LMFDB - Embedded newform 197.3.c.a.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,3,Mod(14,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("197.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	197.c (of order $4$, 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:	$5.36786120790$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			14.2
Character	$\chi$	$=$	197.14
Dual form			197.3.c.a.183.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.60079 + 2.60079i) q^{2} +(-0.624484 + 0.624484i) q^{3} -9.52825i q^{4} +(1.64362 - 1.64362i) q^{5} -3.24831i q^{6} -8.36970i q^{7} +(14.3778 + 14.3778i) q^{8} +8.22004i q^{9} +8.54942i q^{10} +(-2.58710 + 2.58710i) q^{11} +(5.95024 + 5.95024i) q^{12} +(-14.4989 + 14.4989i) q^{13} +(21.7679 + 21.7679i) q^{14} +2.05283i q^{15} -36.6745 q^{16} +(8.22478 + 8.22478i) q^{17} +(-21.3786 - 21.3786i) q^{18} +10.8311i q^{19} +(-15.6608 - 15.6608i) q^{20} +(5.22675 + 5.22675i) q^{21} -13.4570i q^{22} +15.9629 q^{23} -17.9574 q^{24} +19.5970i q^{25} -75.4170i q^{26} +(-10.7536 - 10.7536i) q^{27} -79.7486 q^{28} +8.00527 q^{29} +(-5.33897 - 5.33897i) q^{30} +(-15.9401 + 15.9401i) q^{31} +(37.8715 - 37.8715i) q^{32} -3.23120i q^{33} -42.7819 q^{34} +(-13.7566 - 13.7566i) q^{35} +78.3226 q^{36} -30.3859 q^{37} +(-28.1695 - 28.1695i) q^{38} -18.1086i q^{39} +47.2633 q^{40} +30.8557i q^{41} -27.1874 q^{42} -27.3922i q^{43} +(24.6505 + 24.6505i) q^{44} +(13.5106 + 13.5106i) q^{45} +(-41.5163 + 41.5163i) q^{46} +76.2072i q^{47} +(22.9027 - 22.9027i) q^{48} -21.0519 q^{49} +(-50.9679 - 50.9679i) q^{50} -10.2725 q^{51} +(138.149 + 138.149i) q^{52} -70.0440 q^{53} +55.9360 q^{54} +8.50439i q^{55} +(120.338 - 120.338i) q^{56} +(-6.76387 - 6.76387i) q^{57} +(-20.8201 + 20.8201i) q^{58} +74.9056 q^{59} +19.5598 q^{60} +93.1420 q^{61} -82.9136i q^{62} +68.7993 q^{63} +50.2938i q^{64} +47.6611i q^{65} +(8.40368 + 8.40368i) q^{66} +(-58.1423 + 58.1423i) q^{67} +(78.3677 - 78.3677i) q^{68} +(-9.96859 + 9.96859i) q^{69} +71.5561 q^{70} +(53.8173 + 53.8173i) q^{71} +(-118.186 + 118.186i) q^{72} +(-91.4298 + 91.4298i) q^{73} +(79.0274 - 79.0274i) q^{74} +(-12.2380 - 12.2380i) q^{75} +103.202 q^{76} +(21.6532 + 21.6532i) q^{77} +(47.0967 + 47.0967i) q^{78} +(-8.09237 - 8.09237i) q^{79} +(-60.2789 + 60.2789i) q^{80} -60.5494 q^{81} +(-80.2493 - 80.2493i) q^{82} -114.980i q^{83} +(49.8017 - 49.8017i) q^{84} +27.0368 q^{85} +(71.2414 + 71.2414i) q^{86} +(-4.99917 + 4.99917i) q^{87} -74.3936 q^{88} +(-91.1938 - 91.1938i) q^{89} -70.2765 q^{90} +(121.351 + 121.351i) q^{91} -152.099i q^{92} -19.9086i q^{93} +(-198.199 - 198.199i) q^{94} +(17.8022 + 17.8022i) q^{95} +47.3003i q^{96} -86.1359i q^{97} +(54.7516 - 54.7516i) q^{98} +(-21.2660 - 21.2660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28}+ \cdots - 66 q^{99}+O(q^{100}) $ 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8 + 10 * q^11 + 68 * q^12 + 2 * q^13 - 2 * q^14 - 280 * q^16 - 30 * q^17 - 68 * q^18 + 114 * q^20 - 20 * q^21 + 48 * q^23 + 60 * q^24 + 22 * q^27 + 392 * q^28 + 56 * q^29 - 70 * q^30 - 64 * q^31 - 156 * q^32 - 52 * q^34 - 92 * q^35 - 36 * q^36 - 160 * q^37 + 40 * q^38 + 52 * q^40 + 80 * q^42 + 140 * q^44 + 324 * q^45 + 214 * q^46 + 216 * q^48 - 836 * q^49 + 126 * q^50 + 124 * q^51 - 10 * q^52 - 16 * q^53 + 400 * q^54 - 40 * q^56 + 68 * q^57 - 266 * q^58 - 364 * q^59 - 68 * q^60 - 168 * q^61 - 12 * q^63 + 238 * q^66 - 112 * q^67 - 148 * q^68 - 48 * q^69 + 48 * q^70 + 150 * q^71 - 474 * q^72 + 18 * q^73 + 236 * q^74 + 64 * q^75 - 260 * q^76 - 388 * q^77 - 782 * q^78 + 202 * q^79 + 796 * q^80 - 516 * q^81 + 72 * q^82 - 294 * q^84 - 696 * q^85 + 618 * q^86 + 464 * q^87 - 244 * q^88 - 536 * q^89 + 1484 * q^90 + 212 * q^91 + 132 * q^94 + 370 * q^95 - 530 * q^98 - 66 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.60079	+	2.60079i	−1.30040	+	1.30040i	−0.372273	+	0.928123i	$0.621422\pi$
$2$	−2.60079	+	2.60079i	−1.30040	+	1.30040i	−0.928123	+	0.372273i	$0.878578\pi$
$3$	−0.624484	+	0.624484i	−0.208161	+	0.208161i	−0.803486	−	0.595324i	$-0.797024\pi$
$3$	−0.624484	+	0.624484i	−0.208161	+	0.208161i	0.595324	+	0.803486i	$0.297024\pi$
$4$		−	9.52825i		−	2.38206i
$5$	1.64362	−	1.64362i	0.328723	−	0.328723i	−0.523377	−	0.852101i	$-0.675328\pi$
$5$	1.64362	−	1.64362i	0.328723	−	0.328723i	0.852101	+	0.523377i	$0.175328\pi$
$6$		−	3.24831i		−	0.541385i
$7$		−	8.36970i		−	1.19567i	−0.801619	−	0.597836i	$-0.796027\pi$
$7$		−	8.36970i		−	1.19567i	0.801619	−	0.597836i	$-0.203973\pi$
$8$	14.3778	+	14.3778i	1.79723	+	1.79723i
$9$			8.22004i			0.913338i
$10$			8.54942i			0.854942i
$11$	−2.58710	+	2.58710i	−0.235191	+	0.235191i	−0.814855	−	0.579665i	$-0.803184\pi$
$11$	−2.58710	+	2.58710i	−0.235191	+	0.235191i	0.579665	+	0.814855i	$0.303184\pi$
$12$	5.95024	+	5.95024i	0.495853	+	0.495853i
$13$	−14.4989	+	14.4989i	−1.11530	+	1.11530i	−0.122874	+	0.992422i	$0.539211\pi$
$13$	−14.4989	+	14.4989i	−1.11530	+	1.11530i	−0.992422	+	0.122874i	$0.960789\pi$
$14$	21.7679	+	21.7679i	1.55485	+	1.55485i
$15$			2.05283i			0.136855i
$16$	−36.6745			−2.29216
$17$	8.22478	+	8.22478i	0.483810	+	0.483810i	0.906346	−	0.422536i	$-0.138860\pi$
$17$	8.22478	+	8.22478i	0.483810	+	0.483810i	−0.422536	+	0.906346i	$0.638860\pi$
$18$	−21.3786	−	21.3786i	−1.18770	−	1.18770i
$19$			10.8311i			0.570060i	0.958519	+	0.285030i	$0.0920035\pi$
$19$			10.8311i			0.570060i	−0.958519	+	0.285030i	$0.907997\pi$
$20$	−15.6608	−	15.6608i	−0.783040	−	0.783040i
$21$	5.22675	+	5.22675i	0.248893	+	0.248893i
$22$		−	13.4570i		−	0.611682i
$23$	15.9629			0.694040			0.347020	−	0.937858i	$-0.387194\pi$
$23$	15.9629			0.694040			0.347020	+	0.937858i	$0.387194\pi$
$24$	−17.9574			−0.748227
$25$			19.5970i			0.783882i
$26$		−	75.4170i		−	2.90065i
$27$	−10.7536	−	10.7536i	−0.398283	−	0.398283i
$28$	−79.7486			−2.84816
$29$	8.00527			0.276044			0.138022	−	0.990429i	$-0.455926\pi$
$29$	8.00527			0.276044			0.138022	+	0.990429i	$0.455926\pi$
$30$	−5.33897	−	5.33897i	−0.177966	−	0.177966i
$31$	−15.9401	+	15.9401i	−0.514195	+	0.514195i	−0.915809	−	0.401614i	$-0.868449\pi$
$31$	−15.9401	+	15.9401i	−0.514195	+	0.514195i	0.401614	+	0.915809i	$0.368449\pi$
$32$	37.8715	−	37.8715i	1.18348	−	1.18348i
$33$		−	3.23120i		−	0.0979152i
$34$	−42.7819			−1.25829
$35$	−13.7566	−	13.7566i	−0.393045	−	0.393045i
$36$	78.3226			2.17563
$37$	−30.3859			−0.821240			−0.410620	−	0.911807i	$-0.634688\pi$
$37$	−30.3859			−0.821240			−0.410620	+	0.911807i	$0.634688\pi$
$38$	−28.1695	−	28.1695i	−0.741303	−	0.741303i
$39$		−	18.1086i		−	0.464323i
$40$	47.2633			1.18158
$41$			30.8557i			0.752579i	0.926502	+	0.376289i	$0.122800\pi$
$41$			30.8557i			0.752579i	−0.926502	+	0.376289i	$0.877200\pi$
$42$	−27.1874			−0.647318
$43$		−	27.3922i		−	0.637028i	−0.947918	−	0.318514i	$-0.896816\pi$
$43$		−	27.3922i		−	0.637028i	0.947918	−	0.318514i	$-0.103184\pi$
$44$	24.6505	+	24.6505i	0.560238	+	0.560238i
$45$	13.5106	+	13.5106i	0.300236	+	0.300236i
$46$	−41.5163	+	41.5163i	−0.902527	+	0.902527i
$47$			76.2072i			1.62143i	0.585441	+	0.810715i	$0.300921\pi$
$47$			76.2072i			1.62143i	−0.585441	+	0.810715i	$0.699079\pi$
$48$	22.9027	−	22.9027i	0.477139	−	0.477139i
$49$	−21.0519			−0.429631
$50$	−50.9679	−	50.9679i	−1.01936	−	1.01936i
$51$	−10.2725			−0.201421
$52$	138.149	+	138.149i	2.65670	+	2.65670i
$53$	−70.0440			−1.32158			−0.660792	−	0.750569i	$-0.729779\pi$
$53$	−70.0440			−1.32158			−0.660792	+	0.750569i	$0.729779\pi$
$54$	55.9360			1.03585
$55$			8.50439i			0.154625i
$56$	120.338	−	120.338i	2.14890	−	2.14890i
$57$	−6.76387	−	6.76387i	−0.118664	−	0.118664i
$58$	−20.8201	+	20.8201i	−0.358966	+	0.358966i
$59$	74.9056			1.26959			0.634793	−	0.772682i	$-0.281085\pi$
$59$	74.9056			1.26959			0.634793	+	0.772682i	$0.281085\pi$
$60$	19.5598			0.325997
$61$	93.1420			1.52692			0.763459	−	0.645856i	$-0.223500\pi$
$61$	93.1420			1.52692			0.763459	+	0.645856i	$0.223500\pi$
$62$		−	82.9136i		−	1.33732i
$63$	68.7993			1.09205
$64$			50.2938i			0.785841i
$65$			47.6611i			0.733248i
$66$	8.40368	+	8.40368i	0.127329	+	0.127329i
$67$	−58.1423	+	58.1423i	−0.867795	+	0.867795i	−0.992228	−	0.124433i	$-0.960289\pi$
$67$	−58.1423	+	58.1423i	−0.867795	+	0.867795i	0.124433	+	0.992228i	$0.460289\pi$
$68$	78.3677	−	78.3677i	1.15247	−	1.15247i
$69$	−9.96859	+	9.96859i	−0.144472	+	0.144472i
$70$	71.5561			1.02223
$71$	53.8173	+	53.8173i	0.757990	+	0.757990i	0.975956	−	0.217966i	$-0.0699423\pi$
$71$	53.8173	+	53.8173i	0.757990	+	0.757990i	−0.217966	+	0.975956i	$0.569942\pi$
$72$	−118.186	+	118.186i	−1.64148	+	1.64148i
$73$	−91.4298	+	91.4298i	−1.25246	+	1.25246i	−0.297850	+	0.954613i	$0.596270\pi$
$73$	−91.4298	+	91.4298i	−1.25246	+	1.25246i	−0.954613	+	0.297850i	$0.903730\pi$
$74$	79.0274	−	79.0274i	1.06794	−	1.06794i
$75$	−12.2380	−	12.2380i	−0.163174	−	0.163174i
$76$	103.202			1.35792
$77$	21.6532	+	21.6532i	0.281211	+	0.281211i
$78$	47.0967	+	47.0967i	0.603804	+	0.603804i
$79$	−8.09237	−	8.09237i	−0.102435	−	0.102435i	0.654032	−	0.756467i	$-0.273076\pi$
$79$	−8.09237	−	8.09237i	−0.102435	−	0.102435i	−0.756467	+	0.654032i	$0.773076\pi$
$80$	−60.2789	+	60.2789i	−0.753486	+	0.753486i
$81$	−60.5494			−0.747523
$82$	−80.2493	−	80.2493i	−0.978651	−	0.978651i
$83$		−	114.980i		−	1.38531i	−0.721271	−	0.692653i	$-0.756442\pi$
$83$		−	114.980i		−	1.38531i	0.721271	−	0.692653i	$-0.243558\pi$
$84$	49.8017	−	49.8017i	0.592878	−	0.592878i
$85$	27.0368			0.318080
$86$	71.2414	+	71.2414i	0.828389	+	0.828389i
$87$	−4.99917	+	4.99917i	−0.0574617	+	0.0574617i
$88$	−74.3936			−0.845382
$89$	−91.1938	−	91.1938i	−1.02465	−	1.02465i	−0.999688	−	0.0249612i	$-0.992054\pi$
$89$	−91.1938	−	91.1938i	−1.02465	−	1.02465i	−0.0249612	−	0.999688i	$-0.507946\pi$
$90$	−70.2765			−0.780850
$91$	121.351	+	121.351i	1.33353	+	1.33353i
$92$		−	152.099i		−	1.65325i
$93$		−	19.9086i		−	0.214071i
$94$	−198.199	−	198.199i	−2.10850	−	2.10850i
$95$	17.8022	+	17.8022i	0.187392	+	0.187392i
$96$			47.3003i			0.492712i
$97$		−	86.1359i		−	0.887999i	−0.896027	−	0.443999i	$-0.853559\pi$
$97$		−	86.1359i		−	0.887999i	0.896027	−	0.443999i	$-0.146441\pi$
$98$	54.7516	−	54.7516i	0.558690	−	0.558690i
$99$	−21.2660	−	21.2660i	−0.214808	−	0.214808i
$100$	186.725			1.86725
$101$	60.5394			0.599400			0.299700	−	0.954033i	$-0.403113\pi$
$101$	60.5394			0.599400			0.299700	+	0.954033i	$0.403113\pi$
$102$	26.7166	−	26.7166i	0.261928	−	0.261928i
$103$	−3.27564	+	3.27564i	−0.0318024	+	0.0318024i	−0.722829	−	0.691027i	$-0.757159\pi$
$103$	−3.27564	+	3.27564i	−0.0318024	+	0.0318024i	0.691027	+	0.722829i	$0.257159\pi$
$104$	−416.924			−4.00888
$105$	17.1815			0.163634
$106$	182.170	−	182.170i	1.71858	−	1.71858i
$107$			98.0644i			0.916490i	0.888826	+	0.458245i	$0.151522\pi$
$107$			98.0644i			0.916490i	−0.888826	+	0.458245i	$0.848478\pi$
$108$	−102.463	+	102.463i	−0.948735	+	0.948735i
$109$		−	164.617i		−	1.51025i	−0.655582	−	0.755124i	$-0.727577\pi$
$109$		−	164.617i		−	1.51025i	0.655582	−	0.755124i	$-0.272423\pi$
$110$	−22.1182	−	22.1182i	−0.201074	−	0.201074i
$111$	18.9755	−	18.9755i	0.170950	−	0.170950i
$112$			306.955i			2.74067i
$113$	−59.8495	−	59.8495i	−0.529642	−	0.529642i	0.390824	−	0.920466i	$-0.372190\pi$
$113$	−59.8495	−	59.8495i	−0.529642	−	0.529642i	−0.920466	+	0.390824i	$0.872190\pi$
$114$	35.1828			0.308621
$115$	26.2369	−	26.2369i	0.228147	−	0.228147i
$116$		−	76.2762i		−	0.657554i
$117$	−119.181	−	119.181i	−1.01864	−	1.01864i
$118$	−194.814	+	194.814i	−1.65097	+	1.65097i
$119$	68.8389	−	68.8389i	0.578478	−	0.578478i
$120$	−29.5152	+	29.5152i	−0.245960	+	0.245960i
$121$			107.614i			0.889371i
$122$	−242.243	+	242.243i	−1.98560	+	1.98560i
$123$	−19.2689	−	19.2689i	−0.156658	−	0.156658i
$124$	151.881	+	151.881i	1.22485	+	1.22485i
$125$	73.3005	+	73.3005i	0.586404	+	0.586404i
$126$	−178.933	+	178.933i	−1.42010	+	1.42010i
$127$			79.5090i			0.626055i	0.949744	+	0.313028i	$0.101343\pi$
$127$			79.5090i			0.626055i	−0.949744	+	0.313028i	$0.898657\pi$
$128$	20.6822	+	20.6822i	0.161579	+	0.161579i
$129$	17.1060	+	17.1060i	0.132605	+	0.132605i
$130$	−123.957	−	123.957i	−0.953513	−	0.953513i
$131$	58.1594	−	58.1594i	0.443965	−	0.443965i	−0.449377	−	0.893342i	$-0.648354\pi$
$131$	58.1594	−	58.1594i	0.443965	−	0.443965i	0.893342	+	0.449377i	$0.148354\pi$
$132$	−30.7877			−0.233240
$133$	90.6533			0.681604
$134$		−	302.432i		−	2.25696i
$135$	−35.3497			−0.261850
$136$			236.509i			1.73904i
$137$			93.6626i			0.683669i	0.939760	+	0.341834i	$0.111048\pi$
$137$			93.6626i			0.683669i	−0.939760	+	0.341834i	$0.888952\pi$
$138$		−	51.8525i		−	0.375743i
$139$	75.3266	+	75.3266i	0.541918	+	0.541918i	0.924091	−	0.382173i	$-0.124824\pi$
$139$	75.3266	+	75.3266i	0.541918	+	0.541918i	−0.382173	+	0.924091i	$0.624824\pi$
$140$	−131.076	+	131.076i	−0.936258	+	0.936258i
$141$	−47.5902	−	47.5902i	−0.337519	−	0.337519i
$142$	−279.935			−1.97137
$143$		−	75.0198i		−	0.524614i
$144$		−	301.466i		−	2.09351i
$145$	13.1576	−	13.1576i	0.0907421	−	0.0907421i
$146$		−	475.580i		−	3.25740i
$147$	13.1466	−	13.1466i	0.0894325	−	0.0894325i
$148$			289.524i			1.95625i
$149$	99.4605	+	99.4605i	0.667520	+	0.667520i	0.957141	−	0.289621i	$-0.0935294\pi$
$149$	99.4605	+	99.4605i	0.667520	+	0.667520i	−0.289621	+	0.957141i	$0.593529\pi$
$150$	63.6572			0.424382
$151$	94.6068	+	94.6068i	0.626535	+	0.626535i	0.947195	−	0.320659i	$-0.103904\pi$
$151$	94.6068	+	94.6068i	0.626535	+	0.626535i	−0.320659	+	0.947195i	$0.603904\pi$
$152$	−155.728	+	155.728i	−1.02453	+	1.02453i
$153$	−67.6080	+	67.6080i	−0.441882	+	0.441882i
$154$	−112.631			−0.731371
$155$			52.3987i			0.338056i
$156$	−172.543			−1.10605
$157$		−	97.5493i		−	0.621333i	−0.950519	−	0.310666i	$-0.899448\pi$
$157$		−	97.5493i		−	0.621333i	0.950519	−	0.310666i	$-0.100552\pi$
$158$	42.0932			0.266412
$159$	43.7413	−	43.7413i	0.275103	−	0.275103i
$160$		−	124.493i		−	0.778078i
$161$		−	133.605i		−	0.829844i
$162$	157.476	−	157.476i	0.972077	−	0.972077i
$163$		−	198.133i		−	1.21554i	−0.794112	−	0.607771i	$-0.792064\pi$
$163$		−	198.133i		−	1.21554i	0.794112	−	0.607771i	$-0.207936\pi$
$164$	294.001			1.79269
$165$	−5.31086	−	5.31086i	−0.0321870	−	0.0321870i
$166$	299.040	+	299.040i	1.80145	+	1.80145i
$167$	130.385	−	130.385i	0.780746	−	0.780746i	−0.199211	−	0.979957i	$-0.563838\pi$
$167$	130.385	−	130.385i	0.780746	−	0.780746i	0.979957	+	0.199211i	$0.0638379\pi$
$168$			150.298i			0.894634i
$169$		−	251.433i		−	1.48777i
$170$	−70.3171	+	70.3171i	−0.413630	+	0.413630i
$171$	−89.0323			−0.520657
$172$	−261.000			−1.51744
$173$			37.4801i			0.216648i	0.994116	+	0.108324i	$0.0345484\pi$
$173$			37.4801i			0.216648i	−0.994116	+	0.108324i	$0.965452\pi$
$174$		−	26.0036i		−	0.149446i
$175$	164.021			0.937265
$176$	94.8805	−	94.8805i	0.539094	−	0.539094i
$177$	−46.7774	+	46.7774i	−0.264279	+	0.264279i
$178$	474.352			2.66490
$179$	2.00525	−	2.00525i	0.0112025	−	0.0112025i	−0.701483	−	0.712686i	$-0.747479\pi$
$179$	2.00525	−	2.00525i	0.0112025	−	0.0112025i	0.712686	+	0.701483i	$0.247479\pi$
$180$	128.732	−	128.732i	0.715180	−	0.715180i
$181$		−	195.358i		−	1.07933i	−0.841881	−	0.539663i	$-0.818552\pi$
$181$		−	195.358i		−	1.07933i	0.841881	−	0.539663i	$-0.181448\pi$
$182$	−631.218			−3.46823
$183$	−58.1657	+	58.1657i	−0.317845	+	0.317845i
$184$	229.512	+	229.512i	1.24735	+	1.24735i
$185$	−49.9428	+	49.9428i	−0.269961	+	0.269961i
$186$	51.7782	+	51.7782i	0.278377	+	0.278377i
$187$	−42.5566			−0.227575
$188$	726.121			3.86235
$189$	−90.0048	+	90.0048i	−0.476216	+	0.476216i
$190$	−92.5998			−0.487368
$191$	79.9152			0.418404			0.209202	−	0.977872i	$-0.432913\pi$
$191$	79.9152			0.418404			0.209202	+	0.977872i	$0.432913\pi$
$192$	−31.4077	−	31.4077i	−0.163582	−	0.163582i
$193$	−222.184			−1.15121			−0.575606	−	0.817727i	$-0.695234\pi$
$193$	−222.184			−1.15121			−0.575606	+	0.817727i	$0.695234\pi$
$194$	224.022	+	224.022i	1.15475	+	1.15475i
$195$	−29.7636	−	29.7636i	−0.152634	−	0.152634i
$196$			200.588i			1.02341i
$197$	113.539	+	160.990i	0.576341	+	0.817210i
$197$	113.539	+	160.990i	0.576341	+	0.817210i
$198$	110.617			0.558672
$199$	−159.724	+	159.724i	−0.802633	+	0.802633i	−0.983506	−	0.180874i	$-0.942108\pi$
$199$	−159.724	+	159.724i	−0.802633	+	0.802633i	0.180874	+	0.983506i	$0.442108\pi$
$200$	−281.763	+	281.763i	−1.40881	+	1.40881i
$201$		−	72.6179i		−	0.361283i
$202$	−157.451	+	157.451i	−0.779458	+	0.779458i
$203$		−	67.0017i		−	0.330058i
$204$			97.8788i			0.479798i
$205$	50.7150	+	50.7150i	0.247390	+	0.247390i
$206$		−	17.0385i		−	0.0827114i
$207$			131.216i			0.633893i
$208$	531.738	−	531.738i	2.55643	−	2.55643i
$209$	−28.0212	−	28.0212i	−0.134073	−	0.134073i
$210$	−44.6856	+	44.6856i	−0.212789	+	0.212789i
$211$	−279.107	−	279.107i	−1.32278	−	1.32278i	−0.911516	−	0.411265i	$-0.865087\pi$
$211$	−279.107	−	279.107i	−1.32278	−	1.32278i	−0.411265	−	0.911516i	$-0.634913\pi$
$212$			667.396i			3.14810i
$213$	−67.2161			−0.315568
$214$	−255.045	−	255.045i	−1.19180	−	1.19180i
$215$	−45.0223	−	45.0223i	−0.209406	−	0.209406i
$216$		−	309.228i		−	1.43161i
$217$	133.414	+	133.414i	0.614809	+	0.614809i
$218$	428.135	+	428.135i	1.96392	+	1.96392i
$219$		−	114.193i		−	0.521429i
$220$	81.0320			0.368327
$221$	−238.500			−1.07918
$222$			98.7027i			0.444607i
$223$		−	270.794i		−	1.21432i	−0.794578	−	0.607162i	$-0.792308\pi$
$223$		−	270.794i		−	1.21432i	0.794578	−	0.607162i	$-0.207692\pi$
$224$	−316.973	−	316.973i	−1.41506	−	1.41506i
$225$	−161.088			−0.715949
$226$	311.313			1.37749
$227$	230.378	+	230.378i	1.01488	+	1.01488i	0.999888	+	0.0149918i	$0.00477222\pi$
$227$	230.378	+	230.378i	1.01488	+	1.01488i	0.0149918	+	0.999888i	$0.495228\pi$
$228$	−64.4478	+	64.4478i	−0.282666	+	0.282666i
$229$	−50.3697	+	50.3697i	−0.219955	+	0.219955i	−0.808480	−	0.588524i	$-0.799709\pi$
$229$	−50.3697	+	50.3697i	−0.219955	+	0.219955i	0.588524	+	0.808480i	$0.299709\pi$
$230$			136.474i			0.593364i
$231$	−27.0442			−0.117074
$232$	115.098	+	115.098i	0.496114	+	0.496114i
$233$	265.569			1.13978			0.569890	−	0.821721i	$-0.306986\pi$
$233$	265.569			1.13978			0.569890	+	0.821721i	$0.306986\pi$
$234$	619.931			2.64928
$235$	125.256	+	125.256i	0.533002	+	0.533002i
$236$		−	713.719i		−	3.02423i
$237$	10.1071			0.0426460
$238$			358.072i			1.50450i
$239$	296.870			1.24213			0.621067	−	0.783757i	$-0.286699\pi$
$239$	296.870			1.24213			0.621067	+	0.783757i	$0.286699\pi$
$240$		−	75.2864i		−	0.313693i
$241$	116.921	+	116.921i	0.485148	+	0.485148i	0.906771	−	0.421623i	$-0.138540\pi$
$241$	116.921	+	116.921i	0.485148	+	0.485148i	−0.421623	+	0.906771i	$0.638540\pi$
$242$	−279.881	−	279.881i	−1.15653	−	1.15653i
$243$	134.595	−	134.595i	0.553888	−	0.553888i
$244$		−	887.480i		−	3.63721i
$245$	−34.6013	+	34.6013i	−0.141230	+	0.141230i
$246$	100.229			0.407434
$247$	−157.039	−	157.039i	−0.635785	−	0.635785i
$248$	−458.367			−1.84825
$249$	71.8034	+	71.8034i	0.288367	+	0.288367i
$250$	−381.279			−1.52511
$251$	−144.851			−0.577098			−0.288549	−	0.957465i	$-0.593173\pi$
$251$	−144.851			−0.577098			−0.288549	+	0.957465i	$0.593173\pi$
$252$		−	655.537i		−	2.60134i
$253$	−41.2976	+	41.2976i	−0.163232	+	0.163232i
$254$	−206.787	−	206.787i	−0.814120	−	0.814120i
$255$	−16.8840	+	16.8840i	−0.0662119	+	0.0662119i
$256$	−308.755			−1.20608
$257$	−478.146			−1.86049			−0.930246	−	0.366937i	$-0.880406\pi$
$257$	−478.146			−1.86049			−0.930246	+	0.366937i	$0.880406\pi$
$258$	−88.9783			−0.344877
$259$			254.321i			0.981934i
$260$	454.127			1.74664
$261$			65.8037i			0.252121i
$262$			302.521i			1.15466i
$263$	−211.841	−	211.841i	−0.805477	−	0.805477i	0.178468	−	0.983946i	$-0.442886\pi$
$263$	−211.841	−	211.841i	−0.805477	−	0.805477i	−0.983946	+	0.178468i	$0.942886\pi$
$264$	46.4576	−	46.4576i	0.175976	−	0.175976i
$265$	−115.125	+	115.125i	−0.434436	+	0.434436i
$266$	−235.771	+	235.771i	−0.886355	+	0.886355i
$267$	113.898			0.426585
$268$	553.994	+	553.994i	2.06714	+	2.06714i
$269$	−138.078	+	138.078i	−0.513300	+	0.513300i	−0.915536	−	0.402236i	$-0.868233\pi$
$269$	−138.078	+	138.078i	−0.513300	+	0.513300i	0.402236	+	0.915536i	$0.368233\pi$
$270$	91.9373	−	91.9373i	0.340509	−	0.340509i
$271$	−5.74612	+	5.74612i	−0.0212034	+	0.0212034i	−0.717629	−	0.696426i	$-0.754773\pi$
$271$	−5.74612	+	5.74612i	−0.0212034	+	0.0212034i	0.696426	+	0.717629i	$0.254773\pi$
$272$	−301.640	−	301.640i	−1.10897	−	1.10897i
$273$	−151.564			−0.555178
$274$	−243.597	−	243.597i	−0.889041	−	0.889041i
$275$	−50.6994	−	50.6994i	−0.184362	−	0.184362i
$276$	94.9832	+	94.9832i	0.344142	+	0.344142i
$277$	310.633	−	310.633i	1.12142	−	1.12142i	0.129889	−	0.991529i	$-0.458538\pi$
$277$	310.633	−	310.633i	1.12142	−	1.12142i	0.991529	−	0.129889i	$-0.0414621\pi$
$278$	−391.818			−1.40942
$279$	−131.028	−	131.028i	−0.469634	−	0.469634i
$280$		−	395.580i		−	1.41278i
$281$	−276.302	+	276.302i	−0.983283	+	0.983283i	−0.999863	−	0.0165796i	$-0.994722\pi$
$281$	−276.302	+	276.302i	−0.983283	+	0.983283i	0.0165796	+	0.999863i	$0.494722\pi$
$282$	247.545			0.877817
$283$	−51.4173	−	51.4173i	−0.181686	−	0.181686i	0.610404	−	0.792090i	$-0.291007\pi$
$283$	−51.4173	−	51.4173i	−0.181686	−	0.181686i	−0.792090	+	0.610404i	$0.791007\pi$
$284$	512.784	−	512.784i	1.80558	−	1.80558i
$285$	−22.2344			−0.0780155
$286$	195.111	+	195.111i	0.682207	+	0.682207i
$287$	258.253			0.899837
$288$	311.305	+	311.305i	1.08092	+	1.08092i
$289$		−	153.706i		−	0.531855i
$290$			68.4404i			0.236001i
$291$	53.7905	+	53.7905i	0.184847	+	0.184847i
$292$	871.166	+	871.166i	2.98344	+	2.98344i
$293$			342.169i			1.16781i	0.811821	+	0.583906i	$0.198476\pi$
$293$			342.169i			1.16781i	−0.811821	+	0.583906i	$0.801524\pi$
$294$			68.3831i			0.232595i
$295$	123.116	−	123.116i	0.417343	−	0.417343i
$296$	−436.883	−	436.883i	−1.47596	−	1.47596i
$297$	55.6414			0.187345
$298$	−517.352			−1.73608
$299$	−231.444	+	231.444i	−0.774060	+	0.774060i
$300$	−116.607	+	116.607i	−0.388690	+	0.388690i
$301$	−229.265			−0.761676
$302$	−492.106			−1.62949
$303$	−37.8059	+	37.8059i	−0.124772	+	0.124772i
$304$		−	397.226i		−	1.30667i
$305$	153.090	−	153.090i	0.501934	−	0.501934i
$306$		−	351.669i		−	1.14924i
$307$	−256.870	−	256.870i	−0.836708	−	0.836708i	0.151716	−	0.988424i	$-0.451520\pi$
$307$	−256.870	−	256.870i	−0.836708	−	0.836708i	−0.988424	+	0.151716i	$0.951520\pi$
$308$	206.317	−	206.317i	0.669861	−	0.669861i
$309$		−	4.09118i		−	0.0132401i
$310$	−136.278	−	136.278i	−0.439607	−	0.439607i
$311$	335.465			1.07866			0.539332	−	0.842093i	$-0.318677\pi$
$311$	335.465			1.07866			0.539332	+	0.842093i	$0.318677\pi$
$312$	260.362	−	260.362i	0.834495	−	0.834495i
$313$			121.029i			0.386674i	0.981132	+	0.193337i	$0.0619311\pi$
$313$			121.029i			0.386674i	−0.981132	+	0.193337i	$0.938069\pi$
$314$	253.705	+	253.705i	0.807979	+	0.807979i
$315$	113.080	−	113.080i	0.358983	−	0.358983i
$316$	−77.1061	+	77.1061i	−0.244007	+	0.244007i
$317$	−105.696	+	105.696i	−0.333426	+	0.333426i	−0.853886	−	0.520460i	$-0.825761\pi$
$317$	−105.696	+	105.696i	−0.333426	+	0.333426i	0.520460	+	0.853886i	$0.325761\pi$
$318$			227.524i			0.715485i
$319$	−20.7104	+	20.7104i	−0.0649229	+	0.0649229i
$320$	82.6638	+	82.6638i	0.258324	+	0.258324i
$321$	−61.2396	−	61.2396i	−0.190778	−	0.190778i
$322$	347.479	+	347.479i	1.07913	+	1.07913i
$323$	−89.0836	+	89.0836i	−0.275801	+	0.275801i
$324$			576.930i			1.78065i
$325$	−284.135	−	284.135i	−0.874260	−	0.874260i
$326$	515.304	+	515.304i	1.58069	+	1.58069i
$327$	102.801	+	102.801i	0.314375	+	0.314375i
$328$	−443.638	+	443.638i	−1.35256	+	1.35256i
$329$	637.832			1.93870
$330$	27.6249			0.0837118
$331$			100.952i			0.304990i	0.988304	+	0.152495i	$0.0487309\pi$
$331$			100.952i			0.304990i	−0.988304	+	0.152495i	$0.951269\pi$
$332$	−1095.56			−3.29988
$333$		−	249.773i		−	0.750070i
$334$			678.206i			2.03056i
$335$			191.127i			0.570529i
$336$	−191.688	−	191.688i	−0.570501	−	0.570501i
$337$	−374.454	+	374.454i	−1.11114	+	1.11114i	−0.118142	+	0.992997i	$0.537694\pi$
$337$	−374.454	+	374.454i	−1.11114	+	1.11114i	−0.992997	+	0.118142i	$0.962306\pi$
$338$	653.926	+	653.926i	1.93469	+	1.93469i
$339$	74.7502			0.220502
$340$		−	257.613i		−	0.757686i
$341$		−	82.4769i		−	0.241868i
$342$	231.555	−	231.555i	0.677060	−	0.677060i
$343$		−	233.917i		−	0.681974i
$344$	393.840	−	393.840i	1.14488	−	1.14488i
$345$			32.7691i			0.0949829i
$346$	−97.4779	−	97.4779i	−0.281728	−	0.281728i
$347$	550.050			1.58516			0.792580	−	0.609769i	$-0.208738\pi$
$347$	550.050			1.58516			0.792580	+	0.609769i	$0.208738\pi$
$348$	47.6333	+	47.6333i	0.136877	+	0.136877i
$349$	−41.6734	+	41.6734i	−0.119408	+	0.119408i	−0.764286	−	0.644878i	$-0.776908\pi$
$349$	−41.6734	+	41.6734i	−0.119408	+	0.119408i	0.644878	+	0.764286i	$0.276908\pi$
$350$	−426.586	+	426.586i	−1.21882	+	1.21882i
$351$	311.831			0.888407
$352$			195.954i			0.556689i
$353$	−435.069			−1.23249			−0.616245	−	0.787554i	$-0.711347\pi$
$353$	−435.069			−1.23249			−0.616245	+	0.787554i	$0.711347\pi$
$354$		−	243.316i		−	0.687335i
$355$	176.910			0.498338
$356$	−868.917	+	868.917i	−2.44078	+	2.44078i
$357$			85.9776i			0.240834i
$358$			10.4305i			0.0291354i
$359$	121.931	−	121.931i	0.339642	−	0.339642i	−0.516591	−	0.856232i	$-0.672799\pi$
$359$	121.931	−	121.931i	0.339642	−	0.339642i	0.856232	+	0.516591i	$0.172799\pi$
$360$			388.506i			1.07918i
$361$	243.687			0.675032
$362$	508.086	+	508.086i	1.40355	+	1.40355i
$363$	−67.2031	−	67.2031i	−0.185133	−	0.185133i
$364$	1156.26	−	1156.26i	3.17655	−	3.17655i
$365$			300.551i			0.823428i
$366$		−	302.554i		−	0.826650i
$367$	191.381	−	191.381i	0.521473	−	0.521473i	−0.396543	−	0.918016i	$-0.629790\pi$
$367$	191.381	−	191.381i	0.521473	−	0.521473i	0.918016	+	0.396543i	$0.129790\pi$
$368$	−585.432			−1.59085
$369$	−253.635			−0.687358
$370$		−	259.782i		−	0.702112i
$371$			586.247i			1.58018i
$372$	−189.694			−0.509931
$373$	368.016	−	368.016i	0.986638	−	0.986638i	−0.0132741	−	0.999912i	$-0.504225\pi$
$373$	368.016	−	368.016i	0.986638	−	0.986638i	0.999912	+	0.0132741i	$0.00422539\pi$
$374$	110.681	−	110.681i	0.295938	−	0.295938i
$375$	−91.5500			−0.244133
$376$	−1095.69	+	1095.69i	−2.91408	+	2.91408i
$377$	−116.067	+	116.067i	−0.307871	+	0.307871i
$378$		−	468.167i		−	1.23854i
$379$	−661.843			−1.74629			−0.873143	−	0.487463i	$-0.837922\pi$
$379$	−661.843			−1.74629			−0.873143	+	0.487463i	$0.837922\pi$
$380$	169.624	−	169.624i	0.446379	−	0.446379i
$381$	−49.6521	−	49.6521i	−0.130321	−	0.130321i
$382$	−207.843	+	207.843i	−0.544091	+	0.544091i
$383$	50.4348	+	50.4348i	0.131683	+	0.131683i	0.769876	−	0.638193i	$-0.220318\pi$
$383$	50.4348	+	50.4348i	0.131683	+	0.131683i	−0.638193	+	0.769876i	$0.720318\pi$
$384$	−25.8314			−0.0672692
$385$	71.1792			0.184881
$386$	577.854	−	577.854i	1.49703	−	1.49703i
$387$	225.165			0.581822
$388$	−820.724			−2.11527
$389$	−241.121	−	241.121i	−0.619848	−	0.619848i	0.325645	−	0.945492i	$-0.394419\pi$
$389$	−241.121	−	241.121i	−0.619848	−	0.619848i	−0.945492	+	0.325645i	$0.894419\pi$
$390$	154.818			0.396969
$391$	131.292	+	131.292i	0.335784	+	0.335784i
$392$	−302.681	−	302.681i	−0.772145	−	0.772145i
$393$			72.6393i			0.184833i
$394$	−713.994	−	123.411i	−1.81217	−	0.313225i
$395$	−26.6015			−0.0673456
$396$	−202.628	+	202.628i	−0.511687	+	0.511687i
$397$	−59.0299	+	59.0299i	−0.148690	+	0.148690i	−0.777533	−	0.628843i	$-0.783529\pi$
$397$	−59.0299	+	59.0299i	−0.148690	+	0.148690i	0.628843	+	0.777533i	$0.283529\pi$
$398$		−	830.818i		−	2.08748i
$399$	−56.6116	+	56.6116i	−0.141884	+	0.141884i
$400$		−	718.712i		−	1.79678i
$401$			272.517i			0.679592i	0.940499	+	0.339796i	$0.110358\pi$
$401$			272.517i			0.679592i	−0.940499	+	0.339796i	$0.889642\pi$
$402$	188.864	+	188.864i	0.469811	+	0.469811i
$403$		−	462.225i		−	1.14696i
$404$		−	576.835i		−	1.42781i
$405$	−99.5200	+	99.5200i	−0.245728	+	0.245728i
$406$	174.258	+	174.258i	0.429206	+	0.429206i
$407$	78.6112	−	78.6112i	0.193148	−	0.193148i
$408$	−147.696	−	147.696i	−0.362000	−	0.362000i
$409$		−	450.039i		−	1.10034i	−0.835053	−	0.550170i	$-0.814563\pi$
$409$		−	450.039i		−	1.10034i	0.835053	−	0.550170i	$-0.185437\pi$
$410$	−263.798			−0.643411
$411$	−58.4908	−	58.4908i	−0.142313	−	0.142313i
$412$	31.2112	+	31.2112i	0.0757552	+	0.0757552i
$413$		−	626.938i		−	1.51801i
$414$	−341.265	−	341.265i	−0.824312	−	0.824312i
$415$	−188.984	−	188.984i	−0.455382	−	0.455382i
$416$			1098.19i			2.63987i
$417$	−94.0806			−0.225613
$418$	145.755			0.348695
$419$		−	287.457i		−	0.686056i	−0.939325	−	0.343028i	$-0.888547\pi$
$419$		−	287.457i		−	0.686056i	0.939325	−	0.343028i	$-0.111453\pi$
$420$		−	163.710i		−	0.389786i
$421$	570.167	+	570.167i	1.35432	+	1.35432i	0.880768	+	0.473548i	$0.157027\pi$
$421$	570.167	+	570.167i	1.35432	+	1.35432i	0.473548	+	0.880768i	$0.342973\pi$
$422$	1451.80			3.44028
$423$	−626.426			−1.48091
$424$	−1007.08	−	1007.08i	−2.37519	−	2.37519i
$425$	−161.181	+	161.181i	−0.379250	+	0.379250i
$426$	174.815	−	174.815i	0.410364	−	0.410364i
$427$		−	779.571i		−	1.82569i
$428$	934.382			2.18313
$429$	46.8487	+	46.8487i	0.109204	+	0.109204i
$430$	234.187			0.544622
$431$	−256.098			−0.594194			−0.297097	−	0.954847i	$-0.596019\pi$
$431$	−256.098			−0.594194			−0.297097	+	0.954847i	$0.596019\pi$
$432$	394.385	+	394.385i	0.912927	+	0.912927i
$433$		−	596.148i		−	1.37678i	−0.725338	−	0.688392i	$-0.758317\pi$
$433$		−	596.148i		−	1.37678i	0.725338	−	0.688392i	$-0.241683\pi$
$434$	−693.962			−1.59899
$435$			16.4334i			0.0377780i
$436$	−1568.51			−3.59750
$437$			172.897i			0.395644i
$438$	296.992	+	296.992i	0.678064	+	0.678064i
$439$	508.878	+	508.878i	1.15918	+	1.15918i	0.984653	+	0.174522i	$0.0558381\pi$
$439$	508.878	+	508.878i	1.15918	+	1.15918i	0.174522	+	0.984653i	$0.444162\pi$
$440$	−122.275	+	122.275i	−0.277897	+	0.277897i
$441$		−	173.047i		−	0.392398i
$442$	620.288	−	620.288i	1.40337	−	1.40337i
$443$	710.347			1.60349			0.801746	−	0.597664i	$-0.203904\pi$
$443$	710.347			1.60349			0.801746	+	0.597664i	$0.203904\pi$
$444$	−180.803	−	180.803i	−0.407215	−	0.407215i
$445$	−299.775			−0.673653
$446$	704.280	+	704.280i	1.57910	+	1.57910i
$447$	−124.223			−0.277904
$448$	420.944			0.939608
$449$			575.824i			1.28246i	0.767349	+	0.641229i	$0.221575\pi$
$449$			575.824i			1.28246i	−0.767349	+	0.641229i	$0.778425\pi$
$450$	418.958	−	418.958i	0.931017	−	0.931017i
$451$	−79.8267	−	79.8267i	−0.176999	−	0.176999i
$452$	−570.261	+	570.261i	−1.26164	+	1.26164i
$453$	−118.161			−0.260841
$454$	−1198.33			−2.63949
$455$	398.909			0.876724
$456$		−	194.499i		−	0.426534i
$457$	550.354			1.20428			0.602138	−	0.798392i	$-0.294316\pi$
$457$	550.354			1.20428			0.602138	+	0.798392i	$0.294316\pi$
$458$		−	262.002i		−	0.572058i
$459$		−	176.893i		−	0.385387i
$460$	−249.992	−	249.992i	−0.543461	−	0.543461i
$461$	−76.7874	+	76.7874i	−0.166567	+	0.166567i	−0.785469	−	0.618902i	$-0.787578\pi$
$461$	−76.7874	+	76.7874i	−0.166567	+	0.166567i	0.618902	+	0.785469i	$0.287578\pi$
$462$	70.3363	−	70.3363i	0.152243	−	0.152243i
$463$	−309.182	+	309.182i	−0.667780	+	0.667780i	−0.957202	−	0.289422i	$-0.906537\pi$
$463$	−309.182	+	309.182i	−0.667780	+	0.667780i	0.289422	+	0.957202i	$0.406537\pi$
$464$	−293.589			−0.632736
$465$	−32.7222	−	32.7222i	−0.0703702	−	0.0703702i
$466$	−690.689	+	690.689i	−1.48217	+	1.48217i
$467$	237.080	−	237.080i	0.507666	−	0.507666i	−0.406143	−	0.913810i	$-0.633127\pi$
$467$	237.080	−	237.080i	0.507666	−	0.507666i	0.913810	+	0.406143i	$0.133127\pi$
$468$	−1135.59	+	1135.59i	−2.42647	+	2.42647i
$469$	486.634	+	486.634i	1.03760	+	1.03760i
$470$	−651.527			−1.38623
$471$	60.9180	+	60.9180i	0.129337	+	0.129337i
$472$	1076.98	+	1076.98i	2.28174	+	2.28174i
$473$	70.8663	+	70.8663i	0.149823	+	0.149823i
$474$	−26.2865	+	26.2865i	−0.0554568	+	0.0554568i
$475$	−212.258			−0.446859
$476$	−655.914	−	655.914i	−1.37797	−	1.37797i
$477$		−	575.764i		−	1.20705i
$478$	−772.097	+	772.097i	−1.61527	+	1.61527i
$479$	−606.416			−1.26600			−0.633002	−	0.774150i	$-0.718177\pi$
$479$	−606.416			−1.26600			−0.633002	+	0.774150i	$0.718177\pi$
$480$	77.7436	+	77.7436i	0.161966	+	0.161966i
$481$	440.560	−	440.560i	0.915926	−	0.915926i
$482$	−608.173			−1.26177
$483$	83.4341	+	83.4341i	0.172741	+	0.172741i
$484$	1025.37			2.11854
$485$	−141.574	−	141.574i	−0.291906	−	0.291906i
$486$			700.107i			1.44055i
$487$			459.304i			0.943129i	0.881832	+	0.471565i	$0.156311\pi$
$487$			459.304i			0.943129i	−0.881832	+	0.471565i	$0.843689\pi$
$488$	1339.18	+	1339.18i	2.74422	+	2.74422i
$489$	123.731	+	123.731i	0.253029	+	0.253029i
$490$		−	179.981i		−	0.367309i
$491$			109.257i			0.222518i	0.993791	+	0.111259i	$0.0354884\pi$
$491$			109.257i			0.222518i	−0.993791	+	0.111259i	$0.964512\pi$
$492$	−183.599	+	183.599i	−0.373169	+	0.373169i
$493$	65.8416	+	65.8416i	0.133553	+	0.133553i
$494$	816.852			1.65355
$495$	−69.9064			−0.141225
$496$	584.594	−	584.594i	1.17862	−	1.17862i
$497$	450.435	−	450.435i	0.906307	−	0.906307i
$498$	−373.492			−0.749983
$499$	410.164			0.821972			0.410986	−	0.911642i	$-0.365184\pi$
$499$	410.164			0.821972			0.410986	+	0.911642i	$0.365184\pi$
$500$	698.425	−	698.425i	1.39685	−	1.39685i
$501$			162.846i			0.325042i
$502$	376.729	−	376.729i	0.750456	−	0.750456i
$503$		−	361.862i		−	0.719408i	−0.933066	−	0.359704i	$-0.882878\pi$
$503$		−	361.862i		−	0.719408i	0.933066	−	0.359704i	$-0.117122\pi$
$504$	989.184	+	989.184i	1.96267	+	1.96267i
$505$	99.5037	−	99.5037i	0.197037	−	0.197037i
$506$		−	214.813i		−	0.424532i
$507$	157.016	+	157.016i	0.309696	+	0.309696i
$508$	757.582			1.49130
$509$	222.334	−	222.334i	0.436806	−	0.436806i	−0.454130	−	0.890936i	$-0.650050\pi$
$509$	222.334	−	222.334i	0.436806	−	0.436806i	0.890936	+	0.454130i	$0.150050\pi$
$510$		−	87.8238i		−	0.172203i
$511$	765.240	+	765.240i	1.49753	+	1.49753i
$512$	720.280	−	720.280i	1.40680	−	1.40680i
$513$	116.474	−	116.474i	0.227045	−	0.227045i
$514$	1243.56	−	1243.56i	2.41938	−	2.41938i
$515$			10.7678i			0.0209084i
$516$	162.990	−	162.990i	0.315872	−	0.315872i
$517$	−197.155	−	197.155i	−0.381345	−	0.381345i
$518$	−661.436	−	661.436i	−1.27690	−	1.27690i
$519$	−23.4057	−	23.4057i	−0.0450977	−	0.0450977i
$520$	−685.263	+	685.263i	−1.31781	+	1.31781i
$521$		−	573.279i		−	1.10034i	−0.835051	−	0.550172i	$-0.814562\pi$
$521$		−	573.279i		−	1.10034i	0.835051	−	0.550172i	$-0.185438\pi$
$522$	−171.142	−	171.142i	−0.327858	−	0.327858i
$523$	429.041	+	429.041i	0.820347	+	0.820347i	0.986158	−	0.165811i	$-0.0530242\pi$
$523$	429.041	+	429.041i	0.820347	+	0.820347i	−0.165811	+	0.986158i	$0.553024\pi$
$524$	−554.157	−	554.157i	−1.05755	−	1.05755i
$525$	−102.429	+	102.429i	−0.195102	+	0.195102i
$526$	1101.91			2.09488
$527$	−262.207			−0.497546
$528$			118.503i			0.224437i
$529$	−274.185			−0.518308
$530$		−	598.835i		−	1.12988i
$531$			615.727i			1.15956i
$532$		−	863.767i		−	1.62362i
$533$	−447.373	−	447.373i	−0.839348	−	0.839348i
$534$	−296.226	+	296.226i	−0.554730	+	0.554730i
$535$	161.180	+	161.180i	0.301272	+	0.301272i
$536$	−1671.92			−3.11925
$537$			2.50449i			0.00466386i
$538$		−	718.223i		−	1.33499i
$539$	54.4633	−	54.4633i	0.101045	−	0.101045i
$540$			336.821i			0.623743i
$541$	−223.673	+	223.673i	−0.413444	+	0.413444i	−0.882936	−	0.469493i	$-0.844437\pi$
$541$	−223.673	+	223.673i	−0.413444	+	0.413444i	0.469493	+	0.882936i	$0.344437\pi$
$542$		−	29.8889i		−	0.0551456i
$543$	121.998	+	121.998i	0.224674	+	0.224674i
$544$	622.969			1.14516
$545$	−270.567	−	270.567i	−0.496454	−	0.496454i
$546$	394.186	−	394.186i	0.721952	−	0.721952i
$547$	−199.839	+	199.839i	−0.365337	+	0.365337i	−0.865773	−	0.500436i	$-0.833173\pi$
$547$	−199.839	+	199.839i	−0.365337	+	0.365337i	0.500436	+	0.865773i	$0.333173\pi$
$548$	892.441			1.62854
$549$			765.631i			1.39459i
$550$	263.717			0.479486
$551$			86.7062i			0.157361i
$552$	−286.653			−0.519300
$553$	−67.7307	+	67.7307i	−0.122479	+	0.122479i
$554$			1615.78i			2.91657i
$555$		−	62.3769i		−	0.112391i
$556$	717.731	−	717.731i	1.29088	−	1.29088i
$557$		−	200.211i		−	0.359445i	−0.983717	−	0.179723i	$-0.942480\pi$
$557$		−	200.211i		−	0.359445i	0.983717	−	0.179723i	$-0.0575200\pi$
$558$	681.553			1.22142
$559$	397.155	+	397.155i	0.710475	+	0.710475i
$560$	504.516	+	504.516i	0.900922	+	0.900922i
$561$	26.5759	−	26.5759i	0.0473724	−	0.0473724i
$562$		−	1437.21i		−	2.55732i
$563$		−	789.788i		−	1.40282i	−0.712758	−	0.701410i	$-0.752554\pi$
$563$		−	789.788i		−	1.40282i	0.712758	−	0.701410i	$-0.247446\pi$
$564$	−453.451	+	453.451i	−0.803992	+	0.803992i
$565$	−196.739			−0.348211
$566$	267.451			0.472529
$567$			506.780i			0.893793i
$568$			1547.55i			2.72456i
$569$	643.352			1.13067			0.565335	−	0.824861i	$-0.308747\pi$
$569$	643.352			1.13067			0.565335	+	0.824861i	$0.308747\pi$
$570$	57.8271	−	57.8271i	0.101451	−	0.101451i
$571$	72.6494	−	72.6494i	0.127232	−	0.127232i	−0.640623	−	0.767855i	$-0.721324\pi$
$571$	72.6494	−	72.6494i	0.127232	−	0.127232i	0.767855	+	0.640623i	$0.221324\pi$
$572$	−714.808			−1.24966
$573$	−49.9058	+	49.9058i	−0.0870956	+	0.0870956i
$574$	−671.663	+	671.663i	−1.17014	+	1.17014i
$575$			312.826i			0.544045i
$576$	−413.417			−0.717738
$577$	−383.926	+	383.926i	−0.665384	+	0.665384i	−0.956644	−	0.291260i	$-0.905925\pi$
$577$	−383.926	+	383.926i	−0.665384	+	0.665384i	0.291260	+	0.956644i	$0.405925\pi$
$578$	399.758	+	399.758i	0.691622	+	0.691622i
$579$	138.750	−	138.750i	0.239638	−	0.239638i
$580$	−125.369	−	125.369i	−0.216153	−	0.216153i
$581$	−962.351			−1.65637
$582$	−279.796			−0.480749
$583$	181.210	−	181.210i	0.310824	−	0.310824i
$584$	−2629.12			−4.50192
$585$	−391.776			−0.669703
$586$	−889.911	−	889.911i	−1.51862	−	1.51862i
$587$	881.823			1.50225			0.751127	−	0.660158i	$-0.229511\pi$
$587$	881.823			1.50225			0.751127	+	0.660158i	$0.229511\pi$
$588$	−125.264	−	125.264i	−0.213034	−	0.213034i
$589$	−172.649	−	172.649i	−0.293122	−	0.293122i
$590$			640.399i			1.08542i
$591$	−171.439	−	29.6325i	−0.290083	−	0.0501396i
$592$	1114.39			1.88241
$593$	−569.208	+	569.208i	−0.959879	+	0.959879i	−0.999226	−	0.0393467i	$-0.987472\pi$
$593$	−569.208	+	569.208i	−0.959879	+	0.959879i	0.0393467	+	0.999226i	$0.487472\pi$
$594$	−144.712	+	144.712i	−0.243623	+	0.243623i
$595$		−	226.290i		−	0.380319i
$596$	947.684	−	947.684i	1.59007	−	1.59007i
$597$		−	199.490i		−	0.334154i
$598$		−	1203.88i		−	2.01317i
$599$	466.304	+	466.304i	0.778471	+	0.778471i	0.979571	−	0.201100i	$-0.0644517\pi$
$599$	466.304	+	466.304i	0.778471	+	0.778471i	−0.201100	+	0.979571i	$0.564452\pi$
$600$		−	351.913i		−	0.586522i
$601$			852.861i			1.41907i	0.704670	+	0.709535i	$0.251095\pi$
$601$			852.861i			1.41907i	−0.704670	+	0.709535i	$0.748905\pi$
$602$	596.270	−	596.270i	0.990481	−	0.990481i
$603$	−477.932	−	477.932i	−0.792590	−	0.792590i
$604$	901.437	−	901.437i	1.49245	−	1.49245i
$605$	176.876	+	176.876i	0.292357	+	0.292357i
$606$		−	196.651i		−	0.324506i
$607$	650.935			1.07238			0.536190	−	0.844097i	$-0.319863\pi$
$607$	650.935			1.07238			0.536190	+	0.844097i	$0.319863\pi$
$608$	410.191	+	410.191i	0.674657	+	0.674657i
$609$	41.8415	+	41.8415i	0.0687053	+	0.0687053i
$610$			796.310i			1.30543i
$611$	−1104.92	−	1104.92i	−1.80838	−	1.80838i
$612$	644.186	+	644.186i	1.05259	+	1.05259i
$613$		−	170.873i		−	0.278749i	−0.990240	−	0.139374i	$-0.955491\pi$
$613$		−	170.873i		−	0.278749i	0.990240	−	0.139374i	$-0.0445092\pi$
$614$	1336.13			2.17611
$615$	−63.3414			−0.102994
$616$			622.653i			1.01080i
$617$			645.317i			1.04589i	0.852365	+	0.522947i	$0.175168\pi$
$617$			645.317i			1.04589i	−0.852365	+	0.522947i	$0.824832\pi$
$618$	10.6403	+	10.6403i	0.0172173	+	0.0172173i
$619$	−911.412			−1.47239			−0.736197	−	0.676767i	$-0.763381\pi$
$619$	−911.412			−1.47239			−0.736197	+	0.676767i	$0.763381\pi$
$620$	499.268			0.805271
$621$	−171.660	−	171.660i	−0.276424	−	0.276424i
$622$	−872.474	+	872.474i	−1.40269	+	1.40269i
$623$	−763.265	+	763.265i	−1.22514	+	1.22514i
$624$			664.124i			1.06430i
$625$	−248.970			−0.398352
$626$	−314.771	−	314.771i	−0.502830	−	0.502830i
$627$	34.9976			0.0558175
$628$	−929.473			−1.48005
$629$	−249.917	−	249.917i	−0.397325	−	0.397325i
$630$			588.194i			0.933641i
$631$	−8.88970			−0.0140883			−0.00704414	−	0.999975i	$-0.502242\pi$
$631$	−8.88970			−0.0140883			−0.00704414	+	0.999975i	$0.502242\pi$
$632$		−	232.701i		−	0.368198i
$633$	348.595			0.550704
$634$		−	549.787i		−	0.867173i
$635$	130.682	+	130.682i	0.205799	+	0.205799i
$636$	−416.778	−	416.778i	−0.655312	−	0.655312i
$637$	305.228	−	305.228i	0.479165	−	0.479165i
$638$		−	107.727i		−	0.168851i
$639$	−442.380	+	442.380i	−0.692301	+	0.692301i
$640$	67.9871			0.106230
$641$	313.502	+	313.502i	0.489083	+	0.489083i	0.908017	−	0.418934i	$-0.137596\pi$
$641$	313.502	+	313.502i	0.489083	+	0.489083i	−0.418934	+	0.908017i	$0.637596\pi$
$642$	318.543			0.496173
$643$	199.335	+	199.335i	0.310008	+	0.310008i	0.844913	−	0.534904i	$-0.179652\pi$
$643$	199.335	+	199.335i	0.310008	+	0.310008i	−0.534904	+	0.844913i	$0.679652\pi$
$644$	−1273.02			−1.97674
$645$	56.2314			0.0871805
$646$		−	463.376i		−	0.717301i
$647$	−701.905	+	701.905i	−1.08486	+	1.08486i	−0.0888129	+	0.996048i	$0.528307\pi$
$647$	−701.905	+	701.905i	−1.08486	+	1.08486i	−0.996048	+	0.0888129i	$0.971693\pi$
$648$	−870.569	−	870.569i	−1.34347	−	1.34347i
$649$	−193.788	+	193.788i	−0.298595	+	0.298595i
$650$	1477.95			2.27377
$651$	−166.629			−0.255959
$652$	−1887.86			−2.89550
$653$			812.556i			1.24434i	0.782881	+	0.622172i	$0.213749\pi$
$653$			812.556i			1.24434i	−0.782881	+	0.622172i	$0.786251\pi$
$654$	−534.727			−0.817625
$655$		−	191.184i		−	0.291883i
$656$		−	1131.62i		−	1.72503i
$657$	−751.556	−	751.556i	−1.14392	−	1.14392i
$658$	−1658.87	+	1658.87i	−2.52108	+	2.52108i
$659$	327.628	−	327.628i	0.497160	−	0.497160i	−0.413393	−	0.910553i	$-0.635656\pi$
$659$	327.628	−	327.628i	0.497160	−	0.497160i	0.910553	+	0.413393i	$0.135656\pi$
$660$	−50.6032	+	50.6032i	−0.0766715	+	0.0766715i
$661$	894.445			1.35317			0.676584	−	0.736365i	$-0.263459\pi$
$661$	894.445			1.35317			0.676584	+	0.736365i	$0.263459\pi$
$662$	−262.555	−	262.555i	−0.396608	−	0.396608i
$663$	148.939	−	148.939i	0.224644	−	0.224644i
$664$	1653.17	−	1653.17i	2.48971	−	2.48971i
$665$	148.999	−	148.999i	0.224059	−	0.224059i
$666$	649.608	+	649.608i	0.975388	+	0.975388i
$667$	127.788			0.191586
$668$	−1242.34	−	1242.34i	−1.85978	−	1.85978i
$669$	169.107	+	169.107i	0.252776	+	0.252776i
$670$	−497.083	−	497.083i	−0.741914	−	0.741914i
$671$	−240.967	+	240.967i	−0.359117	+	0.359117i
$672$	395.889			0.589121
$673$	855.939	+	855.939i	1.27183	+	1.27183i	0.945129	+	0.326697i	$0.105936\pi$
$673$	855.939	+	855.939i	1.27183	+	1.27183i	0.326697	+	0.945129i	$0.394064\pi$
$674$		−	1947.75i		−	2.88984i
$675$	210.740	−	210.740i	0.312207	−	0.312207i
$676$	−2395.72			−3.54396
$677$	80.3325	+	80.3325i	0.118659	+	0.118659i	0.763943	−	0.645284i	$-0.223261\pi$
$677$	80.3325	+	80.3325i	0.118659	+	0.118659i	−0.645284	+	0.763943i	$0.723261\pi$
$678$	−194.410	+	194.410i	−0.286740	+	0.286740i
$679$	−720.932			−1.06176
$680$	388.730	+	388.730i	0.571662	+	0.571662i
$681$	−287.734			−0.422517
$682$	214.505	+	214.505i	0.314524	+	0.314524i
$683$			478.188i			0.700129i	0.936726	+	0.350064i	$0.113840\pi$
$683$			478.188i			0.700129i	−0.936726	+	0.350064i	$0.886160\pi$
$684$			848.322i			1.24024i
$685$	153.946	+	153.946i	0.224738	+	0.224738i
$686$	608.370	+	608.370i	0.886837	+	0.886837i
$687$		−	62.9102i		−	0.0915723i
$688$			1004.60i			1.46017i
$689$	1015.56	−	1015.56i	1.47396	−	1.47396i
$690$	−85.2256	−	85.2256i	−0.123515	−	0.123515i
$691$	−17.1704			−0.0248486			−0.0124243	−	0.999923i	$-0.503955\pi$
$691$	−17.1704			−0.0248486			−0.0124243	+	0.999923i	$0.503955\pi$
$692$	357.119			0.516068
$693$	−177.990	+	177.990i	−0.256840	+	0.256840i
$694$	−1430.57	+	1430.57i	−2.06134	+	2.06134i
$695$	247.616			0.356283
$696$	−143.754			−0.206543
$697$	−253.781	+	253.781i	−0.364105	+	0.364105i
$698$		−	216.768i		−	0.310555i
$699$	−165.843	+	165.843i	−0.237258	+	0.237258i
$700$		−	1562.84i		−	2.23262i
$701$	88.9119	+	88.9119i	0.126836	+	0.126836i	0.767675	−	0.640839i	$-0.221413\pi$
$701$	88.9119	+	88.9119i	0.126836	+	0.126836i	−0.640839	+	0.767675i	$0.721413\pi$
$702$	−811.007	+	811.007i	−1.15528	+	1.15528i
$703$		−	329.114i		−	0.468156i
$704$	−130.115	−	130.115i	−0.184822	−	0.184822i
$705$	−156.440			−0.221901
$706$	1131.52	−	1131.52i	1.60273	−	1.60273i
$707$		−	506.697i		−	0.716686i
$708$	445.706	+	445.706i	0.629529	+	0.629529i
$709$	−371.332	+	371.332i	−0.523740	+	0.523740i	−0.918699	−	0.394958i	$-0.870759\pi$
$709$	−371.332	+	371.332i	−0.523740	+	0.523740i	0.394958	+	0.918699i	$0.370759\pi$
$710$	−460.106	+	460.106i	−0.648037	+	0.648037i
$711$	66.5196	−	66.5196i	0.0935578	−	0.0935578i
$712$		−	2622.34i		−	3.68306i
$713$	−254.450	+	254.450i	−0.356872	+	0.356872i
$714$	−223.610	−	223.610i	−0.313179	−	0.313179i
$715$	−123.304	−	123.304i	−0.172453	−	0.172453i
$716$	−19.1065	−	19.1065i	−0.0266851	−	0.0266851i
$717$	−185.391	+	185.391i	−0.258564	+	0.258564i
$718$			634.236i			0.883338i
$719$	169.844	+	169.844i	0.236222	+	0.236222i	0.815284	−	0.579062i	$-0.196581\pi$
$719$	169.844	+	169.844i	0.236222	+	0.236222i	−0.579062	+	0.815284i	$0.696581\pi$
$720$	−495.495	−	495.495i	−0.688187	−	0.688187i
$721$	27.4162	+	27.4162i	0.0380252	+	0.0380252i
$722$	−633.778	+	633.778i	−0.877809	+	0.877809i
$723$	−146.030			−0.201978
$724$	−1861.42			−2.57102
$725$			156.880i			0.216386i
$726$	349.563			0.481492
$727$		−	245.746i		−	0.338028i	−0.985614	−	0.169014i	$-0.945942\pi$
$727$		−	245.746i		−	0.338028i	0.985614	−	0.169014i	$-0.0540583\pi$
$728$			3489.53i			4.79331i
$729$		−	376.840i		−	0.516927i
$730$	−781.671	−	781.671i	−1.07078	−	1.07078i
$731$	225.295	−	225.295i	0.308201	−	0.308201i
$732$	554.217	+	554.217i	0.757127	+	0.757127i
$733$	−22.8694			−0.0311997			−0.0155999	−	0.999878i	$-0.504966\pi$
$733$	−22.8694			−0.0311997			−0.0155999	+	0.999878i	$0.504966\pi$
$734$			995.483i			1.35624i
$735$		−	43.2159i		−	0.0587971i
$736$	604.540	−	604.540i	0.821386	−	0.821386i
$737$		−	300.839i		−	0.408195i
$738$	659.653	−	659.653i	0.893838	−	0.893838i
$739$		−	1401.39i		−	1.89633i	−0.317772	−	0.948167i	$-0.602935\pi$
$739$		−	1401.39i		−	1.89633i	0.317772	−	0.948167i	$-0.397065\pi$
$740$	475.867	+	475.867i	0.643064	+	0.643064i
$741$	196.137			0.264692
$742$	−1524.71	−	1524.71i	−2.05486	−	2.05486i
$743$	261.028	−	261.028i	0.351316	−	0.351316i	−0.509283	−	0.860599i	$-0.670089\pi$
$743$	261.028	−	261.028i	0.351316	−	0.351316i	0.860599	+	0.509283i	$0.170089\pi$
$744$	286.243	−	286.243i	0.384735	−	0.384735i
$745$	326.950			0.438859
$746$			1914.27i			2.56604i
$747$	945.143			1.26525
$748$			405.490i			0.542098i
$749$	820.770			1.09582
$750$	238.102	−	238.102i	0.317470	−	0.317470i
$751$			907.944i			1.20898i	0.796612	+	0.604490i	$0.206623\pi$
$751$			907.944i			1.20898i	−0.796612	+	0.604490i	$0.793377\pi$
$752$		−	2794.86i		−	3.71657i
$753$	90.4574	−	90.4574i	0.120129	−	0.120129i
$754$		−	603.734i		−	0.800708i
$755$	310.995			0.411914
$756$	857.588	+	857.588i	1.13438	+	1.13438i
$757$	800.922	+	800.922i	1.05802	+	1.05802i	0.998210	+	0.0598115i	$0.0190500\pi$
$757$	800.922	+	800.922i	1.05802	+	1.05802i	0.0598115	+	0.998210i	$0.480950\pi$
$758$	1721.32	−	1721.32i	2.27087	−	2.27087i
$759$		−	51.5794i		−	0.0679571i
$760$			511.915i			0.673572i
$761$	487.128	−	487.128i	0.640115	−	0.640115i	−0.310469	−	0.950584i	$-0.600486\pi$
$761$	487.128	−	487.128i	0.640115	−	0.640115i	0.950584	+	0.310469i	$0.100486\pi$
$762$	258.270			0.338937
$763$	−1377.79			−1.80576
$764$		−	761.452i		−	0.996664i
$765$			222.243i			0.290514i
$766$	−262.341			−0.342481
$767$	−1086.05	+	1086.05i	−1.41597	+	1.41597i
$768$	192.813	−	192.813i	0.251058	−	0.251058i
$769$	1342.31			1.74553			0.872763	−	0.488144i	$-0.162326\pi$
$769$	1342.31			1.74553			0.872763	+	0.488144i	$0.162326\pi$
$770$	−185.122	+	185.122i	−0.240419	+	0.240419i
$771$	298.595	−	298.595i	0.387282	−	0.387282i
$772$			2117.02i			2.74226i
$773$	−590.878			−0.764397			−0.382198	−	0.924080i	$-0.624833\pi$
$773$	−590.878			−0.764397			−0.382198	+	0.924080i	$0.624833\pi$
$774$	−585.607	+	585.607i	−0.756599	+	0.756599i
$775$	−312.378	−	312.378i	−0.403068	−	0.403068i
$776$	1238.45	−	1238.45i	1.59594	−	1.59594i
$777$	−158.819	−	158.819i	−0.204401	−	0.204401i
$778$	1254.21			1.61210
$779$	−334.202			−0.429015
$780$	−283.595	+	283.595i	−0.363583	+	0.363583i
$781$	−278.461			−0.356544
$782$	−682.924			−0.873304
$783$	−86.0858	−	86.0858i	−0.109944	−	0.109944i
$784$	772.068			0.984781
$785$	−160.334	−	160.334i	−0.204247	−	0.204247i
$786$	−188.920	−	188.920i	−0.240356	−	0.240356i
$787$		−	573.444i		−	0.728645i	−0.931273	−	0.364323i	$-0.881301\pi$
$787$		−	573.444i		−	0.728645i	0.931273	−	0.364323i	$-0.118699\pi$
$788$	1533.96	−	1081.83i	1.94664	−	1.37288i
$789$	264.582			0.335339
$790$	69.1850	−	69.1850i	0.0875760	−	0.0875760i
$791$	−500.923	+	500.923i	−0.633278	+	0.633278i
$792$		−	611.519i		−	0.772120i
$793$	−1350.45	+	1350.45i	−1.70297	+	1.70297i
$794$		−	307.049i		−	0.386712i
$795$		−	143.788i		−	0.180865i
$796$	1521.89	+	1521.89i	1.91192	+	1.91192i
$797$		−	29.6984i		−	0.0372627i	−0.999826	−	0.0186314i	$-0.994069\pi$
$797$		−	29.6984i		−	0.0372627i	0.999826	−	0.0186314i	$-0.00593089\pi$
$798$		−	294.470i		−	0.369010i
$799$	−626.788	+	626.788i	−0.784465	+	0.784465i
$800$	742.170	+	742.170i	0.927712	+	0.927712i
$801$	749.617	−	749.617i	0.935851	−	0.935851i
$802$	−708.759	−	708.759i	−0.883740	−	0.883740i
$803$		−	473.075i		−	0.589135i
$804$	−691.921			−0.860598
$805$	−219.595	−	219.595i	−0.272789	−	0.272789i
$806$	1202.15	+	1202.15i	1.49150	+	1.49150i
$807$		−	172.455i		−	0.213698i
$808$	870.426	+	870.426i	1.07726	+	1.07726i
$809$	509.263	+	509.263i	0.629496	+	0.629496i	0.947941	−	0.318445i	$-0.103161\pi$
$809$	509.263	+	509.263i	0.629496	+	0.629496i	−0.318445	+	0.947941i	$0.603161\pi$
$810$		−	517.662i		−	0.639089i
$811$	411.509			0.507410			0.253705	−	0.967282i	$-0.418351\pi$
$811$	411.509			0.507410			0.253705	+	0.967282i	$0.418351\pi$
$812$	−638.409			−0.786218
$813$		−	7.17672i		−	0.00882745i
$814$			408.903i			0.502338i
$815$	−325.656	−	325.656i	−0.399577	−	0.399577i
$816$	376.738			0.461689
$817$	296.689			0.363144
$818$	1170.46	+	1170.46i	1.43088	+	1.43088i
$819$	−997.510	+	997.510i	−1.21796	+	1.21796i
$820$	483.225	−	483.225i	0.589299	−	0.589299i
$821$		−	770.794i		−	0.938848i	−0.882973	−	0.469424i	$-0.844462\pi$
$821$		−	770.794i		−	0.938848i	0.882973	−	0.469424i	$-0.155538\pi$
$822$	304.245			0.370128
$823$	835.461	+	835.461i	1.01514	+	1.01514i	0.999884	+	0.0152574i	$0.00485676\pi$
$823$	835.461	+	835.461i	1.01514	+	1.01514i	0.0152574	+	0.999884i	$0.495143\pi$
$824$	−94.1933			−0.114312
$825$	63.3220			0.0767539
$826$	1630.53	+	1630.53i	1.97401	+	1.97401i
$827$			1464.44i			1.77079i	0.464840	+	0.885395i	$0.346112\pi$
$827$			1464.44i			1.77079i	−0.464840	+	0.885395i	$0.653888\pi$
$828$	1250.26			1.50997
$829$			121.690i			0.146791i	0.997303	+	0.0733956i	$0.0233836\pi$
$829$			121.690i			0.146791i	−0.997303	+	0.0733956i	$0.976616\pi$
$830$	983.015			1.18436
$831$			387.970i			0.466872i
$832$	−729.203	−	729.203i	−0.876446	−	0.876446i
$833$	−173.147	−	173.147i	−0.207860	−	0.207860i
$834$	244.684	−	244.684i	0.293386	−	0.293386i
$835$		−	428.605i		−	0.513299i
$836$	−266.993	+	266.993i	−0.319369	+	0.319369i
$837$	342.827			0.409591
$838$	747.617	+	747.617i	0.892145	+	0.892145i
$839$	−1218.77			−1.45265			−0.726324	−	0.687353i	$-0.758773\pi$
$839$	−1218.77			−1.45265			−0.726324	+	0.687353i	$0.758773\pi$
$840$	247.033	+	247.033i	0.294087	+	0.294087i
$841$	−776.916			−0.923800
$842$	−2965.77			−3.52230
$843$		−	345.093i		−	0.409363i
$844$	−2659.40	+	2659.40i	−3.15095	+	3.15095i
$845$	−413.260	−	413.260i	−0.489065	−	0.489065i
$846$	1629.21	−	1629.21i	1.92577	−	1.92577i
$847$	900.696			1.06340
$848$	2568.83			3.02928
$849$	64.2185			0.0756402
$850$		−	838.399i		−	0.986351i
$851$	−485.048			−0.569974
$852$			640.451i			0.751703i
$853$			348.356i			0.408389i	0.978930	+	0.204194i	$0.0654575\pi$
$853$			348.356i			0.408389i	−0.978930	+	0.204194i	$0.934543\pi$
$854$	2027.50	+	2027.50i	2.37412	+	2.37412i
$855$	−146.335	+	146.335i	−0.171152	+	0.171152i
$856$	−1409.95	+	1409.95i	−1.64714	+	1.64714i
$857$	942.949	−	942.949i	1.10029	−	1.10029i	0.105916	−	0.994375i	$-0.466223\pi$
$857$	942.949	−	942.949i	1.10029	−	1.10029i	0.994375	−	0.105916i	$-0.0337775\pi$
$858$	−243.688			−0.284018
$859$	−804.358	−	804.358i	−0.936389	−	0.936389i	0.0617058	−	0.998094i	$-0.480346\pi$
$859$	−804.358	−	804.358i	−0.936389	−	0.936389i	−0.998094	+	0.0617058i	$0.980346\pi$
$860$	−428.984	+	428.984i	−0.498818	+	0.498818i
$861$	−161.275	+	161.275i	−0.187311	+	0.187311i
$862$	666.057	−	666.057i	0.772688	−	0.772688i
$863$	280.823	+	280.823i	0.325403	+	0.325403i	0.850835	−	0.525432i	$-0.176096\pi$
$863$	280.823	+	280.823i	0.325403	+	0.325403i	−0.525432	+	0.850835i	$0.676096\pi$
$864$	−814.513			−0.942724
$865$	61.6029	+	61.6029i	0.0712172	+	0.0712172i
$866$	1550.46	+	1550.46i	1.79037	+	1.79037i
$867$	95.9870	+	95.9870i	0.110712	+	0.110712i
$868$	1271.20	−	1271.20i	1.46451	−	1.46451i
$869$	41.8715			0.0481835
$870$	−42.7399	−	42.7399i	−0.0491264	−	0.0491264i
$871$		−	1685.99i		−	1.93570i
$872$	2366.83	−	2366.83i	2.71426	−	2.71426i
$873$	708.040			0.811043
$874$	−449.668	−	449.668i	−0.514494	−	0.514494i
$875$	613.503	−	613.503i	0.701146	−	0.701146i
$876$	−1088.06			−1.24208
$877$	193.365	+	193.365i	0.220485	+	0.220485i	0.808703	−	0.588218i	$-0.200170\pi$
$877$	193.365	+	193.365i	0.220485	+	0.220485i	−0.588218	+	0.808703i	$0.700170\pi$
$878$	−2646.97			−3.01478
$879$	−213.679	−	213.679i	−0.243093	−	0.243093i
$880$		−	311.894i		−	0.354425i
$881$			186.947i			0.212199i	0.994356	+	0.106099i	$0.0338362\pi$
$881$			186.947i			0.212199i	−0.994356	+	0.106099i	$0.966164\pi$
$882$	450.061	+	450.061i	0.510273	+	0.510273i
$883$	−969.474	−	969.474i	−1.09793	−	1.09793i	−0.994652	−	0.103280i	$-0.967066\pi$
$883$	−969.474	−	969.474i	−1.09793	−	1.09793i	−0.103280	−	0.994652i	$-0.532934\pi$
$884$			2272.48i			2.57068i
$885$			153.768i			0.173749i
$886$	−1847.47	+	1847.47i	−2.08518	+	2.08518i
$887$	−268.392	−	268.392i	−0.302584	−	0.302584i	0.539440	−	0.842024i	$-0.318636\pi$
$887$	−268.392	−	268.392i	−0.302584	−	0.302584i	−0.842024	+	0.539440i	$0.818636\pi$
$888$	545.653			0.614474
$889$	665.467			0.748557
$890$	779.654	−	779.654i	0.876016	−	0.876016i
$891$	156.647	−	156.647i	0.175810	−	0.175810i
$892$	−2580.20			−2.89260
$893$	−825.411			−0.924312
$894$	323.078	−	323.078i	0.361385	−	0.361385i
$895$		−	6.59173i		−	0.00736506i
$896$	173.104	−	173.104i	0.193196	−	0.193196i
$897$		−	289.066i		−	0.322259i
$898$	−1497.60	−	1497.60i	−1.66770	−	1.66770i
$899$	−127.604	+	127.604i	−0.141940	+	0.141940i
$900$			1534.89i			1.70543i
$901$	−576.096	−	576.096i	−0.639396	−	0.639396i
$902$	415.226			0.460339
$903$	143.172	−	143.172i	0.158552	−	0.158552i
$904$		−	1721.01i		−	1.90378i
$905$	−321.094	−	321.094i	−0.354800	−	0.354800i
$906$	307.312	−	307.312i	0.339197	−	0.339197i
$907$	458.963	−	458.963i	0.506024	−	0.506024i	−0.407280	−	0.913303i	$-0.633523\pi$
$907$	458.963	−	458.963i	0.506024	−	0.506024i	0.913303	+	0.407280i	$0.133523\pi$
$908$	2195.10	−	2195.10i	2.41751	−	2.41751i
$909$			497.637i			0.547455i
$910$	−1037.48	+	1037.48i	−1.14009	+	1.14009i
$911$	282.359	+	282.359i	0.309944	+	0.309944i	0.844888	−	0.534944i	$-0.179667\pi$
$911$	282.359	+	282.359i	0.309944	+	0.309944i	−0.534944	+	0.844888i	$0.679667\pi$
$912$	248.062	+	248.062i	0.271997	+	0.271997i
$913$	297.465	+	297.465i	0.325811	+	0.325811i
$914$	−1431.36	+	1431.36i	−1.56604	+	1.56604i
$915$			191.204i			0.208966i
$916$	479.935	+	479.935i	0.523947	+	0.523947i
$917$	−486.777	−	486.777i	−0.530836	−	0.530836i
$918$	460.061	+	460.061i	0.501156	+	0.501156i
$919$	982.147	−	982.147i	1.06871	−	1.06871i	0.0712547	−	0.997458i	$-0.477300\pi$
$919$	982.147	−	982.147i	1.06871	−	1.06871i	0.997458	−	0.0712547i	$-0.0227003\pi$
$920$	754.460			0.820066
$921$	320.822			0.348341
$922$		−	399.416i		−	0.433206i
$923$	−1560.58			−1.69077
$924$			257.684i			0.278878i
$925$		−	595.474i		−	0.643755i
$926$		−	1608.24i		−	1.73676i
$927$	−26.9259	−	26.9259i	−0.0290463	−	0.0290463i
$928$	303.172	−	303.172i	0.326694	−	0.326694i
$929$	−741.619	−	741.619i	−0.798298	−	0.798298i	0.184529	−	0.982827i	$-0.440924\pi$
$929$	−741.619	−	741.619i	−0.798298	−	0.798298i	−0.982827	+	0.184529i	$0.940924\pi$
$930$	170.207			0.183018
$931$		−	228.016i		−	0.244915i
$932$		−	2530.41i		−	2.71503i
$933$	−209.492	+	209.492i	−0.224536	+	0.224536i
$934$			1233.19i			1.32034i
$935$	−69.9467	+	69.9467i	−0.0748093	+	0.0748093i
$936$		−	3427.13i		−	3.66146i
$937$	800.634	+	800.634i	0.854466	+	0.854466i	0.990679	−	0.136214i	$-0.0434934\pi$
$937$	800.634	+	800.634i	0.854466	+	0.854466i	−0.136214	+	0.990679i	$0.543493\pi$
$938$	−2531.27			−2.69858
$939$	−75.5807	−	75.5807i	−0.0804906	−	0.0804906i
$940$	1193.47	−	1193.47i	1.26964	−	1.26964i
$941$	680.519	−	680.519i	0.723187	−	0.723187i	−0.246066	−	0.969253i	$-0.579138\pi$
$941$	680.519	−	680.519i	0.723187	−	0.723187i	0.969253	+	0.246066i	$0.0791381\pi$
$942$	−316.870			−0.336380
$943$			492.548i			0.522320i
$944$	−2747.13			−2.91009
$945$			295.867i			0.313087i
$946$	−368.617			−0.389658
$947$	−835.262	+	835.262i	−0.882009	+	0.882009i	−0.993739	−	0.111730i	$-0.964361\pi$
$947$	−835.262	+	835.262i	−0.882009	+	0.882009i	0.111730	+	0.993739i	$0.464361\pi$
$948$		−	96.3031i		−	0.101586i
$949$		−	2651.25i		−	2.79373i
$950$	552.040	−	552.040i	0.581094	−	0.581094i
$951$		−	132.011i		−	0.138813i
$952$	1979.51			2.07932
$953$	−622.090	−	622.090i	−0.652770	−	0.652770i	0.300889	−	0.953659i	$-0.402717\pi$
$953$	−622.090	−	622.090i	−0.652770	−	0.652770i	−0.953659	+	0.300889i	$0.902717\pi$
$954$	1497.44	+	1497.44i	1.56965	+	1.56965i
$955$	131.350	−	131.350i	0.137539	−	0.137539i
$956$		−	2828.65i		−	2.95884i
$957$		−	25.8666i		−	0.0270289i
$958$	1577.16	−	1577.16i	1.64631	−	1.64631i
$959$	783.928			0.817444
$960$	−103.244			−0.107546
$961$			452.829i			0.471206i
$962$			2291.61i			2.38213i
$963$	−806.093			−0.837064
$964$	1114.05	−	1114.05i	1.15565	−	1.15565i
$965$	−365.185	+	365.185i	−0.378430	+	0.378430i
$966$	−433.990			−0.449265
$967$	−527.505	+	527.505i	−0.545507	+	0.545507i	−0.925138	−	0.379631i	$-0.876051\pi$
$967$	−527.505	+	527.505i	−0.545507	+	0.545507i	0.379631	+	0.925138i	$0.376051\pi$
$968$	−1547.25	+	1547.25i	−1.59840	+	1.59840i
$969$		−	111.263i		−	0.114822i
$970$	736.412			0.759187
$971$	760.995	−	760.995i	0.783723	−	0.783723i	−0.196734	−	0.980457i	$-0.563034\pi$
$971$	760.995	−	760.995i	0.783723	−	0.783723i	0.980457	+	0.196734i	$0.0630335\pi$
$972$	−1282.45	−	1282.45i	−1.31940	−	1.31940i
$973$	630.462	−	630.462i	0.647956	−	0.647956i
$974$	−1194.55	−	1194.55i	−1.22644	−	1.22644i
$975$	354.875			0.363974
$976$	−3415.94			−3.49994
$977$	−182.319	+	182.319i	−0.186611	+	0.186611i	−0.794229	−	0.607618i	$-0.792125\pi$
$977$	−182.319	+	182.319i	−0.186611	+	0.186611i	0.607618	+	0.794229i	$0.292125\pi$
$978$	−643.598			−0.658076
$979$	471.854			0.481976
$980$	329.689	+	329.689i	0.336418	+	0.336418i
$981$	1353.16			1.37937
$982$	−284.154	−	284.154i	−0.289362	−	0.289362i
$983$	−23.0869	−	23.0869i	−0.0234862	−	0.0234862i	0.695266	−	0.718752i	$-0.255286\pi$
$983$	−23.0869	−	23.0869i	−0.0234862	−	0.0234862i	−0.718752	+	0.695266i	$0.755286\pi$
$984$		−	554.090i		−	0.563100i
$985$	451.221	+	77.9915i	0.458093	+	0.0791792i
$986$	−342.481			−0.347343
$987$	−398.316	+	398.316i	−0.403562	+	0.403562i
$988$	−1496.31	+	1496.31i	−1.51448	+	1.51448i
$989$		−	437.260i		−	0.442123i
$990$	181.812	−	181.812i	0.183649	−	0.183649i
$991$			962.512i			0.971253i	0.874166	+	0.485627i	$0.161409\pi$
$991$			962.512i			0.971253i	−0.874166	+	0.485627i	$0.838591\pi$
$992$			1207.35i			1.21708i
$993$	−63.0428	−	63.0428i	−0.0634872	−	0.0634872i
$994$			2342.97i			2.35712i
$995$			525.050i			0.527688i
$996$	684.161	−	684.161i	0.686908	−	0.686908i
$997$	−209.635	−	209.635i	−0.210266	−	0.210266i	0.594114	−	0.804380i	$-0.297503\pi$
$997$	−209.635	−	209.635i	−0.210266	−	0.210266i	−0.804380	+	0.594114i	$0.797503\pi$
$998$	−1066.75	+	1066.75i	−1.06889	+	1.06889i
$999$	326.759	+	326.759i	0.327086	+	0.327086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.3.c.a.14.2	✓	64
197.183	odd	4	inner	197.3.c.a.183.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.3.c.a.14.2	✓	64	1.1	even	1	trivial
197.3.c.a.183.2	yes	64	197.183	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.60079 + 2.60079i) q^{2} +(-0.624484 + 0.624484i) q^{3} -9.52825i q^{4} +(1.64362 - 1.64362i) q^{5} -3.24831i q^{6} -8.36970i q^{7} +(14.3778 + 14.3778i) q^{8} +8.22004i q^{9} +8.54942i q^{10} +(-2.58710 + 2.58710i) q^{11} +(5.95024 + 5.95024i) q^{12} +(-14.4989 + 14.4989i) q^{13} +(21.7679 + 21.7679i) q^{14} +2.05283i q^{15} -36.6745 q^{16} +(8.22478 + 8.22478i) q^{17} +(-21.3786 - 21.3786i) q^{18} +10.8311i q^{19} +(-15.6608 - 15.6608i) q^{20} +(5.22675 + 5.22675i) q^{21} -13.4570i q^{22} +15.9629 q^{23} -17.9574 q^{24} +19.5970i q^{25} -75.4170i q^{26} +(-10.7536 - 10.7536i) q^{27} -79.7486 q^{28} +8.00527 q^{29} +(-5.33897 - 5.33897i) q^{30} +(-15.9401 + 15.9401i) q^{31} +(37.8715 - 37.8715i) q^{32} -3.23120i q^{33} -42.7819 q^{34} +(-13.7566 - 13.7566i) q^{35} +78.3226 q^{36} -30.3859 q^{37} +(-28.1695 - 28.1695i) q^{38} -18.1086i q^{39} +47.2633 q^{40} +30.8557i q^{41} -27.1874 q^{42} -27.3922i q^{43} +(24.6505 + 24.6505i) q^{44} +(13.5106 + 13.5106i) q^{45} +(-41.5163 + 41.5163i) q^{46} +76.2072i q^{47} +(22.9027 - 22.9027i) q^{48} -21.0519 q^{49} +(-50.9679 - 50.9679i) q^{50} -10.2725 q^{51} +(138.149 + 138.149i) q^{52} -70.0440 q^{53} +55.9360 q^{54} +8.50439i q^{55} +(120.338 - 120.338i) q^{56} +(-6.76387 - 6.76387i) q^{57} +(-20.8201 + 20.8201i) q^{58} +74.9056 q^{59} +19.5598 q^{60} +93.1420 q^{61} -82.9136i q^{62} +68.7993 q^{63} +50.2938i q^{64} +47.6611i q^{65} +(8.40368 + 8.40368i) q^{66} +(-58.1423 + 58.1423i) q^{67} +(78.3677 - 78.3677i) q^{68} +(-9.96859 + 9.96859i) q^{69} +71.5561 q^{70} +(53.8173 + 53.8173i) q^{71} +(-118.186 + 118.186i) q^{72} +(-91.4298 + 91.4298i) q^{73} +(79.0274 - 79.0274i) q^{74} +(-12.2380 - 12.2380i) q^{75} +103.202 q^{76} +(21.6532 + 21.6532i) q^{77} +(47.0967 + 47.0967i) q^{78} +(-8.09237 - 8.09237i) q^{79} +(-60.2789 + 60.2789i) q^{80} -60.5494 q^{81} +(-80.2493 - 80.2493i) q^{82} -114.980i q^{83} +(49.8017 - 49.8017i) q^{84} +27.0368 q^{85} +(71.2414 + 71.2414i) q^{86} +(-4.99917 + 4.99917i) q^{87} -74.3936 q^{88} +(-91.1938 - 91.1938i) q^{89} -70.2765 q^{90} +(121.351 + 121.351i) q^{91} -152.099i q^{92} -19.9086i q^{93} +(-198.199 - 198.199i) q^{94} +(17.8022 + 17.8022i) q^{95} +47.3003i q^{96} -86.1359i q^{97} +(54.7516 - 54.7516i) q^{98} +(-21.2660 - 21.2660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28}+ \cdots - 66 q^{99}+O(q^{100}) \) 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8 + 10 * q^11 + 68 * q^12 + 2 * q^13 - 2 * q^14 - 280 * q^16 - 30 * q^17 - 68 * q^18 + 114 * q^20 - 20 * q^21 + 48 * q^23 + 60 * q^24 + 22 * q^27 + 392 * q^28 + 56 * q^29 - 70 * q^30 - 64 * q^31 - 156 * q^32 - 52 * q^34 - 92 * q^35 - 36 * q^36 - 160 * q^37 + 40 * q^38 + 52 * q^40 + 80 * q^42 + 140 * q^44 + 324 * q^45 + 214 * q^46 + 216 * q^48 - 836 * q^49 + 126 * q^50 + 124 * q^51 - 10 * q^52 - 16 * q^53 + 400 * q^54 - 40 * q^56 + 68 * q^57 - 266 * q^58 - 364 * q^59 - 68 * q^60 - 168 * q^61 - 12 * q^63 + 238 * q^66 - 112 * q^67 - 148 * q^68 - 48 * q^69 + 48 * q^70 + 150 * q^71 - 474 * q^72 + 18 * q^73 + 236 * q^74 + 64 * q^75 - 260 * q^76 - 388 * q^77 - 782 * q^78 + 202 * q^79 + 796 * q^80 - 516 * q^81 + 72 * q^82 - 294 * q^84 - 696 * q^85 + 618 * q^86 + 464 * q^87 - 244 * q^88 - 536 * q^89 + 1484 * q^90 + 212 * q^91 + 132 * q^94 + 370 * q^95 - 530 * q^98 - 66 * q^99

Introduction

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