LMFDB - Embedded newform 72.7.p.b.43.4

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			43.4
Character	$\chi$	$=$	72.43
Dual form			72.7.p.b.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.92579 - 1.08711i) q^{2} +(-6.90289 - 26.1027i) q^{3} +(61.6364 + 17.2324i) q^{4} +(42.4034 - 24.4816i) q^{5} +(26.3344 + 214.389i) q^{6} +(-225.391 - 130.130i) q^{7} +(-469.784 - 203.586i) q^{8} +(-633.700 + 360.368i) q^{9} +O(q^{10})$	\(q+(-7.92579 - 1.08711i) q^{2} +(-6.90289 - 26.1027i) q^{3} +(61.6364 + 17.2324i) q^{4} +(42.4034 - 24.4816i) q^{5} +(26.3344 + 214.389i) q^{6} +(-225.391 - 130.130i) q^{7} +(-469.784 - 203.586i) q^{8} +(-633.700 + 360.368i) q^{9} +(-362.695 + 147.939i) q^{10} +(1013.95 - 1756.20i) q^{11} +(24.3423 - 1727.83i) q^{12} +(2836.36 - 1637.57i) q^{13} +(1644.94 + 1276.41i) q^{14} +(-931.742 - 937.849i) q^{15} +(3502.09 + 2124.28i) q^{16} -5091.86 q^{17} +(5414.34 - 2167.30i) q^{18} -11320.0 q^{19} +(3035.47 - 778.247i) q^{20} +(-1840.88 + 6781.59i) q^{21} +(-9945.50 + 12817.0i) q^{22} +(15901.3 - 9180.60i) q^{23} +(-2071.27 + 13667.9i) q^{24} +(-6613.80 + 11455.4i) q^{25} +(-24260.6 + 9895.63i) q^{26} +(13780.9 + 14053.7i) q^{27} +(-11649.9 - 11904.8i) q^{28} +(-15465.1 - 8928.76i) q^{29} +(6365.25 + 8446.10i) q^{30} +(-31033.1 + 17917.0i) q^{31} +(-25447.5 - 20643.8i) q^{32} +(-52840.8 - 14343.8i) q^{33} +(40357.1 + 5535.41i) q^{34} -12743.1 q^{35} +(-45269.0 + 11291.6i) q^{36} +86927.3i q^{37} +(89719.7 + 12306.0i) q^{38} +(-62324.1 - 62732.6i) q^{39} +(-24904.5 + 2868.34i) q^{40} +(34572.7 + 59881.7i) q^{41} +(21962.8 - 51748.2i) q^{42} +(-13530.7 + 23435.9i) q^{43} +(92759.5 - 90773.4i) q^{44} +(-18048.7 + 30794.8i) q^{45} +(-136010. + 55477.1i) q^{46} +(-49394.0 - 28517.6i) q^{47} +(31275.0 - 106078. i) q^{48} +(-24957.0 - 43226.8i) q^{49} +(64872.9 - 83603.5i) q^{50} +(35148.6 + 132911. i) q^{51} +(203042. - 52056.8i) q^{52} +20816.2i q^{53} +(-93946.9 - 126368. i) q^{54} -99292.1i q^{55} +(79392.6 + 107019. i) q^{56} +(78140.5 + 295481. i) q^{57} +(112866. + 87579.7i) q^{58} +(-1221.88 - 2116.36i) q^{59} +(-41267.8 - 73861.8i) q^{60} +(-157808. - 91110.4i) q^{61} +(265440. - 108270. i) q^{62} +(189725. + 1239.45i) q^{63} +(179250. + 191283. i) q^{64} +(80180.8 - 138877. i) q^{65} +(403212. + 171130. i) q^{66} +(31505.5 + 54569.1i) q^{67} +(-313844. - 87745.0i) q^{68} +(-349403. - 351693. i) q^{69} +(101000. + 13853.2i) q^{70} -555937. i q^{71} +(371068. - 40282.7i) q^{72} -462585. q^{73} +(94499.4 - 688968. i) q^{74} +(344672. + 93562.3i) q^{75} +(-697722. - 195070. i) q^{76} +(-457069. + 263889. i) q^{77} +(425771. + 564958. i) q^{78} +(299910. + 173153. i) q^{79} +(200506. + 4340.07i) q^{80} +(271711. - 456730. i) q^{81} +(-208918. - 512194. i) q^{82} +(18478.6 - 32005.8i) q^{83} +(-230328. + 386270. i) q^{84} +(-215912. + 124657. i) q^{85} +(132719. - 171039. i) q^{86} +(-126311. + 465314. i) q^{87} +(-833873. + 618612. i) q^{88} -58224.1 q^{89} +(176527. - 224453. i) q^{90} -852387. q^{91} +(1.13830e6 - 291842. i) q^{92} +(681900. + 686369. i) q^{93} +(360485. + 279721. i) q^{94} +(-480005. + 277131. i) q^{95} +(-363197. + 806750. i) q^{96} +(-111119. + 192463. i) q^{97} +(150812. + 369738. i) q^{98} +(-9657.56 + 1.47830e6i) 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 $

$2$	−7.92579	−	1.08711i	−0.990724	−	0.135889i
$2$	−7.92579	−	1.08711i	−0.990724	−	0.135889i
$3$	−6.90289	−	26.1027i	−0.255663	−	0.966766i
$3$	−6.90289	−	26.1027i	−0.255663	−	0.966766i
$4$	61.6364	+	17.2324i	0.963069	+	0.269256i
$5$	42.4034	−	24.4816i	0.339227	−	0.195853i	−0.320703	−	0.947180i	$-0.603919\pi$
$5$	42.4034	−	24.4816i	0.339227	−	0.195853i	0.659930	+	0.751327i	$0.270586\pi$
$6$	26.3344	+	214.389i	0.121919	+	0.992540i
$7$	−225.391	−	130.130i	−0.657117	−	0.379387i	0.134060	−	0.990973i	$-0.457198\pi$
$7$	−225.391	−	130.130i	−0.657117	−	0.379387i	−0.791178	+	0.611586i	$0.790532\pi$
$8$	−469.784	−	203.586i	−0.917547	−	0.397628i
$9$	−633.700	+	360.368i	−0.869273	+	0.494332i
$10$	−362.695	+	147.939i	−0.362695	+	0.147939i
$11$	1013.95	−	1756.20i	0.761792	−	1.31946i	−0.180134	−	0.983642i	$-0.557653\pi$
$11$	1013.95	−	1756.20i	0.761792	−	1.31946i	0.941926	−	0.335820i	$-0.109013\pi$
$12$	24.3423	−	1727.83i	0.0140870	−	0.999901i
$13$	2836.36	−	1637.57i	1.29101	−	0.745367i	0.312180	−	0.950023i	$-0.398941\pi$
$13$	2836.36	−	1637.57i	1.29101	−	0.745367i	0.978834	+	0.204656i	$0.0656076\pi$
$14$	1644.94	+	1276.41i	0.599468	+	0.465163i
$15$	−931.742	−	937.849i	−0.276072	−	0.277881i
$16$	3502.09	+	2124.28i	0.855002	+	0.518624i
$17$	−5091.86			−1.03641			−0.518203	−	0.855258i	$-0.673399\pi$
$17$	−5091.86			−1.03641			−0.518203	+	0.855258i	$0.673399\pi$
$18$	5414.34	−	2167.30i	0.928384	−	0.371622i
$19$	−11320.0			−1.65038			−0.825190	−	0.564855i	$-0.808932\pi$
$19$	−11320.0			−1.65038			−0.825190	+	0.564855i	$0.808932\pi$
$20$	3035.47	−	778.247i	0.379434	−	0.0972809i
$21$	−1840.88	+	6781.59i	−0.198778	+	0.732274i
$22$	−9945.50	+	12817.0i	−0.934025	+	1.20370i
$23$	15901.3	−	9180.60i	1.30692	−	0.754549i	0.325336	−	0.945598i	$-0.394522\pi$
$23$	15901.3	−	9180.60i	1.30692	−	0.754549i	0.981580	+	0.191050i	$0.0611891\pi$
$24$	−2071.27	+	13667.9i	−0.149831	+	0.988712i
$25$	−6613.80	+	11455.4i	−0.423283	+	0.733148i
$26$	−24260.6	+	9895.63i	−1.38033	+	0.563019i
$27$	13780.9	+	14053.7i	0.700144	+	0.714002i
$28$	−11649.9	−	11904.8i	−0.530697	−	0.542309i
$29$	−15465.1	−	8928.76i	−0.634100	−	0.366098i	0.148238	−	0.988952i	$-0.452640\pi$
$29$	−15465.1	−	8928.76i	−0.634100	−	0.366098i	−0.782338	+	0.622854i	$0.785973\pi$
$30$	6365.25	+	8446.10i	0.235750	+	0.312819i
$31$	−31033.1	+	17917.0i	−1.04169	+	0.601423i	−0.920313	−	0.391183i	$-0.872066\pi$
$31$	−31033.1	+	17917.0i	−1.04169	+	0.601423i	−0.121382	+	0.992606i	$0.538733\pi$
$32$	−25447.5	−	20643.8i	−0.776596	−	0.629998i
$33$	−52840.8	−	14343.8i	−1.47037	−	0.399137i
$34$	40357.1	+	5535.41i	1.02679	+	0.140836i
$35$	−12743.1			−0.297216
$36$	−45269.0	+	11291.6i	−0.970272	+	0.242018i
$37$			86927.3i			1.71613i	0.513538	+	0.858067i	$0.328335\pi$
$37$			86927.3i			1.71613i	−0.513538	+	0.858067i	$0.671665\pi$
$38$	89719.7	+	12306.0i	1.63507	+	0.224268i
$39$	−62324.1	−	62732.6i	−1.05066	−	1.05755i
$40$	−24904.5	+	2868.34i	−0.389134	+	0.0448178i
$41$	34572.7	+	59881.7i	0.501628	+	0.868846i	0.999998	+	0.00188109i	$0.000598771\pi$
$41$	34572.7	+	59881.7i	0.501628	+	0.868846i	−0.498370	+	0.866964i	$0.666068\pi$
$42$	21962.8	−	51748.2i	0.296442	−	0.698470i
$43$	−13530.7	+	23435.9i	−0.170183	+	0.294765i	−0.938484	−	0.345324i	$-0.887769\pi$
$43$	−13530.7	+	23435.9i	−0.170183	+	0.294765i	0.768301	+	0.640089i	$0.221102\pi$
$44$	92759.5	−	90773.4i	1.08893	−	1.06562i
$45$	−18048.7	+	30794.8i	−0.198065	+	0.337941i
$46$	−136010.	+	55477.1i	−1.39733	+	0.569955i
$47$	−49394.0	−	28517.6i	−0.475752	−	0.274675i	0.242893	−	0.970053i	$-0.421904\pi$
$47$	−49394.0	−	28517.6i	−0.475752	−	0.274675i	−0.718644	+	0.695378i	$0.755237\pi$
$48$	31275.0	−	106078.i	0.282796	−	0.959180i
$49$	−24957.0	−	43226.8i	−0.212131	−	0.367422i
$50$	64872.9	−	83603.5i	0.518983	−	0.668828i
$51$	35148.6	+	132911.i	0.264970	+	1.00196i
$52$	203042.	−	52056.8i	1.44403	−	0.370226i
$53$			20816.2i			0.139821i	0.997553	+	0.0699106i	$0.0222714\pi$
$53$			20816.2i			0.139821i	−0.997553	+	0.0699106i	$0.977729\pi$
$54$	−93946.9	−	126368.i	−0.596625	−	0.802520i
$55$		−	99292.1i		−	0.596797i
$56$	79392.6	+	107019.i	0.452081	+	0.609394i
$57$	78140.5	+	295481.i	0.421941	+	1.59553i
$58$	112866.	+	87579.7i	0.578470	+	0.448869i
$59$	−1221.88	−	2116.36i	−0.00594940	−	0.0103047i	0.863035	−	0.505143i	$-0.168560\pi$
$59$	−1221.88	−	2116.36i	−0.00594940	−	0.0103047i	−0.868985	+	0.494839i	$0.835227\pi$
$60$	−41267.8	−	73861.8i	−0.191055	−	0.341953i
$61$	−157808.	−	91110.4i	−0.695247	−	0.401401i	0.110328	−	0.993895i	$-0.464810\pi$
$61$	−157808.	−	91110.4i	−0.695247	−	0.401401i	−0.805575	+	0.592494i	$0.798143\pi$
$62$	265440.	−	108270.i	1.11376	−	0.454290i
$63$	189725.	+	1239.45i	0.758758	+	0.00495687i
$64$	179250.	+	191283.i	0.683783	+	0.729685i
$65$	80180.8	−	138877.i	0.291965	−	0.505698i
$66$	403212.	+	171130.i	1.40250	+	0.595242i
$67$	31505.5	+	54569.1i	0.104752	+	0.181436i	0.913637	−	0.406531i	$-0.133262\pi$
$67$	31505.5	+	54569.1i	0.104752	+	0.181436i	−0.808885	+	0.587967i	$0.799928\pi$
$68$	−313844.	−	87745.0i	−0.998130	−	0.279059i
$69$	−349403.	−	351693.i	−1.06360	−	1.07057i
$70$	101000.	+	13853.2i	0.294459	+	0.0403883i
$71$		−	555937.i		−	1.55328i	−0.629942	−	0.776642i	$-0.716921\pi$
$71$		−	555937.i		−	1.55328i	0.629942	−	0.776642i	$-0.283079\pi$
$72$	371068.	−	40282.7i	0.994159	−	0.107925i
$73$	−462585.			−1.18911			−0.594556	−	0.804054i	$-0.702672\pi$
$73$	−462585.			−1.18911			−0.594556	+	0.804054i	$0.702672\pi$
$74$	94499.4	−	688968.i	0.233203	−	1.70022i
$75$	344672.	+	93562.3i	0.817000	+	0.221777i
$76$	−697722.	−	195070.i	−1.58943	−	0.444375i
$77$	−457069.	+	263889.i	−1.00117	+	0.578028i
$78$	425771.	+	564958.i	0.897205	+	1.19051i
$79$	299910.	+	173153.i	0.608289	+	0.351196i	0.772295	−	0.635264i	$-0.219109\pi$
$79$	299910.	+	173153.i	0.608289	+	0.351196i	−0.164007	+	0.986459i	$0.552442\pi$
$80$	200506.	+	4340.07i	0.391614	+	0.00847670i
$81$	271711.	−	456730.i	0.511272	−	0.859419i
$82$	−208918.	−	512194.i	−0.378909	−	0.928952i
$83$	18478.6	−	32005.8i	0.0323172	−	0.0559751i	−0.849414	−	0.527726i	$-0.823045\pi$
$83$	18478.6	−	32005.8i	0.0323172	−	0.0559751i	0.881732	+	0.471751i	$0.156378\pi$
$84$	−230328.	+	386270.i	−0.388606	+	0.651708i
$85$	−215912.	+	124657.i	−0.351577	+	0.202983i
$86$	132719.	−	171039.i	0.208659	−	0.268905i
$87$	−126311.	+	465314.i	−0.191815	+	0.706624i
$88$	−833873.	+	618612.i	−1.22364	+	0.907758i
$89$	−58224.1			−0.0825910			−0.0412955	−	0.999147i	$-0.513149\pi$
$89$	−58224.1			−0.0825910			−0.0412955	+	0.999147i	$0.513149\pi$
$90$	176527.	−	224453.i	0.242150	−	0.307891i
$91$	−852387.			−1.13113
$92$	1.13830e6	−	291842.i	1.46182	−	0.374787i
$93$	681900.	+	686369.i	0.847758	+	0.853314i
$94$	360485.	+	279721.i	0.434014	+	0.336777i
$95$	−480005.	+	277131.i	−0.559854	+	0.323232i
$96$	−363197.	+	806750.i	−0.410514	+	0.911854i
$97$	−111119.	+	192463.i	−0.121751	+	0.210878i	−0.920458	−	0.390841i	$-0.872184\pi$
$97$	−111119.	+	192463.i	−0.121751	+	0.210878i	0.798707	+	0.601720i	$0.205518\pi$
$98$	150812.	+	369738.i	0.160235	+	0.392840i
$99$	−9657.56	+	1.47830e6i	−0.00995318	+	1.52355i
$100$	−605055.	+	592100.i	−0.605055	+	0.592100i
$101$	−1.27902e6	−	738441.i	−1.24140	−	0.716724i	−0.272023	−	0.962291i	$-0.587693\pi$
$101$	−1.27902e6	−	738441.i	−1.24140	−	0.716724i	−0.969380	+	0.245567i	$0.921026\pi$
$102$	−134091.	−	1.09164e6i	−0.126357	−	1.02867i
$103$	1.23218e6	−	711401.i	1.12762	−	0.651033i	0.184286	−	0.982873i	$-0.441003\pi$
$103$	1.23218e6	−	711401.i	1.12762	−	0.651033i	0.943336	+	0.331840i	$0.107669\pi$
$104$	−1.66586e6	+	191863.i	−1.48094	+	0.170565i
$105$	87964.5	+	332630.i	0.0759871	+	0.287339i
$106$	22629.4	−	164985.i	0.0190001	−	0.138524i
$107$	360274.			0.294091			0.147046	−	0.989130i	$-0.453024\pi$
$107$	360274.			0.294091			0.147046	+	0.989130i	$0.453024\pi$
$108$	607228.	+	1.10370e6i	0.482037	+	0.876151i
$109$		−	150690.i		−	0.116360i	−0.998306	−	0.0581800i	$-0.981470\pi$
$109$		−	150690.i		−	0.116360i	0.998306	−	0.0581800i	$-0.0185297\pi$
$110$	−107941.	+	786968.i	−0.0810978	+	0.591261i
$111$	2.26904e6	−	600050.i	1.65910	−	0.438751i
$112$	−512908.	−	934521.i	−0.365078	−	0.665174i
$113$	−544893.	−	943782.i	−0.377638	−	0.654089i	0.613080	−	0.790021i	$-0.289930\pi$
$113$	−544893.	−	943782.i	−0.377638	−	0.654089i	−0.990718	+	0.135932i	$0.956597\pi$
$114$	−298105.	−	2.42687e6i	−0.201212	−	1.63807i
$115$	449512.	−	778577.i	0.295561	−	0.511927i
$116$	−799347.	−	816837.i	−0.512108	−	0.523313i
$117$	−1.20727e6	+	2.05986e6i	−0.753785	+	1.28612i
$118$	7383.67	+	18102.2i	0.00449393	+	0.0110175i
$119$	1.14766e6	+	662603.i	0.681041	+	0.393199i
$120$	246785.	+	630276.i	0.142815	+	0.364743i
$121$	−1.17039e6	−	2.02717e6i	−0.660654	−	1.14429i
$122$	1.15170e6	+	893676.i	0.634252	+	0.492154i
$123$	1.32442e6	−	1.31580e6i	0.711723	−	0.707088i
$124$	−2.22152e6	+	569563.i	−1.16516	+	0.298729i
$125$			1.41272e6i			0.723311i
$126$	−1.50237e6	−	216075.i	−0.751046	−	0.108017i
$127$		−	410307.i		−	0.200308i	−0.994972	−	0.100154i	$-0.968066\pi$
$127$		−	410307.i		−	0.200308i	0.994972	−	0.100154i	$-0.0319335\pi$
$128$	−1.21275e6	−	1.71093e6i	−0.578285	−	0.815835i
$129$	705140.	+	191413.i	0.328478	+	0.0891664i
$130$	−786471.	+	1.01355e6i	−0.357975	+	0.461332i
$131$	901804.	+	1.56197e6i	0.401142	+	0.694799i	0.993864	−	0.110609i	$-0.0352800\pi$
$131$	901804.	+	1.56197e6i	0.401142	+	0.694799i	−0.592722	+	0.805407i	$0.701947\pi$
$132$	−3.00974e6	−	1.79467e6i	−1.30860	−	0.780304i
$133$	2.55142e6	+	1.47306e6i	1.08449	+	0.626133i
$134$	−190383.	−	466753.i	−0.0791252	−	0.193987i
$135$	928416.	+	258545.i	0.377347	+	0.105084i
$136$	2.39208e6	+	1.03663e6i	0.950951	+	0.412105i
$137$	−151934.	+	263158.i	−0.0590873	+	0.102342i	−0.894056	−	0.447955i	$-0.852152\pi$
$137$	−151934.	+	263158.i	−0.0590873	+	0.102342i	0.834969	+	0.550298i	$0.185486\pi$
$138$	2.38697e6	+	3.16728e6i	0.908258	+	1.20517i
$139$	−2.11663e6	−	3.66611e6i	−0.788135	−	1.36509i	−0.927109	−	0.374793i	$-0.877714\pi$
$139$	−2.11663e6	−	3.66611e6i	−0.788135	−	1.36509i	0.138974	−	0.990296i	$-0.455620\pi$
$140$	−785442.	−	219595.i	−0.286240	−	0.0800273i
$141$	−403425.	+	1.48617e6i	−0.143915	+	0.530165i
$142$	−604364.	+	4.40625e6i	−0.211073	+	1.53888i
$143$		−	6.64163e6i		−	2.27126i
$144$	−2.98480e6	−	84118.8i	−0.999603	−	0.0281712i
$145$	−874362.			−0.286805
$146$	3.66635e6	+	502880.i	1.17808	+	0.161587i
$147$	−956060.	+	949835.i	−0.300977	+	0.299017i
$148$	−1.49797e6	+	5.35789e6i	−0.462079	+	1.65275i
$149$	−2.29842e6	+	1.32699e6i	−0.694816	+	0.401152i	−0.805414	−	0.592713i	$-0.798057\pi$
$149$	−2.29842e6	+	1.32699e6i	−0.694816	+	0.401152i	0.110597	+	0.993865i	$0.464724\pi$
$150$	−2.63009e6	−	1.11625e6i	−0.779285	−	0.330741i
$151$	328136.	+	189450.i	0.0953067	+	0.0550253i	0.546896	−	0.837201i	$-0.315809\pi$
$151$	328136.	+	189450.i	0.0953067	+	0.0550253i	−0.451589	+	0.892226i	$0.649143\pi$
$152$	5.31794e6	+	2.30458e6i	1.51430	+	0.656238i
$153$	3.22672e6	−	1.83494e6i	0.900920	−	0.512329i
$154$	3.90951e6	−	1.59464e6i	1.07043	−	0.436618i
$155$	−877274.	+	1.51948e6i	−0.235581	+	0.408038i
$156$	−2.76040e6	−	4.94060e6i	−0.727107	−	1.30139i
$157$	1.40996e6	−	814040.i	0.364340	−	0.210352i	−0.306643	−	0.951825i	$-0.599206\pi$
$157$	1.40996e6	−	814040.i	0.364340	−	0.210352i	0.670983	+	0.741473i	$0.265872\pi$
$158$	−2.18879e6	−	1.69841e6i	−0.554923	−	0.430598i
$159$	543358.	−	143692.i	0.135174	−	0.0357471i
$160$	−1.58445e6	−	252371.i	−0.386830	−	0.0616139i
$161$	−4.77867e6			−1.14506
$162$	−2.65004e6	+	3.32457e6i	−0.623315	+	0.781971i
$163$	7.35394e6			1.69808			0.849038	−	0.528331i	$-0.177182\pi$
$163$	7.35394e6			1.69808			0.849038	+	0.528331i	$0.177182\pi$
$164$	1.09903e6	+	4.28666e6i	0.249160	+	0.971824i
$165$	−2.59179e6	+	685402.i	−0.576963	+	0.152579i
$166$	−181251.	+	233583.i	−0.0396238	+	0.0510643i
$167$	981167.	−	566477.i	0.210665	−	0.121628i	−0.390955	−	0.920410i	$-0.627855\pi$
$167$	981167.	−	566477.i	0.210665	−	0.121628i	0.601621	+	0.798782i	$0.294522\pi$
$168$	2.24545e6	−	2.81110e6i	0.473561	−	0.592856i
$169$	2.94988e6	−	5.10933e6i	0.611144	−	1.05853i
$170$	1.84679e6	−	753286.i	0.375899	−	0.153325i
$171$	7.17346e6	−	4.07935e6i	1.43463	−	0.815836i
$172$	−1.23784e6	+	1.21134e6i	−0.243265	+	0.238056i
$173$	3.80453e6	+	2.19655e6i	0.734789	+	0.424231i	0.820172	−	0.572118i	$-0.193878\pi$
$173$	3.80453e6	+	2.19655e6i	0.734789	+	0.424231i	−0.0853826	+	0.996348i	$0.527211\pi$
$174$	1.50696e6	−	3.55067e6i	0.286058	−	0.674004i
$175$	2.98139e6	−	1.72130e6i	0.556294	−	0.321176i
$176$	7.28160e6	−	3.99648e6i	1.33564	−	0.733060i
$177$	−46808.2	+	46503.4i	−0.00844116	+	0.00838619i
$178$	461472.	+	63295.9i	0.0818249	+	0.0112232i
$179$	−1.89686e6			−0.330732			−0.165366	−	0.986232i	$-0.552880\pi$
$179$	−1.89686e6			−0.330732			−0.165366	+	0.986232i	$0.552880\pi$
$180$	−1.64312e6	+	1.58706e6i	−0.281743	+	0.272130i
$181$		−	2.01285e6i		−	0.339450i	−0.985491	−	0.169725i	$-0.945712\pi$
$181$		−	2.01285e6i		−	0.339450i	0.985491	−	0.169725i	$-0.0542880\pi$
$182$	6.75584e6	+	926637.i	1.12064	+	0.153708i
$183$	−1.28890e6	+	4.74813e6i	−0.210312	+	0.774764i
$184$	−9.33919e6	+	1.07563e6i	−1.49919	+	0.172666i
$185$	2.12812e6	+	3.68602e6i	0.336110	+	0.582160i
$186$	−4.65844e6	−	6.18132e6i	−0.723938	−	0.960599i
$187$	−5.16287e6	+	8.94235e6i	−0.789526	+	1.36750i
$188$	−2.55304e6	−	2.60890e6i	−0.384224	−	0.392630i
$189$	−1.27730e6	−	4.96089e6i	−0.189194	−	0.734809i
$190$	4.10569e6	−	1.67467e6i	0.598585	−	0.244156i
$191$	−5.05904e6	−	2.92084e6i	−0.726052	−	0.419186i	0.0909242	−	0.995858i	$-0.471018\pi$
$191$	−5.05904e6	−	2.92084e6i	−0.726052	−	0.419186i	−0.816976	+	0.576672i	$0.804351\pi$
$192$	3.75565e6	−	5.99930e6i	0.530617	−	0.847612i
$193$	841533.	+	1.45758e6i	0.117057	+	0.202749i	0.918600	−	0.395188i	$-0.129321\pi$
$193$	841533.	+	1.45758e6i	0.117057	+	0.202749i	−0.801543	+	0.597937i	$0.795987\pi$
$194$	1.08993e6	−	1.40462e6i	0.149277	−	0.192378i
$195$	−4.17855e6	−	1.13428e6i	−0.563536	−	0.152974i
$196$	−793359.	−	3.09441e6i	−0.105366	−	0.410970i
$197$		−	6.99567e6i		−	0.915020i	−0.889204	−	0.457510i	$-0.848741\pi$
$197$		−	6.99567e6i		−	0.915020i	0.889204	−	0.457510i	$-0.151259\pi$
$198$	1.68362e6	−	1.17062e7i	0.216894	−	1.50807i
$199$		−	1.93692e6i		−	0.245783i	−0.992420	−	0.122891i	$-0.960783\pi$
$199$		−	1.93692e6i		−	0.245783i	0.992420	−	0.122891i	$-0.0392167\pi$
$200$	5.43922e6	−	4.03510e6i	0.679903	−	0.504388i
$201$	1.20692e6	−	1.19906e6i	0.148625	−	0.147657i
$202$	9.33447e6	+	7.24317e6i	1.13249	+	0.878768i
$203$	2.32379e6	+	4.02493e6i	0.277786	+	0.481139i
$204$	−123948.	+	8.79787e6i	−0.0145999	+	1.03630i
$205$	2.93200e6	+	1.69279e6i	0.340332	+	0.196491i
$206$	−1.05394e7	+	4.29890e6i	−1.20563	+	0.491763i
$207$	−6.76824e6	+	1.15480e7i	−0.763070	+	1.30196i
$208$	1.34118e7	+	290306.i	1.49038	+	0.0322602i
$209$	−1.14778e7	+	1.98802e7i	−1.25725	+	2.17762i
$210$	−335584.	−	2.73199e6i	−0.0362362	−	0.294999i
$211$	−7.52132e6	−	1.30273e7i	−0.800657	−	1.38678i	−0.919184	−	0.393828i	$-0.871151\pi$
$211$	−7.52132e6	−	1.30273e7i	−0.800657	−	1.38678i	0.118527	−	0.992951i	$-0.462183\pi$
$212$	−358712.	+	1.28303e6i	−0.0376477	+	0.134657i
$213$	−1.45115e7	+	3.83757e6i	−1.50166	+	0.397117i
$214$	−2.85546e6	−	391657.i	−0.291363	−	0.0399636i
$215$			1.32502e6i			0.133323i
$216$	−3.61293e6	−	9.40780e6i	−0.358507	−	0.933527i
$217$	9.32613e6			0.912688
$218$	−163816.	+	1.19433e6i	−0.0158120	+	0.115281i
$219$	3.19317e6	+	1.20747e7i	0.304011	+	1.14959i
$220$	1.71104e6	−	6.12001e6i	0.160691	−	0.574756i
$221$	−1.44423e7	+	8.33829e6i	−1.33801	+	0.772503i
$222$	−1.86362e7	+	2.28918e6i	−1.70333	+	0.209229i
$223$	−2.81386e6	−	1.62458e6i	−0.253740	−	0.146497i	0.367736	−	0.929930i	$-0.380133\pi$
$223$	−2.81386e6	−	1.62458e6i	−0.253740	−	0.146497i	−0.621475	+	0.783434i	$0.713466\pi$
$224$	3.04928e6	+	7.96441e6i	0.271302	+	0.708614i
$225$	62994.7	−	9.64272e6i	0.00553040	−	0.846548i
$226$	3.29272e6	+	8.07258e6i	0.285252	+	0.699338i
$227$	−4.40956e6	+	7.63759e6i	−0.376980	+	0.652948i	−0.990621	−	0.136637i	$-0.956371\pi$
$227$	−4.40956e6	+	7.63759e6i	−0.376980	+	0.652948i	0.613641	+	0.789585i	$0.289704\pi$
$228$	−275554.	+	1.95590e7i	−0.0232489	+	1.65022i
$229$	2.04665e7	−	1.18164e7i	1.70427	−	0.983959i	0.762936	−	0.646473i	$-0.223757\pi$
$229$	2.04665e7	−	1.18164e7i	1.70427	−	0.983959i	0.941331	−	0.337486i	$-0.109576\pi$
$230$	−4.40913e6	+	5.68217e6i	−0.362385	+	0.467015i
$231$	1.00433e7	+	1.01091e7i	0.814780	+	0.820121i
$232$	5.44747e6	+	7.34306e6i	0.436246	+	0.588048i
$233$	362258.			0.0286385			0.0143192	−	0.999897i	$-0.495442\pi$
$233$	362258.			0.0286385			0.0143192	+	0.999897i	$0.495442\pi$
$234$	1.18079e7	−	1.50136e7i	0.921561	−	1.17176i
$235$	−2.79263e6			−0.215184
$236$	−38842.4	−	151501.i	−0.00295509	−	0.0115260i
$237$	2.44952e6	−	9.02372e6i	0.184007	−	0.677861i
$238$	−8.37581e6	−	6.49929e6i	−0.621292	−	0.482097i
$239$	−2.60629e6	+	1.50474e6i	−0.190910	+	0.110222i	−0.592409	−	0.805638i	$-0.701823\pi$
$239$	−2.60629e6	+	1.50474e6i	−0.190910	+	0.110222i	0.401498	+	0.915860i	$0.368490\pi$
$240$	−1.27079e6	−	5.26372e6i	−0.0919261	−	0.380767i
$241$	−7.66704e6	+	1.32797e7i	−0.547743	+	0.948718i	0.450686	+	0.892683i	$0.351179\pi$
$241$	−7.66704e6	+	1.32797e7i	−0.547743	+	0.948718i	−0.998429	+	0.0560357i	$0.982154\pi$
$242$	7.07250e6	+	1.73393e7i	0.499030	+	1.22345i
$243$	−1.37975e7	−	3.93963e6i	−0.961570	−	0.274559i
$244$	−8.15665e6	−	8.33512e6i	−0.561491	−	0.573776i
$245$	−2.11652e6	−	1.22198e6i	−0.143921	−	0.0830930i
$246$	−1.19275e7	+	8.98895e6i	−0.801206	+	0.603815i
$247$	−3.21075e7	+	1.85372e7i	−2.13066	+	1.23014i
$248$	1.82265e7	−	2.09921e6i	1.19495	−	0.137626i
$249$	−962993.	−	261408.i	−0.0623771	−	0.0169325i
$250$	1.53578e6	−	1.11969e7i	0.0982897	−	0.716602i
$251$	−2.29302e7			−1.45006			−0.725032	−	0.688715i	$-0.758175\pi$
$251$	−2.29302e7			−1.45006			−0.725032	+	0.688715i	$0.758175\pi$
$252$	1.16726e7	+	3.34581e6i	0.729401	+	0.209074i
$253$		−	3.72345e7i		−	2.29924i
$254$	−446048.	+	3.25201e6i	−0.0272195	+	0.198450i
$255$	4.74430e6	+	4.77540e6i	0.286122	+	0.287998i
$256$	7.75205e6	+	1.48789e7i	0.462058	+	0.886850i
$257$	−3.55002e6	−	6.14881e6i	−0.209137	−	0.362236i	0.742306	−	0.670061i	$-0.233732\pi$
$257$	−3.55002e6	−	6.14881e6i	−0.209137	−	0.362236i	−0.951443	+	0.307825i	$0.900399\pi$
$258$	−5.38071e6	−	2.28366e6i	−0.313315	−	0.132976i
$259$	1.13118e7	−	1.95927e7i	0.651079	−	1.12770i
$260$	7.33524e6	−	7.17818e6i	0.417344	−	0.408408i
$261$	1.30179e7	+	85044.1i	0.732180	+	0.00478325i
$262$	−5.44948e6	−	1.33602e7i	−0.303006	−	0.742864i
$263$	−1.98990e7	−	1.14887e7i	−1.09386	−	0.631543i	−0.159262	−	0.987236i	$-0.550911\pi$
$263$	−1.98990e7	−	1.14887e7i	−1.09386	−	0.631543i	−0.934603	+	0.355694i	$0.884245\pi$
$264$	2.19036e7	+	1.74961e7i	1.19043	+	0.950889i
$265$	509614.	+	882677.i	0.0273844	+	0.0474312i
$266$	−1.86207e7	−	1.44489e7i	−0.989350	−	0.767695i
$267$	401915.	+	1.51981e6i	0.0211154	+	0.0798462i
$268$	1.00153e6	+	3.90636e6i	0.0520306	+	0.202940i
$269$			1.84284e7i			0.946739i	0.880864	+	0.473370i	$0.156962\pi$
$269$			1.84284e7i			0.946739i	−0.880864	+	0.473370i	$0.843038\pi$
$270$	−7.07737e6	−	3.05846e6i	−0.359567	−	0.155386i
$271$			1.08459e6i			0.0544952i	0.999629	+	0.0272476i	$0.00867425\pi$
$271$			1.08459e6i			0.0544952i	−0.999629	+	0.0272476i	$0.991326\pi$
$272$	−1.78322e7	−	1.08166e7i	−0.886130	−	0.537505i
$273$	5.88393e6	+	2.22496e7i	0.289188	+	1.09354i
$274$	1.49028e6	−	1.92057e6i	0.0724464	−	0.0933636i
$275$	1.34121e7	+	2.32304e7i	0.644907	+	1.11701i
$276$	−1.54754e7	−	2.76981e7i	−0.736063	−	1.31742i
$277$	2.07096e7	+	1.19567e7i	0.974390	+	0.562564i	0.900572	−	0.434707i	$-0.143148\pi$
$277$	2.07096e7	+	1.19567e7i	0.974390	+	0.562564i	0.0738182	+	0.997272i	$0.476482\pi$
$278$	1.27905e7	+	3.13578e7i	0.595324	+	1.45953i
$279$	1.32090e7	−	2.25373e7i	0.608215	−	1.03774i
$280$	5.98652e6	+	2.59432e6i	0.272710	+	0.118182i
$281$	1.49840e7	−	2.59530e7i	0.675317	−	1.16968i	−0.301060	−	0.953605i	$-0.597340\pi$
$281$	1.49840e7	−	2.59530e7i	0.675317	−	1.16968i	0.976376	−	0.216077i	$-0.0693264\pi$
$282$	4.81309e6	−	1.13405e7i	0.214623	−	0.505691i
$283$	−2.32948e6	−	4.03477e6i	−0.102778	−	0.178016i	0.810050	−	0.586360i	$-0.199440\pi$
$283$	−2.32948e6	−	4.03477e6i	−0.102778	−	0.178016i	−0.912828	+	0.408344i	$0.866106\pi$
$284$	9.58013e6	−	3.42660e7i	0.418231	−	1.49592i
$285$	1.05473e7	+	1.06164e7i	0.455624	+	0.458610i
$286$	−7.22017e6	+	5.26402e7i	−0.308638	+	2.25019i
$287$		−	1.79958e7i		−	0.761245i
$288$	2.35655e7	+	3.91151e6i	0.986503	+	0.163744i
$289$	1.78951e6			0.0741379
$290$	6.93002e6	+	950526.i	0.284145	+	0.0389736i
$291$	5.79084e6	+	1.57194e6i	0.234997	+	0.0637907i
$292$	−2.85121e7	−	7.97144e6i	−1.14520	−	0.320176i
$293$	2.69579e7	−	1.55642e7i	1.07173	−	0.618761i	0.143074	−	0.989712i	$-0.454301\pi$
$293$	2.69579e7	−	1.55642e7i	1.07173	−	0.618761i	0.928653	+	0.370951i	$0.120968\pi$
$294$	8.61011e6	−	6.48885e6i	0.338818	−	0.255344i
$295$	−103624.	−	59827.3i	−0.00403640	−	0.00233041i
$296$	1.76972e7	−	4.08371e7i	0.682384	−	1.57463i
$297$	3.86543e7	−	9.95246e6i	1.47546	−	0.379893i
$298$	1.96594e7	−	8.01883e6i	0.742883	−	0.303014i
$299$	3.00678e7	−	5.20789e7i	1.12483	−	1.94827i
$300$	1.96320e7	+	1.17064e7i	0.727113	+	0.433569i
$301$	6.09941e6	−	3.52150e6i	0.223660	−	0.129130i
$302$	−2.39479e6	−	1.85826e6i	−0.0869453	−	0.0674660i
$303$	−1.04464e7	+	3.84832e7i	−0.375524	+	1.38339i
$304$	−3.96435e7	−	2.40468e7i	−1.41108	−	0.855927i
$305$	−8.92212e6			−0.314462
$306$	−2.75691e7	+	1.10356e7i	−0.962183	+	0.385152i
$307$	−9.08272e6			−0.313907			−0.156953	−	0.987606i	$-0.550167\pi$
$307$	−9.08272e6			−0.313907			−0.156953	+	0.987606i	$0.550167\pi$
$308$	−3.27195e7	+	8.38877e6i	−1.11984	+	0.287108i
$309$	−2.70751e7	−	2.72526e7i	−0.917687	−	0.923702i
$310$	8.60493e6	−	1.10894e7i	0.288843	−	0.372240i
$311$	1.55566e7	−	8.98162e6i	0.517171	−	0.298589i	−0.218606	−	0.975813i	$-0.570151\pi$
$311$	1.55566e7	−	8.98162e6i	0.517171	−	0.298589i	0.735776	+	0.677225i	$0.236817\pi$
$312$	1.65074e7	+	4.21590e7i	0.543519	+	1.38812i
$313$	−2.10515e7	+	3.64623e7i	−0.686516	+	1.18908i	0.286442	+	0.958097i	$0.407527\pi$
$313$	−2.10515e7	+	3.64623e7i	−0.686516	+	1.18908i	−0.972958	+	0.230982i	$0.925806\pi$
$314$	−1.20600e7	+	4.91913e6i	−0.389545	+	0.158891i
$315$	8.07534e6	−	4.59222e6i	0.258362	−	0.146923i
$316$	1.55015e7	+	1.58407e7i	0.491262	+	0.502011i
$317$	2.95288e7	+	1.70484e7i	0.926974	+	0.535189i	0.885853	−	0.463966i	$-0.153574\pi$
$317$	2.95288e7	+	1.70484e7i	0.926974	+	0.535189i	0.0411206	+	0.999154i	$0.486907\pi$
$318$	−4.46275e6	+	548182.i	−0.138778	+	0.0170468i
$319$	−3.13615e7	+	1.81065e7i	−0.966105	+	0.557781i
$320$	1.22837e7	+	3.72271e6i	0.374869	+	0.113608i
$321$	−2.48693e6	−	9.40413e6i	−0.0751881	−	0.284317i
$322$	3.78748e7	+	5.19493e6i	1.13444	+	0.155601i
$323$	5.76397e7			1.71047
$324$	2.46178e7	−	2.34690e7i	0.723794	−	0.690016i
$325$			4.33223e7i			1.26201i
$326$	−5.82858e7	−	7.99453e6i	−1.68233	−	0.230749i
$327$	−3.93340e6	+	1.04019e6i	−0.112493	+	0.0297489i
$328$	−4.05064e6	−	3.51700e7i	−0.114790	−	0.996668i
$329$	7.42198e6	+	1.28552e7i	0.208417	+	0.360988i
$330$	2.12871e7	−	2.61480e6i	0.592345	−	0.0727607i
$331$	130329.	−	225736.i	0.00359382	−	0.00622468i	−0.864223	−	0.503109i	$-0.832189\pi$
$331$	130329.	−	225736.i	0.00359382	−	0.00622468i	0.867817	+	0.496884i	$0.165523\pi$
$332$	1.69049e6	−	1.65429e6i	0.0461953	−	0.0452062i
$333$	−3.13258e7	−	5.50859e7i	−0.848340	−	1.49179i
$334$	−8.39234e6	+	3.42314e6i	−0.225239	+	0.0918725i
$335$	2.67188e6	+	1.54261e6i	0.0710694	+	0.0410319i
$336$	−2.08530e7	+	1.98392e7i	−0.549731	+	0.523005i
$337$	−1.21805e7	−	2.10972e7i	−0.318254	−	0.551233i	0.661870	−	0.749619i	$-0.269763\pi$
$337$	−1.21805e7	−	2.10972e7i	−0.318254	−	0.551233i	−0.980124	+	0.198386i	$0.936430\pi$
$338$	−2.89345e7	+	3.72887e7i	−0.749317	+	0.965666i
$339$	−2.08739e7	+	2.07380e7i	−0.535803	+	0.532314i
$340$	−1.54562e7	+	3.96273e6i	−0.393248	+	0.100822i
$341$			7.26674e7i			1.83264i
$342$	−6.12901e7	+	2.45338e7i	−1.53219	+	0.613318i
$343$			4.36099e7i			1.08069i
$344$	1.11277e7	−	8.25514e6i	0.273357	−	0.202791i
$345$	−2.34259e7	−	6.35903e6i	−0.570478	−	0.154858i
$346$	−2.77660e7	−	2.15453e7i	−0.670325	−	0.520145i
$347$	−2.86680e7	−	4.96544e7i	−0.686134	−	1.18842i	−0.973079	−	0.230472i	$-0.925973\pi$
$347$	−2.86680e7	−	4.96544e7i	−0.686134	−	1.18842i	0.286945	−	0.957947i	$-0.407360\pi$
$348$	−1.58038e7	+	2.65036e7i	−0.374994	+	0.628880i
$349$	2.04042e7	+	1.17804e7i	0.480002	+	0.277129i	0.720417	−	0.693541i	$-0.243950\pi$
$349$	2.04042e7	+	1.17804e7i	0.480002	+	0.277129i	−0.240415	+	0.970670i	$0.577284\pi$
$350$	−2.55011e7	+	1.04016e7i	−0.594778	+	0.242603i
$351$	6.21016e7	+	1.72940e7i	1.43609	+	0.399922i
$352$	−6.20571e7	+	2.37594e7i	−1.42286	+	0.544762i
$353$	2.03100e7	−	3.51779e7i	0.461727	−	0.799734i	−0.537320	−	0.843378i	$-0.680563\pi$
$353$	2.03100e7	−	3.51779e7i	0.461727	−	0.799734i	0.999047	+	0.0436441i	$0.0138968\pi$
$354$	421546.	−	317691.i	0.00950245	−	0.00716135i
$355$	−1.36103e7	−	2.35736e7i	−0.304215	−	0.526916i
$356$	−3.58872e6	−	1.00334e6i	−0.0795408	−	0.0222381i
$357$	9.37353e6	−	3.45309e7i	0.206015	−	0.758933i
$358$	1.50341e7	+	2.06209e6i	0.327664	+	0.0449426i
$359$		−	7.09984e7i		−	1.53449i	−0.641352	−	0.767247i	$-0.721626\pi$
$359$		−	7.09984e7i		−	1.53449i	0.641352	−	0.767247i	$-0.278374\pi$
$360$	1.47484e7	−	1.07925e7i	0.316109	−	0.231320i
$361$	8.10957e7			1.72376
$362$	−2.18819e6	+	1.59534e7i	−0.0461274	+	0.336301i
$363$	−4.48356e7	+	4.45436e7i	−0.937352	+	0.931249i
$364$	−5.25380e7	−	1.46887e7i	−1.08936	−	0.304564i
$365$	−1.96152e7	+	1.13248e7i	−0.403379	+	0.232891i
$366$	1.53772e7	−	3.62315e7i	0.313643	−	0.738998i
$367$	−1.63847e7	−	9.45973e6i	−0.331468	−	0.191373i	0.325025	−	0.945705i	$-0.394627\pi$
$367$	−1.63847e7	−	9.45973e6i	−0.331468	−	0.191373i	−0.656493	+	0.754332i	$0.727961\pi$
$368$	7.51898e7	+	1.62752e6i	1.50874	+	0.0326576i
$369$	−4.34882e7	−	2.54882e7i	−0.865550	−	0.507293i
$370$	−1.28600e7	−	3.15281e7i	−0.253883	−	0.622433i
$371$	2.70880e6	−	4.69178e6i	0.0530464	−	0.0918790i
$372$	3.02021e7	+	5.40561e7i	0.586689	+	1.05006i
$373$	5.11698e7	−	2.95429e7i	0.986024	−	0.569281i	0.0819404	−	0.996637i	$-0.473888\pi$
$373$	5.11698e7	−	2.95429e7i	0.986024	−	0.569281i	0.904083	+	0.427356i	$0.140555\pi$
$374$	5.06411e7	−	6.52626e7i	0.968030	−	1.24753i
$375$	3.68757e7	−	9.75183e6i	0.699273	−	0.184924i
$376$	1.73987e7	+	2.34530e7i	0.327306	+	0.441200i
$377$	−5.84859e7			−1.09151
$378$	4.73058e6	+	4.07075e7i	0.0875868	+	0.753702i
$379$	−2.52783e7			−0.464334			−0.232167	−	0.972676i	$-0.574582\pi$
$379$	−2.52783e7			−0.464334			−0.232167	+	0.972676i	$0.574582\pi$
$380$	−3.43614e7	+	8.80973e6i	−0.626210	+	0.160550i
$381$	−1.07101e7	+	2.83230e6i	−0.193651	+	0.0512112i
$382$	3.69216e7	+	2.86497e7i	0.662355	+	0.513960i
$383$	1.53948e7	−	8.88817e6i	0.274017	−	0.158204i	−0.356695	−	0.934221i	$-0.616096\pi$
$383$	1.53948e7	−	8.88817e6i	0.274017	−	0.158204i	0.630712	+	0.776017i	$0.282763\pi$
$384$	−3.62884e7	+	4.34664e7i	−0.640876	+	0.767645i
$385$	−1.29209e7	+	2.23796e7i	−0.226417	+	0.392166i
$386$	−5.08527e6	−	1.24673e7i	−0.0884203	−	0.216776i
$387$	128876.	−	1.97274e7i	0.00222352	−	0.340358i
$388$	−1.01655e7	+	9.94789e6i	−0.174035	+	0.170308i
$389$	6.59426e6	+	3.80720e6i	0.112026	+	0.0646780i	0.554966	−	0.831873i	$-0.312731\pi$
$389$	6.59426e6	+	3.80720e6i	0.112026	+	0.0646780i	−0.442940	+	0.896551i	$0.646065\pi$
$390$	3.18852e7	+	1.35326e7i	0.537521	+	0.228133i
$391$	−8.09670e7	+	4.67463e7i	−1.35450	+	0.782019i
$392$	2.92404e6	+	2.53881e7i	0.0485428	+	0.421476i
$393$	3.45466e7	−	3.43216e7i	0.569151	−	0.565445i
$394$	−7.60505e6	+	5.54462e7i	−0.124341	+	0.906532i
$395$	1.69563e7			0.275131
$396$	−2.60699e7	+	9.09507e7i	−0.419811	+	1.46460i
$397$			5.93878e6i			0.0949130i	0.998873	+	0.0474565i	$0.0151115\pi$
$397$			5.93878e6i			0.0949130i	−0.998873	+	0.0474565i	$0.984888\pi$
$398$	−2.10564e6	+	1.53516e7i	−0.0333991	+	0.243503i
$399$	2.08387e7	−	7.67673e7i	0.328060	−	1.20853i
$400$	−4.74967e7	+	2.60684e7i	−0.742136	+	0.407318i
$401$	−1.41822e7	−	2.45642e7i	−0.219943	−	0.380952i	0.734847	−	0.678232i	$-0.237254\pi$
$401$	−1.41822e7	−	2.45642e7i	−0.219943	−	0.380952i	−0.954790	+	0.297280i	$0.903920\pi$
$402$	−1.08693e7	+	8.19147e6i	−0.167311	+	0.126091i
$403$	−5.86807e7	+	1.01638e8i	−0.896561	+	1.55289i
$404$	−6.61090e7	−	6.75554e7i	−1.00257	−	1.02451i
$405$	339971.	−	2.60189e7i	0.00511772	−	0.391673i
$406$	−1.40424e7	−	3.44270e7i	−0.209828	−	0.514424i
$407$	1.52662e8	+	8.81395e7i	2.26437	+	1.30734i
$408$	1.05466e7	−	6.95953e7i	0.155286	−	1.02471i
$409$	1.81658e7	+	3.14641e7i	0.265513	+	0.459881i	0.967698	−	0.252113i	$-0.0811255\pi$
$409$	1.81658e7	+	3.14641e7i	0.265513	+	0.459881i	−0.702185	+	0.711994i	$0.747792\pi$
$410$	−2.13982e7	−	1.66041e7i	−0.310474	−	0.240915i
$411$	7.91791e6	+	2.14934e6i	0.114047	+	0.0309585i
$412$	8.82065e7	−	2.26148e7i	1.26127	−	0.323370i
$413$			636012.i			0.00902850i
$414$	6.61976e7	−	8.41696e7i	0.932914	−	1.18619i
$415$		−	1.80954e6i		−	0.0253177i
$416$	−1.05984e8	−	1.68810e7i	−1.47218	−	0.234487i
$417$	−8.10844e7	+	8.05564e7i	−1.11823	+	1.11094i
$418$	1.12583e8	−	1.45088e8i	1.54150	−	1.98657i
$419$	3.37780e7	+	5.85051e7i	0.459189	+	0.795338i	0.998918	−	0.0465001i	$-0.0148068\pi$
$419$	3.37780e7	+	5.85051e7i	0.459189	+	0.795338i	−0.539729	+	0.841839i	$0.681473\pi$
$420$	−310198.	+	2.20180e7i	−0.00418689	+	0.297187i
$421$	−1.01829e8	−	5.87912e7i	−1.36467	−	0.787890i	−0.374425	−	0.927257i	$-0.622160\pi$
$421$	−1.01829e8	−	5.87912e7i	−1.36467	−	0.787890i	−0.990241	+	0.139367i	$0.955493\pi$
$422$	4.54503e7	+	1.11428e8i	0.604783	+	1.48272i
$423$	4.15778e7	+	271623.i	0.549339	+	0.00358877i
$424$	4.23788e6	−	9.77910e6i	0.0555969	−	0.128293i
$425$	3.36766e7	−	5.83295e7i	0.438693	−	0.759839i
$426$	1.19187e8	−	1.46403e7i	1.54170	−	0.189374i
$427$	2.37123e7	+	4.10710e7i	0.304572	+	0.527535i
$428$	2.22060e7	+	6.20839e6i	0.283230	+	0.0791859i
$429$	−1.73364e8	+	4.58464e7i	−2.19578	+	0.580676i
$430$	1.44043e6	−	1.05018e7i	0.0181171	−	0.132086i
$431$		−	8.37004e7i		−	1.04543i	−0.852507	−	0.522716i	$-0.824919\pi$
$431$		−	8.37004e7i		−	1.04543i	0.852507	−	0.522716i	$-0.175081\pi$
$432$	1.84080e7	+	7.84919e7i	0.228326	+	0.973585i
$433$	−8.00168e7			−0.985638			−0.492819	−	0.870132i	$-0.664034\pi$
$433$	−8.00168e7			−0.985638			−0.492819	+	0.870132i	$0.664034\pi$
$434$	−7.39170e7	−	1.01385e7i	−0.904222	−	0.124024i
$435$	6.03563e6	+	2.28232e7i	0.0733254	+	0.277274i
$436$	2.59674e6	−	9.28797e6i	0.0313306	−	0.112063i
$437$	−1.80002e8	+	1.03924e8i	−2.15691	+	1.24529i
$438$	−1.21819e7	−	9.91729e7i	−0.144975	−	1.18024i
$439$	−8.30045e7	−	4.79227e7i	−0.981088	−	0.566432i	−0.0784898	−	0.996915i	$-0.525010\pi$
$439$	−8.30045e7	−	4.79227e7i	−0.981088	−	0.566432i	−0.902599	+	0.430483i	$0.858343\pi$
$440$	−2.02145e7	+	4.66458e7i	−0.237303	+	0.547589i
$441$	3.13928e7	+	1.83991e7i	0.366028	+	0.214527i
$442$	1.23532e8	−	5.03872e7i	1.43058	−	0.583517i
$443$	1.88290e7	−	3.26128e7i	0.216579	−	0.375126i	−0.737181	−	0.675696i	$-0.763843\pi$
$443$	1.88290e7	−	3.26128e7i	0.216579	−	0.375126i	0.953760	+	0.300569i	$0.0971767\pi$
$444$	1.50196e8	+	2.11602e6i	1.71596	+	0.0241752i
$445$	−2.46890e6	+	1.42542e6i	−0.0280171	+	0.0161757i
$446$	2.05360e7	+	1.59351e7i	0.231479	+	0.179618i
$447$	5.05038e7	+	5.08348e7i	0.565459	+	0.569165i
$448$	−1.55098e7	−	6.64391e7i	−0.172493	−	0.738907i
$449$	2.93351e6			0.0324077			0.0162039	−	0.999869i	$-0.494842\pi$
$449$	2.93351e6			0.0324077			0.0162039	+	0.999869i	$0.494842\pi$
$450$	−1.09820e7	+	7.63577e7i	−0.120515	+	0.837944i
$451$	1.40219e8			1.52855
$452$	−1.73216e7	−	6.75612e7i	−0.187574	−	0.731614i
$453$	2.68005e6	−	9.87298e6i	0.0288303	−	0.106207i
$454$	4.32522e7	−	5.57403e7i	0.462211	−	0.595664i
$455$	−3.61441e7	+	2.08678e7i	−0.383710	+	0.221535i
$456$	2.34467e7	−	1.54721e8i	0.247279	−	1.63175i
$457$	2.68230e7	−	4.64587e7i	0.281034	−	0.486764i	−0.690606	−	0.723231i	$-0.742656\pi$
$457$	2.68230e7	−	4.64587e7i	0.281034	−	0.486764i	0.971640	+	0.236467i	$0.0759894\pi$
$458$	−1.75059e8	+	7.14047e7i	−1.82217	+	0.743242i
$459$	−7.01706e7	−	7.15595e7i	−0.725633	−	0.739996i
$460$	4.11230e7	−	4.02425e7i	0.422485	−	0.413439i
$461$	1.27641e8	+	7.36935e7i	1.30283	+	0.752188i	0.980888	−	0.194572i	$-0.0623319\pi$
$461$	1.27641e8	+	7.36935e7i	1.30283	+	0.752188i	0.321939	+	0.946760i	$0.395665\pi$
$462$	−6.86114e7	−	9.10410e7i	−0.695778	−	0.923233i
$463$	−1.11110e7	+	6.41493e6i	−0.111946	+	0.0646322i	−0.554928	−	0.831899i	$-0.687254\pi$
$463$	−1.11110e7	+	6.41493e6i	−0.111946	+	0.0646322i	0.442981	+	0.896531i	$0.353921\pi$
$464$	−3.51928e7	−	6.41215e7i	−0.352290	−	0.641874i
$465$	4.57183e7	+	1.24104e7i	0.454707	+	0.123432i
$466$	−2.87118e6	−	393813.i	−0.0283728	−	0.00389164i
$467$	−2.45802e7			−0.241343			−0.120671	−	0.992693i	$-0.538505\pi$
$467$	−2.45802e7			−0.241343			−0.120671	+	0.992693i	$0.538505\pi$
$468$	−1.09908e8	+	1.06158e8i	−1.07224	+	1.03566i
$469$		−	1.63992e7i		−	0.158966i
$470$	2.21338e7	+	3.03589e6i	0.213188	+	0.0292410i
$471$	−3.09814e7	−	3.11845e7i	−0.296509	−	0.298453i
$472$	143159.	+	1.24299e6i	0.00136142	+	0.0118207i
$473$	2.74388e7	+	4.75254e7i	0.259288	+	0.449099i
$474$	−2.92241e7	+	6.88572e7i	−0.274414	+	0.646568i
$475$	7.48680e7	−	1.29675e8i	0.698579	−	1.20997i
$476$	5.93195e7	+	6.06174e7i	0.550018	+	0.562052i
$477$	−7.50148e6	−	1.31912e7i	−0.0691181	−	0.121543i
$478$	2.22928e7	−	9.09297e6i	0.204117	−	0.0832572i
$479$	−1.65994e8	−	9.58369e7i	−1.51038	−	0.872019i	−0.999927	−	0.0121153i	$-0.996143\pi$
$479$	−1.65994e8	−	9.58369e7i	−1.51038	−	0.872019i	−0.510455	−	0.859904i	$-0.670523\pi$
$480$	4.34976e6	+	4.31006e7i	0.0393316	+	0.389726i
$481$	1.42350e8	+	2.46557e8i	1.27915	+	2.21555i
$482$	7.52039e7	−	9.69173e7i	0.671582	−	0.865486i
$483$	3.29867e7	+	1.24736e8i	0.292750	+	1.10701i
$484$	−3.72055e7	−	1.45116e8i	−0.328149	−	1.27991i
$485$			1.08815e7i			0.0953809i
$486$	1.05073e8	+	4.62240e7i	0.915341	+	0.402679i
$487$		−	1.55370e8i		−	1.34518i	−0.740015	−	0.672590i	$-0.765182\pi$
$487$		−	1.55370e8i		−	1.34518i	0.740015	−	0.672590i	$-0.234818\pi$
$488$	5.55868e7	+	7.49296e7i	0.478313	+	0.644754i
$489$	−5.07634e7	−	1.91958e8i	−0.434135	−	1.64164i
$490$	1.54467e7	+	1.19860e7i	0.131295	+	0.101880i
$491$	1.04871e8	+	1.81643e8i	0.885958	+	1.53452i	0.844612	+	0.535379i	$0.179831\pi$
$491$	1.04871e8	+	1.81643e8i	0.885958	+	1.53452i	0.0413456	+	0.999145i	$0.486836\pi$
$492$	1.04307e8	−	5.82781e7i	0.875826	−	0.489339i
$493$	7.87460e7	+	4.54640e7i	0.657185	+	0.379426i
$494$	2.74629e8	−	1.12018e8i	2.27806	−	0.929196i
$495$	3.57817e7	+	6.29214e7i	0.295016	+	0.518780i
$496$	−1.46742e8	−	3.17630e6i	−1.20256	−	0.0260301i
$497$	−7.23440e7	+	1.25303e8i	−0.589296	+	1.02069i
$498$	7.34831e6	+	3.11874e6i	0.0594976	+	0.0252517i
$499$	4.48102e7	+	7.76136e7i	0.360641	+	0.624649i	0.988067	−	0.154028i	$-0.0492245\pi$
$499$	4.48102e7	+	7.76136e7i	0.360641	+	0.624649i	−0.627425	+	0.778677i	$0.715891\pi$
$500$	−2.43445e7	+	8.70748e7i	−0.194756	+	0.696598i
$501$	−2.15594e7	−	2.17008e7i	−0.171445	−	0.172569i
$502$	1.81740e8	+	2.49276e7i	1.43661	+	0.197047i
$503$		−	1.42580e8i		−	1.12035i	−0.828373	−	0.560177i	$-0.810733\pi$
$503$		−	1.42580e8i		−	1.12035i	0.828373	−	0.560177i	$-0.189267\pi$
$504$	−8.88774e7	−	3.92076e7i	−0.694225	−	0.306252i
$505$	−7.23130e7			−0.561490
$506$	−4.04779e7	+	2.95113e8i	−0.312440	+	2.27791i
$507$	−1.53730e8	−	4.17305e7i	−1.17960	−	0.320206i
$508$	7.07057e6	−	2.52898e7i	0.0539341	−	0.192910i
$509$	−5.37602e7	+	3.10385e7i	−0.407669	+	0.235368i	−0.689788	−	0.724012i	$-0.742296\pi$
$509$	−5.37602e7	+	3.10385e7i	−0.407669	+	0.235368i	0.282119	+	0.959379i	$0.408963\pi$
$510$	−3.24110e7	−	4.30064e7i	−0.244333	−	0.324207i
$511$	1.04263e8	+	6.01960e7i	0.781386	+	0.451134i
$512$	−4.52662e7	−	1.26354e8i	−0.337259	−	0.941412i
$513$	−1.56000e8	−	1.59087e8i	−1.15550	−	1.17837i
$514$	2.14523e7	+	5.25935e7i	0.157974	+	0.387296i
$515$	3.48325e7	−	6.03317e7i	0.255014	−	0.441696i
$516$	4.01638e7	+	2.39492e7i	0.292338	+	0.174318i
$517$	−1.00166e8	+	5.78306e7i	−0.724848	+	0.418491i
$518$	−1.10955e8	+	1.42990e8i	−0.798281	+	1.02877i
$519$	3.10735e7	−	1.14471e8i	0.222274	−	0.818829i
$520$	−6.59411e7	+	4.89186e7i	−0.468971	+	0.347908i
$521$	−1.75208e8			−1.23891			−0.619457	−	0.785031i	$-0.712647\pi$
$521$	−1.75208e8			−1.23891			−0.619457	+	0.785031i	$0.712647\pi$
$522$	−1.03084e8	−	1.48259e7i	−0.724739	−	0.104234i
$523$	−9.49026e7			−0.663396			−0.331698	−	0.943386i	$-0.607622\pi$
$523$	−9.49026e7			−0.663396			−0.331698	+	0.943386i	$0.607622\pi$
$524$	2.86675e7	+	1.11814e8i	0.199249	+	0.777149i
$525$	−6.55108e7	−	6.59402e7i	−0.452726	−	0.455693i
$526$	1.45226e8	+	1.12689e8i	0.997898	+	0.774328i
$527$	1.58016e8	−	9.12309e7i	1.07962	−	0.623318i
$528$	−1.54583e8	−	1.62482e8i	−1.05017	−	1.10383i
$529$	9.45487e7	−	1.63763e8i	0.638688	−	1.10624i
$530$	−3.07953e6	−	7.54992e6i	−0.0206850	−	0.0507125i
$531$	1.53697e6	+	900811.i	0.0102656	+	0.00601659i
$532$	1.31876e8	+	1.34761e8i	0.875852	+	0.895016i
$533$	1.96121e8	+	1.13231e8i	1.29522	+	0.747794i
$534$	−1.53330e6	−	1.24826e7i	−0.0100694	−	0.0819749i
$535$	1.52769e7	−	8.82010e6i	0.0997638	−	0.0575987i
$536$	−3.69128e6	−	3.20498e7i	−0.0239708	−	0.208128i
$537$	1.30938e7	+	4.95131e7i	0.0845557	+	0.319740i
$538$	2.00336e7	−	1.46060e8i	0.128651	−	0.937957i
$539$	−1.01220e8			−0.646399
$540$	5.27689e7	+	3.19346e7i	0.335117	+	0.202806i
$541$			3.46141e7i			0.218606i	0.994008	+	0.109303i	$0.0348619\pi$
$541$			3.46141e7i			0.218606i	−0.994008	+	0.109303i	$0.965138\pi$
$542$	1.17907e6	−	8.59625e6i	0.00740527	−	0.0539897i
$543$	−5.25408e7	+	1.38945e7i	−0.328169	+	0.0867847i
$544$	1.29575e8	+	1.05115e8i	0.804869	+	0.652934i
$545$	−3.68913e6	−	6.38976e6i	−0.0227895	−	0.0394725i
$546$	−2.24471e7	−	1.82742e8i	−0.137906	−	1.12269i
$547$	−1.48053e7	+	2.56436e7i	−0.0904600	+	0.156681i	−0.907705	−	0.419609i	$-0.862167\pi$
$547$	−1.48053e7	+	2.56436e7i	−0.0904600	+	0.156681i	0.817245	+	0.576291i	$0.195500\pi$
$548$	−1.38995e7	+	1.36019e7i	−0.0844614	+	0.0826530i
$549$	1.32836e8	+	867802.i	0.802785	+	0.00524450i
$550$	−8.10473e7	−	1.98699e8i	−0.487136	−	1.19429i
$551$	1.75064e8	+	1.01073e8i	1.04651	+	0.604201i
$552$	9.25441e7	+	2.36353e8i	0.550214	+	1.40522i
$553$	−4.50648e7	−	7.80544e7i	−0.266478	−	0.461554i
$554$	−1.51142e8	−	1.17280e8i	−0.888906	−	0.689754i
$555$	8.15247e7	−	8.09939e7i	0.476881	−	0.473776i
$556$	−6.72856e7	−	2.62440e8i	−0.391469	−	1.52688i
$557$		−	1.25420e8i		−	0.725776i	−0.931833	−	0.362888i	$-0.881791\pi$
$557$		−	1.25420e8i		−	0.725776i	0.931833	−	0.362888i	$-0.118209\pi$
$558$	−1.29192e8	+	1.64267e8i	−0.743591	+	0.945468i
$559$			8.86300e7i			0.507394i
$560$	−4.46276e7	−	2.70701e7i	−0.254121	−	0.154144i
$561$	2.69058e8	+	7.30367e7i	1.52390	+	0.413669i
$562$	−1.46973e8	+	1.89409e8i	−0.827999	+	1.06707i
$563$	−8.04925e7	−	1.39417e8i	−0.451056	−	0.781251i	0.547396	−	0.836874i	$-0.315619\pi$
$563$	−8.04925e7	−	1.39417e8i	−0.451056	−	0.781251i	−0.998452	+	0.0556223i	$0.982286\pi$
$564$	−5.04759e7	+	8.46501e7i	−0.281350	+	0.471835i
$565$	−4.62107e7	−	2.66797e7i	−0.256210	−	0.147923i
$566$	1.40767e7	+	3.45112e7i	0.0776341	+	0.190331i
$567$	−1.20675e8	+	6.75854e7i	−0.662018	+	0.370769i
$568$	−1.13181e8	+	2.61170e8i	−0.617630	+	1.42521i
$569$	1.07113e8	−	1.85525e8i	0.581440	−	1.00708i	−0.413868	−	0.910337i	$-0.635823\pi$
$569$	1.07113e8	−	1.85525e8i	0.581440	−	1.00708i	0.995309	−	0.0967477i	$-0.0308440\pi$
$570$	−7.20544e7	−	9.56096e7i	−0.389077	−	0.516270i
$571$	−1.05495e8	−	1.82722e8i	−0.566660	−	0.981485i	−0.996893	−	0.0787666i	$-0.974902\pi$
$571$	−1.05495e8	−	1.82722e8i	−0.566660	−	0.981485i	0.430233	−	0.902718i	$-0.358432\pi$
$572$	1.14451e8	−	4.09366e8i	0.611550	−	2.18738i
$573$	−4.13197e7	+	1.52217e8i	−0.219631	+	0.809093i
$574$	−1.95633e7	+	1.42631e8i	−0.103444	+	0.754184i
$575$			2.42874e8i			1.27755i
$576$	−1.82523e8	−	5.66200e7i	−0.955101	−	0.296280i
$577$	−5.82765e7			−0.303365			−0.151683	−	0.988429i	$-0.548469\pi$
$577$	−5.82765e7			−0.303365			−0.151683	+	0.988429i	$0.548469\pi$
$578$	−1.41833e7	−	1.94539e6i	−0.0734502	−	0.0100745i
$579$	3.22377e7	−	3.20278e7i	0.166084	−	0.165003i
$580$	−5.38925e7	−	1.50674e7i	−0.276213	−	0.0772241i
$581$	−8.32982e6	+	4.80922e6i	−0.0424724	+	0.0245215i
$582$	−4.41881e7	−	1.87542e7i	−0.224149	−	0.0951324i
$583$	3.65575e7	+	2.11065e7i	0.184489	+	0.106515i
$584$	2.17315e8	+	9.41757e7i	1.09107	+	0.472825i
$585$	−763701.	+	1.16901e8i	−0.00381466	+	0.583917i
$586$	−2.30583e8	+	9.40522e7i	−1.14587	+	0.467387i
$587$	−8.13815e7	+	1.40957e8i	−0.402357	+	0.696902i	−0.994010	−	0.109290i	$-0.965142\pi$
$587$	−8.13815e7	+	1.40957e8i	−0.402357	+	0.696902i	0.591653	+	0.806193i	$0.298475\pi$
$588$	−7.52960e7	+	4.20692e7i	−0.370374	+	0.206934i
$589$	3.51294e8	−	2.02820e8i	1.71919	−	0.992577i
$590$	756263.	+	586829.i	0.00368228	+	0.00285730i
$591$	−1.82606e8	+	4.82903e7i	−0.884610	+	0.233936i
$592$	−1.84658e8	+	3.04427e8i	−0.890029	+	1.46730i
$593$	−4.80399e7			−0.230376			−0.115188	−	0.993344i	$-0.536747\pi$
$593$	−4.80399e7			−0.230376			−0.115188	+	0.993344i	$0.536747\pi$
$594$	−3.17185e8	+	3.68597e7i	−1.51340	+	0.175870i
$595$	6.48864e7			0.308037
$596$	−1.64533e8	+	4.21838e7i	−0.777169	+	0.199254i
$597$	−5.05587e7	+	1.33703e7i	−0.237615	+	0.0628375i
$598$	−2.94926e8	+	3.80080e8i	−1.37914	+	1.77734i
$599$	−2.61785e8	+	1.51142e8i	−1.21805	+	0.703240i	−0.964500	−	0.264084i	$-0.914931\pi$
$599$	−2.61785e8	+	1.51142e8i	−1.21805	+	0.703240i	−0.253547	+	0.967323i	$0.581597\pi$
$600$	−1.42873e8	−	1.14124e8i	−0.661451	−	0.528354i
$601$	−8.92051e7	+	1.54508e8i	−0.410928	+	0.711749i	−0.994992	−	0.0999594i	$-0.968129\pi$
$601$	−8.92051e7	+	1.54508e8i	−0.410928	+	0.711749i	0.584063	+	0.811708i	$0.301462\pi$
$602$	−5.21709e7	+	2.12799e7i	−0.239133	+	0.0975395i
$603$	−3.96300e7	−	2.32269e7i	−0.180747	−	0.105935i
$604$	1.69605e7	+	1.73316e7i	0.0769710	+	0.0786551i
$605$	−9.92569e7	−	5.73060e7i	−0.448224	−	0.258782i
$606$	1.24631e8	−	2.93653e8i	0.560027	−	1.31952i
$607$	2.75062e7	−	1.58807e7i	0.122989	−	0.0710075i	−0.437244	−	0.899343i	$-0.644045\pi$
$607$	2.75062e7	−	1.58807e7i	0.122989	−	0.0710075i	0.560232	+	0.828336i	$0.310712\pi$
$608$	2.88065e8	+	2.33687e8i	1.28168	+	1.03974i
$609$	8.90206e7	−	8.84409e7i	0.394129	−	0.391563i
$610$	7.07149e7	+	9.69931e6i	0.311545	+	0.0427318i
$611$	−1.86799e8			−0.818936
$612$	2.30504e8	−	5.74953e7i	1.00560	−	0.250829i
$613$			1.49126e8i			0.647398i	0.946160	+	0.323699i	$0.104927\pi$
$613$			1.49126e8i			0.647398i	−0.946160	+	0.323699i	$0.895073\pi$
$614$	7.19878e7	+	9.87390e6i	0.310995	+	0.0426563i
$615$	2.39471e7	−	8.82183e7i	0.102950	−	0.379257i
$616$	2.68448e8	−	3.09180e7i	1.14846	−	0.132272i
$617$	1.84049e8	+	3.18783e8i	0.783572	+	1.35719i	0.929849	+	0.367943i	$0.119938\pi$
$617$	1.84049e8	+	3.18783e8i	0.783572	+	1.35719i	−0.146277	+	0.989244i	$0.546729\pi$
$618$	1.84965e8	+	2.45432e8i	0.783655	+	1.03984i
$619$	9.65060e7	−	1.67153e8i	0.406895	−	0.704763i	−0.587645	−	0.809119i	$-0.699945\pi$
$619$	9.65060e7	−	1.67153e8i	0.406895	−	0.704763i	0.994540	+	0.104356i	$0.0332782\pi$
$620$	−8.02563e7	+	7.85379e7i	−0.336747	+	0.329537i
$621$	3.48155e8	+	9.69543e7i	1.45378	+	0.404848i
$622$	−1.33063e8	+	5.42747e7i	−0.552948	+	0.225541i
$623$	1.31232e7	+	7.57669e6i	0.0542720	+	0.0313340i
$624$	−8.50027e7	−	3.52089e8i	−0.349848	−	1.44910i
$625$	−6.87550e7	−	1.19087e8i	−0.281621	−	0.487781i
$626$	2.06488e8	−	2.66107e8i	0.841730	−	1.08476i
$627$	5.98156e8	+	1.62371e8i	2.42668	+	0.658729i
$628$	1.00933e8	−	2.58775e7i	0.407523	−	0.104483i
$629$		−	4.42622e8i		−	1.77861i
$630$	−6.89957e7	+	2.76182e7i	−0.275931	+	0.110452i
$631$			3.34674e8i			1.33209i	0.745911	+	0.666046i	$0.232015\pi$
$631$			3.34674e8i			1.33209i	−0.745911	+	0.666046i	$0.767985\pi$
$632$	−1.05641e8	−	1.42402e8i	−0.418488	−	0.564111i
$633$	−2.88129e8	+	2.86253e8i	−1.13599	+	1.12860i
$634$	−2.15505e8	−	1.67223e8i	−0.845649	−	0.656189i
$635$	−1.00450e7	−	1.73984e7i	−0.0392309	−	0.0679498i
$636$	3.59668e7	+	506715.i	0.139807	+	0.00196966i
$637$	−1.41574e8	−	8.17378e7i	−0.547728	−	0.316231i
$638$	2.68248e8	−	1.09415e8i	1.03294	−	0.421324i
$639$	2.00342e8	+	3.52298e8i	0.767838	+	1.35023i
$640$	−9.33111e7	−	4.28592e7i	−0.355954	−	0.163495i
$641$	1.46458e8	−	2.53673e8i	0.556082	−	0.963163i	−0.441736	−	0.897145i	$-0.645637\pi$
$641$	1.46458e8	−	2.53673e8i	0.556082	−	0.963163i	0.997818	−	0.0660177i	$-0.0210294\pi$
$642$	9.48763e6	+	7.72388e7i	0.0358552	+	0.291897i
$643$	3.59494e6	+	6.22662e6i	0.0135226	+	0.0234218i	0.872708	−	0.488243i	$-0.162362\pi$
$643$	3.59494e6	+	6.22662e6i	0.0135226	+	0.0234218i	−0.859185	+	0.511665i	$0.829029\pi$
$644$	−2.94540e8	−	8.23479e7i	−1.10278	−	0.308315i
$645$	3.45864e7	−	9.14643e6i	0.128892	−	0.0340857i
$646$	−4.56840e8	−	6.26606e7i	−1.69460	−	0.232433i
$647$		−	1.84239e8i		−	0.680249i	−0.940380	−	0.340125i	$-0.889531\pi$
$647$		−	1.84239e8i		−	0.680249i	0.940380	−	0.340125i	$-0.110469\pi$
$648$	−2.20629e8	+	1.59248e8i	−0.810845	+	0.585260i
$649$	−4.95568e6			−0.0181288
$650$	4.70960e7	−	3.43363e8i	0.171492	−	1.25030i
$651$	−6.43772e7	−	2.43437e8i	−0.233340	−	0.882356i
$652$	4.53270e8	+	1.26726e8i	1.63536	+	0.457217i
$653$	1.45935e8	−	8.42556e7i	0.524107	−	0.302593i	−0.214507	−	0.976723i	$-0.568814\pi$
$653$	1.45935e8	−	8.42556e7i	0.524107	−	0.302593i	0.738613	+	0.674129i	$0.235481\pi$
$654$	3.23061e7	−	3.96833e6i	0.115492	−	0.0141865i
$655$	7.64791e7	+	4.41553e7i	0.272157	+	0.157130i
$656$	−6.12901e6	+	2.83153e8i	−0.0217109	+	1.00302i
$657$	2.93140e8	−	1.66701e8i	1.03366	−	0.587816i
$658$	−4.48500e7	−	1.09957e8i	−0.157429	−	0.385961i
$659$	1.44347e8	−	2.50017e8i	0.504373	−	0.873600i	−0.495614	−	0.868543i	$-0.665057\pi$
$659$	1.44347e8	−	2.50017e8i	0.504373	−	0.873600i	0.999987	−	0.00505693i	$-0.00160968\pi$
$660$	−1.71560e8	−	2.41700e6i	−0.596738	−	0.00840708i
$661$	3.12804e8	−	1.80597e8i	1.08310	−	0.625327i	0.151367	−	0.988478i	$-0.451632\pi$
$661$	3.12804e8	−	1.80597e8i	1.08310	−	0.625327i	0.931730	+	0.363151i	$0.118299\pi$
$662$	−1.27836e6	+	1.64746e6i	−0.00440635	+	0.00567858i
$663$	3.17346e8	+	3.19426e8i	1.08891	+	1.09605i
$664$	−1.51969e7	+	1.12738e7i	−0.0519098	+	0.0385095i
$665$	1.44252e8			0.490520
$666$	1.88398e8	+	4.70654e8i	0.637754	+	1.59323i
$667$	−3.27885e8			−1.10496
$668$	7.02373e7	−	1.80077e7i	0.235634	−	0.0604129i
$669$	−2.29822e7	+	8.46637e7i	−0.0767563	+	0.282761i
$670$	−1.94998e7	−	1.51310e7i	−0.0648344	−	0.0503088i
$671$	−3.20017e8	+	1.84762e8i	−1.05927	+	0.611568i
$672$	1.86844e8	−	1.34572e8i	0.615702	−	0.443451i
$673$	2.74548e8	−	4.75532e8i	0.900686	−	1.56003i	0.0740812	−	0.997252i	$-0.476398\pi$
$673$	2.74548e8	−	4.75532e8i	0.900686	−	1.56003i	0.826605	−	0.562782i	$-0.190269\pi$
$674$	7.36049e7	+	1.80453e8i	0.240396	+	0.589367i
$675$	−2.52136e8	+	6.49183e7i	−0.819828	+	0.211084i
$676$	2.69866e8	−	2.64088e8i	0.873590	−	0.854885i
$677$	−4.41571e8	−	2.54941e8i	−1.42310	−	0.821625i	−0.426534	−	0.904472i	$-0.640265\pi$
$677$	−4.41571e8	−	2.54941e8i	−1.42310	−	0.821625i	−0.996562	+	0.0828468i	$0.973599\pi$
$678$	1.87987e8	−	1.41673e8i	0.603168	−	0.454567i
$679$	5.00903e7	−	2.89197e7i	0.160009	−	0.0923812i
$680$	1.26811e8	−	1.46052e7i	0.403300	−	0.0464495i
$681$	2.29800e8	+	6.23800e7i	0.727628	+	0.197517i
$682$	7.89973e7	−	5.75946e8i	0.249034	−	1.81564i
$683$	−8.96175e7			−0.281275			−0.140637	−	0.990061i	$-0.544915\pi$
$683$	−8.96175e7			−0.281275			−0.140637	+	0.990061i	$0.544915\pi$
$684$	5.12443e8	−	1.27821e8i	1.60132	−	0.399423i
$685$			1.48784e7i			0.0462897i
$686$	4.74086e7	−	3.45643e8i	0.146854	−	1.07067i
$687$	−4.49717e8	−	4.52664e8i	−1.38698	−	1.39607i
$688$	−9.71702e7	+	5.33315e7i	−0.298379	+	0.163764i
$689$	3.40880e7	+	5.90421e7i	0.104218	+	0.180511i
$690$	1.78756e8	+	7.58668e7i	0.544143	+	0.230943i
$691$	−1.65482e8	+	2.86623e8i	−0.501553	+	0.868715i	0.498445	+	0.866921i	$0.333904\pi$
$691$	−1.65482e8	+	2.86623e8i	−0.501553	+	0.868715i	−0.999998	+	0.00179409i	$0.999429\pi$
$692$	1.96646e8	+	2.00948e8i	0.593426	+	0.606410i
$693$	1.94548e8	−	3.31939e8i	0.584556	−	0.997376i
$694$	1.73237e8	+	4.24716e8i	0.518277	+	1.27063i
$695$	−1.79505e8	−	1.03637e8i	−0.534714	−	0.308717i
$696$	1.54070e8	−	1.92882e8i	0.456973	−	0.572089i
$697$	−1.76040e8	−	3.04909e8i	−0.519891	−	0.900477i
$698$	−1.48913e8	−	1.15550e8i	−0.437891	−	0.339786i
$699$	−2.50062e6	−	9.45590e6i	−0.00732179	−	0.0276867i
$700$	2.13424e8	−	5.47186e7i	0.622228	−	0.159529i
$701$		−	1.21635e8i		−	0.353106i	−0.984291	−	0.176553i	$-0.943505\pi$
$701$		−	1.21635e8i		−	0.353106i	0.984291	−	0.176553i	$-0.0564948\pi$
$702$	−4.73404e8	−	2.04580e8i	−1.36842	−	0.591360i
$703$		−	9.84014e8i		−	2.83228i
$704$	5.17681e8	−	1.20849e8i	1.48369	−	0.346358i
$705$	1.92772e7	+	7.28952e7i	0.0550145	+	0.208033i
$706$	−1.99215e8	+	2.56733e8i	−0.566118	+	0.729572i
$707$	1.92186e8	+	3.32877e8i	0.543831	+	0.941944i
$708$	−3.68645e6	+	2.05968e6i	−0.0103874	+	0.00580365i
$709$	1.14089e7	+	6.58695e6i	0.0320115	+	0.0184818i	0.515920	−	0.856637i	$-0.327450\pi$
$709$	1.14089e7	+	6.58695e6i	0.0320115	+	0.0184818i	−0.483909	+	0.875118i	$0.660783\pi$
$710$	8.22449e7	+	2.01636e8i	0.229792	+	0.563368i
$711$	−2.52452e8	−	1.64924e6i	−0.702376	−	0.00458854i
$712$	2.73528e7	+	1.18536e7i	0.0757811	+	0.0328405i
$713$	−3.28977e8	+	5.69805e8i	−0.907606	+	1.57202i
$714$	−1.11832e8	+	2.63495e8i	−0.307234	+	0.723898i
$715$	−1.62598e8	−	2.81628e8i	−0.444833	−	0.770473i
$716$	−1.16915e8	−	3.26874e7i	−0.318517	−	0.0890515i
$717$	5.72688e7	+	5.76442e7i	0.155368	+	0.156386i
$718$	−7.71829e7	+	5.62718e8i	−0.208520	+	1.52026i
$719$			1.23428e8i			0.332068i	0.986120	+	0.166034i	$0.0530962\pi$
$719$			1.23428e8i			0.332068i	−0.986120	+	0.166034i	$0.946904\pi$
$720$	−1.28625e8	+	6.95058e7i	−0.344610	+	0.186219i
$721$	−3.70298e8			−0.987974
$722$	−6.42748e8	−	8.81598e7i	−1.70777	−	0.234239i
$723$	3.99561e8	+	1.08462e8i	1.05723	+	0.286987i
$724$	3.46862e7	−	1.24065e8i	0.0913990	−	0.326914i
$725$	2.04566e8	−	1.18106e8i	0.536808	−	0.309926i
$726$	4.03781e8	−	3.04302e8i	1.05520	−	0.795235i
$727$	5.21361e8	+	3.01008e8i	1.35686	+	0.783383i	0.989199	−	0.146577i	$-0.0468255\pi$
$727$	5.21361e8	+	3.01008e8i	1.35686	+	0.783383i	0.367661	+	0.929960i	$0.380159\pi$
$728$	4.00438e8	+	1.73534e8i	1.03786	+	0.449769i
$729$	−7.59232e6	+	3.87346e8i	−0.0195971	+	0.999808i
$730$	1.67777e8	−	6.84344e7i	0.431285	−	0.175916i
$731$	6.88965e7	−	1.19332e8i	0.176378	−	0.305496i
$732$	−1.61264e8	+	2.70447e8i	−0.411155	+	0.689523i
$733$	−2.95717e8	+	1.70732e8i	−0.750869	+	0.433514i	−0.826008	−	0.563659i	$-0.809393\pi$
$733$	−2.95717e8	+	1.70732e8i	−0.750869	+	0.433514i	0.0751391	+	0.997173i	$0.476060\pi$
$734$	1.19578e8	+	9.27879e7i	0.302388	+	0.234640i
$735$	−1.72867e7	+	6.36821e7i	−0.0435362	+	0.160382i
$736$	−5.94170e8	−	9.46389e7i	−1.49031	−	0.237376i
$737$	1.27779e8			0.319197
$738$	3.16970e8	+	2.49290e8i	0.788586	+	0.620206i
$739$	−2.25431e8			−0.558574			−0.279287	−	0.960208i	$-0.590098\pi$
$739$	−2.25431e8			−0.558574			−0.279287	+	0.960208i	$0.590098\pi$
$740$	6.76509e7	+	2.63865e8i	0.166947	+	0.651159i
$741$	7.05506e8	+	7.10130e8i	1.73399	+	1.74535i
$742$	−2.65699e7	+	3.42414e7i	−0.0650396	+	0.0838184i
$743$	−6.25965e8	+	3.61401e8i	−1.52610	+	0.881095i	−0.526581	+	0.850125i	$0.676526\pi$
$743$	−6.25965e8	+	3.61401e8i	−1.52610	+	0.881095i	−0.999520	+	0.0309701i	$0.990140\pi$
$744$	−1.80611e8	−	4.61270e8i	−0.438555	−	1.12005i
$745$	−6.49738e7	+	1.12538e8i	−0.157134	+	0.272164i
$746$	−4.37678e8	+	1.78524e8i	−1.05424	+	0.430011i
$747$	−176004.	+	2.69412e7i	−0.000422240	+	0.0646331i
$748$	−4.72319e8	+	4.62206e8i	−1.12858	+	1.10441i
$749$	−8.12027e7	−	4.68824e7i	−0.193253	−	0.111574i
$750$	−3.02870e8	+	3.72031e7i	−0.717915	+	0.0881851i
$751$	−1.01297e8	+	5.84841e7i	−0.239155	+	0.138076i	−0.614788	−	0.788692i	$-0.710758\pi$
$751$	−1.01297e8	+	5.84841e7i	−0.239155	+	0.138076i	0.375634	+	0.926768i	$0.377425\pi$
$752$	−1.12403e8	−	2.04798e8i	−0.264316	−	0.481584i
$753$	1.58285e8	+	5.98541e8i	0.370727	+	1.40187i
$754$	4.63547e8	+	6.35805e7i	1.08138	+	0.148324i
$755$	1.85521e7			0.0431075
$756$	6.75991e6	−	3.27782e8i	0.0156450	−	0.758613i
$757$			4.77238e8i			1.10014i	0.835119	+	0.550069i	$0.185399\pi$
$757$			4.77238e8i			1.10014i	−0.835119	+	0.550069i	$0.814601\pi$
$758$	2.00351e8	+	2.74803e7i	0.460027	+	0.0630977i
$759$	−9.71920e8	+	2.57025e8i	−2.22282	+	0.587829i
$760$	2.81919e8	−	3.24695e7i	0.642219	−	0.0739664i
$761$	−1.17423e8	−	2.03382e8i	−0.266439	−	0.461487i	0.701500	−	0.712669i	$-0.252514\pi$
$761$	−1.17423e8	−	2.03382e8i	−0.266439	−	0.461487i	−0.967940	+	0.251183i	$0.919181\pi$
$762$	8.79652e7	−	1.08052e7i	0.198813	−	0.0244213i
$763$	−1.96092e7	+	3.39641e7i	−0.0441455	+	0.0764622i
$764$	−2.61488e8	−	2.67209e8i	−0.586369	−	0.599199i
$765$	9.19013e7	−	1.56803e8i	0.205276	−	0.350244i
$766$	−1.31678e8	+	5.37100e7i	−0.292973	+	0.119500i
$767$	−6.93138e6	−	4.00184e6i	−0.0153615	−	0.00886897i
$768$	3.34867e8	−	3.05056e8i	0.739245	−	0.673436i
$769$	3.28719e8	+	5.69358e8i	0.722845	+	1.25201i	0.959855	+	0.280498i	$0.0904995\pi$
$769$	3.28719e8	+	5.69358e8i	0.722845	+	1.25201i	−0.237009	+	0.971507i	$0.576167\pi$
$770$	1.26737e8	−	1.63329e8i	0.277608	−	0.357761i
$771$	−1.35995e8	+	1.35110e8i	−0.296729	+	0.294797i
$772$	2.67515e7	+	1.04341e8i	0.0581428	+	0.226780i
$773$			1.10532e7i			0.0239305i	0.999928	+	0.0119652i	$0.00380875\pi$
$773$			1.10532e7i			0.0239305i	−0.999928	+	0.0119652i	$0.996191\pi$
$774$	−2.24672e7	+	1.56215e8i	−0.0484536	+	0.336899i
$775$		−	4.73997e8i		−	1.01829i
$776$	9.13844e7	−	6.77938e7i	0.195563	−	0.145079i
$777$	−5.89506e8	−	1.60023e8i	−1.25668	−	0.341130i
$778$	−4.81259e7	−	3.73437e7i	−0.102197	−	0.0793010i
$779$	−3.91362e8	−	6.77859e8i	−0.827878	−	1.43393i
$780$	−2.38004e8	−	1.41919e8i	−0.501535	−	0.299060i
$781$	−9.76340e8	−	5.63690e8i	−2.04950	−	1.18328i
$782$	6.92546e8	−	2.82482e8i	1.44820	−	0.590705i
$783$	−8.76410e7	−	3.40388e8i	−0.182567	−	0.709070i
$784$	4.42435e6	−	2.04400e8i	0.00918123	−	0.424163i
$785$	3.98580e7	−	6.90361e7i	0.0823961	−	0.142714i
$786$	−3.11120e8	+	2.34470e8i	−0.640709	+	0.482859i
$787$	3.25839e8	+	5.64370e8i	0.668465	+	1.15782i	0.978333	+	0.207036i	$0.0663819\pi$
$787$	3.25839e8	+	5.64370e8i	0.668465	+	1.15782i	−0.309868	+	0.950780i	$0.600285\pi$
$788$	1.20552e8	−	4.31188e8i	0.246375	−	0.881227i
$789$	−1.62525e8	+	5.98722e8i	−0.330894	+	1.21897i
$790$	−1.34392e8	−	1.84333e7i	−0.272579	−	0.0373871i
$791$			2.83627e8i			0.573084i
$792$	3.05498e8	−	6.92515e8i	0.614940	−	1.39397i
$793$	−5.96799e8			−1.19676
$794$	6.45610e6	−	4.70695e7i	0.0128976	−	0.0940326i
$795$	1.95224e7	−	1.93953e7i	0.0388537	−	0.0386007i
$796$	3.33777e7	−	1.19385e8i	0.0661786	−	0.236706i
$797$	7.43295e7	−	4.29141e7i	0.146820	−	0.0847667i	−0.424790	−	0.905292i	$-0.639652\pi$
$797$	7.43295e7	−	4.29141e7i	0.146820	−	0.0847667i	0.571611	+	0.820525i	$0.306319\pi$
$798$	−2.48618e8	+	5.85788e8i	−0.489242	+	1.15274i
$799$	2.51507e8	+	1.45208e8i	0.493072	+	0.284675i
$800$	4.04788e8	−	1.54979e8i	0.790602	−	0.302692i
$801$	3.68966e7	−	2.09821e7i	0.0717942	−	0.0408274i
$802$	8.57010e7	+	2.10109e8i	0.166136	+	0.407306i
$803$	−4.69036e8	+	8.12393e8i	−0.905856	+	1.56899i
$804$	9.50530e7	−	5.31077e7i	0.182893	−	0.102186i
$805$	−2.02632e8	+	1.16990e8i	−0.388437	+	0.224264i
$806$	5.75582e8	−	7.41769e8i	1.09926	−	1.41665i
$807$	4.81030e8	−	1.27209e8i	0.915275	−	0.242046i
$808$	4.50526e8	+	6.07298e8i	0.854055	+	1.15124i
$809$	−4.23829e8			−0.800471			−0.400235	−	0.916412i	$-0.631072\pi$
$809$	−4.23829e8			−0.800471			−0.400235	+	0.916412i	$0.631072\pi$
$810$	−3.09798e7	+	2.05850e8i	−0.0582940	+	0.387344i
$811$	6.49000e8			1.21670			0.608348	−	0.793671i	$-0.291833\pi$
$811$	6.49000e8			1.21670			0.608348	+	0.793671i	$0.291833\pi$
$812$	7.38712e7	+	2.88127e8i	0.137977	+	0.538165i
$813$	2.83107e7	−	7.48681e6i	0.0526841	−	0.0139324i
$814$	−1.11415e9	−	8.64536e8i	−2.06572	−	1.60291i
$815$	3.11832e8	−	1.80036e8i	0.576034	−	0.332573i
$816$	−1.59248e8	+	5.40133e8i	−0.293092	+	0.994100i
$817$	1.53167e8	−	2.65293e8i	0.280866	−	0.486475i
$818$	−1.09774e8	−	2.69126e8i	−0.200557	−	0.491696i
$819$	5.40158e8	−	3.07173e8i	0.983261	−	0.559154i
$820$	1.51547e8	+	1.54863e8i	0.274857	+	0.280871i
$821$	−3.48162e8	−	2.01011e8i	−0.629147	−	0.363238i	0.151275	−	0.988492i	$-0.451662\pi$
$821$	−3.48162e8	−	2.01011e8i	−0.629147	−	0.363238i	−0.780421	+	0.625254i	$0.784995\pi$
$822$	−6.04192e7	−	2.56429e7i	−0.108783	−	0.0461691i
$823$	3.90726e8	−	2.25586e8i	0.700927	−	0.404681i	−0.106765	−	0.994284i	$-0.534049\pi$
$823$	3.90726e8	−	2.25586e8i	0.700927	−	0.404681i	0.807693	+	0.589604i	$0.200716\pi$
$824$	−7.23691e8	+	8.33499e7i	−1.29352	+	0.148978i
$825$	5.13793e8	−	5.10447e8i	0.915011	−	0.909053i
$826$	691414.	−	5.04090e6i	0.00122687	−	0.00894475i
$827$	−7.92713e8			−1.40152			−0.700760	−	0.713397i	$-0.747156\pi$
$827$	−7.92713e8			−1.40152			−0.700760	+	0.713397i	$0.747156\pi$
$828$	−6.16170e8	+	5.95147e8i	−1.08545	+	1.04842i
$829$			6.55850e8i			1.15117i	0.817741	+	0.575587i	$0.195226\pi$
$829$			6.55850e8i			1.15117i	−0.817741	+	0.575587i	$0.804774\pi$
$830$	−1.96717e6	+	1.43421e7i	−0.00344038	+	0.0250829i
$831$	1.69146e8	−	6.23112e8i	0.294753	−	1.08583i
$832$	8.21655e8	+	2.49012e8i	1.42666	+	0.432364i
$833$	1.27078e8	+	2.20105e8i	0.219854	+	0.380798i
$834$	7.30232e8	−	5.50326e8i	1.25882	−	0.948685i
$835$	2.77365e7	−	4.80411e7i	0.0476423	−	0.0825189i
$836$	−1.05003e9	+	1.02755e9i	−1.79715	+	1.75867i
$837$	−6.79465e8	−	1.89217e8i	−1.15875	−	0.322689i
$838$	−2.04116e8	−	5.00420e8i	−0.346852	−	0.850360i
$839$	3.57004e8	+	2.06117e8i	0.604488	+	0.349001i	0.770805	−	0.637071i	$-0.219854\pi$
$839$	3.57004e8	+	2.06117e8i	0.604488	+	0.349001i	−0.166317	+	0.986072i	$0.553188\pi$
$840$	2.63945e7	−	1.74173e8i	0.0445323	−	0.293861i
$841$	−1.37966e8	−	2.38964e8i	−0.231945	−	0.401740i
$842$	7.43165e8	+	5.76666e8i	1.24494	+	0.966024i
$843$	−7.80875e8	−	2.11971e8i	−1.30346	−	0.353829i
$844$	−2.39095e8	−	9.32566e8i	−0.397689	−	1.55115i
$845$		−	2.88871e8i		−	0.478777i
$846$	−3.29242e8	−	4.73524e7i	−0.543756	−	0.0782044i
$847$			6.09209e8i			1.00257i
$848$	−4.42195e7	+	7.29001e7i	−0.0725147	+	0.119548i
$849$	−8.92383e7	+	8.86572e7i	−0.145824	+	0.144874i
$850$	−3.30324e8	+	4.25698e8i	−0.537878	+	0.693178i
$851$	7.98045e8	+	1.38225e9i	1.29491	+	2.24284i
$852$	−9.60565e8	−	1.35328e7i	−1.55313	−	0.0218811i
$853$	3.06953e8	+	1.77220e8i	0.494567	+	0.285538i	0.726467	−	0.687201i	$-0.241161\pi$
$853$	3.06953e8	+	1.77220e8i	0.494567	+	0.285538i	−0.231900	+	0.972740i	$0.574494\pi$
$854$	−1.43290e8	−	3.51298e8i	−0.230061	−	0.564030i
$855$	2.04310e8	−	3.48596e8i	0.326883	−	0.557731i
$856$	−1.69251e8	−	7.33468e7i	−0.269842	−	0.116939i
$857$	2.90252e8	−	5.02732e8i	0.461141	−	0.798719i	−0.537877	−	0.843023i	$-0.680774\pi$
$857$	2.90252e8	−	5.02732e8i	0.461141	−	0.798719i	0.999018	+	0.0443040i	$0.0141070\pi$
$858$	1.42389e9	−	1.74904e8i	2.25431	−	0.276909i
$859$	−1.48820e8	−	2.57764e8i	−0.234792	−	0.406671i	0.724420	−	0.689358i	$-0.242107\pi$
$859$	−1.48820e8	−	2.57764e8i	−0.234792	−	0.406671i	−0.959212	+	0.282687i	$0.908774\pi$
$860$	−2.28332e7	+	8.16691e7i	−0.0358981	+	0.128399i
$861$	−4.69737e8	+	1.24223e8i	−0.735946	+	0.194622i
$862$	−9.09913e7	+	6.63392e8i	−0.142062	+	1.03573i
$863$			6.34567e8i			0.987291i	0.869663	+	0.493646i	$0.164336\pi$
$863$			6.34567e8i			0.987291i	−0.869663	+	0.493646i	$0.835664\pi$
$864$	−6.05689e7	−	6.42122e8i	−0.0939092	−	0.995581i
$865$	2.15100e8			0.332347
$866$	6.34197e8	+	8.69869e7i	0.976496	+	0.133937i
$867$	−1.23528e7	−	4.67110e7i	−0.0189543	−	0.0716740i
$868$	5.74829e8	+	1.60711e8i	0.878981	+	0.245747i
$869$	6.08185e8	−	3.51136e8i	0.926779	−	0.535076i
$870$	−2.30258e7	−	1.87453e8i	−0.0349669	−	0.284666i
$871$	1.78722e8	+	1.03185e8i	0.270472	+	0.156157i
$872$	−3.06783e7	+	7.07916e7i	−0.0462681	+	0.106766i
$873$	1.05838e6	−	1.62007e8i	0.00159073	−	0.243496i
$874$	1.53963e9	−	6.27999e8i	2.30612	−	0.940642i
$875$	1.83836e8	−	3.18414e8i	0.274415	−	0.475300i
$876$	−1.12604e7	+	7.99267e8i	−0.0167510	+	1.18899i
$877$	1.37665e8	−	7.94808e7i	0.204091	−	0.117832i	−0.394471	−	0.918908i	$-0.629072\pi$
$877$	1.37665e8	−	7.94808e7i	0.204091	−	0.117832i	0.598562	+	0.801076i	$0.295739\pi$
$878$	6.05779e8	+	4.70060e8i	0.895016	+	0.694496i
$879$	−5.92354e8	−	5.96237e8i	−0.872198	−	0.877914i
$880$	2.10925e8	−	3.47730e8i	0.309513	−	0.510263i
$881$	4.67388e8			0.683517			0.341759	−	0.939788i	$-0.388977\pi$
$881$	4.67388e8			0.683517			0.341759	+	0.939788i	$0.388977\pi$
$882$	−2.28811e8	−	1.79955e8i	−0.333481	−	0.262276i
$883$	1.12432e9			1.63307			0.816537	−	0.577293i	$-0.195891\pi$
$883$	1.12432e9			1.63307			0.816537	+	0.577293i	$0.195891\pi$
$884$	−1.03386e9	+	2.65066e8i	−1.49660	+	0.383705i
$885$	−846348.	+	3.11784e6i	−0.00122101	+	0.00449805i
$886$	−1.84689e8	+	2.38013e8i	−0.265546	+	0.342216i
$887$	9.50907e8	−	5.49006e8i	1.36260	−	0.786695i	0.372627	−	0.927981i	$-0.378457\pi$
$887$	9.50907e8	−	5.49006e8i	1.36260	−	0.786695i	0.989969	+	0.141286i	$0.0451237\pi$
$888$	−1.18812e9	−	1.80050e8i	−1.69676	−	0.257131i
$889$	−5.33931e7	+	9.24796e7i	−0.0759941	+	0.131626i
$890$	2.11176e7	−	8.61363e6i	0.0299553	−	0.0122185i
$891$	−5.26612e8	−	9.40280e8i	−0.744488	−	1.32930i
$892$	−1.45441e8	−	1.48623e8i	−0.204924	−	0.209407i
$893$	5.59138e8	+	3.22818e8i	0.785172	+	0.453319i
$894$	−3.45020e8	−	4.57809e8i	−0.482871	−	0.640725i
$895$	−8.04332e7	+	4.64381e7i	−0.112193	+	0.0647748i
$896$	5.07007e7	+	5.43444e8i	0.0704839	+	0.755493i
$897$	−1.56695e9	−	4.25354e8i	−2.17109	−	0.589350i
$898$	−2.32504e7	−	3.18904e6i	−0.0321071	−	0.00440383i
$899$	6.39906e8			0.880719
$900$	1.70050e8	−	5.93257e8i	0.233264	−	0.813795i
$901$		−	1.05993e8i		−	0.144912i
$902$	−1.11135e9	−	1.52434e8i	−1.51437	−	0.207712i
$903$	−1.34024e8	−	1.34902e8i	−0.182020	−	0.183213i
$904$	6.38413e7	+	5.54306e8i	0.0864164	+	0.750316i
$905$	−4.92779e7	−	8.53518e7i	−0.0664823	−	0.115151i
$906$	−3.19745e7	+	7.53377e7i	−0.0429952	+	0.101304i
$907$	−2.53070e8	+	4.38330e8i	−0.339171	+	0.587461i	−0.984277	−	0.176632i	$-0.943480\pi$
$907$	−2.53070e8	+	4.38330e8i	−0.339171	+	0.587461i	0.645106	+	0.764093i	$0.276813\pi$
$908$	−4.03403e8	+	3.94766e8i	−0.538868	+	0.527330i
$909$	1.07662e9	+	7.03346e6i	1.43342	+	0.00936435i
$910$	3.09156e8	−	1.26101e8i	0.410255	−	0.167338i
$911$	9.50684e8	+	5.48878e8i	1.25742	+	0.725973i	0.972573	−	0.232599i	$-0.0747230\pi$
$911$	9.50684e8	+	5.48878e8i	1.25742	+	0.725973i	0.284850	+	0.958572i	$0.408056\pi$
$912$	−3.54032e8	+	1.20079e9i	−0.466721	+	1.58301i
$913$	−3.74725e7	−	6.49043e7i	−0.0492380	−	0.0852827i
$914$	−2.63099e8	+	3.39063e8i	−0.344572	+	0.444060i
$915$	6.15884e7	+	2.32891e8i	0.0803962	+	0.304011i
$916$	1.46511e9	−	3.75630e8i	1.90626	−	0.488736i
$917$		−	4.69406e8i		−	0.608752i
$918$	4.78365e8	+	6.43449e8i	0.618346	+	0.831737i
$919$		−	1.24645e9i		−	1.60593i	−0.596025	−	0.802966i	$-0.703254\pi$
$919$		−	1.24645e9i		−	1.60593i	0.596025	−	0.802966i	$-0.296746\pi$
$920$	−3.69681e8	+	2.74249e8i	−0.474748	+	0.352193i
$921$	6.26970e7	+	2.37083e8i	0.0802542	+	0.303475i
$922$	−9.31542e8	−	7.22839e8i	−1.18853	−	0.922250i
$923$	−9.10387e8	−	1.57684e9i	−1.15777	−	2.00531i
$924$	4.44828e8	+	7.96160e8i	0.563867	+	1.00922i
$925$	−9.95791e8	−	5.74920e8i	−1.25818	−	0.726411i
$926$	9.50371e7	−	3.87646e7i	0.119691	−	0.0488205i
$927$	−5.24469e8	+	8.94854e8i	−0.658386	+	1.12335i
$928$	2.09224e8	+	5.46472e8i	0.261799	+	0.683792i
$929$	1.90666e8	−	3.30243e8i	0.237808	−	0.411895i	−0.722277	−	0.691604i	$-0.756904\pi$
$929$	1.90666e8	−	3.30243e8i	0.237808	−	0.411895i	0.960085	+	0.279708i	$0.0902378\pi$
$930$	−3.48862e8	−	1.48063e8i	−0.433716	−	0.184076i
$931$	2.82512e8	+	4.89326e8i	0.350097	+	0.606386i
$932$	2.23283e7	+	6.24257e6i	0.0275808	+	0.00771108i
$933$	−3.41830e8	−	3.44070e8i	−0.420887	−	0.423645i
$934$	1.94817e8	+	2.67213e7i	0.239104	+	0.0327957i
$935$			5.05582e8i			0.618524i
$936$	9.86515e8	−	7.21906e8i	1.20303	−	0.880346i
$937$	1.60160e9			1.94686			0.973429	−	0.228987i	$-0.0735414\pi$
$937$	1.60160e9			1.94686			0.973429	+	0.228987i	$0.0735414\pi$
$938$	−1.78277e7	+	1.29977e8i	−0.0216017	+	0.157491i
$939$	1.09708e9	+	2.97806e8i	1.32508	+	0.359697i
$940$	−1.72128e8	−	4.81237e7i	−0.207237	−	0.0579396i
$941$	−1.15588e9	+	6.67349e8i	−1.38722	+	0.800911i	−0.993001	−	0.118106i	$-0.962318\pi$
$941$	−1.15588e9	+	6.67349e8i	−1.38722	+	0.800911i	−0.394218	+	0.919017i	$0.628984\pi$
$942$	2.11651e8	+	2.80842e8i	0.253203	+	0.335977i
$943$	1.09950e9	+	6.34796e8i	1.31117	+	0.757006i
$944$	216614.	−	1.00073e7i	0.000257495	−	0.0118960i
$945$	−1.75612e8	−	1.79088e8i	−0.208094	−	0.212213i
$946$	−1.65809e8	−	4.06505e8i	−0.195855	−	0.480168i
$947$	9.45923e7	−	1.63839e8i	0.111380	−	0.192915i	−0.804947	−	0.593347i	$-0.797806\pi$
$947$	9.45923e7	−	1.63839e8i	0.111380	−	0.192915i	0.916327	+	0.400431i	$0.131140\pi$
$948$	3.06480e8	−	5.13978e8i	0.359730	−	0.603281i
$949$	−1.31206e9	+	7.57516e8i	−1.53516	+	0.886325i
$950$	−7.34359e8	+	9.46389e8i	−0.856520	+	1.10382i
$951$	2.41176e8	−	8.88463e8i	0.280410	−	1.03299i
$952$	−4.04256e8	−	5.44928e8i	−0.468539	−	0.631580i
$953$	1.40847e9			1.62730			0.813652	−	0.581353i	$-0.197476\pi$
$953$	1.40847e9			1.62730			0.813652	+	0.581353i	$0.197476\pi$
$954$	4.51149e7	+	1.12706e8i	0.0519607	+	0.129808i
$955$	−2.86027e8			−0.328396
$956$	−1.86573e8	+	4.78343e7i	−0.213538	+	0.0547477i
$957$	6.89114e8	+	6.93631e8i	0.786240	+	0.791394i
$958$	1.21145e9	+	9.40037e8i	1.37787	+	1.06917i
$959$	6.84893e7	−	3.95423e7i	0.0776546	−	0.0448339i
$960$	1.23797e7	−	3.46335e8i	0.0139925	−	0.391456i
$961$	1.98285e8	−	3.43440e8i	0.223419	−	0.386973i
$962$	−8.60200e8	−	2.10891e9i	−0.966216	−	2.36882i
$963$	−2.28306e8	+	1.29831e8i	−0.255646	+	0.145379i
$964$	−7.01410e8	+	6.86392e8i	−0.782962	+	0.766198i
$965$	7.13677e7	+	4.12042e7i	0.0794182	+	0.0458521i
$966$	−1.25844e8	−	1.02449e9i	−0.139605	−	1.13652i
$967$	3.80759e8	−	2.19831e8i	0.421086	−	0.243114i	−0.274456	−	0.961600i	$-0.588498\pi$
$967$	3.80759e8	−	2.19831e8i	0.421086	−	0.243114i	0.695542	+	0.718486i	$0.255164\pi$
$968$	1.37126e8	+	1.19061e9i	0.151180	+	1.31263i
$969$	−3.97881e8	−	1.50455e9i	−0.437302	−	1.65362i
$970$	1.18293e7	−	8.62441e7i	0.0129612	−	0.0944962i
$971$	−7.93450e7			−0.0866686			−0.0433343	−	0.999061i	$-0.513798\pi$
$971$	−7.93450e7			−0.0866686			−0.0433343	+	0.999061i	$0.513798\pi$
$972$	−7.82538e8	−	4.80588e8i	−0.852131	−	0.523328i
$973$			1.10175e9i			1.19603i
$974$	−1.68904e8	+	1.23143e9i	−0.182795	+	1.33270i
$975$	1.13083e9	−	2.99049e8i	1.22006	−	0.322648i
$976$	−3.59113e8	−	6.54305e8i	−0.386261	−	0.703770i
$977$	−1.71910e8	−	2.97757e8i	−0.184339	−	0.319284i	0.759015	−	0.651074i	$-0.225681\pi$
$977$	−1.71910e8	−	2.97757e8i	−0.184339	−	0.319284i	−0.943354	+	0.331789i	$0.892348\pi$
$978$	1.93662e8	+	1.57660e9i	0.207027	+	1.68541i
$979$	−5.90361e7	+	1.02253e8i	−0.0629172	+	0.108976i
$980$	−1.09397e8	−	1.11791e8i	−0.116233	−	0.118776i
$981$	5.43037e7	+	9.54921e7i	0.0575205	+	0.101149i
$982$	−6.33724e8	−	1.55367e9i	−0.669216	−	1.64068i
$983$	−6.53785e7	−	3.77463e7i	−0.0688295	−	0.0397387i	0.465190	−	0.885211i	$-0.345986\pi$
$983$	−6.53785e7	−	3.77463e7i	−0.0688295	−	0.0397387i	−0.534020	+	0.845472i	$0.679319\pi$
$984$	−8.90069e8	+	3.48507e8i	−0.934197	+	0.365785i
$985$	−1.71265e8	−	2.96640e8i	−0.179209	−	0.310400i
$986$	−5.74700e8	−	4.45944e8i	−0.599530	−	0.465211i
$987$	2.84323e8	−	2.82472e8i	0.295707	−	0.293781i
$988$	−2.29843e9	+	5.89281e8i	−2.38320	+	0.611015i
$989$			4.96880e8i			0.513644i
$990$	−2.15196e8	−	5.37601e8i	−0.221783	−	0.554057i
$991$		−	1.04865e9i		−	1.07748i	−0.842472	−	0.538741i	$-0.818900\pi$
$991$		−	1.04865e9i		−	1.07748i	0.842472	−	0.538741i	$-0.181100\pi$
$992$	1.15959e9	+	1.84699e8i	1.18787	+	0.189203i
$993$	−6.79197e6	−	1.84370e6i	−0.00693662	−	0.00188297i
$994$	7.09602e8	−	9.14484e8i	0.722530	−	0.931144i
$995$	−4.74189e7	−	8.21319e7i	−0.0481373	−	0.0833763i
$996$	−5.48508e7	−	3.27069e7i	−0.0555143	−	0.0331025i
$997$	−9.92876e8	−	5.73237e8i	−1.00187	−	0.578428i	−0.0930661	−	0.995660i	$-0.529667\pi$
$997$	−9.92876e8	−	5.73237e8i	−1.00187	−	0.578428i	−0.908800	+	0.417232i	$0.863000\pi$
$998$	−2.70782e8	−	6.63863e8i	−0.272413	−	0.667862i
$999$	−1.22165e9	+	1.19794e9i	−1.22532	+	1.20154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.p.b.43.4	✓	136
8.3	odd	2	inner	72.7.p.b.43.48	yes	136
9.4	even	3	inner	72.7.p.b.67.48	yes	136
72.67	odd	6	inner	72.7.p.b.67.4	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.p.b.43.4	✓	136	1.1	even	1	trivial
72.7.p.b.43.48	yes	136	8.3	odd	2	inner
72.7.p.b.67.4	yes	136	72.67	odd	6	inner
72.7.p.b.67.48	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)

\(f(q)\)	\(=\)	\(q+(-7.92579 - 1.08711i) q^{2} +(-6.90289 - 26.1027i) q^{3} +(61.6364 + 17.2324i) q^{4} +(42.4034 - 24.4816i) q^{5} +(26.3344 + 214.389i) q^{6} +(-225.391 - 130.130i) q^{7} +(-469.784 - 203.586i) q^{8} +(-633.700 + 360.368i) q^{9} +O(q^{10})\)	\(q+(-7.92579 - 1.08711i) q^{2} +(-6.90289 - 26.1027i) q^{3} +(61.6364 + 17.2324i) q^{4} +(42.4034 - 24.4816i) q^{5} +(26.3344 + 214.389i) q^{6} +(-225.391 - 130.130i) q^{7} +(-469.784 - 203.586i) q^{8} +(-633.700 + 360.368i) q^{9} +(-362.695 + 147.939i) q^{10} +(1013.95 - 1756.20i) q^{11} +(24.3423 - 1727.83i) q^{12} +(2836.36 - 1637.57i) q^{13} +(1644.94 + 1276.41i) q^{14} +(-931.742 - 937.849i) q^{15} +(3502.09 + 2124.28i) q^{16} -5091.86 q^{17} +(5414.34 - 2167.30i) q^{18} -11320.0 q^{19} +(3035.47 - 778.247i) q^{20} +(-1840.88 + 6781.59i) q^{21} +(-9945.50 + 12817.0i) q^{22} +(15901.3 - 9180.60i) q^{23} +(-2071.27 + 13667.9i) q^{24} +(-6613.80 + 11455.4i) q^{25} +(-24260.6 + 9895.63i) q^{26} +(13780.9 + 14053.7i) q^{27} +(-11649.9 - 11904.8i) q^{28} +(-15465.1 - 8928.76i) q^{29} +(6365.25 + 8446.10i) q^{30} +(-31033.1 + 17917.0i) q^{31} +(-25447.5 - 20643.8i) q^{32} +(-52840.8 - 14343.8i) q^{33} +(40357.1 + 5535.41i) q^{34} -12743.1 q^{35} +(-45269.0 + 11291.6i) q^{36} +86927.3i q^{37} +(89719.7 + 12306.0i) q^{38} +(-62324.1 - 62732.6i) q^{39} +(-24904.5 + 2868.34i) q^{40} +(34572.7 + 59881.7i) q^{41} +(21962.8 - 51748.2i) q^{42} +(-13530.7 + 23435.9i) q^{43} +(92759.5 - 90773.4i) q^{44} +(-18048.7 + 30794.8i) q^{45} +(-136010. + 55477.1i) q^{46} +(-49394.0 - 28517.6i) q^{47} +(31275.0 - 106078. i) q^{48} +(-24957.0 - 43226.8i) q^{49} +(64872.9 - 83603.5i) q^{50} +(35148.6 + 132911. i) q^{51} +(203042. - 52056.8i) q^{52} +20816.2i q^{53} +(-93946.9 - 126368. i) q^{54} -99292.1i q^{55} +(79392.6 + 107019. i) q^{56} +(78140.5 + 295481. i) q^{57} +(112866. + 87579.7i) q^{58} +(-1221.88 - 2116.36i) q^{59} +(-41267.8 - 73861.8i) q^{60} +(-157808. - 91110.4i) q^{61} +(265440. - 108270. i) q^{62} +(189725. + 1239.45i) q^{63} +(179250. + 191283. i) q^{64} +(80180.8 - 138877. i) q^{65} +(403212. + 171130. i) q^{66} +(31505.5 + 54569.1i) q^{67} +(-313844. - 87745.0i) q^{68} +(-349403. - 351693. i) q^{69} +(101000. + 13853.2i) q^{70} -555937. i q^{71} +(371068. - 40282.7i) q^{72} -462585. q^{73} +(94499.4 - 688968. i) q^{74} +(344672. + 93562.3i) q^{75} +(-697722. - 195070. i) q^{76} +(-457069. + 263889. i) q^{77} +(425771. + 564958. i) q^{78} +(299910. + 173153. i) q^{79} +(200506. + 4340.07i) q^{80} +(271711. - 456730. i) q^{81} +(-208918. - 512194. i) q^{82} +(18478.6 - 32005.8i) q^{83} +(-230328. + 386270. i) q^{84} +(-215912. + 124657. i) q^{85} +(132719. - 171039. i) q^{86} +(-126311. + 465314. i) q^{87} +(-833873. + 618612. i) q^{88} -58224.1 q^{89} +(176527. - 224453. i) q^{90} -852387. q^{91} +(1.13830e6 - 291842. i) q^{92} +(681900. + 686369. i) q^{93} +(360485. + 279721. i) q^{94} +(-480005. + 277131. i) q^{95} +(-363197. + 806750. i) q^{96} +(-111119. + 192463. i) q^{97} +(150812. + 369738. i) q^{98} +(-9657.56 + 1.47830e6i) 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

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Database

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