LMFDB - Embedded newform 300.3.l.g.107.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(107,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("300.107");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.l (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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.20
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99497 - 0.141758i) q^{2} +(2.06649 + 2.17477i) q^{3} +(3.95981 - 0.565605i) q^{4} +(4.43087 + 4.04566i) q^{6} +(5.18766 - 5.18766i) q^{7} +(7.81952 - 1.68970i) q^{8} +(-0.459255 + 8.98827i) q^{9} +O(q^{10})$	\(q+(1.99497 - 0.141758i) q^{2} +(2.06649 + 2.17477i) q^{3} +(3.95981 - 0.565605i) q^{4} +(4.43087 + 4.04566i) q^{6} +(5.18766 - 5.18766i) q^{7} +(7.81952 - 1.68970i) q^{8} +(-0.459255 + 8.98827i) q^{9} -7.14796 q^{11} +(9.41296 + 7.44286i) q^{12} +(7.93751 - 7.93751i) q^{13} +(9.61384 - 11.0846i) q^{14} +(15.3602 - 4.47938i) q^{16} +(-16.5858 + 16.5858i) q^{17} +(0.357959 + 17.9964i) q^{18} -12.1545 q^{19} +(22.0022 + 0.561734i) q^{21} +(-14.2600 + 1.01328i) q^{22} +(11.0852 - 11.0852i) q^{23} +(19.8337 + 13.5139i) q^{24} +(14.7099 - 16.9603i) q^{26} +(-20.4965 + 17.5754i) q^{27} +(17.6080 - 23.4763i) q^{28} -26.1010 q^{29} +8.74184i q^{31} +(30.0081 - 11.1137i) q^{32} +(-14.7712 - 15.5452i) q^{33} +(-30.7369 + 35.4392i) q^{34} +(3.26525 + 35.8516i) q^{36} +(26.7167 + 26.7167i) q^{37} +(-24.2478 + 1.72299i) q^{38} +(33.6650 + 0.859495i) q^{39} +35.4164i q^{41} +(43.9734 - 1.99834i) q^{42} +(-24.6907 - 24.6907i) q^{43} +(-28.3045 + 4.04292i) q^{44} +(20.5431 - 23.6860i) q^{46} +(-58.6014 - 58.6014i) q^{47} +(41.4833 + 24.1483i) q^{48} -4.82369i q^{49} +(-70.3445 - 1.79595i) q^{51} +(26.9415 - 35.9205i) q^{52} +(-20.4453 - 20.4453i) q^{53} +(-38.3984 + 37.9679i) q^{54} +(31.7994 - 49.3306i) q^{56} +(-25.1171 - 26.4332i) q^{57} +(-52.0707 + 3.70002i) q^{58} -59.4125i q^{59} +7.42905 q^{61} +(1.23923 + 17.4397i) q^{62} +(44.2457 + 49.0106i) q^{63} +(58.2898 - 26.4253i) q^{64} +(-31.6717 - 28.9182i) q^{66} +(35.8479 - 35.8479i) q^{67} +(-56.2954 + 75.0574i) q^{68} +(47.0150 + 1.20033i) q^{69} +46.2359 q^{71} +(11.5963 + 71.0600i) q^{72} +(-10.6280 + 10.6280i) q^{73} +(57.0864 + 49.5118i) q^{74} +(-48.1294 + 6.87464i) q^{76} +(-37.0812 + 37.0812i) q^{77} +(67.2826 - 3.05762i) q^{78} -68.3530 q^{79} +(-80.5782 - 8.25582i) q^{81} +(5.02056 + 70.6547i) q^{82} +(76.6461 - 76.6461i) q^{83} +(87.4423 - 10.2202i) q^{84} +(-52.7574 - 45.7572i) q^{86} +(-53.9374 - 56.7637i) q^{87} +(-55.8936 + 12.0779i) q^{88} -41.0916 q^{89} -82.3543i q^{91} +(37.6253 - 50.1649i) q^{92} +(-19.0115 + 18.0649i) q^{93} +(-125.215 - 108.601i) q^{94} +(86.1810 + 42.2945i) q^{96} +(-81.7315 - 81.7315i) q^{97} +(-0.683795 - 9.62311i) q^{98} +(3.28274 - 64.2478i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.99497	−	0.141758i	0.997485	−	0.0708789i
$2$	1.99497	−	0.141758i	0.997485	−	0.0708789i
$3$	2.06649	+	2.17477i	0.688829	+	0.724924i
$3$	2.06649	+	2.17477i	0.688829	+	0.724924i
$4$	3.95981	−	0.565605i	0.989952	−	0.141401i
$5$		0			0
$5$		0			0
$6$	4.43087	+	4.04566i	0.738479	+	0.674277i
$7$	5.18766	−	5.18766i	0.741095	−	0.741095i	−0.231694	−	0.972789i	$-0.574427\pi$
$7$	5.18766	−	5.18766i	0.741095	−	0.741095i	0.972789	+	0.231694i	$0.0744268\pi$
$8$	7.81952	−	1.68970i	0.977440	−	0.211212i
$9$	−0.459255	+	8.98827i	−0.0510283	+	0.998697i
$10$		0			0
$11$	−7.14796			−0.649814			−0.324907	−	0.945746i	$-0.605333\pi$
$11$	−7.14796			−0.649814			−0.324907	+	0.945746i	$0.605333\pi$
$12$	9.41296	+	7.44286i	0.784413	+	0.620238i
$13$	7.93751	−	7.93751i	0.610578	−	0.610578i	−0.332519	−	0.943097i	$-0.607898\pi$
$13$	7.93751	−	7.93751i	0.610578	−	0.610578i	0.943097	+	0.332519i	$0.107898\pi$
$14$	9.61384	−	11.0846i	0.686703	−	0.791759i
$15$		0			0
$16$	15.3602	−	4.47938i	0.960011	−	0.279961i
$17$	−16.5858	+	16.5858i	−0.975633	+	0.975633i	−0.999710	−	0.0240774i	$-0.992335\pi$
$17$	−16.5858	+	16.5858i	−0.975633	+	0.975633i	0.0240774	+	0.999710i	$0.492335\pi$
$18$	0.357959	+	17.9964i	0.0198866	+	0.999802i
$19$	−12.1545			−0.639709			−0.319855	−	0.947467i	$-0.603634\pi$
$19$	−12.1545			−0.639709			−0.319855	+	0.947467i	$0.603634\pi$
$20$		0			0
$21$	22.0022	+	0.561734i	1.04772	+	0.0267492i
$22$	−14.2600	+	1.01328i	−0.648180	+	0.0460581i
$23$	11.0852	−	11.0852i	0.481963	−	0.481963i	−0.423795	−	0.905758i	$-0.639302\pi$
$23$	11.0852	−	11.0852i	0.481963	−	0.481963i	0.905758	+	0.423795i	$0.139302\pi$
$24$	19.8337	+	13.5139i	0.826402	+	0.563080i
$25$		0			0
$26$	14.7099	−	16.9603i	0.565765	−	0.652319i
$27$	−20.4965	+	17.5754i	−0.759129	+	0.650940i
$28$	17.6080	−	23.4763i	0.628857	−	0.838440i
$29$	−26.1010			−0.900034			−0.450017	−	0.893020i	$-0.648582\pi$
$29$	−26.1010			−0.900034			−0.450017	+	0.893020i	$0.648582\pi$
$30$		0			0
$31$			8.74184i			0.281995i	0.990010	+	0.140997i	$0.0450309\pi$
$31$			8.74184i			0.281995i	−0.990010	+	0.140997i	$0.954969\pi$
$32$	30.0081	−	11.1137i	0.937753	−	0.347302i
$33$	−14.7712	−	15.5452i	−0.447611	−	0.471066i
$34$	−30.7369	+	35.4392i	−0.904027	+	1.04233i
$35$		0			0
$36$	3.26525	+	35.8516i	0.0907015	+	0.995878i
$37$	26.7167	+	26.7167i	0.722074	+	0.722074i	0.969027	−	0.246953i	$-0.0794294\pi$
$37$	26.7167	+	26.7167i	0.722074	+	0.722074i	−0.246953	+	0.969027i	$0.579429\pi$
$38$	−24.2478	+	1.72299i	−0.638100	+	0.0453419i
$39$	33.6650	+	0.859495i	0.863206	+	0.0220383i
$40$		0			0
$41$			35.4164i			0.863815i	0.901918	+	0.431908i	$0.142159\pi$
$41$			35.4164i			0.863815i	−0.901918	+	0.431908i	$0.857841\pi$
$42$	43.9734	−	1.99834i	1.04699	−	0.0475796i
$43$	−24.6907	−	24.6907i	−0.574203	−	0.574203i	0.359097	−	0.933300i	$-0.383085\pi$
$43$	−24.6907	−	24.6907i	−0.574203	−	0.574203i	−0.933300	+	0.359097i	$0.883085\pi$
$44$	−28.3045	+	4.04292i	−0.643285	+	0.0918846i
$45$		0			0
$46$	20.5431	−	23.6860i	0.446590	−	0.514912i
$47$	−58.6014	−	58.6014i	−1.24684	−	1.24684i	−0.957109	−	0.289728i	$-0.906435\pi$
$47$	−58.6014	−	58.6014i	−1.24684	−	1.24684i	−0.289728	−	0.957109i	$-0.593565\pi$
$48$	41.4833	+	24.1483i	0.864234	+	0.503089i
$49$		−	4.82369i		−	0.0984426i
$50$		0			0
$51$	−70.3445	−	1.79595i	−1.37930	−	0.0352147i
$52$	26.9415	−	35.9205i	0.518106	−	0.690779i
$53$	−20.4453	−	20.4453i	−0.385761	−	0.385761i	0.487411	−	0.873172i	$-0.337941\pi$
$53$	−20.4453	−	20.4453i	−0.385761	−	0.385761i	−0.873172	+	0.487411i	$0.837941\pi$
$54$	−38.3984	+	37.9679i	−0.711082	+	0.703109i
$55$		0			0
$56$	31.7994	−	49.3306i	0.567847	−	0.880904i
$57$	−25.1171	−	26.4332i	−0.440651	−	0.463740i
$58$	−52.0707	+	3.70002i	−0.897771	+	0.0637935i
$59$		−	59.4125i		−	1.00699i	−0.863998	−	0.503496i	$-0.832047\pi$
$59$		−	59.4125i		−	1.00699i	0.863998	−	0.503496i	$-0.167953\pi$
$60$		0			0
$61$	7.42905			0.121788			0.0608939	−	0.998144i	$-0.480605\pi$
$61$	7.42905			0.121788			0.0608939	+	0.998144i	$0.480605\pi$
$62$	1.23923	+	17.4397i	0.0199875	+	0.281286i
$63$	44.2457	+	49.0106i	0.702312	+	0.777946i
$64$	58.2898	−	26.4253i	0.910779	−	0.412895i
$65$		0			0
$66$	−31.6717	−	28.9182i	−0.479874	−	0.438155i
$67$	35.8479	−	35.8479i	0.535044	−	0.535044i	−0.387025	−	0.922069i	$-0.626497\pi$
$67$	35.8479	−	35.8479i	0.535044	−	0.535044i	0.922069	+	0.387025i	$0.126497\pi$
$68$	−56.2954	+	75.0574i	−0.827874	+	1.10379i
$69$	47.0150	+	1.20033i	0.681377	+	0.0173961i
$70$		0			0
$71$	46.2359			0.651210			0.325605	−	0.945506i	$-0.394432\pi$
$71$	46.2359			0.651210			0.325605	+	0.945506i	$0.394432\pi$
$72$	11.5963	+	71.0600i	0.161060	+	0.986945i
$73$	−10.6280	+	10.6280i	−0.145589	+	0.145589i	−0.776144	−	0.630555i	$-0.782827\pi$
$73$	−10.6280	+	10.6280i	−0.145589	+	0.145589i	0.630555	+	0.776144i	$0.282827\pi$
$74$	57.0864	+	49.5118i	0.771438	+	0.669078i
$75$		0			0
$76$	−48.1294	+	6.87464i	−0.633282	+	0.0904558i
$77$	−37.0812	+	37.0812i	−0.481574	+	0.481574i
$78$	67.2826	−	3.05762i	0.862597	−	0.0392002i
$79$	−68.3530			−0.865228			−0.432614	−	0.901579i	$-0.642409\pi$
$79$	−68.3530			−0.865228			−0.432614	+	0.901579i	$0.642409\pi$
$80$		0			0
$81$	−80.5782	−	8.25582i	−0.994792	−	0.101924i
$82$	5.02056	+	70.6547i	0.0612263	+	0.861643i
$83$	76.6461	−	76.6461i	0.923447	−	0.923447i	−0.0738244	−	0.997271i	$-0.523520\pi$
$83$	76.6461	−	76.6461i	0.923447	−	0.923447i	0.997271	+	0.0738244i	$0.0235204\pi$
$84$	87.4423	−	10.2202i	1.04098	−	0.121669i
$85$		0			0
$86$	−52.7574	−	45.7572i	−0.613458	−	0.532060i
$87$	−53.9374	−	56.7637i	−0.619970	−	0.652456i
$88$	−55.8936	+	12.0779i	−0.635155	+	0.137249i
$89$	−41.0916			−0.461703			−0.230852	−	0.972989i	$-0.574151\pi$
$89$	−41.0916			−0.461703			−0.230852	+	0.972989i	$0.574151\pi$
$90$		0			0
$91$		−	82.3543i		−	0.904992i
$92$	37.6253	−	50.1649i	0.408970	−	0.545271i
$93$	−19.0115	+	18.0649i	−0.204425	+	0.194246i
$94$	−125.215	−	108.601i	−1.33208	−	1.15533i
$95$		0			0
$96$	86.1810	+	42.2945i	0.897719	+	0.440568i
$97$	−81.7315	−	81.7315i	−0.842593	−	0.842593i	0.146602	−	0.989196i	$-0.453166\pi$
$97$	−81.7315	−	81.7315i	−0.842593	−	0.842593i	−0.989196	+	0.146602i	$0.953166\pi$
$98$	−0.683795	−	9.62311i	−0.00697750	−	0.0981950i
$99$	3.28274	−	64.2478i	0.0331589	−	0.648968i
$100$		0			0
$101$			125.873i			1.24626i	0.782117	+	0.623132i	$0.214140\pi$
$101$			125.873i			1.24626i	−0.782117	+	0.623132i	$0.785860\pi$
$102$	−140.590	+	6.38902i	−1.37833	+	0.0626374i
$103$	−46.2904	−	46.2904i	−0.449421	−	0.449421i	0.445741	−	0.895162i	$-0.352940\pi$
$103$	−46.2904	−	46.2904i	−0.449421	−	0.449421i	−0.895162	+	0.445741i	$0.852940\pi$
$104$	48.6555	−	75.4796i	0.467842	−	0.725765i
$105$		0			0
$106$	−43.6861	−	37.8895i	−0.412133	−	0.357448i
$107$	107.270	+	107.270i	1.00252	+	1.00252i	0.999997	+	0.00252770i	$0.000804591\pi$
$107$	107.270	+	107.270i	1.00252	+	1.00252i	0.00252770	+	0.999997i	$0.499195\pi$
$108$	−71.2214	+	81.1881i	−0.659458	+	0.751742i
$109$		−	22.8980i		−	0.210073i	−0.994468	−	0.105037i	$-0.966504\pi$
$109$		−	22.8980i		−	0.210073i	0.994468	−	0.105037i	$-0.0334960\pi$
$110$		0			0
$111$	−2.89296	+	113.313i	−0.0260627	+	1.02083i
$112$	56.4459	−	102.921i	0.503982	−	0.918937i
$113$	85.7431	+	85.7431i	0.758788	+	0.758788i	0.976102	−	0.217314i	$-0.0697294\pi$
$113$	85.7431	+	85.7431i	0.758788	+	0.758788i	−0.217314	+	0.976102i	$0.569729\pi$
$114$	−53.8549	−	49.1729i	−0.472412	−	0.431341i
$115$		0			0
$116$	−103.355	+	14.7629i	−0.890991	+	0.127266i
$117$	67.6992	+	74.9899i	0.578626	+	0.640939i
$118$	−8.42219	−	118.526i	−0.0713745	−	1.00446i
$119$			172.083i			1.44607i
$120$		0			0
$121$	−69.9067			−0.577741
$122$	14.8207	−	1.05313i	0.121481	−	0.00863219i
$123$	−77.0226	+	73.1876i	−0.626200	+	0.595021i
$124$	4.94443	+	34.6160i	0.0398745	+	0.279162i
$125$		0			0
$126$	95.2164	+	91.5025i	0.755686	+	0.726210i
$127$	−77.5158	+	77.5158i	−0.610361	+	0.610361i	−0.943040	−	0.332679i	$-0.892047\pi$
$127$	−77.5158	+	77.5158i	−0.610361	+	0.610361i	0.332679	+	0.943040i	$0.392047\pi$
$128$	112.540	−	60.9807i	0.879222	−	0.476412i
$129$	2.67358	−	104.720i	0.0207254	−	0.811781i
$130$		0			0
$131$	−20.0258			−0.152869			−0.0764345	−	0.997075i	$-0.524354\pi$
$131$	−20.0258			−0.152869			−0.0764345	+	0.997075i	$0.524354\pi$
$132$	−67.2834	−	53.2013i	−0.509723	−	0.403040i
$133$	−63.0533	+	63.0533i	−0.474085	+	0.474085i
$134$	66.4338	−	76.5972i	0.495775	−	0.571621i
$135$		0			0
$136$	−101.668	+	157.718i	−0.747557	+	1.15969i
$137$	−8.45410	+	8.45410i	−0.0617088	+	0.0617088i	−0.737288	−	0.675579i	$-0.763894\pi$
$137$	−8.45410	+	8.45410i	−0.0617088	+	0.0617088i	0.675579	+	0.737288i	$0.263894\pi$
$138$	93.9637	−	4.27012i	0.680896	−	0.0309429i
$139$	165.614			1.19147			0.595734	−	0.803182i	$-0.296861\pi$
$139$	165.614			1.19147			0.595734	+	0.803182i	$0.296861\pi$
$140$		0			0
$141$	6.34551	−	248.543i	0.0450036	−	1.76272i
$142$	92.2392	−	6.55430i	0.649572	−	0.0461571i
$143$	−56.7370	+	56.7370i	−0.396762	+	0.396762i
$144$	33.2076	+	140.119i	0.230609	+	0.973047i
$145$		0			0
$146$	−19.6960	+	22.7092i	−0.134904	+	0.155542i
$147$	10.4904	−	9.96809i	0.0713633	−	0.0678101i
$148$	120.904	+	90.6821i	0.816921	+	0.612717i
$149$	−26.8277			−0.180052			−0.0900259	−	0.995939i	$-0.528695\pi$
$149$	−26.8277			−0.180052			−0.0900259	+	0.995939i	$0.528695\pi$
$150$		0			0
$151$		−	6.88363i		−	0.0455870i	−0.999740	−	0.0227935i	$-0.992744\pi$
$151$		−	6.88363i		−	0.0455870i	0.999740	−	0.0227935i	$-0.00725602\pi$
$152$	−95.0422	+	20.5374i	−0.625278	+	0.135115i
$153$	−141.460	−	156.694i	−0.924577	−	1.02415i
$154$	−68.7193	+	79.2324i	−0.446229	+	0.514496i
$155$		0			0
$156$	133.793	−	15.6377i	0.857649	−	0.100242i
$157$	33.6577	+	33.6577i	0.214380	+	0.214380i	0.806125	−	0.591745i	$-0.201561\pi$
$157$	33.6577	+	33.6577i	0.214380	+	0.214380i	−0.591745	+	0.806125i	$0.701561\pi$
$158$	−136.362	+	9.68957i	−0.863051	+	0.0613264i
$159$	2.21388	−	86.7139i	0.0139237	−	0.545371i
$160$		0			0
$161$		−	115.012i		−	0.714361i
$162$	−161.921	−	5.04752i	−0.999514	−	0.0311576i
$163$	−1.81560	−	1.81560i	−0.0111386	−	0.0111386i	0.701516	−	0.712654i	$-0.252507\pi$
$163$	−1.81560	−	1.81560i	−0.0111386	−	0.0111386i	−0.712654	+	0.701516i	$0.752507\pi$
$164$	20.0317	+	140.242i	0.122145	+	0.855136i
$165$		0			0
$166$	142.041	−	163.772i	0.855671	−	0.986577i
$167$	110.613	+	110.613i	0.662355	+	0.662355i	0.955935	−	0.293579i	$-0.0948465\pi$
$167$	110.613	+	110.613i	0.662355	+	0.662355i	−0.293579	+	0.955935i	$0.594847\pi$
$168$	172.996	−	32.7846i	1.02974	−	0.195147i
$169$			42.9918i			0.254389i
$170$		0			0
$171$	5.58200	−	109.248i	0.0326433	−	0.638876i
$172$	−111.736	−	83.8054i	−0.649627	−	0.487241i
$173$	58.8176	+	58.8176i	0.339986	+	0.339986i	0.856362	−	0.516376i	$-0.172719\pi$
$173$	58.8176	+	58.8176i	0.339986	+	0.339986i	−0.516376	+	0.856362i	$0.672719\pi$
$174$	−115.650	−	105.596i	−0.664656	−	0.606872i
$175$		0			0
$176$	−109.794	+	32.0184i	−0.623829	+	0.181923i
$177$	129.209	−	122.775i	0.729992	−	0.693646i
$178$	−81.9764	+	5.82505i	−0.460542	+	0.0327250i
$179$			221.072i			1.23504i	0.786555	+	0.617520i	$0.211862\pi$
$179$			221.072i			1.23504i	−0.786555	+	0.617520i	$0.788138\pi$
$180$		0			0
$181$	184.455			1.01909			0.509545	−	0.860444i	$-0.329814\pi$
$181$	184.455			1.01909			0.509545	+	0.860444i	$0.329814\pi$
$182$	−11.6744	−	164.294i	−0.0641449	−	0.902716i
$183$	15.3520	+	16.1565i	0.0838910	+	0.0882868i
$184$	67.9500	−	105.411i	0.369294	−	0.572887i
$185$		0			0
$186$	−35.3665	+	38.7340i	−0.190143	+	0.208247i
$187$	118.554	−	118.554i	0.633980	−	0.633980i
$188$	−265.195	−	198.905i	−1.41061	−	1.05801i
$189$	−15.1537	+	197.504i	−0.0801780	+	1.04499i
$190$		0			0
$191$	247.515			1.29589			0.647944	−	0.761688i	$-0.275629\pi$
$191$	247.515			1.29589			0.647944	+	0.761688i	$0.275629\pi$
$192$	177.924	+	72.1595i	0.926688	+	0.375831i
$193$	218.501	−	218.501i	1.13213	−	1.13213i	0.142305	−	0.989823i	$-0.454549\pi$
$193$	218.501	−	218.501i	1.13213	−	1.13213i	0.989823	−	0.142305i	$-0.0454513\pi$
$194$	−174.638	−	151.466i	−0.900196	−	0.780752i
$195$		0			0
$196$	−2.72830	−	19.1009i	−0.0139199	−	0.0974534i
$197$	199.518	−	199.518i	1.01278	−	1.01278i	0.0128655	−	0.999917i	$-0.495905\pi$
$197$	199.518	−	199.518i	1.01278	−	1.01278i	0.999917	−	0.0128655i	$-0.00409532\pi$
$198$	−2.55867	−	128.638i	−0.0129226	−	0.649686i
$199$	−278.384			−1.39891			−0.699457	−	0.714674i	$-0.746575\pi$
$199$	−278.384			−1.39891			−0.699457	+	0.714674i	$0.746575\pi$
$200$		0			0
$201$	152.040	+	3.88171i	0.756419	+	0.0193120i
$202$	17.8434	+	251.112i	0.0883338	+	1.24313i
$203$	−135.403	+	135.403i	−0.667011	+	0.667011i
$204$	−279.567	+	32.6756i	−1.37042	+	0.160174i
$205$		0			0
$206$	−98.9099	−	85.7859i	−0.480145	−	0.416436i
$207$	94.5455	+	104.727i	0.456742	+	0.505929i
$208$	86.3665	−	157.477i	0.415224	−	0.757100i
$209$	86.8797			0.415692
$210$		0			0
$211$			85.1758i			0.403677i	0.979419	+	0.201838i	$0.0646916\pi$
$211$			85.1758i			0.403677i	−0.979419	+	0.201838i	$0.935308\pi$
$212$	−92.5236	−	69.3956i	−0.436432	−	0.327338i
$213$	95.5459	+	100.552i	0.448572	+	0.472077i
$214$	229.207	+	198.794i	1.07106	+	0.928945i
$215$		0			0
$216$	−130.576	+	172.064i	−0.604516	+	0.796593i
$217$	45.3497	+	45.3497i	0.208985	+	0.208985i
$218$	−3.24597	−	45.6808i	−0.0148898	−	0.209545i
$219$	−45.0762	−	1.15083i	−0.205827	−	0.00525494i
$220$		0			0
$221$			263.299i			1.19140i
$222$	10.2916	+	226.465i	0.0463585	+	1.02011i
$223$	222.212	+	222.212i	0.996466	+	0.996466i	0.999994	−	0.00352781i	$-0.00112294\pi$
$223$	222.212	+	222.212i	0.996466	+	0.996466i	−0.00352781	+	0.999994i	$0.501123\pi$
$224$	98.0181	−	213.326i	0.437581	−	0.952347i
$225$		0			0
$226$	183.210	+	158.900i	0.810662	+	0.703098i
$227$	−33.6138	−	33.6138i	−0.148078	−	0.148078i	0.629181	−	0.777259i	$-0.283391\pi$
$227$	−33.6138	−	33.6138i	−0.148078	−	0.148078i	−0.777259	+	0.629181i	$0.783391\pi$
$228$	−114.410	−	90.4641i	−0.501797	−	0.396772i
$229$			127.633i			0.557349i	0.960386	+	0.278675i	$0.0898951\pi$
$229$			127.633i			0.557349i	−0.960386	+	0.278675i	$0.910105\pi$
$230$		0			0
$231$	−157.271	−	4.01525i	−0.680827	−	0.0173820i
$232$	−204.097	+	44.1029i	−0.879730	+	0.190098i
$233$	190.936	+	190.936i	0.819467	+	0.819467i	0.986031	−	0.166564i	$-0.0532671\pi$
$233$	190.936	+	190.936i	0.819467	+	0.819467i	−0.166564	+	0.986031i	$0.553267\pi$
$234$	145.688	+	140.006i	0.622599	+	0.598315i
$235$		0			0
$236$	−33.6040	−	235.262i	−0.142390	−	0.996874i
$237$	−141.251	−	148.652i	−0.595994	−	0.627224i
$238$	24.3941	+	343.300i	0.102496	+	1.44244i
$239$		−	164.867i		−	0.689820i	−0.938636	−	0.344910i	$-0.887910\pi$
$239$		−	164.867i		−	0.689820i	0.938636	−	0.344910i	$-0.112090\pi$
$240$		0			0
$241$	−20.3865			−0.0845915			−0.0422957	−	0.999105i	$-0.513467\pi$
$241$	−20.3865			−0.0845915			−0.0422957	+	0.999105i	$0.513467\pi$
$242$	−139.462	+	9.90982i	−0.576288	+	0.0409497i
$243$	−148.559	−	192.300i	−0.611355	−	0.791356i
$244$	29.4176	−	4.20191i	0.120564	−	0.0172209i
$245$		0			0
$246$	−143.283	+	156.926i	−0.582451	+	0.637909i
$247$	−96.4763	+	96.4763i	−0.390592	+	0.390592i
$248$	14.7711	+	68.3570i	0.0595609	+	0.275633i
$249$	325.076	+	8.29945i	1.30553	+	0.0333311i
$250$		0			0
$251$	425.326			1.69452			0.847262	−	0.531175i	$-0.178249\pi$
$251$	425.326			1.69452			0.847262	+	0.531175i	$0.178249\pi$
$252$	202.925	+	169.047i	0.805258	+	0.670822i
$253$	−79.2362	+	79.2362i	−0.313187	+	0.313187i
$254$	−143.653	+	165.630i	−0.565564	+	0.652087i
$255$		0			0
$256$	215.870	−	137.608i	0.843243	−	0.537532i
$257$	−162.977	+	162.977i	−0.634150	+	0.634150i	−0.949106	−	0.314956i	$-0.898010\pi$
$257$	−162.977	+	162.977i	−0.634150	+	0.634150i	0.314956	+	0.949106i	$0.398010\pi$
$258$	−9.51114	−	209.292i	−0.0368649	−	0.811209i
$259$	277.195			1.07025
$260$		0			0
$261$	11.9870	−	234.603i	0.0459273	−	0.898862i
$262$	−39.9510	+	2.83882i	−0.152485	+	0.0108352i
$263$	216.217	−	216.217i	0.822117	−	0.822117i	−0.164294	−	0.986411i	$-0.552535\pi$
$263$	216.217	−	216.217i	0.822117	−	0.822117i	0.986411	+	0.164294i	$0.0525346\pi$
$264$	−141.770	−	96.5969i	−0.537008	−	0.365898i
$265$		0			0
$266$	−116.851	+	134.728i	−0.439290	+	0.506495i
$267$	−84.9152	−	89.3647i	−0.318035	−	0.334699i
$268$	121.675	−	162.227i	0.454012	−	0.605324i
$269$	90.1584			0.335161			0.167581	−	0.985858i	$-0.446405\pi$
$269$	90.1584			0.335161			0.167581	+	0.985858i	$0.446405\pi$
$270$		0			0
$271$			406.310i			1.49930i	0.661836	+	0.749649i	$0.269777\pi$
$271$			406.310i			1.49930i	−0.661836	+	0.749649i	$0.730223\pi$
$272$	−180.466	+	329.054i	−0.663479	+	1.20976i
$273$	179.102	−	170.184i	0.656050	−	0.623385i
$274$	−15.6672	+	18.0641i	−0.0571797	+	0.0659274i
$275$		0			0
$276$	186.849	−	21.8389i	0.676991	−	0.0791263i
$277$	190.299	+	190.299i	0.687001	+	0.687001i	0.961568	−	0.274567i	$-0.0885344\pi$
$277$	190.299	+	190.299i	0.687001	+	0.687001i	−0.274567	+	0.961568i	$0.588534\pi$
$278$	330.395	−	23.4771i	1.18847	−	0.0844500i
$279$	−78.5741	−	4.01474i	−0.281628	−	0.0143897i
$280$		0			0
$281$		−	150.443i		−	0.535385i	−0.963504	−	0.267692i	$-0.913739\pi$
$281$		−	150.443i		−	0.535385i	0.963504	−	0.267692i	$-0.0862611\pi$
$282$	−22.5739	−	496.736i	−0.0800492	−	1.76148i
$283$	−152.489	−	152.489i	−0.538830	−	0.538830i	0.384355	−	0.923185i	$-0.374424\pi$
$283$	−152.489	−	152.489i	−0.538830	−	0.538830i	−0.923185	+	0.384355i	$0.874424\pi$
$284$	183.085	−	26.1513i	0.644667	−	0.0920819i
$285$		0			0
$286$	−105.146	+	121.232i	−0.367642	+	0.423886i
$287$	183.728	+	183.728i	0.640169	+	0.640169i
$288$	86.1112	+	274.825i	0.298997	+	0.954254i
$289$		−	261.175i		−	0.903718i
$290$		0			0
$291$	8.85011	−	346.645i	0.0304128	−	1.19122i
$292$	−36.0737	+	48.0962i	−0.123540	+	0.164713i
$293$	−132.745	−	132.745i	−0.453054	−	0.453054i	0.443313	−	0.896367i	$-0.353803\pi$
$293$	−132.745	−	132.745i	−0.453054	−	0.453054i	−0.896367	+	0.443313i	$0.853803\pi$
$294$	19.5150	−	21.3731i	0.0663775	−	0.0726977i
$295$		0			0
$296$	254.055	+	163.769i	0.858295	+	0.553273i
$297$	146.508	−	125.628i	0.493293	−	0.422990i
$298$	−53.5205	+	3.80304i	−0.179599	+	0.0127619i
$299$		−	175.977i		−	0.588552i
$300$		0			0
$301$	−256.174			−0.851078
$302$	−0.975809	−	13.7326i	−0.00323115	−	0.0454723i
$303$	−273.744	+	260.114i	−0.903446	+	0.858463i
$304$	−186.695	+	54.4445i	−0.614128	+	0.179094i
$305$		0			0
$306$	−304.422	−	292.548i	−0.994842	−	0.956038i
$307$	−88.3919	+	88.3919i	−0.287922	+	0.287922i	−0.836258	−	0.548336i	$-0.815261\pi$
$307$	−88.3919	+	88.3919i	−0.287922	+	0.287922i	0.548336	+	0.836258i	$0.315261\pi$
$308$	−125.861	+	167.808i	−0.408640	+	0.544830i
$309$	5.01245	−	196.329i	0.0162215	−	0.635370i
$310$		0			0
$311$	−514.733			−1.65509			−0.827545	−	0.561399i	$-0.810263\pi$
$311$	−514.733			−1.65509			−0.827545	+	0.561399i	$0.810263\pi$
$312$	264.697	−	50.1630i	0.848387	−	0.160779i
$313$	−387.047	+	387.047i	−1.23657	+	1.23657i	−0.275179	+	0.961393i	$0.588737\pi$
$313$	−387.047	+	387.047i	−1.23657	+	1.23657i	−0.961393	+	0.275179i	$0.911263\pi$
$314$	71.9174	+	62.3749i	0.229036	+	0.198646i
$315$		0			0
$316$	−270.665	+	38.6608i	−0.856534	+	0.122344i
$317$	−3.71813	+	3.71813i	−0.0117291	+	0.0117291i	−0.712947	−	0.701218i	$-0.752640\pi$
$317$	−3.71813	+	3.71813i	−0.0117291	+	0.0117291i	0.701218	+	0.712947i	$0.252640\pi$
$318$	−7.87577	−	173.306i	−0.0247666	−	0.544986i
$319$	186.569			0.584855
$320$		0			0
$321$	−11.6155	+	454.960i	−0.0361854	+	1.41732i
$322$	−16.3039	−	229.446i	−0.0506331	−	0.712564i
$323$	201.591	−	201.591i	0.624121	−	0.624121i
$324$	−323.744	+	12.8840i	−0.999209	+	0.0397653i
$325$		0			0
$326$	−3.87944	−	3.36469i	−0.0119001	−	0.0103211i
$327$	49.7978	−	47.3184i	0.152287	−	0.144705i
$328$	59.8431	+	276.939i	0.182449	+	0.844328i
$329$	−608.008			−1.84805
$330$		0			0
$331$		−	573.217i		−	1.73177i	−0.500241	−	0.865886i	$-0.666755\pi$
$331$		−	573.217i		−	1.73177i	0.500241	−	0.865886i	$-0.333245\pi$
$332$	260.152	−	346.855i	0.783592	−	1.04474i
$333$	−252.407	+	227.868i	−0.757980	+	0.684287i
$334$	236.351	+	204.990i	0.707636	+	0.613742i
$335$		0			0
$336$	340.474	−	89.9279i	1.01332	−	0.267643i
$337$	−143.969	−	143.969i	−0.427209	−	0.427209i	0.460468	−	0.887676i	$-0.347682\pi$
$337$	−143.969	−	143.969i	−0.427209	−	0.427209i	−0.887676	+	0.460468i	$0.847682\pi$
$338$	6.09443	+	85.7674i	0.0180309	+	0.253750i
$339$	−9.28449	+	363.659i	−0.0273879	+	1.07274i
$340$		0			0
$341$		−	62.4863i		−	0.183244i
$342$	−4.35080	−	218.737i	−0.0127216	−	0.639583i
$343$	229.172	+	229.172i	0.668139	+	0.668139i
$344$	−234.790	−	151.350i	−0.682528	−	0.439970i
$345$		0			0
$346$	125.677	+	109.002i	0.363229	+	0.315033i
$347$	−358.220	−	358.220i	−1.03233	−	1.03233i	−0.999459	−	0.0328744i	$-0.989534\pi$
$347$	−358.220	−	358.220i	−1.03233	−	1.03233i	−0.0328744	−	0.999459i	$-0.510466\pi$
$348$	−245.688	−	194.266i	−0.705999	−	0.558236i
$349$		−	153.076i		−	0.438613i	−0.975656	−	0.219307i	$-0.929621\pi$
$349$		−	153.076i		−	0.438613i	0.975656	−	0.219307i	$-0.0703795\pi$
$350$		0			0
$351$	−23.1862	+	302.196i	−0.0660576	+	0.860957i
$352$	−214.497	+	79.4399i	−0.609366	+	0.225682i
$353$	−199.291	−	199.291i	−0.564563	−	0.564563i	0.366037	−	0.930600i	$-0.380714\pi$
$353$	−199.291	−	199.291i	−0.564563	−	0.564563i	−0.930600	+	0.366037i	$0.880714\pi$
$354$	240.363	−	263.249i	0.678991	−	0.743642i
$355$		0			0
$356$	−162.715	+	23.2416i	−0.457064	+	0.0652854i
$357$	−374.240	+	355.607i	−1.04829	+	0.996097i
$358$	31.3387	+	441.032i	0.0875383	+	1.23193i
$359$		−	54.0713i		−	0.150616i	−0.997160	−	0.0753082i	$-0.976006\pi$
$359$		−	54.0713i		−	0.150616i	0.997160	−	0.0753082i	$-0.0239941\pi$
$360$		0			0
$361$	−213.269			−0.590772
$362$	367.983	−	26.1480i	1.01653	−	0.0722321i
$363$	−144.461	−	152.031i	−0.397965	−	0.418818i
$364$	−46.5800	−	326.107i	−0.127967	−	0.895899i
$365$		0			0
$366$	32.9172	+	30.0554i	0.0899376	+	0.0821187i
$367$	8.93510	−	8.93510i	0.0243463	−	0.0243463i	−0.694829	−	0.719175i	$-0.744520\pi$
$367$	8.93510	−	8.93510i	0.0243463	−	0.0243463i	0.719175	+	0.694829i	$0.244520\pi$
$368$	120.615	−	219.925i	0.327759	−	0.597621i
$369$	−318.333	−	16.2652i	−0.862690	−	0.0440791i
$370$		0			0
$371$	−212.127			−0.571771
$372$	−65.0643	+	82.2866i	−0.174904	+	0.221201i
$373$	409.810	−	409.810i	1.09869	−	1.09869i	0.104121	−	0.994565i	$-0.466797\pi$
$373$	409.810	−	409.810i	1.09869	−	1.09869i	0.994565	−	0.104121i	$-0.0332030\pi$
$374$	219.706	−	253.318i	0.587450	−	0.677321i
$375$		0			0
$376$	−557.253	−	359.216i	−1.48206	−	0.955361i
$377$	−207.177	+	207.177i	−0.549541	+	0.549541i
$378$	−2.23333	+	396.163i	−0.00590828	+	1.04805i
$379$	−5.84018			−0.0154095			−0.00770473	−	0.999970i	$-0.502453\pi$
$379$	−5.84018			−0.0154095			−0.00770473	+	0.999970i	$0.502453\pi$
$380$		0			0
$381$	−328.765	−	8.39362i	−0.862899	−	0.0220305i
$382$	493.784	−	35.0872i	1.29263	−	0.0918512i
$383$	−137.693	+	137.693i	−0.359513	+	0.359513i	−0.863633	−	0.504121i	$-0.831817\pi$
$383$	−137.693	+	137.693i	−0.359513	+	0.359513i	0.504121	+	0.863633i	$0.331817\pi$
$384$	365.183	+	118.734i	0.950996	+	0.309203i
$385$		0			0
$386$	404.928	−	466.876i	1.04904	−	1.20952i
$387$	233.266	−	210.588i	0.602756	−	0.544155i
$388$	−369.869	−	277.414i	−0.953271	−	0.714983i
$389$	34.5568			0.0888349			0.0444174	−	0.999013i	$-0.485857\pi$
$389$	34.5568			0.0888349			0.0444174	+	0.999013i	$0.485857\pi$
$390$		0			0
$391$			367.711i			0.940438i
$392$	−8.15058	−	37.7189i	−0.0207923	−	0.0962217i
$393$	−41.3832	−	43.5516i	−0.105301	−	0.110818i
$394$	369.750	−	426.316i	0.938451	−	1.08202i
$395$		0			0
$396$	−23.3399	−	256.266i	−0.0589391	−	0.647136i
$397$	−446.029	−	446.029i	−1.12350	−	1.12350i	−0.991212	−	0.132286i	$-0.957768\pi$
$397$	−446.029	−	446.029i	−1.12350	−	1.12350i	−0.132286	−	0.991212i	$-0.542232\pi$
$398$	−555.368	+	39.4631i	−1.39540	+	0.0991536i
$399$	−267.425	−	6.82759i	−0.670239	−	0.0171117i
$400$		0			0
$401$		−	103.887i		−	0.259071i	−0.991575	−	0.129535i	$-0.958651\pi$
$401$		−	103.887i		−	0.259071i	0.991575	−	0.129535i	$-0.0413486\pi$
$402$	303.866	−	13.8090i	0.755886	−	0.0343508i
$403$	69.3885	+	69.3885i	0.172180	+	0.172180i
$404$	71.1942	+	498.432i	0.176223	+	1.23374i
$405$		0			0
$406$	−250.931	+	289.320i	−0.618056	+	0.712610i
$407$	−190.970	−	190.970i	−0.469214	−	0.469214i
$408$	−553.095	+	104.818i	−1.35562	+	0.256906i
$409$			583.243i			1.42602i	0.701153	+	0.713011i	$0.252669\pi$
$409$			583.243i			1.42602i	−0.701153	+	0.713011i	$0.747331\pi$
$410$		0			0
$411$	−35.8560	−	0.915433i	−0.0872409	−	0.00222733i
$412$	−209.483	−	157.119i	−0.508454	−	0.381357i
$413$	−308.212	−	308.212i	−0.746276	−	0.746276i
$414$	203.461	+	195.525i	0.491453	+	0.472283i
$415$		0			0
$416$	149.975	−	326.404i	0.360517	−	0.784626i
$417$	342.240	+	360.173i	0.820719	+	0.863724i
$418$	173.322	−	12.3159i	0.414647	−	0.0294638i
$419$			231.688i			0.552954i	0.961021	+	0.276477i	$0.0891669\pi$
$419$			231.688i			0.552954i	−0.961021	+	0.276477i	$0.910833\pi$
$420$		0			0
$421$	252.861			0.600620			0.300310	−	0.953842i	$-0.402910\pi$
$421$	252.861			0.600620			0.300310	+	0.953842i	$0.402910\pi$
$422$	12.0743	+	169.923i	0.0286122	+	0.402662i
$423$	553.638	−	499.812i	1.30884	−	1.18159i
$424$	−194.419	−	125.326i	−0.458536	−	0.295581i
$425$		0			0
$426$	204.865	+	187.055i	0.480905	+	0.439096i
$427$	38.5394	−	38.5394i	0.0902562	−	0.0902562i
$428$	485.442	+	364.097i	1.13421	+	0.850693i
$429$	−240.636	−	6.14364i	−0.560924	−	0.0143208i
$430$		0			0
$431$	−122.832			−0.284993			−0.142496	−	0.989795i	$-0.545513\pi$
$431$	−122.832			−0.284993			−0.142496	+	0.989795i	$0.545513\pi$
$432$	−236.103	+	361.773i	−0.546534	+	0.837437i
$433$	−317.452	+	317.452i	−0.733145	+	0.733145i	−0.971241	−	0.238097i	$-0.923477\pi$
$433$	−317.452	+	317.452i	−0.733145	+	0.733145i	0.238097	+	0.971241i	$0.423477\pi$
$434$	96.9000	+	84.0427i	0.223272	+	0.193647i
$435$		0			0
$436$	−12.9512	−	90.6716i	−0.0297046	−	0.207962i
$437$	−134.734	+	134.734i	−0.308316	+	0.308316i
$438$	−90.0888	+	4.09403i	−0.205682	+	0.00934710i
$439$	−238.776			−0.543908			−0.271954	−	0.962310i	$-0.587670\pi$
$439$	−238.776			−0.543908			−0.271954	+	0.962310i	$0.587670\pi$
$440$		0			0
$441$	43.3566	+	2.21530i	0.0983143	+	0.00502336i
$442$	37.3247	+	525.274i	0.0844451	+	1.18840i
$443$	−228.090	+	228.090i	−0.514875	+	0.514875i	−0.916016	−	0.401141i	$-0.868614\pi$
$443$	−228.090	+	228.090i	−0.514875	+	0.514875i	0.401141	+	0.916016i	$0.368614\pi$
$444$	52.6346	+	450.333i	0.118547	+	1.01426i
$445$		0			0
$446$	474.806	+	411.806i	1.06459	+	0.923331i
$447$	−55.4392	−	58.3442i	−0.124025	−	0.130524i
$448$	165.303	−	439.473i	0.368979	−	0.980967i
$449$	483.206			1.07618			0.538091	−	0.842887i	$-0.319146\pi$
$449$	483.206			1.07618			0.538091	+	0.842887i	$0.319146\pi$
$450$		0			0
$451$		−	253.155i		−	0.561320i
$452$	388.023	+	291.030i	0.858458	+	0.643871i
$453$	14.9703	−	14.2249i	0.0330471	−	0.0314016i
$454$	−71.8235	−	62.2934i	−0.158202	−	0.137210i
$455$		0			0
$456$	−241.068	−	164.255i	−0.528657	−	0.360208i
$457$	−48.6424	−	48.6424i	−0.106438	−	0.106438i	0.651882	−	0.758320i	$-0.273980\pi$
$457$	−48.6424	−	48.6424i	−0.106438	−	0.106438i	−0.758320	+	0.651882i	$0.773980\pi$
$458$	18.0930	+	254.624i	0.0395043	+	0.555947i
$459$	48.4486	−	631.451i	0.105552	−	1.37571i
$460$		0			0
$461$			436.442i			0.946728i	0.880867	+	0.473364i	$0.156960\pi$
$461$			436.442i			0.946728i	−0.880867	+	0.473364i	$0.843040\pi$
$462$	−314.320	+	14.2841i	−0.680346	+	0.0309179i
$463$	31.1103	+	31.1103i	0.0671929	+	0.0671929i	0.739905	−	0.672712i	$-0.234871\pi$
$463$	31.1103	+	31.1103i	0.0671929	+	0.0671929i	−0.672712	+	0.739905i	$0.734871\pi$
$464$	−400.916	+	116.916i	−0.864043	+	0.251975i
$465$		0			0
$466$	407.978	+	353.845i	0.875489	+	0.759323i
$467$	−228.219	−	228.219i	−0.488693	−	0.488693i	0.419201	−	0.907894i	$-0.362310\pi$
$467$	−228.219	−	228.219i	−0.488693	−	0.488693i	−0.907894	+	0.419201i	$0.862310\pi$
$468$	310.491	+	258.655i	0.663441	+	0.552681i
$469$		−	371.934i		−	0.793036i
$470$		0			0
$471$	−3.64455	+	142.751i	−0.00773790	+	0.303081i
$472$	−100.389	−	464.577i	−0.212689	−	0.984274i
$473$	176.488	+	176.488i	0.373125	+	0.373125i
$474$	−302.863	−	276.533i	−0.638952	−	0.583403i
$475$		0			0
$476$	97.3308	+	681.414i	0.204477	+	1.43154i
$477$	193.158	−	174.379i	0.404943	−	0.365574i
$478$	−23.3712	−	328.904i	−0.0488937	−	0.688085i
$479$		−	698.050i		−	1.45731i	−0.684883	−	0.728653i	$-0.740147\pi$
$479$		−	698.050i		−	1.45731i	0.684883	−	0.728653i	$-0.259853\pi$
$480$		0			0
$481$	424.129			0.881765
$482$	−40.6705	+	2.88995i	−0.0843787	+	0.00599575i
$483$	250.125	−	237.671i	0.517857	−	0.492073i
$484$	−276.817	+	39.5396i	−0.571936	+	0.0816934i
$485$		0			0
$486$	−323.631	−	362.572i	−0.665908	−	0.746034i
$487$	−521.267	+	521.267i	−1.07036	+	1.07036i	−0.0730343	+	0.997329i	$0.523268\pi$
$487$	−521.267	+	521.267i	−1.07036	+	1.07036i	−0.997329	+	0.0730343i	$0.976732\pi$
$488$	58.0916	−	12.5529i	0.119040	−	0.0257231i
$489$	0.196598	−	7.70043i	0.000402041	−	0.0157473i
$490$		0			0
$491$	−423.603			−0.862736			−0.431368	−	0.902176i	$-0.641969\pi$
$491$	−423.603			−0.862736			−0.431368	+	0.902176i	$0.641969\pi$
$492$	−263.600	+	333.373i	−0.535771	+	0.677588i
$493$	432.905	−	432.905i	0.878103	−	0.878103i
$494$	−178.791	+	206.144i	−0.361925	+	0.417295i
$495$		0			0
$496$	39.1580	+	134.276i	0.0789476	+	0.270718i
$497$	239.856	−	239.856i	0.482608	−	0.482608i
$498$	649.693	−	29.5249i	1.30460	−	0.0592870i
$499$	422.547			0.846787			0.423393	−	0.905946i	$-0.360839\pi$
$499$	422.547			0.846787			0.423393	+	0.905946i	$0.360839\pi$
$500$		0			0
$501$	−11.9775	+	469.140i	−0.0239072	+	0.936407i
$502$	848.512	−	60.2933i	1.69026	−	0.120106i
$503$	71.8560	−	71.8560i	0.142855	−	0.142855i	−0.632063	−	0.774917i	$-0.717791\pi$
$503$	71.8560	−	71.8560i	0.142855	−	0.142855i	0.774917	+	0.632063i	$0.217791\pi$
$504$	428.793	+	308.478i	0.850780	+	0.612059i
$505$		0			0
$506$	−146.842	+	169.306i	−0.290201	+	0.334597i
$507$	−93.4973	+	88.8421i	−0.184413	+	0.175231i
$508$	−263.104	+	350.791i	−0.517922	+	0.690534i
$509$	196.155			0.385374			0.192687	−	0.981260i	$-0.438280\pi$
$509$	196.155			0.385374			0.192687	+	0.981260i	$0.438280\pi$
$510$		0			0
$511$			110.269i			0.215791i
$512$	411.148	−	305.125i	0.803023	−	0.595948i
$513$	249.124	−	213.620i	0.485622	−	0.416413i
$514$	−302.030	+	348.237i	−0.587608	+	0.677503i
$515$		0			0
$516$	−48.6432	−	416.183i	−0.0942698	−	0.806556i
$517$	418.880	+	418.880i	0.810213	+	0.810213i
$518$	552.995	−	39.2946i	1.06756	−	0.0758582i
$519$	−6.36893	+	249.461i	−0.0122715	+	0.480657i
$520$		0			0
$521$			22.8866i			0.0439282i	0.999759	+	0.0219641i	$0.00699195\pi$
$521$			22.8866i			0.0439282i	−0.999759	+	0.0219641i	$0.993008\pi$
$522$	−9.34308	−	469.725i	−0.0178986	−	0.899856i
$523$	−665.171	−	665.171i	−1.27184	−	1.27184i	−0.945123	−	0.326715i	$-0.894058\pi$
$523$	−665.171	−	665.171i	−1.27184	−	1.27184i	−0.326715	−	0.945123i	$-0.605942\pi$
$524$	−79.2985	+	11.3267i	−0.151333	+	0.0216159i
$525$		0			0
$526$	400.696	−	461.997i	0.761779	−	0.878320i
$527$	−144.990	−	144.990i	−0.275124	−	0.275124i
$528$	−296.521	−	172.611i	−0.561592	−	0.326915i
$529$			283.239i			0.535423i
$530$		0			0
$531$	534.016	+	27.2855i	1.00568	+	0.0513851i
$532$	−214.016	+	285.342i	−0.402285	+	0.536358i
$533$	281.118	+	281.118i	0.527426	+	0.527426i
$534$	−182.071	−	166.243i	−0.340958	−	0.311316i
$535$		0			0
$536$	219.741	−	340.886i	0.409965	−	0.635981i
$537$	−480.781	+	456.843i	−0.895309	+	0.850731i
$538$	179.863	−	12.7807i	0.334318	−	0.0237559i
$539$			34.4795i			0.0639694i
$540$		0			0
$541$	197.624			0.365294			0.182647	−	0.983179i	$-0.441533\pi$
$541$	197.624			0.365294			0.182647	+	0.983179i	$0.441533\pi$
$542$	57.5976	+	810.575i	0.106269	+	1.49553i
$543$	381.175	+	401.148i	0.701979	+	0.738763i
$544$	−313.379	+	682.036i	−0.576064	+	1.25374i
$545$		0			0
$546$	333.177	−	364.901i	0.610215	−	0.668317i
$547$	547.610	−	547.610i	1.00111	−	1.00111i	0.00111506	−	0.999999i	$-0.499645\pi$
$547$	547.610	−	547.610i	1.00111	−	1.00111i	0.999999	−	0.00111506i	$-0.000354935\pi$
$548$	−28.6949	+	38.2583i	−0.0523630	+	0.0698144i
$549$	−3.41183	+	66.7744i	−0.00621463	+	0.121629i
$550$		0			0
$551$	317.244			0.575760
$552$	369.663	−	70.0552i	0.669679	−	0.126912i
$553$	−354.592	+	354.592i	−0.641216	+	0.641216i
$554$	406.618	+	352.665i	0.733967	+	0.636579i
$555$		0			0
$556$	655.800	−	93.6722i	1.17950	−	0.168475i
$557$	−13.7649	+	13.7649i	−0.0247126	+	0.0247126i	−0.719355	−	0.694643i	$-0.755563\pi$
$557$	−13.7649	+	13.7649i	−0.0247126	+	0.0247126i	0.694643	+	0.719355i	$0.255563\pi$
$558$	−157.322	+	3.12922i	−0.281939	+	0.00560792i
$559$	−391.966			−0.701192
$560$		0			0
$561$	502.819	+	12.8374i	0.896291	+	0.0228830i
$562$	−21.3265	−	300.130i	−0.0379475	−	0.534038i
$563$	−50.4772	+	50.4772i	−0.0896575	+	0.0896575i	−0.750513	−	0.660856i	$-0.770194\pi$
$563$	−50.4772	+	50.4772i	−0.0896575	+	0.0896575i	0.660856	+	0.750513i	$0.270194\pi$
$564$	−115.450	−	987.774i	−0.204699	−	1.75137i
$565$		0			0
$566$	−325.827	−	282.594i	−0.575667	−	0.499283i
$567$	−460.841	+	375.184i	−0.812770	+	0.661700i
$568$	361.543	−	78.1248i	0.636519	−	0.137544i
$569$	981.959			1.72576			0.862882	−	0.505406i	$-0.168657\pi$
$569$	981.959			1.72576			0.862882	+	0.505406i	$0.168657\pi$
$570$		0			0
$571$		−	721.470i		−	1.26352i	−0.775164	−	0.631760i	$-0.782333\pi$
$571$		−	721.470i		−	1.26352i	0.775164	−	0.631760i	$-0.217667\pi$
$572$	−192.577	+	256.758i	−0.336673	+	0.448878i
$573$	511.486	+	538.288i	0.892646	+	0.939420i
$574$	392.578	+	340.488i	0.683933	+	0.593184i
$575$		0			0
$576$	210.748	+	536.061i	0.365882	+	0.930661i
$577$	581.890	+	581.890i	1.00847	+	1.00847i	0.999964	+	0.00851059i	$0.00270904\pi$
$577$	581.890	+	581.890i	1.00847	+	1.00847i	0.00851059	+	0.999964i	$0.497291\pi$
$578$	−37.0236	−	521.035i	−0.0640546	−	0.901445i
$579$	926.718	+	23.6598i	1.60055	+	0.0408633i
$580$		0			0
$581$		−	795.228i		−	1.36872i
$582$	−31.4839	−	692.800i	−0.0540960	−	1.19038i
$583$	146.142	+	146.142i	0.250673	+	0.250673i
$584$	−65.1479	+	101.064i	−0.111555	+	0.173055i
$585$		0			0
$586$	−283.640	−	246.005i	−0.484027	−	0.419803i
$587$	681.614	+	681.614i	1.16118	+	1.16118i	0.984217	+	0.176965i	$0.0566280\pi$
$587$	681.614	+	681.614i	1.16118	+	1.16118i	0.176965	+	0.984217i	$0.443372\pi$
$588$	35.9020	−	45.4052i	0.0610579	−	0.0772197i
$589$		−	106.253i		−	0.180395i
$590$		0			0
$591$	846.208	+	21.6044i	1.43182	+	0.0365556i
$592$	530.048	+	290.700i	0.895352	+	0.491047i
$593$	−428.337	−	428.337i	−0.722322	−	0.722322i	0.246756	−	0.969078i	$-0.420635\pi$
$593$	−428.337	−	428.337i	−0.722322	−	0.722322i	−0.969078	+	0.246756i	$0.920635\pi$
$594$	274.470	−	271.393i	0.462071	−	0.456891i
$595$		0			0
$596$	−106.233	+	15.1739i	−0.178243	+	0.0254596i
$597$	−575.277	−	605.422i	−0.963614	−	1.01411i
$598$	−24.9461	−	351.069i	−0.0417159	−	0.587072i
$599$			798.031i			1.33227i	0.745830	+	0.666136i	$0.232053\pi$
$599$			798.031i			1.33227i	−0.745830	+	0.666136i	$0.767947\pi$
$600$		0			0
$601$	−20.9629			−0.0348801			−0.0174400	−	0.999848i	$-0.505552\pi$
$601$	−20.9629			−0.0348801			−0.0174400	+	0.999848i	$0.505552\pi$
$602$	−511.060	+	36.3147i	−0.848937	+	0.0603235i
$603$	305.748	+	338.674i	0.507044	+	0.561649i
$604$	−3.89342	−	27.2579i	−0.00644606	−	0.0451289i
$605$		0			0
$606$	−509.238	+	557.725i	−0.840327	+	0.920339i
$607$	648.167	−	648.167i	1.06782	−	1.06782i	0.0702937	−	0.997526i	$-0.477606\pi$
$607$	648.167	−	648.167i	1.06782	−	1.06782i	0.997526	−	0.0702937i	$-0.0223936\pi$
$608$	−364.733	+	135.081i	−0.599890	+	0.222172i
$609$	−574.280	−	14.6618i	−0.942988	−	0.0240752i
$610$		0			0
$611$	−930.298			−1.52258
$612$	−648.783	−	540.469i	−1.06010	−	0.883120i
$613$	394.049	−	394.049i	0.642821	−	0.642821i	−0.308427	−	0.951248i	$-0.599803\pi$
$613$	394.049	−	394.049i	0.642821	−	0.642821i	0.951248	+	0.308427i	$0.0998026\pi$
$614$	−163.809	+	188.870i	−0.266790	+	0.307605i
$615$		0			0
$616$	−227.301	+	352.613i	−0.368995	+	0.572424i
$617$	597.558	−	597.558i	0.968489	−	0.968489i	−0.0310296	−	0.999518i	$-0.509879\pi$
$617$	597.558	−	597.558i	0.968489	−	0.968489i	0.999518	+	0.0310296i	$0.00987863\pi$
$618$	−17.8316	−	392.382i	−0.0288537	−	0.634922i
$619$	−541.863			−0.875384			−0.437692	−	0.899125i	$-0.644204\pi$
$619$	−541.863			−0.875384			−0.437692	+	0.899125i	$0.644204\pi$
$620$		0			0
$621$	−32.3808	+	422.033i	−0.0521430	+	0.679602i
$622$	−1026.88	+	72.9675i	−1.65093	+	0.117311i
$623$	−213.169	+	213.169i	−0.342166	+	0.342166i
$624$	520.951	−	137.596i	0.834858	−	0.220507i
$625$		0			0
$626$	−717.280	+	827.014i	−1.14582	+	1.32111i
$627$	179.536	+	188.943i	0.286341	+	0.301345i
$628$	152.315	+	114.241i	0.242540	+	0.181913i
$629$	−886.235			−1.40896
$630$		0			0
$631$			941.798i			1.49255i	0.665638	+	0.746274i	$0.268159\pi$
$631$			941.798i			1.49255i	−0.665638	+	0.746274i	$0.731841\pi$
$632$	−534.488	+	115.496i	−0.845708	+	0.182747i
$633$	−185.238	+	176.015i	−0.292635	+	0.278064i
$634$	−6.89048	+	7.94463i	−0.0108683	+	0.0125310i
$635$		0			0
$636$	−40.2793	−	344.623i	−0.0633323	−	0.541860i
$637$	−38.2881	−	38.2881i	−0.0601068	−	0.0601068i
$638$	372.199	−	26.4476i	0.583384	−	0.0414539i
$639$	−21.2341	+	415.581i	−0.0332302	+	0.650361i
$640$		0			0
$641$		−	563.904i		−	0.879726i	−0.898065	−	0.439863i	$-0.855027\pi$
$641$		−	563.904i		−	0.879726i	0.898065	−	0.439863i	$-0.144973\pi$
$642$	41.3216	+	909.279i	0.0643639	+	1.41632i
$643$	−41.5913	−	41.5913i	−0.0646832	−	0.0646832i	0.674025	−	0.738708i	$-0.264564\pi$
$643$	−41.5913	−	41.5913i	−0.0646832	−	0.0646832i	−0.738708	+	0.674025i	$0.764564\pi$
$644$	−65.0514	−	455.426i	−0.101012	−	0.707183i
$645$		0			0
$646$	373.591	−	430.745i	0.578315	−	0.666789i
$647$	−28.6494	−	28.6494i	−0.0442804	−	0.0442804i	0.684620	−	0.728900i	$-0.259968\pi$
$647$	−28.6494	−	28.6494i	−0.0442804	−	0.0442804i	−0.728900	+	0.684620i	$0.759968\pi$
$648$	−644.033	+	71.5963i	−0.993877	+	0.110488i
$649$			424.678i			0.654358i
$650$		0			0
$651$	−4.91059	+	192.340i	−0.00754315	+	0.295453i
$652$	−8.21634	−	6.16252i	−0.0126018	−	0.00945171i
$653$	−386.414	−	386.414i	−0.591753	−	0.591753i	0.346352	−	0.938105i	$-0.387420\pi$
$653$	−386.414	−	386.414i	−0.591753	−	0.591753i	−0.938105	+	0.346352i	$0.887420\pi$
$654$	92.6374	−	101.458i	0.141647	−	0.155135i
$655$		0			0
$656$	158.644	+	544.003i	0.241835	+	0.829272i
$657$	−90.6466	−	100.409i	−0.137970	−	0.152829i
$658$	−1212.96	+	86.1899i	−1.84340	+	0.130988i
$659$		−	851.849i		−	1.29264i	−0.763067	−	0.646320i	$-0.776307\pi$
$659$		−	851.849i		−	1.29264i	0.763067	−	0.646320i	$-0.223693\pi$
$660$		0			0
$661$	−523.764			−0.792381			−0.396191	−	0.918168i	$-0.629668\pi$
$661$	−523.764			−0.792381			−0.396191	+	0.918168i	$0.629668\pi$
$662$	−81.2580	−	1143.55i	−0.122746	−	1.72742i
$663$	−572.616	+	544.105i	−0.863673	+	0.820671i
$664$	469.827	−	728.845i	0.707571	−	1.09766i
$665$		0			0
$666$	−471.243	+	490.370i	−0.707572	+	0.736291i
$667$	−289.334	+	289.334i	−0.433784	+	0.433784i
$668$	500.571	+	375.444i	0.749358	+	0.562042i
$669$	−24.0617	+	942.458i	−0.0359667	+	1.40876i
$670$		0			0
$671$	−53.1026			−0.0791394
$672$	666.488	−	227.668i	0.991798	−	0.338792i
$673$	319.629	−	319.629i	0.474931	−	0.474931i	−0.428575	−	0.903506i	$-0.640984\pi$
$673$	319.629	−	319.629i	0.474931	−	0.474931i	0.903506	+	0.428575i	$0.140984\pi$
$674$	−307.623	−	266.806i	−0.456414	−	0.395854i
$675$		0			0
$676$	24.3164	+	170.239i	0.0359710	+	0.251833i
$677$	509.574	−	509.574i	0.752694	−	0.752694i	−0.222288	−	0.974981i	$-0.571352\pi$
$677$	509.574	−	509.574i	0.752694	−	0.752694i	0.974981	+	0.222288i	$0.0713524\pi$
$678$	33.0292	+	726.804i	0.0487156	+	1.07198i
$679$	−847.991			−1.24888
$680$		0			0
$681$	3.63979	−	142.565i	0.00534477	−	0.209346i
$682$	−8.85793	−	124.658i	−0.0129882	−	0.182784i
$683$	−278.938	+	278.938i	−0.408402	+	0.408402i	−0.881181	−	0.472779i	$-0.843251\pi$
$683$	−278.938	+	278.938i	−0.408402	+	0.408402i	0.472779	+	0.881181i	$0.343251\pi$
$684$	−39.6875	−	435.758i	−0.0580226	−	0.637073i
$685$		0			0
$686$	489.678	+	424.704i	0.713816	+	0.619102i
$687$	−277.572	+	263.752i	−0.404035	+	0.383918i
$688$	−489.853	−	268.655i	−0.711996	−	0.390487i
$689$	−324.570			−0.471074
$690$		0			0
$691$			108.692i			0.157297i	0.996902	+	0.0786483i	$0.0250604\pi$
$691$			108.692i			0.157297i	−0.996902	+	0.0786483i	$0.974940\pi$
$692$	266.174	+	199.639i	0.384645	+	0.288496i
$693$	−316.266	−	350.326i	−0.456373	−	0.505520i
$694$	−765.418	−	663.857i	−1.10291	−	0.956567i
$695$		0			0
$696$	−517.678	−	352.727i	−0.743791	−	0.506791i
$697$	−587.408	−	587.408i	−0.842766	−	0.842766i
$698$	−21.6997	−	305.382i	−0.0310884	−	0.437510i
$699$	−20.6751	+	809.808i	−0.0295780	+	1.15852i
$700$		0			0
$701$		−	1299.56i		−	1.85387i	−0.375224	−	0.926934i	$-0.622434\pi$
$701$		−	1299.56i		−	1.85387i	0.375224	−	0.926934i	$-0.377566\pi$
$702$	−3.41716	+	606.159i	−0.00486775	+	0.863474i
$703$	−324.728	−	324.728i	−0.461918	−	0.461918i
$704$	−416.653	+	188.887i	−0.591837	+	0.268305i
$705$		0			0
$706$	−425.830	−	369.328i	−0.603158	−	0.523127i
$707$	652.985	+	652.985i	0.923599	+	0.923599i
$708$	442.199	−	559.248i	0.624575	−	0.789898i
$709$		−	1025.36i		−	1.44620i	−0.690743	−	0.723100i	$-0.742717\pi$
$709$		−	1025.36i		−	1.44620i	0.690743	−	0.723100i	$-0.257283\pi$
$710$		0			0
$711$	31.3914	−	614.375i	0.0441511	−	0.864100i
$712$	−321.316	+	69.4324i	−0.451287	+	0.0975174i
$713$	96.9047	+	96.9047i	0.135911	+	0.135911i
$714$	−696.188	+	762.476i	−0.975053	+	1.06789i
$715$		0			0
$716$	125.040	+	875.403i	0.174636	+	1.22263i
$717$	358.548	−	340.695i	0.500066	−	0.475168i
$718$	−7.66503	−	107.871i	−0.0106755	−	0.150238i
$719$			873.333i			1.21465i	0.794454	+	0.607325i	$0.207757\pi$
$719$			873.333i			1.21465i	−0.794454	+	0.607325i	$0.792243\pi$
$720$		0			0
$721$	−480.278			−0.666127
$722$	−425.465	+	30.2325i	−0.589286	+	0.0418733i
$723$	−42.1285	−	44.3361i	−0.0582691	−	0.0613224i
$724$	730.408	−	104.329i	1.00885	−	0.144101i
$725$		0			0
$726$	−309.748	−	282.819i	−0.426650	−	0.389558i
$727$	165.684	−	165.684i	0.227901	−	0.227901i	−0.583914	−	0.811815i	$-0.698480\pi$
$727$	165.684	−	165.684i	0.227901	−	0.227901i	0.811815	+	0.583914i	$0.198480\pi$
$728$	−139.154	−	643.971i	−0.191146	−	0.884575i
$729$	111.212	−	720.467i	0.152554	−	0.988295i
$730$		0			0
$731$	819.029			1.12042
$732$	69.9294	+	55.2934i	0.0955319	+	0.0755374i
$733$	−896.646	+	896.646i	−1.22325	+	1.22325i	−0.256786	+	0.966468i	$0.582664\pi$
$733$	−896.646	+	896.646i	−1.22325	+	1.22325i	−0.966468	+	0.256786i	$0.917336\pi$
$734$	16.5586	−	19.0919i	0.0225594	−	0.0260107i
$735$		0			0
$736$	209.448	−	455.841i	0.284576	−	0.619349i
$737$	−256.239	+	256.239i	−0.347679	+	0.347679i
$738$	−637.370	+	12.6776i	−0.863644	+	0.0171783i
$739$	135.132			0.182858			0.0914290	−	0.995812i	$-0.470857\pi$
$739$	135.132			0.182858			0.0914290	+	0.995812i	$0.470857\pi$
$740$		0			0
$741$	−409.181	−	10.4467i	−0.552201	−	0.0140981i
$742$	−423.187	+	30.0707i	−0.570333	+	0.0405265i
$743$	−472.574	+	472.574i	−0.636035	+	0.636035i	−0.949575	−	0.313540i	$-0.898485\pi$
$743$	−472.574	+	472.574i	−0.636035	+	0.636035i	0.313540	+	0.949575i	$0.398485\pi$
$744$	−118.137	+	173.383i	−0.158786	+	0.233041i
$745$		0			0
$746$	759.465	−	875.652i	1.01805	−	1.17380i
$747$	653.716	+	724.116i	0.875122	+	0.969366i
$748$	402.397	−	536.507i	0.537964	−	0.717256i
$749$	1112.96			1.48593
$750$		0			0
$751$		−	643.372i		−	0.856687i	−0.903616	−	0.428344i	$-0.859097\pi$
$751$		−	643.372i		−	0.856687i	0.903616	−	0.428344i	$-0.140903\pi$
$752$	−1162.63	−	637.630i	−1.54604	−	0.847912i
$753$	878.930	+	924.986i	1.16724	+	1.22840i
$754$	−383.943	+	442.681i	−0.509208	+	0.587110i
$755$		0			0
$756$	51.7037	+	790.649i	0.0683912	+	1.04583i
$757$	−205.600	−	205.600i	−0.271598	−	0.271598i	0.558145	−	0.829743i	$-0.311513\pi$
$757$	−205.600	−	205.600i	−0.271598	−	0.271598i	−0.829743	+	0.558145i	$0.811513\pi$
$758$	−11.6510	+	0.827892i	−0.0153707	+	0.00109221i
$759$	−336.061	−	8.57991i	−0.442768	−	0.0113042i
$760$		0			0
$761$			477.527i			0.627499i	0.949506	+	0.313750i	$0.101585\pi$
$761$			477.527i			0.627499i	−0.949506	+	0.313750i	$0.898415\pi$
$762$	−657.065	+	29.8599i	−0.862290	+	0.0391863i
$763$	−118.787	−	118.787i	−0.155684	−	0.155684i
$764$	980.111	−	139.996i	1.28287	−	0.183240i
$765$		0			0
$766$	−255.175	+	294.213i	−0.333126	+	0.384090i
$767$	−471.588	−	471.588i	−0.614847	−	0.614847i
$768$	745.360	+	185.103i	0.970520	+	0.241019i
$769$		−	743.814i		−	0.967249i	−0.875276	−	0.483624i	$-0.839320\pi$
$769$		−	743.814i		−	0.967249i	0.875276	−	0.483624i	$-0.160680\pi$
$770$		0			0
$771$	−691.226	−	17.6476i	−0.896532	−	0.0228892i
$772$	741.636	−	988.806i	0.960668	−	1.28084i
$773$	357.445	+	357.445i	0.462412	+	0.462412i	0.899445	−	0.437033i	$-0.143971\pi$
$773$	357.445	+	357.445i	0.462412	+	0.462412i	−0.437033	+	0.899445i	$0.643971\pi$
$774$	435.507	−	453.184i	0.562671	−	0.585509i
$775$		0			0
$776$	−777.203	−	501.000i	−1.00155	−	0.645618i
$777$	572.820	+	602.835i	0.737220	+	0.775850i
$778$	68.9397	−	4.89869i	0.0886114	−	0.00629652i
$779$		−	430.468i		−	0.552591i
$780$		0			0
$781$	−330.492			−0.423165
$782$	52.1260	+	733.573i	0.0666573	+	0.938073i
$783$	534.979	−	458.735i	0.683242	−	0.585869i
$784$	−21.6071	−	74.0927i	−0.0275601	−	0.0945060i
$785$		0			0
$786$	−88.7319	−	81.0178i	−0.112891	−	0.103076i
$787$	188.018	−	188.018i	0.238905	−	0.238905i	−0.577492	−	0.816396i	$-0.695968\pi$
$787$	188.018	−	188.018i	0.238905	−	0.238905i	0.816396	+	0.577492i	$0.195968\pi$
$788$	677.205	−	902.903i	0.859398	−	1.14582i
$789$	917.032	+	23.4126i	1.16227	+	0.0296737i
$790$		0			0
$791$	889.612			1.12467
$792$	−82.8901	−	507.934i	−0.104659	−	0.641331i
$793$	58.9682	−	58.9682i	0.0743609	−	0.0743609i
$794$	−953.042	−	826.586i	−1.20030	−	1.04104i
$795$		0			0
$796$	−1102.35	+	157.456i	−1.38486	+	0.197808i
$797$	−651.365	+	651.365i	−0.817271	+	0.817271i	−0.985712	−	0.168441i	$-0.946127\pi$
$797$	−651.365	+	651.365i	−0.817271	+	0.817271i	0.168441	+	0.985712i	$0.446127\pi$
$798$	−534.474	+	24.2888i	−0.669766	+	0.0304371i
$799$	1943.90			2.43291
$800$		0			0
$801$	18.8715	−	369.342i	0.0235599	−	0.461102i
$802$	−14.7269	−	207.252i	−0.0183627	−	0.258419i
$803$	75.9686	−	75.9686i	0.0946060	−	0.0946060i
$804$	604.246	−	70.6240i	0.751550	−	0.0878408i
$805$		0			0
$806$	148.264	+	128.592i	0.183951	+	0.159543i
$807$	186.311	+	196.074i	0.230869	+	0.242966i
$808$	212.687	+	984.264i	0.263226	+	1.21815i
$809$	−735.550			−0.909209			−0.454604	−	0.890694i	$-0.650219\pi$
$809$	−735.550			−0.909209			−0.454604	+	0.890694i	$0.650219\pi$
$810$		0			0
$811$		−	92.4709i		−	0.114021i	−0.998374	−	0.0570104i	$-0.981843\pi$
$811$		−	92.4709i		−	0.114021i	0.998374	−	0.0570104i	$-0.0181568\pi$
$812$	−459.586	+	612.756i	−0.565993	+	0.754625i
$813$	−883.630	+	839.634i	−1.08688	+	1.03276i
$814$	−408.051	−	353.908i	−0.501291	−	0.434777i
$815$		0			0
$816$	−1088.55	+	287.513i	−1.33401	+	0.352345i
$817$	300.103	+	300.103i	0.367323	+	0.367323i
$818$	82.6793	+	1163.55i	0.101075	+	1.42244i
$819$	740.223	+	37.8216i	0.903813	+	0.0461802i
$820$		0			0
$821$			593.249i			0.722593i	0.932451	+	0.361296i	$0.117666\pi$
$821$			593.249i			0.722593i	−0.932451	+	0.361296i	$0.882334\pi$
$822$	−71.6615	+	3.25661i	−0.0871794	+	0.00396182i
$823$	468.289	+	468.289i	0.569003	+	0.569003i	0.931849	−	0.362846i	$-0.118195\pi$
$823$	468.289	+	468.289i	0.569003	+	0.569003i	−0.362846	+	0.931849i	$0.618195\pi$
$824$	−440.185	−	283.752i	−0.534206	−	0.344359i
$825$		0			0
$826$	−658.565	−	571.182i	−0.797295	−	0.691504i
$827$	−337.326	−	337.326i	−0.407891	−	0.407891i	0.473111	−	0.881003i	$-0.343131\pi$
$827$	−337.326	−	337.326i	−0.407891	−	0.407891i	−0.881003	+	0.473111i	$0.843131\pi$
$828$	433.617	+	361.225i	0.523691	+	0.436262i
$829$			483.086i			0.582733i	0.956611	+	0.291367i	$0.0941099\pi$
$829$			483.086i			0.582733i	−0.956611	+	0.291367i	$0.905890\pi$
$830$		0			0
$831$	−20.6061	+	807.109i	−0.0247968	+	0.971250i
$832$	252.925	−	672.427i	0.303997	−	0.808206i
$833$	80.0045	+	80.0045i	0.0960438	+	0.0960438i
$834$	733.815	+	670.019i	0.879874	+	0.803380i
$835$		0			0
$836$	344.027	−	49.1396i	0.411516	−	0.0587794i
$837$	−153.641	−	179.177i	−0.183562	−	0.214071i
$838$	32.8435	+	462.210i	0.0391928	+	0.551563i
$839$		−	835.860i		−	0.996257i	−0.867103	−	0.498129i	$-0.834021\pi$
$839$		−	835.860i		−	0.996257i	0.867103	−	0.498129i	$-0.165979\pi$
$840$		0			0
$841$	−159.738			−0.189938
$842$	504.450	−	35.8451i	0.599110	−	0.0425713i
$843$	327.179	−	310.889i	0.388113	−	0.368789i
$844$	48.1759	+	337.280i	0.0570804	+	0.399621i
$845$		0			0
$846$	1033.64	−	1075.59i	1.22180	−	1.27139i
$847$	−362.652	+	362.652i	−0.428161	+	0.428161i
$848$	−405.626	−	222.462i	−0.478333	−	0.262337i
$849$	16.5119	−	646.745i	0.0194487	−	0.761773i
$850$		0			0
$851$	592.319			0.696026
$852$	435.217	+	344.127i	0.510818	+	0.403905i
$853$	306.961	−	306.961i	0.359861	−	0.359861i	−0.503901	−	0.863762i	$-0.668102\pi$
$853$	306.961	−	306.961i	0.359861	−	0.359861i	0.863762	+	0.503901i	$0.168102\pi$
$854$	71.4217	−	82.3482i	0.0836320	−	0.0964265i
$855$		0			0
$856$	1020.06	+	657.547i	1.19165	+	0.768162i
$857$	861.944	−	861.944i	1.00577	−	1.00577i	0.00578611	−	0.999983i	$-0.498158\pi$
$857$	861.944	−	861.944i	1.00577	−	1.00577i	0.999983	−	0.00578611i	$-0.00184179\pi$
$858$	−480.933	+	21.8557i	−0.560528	+	0.0254729i
$859$	−518.926			−0.604104			−0.302052	−	0.953291i	$-0.597672\pi$
$859$	−518.926			−0.604104			−0.302052	+	0.953291i	$0.597672\pi$
$860$		0			0
$861$	−19.8946	+	779.240i	−0.0231064	+	0.905041i
$862$	−245.046	+	17.4124i	−0.284276	+	0.0202000i
$863$	284.726	−	284.726i	0.329926	−	0.329926i	−0.522633	−	0.852558i	$-0.675050\pi$
$863$	284.726	−	284.726i	0.329926	−	0.329926i	0.852558	+	0.522633i	$0.175050\pi$
$864$	−419.734	+	755.195i	−0.485803	+	0.874068i
$865$		0			0
$866$	−588.305	+	678.308i	−0.679336	+	0.783266i
$867$	567.995	−	539.714i	0.655127	−	0.622508i
$868$	205.226	+	153.926i	0.236436	+	0.177334i
$869$	488.584			0.562237
$870$		0			0
$871$		−	569.087i		−	0.653372i
$872$	−38.6907	−	179.051i	−0.0443701	−	0.205334i
$873$	772.161	−	697.090i	0.884492	−	0.798499i
$874$	−249.691	+	287.890i	−0.285688	+	0.329394i
$875$		0			0
$876$	−179.144	+	20.9383i	−0.204502	+	0.0239021i
$877$	127.814	+	127.814i	0.145740	+	0.145740i	0.776212	−	0.630472i	$-0.217139\pi$
$877$	127.814	+	127.814i	0.145740	+	0.145740i	−0.630472	+	0.776212i	$0.717139\pi$
$878$	−476.350	+	33.8483i	−0.542540	+	0.0385516i
$879$	14.3740	−	563.006i	0.0163527	−	0.640507i
$880$		0			0
$881$			833.425i			0.945999i	0.881063	+	0.472999i	$0.156829\pi$
$881$			833.425i			0.945999i	−0.881063	+	0.472999i	$0.843171\pi$
$882$	86.8092	−	1.72668i	0.0984231	−	0.00195769i
$883$	−314.080	−	314.080i	−0.355696	−	0.355696i	0.506527	−	0.862224i	$-0.330929\pi$
$883$	−314.080	−	314.080i	−0.355696	−	0.355696i	−0.862224	+	0.506527i	$0.830929\pi$
$884$	148.923	+	1042.61i	0.168465	+	1.17943i
$885$		0			0
$886$	−422.698	+	487.365i	−0.477086	+	0.550074i
$887$	341.814	+	341.814i	0.385359	+	0.385359i	0.873029	−	0.487669i	$-0.162153\pi$
$887$	341.814	+	341.814i	0.385359	+	0.385359i	−0.487669	+	0.873029i	$0.662153\pi$
$888$	168.843	+	890.939i	0.190138	+	1.00331i
$889$			804.252i			0.904670i
$890$		0			0
$891$	575.969	+	59.0123i	0.646430	+	0.0662315i
$892$	1005.60	+	754.233i	1.12736	+	0.845552i
$893$	712.269	+	712.269i	0.797613	+	0.797613i
$894$	−118.870	−	108.536i	−0.132964	−	0.121405i
$895$		0			0
$896$	267.475	−	900.169i	0.298521	−	1.00465i
$897$	382.710	−	363.655i	0.426655	−	0.405412i
$898$	963.981	−	68.4982i	1.07348	−	0.0762787i
$899$		−	228.171i		−	0.253805i
$900$		0			0
$901$	678.202			0.752722
$902$	−35.8867	−	505.037i	−0.0397857	−	0.559908i
$903$	−529.381	−	557.121i	−0.586247	−	0.616966i
$904$	815.350	+	525.590i	0.901936	+	0.581405i
$905$		0			0
$906$	27.8488	−	30.5005i	0.0307382	−	0.0336650i
$907$	−542.622	+	542.622i	−0.598261	+	0.598261i	−0.939850	−	0.341589i	$-0.889035\pi$
$907$	−542.622	+	542.622i	−0.598261	+	0.598261i	0.341589	+	0.939850i	$0.389035\pi$
$908$	−152.116	−	114.092i	−0.167529	−	0.125652i
$909$	−1131.38	−	57.8076i	−1.24464	−	0.0635948i
$910$		0			0
$911$	−695.346			−0.763277			−0.381639	−	0.924312i	$-0.624640\pi$
$911$	−695.346			−0.763277			−0.381639	+	0.924312i	$0.624640\pi$
$912$	−504.207	−	293.510i	−0.552859	−	0.321831i
$913$	−547.863	+	547.863i	−0.600069	+	0.600069i
$914$	−103.935	−	90.1446i	−0.113715	−	0.0986265i
$915$		0			0
$916$	72.1899	+	505.402i	0.0788099	+	0.551749i
$917$	−103.887	+	103.887i	−0.113290	+	0.113290i
$918$	7.14030	−	1266.59i	0.00777811	−	1.37973i
$919$	−718.456			−0.781780			−0.390890	−	0.920437i	$-0.627833\pi$
$919$	−718.456			−0.781780			−0.390890	+	0.920437i	$0.627833\pi$
$920$		0			0
$921$	−374.893	−	9.57132i	−0.407050	−	0.0103923i
$922$	61.8690	+	870.688i	0.0671031	+	0.944347i
$923$	366.998	−	366.998i	0.397614	−	0.397614i
$924$	−625.034	+	73.0536i	−0.676444	+	0.0790624i
$925$		0			0
$926$	66.4743	+	57.6540i	0.0717865	+	0.0622613i
$927$	437.330	−	394.812i	0.471769	−	0.425902i
$928$	−783.242	+	290.077i	−0.844010	+	0.312583i
$929$	832.286			0.895895			0.447947	−	0.894060i	$-0.352155\pi$
$929$	832.286			0.895895			0.447947	+	0.894060i	$0.352155\pi$
$930$		0			0
$931$			58.6294i			0.0629746i
$932$	864.064	+	648.075i	0.927107	+	0.695360i
$933$	−1063.69	−	1119.43i	−1.14008	−	1.19981i
$934$	−487.643	−	422.939i	−0.522102	−	0.452826i
$935$		0			0
$936$	656.086	+	471.994i	0.700946	+	0.504267i
$937$	−1098.42	−	1098.42i	−1.17227	−	1.17227i	−0.981667	−	0.190603i	$-0.938956\pi$
$937$	−1098.42	−	1098.42i	−1.17227	−	1.17227i	−0.190603	−	0.981667i	$-0.561044\pi$
$938$	−52.7245	−	741.997i	−0.0562095	−	0.791041i
$939$	−1641.57	−	41.9105i	−1.74821	−	0.0446331i
$940$		0			0
$941$		−	1235.22i		−	1.31267i	−0.754470	−	0.656334i	$-0.772106\pi$
$941$		−	1235.22i		−	1.31267i	0.754470	−	0.656334i	$-0.227894\pi$
$942$	12.9653	+	285.301i	0.0137636	+	0.302867i
$943$	392.597	+	392.597i	0.416327	+	0.416327i
$944$	−266.131	−	912.587i	−0.281919	−	0.966724i
$945$		0			0
$946$	377.108	+	327.070i	0.398634	+	0.345740i
$947$	−1168.65	−	1168.65i	−1.23405	−	1.23405i	−0.962394	−	0.271656i	$-0.912429\pi$
$947$	−1168.65	−	1168.65i	−1.23405	−	1.23405i	−0.271656	−	0.962394i	$-0.587571\pi$
$948$	−643.404	−	508.742i	−0.678696	−	0.536647i
$949$			168.720i			0.177787i
$950$		0			0
$951$	−15.7696	−	0.402609i	−0.0165821	−	0.000423354i
$952$	290.768	+	1345.60i	0.305428	+	1.41345i
$953$	−756.942	−	756.942i	−0.794273	−	0.794273i	0.187913	−	0.982186i	$-0.439828\pi$
$953$	−756.942	−	756.942i	−0.794273	−	0.794273i	−0.982186	+	0.187913i	$0.939828\pi$
$954$	360.625	−	375.262i	0.378013	−	0.393356i
$955$		0			0
$956$	−93.2496	−	652.841i	−0.0975414	−	0.682888i
$957$	385.542	+	405.744i	0.402865	+	0.423975i
$958$	−98.9541	−	1392.59i	−0.103292	−	1.45364i
$959$			87.7140i			0.0914641i
$960$		0			0
$961$	884.580			0.920479
$962$	846.124	−	60.1236i	0.879547	−	0.0624986i
$963$	−1013.44	+	914.909i	−1.05238	+	0.950061i
$964$	−80.7268	+	11.5307i	−0.0837415	+	0.0119613i
$965$		0			0
$966$	465.300	−	509.604i	0.481677	−	0.527540i
$967$	−366.482	+	366.482i	−0.378989	+	0.378989i	−0.870737	−	0.491749i	$-0.836358\pi$
$967$	−366.482	+	366.482i	−0.378989	+	0.378989i	0.491749	+	0.870737i	$0.336358\pi$
$968$	−546.637	+	118.121i	−0.564708	+	0.122026i
$969$	855.000	+	21.8288i	0.882353	+	0.0225272i
$970$		0			0
$971$	−1773.80			−1.82678			−0.913390	−	0.407086i	$-0.866545\pi$
$971$	−1773.80			−1.82678			−0.913390	+	0.407086i	$0.866545\pi$
$972$	−697.032	−	677.444i	−0.717111	−	0.696959i
$973$	859.150	−	859.150i	0.882991	−	0.882991i
$974$	−966.018	+	1113.81i	−0.991805	+	1.14354i
$975$		0			0
$976$	114.112	−	33.2775i	0.116918	−	0.0340958i
$977$	−887.249	+	887.249i	−0.908136	+	0.908136i	−0.996122	−	0.0879854i	$-0.971957\pi$
$977$	−887.249	+	887.249i	−0.908136	+	0.908136i	0.0879854	+	0.996122i	$0.471957\pi$
$978$	−0.699389	−	15.3900i	−0.000715122	−	0.0157362i
$979$	293.721			0.300021
$980$		0			0
$981$	205.813	+	10.5160i	0.209799	+	0.0107197i
$982$	−845.076	+	60.0491i	−0.860566	+	0.0611498i
$983$	297.097	−	297.097i	0.302235	−	0.302235i	−0.539653	−	0.841888i	$-0.681444\pi$
$983$	297.097	−	297.097i	0.302235	−	0.302235i	0.841888	+	0.539653i	$0.181444\pi$
$984$	−478.615	+	702.437i	−0.486397	+	0.713859i
$985$		0			0
$986$	802.264	−	925.000i	0.813656	−	0.938134i
$987$	−1256.44	−	1322.28i	−1.27299	−	1.33969i
$988$	−327.460	+	436.595i	−0.331438	+	0.441898i
$989$	−547.401			−0.553490
$990$		0			0
$991$			1518.20i			1.53198i	0.642850	+	0.765992i	$0.277752\pi$
$991$			1518.20i			1.53198i	−0.642850	+	0.765992i	$0.722248\pi$
$992$	97.1538	+	262.326i	0.0979373	+	0.264442i
$993$	1246.61	−	1184.55i	1.25540	−	1.19290i
$994$	444.504	−	512.507i	0.447188	−	0.515601i
$995$		0			0
$996$	1291.93	−	151.000i	1.29712	−	0.151607i
$997$	566.238	+	566.238i	0.567942	+	0.567942i	0.931551	−	0.363610i	$-0.118456\pi$
$997$	566.238	+	566.238i	0.567942	+	0.567942i	−0.363610	+	0.931551i	$0.618456\pi$
$998$	842.968	−	59.8993i	0.844657	−	0.0600193i
$999$	−1017.16	−	78.0421i	−1.01817	−	0.0781203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.l.g.107.20		40
3.2	odd	2	inner	300.3.l.g.107.1		40
4.3	odd	2	inner	300.3.l.g.107.11		40
5.2	odd	4		60.3.l.a.23.11	yes	40
5.3	odd	4	inner	300.3.l.g.143.10		40
5.4	even	2		60.3.l.a.47.1	yes	40
12.11	even	2	inner	300.3.l.g.107.10		40
15.2	even	4		60.3.l.a.23.10	yes	40
15.8	even	4	inner	300.3.l.g.143.11		40
15.14	odd	2		60.3.l.a.47.20	yes	40
20.3	even	4	inner	300.3.l.g.143.1		40
20.7	even	4		60.3.l.a.23.20	yes	40
20.19	odd	2		60.3.l.a.47.10	yes	40
60.23	odd	4	inner	300.3.l.g.143.20		40
60.47	odd	4		60.3.l.a.23.1	✓	40
60.59	even	2		60.3.l.a.47.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.1	✓	40	60.47	odd	4
60.3.l.a.23.10	yes	40	15.2	even	4
60.3.l.a.23.11	yes	40	5.2	odd	4
60.3.l.a.23.20	yes	40	20.7	even	4
60.3.l.a.47.1	yes	40	5.4	even	2
60.3.l.a.47.10	yes	40	20.19	odd	2
60.3.l.a.47.11	yes	40	60.59	even	2
60.3.l.a.47.20	yes	40	15.14	odd	2
300.3.l.g.107.1		40	3.2	odd	2	inner
300.3.l.g.107.10		40	12.11	even	2	inner
300.3.l.g.107.11		40	4.3	odd	2	inner
300.3.l.g.107.20		40	1.1	even	1	trivial
300.3.l.g.143.1		40	20.3	even	4	inner
300.3.l.g.143.10		40	5.3	odd	4	inner
300.3.l.g.143.11		40	15.8	even	4	inner
300.3.l.g.143.20		40	60.23	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99497 - 0.141758i) q^{2} +(2.06649 + 2.17477i) q^{3} +(3.95981 - 0.565605i) q^{4} +(4.43087 + 4.04566i) q^{6} +(5.18766 - 5.18766i) q^{7} +(7.81952 - 1.68970i) q^{8} +(-0.459255 + 8.98827i) q^{9} +O(q^{10})\)	\(q+(1.99497 - 0.141758i) q^{2} +(2.06649 + 2.17477i) q^{3} +(3.95981 - 0.565605i) q^{4} +(4.43087 + 4.04566i) q^{6} +(5.18766 - 5.18766i) q^{7} +(7.81952 - 1.68970i) q^{8} +(-0.459255 + 8.98827i) q^{9} -7.14796 q^{11} +(9.41296 + 7.44286i) q^{12} +(7.93751 - 7.93751i) q^{13} +(9.61384 - 11.0846i) q^{14} +(15.3602 - 4.47938i) q^{16} +(-16.5858 + 16.5858i) q^{17} +(0.357959 + 17.9964i) q^{18} -12.1545 q^{19} +(22.0022 + 0.561734i) q^{21} +(-14.2600 + 1.01328i) q^{22} +(11.0852 - 11.0852i) q^{23} +(19.8337 + 13.5139i) q^{24} +(14.7099 - 16.9603i) q^{26} +(-20.4965 + 17.5754i) q^{27} +(17.6080 - 23.4763i) q^{28} -26.1010 q^{29} +8.74184i q^{31} +(30.0081 - 11.1137i) q^{32} +(-14.7712 - 15.5452i) q^{33} +(-30.7369 + 35.4392i) q^{34} +(3.26525 + 35.8516i) q^{36} +(26.7167 + 26.7167i) q^{37} +(-24.2478 + 1.72299i) q^{38} +(33.6650 + 0.859495i) q^{39} +35.4164i q^{41} +(43.9734 - 1.99834i) q^{42} +(-24.6907 - 24.6907i) q^{43} +(-28.3045 + 4.04292i) q^{44} +(20.5431 - 23.6860i) q^{46} +(-58.6014 - 58.6014i) q^{47} +(41.4833 + 24.1483i) q^{48} -4.82369i q^{49} +(-70.3445 - 1.79595i) q^{51} +(26.9415 - 35.9205i) q^{52} +(-20.4453 - 20.4453i) q^{53} +(-38.3984 + 37.9679i) q^{54} +(31.7994 - 49.3306i) q^{56} +(-25.1171 - 26.4332i) q^{57} +(-52.0707 + 3.70002i) q^{58} -59.4125i q^{59} +7.42905 q^{61} +(1.23923 + 17.4397i) q^{62} +(44.2457 + 49.0106i) q^{63} +(58.2898 - 26.4253i) q^{64} +(-31.6717 - 28.9182i) q^{66} +(35.8479 - 35.8479i) q^{67} +(-56.2954 + 75.0574i) q^{68} +(47.0150 + 1.20033i) q^{69} +46.2359 q^{71} +(11.5963 + 71.0600i) q^{72} +(-10.6280 + 10.6280i) q^{73} +(57.0864 + 49.5118i) q^{74} +(-48.1294 + 6.87464i) q^{76} +(-37.0812 + 37.0812i) q^{77} +(67.2826 - 3.05762i) q^{78} -68.3530 q^{79} +(-80.5782 - 8.25582i) q^{81} +(5.02056 + 70.6547i) q^{82} +(76.6461 - 76.6461i) q^{83} +(87.4423 - 10.2202i) q^{84} +(-52.7574 - 45.7572i) q^{86} +(-53.9374 - 56.7637i) q^{87} +(-55.8936 + 12.0779i) q^{88} -41.0916 q^{89} -82.3543i q^{91} +(37.6253 - 50.1649i) q^{92} +(-19.0115 + 18.0649i) q^{93} +(-125.215 - 108.601i) q^{94} +(86.1810 + 42.2945i) q^{96} +(-81.7315 - 81.7315i) q^{97} +(-0.683795 - 9.62311i) q^{98} +(3.28274 - 64.2478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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