LMFDB - Embedded newform 300.3.l.g.107.11

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			107.11
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.141758 - 1.99497i) q^{2} +(-2.06649 - 2.17477i) q^{3} +(-3.95981 - 0.565605i) q^{4} +(-4.63154 + 3.81429i) q^{6} +(-5.18766 + 5.18766i) q^{7} +(-1.68970 + 7.81952i) q^{8} +(-0.459255 + 8.98827i) q^{9} +O(q^{10})$	\(q+(0.141758 - 1.99497i) q^{2} +(-2.06649 - 2.17477i) q^{3} +(-3.95981 - 0.565605i) q^{4} +(-4.63154 + 3.81429i) q^{6} +(-5.18766 + 5.18766i) q^{7} +(-1.68970 + 7.81952i) q^{8} +(-0.459255 + 8.98827i) q^{9} +7.14796 q^{11} +(6.95284 + 9.78049i) 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} +(17.8662 + 2.19036i) q^{18} +12.1545 q^{19} +(22.0022 + 0.561734i) q^{21} +(1.01328 - 14.2600i) q^{22} +(-11.0852 + 11.0852i) q^{23} +(20.4974 - 12.4842i) q^{24} +(-14.7099 - 16.9603i) q^{26} +(20.4965 - 17.5754i) q^{27} +(23.4763 - 17.6080i) q^{28} -26.1010 q^{29} -8.74184i q^{31} +(11.1137 - 30.0081i) q^{32} +(-14.7712 - 15.5452i) q^{33} +(30.7369 + 35.4392i) q^{34} +(6.90238 - 35.3321i) q^{36} +(26.7167 + 26.7167i) q^{37} +(1.72299 - 24.2478i) q^{38} +(-33.6650 - 0.859495i) q^{39} +35.4164i q^{41} +(4.23963 - 43.8141i) 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} +(-22.0000 - 42.6615i) q^{48} -4.82369i q^{49} +(70.3445 + 1.79595i) q^{51} +(-35.9205 + 26.9415i) q^{52} +(-20.4453 - 20.4453i) q^{53} +(-32.1568 - 43.3813i) q^{54} +(-31.7994 - 49.3306i) q^{56} +(-25.1171 - 26.4332i) q^{57} +(-3.70002 + 52.0707i) q^{58} +59.4125i q^{59} +7.42905 q^{61} +(-17.4397 - 1.23923i) q^{62} +(-44.2457 - 49.0106i) q^{63} +(-58.2898 - 26.4253i) q^{64} +(-33.1061 + 27.2644i) q^{66} +(-35.8479 + 35.8479i) q^{67} +(75.0574 - 56.2954i) q^{68} +(47.0150 + 1.20033i) q^{69} -46.2359 q^{71} +(-69.5080 - 18.7786i) 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} +(-6.48695 + 67.0389i) q^{78} +68.3530 q^{79} +(-80.5782 - 8.25582i) q^{81} +(70.6547 + 5.02056i) q^{82} +(-76.6461 + 76.6461i) q^{83} +(-86.8069 - 14.6689i) q^{84} +(52.7574 - 45.7572i) q^{86} +(53.9374 + 56.7637i) q^{87} +(-12.0779 + 55.8936i) q^{88} -41.0916 q^{89} +82.3543i q^{91} +(50.1649 - 37.6253i) q^{92} +(-19.0115 + 18.0649i) q^{93} +(125.215 - 108.601i) q^{94} +(-88.2270 + 37.8418i) q^{96} +(-81.7315 - 81.7315i) q^{97} +(-9.62311 - 0.683795i) 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 $

$2$	0.141758	−	1.99497i	0.0708789	−	0.997485i
$2$	0.141758	−	1.99497i	0.0708789	−	0.997485i
$3$	−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
$6$	−4.63154	+	3.81429i	−0.771924	+	0.635715i
$7$	−5.18766	+	5.18766i	−0.741095	+	0.741095i	−0.972789	−	0.231694i	$-0.925573\pi$
$7$	−5.18766	+	5.18766i	−0.741095	+	0.741095i	0.231694	+	0.972789i	$0.425573\pi$
$8$	−1.68970	+	7.81952i	−0.211212	+	0.977440i
$9$	−0.459255	+	8.98827i	−0.0510283	+	0.998697i
$10$		0			0
$11$	7.14796			0.649814			0.324907	−	0.945746i	$-0.394667\pi$
$11$	7.14796			0.649814			0.324907	+	0.945746i	$0.394667\pi$
$12$	6.95284	+	9.78049i	0.579403	+	0.815041i
$13$	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	$0.492335\pi$
$18$	17.8662	+	2.19036i	0.992569	+	0.121687i
$19$	12.1545			0.639709			0.319855	−	0.947467i	$-0.396366\pi$
$19$	12.1545			0.639709			0.319855	+	0.947467i	$0.396366\pi$
$20$		0			0
$21$	22.0022	+	0.561734i	1.04772	+	0.0267492i
$22$	1.01328	−	14.2600i	0.0460581	−	0.648180i
$23$	−11.0852	+	11.0852i	−0.481963	+	0.481963i	−0.905758	−	0.423795i	$-0.860698\pi$
$23$	−11.0852	+	11.0852i	−0.481963	+	0.481963i	0.423795	+	0.905758i	$0.360698\pi$
$24$	20.4974	−	12.4842i	0.854059	−	0.520177i
$25$		0			0
$26$	−14.7099	−	16.9603i	−0.565765	−	0.652319i
$27$	20.4965	−	17.5754i	0.759129	−	0.650940i
$28$	23.4763	−	17.6080i	0.838440	−	0.628857i
$29$	−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	$-0.954969\pi$
$31$		−	8.74184i		−	0.281995i	0.990010	−	0.140997i	$-0.0450309\pi$
$32$	11.1137	−	30.0081i	0.347302	−	0.937753i
$33$	−14.7712	−	15.5452i	−0.447611	−	0.471066i
$34$	30.7369	+	35.4392i	0.904027	+	1.04233i
$35$		0			0
$36$	6.90238	−	35.3321i	0.191733	−	0.981447i
$37$	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	$0.579429\pi$
$38$	1.72299	−	24.2478i	0.0453419	−	0.638100i
$39$	−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	$0.857841\pi$
$42$	4.23963	−	43.8141i	0.100944	−	1.04319i
$43$	24.6907	+	24.6907i	0.574203	+	0.574203i	0.933300	−	0.359097i	$-0.116915\pi$
$43$	24.6907	+	24.6907i	0.574203	+	0.574203i	−0.359097	+	0.933300i	$0.616915\pi$
$44$	−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	$0.0935650\pi$
$47$	58.6014	+	58.6014i	1.24684	+	1.24684i	0.289728	+	0.957109i	$0.406435\pi$
$48$	−22.0000	−	42.6615i	−0.458334	−	0.888780i
$49$		−	4.82369i		−	0.0984426i
$50$		0			0
$51$	70.3445	+	1.79595i	1.37930	+	0.0352147i
$52$	−35.9205	+	26.9415i	−0.690779	+	0.518106i
$53$	−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	$0.837941\pi$
$54$	−32.1568	−	43.3813i	−0.595497	−	0.803358i
$55$		0			0
$56$	−31.7994	−	49.3306i	−0.567847	−	0.880904i
$57$	−25.1171	−	26.4332i	−0.440651	−	0.463740i
$58$	−3.70002	+	52.0707i	−0.0637935	+	0.897771i
$59$			59.4125i			1.00699i	0.863998	+	0.503496i	$0.167953\pi$
$59$			59.4125i			1.00699i	−0.863998	+	0.503496i	$0.832047\pi$
$60$		0			0
$61$	7.42905			0.121788			0.0608939	−	0.998144i	$-0.480605\pi$
$61$	7.42905			0.121788			0.0608939	+	0.998144i	$0.480605\pi$
$62$	−17.4397	−	1.23923i	−0.281286	−	0.0199875i
$63$	−44.2457	−	49.0106i	−0.702312	−	0.777946i
$64$	−58.2898	−	26.4253i	−0.910779	−	0.412895i
$65$		0			0
$66$	−33.1061	+	27.2644i	−0.501607	+	0.413097i
$67$	−35.8479	+	35.8479i	−0.535044	+	0.535044i	−0.922069	−	0.387025i	$-0.873503\pi$
$67$	−35.8479	+	35.8479i	−0.535044	+	0.535044i	0.387025	+	0.922069i	$0.373503\pi$
$68$	75.0574	−	56.2954i	1.10379	−	0.827874i
$69$	47.0150	+	1.20033i	0.681377	+	0.0173961i
$70$		0			0
$71$	−46.2359			−0.651210			−0.325605	−	0.945506i	$-0.605568\pi$
$71$	−46.2359			−0.651210			−0.325605	+	0.945506i	$0.605568\pi$
$72$	−69.5080	−	18.7786i	−0.965389	−	0.260814i
$73$	−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
$78$	−6.48695	+	67.0389i	−0.0831660	+	0.859473i
$79$	68.3530			0.865228			0.432614	−	0.901579i	$-0.357591\pi$
$79$	68.3530			0.865228			0.432614	+	0.901579i	$0.357591\pi$
$80$		0			0
$81$	−80.5782	−	8.25582i	−0.994792	−	0.101924i
$82$	70.6547	+	5.02056i	0.861643	+	0.0612263i
$83$	−76.6461	+	76.6461i	−0.923447	+	0.923447i	−0.997271	−	0.0738244i	$-0.976480\pi$
$83$	−76.6461	+	76.6461i	−0.923447	+	0.923447i	0.0738244	+	0.997271i	$0.476480\pi$
$84$	−86.8069	−	14.6689i	−1.03342	−	0.174630i
$85$		0			0
$86$	52.7574	−	45.7572i	0.613458	−	0.532060i
$87$	53.9374	+	56.7637i	0.619970	+	0.652456i
$88$	−12.0779	+	55.8936i	−0.137249	+	0.635155i
$89$	−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
$92$	50.1649	−	37.6253i	0.545271	−	0.408970i
$93$	−19.0115	+	18.0649i	−0.204425	+	0.194246i
$94$	125.215	−	108.601i	1.33208	−	1.15533i
$95$		0			0
$96$	−88.2270	+	37.8418i	−0.919031	+	0.394185i
$97$	−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	$0.953166\pi$
$98$	−9.62311	−	0.683795i	−0.0981950	−	0.00697750i
$99$	−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	$0.785860\pi$
$102$	13.5548	−	140.081i	0.132890	−	1.37334i
$103$	46.2904	+	46.2904i	0.449421	+	0.449421i	0.895162	−	0.445741i	$-0.147060\pi$
$103$	46.2904	+	46.2904i	0.449421	+	0.449421i	−0.445741	+	0.895162i	$0.647060\pi$
$104$	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	$-0.999195\pi$
$107$	−107.270	−	107.270i	−1.00252	−	1.00252i	−0.00252770	−	0.999997i	$-0.500805\pi$
$108$	−91.1029	+	58.0023i	−0.843545	+	0.537058i
$109$		−	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
$112$	−102.921	+	56.4459i	−0.918937	+	0.503982i
$113$	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	$0.569729\pi$
$114$	−56.2940	+	46.3607i	−0.493807	+	0.406673i
$115$		0			0
$116$	103.355	+	14.7629i	0.890991	+	0.127266i
$117$	67.6992	+	74.9899i	0.578626	+	0.640939i
$118$	118.526	+	8.42219i	1.00446	+	0.0713745i
$119$		−	172.083i		−	1.44607i
$120$		0			0
$121$	−69.9067			−0.577741
$122$	1.05313	−	14.8207i	0.00863219	−	0.121481i
$123$	77.0226	−	73.1876i	0.626200	−	0.595021i
$124$	−4.94443	+	34.6160i	−0.0398745	+	0.279162i
$125$		0			0
$126$	−104.047	+	81.3212i	−0.825769	+	0.645406i
$127$	77.5158	−	77.5158i	0.610361	−	0.610361i	−0.332679	−	0.943040i	$-0.607953\pi$
$127$	77.5158	−	77.5158i	0.610361	−	0.610361i	0.943040	+	0.332679i	$0.107953\pi$
$128$	−60.9807	+	112.540i	−0.476412	+	0.879222i
$129$	2.67358	−	104.720i	0.0207254	−	0.811781i
$130$		0			0
$131$	20.0258			0.152869			0.0764345	−	0.997075i	$-0.475646\pi$
$131$	20.0258			0.152869			0.0764345	+	0.997075i	$0.475646\pi$
$132$	49.6986	+	69.9106i	0.376504	+	0.529625i
$133$	−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	$0.263894\pi$
$138$	9.05937	−	93.6234i	0.0656476	−	0.678430i
$139$	−165.614			−1.19147			−0.595734	−	0.803182i	$-0.703139\pi$
$139$	−165.614			−1.19147			−0.595734	+	0.803182i	$0.703139\pi$
$140$		0			0
$141$	6.34551	−	248.543i	0.0450036	−	1.76272i
$142$	−6.55430	+	92.2392i	−0.0461571	+	0.649572i
$143$	56.7370	−	56.7370i	0.396762	−	0.396762i
$144$	−47.3161	+	136.004i	−0.328584	+	0.944475i
$145$		0			0
$146$	19.6960	+	22.7092i	0.134904	+	0.155542i
$147$	−10.4904	+	9.96809i	−0.0713633	+	0.0678101i
$148$	−90.6821	−	120.904i	−0.612717	−	0.816921i
$149$	−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	$0.00725602\pi$
$151$			6.88363i			0.0455870i	−0.999740	+	0.0227935i	$0.992744\pi$
$152$	−20.5374	+	95.0422i	−0.135115	+	0.625278i
$153$	−141.460	−	156.694i	−0.924577	−	1.02415i
$154$	68.7193	+	79.2324i	0.446229	+	0.514496i
$155$		0			0
$156$	132.821	+	22.4446i	0.851417	+	0.143875i
$157$	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	$0.701561\pi$
$158$	9.68957	−	136.362i	0.0613264	−	0.863051i
$159$	−2.21388	+	86.7139i	−0.0139237	+	0.545371i
$160$		0			0
$161$		−	115.012i		−	0.714361i
$162$	−27.8927	+	159.581i	−0.172177	+	0.985066i
$163$	1.81560	+	1.81560i	0.0111386	+	0.0111386i	0.712654	−	0.701516i	$-0.247493\pi$
$163$	1.81560	+	1.81560i	0.0111386	+	0.0111386i	−0.701516	+	0.712654i	$0.747493\pi$
$164$	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	0.293579	−	0.955935i	$-0.405153\pi$
$167$	−110.613	−	110.613i	−0.662355	−	0.662355i	−0.955935	+	0.293579i	$0.905153\pi$
$168$	−41.5696	+	171.098i	−0.247438	+	1.01844i
$169$			42.9918i			0.254389i
$170$		0			0
$171$	−5.58200	+	109.248i	−0.0326433	+	0.638876i
$172$	−83.8054	−	111.736i	−0.487241	−	0.649627i
$173$	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	$0.672719\pi$
$174$	120.888	−	99.5568i	0.694758	−	0.572165i
$175$		0			0
$176$	109.794	+	32.0184i	0.623829	+	0.181923i
$177$	129.209	−	122.775i	0.729992	−	0.693646i
$178$	−5.82505	+	81.9764i	−0.0327250	+	0.460542i
$179$		−	221.072i		−	1.23504i	−0.786555	−	0.617520i	$-0.788138\pi$
$179$		−	221.072i		−	1.23504i	0.786555	−	0.617520i	$-0.211862\pi$
$180$		0			0
$181$	184.455			1.01909			0.509545	−	0.860444i	$-0.329814\pi$
$181$	184.455			1.01909			0.509545	+	0.860444i	$0.329814\pi$
$182$	164.294	+	11.6744i	0.902716	+	0.0641449i
$183$	−15.3520	−	16.1565i	−0.0838910	−	0.0882868i
$184$	−67.9500	−	105.411i	−0.369294	−	0.572887i
$185$		0			0
$186$	33.3439	+	40.4882i	0.179268	+	0.217679i
$187$	−118.554	+	118.554i	−0.633980	+	0.633980i
$188$	−198.905	−	265.195i	−1.05801	−	1.41061i
$189$	−15.1537	+	197.504i	−0.0801780	+	1.04499i
$190$		0			0
$191$	−247.515			−1.29589			−0.647944	−	0.761688i	$-0.724371\pi$
$191$	−247.515			−1.29589			−0.647944	+	0.761688i	$0.724371\pi$
$192$	62.9863	+	181.375i	0.328054	+	0.944659i
$193$	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	$-0.00409532\pi$
$198$	127.707	+	15.6566i	0.644985	+	0.0790737i
$199$	278.384			1.39891			0.699457	−	0.714674i	$-0.253425\pi$
$199$	278.384			1.39891			0.699457	+	0.714674i	$0.253425\pi$
$200$		0			0
$201$	152.040	+	3.88171i	0.756419	+	0.0193120i
$202$	251.112	+	17.8434i	1.24313	+	0.0883338i
$203$	135.403	−	135.403i	0.667011	−	0.667011i
$204$	−277.535	−	46.8988i	−1.36047	−	0.229896i
$205$		0			0
$206$	98.9099	−	85.7859i	0.480145	−	0.416436i
$207$	−94.5455	−	104.727i	−0.456742	−	0.505929i
$208$	157.477	−	86.3665i	0.757100	−	0.415224i
$209$	86.8797			0.415692
$210$		0			0
$211$		−	85.1758i		−	0.403677i	−0.979419	−	0.201838i	$-0.935308\pi$
$211$		−	85.1758i		−	0.403677i	0.979419	−	0.201838i	$-0.0646916\pi$
$212$	69.3956	+	92.5236i	0.327338	+	0.436432i
$213$	95.5459	+	100.552i	0.448572	+	0.472077i
$214$	−229.207	+	198.794i	−1.07106	+	0.928945i
$215$		0			0
$216$	102.798	+	189.970i	0.475918	+	0.879490i
$217$	45.3497	+	45.3497i	0.208985	+	0.208985i
$218$	−45.6808	−	3.24597i	−0.209545	−	0.0148898i
$219$	45.0762	+	1.15083i	0.205827	+	0.00525494i
$220$		0			0
$221$			263.299i			1.19140i
$222$	−225.645	−	21.8343i	−1.01642	−	0.0983528i
$223$	−222.212	−	222.212i	−0.996466	−	0.996466i	0.00352781	−	0.999994i	$-0.498877\pi$
$223$	−222.212	−	222.212i	−0.996466	−	0.996466i	−0.999994	+	0.00352781i	$0.998877\pi$
$224$	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	0.777259	−	0.629181i	$-0.216609\pi$
$227$	33.6138	+	33.6138i	0.148078	+	0.148078i	−0.629181	+	0.777259i	$0.716609\pi$
$228$	84.5081	+	118.877i	0.370650	+	0.521389i
$229$			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
$232$	44.1029	−	204.097i	0.190098	−	0.879730i
$233$	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	$0.553267\pi$
$234$	159.199	−	124.427i	0.680339	−	0.531741i
$235$		0			0
$236$	33.6040	−	235.262i	0.142390	−	0.996874i
$237$	−141.251	−	148.652i	−0.595994	−	0.627224i
$238$	−343.300	−	24.3941i	−1.44244	−	0.102496i
$239$			164.867i			0.689820i	0.938636	+	0.344910i	$0.112090\pi$
$239$			164.867i			0.689820i	−0.938636	+	0.344910i	$0.887910\pi$
$240$		0			0
$241$	−20.3865			−0.0845915			−0.0422957	−	0.999105i	$-0.513467\pi$
$241$	−20.3865			−0.0845915			−0.0422957	+	0.999105i	$0.513467\pi$
$242$	−9.90982	+	139.462i	−0.0409497	+	0.576288i
$243$	148.559	+	192.300i	0.611355	+	0.791356i
$244$	−29.4176	−	4.20191i	−0.120564	−	0.0172209i
$245$		0			0
$246$	−135.089	−	164.033i	−0.549140	−	0.666800i
$247$	96.4763	−	96.4763i	0.390592	−	0.390592i
$248$	68.3570	+	14.7711i	0.275633	+	0.0595609i
$249$	325.076	+	8.29945i	1.30553	+	0.0333311i
$250$		0			0
$251$	−425.326			−1.69452			−0.847262	−	0.531175i	$-0.821751\pi$
$251$	−425.326			−1.69452			−0.847262	+	0.531175i	$0.821751\pi$
$252$	147.484	+	219.098i	0.585253	+	0.869437i
$253$	−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	$0.398010\pi$
$258$	−208.534	−	20.1786i	−0.808271	−	0.0782115i
$259$	−277.195			−1.07025
$260$		0			0
$261$	11.9870	−	234.603i	0.0459273	−	0.898862i
$262$	2.83882	−	39.9510i	0.0108352	−	0.152485i
$263$	−216.217	+	216.217i	−0.822117	+	0.822117i	−0.986411	−	0.164294i	$-0.947465\pi$
$263$	−216.217	+	216.217i	−0.822117	+	0.822117i	0.164294	+	0.986411i	$0.447465\pi$
$264$	146.515	−	89.2368i	0.554980	−	0.338018i
$265$		0			0
$266$	116.851	+	134.728i	0.439290	+	0.506495i
$267$	84.9152	+	89.3647i	0.318035	+	0.334699i
$268$	162.227	−	121.675i	0.605324	−	0.454012i
$269$	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	$-0.730223\pi$
$271$		−	406.310i		−	1.49930i	0.661836	−	0.749649i	$-0.269777\pi$
$272$	−329.054	+	180.466i	−1.20976	+	0.663479i
$273$	179.102	−	170.184i	0.656050	−	0.623385i
$274$	15.6672	+	18.0641i	0.0571797	+	0.0659274i
$275$		0			0
$276$	−185.492	−	31.3450i	−0.672071	−	0.113569i
$277$	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	$0.588534\pi$
$278$	−23.4771	+	330.395i	−0.0844500	+	1.18847i
$279$	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	$-0.0862611\pi$
$282$	−494.937	−	47.8921i	−1.75510	−	0.169830i
$283$	152.489	+	152.489i	0.538830	+	0.538830i	0.923185	−	0.384355i	$-0.125576\pi$
$283$	152.489	+	152.489i	0.538830	+	0.538830i	−0.384355	+	0.923185i	$0.625576\pi$
$284$	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
$288$	264.617	+	113.674i	0.918810	+	0.394701i
$289$		−	261.175i		−	0.903718i
$290$		0			0
$291$	−8.85011	+	346.645i	−0.0304128	+	1.19122i
$292$	48.0962	−	36.0737i	0.164713	−	0.123540i
$293$	−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	$0.853803\pi$
$294$	18.3989	+	22.3411i	0.0625814	+	0.0759902i
$295$		0			0
$296$	−254.055	+	163.769i	−0.858295	+	0.553273i
$297$	146.508	−	125.628i	0.493293	−	0.422990i
$298$	−3.80304	+	53.5205i	−0.0127619	+	0.179599i
$299$			175.977i			0.588552i
$300$		0			0
$301$	−256.174			−0.851078
$302$	13.7326	+	0.975809i	0.0454723	+	0.00323115i
$303$	273.744	−	260.114i	0.903446	−	0.858463i
$304$	186.695	+	54.4445i	0.614128	+	0.179094i
$305$		0			0
$306$	−332.654	+	259.996i	−1.08710	+	0.849661i
$307$	88.3919	−	88.3919i	0.287922	−	0.287922i	−0.548336	−	0.836258i	$-0.684739\pi$
$307$	88.3919	−	88.3919i	0.287922	−	0.287922i	0.836258	+	0.548336i	$0.184739\pi$
$308$	167.808	−	125.861i	0.544830	−	0.408640i
$309$	5.01245	−	196.329i	0.0162215	−	0.635370i
$310$		0			0
$311$	514.733			1.65509			0.827545	−	0.561399i	$-0.189737\pi$
$311$	514.733			1.65509			0.827545	+	0.561399i	$0.189737\pi$
$312$	63.6047	−	261.792i	0.203861	−	0.839078i
$313$	−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	$0.252640\pi$
$318$	172.678	+	16.7090i	0.543012	+	0.0525440i
$319$	−186.569			−0.584855
$320$		0			0
$321$	−11.6155	+	454.960i	−0.0361854	+	1.41732i
$322$	−229.446	−	16.3039i	−0.712564	−	0.0506331i
$323$	−201.591	+	201.591i	−0.624121	+	0.624121i
$324$	314.405	+	78.2669i	0.970385	+	0.241565i
$325$		0			0
$326$	3.87944	−	3.36469i	0.0119001	−	0.0103211i
$327$	−49.7978	+	47.3184i	−0.152287	+	0.144705i
$328$	−276.939	−	59.8431i	−0.844328	−	0.182449i
$329$	−608.008			−1.84805
$330$		0			0
$331$			573.217i			1.73177i	0.500241	+	0.865886i	$0.333245\pi$
$331$			573.217i			1.73177i	−0.500241	+	0.865886i	$0.666755\pi$
$332$	346.855	−	260.152i	1.04474	−	0.783592i
$333$	−252.407	+	227.868i	−0.757980	+	0.684287i
$334$	−236.351	+	204.990i	−0.707636	+	0.613742i
$335$		0			0
$336$	335.442	+	107.185i	0.998339	+	0.319002i
$337$	−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	$0.847682\pi$
$338$	85.7674	+	6.09443i	0.253750	+	0.0180309i
$339$	9.28449	−	363.659i	0.0273879	−	1.07274i
$340$		0			0
$341$		−	62.4863i		−	0.183244i
$342$	217.155	+	26.6227i	0.634955	+	0.0778440i
$343$	−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	$0.0104661\pi$
$347$	358.220	+	358.220i	1.03233	+	1.03233i	0.0328744	+	0.999459i	$0.489534\pi$
$348$	−181.476	−	255.281i	−0.521483	−	0.733565i
$349$		−	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
$352$	79.4399	−	214.497i	0.225682	−	0.609366i
$353$	−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	$0.880714\pi$
$354$	−226.617	−	275.172i	−0.640160	−	0.777321i
$355$		0			0
$356$	162.715	+	23.2416i	0.457064	+	0.0652854i
$357$	−374.240	+	355.607i	−1.04829	+	0.996097i
$358$	−441.032	−	31.3387i	−1.23193	−	0.0875383i
$359$			54.0713i			0.150616i	0.997160	+	0.0753082i	$0.0239941\pi$
$359$			54.0713i			0.150616i	−0.997160	+	0.0753082i	$0.976006\pi$
$360$		0			0
$361$	−213.269			−0.590772
$362$	26.1480	−	367.983i	0.0722321	−	1.01653i
$363$	144.461	+	152.031i	0.397965	+	0.418818i
$364$	46.5800	−	326.107i	0.127967	−	0.895899i
$365$		0			0
$366$	−34.4080	+	28.3366i	−0.0940109	+	0.0774223i
$367$	−8.93510	+	8.93510i	−0.0243463	+	0.0243463i	−0.719175	−	0.694829i	$-0.755480\pi$
$367$	−8.93510	+	8.93510i	−0.0243463	+	0.0243463i	0.694829	+	0.719175i	$0.255480\pi$
$368$	−219.925	+	120.615i	−0.597621	+	0.327759i
$369$	−318.333	−	16.2652i	−0.862690	−	0.0440791i
$370$		0			0
$371$	212.127			0.571771
$372$	85.4996	−	60.7806i	0.229838	−	0.163389i
$373$	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
$378$	391.866	+	58.2288i	1.03668	+	0.154045i
$379$	5.84018			0.0154095			0.00770473	−	0.999970i	$-0.497547\pi$
$379$	5.84018			0.0154095			0.00770473	+	0.999970i	$0.497547\pi$
$380$		0			0
$381$	−328.765	−	8.39362i	−0.862899	−	0.0220305i
$382$	−35.0872	+	493.784i	−0.0918512	+	1.29263i
$383$	137.693	−	137.693i	0.359513	−	0.359513i	−0.504121	−	0.863633i	$-0.668183\pi$
$383$	137.693	−	137.693i	0.359513	−	0.359513i	0.863633	+	0.504121i	$0.168183\pi$
$384$	370.766	−	99.9445i	0.965535	−	0.260272i
$385$		0			0
$386$	−404.928	−	466.876i	−1.04904	−	1.20952i
$387$	−233.266	+	210.588i	−0.602756	+	0.544155i
$388$	277.414	+	369.869i	0.714983	+	0.953271i
$389$	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
$392$	37.7189	+	8.15058i	0.0962217	+	0.0207923i
$393$	−41.3832	−	43.5516i	−0.105301	−	0.110818i
$394$	−369.750	−	426.316i	−0.938451	−	1.08202i
$395$		0			0
$396$	49.3379	−	252.552i	0.124591	−	0.637758i
$397$	−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	$-0.542232\pi$
$398$	39.4631	−	555.368i	0.0991536	−	1.39540i
$399$	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	$-0.0413486\pi$
$402$	29.2968	−	302.766i	0.0728776	−	0.753148i
$403$	−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
$408$	−132.905	+	547.026i	−0.325746	+	1.34075i
$409$			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
$412$	−157.119	−	209.483i	−0.381357	−	0.508454i
$413$	−308.212	−	308.212i	−0.746276	−	0.746276i
$414$	−222.330	+	173.770i	−0.537030	+	0.419733i
$415$		0			0
$416$	−149.975	−	326.404i	−0.360517	−	0.784626i
$417$	342.240	+	360.173i	0.820719	+	0.863724i
$418$	12.3159	−	173.322i	0.0294638	−	0.414647i
$419$		−	231.688i		−	0.552954i	−0.961021	−	0.276477i	$-0.910833\pi$
$419$		−	231.688i		−	0.552954i	0.961021	−	0.276477i	$-0.0891669\pi$
$420$		0			0
$421$	252.861			0.600620			0.300310	−	0.953842i	$-0.402910\pi$
$421$	252.861			0.600620			0.300310	+	0.953842i	$0.402910\pi$
$422$	−169.923	−	12.0743i	−0.402662	−	0.0286122i
$423$	−553.638	+	499.812i	−1.30884	+	1.18159i
$424$	194.419	−	125.326i	0.458536	−	0.295581i
$425$		0			0
$426$	214.144	−	176.357i	0.502684	−	0.413984i
$427$	−38.5394	+	38.5394i	−0.0902562	+	0.0902562i
$428$	364.097	+	485.442i	0.850693	+	1.13421i
$429$	−240.636	−	6.14364i	−0.560924	−	0.0143208i
$430$		0			0
$431$	122.832			0.284993			0.142496	−	0.989795i	$-0.454487\pi$
$431$	122.832			0.284993			0.142496	+	0.989795i	$0.454487\pi$
$432$	393.556	−	178.150i	0.911010	−	0.412383i
$433$	−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
$438$	8.68578	−	89.7625i	0.0198305	−	0.204937i
$439$	238.776			0.543908			0.271954	−	0.962310i	$-0.412330\pi$
$439$	238.776			0.543908			0.271954	+	0.962310i	$0.412330\pi$
$440$		0			0
$441$	43.3566	+	2.21530i	0.0983143	+	0.00502336i
$442$	525.274	+	37.3247i	1.18840	+	0.0844451i
$443$	228.090	−	228.090i	0.514875	−	0.514875i	−0.401141	−	0.916016i	$-0.631386\pi$
$443$	228.090	−	228.090i	0.514875	−	0.514875i	0.916016	+	0.401141i	$0.131386\pi$
$444$	−75.5458	+	447.060i	−0.170148	+	1.00689i
$445$		0			0
$446$	−474.806	+	411.806i	−1.06459	+	0.923331i
$447$	55.4392	+	58.3442i	0.124025	+	0.130524i
$448$	439.473	−	165.303i	0.980967	−	0.368979i
$449$	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
$452$	−291.030	−	388.023i	−0.643871	−	0.858458i
$453$	14.9703	−	14.2249i	0.0330471	−	0.0314016i
$454$	71.8235	−	62.2934i	0.158202	−	0.137210i
$455$		0			0
$456$	249.135	−	151.739i	0.546349	−	0.332762i
$457$	−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	$0.773980\pi$
$458$	254.624	+	18.0930i	0.555947	+	0.0395043i
$459$	−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	$0.843040\pi$
$462$	30.3047	−	313.182i	0.0655946	−	0.677882i
$463$	−31.1103	−	31.1103i	−0.0671929	−	0.0671929i	0.672712	−	0.739905i	$-0.265129\pi$
$463$	−31.1103	−	31.1103i	−0.0671929	−	0.0671929i	−0.739905	+	0.672712i	$0.765129\pi$
$464$	−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	0.907894	−	0.419201i	$-0.137690\pi$
$467$	228.219	+	228.219i	0.488693	+	0.488693i	−0.419201	+	0.907894i	$0.637690\pi$
$468$	−225.661	−	335.237i	−0.482182	−	0.716318i
$469$		−	371.934i		−	0.793036i
$470$		0			0
$471$	3.64455	−	142.751i	0.00773790	−	0.303081i
$472$	−464.577	−	100.389i	−0.984274	−	0.212689i
$473$	176.488	+	176.488i	0.373125	+	0.373125i
$474$	−316.580	+	260.718i	−0.667890	+	0.550038i
$475$		0			0
$476$	−97.3308	+	681.414i	−0.204477	+	1.43154i
$477$	193.158	−	174.379i	0.404943	−	0.365574i
$478$	328.904	+	23.3712i	0.688085	+	0.0488937i
$479$			698.050i			1.45731i	0.684883	+	0.728653i	$0.259853\pi$
$479$			698.050i			1.45731i	−0.684883	+	0.728653i	$0.740147\pi$
$480$		0			0
$481$	424.129			0.881765
$482$	−2.88995	+	40.6705i	−0.00599575	+	0.0843787i
$483$	−250.125	+	237.671i	−0.517857	+	0.492073i
$484$	276.817	+	39.5396i	0.571936	+	0.0816934i
$485$		0			0
$486$	404.691	−	269.111i	0.832698	−	0.553727i
$487$	521.267	−	521.267i	1.07036	−	1.07036i	0.0730343	−	0.997329i	$-0.476732\pi$
$487$	521.267	−	521.267i	1.07036	−	1.07036i	0.997329	−	0.0730343i	$-0.0232683\pi$
$488$	−12.5529	+	58.0916i	−0.0257231	+	0.119040i
$489$	0.196598	−	7.70043i	0.000402041	−	0.0157473i
$490$		0			0
$491$	423.603			0.862736			0.431368	−	0.902176i	$-0.358031\pi$
$491$	423.603			0.862736			0.431368	+	0.902176i	$0.358031\pi$
$492$	−346.390	+	246.245i	−0.704045	+	0.500497i
$493$	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
$498$	62.6392	−	647.340i	0.125782	−	1.29988i
$499$	−422.547			−0.846787			−0.423393	−	0.905946i	$-0.639161\pi$
$499$	−422.547			−0.846787			−0.423393	+	0.905946i	$0.639161\pi$
$500$		0			0
$501$	−11.9775	+	469.140i	−0.0239072	+	0.936407i
$502$	−60.2933	+	848.512i	−0.120106	+	1.69026i
$503$	−71.8560	+	71.8560i	−0.142855	+	0.142855i	−0.774917	−	0.632063i	$-0.782209\pi$
$503$	−71.8560	+	71.8560i	−0.142855	+	0.142855i	0.632063	+	0.774917i	$0.282209\pi$
$504$	458.001	−	263.167i	0.908733	−	0.522156i
$505$		0			0
$506$	146.842	+	169.306i	0.290201	+	0.334597i
$507$	93.4973	−	88.8421i	0.184413	−	0.175231i
$508$	−350.791	+	263.104i	−0.690534	+	0.517922i
$509$	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
$512$	305.125	−	411.148i	0.595948	−	0.803023i
$513$	249.124	−	213.620i	0.485622	−	0.416413i
$514$	302.030	+	348.237i	0.587608	+	0.677503i
$515$		0			0
$516$	−69.8170	+	413.158i	−0.135304	+	0.800694i
$517$	418.880	+	418.880i	0.810213	+	0.810213i
$518$	−39.2946	+	552.995i	−0.0758582	+	1.06756i
$519$	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	$0.993008\pi$
$522$	−466.327	−	57.1705i	−0.893346	−	0.109522i
$523$	665.171	+	665.171i	1.27184	+	1.27184i	0.945123	+	0.326715i	$0.105942\pi$
$523$	665.171	+	665.171i	1.27184	+	1.27184i	0.326715	+	0.945123i	$0.394058\pi$
$524$	−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
$528$	−157.255	−	304.942i	−0.297832	−	0.577542i
$529$			283.239i			0.535423i
$530$		0			0
$531$	−534.016	−	27.2855i	−1.00568	−	0.0513851i
$532$	285.342	−	214.016i	0.536358	−	0.402285i
$533$	281.118	+	281.118i	0.527426	+	0.527426i
$534$	190.317	−	156.735i	0.356400	−	0.293512i
$535$		0			0
$536$	−219.741	−	340.886i	−0.409965	−	0.635981i
$537$	−480.781	+	456.843i	−0.895309	+	0.850731i
$538$	12.7807	−	179.863i	0.0237559	−	0.334318i
$539$		−	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	$0.441533\pi$
$542$	−810.575	−	57.5976i	−1.49553	−	0.106269i
$543$	−381.175	−	401.148i	−0.701979	−	0.738763i
$544$	313.379	+	682.036i	0.576064	+	1.25374i
$545$		0			0
$546$	−314.123	−	381.427i	−0.575317	−	0.698585i
$547$	−547.610	+	547.610i	−1.00111	+	1.00111i	−0.00111506	+	0.999999i	$0.500355\pi$
$547$	−547.610	+	547.610i	−1.00111	+	1.00111i	−0.999999	+	0.00111506i	$0.999645\pi$
$548$	38.2583	−	28.6949i	0.0698144	−	0.0523630i
$549$	−3.41183	+	66.7744i	−0.00621463	+	0.121629i
$550$		0			0
$551$	−317.244			−0.575760
$552$	−88.8273	+	365.607i	−0.160919	+	0.662331i
$553$	−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	$0.255563\pi$
$558$	19.1478	−	156.184i	0.0343150	−	0.279899i
$559$	391.966			0.701192
$560$		0			0
$561$	502.819	+	12.8374i	0.896291	+	0.0228830i
$562$	−300.130	−	21.3265i	−0.534038	−	0.0379475i
$563$	50.4772	−	50.4772i	0.0896575	−	0.0896575i	−0.660856	−	0.750513i	$-0.729806\pi$
$563$	50.4772	−	50.4772i	0.0896575	−	0.0896575i	0.750513	+	0.660856i	$0.229806\pi$
$564$	−165.705	+	980.596i	−0.293802	+	1.73865i
$565$		0			0
$566$	325.827	−	282.594i	0.575667	−	0.499283i
$567$	460.841	−	375.184i	0.812770	−	0.661700i
$568$	78.1248	−	361.543i	0.137544	−	0.636519i
$569$	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	$0.217667\pi$
$571$			721.470i			1.26352i	−0.775164	+	0.631760i	$0.782333\pi$
$572$	−256.758	+	192.577i	−0.448878	+	0.336673i
$573$	511.486	+	538.288i	0.892646	+	0.939420i
$574$	−392.578	+	340.488i	−0.683933	+	0.593184i
$575$		0			0
$576$	264.288	−	511.789i	0.458833	−	0.888523i
$577$	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	$0.497291\pi$
$578$	−521.035	−	37.0236i	−0.901445	−	0.0640546i
$579$	−926.718	−	23.6598i	−1.60055	−	0.0408633i
$580$		0			0
$581$		−	795.228i		−	1.36872i
$582$	690.291	+	66.7953i	1.18607	+	0.114769i
$583$	−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	$-0.943372\pi$
$587$	−681.614	−	681.614i	−1.16118	−	1.16118i	−0.176965	−	0.984217i	$-0.556628\pi$
$588$	47.1780	−	33.5383i	0.0802347	−	0.0570379i
$589$		−	106.253i		−	0.180395i
$590$		0			0
$591$	−846.208	−	21.6044i	−1.43182	−	0.0365556i
$592$	290.700	+	530.048i	0.491047	+	0.895352i
$593$	−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	$0.920635\pi$
$594$	−229.856	−	310.088i	−0.386962	−	0.522033i
$595$		0			0
$596$	106.233	+	15.1739i	0.178243	+	0.0254596i
$597$	−575.277	−	605.422i	−0.963614	−	1.01411i
$598$	351.069	+	24.9461i	0.587072	+	0.0417159i
$599$		−	798.031i		−	1.33227i	−0.745830	−	0.666136i	$-0.767947\pi$
$599$		−	798.031i		−	1.33227i	0.745830	−	0.666136i	$-0.232053\pi$
$600$		0			0
$601$	−20.9629			−0.0348801			−0.0174400	−	0.999848i	$-0.505552\pi$
$601$	−20.9629			−0.0348801			−0.0174400	+	0.999848i	$0.505552\pi$
$602$	−36.3147	+	511.060i	−0.0603235	+	0.848937i
$603$	−305.748	−	338.674i	−0.507044	−	0.561649i
$604$	3.89342	−	27.2579i	0.00644606	−	0.0451289i
$605$		0			0
$606$	−480.115	−	582.984i	−0.792269	−	0.962021i
$607$	−648.167	+	648.167i	−1.06782	+	1.06782i	−0.0702937	+	0.997526i	$0.522394\pi$
$607$	−648.167	+	648.167i	−1.06782	+	1.06782i	−0.997526	+	0.0702937i	$0.977606\pi$
$608$	135.081	−	364.733i	0.222172	−	0.599890i
$609$	−574.280	−	14.6618i	−0.942988	−	0.0240752i
$610$		0			0
$611$	930.298			1.52258
$612$	471.528	+	700.491i	0.770471	+	1.14459i
$613$	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	$0.00987863\pi$
$618$	−390.961	−	37.8309i	−0.632623	−	0.0612151i
$619$	541.863			0.875384			0.437692	−	0.899125i	$-0.355796\pi$
$619$	541.863			0.875384			0.437692	+	0.899125i	$0.355796\pi$
$620$		0			0
$621$	−32.3808	+	422.033i	−0.0521430	+	0.679602i
$622$	72.9675	−	1026.88i	0.117311	−	1.65093i
$623$	213.169	−	213.169i	0.342166	−	0.342166i
$624$	−513.251	−	164.000i	−0.822518	−	0.262821i
$625$		0			0
$626$	717.280	+	827.014i	1.14582	+	1.32111i
$627$	−179.536	−	188.943i	−0.286341	−	0.301345i
$628$	−114.241	−	152.315i	−0.181913	−	0.242540i
$629$	−886.235			−1.40896
$630$		0			0
$631$		−	941.798i		−	1.49255i	−0.665638	−	0.746274i	$-0.731841\pi$
$631$		−	941.798i		−	1.49255i	0.665638	−	0.746274i	$-0.268159\pi$
$632$	−115.496	+	534.488i	−0.182747	+	0.845708i
$633$	−185.238	+	176.015i	−0.292635	+	0.278064i
$634$	6.89048	+	7.94463i	0.0108683	+	0.0125310i
$635$		0			0
$636$	57.8124	−	342.118i	0.0909000	−	0.537922i
$637$	−38.2881	−	38.2881i	−0.0601068	−	0.0601068i
$638$	−26.4476	+	372.199i	−0.0414539	+	0.583384i
$639$	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	$-0.144973\pi$
$642$	905.986	+	87.6668i	1.41119	+	0.136553i
$643$	41.5913	+	41.5913i	0.0646832	+	0.0646832i	0.738708	−	0.674025i	$-0.235436\pi$
$643$	41.5913	+	41.5913i	0.0646832	+	0.0646832i	−0.674025	+	0.738708i	$0.735436\pi$
$644$	−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	0.728900	−	0.684620i	$-0.240032\pi$
$647$	28.6494	+	28.6494i	0.0442804	+	0.0442804i	−0.684620	+	0.728900i	$0.740032\pi$
$648$	200.709	−	616.133i	0.309737	−	0.950822i
$649$			424.678i			0.654358i
$650$		0			0
$651$	4.91059	−	192.340i	0.00754315	−	0.295453i
$652$	−6.16252	−	8.21634i	−0.00945171	−	0.0126018i
$653$	−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	$0.887420\pi$
$654$	87.3395	+	106.053i	0.133547	+	0.162160i
$655$		0			0
$656$	−158.644	+	544.003i	−0.241835	+	0.829272i
$657$	−90.6466	−	100.409i	−0.137970	−	0.152829i
$658$	−86.1899	+	1212.96i	−0.130988	+	1.84340i
$659$			851.849i			1.29264i	0.763067	+	0.646320i	$0.223693\pi$
$659$			851.849i			1.29264i	−0.763067	+	0.646320i	$0.776307\pi$
$660$		0			0
$661$	−523.764			−0.792381			−0.396191	−	0.918168i	$-0.629668\pi$
$661$	−523.764			−0.792381			−0.396191	+	0.918168i	$0.629668\pi$
$662$	1143.55	+	81.2580i	1.72742	+	0.122746i
$663$	572.616	−	544.105i	0.863673	−	0.820671i
$664$	−469.827	−	728.845i	−0.707571	−	1.09766i
$665$		0			0
$666$	418.808	+	535.847i	0.628841	+	0.804575i
$667$	289.334	−	289.334i	0.433784	−	0.433784i
$668$	375.444	+	500.571i	0.562042	+	0.749358i
$669$	−24.0617	+	942.458i	−0.0359667	+	1.40876i
$670$		0			0
$671$	53.1026			0.0791394
$672$	261.382	−	654.002i	0.388961	−	0.973217i
$673$	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	$0.0713524\pi$
$678$	−724.172	−	70.0737i	−1.06810	−	0.103354i
$679$	847.991			1.24888
$680$		0			0
$681$	3.63979	−	142.565i	0.00534477	−	0.209346i
$682$	−124.658	−	8.85793i	−0.182784	−	0.0129882i
$683$	278.938	−	278.938i	0.408402	−	0.408402i	−0.472779	−	0.881181i	$-0.656749\pi$
$683$	278.938	−	278.938i	0.408402	−	0.408402i	0.881181	+	0.472779i	$0.156749\pi$
$684$	83.8948	−	429.443i	0.122653	−	0.627841i
$685$		0			0
$686$	−489.678	+	424.704i	−0.713816	+	0.619102i
$687$	277.572	−	263.752i	0.404035	−	0.383918i
$688$	268.655	+	489.853i	0.390487	+	0.711996i
$689$	−324.570			−0.471074
$690$		0			0
$691$		−	108.692i		−	0.157297i	−0.996902	−	0.0786483i	$-0.974940\pi$
$691$		−	108.692i		−	0.157297i	0.996902	−	0.0786483i	$-0.0250604\pi$
$692$	−199.639	−	266.174i	−0.288496	−	0.384645i
$693$	−316.266	−	350.326i	−0.456373	−	0.505520i
$694$	765.418	−	663.857i	1.10291	−	0.956567i
$695$		0			0
$696$	−535.003	+	325.851i	−0.768682	+	0.468177i
$697$	−587.408	−	587.408i	−0.842766	−	0.842766i
$698$	−305.382	−	21.6997i	−0.437510	−	0.0310884i
$699$	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	$-0.377566\pi$
$702$	−599.585	−	89.0945i	−0.854110	−	0.126915i
$703$	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
$708$	−581.084	+	413.086i	−0.820740	+	0.583454i
$709$		−	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
$712$	69.4324	−	321.316i	0.0975174	−	0.451287i
$713$	96.9047	+	96.9047i	0.135911	+	0.135911i
$714$	656.373	+	797.008i	0.919290	+	1.11626i
$715$		0			0
$716$	−125.040	+	875.403i	−0.174636	+	1.22263i
$717$	358.548	−	340.695i	0.500066	−	0.475168i
$718$	107.871	+	7.66503i	0.150238	+	0.0106755i
$719$		−	873.333i		−	1.21465i	−0.794454	−	0.607325i	$-0.792243\pi$
$719$		−	873.333i		−	1.21465i	0.794454	−	0.607325i	$-0.207757\pi$
$720$		0			0
$721$	−480.278			−0.666127
$722$	−30.2325	+	425.465i	−0.0418733	+	0.589286i
$723$	42.1285	+	44.3361i	0.0582691	+	0.0613224i
$724$	−730.408	−	104.329i	−1.00885	−	0.144101i
$725$		0			0
$726$	323.776	−	266.644i	0.445972	−	0.367279i
$727$	−165.684	+	165.684i	−0.227901	+	0.227901i	−0.811815	−	0.583914i	$-0.801520\pi$
$727$	−165.684	+	165.684i	−0.227901	+	0.227901i	0.583914	+	0.811815i	$0.301520\pi$
$728$	−643.971	−	139.154i	−0.884575	−	0.191146i
$729$	111.212	−	720.467i	0.152554	−	0.988295i
$730$		0			0
$731$	−819.029			−1.12042
$732$	51.6530	+	72.6598i	0.0705642	+	0.0992620i
$733$	−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
$738$	−77.5747	+	632.758i	−0.105115	+	0.857396i
$739$	−135.132			−0.182858			−0.0914290	−	0.995812i	$-0.529143\pi$
$739$	−135.132			−0.182858			−0.0914290	+	0.995812i	$0.529143\pi$
$740$		0			0
$741$	−409.181	−	10.4467i	−0.552201	−	0.0140981i
$742$	30.0707	−	423.187i	0.0405265	−	0.570333i
$743$	472.574	−	472.574i	0.636035	−	0.636035i	−0.313540	−	0.949575i	$-0.601515\pi$
$743$	472.574	−	472.574i	0.636035	−	0.636035i	0.949575	+	0.313540i	$0.101515\pi$
$744$	−109.135	−	179.185i	−0.146687	−	0.240840i
$745$		0			0
$746$	−759.465	−	875.652i	−1.01805	−	1.17380i
$747$	−653.716	−	724.116i	−0.875122	−	0.969366i
$748$	536.507	−	402.397i	0.717256	−	0.537964i
$749$	1112.96			1.48593
$750$		0			0
$751$			643.372i			0.856687i	0.903616	+	0.428344i	$0.140903\pi$
$751$			643.372i			0.856687i	−0.903616	+	0.428344i	$0.859097\pi$
$752$	637.630	+	1162.63i	0.847912	+	1.54604i
$753$	878.930	+	924.986i	1.16724	+	1.22840i
$754$	383.943	+	442.681i	0.509208	+	0.587110i
$755$		0			0
$756$	171.715	−	773.507i	0.227136	−	1.02316i
$757$	−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	$0.811513\pi$
$758$	0.827892	−	11.6510i	0.00109221	−	0.0153707i
$759$	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	$0.898415\pi$
$762$	−63.3500	+	654.686i	−0.0831365	+	0.859167i
$763$	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
$768$	−146.827	−	753.834i	−0.191181	−	0.981555i
$769$		−	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
$772$	−988.806	+	741.636i	−1.28084	+	0.960668i
$773$	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	$0.643971\pi$
$774$	387.049	+	495.212i	0.500063	+	0.639809i
$775$		0			0
$776$	777.203	−	501.000i	1.00155	−	0.645618i
$777$	572.820	+	602.835i	0.737220	+	0.775850i
$778$	4.89869	−	68.9397i	0.00629652	−	0.0886114i
$779$			430.468i			0.552591i
$780$		0			0
$781$	−330.492			−0.423165
$782$	−733.573	−	52.1260i	−0.938073	−	0.0666573i
$783$	−534.979	+	458.735i	−0.683242	+	0.585869i
$784$	21.6071	−	74.0927i	0.0275601	−	0.0945060i
$785$		0			0
$786$	−92.7506	+	76.3844i	−0.118003	+	0.0971811i
$787$	−188.018	+	188.018i	−0.238905	+	0.238905i	−0.816396	−	0.577492i	$-0.804032\pi$
$787$	−188.018	+	188.018i	−0.238905	+	0.238905i	0.577492	+	0.816396i	$0.304032\pi$
$788$	−902.903	+	677.205i	−1.14582	+	0.859398i
$789$	917.032	+	23.4126i	1.16227	+	0.0296737i
$790$		0			0
$791$	−889.612			−1.12467
$792$	−496.840	−	134.229i	−0.627324	−	0.169481i
$793$	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	$0.446127\pi$
$798$	51.5305	−	532.538i	0.0645746	−	0.667341i
$799$	−1943.90			−2.43291
$800$		0			0
$801$	18.8715	−	369.342i	0.0235599	−	0.461102i
$802$	−207.252	−	14.7269i	−0.258419	−	0.0183627i
$803$	−75.9686	+	75.9686i	−0.0946060	+	0.0946060i
$804$	−599.855	−	101.366i	−0.746088	−	0.126077i
$805$		0			0
$806$	−148.264	+	128.592i	−0.183951	+	0.159543i
$807$	−186.311	−	196.074i	−0.230869	−	0.242966i
$808$	−984.264	−	212.687i	−1.21815	−	0.263226i
$809$	−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	$0.0181568\pi$
$811$			92.4709i			0.114021i	−0.998374	+	0.0570104i	$0.981843\pi$
$812$	−612.756	+	459.586i	−0.754625	+	0.565993i
$813$	−883.630	+	839.634i	−1.08688	+	1.03276i
$814$	408.051	−	353.908i	0.501291	−	0.434777i
$815$		0			0
$816$	1072.46	+	342.686i	1.31429	+	0.419958i
$817$	300.103	+	300.103i	0.367323	+	0.367323i
$818$	1163.55	+	82.6793i	1.42244	+	0.101075i
$819$	−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	$0.882334\pi$
$822$	6.90913	−	71.4019i	0.00840527	−	0.0868636i
$823$	−468.289	−	468.289i	−0.569003	−	0.569003i	0.362846	−	0.931849i	$-0.381805\pi$
$823$	−468.289	−	468.289i	−0.569003	−	0.569003i	−0.931849	+	0.362846i	$0.881805\pi$
$824$	−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	0.881003	−	0.473111i	$-0.156869\pi$
$827$	337.326	+	337.326i	0.407891	+	0.407891i	−0.473111	+	0.881003i	$0.656869\pi$
$828$	315.148	+	468.176i	0.380613	+	0.565430i
$829$			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
$832$	−672.427	+	252.925i	−0.808206	+	0.303997i
$833$	80.0045	+	80.0045i	0.0960438	+	0.0960438i
$834$	767.049	−	631.700i	0.919723	−	0.757435i
$835$		0			0
$836$	−344.027	−	49.1396i	−0.411516	−	0.0587794i
$837$	−153.641	−	179.177i	−0.183562	−	0.214071i
$838$	−462.210	−	32.8435i	−0.551563	−	0.0391928i
$839$			835.860i			0.996257i	0.867103	+	0.498129i	$0.165979\pi$
$839$			835.860i			0.996257i	−0.867103	+	0.498129i	$0.834021\pi$
$840$		0			0
$841$	−159.738			−0.189938
$842$	35.8451	−	504.450i	0.0425713	−	0.599110i
$843$	−327.179	+	310.889i	−0.388113	+	0.368789i
$844$	−48.1759	+	337.280i	−0.0570804	+	0.399621i
$845$		0			0
$846$	918.628	+	1175.34i	1.08585	+	1.38929i
$847$	362.652	−	362.652i	0.428161	−	0.428161i
$848$	−222.462	−	405.626i	−0.262337	−	0.478333i
$849$	16.5119	−	646.745i	0.0194487	−	0.761773i
$850$		0			0
$851$	−592.319			−0.696026
$852$	−321.471	−	452.210i	−0.377313	−	0.530763i
$853$	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	$-0.00184179\pi$
$858$	−46.3685	+	479.191i	−0.0540425	+	0.558498i
$859$	518.926			0.604104			0.302052	−	0.953291i	$-0.402328\pi$
$859$	518.926			0.604104			0.302052	+	0.953291i	$0.402328\pi$
$860$		0			0
$861$	−19.8946	+	779.240i	−0.0231064	+	0.905041i
$862$	17.4124	−	245.046i	0.0202000	−	0.284276i
$863$	−284.726	+	284.726i	−0.329926	+	0.329926i	−0.852558	−	0.522633i	$-0.824950\pi$
$863$	−284.726	+	284.726i	−0.329926	+	0.329926i	0.522633	+	0.852558i	$0.324950\pi$
$864$	−299.613	−	810.387i	−0.346775	−	0.937948i
$865$		0			0
$866$	588.305	+	678.308i	0.679336	+	0.783266i
$867$	−567.995	+	539.714i	−0.655127	+	0.622508i
$868$	−153.926	−	205.226i	−0.177334	−	0.236436i
$869$	488.584			0.562237
$870$		0			0
$871$			569.087i			0.653372i
$872$	179.051	+	38.6907i	0.205334	+	0.0443701i
$873$	772.161	−	697.090i	0.884492	−	0.798499i
$874$	249.691	+	287.890i	0.285688	+	0.329394i
$875$		0			0
$876$	−177.842	−	30.0524i	−0.203016	−	0.0343064i
$877$	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	$0.717139\pi$
$878$	33.8483	−	476.350i	0.0385516	−	0.542540i
$879$	−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	$0.843171\pi$
$882$	10.5656	−	86.1811i	0.0119791	−	0.0977110i
$883$	314.080	+	314.080i	0.355696	+	0.355696i	0.862224	−	0.506527i	$-0.169071\pi$
$883$	314.080	+	314.080i	0.355696	+	0.355696i	−0.506527	+	0.862224i	$0.669071\pi$
$884$	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	0.487669	−	0.873029i	$-0.337847\pi$
$887$	−341.814	−	341.814i	−0.385359	−	0.385359i	−0.873029	+	0.487669i	$0.837847\pi$
$888$	881.162	+	214.086i	0.992300	+	0.241088i
$889$			804.252i			0.904670i
$890$		0			0
$891$	−575.969	−	59.0123i	−0.646430	−	0.0662315i
$892$	754.233	+	1005.60i	0.845552	+	1.12736i
$893$	712.269	+	712.269i	0.797613	+	0.797613i
$894$	124.254	−	102.329i	0.138986	−	0.114462i
$895$		0			0
$896$	−267.475	−	900.169i	−0.298521	−	1.00465i
$897$	382.710	−	363.655i	0.426655	−	0.405412i
$898$	68.4982	−	963.981i	0.0762787	−	1.07348i
$899$			228.171i			0.253805i
$900$		0			0
$901$	678.202			0.752722
$902$	505.037	+	35.8867i	0.559908	+	0.0397857i
$903$	529.381	+	557.121i	0.586247	+	0.616966i
$904$	−815.350	+	525.590i	−0.901936	+	0.581405i
$905$		0			0
$906$	−26.2562	−	31.8818i	−0.0289803	−	0.0351897i
$907$	542.622	−	542.622i	0.598261	−	0.598261i	−0.341589	−	0.939850i	$-0.610965\pi$
$907$	542.622	−	542.622i	0.598261	−	0.598261i	0.939850	+	0.341589i	$0.110965\pi$
$908$	−114.092	−	152.116i	−0.125652	−	0.167529i
$909$	−1131.38	−	57.8076i	−1.24464	−	0.0635948i
$910$		0			0
$911$	695.346			0.763277			0.381639	−	0.924312i	$-0.375360\pi$
$911$	695.346			0.763277			0.381639	+	0.924312i	$0.375360\pi$
$912$	−267.399	−	518.528i	−0.293200	−	0.568561i
$913$	−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
$918$	1252.86	+	186.167i	1.36477	+	0.202796i
$919$	718.456			0.781780			0.390890	−	0.920437i	$-0.372167\pi$
$919$	718.456			0.781780			0.390890	+	0.920437i	$0.372167\pi$
$920$		0			0
$921$	−374.893	−	9.57132i	−0.407050	−	0.0103923i
$922$	870.688	+	61.8690i	0.944347	+	0.0671031i
$923$	−366.998	+	366.998i	−0.397614	+	0.397614i
$924$	−620.492	−	104.853i	−0.671528	−	0.113477i
$925$		0			0
$926$	−66.4743	+	57.6540i	−0.0717865	+	0.0622613i
$927$	−437.330	+	394.812i	−0.471769	+	0.425902i
$928$	−290.077	+	783.242i	−0.312583	+	0.844010i
$929$	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
$932$	−648.075	−	864.064i	−0.695360	−	0.927107i
$933$	−1063.69	−	1119.43i	−1.14008	−	1.19981i
$934$	487.643	−	422.939i	0.522102	−	0.452826i
$935$		0			0
$936$	−700.776	+	402.665i	−0.748693	+	0.430198i
$937$	−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	$-0.561044\pi$
$938$	−741.997	−	52.7245i	−0.791041	−	0.0562095i
$939$	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	$-0.227894\pi$
$942$	−284.268	−	27.5069i	−0.301770	−	0.0292005i
$943$	−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	$0.0875713\pi$
$947$	1168.65	+	1168.65i	1.23405	+	1.23405i	0.271656	+	0.962394i	$0.412429\pi$
$948$	475.247	+	668.526i	0.501315	+	0.705196i
$949$			168.720i			0.177787i
$950$		0			0
$951$	15.7696	+	0.402609i	0.0165821	+	0.000423354i
$952$	1345.60	+	290.768i	1.41345	+	0.305428i
$953$	−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	$0.939828\pi$
$954$	−320.498	−	410.064i	−0.335952	−	0.429836i
$955$		0			0
$956$	93.2496	−	652.841i	0.0975414	−	0.682888i
$957$	385.542	+	405.744i	0.402865	+	0.423975i
$958$	1392.59	+	98.9541i	1.45364	+	0.103292i
$959$		−	87.7140i		−	0.0914641i
$960$		0			0
$961$	884.580			0.920479
$962$	60.1236	−	846.124i	0.0624986	−	0.879547i
$963$	1013.44	−	914.909i	1.05238	−	0.950061i
$964$	80.7268	+	11.5307i	0.0837415	+	0.0119613i
$965$		0			0
$966$	438.689	+	532.683i	0.454130	+	0.551432i
$967$	366.482	−	366.482i	0.378989	−	0.378989i	−0.491749	−	0.870737i	$-0.663642\pi$
$967$	366.482	−	366.482i	0.378989	−	0.378989i	0.870737	+	0.491749i	$0.163642\pi$
$968$	118.121	−	546.637i	0.122026	−	0.564708i
$969$	855.000	+	21.8288i	0.882353	+	0.0225272i
$970$		0			0
$971$	1773.80			1.82678			0.913390	−	0.407086i	$-0.133455\pi$
$971$	1773.80			1.82678			0.913390	+	0.407086i	$0.133455\pi$
$972$	−479.501	−	845.496i	−0.493314	−	0.869852i
$973$	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	$0.471957\pi$
$978$	−15.3343	−	1.48380i	−0.0156792	−	0.00151718i
$979$	−293.721			−0.300021
$980$		0			0
$981$	205.813	+	10.5160i	0.209799	+	0.0107197i
$982$	60.0491	−	845.076i	0.0611498	−	0.860566i
$983$	−297.097	+	297.097i	−0.302235	+	0.302235i	−0.841888	−	0.539653i	$-0.818556\pi$
$983$	−297.097	+	297.097i	−0.302235	+	0.302235i	0.539653	+	0.841888i	$0.318556\pi$
$984$	442.147	+	725.945i	0.449336	+	0.737749i
$985$		0			0
$986$	−802.264	−	925.000i	−0.813656	−	0.938134i
$987$	1256.44	+	1322.28i	1.27299	+	1.33969i
$988$	−436.595	+	327.460i	−0.441898	+	0.331438i
$989$	−547.401			−0.553490
$990$		0			0
$991$		−	1518.20i		−	1.53198i	−0.642850	−	0.765992i	$-0.722248\pi$
$991$		−	1518.20i		−	1.53198i	0.642850	−	0.765992i	$-0.277752\pi$
$992$	−262.326	−	97.1538i	−0.264442	−	0.0979373i
$993$	1246.61	−	1184.55i	1.25540	−	1.19290i
$994$	−444.504	−	512.507i	−0.447188	−	0.515601i
$995$		0			0
$996$	−1282.54	−	216.729i	−1.28770	−	0.217599i
$997$	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	$0.618456\pi$
$998$	−59.8993	+	842.968i	−0.0600193	+	0.844657i
$999$	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.107.11		40
3.2	odd	2	inner	300.3.l.g.107.10		40
4.3	odd	2	inner	300.3.l.g.107.20		40
5.2	odd	4		60.3.l.a.23.20	yes	40
5.3	odd	4	inner	300.3.l.g.143.1		40
5.4	even	2		60.3.l.a.47.10	yes	40
12.11	even	2	inner	300.3.l.g.107.1		40
15.2	even	4		60.3.l.a.23.1	✓	40
15.8	even	4	inner	300.3.l.g.143.20		40
15.14	odd	2		60.3.l.a.47.11	yes	40
20.3	even	4	inner	300.3.l.g.143.10		40
20.7	even	4		60.3.l.a.23.11	yes	40
20.19	odd	2		60.3.l.a.47.1	yes	40
60.23	odd	4	inner	300.3.l.g.143.11		40
60.47	odd	4		60.3.l.a.23.10	yes	40
60.59	even	2		60.3.l.a.47.20	yes	40

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

\(f(q)\)	\(=\)	\(q+(0.141758 - 1.99497i) q^{2} +(-2.06649 - 2.17477i) q^{3} +(-3.95981 - 0.565605i) q^{4} +(-4.63154 + 3.81429i) q^{6} +(-5.18766 + 5.18766i) q^{7} +(-1.68970 + 7.81952i) q^{8} +(-0.459255 + 8.98827i) q^{9} +O(q^{10})\)	\(q+(0.141758 - 1.99497i) q^{2} +(-2.06649 - 2.17477i) q^{3} +(-3.95981 - 0.565605i) q^{4} +(-4.63154 + 3.81429i) q^{6} +(-5.18766 + 5.18766i) q^{7} +(-1.68970 + 7.81952i) q^{8} +(-0.459255 + 8.98827i) q^{9} +7.14796 q^{11} +(6.95284 + 9.78049i) 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} +(17.8662 + 2.19036i) q^{18} +12.1545 q^{19} +(22.0022 + 0.561734i) q^{21} +(1.01328 - 14.2600i) q^{22} +(-11.0852 + 11.0852i) q^{23} +(20.4974 - 12.4842i) q^{24} +(-14.7099 - 16.9603i) q^{26} +(20.4965 - 17.5754i) q^{27} +(23.4763 - 17.6080i) q^{28} -26.1010 q^{29} -8.74184i q^{31} +(11.1137 - 30.0081i) q^{32} +(-14.7712 - 15.5452i) q^{33} +(30.7369 + 35.4392i) q^{34} +(6.90238 - 35.3321i) q^{36} +(26.7167 + 26.7167i) q^{37} +(1.72299 - 24.2478i) q^{38} +(-33.6650 - 0.859495i) q^{39} +35.4164i q^{41} +(4.23963 - 43.8141i) 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} +(-22.0000 - 42.6615i) q^{48} -4.82369i q^{49} +(70.3445 + 1.79595i) q^{51} +(-35.9205 + 26.9415i) q^{52} +(-20.4453 - 20.4453i) q^{53} +(-32.1568 - 43.3813i) q^{54} +(-31.7994 - 49.3306i) q^{56} +(-25.1171 - 26.4332i) q^{57} +(-3.70002 + 52.0707i) q^{58} +59.4125i q^{59} +7.42905 q^{61} +(-17.4397 - 1.23923i) q^{62} +(-44.2457 - 49.0106i) q^{63} +(-58.2898 - 26.4253i) q^{64} +(-33.1061 + 27.2644i) q^{66} +(-35.8479 + 35.8479i) q^{67} +(75.0574 - 56.2954i) q^{68} +(47.0150 + 1.20033i) q^{69} -46.2359 q^{71} +(-69.5080 - 18.7786i) 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} +(-6.48695 + 67.0389i) q^{78} +68.3530 q^{79} +(-80.5782 - 8.25582i) q^{81} +(70.6547 + 5.02056i) q^{82} +(-76.6461 + 76.6461i) q^{83} +(-86.8069 - 14.6689i) q^{84} +(52.7574 - 45.7572i) q^{86} +(53.9374 + 56.7637i) q^{87} +(-12.0779 + 55.8936i) q^{88} -41.0916 q^{89} +82.3543i q^{91} +(50.1649 - 37.6253i) q^{92} +(-19.0115 + 18.0649i) q^{93} +(125.215 - 108.601i) q^{94} +(-88.2270 + 37.8418i) q^{96} +(-81.7315 - 81.7315i) q^{97} +(-9.62311 - 0.683795i) 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

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Representations

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Database

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