	0.116137	−	0.201155i
$980$	−6.79157e9	−	4.44354e8i	−0.230504	−	0.0150813i
$981$	−8.81433e9	−	1.76573e10i	−0.298090	−	0.597150i
$982$	7.89397e8	−	2.41563e10i	0.0266015	−	0.814030i
$983$	−8.76196e9	+	1.51762e10i	−0.294215	+	0.509595i	−0.974802	−	0.223072i	$-0.928391\pi$
$983$	−8.76196e9	+	1.51762e10i	−0.294215	+	0.509595i	0.680587	+	0.732667i	$0.261725\pi$
$984$	−2.77655e10	−	3.59907e10i	−0.929014	−	1.20422i
$985$	−2.55681e8	−	4.42853e8i	−0.00852456	−	0.0147650i
$986$	−4.11527e10	+	2.19996e10i	−1.36719	+	0.730880i
$987$	−7.61521e9	−	8.09126e9i	−0.252099	−	0.267859i
$988$	−4.82803e10	−	3.22518e10i	−1.59265	−	1.06391i
$989$	3.84194e10			1.26288
$990$	−2.57131e10	−	2.40518e9i	−0.842230	−	0.0787816i
$991$			2.48465e10i			0.810976i	0.914100	+	0.405488i	$0.132898\pi$
$991$			2.48465e10i			0.810976i	−0.914100	+	0.405488i	$0.867102\pi$
$992$	−2.09877e10	−	1.72140e10i	−0.682613	−	0.559876i
$993$	3.99411e10	+	1.20103e10i	1.29449	+	0.389253i
$994$	1.57532e10	−	8.42144e9i	0.508764	−	0.271978i
$995$	1.73077e9	−	9.99259e8i	0.0557003	−	0.0321586i
$996$	1.30667e10	−	2.19143e9i	0.419042	−	0.0702780i
$997$	−3.24619e10	−	1.87419e10i	−1.03739	−	0.598935i	−0.118294	−	0.992979i	$-0.537743\pi$
$997$	−3.24619e10	−	1.87419e10i	−1.03739	−	0.598935i	−0.919092	+	0.394044i	$0.871076\pi$
$998$	1.44978e10	+	4.73769e8i	0.461684	+	0.0150872i
$999$	−2.19922e10	+	1.83178e10i	−0.697894	+	0.581293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.8.l.b.11.55	yes	160
8.3	odd	2	inner	72.8.l.b.11.27	✓	160
9.5	odd	6	inner	72.8.l.b.59.27	yes	160
72.59	even	6	inner	72.8.l.b.59.55	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.8.l.b.11.27	✓	160	8.3	odd	2	inner
72.8.l.b.11.55	yes	160	1.1	even	1	trivial
72.8.l.b.59.27	yes	160	9.5	odd	6	inner
72.8.l.b.59.55	yes	160	72.59	even	6	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.97385 - 9.60797i) q^{2} +(-10.7297 - 45.5178i) q^{3} +(-56.6262 - 114.793i) q^{4} +(90.9504 + 157.531i) q^{5} +(-501.432 - 168.826i) q^{6} +(-631.205 - 364.426i) q^{7} +(-1441.21 - 141.694i) q^{8} +(-1956.75 + 976.785i) q^{9} +O(q^{10})\)	\(q+(5.97385 - 9.60797i) q^{2} +(-10.7297 - 45.5178i) q^{3} +(-56.6262 - 114.793i) q^{4} +(90.9504 + 157.531i) q^{5} +(-501.432 - 168.826i) q^{6} +(-631.205 - 364.426i) q^{7} +(-1441.21 - 141.694i) q^{8} +(-1956.75 + 976.785i) q^{9} +(2056.87 + 67.2160i) q^{10} +(4969.22 + 2868.98i) q^{11} +(-4617.55 + 3809.20i) q^{12} +(-10351.5 + 5976.45i) q^{13} +(-7272.12 + 3887.57i) q^{14} +(6194.59 - 5830.12i) q^{15} +(-9970.94 + 13000.6i) q^{16} -20155.9i q^{17} +(-2304.39 + 24635.5i) q^{18} -37949.6 q^{19} +(12933.3 - 19360.8i) q^{20} +(-9815.27 + 32641.3i) q^{21} +(57250.4 - 30605.2i) q^{22} +(44422.2 + 76941.5i) q^{23} +(9014.10 + 67120.9i) q^{24} +(22518.6 - 39003.3i) q^{25} +(-4416.83 + 135159. i) q^{26} +(65456.4 + 78586.3i) q^{27} +(-6090.90 + 93094.1i) q^{28} +(102316. - 177217. i) q^{29} +(-19010.1 - 94345.7i) q^{30} +(-126819. + 73218.7i) q^{31} +(65344.6 + 173464. i) q^{32} +(77271.5 - 256971. i) q^{33} +(-193657. - 120408. i) q^{34} -132579. i q^{35} +(222931. + 169310. i) q^{36} +279848. i q^{37} +(-226705. + 364619. i) q^{38} +(383104. + 407053. i) q^{39} +(-108757. - 239921. i) q^{40} +(-581277. + 335600. i) q^{41} +(254982. + 289299. i) q^{42} +(216217. - 374499. i) q^{43} +(47951.1 - 732891. i) q^{44} +(-331840. - 219409. i) q^{45} +(1.00462e6 + 32829.8i) q^{46} +(-162993. + 282312. i) q^{47} +(698745. + 314363. i) q^{48} +(-146158. - 253154. i) q^{49} +(-240220. - 449358. i) q^{50} +(-917452. + 216266. i) q^{51} +(1.27222e6 + 849859. i) q^{52} -386950. q^{53} +(1.14608e6 - 159441. i) q^{54} +1.04374e6i q^{55} +(858060. + 614651. i) q^{56} +(407188. + 1.72738e6i) q^{57} +(-1.09147e6 - 2.04172e6i) q^{58} +(-1.71965e6 + 992841. i) q^{59} +(-1.02003e6 - 380958. i) q^{60} +(-659668. - 380859. i) q^{61} +(-54111.6 + 1.65587e6i) q^{62} +(1.59108e6 + 96538.8i) q^{63} +(2.05700e6 + 408420. i) q^{64} +(-1.88295e6 - 1.08712e6i) q^{65} +(-2.00736e6 - 2.27753e6i) q^{66} +(-1.02078e6 - 1.76804e6i) q^{67} +(-2.31376e6 + 1.14135e6i) q^{68} +(3.02557e6 - 2.84756e6i) q^{69} +(-1.27381e6 - 792006. i) q^{70} -2.16625e6 q^{71} +(2.95848e6 - 1.13049e6i) q^{72} -6.07704e6 q^{73} +(2.68877e6 + 1.67177e6i) q^{74} +(-2.01696e6 - 606503. i) q^{75} +(2.14894e6 + 4.35635e6i) q^{76} +(-2.09106e6 - 3.62183e6i) q^{77} +(6.19956e6 - 1.24917e6i) q^{78} +(1.38089e6 + 797260. i) q^{79} +(-2.95485e6 - 388319. i) q^{80} +(2.87475e6 - 3.82264e6i) q^{81} +(-248022. + 7.58972e6i) q^{82} +(-1.91684e6 - 1.10669e6i) q^{83} +(4.30280e6 - 721627. i) q^{84} +(3.17517e6 - 1.83318e6i) q^{85} +(-2.30653e6 - 4.31461e6i) q^{86} +(-9.16436e6 - 2.75573e6i) q^{87} +(-6.75515e6 - 4.83890e6i) q^{88} -1.18845e6i q^{89} +(-4.09044e6 + 1.87760e6i) q^{90} +8.71190e6 q^{91} +(6.31690e6 - 9.45627e6i) q^{92} +(4.69348e6 + 4.98689e6i) q^{93} +(1.73875e6 + 3.25252e6i) q^{94} +(-3.45153e6 - 5.97822e6i) q^{95} +(7.19459e6 - 4.83556e6i) q^{96} +(4.45411e6 - 7.71475e6i) q^{97} +(-3.30542e6 - 108017. i) q^{98} +(-1.25259e7 - 760010. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9}+O(q^{10}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9	\( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9} + 252 q^{10} - 26448 q^{11} - 27234 q^{12} - 43488 q^{14} + 32767 q^{16} + 21762 q^{18} - 119452 q^{19} + 130806 q^{20} - 6049 q^{22} - 83379 q^{24} - 1312502 q^{25} - 94428 q^{27} - 32772 q^{28} + 735060 q^{30} + 308907 q^{32} - 1249812 q^{33} - 188203 q^{34} - 1410345 q^{36} + 353415 q^{38} - 477876 q^{40} - 1612476 q^{41} - 39360 q^{42} + 220508 q^{43} + 1082496 q^{46} - 3515619 q^{48} + 9882514 q^{49} - 136947 q^{50} - 2358786 q^{51} + 1089018 q^{52} - 8083005 q^{54} - 1285266 q^{56} - 2070294 q^{57} + 1295022 q^{58} - 8748744 q^{59} - 3070044 q^{60} + 16058050 q^{64} - 6 q^{65} - 19546374 q^{66} + 3851300 q^{67} + 10545975 q^{68} + 979920 q^{70} + 12593427 q^{72} - 9731236 q^{73} + 13246572 q^{74} + 8347746 q^{75} - 4009903 q^{76} - 9123732 q^{78} - 6855198 q^{81} + 21020522 q^{82} - 14348826 q^{83} + 44644836 q^{84} + 80099985 q^{86} + 10463891 q^{88} + 7437678 q^{90} - 3294180 q^{91} - 57890184 q^{92} - 1609122 q^{94} + 69780834 q^{96} + 9938888 q^{97} - 16049670 q^{99}+O(q^{100}) \) 160 * q - 3 * q^2 - 90 * q^3 - 257 * q^4 - 459 * q^6 + 3018 * q^9 + 252 * q^10 - 26448 * q^11 - 27234 * q^12 - 43488 * q^14 + 32767 * q^16 + 21762 * q^18 - 119452 * q^19 + 130806 * q^20 - 6049 * q^22 - 83379 * q^24 - 1312502 * q^25 - 94428 * q^27 - 32772 * q^28 + 735060 * q^30 + 308907 * q^32 - 1249812 * q^33 - 188203 * q^34 - 1410345 * q^36 + 353415 * q^38 - 477876 * q^40 - 1612476 * q^41 - 39360 * q^42 + 220508 * q^43 + 1082496 * q^46 - 3515619 * q^48 + 9882514 * q^49 - 136947 * q^50 - 2358786 * q^51 + 1089018 * q^52 - 8083005 * q^54 - 1285266 * q^56 - 2070294 * q^57 + 1295022 * q^58 - 8748744 * q^59 - 3070044 * q^60 + 16058050 * q^64 - 6 * q^65 - 19546374 * q^66 + 3851300 * q^67 + 10545975 * q^68 + 979920 * q^70 + 12593427 * q^72 - 9731236 * q^73 + 13246572 * q^74 + 8347746 * q^75 - 4009903 * q^76 - 9123732 * q^78 - 6855198 * q^81 + 21020522 * q^82 - 14348826 * q^83 + 44644836 * q^84 + 80099985 * q^86 + 10463891 * q^88 + 7437678 * q^90 - 3294180 * q^91 - 57890184 * q^92 - 1609122 * q^94 + 69780834 * q^96 + 9938888 * q^97 - 16049670 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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