LMFDB - Embedded newform 197.4.e.a.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(6,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(14))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("197.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.e (of order $14$, 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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	197.33
Dual form			197.4.e.a.6.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.93087 - 1.12544i) q^{2} +(8.18390 - 1.86792i) q^{3} +(15.8391 + 7.62772i) q^{4} +(3.18930 + 6.62265i) q^{5} -42.4560 q^{6} +(1.15067 + 5.04140i) q^{7} +(-37.8821 - 30.2100i) q^{8} +(39.1609 - 18.8589i) q^{9} +O(q^{10})$	\(q+(-4.93087 - 1.12544i) q^{2} +(8.18390 - 1.86792i) q^{3} +(15.8391 + 7.62772i) q^{4} +(3.18930 + 6.62265i) q^{5} -42.4560 q^{6} +(1.15067 + 5.04140i) q^{7} +(-37.8821 - 30.2100i) q^{8} +(39.1609 - 18.8589i) q^{9} +(-8.27264 - 36.2448i) q^{10} +(25.8971 + 5.91085i) q^{11} +(143.874 + 32.8382i) q^{12} +(23.1694 - 18.4770i) q^{13} -26.1535i q^{14} +(38.4715 + 48.2418i) q^{15} +(65.1043 + 81.6382i) q^{16} +(7.25208 + 15.0591i) q^{17} +(-214.322 + 48.9176i) q^{18} -31.0913 q^{19} +129.224i q^{20} +(18.8339 + 39.1089i) q^{21} +(-121.043 - 58.2913i) q^{22} +(-32.9563 + 144.391i) q^{23} +(-366.453 - 176.475i) q^{24} +(44.2483 - 55.4857i) q^{25} +(-135.040 + 65.0318i) q^{26} +(108.062 - 86.1762i) q^{27} +(-20.2288 + 88.6283i) q^{28} +(-29.7563 + 130.371i) q^{29} +(-135.405 - 281.171i) q^{30} +(159.752 + 36.4624i) q^{31} +(-60.9580 - 126.581i) q^{32} +222.980 q^{33} +(-18.8110 - 82.4162i) q^{34} +(-29.7176 + 23.6990i) q^{35} +764.125 q^{36} +(221.822 - 278.156i) q^{37} +(153.307 + 34.9914i) q^{38} +(155.102 - 194.492i) q^{39} +(79.2528 - 347.229i) q^{40} +(-143.467 + 69.0900i) q^{41} +(-48.8527 - 214.038i) q^{42} +(-98.5804 + 431.909i) q^{43} +(365.101 + 291.159i) q^{44} +(249.792 + 199.202i) q^{45} +(325.007 - 674.884i) q^{46} +(219.251 - 274.932i) q^{47} +(685.301 + 546.509i) q^{48} +(284.941 - 137.220i) q^{49} +(-280.629 + 223.794i) q^{50} +(87.4795 + 109.696i) q^{51} +(507.920 - 115.929i) q^{52} +(-68.0744 - 32.7829i) q^{53} +(-629.824 + 303.307i) q^{54} +(43.4482 + 190.359i) q^{55} +(108.711 - 225.741i) q^{56} +(-254.448 + 58.0762i) q^{57} +(293.449 - 609.353i) q^{58} +(-33.1654 + 145.307i) q^{59} +(241.381 + 1057.56i) q^{60} +(157.755 - 691.172i) q^{61} +(-746.682 - 359.583i) q^{62} +(140.136 + 175.725i) q^{63} +(-27.7662 - 121.652i) q^{64} +(196.261 + 94.5142i) q^{65} +(-1099.49 - 250.951i) q^{66} +(150.033 + 119.648i) q^{67} +293.840i q^{68} +1243.24i q^{69} +(173.205 - 83.4114i) q^{70} +(-437.257 - 907.974i) q^{71} +(-2053.23 - 468.635i) q^{72} +(-210.444 - 167.824i) q^{73} +(-1406.82 + 1121.90i) q^{74} +(258.481 - 536.741i) q^{75} +(-492.460 - 237.156i) q^{76} +137.359i q^{77} +(-983.679 + 784.458i) q^{78} +(-247.535 + 514.012i) q^{79} +(-333.024 + 691.532i) q^{80} +(-8.31079 + 10.4214i) q^{81} +(785.173 - 179.211i) q^{82} +514.603 q^{83} +763.111i q^{84} +(-76.6021 + 96.0560i) q^{85} +(972.174 - 2018.74i) q^{86} +1122.52i q^{87} +(-802.471 - 1006.27i) q^{88} +(-485.482 + 110.808i) q^{89} +(-1007.50 - 1263.37i) q^{90} +(119.810 + 95.5453i) q^{91} +(-1623.37 + 2035.65i) q^{92} +1375.51 q^{93} +(-1390.52 + 1108.90i) q^{94} +(-99.1597 - 205.907i) q^{95} +(-735.317 - 922.058i) q^{96} +(-227.636 + 109.624i) q^{97} +(-1559.44 + 355.932i) q^{98} +(1125.63 - 256.917i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9}+O(q^{10}) $ 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9	\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + 149 q^{10} + 91 q^{11} - 63 q^{12} - 7 q^{13} - 473 q^{15} - 1113 q^{16} - 7 q^{17} - 196 q^{18} + 464 q^{19} - 7 q^{21} + 807 q^{22} + 413 q^{23} - 1425 q^{24} + 1195 q^{25} - 543 q^{26} + 455 q^{27} + 174 q^{28} - 906 q^{29} + 798 q^{30} + 917 q^{31} + 945 q^{32} + 894 q^{33} - 219 q^{34} - 7 q^{35} + 3250 q^{36} + 1734 q^{37} - 63 q^{38} - 825 q^{39} + 141 q^{40} + 563 q^{41} + 432 q^{42} - 423 q^{43} + 2149 q^{44} - 3808 q^{45} - 2569 q^{46} - 289 q^{47} - 3703 q^{48} - 3747 q^{49} - 4963 q^{50} - 87 q^{51} + 3654 q^{52} - 1573 q^{53} - 1228 q^{54} + 2825 q^{55} + 98 q^{56} - 518 q^{57} - 5103 q^{58} + 2045 q^{59} + 3375 q^{60} + 287 q^{61} - 2547 q^{62} + 1453 q^{63} + 6475 q^{64} + 1268 q^{65} + 4634 q^{66} - 3577 q^{67} - 814 q^{70} - 273 q^{71} - 1008 q^{72} - 679 q^{73} - 315 q^{74} - 1281 q^{75} + 6078 q^{76} + 4739 q^{78} + 1463 q^{79} + 441 q^{80} - 4427 q^{81} - 7 q^{82} + 4900 q^{83} - 3351 q^{85} + 3472 q^{86} + 3738 q^{88} + 147 q^{89} + 7133 q^{90} - 14133 q^{91} - 803 q^{92} - 4894 q^{93} - 7833 q^{94} - 7700 q^{95} - 16450 q^{96} + 1233 q^{97} - 2030 q^{98} + 2464 q^{99}+O(q^{100}) \) 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9 + 149 * q^10 + 91 * q^11 - 63 * q^12 - 7 * q^13 - 473 * q^15 - 1113 * q^16 - 7 * q^17 - 196 * q^18 + 464 * q^19 - 7 * q^21 + 807 * q^22 + 413 * q^23 - 1425 * q^24 + 1195 * q^25 - 543 * q^26 + 455 * q^27 + 174 * q^28 - 906 * q^29 + 798 * q^30 + 917 * q^31 + 945 * q^32 + 894 * q^33 - 219 * q^34 - 7 * q^35 + 3250 * q^36 + 1734 * q^37 - 63 * q^38 - 825 * q^39 + 141 * q^40 + 563 * q^41 + 432 * q^42 - 423 * q^43 + 2149 * q^44 - 3808 * q^45 - 2569 * q^46 - 289 * q^47 - 3703 * q^48 - 3747 * q^49 - 4963 * q^50 - 87 * q^51 + 3654 * q^52 - 1573 * q^53 - 1228 * q^54 + 2825 * q^55 + 98 * q^56 - 518 * q^57 - 5103 * q^58 + 2045 * q^59 + 3375 * q^60 + 287 * q^61 - 2547 * q^62 + 1453 * q^63 + 6475 * q^64 + 1268 * q^65 + 4634 * q^66 - 3577 * q^67 - 814 * q^70 - 273 * q^71 - 1008 * q^72 - 679 * q^73 - 315 * q^74 - 1281 * q^75 + 6078 * q^76 + 4739 * q^78 + 1463 * q^79 + 441 * q^80 - 4427 * q^81 - 7 * q^82 + 4900 * q^83 - 3351 * q^85 + 3472 * q^86 + 3738 * q^88 + 147 * q^89 + 7133 * q^90 - 14133 * q^91 - 803 * q^92 - 4894 * q^93 - 7833 * q^94 - 7700 * q^95 - 16450 * q^96 + 1233 * q^97 - 2030 * q^98 + 2464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−4.93087	−	1.12544i	−1.74333	−	0.397903i	−0.771994	−	0.635630i	$-0.780741\pi$
$2$	−4.93087	−	1.12544i	−1.74333	−	0.397903i	−0.971332	+	0.237727i	$0.923598\pi$
$3$	8.18390	−	1.86792i	1.57499	−	0.359482i	0.656314	−	0.754488i	$-0.272115\pi$
$3$	8.18390	−	1.86792i	1.57499	−	0.359482i	0.918678	+	0.395007i	$0.129258\pi$
$4$	15.8391	+	7.62772i	1.97989	+	0.953465i
$5$	3.18930	+	6.62265i	0.285260	+	0.592348i	0.993527	−	0.113596i	$-0.0362371\pi$
$5$	3.18930	+	6.62265i	0.285260	+	0.592348i	−0.708267	+	0.705944i	$0.750523\pi$
$6$	−42.4560			−2.88876
$7$	1.15067	+	5.04140i	0.0621301	+	0.272210i	0.996446	−	0.0842369i	$-0.0268452\pi$
$7$	1.15067	+	5.04140i	0.0621301	+	0.272210i	−0.934316	+	0.356447i	$0.883988\pi$
$8$	−37.8821	−	30.2100i	−1.67417	−	1.33511i
$9$	39.1609	−	18.8589i	1.45040	−	0.698478i
$10$	−8.27264	−	36.2448i	−0.261604	−	1.14616i
$11$	25.8971	+	5.91085i	0.709843	+	0.162017i	0.562173	−	0.827020i	$-0.309965\pi$
$11$	25.8971	+	5.91085i	0.709843	+	0.162017i	0.147670	+	0.989037i	$0.452823\pi$
$12$	143.874	+	32.8382i	3.46106	+	0.789965i
$13$	23.1694	−	18.4770i	0.494310	−	0.394199i	−0.344361	−	0.938837i	$-0.611904\pi$
$13$	23.1694	−	18.4770i	0.494310	−	0.394199i	0.838671	+	0.544638i	$0.183333\pi$
$14$		−	26.1535i		−	0.499272i
$15$	38.4715	+	48.2418i	0.662220	+	0.830398i
$16$	65.1043	+	81.6382i	1.01725	+	1.27560i
$17$	7.25208	+	15.0591i	0.103464	+	0.214845i	0.946274	−	0.323366i	$-0.104815\pi$
$17$	7.25208	+	15.0591i	0.103464	+	0.214845i	−0.842810	+	0.538211i	$0.819100\pi$
$18$	−214.322	+	48.9176i	−2.80645	+	0.640555i
$19$	−31.0913			−0.375413			−0.187706	−	0.982225i	$-0.560105\pi$
$19$	−31.0913			−0.375413			−0.187706	+	0.982225i	$0.560105\pi$
$20$			129.224i			1.44477i
$21$	18.8339	+	39.1089i	0.195709	+	0.406394i
$22$	−121.043	−	58.2913i	−1.17302	−	0.564897i
$23$	−32.9563	+	144.391i	−0.298777	+	1.30903i	0.573174	+	0.819434i	$0.305712\pi$
$23$	−32.9563	+	144.391i	−0.298777	+	1.30903i	−0.871951	+	0.489593i	$0.837145\pi$
$24$	−366.453	−	176.475i	−3.11675	−	1.50095i
$25$	44.2483	−	55.4857i	0.353987	−	0.443885i
$26$	−135.040	+	65.0318i	−1.01860	+	0.490530i
$27$	108.062	−	86.1762i	0.770239	−	0.614245i
$28$	−20.2288	+	88.6283i	−0.136532	+	0.598185i
$29$	−29.7563	+	130.371i	−0.190538	+	0.834803i	0.785787	+	0.618497i	$0.212258\pi$
$29$	−29.7563	+	130.371i	−0.190538	+	0.834803i	−0.976326	+	0.216306i	$0.930599\pi$
$30$	−135.405	−	281.171i	−0.824048	−	1.71115i
$31$	159.752	+	36.4624i	0.925560	+	0.211253i	0.658634	−	0.752464i	$-0.271135\pi$
$31$	159.752	+	36.4624i	0.925560	+	0.211253i	0.266927	+	0.963717i	$0.413992\pi$
$32$	−60.9580	−	126.581i	−0.336749	−	0.699266i
$33$	222.980			1.17624
$34$	−18.8110	−	82.4162i	−0.0948839	−	0.415714i
$35$	−29.7176	+	23.6990i	−0.143520	+	0.114453i
$36$	764.125			3.53761
$37$	221.822	−	278.156i	0.985602	−	1.23591i	0.0138492	−	0.999904i	$-0.495592\pi$
$37$	221.822	−	278.156i	0.985602	−	1.23591i	0.971753	−	0.236002i	$-0.0758370\pi$
$38$	153.307	+	34.9914i	0.654467	+	0.149378i
$39$	155.102	−	194.492i	0.636827	−	0.798556i
$40$	79.2528	−	347.229i	0.313274	−	1.37254i
$41$	−143.467	+	69.0900i	−0.546482	+	0.263172i	−0.686690	−	0.726950i	$-0.740937\pi$
$41$	−143.467	+	69.0900i	−0.546482	+	0.263172i	0.140208	+	0.990122i	$0.455223\pi$
$42$	−48.8527	−	214.038i	−0.179479	−	0.786350i
$43$	−98.5804	+	431.909i	−0.349613	+	1.53176i	0.428447	+	0.903567i	$0.359061\pi$
$43$	−98.5804	+	431.909i	−0.349613	+	1.53176i	−0.778061	+	0.628189i	$0.783796\pi$
$44$	365.101	+	291.159i	1.25093	+	0.997587i
$45$	249.792	+	199.202i	0.827484	+	0.659896i
$46$	325.007	−	674.884i	1.04173	−	2.16318i
$47$	219.251	−	274.932i	0.680447	−	0.853254i	−0.314948	−	0.949109i	$-0.601987\pi$
$47$	219.251	−	274.932i	0.680447	−	0.853254i	0.995395	+	0.0958552i	$0.0305586\pi$
$48$	685.301	+	546.509i	2.06072	+	1.64337i
$49$	284.941	−	137.220i	0.830731	−	0.400059i
$50$	−280.629	+	223.794i	−0.793737	+	0.632985i
$51$	87.4795	+	109.696i	0.240188	+	0.301186i
$52$	507.920	−	115.929i	1.35454	−	0.309164i
$53$	−68.0744	−	32.7829i	−0.176429	−	0.0849638i	0.343584	−	0.939122i	$-0.388359\pi$
$53$	−68.0744	−	32.7829i	−0.176429	−	0.0849638i	−0.520014	+	0.854158i	$0.674073\pi$
$54$	−629.824	+	303.307i	−1.58719	+	0.764349i
$55$	43.4482	+	190.359i	0.106519	+	0.466691i
$56$	108.711	−	225.741i	0.259413	−	0.538676i
$57$	−254.448	+	58.0762i	−0.591272	+	0.134954i
$58$	293.449	−	609.353i	0.664341	−	1.37952i
$59$	−33.1654	+	145.307i	−0.0731826	+	0.320634i	−0.998248	−	0.0591749i	$-0.981153\pi$
$59$	−33.1654	+	145.307i	−0.0731826	+	0.320634i	0.925065	+	0.379809i	$0.124010\pi$
$60$	241.381	+	1057.56i	0.519368	+	2.27550i
$61$	157.755	−	691.172i	0.331123	−	1.45075i	−0.485836	−	0.874050i	$-0.661485\pi$
$61$	157.755	−	691.172i	0.331123	−	1.45075i	0.816959	−	0.576696i	$-0.195658\pi$
$62$	−746.682	−	359.583i	−1.52950	−	0.736566i
$63$	140.136	+	175.725i	0.280246	+	0.351418i
$64$	−27.7662	−	121.652i	−0.0542309	−	0.237601i
$65$	196.261	+	94.5142i	0.374510	+	0.180355i
$66$	−1099.49	−	250.951i	−2.05057	−	0.468029i
$67$	150.033	+	119.648i	0.273574	+	0.218168i	0.750660	−	0.660688i	$-0.229736\pi$
$67$	150.033	+	119.648i	0.273574	+	0.218168i	−0.477086	+	0.878857i	$0.658307\pi$
$68$			293.840i			0.524019i
$69$			1243.24i			2.16911i
$70$	173.205	−	83.4114i	0.295743	−	0.142422i
$71$	−437.257	−	907.974i	−0.730886	−	1.51770i	−0.851130	−	0.524955i	$-0.824082\pi$
$71$	−437.257	−	907.974i	−0.730886	−	1.51770i	0.120244	−	0.992744i	$-0.461632\pi$
$72$	−2053.23	−	468.635i	−3.36076	−	0.767072i
$73$	−210.444	−	167.824i	−0.337406	−	0.269072i	0.440099	−	0.897949i	$-0.354943\pi$
$73$	−210.444	−	167.824i	−0.337406	−	0.269072i	−0.777505	+	0.628877i	$0.783515\pi$
$74$	−1406.82	+	1121.90i	−2.21000	+	1.76241i
$75$	258.481	−	536.741i	0.397958	−	0.826367i
$76$	−492.460	−	237.156i	−0.743276	−	0.357943i
$77$			137.359i			0.203292i
$78$	−983.679	+	784.458i	−1.42795	+	1.13875i
$79$	−247.535	+	514.012i	−0.352530	+	0.732036i	−0.999536	−	0.0304487i	$-0.990306\pi$
$79$	−247.535	+	514.012i	−0.352530	+	0.732036i	0.647006	+	0.762485i	$0.276021\pi$
$80$	−333.024	+	691.532i	−0.465415	+	0.966445i
$81$	−8.31079	+	10.4214i	−0.0114003	+	0.0142955i
$82$	785.173	−	179.211i	1.05741	−	0.241348i
$83$	514.603			0.680542			0.340271	−	0.940327i	$-0.389481\pi$
$83$	514.603			0.680542			0.340271	+	0.940327i	$0.389481\pi$
$84$			763.111i			0.991217i
$85$	−76.6021	+	96.0560i	−0.0977490	+	0.122573i
$86$	972.174	−	2018.74i	1.21898	−	2.53124i
$87$			1122.52i			1.38330i
$88$	−802.471	−	1006.27i	−0.972088	−	1.21896i
$89$	−485.482	+	110.808i	−0.578213	+	0.131973i	−0.501619	−	0.865089i	$-0.667262\pi$
$89$	−485.482	+	110.808i	−0.578213	+	0.131973i	−0.0765948	+	0.997062i	$0.524405\pi$
$90$	−1007.50	−	1263.37i	−1.18000	−	1.47967i
$91$	119.810	+	95.5453i	0.138017	+	0.110064i
$92$	−1623.37	+	2035.65i	−1.83966	+	2.30686i
$93$	1375.51			1.53369
$94$	−1390.52	+	1108.90i	−1.52575	+	1.21675i
$95$	−99.1597	−	205.907i	−0.107090	−	0.222375i
$96$	−735.317	−	922.058i	−0.781750	−	0.980283i
$97$	−227.636	+	109.624i	−0.238277	+	0.114748i	−0.549212	−	0.835683i	$-0.685072\pi$
$97$	−227.636	+	109.624i	−0.238277	+	0.114748i	0.310935	+	0.950431i	$0.399358\pi$
$98$	−1559.44	+	355.932i	−1.60742	+	0.366883i
$99$	1125.63	−	256.917i	1.14272	−	0.260819i
$100$	1124.08	−	541.330i	1.12408	−	0.541330i
$101$	982.433	+	1231.93i	0.967878	+	1.21368i	0.976895	+	0.213722i	$0.0685586\pi$
$101$	982.433	+	1231.93i	0.967878	+	1.21368i	−0.00901624	+	0.999959i	$0.502870\pi$
$102$	−307.894	−	639.348i	−0.298883	−	0.620637i
$103$	1421.75	−	1133.81i	1.36009	−	1.08463i	0.372422	−	0.928063i	$-0.378527\pi$
$103$	1421.75	−	1133.81i	1.36009	−	1.08463i	0.987667	−	0.156571i	$-0.0500441\pi$
$104$	−1435.90			−1.35386
$105$	−198.938	+	249.460i	−0.184899	+	0.231856i
$106$	298.771	+	238.262i	0.273766	+	0.218321i
$107$	−121.634	−	152.524i	−0.109895	−	0.137805i	0.723842	−	0.689966i	$-0.242375\pi$
$107$	−121.634	−	152.524i	−0.109895	−	0.137805i	−0.833737	+	0.552162i	$0.813803\pi$
$108$	2368.93	−	540.692i	2.11065	−	0.481742i
$109$	−1019.25	−	1278.10i	−0.895657	−	1.12312i	−0.991806	−	0.127751i	$-0.959224\pi$
$109$	−1019.25	−	1278.10i	−0.895657	−	1.12312i	0.0961497	−	0.995367i	$-0.469347\pi$
$110$		−	987.534i		−	0.855979i
$111$	1295.79	−	2690.74i	1.10803	−	2.30085i
$112$	−336.657	+	422.155i	−0.284028	+	0.356160i
$113$			1411.04i			1.17469i	0.809338	+	0.587344i	$0.199826\pi$
$113$			1411.04i			1.17469i	−0.809338	+	0.587344i	$0.800174\pi$
$114$	1320.01			1.08448
$115$	−1061.36	+	242.248i	−0.860629	+	0.196433i
$116$	−1465.75	+	1837.99i	−1.17320	+	1.47115i
$117$	558.879	−	1160.52i	0.441610	−	0.917013i
$118$	327.069	−	679.166i	0.255162	−	0.529850i
$119$	−67.5742	+	53.8886i	−0.0520547	+	0.0415123i
$120$		−	2989.72i		−	2.27436i
$121$	−563.467	−	271.351i	−0.423341	−	0.203870i
$122$	−1555.74	+	3230.53i	−1.15451	+	2.39737i
$123$	−1045.06	+	833.410i	−0.766099	+	0.610944i
$124$	2252.21	+	1796.08i	1.63109	+	1.30075i
$125$	1404.37	+	320.538i	1.00489	+	0.229359i
$126$	−493.226	−	1024.19i	−0.348731	−	0.724147i
$127$	−1868.53	+	899.838i	−1.30555	+	0.628722i	−0.951830	−	0.306627i	$-0.900799\pi$
$127$	−1868.53	+	899.838i	−1.30555	+	0.628722i	−0.353725	+	0.935349i	$0.615085\pi$
$128$			1755.05i			1.21192i
$129$			3718.84i			2.53818i
$130$	−861.366	−	686.917i	−0.581130	−	0.463435i
$131$	−2394.16	−	546.452i	−1.59679	−	0.364456i	−0.670688	−	0.741740i	$-0.734001\pi$
$131$	−2394.16	−	546.452i	−1.59679	−	0.364456i	−0.926098	+	0.377284i	$0.876858\pi$
$132$	3531.81	+	1700.83i	2.32883	+	1.12150i
$133$	−35.7758	−	156.744i	−0.0233245	−	0.102191i
$134$	−605.139	−	758.820i	−0.390120	−	0.489195i
$135$	915.356	+	440.812i	0.583565	+	0.281030i
$136$	180.211	−	789.556i	0.113625	−	0.497822i
$137$	−133.234	−	583.736i	−0.0830872	−	0.364029i	0.916243	−	0.400623i	$-0.131206\pi$
$137$	−133.234	−	583.736i	−0.0830872	−	0.364029i	−0.999330	+	0.0365941i	$0.988349\pi$
$138$	1399.19	−	6130.27i	0.863096	−	3.78147i
$139$	251.809	−	522.886i	0.153656	−	0.319069i	−0.809904	−	0.586562i	$-0.800481\pi$
$139$	251.809	−	522.886i	0.153656	−	0.319069i	0.963560	+	0.267493i	$0.0861953\pi$
$140$	−651.470	+	148.694i	−0.393281	+	0.0897637i
$141$	1280.78	−	2659.56i	0.764970	−	1.58848i
$142$	1134.19	+	4969.21i	0.670275	+	2.93667i
$143$	709.235	−	341.550i	0.414750	−	0.199733i
$144$	4089.15	+	1969.23i	2.36641	+	1.13960i
$145$	−958.303	+	218.726i	−0.548847	+	0.125271i
$146$	848.797	+	1064.36i	0.481144	+	0.603335i
$147$	2075.61	−	1655.24i	1.16458	−	0.928722i
$148$	5635.16	−	2713.75i	3.12978	−	1.50722i
$149$	−2012.64	−	1605.03i	−1.10659	−	0.882476i	−0.112786	−	0.993619i	$-0.535977\pi$
$149$	−2012.64	−	1605.03i	−1.10659	−	0.882476i	−0.993804	+	0.111143i	$0.964549\pi$
$150$	−1878.61	+	2355.70i	−1.02258	+	1.28228i
$151$	668.098	−	1387.32i	0.360060	−	0.747672i	−0.639721	−	0.768607i	$-0.720950\pi$
$151$	668.098	−	1387.32i	0.360060	−	0.747672i	0.999781	+	0.0209355i	$0.00666447\pi$
$152$	1177.81	+	939.269i	0.628505	+	0.501216i
$153$	567.996	+	452.961i	0.300129	+	0.239345i
$154$	154.589	−	677.300i	0.0808906	−	0.354405i
$155$	268.020	+	1174.27i	0.138890	+	0.608516i
$156$	3940.22	−	1897.51i	2.02224	−	0.973861i
$157$	−391.959	+	1717.28i	−0.199247	+	0.872956i	0.772140	+	0.635452i	$0.219186\pi$
$157$	−391.959	+	1717.28i	−0.199247	+	0.872956i	−0.971387	+	0.237504i	$0.923671\pi$
$158$	1799.05	−	2255.94i	0.905854	−	1.13590i
$159$	−618.350	−	141.134i	−0.308417	−	0.0703942i
$160$	643.886	−	807.408i	0.318148	−	0.398945i
$161$	−765.855			−0.374893
$162$	52.7081	−	42.0333i	0.0255626	−	0.0203855i
$163$	153.746	+	673.606i	0.0738793	+	0.323687i	0.998340	−	0.0575901i	$-0.0183417\pi$
$163$	153.746	+	673.606i	0.0738793	+	0.323687i	−0.924461	+	0.381277i	$0.875485\pi$
$164$	−2799.39			−1.33290
$165$	711.152	+	1476.72i	0.335534	+	0.696743i
$166$	−2537.44	−	579.154i	−1.18641	−	0.270790i
$167$	−406.062	−	843.197i	−0.188156	−	0.390710i	0.785457	−	0.618917i	$-0.212428\pi$
$167$	−406.062	−	843.197i	−0.188156	−	0.390710i	−0.973613	+	0.228207i	$0.926714\pi$
$168$	468.013	−	2050.50i	0.214929	−	0.941664i
$169$	−293.456	+	1285.72i	−0.133571	+	0.585214i
$170$	485.820	−	387.429i	0.219181	−	0.174791i
$171$	−1217.57	+	586.348i	−0.544500	+	0.262217i
$172$	−4855.91	+	6089.12i	−2.15267	+	2.69936i
$173$	−2500.87	−	1204.35i	−1.09906	−	0.529279i	−0.205697	−	0.978616i	$-0.565946\pi$
$173$	−2500.87	−	1204.35i	−1.09906	−	0.529279i	−0.893363	+	0.449336i	$0.851661\pi$
$174$	1263.33	−	5535.03i	0.550420	−	2.41155i
$175$	330.640	+	159.228i	0.142823	+	0.0687800i
$176$	1203.46	+	2499.02i	0.515423	+	1.07029i
$177$			1251.13i			0.531303i
$178$	2518.56			1.06053
$179$	−3071.46	+	701.040i	−1.28252	+	0.292727i	−0.808872	−	0.587985i	$-0.799921\pi$
$179$	−3071.46	+	701.040i	−1.28252	+	0.292727i	−0.473651	+	0.880713i	$0.657064\pi$
$180$	2437.02	+	5060.53i	1.00914	+	2.09550i
$181$	1494.15	+	1873.60i	0.613585	+	0.769412i	0.987426	−	0.158081i	$-0.0505307\pi$
$181$	1494.15	+	1873.60i	0.613585	+	0.769412i	−0.373841	+	0.927493i	$0.621959\pi$
$182$	−483.237	−	605.960i	−0.196813	−	0.246795i
$183$		−	5951.15i		−	2.40395i
$184$	5610.51	−	4474.23i	2.24789	−	1.79263i
$185$	2549.58	+	581.926i	1.01324	+	0.231265i
$186$	−6782.44	−	1548.05i	−2.67372	−	0.610260i
$187$	98.7959	+	432.853i	0.0386346	+	0.169269i
$188$	5569.84	−	2682.30i	2.16076	−	1.04057i
$189$	558.791	+	445.621i	0.215059	+	0.171504i
$190$	257.208	+	1126.90i	0.0982095	+	0.430284i
$191$	742.930			0.281448			0.140724	−	0.990049i	$-0.455057\pi$
$191$	742.930			0.281448			0.140724	+	0.990049i	$0.455057\pi$
$192$	−454.472	−	943.721i	−0.170827	−	0.354725i
$193$	−2311.74	−	1113.28i	−0.862192	−	0.415210i	−0.0501033	−	0.998744i	$-0.515955\pi$
$193$	−2311.74	−	1113.28i	−0.862192	−	0.415210i	−0.812088	+	0.583534i	$0.801669\pi$
$194$	1245.82	−	284.350i	0.461054	−	0.105233i
$195$	1782.72	+	406.895i	0.654684	+	0.149427i
$196$	5559.89			2.02620
$197$	1207.29	+	2487.54i	0.436627	+	0.899643i
$197$	1207.29	+	2487.54i	0.436627	+	0.899643i
$198$	−5839.46			−2.09592
$199$	−4264.88	−	973.432i	−1.51924	−	0.346758i	−0.620139	−	0.784492i	$-0.712924\pi$
$199$	−4264.88	−	973.432i	−1.51924	−	0.346758i	−0.899105	+	0.437734i	$0.855781\pi$
$200$	−3352.44	+	765.173i	−1.18527	+	0.270530i
$201$	1451.35	+	698.933i	0.509305	+	0.245268i
$202$	−3457.79	−	7180.16i	−1.20440	−	2.50096i
$203$	−691.491			−0.239080
$204$	548.869	+	2404.75i	0.188375	+	0.825326i
$205$	−915.118	−	729.782i	−0.311779	−	0.248635i
$206$	−8286.50	+	3990.57i	−2.80266	+	1.34969i
$207$	1432.46	+	6276.01i	0.480979	+	2.10731i
$208$	3016.85	+	688.577i	1.00568	+	0.229540i
$209$	−805.176	−	183.776i	−0.266484	−	0.0608233i
$210$	1261.69	−	1006.16i	0.414595	−	0.330628i
$211$		−	2905.68i		−	0.948033i	−0.880516	−	0.474017i	$-0.842804\pi$
$211$		−	2905.68i		−	0.948033i	0.880516	−	0.474017i	$-0.157196\pi$
$212$	−828.180	−	1038.51i	−0.268300	−	0.336438i
$213$	−5274.49	−	6614.00i	−1.69672	−	2.12762i
$214$	428.105	+	888.970i	0.136751	+	0.283966i
$215$	−3174.79	+	724.624i	−1.00706	+	0.229856i
$216$	−6696.98			−2.10959
$217$			847.331i			0.265072i
$218$	3587.37	+	7449.25i	1.11453	+	2.31434i
$219$	−2035.73	−	980.358i	−0.628138	−	0.302495i
$220$	−763.824	+	3346.53i	−0.234077	+	1.02556i
$221$	446.273	+	214.914i	0.135835	+	0.0654147i
$222$	−9417.66	+	11809.4i	−2.84717	+	3.57024i
$223$	−3963.09	+	1908.52i	−1.19008	+	0.573113i	−0.920833	−	0.389958i	$-0.872489\pi$
$223$	−3963.09	+	1908.52i	−1.19008	+	0.573113i	−0.269248	+	0.963071i	$0.586775\pi$
$224$	568.001	−	452.966i	0.169425	−	0.135112i
$225$	686.406	−	3007.34i	0.203380	−	0.891065i
$226$	1588.04	−	6957.67i	0.467411	−	2.04786i
$227$	−43.3395	−	89.9955i	−0.0126720	−	0.0263137i	0.894537	−	0.446994i	$-0.147506\pi$
$227$	−43.3395	−	89.9955i	−0.0126720	−	0.0263137i	−0.907209	+	0.420681i	$0.861791\pi$
$228$	−4473.23	−	1020.99i	−1.29933	−	0.296563i
$229$	450.892	+	936.286i	0.130112	+	0.270181i	0.955840	−	0.293888i	$-0.0949493\pi$
$229$	450.892	+	936.286i	0.130112	+	0.270181i	−0.825727	+	0.564069i	$0.809235\pi$
$230$	5506.06			1.57852
$231$	256.576	+	1124.13i	0.0730799	+	0.320184i
$232$	5065.74	−	4039.79i	1.43354	−	1.14321i
$233$	2411.10			0.677925			0.338962	−	0.940800i	$-0.389924\pi$
$233$	2411.10			0.677925			0.338962	+	0.940800i	$0.389924\pi$
$234$	−4061.86	+	5093.41i	−1.13475	+	1.42293i
$235$	2520.03	+	575.181i	0.699527	+	0.159663i
$236$	−1633.67	+	2048.56i	−0.450606	+	0.565043i
$237$	−1065.67	+	4669.00i	−0.292078	+	1.27968i
$238$	393.848	−	189.667i	0.107266	−	0.0516567i
$239$	−799.412	−	3502.45i	−0.216359	−	0.947929i	−0.960143	−	0.279509i	$-0.909828\pi$
$239$	−799.412	−	3502.45i	−0.216359	−	0.947929i	0.743784	−	0.668420i	$-0.233029\pi$
$240$	−1433.71	+	6281.49i	−0.385606	+	1.68945i
$241$	855.419	+	682.174i	0.228641	+	0.182335i	0.731109	−	0.682261i	$-0.239003\pi$
$241$	855.419	+	682.174i	0.228641	+	0.182335i	−0.502468	+	0.864596i	$0.667575\pi$
$242$	2472.99	+	1972.15i	0.656901	+	0.523861i
$243$	−1667.73	+	3463.07i	−0.440267	+	0.914223i
$244$	7770.77	−	9744.24i	2.03882	−	2.55660i
$245$	1817.52	+	1449.43i	0.473948	+	0.377961i
$246$	6091.03	−	2933.28i	1.57866	−	0.760241i
$247$	−720.368	+	574.474i	−0.185570	+	0.147987i
$248$	−4950.23	−	6207.39i	−1.26750	−	1.58939i
$249$	4211.46	−	961.237i	1.07185	−	0.244642i
$250$	−6564.02	−	3161.07i	−1.66058	−	0.799694i
$251$	5882.83	−	2833.02i	1.47937	−	0.712426i	0.491959	−	0.870618i	$-0.336281\pi$
$251$	5882.83	−	2833.02i	1.47937	−	0.712426i	0.987408	+	0.158193i	$0.0505667\pi$
$252$	879.253	+	3852.26i	0.219792	+	0.962974i
$253$	−1706.95	+	3544.51i	−0.424169	+	0.880797i
$254$	10226.2	−	2334.06i	2.52618	−	0.576584i
$255$	−447.479	+	929.199i	−0.109891	+	0.228191i
$256$	1753.07	−	7680.71i	0.427996	−	1.87517i
$257$	412.589	+	1807.67i	0.100142	+	0.438752i	0.999997	+	0.00256171i	$0.000815419\pi$
$257$	412.589	+	1807.67i	0.100142	+	0.438752i	−0.899854	+	0.436190i	$0.856327\pi$
$258$	4185.33	−	18337.1i	1.00995	−	4.42488i
$259$	1657.54	+	798.227i	0.397661	+	0.191504i
$260$	2387.67	+	2994.04i	0.569527	+	0.714164i
$261$	1293.37	+	5666.61i	0.306734	+	1.34389i
$262$	11190.3	+	5388.97i	2.63870	+	1.27073i
$263$	5057.30	+	1154.30i	1.18573	+	0.270635i	0.769513	−	0.638631i	$-0.220499\pi$
$263$	5057.30	+	1154.30i	1.18573	+	0.270635i	0.416216	+	0.909266i	$0.363356\pi$
$264$	−8446.97	−	6736.23i	−1.96922	−	1.57040i
$265$		−	555.388i		−	0.128744i
$266$			813.147i			0.187433i
$267$	−3766.15	+	1813.68i	−0.863239	+	0.415714i
$268$	1463.76	+	3039.53i	0.333632	+	0.692793i
$269$	−6221.12	−	1419.93i	−1.41007	−	0.321839i	−0.551345	−	0.834278i	$-0.685885\pi$
$269$	−6221.12	−	1419.93i	−1.41007	−	0.321839i	−0.858724	+	0.512439i	$0.828742\pi$
$270$	−4017.39	−	3203.76i	−0.905522	−	0.722129i
$271$	3833.82	−	3057.37i	0.859365	−	0.685320i	−0.0912050	−	0.995832i	$-0.529072\pi$
$271$	3833.82	−	3057.37i	0.859365	−	0.685320i	0.950570	+	0.310512i	$0.100500\pi$
$272$	−757.256	+	1572.46i	−0.168807	+	0.350530i
$273$	1158.98	+	558.137i	0.256941	+	0.123736i
$274$			3028.28i			0.667682i
$275$	1473.87	−	1175.37i	0.323192	−	0.257737i
$276$	−9483.10	+	19691.9i	−2.06817	+	4.29460i
$277$	676.200	−	1404.14i	0.146675	−	0.304573i	−0.814668	−	0.579928i	$-0.803081\pi$
$277$	676.200	−	1404.14i	0.146675	−	0.304573i	0.961343	+	0.275354i	$0.0887951\pi$
$278$	−1830.11	+	2294.89i	−0.394830	+	0.495101i
$279$	6943.69	−	1584.85i	1.48999	−	0.340081i
$280$	1841.71			0.393084
$281$		−	5235.77i		−	1.11153i	−0.831339	−	0.555765i	$-0.812425\pi$
$281$		−	5235.77i		−	1.11153i	0.831339	−	0.555765i	$-0.187575\pi$
$282$	−9308.51	+	11672.5i	−1.96565	+	2.46485i
$283$	−1443.36	+	2997.18i	−0.303177	+	0.629553i	−0.995781	−	0.0917649i	$-0.970749\pi$
$283$	−1443.36	+	2997.18i	−0.303177	+	0.629553i	0.692604	+	0.721318i	$0.256463\pi$
$284$		−	17716.8i		−	3.70175i
$285$	−1196.13	−	1499.90i	−0.248606	−	0.311742i
$286$	−3881.54	+	885.936i	−0.802518	+	0.183170i
$287$	−513.393	−	643.774i	−0.105591	−	0.132407i
$288$	−4774.34	−	3807.41i	−0.976843	−	0.779006i
$289$	2889.02	−	3622.72i	0.588036	−	0.737374i
$290$	4971.43			1.00666
$291$	−1658.18	+	1322.35i	−0.334035	+	0.266384i
$292$	−2053.14	−	4263.39i	−0.411475	−	0.854438i
$293$	−5277.94	−	6618.32i	−1.05236	−	1.31961i	−0.945602	−	0.325327i	$-0.894526\pi$
$293$	−5277.94	−	6618.32i	−1.05236	−	1.31961i	−0.106754	−	0.994285i	$-0.534046\pi$
$294$	−12097.4	+	5825.82i	−2.39978	+	1.15568i
$295$	−1068.09	+	243.785i	−0.210803	+	0.0481144i
$296$	−16806.2	+	3835.90i	−3.30013	+	0.753233i
$297$	3307.86	−	1592.98i	0.646267	−	0.311226i
$298$	8117.71	+	10179.3i	1.57801	+	1.97876i
$299$	1904.33	+	3954.39i	0.368329	+	0.764843i
$300$	8188.23	−	6529.89i	1.57582	−	1.25668i
$301$	−2290.86			−0.438681
$302$	−4855.65	+	6088.79i	−0.925202	+	1.16017i
$303$	10341.3	+	8246.90i	1.96070	+	1.56360i
$304$	−2024.18	−	2538.24i	−0.381890	−	0.478875i
$305$	5080.52	−	1159.60i	0.953802	−	0.217699i
$306$	−2290.93	−	2872.74i	−0.427987	−	0.536678i
$307$			2403.66i			0.446854i	0.974721	+	0.223427i	$0.0717245\pi$
$307$			2403.66i			0.446854i	−0.974721	+	0.223427i	$0.928275\pi$
$308$	−1047.74	+	2175.65i	−0.193832	+	0.402497i
$309$	9517.59	−	11934.7i	1.75222	−	2.19722i
$310$		−	6091.83i		−	1.11611i
$311$	5873.77			1.07097			0.535483	−	0.844546i	$-0.320129\pi$
$311$	5873.77			1.07097			0.535483	+	0.844546i	$0.320129\pi$
$312$	−11751.2	+	2682.14i	−2.13231	+	0.486687i
$313$	−4376.66	+	5488.16i	−0.790363	+	0.991084i	0.209549	+	0.977798i	$0.432800\pi$
$313$	−4376.66	+	5488.16i	−0.790363	+	0.991084i	−0.999912	+	0.0132855i	$0.995771\pi$
$314$	3865.40	−	8026.58i	0.694703	−	1.44257i
$315$	−716.831	+	1488.52i	−0.128219	+	0.266249i
$316$	−7841.48	+	6253.37i	−1.39594	+	1.11323i
$317$		−	5942.72i		−	1.05292i	−0.850199	−	0.526461i	$-0.823519\pi$
$317$		−	5942.72i		−	1.05292i	0.850199	−	0.526461i	$-0.176481\pi$
$318$	2890.17	+	1391.83i	0.509662	+	0.245440i
$319$	−1541.21	+	3200.35i	−0.270504	+	0.561708i
$320$	717.103	−	571.870i	0.125273	−	0.0999017i
$321$	−1280.34	−	1021.04i	−0.222623	−	0.177536i
$322$	3776.33	+	861.923i	0.653561	+	0.149171i
$323$	−225.477	−	468.207i	−0.0388417	−	0.0806556i
$324$	−211.127	+	101.674i	−0.0362015	+	0.0174337i
$325$		−	2103.14i		−	0.358958i
$326$		−	3494.50i		−	0.593688i
$327$	−10728.8	−	8555.96i	−1.81439	−	1.44693i
$328$	7522.04	+	1716.86i	1.26627	+	0.289017i
$329$	1638.33	+	788.976i	0.274540	+	0.132212i
$330$	−1844.64	−	8081.88i	−0.307709	−	1.34816i
$331$	−1002.72	−	1257.37i	−0.166509	−	0.208795i	0.691576	−	0.722304i	$-0.256917\pi$
$331$	−1002.72	−	1257.37i	−0.166509	−	0.208795i	−0.858084	+	0.513509i	$0.828345\pi$
$332$	8150.86	+	3925.25i	1.34740	+	0.648873i
$333$	3441.03	−	15076.1i	0.566268	−	2.48098i
$334$	1053.27	+	4614.70i	0.172553	+	0.756003i
$335$	−313.883	+	1375.21i	−0.0511918	+	0.224286i
$336$	−1966.62	+	4083.72i	−0.319309	+	0.663052i
$337$	−3134.39	+	715.404i	−0.506650	+	0.115640i	−0.468203	−	0.883621i	$-0.655098\pi$
$337$	−3134.39	+	715.404i	−0.506650	+	0.115640i	−0.0384473	+	0.999261i	$0.512241\pi$
$338$	2893.99	−	6009.43i	0.465717	−	0.967071i
$339$	2635.72	+	11547.8i	0.422279	+	1.85012i
$340$	−1946.00	+	937.143i	−0.310402	+	0.149482i
$341$	3921.60	+	1888.54i	0.622776	+	0.299913i
$342$	6663.56	−	1520.91i	1.05358	−	0.240472i
$343$	2125.52	+	2665.32i	0.334598	+	0.419573i
$344$	16782.4	−	13383.5i	2.63037	−	2.09765i
$345$	−8233.56	+	3965.07i	−1.28487	+	0.618760i
$346$	10976.0	+	8753.09i	1.70542	+	1.36003i
$347$	−2270.66	+	2847.32i	−0.351284	+	0.440496i	−0.925809	−	0.377991i	$-0.876615\pi$
$347$	−2270.66	+	2847.32i	−0.351284	+	0.440496i	0.574526	+	0.818487i	$0.305187\pi$
$348$	−8562.31	+	17779.8i	−1.31893	+	2.73879i
$349$	−3961.91	−	3159.51i	−0.607667	−	0.484599i	0.270649	−	0.962678i	$-0.412762\pi$
$349$	−3961.91	−	3159.51i	−0.607667	−	0.484599i	−0.878317	+	0.478079i	$0.841333\pi$
$350$	−1451.14	−	1157.25i	−0.221620	−	0.176736i
$351$	911.445	−	3993.30i	0.138602	−	0.607255i
$352$	−830.438	−	3638.39i	−0.125746	−	0.550928i
$353$	−4819.09	+	2320.75i	−0.726613	+	0.349918i	−0.760351	−	0.649513i	$-0.774973\pi$
$353$	−4819.09	+	2320.75i	−0.726613	+	0.349918i	0.0337383	+	0.999431i	$0.489259\pi$
$354$	1408.07	−	6169.16i	0.211407	−	0.926235i
$355$	4618.65	−	5791.61i	0.690514	−	0.865877i
$356$	−8534.82	−	1948.02i	−1.27063	−	0.290013i
$357$	−452.360	+	567.242i	−0.0670629	+	0.0840942i
$358$	15933.9			2.35233
$359$	−4281.72	+	3414.56i	−0.629472	+	0.501987i	−0.885474	−	0.464689i	$-0.846166\pi$
$359$	−4281.72	+	3414.56i	−0.629472	+	0.501987i	0.256002	+	0.966676i	$0.417595\pi$
$360$	−3444.75	−	15092.4i	−0.504317	−	2.20956i
$361$	−5892.33			−0.859065
$362$	−5258.82	−	10920.0i	−0.763528	−	1.58548i
$363$	−5118.22	−	1168.20i	−0.740047	−	0.168911i
$364$	1168.89	+	2427.23i	0.168315	+	0.349510i
$365$	440.267	−	1928.94i	0.0631360	−	0.276617i
$366$	−6697.66	+	29344.4i	−0.956537	+	4.19086i
$367$	−3145.42	+	2508.39i	−0.447383	+	0.356776i	−0.821117	−	0.570760i	$-0.806649\pi$
$367$	−3145.42	+	2508.39i	−0.447383	+	0.356776i	0.373734	+	0.927536i	$0.378077\pi$
$368$	−13933.4	+	6709.98i	−1.97372	+	0.950495i
$369$	−4315.33	+	5411.25i	−0.608800	+	0.763411i
$370$	−11916.8	−	5738.81i	−1.67438	−	0.806341i
$371$	86.9408	−	380.912i	0.0121664	−	0.0533046i
$372$	21786.8	+	10492.0i	3.03654	+	1.46232i
$373$	−1948.19	−	4045.46i	−0.270438	−	0.561571i	0.720879	−	0.693061i	$-0.243738\pi$
$373$	−1948.19	−	4045.46i	−0.270438	−	0.561571i	−0.991317	+	0.131490i	$0.958024\pi$
$374$		−	2245.53i		−	0.310464i
$375$	12092.0			1.66514
$376$	−16611.4	+	3791.44i	−2.27837	+	0.520023i
$377$	1719.42	+	3570.42i	0.234894	+	0.487761i
$378$	−2253.81	−	2826.19i	−0.306676	−	0.384559i
$379$	−426.356	−	534.634i	−0.0577848	−	0.0724599i	0.752099	−	0.659050i	$-0.229041\pi$
$379$	−426.356	−	534.634i	−0.0577848	−	0.0724599i	−0.809884	+	0.586590i	$0.800470\pi$
$380$		−	4017.75i		−	0.542385i
$381$	−13611.1	+	10854.5i	−1.83022	+	1.45956i
$382$	−3663.29	−	836.122i	−0.490655	−	0.111989i
$383$	−4753.47	−	1084.95i	−0.634180	−	0.144747i	−0.106668	−	0.994295i	$-0.534018\pi$
$383$	−4753.47	−	1084.95i	−0.634180	−	0.144747i	−0.527512	+	0.849547i	$0.676875\pi$
$384$	3278.30	+	14363.2i	0.435664	+	1.90877i
$385$	−909.682	+	438.080i	−0.120420	+	0.0579912i
$386$	10146.0	+	8091.16i	1.33787	+	1.06691i
$387$	4284.83	+	18773.1i	0.562817	+	2.46586i
$388$	−4441.73			−0.581172
$389$	−5299.96	−	11005.5i	−0.690793	−	1.43445i	−0.890681	−	0.454628i	$-0.849772\pi$
$389$	−5299.96	−	11005.5i	−0.690793	−	1.43445i	0.199888	−	0.979819i	$-0.435942\pi$
$390$	−8332.44	−	4012.69i	−1.08187	−	0.521002i
$391$	−2413.40	+	550.843i	−0.312151	+	0.0712464i
$392$	−14939.6	−	3409.86i	−1.92490	−	0.439347i
$393$	−20614.3			−2.64594
$394$	−3153.40	−	13624.4i	−0.403213	−	1.74211i
$395$	−4193.58			−0.534183
$396$	19788.6	+	4516.63i	2.51115	+	0.573154i
$397$	−6865.68	+	1567.05i	−0.867956	+	0.198105i	−0.633237	−	0.773958i	$-0.718274\pi$
$397$	−6865.68	+	1567.05i	−0.867956	+	0.198105i	−0.234719	+	0.972063i	$0.575417\pi$
$398$	19934.1	+	9599.73i	2.51056	+	1.20902i
$399$	−585.570	−	1215.95i	−0.0734716	−	0.152565i
$400$	7410.51			0.926313
$401$	−802.134	−	3514.38i	−0.0998919	−	0.437655i	−0.999998	−	0.00198432i	$-0.999368\pi$
$401$	−802.134	−	3514.38i	−0.0998919	−	0.437655i	0.900106	−	0.435671i	$-0.143489\pi$
$402$	−6369.81	−	5079.76i	−0.790292	−	0.630237i
$403$	4375.08	−	2106.93i	0.540790	−	0.260431i
$404$	6164.04	+	27006.4i	0.759091	+	3.32579i
$405$	−95.5230	−	21.8025i	−0.0117199	−	0.00267500i
$406$	3409.65	+	778.231i	0.416794	+	0.0951305i
$407$	7388.68	−	5892.27i	0.899860	−	0.717615i
$408$		−	6798.26i		−	0.824912i
$409$	−1923.71	−	2412.25i	−0.232570	−	0.291634i	0.651828	−	0.758367i	$-0.274002\pi$
$409$	−1923.71	−	2412.25i	−0.232570	−	0.291634i	−0.884398	+	0.466733i	$0.845431\pi$
$410$	3691.00	+	4628.37i	0.444599	+	0.557510i
$411$	−2180.75	−	4528.37i	−0.261723	−	0.543474i
$412$	31167.6	−	7113.81i	3.72699	−	0.850661i
$413$	−770.714			−0.0918265
$414$		−	32558.3i		−	3.86511i
$415$	1641.22	+	3408.04i	0.194131	+	0.403118i
$416$	−3751.19	−	1806.48i	−0.442108	−	0.212908i
$417$	1084.07	−	4749.60i	0.127307	−	0.557768i
$418$	3763.39	+	1812.35i	0.440367	+	0.212070i
$419$	−1084.06	+	1359.37i	−0.126395	+	0.158495i	−0.841003	−	0.541031i	$-0.818034\pi$
$419$	−1084.06	+	1359.37i	−0.126395	+	0.158495i	0.714607	+	0.699526i	$0.246606\pi$
$420$	−5053.82	+	2433.79i	−0.587145	+	0.282754i
$421$	1930.01	−	1539.13i	0.223427	−	0.178177i	−0.505379	−	0.862898i	$-0.668647\pi$
$421$	1930.01	−	1539.13i	0.223427	−	0.178177i	0.728806	+	0.684720i	$0.240076\pi$
$422$	−3270.16	+	14327.5i	−0.377225	+	1.65273i
$423$	3401.15	−	14901.4i	0.390944	−	1.71284i
$424$	1588.43	+	3298.41i	0.181937	+	0.377795i
$425$	1156.46	+	263.954i	0.131991	+	0.0301262i
$426$	18564.2	+	38548.9i	2.11136	+	4.38428i
$427$	3666.00			0.415480
$428$	−763.165	−	3343.64i	−0.0861892	−	0.377619i
$429$	5166.32	−	4120.00i	0.581427	−	0.463673i
$430$	16470.0			1.84710
$431$	4064.02	−	5096.11i	0.454192	−	0.569539i	−0.501030	−	0.865430i	$-0.667045\pi$
$431$	4064.02	−	5096.11i	0.454192	−	0.569539i	0.955222	+	0.295891i	$0.0956167\pi$
$432$	14070.5	+	3211.51i	1.56706	+	0.357671i
$433$	5741.55	−	7199.68i	0.637232	−	0.799063i	−0.353422	−	0.935464i	$-0.614982\pi$
$433$	5741.55	−	7199.68i	0.637232	−	0.799063i	0.990654	+	0.136401i	$0.0435534\pi$
$434$	953.620	−	4178.08i	0.105473	−	0.462107i
$435$	−7434.09	+	3580.07i	−0.819396	+	0.394601i
$436$	−6395.05	−	28018.6i	−0.702448	−	3.07763i
$437$	1024.66	−	4489.31i	0.112165	−	0.491426i
$438$	8934.61	+	7125.11i	0.974685	+	0.777285i
$439$	8514.72	+	6790.26i	0.925707	+	0.738227i	0.965342	−	0.260987i	$-0.0840480\pi$
$439$	8514.72	+	6790.26i	0.925707	+	0.738227i	−0.0396348	+	0.999214i	$0.512619\pi$
$440$	4104.84	−	8523.78i	0.444751	−	0.923534i
$441$	8570.71	−	10747.3i	0.925463	−	1.16049i
$442$	−1958.64	−	1561.96i	−0.210776	−	0.168088i
$443$	605.667	−	291.674i	0.0649574	−	0.0312818i	−0.401123	−	0.916024i	$-0.631380\pi$
$443$	605.667	−	291.674i	0.0649574	−	0.0312818i	0.466080	+	0.884742i	$0.345666\pi$
$444$	41048.5	−	32735.1i	4.38755	−	3.49896i
$445$	−2282.19	−	2861.78i	−0.243115	−	0.304857i
$446$	21689.4	−	4950.46i	2.30274	−	0.525586i
$447$	−19469.3	−	9375.92i	−2.06010	−	0.992094i
$448$	581.346	−	279.961i	0.0613080	−	0.0295244i
$449$	2171.74	+	9515.02i	0.228265	+	1.00009i	0.951054	+	0.309025i	$0.100003\pi$
$449$	2171.74	+	9515.02i	0.228265	+	1.00009i	−0.722789	+	0.691068i	$0.757140\pi$
$450$	−6769.16	+	14056.3i	−0.709114	+	1.47249i
$451$	−4123.76	+	941.221i	−0.430555	+	0.0982713i
$452$	−10763.0	+	22349.7i	−1.12002	+	2.32575i
$453$	2876.24	−	12601.6i	0.298317	−	1.30701i
$454$	112.417	+	492.532i	0.0116212	+	0.0509156i
$455$	−250.653	+	1098.18i	−0.0258259	+	0.113151i
$456$	11393.5	+	5486.83i	1.17007	+	0.563475i
$457$	1781.57	+	2234.02i	0.182360	+	0.228672i	0.864606	−	0.502451i	$-0.167568\pi$
$457$	1781.57	+	2234.02i	0.182360	+	0.228672i	−0.682246	+	0.731123i	$0.738997\pi$
$458$	−1169.56	−	5124.16i	−0.119323	−	0.522786i
$459$	2081.41	+	1002.35i	0.211659	+	0.101930i
$460$	−18658.8	−	4258.75i	−1.89124	−	0.431664i
$461$	−2617.24	−	2087.18i	−0.264419	−	0.210867i	0.482301	−	0.876005i	$-0.339801\pi$
$461$	−2617.24	−	2087.18i	−0.264419	−	0.210867i	−0.746720	+	0.665139i	$0.768372\pi$
$462$		−	5831.71i		−	0.587264i
$463$			11834.6i			1.18790i	0.804501	+	0.593951i	$0.202433\pi$
$463$			11834.6i			1.18790i	−0.804501	+	0.593951i	$0.797567\pi$
$464$	−12580.5	+	6058.45i	−1.25870	+	0.606157i
$465$	4386.90	+	9109.50i	0.437501	+	0.908479i
$466$	−11888.8	−	2713.55i	−1.18184	−	0.269748i
$467$	365.121	+	291.174i	0.0361794	+	0.0288521i	0.641413	−	0.767196i	$-0.278349\pi$
$467$	365.121	+	291.174i	0.0361794	+	0.0288521i	−0.605233	+	0.796048i	$0.706920\pi$
$468$	17704.3	−	14118.7i	1.74868	−	1.39453i
$469$	−430.553	+	894.052i	−0.0423904	+	0.0880245i
$470$	−11778.6	−	5672.29i	−1.15597	−	0.556688i
$471$			14786.2i			1.44652i
$472$	5646.11	−	4502.62i	0.550600	−	0.439089i
$473$	−5105.90	+	10602.5i	−0.496341	+	1.03066i
$474$	10509.3	−	21822.9i	1.01838	−	2.11468i
$475$	−1375.74	+	1725.12i	−0.132891	+	0.166640i
$476$	−1481.36	+	338.111i	−0.142643	+	0.0325574i
$477$	−3284.11			−0.315239
$478$			18169.8i			1.73864i
$479$	6461.40	−	8102.33i	0.616344	−	0.772871i	−0.371481	−	0.928441i	$-0.621150\pi$
$479$	6461.40	−	8102.33i	0.616344	−	0.772871i	0.987825	+	0.155570i	$0.0497213\pi$
$480$	3761.33	−	7810.47i	0.357667	−	0.742703i
$481$		−	10543.3i		−	0.999444i
$482$	−3450.22	−	4326.43i	−0.326044	−	0.408846i
$483$	−6267.68	+	1430.56i	−0.590454	+	0.134767i
$484$	−6855.03	−	8595.94i	−0.643786	−	0.807282i
$485$	−1452.00	−	1157.93i	−0.135942	−	0.108410i
$486$	12120.8	−	15199.0i	1.13130	−	1.41861i
$487$	17074.4			1.58874			0.794369	−	0.607435i	$-0.207802\pi$
$487$	17074.4			1.58874			0.794369	+	0.607435i	$0.207802\pi$
$488$	−26856.4	+	21417.3i	−2.49125	+	1.98671i
$489$	2516.49	+	5225.54i	0.232719	+	0.483245i
$490$	−7330.73	−	9192.45i	−0.675855	−	0.847495i
$491$	5590.95	−	2692.46i	0.513882	−	0.247473i	−0.158925	−	0.987291i	$-0.550803\pi$
$491$	5590.95	−	2692.46i	0.513882	−	0.247473i	0.672807	+	0.739818i	$0.265088\pi$
$492$	−22909.9	+	5229.04i	−2.09931	+	0.479153i
$493$	−2179.06	+	497.357i	−0.199067	+	0.0454358i
$494$	4198.57	−	2021.93i	0.382394	−	0.184151i
$495$	5291.43	+	6635.25i	0.480469	+	0.602489i
$496$	7423.83	+	15415.8i	0.672056	+	1.39554i
$497$	4074.32	−	3249.16i	0.367723	−	0.293249i
$498$	−21848.0			−1.96592
$499$	2591.61	−	3249.78i	0.232498	−	0.291543i	−0.651873	−	0.758328i	$-0.726016\pi$
$499$	2591.61	−	3249.78i	0.232498	−	0.291543i	0.884371	+	0.466785i	$0.154588\pi$
$500$	19799.0	+	15789.2i	1.77088	+	1.41223i
$501$	−4898.20	−	6142.15i	−0.436797	−	0.547727i
$502$	−32195.9	+	7348.50i	−2.86250	+	0.653346i
$503$	8896.36	+	11155.7i	0.788607	+	0.988882i	0.999934	+	0.0114663i	$0.00364993\pi$
$503$	8896.36	+	11155.7i	0.788607	+	0.988882i	−0.211327	+	0.977415i	$0.567779\pi$
$504$		−	10890.4i		−	0.962491i
$505$	−5025.38	+	10435.3i	−0.442825	+	0.919535i
$506$	12405.9	−	15556.5i	1.08994	−	1.36674i
$507$			11070.3i			0.969725i
$508$	−36459.6			−3.18432
$509$	15123.6	−	3451.87i	1.31698	−	0.300592i	0.494396	−	0.869237i	$-0.335389\pi$
$509$	15123.6	−	3451.87i	1.31698	−	0.300592i	0.822583	+	0.568645i	$0.192532\pi$
$510$	3252.22	−	4078.15i	0.282374	−	0.354085i
$511$	603.914	−	1254.04i	0.0522810	−	0.108563i
$512$	−11196.4	+	23249.7i	−0.966441	+	2.00683i
$513$	−3359.78	+	2679.33i	−0.289158	+	0.230595i
$514$		−	9377.72i		−	0.804735i
$515$	12043.2	+	5799.70i	1.03046	+	0.496243i
$516$	−28366.3	+	58903.2i	−2.42007	+	5.02532i
$517$	7303.04	−	5823.98i	0.621252	−	0.495432i
$518$	−7274.74	−	5801.41i	−0.617054	−	0.492084i
$519$	−22716.5	−	5184.89i	−1.92128	−	0.438519i
$520$	−4579.50	−	9509.43i	−0.386201	−	0.801954i
$521$	−15131.9	+	7287.12i	−1.27244	+	0.612773i	−0.943435	−	0.331557i	$-0.892426\pi$
$521$	−15131.9	+	7287.12i	−1.27244	+	0.612773i	−0.329000	+	0.944330i	$0.606712\pi$
$522$		−	29397.0i		−	2.46488i
$523$			21111.7i			1.76511i	0.470211	+	0.882554i	$0.344178\pi$
$523$			21111.7i			1.76511i	−0.470211	+	0.882554i	$0.655822\pi$
$524$	−33753.2	−	26917.3i	−2.81396	−	2.24406i
$525$	3003.35	+	685.496i	0.249671	+	0.0569857i
$526$	−23637.8	−	11383.4i	−1.95943	−	0.943610i
$527$	609.445	+	2670.15i	0.0503754	+	0.220709i
$528$	14517.0	+	18203.7i	1.19653	+	1.50041i
$529$	−8800.58	−	4238.14i	−0.723316	−	0.348330i
$530$	−625.055	+	2738.55i	−0.0512277	+	0.224443i
$531$	1441.55	+	6315.83i	0.117811	+	0.516165i
$532$	628.942	−	2755.57i	0.0512558	−	0.224566i
$533$	−2047.47	+	4251.61i	−0.166389	+	0.345511i
$534$	20611.6	−	4704.47i	1.67032	−	0.381240i
$535$	622.188	−	1291.99i	0.0502795	−	0.104406i
$536$	−2069.03	−	9065.01i	−0.166732	−	0.730502i
$537$	−23827.0	+	11474.5i	−1.91473	+	0.922087i
$538$	29077.5	+	14003.0i	2.33015	+	1.12214i
$539$	8190.23	−	1869.37i	0.654505	−	0.149386i
$540$	11136.0	+	13964.2i	0.887443	+	1.11282i
$541$	15564.3	−	12412.1i	1.23690	−	0.986395i	0.237011	−	0.971507i	$-0.423832\pi$
$541$	15564.3	−	12412.1i	1.23690	−	0.986395i	0.999889	−	0.0148882i	$-0.00473925\pi$
$542$	−22344.9	+	10760.8i	−1.77084	+	0.852793i
$543$	15727.7	+	12542.4i	1.24298	+	0.991245i
$544$	1464.12	−	1835.95i	0.115392	−	0.144698i
$545$	5213.72	−	10826.4i	0.409782	−	0.850921i
$546$	−5086.65	−	4056.47i	−0.398697	−	0.317950i
$547$	−16126.6	−	12860.5i	−1.26056	−	1.00526i	−0.999199	−	0.0400178i	$-0.987259\pi$
$547$	−16126.6	−	12860.5i	−1.26056	−	1.00526i	−0.261357	−	0.965242i	$-0.584170\pi$
$548$	2342.27	−	10262.1i	0.182585	−	0.799958i
$549$	−6856.89	−	30042.0i	−0.533051	−	2.33545i
$550$	−8590.28	+	4136.86i	−0.665983	+	0.320721i
$551$	925.164	−	4053.41i	0.0715305	−	0.313396i
$552$	37558.3	−	47096.7i	2.89599	−	3.63146i
$553$	−2876.17	−	656.467i	−0.221170	−	0.0504806i
$554$	−4914.53	+	6162.63i	−0.376893	+	0.472608i
$555$	21952.5			1.67898
$556$	7976.85	−	6361.33i	0.608442	−	0.485217i
$557$	2550.31	+	11173.6i	0.194004	+	0.849986i	0.974422	+	0.224728i	$0.0721493\pi$
$557$	2550.31	+	11173.6i	0.194004	+	0.849986i	−0.780418	+	0.625258i	$0.784994\pi$
$558$	−36022.1			−2.73286
$559$	5696.32	+	11828.5i	0.431000	+	0.894980i
$560$	−3869.49	−	883.185i	−0.291992	−	0.0666453i
$561$	1617.07	+	3357.88i	0.121698	+	0.252709i
$562$	−5892.54	+	25816.9i	−0.442281	+	1.93776i
$563$	4585.66	−	20091.1i	0.343273	−	1.50398i	−0.448846	−	0.893609i	$-0.648165\pi$
$563$	4585.66	−	20091.1i	0.343273	−	1.50398i	0.792119	−	0.610367i	$-0.208978\pi$
$564$	40572.7	−	32355.7i	3.02911	−	2.41564i
$565$	−9344.84	+	4500.24i	−0.695824	+	0.335091i
$566$	10490.2	−	13154.3i	0.779037	−	0.976882i
$567$	−62.1014	−	29.9065i	−0.00459967	−	0.00221509i
$568$	−10865.7	+	47605.5i	−0.802663	+	3.51670i
$569$	2412.82	+	1161.95i	0.177769	+	0.0856093i	0.520652	−	0.853769i	$-0.325689\pi$
$569$	2412.82	+	1161.95i	0.177769	+	0.0856093i	−0.342882	+	0.939378i	$0.611403\pi$
$570$	4209.92	+	8741.99i	0.309358	+	0.642389i
$571$			8308.34i			0.608920i	0.952525	+	0.304460i	$0.0984760\pi$
$571$			8308.34i			0.608920i	−0.952525	+	0.304460i	$0.901524\pi$
$572$	13838.9			1.01160
$573$	6080.06	−	1387.73i	0.443278	−	0.101175i
$574$	1806.94	+	3752.16i	0.131394	+	0.272843i
$575$	6553.37	+	8217.67i	0.475295	+	0.596001i
$576$	−3381.57	−	4240.35i	−0.244616	−	0.306739i
$577$			1046.82i			0.0755279i	0.999287	+	0.0377640i	$0.0120235\pi$
$577$			1046.82i			0.0755279i	−0.999287	+	0.0377640i	$0.987977\pi$
$578$	−18322.5	+	14611.7i	−1.31854	+	1.05150i
$579$	−20998.6	−	4792.79i	−1.50721	−	0.344010i
$580$	−16847.1	−	3845.23i	−1.20610	−	0.275284i
$581$	592.136	+	2594.32i	0.0422822	+	0.185250i
$582$	9664.50	−	4654.18i	0.688327	−	0.331481i
$583$	−1569.16	−	1251.36i	−0.111471	−	0.0888955i
$584$	2902.12	+	12715.0i	0.205635	+	0.900944i
$585$	9468.18			0.669164
$586$	18576.3	+	38574.1i	1.30952	+	2.71925i
$587$	3992.83	+	1922.85i	0.280753	+	0.135203i	0.568961	−	0.822364i	$-0.307345\pi$
$587$	3992.83	+	1922.85i	0.280753	+	0.135203i	−0.288209	+	0.957568i	$0.593060\pi$
$588$	45501.6	−	10385.4i	3.19125	−	0.728381i
$589$	−4966.91	−	1133.67i	−0.347467	−	0.0793071i
$590$	5541.00			0.386643
$591$	14526.8	+	18102.6i	1.01109	+	1.25997i
$592$	37149.7			2.57912
$593$	11039.0	+	2519.58i	0.764446	+	0.174480i	0.586930	−	0.809638i	$-0.300336\pi$
$593$	11039.0	+	2519.58i	0.764446	+	0.174480i	0.177517	+	0.984118i	$0.443194\pi$
$594$	−18103.4	+	4131.99i	−1.25049	+	0.285417i
$595$	−572.400	−	275.653i	−0.0394388	−	0.0189927i
$596$	−19635.8	−	40774.1i	−1.34952	−	2.80230i
$597$	−36721.7			−2.51745
$598$	−4939.60	−	21641.8i	−0.337784	−	1.47993i
$599$	−21.4948	−	17.1416i	−0.00146620	−	0.00116926i	0.622756	−	0.782416i	$-0.286013\pi$
$599$	−21.4948	−	17.1416i	−0.00146620	−	0.00116926i	−0.624223	+	0.781247i	$0.714584\pi$
$600$	−26006.8	+	12524.2i	−1.76954	+	0.852164i
$601$	346.330	+	1517.37i	0.0235060	+	0.102986i	0.985320	−	0.170717i	$-0.0546084\pi$
$601$	346.330	+	1517.37i	0.0235060	+	0.102986i	−0.961814	+	0.273704i	$0.911751\pi$
$602$	11295.9	+	2578.22i	0.764763	+	0.174552i
$603$	8131.86	+	1856.04i	0.549179	+	0.125347i
$604$	21164.2	−	16877.9i	1.42576	−	1.13700i
$605$		−	4597.07i		−	0.308921i
$606$	−41710.1	−	52302.9i	−2.79597	−	3.50604i
$607$	17091.6	+	21432.2i	1.14288	+	1.43312i	0.884170	+	0.467166i	$0.154725\pi$
$607$	17091.6	+	21432.2i	1.14288	+	1.43312i	0.258707	+	0.965956i	$0.416704\pi$
$608$	1895.27	+	3935.56i	0.126420	+	0.262513i
$609$	−5659.10	+	1291.65i	−0.376549	+	0.0859448i
$610$	−26356.4			−1.74941
$611$		−	10421.1i		−	0.690004i
$612$	5541.49	+	11507.0i	0.366016	+	0.760039i
$613$	−25115.0	−	12094.7i	−1.65479	−	0.796904i	−0.999124	−	0.0418502i	$-0.986675\pi$
$613$	−25115.0	−	12094.7i	−1.65479	−	0.796904i	−0.655663	−	0.755053i	$-0.727611\pi$
$614$	2705.18	−	11852.2i	0.177805	−	0.779013i
$615$	−8852.41	−	4263.10i	−0.580429	−	0.279520i
$616$	4149.62	−	5203.45i	0.271417	−	0.340346i
$617$	−21335.1	+	10274.5i	−1.39209	+	0.670396i	−0.971540	−	0.236874i	$-0.923877\pi$
$617$	−21335.1	+	10274.5i	−1.39209	+	0.670396i	−0.420550	+	0.907269i	$0.638163\pi$
$618$	−60361.8	+	48136.9i	−3.92898	+	3.13325i
$619$	970.737	−	4253.08i	0.0630327	−	0.276164i	−0.933584	−	0.358360i	$-0.883336\pi$
$619$	970.737	−	4253.08i	0.0630327	−	0.276164i	0.996616	+	0.0821956i	$0.0261932\pi$
$620$	−4711.83	+	20643.9i	−0.305212	+	1.33722i
$621$	8881.76	+	18443.2i	0.573934	+	1.19179i
$622$	−28962.8	−	6610.57i	−1.86704	−	0.426141i
$623$	−1117.26	−	2320.01i	−0.0718490	−	0.149196i
$624$	25975.8			1.66645
$625$	382.140	+	1674.27i	0.0244570	+	0.107153i
$626$	27757.3	−	22135.7i	1.77222	−	1.41329i
$627$	−6932.76			−0.441575
$628$	−19307.2	+	24210.5i	−1.22682	+	1.53838i
$629$	5797.44	+	1323.23i	0.367502	+	0.0838800i
$630$	5209.84	−	6532.93i	0.329468	−	0.413140i
$631$	192.008	−	841.243i	0.0121137	−	0.0530735i	−0.968510	−	0.248975i	$-0.919906\pi$
$631$	192.008	−	841.243i	0.0121137	−	0.0530735i	0.980624	+	0.195902i	$0.0627634\pi$
$632$	24905.4	−	11993.8i	1.56754	−	0.754888i
$633$	−5427.58	−	23779.8i	−0.340801	−	1.49314i
$634$	−6688.17	+	29302.8i	−0.418961	+	1.83559i
$635$	−11918.6	−	9504.79i	−0.744845	−	0.593994i
$636$	−8717.59	−	6952.05i	−0.543514	−	0.433438i
$637$	4066.49	−	8444.15i	0.252936	−	0.525227i
$638$	11201.3	−	14046.0i	0.695083	−	0.871606i
$639$	−34246.8	−	27310.9i	−2.12016	−	1.69077i
$640$	−11623.1	+	5597.38i	−0.717879	+	0.345713i
$641$	20008.5	−	15956.3i	1.23290	−	0.983205i	0.232957	−	0.972487i	$-0.425160\pi$
$641$	20008.5	−	15956.3i	1.23290	−	0.983205i	0.999943	−	0.0107177i	$-0.00341161\pi$
$642$	5164.10	+	6475.57i	0.317462	+	0.398085i
$643$	22962.2	−	5240.97i	1.40830	−	0.321436i	0.550252	−	0.834999i	$-0.314532\pi$
$643$	22962.2	−	5240.97i	1.40830	−	0.321436i	0.858052	+	0.513562i	$0.171674\pi$
$644$	−12130.5	−	5841.73i	−0.742248	−	0.357448i
$645$	−24628.6	+	11860.5i	−1.50349	+	0.724041i
$646$	584.858	+	2562.43i	0.0356206	+	0.156064i
$647$	−5850.78	+	12149.3i	−0.355514	+	0.738233i	−0.999644	−	0.0266831i	$-0.991505\pi$
$647$	−5850.78	+	12149.3i	−0.355514	+	0.738233i	0.644129	+	0.764916i	$0.277220\pi$
$648$	629.661	−	143.716i	0.0381720	−	0.00871250i
$649$	−1717.78	+	3567.00i	−0.103896	+	0.215743i
$650$	−2366.96	+	10370.3i	−0.142831	+	0.625781i
$651$	1582.75	+	6934.47i	0.0952885	+	0.417486i
$652$	−2702.87	+	11842.1i	−0.162351	+	0.711305i
$653$	1970.95	+	949.158i	0.118115	+	0.0568812i	0.492008	−	0.870591i	$-0.336263\pi$
$653$	1970.95	+	949.158i	0.118115	+	0.0568812i	−0.373893	+	0.927472i	$0.621977\pi$
$654$	43273.3	+	54263.0i	2.58734	+	3.24442i
$655$	−4016.74	−	17598.5i	−0.239614	−	1.04982i
$656$	−14980.7	−	7214.32i	−0.891612	−	0.429378i
$657$	−11406.1	−	2603.38i	−0.677315	−	0.154593i
$658$	−7190.43	−	5734.17i	−0.426006	−	0.339728i
$659$			24590.5i			1.45358i	0.686858	+	0.726792i	$0.258989\pi$
$659$			24590.5i			1.45358i	−0.686858	+	0.726792i	$0.741011\pi$
$660$			28814.4i			1.69939i
$661$	11931.4	−	5745.84i	0.702081	−	0.338105i	−0.0485546	−	0.998821i	$-0.515461\pi$
$661$	11931.4	−	5745.84i	0.702081	−	0.338105i	0.750636	+	0.660716i	$0.229747\pi$
$662$	3529.18	+	7328.43i	0.207199	+	0.430253i
$663$	4053.69	+	925.229i	0.237454	+	0.0541974i
$664$	−19494.2	−	15546.1i	−1.13934	−	0.908596i
$665$	923.960	−	736.834i	0.0538792	−	0.0429672i
$666$	−33934.6	+	70465.8i	−1.97438	+	4.09984i
$667$	−17843.7	−	8593.09i	−1.03585	−	0.498839i
$668$		−	16452.8i		−	0.952963i
$669$	−28868.5	+	23021.9i	−1.66834	+	1.33046i
$670$	3095.43	−	6427.73i	0.178488	−	0.370634i
$671$	8170.82	−	16966.9i	0.470091	−	0.976154i
$672$	3802.36	−	4768.01i	0.218273	−	0.273705i
$673$	19423.7	−	4433.34i	1.11253	−	0.253927i	0.373517	−	0.927623i	$-0.378152\pi$
$673$	19423.7	−	4433.34i	1.11253	−	0.253927i	0.739008	+	0.673696i	$0.235294\pi$
$674$	16260.4			0.929269
$675$		−	9809.02i		−	0.559332i
$676$	−14455.2	+	18126.2i	−0.822438	+	1.03130i
$677$	8519.78	−	17691.5i	0.483666	−	1.00434i	−0.506211	−	0.862410i	$-0.668954\pi$
$677$	8519.78	−	17691.5i	0.483666	−	1.00434i	0.989876	−	0.141932i	$-0.0453315\pi$
$678$		−	59907.2i		−	3.39339i
$679$	−814.589	−	1021.46i	−0.0460399	−	0.0577322i
$680$	5803.70	−	1324.66i	0.327297	−	0.0747033i
$681$	−522.791	−	655.559i	−0.0294176	−	0.0368885i
$682$	−17211.5	−	13725.7i	−0.966365	−	0.770651i
$683$	11327.0	−	14203.6i	0.634576	−	0.795733i	−0.355737	−	0.934586i	$-0.615770\pi$
$683$	11327.0	−	14203.6i	0.634576	−	0.795733i	0.990313	+	0.138853i	$0.0443416\pi$
$684$	−23757.7			−1.32807
$685$	3440.96	−	2744.07i	0.191930	−	0.153059i
$686$	−7481.00	−	15534.5i	−0.416365	−	0.864590i
$687$	5438.96	+	6820.24i	0.302051	+	0.378760i
$688$	−41678.3	+	20071.2i	−2.30955	+	1.11222i
$689$	−2182.97	+	498.249i	−0.120703	+	0.0275498i
$690$	45061.1	−	10284.9i	2.48615	−	0.567448i
$691$	29849.1	−	14374.5i	1.64329	−	0.791365i	0.643626	−	0.765340i	$-0.277429\pi$
$691$	29849.1	−	14374.5i	1.64329	−	0.791365i	0.999661	−	0.0260254i	$-0.00828507\pi$
$692$	−30425.1	−	38151.8i	−1.67137	−	2.09583i
$693$	2590.44	+	5379.11i	0.141995	+	0.294856i
$694$	14400.8	−	11484.3i	0.787677	−	0.628151i
$695$	4265.98			0.232832
$696$	33911.5	−	42523.6i	1.84685	−	2.31588i
$697$	−2080.87	−	1659.43i	−0.113082	−	0.0901802i
$698$	15979.8	+	20038.0i	0.866539	+	1.08661i
$699$	19732.2	−	4503.75i	1.06773	−	0.243702i
$700$	4022.51	+	5044.06i	0.217195	+	0.272354i
$701$		−	2400.97i		−	0.129363i	−0.997906	−	0.0646816i	$-0.979397\pi$
$701$		−	2400.97i		−	0.129363i	0.997906	−	0.0646816i	$-0.0206032\pi$
$702$	−8988.43	+	18664.7i	−0.483257	+	1.00349i
$703$	−6896.74	+	8648.23i	−0.370008	+	0.463975i
$704$		−	3314.55i		−	0.177446i
$705$	21698.1			1.15915
$706$	26374.2	−	6019.73i	1.40596	−	0.320900i
$707$	−5080.21	+	6370.38i	−0.270242	+	0.338872i
$708$	−9543.27	+	19816.8i	−0.506579	+	1.05192i
$709$	−6737.87	+	13991.3i	−0.356906	+	0.741122i	−0.999689	−	0.0249255i	$-0.992065\pi$
$709$	−6737.87	+	13991.3i	−0.356906	+	0.741122i	0.642784	+	0.766048i	$0.277779\pi$
$710$	−29292.1	+	23359.6i	−1.54833	+	1.23475i
$711$			24797.4i			1.30798i
$712$	21738.6	+	10468.8i	1.14423	+	0.551030i
$713$	−10529.7	+	21865.1i	−0.553072	+	1.14847i
$714$	2868.93	−	2287.89i	0.150374	−	0.119919i
$715$	4523.93	+	3607.71i	0.236623	+	0.188700i
$716$	−53996.6	−	12324.4i	−2.81836	−	0.643272i
$717$	−13084.6	−	27170.5i	−0.681526	−	1.41520i
$718$	24955.5	−	12017.9i	1.29712	−	0.624659i
$719$		−	23552.1i		−	1.22162i	−0.791777	−	0.610811i	$-0.790844\pi$
$719$		−	23552.1i		−	1.22162i	0.791777	−	0.610811i	$-0.209156\pi$
$720$			33361.5i			1.72682i
$721$	7351.94	+	5862.97i	0.379751	+	0.302841i
$722$	29054.3	+	6631.46i	1.49763	+	0.341824i
$723$	8274.91	+	3984.99i	0.425653	+	0.204984i
$724$	9374.67	+	41073.1i	0.481225	+	2.10838i
$725$	5917.05	+	7419.75i	0.303109	+	0.380086i
$726$	23922.5	+	11520.5i	1.22293	+	0.588933i
$727$	2433.75	−	10663.0i	0.124158	−	0.543972i	−0.874141	−	0.485672i	$-0.838575\pi$
$727$	2433.75	−	10663.0i	0.124158	−	0.543972i	0.998299	−	0.0583000i	$-0.0185680\pi$
$728$	−1652.24	−	7238.92i	−0.0841153	−	0.368533i
$729$	−7099.68	+	31105.8i	−0.360701	+	1.58034i
$730$	−4341.80	+	9015.85i	−0.220133	+	0.457112i
$731$	−7219.07	+	1647.71i	−0.365263	+	0.0833688i
$732$	45393.7	−	94261.1i	2.29208	−	4.75955i
$733$	5774.54	+	25299.9i	0.290979	+	1.27486i	0.883166	+	0.469061i	$0.155408\pi$
$733$	5774.54	+	25299.9i	0.290979	+	1.27486i	−0.592187	+	0.805801i	$0.701735\pi$
$734$	18332.7	−	8828.57i	0.921897	−	0.443962i
$735$	17581.8	+	8466.97i	0.882335	+	0.424910i
$736$	20286.1	−	4630.16i	1.01597	−	0.231889i
$737$	3178.21	+	3985.35i	0.158848	+	0.199189i
$738$	27368.4	−	21825.5i	1.36510	−	1.08863i
$739$	−23023.0	+	11087.3i	−1.14603	+	0.551898i	−0.907838	−	0.419321i	$-0.862268\pi$
$739$	−23023.0	+	11087.3i	−1.14603	+	0.551898i	−0.238189	+	0.971219i	$0.576554\pi$
$740$	35944.4	+	28664.7i	1.78560	+	1.42397i
$741$	−4822.34	+	6047.03i	−0.239073	+	0.299788i
$742$	−857.388	+	1780.38i	−0.0424201	+	0.0880862i
$743$	−10226.5	−	8155.36i	−0.504945	−	0.402680i	0.337614	−	0.941285i	$-0.390380\pi$
$743$	−10226.5	−	8155.36i	−0.504945	−	0.402680i	−0.842559	+	0.538605i	$0.818952\pi$
$744$	−52107.1	−	41554.0i	−2.56766	−	2.04764i
$745$	4210.62	−	18447.9i	0.207067	−	0.907221i
$746$	5053.36	+	22140.2i	0.248011	+	1.08661i
$747$	20152.3	−	9704.84i	0.987061	−	0.475343i
$748$	−1736.84	+	7609.60i	−0.0849000	+	0.371971i
$749$	628.976	−	788.711i	0.0306839	−	0.0384765i
$750$	−59623.9	−	13608.8i	−2.90288	−	0.662563i
$751$	−16081.8	+	20166.0i	−0.781404	+	0.979850i	0.218588	+	0.975817i	$0.429855\pi$
$751$	−16081.8	+	20166.0i	−0.781404	+	0.979850i	−0.999992	+	0.00403251i	$0.998716\pi$
$752$	36719.1			1.78060
$753$	42852.7	−	34173.9i	2.07389	−	1.65387i
$754$	−4459.97	−	19540.4i	−0.215414	−	0.943792i
$755$	11318.5			0.545592
$756$	5451.69	+	11320.6i	0.262270	+	0.544609i
$757$	30795.7	+	7028.92i	1.47858	+	0.337477i	0.884354	−	0.466817i	$-0.154599\pi$
$757$	30795.7	+	7028.92i	1.47858	+	0.337477i	0.594231	+	0.804294i	$0.297456\pi$
$758$	1500.61	+	3116.05i	0.0719058	+	0.149314i
$759$	−7348.61	+	32196.4i	−0.351433	+	1.53973i
$760$	−2464.07	+	10795.8i	−0.117607	+	0.515270i
$761$	−13750.2	+	10965.4i	−0.654985	+	0.522333i	−0.893648	−	0.448769i	$-0.851863\pi$
$761$	−13750.2	+	10965.4i	−0.654985	+	0.522333i	0.238662	+	0.971103i	$0.423291\pi$
$762$	79330.4	−	38203.5i	3.77144	−	1.81623i
$763$	5270.60	−	6609.12i	0.250077	−	0.313586i
$764$	11767.4	+	5666.86i	0.557236	+	0.268350i
$765$	−1188.30	+	5206.27i	−0.0561607	+	0.246056i
$766$	22217.7	+	10699.5i	1.04799	+	0.504684i
$767$	1916.41	+	3979.48i	0.0902187	+

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.93087 - 1.12544i) q^{2} +(8.18390 - 1.86792i) q^{3} +(15.8391 + 7.62772i) q^{4} +(3.18930 + 6.62265i) q^{5} -42.4560 q^{6} +(1.15067 + 5.04140i) q^{7} +(-37.8821 - 30.2100i) q^{8} +(39.1609 - 18.8589i) q^{9} +O(q^{10})\)	\(q+(-4.93087 - 1.12544i) q^{2} +(8.18390 - 1.86792i) q^{3} +(15.8391 + 7.62772i) q^{4} +(3.18930 + 6.62265i) q^{5} -42.4560 q^{6} +(1.15067 + 5.04140i) q^{7} +(-37.8821 - 30.2100i) q^{8} +(39.1609 - 18.8589i) q^{9} +(-8.27264 - 36.2448i) q^{10} +(25.8971 + 5.91085i) q^{11} +(143.874 + 32.8382i) q^{12} +(23.1694 - 18.4770i) q^{13} -26.1535i q^{14} +(38.4715 + 48.2418i) q^{15} +(65.1043 + 81.6382i) q^{16} +(7.25208 + 15.0591i) q^{17} +(-214.322 + 48.9176i) q^{18} -31.0913 q^{19} +129.224i q^{20} +(18.8339 + 39.1089i) q^{21} +(-121.043 - 58.2913i) q^{22} +(-32.9563 + 144.391i) q^{23} +(-366.453 - 176.475i) q^{24} +(44.2483 - 55.4857i) q^{25} +(-135.040 + 65.0318i) q^{26} +(108.062 - 86.1762i) q^{27} +(-20.2288 + 88.6283i) q^{28} +(-29.7563 + 130.371i) q^{29} +(-135.405 - 281.171i) q^{30} +(159.752 + 36.4624i) q^{31} +(-60.9580 - 126.581i) q^{32} +222.980 q^{33} +(-18.8110 - 82.4162i) q^{34} +(-29.7176 + 23.6990i) q^{35} +764.125 q^{36} +(221.822 - 278.156i) q^{37} +(153.307 + 34.9914i) q^{38} +(155.102 - 194.492i) q^{39} +(79.2528 - 347.229i) q^{40} +(-143.467 + 69.0900i) q^{41} +(-48.8527 - 214.038i) q^{42} +(-98.5804 + 431.909i) q^{43} +(365.101 + 291.159i) q^{44} +(249.792 + 199.202i) q^{45} +(325.007 - 674.884i) q^{46} +(219.251 - 274.932i) q^{47} +(685.301 + 546.509i) q^{48} +(284.941 - 137.220i) q^{49} +(-280.629 + 223.794i) q^{50} +(87.4795 + 109.696i) q^{51} +(507.920 - 115.929i) q^{52} +(-68.0744 - 32.7829i) q^{53} +(-629.824 + 303.307i) q^{54} +(43.4482 + 190.359i) q^{55} +(108.711 - 225.741i) q^{56} +(-254.448 + 58.0762i) q^{57} +(293.449 - 609.353i) q^{58} +(-33.1654 + 145.307i) q^{59} +(241.381 + 1057.56i) q^{60} +(157.755 - 691.172i) q^{61} +(-746.682 - 359.583i) q^{62} +(140.136 + 175.725i) q^{63} +(-27.7662 - 121.652i) q^{64} +(196.261 + 94.5142i) q^{65} +(-1099.49 - 250.951i) q^{66} +(150.033 + 119.648i) q^{67} +293.840i q^{68} +1243.24i q^{69} +(173.205 - 83.4114i) q^{70} +(-437.257 - 907.974i) q^{71} +(-2053.23 - 468.635i) q^{72} +(-210.444 - 167.824i) q^{73} +(-1406.82 + 1121.90i) q^{74} +(258.481 - 536.741i) q^{75} +(-492.460 - 237.156i) q^{76} +137.359i q^{77} +(-983.679 + 784.458i) q^{78} +(-247.535 + 514.012i) q^{79} +(-333.024 + 691.532i) q^{80} +(-8.31079 + 10.4214i) q^{81} +(785.173 - 179.211i) q^{82} +514.603 q^{83} +763.111i q^{84} +(-76.6021 + 96.0560i) q^{85} +(972.174 - 2018.74i) q^{86} +1122.52i q^{87} +(-802.471 - 1006.27i) q^{88} +(-485.482 + 110.808i) q^{89} +(-1007.50 - 1263.37i) q^{90} +(119.810 + 95.5453i) q^{91} +(-1623.37 + 2035.65i) q^{92} +1375.51 q^{93} +(-1390.52 + 1108.90i) q^{94} +(-99.1597 - 205.907i) q^{95} +(-735.317 - 922.058i) q^{96} +(-227.636 + 109.624i) q^{97} +(-1559.44 + 355.932i) q^{98} +(1125.63 - 256.917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9}+O(q^{10}) \) 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9	\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + 149 q^{10} + 91 q^{11} - 63 q^{12} - 7 q^{13} - 473 q^{15} - 1113 q^{16} - 7 q^{17} - 196 q^{18} + 464 q^{19} - 7 q^{21} + 807 q^{22} + 413 q^{23} - 1425 q^{24} + 1195 q^{25} - 543 q^{26} + 455 q^{27} + 174 q^{28} - 906 q^{29} + 798 q^{30} + 917 q^{31} + 945 q^{32} + 894 q^{33} - 219 q^{34} - 7 q^{35} + 3250 q^{36} + 1734 q^{37} - 63 q^{38} - 825 q^{39} + 141 q^{40} + 563 q^{41} + 432 q^{42} - 423 q^{43} + 2149 q^{44} - 3808 q^{45} - 2569 q^{46} - 289 q^{47} - 3703 q^{48} - 3747 q^{49} - 4963 q^{50} - 87 q^{51} + 3654 q^{52} - 1573 q^{53} - 1228 q^{54} + 2825 q^{55} + 98 q^{56} - 518 q^{57} - 5103 q^{58} + 2045 q^{59} + 3375 q^{60} + 287 q^{61} - 2547 q^{62} + 1453 q^{63} + 6475 q^{64} + 1268 q^{65} + 4634 q^{66} - 3577 q^{67} - 814 q^{70} - 273 q^{71} - 1008 q^{72} - 679 q^{73} - 315 q^{74} - 1281 q^{75} + 6078 q^{76} + 4739 q^{78} + 1463 q^{79} + 441 q^{80} - 4427 q^{81} - 7 q^{82} + 4900 q^{83} - 3351 q^{85} + 3472 q^{86} + 3738 q^{88} + 147 q^{89} + 7133 q^{90} - 14133 q^{91} - 803 q^{92} - 4894 q^{93} - 7833 q^{94} - 7700 q^{95} - 16450 q^{96} + 1233 q^{97} - 2030 q^{98} + 2464 q^{99}+O(q^{100}) \) 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9 + 149 * q^10 + 91 * q^11 - 63 * q^12 - 7 * q^13 - 473 * q^15 - 1113 * q^16 - 7 * q^17 - 196 * q^18 + 464 * q^19 - 7 * q^21 + 807 * q^22 + 413 * q^23 - 1425 * q^24 + 1195 * q^25 - 543 * q^26 + 455 * q^27 + 174 * q^28 - 906 * q^29 + 798 * q^30 + 917 * q^31 + 945 * q^32 + 894 * q^33 - 219 * q^34 - 7 * q^35 + 3250 * q^36 + 1734 * q^37 - 63 * q^38 - 825 * q^39 + 141 * q^40 + 563 * q^41 + 432 * q^42 - 423 * q^43 + 2149 * q^44 - 3808 * q^45 - 2569 * q^46 - 289 * q^47 - 3703 * q^48 - 3747 * q^49 - 4963 * q^50 - 87 * q^51 + 3654 * q^52 - 1573 * q^53 - 1228 * q^54 + 2825 * q^55 + 98 * q^56 - 518 * q^57 - 5103 * q^58 + 2045 * q^59 + 3375 * q^60 + 287 * q^61 - 2547 * q^62 + 1453 * q^63 + 6475 * q^64 + 1268 * q^65 + 4634 * q^66 - 3577 * q^67 - 814 * q^70 - 273 * q^71 - 1008 * q^72 - 679 * q^73 - 315 * q^74 - 1281 * q^75 + 6078 * q^76 + 4739 * q^78 + 1463 * q^79 + 441 * q^80 - 4427 * q^81 - 7 * q^82 + 4900 * q^83 - 3351 * q^85 + 3472 * q^86 + 3738 * q^88 + 147 * q^89 + 7133 * q^90 - 14133 * q^91 - 803 * q^92 - 4894 * q^93 - 7833 * q^94 - 7700 * q^95 - 16450 * q^96 + 1233 * q^97 - 2030 * q^98 + 2464 * q^99

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