LMFDB - Embedded newform 76.6.k.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	76.3
Dual form			76.6.k.a.51.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.83109 - 2.94288i) q^{2} +(0.477768 - 0.173893i) q^{3} +(14.6789 + 28.4347i) q^{4} +(2.39951 - 13.6083i) q^{5} +(-2.81989 - 0.565922i) q^{6} +(49.8634 - 28.7886i) q^{7} +(12.7651 - 180.569i) q^{8} +(-185.951 + 156.031i) q^{9} +O(q^{10})$	\(q+(-4.83109 - 2.94288i) q^{2} +(0.477768 - 0.173893i) q^{3} +(14.6789 + 28.4347i) q^{4} +(2.39951 - 13.6083i) q^{5} +(-2.81989 - 0.565922i) q^{6} +(49.8634 - 28.7886i) q^{7} +(12.7651 - 180.569i) q^{8} +(-185.951 + 156.031i) q^{9} +(-51.6398 + 58.6813i) q^{10} +(2.23061 + 1.28784i) q^{11} +(11.9577 + 11.0326i) q^{12} +(-166.175 + 456.562i) q^{13} +(-325.616 - 7.66167i) q^{14} +(-1.21998 - 6.91886i) q^{15} +(-593.062 + 834.778i) q^{16} +(72.0101 + 60.4237i) q^{17} +(1357.53 - 206.569i) q^{18} +(1430.28 + 656.055i) q^{19} +(422.169 - 131.525i) q^{20} +(18.8170 - 22.4252i) q^{21} +(-6.98631 - 12.7861i) q^{22} +(1590.17 - 280.389i) q^{23} +(-25.3010 - 88.4898i) q^{24} +(2757.11 + 1003.51i) q^{25} +(2146.41 - 1716.66i) q^{26} +(-123.483 + 213.879i) q^{27} +(1550.53 + 995.265i) q^{28} +(3786.95 + 4513.11i) q^{29} +(-14.4676 + 37.0159i) q^{30} +(2756.34 + 4774.13i) q^{31} +(5321.79 - 2287.57i) q^{32} +(1.28966 + 0.227403i) q^{33} +(-170.068 - 503.830i) q^{34} +(-272.116 - 747.633i) q^{35} +(-7166.24 - 2997.09i) q^{36} +3469.13i q^{37} +(-4979.10 - 7378.60i) q^{38} +247.027i q^{39} +(-2426.60 - 606.986i) q^{40} +(2911.76 + 8000.01i) q^{41} +(-156.901 + 52.9620i) q^{42} +(-10752.1 - 1895.88i) q^{43} +(-3.87660 + 82.3309i) q^{44} +(1677.13 + 2904.87i) q^{45} +(-8507.39 - 3325.09i) q^{46} +(-6078.60 - 7244.19i) q^{47} +(-138.184 + 501.960i) q^{48} +(-6745.93 + 11684.3i) q^{49} +(-10366.7 - 12961.9i) q^{50} +(44.9114 + 16.3464i) q^{51} +(-15421.4 + 1976.68i) q^{52} +(21259.3 - 3748.59i) q^{53} +(1225.98 - 669.871i) q^{54} +(22.8777 - 27.2646i) q^{55} +(-4561.82 - 9371.25i) q^{56} +(797.424 + 64.7266i) q^{57} +(-5013.53 - 32947.8i) q^{58} +(-22182.9 - 18613.6i) q^{59} +(178.828 - 136.251i) q^{60} +(3647.66 + 20686.9i) q^{61} +(733.560 - 31175.8i) q^{62} +(-4780.21 + 13133.5i) q^{63} +(-32442.1 - 4609.94i) q^{64} +(5814.28 + 3356.88i) q^{65} +(-5.56126 - 4.89393i) q^{66} +(-11452.4 + 9609.69i) q^{67} +(-661.101 + 2934.54i) q^{68} +(710.974 - 410.481i) q^{69} +(-885.580 + 4412.69i) q^{70} +(-5232.36 + 29674.2i) q^{71} +(25800.7 + 35568.6i) q^{72} +(13331.7 - 4852.34i) q^{73} +(10209.2 - 16759.7i) q^{74} +1491.76 q^{75} +(2340.12 + 50299.6i) q^{76} +148.301 q^{77} +(726.973 - 1193.41i) q^{78} +(-8739.49 + 3180.92i) q^{79} +(9936.83 + 10073.6i) q^{80} +(10221.0 - 57966.4i) q^{81} +(9476.10 - 47217.7i) q^{82} +(88157.9 - 50898.0i) q^{83} +(913.865 + 205.878i) q^{84} +(995.051 - 834.947i) q^{85} +(46364.9 + 40801.3i) q^{86} +(2594.08 + 1497.69i) q^{87} +(261.018 - 386.339i) q^{88} +(1307.30 - 3591.78i) q^{89} +(446.342 - 18969.3i) q^{90} +(4857.75 + 27549.6i) q^{91} +(31314.6 + 41100.1i) q^{92} +(2147.08 + 1801.62i) q^{93} +(8047.44 + 52886.0i) q^{94} +(12359.7 - 17889.4i) q^{95} +(2144.79 - 2018.35i) q^{96} +(-65250.3 + 77762.3i) q^{97} +(66975.7 - 36595.4i) q^{98} +(-615.728 + 108.569i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) $ 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−4.83109	−	2.94288i	−0.854024	−	0.520233i
$2$	−4.83109	−	2.94288i	−0.854024	−	0.520233i
$3$	0.477768	−	0.173893i	0.0306489	−	0.0111553i	−0.326650	−	0.945145i	$-0.605920\pi$
$3$	0.477768	−	0.173893i	0.0306489	−	0.0111553i	0.357299	+	0.933990i	$0.383698\pi$
$4$	14.6789	+	28.4347i	0.458714	+	0.888584i
$5$	2.39951	−	13.6083i	0.0429237	−	0.243432i	−0.955795	−	0.294033i	$-0.905002\pi$
$5$	2.39951	−	13.6083i	0.0429237	−	0.243432i	0.998719	+	0.0506007i	$0.0161136\pi$
$6$	−2.81989	−	0.565922i	−0.0319782	−	0.00641769i
$7$	49.8634	−	28.7886i	0.384624	−	0.222063i	−0.295204	−	0.955434i	$-0.595388\pi$
$7$	49.8634	−	28.7886i	0.384624	−	0.222063i	0.679828	+	0.733371i	$0.262054\pi$
$8$	12.7651	−	180.569i	0.0705177	−	0.997511i
$9$	−185.951	+	156.031i	−0.765230	+	0.642104i
$10$	−51.6398	+	58.6813i	−0.163299	+	0.185567i
$11$	2.23061	+	1.28784i	0.00555831	+	0.00320909i	0.502777	−	0.864416i	$-0.332312\pi$
$11$	2.23061	+	1.28784i	0.00555831	+	0.00320909i	−0.497218	+	0.867625i	$0.665645\pi$
$12$	11.9577	+	11.0326i	0.0239715	+	0.0221170i
$13$	−166.175	+	456.562i	−0.272714	+	0.749275i	0.725426	+	0.688301i	$0.241643\pi$
$13$	−166.175	+	456.562i	−0.272714	+	0.749275i	−0.998139	+	0.0609742i	$0.980579\pi$
$14$	−325.616	−	7.66167i	−0.444003	−	0.0104473i
$15$	−1.21998	−	6.91886i	−0.00139999	−	0.00793974i
$16$	−593.062	+	834.778i	−0.579162	+	0.815212i
$17$	72.0101	+	60.4237i	0.0604326	+	0.0507090i	0.672504	−	0.740094i	$-0.265219\pi$
$17$	72.0101	+	60.4237i	0.0604326	+	0.0507090i	−0.612071	+	0.790803i	$0.709663\pi$
$18$	1357.53	−	206.569i	0.987568	−	0.150274i
$19$	1430.28	+	656.055i	0.908942	+	0.416923i
$19$	1430.28	+	656.055i	0.908942	+	0.416923i
$20$	422.169	−	131.525i	0.236000	−	0.0735246i
$21$	18.8170	−	22.4252i	0.00931112	−	0.0110966i
$22$	−6.98631	−	12.7861i	−0.00307745	−	0.00563226i
$23$	1590.17	−	280.389i	0.626792	−	0.110520i	0.148775	−	0.988871i	$-0.452467\pi$
$23$	1590.17	−	280.389i	0.626792	−	0.110520i	0.478017	+	0.878351i	$0.341356\pi$
$24$	−25.3010	−	88.4898i	−0.00896621	−	0.0313592i
$25$	2757.11	+	1003.51i	0.882276	+	0.321122i
$26$	2146.41	−	1716.66i	0.622702	−	0.498024i
$27$	−123.483	+	213.879i	−0.0325985	+	0.0564622i
$28$	1550.53	+	995.265i	0.373754	+	0.239907i
$29$	3786.95	+	4513.11i	0.836169	+	0.996507i	0.999950	+	0.0100107i	$0.00318654\pi$
$29$	3786.95	+	4513.11i	0.836169	+	0.996507i	−0.163781	+	0.986497i	$0.552369\pi$
$30$	−14.4676	+	37.0159i	−0.00293489	+	0.00750905i
$31$	2756.34	+	4774.13i	0.515144	+	0.892256i	0.999846	+	0.0175764i	$0.00559504\pi$
$31$	2756.34	+	4774.13i	0.515144	+	0.892256i	−0.484701	+	0.874680i	$0.661072\pi$
$32$	5321.79	−	2287.57i	0.918719	−	0.394912i
$33$	1.28966	+	0.227403i	0.000206154	+	3.63505e-5i
$34$	−170.068	−	503.830i	−0.0252304	−	0.0747458i
$35$	−272.116	−	747.633i	−0.0375478	−	0.103162i
$36$	−7166.24	−	2997.09i	−0.921585	−	0.385428i
$37$			3469.13i			0.416597i	0.978065	+	0.208299i	$0.0667926\pi$
$37$			3469.13i			0.416597i	−0.978065	+	0.208299i	$0.933207\pi$
$38$	−4979.10	−	7378.60i	−0.559361	−	0.828924i
$39$			247.027i			0.0260066i
$40$	−2426.60	−	606.986i	−0.239799	−	0.0599831i
$41$	2911.76	+	8000.01i	0.270518	+	0.743243i	0.998346	+	0.0574833i	$0.0183076\pi$
$41$	2911.76	+	8000.01i	0.270518	+	0.743243i	−0.727828	+	0.685760i	$0.759470\pi$
$42$	−156.901	+	52.9620i	−0.0137247	+	0.00463277i
$43$	−10752.1	−	1895.88i	−0.886790	−	0.156365i	−0.288343	−	0.957527i	$-0.593104\pi$
$43$	−10752.1	−	1895.88i	−0.886790	−	0.156365i	−0.598447	+	0.801162i	$0.704215\pi$
$44$	−3.87660	+	82.3309i	−0.000301869	+	0.00641108i
$45$	1677.13	+	2904.87i	0.123462	+	0.213843i
$46$	−8507.39	−	3325.09i	−0.592791	−	0.231691i
$47$	−6078.60	−	7244.19i	−0.401383	−	0.478350i	0.527058	−	0.849829i	$-0.323295\pi$
$47$	−6078.60	−	7244.19i	−0.401383	−	0.478350i	−0.928441	+	0.371480i	$0.878851\pi$
$48$	−138.184	+	501.960i	−0.00865674	+	0.0314460i
$49$	−6745.93	+	11684.3i	−0.401376	+	0.695204i
$50$	−10366.7	−	12961.9i	−0.586426	−	0.733235i
$51$	44.9114	+	16.3464i	0.00241786	+	0.000880030i
$52$	−15421.4	+	1976.68i	−0.790891	+	0.101374i
$53$	21259.3	−	3748.59i	1.03958	−	0.183307i	0.372301	−	0.928112i	$-0.378569\pi$
$53$	21259.3	−	3748.59i	1.03958	−	0.183307i	0.667282	+	0.744805i	$0.267458\pi$
$54$	1225.98	−	669.871i	0.0572134	−	0.0312613i
$55$	22.8777	−	27.2646i	0.00101978	−	0.00121533i
$56$	−4561.82	−	9371.25i	−0.194387	−	0.399326i
$57$	797.424	+	64.7266i	0.0325089	+	0.00263873i
$58$	−5013.53	−	32947.8i	−0.195692	−	1.28604i
$59$	−22182.9	−	18613.6i	−0.829637	−	0.696148i	0.125571	−	0.992085i	$-0.459924\pi$
$59$	−22182.9	−	18613.6i	−0.829637	−	0.696148i	−0.955207	+	0.295937i	$0.904368\pi$
$60$	178.828	−	136.251i	0.00641293	−	0.00488608i
$61$	3647.66	+	20686.9i	0.125513	+	0.711821i	0.981002	+	0.193999i	$0.0621459\pi$
$61$	3647.66	+	20686.9i	0.125513	+	0.711821i	−0.855488	+	0.517822i	$0.826743\pi$
$62$	733.560	−	31175.8i	0.0242357	−	1.03000i
$63$	−4780.21	+	13133.5i	−0.151738	+	0.416898i
$64$	−32442.1	−	4609.94i	−0.990055	−	0.140684i
$65$	5814.28	+	3356.88i	0.170692	+	0.0985489i
$66$	−5.56126	−	4.89393i	−0.000157150	−	0.000138292i
$67$	−11452.4	+	9609.69i	−0.311680	+	0.261531i	−0.785186	−	0.619260i	$-0.787433\pi$
$67$	−11452.4	+	9609.69i	−0.311680	+	0.261531i	0.473506	+	0.880791i	$0.342988\pi$
$68$	−661.101	+	2934.54i	−0.0173379	+	0.0769604i
$69$	710.974	−	410.481i	0.0179776	−	0.0103793i
$70$	−885.580	+	4412.69i	−0.0216014	+	0.107636i
$71$	−5232.36	+	29674.2i	−0.123183	+	0.698608i	0.859187	+	0.511662i	$0.170970\pi$
$71$	−5232.36	+	29674.2i	−0.123183	+	0.698608i	−0.982370	+	0.186946i	$0.940141\pi$
$72$	25800.7	+	35568.6i	0.586543	+	0.808604i
$73$	13331.7	−	4852.34i	0.292805	−	0.106572i	−0.191441	−	0.981504i	$-0.561316\pi$
$73$	13331.7	−	4852.34i	0.292805	−	0.106572i	0.484246	+	0.874932i	$0.339094\pi$
$74$	10209.2	−	16759.7i	0.216728	−	0.355784i
$75$	1491.76			0.0306229
$76$	2340.12	+	50299.6i	0.0464734	+	0.998920i
$77$	148.301			0.00285048
$78$	726.973	−	1193.41i	0.0135295	−	0.0222103i
$79$	−8739.49	+	3180.92i	−0.157550	+	0.0573435i	−0.419591	−	0.907713i	$-0.637827\pi$
$79$	−8739.49	+	3180.92i	−0.157550	+	0.0573435i	0.262041	+	0.965057i	$0.415604\pi$
$80$	9936.83	+	10073.6i	0.173589	+	0.175979i
$81$	10221.0	−	57966.4i	0.173094	−	0.981666i
$82$	9476.10	−	47217.7i	0.155631	−	0.775480i
$83$	88157.9	−	50898.0i	1.40464	−	0.810971i	0.409778	−	0.912185i	$-0.365606\pi$
$83$	88157.9	−	50898.0i	1.40464	−	0.810971i	0.994865	+	0.101215i	$0.0322729\pi$
$84$	913.865	+	205.878i	0.0141314	+	0.00318356i
$85$	995.051	−	834.947i	0.0149382	−	0.0125346i
$86$	46364.9	+	40801.3i	0.675994	+	0.594877i
$87$	2594.08	+	1497.69i	0.0367439	+	0.0212141i
$88$	261.018	−	386.339i	0.00359306	−	0.00531817i
$89$	1307.30	−	3591.78i	0.0174945	−	0.0480656i	−0.930638	−	0.365941i	$-0.880747\pi$
$89$	1307.30	−	3591.78i	0.0174945	−	0.0480656i	0.948132	+	0.317875i	$0.102969\pi$
$90$	446.342	−	18969.3i	0.00580847	−	0.246856i
$91$	4857.75	+	27549.6i	0.0614938	+	0.348749i
$92$	31314.6	+	41100.1i	0.385725	+	0.506260i
$93$	2147.08	+	1801.62i	0.0257419	+	0.0216001i
$94$	8047.44	+	52886.0i	0.0939373	+	0.617335i
$95$	12359.7	−	17889.4i	0.140508	−	0.203370i
$96$	2144.79	−	2018.35i	0.0237523	−	0.0223521i
$97$	−65250.3	+	77762.3i	−0.704130	+	0.839150i	−0.992987	−	0.118222i	$-0.962280\pi$
$97$	−65250.3	+	77762.3i	−0.704130	+	0.839150i	0.288857	+	0.957372i	$0.406725\pi$
$98$	66975.7	−	36595.4i	0.704453	−	0.384912i
$99$	−615.728	+	108.569i	−0.00631395	+	0.00111332i
$100$	11936.9	+	93127.9i	0.119369	+	0.931279i
$101$	−137150.	−	49918.4i	−1.33780	−	0.486919i	−0.428681	−	0.903456i	$-0.641022\pi$
$101$	−137150.	−	49918.4i	−1.33780	−	0.486919i	−0.909119	+	0.416537i	$0.863244\pi$
$102$	−168.866	−	211.140i	−0.00160709	−	0.00200942i
$103$	39044.2	−	67626.6i	0.362630	−	0.628093i	−0.625763	−	0.780013i	$-0.715212\pi$
$103$	39044.2	−	67626.6i	0.362630	−	0.628093i	0.988393	+	0.151920i	$0.0485456\pi$
$104$	80319.5	+	35834.0i	0.728178	+	0.324872i
$105$	−260.017	−	309.876i	−0.00230159	−	0.00274293i
$106$	−113737.	−	44453.9i	−0.983191	−	0.384278i
$107$	79698.4	+	138042.i	0.672961	+	1.16560i	0.977060	+	0.212962i	$0.0683112\pi$
$107$	79698.4	+	138042.i	0.672961	+	1.16560i	−0.304099	+	0.952640i	$0.598355\pi$
$108$	−7894.16	−	371.701i	−0.0651248	−	0.00306644i
$109$	−38532.7	−	6794.36i	−0.310644	−	0.0547750i	0.0161526	−	0.999870i	$-0.494858\pi$
$109$	−38532.7	−	6794.36i	−0.310644	−	0.0547750i	−0.326797	+	0.945095i	$0.605969\pi$
$110$	−190.761	+	64.3913i	−0.00150317	+	0.000507394i
$111$	603.259	+	1657.44i	0.00464725	+	0.0127682i
$112$	−5539.97	+	58698.3i	−0.0417313	+	0.442161i
$113$		−	65644.7i		−	0.483619i	−0.970324	−	0.241810i	$-0.922259\pi$
$113$		−	65644.7i		−	0.483619i	0.970324	−	0.241810i	$-0.0777410\pi$
$114$	−3661.95	−	2659.43i	−0.0263906	−	0.0191658i
$115$		−	22312.2i		−	0.157325i
$116$	−72740.7	+	173928.i	−0.501917	+	1.20012i
$117$	−40337.5	−	110826.i	−0.272424	−	0.748478i
$118$	52389.7	+	155206.i	0.346370	+	1.02613i
$119$	5330.18	+	939.855i	0.0345044	+	0.00608406i
$120$	−1264.90	+	131.971i	−0.00801870	+	0.000836613i
$121$	−80522.2	−	139469.i	−0.499979	−	0.865990i
$122$	43257.0	−	110675.i	0.263122	−	0.673208i
$123$	2782.30	+	3315.81i	0.0165821	+	0.0197618i
$124$	−95290.8	+	148454.i	−0.556540	+	0.867040i
$125$	41862.7	−	72508.2i	0.239636	−	0.415061i
$126$	61744.0	−	49381.6i	0.346472	−	0.277101i
$127$	−163995.	−	59689.4i	−0.902240	−	0.328388i	−0.151090	−	0.988520i	$-0.548278\pi$
$127$	−163995.	−	59689.4i	−0.902240	−	0.328388i	−0.751150	+	0.660132i	$0.770501\pi$
$128$	143164.	+	117744.i	0.772342	+	0.635207i
$129$	−5466.68	+	963.923i	−0.0289234	+	0.00509998i
$130$	−18210.4	−	33328.1i	−0.0945064	−	0.172963i
$131$	116205.	−	138487.i	0.591623	−	0.705068i	−0.384294	−	0.923211i	$-0.625555\pi$
$131$	116205.	−	138487.i	0.591623	−	0.705068i	0.975917	+	0.218142i	$0.0699997\pi$
$132$	12.4647	+	40.0092i	6.22653e−5	+	0.000199860i
$133$	90205.3	−	8462.59i	0.442184	−	0.0414834i
$134$	83607.7	−	12722.2i	0.402239	−	0.0612071i
$135$	2614.22	+	2193.59i	0.0123455	+	0.0103591i
$136$	11829.8	−	12231.5i	0.0548443	−	0.0567063i
$137$	10386.7	+	58905.6i	0.0472796	+	0.268136i	0.999279	−	0.0379635i	$-0.0120870\pi$
$137$	10386.7	+	58905.6i	0.0472796	+	0.268136i	−0.951999	+	0.306100i	$0.900976\pi$
$138$	−4642.77	−	109.243i	−0.0207530	−	0.000488312i
$139$	−34255.1	+	94115.0i	−0.150379	+	0.413163i	−0.991894	−	0.127071i	$-0.959442\pi$
$139$	−34255.1	+	94115.0i	−0.150379	+	0.413163i	0.841514	+	0.540235i	$0.181665\pi$
$140$	17264.3	−	18711.9i	0.0744441	−	0.0806861i
$141$	−4163.88	−	2404.02i	−0.0176380	−	0.0101833i
$142$	112606.	−	127961.i	0.468641	−	0.532544i
$143$	−958.652	+	804.405i	−0.00392032	+	0.00328954i
$144$	−19971.0	−	247764.i	−0.0802591	−	0.995707i
$145$	70502.4	−	40704.6i	0.278473	−	0.160777i
$146$	−78686.6	−	15791.6i	−0.305505	−	0.0613116i
$147$	−1191.17	+	6755.46i	−0.00454653	+	0.0257847i
$148$	−98643.6	+	50922.9i	−0.370181	+	0.191099i
$149$	−10216.5	+	3718.49i	−0.0376995	+	0.0137215i	−0.360801	−	0.932643i	$-0.617497\pi$
$149$	−10216.5	+	3718.49i	−0.0376995	+	0.0137215i	0.323102	+	0.946364i	$0.395274\pi$
$150$	−7206.85	−	4390.09i	−0.0261527	−	0.0159311i
$151$	−386778.			−1.38045			−0.690223	−	0.723597i	$-0.742488\pi$
$151$	−386778.			−1.38045			−0.690223	+	0.723597i	$0.742488\pi$
$152$	136721.	−	249889.i	0.479982	−	0.877278i
$153$	−22818.3			−0.0788053
$154$	−716.456	−	436.433i	−0.00243438	−	0.00148291i
$155$	71581.5	−	26053.5i	0.239316	−	0.0871038i
$156$	−7024.15	+	3626.08i	−0.0231090	+	0.0119296i
$157$	12079.9	−	68508.7i	0.0391125	−	0.221818i	−0.958986	−	0.283452i	$-0.908520\pi$
$157$	12079.9	−	68508.7i	0.0391125	−	0.221818i	0.998099	+	0.0616346i	$0.0196313\pi$
$158$	51582.3	+	10352.0i	0.164384	+	0.0329900i
$159$	9505.16	−	5487.81i	0.0298172	−	0.0172150i
$160$	−18360.3	−	77909.4i	−0.0566994	−	0.240597i
$161$	71219.1	−	59759.9i	0.216537	−	0.181696i
$162$	−219967.	+	249962.i	−0.658522	+	0.748317i
$163$	−168550.	−	97312.2i	−0.496889	−	0.286879i	0.230539	−	0.973063i	$-0.425951\pi$
$163$	−168550.	−	97312.2i	−0.496889	−	0.286879i	−0.727428	+	0.686184i	$0.759284\pi$
$164$	−184736.	+	200226.i	−0.536343	+	0.581314i
$165$	6.18911	−	17.0044i	1.76978e−5	−	4.86242e-5i
$166$	−575685.	−	13545.7i	−1.62149	−	0.0381533i
$167$	63448.8	+	359836.i	0.176048	+	0.998420i	0.936927	+	0.349525i	$0.113657\pi$
$167$	63448.8	+	359836.i	0.176048	+	0.998420i	−0.760879	+	0.648894i	$0.775232\pi$
$168$	−3809.09	−	3684.02i	−0.0104123	−	0.0100704i
$169$	103592.	+	86924.4i	0.279005	+	0.234113i
$170$	−7264.33	+	1105.38i	−0.0192785	+	0.00293353i
$171$	−368326.	+	101174.i	−0.963257	+	0.264593i
$172$	−103919.	−	333561.i	−0.267840	−	0.859714i
$173$	−232932.	+	277598.i	−0.591717	+	0.705181i	−0.975935	−	0.218062i	$-0.930027\pi$
$173$	−232932.	+	277598.i	−0.591717	+	0.705181i	0.384218	+	0.923242i	$0.374471\pi$
$174$	−8124.70	−	14869.6i	−0.0203439	−	0.0372328i
$175$	166368.	−	29335.2i	0.410654	−	0.0724093i
$176$	−2397.96	+	1098.29i	−0.00583525	+	0.00267262i
$177$	−13835.1	−	5035.55i	−0.0331931	−	0.0120813i
$178$	−16885.9	+	13505.0i	−0.0399460	+	0.0319480i
$179$	223852.	−	387723.i	0.522190	−	0.904459i	−0.477477	−	0.878644i	$-0.658449\pi$
$179$	223852.	−	387723.i	0.522190	−	0.904459i	0.999667	−	0.0258147i	$-0.00821799\pi$
$180$	−57980.7	+	90328.7i	−0.133383	+	0.207799i
$181$	42883.6	+	51106.7i	0.0972961	+	0.115953i	0.812495	−	0.582968i	$-0.198109\pi$
$181$	42883.6	+	51106.7i	0.0972961	+	0.115953i	−0.715199	+	0.698921i	$0.753664\pi$
$182$	57607.2	−	147391.i	0.128914	−	0.329831i
$183$	5340.05	+	9249.24i	0.0117874	+	0.0204164i
$184$	−30331.0	−	290714.i	−0.0660452	−	0.633025i
$185$	47208.9	+	8324.20i	0.101413	+	0.0178819i
$186$	−5070.80	−	15022.4i	−0.0107472	−	0.0318388i
$187$	82.8104	+	227.520i	0.000173173	+	0.000475790i
$188$	116759.	−	279180.i	0.240934	−	0.576088i
$189$			14219.6i			0.0289556i
$190$	−112357.	+	50052.0i	−0.225797	+	0.100586i
$191$		−	559312.i		−	1.10935i	−0.832066	−	0.554677i	$-0.812842\pi$
$191$		−	559312.i		−	1.10935i	0.832066	−	0.554677i	$-0.187158\pi$
$192$	−16301.4	+	3438.98i	−0.0319134	+	0.00673251i
$193$	276884.	+	760734.i	0.535064	+	1.47008i	0.852974	+	0.521954i	$0.174797\pi$
$193$	276884.	+	760734.i	0.535064	+	1.47008i	−0.317910	+	0.948121i	$0.602981\pi$
$194$	544075.	−	183652.i	1.03790	−	0.350342i
$195$	3361.62	+	592.744i	0.00633085	+	0.00111630i
$196$	−431262.	−	20306.2i	−0.801864	−	0.0377562i
$197$	379877.	+	657966.i	0.697393	+	1.20792i	0.969367	+	0.245615i	$0.0789900\pi$
$197$	379877.	+	657966.i	0.697393	+	1.20792i	−0.271975	+	0.962304i	$0.587677\pi$
$198$	3294.15	+	1287.51i	0.00597145	+	0.00233393i
$199$	171205.	+	204034.i	0.306467	+	0.365234i	0.897193	−	0.441639i	$-0.145603\pi$
$199$	171205.	+	204034.i	0.306467	+	0.365234i	−0.590725	+	0.806873i	$0.701158\pi$
$200$	216397.	−	485038.i	0.382539	−	0.857435i
$201$	−3800.52	+	6582.70i	−0.00663519	+	0.0114925i
$202$	515678.	+	644776.i	0.889202	+	1.11181i
$203$	318756.	+	116018.i	0.542898	+	0.197599i
$204$	194.443	+	1516.99i	0.000327128	+	0.00255216i
$205$	115853.	−	20428.0i	0.192541	−	0.0339502i
$206$	−387643.	+	211807.i	−0.636450	+	0.347755i
$207$	−251943.	+	300254.i	−0.408674	+	0.487039i
$208$	−282575.	−	409488.i	−0.452873	−	0.656271i
$209$	2345.50	+	3305.38i	0.00371423	+	0.00523426i
$210$	344.236	+	2262.24i	0.000538651	+	0.00353989i
$211$	544969.	+	457283.i	0.842686	+	0.707098i	0.958166	−	0.286212i	$-0.0923962\pi$
$211$	544969.	+	457283.i	0.842686	+	0.707098i	−0.115480	+	0.993310i	$0.536841\pi$
$212$	418652.	+	549476.i	0.639755	+	0.839671i
$213$	2660.29	+	15087.3i	0.00401773	+	0.0227857i
$214$	21210.5	−	901435.i	0.0316605	−	1.34555i
$215$	−51599.3	+	141768.i	−0.0761286	+	0.209162i
$216$	37043.5	+	25027.3i	0.0540229	+	0.0364989i
$217$	274881.	+	158703.i	0.396274	+	0.228789i
$218$	166160.	+	146222.i	0.236802	+	0.208387i
$219$	5525.68	−	4636.59i	0.00778530	−	0.00653264i
$220$	1111.08	+	250.307i	0.00154771	+	0.000348672i
$221$	−39553.4	+	22836.2i	−0.0544758	+	0.0314516i
$222$	1963.26	−	9782.56i	0.00267359	−	0.0133220i
$223$	−74233.3	+	420998.i	−0.0999624	+	0.566915i	0.893151	+	0.449757i	$0.148489\pi$
$223$	−74233.3	+	420998.i	−0.0999624	+	0.566915i	−0.993113	+	0.117158i	$0.962622\pi$
$224$	199506.	−	267273.i	0.265666	−	0.355906i
$225$	−669265.	+	243593.i	−0.881337	+	0.320781i
$226$	−193185.	+	317136.i	−0.251595	+	0.413023i
$227$	898850.			1.15777			0.578886	−	0.815409i	$-0.303488\pi$
$227$	898850.			1.15777			0.578886	+	0.815409i	$0.303488\pi$
$228$	9864.80	+	23624.6i	0.0125676	+	0.0300973i
$229$	918878.			1.15790			0.578948	−	0.815365i	$-0.303464\pi$
$229$	918878.			1.15790			0.578948	+	0.815365i	$0.303464\pi$
$230$	−65662.3	+	107792.i	−0.0818458	+	0.134360i
$231$	70.8536	−	25.7886i	8.73639e−5	−	3.17978e-5i
$232$	863266.	−	626194.i	1.05299	−	0.763816i
$233$	107232.	−	608144.i	0.129400	−	0.733866i	−0.849196	−	0.528078i	$-0.822913\pi$
$233$	107232.	−	608144.i	0.129400	−	0.733866i	0.978596	−	0.205789i	$-0.0659759\pi$
$234$	−131275.	+	654121.i	−0.156727	+	0.780942i
$235$	−113167.	+	65336.8i	−0.133675	+	0.0771770i
$236$	203654.	−	903990.i	0.238019	−	1.05653i
$237$	−3622.31	+	3039.48i	−0.00418905	+	0.00351503i
$238$	−22984.7	−	20226.6i	−0.0263025	−	0.0231463i
$239$	−883590.	−	510141.i	−1.00059	−	0.577691i	−0.0921670	−	0.995744i	$-0.529379\pi$
$239$	−883590.	−	510141.i	−1.00059	−	0.577691i	−0.908423	+	0.418053i	$0.862713\pi$
$240$	6499.23	+	3084.90i	0.00728340	+	0.00345711i
$241$	26597.6	−	73076.2i	0.0294984	−	0.0810463i	−0.924069	−	0.382225i	$-0.875158\pi$
$241$	26597.6	−	73076.2i	0.0294984	−	0.0810463i	0.953568	+	0.301179i	$0.0973801\pi$
$242$	−21429.8	+	910752.i	−0.0235223	+	0.999682i
$243$	−15617.8	−	88572.8i	−0.0169669	−	0.0962243i
$244$	−534682.	+	407380.i	−0.574938	+	0.438052i
$245$	142816.	+	119837.i	0.152007	+	0.127549i
$246$	−3683.48	−	24207.0i	−0.00388079	−	0.0255037i
$247$	−537206.	+	543990.i	−0.560271	+	0.567346i
$248$	897243.	−	436767.i	0.926362	−	0.450942i
$249$	33268.2	−	39647.5i	0.0340041	−	0.0405245i
$250$	−415626.	+	227097.i	−0.420584	+	0.229806i
$251$	1.27362e6	−	224573.i	1.27601	−	0.224995i	0.505725	−	0.862695i	$-0.331225\pi$
$251$	1.27362e6	−	224573.i	1.27601	−	0.224995i	0.770285	+	0.637700i	$0.220114\pi$
$252$	−443615.	+	56861.3i	−0.440053	+	0.0564048i
$253$	3908.14	+	1422.45i	0.00383857	+	0.00139712i
$254$	616617.	+	770984.i	0.599696	+	0.749827i
$255$	330.212	−	571.944i	0.000318011	−	0.000550812i
$256$	−345131.	−	990150.i	−0.329143	−	0.944280i
$257$	61472.2	+	73259.8i	0.0580559	+	0.0691883i	0.794291	−	0.607538i	$-0.207843\pi$
$257$	61472.2	+	73259.8i	0.0580559	+	0.0691883i	−0.736235	+	0.676726i	$0.763398\pi$
$258$	29246.7	+	11431.0i	0.0273545	+	0.0106914i
$259$	99871.5	+	172982.i	0.0925107	+	0.160233i
$260$	−10104.7	+	214602.i	−0.00927020	+	0.196880i
$261$	−1.40837e6	−	248334.i	−1.27972	−	0.225650i
$262$	−968946.	+	327067.i	−0.872060	+	0.294364i
$263$	−563817.	−	1.54908e6i	−0.502631	−	1.38097i	−0.888697	−	0.458496i	$-0.848388\pi$
$263$	−563817.	−	1.54908e6i	−0.502631	−	1.38097i	0.386066	−	0.922471i	$-0.373834\pi$
$264$	57.5244	−	229.970i	5.07975e−5	−	0.000203077i
$265$		−	298297.i		−	0.260936i
$266$	−460694.	−	224580.i	−0.399217	−	0.194611i
$267$		−	1943.37i		−	0.00166831i
$268$	−441356.	−	184585.i	−0.375364	−	0.156986i
$269$	260467.	+	715627.i	0.219468	+	0.602984i	0.999748	−	0.0224466i	$-0.00714556\pi$
$269$	260467.	+	715627.i	0.219468	+	0.602984i	−0.780280	+	0.625431i	$0.784923\pi$
$270$	−6174.05	−	18290.8i	−0.00515419	−	0.0152694i
$271$	−1.25762e6	−	221753.i	−1.04022	−	0.183419i	−0.372657	−	0.927969i	$-0.621553\pi$
$271$	−1.25762e6	−	221753.i	−1.04022	−	0.183419i	−0.667567	+	0.744550i	$0.732664\pi$
$272$	−93146.8	+	24277.5i	−0.0763389	+	0.0198967i
$273$	7111.58	+	12317.6i	0.00577510	+	0.0100028i
$274$	123174.	−	315145.i	0.0991154	−	0.253591i
$275$	4857.69	+	5789.17i	0.00387345	+	0.00461620i
$276$	22108.2	+	14190.9i	0.0174695	+	0.0112134i
$277$	1.06503e6	−	1.84468e6i	0.833991	−	1.44451i	−0.0608589	−	0.998146i	$-0.519384\pi$
$277$	1.06503e6	−	1.84468e6i	0.833991	−	1.44451i	0.894850	−	0.446368i	$-0.147283\pi$
$278$	442459.	−	353869.i	0.343369	−	0.274619i
$279$	−1.25746e6	−	457677.i	−0.967125	−	0.352005i
$280$	−138473.	+	39592.1i	−0.105553	+	0.0301796i
$281$	−2.14787e6	+	378728.i	−1.62272	+	0.286129i	−0.909778	−	0.415096i	$-0.863748\pi$
$281$	−2.14787e6	+	378728.i	−1.62272	+	0.286129i	−0.712940	+	0.701225i	$0.752637\pi$
$282$	13041.3	+	23867.8i	0.00976561	+	0.0178727i
$283$	163383.	−	194713.i	0.121267	−	0.144520i	−0.701995	−	0.712182i	$-0.747707\pi$
$283$	163383.	−	194713.i	0.121267	−	0.144520i	0.823262	+	0.567661i	$0.192152\pi$
$284$	−920582.	+	286803.i	−0.677277	+	0.211003i
$285$	2794.24	−	10696.3i	0.00203775	−	0.00780045i
$286$	6998.61	−	1064.95i	0.00505937	−	0.000769864i
$287$	375500.	+	315082.i	0.269094	+	0.225797i
$288$	−632658.	+	1.25574e6i	−0.449457	+	0.892111i
$289$	−245021.	−	1.38958e6i	−0.172567	−	0.978679i
$290$	−460392.	−	10832.9i	−0.321465	−	0.00756398i
$291$	−17652.2	+	48498.9i	−0.0122198	+	0.0335737i
$292$	333669.	+	307856.i	0.229012	+	0.211296i
$293$	−2.06699e6	−	1.19338e6i	−1.40660	−	0.812098i	−0.411537	−	0.911393i	$-0.635008\pi$
$293$	−2.06699e6	−	1.19338e6i	−1.40660	−	0.812098i	−0.995058	+	0.0992947i	$0.968341\pi$
$294$	25635.2	−	29130.8i	0.0172969	−	0.0196555i
$295$	−306528.	+	257207.i	−0.205076	+	0.172079i
$296$	626416.	+	44283.7i	0.415560	+	0.0293775i
$297$	−550.885	+	318.054i	−0.000362385	+	0.000209223i
$298$	60299.8	+	12101.5i	0.0393346	+	0.00789405i
$299$	−136231.	+	772603.i	−0.0881246	+	0.499779i
$300$	21897.4	+	42417.8i	0.0140472	+	0.0272110i
$301$	−590714.	+	215002.i	−0.375804	+	0.136781i
$302$	1.86856e6	+	1.13824e6i	1.17893	+	0.718154i
$303$	−74206.2			−0.0464337
$304$	−1.39590e6	+	804881.i	−0.866306	+	0.499514i
$305$	290266.			0.178668
$306$	110237.	+	67151.7i	0.0673016	+	0.0409971i
$307$	894313.	−	325503.i	0.541556	−	0.197110i	−0.0567347	−	0.998389i	$-0.518069\pi$
$307$	894313.	−	325503.i	0.541556	−	0.197110i	0.598291	+	0.801279i	$0.295847\pi$
$308$	2176.89	+	4216.90i	0.00130756	+	0.00253289i
$309$	6894.27	−	39099.4i	0.00410764	−	0.0232956i
$310$	−422489.	−	84789.1i	−0.249696	−	0.0501113i
$311$	−892578.	+	515330.i	−0.523293	+	0.302123i	−0.738281	−	0.674493i	$-0.764362\pi$
$311$	−892578.	+	515330.i	−0.523293	+	0.302123i	0.214988	+	0.976617i	$0.431029\pi$
$312$	44605.4	+	3153.32i	0.0259419	+	0.00183393i
$313$	2.06421e6	−	1.73208e6i	1.19095	−	0.999324i	0.191106	−	0.981569i	$-0.438793\pi$
$313$	2.06421e6	−	1.73208e6i	1.19095	−	0.999324i	0.999842	−	0.0177546i	$-0.00565177\pi$
$314$	−259972.	+	295422.i	−0.148800	+	0.169090i
$315$	167254.	+	96564.3i	0.0949732	+	0.0548328i
$316$	−218734.	−	201812.i	−0.123225	−	0.113692i
$317$	380425.	−	1.04521e6i	0.212628	−	0.584191i	−0.786828	−	0.617173i	$-0.788278\pi$
$317$	380425.	−	1.04521e6i	0.212628	−	0.584191i	0.999456	+	0.0329815i	$0.0105002\pi$
$318$	−62070.3	−	1460.50i	−0.0344204	−	0.000809904i
$319$	2635.03	+	14944.0i	0.00144980	+	0.00822223i
$320$	−140578.	+	430420.i	−0.0767439	+	0.234973i
$321$	62081.9	+	52092.9i	0.0336281	+	0.0282173i
$322$	−519932.	+	79115.9i	−0.279452	+	0.0425230i
$323$	63353.2	+	133665.i	0.0337880	+	0.0712873i
$324$	1.79829e6	−	560249.i	0.951693	−	0.296496i
$325$	−916325.	+	1.09203e6i	−0.481217	+	0.573493i
$326$	527900.	+	966146.i	0.275111	+	0.503499i
$327$	−19591.2	+	3454.46i	−0.0101319	+	0.00178653i
$328$	1.48172e6	−	423653.i	0.760469	−	0.217433i
$329$	−511650.	−	186225.i	−0.260605	−	0.0948525i
$330$	−79.9423	+	63.9362i	−4.04103e−5	+	3.23193e-5i
$331$	1.63893e6	−	2.83871e6i	0.822224	−	1.42413i	−0.0817980	−	0.996649i	$-0.526066\pi$
$331$	1.63893e6	−	2.83871e6i	0.822224	−	1.42413i	0.904022	−	0.427485i	$-0.140600\pi$
$332$	2.74132e6	+	1.75962e6i	1.36495	+	0.876138i
$333$	−541293.	−	645087.i	−0.267499	−	0.318792i
$334$	752428.	−	1.92512e6i	0.369062	−	0.944261i
$335$	103291.	+	178906.i	0.0502865	+	0.0870988i
$336$	7560.42	+	29007.5i	0.00365340	+	0.0140172i
$337$	853200.	+	150442.i	0.409238	+	0.0721597i	0.374478	−	0.927236i	$-0.377822\pi$
$337$	853200.	+	150442.i	0.409238	+	0.0721597i	0.0347605	+	0.999396i	$0.488933\pi$
$338$	−244656.	−	724800.i	−0.116483	−	0.345085i
$339$	−11415.2	−	31363.0i	−0.00539490	−	0.0148224i
$340$	38347.7	+	16037.9i	0.0179904	+	0.00752402i
$341$			14199.0i			0.00661258i
$342$	2.07716e6	+	595161.i	0.960295	+	0.275150i
$343$			1.74453e6i			0.800649i
$344$	−479587.	+	1.91729e6i	−0.218510	+	0.873556i
$345$	−3879.95	−	10660.1i	−0.00175501	−	0.00482184i
$346$	1.94225e6	−	655607.i	0.872199	−	0.294410i
$347$	2.99320e6	+	527783.i	1.33448	+	0.235305i	0.794958	−	0.606665i	$-0.207493\pi$
$347$	2.99320e6	+	527783.i	1.33448	+	0.235305i	0.539524	+	0.841970i	$0.318604\pi$
$348$	−4508.27	+	95746.3i	−0.00199555	+	0.0423813i
$349$	746444.	+	1.29288e6i	0.328045	+	0.568191i	0.982124	−	0.188235i	$-0.0602768\pi$
$349$	746444.	+	1.29288e6i	0.328045	+	0.568191i	−0.654079	+	0.756427i	$0.726943\pi$
$350$	−890071.	−	347882.i	−0.388378	−	0.151796i
$351$	−77129.0	−	91918.8i	−0.0334157	−	0.0398232i
$352$	14816.9	+	1750.95i	0.00637383	+	0.000753212i
$353$	−112527.	+	194902.i	−0.0480639	+	0.0832492i	−0.889056	−	0.457798i	$-0.848638\pi$
$353$	−112527.	+	194902.i	−0.0480639	+	0.0832492i	0.840993	+	0.541047i	$0.181972\pi$
$354$	52019.4	+	65042.2i	0.0220626	+	0.0275859i
$355$	391260.	+	142407.i	0.164776	+	0.0599736i
$356$	121321.	−	15550.6i	0.0507353	−	0.00650311i
$357$	2710.03	−	477.851i	0.00112539	−	0.000198437i
$358$	−2.22247e6	+	1.21435e6i	−0.916492	+	0.500769i
$359$	−41531.3	+	49495.1i	−0.0170075	+	0.0202687i	−0.774481	−	0.632597i	$-0.781989\pi$
$359$	−41531.3	+	49495.1i	−0.0170075	+	0.0202687i	0.757474	+	0.652866i	$0.226433\pi$
$360$	545937.	−	265756.i	0.222017	−	0.108075i
$361$	1.61528e6	+	1.87668e6i	0.652350	+	0.757918i
$362$	−56773.5	−	373103.i	−0.0227706	−	0.149643i
$363$	−62723.6	−	52631.4i	−0.0249841	−	0.0209642i
$364$	−712059.	+	542526.i	−0.281684	+	0.214618i
$365$	−34042.5	−	193065.i	−0.0133749	−	0.0758527i
$366$	1421.18	−	60399.1i	0.000554556	−	0.0235683i
$367$	−803664.	+	2.20805e6i	−0.311465	+	0.855743i	0.680897	+	0.732380i	$0.261590\pi$
$367$	−803664.	+	2.20805e6i	−0.311465	+	0.855743i	−0.992362	+	0.123363i	$0.960632\pi$
$368$	−709005.	+	1.49372e6i	−0.272916	+	0.574977i
$369$	−1.78970e6	−	1.03328e6i	−0.684248	−	0.395051i
$370$	−203573.	−	179145.i	−0.0773065	−	0.0680301i
$371$	952143.	−	798943.i	0.359143	−	0.301357i
$372$	−19711.6	+	87497.3i	−0.00738526	+	0.0327821i
$373$	680096.	−	392653.i	0.253103	−	0.146129i	−0.368081	−	0.929794i	$-0.619985\pi$
$373$	680096.	−	392653.i	0.253103	−	0.146129i	0.621184	+	0.783664i	$0.286652\pi$
$374$	269.500	−	1342.87i	9.96275e−5	−	0.000496426i
$375$	7391.94	−	41921.8i	0.00271444	−	0.0153944i
$376$	−1.38567e6	+	1.00513e6i	−0.505463	+	0.366652i
$377$	−2.68981e6	+	979009.i	−0.974693	+	0.354759i
$378$	41846.7	−	68696.2i	0.0150637	−	0.0247288i
$379$	850624.			0.304186			0.152093	−	0.988366i	$-0.451399\pi$
$379$	850624.			0.304186			0.152093	+	0.988366i	$0.451399\pi$
$380$	690106.	+	88849.2i	0.245164	+	0.0315642i
$381$	−88731.3			−0.0313159
$382$	−1.64599e6	+	2.70208e6i	−0.577123	+	0.947416i
$383$	−2.26572e6	+	824655.i	−0.789241	+	0.287260i	−0.705020	−	0.709187i	$-0.749062\pi$
$383$	−2.26572e6	+	824655.i	−0.789241	+	0.287260i	−0.0842204	+	0.996447i	$0.526840\pi$
$384$	88874.3	+	31359.2i	0.0307573	+	0.0108527i
$385$	355.850	−	2018.12i	0.000122353	−	0.000693898i
$386$	901098.	−	4.49001e6i	0.307825	−	1.53384i
$387$	2.29517e6	−	1.32512e6i	0.779001	−	0.449756i
$388$	−3.16894e6	−	713909.i	−1.06865	−	0.240749i
$389$	847906.	−	711477.i	0.284102	−	0.238389i	−0.489589	−	0.871953i	$-0.662853\pi$
$389$	847906.	−	711477.i	0.284102	−	0.238389i	0.773690	+	0.633564i	$0.218409\pi$
$390$	−14495.9	−	12756.5i	−0.00482596	−	0.00424686i
$391$	131450.	+	75892.9i	0.0434830	+	0.0251049i
$392$	2.02371e6	+	1.36725e6i	0.665169	+	0.449401i
$393$	31436.8	−	86372.0i	0.0102673	−	0.0282092i
$394$	101099.	−	4.29663e6i	0.0328099	−	1.39440i
$395$	22316.3	+	126562.i	0.00719664	+	0.0408142i
$396$	−12125.3	−	15914.4i	−0.00388558	−	0.00509978i
$397$	2.14800e6	+	1.80239e6i	0.684004	+	0.573948i	0.917173	−	0.398488i	$-0.130465\pi$
$397$	2.14800e6	+	1.80239e6i	0.684004	+	0.573948i	−0.233169	+	0.972436i	$0.574910\pi$
$398$	−226658.	−	1.48955e6i	−0.0717238	−	0.471353i
$399$	41625.7	−	19729.3i	0.0130897	−	0.00620410i
$400$	−2.47284e6	+	1.70643e6i	−0.772763	+	0.533260i
$401$	−2.24101e6	+	2.67073e6i	−0.695958	+	0.829411i	−0.992063	−	0.125745i	$-0.959868\pi$
$401$	−2.24101e6	+	2.67073e6i	−0.695958	+	0.829411i	0.296105	+	0.955156i	$0.404312\pi$
$402$	37732.8	−	20617.1i	0.0116454	−	0.00636301i
$403$	−2.63772e6	+	465101.i	−0.809032	+	0.142654i
$404$	−593787.	−	4.63255e6i	−0.181000	−	1.41210i
$405$	−764297.	−	278181.i	−0.231539	−	0.0842734i
$406$	−1.19851e6	−	1.49855e6i	−0.360851	−	0.451188i
$407$	−4467.70	+	7738.28i	−0.00133690	+	0.00231557i
$408$	3524.95	−	7900.94i	0.00104834	−	0.00234979i
$409$	3.97539e6	+	4.73768e6i	1.17509	+	1.40042i	0.898240	+	0.439505i	$0.144846\pi$
$409$	3.97539e6	+	4.73768e6i	1.17509	+	1.40042i	0.276850	+	0.960913i	$0.410710\pi$
$410$	−619814.	−	242253.i	−0.182097	−	0.0711720i
$411$	15205.7	+	26337.1i	0.00444020	+	0.00769065i
$412$	2.49606e6	+	117529.i	0.724457	+	0.0341115i
$413$	−1.64197e6	−	289524.i	−0.473687	−	0.0835238i
$414$	2.10077e6	−	709116.i	0.602391	−	0.203337i
$415$	−481098.	−	1.32181e6i	−0.137124	−	0.376745i
$416$	160070.	+	2.80986e6i	0.0453500	+	0.796071i
$417$			50921.9i			0.0143405i
$418$	−1603.95	−	22871.1i	−0.000449005	−	0.00640245i
$419$		−	314969.i		−	0.0876461i	−0.999039	−	0.0438231i	$-0.986046\pi$
$419$		−	314969.i		−	0.0876461i	0.999039	−	0.0438231i	$-0.0139538\pi$
$420$	4994.48	−	11942.1i	0.00138155	−	0.00330338i
$421$	2.06020e6	+	5.66036e6i	0.566506	+	1.55646i	0.809920	+	0.586540i	$0.199510\pi$
$421$	2.06020e6	+	5.66036e6i	0.566506	+	1.55646i	−0.243414	+	0.969922i	$0.578268\pi$
$422$	−1.28706e6	−	3.81296e6i	−0.351818	−	1.04227i
$423$	2.26064e6	+	398612.i	0.614300	+	0.108318i
$424$	−405501.	−	3.88661e6i	−0.109541	−	1.04992i
$425$	137904.	+	238858.i	0.0370345	+	0.0641456i
$426$	31548.0	−	80716.9i	0.00842263	−	0.0215497i
$427$	777432.	+	926507.i	0.206344	+	0.245912i
$428$	−2.75529e6	+	4.29249e6i	−0.727039	+	1.13266i
$429$	−318.133	+	551.022i	−8.34575e−5	+	0.000144553i
$430$	666488.	−	533043.i	0.173828	−	0.139024i
$431$	−4.94455e6	−	1.79967e6i	−1.28213	−	0.466659i	−0.390997	−	0.920392i	$-0.627870\pi$
$431$	−4.94455e6	−	1.79967e6i	−1.28213	−	0.466659i	−0.891137	+	0.453733i	$0.850092\pi$
$432$	−105308.	−	229924.i	−0.0271489	−	0.0592755i
$433$	3.20352e6	−	564868.i	0.821123	−	0.144786i	0.252723	−	0.967539i	$-0.418674\pi$
$433$	3.20352e6	−	564868.i	0.821123	−	0.144786i	0.568400	+	0.822752i	$0.307563\pi$
$434$	−860932.	−	1.57565e6i	−0.219404	−	0.401546i
$435$	26605.5	−	31707.3i	0.00674138	−	0.00803407i
$436$	−372421.	−	1.19540e6i	−0.0938249	−	0.301160i
$437$	2.45833e6	+	642203.i	0.615795	+	0.160868i
$438$	−40340.0	+	6138.37i	−0.0100473	+	0.00152886i
$439$	−5.09568e6	−	4.27579e6i	−1.26195	−	1.05890i	−0.995472	−	0.0950579i	$-0.969696\pi$
$439$	−5.09568e6	−	4.27579e6i	−1.26195	−	1.05890i	−0.266476	−	0.963842i	$-0.585859\pi$
$440$	−4631.10	−	4479.03i	−0.00114039	−	0.00110294i
$441$	−568704.	−	3.22528e6i	−0.139248	−	0.789716i
$442$	258290.	+	6077.51i	0.0628858	+	0.00147969i
$443$	−893118.	+	2.45382e6i	−0.216222	+	0.594064i	−0.999623	−	0.0274517i	$-0.991261\pi$
$443$	−893118.	+	2.45382e6i	−0.216222	+	0.594064i	0.783401	+	0.621516i	$0.213483\pi$
$444$	−38273.6	+	41482.8i	−0.00921387	+	0.00998644i
$445$	−45741.0	−	26408.6i	−0.0109498	−	0.00632187i
$446$	1.59758e6	−	1.81542e6i	0.380298	−	0.432155i
$447$	−4234.49	+	3553.16i	−0.00100238	+	0.000841096i
$448$	−1.75039e6	+	704096.i	−0.412040	+	0.165744i
$449$	4.23785e6	−	2.44672e6i	0.992041	−	0.572755i	0.0861574	−	0.996282i	$-0.472541\pi$
$449$	4.23785e6	−	2.44672e6i	0.992041	−	0.572755i	0.905884	+	0.423526i	$0.139208\pi$
$450$	3.95015e6	+	792753.i	0.919564	+	0.184547i
$451$	−3807.75	+	21594.8i	−0.000881509	+	0.00499929i
$452$	1.86659e6	−	963590.i	0.429736	−	0.221843i
$453$	−184790.	+	67258.2i	−0.0423091	+	0.0153992i
$454$	−4.34243e6	−	2.64521e6i	−0.988765	−	0.602311i
$455$	386559.			0.0875362
$456$	21866.8	−	143164.i	0.00492462	−	0.0322419i
$457$	963186.			0.215734			0.107867	−	0.994165i	$-0.465598\pi$
$457$	963186.			0.215734			0.107867	+	0.994165i	$0.465598\pi$
$458$	−4.43918e6	−	2.70415e6i	−0.988871	−	0.602376i
$459$	−21815.4	+	7940.14i	−0.00483315	+	0.00175912i
$460$	634441.	−	327518.i	0.139797	−	0.0721674i
$461$	1.07412e6	−	6.09161e6i	0.235396	−	1.33500i	−0.606383	−	0.795173i	$-0.707380\pi$
$461$	1.07412e6	−	6.09161e6i	0.235396	−	1.33500i	0.841779	−	0.539823i	$-0.181509\pi$
$462$	−418.193	−	83.9269i	−9.11532e−5	−	1.82935e-5i
$463$	−2.44339e6	+	1.41069e6i	−0.529713	+	0.305830i	−0.740900	−	0.671616i	$-0.765601\pi$
$463$	−2.44339e6	+	1.41069e6i	−0.529713	+	0.305830i	0.211186	+	0.977446i	$0.432267\pi$
$464$	−6.01333e6	+	484705.i	−1.29664	+	0.104516i
$465$	29668.8	−	24895.1i	0.00636309	−	0.00533927i
$466$	−2.30775e6	+	2.62243e6i	−0.492293	+	0.559421i
$467$	5.56275e6	+	3.21166e6i	1.18031	+	0.681455i	0.956087	−	0.293082i	$-0.0946810\pi$
$467$	5.56275e6	+	3.21166e6i	1.18031	+	0.681455i	0.224227	+	0.974537i	$0.428014\pi$
$468$	2.55921e6	−	2.77379e6i	0.540120	−	0.585409i
$469$	−294405.	+	808870.i	−0.0618034	+	0.169803i
$470$	738997.	+	17388.4i	0.154311	+	0.00363091i
$471$	−6141.80	−	34831.9i	−0.00127568	−	0.00723477i
$472$	−3.64421e6	+	3.76793e6i	−0.752919	+	0.778480i
$473$	−21542.1	−	18076.0i	−0.00442726	−	0.00371491i
$474$	26444.6	−	4023.96i	0.00540618	−	0.000822636i
$475$	3.28508e6	+	3.24411e6i	0.668054	+	0.659723i
$476$	51516.6	+	165358.i	0.0104215	+	0.0334509i
$477$	−3.36829e6	+	4.01417e6i	−0.677818	+	0.807792i
$478$	2.76742e6	+	5.06484e6i	0.553994	+	1.01390i
$479$	−9.21710e6	+	1.62522e6i	−1.83551	+	0.323649i	−0.980733	−	0.195353i	$-0.937415\pi$
$479$	−9.21710e6	+	1.62522e6i	−1.83551	+	0.323649i	−0.854773	+	0.519003i	$0.826304\pi$
$480$	−22319.9	−	34029.9i	−0.00442170	−	0.00674152i
$481$	−1.58387e6	−	576482.i	−0.312146	−	0.113612i
$482$	−343550.	+	274764.i	−0.0673554	+	0.0538694i
$483$	23634.4	−	40935.9i	0.00460973	−	0.00798429i
$484$	2.78377e6	−	4.33686e6i	0.540157	−	0.841516i
$485$	901642.	+	1.07453e6i	0.174052	+	0.207427i
$486$	−185209.	+	473865.i	−0.0355689	+	0.0910047i
$487$	−193922.	−	335883.i	−0.0370514	−	0.0641749i	0.846905	−	0.531744i	$-0.178463\pi$
$487$	−193922.	−	335883.i	−0.0370514	−	0.0641749i	−0.883956	+	0.467569i	$0.845130\pi$
$488$	3.78197e6	−	394583.i	0.718900	−	0.0750048i
$489$	−97449.7	−	17183.0i	−0.0184293	−	0.00324958i
$490$	−337291.	−	999235.i	−0.0634622	−	0.188008i
$491$	−2.08008e6	−	5.71498e6i	−0.389383	−	1.06982i	−0.967280	−	0.253711i	$-0.918349\pi$
$491$	−2.08008e6	−	5.71498e6i	−0.389383	−	1.06982i	0.577897	−	0.816109i	$-0.303873\pi$
$492$	−53443.1	+	127786.i	−0.00995357	+	0.0237997i
$493$			553811.i			0.102623i
$494$	4.19619e6	−	1.04713e6i	0.773637	−	0.193056i
$495$			8639.51i			0.00158481i
$496$	−5.62001e6	−	530420.i	−1.02573	−	0.0968089i
$497$	593377.	+	1.63029e6i	0.107756	+	0.296056i
$498$	−277400.	+	93636.2i	−0.0501225	+	0.0169188i
$499$	4.21359e6	+	742969.i	0.757531	+	0.133573i	0.539057	−	0.842269i	$-0.318781\pi$
$499$	4.21359e6	+	742969.i	0.757531	+	0.133573i	0.218474	+	0.975843i	$0.429892\pi$
$500$	2.67624e6	+	126013.i	0.478741	+	0.0225418i
$501$	92886.9	+	160885.i	0.0165333	+	0.0286366i
$502$	−6.81384e6	−	2.66317e6i	−1.20679	−	0.471672i
$503$	−1.40164e6	−	1.67041e6i	−0.247011	−	0.294377i	0.628265	−	0.777999i	$-0.283765\pi$
$503$	−1.40164e6	−	1.67041e6i	−0.247011	−	0.294377i	−0.875277	+	0.483622i	$0.839321\pi$
$504$	2.31048e6	+	1.03081e6i	0.405160	+	0.180759i
$505$	−1.00839e6	+	1.74659e6i	−0.175955	+	0.304763i
$506$	−14694.5	−	18373.2i	−0.00255140	−	0.00319013i
$507$	64608.8	+	23515.7i	0.0111628	+	0.00406291i
$508$	−710015.	−	5.53933e6i	−0.122070	−	0.952352i
$509$	173883.	−	30660.3i	0.0297484	−	0.00524544i	−0.158754	−	0.987318i	$-0.550748\pi$
$509$	173883.	−	30660.3i	0.0297484	−	0.00524544i	0.188503	+	0.982073i	$0.439637\pi$
$510$	−3278.45	+	1791.34i	−0.000558140	+	0.000304966i
$511$	525071.	−	625756.i	0.0889541	−	0.106011i
$512$	−1.24654e6	+	5.79918e6i	−0.210150	+	0.977669i
$513$	−316931.	+	224894.i	−0.0531705	+	0.0377298i
$514$	−81382.9	−	534830.i	−0.0135871	−	0.0892911i
$515$	−826594.	−	693595.i	−0.137333	−	0.115236i
$516$	−107653.	−	141294.i	−0.0177993	−	0.0233614i
$517$	−4229.61	−	23987.3i	−0.000695943	−	0.00394689i
$518$	26579.3	−	1.12960e6i	0.00435231	−	0.184970i
$519$	−63015.1	+	173133.i	−0.0102690	+	0.0282137i
$520$	680366.	−	1.00703e6i	0.110340	−	0.163317i
$521$	−9.90789e6	−	5.72032e6i	−1.59914	−	0.923265i	−0.991653	−	0.128937i	$-0.958844\pi$
$521$	−9.90789e6	−	5.72032e6i	−1.59914	−	0.923265i	−0.607489	−	0.794328i	$-0.707823\pi$
$522$	6.07315e6	+	5.34440e6i	0.975523	+	0.858465i
$523$	6.55142e6	−	5.49730e6i	1.04733	−	0.878810i	0.0545153	−	0.998513i	$-0.482639\pi$
$523$	6.55142e6	−	5.49730e6i	1.04733	−	0.878810i	0.992810	+	0.119703i	$0.0381942\pi$
$524$	5.64359e6	+	1.27140e6i	0.897898	+	0.202281i
$525$	74384.4	−	42945.8i	0.0117783	−	0.00680022i
$526$	−1.83490e6	+	9.14297e6i	−0.289166	+	1.44086i
$527$	−89985.6	+	510334.i	−0.0141139	+	0.0800438i
$528$	−954.681	+	941.719i	−0.000149030	+	0.000147006i
$529$	−3.59817e6	+	1.30963e6i	−0.559040	+	0.203474i
$530$	−877854.	+	1.44110e6i	−0.135748	+	0.222846i
$531$	7.02923e6			1.08186
$532$	1.56474e6	+	2.44074e6i	0.239698	+	0.373889i
$533$	−4.13636e6			−0.630667
$534$	−5719.11	+	9388.59i	−0.000867911	+	0.00142478i
$535$	2.06975e6	−	753326.i	0.312631	−	0.113788i
$536$	1.58902e6	+	2.19061e6i	0.238900	+	0.329347i
$537$	39526.9	−	224168.i	0.00591503	−	0.0335458i
$538$	847668.	−	4.22378e6i	0.126261	−	0.629138i
$539$	−30095.1	+	17375.4i	−0.00446194	+	0.00257610i
$540$	−24000.3	+	106534.i	−0.00354187	+	0.0157219i
$541$	9.29745e6	−	7.80149e6i	1.36575	−	1.14600i	0.391589	−	0.920140i	$-0.371926\pi$
$541$	9.29745e6	−	7.80149e6i	1.36575	−	1.14600i	0.974160	−	0.225859i	$-0.0725188\pi$
$542$	5.42309e6	+	4.77234e6i	0.792955	+	0.697804i
$543$	29375.6	+	16960.0i	0.00427550	+	0.00246846i
$544$	521446.	+	156834.i	0.0755462	+	0.0227218i
$545$	−184919.	+	508061.i	−0.0266680	+	0.0732697i
$546$	1892.64	−	80436.1i	0.000271698	−	0.0115470i
$547$	384282.	+	2.17937e6i	0.0549138	+	0.311432i	0.999876	−	0.0157478i	$-0.00501288\pi$
$547$	384282.	+	2.17937e6i	0.0549138	+	0.311432i	−0.944962	+	0.327180i	$0.893902\pi$
$548$	−1.52250e6	+	1.16001e6i	−0.216574	+	0.165010i
$549$	−3.90609e6	−	3.27760e6i	−0.553109	−	0.464114i
$550$	−6431.08	−	42263.6i	−0.000906519	−	0.00595744i
$551$	2.45553e6	+	8.93943e6i	0.344562	+	1.25439i
$552$	−65044.3	−	133619.i	−0.00908577	−	0.0186647i
$553$	−344206.	+	410209.i	−0.0478637	+	0.0570417i
$554$	−1.05739e7	+	5.77757e6i	−1.46373	+	0.799780i
$555$	24002.4	−	4232.28i	0.00330767	−	0.000583232i
$556$	−3.17896e6	+	407470.i	−0.436111	+	0.0558995i
$557$	−8.12539e6	−	2.95740e6i	−1.10970	−	0.403898i	−0.278818	−	0.960344i	$-0.589942\pi$
$557$	−8.12539e6	−	2.95740e6i	−1.10970	−	0.403898i	−0.830884	+	0.556446i	$0.812165\pi$
$558$	4.72800e6	+	5.91163e6i	0.642823	+	0.803751i
$559$	2.65231e6	−	4.59394e6i	0.359000	−	0.621807i
$560$	785489.	+	216236.i	0.105845	+	0.0291379i
$561$	79.1284	+	94.3015i	1.06151e−5	+	1.26506e-5i
$562$	1.14911e7	+	4.49128e6i	1.53469	+	0.599831i
$563$	−3.78370e6	−	6.55356e6i	−0.503090	−	0.871377i	−0.999994	−	0.00357166i	$-0.998863\pi$
$563$	−3.78370e6	−	6.55356e6i	−0.503090	−	0.871377i	0.496904	−	0.867806i	$-0.334470\pi$
$564$	7236.44	−	153687.i	0.000957915	−	0.0203441i
$565$	−893311.	−	157515.i	−0.117729	−	0.0207587i
$566$	−1.36234e6	+	459856.i	−0.178749	+	0.0603366i
$567$	−1.15912e6	−	3.18465e6i	−0.151415	−	0.416010i
$568$	5.29144e6	+	1.32359e6i	0.688182	+	0.172141i
$569$			2.37422e6i			0.307426i	0.988116	+	0.153713i	$0.0491231\pi$
$569$			2.37422e6i			0.307426i	−0.988116	+	0.153713i	$0.950877\pi$
$570$	−44977.1	+	43451.5i	−0.00579835	+	0.00560167i
$571$			1.39286e7i			1.78780i	0.448268	+	0.893899i	$0.352041\pi$
$571$			1.39286e7i			1.78780i	−0.448268	+	0.893899i	$0.647959\pi$
$572$	−36944.9	−	15451.2i	−0.00472133	−	0.00197457i
$573$	−97260.6	−	267221.i	−0.0123752	−	0.0340004i
$574$	−886824.	−	2.62724e6i	−0.112346	−	0.332828i
$575$	4.66564e6	+	822678.i	0.588494	+	0.103767i
$576$	6.75193e6	−	4.20476e6i	0.847953	−	0.528062i
$577$	−735267.	−	1.27352e6i	−0.0919403	−	0.159245i	0.816387	−	0.577505i	$-0.195974\pi$
$577$	−735267.	−	1.27352e6i	−0.0919403	−	0.159245i	−0.908328	+	0.418260i	$0.862640\pi$
$578$	−2.90567e6	+	7.43427e6i	−0.361765	+	0.925591i
$579$	264573.	+	315306.i	0.0327982	+	0.0390873i
$580$	2.19232e6	+	1.40722e6i	0.270603	+	0.173696i
$581$	2.93057e6	−	5.07589e6i	0.360173	−	0.623838i
$582$	228006.	−	182354.i	0.0279022	−	0.0223156i
$583$	52248.9	+	19017.0i	0.00636657	+	0.00231724i
$584$	−706001.	−	2.46923e6i	−0.0856591	−	0.299591i
$585$	−1.60495e6	+	282996.i	−0.193897	+	0.0341893i
$586$	6.47384e6	+	1.18482e7i	0.778786	+	1.42531i
$587$	−3.29246e6	+	3.92380e6i	−0.394389	+	0.470014i	−0.926301	−	0.376785i	$-0.877029\pi$
$587$	−3.29246e6	+	3.92380e6i	−0.394389	+	0.470014i	0.531912	+	0.846800i	$0.321474\pi$
$588$	−209574.	+	65291.9i	−0.0249974	+	0.00778782i
$589$	810243.	+	8.63663e6i	0.0962337	+	1.02578i
$590$	2.23779e6	−	340516.i	0.264661	−	0.0402724i
$591$	295909.	+	248297.i	0.0348490	+	0.0292417i
$592$	−2.89595e6	−	2.05741e6i	−0.339615	−	0.241277i
$593$	−2.46487e6	−	1.39790e7i	−0.287845	−	1.63245i	−0.694944	−	0.719064i	$-0.744571\pi$
$593$	−2.46487e6	−	1.39790e7i	−0.287845	−	1.63245i	0.407099	−	0.913384i	$-0.366540\pi$
$594$	3597.37	+	84.6453i	0.000418330	+	9.84321e-6i
$595$	25579.6	−	70279.4i	0.00296211	−	0.00813834i
$596$	−255700.	−	235919.i	−0.0294860	−	0.0272049i
$597$	117277.	+	67709.7i	0.0134671	+	0.00777526i
$598$	2.93182e6	−	3.33160e6i	0.335263	−	0.380978i
$599$	−1.80825e6	+	1.51730e6i	−0.205916	+	0.172784i	−0.739914	−	0.672702i	$-0.765134\pi$
$599$	−1.80825e6	+	1.51730e6i	−0.205916	+	0.172784i	0.533997	+	0.845486i	$0.320689\pi$
$600$	19042.5	−	269366.i	0.00215946	−	0.0305467i
$601$	1.16413e7	−	6.72111e6i	1.31467	−	0.759023i	0.331801	−	0.943349i	$-0.392344\pi$
$601$	1.16413e7	−	6.72111e6i	1.31467	−	0.759023i	0.982865	+	0.184327i	$0.0590104\pi$
$602$	3.48652e6	+	699708.i	0.392104	+	0.0786911i
$603$	630168.	−	3.57386e6i	0.0705769	−	0.400262i
$604$	−5.67746e6	−	1.09979e7i	−0.633231	−	1.22664i
$605$	−2.09114e6	+	761113.i	−0.232271	+	0.0845397i
$606$	358497.	+	218380.i	0.0396555	+	0.0241564i
$607$	1.42537e7			1.57021			0.785103	−	0.619365i	$-0.212610\pi$
$607$	1.42537e7			1.57021			0.785103	+	0.619365i	$0.212610\pi$
$608$	9.11240e6	+	219525.i	0.999710	+	0.0240838i
$609$	172466.			0.0188435
$610$	−1.40230e6	−	854218.i	−0.152586	−	0.0929489i
$611$	4.31753e6	−	1.57145e6i	0.467878	−	0.170294i
$612$	−334947.	−	648832.i	−0.0361491	−	0.0700251i
$613$	803907.	−	4.55918e6i	0.0864081	−	0.490045i	−0.910636	−	0.413210i	$-0.864408\pi$
$613$	803907.	−	4.55918e6i	0.0864081	−	0.490045i	0.997044	−	0.0768347i	$-0.0244814\pi$
$614$	−5.27843e6	−	1.05932e6i	−0.565046	−	0.113399i
$615$	51798.6	−	29906.0i	0.00552243	−	0.00318838i
$616$	1893.07	−	26778.5i	0.000201009	−	0.00284338i
$617$	−5.22283e6	+	4.38248e6i	−0.552323	+	0.463454i	−0.875727	−	0.482807i	$-0.839617\pi$
$617$	−5.22283e6	+	4.38248e6i	−0.552323	+	0.463454i	0.323404	+	0.946261i	$0.395173\pi$
$618$	−148372.	+	168603.i	−0.0156272	+	0.0177581i
$619$	−7.19849e6	−	4.15605e6i	−0.755118	−	0.435968i	0.0724222	−	0.997374i	$-0.476927\pi$
$619$	−7.19849e6	−	4.15605e6i	−0.755118	−	0.435968i	−0.827540	+	0.561406i	$0.810260\pi$
$620$	1.79156e6	+	1.65296e6i	0.187177	+	0.172696i
$621$	−136389.	+	374726.i	−0.0141922	+	0.0389928i
$622$	5.82868e6	+	137147.i	0.604080	+	0.0142139i
$623$	−38216.0	−	216734.i	−0.00394480	−	0.0223721i
$624$	−206213.	−	146503.i	−0.0212009	−	0.0150620i
$625$	6.13754e6	+	5.15001e6i	0.628485	+	0.527361i
$626$	−1.50697e7	+	2.29309e6i	−1.53698	+	0.233876i
$627$	1695.39	+	1171.34i	0.000172227	+	0.000118991i
$628$	2.12534e6	−	662140.i	0.215045	−	0.0669963i
$629$	−209618.	+	249813.i	−0.0211252	+	0.0251761i
$630$	−523843.	−	958721.i	−0.0525835	−	0.0962367i
$631$	−1.33145e7	+	2.34770e6i	−1.33122	+	0.234730i	−0.793592	−	0.608450i	$-0.791792\pi$
$631$	−1.33145e7	+	2.34770e6i	−1.33122	+	0.234730i	−0.537631	+	0.843181i	$0.680680\pi$
$632$	462814.	+	1.61868e6i	0.0460907	+	0.161202i
$633$	339888.	+	123709.i	0.0337152	+	0.0122713i
$634$	−4.91380e6	+	3.92995e6i	−0.485505	+	0.388297i
$635$	−1.20578e6	+	2.08847e6i	−0.118668	+	0.205539i
$636$	295569.	+	189721.i	0.0289745	+	0.0185983i
$637$	−4.21360e6	−	5.02157e6i	−0.411438	−	0.490333i
$638$	31248.4	−	79950.3i	0.00303931	−	0.00777622i
$639$	−3.65714e6	−	6.33436e6i	−0.354315	−	0.613692i
$640$	1.94582e6	−	1.66569e6i	0.187782	−	0.160747i
$641$	5.37347e6	+	947487.i	0.516547	+	0.0910811i	0.425843	−	0.904797i	$-0.359977\pi$
$641$	5.37347e6	+	947487.i	0.516547	+	0.0910811i	0.0907031	+	0.995878i	$0.471089\pi$
$642$	−146620.	−	434365.i	−0.0140396	−	0.0415927i
$643$	−6.41487e6	−	1.76247e7i	−0.611872	−	1.68110i	−0.726049	−	0.687643i	$-0.758645\pi$
$643$	−6.41487e6	−	1.76247e7i	−0.611872	−	1.68110i	0.114178	−	0.993460i	$-0.463577\pi$
$644$	2.74467e6	+	1.14788e6i	0.260781	+	0.109064i
$645$			76705.0i			0.00725980i
$646$	87296.4	−	832190.i	0.00823029	−	0.0784587i
$647$			8.54262e6i			0.802289i	0.916015	+	0.401144i	$0.131387\pi$
$647$			8.54262e6i			0.802289i	−0.916015	+	0.401144i	$0.868613\pi$
$648$	−1.03364e7	−	2.58554e6i	−0.967016	−	0.241888i
$649$	−25509.9	−	70087.9i	−0.00237737	−	0.00653178i
$650$	7.64058e6	−	2.57908e6i	0.709321	−	0.239431i
$651$	158927.	+	28023.1i	0.0146975	+	0.00259157i
$652$	292924.	−	6.22109e6i	0.0269858	−	0.573122i
$653$	1.00296e6	+	1.73718e6i	0.0920453	+	0.159427i	0.908372	−	0.418164i	$-0.137326\pi$
$653$	1.00296e6	+	1.73718e6i	0.0920453	+	0.159427i	−0.816326	+	0.577591i	$0.803993\pi$
$654$	104813.	+	40965.9i	0.00958232	+	0.00374522i
$655$	−1.60574e6	−	1.91364e6i	−0.146242	−	0.174284i
$656$	−8.40508e6	−	2.31382e6i	−0.762575	−	0.209928i
$657$	−1.72192e6	+	2.98246e6i	−0.155633	+	0.269564i
$658$	1.92379e6	+	2.40540e6i	0.173218	+	0.216582i
$659$	−1.63917e7	−	5.96609e6i	−1.47031	−	0.535151i	−0.522129	−	0.852867i	$-0.674862\pi$
$659$	−1.63917e7	−	5.96609e6i	−1.47031	−	0.535151i	−0.948186	+	0.317716i	$0.897084\pi$
$660$	574.365	−	73.6205i	5.13249e−5	−	6.57868e-6i
$661$	−6.68744e6	+	1.17918e6i	−0.595328	+	0.104972i	−0.463190	−	0.886259i	$-0.653295\pi$
$661$	−6.68744e6	+	1.17918e6i	−0.595328	+	0.104972i	−0.132138	+	0.991231i	$0.542184\pi$
$662$	−1.62718e7	+	8.89088e6i	−1.44308	+	0.788496i
$663$	−14926.3	+	17788.5i	−0.00131877	+	0.00157165i
$664$	−8.06524e6	−	1.65683e7i	−0.709900	−	1.45833i
$665$	101287.	−	1.24785e6i	0.00888177	−	0.109422i
$666$	716616.	+	4.70944e6i	0.0626038	+	0.411418i
$667$	7.28730e6	+	6.11477e6i	0.634238	+	0.532189i
$668$	−9.30046e6	+	7.08613e6i	−0.806424	+	0.614423i
$669$	37742.5	+	214048.i	0.00326036	+	0.0184904i
$670$	27489.4	−	1.16828e6i	0.00236580	−	0.100545i
$671$	−18505.0	+	50842.1i	−0.00158666	+	0.00435930i
$672$	48840.7	−	162387.i	0.00417214	−	0.0138717i
$673$	208970.	+	120649.i	0.0177847	+	0.0102680i	0.508866	−	0.860846i	$-0.330065\pi$
$673$	208970.	+	120649.i	0.0177847	+	0.0102680i	−0.491081	+	0.871114i	$0.663398\pi$
$674$	−3.67915e6	−	3.23767e6i	−0.311959	−	0.274525i
$675$	−555085.	+	465771.i	−0.0468921	+	0.0393472i
$676$	−951048.	+	4.22157e6i	−0.0800452	+	0.355310i
$677$	−8.45434e6	+	4.88111e6i	−0.708938	+	0.409305i	−0.810668	−	0.585507i	$-0.800896\pi$
$677$	−8.45434e6	+	4.88111e6i	−0.708938	+	0.409305i	0.101730	+	0.994812i	$0.467562\pi$
$678$	−37149.8	+	185111.i	−0.00310372	+	0.0154653i
$679$	−1.01493e6	+	5.75595e6i	−0.0844815	+	0.479118i
$680$	−138063.	−	190333.i	−0.0114500	−	0.0157849i
$681$	429442.	−	156304.i	0.0354844	−	0.0129153i
$682$	41785.9	−	68596.5i	0.00344008	−	0.00564730i
$683$	8.97539e6			0.736209			0.368105	−	0.929784i	$-0.380007\pi$
$683$	8.97539e6			0.736209			0.368105	+	0.929784i	$0.380007\pi$
$684$	−8.28345e6	−	8.98812e6i	−0.676973	−	0.734562i
$685$	826527.			0.0673024
$686$	5.13394e6	−	8.42796e6i	0.416524	−	0.683773i
$687$	439011.	−	159787.i	0.0354882	−	0.0129166i
$688$	7.95928e6	−	7.85121e6i	0.641066	−	0.632362i
$689$	−1.82130e6	+	1.03291e7i	−0.146162	+	0.828924i
$690$	−12627.0	+	62918.0i	−0.00100966	+	0.00503098i
$691$	−1.14835e7	+	6.62997e6i	−0.914908	+	0.528222i	−0.882007	−	0.471236i	$-0.843808\pi$
$691$	−1.14835e7	+	6.62997e6i	−0.914908	+	0.528222i	−0.0329009	+	0.999459i	$0.510475\pi$
$692$	−1.13126e7	−	2.54853e6i	−0.898041	−	0.202313i
$693$	−27576.7	+	23139.6i	−0.00218127	+	0.00183030i
$694$	−1.29072e7	−	1.13584e7i	−1.01727	−	0.895198i
$695$	1.19855e6	+	691982.i	0.0941225	+	0.0543416i
$696$	303550.	−	449292.i	0.0237524	−	0.0351565i
$697$	−273713.	+	752021.i	−0.0213410	+	0.0586338i
$698$	198655.	−	8.44272e6i	0.0154334	−	0.655909i
$699$	−54520.1	−	309199.i	−0.00422050	−	0.0239357i
$700$	3.27624e6	+	4.30003e6i	0.252715	+	0.331685i
$701$	6.59334e6	+	5.53247e6i	0.506769	+	0.425230i	0.859991	−	0.510310i	$-0.170469\pi$
$701$	6.59334e6	+	5.53247e6i	0.506769	+	0.425230i	−0.353221	+	0.935540i	$0.614914\pi$
$702$	102111.	+	671050.i	0.00782041	+	0.0513939i
$703$	−2.27594e6	+	4.96181e6i	−0.173689	+	0.378662i
$704$	−66428.9	−	52063.4i	−0.00505156	−	0.00395914i
$705$	−42705.8	+	50894.8i	−0.00323604	+	0.00385656i
$706$	1.11720e6	−	610437.i	0.0843568	−	0.0460924i
$707$	−8.27582e6	+	1.45925e6i	−0.622677	+	0.109795i
$708$	−59898.7	−	467312.i	−0.00449091	−	0.0350367i
$709$	1.43253e7	+	5.21397e6i	1.07025	+	0.389541i	0.816272	−	0.577668i	$-0.196037\pi$
$709$	1.43253e7	+	5.21397e6i	1.07025	+	0.389541i	0.253983	+	0.967209i	$0.418259\pi$
$710$	−1.47112e6	−	1.83941e6i	−0.109523	−	0.136941i
$711$	1.12879e6	−	1.95513e6i	0.0837414	−	0.145044i
$712$	−631875.	−	281907.i	−0.0467123	−	0.0208404i
$713$	5.72166e6	+	6.81881e6i	0.421501	+	0.502325i
$714$	−14498.6	−	5666.76i	−0.00106434	−	0.000415996i
$715$	8646.27	+	14975.8i	0.000632505	+	0.00109553i
$716$	1.43107e7	+	673826.i	1.04322	+	0.0491208i
$717$	−510861.	−	90078.7i	−0.0371112	−	0.00654371i
$718$	346300.	−	116893.i	0.0250692	−	0.00846211i
$719$	−7.06984e6	−	1.94242e7i	−0.510020	−	1.40127i	−0.881216	−	0.472714i	$-0.843274\pi$
$719$	−7.06984e6	−	1.94242e7i	−0.510020	−	1.40127i	0.371196	−	0.928554i	$-0.378948\pi$
$720$	−3.41956e6	−	322739.i	−0.245832	−	0.0232017i
$721$		−	4.49612e6i		−	0.322106i
$722$	−2.28072e6	−	1.38200e7i	−0.162828	−	0.986654i
$723$		−	39538.6i		−	0.00281304i
$724$	−823721.	+	1.96957e6i	−0.0584028	+	0.139645i
$725$	5.91210e6	+	1.62434e7i	0.417731	+	1.14771i
$726$	148135.	+	438855.i	0.0104308	+	0.0309015i
$727$	1.30653e7	+	2.30376e6i	0.916818	+	0.161660i	0.612098	−	0.790782i	$-0.290326\pi$
$727$	1.30653e7	+	2.30376e6i	0.916818	+	0.161660i	0.304720	+	0.952442i	$0.401437\pi$
$728$	5.03661e6	−	525484.i	0.352217	−	0.0367478i
$729$	7.12870e6	+	1.23473e7i	0.496811	+	0.860503i
$730$	−403705.	+	1.03290e6i	−0.0280386	+	0.0717381i
$731$	−659702.	−	786202.i	−0.0456619	−	0.0544178i
$732$	−184613.	+	287611.i	−0.0127346	+	0.0198394i
$733$	4.18350e6	−	7.24603e6i	0.287594	−	0.498127i	−0.685641	−	0.727940i	$-0.740478\pi$
$733$	4.18350e6	−	7.24603e6i	0.287594	−	0.498127i	0.973235	+	0.229813i	$0.0738114\pi$
$734$	1.03806e7	−	8.30219e6i	0.711185	−	0.568791i
$735$	89071.9	+	32419.5i	0.00608166	+	0.00221354i
$736$	7.82112e6	−	5.12980e6i	0.532200	−	0.349064i
$737$	−37921.6	+	6686.60i	−0.00257169	+	0.000453458i
$738$	5.60535e6	+	1.02587e7i	0.378846	+	0.693351i
$739$	4.63914e6	−	5.52871e6i	0.312483	−	0.372402i	−0.586829	−	0.809711i	$-0.699624\pi$
$739$	4.63914e6	−	5.52871e6i	0.312483	−	0.372402i	0.899312	+	0.437309i	$0.144068\pi$
$740$	456277.	+	1.46456e6i	0.0306301	+	0.0983168i
$741$	−162064.	+	353318.i	−0.0108428	+	0.0236385i
$742$	−6.95109e6	+	1.05772e6i	−0.463493	+	0.0705278i
$743$	1.52003e7	+	1.27545e7i	1.01013	+	0.847604i	0.988356	−	0.152159i	$-0.0486226\pi$
$743$	1.52003e7	+	1.27545e7i	1.01013	+	0.847604i	0.0217788	+	0.999763i	$0.493067\pi$
$744$	352723.	−	364698.i	0.0233615	−	0.0241547i
$745$	26087.8	+	147951.i	0.00172205	+	0.00976625i
$746$	−4.44114e6	−	104499.i	−0.292178	−	0.00687487i
$747$	−8.45135e6	+	2.32199e7i	−0.554147	+	1.52251i
$748$	−5253.89	+	5694.42i	−0.000343342	+	0.000372131i
$749$	7.94806e6	+	4.58881e6i	0.517674	+	0.298879i
$750$	−159082.	+	180774.i	−0.0103269	+	0.0117350i
$751$	1.92002e7	−	1.61109e7i	1.24224	−	1.04237i	0.244899	−	0.969549i	$-0.421245\pi$
$751$	1.92002e7	−	1.61109e7i	1.24224	−	1.04237i	0.997345	−	0.0728180i	$-0.0231992\pi$
$752$	9.65228e6	−	778023.i	0.622422	−	0.0501704i
$753$	569441.	−	328767.i	0.0365984	−	0.0211301i
$754$	1.58758e7	+	3.18611e6i	1.01697	+	0.204095i
$755$	−928076.	+	5.26338e6i	−0.0592538	+	0.336045i
$756$	−404330.	+	208728.i	−0.0257295	+	0.0132824i
$757$	4.04696e6	−	1.47297e6i	0.256679	−	0.0934234i	−0.210476	−	0.977599i	$-0.567501\pi$
$757$	4.04696e6	−	1.47297e6i	0.256679	−	0.0934234i	0.467155	+	0.884176i	$0.345279\pi$
$758$	−4.10944e6	−	2.50329e6i	−0.259782	−	0.158248i
$759$	2114.54			0.000133233
$760$	−3.07249e6	−	2.46014e6i	−0.192955	−	0.154499i
$761$	5.68082e6			0.355590			0.177795	−	0.984068i	$-0.443104\pi$
$761$	5.68082e6			0.355590			0.177795	+	0.984068i	$0.443104\pi$
$762$	428669.	+	261126.i	0.0267445	+	0.0162916i
$763$	−2.11697e6	+	770515.i	−0.131645	+	0.0479148i
$764$	1.59038e7	−	8.21006e6i	0.985755	−	0.508877i
$765$	−54752.7	+	310518.i	−0.00338261	+	0.0191837i
$766$	1.33728e7	+	2.68377e6i	0.823473	+	0.165262i
$767$	1.21845e7	−	7.03473e6i	0.747859	−	0.431777i
$768$	−337073.	−	413046.i	−0.0206215	−	0.0252694i
$769$	−2.16905e6	+	1.82005e6i	−0.132267	+	0.110986i	−0.706521	−	0.707692i	$-0.749737\pi$
$769$	−2.16905e6	+	1.82005e6i	−0.132267	+	0.110986i	0.574254	+	0.818677i	$0.305292\pi$
$770$	−7658.24	+	8702.51i	−0.000465481	+	0.000528954i
$771$	42108.9	+	24311.6i	0.00255116	+	0.00147291i
$772$	−1.75669e7	+	1.90398e7i	−1.06084	+	1.14979i
$773$	6.92848e6	−	1.90358e7i	0.417051	−	1.14584i	−0.536314	−	0.844019i	$-0.680184\pi$
$773$	6.92848e6	−	1.90358e7i	0.417051	−	1.14584i	0.953365	−	0.301820i	$-0.0975941\pi$
$774$	−1.49879e7	−	352661.i	−0.899264	−	0.0211595i
$775$	2.80868e6	+	1.59288e7i	0.167976	+	0.952640i
$776$	1.32085e7	+	1.27748e7i	0.787407	+	0.761552i
$777$	77795.9	+	65278.5i	0.00462279	+	0.00387898i
$778$	−6.19011e6	+	941923.i	−0.366648	+	0.0557913i
$779$	−1.08382e6	+	1.33525e7i	−0.0639900	+	0.788350i
$780$	32490.2	+	104287.i	0.00191213	+	0.00613755i
$781$	−49887.2	+	59453.2i	−0.00292659	+	0.00348777i
$782$	−411704.	−	753488.i	−0.0240751	−	0.0440615i
$783$	−1.43288e6	+	252655.i	−0.0835229	+	0.0147273i
$784$	−5.75303e6	−	1.25609e7i	−0.334277	−	0.729843i
$785$	−903299.	−	328774.i	−0.0523187	−	0.0190425i
$786$	−406057.	+	324756.i	−0.0234439	+	0.0187500i
$787$	8.78473e6	−	1.52156e7i	0.505582	−	0.875694i	−0.494397	−	0.869236i	$-0.664611\pi$
$787$	8.78473e6	−	1.52156e7i	0.505582	−	0.875694i	0.999979	−	0.00645745i	$-0.00205548\pi$
$788$	−1.31329e7	+	2.04599e7i	−0.753434	+	1.17378i
$789$	−538748.	−	642055.i	−0.0308101	−	0.0367181i
$790$	264645.	−	677107.i	0.0150868	−	0.0386002i
$791$	−1.88982e6	−	3.27327e6i	−0.107394	−	0.186012i
$792$	11744.4	+	112567.i	0.000665303	+	0.00637674i
$793$	−1.00510e7	−	1.77226e6i	−0.567579	−	0.100079i
$794$	−5.07298e6	−	1.50288e7i	−0.285569	−	0.846007i
$795$	−51871.9	−	142517.i	−0.00291081	−	0.00799740i
$796$	−3.28855e6	+	7.86316e6i	−0.183960	+	0.439860i
$797$			2.15430e7i			1.20132i	0.799503	+	0.600662i	$0.205096\pi$
$797$			2.15430e7i			1.20132i	−0.799503	+	0.600662i	$0.794904\pi$
$798$	−259158.	−	27185.6i	−0.0144065	−	0.00151123i
$799$		−	888947.i		−	0.0492616i
$800$	1.69684e7	−	966642.i	0.937379	−	0.0533999i
$801$	317336.	+	871874.i	0.0174758	+	0.0480145i
$802$	1.86862e7	−	6.30752e6i	1.02585	−	0.346276i
$803$	35986.9	+	6345.47i	0.00196950	+	0.000347276i
$804$	−242964.	−	11440.1i	−0.0132557	−	0.000624152i
$805$	−642338.	−	1.11256e6i	−0.0349361	−	0.0605111i
$806$	1.41118e7	+	5.51555e6i	0.765146	+	0.299055i
$807$	248886.	+	296610.i	0.0134529	+	0.0160325i
$808$	−1.07644e7	+	2.41277e7i	−0.580046	+	1.30013i
$809$	−2.89168e6	+	5.00853e6i	−0.155338	+	0.269054i	−0.933182	−	0.359404i	$-0.882980\pi$
$809$	−2.89168e6	+	5.00853e6i	−0.155338	+	0.269054i	0.777844	+	0.628458i	$0.216313\pi$
$810$	2.87373e6	+	3.59316e6i	0.153898	+	0.192426i
$811$	−1.58346e7	−	5.76331e6i	−0.845384	−	0.307694i	−0.117227	−	0.993105i	$-0.537400\pi$
$811$	−1.58346e7	−	5.76331e6i	−0.845384	−	0.307694i	−0.728157	+	0.685411i	$0.759623\pi$
$812$	1.38005e6	+	1.07667e7i	0.0734522	+	0.573052i
$813$	−639413.	+	112746.i	−0.0339278	+	0.00598238i
$814$	44356.7	−	24236.4i	0.00234638	−	0.00128206i
$815$	−1.72869e6	+	2.06017e6i	−0.0911638	+	0.108645i
$816$	−40280.9	+	27796.6i	−0.00211775	+	0.00146139i
$817$	−1.41346e7	−	9.76558e6i	−0.740848	−	0.511850i
$818$	−5.26300e6	−	3.45873e7i	−0.275011	−	1.80731i
$819$	−5.20191e6	−	4.36492e6i	−0.270990	−	0.227387i
$820$	2.28146e6	+	2.99439e6i	0.118489	+	0.155515i
$821$	1.59047e6	+	9.01999e6i	0.0823507	+	0.467034i	0.997897	+	0.0648211i	$0.0206477\pi$
$821$	1.59047e6	+	9.01999e6i	0.0823507	+	0.467034i	−0.915546	+	0.402213i	$0.868241\pi$
$822$	4046.78	−	171985.i	0.000208896	−	0.00887794i
$823$	−1.23920e7	+	3.40469e7i	−0.637740	+	1.75218i	0.0209718	+	0.999780i	$0.493324\pi$
$823$	−1.23920e7	+	3.40469e7i	−0.637740	+	1.75218i	−0.658712	+	0.752396i	$0.728898\pi$
$824$	−1.17128e7	−	7.91342e6i	−0.600958	−	0.406019i
$825$	3327.55	+	1921.16i	0.000170212	+	9.82718e-5i
$826$	7.08049e6	+	6.23086e6i	0.361088	+	0.317759i
$827$	1.83678e7	−	1.54124e7i	0.933885	−	0.783622i	−0.0426259	−	0.999091i	$-0.513572\pi$
$827$	1.83678e7	−	1.54124e7i	0.933885	−	0.783622i	0.976511	+	0.215469i	$0.0691279\pi$
$828$	−1.22359e7	−	2.75653e6i	−0.620239	−	0.139729i
$829$	−1.96544e7	+	1.13475e7i	−0.993287	+	0.573474i	−0.906255	−	0.422731i	$-0.861071\pi$
$829$	−1.96544e7	+	1.13475e7i	−0.993287	+	0.573474i	−0.0870315	+	0.996206i	$0.527738\pi$
$830$	−1.56569e6	+	7.80158e6i	−0.0788882	+	0.393086i
$831$	188058.	−	1.06653e6i	0.00944691	−	0.0535761i
$832$	7.49579e6	−	1.40458e7i	0.375413	−	0.703456i
$833$	−1.19178e6	+	433774.i	−0.0595093	+	0.0216596i
$834$	149857.	−	246008.i	0.00746041	−	0.0122471i
$835$	5.04899e6			0.250604
$836$	−59558.2	+	115213.i	−0.00294731	+	0.00570144i
$837$	−1.36144e6			−0.0671717
$838$	−926917.	+	1.52164e6i	−0.0455964	+	0.0748519i
$839$	2.76524e7	−	1.00647e7i	1.35621	−	0.493622i	0.441333	−	0.897344i	$-0.354506\pi$
$839$	2.76524e7	−	1.00647e7i	1.35621	−	0.493622i	0.914882	+	0.403722i	$0.132284\pi$
$840$	−59273.1	+	42995.3i	−0.00289841	+	0.00210244i
$841$	−2.46544e6	+	1.39822e7i	−0.120200	+	0.681689i
$842$	6.70476e6	−	3.34086e7i	0.325914	−	1.62397i
$843$	−960328.	+	554445.i	−0.0465426	+	0.0268714i
$844$	−5.00318e6	+	2.22084e7i	−0.241763	+	1.07315i
$845$	1.43146e6	−	1.20114e6i	0.0689665	−	0.0578697i
$846$	−9.74829e6	−	8.57854e6i	−0.468277	−	0.412085i
$847$	−8.03021e6	−	4.63625e6i	−0.384608	−	0.222054i
$848$	−9.47884e6	+	1.99699e7i	−0.452653	+	0.953645i
$849$	44200.1	−	121439.i	0.00210453	−	0.00578214i
$850$	36701.2	−	1.55978e6i	0.00174234	−	0.0740484i
$851$	972707.	+	5.51650e6i	0.0460424	+	0.261120i
$852$	−389952.	+	297109.i	−0.0184040	+	0.0140222i
$853$	−2.41799e7	−	2.02893e7i	−1.13784	−	0.954762i	−0.138475	−	0.990366i	$-0.544220\pi$
$853$	−2.41799e7	−	2.02893e7i	−1.13784	−	0.954762i	−0.999366	+	0.0356044i	$0.988664\pi$
$854$	−1.02924e6	−	6.76393e6i	−0.0482916	−	0.317362i
$855$	493001.	+	5.25505e6i	0.0230639	+	0.245845i
$856$	2.59433e7	−	1.26289e7i	1.21016	−	0.589090i
$857$	1.69580e7	−	2.02098e7i	0.788722	−	0.939962i	−0.210571	−	0.977579i	$-0.567532\pi$
$857$	1.69580e7	−	2.02098e7i	0.788722	−	0.939962i	0.999292	+	0.0376168i	$0.0119766\pi$
$858$	3158.52	−	1725.81i	0.000146476	−	8.00341e-5i
$859$	−3.14827e7	+	5.55125e6i	−1.45576	+	0.256689i	−0.844846	−	0.535010i	$-0.820308\pi$
$859$	−3.14827e7	+	5.55125e6i	−1.45576	+	0.256689i	−0.610911	+	0.791699i	$0.709197\pi$
$860$	−4.78855e6	+	613782.i	−0.220779	+	0.0282988i
$861$	234192.	+	85239.1i	0.0107663	+	0.00391860i
$862$	1.85913e7	+	2.32456e7i	0.852202	+	1.06555i
$863$	1.94264e7	−	3.36475e7i	0.887902	−	1.53789i	0.0455510	−	0.998962i	$-0.485496\pi$
$863$	1.94264e7	−	3.36475e7i	0.887902	−	1.53789i	0.842351	−	0.538929i	$-0.181171\pi$
$864$	−167887.	+	1.42069e6i	−0.00765126	+	0.0647464i
$865$	3.21870e6	+	3.83590e6i	0.146265	+	0.174312i
$866$	−1.71389e7	−	6.69867e6i	−0.776581	−	0.303525i
$867$	−358703.	−	621292.i	−0.0162064	−	0.0280703i
$868$	−477718.	+	1.01457e7i	−0.0215215	+	0.457071i
$869$	−23591.0	−	4159.72i	−0.00105973	−	0.000186859i
$870$	−221845.	+	74883.6i	−0.00993690	+	0.00335420i
$871$	−2.48432e6	−	6.82561e6i	−0.110959	−	0.304857i
$872$	−1.71872e6	+	6.87107e6i	−0.0765445	+	0.306008i
$873$		−	2.46410e7i		−	1.09427i
$874$	−9.98648e6	−	1.03371e7i	−0.442215	−	0.457742i
$875$		−	4.82067e6i		−	0.212857i
$876$	212951.	+	89060.9i	0.00937602	+	0.00392127i
$877$	−9.94009e6	−	2.73102e7i	−0.436407	−	1.19902i	−0.941813	−	0.336136i	$-0.890880\pi$
$877$	−9.94009e6	−	2.73102e7i	−0.436407	−	1.19902i	0.505407	−	0.862881i	$-0.331342\pi$
$878$	1.20346e7	+	3.56527e7i	0.526859	+	1.56083i
$879$	−1.19506e6	−	210722.i	−0.0521697	−	0.00919893i
$880$	9191.97	+	35267.4i	0.000400131	+	0.00153521i
$881$	−1.15245e7	−	1.99610e7i	−0.500243	−	0.866446i	−1.00000		0.000280706i	$-0.999911\pi$
$881$	−1.15245e7	−	1.99610e7i	−0.500243	−	0.866446i	0.499757	−	0.866166i	$-0.333423\pi$
$882$	−6.74416e6	+	1.72552e7i	−0.291915	+	0.746878i
$883$	−2.01871e7	−	2.40580e7i	−0.871307	−	1.03838i	−0.998916	−	0.0465586i	$-0.985175\pi$
$883$	−2.01871e7	−	2.40580e7i	−0.871307	−	1.03838i	0.127609	−	0.991825i	$-0.459270\pi$
$884$	−1.22994e6	−	789480.i	−0.0529362	−	0.0339790i
$885$	−101723.	+	176189.i	−0.00436575	+	0.00756170i
$886$	1.15360e7	−	9.22629e6i	0.493711	−	0.394860i
$887$	−2.02127e7	−	7.35683e6i	−0.862612	−	0.313965i	−0.127441	−	0.991846i	$-0.540676\pi$
$887$	−2.02127e7	−	7.35683e6i	−0.862612	−	0.313965i	−0.735172	+	0.677881i	$0.762898\pi$
$888$	306982.	−	87772.3i	0.0130641	−	0.00373530i
$889$	−9.89573e6	+	1.74488e6i	−0.419946	+	0.0740478i
$890$	143262.	+	262193.i	0.00606254	+	0.0110955i
$891$	97450.9	−	116137.i	0.00411236	−	0.00490093i
$892$	−1.30606e7	+	4.06897e6i	−0.549606	+	0.171227i
$893$	−3.94149e6	−	1.43491e7i	−0.165399	−	0.602138i
$894$	30913.7	−	4704.01i	0.00129362	−	0.000196845i
$895$	−4.73911e6	−	3.97658e6i	−0.197760	−	0.165940i
$896$	1.05283e7	+	1.74963e6i	0.438117	+	0.0728076i
$897$	69263.9	+	392815.i	0.00287426	+	0.0163007i
$898$	−2.76739e7	−	651159.i	−1.14519	−	0.0269461i
$899$	−1.11080e7	+	3.05190e7i	−0.458392	+	1.25942i
$900$	−1.67505e7	−	1.54547e7i	−0.689322	−	0.635995i
$901$	1.75739e6	+	1.01463e6i	0.0721200	+	0.0416385i
$902$	81946.6	−	93120.7i	0.00335363	−	0.00381092i
$903$	−244837.	+	205443.i	−0.00999212	+	0.00838438i
$904$	−1.18534e7	−	837959.i	−0.482415	−	0.0341037i
$905$	798374.	−	460942.i	0.0324030	−	0.0187079i
$906$	1.09067e6	+	218886.i	0.0441442	+	0.00885927i
$907$	−7.31570e6	+	4.14894e7i	−0.295282	+	1.67463i	0.370771	+	0.928724i	$0.379094\pi$
$907$	−7.31570e6	+	4.14894e7i	−0.295282	+	1.67463i	−0.666053	+	0.745905i	$0.732017\pi$
$908$	1.31941e7	+	2.55585e7i	0.531086	+	1.02878i
$909$	3.32919e7	−	1.21173e7i	1.33638	−	0.486401i
$910$	−1.86750e6	−	1.13760e6i	−0.0747580	−	0.0455393i
$911$	1.29837e7			0.518324			0.259162	−	0.965834i	$-0.416554\pi$
$911$	1.29837e7			0.518324			0.259162	+	0.965834i	$0.416554\pi$
$912$	−526954.	+	627285.i	−0.0209791	+	0.0249734i
$913$	262195.			0.0104099
$914$	−4.65324e6	−	2.83454e6i	−0.184242	−	0.112232i
$915$	138680.	−	50475.3i	0.00547596	−	0.00199309i
$916$	1.34881e7	+	2.61280e7i	0.531143	+	1.02889i
$917$	1.80749e6	−	1.02508e7i	0.0709828	−	0.402564i
$918$	128759.	+	25840.5i	0.00504278	+	0.00101203i
$919$	3.41265e7	−	1.97030e7i	1.33292	−	0.769560i	0.347171	−	0.937802i	$-0.387142\pi$
$919$	3.41265e7	−	1.97030e7i	1.33292	−	0.769560i	0.985746	+	0.168242i	$0.0538089\pi$
$920$	−4.02889e6	−	284817.i	−0.156934	−	0.0110942i
$921$	370672.	−	311030.i	0.0143993	−	0.0120824i
$922$	−2.31161e7	+	2.62681e7i	−0.895543	+	1.01766i
$923$	−1.26786e7	−	7.32001e6i	−0.489855	−	0.282818i
$924$	1773.34	+	1636.15i	6.83301e−5	+	6.30440e-5i
$925$	−3.48129e6	+	9.56478e6i	−0.133779	+	0.367554i
$926$	1.59558e7	+	375435.i	0.611491	+	0.0143882i
$927$	3.29155e6	+	1.86673e7i	0.125806	+	0.713482i
$928$	3.04774e7	+	1.53549e7i	1.16174	+	0.585298i
$929$	1.01327e7	+	8.50235e6i	0.385200	+	0.323221i	0.814740	−	0.579827i	$-0.196880\pi$
$929$	1.01327e7	+	8.50235e6i	0.385200	+	0.323221i	−0.429540	+	0.903048i	$0.641324\pi$
$930$	−216596.	+	32958.5i	−0.00821190	+	0.00124957i
$931$	−1.73141e7	+	1.22861e7i	−0.654674	+	0.464557i
$932$	1.88664e7	−	5.87775e6i	0.711459	−	0.221652i
$933$	−336833.	+	401422.i	−0.0126681	+	0.0150972i
$934$	−1.74226e7	−	3.18863e7i	−0.653501	−	1.19602i
$935$	3294.86	−	580.972i	0.000123256	−	2.17333e-5i
$936$	−2.05267e7	+	5.86899e6i	−0.765825	+	0.218964i
$937$	−3.80463e7	−	1.38477e7i	−1.41567	−	0.515263i	−0.482884	−	0.875684i	$-0.660411\pi$
$937$	−3.80463e7	−	1.38477e7i	−1.41567	−	0.515263i	−0.932790	+	0.360421i	$0.882633\pi$
$938$	3.80271e6	−	3.04132e6i	0.141119	−	0.112864i
$939$	685017.	−	1.18648e6i	0.0253535	−	0.0439135i
$940$	−3.51899e6	−	2.25879e6i	−0.129897	−	0.0833788i
$941$	−8.16924e6	−	9.73572e6i	−0.300751	−	0.358422i	0.594411	−	0.804161i	$-0.297385\pi$
$941$	−8.16924e6	−	9.73572e6i	−0.300751	−	0.358422i	−0.895163	+	0.445740i	$0.852941\pi$
$942$	−72834.6	+	186351.i	−0.00267430	+	0.00684232i
$943$	6.87331e6	+	1.19049e7i	0.251702	+	0.435961i
$944$	2.86941e7	−	7.47872e6i	1.04800	−	0.273148i
$945$	193504.	+	34120.0i	0.00704874	+	0.00124288i
$946$	50876.3	+	150723.i	0.00184837	+	0.00547584i
$947$	−1.41157e7	−	3.87827e7i	−0.511480	−	1.40528i	−0.879694	−	0.475540i	$-0.842253\pi$
$947$	−1.41157e7	−	3.87827e7i	−0.511480	−	1.40528i	0.368214	−	0.929741i	$-0.379969\pi$
$948$	−139598.	−	58383.2i	−0.00504497	−	0.00210992i
$949$			6.89308e6i			0.248455i
$950$	−6.32346e6	−	2.53402e7i	−0.227324	−	0.910963i
$951$		−	565521.i		−	0.0202767i
$952$	237749.	−	950467.i	0.00850209	−	0.0339895i
$953$	−1.12726e7	−	3.09712e7i	−0.402060	−	1.10465i	−0.961266	−	0.275623i	$-0.911116\pi$
$953$	−1.12726e7	−	3.09712e7i	−0.402060	−	1.10465i	0.559206	−	0.829029i	$-0.311106\pi$
$954$	2.80857e7	−	9.48033e6i	0.999113	−	0.337250i
$955$	−7.61127e6	−	1.34207e6i	−0.270053	−	0.0476176i
$956$	1.53560e6	−	3.26129e7i	0.0543416	−	1.15410i
$957$	3857.59	+	6681.55i	0.000136156	+	0.000235829i
$958$	4.93115e7	+	1.92733e7i	1.73594	+	0.678487i
$959$	2.21373e6	+	2.63822e6i	0.0777280	+	0.0926326i
$960$	7683.23	+	230086.i	0.000269070	+	0.00805774i
$961$	−880275.	+	1.52468e6i	−0.0307475	+	0.0532562i
$962$	5.95531e6	+	7.44619e6i	0.207475	+	0.259416i
$963$	−3.63588e7	−	1.32335e7i	−1.26341	−	0.459843i
$964$	2.46832e6	−	316382.i	0.0855478	−	0.0109653i
$965$	1.10167e7	−	1.94254e6i	0.380831	−	0.0671507i
$966$	−234649.	+	128212.i	−0.00809052	+	0.00442064i
$967$	2.33743e7	−	2.78564e7i	0.803844	−	0.957984i	−0.195900	−	0.980624i	$-0.562763\pi$
$967$	2.33743e7	−	2.78564e7i	0.803844	−	0.957984i	0.999744	+	0.0226401i	$0.00720718\pi$
$968$	−2.62115e7	+	1.27595e7i	−0.899091	+	0.437667i
$969$	53511.6	+	52844.3i	0.00183079	+	0.00180796i
$970$	−1.19368e6	−	7.84460e6i	−0.0407342	−	0.267696i
$971$	2.48660e7	+	2.08650e7i	0.846365	+	0.710184i	0.958986	−	0.283454i	$-0.0914802\pi$
$971$	2.48660e7	+	2.08650e7i	0.846365	+	0.710184i	−0.112621	+	0.993638i	$0.535925\pi$
$972$	2.28929e6	−	1.74423e6i	0.0777204	−	0.0592160i
$973$	1.00137e6	+	5.67905e6i	0.0339088	+	0.192306i
$974$	−51609.5	+	2.19337e6i	−0.00174314	+	0.0740823i
$975$	−247894.	+	681082.i	−0.00835130	+	0.0229450i
$976$	−1.94322e7	−	9.22363e6i	−0.652978	−	0.309940i
$977$	4.05483e7	+	2.34105e7i	1.35905	+	0.784649i	0.989496	−	0.144560i	$-0.0461768\pi$
$977$	4.05483e7	+	2.34105e7i	1.35905	+	0.784649i	0.369555	+	0.929209i	$0.379510\pi$
$978$	420220.	+	369796.i	0.0140485	+	0.0123627i
$979$	7541.73	−	6328.27i	0.000251486	−	0.000211022i
$980$	−1.31115e6	+	5.82000e6i	−0.0436100	+	0.193579i
$981$	8.22532e6	−	4.74889e6i	0.272885	−	0.157550i
$982$	−6.76946e6	+	3.37310e7i	−0.224014	+	1.11622i
$983$	−6.44307e6	+	3.65405e7i	−0.212672	+	1.20612i	0.672230	+	0.740342i	$0.265337\pi$
$983$	−6.44307e6	+	3.65405e7i	−0.212672	+	1.20612i	−0.884902	+	0.465778i	$0.845775\pi$
$984$	634248.	−	460069.i	0.0208820	−	0.0151473i
$985$	9.86530e6	−	3.59068e6i	0.323981	−	0.117920i
$986$	1.62980e6	−	2.67551e6i	0.0533878	−	0.0876424i
$987$	−276833.			−0.00904536
$988$	−2.33537e7	−	7.29012e6i	−0.761139	−	0.237598i
$989$	−1.76292e7			−0.573114
$990$	25425.1	−	41738.3i	0.000824469	−	0.00135346i
$991$	2.79109e7	−	1.01587e7i	0.902795	−	0.328590i	0.151423	−	0.988469i	$-0.451615\pi$
$991$	2.79109e7	−	1.01587e7i	0.902795	−	0.328590i	0.751372	+	0.659879i	$0.229392\pi$
$992$	2.55898e7	+	1.91016e7i	0.825635	+	0.616296i
$993$	289396.	−	1.64124e6i	0.00931363	−	0.0528202i
$994$	1.93110e6	−	9.62231e6i	0.0619923	−	0.308897i
$995$	3.18736e6	−	1.84023e6i	0.102064	−	0.0589269i
$996$	1.61570e6	+	363991.i	0.0516076	+	0.0116263i
$997$	−2.06396e7	+	1.73187e7i	−0.657603	+	0.551794i	−0.909367	−	0.415994i	$-0.863434\pi$
$997$	−2.06396e7	+	1.73187e7i	−0.657603	+	0.551794i	0.251764	+	0.967789i	$0.418989\pi$
$998$	−1.81697e7	−	1.59894e7i	−0.577461	−	0.508168i
$999$	−741973.	−	428378.i	−0.0235220	−	0.0135804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.k.a.3.8	✓	288
4.3	odd	2	inner	76.6.k.a.3.35	yes	288
19.13	odd	18	inner	76.6.k.a.51.35	yes	288
76.51	even	18	inner	76.6.k.a.51.8	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.k.a.3.8	✓	288	1.1	even	1	trivial
76.6.k.a.3.35	yes	288	4.3	odd	2	inner
76.6.k.a.51.8	yes	288	76.51	even	18	inner
76.6.k.a.51.35	yes	288	19.13	odd	18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.83109 - 2.94288i) q^{2} +(0.477768 - 0.173893i) q^{3} +(14.6789 + 28.4347i) q^{4} +(2.39951 - 13.6083i) q^{5} +(-2.81989 - 0.565922i) q^{6} +(49.8634 - 28.7886i) q^{7} +(12.7651 - 180.569i) q^{8} +(-185.951 + 156.031i) q^{9} +O(q^{10})\)	\(q+(-4.83109 - 2.94288i) q^{2} +(0.477768 - 0.173893i) q^{3} +(14.6789 + 28.4347i) q^{4} +(2.39951 - 13.6083i) q^{5} +(-2.81989 - 0.565922i) q^{6} +(49.8634 - 28.7886i) q^{7} +(12.7651 - 180.569i) q^{8} +(-185.951 + 156.031i) q^{9} +(-51.6398 + 58.6813i) q^{10} +(2.23061 + 1.28784i) q^{11} +(11.9577 + 11.0326i) q^{12} +(-166.175 + 456.562i) q^{13} +(-325.616 - 7.66167i) q^{14} +(-1.21998 - 6.91886i) q^{15} +(-593.062 + 834.778i) q^{16} +(72.0101 + 60.4237i) q^{17} +(1357.53 - 206.569i) q^{18} +(1430.28 + 656.055i) q^{19} +(422.169 - 131.525i) q^{20} +(18.8170 - 22.4252i) q^{21} +(-6.98631 - 12.7861i) q^{22} +(1590.17 - 280.389i) q^{23} +(-25.3010 - 88.4898i) q^{24} +(2757.11 + 1003.51i) q^{25} +(2146.41 - 1716.66i) q^{26} +(-123.483 + 213.879i) q^{27} +(1550.53 + 995.265i) q^{28} +(3786.95 + 4513.11i) q^{29} +(-14.4676 + 37.0159i) q^{30} +(2756.34 + 4774.13i) q^{31} +(5321.79 - 2287.57i) q^{32} +(1.28966 + 0.227403i) q^{33} +(-170.068 - 503.830i) q^{34} +(-272.116 - 747.633i) q^{35} +(-7166.24 - 2997.09i) q^{36} +3469.13i q^{37} +(-4979.10 - 7378.60i) q^{38} +247.027i q^{39} +(-2426.60 - 606.986i) q^{40} +(2911.76 + 8000.01i) q^{41} +(-156.901 + 52.9620i) q^{42} +(-10752.1 - 1895.88i) q^{43} +(-3.87660 + 82.3309i) q^{44} +(1677.13 + 2904.87i) q^{45} +(-8507.39 - 3325.09i) q^{46} +(-6078.60 - 7244.19i) q^{47} +(-138.184 + 501.960i) q^{48} +(-6745.93 + 11684.3i) q^{49} +(-10366.7 - 12961.9i) q^{50} +(44.9114 + 16.3464i) q^{51} +(-15421.4 + 1976.68i) q^{52} +(21259.3 - 3748.59i) q^{53} +(1225.98 - 669.871i) q^{54} +(22.8777 - 27.2646i) q^{55} +(-4561.82 - 9371.25i) q^{56} +(797.424 + 64.7266i) q^{57} +(-5013.53 - 32947.8i) q^{58} +(-22182.9 - 18613.6i) q^{59} +(178.828 - 136.251i) q^{60} +(3647.66 + 20686.9i) q^{61} +(733.560 - 31175.8i) q^{62} +(-4780.21 + 13133.5i) q^{63} +(-32442.1 - 4609.94i) q^{64} +(5814.28 + 3356.88i) q^{65} +(-5.56126 - 4.89393i) q^{66} +(-11452.4 + 9609.69i) q^{67} +(-661.101 + 2934.54i) q^{68} +(710.974 - 410.481i) q^{69} +(-885.580 + 4412.69i) q^{70} +(-5232.36 + 29674.2i) q^{71} +(25800.7 + 35568.6i) q^{72} +(13331.7 - 4852.34i) q^{73} +(10209.2 - 16759.7i) q^{74} +1491.76 q^{75} +(2340.12 + 50299.6i) q^{76} +148.301 q^{77} +(726.973 - 1193.41i) q^{78} +(-8739.49 + 3180.92i) q^{79} +(9936.83 + 10073.6i) q^{80} +(10221.0 - 57966.4i) q^{81} +(9476.10 - 47217.7i) q^{82} +(88157.9 - 50898.0i) q^{83} +(913.865 + 205.878i) q^{84} +(995.051 - 834.947i) q^{85} +(46364.9 + 40801.3i) q^{86} +(2594.08 + 1497.69i) q^{87} +(261.018 - 386.339i) q^{88} +(1307.30 - 3591.78i) q^{89} +(446.342 - 18969.3i) q^{90} +(4857.75 + 27549.6i) q^{91} +(31314.6 + 41100.1i) q^{92} +(2147.08 + 1801.62i) q^{93} +(8047.44 + 52886.0i) q^{94} +(12359.7 - 17889.4i) q^{95} +(2144.79 - 2018.35i) q^{96} +(-65250.3 + 77762.3i) q^{97} +(66975.7 - 36595.4i) q^{98} +(-615.728 + 108.569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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