LMFDB - Embedded newform 7.5.d.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,5,Mod(3,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	7.d (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:	$0.723589741587$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 22x^{2} + 484 $ x^4 + 22*x^2 + 484
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$-2.34521 + 4.06202i$ of defining polynomial
Character	$\chi$	$=$	7.5
Dual form			7.5.d.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.34521 + 5.79407i) q^{2} +(8.53562 - 4.92804i) q^{3} +(-14.3808 - 24.9083i) q^{4} +(6.57125 + 3.79391i) q^{5} +65.9413i q^{6} +(-32.8329 - 36.3731i) q^{7} +85.3808 q^{8} +(8.07125 - 13.9798i) q^{9} +O(q^{10})$	\(q+(-3.34521 + 5.79407i) q^{2} +(8.53562 - 4.92804i) q^{3} +(-14.3808 - 24.9083i) q^{4} +(6.57125 + 3.79391i) q^{5} +65.9413i q^{6} +(-32.8329 - 36.3731i) q^{7} +85.3808 q^{8} +(8.07125 - 13.9798i) q^{9} +(-43.9644 + 25.3828i) q^{10} +(25.3685 + 43.9396i) q^{11} +(-245.499 - 141.739i) q^{12} +7.50702i q^{13} +(320.581 - 68.5607i) q^{14} +74.7863 q^{15} +(-55.5233 + 96.1692i) q^{16} +(-300.711 + 173.616i) q^{17} +(54.0000 + 93.5307i) q^{18} +(420.818 + 242.959i) q^{19} -218.238i q^{20} +(-459.497 - 148.665i) q^{21} -339.452 q^{22} +(168.654 - 292.116i) q^{23} +(728.779 - 420.761i) q^{24} +(-283.712 - 491.404i) q^{25} +(-43.4962 - 25.1125i) q^{26} +639.241i q^{27} +(-433.828 + 1340.89i) q^{28} -215.671 q^{29} +(-250.176 + 433.317i) q^{30} +(1108.53 - 640.012i) q^{31} +(311.573 + 539.659i) q^{32} +(433.073 + 250.035i) q^{33} -2323.12i q^{34} +(-77.7570 - 363.582i) q^{35} -464.285 q^{36} +(176.402 - 305.537i) q^{37} +(-2815.45 + 1625.50i) q^{38} +(36.9949 + 64.0771i) q^{39} +(561.059 + 323.927i) q^{40} +1040.97i q^{41} +(2398.49 - 2165.05i) q^{42} -1023.65 q^{43} +(729.641 - 1263.78i) q^{44} +(106.076 - 61.2432i) q^{45} +(1128.36 + 1954.38i) q^{46} +(-1701.16 - 982.166i) q^{47} +1094.49i q^{48} +(-245.000 + 2388.47i) q^{49} +3796.31 q^{50} +(-1711.17 + 2963.84i) q^{51} +(186.987 - 107.957i) q^{52} +(-1924.87 - 3333.97i) q^{53} +(-3703.81 - 2138.40i) q^{54} +384.984i q^{55} +(-2803.30 - 3105.56i) q^{56} +4789.26 q^{57} +(721.464 - 1249.61i) q^{58} +(3790.50 - 2188.44i) q^{59} +(-1075.49 - 1862.80i) q^{60} +(1618.05 + 934.181i) q^{61} +8563.89i q^{62} +(-773.491 + 165.422i) q^{63} -5945.85 q^{64} +(-28.4810 + 49.3305i) q^{65} +(-2897.44 + 1672.83i) q^{66} +(-223.966 - 387.920i) q^{67} +(8648.95 + 4993.48i) q^{68} -3324.53i q^{69} +(2366.73 + 765.727i) q^{70} -1485.68 q^{71} +(689.130 - 1193.61i) q^{72} +(-610.190 + 352.293i) q^{73} +(1180.20 + 2044.17i) q^{74} +(-4843.33 - 2796.30i) q^{75} -13975.8i q^{76} +(765.295 - 2365.40i) q^{77} -495.023 q^{78} +(-2850.67 + 4937.50i) q^{79} +(-729.715 + 421.301i) q^{80} +(3803.98 + 6588.69i) q^{81} +(-6031.44 - 3482.25i) q^{82} -4028.74i q^{83} +(2904.96 + 13583.2i) q^{84} -2634.73 q^{85} +(3424.31 - 5931.07i) q^{86} +(-1840.89 + 1062.84i) q^{87} +(2165.99 + 3751.60i) q^{88} +(5852.11 + 3378.71i) q^{89} +819.485i q^{90} +(273.053 - 246.477i) q^{91} -9701.51 q^{92} +(6308.01 - 10925.8i) q^{93} +(11381.5 - 6571.10i) q^{94} +(1843.53 + 3193.09i) q^{95} +(5318.93 + 3070.89i) q^{96} +11538.2i q^{97} +(-13019.4 - 9409.47i) q^{98} +819.023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 20 q^{4} - 30 q^{5} + 304 q^{8} - 24 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 20 * q^4 - 30 * q^5 + 304 * q^8 - 24 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 20 q^{4} - 30 q^{5} + 304 q^{8} - 24 q^{9} - 204 q^{10} - 58 q^{11} - 588 q^{12} + 560 q^{14} + 468 q^{15} - 72 q^{16} - 246 q^{17} + 216 q^{18} + 642 q^{19} - 1050 q^{21} - 1264 q^{22} + 290 q^{23} + 720 q^{24} - 572 q^{25} + 1008 q^{26} - 28 q^{28} - 2176 q^{29} - 72 q^{30} + 3618 q^{31} + 1584 q^{32} + 2070 q^{33} - 2478 q^{35} - 1632 q^{36} - 270 q^{37} - 6168 q^{38} - 1428 q^{39} - 1752 q^{40} + 6048 q^{42} + 2472 q^{43} + 2412 q^{44} + 1944 q^{45} + 2384 q^{46} - 1542 q^{47} - 980 q^{49} + 7568 q^{50} - 4734 q^{51} - 3192 q^{52} - 4510 q^{53} - 11016 q^{54} - 1232 q^{56} + 11052 q^{57} - 904 q^{58} + 2526 q^{59} - 756 q^{60} - 282 q^{61} - 336 q^{63} - 5472 q^{64} + 5796 q^{65} - 2556 q^{66} - 1318 q^{67} + 20412 q^{68} + 3360 q^{70} - 10408 q^{71} - 1296 q^{72} + 5214 q^{73} + 4036 q^{74} - 9636 q^{75} - 8890 q^{77} - 9072 q^{78} - 8110 q^{79} - 3144 q^{80} + 9306 q^{81} - 4032 q^{82} + 588 q^{84} - 15492 q^{85} + 12928 q^{86} + 5976 q^{87} - 2912 q^{88} + 33990 q^{89} + 17640 q^{91} - 20232 q^{92} + 7446 q^{93} + 27768 q^{94} + 6558 q^{95} - 37828 q^{98} + 10368 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 20 * q^4 - 30 * q^5 + 304 * q^8 - 24 * q^9 - 204 * q^10 - 58 * q^11 - 588 * q^12 + 560 * q^14 + 468 * q^15 - 72 * q^16 - 246 * q^17 + 216 * q^18 + 642 * q^19 - 1050 * q^21 - 1264 * q^22 + 290 * q^23 + 720 * q^24 - 572 * q^25 + 1008 * q^26 - 28 * q^28 - 2176 * q^29 - 72 * q^30 + 3618 * q^31 + 1584 * q^32 + 2070 * q^33 - 2478 * q^35 - 1632 * q^36 - 270 * q^37 - 6168 * q^38 - 1428 * q^39 - 1752 * q^40 + 6048 * q^42 + 2472 * q^43 + 2412 * q^44 + 1944 * q^45 + 2384 * q^46 - 1542 * q^47 - 980 * q^49 + 7568 * q^50 - 4734 * q^51 - 3192 * q^52 - 4510 * q^53 - 11016 * q^54 - 1232 * q^56 + 11052 * q^57 - 904 * q^58 + 2526 * q^59 - 756 * q^60 - 282 * q^61 - 336 * q^63 - 5472 * q^64 + 5796 * q^65 - 2556 * q^66 - 1318 * q^67 + 20412 * q^68 + 3360 * q^70 - 10408 * q^71 - 1296 * q^72 + 5214 * q^73 + 4036 * q^74 - 9636 * q^75 - 8890 * q^77 - 9072 * q^78 - 8110 * q^79 - 3144 * q^80 + 9306 * q^81 - 4032 * q^82 + 588 * q^84 - 15492 * q^85 + 12928 * q^86 + 5976 * q^87 - 2912 * q^88 + 33990 * q^89 + 17640 * q^91 - 20232 * q^92 + 7446 * q^93 + 27768 * q^94 + 6558 * q^95 - 37828 * q^98 + 10368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−3.34521	+	5.79407i	−0.836302	+	1.44852i	0.0566640	+	0.998393i	$0.481954\pi$
$2$	−3.34521	+	5.79407i	−0.836302	+	1.44852i	−0.892966	+	0.450124i	$0.851380\pi$
$3$	8.53562	−	4.92804i	0.948403	−	0.547561i	0.0558183	−	0.998441i	$-0.482223\pi$
$3$	8.53562	−	4.92804i	0.948403	−	0.547561i	0.892584	+	0.450880i	$0.148890\pi$
$4$	−14.3808	−	24.9083i	−0.898802	−	1.55677i
$5$	6.57125	+	3.79391i	0.262850	+	0.151756i	0.625634	−	0.780117i	$-0.284840\pi$
$5$	6.57125	+	3.79391i	0.262850	+	0.151756i	−0.362784	+	0.931873i	$0.618174\pi$
$6$			65.9413i			1.83170i
$7$	−32.8329	−	36.3731i	−0.670059	−	0.742307i
$7$	−32.8329	−	36.3731i	−0.670059	−	0.742307i
$8$	85.3808			1.33408
$9$	8.07125	−	13.9798i	0.0996450	−	0.172590i
$10$	−43.9644	+	25.3828i	−0.439644	+	0.253828i
$11$	25.3685	+	43.9396i	0.209657	+	0.363137i	0.951607	−	0.307319i	$-0.0994318\pi$
$11$	25.3685	+	43.9396i	0.209657	+	0.363137i	−0.741949	+	0.670456i	$0.766098\pi$
$12$	−245.499	−	141.739i	−1.70485	−	0.984297i
$13$			7.50702i			0.0444202i	0.999753	+	0.0222101i	$0.00707028\pi$
$13$			7.50702i			0.0444202i	−0.999753	+	0.0222101i	$0.992930\pi$
$14$	320.581	−	68.5607i	1.63562	−	0.349800i
$15$	74.7863			0.332383
$16$	−55.5233	+	96.1692i	−0.216888	+	0.375661i
$17$	−300.711	+	173.616i	−1.04052	+	0.600746i	−0.919981	−	0.391962i	$-0.871796\pi$
$17$	−300.711	+	173.616i	−1.04052	+	0.600746i	−0.120542	+	0.992708i	$0.538463\pi$
$18$	54.0000	+	93.5307i	0.166667	+	0.288675i
$19$	420.818	+	242.959i	1.16570	+	0.673018i	0.952664	−	0.304026i	$-0.0983311\pi$
$19$	420.818	+	242.959i	1.16570	+	0.673018i	0.213037	+	0.977044i	$0.431664\pi$
$20$		−	218.238i		−	0.545596i
$21$	−459.497	−	148.665i	−1.04194	−	0.337108i
$22$	−339.452			−0.701347
$23$	168.654	−	292.116i	0.318816	−	0.552205i	−0.661425	−	0.750011i	$-0.730048\pi$
$23$	168.654	−	292.116i	0.318816	−	0.552205i	0.980241	+	0.197806i	$0.0633816\pi$
$24$	728.779	−	420.761i	1.26524	−	0.730487i
$25$	−283.712	−	491.404i	−0.453940	−	0.786247i
$26$	−43.4962	−	25.1125i	−0.0643435	−	0.0371487i
$27$			639.241i			0.876874i
$28$	−433.828	+	1340.89i	−0.553352	+	1.71032i
$29$	−215.671			−0.256446			−0.128223	−	0.991745i	$-0.540927\pi$
$29$	−215.671			−0.256446			−0.128223	+	0.991745i	$0.540927\pi$
$30$	−250.176	+	433.317i	−0.277973	+	0.481463i
$31$	1108.53	−	640.012i	1.15352	−	0.665985i	0.203778	−	0.979017i	$-0.434678\pi$
$31$	1108.53	−	640.012i	1.15352	−	0.665985i	0.949743	+	0.313032i	$0.101345\pi$
$32$	311.573	+	539.659i	0.304270	+	0.527011i
$33$	433.073	+	250.035i	0.397679	+	0.229600i
$34$		−	2323.12i		−	2.00962i
$35$	−77.7570	−	363.582i	−0.0634751	−	0.296801i
$36$	−464.285			−0.358245
$37$	176.402	−	305.537i	0.128854	−	0.223182i	−0.794379	−	0.607423i	$-0.792203\pi$
$37$	176.402	−	305.537i	0.128854	−	0.223182i	0.923233	+	0.384241i	$0.125537\pi$
$38$	−2815.45	+	1625.50i	−1.94976	+	1.12569i
$39$	36.9949	+	64.0771i	0.0243228	+	0.0421283i
$40$	561.059	+	323.927i	0.350662	+	0.202455i
$41$			1040.97i			0.619255i	0.950858	+	0.309627i	$0.100204\pi$
$41$			1040.97i			0.619255i	−0.950858	+	0.309627i	$0.899796\pi$
$42$	2398.49	−	2165.05i	1.35969	−	1.22735i
$43$	−1023.65			−0.553621			−0.276811	−	0.960925i	$-0.589277\pi$
$43$	−1023.65			−0.553621			−0.276811	+	0.960925i	$0.589277\pi$
$44$	729.641	−	1263.78i	0.376881	−	0.652777i
$45$	106.076	−	61.2432i	0.0523834	−	0.0302436i
$46$	1128.36	+	1954.38i	0.533252	+	0.923620i
$47$	−1701.16	−	982.166i	−0.770105	−	0.444620i	0.0628072	−	0.998026i	$-0.479995\pi$
$47$	−1701.16	−	982.166i	−0.770105	−	0.444620i	−0.832912	+	0.553405i	$0.813328\pi$
$48$			1094.49i			0.475037i
$49$	−245.000	+	2388.47i	−0.102041	+	0.994780i
$50$	3796.31			1.51852
$51$	−1711.17	+	2963.84i	−0.657890	+	1.13950i
$52$	186.987	−	107.957i	0.0691521	−	0.0399250i
$53$	−1924.87	−	3333.97i	−0.685251	−	1.18689i	−0.973358	−	0.229292i	$-0.926359\pi$
$53$	−1924.87	−	3333.97i	−0.685251	−	1.18689i	0.288107	−	0.957598i	$-0.406974\pi$
$54$	−3703.81	−	2138.40i	−1.27017	−	0.733332i
$55$			384.984i			0.127267i
$56$	−2803.30	−	3105.56i	−0.893910	−	0.990294i
$57$	4789.26			1.47407
$58$	721.464	−	1249.61i	0.214466	−	0.371466i
$59$	3790.50	−	2188.44i	1.08891	−	0.628682i	0.155624	−	0.987816i	$-0.450261\pi$
$59$	3790.50	−	2188.44i	1.08891	−	0.628682i	0.933286	+	0.359134i	$0.116928\pi$
$60$	−1075.49	−	1862.80i	−0.298747	−	0.517445i
$61$	1618.05	+	934.181i	0.434843	+	0.251057i	0.701408	−	0.712760i	$-0.252555\pi$
$61$	1618.05	+	934.181i	0.434843	+	0.251057i	−0.266565	+	0.963817i	$0.585889\pi$
$62$			8563.89i			2.22786i
$63$	−773.491	+	165.422i	−0.194883	+	0.0416785i
$64$	−5945.85			−1.45162
$65$	−28.4810	+	49.3305i	−0.00674106	+	0.0116759i
$66$	−2897.44	+	1672.83i	−0.665160	+	0.384030i
$67$	−223.966	−	387.920i	−0.0498921	−	0.0864157i	0.840001	−	0.542585i	$-0.182554\pi$
$67$	−223.966	−	387.920i	−0.0498921	−	0.0864157i	−0.889893	+	0.456169i	$0.849221\pi$
$68$	8648.95	+	4993.48i	1.87045	+	1.07990i
$69$		−	3324.53i		−	0.698284i
$70$	2366.73	+	765.727i	0.483006	+	0.156271i
$71$	−1485.68			−0.294720			−0.147360	−	0.989083i	$-0.547078\pi$
$71$	−1485.68			−0.294720			−0.147360	+	0.989083i	$0.547078\pi$
$72$	689.130	−	1193.61i	0.132934	−	0.230248i
$73$	−610.190	+	352.293i	−0.114504	+	0.0661087i	−0.556158	−	0.831077i	$-0.687725\pi$
$73$	−610.190	+	352.293i	−0.114504	+	0.0661087i	0.441654	+	0.897185i	$0.354392\pi$
$74$	1180.20	+	2044.17i	0.215522	+	0.373296i
$75$	−4843.33	−	2796.30i	−0.861036	−	0.497119i
$76$		−	13975.8i		−	2.41964i
$77$	765.295	−	2365.40i	0.129077	−	0.398954i
$78$	−495.023			−0.0813647
$79$	−2850.67	+	4937.50i	−0.456765	+	0.791140i	−0.998788	−	0.0492240i	$-0.984325\pi$
$79$	−2850.67	+	4937.50i	−0.456765	+	0.791140i	0.542023	+	0.840364i	$0.317659\pi$
$80$	−729.715	+	421.301i	−0.114018	+	0.0658283i
$81$	3803.98	+	6588.69i	0.579787	+	1.00422i
$82$	−6031.44	−	3482.25i	−0.897001	−	0.517884i
$83$		−	4028.74i		−	0.584808i	−0.956295	−	0.292404i	$-0.905545\pi$
$83$		−	4028.74i		−	0.584808i	0.956295	−	0.292404i	$-0.0944552\pi$
$84$	2904.96	+	13583.2i	0.411701	+	1.92506i
$85$	−2634.73			−0.364669
$86$	3424.31	−	5931.07i	0.462994	−	0.801930i
$87$	−1840.89	+	1062.84i	−0.243214	+	0.140420i
$88$	2165.99	+	3751.60i	0.279699	+	0.484452i
$89$	5852.11	+	3378.71i	0.738809	+	0.426552i	0.821636	−	0.570012i	$-0.193062\pi$
$89$	5852.11	+	3378.71i	0.738809	+	0.426552i	−0.0828272	+	0.996564i	$0.526395\pi$
$90$			819.485i			0.101171i
$91$	273.053	−	246.477i	0.0329735	−	0.0297642i
$92$	−9701.51			−1.14621
$93$	6308.01	−	10925.8i	0.729335	−	1.26324i
$94$	11381.5	−	6571.10i	1.28808	−	0.743674i
$95$	1843.53	+	3193.09i	0.204270	+	0.353805i
$96$	5318.93	+	3070.89i	0.577141	+	0.333213i
$97$			11538.2i			1.22630i	0.789968	+	0.613148i	$0.210097\pi$
$97$			11538.2i			1.22630i	−0.789968	+	0.613148i	$0.789903\pi$
$98$	−13019.4	−	9409.47i	−1.35562	−	0.979745i
$99$	819.023			0.0835652
$100$	−8160.04	+	14133.6i	−0.816004	+	1.41336i
$101$	−14199.7	+	8198.21i	−1.39199	+	0.803667i	−0.993536	−	0.113520i	$-0.963788\pi$
$101$	−14199.7	+	8198.21i	−1.39199	+	0.803667i	−0.398457	+	0.917187i	$0.630454\pi$
$102$	−11448.5	−	19829.3i	−1.10039	−	1.90593i
$103$	2405.70	+	1388.93i	0.226760	+	0.130920i	0.609077	−	0.793111i	$-0.291540\pi$
$103$	2405.70	+	1388.93i	0.226760	+	0.130920i	−0.382316	+	0.924032i	$0.624874\pi$
$104$			640.956i			0.0592599i
$105$	−2455.45	−	2720.21i	−0.222717	−	0.246731i
$106$	25756.4			2.29231
$107$	3526.64	−	6108.32i	0.308030	−	0.533524i	−0.669901	−	0.742450i	$-0.733663\pi$
$107$	3526.64	−	6108.32i	0.308030	−	0.533524i	0.977931	+	0.208926i	$0.0669968\pi$
$108$	15922.4	−	9192.82i	1.36509	−	0.788136i
$109$	−5484.31	−	9499.10i	−0.461603	−	0.799520i	0.537438	−	0.843303i	$-0.319392\pi$
$109$	−5484.31	−	9499.10i	−0.461603	−	0.799520i	−0.999041	+	0.0437831i	$0.986059\pi$
$110$	−2230.62	−	1287.85i	−0.184349	−	0.106434i
$111$		−	3477.26i		−	0.282222i
$112$	5320.96	−	1137.96i	0.424184	−	0.0907176i
$113$	−12985.5			−1.01696			−0.508478	−	0.861075i	$-0.669792\pi$
$113$	−12985.5			−1.01696			−0.508478	+	0.861075i	$0.669792\pi$
$114$	−16021.1	+	27749.3i	−1.23277	+	2.13522i
$115$	2216.53	−	1279.71i	0.167601	−	0.0967647i
$116$	3101.53	+	5372.00i	0.230494	+	0.399227i
$117$	104.947	+	60.5910i	0.00766650	+	0.00442626i
$118$			29283.2i			2.10307i
$119$	16188.2	+	5237.48i	1.14315	+	0.369852i
$120$	6385.31			0.443425
$121$	6033.37	−	10450.1i	0.412088	−	0.713757i
$122$	−10825.4	+	6250.06i	−0.727320	+	0.419918i
$123$	5129.93	+	8885.30i	0.339079	+	0.587303i
$124$	−31883.3	−	18407.8i	−2.07357	−	1.19718i
$125$		−	9047.91i		−	0.579066i
$126$	1629.02	−	5035.03i	0.102609	−	0.317147i
$127$	14948.9			0.926836			0.463418	−	0.886140i	$-0.346623\pi$
$127$	14948.9			0.926836			0.463418	+	0.886140i	$0.346623\pi$
$128$	14904.9	−	25816.1i	0.909725	−	1.57569i
$129$	−8737.45	+	5044.57i	−0.525056	+	0.303141i
$130$	−190.549	−	330.041i	−0.0112751	−	0.0195291i
$131$	−2880.21	−	1662.89i	−0.167834	−	0.0968993i	0.413730	−	0.910400i	$-0.364226\pi$
$131$	−2880.21	−	1662.89i	−0.167834	−	0.0968993i	−0.581564	+	0.813500i	$0.697559\pi$
$132$		−	14382.8i		−	0.825460i
$133$	−4979.50	−	23283.5i	−0.281503	−	1.31627i
$134$	2996.85			0.166899
$135$	−2425.23	+	4200.61i	−0.133071	+	0.230486i
$136$	−25675.0	+	14823.5i	−1.38814	+	0.801441i
$137$	17514.5	+	30336.0i	0.933162	+	1.61628i	0.777879	+	0.628414i	$0.216296\pi$
$137$	17514.5	+	30336.0i	0.933162	+	1.61628i	0.155283	+	0.987870i	$0.450371\pi$
$138$	19262.5	+	11121.2i	1.01148	+	0.583976i
$139$		−	5437.55i		−	0.281432i	−0.990050	−	0.140716i	$-0.955060\pi$
$139$		−	5437.55i		−	0.281432i	0.990050	−	0.140716i	$-0.0449405\pi$
$140$	−7938.00	+	7165.40i	−0.405000	+	0.365582i
$141$	−19360.6			−0.973826
$142$	4969.91	−	8608.14i	0.246475	−	0.426906i
$143$	−329.855	+	190.442i	−0.0161306	+	0.00931303i
$144$	896.285	+	1552.41i	0.0432236	+	0.0748655i
$145$	−1417.23	−	818.236i	−0.0674067	−	0.0389173i
$146$		−	4713.98i		−	0.221147i
$147$	9679.25	+	21594.4i	0.447927	+	0.999326i
$148$	−10147.2			−0.463258
$149$	−11297.9	+	19568.5i	−0.508891	+	0.881424i	0.491056	+	0.871128i	$0.336611\pi$
$149$	−11297.9	+	19568.5i	−0.508891	+	0.881424i	−0.999947	+	0.0102966i	$0.996722\pi$
$150$	32403.9	−	18708.4i	1.44017	−	0.831484i
$151$	−15871.4	−	27490.1i	−0.696085	−	1.20565i	−0.969814	−	0.243848i	$-0.921590\pi$
$151$	−15871.4	−	27490.1i	−0.696085	−	1.20565i	0.273728	−	0.961807i	$-0.411743\pi$
$152$	35929.8	+	20744.1i	1.55513	+	0.897857i
$153$			5605.18i			0.239446i
$154$	11145.2	+	12346.9i	0.469944	+	0.520615i
$155$	9712.59			0.404270
$156$	1064.04	−	1842.96i	0.0437227	−	0.0757299i
$157$	18523.5	−	10694.6i	0.751492	−	0.433874i	−0.0747405	−	0.997203i	$-0.523813\pi$
$157$	18523.5	−	10694.6i	0.751492	−	0.433874i	0.826233	+	0.563329i	$0.190480\pi$
$158$	−19072.2	−	33033.9i	−0.763986	−	1.32326i
$159$	−32859.9	−	18971.7i	−1.29979	−	0.750433i
$160$			4728.31i			0.184700i
$161$	−16162.6	+	3456.59i	−0.623531	+	0.133351i
$162$	−50900.4			−1.93951
$163$	−21528.6	+	37288.6i	−0.810290	+	1.40346i	0.102371	+	0.994746i	$0.467357\pi$
$163$	−21528.6	+	37288.6i	−0.810290	+	1.40346i	−0.912661	+	0.408717i	$0.865976\pi$
$164$	25928.7	−	14970.0i	0.964037	−	0.556587i
$165$	1897.22	+	3286.08i	0.0696866	+	0.120701i
$166$	23342.8	+	13477.0i	0.847104	+	0.489076i
$167$		−	24861.8i		−	0.891457i	−0.895168	−	0.445728i	$-0.852945\pi$
$167$		−	24861.8i		−	0.891457i	0.895168	−	0.445728i	$-0.147055\pi$
$168$	−39232.3	−	12693.1i	−1.39003	−	0.449728i
$169$	28504.6			0.998027
$170$	8813.72	−	15265.8i	0.304973	−	0.528229i
$171$	6793.05	−	3921.97i	0.232313	−	0.134126i
$172$	14720.9	+	25497.3i	0.497596	+	0.861861i
$173$	32456.1	+	18738.5i	1.08444	+	0.626099i	0.932089	−	0.362228i	$-0.117984\pi$
$173$	32456.1	+	18738.5i	1.08444	+	0.626099i	0.152346	+	0.988327i	$0.451317\pi$
$174$		−	14221.6i		−	0.469733i
$175$	−8558.78	+	26453.7i	−0.279470	+	0.863795i
$176$	−5634.18			−0.181889
$177$	21569.5	−	37359.5i	0.688483	−	1.19249i
$178$	−39153.0	+	22605.0i	−1.23573	+	0.713452i
$179$	−11768.6	−	20383.8i	−0.367298	−	0.636178i	0.621844	−	0.783141i	$-0.286384\pi$
$179$	−11768.6	−	20383.8i	−0.367298	−	0.636178i	−0.989142	+	0.146963i	$0.953050\pi$
$180$	−3050.93	−	1761.46i	−0.0941646	−	0.0543659i
$181$			9211.05i			0.281159i	0.990069	+	0.140580i	$0.0448966\pi$
$181$			9211.05i			0.281159i	−0.990069	+	0.140580i	$0.955103\pi$
$182$	514.687	+	2406.61i	0.0155382	+	0.0726545i
$183$	18414.8			0.549875
$184$	14399.8	−	24941.1i	0.425324	−	0.736683i
$185$	2318.36	−	1338.50i	0.0677387	−	0.0391090i
$186$	42203.2	+	73098.2i	1.21989	+	2.11291i
$187$	−15257.2	−	8808.75i	−0.436307	−	0.251902i
$188$			56497.5i			1.59850i
$189$	23251.2	−	20988.2i	0.650910	−	0.587558i
$190$	−24668.0			−0.683324
$191$	−6033.47	+	10450.3i	−0.165387	+	0.286458i	−0.936793	−	0.349885i	$-0.886221\pi$
$191$	−6033.47	+	10450.3i	−0.165387	+	0.286458i	0.771406	+	0.636343i	$0.219554\pi$
$192$	−50751.5	+	29301.4i	−1.37672	+	0.794851i
$193$	−4276.53	−	7407.17i	−0.114809	−	0.198856i	0.802894	−	0.596122i	$-0.203292\pi$
$193$	−4276.53	−	7407.17i	−0.114809	−	0.198856i	−0.917704	+	0.397266i	$0.869959\pi$
$194$	−66853.2	−	38597.7i	−1.77631	−	1.02555i
$195$			561.422i			0.0147645i
$196$	63016.0	−	28245.6i	1.64036	−	0.735256i
$197$	−15909.4			−0.409942			−0.204971	−	0.978768i	$-0.565710\pi$
$197$	−15909.4			−0.409942			−0.204971	+	0.978768i	$0.565710\pi$
$198$	−2739.80	+	4745.48i	−0.0698858	+	0.121046i
$199$	23829.4	−	13757.9i	0.601737	−	0.347413i	−0.167988	−	0.985789i	$-0.553727\pi$
$199$	23829.4	−	13757.9i	0.601737	−	0.347413i	0.769725	+	0.638376i	$0.220393\pi$
$200$	−24223.6	−	41956.5i	−0.605590	−	1.04891i
$201$	−3823.37	−	2207.43i	−0.0946356	−	0.0546379i
$202$		−	109699.i		−	2.68843i
$203$	7081.10	+	7844.61i	0.171834	+	0.190362i
$204$	98432.3			2.36525
$205$	−3949.34	+	6840.45i	−0.0939759	+	0.162771i
$206$	−16095.1	+	9292.53i	−0.379280	+	0.218978i
$207$	−2722.49	−	4715.49i	−0.0635368	−	0.110049i
$208$	−721.944	−	416.815i	−0.0166869	−	0.00963421i
$209$			24654.1i			0.564412i
$210$	23975.1	−	5127.40i	0.543652	−	0.116268i
$211$	−50656.9			−1.13782			−0.568910	−	0.822400i	$-0.692635\pi$
$211$	−50656.9			−1.13782			−0.568910	+	0.822400i	$0.692635\pi$
$212$	−55362.5	+	95890.6i	−1.23181	+	2.13356i
$213$	−12681.2	+	7321.50i	−0.279513	+	0.161377i
$214$	23594.7	+	40867.2i	0.515213	+	0.892375i
$215$	−6726.63	−	3883.62i	−0.145519	−	0.0840156i
$216$			54579.0i			1.16982i
$217$	−59675.6	−	19307.3i	−1.26729	−	0.410017i
$218$	73384.6			1.54416
$219$	−3472.23	+	6014.08i	−0.0723970	+	0.125395i
$220$	9589.31	−	5536.39i	0.198126	−	0.114388i
$221$	−1303.34	−	2257.44i	−0.0266853	−	0.0462203i
$222$	20147.5	+	11632.2i	0.408804	+	0.236023i
$223$			82476.6i			1.65852i	0.558862	+	0.829261i	$0.311238\pi$
$223$			82476.6i			1.65852i	−0.558862	+	0.829261i	$0.688762\pi$
$224$	9399.24	−	29051.4i	0.187325	−	0.578991i
$225$	−9159.65			−0.180931
$226$	43439.3	−	75239.0i	0.850483	−	1.47308i
$227$	28408.6	−	16401.7i	0.551314	−	0.318301i	−0.198338	−	0.980134i	$-0.563554\pi$
$227$	28408.6	−	16401.7i	0.551314	−	0.318301i	0.749652	+	0.661833i	$0.230221\pi$
$228$	−68873.5	−	119292.i	−1.32490	−	2.29479i
$229$	89549.0	+	51701.1i	1.70761	+	0.985892i	0.937500	+	0.347986i	$0.113134\pi$
$229$	89549.0	+	51701.1i	1.70761	+	0.985892i	0.770115	+	0.637905i	$0.220199\pi$
$230$			17123.6i			0.323698i
$231$	−5124.51	−	23961.5i	−0.0960347	−	0.449046i
$232$	−18414.2			−0.342118
$233$	35601.4	−	61663.5i	0.655776	−	1.13584i	−0.325922	−	0.945397i	$-0.605675\pi$
$233$	35601.4	−	61663.5i	0.655776	−	1.13584i	0.981699	−	0.190441i	$-0.0609919\pi$
$234$	−702.137	+	405.379i	−0.0128230	+	0.00740337i
$235$	−7452.50	−	12908.1i	−0.134948	−	0.233737i
$236$	−109021.	−	62943.3i	−1.95743	−	1.13012i
$237$			56192.9i			1.00043i
$238$	−84499.1	+	76274.9i	−1.49176	+	1.34657i
$239$	8170.08			0.143031			0.0715156	−	0.997439i	$-0.477216\pi$
$239$	8170.08			0.143031			0.0715156	+	0.997439i	$0.477216\pi$
$240$	−4152.38	+	7192.14i	−0.0720900	+	0.124863i
$241$	−3341.65	+	1929.30i	−0.0575343	+	0.0332174i	−0.528491	−	0.848939i	$-0.677242\pi$
$241$	−3341.65	+	1929.30i	−0.0575343	+	0.0332174i	0.470957	+	0.882156i	$0.343909\pi$
$242$	40365.8	+	69915.6i	0.689259	+	1.19383i
$243$	20097.2	+	11603.1i	0.340347	+	0.196500i
$244$		−	53737.2i		−	0.902600i
$245$	−10671.6	+	14765.7i	−0.177786	+	0.245993i
$246$	−68642.7			−1.13429
$247$	−1823.90	+	3159.09i	−0.0298956	+	0.0517807i
$248$	94647.5	−	54644.7i	1.53888	−	0.888475i
$249$	−19853.8	−	34387.8i	−0.320218	−	0.554633i
$250$	52424.2	+	30267.1i	0.838788	+	0.484274i
$251$		−	93998.6i		−	1.49202i	−0.665936	−	0.746008i	$-0.731968\pi$
$251$		−	93998.6i		−	1.49202i	0.665936	−	0.746008i	$-0.268032\pi$
$252$	15243.8	+	16887.5i	0.240045	+	0.265928i
$253$	17114.0			0.267368
$254$	−50007.3	+	86615.2i	−0.775115	+	1.34254i
$255$	−22489.1	+	12984.1i	−0.345853	+	0.199678i
$256$	52153.4	+	90332.4i	0.795798	+	1.37836i
$257$	−46558.9	−	26880.8i	−0.704915	−	0.406983i	0.104260	−	0.994550i	$-0.466752\pi$
$257$	−46558.9	−	26880.8i	−0.704915	−	0.406983i	−0.809175	+	0.587567i	$0.800086\pi$
$258$		−	67500.6i		−	1.01407i
$259$	−16905.1	+	3615.39i	−0.252010	+	0.0538958i
$260$	1638.32			0.0242355
$261$	−1740.73	+	3015.04i	−0.0255535	+	0.0442600i
$262$	19269.8	−	11125.4i	0.280721	−	0.162074i
$263$	25434.8	+	44054.3i	0.367719	+	0.636909i	0.989209	−	0.146514i	$-0.0468054\pi$
$263$	25434.8	+	44054.3i	0.367719	+	0.636909i	−0.621489	+	0.783423i	$0.713472\pi$
$264$	36976.1	+	21348.2i	0.530534	+	0.306304i
$265$		−	29211.2i		−	0.415965i
$266$	151564.	+	49036.6i	2.14206	+	0.693038i
$267$	66601.8			0.934251
$268$	−6441.62	+	11157.2i	−0.0896862	+	0.155341i
$269$	−102004.	+	58892.1i	−1.40965	+	0.813865i	−0.995355	−	0.0962757i	$-0.969307\pi$
$269$	−102004.	+	58892.1i	−1.40965	+	0.813865i	−0.414300	+	0.910140i	$0.635974\pi$
$270$	−16225.8	−	28103.8i	−0.222576	−	0.385512i
$271$	593.717	+	342.782i	0.00808427	+	0.00466745i	0.504037	−	0.863682i	$-0.331848\pi$
$271$	593.717	+	342.782i	0.00808427	+	0.00466745i	−0.495952	+	0.868350i	$0.665181\pi$
$272$		−	38558.9i		−	0.521179i
$273$	1116.03	−	3449.46i	0.0149744	−	0.0462834i
$274$	−234359.			−3.12162
$275$	14394.7	−	24932.4i	0.190344	−	0.329685i
$276$	−82808.5	+	47809.5i	−1.08707	+	0.627619i
$277$	−18426.9	−	31916.3i	−0.240156	−	0.415962i	0.720603	−	0.693348i	$-0.243865\pi$
$277$	−18426.9	−	31916.3i	−0.240156	−	0.415962i	−0.960758	+	0.277386i	$0.910532\pi$
$278$	31505.6	+	18189.7i	0.407660	+	0.235362i
$279$		−	20662.8i		−	0.265448i
$280$	−6638.96	−	31042.9i	−0.0846806	−	0.395955i
$281$	−53123.9			−0.672787			−0.336393	−	0.941722i	$-0.609207\pi$
$281$	−53123.9			−0.672787			−0.336393	+	0.941722i	$0.609207\pi$
$282$	64765.3	−	112177.i	0.814413	−	1.41060i
$283$	74715.1	−	43136.8i	0.932901	−	0.538611i	0.0451732	−	0.998979i	$-0.485616\pi$
$283$	74715.1	−	43136.8i	0.932901	−	0.538611i	0.887728	+	0.460368i	$0.152283\pi$
$284$	21365.3	+	37005.8i	0.264894	+	0.458811i
$285$	31471.4	+	18170.0i	0.387460	+	0.223700i
$286$		−	2548.27i		−	0.0311540i
$287$	37863.2	−	34178.0i	0.459677	−	0.414937i
$288$	10059.1			0.121276
$289$	18524.3	−	32085.1i	0.221792	−	0.384156i
$290$	9481.84	−	5474.34i	0.112745	−	0.0650932i
$291$	56860.8	+	98485.8i	0.671471	+	1.16302i
$292$	17550.1	+	10132.5i	0.205832	+	0.118837i
$293$		−	54510.6i		−	0.634959i	−0.948265	−	0.317480i	$-0.897164\pi$
$293$		−	54510.6i		−	0.634959i	0.948265	−	0.317480i	$-0.102836\pi$
$294$	−157499.	−	16155.6i	−1.82214	−	0.186909i
$295$	33211.0			0.381626
$296$	15061.3	−	26087.0i	0.171901	−	0.297742i
$297$	−28088.0	+	16216.6i	−0.318426	+	0.183843i
$298$	−75587.5	−	130921.i	−0.851173	−	1.47427i
$299$	2192.92	+	1266.09i	0.0245291	+	0.0141619i
$300$			160852.i			1.78725i
$301$	33609.3	+	37233.1i	0.370959	+	0.410957i
$302$	212373.			2.32855
$303$	−80802.3	+	139954.i	−0.880113	+	1.52440i
$304$	−46730.4	+	26979.8i	−0.505653	+	0.291939i
$305$	7088.40	+	12277.5i	0.0761989	+	0.131980i
$306$	−32476.8	−	18750.5i	−0.346841	−	0.200249i
$307$			62508.0i			0.663222i	0.943416	+	0.331611i	$0.107592\pi$
$307$			62508.0i			0.663222i	−0.943416	+	0.331611i	$0.892408\pi$
$308$	−69923.6	+	14954.1i	−0.737094	+	0.157638i
$309$	27378.9			0.286747
$310$	−32490.6	+	56275.4i	−0.338092	+	0.585593i
$311$	87021.0	−	50241.6i	0.899712	−	0.519449i	0.0226052	−	0.999744i	$-0.492804\pi$
$311$	87021.0	−	50241.6i	0.899712	−	0.519449i	0.877107	+	0.480296i	$0.159471\pi$
$312$	3158.66	+	5470.96i	0.0324484	+	0.0562023i
$313$	−141974.	−	81968.7i	−1.44917	−	0.836680i	−0.450740	−	0.892655i	$-0.648840\pi$
$313$	−141974.	−	81968.7i	−1.44917	−	0.836680i	−0.998432	+	0.0559755i	$0.982173\pi$
$314$			143102.i			1.45140i
$315$	−5710.40	−	1847.53i	−0.0575500	−	0.0186196i
$316$	163980.			1.64216
$317$	−60956.2	+	105579.i	−0.606596	+	1.05066i	0.385201	+	0.922833i	$0.374132\pi$
$317$	−60956.2	+	105579.i	−0.606596	+	1.05066i	−0.991797	+	0.127822i	$0.959201\pi$
$318$	219847.	−	126929.i	2.17403	−	1.25518i
$319$	−5471.25	−	9476.49i	−0.0537657	−	0.0931250i
$320$	−39071.6	−	22558.0i	−0.381559	−	0.220293i
$321$		−	69517.8i		−	0.674661i
$322$	34039.4	−	105210.i	0.328299	−	1.01472i
$323$	−168726.			−1.61725
$324$	109409.	−	189502.i	1.04223	−	1.80519i
$325$	3688.98	−	2129.83i	0.0349253	−	0.0201641i
$326$	−144035.	−	249476.i	−1.35529	−	2.34744i
$327$	−93624.0	−	54053.8i	−0.875572	−	0.505511i
$328$			88878.6i			0.826132i
$329$	20129.7	+	94123.8i	0.185971	+	0.869577i
$330$	−25386.4			−0.233116
$331$	22437.7	−	38863.2i	0.204796	−	0.354717i	−0.745272	−	0.666761i	$-0.767680\pi$
$331$	22437.7	−	38863.2i	0.204796	−	0.354717i	0.950068	+	0.312044i	$0.101014\pi$
$332$	−100349.	+	57936.7i	−0.910412	+	0.525626i
$333$	−2847.56	−	4932.12i	−0.0256794	−	0.0444780i
$334$	144051.	+	83168.0i	1.29129	+	0.745527i
$335$		−	3398.82i		−	0.0302858i
$336$	39809.8	−	35935.2i	0.352624	−	0.318303i
$337$	128343.			1.13009			0.565045	−	0.825060i	$-0.308859\pi$
$337$	128343.			1.13009			0.565045	+	0.825060i	$0.308859\pi$
$338$	−95354.0	+	165158.i	−0.834652	+	1.44566i
$339$	−110840.	+	63993.2i	−0.964485	+	0.556845i
$340$	37889.6	+	65626.7i	0.327765	+	0.567705i
$341$	56243.7	+	32472.3i	0.483688	+	0.279257i
$342$			52479.2i			0.448679i
$343$	94919.9	−	69508.9i	0.806806	−	0.590816i
$344$	−87399.7			−0.738572
$345$	12613.0	−	21846.3i	0.105969	−	0.183544i
$346$	−217145.	+	125368.i	−1.81383	+	1.04722i
$347$	−6153.32	−	10657.9i	−0.0511035	−	0.0885138i	0.839342	−	0.543604i	$-0.182940\pi$
$347$	−6153.32	−	10657.9i	−0.0511035	−	0.0885138i	−0.890446	+	0.455090i	$0.849607\pi$
$348$	52946.9	+	30568.9i	0.437202	+	0.252419i
$349$			8868.22i			0.0728091i	0.999337	+	0.0364046i	$0.0115905\pi$
$349$			8868.22i			0.0728091i	−0.999337	+	0.0364046i	$0.988410\pi$
$350$	−124644.	−	138083.i	−1.01750	−	1.12721i
$351$	−4798.80			−0.0389510
$352$	−15808.3	+	27380.7i	−0.127585	+	0.220983i
$353$	94106.1	−	54332.2i	0.755211	−	0.436021i	−0.0723626	−	0.997378i	$-0.523054\pi$
$353$	94106.1	−	54332.2i	0.755211	−	0.436021i	0.827574	+	0.561357i	$0.189721\pi$
$354$	144309.	+	249950.i	1.15156	+	1.99456i
$355$	−9762.78	−	5636.54i	−0.0774670	−	0.0447256i
$356$		−	194355.i		−	1.53354i
$357$	163987.	−	35070.8i	1.28668	−	0.275175i
$358$	157473.			1.22869
$359$	114037.	−	197517.i	0.884821	−	1.53256i	0.0389030	−	0.999243i	$-0.487614\pi$
$359$	114037.	−	197517.i	0.884821	−	1.53256i	0.845918	−	0.533313i	$-0.179053\pi$
$360$	9056.88	−	5228.99i	0.0698834	−	0.0403472i
$361$	52898.1	+	91622.1i	0.405906	+	0.703050i
$362$	−53369.5	−	30812.9i	−0.407264	−	0.235134i
$363$		−	118931.i		−	0.902572i
$364$	−10066.1	−	3256.75i	−0.0759726	−	0.0245800i
$365$	−5346.28			−0.0401297
$366$	−61601.2	+	106696.i	−0.459861	+	0.796503i
$367$	−207527.	+	119816.i	−1.54079	+	0.889576i	−0.542001	+	0.840378i	$0.682333\pi$
$367$	−207527.	+	119816.i	−1.54079	+	0.889576i	−0.998789	+	0.0491977i	$0.984334\pi$
$368$	18728.4	+	32438.6i	0.138295	+	0.239533i
$369$	14552.5	+	8401.90i	0.106877	+	0.0617056i
$370$			17910.3i			0.130828i
$371$	−58067.7	+	179478.i	−0.421878	+	1.30395i
$372$	−362858.			−2.62211
$373$	10718.0	−	18564.1i	0.0770363	−	0.133431i	−0.824934	−	0.565230i	$-0.808788\pi$
$373$	10718.0	−	18564.1i	0.0770363	−	0.133431i	0.901970	+	0.431799i	$0.142121\pi$
$374$	102077.	−	58934.2i	0.729768	−	0.421332i
$375$	−44588.5	−	77229.5i	−0.317074	−	0.549188i
$376$	−145247.	−	83858.2i	−1.02738	−	0.593157i
$377$		−	1619.05i		−	0.0113914i
$378$	43826.8	+	204929.i	0.306730	+	1.43423i
$379$	−42375.1			−0.295007			−0.147504	−	0.989062i	$-0.547124\pi$
$379$	−42375.1			−0.295007			−0.147504	+	0.989062i	$0.547124\pi$
$380$	53023.1	−	91838.7i	0.367196	−	0.636002i
$381$	127599.	−	73669.1i	0.879014	−	0.507499i
$382$	−40366.4	−	69916.7i	−0.276626	−	0.479131i
$383$	24769.1	+	14300.4i	0.168854	+	0.0974882i	0.582046	−	0.813156i	$-0.302253\pi$
$383$	24769.1	+	14300.4i	0.168854	+	0.0974882i	−0.413191	+	0.910644i	$0.635586\pi$
$384$		−	293809.i		−	1.99252i
$385$	14003.0	−	12640.1i	0.0944715	−	0.0852767i
$386$	57223.6			0.384061
$387$	−8262.10	+	14310.4i	−0.0551656	+	0.0955496i
$388$	287398.	−	165929.i	1.90906	−	1.10220i
$389$	21801.6	+	37761.5i	0.144075	+	0.249546i	0.929028	−	0.370010i	$-0.120646\pi$
$389$	21801.6	+	37761.5i	0.144075	+	0.249546i	−0.784952	+	0.619556i	$0.787313\pi$
$390$	−3252.92	−	1878.07i	−0.0213867	−	0.0123476i
$391$			117124.i			0.766110i
$392$	−20918.3	+	203929.i	−0.136130	+	1.32711i
$393$	−32779.2			−0.212233
$394$	53220.3	−	92180.3i	0.342835	−	0.593808i
$395$	−37464.9	+	21630.4i	−0.240121	+	0.138634i
$396$	−11778.2	−	20400.5i	−0.0751086	−	0.130092i
$397$	−145187.	−	83823.6i	−0.921183	−	0.531845i	−0.0371710	−	0.999309i	$-0.511835\pi$
$397$	−145187.	−	83823.6i	−0.921183	−	0.531845i	−0.884012	+	0.467463i	$0.845168\pi$
$398$			184092.i			1.16217i
$399$	−157245.	−	174200.i	−0.987716	−	1.09421i
$400$	63010.6			0.393817
$401$	−62660.0	+	108530.i	−0.389674	+	0.674936i	−0.992406	−	0.123008i	$-0.960746\pi$
$401$	−62660.0	+	108530.i	−0.389674	+	0.674936i	0.602731	+	0.797944i	$0.294079\pi$
$402$	25580.0	−	14768.6i	0.158288	−	0.0913875i
$403$	4804.58	+	8321.78i	0.0295832	+	0.0512396i
$404$	408408.	+	235794.i	2.50225	+	1.44468i
$405$			57727.9i			0.351946i
$406$	−69140.0	+	14786.5i	−0.419447	+	0.0897046i
$407$	17900.2			0.108061
$408$	−146101.	+	253055.i	−0.877675	+	1.52018i
$409$	−62991.3	+	36368.0i	−0.376560	+	0.217407i	−0.676320	−	0.736608i	$-0.736427\pi$
$409$	−62991.3	+	36368.0i	−0.376560	+	0.217407i	0.299761	+	0.954014i	$0.403093\pi$
$410$	−26422.7	−	45765.5i	−0.157184	−	0.272251i
$411$	298995.	+	172625.i	1.77003	+	1.02193i
$412$		−	79896.0i		−	0.470685i
$413$	−204053.	−	66019.0i	−1.19631	−	0.387051i
$414$	36429.2			0.212544
$415$	15284.7	−	26473.9i	0.0887484	−	0.153717i
$416$	−4051.23	+	2338.98i	−0.0234100	+	0.0135157i
$417$	−26796.5	−	46412.9i	−0.154101	−	0.266911i
$418$	−142848.	−	82473.1i	−0.817561	−	0.472019i
$419$			48455.0i			0.276001i	0.990432	+	0.138000i	$0.0440675\pi$
$419$			48455.0i			0.276001i	−0.990432	+	0.138000i	$0.955932\pi$
$420$	−32444.4	+	100280.i	−0.183925	+	0.568481i
$421$	−67350.5			−0.379994			−0.189997	−	0.981785i	$-0.560848\pi$
$421$	−67350.5			−0.379994			−0.189997	+	0.981785i	$0.560848\pi$
$422$	169458.	−	293510.i	0.951561	−	1.64815i
$423$	−27461.0	+	15854.6i	−0.153474	+	0.0886084i
$424$	−164347.	−	284657.i	−0.914177	−	1.58340i
$425$	170631.	+	98513.9i	0.944670	+	0.545406i
$426$		−	97967.8i		−	0.539839i
$427$	−19146.2	−	89525.3i	−0.105009	−	0.491010i
$428$	−202864.			−1.10743
$429$	−1877.01	+	3251.08i	−0.0101989	+	0.0176650i
$430$	45003.9	−	25983.0i	0.243396	−	0.140525i
$431$	60765.0	+	105248.i	0.327114	+	0.566578i	0.981938	−	0.189204i	$-0.0605906\pi$
$431$	60765.0	+	105248.i	0.327114	+	0.566578i	−0.654824	+	0.755781i	$0.727257\pi$
$432$	−61475.3	−	35492.8i	−0.329407	−	0.190184i
$433$		−	21137.1i		−	0.112738i	−0.998410	−	0.0563689i	$-0.982048\pi$
$433$		−	21137.1i		−	0.112738i	0.998410	−	0.0563689i	$-0.0179523\pi$
$434$	311495.	−	281177.i	1.65376	−	1.49280i
$435$	−16129.2			−0.0852383
$436$	−157738.	+	273210.i	−0.829780	+	1.43722i
$437$	141945.	−	81951.9i	0.743288	−	0.429137i
$438$	−23230.7	−	40236.7i	−0.121092	−	0.209737i
$439$	15020.7	+	8672.20i	0.0779400	+	0.0449987i	0.538464	−	0.842649i	$-0.319005\pi$
$439$	15020.7	+	8672.20i	0.0779400	+	0.0449987i	−0.460523	+	0.887648i	$0.652338\pi$
$440$			32870.2i			0.169784i
$441$	31412.9	+	22703.0i	0.161522	+	0.116736i
$442$	17439.7			0.0892678
$443$	94338.1	−	163398.i	0.480706	−	0.832607i	−0.519049	−	0.854745i	$-0.673714\pi$
$443$	94338.1	−	163398.i	0.480706	−	0.832607i	0.999755	+	0.0221372i	$0.00704707\pi$
$444$	−86612.7	+	50005.9i	−0.439355	+	0.253662i
$445$	25637.1	+	44404.7i	0.129464	+	0.224238i
$446$	−477875.	−	275901.i	−2.40240	−	1.38702i
$447$			222706.i			1.11459i
$448$	195219.	+	216269.i	0.972673	+	1.07755i
$449$	64161.0			0.318257			0.159129	−	0.987258i	$-0.449132\pi$
$449$	64161.0			0.318257			0.159129	+	0.987258i	$0.449132\pi$
$450$	30640.9	−	53071.7i	0.151313	−	0.262082i
$451$	−45739.7	+	26407.8i	−0.224874	+	0.129831i
$452$	186743.	+	323448.i	0.914043	+	1.58317i
$453$	−270945.	−	156430.i	−1.32034	−	0.762297i
$454$			219469.i			1.06478i
$455$	2729.41	−	583.723i	0.0131840	−	0.00281958i
$456$	408911.			1.96652
$457$	−127623.	+	221050.i	−0.611078	+	1.05842i	0.379981	+	0.924994i	$0.375930\pi$
$457$	−127623.	+	221050.i	−0.611078	+	1.05842i	−0.991059	+	0.133424i	$0.957403\pi$
$458$	−599120.	+	345902.i	−2.85616	+	1.64901i
$459$	−110982.	−	192227.i	−0.526779	−	0.912408i
$460$	−63751.0	−	36806.7i	−0.301281	−	0.173945i
$461$		−	301500.i		−	1.41868i	−0.704865	−	0.709341i	$-0.748992\pi$
$461$		−	301500.i		−	1.41868i	0.704865	−	0.709341i	$-0.251008\pi$
$462$	155977.	+	50464.6i	0.730765	+	0.236430i
$463$	297623.			1.38837			0.694183	−	0.719798i	$-0.255766\pi$
$463$	297623.			1.38837			0.694183	+	0.719798i	$0.255766\pi$
$464$	11974.8	−	20740.9i	0.0556200	−	0.0963367i
$465$	82903.0	−	47864.1i	0.383411	−	0.221362i
$466$	238188.	+	412555.i	1.09685	+	1.89981i
$467$	219771.	+	126885.i	1.00771	+	0.581803i	0.910521	−	0.413462i	$-0.135681\pi$
$467$	219771.	+	126885.i	1.00771	+	0.581803i	0.0971917	+	0.995266i	$0.469014\pi$
$468$		−	3485.40i		−	0.0159133i
$469$	−6756.39	+	20882.9i	−0.0307163	+	0.0949389i
$470$	99720.7			0.451429
$471$	105407.	−	182570.i	0.475145	−	0.822975i
$472$	323636.	−	186851.i	1.45269	−	0.838710i
$473$	−25968.4	−	44978.6i	−0.116071	−	0.201040i
$474$	−325585.	−	187977.i	−1.44913	−	0.836657i
$475$		−	275722.i		−	1.22204i
$476$	−102342.	−	478539.i	−0.451691	−	2.11205i
$477$	−62144.4			−0.273128
$478$	−27330.6	+	47338.0i	−0.119617	+	0.207183i
$479$	−162787.	+	93985.3i	−0.709496	+	0.409627i	−0.810874	−	0.585220i	$-0.801008\pi$
$479$	−162787.	+	93985.3i	−0.709496	+	0.409627i	0.101379	+	0.994848i	$0.467675\pi$
$480$	23301.3	+	40359.1i	0.101134	+	0.175170i
$481$	2293.67	+	1324.25i	0.00991381	+	0.00572374i
$482$		−	25815.7i		−	0.111119i
$483$	−120923.	+	109154.i	−0.518341	+	0.467892i
$484$	−347060.			−1.48154
$485$	−43775.0	+	75820.4i	−0.186098	+	0.322332i
$486$	−134458.	+	77629.6i	−0.569266	+	0.328666i
$487$	−91840.8	−	159073.i	−0.387238	−	0.670716i	0.604839	−	0.796348i	$-0.293237\pi$
$487$	−91840.8	−	159073.i	−0.387238	−	0.670716i	−0.992077	+	0.125632i	$0.959904\pi$
$488$	138150.	+	79761.2i	0.580113	+	0.334928i
$489$			424375.i			1.77473i
$490$	−49854.8	−	111226.i	−0.207642	−	0.463250i
$491$	−135410.			−0.561681			−0.280840	−	0.959755i	$-0.590613\pi$
$491$	−135410.			−0.561681			−0.280840	+	0.959755i	$0.590613\pi$
$492$	147545.	−	255556.i	0.609530	−	1.05574i
$493$	64854.7	−	37443.9i	0.266838	−	0.154059i
$494$	−12202.7	−	21135.6i	−0.0500035	−	0.0866086i
$495$	5382.00	+	3107.30i	0.0219651	+	0.0126816i
$496$			142142.i			0.577777i
$497$	48779.2	+	54038.8i	0.197480	+	0.218772i
$498$	265661.			1.07119
$499$	89910.7	−	155730.i	0.361086	−	0.625419i	−0.627054	−	0.778976i	$-0.715739\pi$
$499$	89910.7	−	155730.i	0.361086	−	0.625419i	0.988140	+	0.153557i	$0.0490728\pi$
$500$	−225368.	+	130116.i	−0.901473	+	0.520466i
$501$	−122520.	−	212211.i	−0.488127	−	0.845460i
$502$	544634.	+	314445.i	2.16121	+	1.24778i
$503$			372946.i			1.47404i	0.675869	+	0.737022i	$0.263769\pi$
$503$			372946.i			1.47404i	−0.675869	+	0.737022i	$0.736231\pi$
$504$	−66041.3	+	14123.9i	−0.259989	+	0.0556022i
$505$	−124413.			−0.487847
$506$	−57249.8	+	99159.5i	−0.223601	+	0.387288i
$507$	243305.	−	140472.i	0.946531	−	0.546480i
$508$	−214978.	−	372353.i	−0.833042	−	1.44287i
$509$	−268892.	−	155245.i	−1.03787	−	0.599213i	−0.118638	−	0.992938i	$-0.537853\pi$
$509$	−268892.	−	155245.i	−1.03787	−	0.599213i	−0.919228	+	0.393725i	$0.871186\pi$
$510$		−	173738.i		−	0.667965i
$511$	32848.3	+	10627.7i	0.125797	+	0.0407001i
$512$	−220898.			−0.842660
$513$	−155310.	+	269004.i	−0.590152	+	1.02217i
$514$	311499.	−	179844.i	1.17904	−	0.680721i
$515$	10539.0	+	18254.0i	0.0397360	+	0.0688247i
$516$	251304.	+	145090.i	0.943842	+	0.544928i
$517$		−	99664.5i		−	0.372872i
$518$	35603.2	−	110043.i	0.132687	−	0.410114i
$519$	369377.			1.37131
$520$	−2431.73	+	4211.88i	−0.00899308	+	0.0155765i
$521$	374408.	−	216164.i	1.37933	−	0.796359i	0.387255	−	0.921973i	$-0.373423\pi$
$521$	374408.	−	216164.i	1.37933	−	0.796359i	0.992079	+	0.125614i	$0.0400901\pi$
$522$	−11646.2	−	20171.9i	−0.0427410	−	0.0740295i
$523$	122106.	+	70497.7i	0.446408	+	0.257734i	0.706312	−	0.707901i	$-0.250358\pi$
$523$	122106.	+	70497.7i	0.446408	+	0.257734i	−0.259904	+	0.965634i	$0.583691\pi$
$524$			95654.9i			0.348373i
$525$	57310.6	+	267977.i	0.207930	+	0.972253i
$526$	−340339.			−1.23010
$527$	−222232.	+	384917.i	−0.800176	+	1.38595i
$528$	−48091.3	+	27765.5i	−0.172504	+	0.0995950i
$529$	83032.5	+	143816.i	0.296713	+	0.513922i
$530$	169251.	+	97717.4i	0.602533	+	0.347873i
$531$		−	70653.9i		−	0.250580i
$532$	−508344.	+	458867.i	−1.79612	+	1.62130i
$533$	−7814.56			−0.0275074
$534$	−222797.	+	385896.i	−0.781316	+	1.35328i
$535$	46348.9	−	26759.5i	0.161932	−	0.0934912i
$536$	−19122.4	−	33120.9i	−0.0665598	−	0.115285i
$537$	−200904.	−	115992.i	−0.696692	−	0.402235i
$538$		−	788025.i		−	2.72255i
$539$	−111164.	+	49826.7i	−0.382635	+	0.171508i
$540$	139507.			0.478419
$541$	36434.9	−	63107.0i	0.124487	−	0.215617i	−0.797046	−	0.603919i	$-0.793605\pi$
$541$	36434.9	−	63107.0i	0.124487	−	0.215617i	0.921532	+	0.388302i	$0.126938\pi$
$542$	−3972.21	+	2293.36i	−0.0135218	+	0.00780680i
$543$	45392.5	+	78622.1i	0.153952	+	0.266652i
$544$	−187387.	−	108188.i	−0.633200	−	0.365578i
$545$		−	83227.9i		−	0.280205i
$546$	16253.0	+	18005.5i	0.0545192	+	0.0603976i
$547$	−422856.			−1.41325			−0.706623	−	0.707590i	$-0.749782\pi$
$547$	−422856.			−1.41325			−0.706623	+	0.707590i	$0.749782\pi$
$548$	503747.	−	872515.i	1.67746	−	2.90544i
$549$	26119.4	−	15080.0i	0.0866598	−	0.0500331i
$550$	96306.8	+	166808.i	0.318370	+	0.551432i
$551$	−90758.2	−	52399.3i	−0.298939	−	0.172593i
$552$		−	283851.i		−	0.931563i
$553$	273188.	−	58425.0i	0.893328	−	0.191051i
$554$	246567.			0.803371
$555$	13192.4	−	22849.9i	0.0428290	−	0.0741821i
$556$	−135440.	+	78196.5i	−0.438125	+	0.252952i
$557$	−139947.	−	242396.i	−0.451080	−	0.781294i	0.547373	−	0.836889i	$-0.315628\pi$
$557$	−139947.	−	242396.i	−0.451080	−	0.781294i	−0.998453	+	0.0555948i	$0.982295\pi$
$558$	119722.	+	69121.3i	0.384507	+	0.221995i
$559$		−	7684.53i		−	0.0245920i
$560$	39282.7	+	12709.4i	0.125264	+	0.0405275i
$561$	−173640.			−0.551726
$562$	177711.	−	307804.i	0.562653	−	0.974543i
$563$	−93652.7	+	54070.4i	−0.295463	+	0.170586i	−0.640403	−	0.768039i	$-0.721233\pi$
$563$	−93652.7	+	54070.4i	−0.295463	+	0.170586i	0.344940	+	0.938625i	$0.387899\pi$
$564$	278422.	+	482241.i	0.875277	+	1.51602i
$565$	−85331.1	−	49265.9i	−0.267307	−	0.154330i
$566$			577206.i			1.80176i
$567$	114755.	−	354688.i	0.356949	−	1.10327i
$568$	−126849.			−0.393178
$569$	7795.85	−	13502.8i	0.0240790	−	0.0417061i	−0.853735	−	0.520708i	$-0.825668\pi$
$569$	7795.85	−	13502.8i	0.0240790	−	0.0417061i	0.877814	+	0.479002i	$0.159001\pi$
$570$	−210557.	+	121565.i	−0.648067	+	0.374161i
$571$	246603.	+	427128.i	0.756355	+	1.31004i	0.944698	+	0.327942i	$0.106355\pi$
$571$	246603.	+	427128.i	0.756355	+	1.31004i	−0.188343	+	0.982103i	$0.560312\pi$
$572$	9487.19	+	5477.43i	0.0289965	+	0.0167411i
$573$			118933.i			0.362237i
$574$	71369.4	+	333714.i	0.216615	+	1.01286i
$575$	−191396.			−0.578893
$576$	−47990.4	+	83121.8i	−0.144647	+	0.250536i
$577$	−280469.	+	161929.i	−0.842429	+	0.486377i	−0.858089	−	0.513501i	$-0.828348\pi$
$577$	−280469.	+	161929.i	−0.842429	+	0.486377i	0.0156601	+	0.999877i	$0.495015\pi$
$578$	123935.	+	214662.i	0.370971	+	0.642540i
$579$	−73005.7	−	42149.9i	−0.217771	−	0.125730i
$580$			47067.7i			0.139916i
$581$	−146538.	+	132275.i	−0.434107	+	0.391856i
$582$	−760845.			−2.24621
$583$	97662.3	−	169156.i	0.287336	−	0.497680i
$584$	−52098.5	+	30079.1i	−0.152756	+	0.0881940i
$585$	459.754	+	796.317i	0.00134343	+	0.00232688i
$586$	315838.	+	182349.i	0.919749	+	0.531018i
$587$		−	318676.i		−	0.924854i	−0.886657	−	0.462427i	$-0.846979\pi$
$587$		−	318676.i		−	0.924854i	0.886657	−	0.462427i	$-0.153021\pi$
$588$	398686.	−	551640.i	1.15312	−	1.59551i
$589$	621988.			1.79288
$590$	−111098.	+	192427.i	−0.319155	+	0.552793i
$591$	−135797.	+	78402.3i	−0.388790	+	0.224468i
$592$	19588.8	+	33928.8i	0.0558939	+	0.0968111i
$593$	497448.	+	287202.i	1.41461	+	0.816728i	0.995819	−	0.0913521i	$-0.0291189\pi$
$593$	497448.	+	287202.i	1.41461	+	0.816728i	0.418796	+	0.908080i	$0.362452\pi$
$594$		−	216992.i		−	0.614993i
$595$	86505.9	+	95833.2i	0.244350	+	0.270696i
$596$	649892.			1.82957
$597$	135599.	−	234865.i	0.380459	−	0.658975i
$598$	−14671.6	+	8470.64i	−0.0410274	+	0.0236872i
$599$	−158653.	−	274795.i	−0.442176	−	0.765871i	0.555675	−	0.831400i	$-0.312460\pi$
$599$	−158653.	−	274795.i	−0.442176	−	0.765871i	−0.997851	+	0.0655285i	$0.979127\pi$
$600$	−413527.	−	238750.i	−1.14869	−	0.663195i
$601$		−	540394.i		−	1.49610i	−0.663640	−	0.748052i	$-0.730989\pi$
$601$		−	540394.i		−	1.49610i	0.663640	−	0.748052i	$-0.269011\pi$
$602$	−328161.	+	70181.9i	−0.905512	+	0.193656i
$603$	−7230.73			−0.0198860
$604$	−456489.	+	790662.i	−1.25129	+	2.16729i
$605$	79293.6	−	45780.2i	0.216634	−	0.125074i
$606$	−540601.	−	936348.i	−1.47208	−	2.54972i
$607$	−295743.	−	170747.i	−0.802669	−	0.463421i	0.0417345	−	0.999129i	$-0.486712\pi$
$607$	−295743.	−	170747.i	−0.802669	−	0.463421i	−0.844404	+	0.535707i	$0.820045\pi$
$608$			302798.i			0.819117i
$609$	99100.2	+	32062.7i	0.267202	+	0.0864500i
$610$	−94848.7			−0.254901
$611$	7373.14	−	12770.7i	0.0197501	−	0.0342082i
$612$	139616.	−	80607.2i	0.372762	−	0.215214i
$613$	190344.	+	329686.i	0.506545	+	0.877362i	0.999971	+	0.00757447i	$0.00241105\pi$
$613$	190344.	+	329686.i	0.506545	+	0.877362i	−0.493426	+	0.869788i	$0.664256\pi$
$614$	−362176.	−	209102.i	−0.960689	−	0.554654i
$615$			77850.0i			0.205830i
$616$	65341.5	−	201959.i	0.172198	−	0.532234i
$617$	658048.			1.72857			0.864286	−	0.503001i	$-0.167771\pi$
$617$	658048.			1.72857			0.864286	+	0.503001i	$0.167771\pi$
$618$	−91588.0	+	158635.i	−0.239807	+	0.415358i
$619$	−53221.2	+	30727.3i	−0.138900	+	0.0801942i	−0.567840	−	0.823139i	$-0.692221\pi$
$619$	−53221.2	+	30727.3i	−0.138900	+	0.0801942i	0.428939	+	0.903333i	$0.358887\pi$
$620$	−139675.	−	241924.i	−0.363359	−	0.629356i
$621$	186733.	+	107810.i	0.484214	+	0.279561i
$622$			672275.i			1.73766i
$623$	−69247.4	−	323792.i	−0.178413	−	0.834238i
$624$	−8216.32			−0.0211013
$625$	−142993.	+	247672.i	−0.366063	+	0.634040i
$626$	949865.	−	548405.i	2.42389	−	1.39943i
$627$	121496.	+	210438.i	0.309050	+	0.535290i
$628$	−532768.	−	307594.i	−1.35089	−	0.779934i
$629$			122504.i			0.309635i
$630$	29807.2	−	26906.1i	0.0751000	−	0.0677906i
$631$	−253942.			−0.637786			−0.318893	−	0.947791i	$-0.603311\pi$
$631$	−253942.			−0.637786			−0.318893	+	0.947791i	$0.603311\pi$
$632$	−243392.	+	421568.i	−0.609358	+	1.05544i
$633$	−432388.	+	249639.i	−1.07911	+	0.623025i
$634$	−407822.	−	706369.i	−1.01459	−	1.75733i
$635$	98233.2	+	56715.0i	0.243619	+	0.140653i
$636$			1.09132e6i			2.69796i
$637$	−17930.3	−	1839.22i	−0.0441884	−	0.00453268i
$638$	73209.9			0.179858
$639$	−11991.3	+	20769.5i	−0.0293673	+	0.0508657i
$640$	195888.	−	113096.i	0.478242	−	0.276113i
$641$	−223890.	−	387789.i	−0.544903	−	0.943800i	−0.998613	−	0.0526504i	$-0.983233\pi$
$641$	−223890.	−	387789.i	−0.544903	−	0.943800i	0.453710	−	0.891149i	$-0.350100\pi$
$642$	402791.	+	232551.i	0.977259	+	0.564221i
$643$			229530.i			0.555160i	0.960702	+	0.277580i	$0.0895324\pi$
$643$			229530.i			0.555160i	−0.960702	+	0.277580i	$0.910468\pi$
$644$	318529.	+	352874.i	0.768028	+	0.850839i
$645$	−76554.6			−0.184014
$646$	564424.	−	977612.i	1.35251	−	2.34262i
$647$	−273365.	+	157828.i	−0.653033	+	0.377029i	−0.789617	−	0.613600i	$-0.789721\pi$
$647$	−273365.	+	157828.i	−0.653033	+	0.377029i	0.136584	+	0.990628i	$0.456388\pi$
$648$	324787.	+	562548.i	0.773479	+	1.33971i
$649$	192319.	+	111035.i	0.456596	+	0.263616i
$650$			28499.0i			0.0674532i
$651$	−604515.	+	129284.i	−1.42641	+	0.305058i
$652$	1.23840e6			2.91316
$653$	303655.	−	525945.i	0.712121	−	1.23343i	−0.251939	−	0.967743i	$-0.581068\pi$
$653$	303655.	−	525945.i	0.712121	−	1.23343i	0.964060	−	0.265686i	$-0.0855984\pi$
$654$	626383.	−	361643.i	1.46448	−	0.845520i
$655$	−12617.7	−	21854.5i	−0.0294102	−	0.0509399i
$656$	−100109.	−	57797.9i	−0.232630	−	0.134309i
$657$			11373.8i			0.0263496i
$658$	−612698.	−	198231.i	−1.41512	−	0.457846i
$659$	−780948.			−1.79826			−0.899128	−	0.437686i	$-0.855798\pi$
$659$	−780948.			−1.79826			−0.899128	+	0.437686i	$0.855798\pi$
$660$	54567.1	−	94513.1i	0.125269	−	0.216972i
$661$	−503807.	+	290873.i	−1.15309	+	0.665734i	−0.949637	−	0.313351i	$-0.898548\pi$
$661$	−503807.	+	290873.i	−1.15309	+	0.665734i	−0.203448	+	0.979086i	$0.565215\pi$
$662$	150117.	+	260011.i	0.342543	+	0.593301i
$663$	−22249.6	−	12845.8i	−0.0506168	−	0.0292236i
$664$		−	343977.i		−	0.780178i
$665$	55614.0	−	171893.i	0.125760	−	0.388701i
$666$	38102.7			0.0859029
$667$	−36373.7	+	63001.0i	−0.0817589	+	0.141611i
$668$	−619267.	+	357534.i	−1.38779	+	0.801243i
$669$	406448.	+	703989.i	0.908141	+	1.57295i
$670$	19693.0	+	11369.8i	0.0438695	+	0.0253281i
$671$			94795.3i			0.210543i
$672$	−62938.4	−	294292.i	−0.139373	−	0.651688i
$673$	−566904.			−1.25164			−0.625820	−	0.779968i	$-0.715235\pi$
$673$	−566904.			−1.25164			−0.625820	+	0.779968i	$0.715235\pi$
$674$	−429335.	+	743630.i	−0.945097	+	1.63696i
$675$	314126.	−	181361.i	0.689440	−	0.398048i
$676$	−409920.	−	710003.i	−0.897028	−	1.55370i
$677$	−290467.	−	167701.i	−0.633753	−	0.365897i	0.148451	−	0.988920i	$-0.452571\pi$
$677$	−290467.	−	167701.i	−0.633753	−	0.365897i	−0.782204	+	0.623022i	$0.785905\pi$
$678$		−	856283.i		−	1.86276i
$679$	419680.	−	378833.i	0.910288	−	0.821691i
$680$	−224955.			−0.486495
$681$	161657.	−	279998.i	0.348578	−	0.603755i
$682$	−376294.	+	217253.i	−0.809018	+	0.467087i
$683$	320814.	+	555666.i	0.687720	+	1.19117i	0.972574	+	0.232595i	$0.0747217\pi$
$683$	320814.	+	555666.i	0.687720	+	1.19117i	−0.284854	+	0.958571i	$0.591945\pi$
$684$	−195380.	−	112802.i	−0.417606	−	0.241105i
$685$			265794.i			0.566454i
$686$	85212.7	+	782495.i	0.181074	+	1.66277i
$687$	1.01914e6			2.15934
$688$	56836.2	−	98443.2i	0.120074	−	0.207974i
$689$	25028.2	−	14450.0i	0.0527219	−	0.0304390i
$690$	84386.0	+	146161.i	0.177244	+	0.306996i
$691$	277213.	+	160049.i	0.580573	+	0.335194i	0.761361	−	0.648328i	$-0.224531\pi$
$691$	277213.	+	160049.i	0.580573	+	0.335194i	−0.180788	+	0.983522i	$0.557865\pi$
$692$		−	1.07790e6i		−	2.25096i
$693$	−26890.9	−	29790.4i	−0.0559937	−	0.0620311i
$694$	82336.5			0.170952
$695$	20629.6	−	35731.5i	0.0427092	−	0.0739744i
$696$	−157176.	+	90745.8i	−0.324466	+	0.187330i
$697$	−180728.	−	313030.i	−0.372015	−	0.644349i
$698$	−51383.1	−	29666.0i	−0.105465	−	0.0608904i
$699$		−	701782.i		−	1.43631i
$700$	782001.	−	167242.i	1.59592	−	0.341310i
$701$	−403113.			−0.820333			−0.410167	−	0.912011i	$-0.634529\pi$
$701$	−403113.			−0.820333			−0.410167	+	0.912011i	$0.634529\pi$
$702$	16053.0	−	27804.6i	0.0325748	−	0.0564211i
$703$	148466.	−	85716.9i	0.300411	−	0.173443i
$704$	−150837.	−	261258.i	−0.304343	−	0.527138i
$705$	−127224.	−	73452.5i	−0.255970	−	0.147784i
$706$			727010.i			1.45858i
$707$	764412.	+	247316.i	1.52929	+	0.494782i
$708$	−1.24075e6			−2.47524
$709$	−59075.5	+	102322.i	−0.117521	+	0.203552i	−0.918785	−	0.394759i	$-0.870828\pi$
$709$	−59075.5	+	102322.i	−0.117521	+	0.203552i	0.801264	+	0.598311i	$0.204161\pi$
$710$	65317.0	−	37710.8i	0.129572	−	0.0748082i
$711$	46016.9	+	79703.6i	0.0910286	+	0.157666i
$712$	499658.	+	288477.i	0.985627	+	0.569052i
$713$		−	431761.i		−	0.849306i
$714$	−345366.	+	1.06747e6i	−0.677460	+	2.09391i
$715$	−2890.08			−0.00565325
$716$	−338484.	+	586271.i	−0.660256	+	1.14360i
$717$	69736.7	−	40262.5i	0.135651	−	0.0783182i
$718$	762953.	+	1.32147e6i	1.47996	+	2.56336i
$719$	−274033.	−	158213.i	−0.530085	−	0.306045i	0.210966	−	0.977493i	$-0.432339\pi$
$719$	−274033.	−	158213.i	−0.530085	−	0.306045i	−0.741051	+	0.671448i	$0.765672\pi$
$720$			13601.7i			0.0262379i
$721$	−28466.4	−	133105.i	−0.0547599	−	0.256050i
$722$	−707820.			−1.35784
$723$	−19015.4	+	32935.6i	−0.0363771	+	0.0630070i
$724$	229432.	−	132463.i	0.437700	−	0.252706i
$725$	61188.5	+	105982.i	0.116411	+	0.201630i
$726$	689094.	+	397849.i	1.30739	+	0.754822i
$727$			773616.i			1.46371i	0.681458	+	0.731857i	$0.261346\pi$
$727$			773616.i			1.46371i	−0.681458	+	0.731857i	$0.738654\pi$
$728$	23313.5	−	21044.4i	0.0439891	−	0.0397077i
$729$	−387523.			−0.729192
$730$	17884.4	−	30976.7i	0.0335605	−	0.0581285i
$731$	307822.	−	177721.i	0.576056	−	0.332586i
$732$	−264819.	−	458681.i	−0.494228	−	0.856029i
$733$	144928.	+	83674.1i	0.269739	+	0.155734i	0.628769	−	0.777592i	$-0.283559\pi$
$733$	144928.	+	83674.1i	0.269739	+	0.155734i	−0.359030	+	0.933326i	$0.616892\pi$
$734$		−	1.60324e6i		−	2.97582i
$735$	−18322.6	+	178625.i	−0.0339167	+	0.330648i
$736$	210191.			0.388024
$737$	11363.4	−	19681.9i	0.0209205	−	0.0362353i
$738$	−97362.4	+	56212.2i	−0.178763	+	0.103209i
$739$	−327676.	−	567552.i	−0.600007	−	1.03924i	−0.992819	−	0.119623i	$-0.961831\pi$
$739$	−327676.	−	567552.i	−0.600007	−	1.03924i	0.392813	−	0.919618i	$-0.371502\pi$
$740$	−66679.8	−	38497.6i	−0.121767	−	0.0703024i
$741$			35953.1i			0.0654786i
$742$	−845657.	−	936838.i	−1.53598	−	1.70160i
$743$	322777.			0.584690			0.292345	−	0.956313i	$-0.405565\pi$
$743$	322777.			0.584690			0.292345	+	0.956313i	$0.405565\pi$
$744$	538583.	−	932854.i	0.972987	−	1.68526i
$745$	−148482.	+	85726.3i	−0.267524	+	0.154455i
$746$	71707.8	+	124202.i	0.128851	+	0.223177i
$747$	−56321.0	−	32517.0i	−0.100932	−	0.0582732i
$748$			506709.i			0.905639i
$749$	−337968.	+	72279.2i	−0.602438	+	0.128840i
$750$	596631.			1.06068
$751$	−2637.27	+	4567.89i	−0.00467601	+	0.00809908i	−0.868354	−	0.495945i	$-0.834822\pi$
$751$	−2637.27	+	4567.89i	−0.00467601	+	0.00809908i	0.863678	+	0.504044i	$0.168155\pi$
$752$	188908.	−	109066.i	0.334053	−	0.192866i
$753$	−463229.	−	802336.i	−0.816970	−	1.41503i
$754$	9380.86	+	5416.04i	0.0165006	+	0.00952663i
$755$		−	240859.i		−	0.422542i
$756$	−857151.	−	277321.i	−1.49973	−	0.485220i
$757$	469746.			0.819732			0.409866	−	0.912146i	$-0.365576\pi$
$757$	469746.			0.819732			0.409866	+	0.912146i	$0.365576\pi$
$758$	141754.	−	245524.i	0.246715	−	0.427323i
$759$	146078.	−	84338.4i	0.253573	−	0.146400i
$760$	157402.	+	272629.i	0.272511	+	0.472003i
$761$	104873.	+	60548.6i	0.181090	+	0.104553i	0.587805	−	0.809003i	$-0.299992\pi$
$761$	104873.	+	60548.6i	0.181090	+	0.104553i	−0.406715	+	0.913555i	$0.633326\pi$
$762$			985753.i			1.69769i
$763$	−165446.	+	511364.i	−0.284188	+	0.878378i
$764$	347065.			0.594599
$765$	−21265.6	+	36833.0i	−0.0363374	+	0.0629382i
$766$	−165716.	+	95675.9i	−0.282427	+	0.163059i
$767$	16428.7	+	28455.3i	0.0279262	+	0.0483696i
$768$	890324.	+	514029.i	1.50947	+	0.871495i
$769$			268249.i			0.453613i	0.973940	+	0.226807i	$0.0728285\pi$
$769$			268249.i			0.453613i	−0.973940	+	0.226807i	$0.927171\pi$
$770$	26394.8	+	123419.i	0.0445181	+	0.208161i
$771$	−529879.			−0.891391
$772$	−123000.	+	213043.i	−0.206382	+	0.357464i
$773$	−209245.	+	120807.i	−0.350183	+	0.202178i	−0.664766	−	0.747052i	$-0.731469\pi$
$773$	−209245.	+	120807.i	−0.350183	+	0.202178i	0.314583	+	0.949230i	$0.398135\pi$
$774$	−55276.9	−	95742.3i	−0.0922702	−	0.159817i
$775$	−629009.	−	363159.i	−1.04726	−	0.604635i
$776$			985142.i			1.63597i
$777$	−126479.	+	114169.i	−0.209496	+	0.189106i
$778$	−291724.			−0.481962
$779$	−252913.	+	438058.i	−0.416769	+	0.721866i
$780$	13984.1	−	8073.71i	0.0229850	−	0.0132704i
$781$	−37689.6	−	65280.2i	−0.0617901	−	0.107024i
$782$	−678622.	−	391803.i	−1.10972	−	0.640699i
$783$		−	137866.i		−	0.224871i
$784$	−216094.	−	156177.i	−0.351569	−	0.254089i
$785$	162297.			0.263373
$786$	109653.	−	189925.i	0.177491	−	0.307423i
$787$	974603.	−	562687.i	1.57354	−	0.908484i	0.577811	−	0.816170i	$-0.303907\pi$
$787$	974603.	−	562687.i	1.57354	−	0.908484i	0.995730	−	0.0923139i	$-0.0294263\pi$
$788$	228791.	+	396277.i	0.368456	+	0.638185i
$789$	434203.	+	250687.i	0.697492	+	0.402697i
$790$		−	289432.i		−	0.463759i
$791$	426353.	+	472323.i	0.681422	+	0.754895i
$792$	69928.9			0.111482
$793$	−7012.92	+	12146.7i	−0.0111520	+	0.0193158i
$794$	971360.	−	560815.i	1.54077	−	0.889567i
$795$	−143954.	−	249335.i	−0.227766	−	0.394502i
$796$	−685373.	−	395700.i	−1.08169	−	0.624511i
$797$			875198.i			1.37781i	0.724851	+	0.688905i	$0.241908\pi$
$797$			875198.i			1.37781i	−0.724851	+	0.688905i	$0.758092\pi$
$798$	1.53535e6	−	328355.i	2.41102	−	0.515630i
$799$	682078.			1.06842
$800$	176794.	−	306216.i	0.276241	−	0.478463i
$801$	94467.6	−	54540.9i	0.147237	−	0.0850075i
$802$	−419222.	−	726113.i	−0.651771	−	1.12890i
$803$	−30959.2	−	17874.3i	−0.0480130	−	0.0277203i
$804$			126978.i			0.196435i
$805$	−119322.	−	38605.2i	−0.184132	−	0.0595737i
$806$	−64289.3			−0.0989620
$807$	−580445.	+	1.00536e6i	−0.891280	+	1.54374i
$808$	−1.21238e6	+	699970.i	−1.85702	+	1.07215i
$809$	272358.	+	471738.i	0.416144	+	0.720782i	0.995548	−	0.0942585i	$-0.0300480\pi$
$809$	272358.	+	471738.i	0.416144	+	0.720782i	−0.579404	+	0.815040i	$0.696715\pi$
$810$	−334479.	−	193112.i	−0.509799	−	0.294333i
$811$		−	786948.i		−	1.19648i	−0.801318	−	0.598238i	$-0.795868\pi$
$811$		−	786948.i		−	1.19648i	0.801318	−	0.598238i	$-0.204132\pi$
$812$	93564.0	−	289191.i	0.141905	−	0.438603i
$813$	6756.99			0.0102229
$814$	−59879.9	+	103715.i	−0.0903717	+	0.156528i
$815$	−282939.	+	163355.i	−0.425969	+	0.245933i
$816$	−190020.	−	329124.i	−0.285377	−	0.494287i
$817$	−430769.	−	248704.i	−0.645357	−	0.372597i
$818$		−	486635.i		−	0.727271i
$819$	−1241.82	−	5806.61i	−0.00185137	−	0.00865675i
$820$	227179.			0.337863
$821$	−287810.	+	498502.i	−0.426992	+	0.739572i	−0.996604	−	0.0823419i	$-0.973760\pi$
$821$	−287810.	+	498502.i	−0.426992	+	0.739572i	0.569612	+	0.821914i	$0.307093\pi$
$822$	−2.00040e6	+	1.15493e6i	−2.96055	+	1.70928i
$823$	−217990.	−	377569.i	−0.321837	−	0.557438i	0.659030	−	0.752117i	$-0.270967\pi$
$823$	−217990.	−	377569.i	−0.321837	−	0.557438i	−0.980867	+	0.194678i	$0.937634\pi$
$824$	205401.	+	118588.i	0.302516	+	0.174657i
$825$		−	283752.i		−	0.416899i
$826$	1.06512e6	−	961452.i	1.56113	−	1.40918i
$827$	567533.			0.829813			0.414907	−	0.909864i	$-0.363814\pi$
$827$	567533.			0.829813			0.414907	+	0.909864i	$0.363814\pi$
$828$	−78303.3	+	135625.i	−0.114214	+	0.197824i
$829$	451387.	−	260608.i	0.656810	−	0.379209i	−0.134250	−	0.990947i	$-0.542863\pi$
$829$	451387.	−	260608.i	0.656810	−	0.379209i	0.791060	+	0.611738i	$0.209529\pi$
$830$	102261.	+	177121.i	0.148441	+	0.257107i
$831$	−314570.	−	181617.i	−0.455529	−	0.263000i
$832$		−	44635.6i		−	0.0644814i
$833$	−341001.	−	760775.i	−0.491435	−	1.09639i
$834$	358559.			0.515500
$835$	94323.6	−	163373.i	0.135284	−	0.234319i
$836$	614092.	−	354546.i	0.878661	−	0.507295i
$837$	409122.	+	708620.i	0.583985	+	1.01149i
$838$	−280752.	−	162092.i	−0.399792	−	0.230820i
$839$			426309.i			0.605620i	0.953051	+	0.302810i	$0.0979247\pi$
$839$			426309.i			0.605620i	−0.953051	+	0.302810i	$0.902075\pi$
$840$	−209648.	−	232253.i	−0.297121	−	0.329157i
$841$	−660767.			−0.934236
$842$	225301.	−	390234.i	0.317790	−	0.550428i
$843$	−453446.	+	261797.i	−0.638073	+	0.368391i
$844$	728488.	+	1.26178e6i	1.02267	+	1.77132i
$845$	187311.	+	108144.i	0.262331	+	0.151457i
$846$		−	212148.i		−	0.296413i
$847$	−578196.	+	123655.i	−0.805950	+	0.172364i
$848$	427501.			0.594491
$849$	425160.	−	736399.i	0.589844	−	1.02164i
$850$	−1.14159e6	+	659099.i	−1.58006	+	0.912247i
$851$	−59501.5	−	103060.i	−0.0821616	−	0.142308i
$852$	364733.	+	210579.i	0.502453	+	0.290092i
$853$		−	200874.i		−	0.276074i	−0.990427	−	0.138037i	$-0.955921\pi$
$853$		−	200874.i		−	0.276074i	0.990427	−	0.138037i	$-0.0440793\pi$
$854$	582764.	+	188546.i	0.799056	+	0.258525i
$855$	59518.4			0.0814178
$856$	301108.	−	521534.i	0.410936	−	0.711762i
$857$	580831.	−	335343.i	0.790839	−	0.456591i	−0.0494189	−	0.998778i	$-0.515737\pi$
$857$	580831.	−	335343.i	0.790839	−	0.456591i	0.840258	+	0.542187i	$0.182404\pi$
$858$	−12558.0	−	21751.1i	−0.0170587	−	0.0295465i
$859$	670028.	+	386841.i	0.908044	+	0.524259i	0.879801	−	0.475342i	$-0.157676\pi$
$859$	670028.	+	386841.i	0.908044	+	0.524259i	0.0282427	+	0.999601i	$0.491009\pi$
$860$			223399.i			0.302053i
$861$	154755.	−	478322.i	0.208756	−	0.645229i
$862$	−813086.			−1.09426
$863$	−8329.28	+	14426.7i	−0.0111837	+	0.0193707i	−0.871563	−	0.490283i	$-0.836893\pi$
$863$	−8329.28	+	14426.7i	−0.0111837	+	0.0193707i	0.860379	+	0.509654i	$0.170227\pi$
$864$	−344973.	+	199170.i	−0.462123	+	0.266807i
$865$	142185.	+	246271.i	0.190029	+	0.329140i
$866$	122470.	+	70707.9i	0.163303	+	0.0942828i
$867$		−	365155.i		−	0.485779i
$868$	377272.	+	1.76407e6i	0.500743	+	2.34141i
$869$	−289269.			−0.383056
$870$	53955.6	−	93453.8i	0.0712850	−	0.123469i
$871$	2912.12	−	1681.31i	0.00383860	−	0.00221622i
$872$	−468255.	−	811041.i	−0.615814	−	1.06662i
$873$	161302.	+	93127.8i	0.211647	+	0.122194i
$874$			1.09658e6i			1.43555i
$875$	−329100.	+	297069.i	−0.429845	+	0.388009i
$876$	199734.			0.260282
$877$	243088.	−	421040.i	0.316056	−	0.547425i	−0.663606	−	0.748083i	$-0.730975\pi$
$877$	243088.	−	421040.i	0.316056	−	0.547425i	0.979661	+	0.200658i	$0.0643080\pi$
$878$	−100495.	+	58020.6i	−0.130363	+	0.0752650i
$879$	−268631.	−	465282.i	−0.347679	−	0.602197i
$880$	−37023.6	−	21375.6i	−0.0478094	−	0.0276028i
$881$			867783.i			1.11805i	0.829152	+	0.559023i	$0.188824\pi$
$881$			867783.i			1.11805i	−0.829152	+	0.559023i	$0.811176\pi$
$882$	−236625.	+	106062.i	−0.304175	+	0.136340i
$883$	103207.			0.132369			0.0661845	−	0.997807i	$-0.478917\pi$
$883$	103207.			0.132369			0.0661845	+	0.997807i	$0.478917\pi$
$884$	−37486.1	+	64927.9i	−0.0479696	+	0.0830858i
$885$	283477.	−	163665.i	0.361936	−	0.208964i
$886$	631161.	+	1.09320e6i	0.804031	+	1.39262i
$887$	−752733.	−	434591.i	−0.956740	−	0.552374i	−0.0615718	−	0.998103i	$-0.519611\pi$
$887$	−752733.	−	434591.i	−0.956740	−	0.552374i	−0.895168	+	0.445729i	$0.852945\pi$
$888$		−	296891.i		−	0.376506i
$889$	−490817.	−	543739.i	−0.621035	−	0.687997i
$890$	−343046.			−0.433084
$891$	−193003.	+	334291.i	−0.243113	+	0.421084i
$892$	2.05435e6	−	1.18608e6i	2.58194	−	1.49068i
$893$	−477253.	−	826627.i	−0.598475	−	1.03659i
$894$	−1.29037e6	−	744997.i	−1.61451	−	0.932137i
$895$		−	178596.i		−	0.222959i
$896$	−1.42838e6	+	305480.i	−1.77922	+	0.380510i
$897$	24957.3			0.0310179
$898$	−214632.	+	371753.i	−0.266159	+	0.461001i
$899$	−239078.	+	138032.i	−0.295815	+	0.170789i
$900$	131723.	+	228152.i	0.162622	+	0.281669i
$901$	1.15766e6	+	668376.i	1.42604	+	0.823324i
$902$		−	353358.i		−	0.434313i
$903$	470363.	+	152180.i	0.576842	+	0.186630i
$904$	−1.10871e6			−1.35670
$905$	−34945.9	+	60528.1i	−0.0426677	+	0.0739027i
$906$	1.81274e6	−	1.04658e6i	2.20840	−	1.27502i
$907$	−270302.	−	468177.i	−0.328575	−	0.569109i	0.653654	−	0.756793i	$-0.273235\pi$
$907$	−270302.	−	468177.i	−0.328575	−	0.569109i	−0.982229	+	0.187685i	$0.939902\pi$
$908$	−817080.	−	471741.i	−0.991044	−	0.572179i
$909$			264679.i			0.320326i
$910$	−5748.32	+	17767.1i	−0.00694158	+	0.0214552i
$911$	1.10640e6			1.33314			0.666572	−	0.745441i	$-0.267761\pi$
$911$	1.10640e6			1.33314			0.666572	+	0.745441i	$0.267761\pi$
$912$	−265916.	+	460579.i	−0.319708	+	0.553751i
$913$	177021.	−	102203.i	0.212365	−	0.122609i
$914$	−853851.	−	1.47891e6i	−1.02209	−	1.77031i
$915$	121008.	+	69863.9i	0.144534	+	0.0834470i
$916$		−	2.97402e6i		−	3.54449i
$917$	34081.2	+	159359.i	0.0405300	+	0.189513i
$918$	1.48504e6			1.76219
$919$	−40794.0	+	70657.3i	−0.0483020	+	0.0836616i	−0.889166	−	0.457586i	$-0.848714\pi$
$919$	−40794.0	+	70657.3i	−0.0483020	+	0.0836616i	0.840864	+	0.541247i	$0.182048\pi$
$920$	189249.	−	109263.i	0.223593	−	0.129091i
$921$	308042.	+	533545.i	0.363154	+	0.629002i
$922$	1.74691e6	+	1.00858e6i	2.05499	+	1.18645i
$923$		−	11153.0i		−	0.0130915i
$924$	−523147.	+	472230.i	−0.612745	+	0.553107i
$925$	−200189.			−0.233969
$926$	−995610.	+	1.72445e6i	−1.16109	+	2.01107i
$927$	38834.0	−	22420.8i	0.0451911	−	0.0260911i
$928$	−67197.1	−	116389.i	−0.0780288	−	0.135150i
$929$	949898.	+	548424.i	1.10064	+	0.635455i	0.936389	−	0.350963i	$-0.114146\pi$
$929$	949898.	+	548424.i	1.10064	+	0.635455i	0.164252	+	0.986418i	$0.447479\pi$
$930$			640461.i			0.740503i
$931$	−683401.	+	945585.i	−0.788454	+	1.09094i
$932$	−2.04791e6			−2.35765
$933$	495186.	−	857687.i	0.568859	−	0.985293i
$934$	−1.47036e6	+	848913.i	−1.68550	+	0.973126i
$935$	−66839.2	−	115769.i	−0.0764554	−	0.132425i
$936$	8960.44	+	5173.31i	0.0102277	+	0.00590496i
$937$			280065.i			0.318992i	0.987199	+	0.159496i	$0.0509869\pi$
$937$			280065.i			0.318992i	−0.987199	+	0.159496i	$0.949013\pi$
$938$	−98395.2	−	109005.i	−0.111833	−	0.123891i
$939$	−1.61578e6			−1.83253
$940$	−214346.	+	371259.i	−0.242583	+	0.420166i
$941$	−1.04479e6	+	603208.i	−1.17991	+	0.681221i	−0.955994	−	0.293387i	$-0.905217\pi$
$941$	−1.04479e6	+	603208.i	−1.17991	+	0.681221i	−0.223916	+	0.974608i	$0.571884\pi$
$942$	705214.	+	1.22147e6i	0.794729	+	1.37651i
$943$	304084.	+	175563.i	0.341955	+	0.197428i
$944$			486039.i			0.545415i
$945$	232416.	−	49705.5i	0.260257	−	0.0556597i
$946$	347479.			0.388281
$947$	484847.	−	839780.i	0.540636	−	0.936409i	−0.458232	−	0.888833i	$-0.651517\pi$
$947$	484847.	−	839780.i	0.540636	−	0.936409i	0.998868	−	0.0475763i	$-0.0151497\pi$
$948$	1.39967e6	−	808100.i	1.55743	−	0.899184i
$949$	−2644.67	−	4580.71i	−0.00293656	−	0.00508628i
$950$	1.59756e6	+	922349.i	1.77014	+	1.02199i
$951$			1.20158e6i			1.32859i
$952$	1.38216e6	+	447180.i	1.52505	+	0.493411i
$953$	566973.			0.624275			0.312138	−	0.950037i	$-0.398955\pi$
$953$	566973.			0.624275			0.312138	+	0.950037i	$0.398955\pi$
$954$	207886.	−	360069.i	0.228417	−	0.395630i
$955$	−79294.9	+	45780.9i	−0.0869437	+	0.0501970i
$956$	−117493.	−	203503.i	−0.128557	−	0.222667i
$957$	−93401.1	−	53925.2i	−0.101983	−	0.0588800i
$958$		−	1.25760e6i		−	1.37029i
$959$	528362.	−	1.63308e6i	0.574506	−	1.77570i
$960$	−444668.			−0.482495
$961$	357470.	−	619156.i	0.387073	−	0.670430i
$962$	−15345.6	+	8859.78i	−0.0165819	+	0.00957355i
$963$	−56928.8	−	98603.5i	−0.0613874	−	0.106326i
$964$	96111.4	+	55489.9i	0.103424	+	0.0597118i
$965$		−	64899.1i		−	0.0696922i
$966$	−227932.	−	1.06578e6i	−0.244259	−	1.14212i
$967$	−1.18372e6			−1.26590			−0.632948	−	0.774195i	$-0.718155\pi$
$967$	−1.18372e6			−1.26590			−0.632948	+	0.774195i	$0.718155\pi$
$968$	515135.	−	892239.i	0.549756	−	0.952205i
$969$	−1.44018e6	+	831491.i	−1.53381	+	0.885543i
$970$	−292873.	−	507270.i	−0.311269	−	0.539133i
$971$	−995192.	−	574574.i	−1.05552	−	0.609408i	−0.131334	−	0.991338i	$-0.541926\pi$
$971$	−995192.	−	574574.i	−1.05552	−	0.609408i	−0.924191	+	0.381931i	$0.875259\pi$
$972$		−	667449.i		−	0.706457i
$973$	−197780.	+	178531.i	−0.208909	+	0.188576i
$974$	1.22891e6			1.29539
$975$	20991.8	−	36358.9i	0.0220821	−	0.0382474i
$976$	−179679.	+	103738.i	−0.188624	+	0.108902i
$977$	505838.	+	876138.i	0.529935	+	0.917875i	0.999390	+	0.0349182i	$0.0111171\pi$
$977$	505838.	+	876138.i	0.529935	+	0.917875i	−0.469455	+	0.882956i	$0.655550\pi$
$978$	−2.45886e6	−	1.41962e6i	−2.57073	−	1.48421i
$979$			342852.i			0.357719i
$980$	521255.	+	53468.4i	0.542748	+	0.0556731i
$981$	−177061.			−0.183986
$982$	452976.	−	784578.i	0.469735	−	0.813604i
$983$	−572273.	+	330402.i	−0.592238	+	0.341929i	−0.765982	−	0.642862i	$-0.777747\pi$
$983$	−572273.	+	330402.i	−0.592238	+	0.341929i	0.173744	+	0.984791i	$0.444414\pi$
$984$	437998.	+	758634.i	0.452357	+	0.783506i
$985$	−104545.	−	60358.9i	−0.107753	−	0.0622113i
$986$			501030.i			0.515359i
$987$	635666.	+	704206.i	0.652521	+	0.722878i
$988$	104917.			0.107481
$989$	−172641.	+	299024.i	−0.176503	+	0.305712i
$990$	−36007.8	+	20789.1i	−0.0367389	+	0.0212112i
$991$	−20806.4	−	36037.7i	−0.0211860	−	0.0366953i	0.855238	−	0.518235i	$-0.173411\pi$
$991$	−20806.4	−	36037.7i	−0.0211860	−	0.0366953i	−0.876424	+	0.481540i	$0.840078\pi$
$992$	690777.	+	398820.i	0.701963	+	0.405279i
$993$		−	442295.i		−	0.448553i
$994$	−476281.	+	101859.i	−0.482048	+	0.103093i
$995$	208785.			0.210889
$996$	−571029.	+	989051.i	−0.575625	+	0.997011i
$997$	345563.	−	199511.i	0.347646	−	0.200713i	−0.316002	−	0.948758i	$-0.602341\pi$
$997$	345563.	−	199511.i	0.347646	−	0.200713i	0.663648	+	0.748045i	$0.269007\pi$
$998$	601540.	+	1.04190e6i	0.603953	+	1.04608i
$999$	195312.	+	112763.i	0.195703	+	0.112989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.5.d.a.5.1	yes	4
3.2	odd	2		63.5.m.d.19.2		4
4.3	odd	2		112.5.s.a.33.1		4
5.2	odd	4		175.5.j.a.124.1		8
5.3	odd	4		175.5.j.a.124.4		8
5.4	even	2		175.5.i.a.26.2		4
7.2	even	3		49.5.b.a.48.4		4
7.3	odd	6	inner	7.5.d.a.3.1	✓	4
7.4	even	3		49.5.d.b.31.1		4
7.5	odd	6		49.5.b.a.48.3		4
7.6	odd	2		49.5.d.b.19.1		4
21.2	odd	6		441.5.d.d.244.2		4
21.5	even	6		441.5.d.d.244.1		4
21.17	even	6		63.5.m.d.10.2		4
28.3	even	6		112.5.s.a.17.1		4
28.19	even	6		784.5.c.c.97.4		4
28.23	odd	6		784.5.c.c.97.1		4
35.3	even	12		175.5.j.a.24.1		8
35.17	even	12		175.5.j.a.24.4		8
35.24	odd	6		175.5.i.a.101.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.5.d.a.3.1	✓	4	7.3	odd	6	inner
7.5.d.a.5.1	yes	4	1.1	even	1	trivial
49.5.b.a.48.3		4	7.5	odd	6
49.5.b.a.48.4		4	7.2	even	3
49.5.d.b.19.1		4	7.6	odd	2
49.5.d.b.31.1		4	7.4	even	3
63.5.m.d.10.2		4	21.17	even	6
63.5.m.d.19.2		4	3.2	odd	2
112.5.s.a.17.1		4	28.3	even	6
112.5.s.a.33.1		4	4.3	odd	2
175.5.i.a.26.2		4	5.4	even	2
175.5.i.a.101.2		4	35.24	odd	6
175.5.j.a.24.1		8	35.3	even	12
175.5.j.a.24.4		8	35.17	even	12
175.5.j.a.124.1		8	5.2	odd	4
175.5.j.a.124.4		8	5.3	odd	4
441.5.d.d.244.1		4	21.5	even	6
441.5.d.d.244.2		4	21.2	odd	6
784.5.c.c.97.1		4	28.23	odd	6
784.5.c.c.97.4		4	28.19	even	6

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.34521 + 5.79407i) q^{2} +(8.53562 - 4.92804i) q^{3} +(-14.3808 - 24.9083i) q^{4} +(6.57125 + 3.79391i) q^{5} +65.9413i q^{6} +(-32.8329 - 36.3731i) q^{7} +85.3808 q^{8} +(8.07125 - 13.9798i) q^{9} +O(q^{10})\)	\(q+(-3.34521 + 5.79407i) q^{2} +(8.53562 - 4.92804i) q^{3} +(-14.3808 - 24.9083i) q^{4} +(6.57125 + 3.79391i) q^{5} +65.9413i q^{6} +(-32.8329 - 36.3731i) q^{7} +85.3808 q^{8} +(8.07125 - 13.9798i) q^{9} +(-43.9644 + 25.3828i) q^{10} +(25.3685 + 43.9396i) q^{11} +(-245.499 - 141.739i) q^{12} +7.50702i q^{13} +(320.581 - 68.5607i) q^{14} +74.7863 q^{15} +(-55.5233 + 96.1692i) q^{16} +(-300.711 + 173.616i) q^{17} +(54.0000 + 93.5307i) q^{18} +(420.818 + 242.959i) q^{19} -218.238i q^{20} +(-459.497 - 148.665i) q^{21} -339.452 q^{22} +(168.654 - 292.116i) q^{23} +(728.779 - 420.761i) q^{24} +(-283.712 - 491.404i) q^{25} +(-43.4962 - 25.1125i) q^{26} +639.241i q^{27} +(-433.828 + 1340.89i) q^{28} -215.671 q^{29} +(-250.176 + 433.317i) q^{30} +(1108.53 - 640.012i) q^{31} +(311.573 + 539.659i) q^{32} +(433.073 + 250.035i) q^{33} -2323.12i q^{34} +(-77.7570 - 363.582i) q^{35} -464.285 q^{36} +(176.402 - 305.537i) q^{37} +(-2815.45 + 1625.50i) q^{38} +(36.9949 + 64.0771i) q^{39} +(561.059 + 323.927i) q^{40} +1040.97i q^{41} +(2398.49 - 2165.05i) q^{42} -1023.65 q^{43} +(729.641 - 1263.78i) q^{44} +(106.076 - 61.2432i) q^{45} +(1128.36 + 1954.38i) q^{46} +(-1701.16 - 982.166i) q^{47} +1094.49i q^{48} +(-245.000 + 2388.47i) q^{49} +3796.31 q^{50} +(-1711.17 + 2963.84i) q^{51} +(186.987 - 107.957i) q^{52} +(-1924.87 - 3333.97i) q^{53} +(-3703.81 - 2138.40i) q^{54} +384.984i q^{55} +(-2803.30 - 3105.56i) q^{56} +4789.26 q^{57} +(721.464 - 1249.61i) q^{58} +(3790.50 - 2188.44i) q^{59} +(-1075.49 - 1862.80i) q^{60} +(1618.05 + 934.181i) q^{61} +8563.89i q^{62} +(-773.491 + 165.422i) q^{63} -5945.85 q^{64} +(-28.4810 + 49.3305i) q^{65} +(-2897.44 + 1672.83i) q^{66} +(-223.966 - 387.920i) q^{67} +(8648.95 + 4993.48i) q^{68} -3324.53i q^{69} +(2366.73 + 765.727i) q^{70} -1485.68 q^{71} +(689.130 - 1193.61i) q^{72} +(-610.190 + 352.293i) q^{73} +(1180.20 + 2044.17i) q^{74} +(-4843.33 - 2796.30i) q^{75} -13975.8i q^{76} +(765.295 - 2365.40i) q^{77} -495.023 q^{78} +(-2850.67 + 4937.50i) q^{79} +(-729.715 + 421.301i) q^{80} +(3803.98 + 6588.69i) q^{81} +(-6031.44 - 3482.25i) q^{82} -4028.74i q^{83} +(2904.96 + 13583.2i) q^{84} -2634.73 q^{85} +(3424.31 - 5931.07i) q^{86} +(-1840.89 + 1062.84i) q^{87} +(2165.99 + 3751.60i) q^{88} +(5852.11 + 3378.71i) q^{89} +819.485i q^{90} +(273.053 - 246.477i) q^{91} -9701.51 q^{92} +(6308.01 - 10925.8i) q^{93} +(11381.5 - 6571.10i) q^{94} +(1843.53 + 3193.09i) q^{95} +(5318.93 + 3070.89i) q^{96} +11538.2i q^{97} +(-13019.4 - 9409.47i) q^{98} +819.023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 20 q^{4} - 30 q^{5} + 304 q^{8} - 24 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 20 * q^4 - 30 * q^5 + 304 * q^8 - 24 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 20 q^{4} - 30 q^{5} + 304 q^{8} - 24 q^{9} - 204 q^{10} - 58 q^{11} - 588 q^{12} + 560 q^{14} + 468 q^{15} - 72 q^{16} - 246 q^{17} + 216 q^{18} + 642 q^{19} - 1050 q^{21} - 1264 q^{22} + 290 q^{23} + 720 q^{24} - 572 q^{25} + 1008 q^{26} - 28 q^{28} - 2176 q^{29} - 72 q^{30} + 3618 q^{31} + 1584 q^{32} + 2070 q^{33} - 2478 q^{35} - 1632 q^{36} - 270 q^{37} - 6168 q^{38} - 1428 q^{39} - 1752 q^{40} + 6048 q^{42} + 2472 q^{43} + 2412 q^{44} + 1944 q^{45} + 2384 q^{46} - 1542 q^{47} - 980 q^{49} + 7568 q^{50} - 4734 q^{51} - 3192 q^{52} - 4510 q^{53} - 11016 q^{54} - 1232 q^{56} + 11052 q^{57} - 904 q^{58} + 2526 q^{59} - 756 q^{60} - 282 q^{61} - 336 q^{63} - 5472 q^{64} + 5796 q^{65} - 2556 q^{66} - 1318 q^{67} + 20412 q^{68} + 3360 q^{70} - 10408 q^{71} - 1296 q^{72} + 5214 q^{73} + 4036 q^{74} - 9636 q^{75} - 8890 q^{77} - 9072 q^{78} - 8110 q^{79} - 3144 q^{80} + 9306 q^{81} - 4032 q^{82} + 588 q^{84} - 15492 q^{85} + 12928 q^{86} + 5976 q^{87} - 2912 q^{88} + 33990 q^{89} + 17640 q^{91} - 20232 q^{92} + 7446 q^{93} + 27768 q^{94} + 6558 q^{95} - 37828 q^{98} + 10368 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 20 * q^4 - 30 * q^5 + 304 * q^8 - 24 * q^9 - 204 * q^10 - 58 * q^11 - 588 * q^12 + 560 * q^14 + 468 * q^15 - 72 * q^16 - 246 * q^17 + 216 * q^18 + 642 * q^19 - 1050 * q^21 - 1264 * q^22 + 290 * q^23 + 720 * q^24 - 572 * q^25 + 1008 * q^26 - 28 * q^28 - 2176 * q^29 - 72 * q^30 + 3618 * q^31 + 1584 * q^32 + 2070 * q^33 - 2478 * q^35 - 1632 * q^36 - 270 * q^37 - 6168 * q^38 - 1428 * q^39 - 1752 * q^40 + 6048 * q^42 + 2472 * q^43 + 2412 * q^44 + 1944 * q^45 + 2384 * q^46 - 1542 * q^47 - 980 * q^49 + 7568 * q^50 - 4734 * q^51 - 3192 * q^52 - 4510 * q^53 - 11016 * q^54 - 1232 * q^56 + 11052 * q^57 - 904 * q^58 + 2526 * q^59 - 756 * q^60 - 282 * q^61 - 336 * q^63 - 5472 * q^64 + 5796 * q^65 - 2556 * q^66 - 1318 * q^67 + 20412 * q^68 + 3360 * q^70 - 10408 * q^71 - 1296 * q^72 + 5214 * q^73 + 4036 * q^74 - 9636 * q^75 - 8890 * q^77 - 9072 * q^78 - 8110 * q^79 - 3144 * q^80 + 9306 * q^81 - 4032 * q^82 + 588 * q^84 - 15492 * q^85 + 12928 * q^86 + 5976 * q^87 - 2912 * q^88 + 33990 * q^89 + 17640 * q^91 - 20232 * q^92 + 7446 * q^93 + 27768 * q^94 + 6558 * q^95 - 37828 * q^98 + 10368 * q^99

Introduction

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