LMFDB - Embedded newform 287.3.g.a.132.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(132,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("287.132");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.g (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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			132.17
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.66337i q^{2} +(-2.23909 + 2.23909i) q^{3} +1.23319 q^{4} -6.64247 q^{5} +(3.72444 + 3.72444i) q^{6} +(6.99925 - 0.102623i) q^{7} -8.70475i q^{8} -1.02704i q^{9} +O(q^{10})$	\(q-1.66337i q^{2} +(-2.23909 + 2.23909i) q^{3} +1.23319 q^{4} -6.64247 q^{5} +(3.72444 + 3.72444i) q^{6} +(6.99925 - 0.102623i) q^{7} -8.70475i q^{8} -1.02704i q^{9} +11.0489i q^{10} +(-3.18102 - 3.18102i) q^{11} +(-2.76121 + 2.76121i) q^{12} +(-2.77474 + 2.77474i) q^{13} +(-0.170701 - 11.6424i) q^{14} +(14.8731 - 14.8731i) q^{15} -9.54651 q^{16} +(-4.86501 - 4.86501i) q^{17} -1.70835 q^{18} +(-13.5114 - 13.5114i) q^{19} -8.19139 q^{20} +(-15.4422 + 15.9017i) q^{21} +(-5.29123 + 5.29123i) q^{22} -39.7354 q^{23} +(19.4907 + 19.4907i) q^{24} +19.1224 q^{25} +(4.61543 + 4.61543i) q^{26} +(-17.8522 - 17.8522i) q^{27} +(8.63137 - 0.126554i) q^{28} +(-31.5812 - 31.5812i) q^{29} +(-24.7395 - 24.7395i) q^{30} -10.8067i q^{31} -18.9396i q^{32} +14.2452 q^{33} +(-8.09233 + 8.09233i) q^{34} +(-46.4923 + 0.681672i) q^{35} -1.26653i q^{36} -12.6510 q^{37} +(-22.4745 + 22.4745i) q^{38} -12.4258i q^{39} +57.8210i q^{40} +(39.6234 + 10.5350i) q^{41} +(26.4505 + 25.6861i) q^{42} +13.8876i q^{43} +(-3.92279 - 3.92279i) q^{44} +6.82205i q^{45} +66.0949i q^{46} +(20.5919 + 20.5919i) q^{47} +(21.3755 - 21.3755i) q^{48} +(48.9789 - 1.43657i) q^{49} -31.8076i q^{50} +21.7864 q^{51} +(-3.42176 + 3.42176i) q^{52} +(-6.26284 - 6.26284i) q^{53} +(-29.6948 + 29.6948i) q^{54} +(21.1298 + 21.1298i) q^{55} +(-0.893310 - 60.9267i) q^{56} +60.5065 q^{57} +(-52.5313 + 52.5313i) q^{58} -16.2701i q^{59} +(18.3413 - 18.3413i) q^{60} -41.0771 q^{61} -17.9755 q^{62} +(-0.105398 - 7.18848i) q^{63} -69.6896 q^{64} +(18.4311 - 18.4311i) q^{65} -23.6951i q^{66} +(-24.3946 + 24.3946i) q^{67} +(-5.99946 - 5.99946i) q^{68} +(88.9712 - 88.9712i) q^{69} +(1.13388 + 77.3340i) q^{70} +(13.8364 + 13.8364i) q^{71} -8.94009 q^{72} +51.0950 q^{73} +21.0434i q^{74} +(-42.8166 + 42.8166i) q^{75} +(-16.6621 - 16.6621i) q^{76} +(-22.5912 - 21.9383i) q^{77} -20.6687 q^{78} +(18.2038 + 18.2038i) q^{79} +63.4124 q^{80} +89.1885 q^{81} +(17.5236 - 65.9086i) q^{82} -46.2697i q^{83} +(-19.0430 + 19.6098i) q^{84} +(32.3157 + 32.3157i) q^{85} +23.1003 q^{86} +141.426 q^{87} +(-27.6900 + 27.6900i) q^{88} +(-71.9192 + 71.9192i) q^{89} +11.3476 q^{90} +(-19.1363 + 19.7058i) q^{91} -49.0012 q^{92} +(24.1971 + 24.1971i) q^{93} +(34.2520 - 34.2520i) q^{94} +(89.7491 + 89.7491i) q^{95} +(42.4074 + 42.4074i) q^{96} +(-46.8338 - 46.8338i) q^{97} +(-2.38956 - 81.4703i) q^{98} +(-3.26702 + 3.26702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) $ 108 * q - 216 * q^4 - 2 * q^7	$ 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) $ 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.66337i		−	0.831687i	−0.909436	−	0.415844i	$-0.863486\pi$
$2$		−	1.66337i		−	0.831687i	0.909436	−	0.415844i	$-0.136514\pi$
$3$	−2.23909	+	2.23909i	−0.746363	+	0.746363i	−0.973794	−	0.227431i	$-0.926967\pi$
$3$	−2.23909	+	2.23909i	−0.746363	+	0.746363i	0.227431	+	0.973794i	$0.426967\pi$
$4$	1.23319			0.308296
$5$	−6.64247			−1.32849			−0.664247	−	0.747514i	$-0.731248\pi$
$5$	−6.64247			−1.32849			−0.664247	+	0.747514i	$0.731248\pi$
$6$	3.72444	+	3.72444i	0.620741	+	0.620741i
$7$	6.99925	−	0.102623i	0.999893	−	0.0146605i
$7$	6.99925	−	0.102623i	0.999893	−	0.0146605i
$8$		−	8.70475i		−	1.08809i
$9$		−	1.02704i		−	0.114115i
$10$			11.0489i			1.10489i
$11$	−3.18102	−	3.18102i	−0.289184	−	0.289184i	0.547574	−	0.836757i	$-0.315552\pi$
$11$	−3.18102	−	3.18102i	−0.289184	−	0.289184i	−0.836757	+	0.547574i	$0.815552\pi$
$12$	−2.76121	+	2.76121i	−0.230101	+	0.230101i
$13$	−2.77474	+	2.77474i	−0.213441	+	0.213441i	−0.805728	−	0.592286i	$-0.798225\pi$
$13$	−2.77474	+	2.77474i	−0.213441	+	0.213441i	0.592286	+	0.805728i	$0.298225\pi$
$14$	−0.170701	−	11.6424i	−0.0121929	−	0.831598i
$15$	14.8731	−	14.8731i	0.991538	−	0.991538i
$16$	−9.54651			−0.596657
$17$	−4.86501	−	4.86501i	−0.286177	−	0.286177i	0.549389	−	0.835566i	$-0.314860\pi$
$17$	−4.86501	−	4.86501i	−0.286177	−	0.286177i	−0.835566	+	0.549389i	$0.814860\pi$
$18$	−1.70835			−0.0949081
$19$	−13.5114	−	13.5114i	−0.711127	−	0.711127i	0.255644	−	0.966771i	$-0.417712\pi$
$19$	−13.5114	−	13.5114i	−0.711127	−	0.711127i	−0.966771	+	0.255644i	$0.917712\pi$
$20$	−8.19139			−0.409570
$21$	−15.4422	+	15.9017i	−0.735341	+	0.757225i
$22$	−5.29123	+	5.29123i	−0.240510	+	0.240510i
$23$	−39.7354			−1.72763			−0.863814	−	0.503811i	$-0.831931\pi$
$23$	−39.7354			−1.72763			−0.863814	+	0.503811i	$0.831931\pi$
$24$	19.4907	+	19.4907i	0.812113	+	0.812113i
$25$	19.1224			0.764894
$26$	4.61543	+	4.61543i	0.177516	+	0.177516i
$27$	−17.8522	−	17.8522i	−0.661192	−	0.661192i
$28$	8.63137	−	0.126554i	0.308263	−	0.00451977i
$29$	−31.5812	−	31.5812i	−1.08901	−	1.08901i	−0.995631	−	0.0933745i	$-0.970235\pi$
$29$	−31.5812	−	31.5812i	−1.08901	−	1.08901i	−0.0933745	−	0.995631i	$-0.529765\pi$
$30$	−24.7395	−	24.7395i	−0.824650	−	0.824650i
$31$		−	10.8067i		−	0.348602i	−0.984692	−	0.174301i	$-0.944233\pi$
$31$		−	10.8067i		−	0.348602i	0.984692	−	0.174301i	$-0.0557666\pi$
$32$		−	18.9396i		−	0.591861i
$33$	14.2452			0.431672
$34$	−8.09233	+	8.09233i	−0.238010	+	0.238010i
$35$	−46.4923	+	0.681672i	−1.32835	+	0.0194763i
$36$		−	1.26653i		−	0.0351813i
$37$	−12.6510			−0.341920			−0.170960	−	0.985278i	$-0.554687\pi$
$37$	−12.6510			−0.341920			−0.170960	+	0.985278i	$0.554687\pi$
$38$	−22.4745	+	22.4745i	−0.591435	+	0.591435i
$39$		−	12.4258i		−	0.318609i
$40$			57.8210i			1.44552i
$41$	39.6234	+	10.5350i	0.966424	+	0.256951i
$41$	39.6234	+	10.5350i	0.966424	+	0.256951i
$42$	26.4505	+	25.6861i	0.629774	+	0.611573i
$43$			13.8876i			0.322968i	0.986875	+	0.161484i	$0.0516280\pi$
$43$			13.8876i			0.322968i	−0.986875	+	0.161484i	$0.948372\pi$
$44$	−3.92279	−	3.92279i	−0.0891543	−	0.0891543i
$45$			6.82205i			0.151601i
$46$			66.0949i			1.43685i
$47$	20.5919	+	20.5919i	0.438125	+	0.438125i	0.891381	−	0.453255i	$-0.149737\pi$
$47$	20.5919	+	20.5919i	0.438125	+	0.438125i	−0.453255	+	0.891381i	$0.649737\pi$
$48$	21.3755	−	21.3755i	0.445323	−	0.445323i
$49$	48.9789	−	1.43657i	0.999570	−	0.0293178i
$50$		−	31.8076i		−	0.636153i
$51$	21.7864			0.427184
$52$	−3.42176	+	3.42176i	−0.0658032	+	0.0658032i
$53$	−6.26284	−	6.26284i	−0.118167	−	0.118167i	0.645551	−	0.763717i	$-0.276628\pi$
$53$	−6.26284	−	6.26284i	−0.118167	−	0.118167i	−0.763717	+	0.645551i	$0.776628\pi$
$54$	−29.6948	+	29.6948i	−0.549905	+	0.549905i
$55$	21.1298	+	21.1298i	0.384179	+	0.384179i
$56$	−0.893310	−	60.9267i	−0.0159520	−	1.08798i
$57$	60.5065			1.06152
$58$	−52.5313	+	52.5313i	−0.905712	+	0.905712i
$59$		−	16.2701i		−	0.275765i	−0.990449	−	0.137882i	$-0.955970\pi$
$59$		−	16.2701i		−	0.275765i	0.990449	−	0.137882i	$-0.0440296\pi$
$60$	18.3413	−	18.3413i	0.305688	−	0.305688i
$61$	−41.0771			−0.673395			−0.336697	−	0.941613i	$-0.609310\pi$
$61$	−41.0771			−0.673395			−0.336697	+	0.941613i	$0.609310\pi$
$62$	−17.9755			−0.289928
$63$	−0.105398	−	7.18848i	−0.00167298	−	0.114103i
$64$	−69.6896			−1.08890
$65$	18.4311	−	18.4311i	0.283555	−	0.283555i
$66$		−	23.6951i		−	0.359016i
$67$	−24.3946	+	24.3946i	−0.364098	+	0.364098i	−0.865319	−	0.501221i	$-0.832884\pi$
$67$	−24.3946	+	24.3946i	−0.364098	+	0.364098i	0.501221	+	0.865319i	$0.332884\pi$
$68$	−5.99946	−	5.99946i	−0.0882273	−	0.0882273i
$69$	88.9712	−	88.9712i	1.28944	−	1.28944i
$70$	1.13388	+	77.3340i	0.0161982	+	1.10477i
$71$	13.8364	+	13.8364i	0.194879	+	0.194879i	0.797801	−	0.602921i	$-0.205997\pi$
$71$	13.8364	+	13.8364i	0.194879	+	0.194879i	−0.602921	+	0.797801i	$0.705997\pi$
$72$	−8.94009			−0.124168
$73$	51.0950			0.699932			0.349966	−	0.936762i	$-0.386193\pi$
$73$	51.0950			0.699932			0.349966	+	0.936762i	$0.386193\pi$
$74$			21.0434i			0.284371i
$75$	−42.8166	+	42.8166i	−0.570889	+	0.570889i
$76$	−16.6621	−	16.6621i	−0.219238	−	0.219238i
$77$	−22.5912	−	21.9383i	−0.293392	−	0.284913i
$78$	−20.6687			−0.264983
$79$	18.2038	+	18.2038i	0.230428	+	0.230428i	0.812871	−	0.582444i	$-0.197903\pi$
$79$	18.2038	+	18.2038i	0.230428	+	0.230428i	−0.582444	+	0.812871i	$0.697903\pi$
$80$	63.4124			0.792655
$81$	89.1885			1.10109
$82$	17.5236	−	65.9086i	0.213703	−	0.803763i
$83$		−	46.2697i		−	0.557467i	−0.960369	−	0.278733i	$-0.910085\pi$
$83$		−	46.2697i		−	0.557467i	0.960369	−	0.278733i	$-0.0899146\pi$
$84$	−19.0430	+	19.6098i	−0.226703	+	0.233450i
$85$	32.3157	+	32.3157i	0.380184	+	0.380184i
$86$	23.1003			0.268608
$87$	141.426			1.62559
$88$	−27.6900	+	27.6900i	−0.314659	+	0.314659i
$89$	−71.9192	+	71.9192i	−0.808081	+	0.808081i	−0.984343	−	0.176262i	$-0.943599\pi$
$89$	−71.9192	+	71.9192i	−0.808081	+	0.808081i	0.176262	+	0.984343i	$0.443599\pi$
$90$	11.3476			0.126085
$91$	−19.1363	+	19.7058i	−0.210289	+	0.216548i
$92$	−49.0012			−0.532621
$93$	24.1971	+	24.1971i	0.260184	+	0.260184i
$94$	34.2520	−	34.2520i	0.364383	−	0.364383i
$95$	89.7491	+	89.7491i	0.944727	+	0.944727i
$96$	42.4074	+	42.4074i	0.441743	+	0.441743i
$97$	−46.8338	−	46.8338i	−0.482822	−	0.482822i	0.423209	−	0.906032i	$-0.360903\pi$
$97$	−46.8338	−	46.8338i	−0.482822	−	0.482822i	−0.906032	+	0.423209i	$0.860903\pi$
$98$	−2.38956	−	81.4703i	−0.0243833	−	0.831330i
$99$	−3.26702	+	3.26702i	−0.0330002	+	0.0330002i
$100$	23.5814			0.235814
$101$	−29.3393	−	29.3393i	−0.290489	−	0.290489i	0.546785	−	0.837273i	$-0.315852\pi$
$101$	−29.3393	−	29.3393i	−0.290489	−	0.290489i	−0.837273	+	0.546785i	$0.815852\pi$
$102$		−	36.2389i		−	0.355283i
$103$	−75.6033			−0.734012			−0.367006	−	0.930219i	$-0.619617\pi$
$103$	−75.6033			−0.734012			−0.367006	+	0.930219i	$0.619617\pi$
$104$	24.1534	+	24.1534i	0.232244	+	0.232244i
$105$	102.574	−	105.627i	0.976895	−	1.00597i
$106$	−10.4174	+	10.4174i	−0.0982778	+	0.0982778i
$107$	195.729			1.82924			0.914621	−	0.404312i	$-0.132489\pi$
$107$	195.729			1.82924			0.914621	+	0.404312i	$0.132489\pi$
$108$	−22.0150	−	22.0150i	−0.203843	−	0.203843i
$109$	70.6126	−	70.6126i	0.647822	−	0.647822i	−0.304644	−	0.952466i	$-0.598537\pi$
$109$	70.6126	−	70.6126i	0.647822	−	0.647822i	0.952466	+	0.304644i	$0.0985375\pi$
$110$	35.1468	−	35.1468i	0.319516	−	0.319516i
$111$	28.3268	−	28.3268i	0.255197	−	0.255197i
$112$	−66.8184	+	0.979695i	−0.596593	+	0.00874728i
$113$	−57.0334			−0.504721			−0.252360	−	0.967633i	$-0.581207\pi$
$113$	−57.0334			−0.504721			−0.252360	+	0.967633i	$0.581207\pi$
$114$		−	100.645i		−	0.882851i
$115$	263.941			2.29514
$116$	−38.9454	−	38.9454i	−0.335736	−	0.335736i
$117$	2.84976	+	2.84976i	0.0243569	+	0.0243569i
$118$	−27.0633			−0.229350
$119$	−34.5507	−	33.5521i	−0.290342	−	0.281951i
$120$	−129.466	−	129.466i	−1.07889	−	1.07889i
$121$		−	100.762i		−	0.832746i
$122$			68.3265i			0.560054i
$123$	−112.309	+	65.1315i	−0.913082	+	0.529525i
$124$		−	13.3266i		−	0.107473i
$125$	39.0421			0.312337
$126$	−11.9571	+	0.175316i	−0.0948979	+	0.00139140i
$127$	107.101			0.843312			0.421656	−	0.906756i	$-0.361449\pi$
$127$	107.101			0.843312			0.421656	+	0.906756i	$0.361449\pi$
$128$			40.1617i			0.313763i
$129$	−31.0956	−	31.0956i	−0.241051	−	0.241051i
$130$	−30.6578	−	30.6578i	−0.235829	−	0.235829i
$131$	−101.394			−0.774001			−0.387000	−	0.922080i	$-0.626489\pi$
$131$	−101.394			−0.774001			−0.387000	+	0.922080i	$0.626489\pi$
$132$	17.5669			0.133083
$133$	−95.9563	−	93.1831i	−0.721476	−	0.700625i
$134$	40.5773	+	40.5773i	0.302816	+	0.302816i
$135$	118.582	+	118.582i	0.878389	+	0.878389i
$136$	−42.3487	+	42.3487i	−0.311387	+	0.311387i
$137$	−192.256	+	192.256i	−1.40333	+	1.40333i	−0.614089	+	0.789236i	$0.710477\pi$
$137$	−192.256	+	192.256i	−1.40333	+	1.40333i	−0.789236	+	0.614089i	$0.789523\pi$
$138$	−147.992	−	147.992i	−1.07241	−	1.07241i
$139$		−	84.5393i		−	0.608196i	−0.952641	−	0.304098i	$-0.901645\pi$
$139$		−	84.5393i		−	0.608196i	0.952641	−	0.304098i	$-0.0983551\pi$
$140$	−57.3336	+	0.840628i	−0.409526	+	0.00600449i
$141$	−92.2141			−0.654001
$142$	23.0151	−	23.0151i	0.162078	−	0.162078i
$143$	17.6530			0.123448
$144$			9.80461i			0.0680876i
$145$	209.777	+	209.777i	1.44674	+	1.44674i
$146$		−	84.9902i		−	0.582124i
$147$	−106.452	+	112.885i	−0.724160	+	0.767924i
$148$	−15.6011			−0.105413
$149$	83.5605	−	83.5605i	0.560809	−	0.560809i	−0.368728	−	0.929537i	$-0.620207\pi$
$149$	83.5605	−	83.5605i	0.560809	−	0.560809i	0.929537	+	0.368728i	$0.120207\pi$
$150$	71.2201	+	71.2201i	0.474801	+	0.474801i
$151$	110.409	+	110.409i	0.731183	+	0.731183i	0.970854	−	0.239671i	$-0.0770397\pi$
$151$	110.409	+	110.409i	0.731183	+	0.731183i	−0.239671	+	0.970854i	$0.577040\pi$
$152$	−117.613	+	117.613i	−0.773772	+	0.773772i
$153$	−4.99654	+	4.99654i	−0.0326571	+	0.0326571i
$154$	−36.4916	+	37.5776i	−0.236959	+	0.244011i
$155$			71.7829i			0.463115i
$156$		−	15.3233i		−	0.0982261i
$157$	−47.6824	+	47.6824i	−0.303710	+	0.303710i	−0.842463	−	0.538754i	$-0.818895\pi$
$157$	−47.6824	+	47.6824i	−0.303710	+	0.303710i	0.538754	+	0.842463i	$0.318895\pi$
$158$	30.2797	−	30.2797i	0.191644	−	0.191644i
$159$	28.0461			0.176391
$160$			125.805i			0.786284i
$161$	−278.118	+	4.07779i	−1.72744	+	0.0253279i
$162$		−	148.354i		−	0.915765i
$163$	−249.804			−1.53254			−0.766270	−	0.642518i	$-0.777890\pi$
$163$	−249.804			−1.53254			−0.766270	+	0.642518i	$0.777890\pi$
$164$	48.8630	+	12.9916i	0.297945	+	0.0792171i
$165$	−94.6231			−0.573473
$166$	−76.9639			−0.463638
$167$	−188.326	+	188.326i	−1.12770	+	1.12770i	−0.137147	+	0.990551i	$0.543793\pi$
$167$	−188.326	+	188.326i	−1.12770	+	1.12770i	−0.990551	+	0.137147i	$0.956207\pi$
$168$	138.420	+	134.420i	0.823931	+	0.800119i
$169$			153.602i			0.908886i
$170$	53.7530	−	53.7530i	0.316194	−	0.316194i
$171$	−13.8767	+	13.8767i	−0.0811503	+	0.0811503i
$172$			17.1260i			0.0995697i
$173$	−212.654			−1.22921			−0.614606	−	0.788835i	$-0.710685\pi$
$173$	−212.654			−1.22921			−0.614606	+	0.788835i	$0.710685\pi$
$174$		−	235.244i		−	1.35198i
$175$	133.842	−	1.96240i	0.764812	−	0.0112137i
$176$	30.3677	+	30.3677i	0.172544	+	0.172544i
$177$	36.4303	+	36.4303i	0.205821	+	0.205821i
$178$	119.629	+	119.629i	0.672071	+	0.672071i
$179$	183.808	−	183.808i	1.02686	−	1.02686i	0.0272338	−	0.999629i	$-0.491330\pi$
$179$	183.808	−	183.808i	1.02686	−	1.02686i	0.999629	−	0.0272338i	$-0.00866987\pi$
$180$			8.41285i			0.0467381i
$181$	234.711	+	234.711i	1.29674	+	1.29674i	0.930531	+	0.366212i	$0.119346\pi$
$181$	234.711	+	234.711i	1.29674	+	1.29674i	0.366212	+	0.930531i	$0.380654\pi$
$182$	32.7782	+	31.8309i	0.180100	+	0.174895i
$183$	91.9752	−	91.9752i	0.502597	−	0.502597i
$184$			345.887i			1.87982i
$185$	84.0341			0.454239
$186$	40.2488	−	40.2488i	0.216391	−	0.216391i
$187$			30.9514i			0.165515i
$188$	25.3936	+	25.3936i	0.135072	+	0.135072i
$189$	−126.784	−	123.120i	−0.670814	−	0.651427i
$190$	149.286	−	149.286i	0.785718	−	0.785718i
$191$	106.658	−	106.658i	0.558417	−	0.558417i	−0.370440	−	0.928857i	$-0.620793\pi$
$191$	106.658	−	106.658i	0.558417	−	0.558417i	0.928857	+	0.370440i	$0.120793\pi$
$192$	156.041	−	156.041i	0.812715	−	0.812715i
$193$	−191.406	−	191.406i	−0.991740	−	0.991740i	0.00822612	−	0.999966i	$-0.497382\pi$
$193$	−191.406	−	191.406i	−0.991740	−	0.991740i	−0.999966	+	0.00822612i	$0.997382\pi$
$194$	−77.9021	+	77.9021i	−0.401557	+	0.401557i
$195$			82.5377i			0.423270i
$196$	60.4001	−	1.77156i	0.308164	−	0.00903857i
$197$			262.352i			1.33174i	0.746069	+	0.665868i	$0.231939\pi$
$197$			262.352i			1.33174i	−0.746069	+	0.665868i	$0.768061\pi$
$198$	5.43428	+	5.43428i	0.0274459	+	0.0274459i
$199$	157.423	+	157.423i	0.791070	+	0.791070i	0.981668	−	0.190598i	$-0.0610427\pi$
$199$	157.423	+	157.423i	0.791070	+	0.791070i	−0.190598	+	0.981668i	$0.561043\pi$
$200$		−	166.455i		−	0.832276i
$201$		−	109.243i		−	0.543499i
$202$	−48.8023	+	48.8023i	−0.241596	+	0.241596i
$203$	−224.285	−	217.803i	−1.10485	−	1.07292i
$204$	26.8666			0.131699
$205$	−263.197	−	69.9783i	−1.28389	−	0.341358i
$206$			125.757i			0.610469i
$207$			40.8097i			0.197148i
$208$	26.4891	−	26.4891i	0.127351	−	0.127351i
$209$			85.9602i			0.411293i
$210$	−175.697	−	170.619i	−0.836651	−	0.812471i
$211$	−4.35136	+	4.35136i	−0.0206226	+	0.0206226i	−0.717343	−	0.696720i	$-0.754642\pi$
$211$	−4.35136	+	4.35136i	−0.0206226	+	0.0206226i	0.696720	+	0.717343i	$0.254642\pi$
$212$	−7.72324	−	7.72324i	−0.0364304	−	0.0364304i
$213$	−61.9619			−0.290901
$214$		−	325.571i		−	1.52136i
$215$		−	92.2480i		−	0.429060i
$216$	−155.399	+	155.399i	−0.719438	+	0.719438i
$217$	−1.10902	−	75.6385i	−0.00511067	−	0.348564i
$218$	−117.455	−	117.455i	−0.538786	−	0.538786i
$219$	−114.406	+	114.406i	−0.522403	+	0.522403i
$220$	26.0570	+	26.0570i	0.118441	+	0.118441i
$221$	26.9982			0.122164
$222$	−47.1181	−	47.1181i	−0.212244	−	0.212244i
$223$		−	67.0770i		−	0.300794i	−0.988626	−	0.150397i	$-0.951945\pi$
$223$		−	67.0770i		−	0.300794i	0.988626	−	0.150397i	$-0.0480551\pi$
$224$	−1.94364	−	132.563i	−0.00867697	−	0.591798i
$225$		−	19.6393i		−	0.0872860i
$226$			94.8680i			0.419770i
$227$	169.622	+	169.622i	0.747236	+	0.747236i	0.973959	−	0.226724i	$-0.0728014\pi$
$227$	169.622	+	169.622i	0.747236	+	0.747236i	−0.226724	+	0.973959i	$0.572801\pi$
$228$	74.6157			0.327262
$229$	−246.442	−	246.442i	−1.07616	−	1.07616i	−0.996850	−	0.0793154i	$-0.974727\pi$
$229$	−246.442	−	246.442i	−1.07616	−	1.07616i	−0.0793154	−	0.996850i	$-0.525273\pi$
$230$		−	439.033i		−	1.90884i
$231$	99.7055	−	1.46189i	0.431626	−	0.00632852i
$232$	−274.906	+	274.906i	−1.18494	+	1.18494i
$233$	−196.386	−	196.386i	−0.842858	−	0.842858i	0.146372	−	0.989230i	$-0.453240\pi$
$233$	−196.386	−	196.386i	−0.842858	−	0.842858i	−0.989230	+	0.146372i	$0.953240\pi$
$234$	4.74021	−	4.74021i	0.0202573	−	0.0202573i
$235$	−136.781	−	136.781i	−0.582046	−	0.582046i
$236$		−	20.0641i		−	0.0850173i
$237$	−81.5198			−0.343965
$238$	−55.8098	+	57.4707i	−0.234495	+	0.241474i
$239$	239.529	+	239.529i	1.00221	+	1.00221i	0.999998	+	0.00221493i	$0.000705035\pi$
$239$	239.529	+	239.529i	1.00221	+	1.00221i	0.00221493	+	0.999998i	$0.499295\pi$
$240$	−141.986	+	141.986i	−0.591608	+	0.591608i
$241$	17.8130			0.0739127			0.0369563	−	0.999317i	$-0.488234\pi$
$241$	17.8130			0.0739127			0.0369563	+	0.999317i	$0.488234\pi$
$242$	−167.605			−0.692584
$243$	−39.0315	+	39.0315i	−0.160623	+	0.160623i
$244$	−50.6556			−0.207605
$245$	−325.341	+	9.54239i	−1.32792	+	0.0389485i
$246$	108.338	+	186.812i	0.440399	+	0.759399i
$247$	74.9812			0.303568
$248$	−94.0692			−0.379311
$249$	103.602	+	103.602i	0.416072	+	0.416072i
$250$		−	64.9416i		−	0.259766i
$251$	252.831			1.00730			0.503648	−	0.863909i	$-0.331991\pi$
$251$	252.831			1.00730			0.503648	+	0.863909i	$0.331991\pi$
$252$	−0.129975	−	8.86473i	−0.000515774	−	0.0351775i
$253$	126.399	+	126.399i	0.499602	+	0.499602i
$254$		−	178.148i		−	0.701371i
$255$	−144.715			−0.567511
$256$	−211.955			−0.827948
$257$	−16.9557	+	16.9557i	−0.0659757	+	0.0659757i	−0.739325	−	0.673349i	$-0.764855\pi$
$257$	−16.9557	+	16.9557i	−0.0659757	+	0.0659757i	0.673349	+	0.739325i	$0.264855\pi$
$258$	−51.7236	+	51.7236i	−0.200479	+	0.200479i
$259$	−88.5478	+	1.29829i	−0.341883	+	0.00501271i
$260$	22.7290	−	22.7290i	0.0874191	−	0.0874191i
$261$	−32.4350	+	32.4350i	−0.124272	+	0.124272i
$262$			168.656i			0.643726i
$263$	−17.1502	+	17.1502i	−0.0652100	+	0.0652100i	−0.738960	−	0.673750i	$-0.764683\pi$
$263$	−17.1502	+	17.1502i	−0.0652100	+	0.0652100i	0.673750	+	0.738960i	$0.264683\pi$
$264$		−	124.001i		−	0.469699i
$265$	41.6007	+	41.6007i	0.156984	+	0.156984i
$266$	−154.998	+	159.611i	−0.582701	+	0.600042i
$267$		−	322.067i		−	1.20624i
$268$	−30.0830	+	30.0830i	−0.112250	+	0.112250i
$269$		−	501.585i		−	1.86463i	−0.361651	−	0.932314i	$-0.617787\pi$
$269$		−	501.585i		−	1.86463i	0.361651	−	0.932314i	$-0.382213\pi$
$270$	197.247	−	197.247i	0.730545	−	0.730545i
$271$		−	248.468i		−	0.916857i	−0.888731	−	0.458428i	$-0.848413\pi$
$271$		−	248.468i		−	0.916857i	0.888731	−	0.458428i	$-0.151587\pi$
$272$	46.4439	+	46.4439i	0.170750	+	0.170750i
$273$	−1.27517	−	86.9710i	−0.00467097	−	0.318575i
$274$	319.793	+	319.793i	1.16713	+	1.16713i
$275$	−60.8286	−	60.8286i	−0.221195	−	0.221195i
$276$	109.718	−	109.718i	0.397529	−	0.397529i
$277$	−89.7821			−0.324123			−0.162062	−	0.986781i	$-0.551814\pi$
$277$	−89.7821			−0.324123			−0.162062	+	0.986781i	$0.551814\pi$
$278$	−140.621			−0.505829
$279$	−11.0988			−0.0397808
$280$	5.93378	+	404.703i	0.0211921	+	1.44537i
$281$	239.382	−	239.382i	0.851895	−	0.851895i	−0.138472	−	0.990366i	$-0.544219\pi$
$281$	239.382	−	239.382i	0.851895	−	0.851895i	0.990366	+	0.138472i	$0.0442189\pi$
$282$			153.387i			0.543924i
$283$		−	470.578i		−	1.66282i	−0.555659	−	0.831410i	$-0.687534\pi$
$283$		−	470.578i		−	1.66282i	0.555659	−	0.831410i	$-0.312466\pi$
$284$	17.0629	+	17.0629i	0.0600805	+	0.0600805i
$285$	−401.912			−1.41022
$286$		−	29.3635i		−	0.102670i
$287$	278.415	+	69.6708i	0.970088	+	0.242755i
$288$	−19.4516			−0.0675403
$289$		−	241.663i		−	0.836205i
$290$	348.937	−	348.937i	1.20323	−	1.20323i
$291$	209.730			0.720722
$292$	63.0096			0.215786
$293$	266.815	+	266.815i	0.910633	+	0.910633i	0.996322	−	0.0856893i	$-0.0273092\pi$
$293$	266.815	+	266.815i	0.910633	+	0.910633i	−0.0856893	+	0.996322i	$0.527309\pi$
$294$	187.770	+	177.069i	0.638672	+	0.602275i
$295$			108.074i			0.366352i
$296$			110.124i			0.372041i
$297$			113.576i			0.382412i
$298$	−138.992	−	138.992i	−0.466418	−	0.466418i
$299$	110.255	−	110.255i	0.368747	−	0.368747i
$300$	−52.8009	+	52.8009i	−0.176003	+	0.176003i
$301$	1.42519	+	97.2028i	0.00473486	+	0.322933i
$302$	183.651	−	183.651i	0.608115	−	0.608115i
$303$	131.387			0.433620
$304$	128.987	+	128.987i	0.424299	+	0.424299i
$305$	272.853			0.894600
$306$	8.31112	+	8.31112i	0.0271605	+	0.0271605i
$307$	393.282			1.28105			0.640524	−	0.767938i	$-0.278717\pi$
$307$	393.282			1.28105			0.640524	+	0.767938i	$0.278717\pi$
$308$	−27.8591	−	27.0540i	−0.0904517	−	0.0878376i
$309$	169.282	−	169.282i	0.547840	−	0.547840i
$310$	119.402			0.385167
$311$	65.0289	+	65.0289i	0.209096	+	0.209096i	0.803883	−	0.594787i	$-0.202764\pi$
$311$	65.0289	+	65.0289i	0.209096	+	0.209096i	−0.594787	+	0.803883i	$0.702764\pi$
$312$	−108.163			−0.346677
$313$	−2.22225	−	2.22225i	−0.00709984	−	0.00709984i	0.703548	−	0.710648i	$-0.251598\pi$
$313$	−2.22225	−	2.22225i	−0.00709984	−	0.00709984i	−0.710648	+	0.703548i	$0.751598\pi$
$314$	79.3137	+	79.3137i	0.252591	+	0.252591i
$315$	0.700102	+	47.7492i	0.00222255	+	0.151585i
$316$	22.4486	+	22.4486i	0.0710400	+	0.0710400i
$317$	−377.460	−	377.460i	−1.19072	−	1.19072i	−0.976864	−	0.213860i	$-0.931396\pi$
$317$	−377.460	−	377.460i	−1.19072	−	1.19072i	−0.213860	−	0.976864i	$-0.568604\pi$
$318$		−	46.6512i		−	0.146702i
$319$			200.921i			0.629845i
$320$	462.911			1.44660
$321$	−438.255	+	438.255i	−1.36528	+	1.36528i
$322$	6.78288	+	462.615i	0.0210649	+	1.43669i
$323$			131.466i			0.407016i
$324$	109.986			0.339463
$325$	−53.0595	+	53.0595i	−0.163260	+	0.163260i
$326$			415.518i			1.27459i
$327$			316.216i			0.967021i
$328$	91.7045	−	344.912i	0.279587	−	1.05156i
$329$	146.241	+	142.015i	0.444501	+	0.431655i
$330$			157.394i			0.476950i
$331$	337.252	+	337.252i	1.01889	+	1.01889i	0.999818	+	0.0190686i	$0.00607008\pi$
$331$	337.252	+	337.252i	1.01889	+	1.01889i	0.0190686	+	0.999818i	$0.493930\pi$
$332$		−	57.0592i		−	0.171865i
$333$			12.9931i			0.0390183i
$334$	313.256	+	313.256i	0.937892	+	0.937892i
$335$	162.040	−	162.040i	0.483702	−	0.483702i
$336$	147.419	−	151.806i	0.438746	−	0.451803i
$337$		−	82.3054i		−	0.244230i	−0.992516	−	0.122115i	$-0.961032\pi$
$337$		−	82.3054i		−	0.244230i	0.992516	−	0.122115i	$-0.0389676\pi$
$338$	255.497			0.755909
$339$	127.703	−	127.703i	0.376705	−	0.376705i
$340$	39.8512	+	39.8512i	0.117209	+	0.117209i
$341$	−34.3762	+	34.3762i	−0.100810	+	0.100810i
$342$	23.0822	+	23.0822i	0.0674917	+	0.0674917i
$343$	342.668	−	15.0813i	0.999033	−	0.0439688i
$344$	120.888			0.351419
$345$	−590.988	+	590.988i	−1.71301	+	1.71301i
$346$			353.722i			1.02232i
$347$	−435.309	+	435.309i	−1.25449	+	1.25449i	−0.300809	+	0.953684i	$0.597257\pi$
$347$	−435.309	+	435.309i	−1.25449	+	1.25449i	−0.953684	+	0.300809i	$0.902743\pi$
$348$	174.405			0.501162
$349$	−448.942			−1.28637			−0.643183	−	0.765712i	$-0.722387\pi$
$349$	−448.942			−1.28637			−0.643183	+	0.765712i	$0.722387\pi$
$350$	−3.26421	−	222.630i	−0.00932630	−	0.636084i
$351$	99.0702			0.282251
$352$	−60.2471	+	60.2471i	−0.171157	+	0.171157i
$353$		−	524.419i		−	1.48561i	−0.669510	−	0.742803i	$-0.733496\pi$
$353$		−	524.419i		−	1.48561i	0.669510	−	0.742803i	$-0.266504\pi$
$354$	60.5972	−	60.5972i	0.171179	−	0.171179i
$355$	−91.9079	−	91.9079i	−0.258896	−	0.258896i
$356$	−88.6897	+	88.6897i	−0.249129	+	0.249129i
$357$	152.488	−	2.23579i	0.427138	−	0.00626272i
$358$	−305.742	−	305.742i	−0.854029	−	0.854029i
$359$	315.335			0.878369			0.439185	−	0.898397i	$-0.355267\pi$
$359$	315.335			0.878369			0.439185	+	0.898397i	$0.355267\pi$
$360$	59.3842			0.164956
$361$			4.11649i			0.0114030i
$362$	390.412	−	390.412i	1.07849	−	1.07849i
$363$	225.616	+	225.616i	0.621530	+	0.621530i
$364$	−23.5986	+	24.3009i	−0.0648314	+	0.0667608i
$365$	−339.397			−0.929855
$366$	−152.989	−	152.989i	−0.418003	−	0.418003i
$367$	−221.393			−0.603251			−0.301626	−	0.953426i	$-0.597529\pi$
$367$	−221.393			−0.603251			−0.301626	+	0.953426i	$0.597529\pi$
$368$	379.335			1.03080
$369$	10.8198	−	40.6947i	0.0293220	−	0.110284i
$370$		−	139.780i		−	0.377784i
$371$	−44.4779	−	43.1925i	−0.119886	−	0.116422i
$372$	29.8395	+	29.8395i	0.0802136	+	0.0802136i
$373$	−280.655			−0.752427			−0.376213	−	0.926533i	$-0.622774\pi$
$373$	−280.655			−0.752427			−0.376213	+	0.926533i	$0.622774\pi$
$374$	51.4838			0.137657
$375$	−87.4186	+	87.4186i	−0.233116	+	0.233116i
$376$	179.247	−	179.247i	0.476721	−	0.476721i
$377$	175.259			0.464878
$378$	−204.794	+	210.889i	−0.541784	+	0.557907i
$379$	−371.393			−0.979927			−0.489964	−	0.871743i	$-0.662990\pi$
$379$	−371.393			−0.979927			−0.489964	+	0.871743i	$0.662990\pi$
$380$	110.677	+	110.677i	0.291256	+	0.291256i
$381$	−239.808	+	239.808i	−0.629416	+	0.629416i
$382$	−177.412	−	177.412i	−0.464428	−	0.464428i
$383$	−322.678	−	322.678i	−0.842501	−	0.842501i	0.146683	−	0.989184i	$-0.453140\pi$
$383$	−322.678	−	322.678i	−0.842501	−	0.842501i	−0.989184	+	0.146683i	$0.953140\pi$
$384$	−89.9257	−	89.9257i	−0.234181	−	0.234181i
$385$	150.061	+	145.724i	0.389770	+	0.378505i
$386$	−318.380	+	318.380i	−0.824818	+	0.824818i
$387$	14.2631			0.0368555
$388$	−57.7547	−	57.7547i	−0.148852	−	0.148852i
$389$			491.989i			1.26475i	0.774661	+	0.632377i	$0.217921\pi$
$389$			491.989i			1.26475i	−0.774661	+	0.632377i	$0.782079\pi$
$390$	137.291			0.352029
$391$	193.313	+	193.313i	0.494407	+	0.494407i
$392$	−12.5050	−	426.349i	−0.0319005	−	1.08763i
$393$	227.030	−	227.030i	0.577685	−	0.577685i
$394$	436.390			1.10759
$395$	−120.918	−	120.918i	−0.306122	−	0.306122i
$396$	−4.02884	+	4.02884i	−0.0101739	+	0.0101739i
$397$	−392.372	+	392.372i	−0.988344	+	0.988344i	−0.999933	−	0.0115891i	$-0.996311\pi$
$397$	−392.372	+	392.372i	−0.988344	+	0.988344i	0.0115891	+	0.999933i	$0.496311\pi$
$398$	261.853	−	261.853i	0.657923	−	0.657923i
$399$	423.500	−	6.20938i	1.06140	−	0.0155624i
$400$	−182.552			−0.456380
$401$		−	708.930i		−	1.76790i	−0.467577	−	0.883952i	$-0.654873\pi$
$401$		−	708.930i		−	1.76790i	0.467577	−	0.883952i	$-0.345127\pi$
$402$	−181.712			−0.452021
$403$	29.9856	+	29.9856i	0.0744061	+	0.0744061i
$404$	−36.1809	−	36.1809i	−0.0895566	−	0.0895566i
$405$	−592.432			−1.46279
$406$	−362.289	+	373.071i	−0.892337	+	0.918893i
$407$	40.2432	+	40.2432i	0.0988777	+	0.0988777i
$408$		−	189.645i		−	0.464816i
$409$			210.195i			0.513925i	0.966421	+	0.256962i	$0.0827217\pi$
$409$			210.195i			0.513925i	−0.966421	+	0.256962i	$0.917278\pi$
$410$	−116.400	+	437.795i	−0.283903	+	1.06779i
$411$		−	860.955i		−	2.09478i
$412$	−93.2328			−0.226293
$413$	−1.66970	−	113.879i	−0.00404285	−	0.275735i
$414$	67.8819			0.163966
$415$			307.345i			0.740591i
$416$	52.5523	+	52.5523i	0.126328	+	0.126328i
$417$	189.291	+	189.291i	0.453935	+	0.453935i
$418$	142.984			0.342067
$419$	59.4123			0.141795			0.0708977	−	0.997484i	$-0.477414\pi$
$419$	59.4123			0.141795			0.0708977	+	0.997484i	$0.477414\pi$
$420$	126.493	−	130.257i	0.301173	−	0.310136i
$421$	−156.713	−	156.713i	−0.372240	−	0.372240i	0.496052	−	0.868293i	$-0.334782\pi$
$421$	−156.713	−	156.713i	−0.372240	−	0.372240i	−0.868293	+	0.496052i	$0.834782\pi$
$422$	7.23794	+	7.23794i	0.0171515	+	0.0171515i
$423$	21.1486	−	21.1486i	0.0499967	−	0.0499967i
$424$	−54.5164	+	54.5164i	−0.128577	+	0.128577i
$425$	−93.0304	−	93.0304i	−0.218895	−	0.218895i
$426$			103.066i			0.241939i
$427$	−287.509	+	4.21547i	−0.673322	+	0.00987229i
$428$	241.370			0.563949
$429$	−39.5266	+	39.5266i	−0.0921366	+	0.0921366i
$430$	−153.443			−0.356844
$431$		−	235.492i		−	0.546384i	−0.961959	−	0.273192i	$-0.911921\pi$
$431$		−	235.492i		−	0.546384i	0.961959	−	0.273192i	$-0.0880795\pi$
$432$	170.426	+	170.426i	0.394505	+	0.394505i
$433$			334.485i			0.772484i	0.922398	+	0.386242i	$0.126227\pi$
$433$			334.485i			0.772484i	−0.922398	+	0.386242i	$0.873773\pi$
$434$	−125.815	+	1.84471i	−0.289897	+	0.00425048i
$435$	−939.418			−2.15958
$436$	87.0785	−	87.0785i	0.199721	−	0.199721i
$437$	536.882	+	536.882i	1.22856	+	1.22856i
$438$	190.300	+	190.300i	0.434476	+	0.434476i
$439$	314.621	−	314.621i	0.716677	−	0.716677i	−0.251246	−	0.967923i	$-0.580840\pi$
$439$	314.621	−	314.621i	0.716677	−	0.716677i	0.967923	+	0.251246i	$0.0808404\pi$
$440$	183.930	−	183.930i	0.418022	−	0.418022i
$441$	−1.47541	−	50.3031i	−0.00334561	−	0.114066i
$442$		−	44.9082i		−	0.101602i
$443$		−	384.808i		−	0.868642i	−0.900758	−	0.434321i	$-0.856988\pi$
$443$		−	384.808i		−	0.868642i	0.900758	−	0.434321i	$-0.143012\pi$
$444$	34.9322	−	34.9322i	0.0786761	−	0.0786761i
$445$	477.721	−	477.721i	1.07353	−	1.07353i
$446$	−111.574			−0.250166
$447$			374.199i			0.837134i
$448$	−487.775	+	7.15179i	−1.08878	+	0.0159638i
$449$		−	271.399i		−	0.604451i	−0.953236	−	0.302226i	$-0.902270\pi$
$449$		−	271.399i		−	0.604451i	0.953236	−	0.302226i	$-0.0977296\pi$
$450$	−32.6676			−0.0725946
$451$	−92.5308	−	159.555i	−0.205168	−	0.353780i
$452$	−70.3328			−0.155604
$453$	−494.429			−1.09146
$454$	282.146	−	282.146i	0.621466	−	0.621466i
$455$	127.112	−	130.895i	0.279368	−	0.287682i
$456$		−	526.694i		−	1.15503i
$457$	350.559	−	350.559i	0.767089	−	0.767089i	−0.210504	−	0.977593i	$-0.567511\pi$
$457$	350.559	−	350.559i	0.767089	−	0.767089i	0.977593	+	0.210504i	$0.0675106\pi$
$458$	−409.925	+	409.925i	−0.895033	+	0.895033i
$459$			173.702i			0.378436i
$460$	325.489			0.707584
$461$			375.893i			0.815387i	0.913119	+	0.407693i	$0.133667\pi$
$461$			375.893i			0.815387i	−0.913119	+	0.407693i	$0.866333\pi$
$462$	−2.43167	−	165.848i	−0.00526335	−	0.358977i
$463$	−586.857	−	586.857i	−1.26751	−	1.26751i	−0.947370	−	0.320140i	$-0.896270\pi$
$463$	−586.857	−	586.857i	−1.26751	−	1.26751i	−0.320140	−	0.947370i	$-0.603730\pi$
$464$	301.490	+	301.490i	0.649763	+	0.649763i
$465$	−160.728	−	160.728i	−0.345652	−	0.345652i
$466$	−326.663	+	326.663i	−0.700994	+	0.700994i
$467$			143.060i			0.306338i	0.988200	+	0.153169i	$0.0489479\pi$
$467$			143.060i			0.306338i	−0.988200	+	0.153169i	$0.951052\pi$
$468$	3.51428	+	3.51428i	0.00750914	+	0.00750914i
$469$	−168.240	+	173.247i	−0.358721	+	0.369397i
$470$	−227.518	+	227.518i	−0.484081	+	0.484081i
$471$		−	213.530i		−	0.453355i
$472$	−141.627			−0.300058
$473$	44.1768	−	44.1768i	0.0933970	−	0.0933970i
$474$			135.598i			0.286072i
$475$	−258.370	−	258.370i	−0.543937	−	0.543937i
$476$	−42.6074	−	41.3760i	−0.0895113	−	0.0869244i
$477$	−6.43216	+	6.43216i	−0.0134846	+	0.0134846i
$478$	398.426	−	398.426i	0.833527	−	0.833527i
$479$	−527.110	+	527.110i	−1.10044	+	1.10044i	−0.106082	+	0.994357i	$0.533831\pi$
$479$	−527.110	+	527.110i	−1.10044	+	1.10044i	−0.994357	+	0.106082i	$0.966169\pi$
$480$	−281.689	−	281.689i	−0.586853	−	0.586853i
$481$	35.1033	−	35.1033i	0.0729799	−	0.0729799i
$482$		−	29.6296i		−	0.0614722i
$483$	613.601	−	631.862i	1.27040	−	1.30820i
$484$		−	124.258i		−	0.256732i
$485$	311.092	+	311.092i	0.641426	+	0.641426i
$486$	64.9239	+	64.9239i	0.133588	+	0.133588i
$487$		−	244.973i		−	0.503024i	−0.967854	−	0.251512i	$-0.919072\pi$
$487$		−	244.973i		−	0.503024i	0.967854	−	0.251512i	$-0.0809278\pi$
$488$			357.565i			0.732716i
$489$	559.334	−	559.334i	1.14383	−	1.14383i
$490$	15.8726	+	541.164i	0.0323930	+	1.10442i
$491$	−244.999			−0.498981			−0.249490	−	0.968377i	$-0.580263\pi$
$491$	−244.999			−0.498981			−0.249490	+	0.968377i	$0.580263\pi$
$492$	−138.498	+	80.3192i	−0.281500	+	0.163250i
$493$			307.285i			0.623297i
$494$		−	124.722i		−	0.252473i
$495$	21.7011	−	21.7011i	0.0438406	−	0.0438406i
$496$			103.166i			0.207996i
$497$	98.2644	+	95.4246i	0.197715	+	0.192001i
$498$	172.329	−	172.329i	0.346042	−	0.346042i
$499$	398.812	+	398.812i	0.799223	+	0.799223i	0.982973	−	0.183750i	$-0.0588237\pi$
$499$	398.812	+	398.812i	0.799223	+	0.799223i	−0.183750	+	0.982973i	$0.558824\pi$
$500$	48.1461			0.0962922
$501$		−	843.355i		−	1.68334i
$502$		−	420.553i		−	0.837756i
$503$	−315.401	+	315.401i	−0.627039	+	0.627039i	−0.947322	−	0.320283i	$-0.896222\pi$
$503$	−315.401	+	315.401i	−0.627039	+	0.627039i	0.320283	+	0.947322i	$0.396222\pi$
$504$	−62.5739	+	0.917462i	−0.124155	+	0.00182036i
$505$	194.886	+	194.886i	0.385912	+	0.385912i
$506$	210.249	−	210.249i	0.415513	−	0.415513i
$507$	−343.928	−	343.928i	−0.678358	−	0.678358i
$508$	132.075			0.259990
$509$	−608.632	−	608.632i	−1.19574	−	1.19574i	−0.975430	−	0.220310i	$-0.929293\pi$
$509$	−608.632	−	608.632i	−1.19574	−	1.19574i	−0.220310	−	0.975430i	$-0.570707\pi$
$510$			240.716i			0.471991i
$511$	357.627	−	5.24354i	0.699857	−	0.0102613i
$512$			513.207i			1.00236i
$513$			482.416i			0.940382i
$514$	28.2038	+	28.2038i	0.0548711	+	0.0548711i
$515$	502.192			0.975130
$516$	−38.3466	−	38.3466i	−0.0743152	−	0.0743152i
$517$		−	131.006i		−	0.253397i
$518$	2.15955	+	147.288i	0.00416901	+	0.284340i
$519$	476.150	−	476.150i	0.917438	−	0.917438i
$520$	−160.438	−	160.438i	−0.308535	−	0.308535i
$521$	450.426	−	450.426i	0.864541	−	0.864541i	−0.127321	−	0.991862i	$-0.540638\pi$
$521$	450.426	−	450.426i	0.864541	−	0.864541i	0.991862	+	0.127321i	$0.0406377\pi$
$522$	53.9515	+	53.9515i	0.103355	+	0.103355i
$523$			720.116i			1.37689i	0.725286	+	0.688447i	$0.241707\pi$
$523$			720.116i			1.37689i	−0.725286	+	0.688447i	$0.758293\pi$
$524$	−125.038			−0.238622
$525$	−295.290	+	304.078i	−0.562458	+	0.579197i
$526$	28.5273	+	28.5273i	0.0542344	+	0.0542344i
$527$	−52.5745	+	52.5745i	−0.0997619	+	0.0997619i
$528$	−135.992			−0.257560
$529$	1049.91			1.98470
$530$	69.1975	−	69.1975i	0.130561	−	0.130561i
$531$	−16.7100			−0.0314690
$532$	−118.332	−	114.912i	−0.222428	−	0.216000i
$533$	−139.176	+	80.7127i	−0.261119	+	0.151431i
$534$	−535.718			−1.00322
$535$	−1300.12			−2.43014
$536$	212.349	+	212.349i	0.396173	+	0.396173i
$537$			823.127i			1.53282i
$538$	−834.323			−1.55079
$539$	−160.373	−	151.233i	−0.297538	−	0.280581i
$540$	146.234	+	146.234i	0.270804	+	0.270804i
$541$		−	625.679i		−	1.15652i	−0.815851	−	0.578262i	$-0.803731\pi$
$541$		−	625.679i		−	1.15652i	0.815851	−	0.578262i	$-0.196269\pi$
$542$	−413.296			−0.762538
$543$	−1051.08			−1.93568
$544$	−92.1411	+	92.1411i	−0.169377	+	0.169377i
$545$	−469.042	+	469.042i	−0.860628	+	0.860628i
$546$	−144.665	+	2.12109i	−0.264955	+	0.00388478i
$547$	−332.460	+	332.460i	−0.607788	+	0.607788i	−0.942368	−	0.334579i	$-0.891406\pi$
$547$	−332.460	+	332.460i	−0.607788	+	0.607788i	0.334579	+	0.942368i	$0.391406\pi$
$548$	−237.087	+	237.087i	−0.432640	+	0.432640i
$549$			42.1876i			0.0768445i
$550$	−101.181	+	101.181i	−0.183965	+	0.183965i
$551$			853.412i			1.54884i
$552$	−774.472	−	774.472i	−1.40303	−	1.40303i
$553$	129.281	+	125.545i	0.233781	+	0.227025i
$554$			149.341i			0.269569i
$555$	−188.160	+	188.160i	−0.339027	+	0.339027i
$556$		−	104.253i		−	0.187505i
$557$	684.259	−	684.259i	1.22847	−	1.22847i	0.263930	−	0.964542i	$-0.414981\pi$
$557$	684.259	−	684.259i	1.22847	−	1.22847i	0.964542	−	0.263930i	$-0.0850186\pi$
$558$			18.4615i			0.0330851i
$559$	−38.5345	−	38.5345i	−0.0689346	−	0.0689346i
$560$	443.839	−	6.50759i	0.792570	−	0.0116207i
$561$	−69.3029	−	69.3029i	−0.123535	−	0.123535i
$562$	−398.183	−	398.183i	−0.708510	−	0.708510i
$563$	168.561	−	168.561i	0.299397	−	0.299397i	−0.541381	−	0.840778i	$-0.682098\pi$
$563$	168.561	−	168.561i	0.299397	−	0.299397i	0.840778	+	0.541381i	$0.182098\pi$
$564$	−113.717			−0.201626
$565$	378.843			0.670518
$566$	−782.748			−1.38295
$567$	624.253	−	9.15283i	1.10097	−	0.0161426i
$568$	120.443	−	120.443i	0.212047	−	0.212047i
$569$			496.683i			0.872904i	0.899727	+	0.436452i	$0.143765\pi$
$569$			496.683i			0.872904i	−0.899727	+	0.436452i	$0.856235\pi$
$570$			668.531i			1.17286i
$571$	286.208	+	286.208i	0.501240	+	0.501240i	0.911823	−	0.410583i	$-0.134675\pi$
$571$	286.208	+	286.208i	0.501240	+	0.501240i	−0.410583	+	0.911823i	$0.634675\pi$
$572$	21.7694			0.0380584
$573$			477.632i			0.833563i
$574$	115.889	−	463.109i	0.201896	−	0.806809i
$575$	−759.835			−1.32145
$576$			71.5738i			0.124260i
$577$	−275.423	+	275.423i	−0.477337	+	0.477337i	−0.904279	−	0.426942i	$-0.859591\pi$
$577$	−275.423	+	275.423i	−0.477337	+	0.477337i	0.426942	+	0.904279i	$0.359591\pi$
$578$	−401.977			−0.695461
$579$	857.149			1.48040
$580$	258.694	+	258.694i	0.446024	+	0.446024i
$581$	−4.74836	−	323.853i	−0.00817273	−	0.557407i
$582$		−	348.859i		−	0.599415i
$583$			39.8444i			0.0683438i
$584$		−	444.769i		−	0.761591i
$585$	−18.9294	−	18.9294i	−0.0323580	−	0.0323580i
$586$	443.814	−	443.814i	0.757362	−	0.757362i
$587$	516.506	−	516.506i	0.879908	−	0.879908i	−0.113616	−	0.993525i	$-0.536243\pi$
$587$	516.506	−	516.506i	0.879908	−	0.879908i	0.993525	+	0.113616i	$0.0362434\pi$
$588$	−131.275	+	139.208i	−0.223256	+	0.236748i
$589$	−146.013	+	146.013i	−0.247900	+	0.247900i
$590$	179.767			0.304690
$591$	−587.430	−	587.430i	−0.993959	−	0.993959i
$592$	120.773			0.204009
$593$	743.392	+	743.392i	1.25361	+	1.25361i	0.954089	+	0.299524i	$0.0968278\pi$
$593$	743.392	+	743.392i	1.25361	+	1.25361i	0.299524	+	0.954089i	$0.403172\pi$
$594$	188.920			0.318047
$595$	229.502	+	222.869i	0.385717	+	0.374570i
$596$	103.046	−	103.046i	0.172895	−	0.172895i
$597$	−704.968			−1.18085
$598$	−183.396	−	183.396i	−0.306682	−	0.306682i
$599$	−873.768			−1.45871			−0.729355	−	0.684135i	$-0.760180\pi$
$599$	−873.768			−1.45871			−0.729355	+	0.684135i	$0.760180\pi$
$600$	372.708	+	372.708i	0.621180	+	0.621180i
$601$	−515.697	−	515.697i	−0.858065	−	0.858065i	0.133045	−	0.991110i	$-0.457525\pi$
$601$	−515.697	−	515.697i	−0.858065	−	0.858065i	−0.991110	+	0.133045i	$0.957525\pi$
$602$	161.685	−	2.37063i	0.268579	−	0.00393792i
$603$	25.0541	+	25.0541i	0.0415491	+	0.0415491i
$604$	136.154	+	136.154i	0.225421	+	0.225421i
$605$			669.310i			1.10630i
$606$		−	218.545i		−	0.360636i
$607$	263.884			0.434735			0.217368	−	0.976090i	$-0.430253\pi$
$607$	263.884			0.434735			0.217368	+	0.976090i	$0.430253\pi$
$608$	−255.900	+	255.900i	−0.420888	+	0.420888i
$609$	989.876	−	14.5136i	1.62541	−	0.0238319i
$610$		−	453.857i		−	0.744027i
$611$	−114.274			−0.187028
$612$	−6.16166	+	6.16166i	−0.0100681	+	0.0100681i
$613$			397.780i			0.648908i	0.945902	+	0.324454i	$0.105180\pi$
$613$			397.780i			0.648908i	−0.945902	+	0.324454i	$0.894820\pi$
$614$		−	654.175i		−	1.06543i
$615$	746.009	−	432.634i	1.21302	−	0.703470i
$616$	−190.967	+	196.651i	−0.310012	+	0.319238i
$617$			19.4730i			0.0315607i	0.999875	+	0.0157804i	$0.00502325\pi$
$617$			19.4730i			0.0315607i	−0.999875	+	0.0157804i	$0.994977\pi$
$618$	−281.580	−	281.580i	−0.455631	−	0.455631i
$619$		−	897.516i		−	1.44994i	−0.688778	−	0.724972i	$-0.741852\pi$
$619$		−	897.516i		−	1.44994i	0.688778	−	0.724972i	$-0.258148\pi$
$620$			88.5216i			0.142777i
$621$	709.364	+	709.364i	1.14229	+	1.14229i
$622$	108.167	−	108.167i	0.173903	−	0.173903i
$623$	−496.000	+	510.761i	−0.796148	+	0.819841i
$624$			118.623i			0.190101i
$625$	−737.394			−1.17983
$626$	−3.69643	+	3.69643i	−0.00590484	+	0.00590484i
$627$	−192.472	−	192.472i	−0.306974	−	0.306974i
$628$	−58.8012	+	58.8012i	−0.0936326	+	0.0936326i
$629$	61.5475	+	61.5475i	0.0978497	+	0.0978497i
$630$	79.4249	−	1.16453i	0.126071	−	0.00184846i
$631$	105.852			0.167753			0.0838763	−	0.996476i	$-0.473270\pi$
$631$	105.852			0.167753			0.0838763	+	0.996476i	$0.473270\pi$
$632$	158.459	−	158.459i	0.250727	−	0.250727i
$633$		−	19.4862i		−	0.0307838i
$634$	−627.857	+	627.857i	−0.990310	+	0.990310i
$635$	−711.412			−1.12033
$636$	34.5860			0.0543806
$637$	−131.918	+	139.890i	−0.207092	+	0.219607i
$638$	334.206			0.523834
$639$	14.2105	−	14.2105i	0.0222387	−	0.0222387i
$640$		−	266.773i		−	0.416833i
$641$	−145.539	+	145.539i	−0.227049	+	0.227049i	−0.811459	−	0.584410i	$-0.801326\pi$
$641$	−145.539	+	145.539i	−0.227049	+	0.227049i	0.584410	+	0.811459i	$0.301326\pi$
$642$	728.981	+	728.981i	1.13548	+	1.13548i
$643$	108.037	−	108.037i	0.168020	−	0.168020i	−0.618089	−	0.786108i	$-0.712093\pi$
$643$	108.037	−	108.037i	0.168020	−	0.168020i	0.786108	+	0.618089i	$0.212093\pi$
$644$	−342.971	+	5.02866i	−0.532564	+	0.00780849i
$645$	206.551	+	206.551i	0.320235	+	0.320235i
$646$	218.678			0.338510
$647$	878.729			1.35816			0.679080	−	0.734065i	$-0.262379\pi$
$647$	878.729			1.35816			0.679080	+	0.734065i	$0.262379\pi$
$648$		−	776.364i		−	1.19809i
$649$	−51.7556	+	51.7556i	−0.0797467	+	0.0797467i
$650$	88.2578	+	88.2578i	0.135781	+	0.135781i
$651$	171.844	+	166.878i	0.263970	+	0.256341i
$652$	−308.055			−0.472477
$653$	−290.301	−	290.301i	−0.444564	−	0.444564i	0.448978	−	0.893543i	$-0.351788\pi$
$653$	−290.301	−	290.301i	−0.444564	−	0.444564i	−0.893543	+	0.448978i	$0.851788\pi$
$654$	525.986			0.804259
$655$	673.507			1.02825
$656$	−378.265	−	100.572i	−0.576624	−	0.153312i
$657$		−	52.4764i		−	0.0798728i
$658$	236.223	−	243.253i	0.359002	−	0.369686i
$659$	346.814	+	346.814i	0.526274	+	0.526274i	0.919459	−	0.393186i	$-0.128627\pi$
$659$	346.814	+	346.814i	0.526274	+	0.526274i	−0.393186	+	0.919459i	$0.628627\pi$
$660$	−116.688			−0.176800
$661$	−476.749			−0.721254			−0.360627	−	0.932710i	$-0.617437\pi$
$661$	−476.749			−0.721254			−0.360627	+	0.932710i	$0.617437\pi$
$662$	560.976	−	560.976i	0.847395	−	0.847395i
$663$	−60.4515	+	60.4515i	−0.0911787	+	0.0911787i
$664$	−402.766			−0.606576
$665$	637.386	+	618.966i	0.958476	+	0.930776i
$666$	21.6124			0.0324510
$667$	1254.89	+	1254.89i	1.88140	+	1.88140i
$668$	−232.240	+	232.240i	−0.347665	+	0.347665i
$669$	150.191	+	150.191i	0.224501	+	0.224501i
$670$	−269.534	−	269.534i	−0.402289	−	0.402289i
$671$	130.667	+	130.667i	0.194735	+	0.194735i
$672$	301.172	+	292.468i	0.448172	+	0.435220i
$673$	620.343	−	620.343i	0.921758	−	0.921758i	−0.0753960	−	0.997154i	$-0.524022\pi$
$673$	620.343	−	620.343i	0.921758	−	0.921758i	0.997154	+	0.0753960i	$0.0240221\pi$
$674$	−136.905			−0.203123
$675$	−341.376	−	341.376i	−0.505742	−	0.505742i
$676$			189.419i			0.280206i
$677$	−1027.38			−1.51754			−0.758772	−	0.651356i	$-0.774201\pi$
$677$	−1027.38			−1.51754			−0.758772	+	0.651356i	$0.774201\pi$
$678$	−212.418	−	212.418i	−0.313301	−	0.313301i
$679$	−332.607	−	322.995i	−0.489849	−	0.475692i
$680$	281.300	−	281.300i	0.413676	−	0.413676i
$681$	−759.600			−1.11542
$682$	57.1805	+	57.1805i	0.0838424	+	0.0838424i
$683$	−624.740	+	624.740i	−0.914699	+	0.914699i	−0.996637	−	0.0819380i	$-0.973889\pi$
$683$	−624.740	+	624.740i	−0.914699	+	0.914699i	0.0819380	+	0.996637i	$0.473889\pi$
$684$	−17.1126	+	17.1126i	−0.0250183	+	0.0250183i
$685$	1277.05	−	1277.05i	1.86431	−	1.86431i
$686$	−25.0859	−	569.986i	−0.0365683	−	0.830883i
$687$	1103.61			1.60642
$688$		−	132.578i		−	0.192701i
$689$	34.7555			0.0504434
$690$	983.034	+	983.034i	1.42469	+	1.42469i
$691$	−559.233	−	559.233i	−0.809309	−	0.809309i	0.175220	−	0.984529i	$-0.443936\pi$
$691$	−559.233	−	559.233i	−0.809309	−	0.809309i	−0.984529	+	0.175220i	$0.943936\pi$
$692$	−262.241			−0.378961
$693$	−22.5314	+	23.2020i	−0.0325129	+	0.0334805i
$694$	724.082	+	724.082i	1.04335	+	1.04335i
$695$			561.549i			0.807985i
$696$		−	1231.08i		−	1.76879i
$697$	−141.515	−	244.021i	−0.203035	−	0.350102i
$698$			746.759i			1.06985i
$699$	879.451			1.25816
$700$	165.052	−	2.42000i	0.235789	−	0.00345715i
$701$	−195.759			−0.279256			−0.139628	−	0.990204i	$-0.544591\pi$
$701$	−195.759			−0.279256			−0.139628	+	0.990204i	$0.544591\pi$
$702$		−	164.791i		−	0.234745i
$703$	170.933	+	170.933i	0.243149	+	0.243149i
$704$	221.684	+	221.684i	0.314892	+	0.314892i
$705$	612.529			0.868836
$706$	−872.305			−1.23556
$707$	−208.364	−	202.342i	−0.294716	−	0.286199i
$708$	44.9253	+	44.9253i	0.0634538	+	0.0634538i
$709$	−390.072	−	390.072i	−0.550173	−	0.550173i	0.376318	−	0.926491i	$-0.377190\pi$
$709$	−390.072	−	390.072i	−0.550173	−	0.550173i	−0.926491	+	0.376318i	$0.877190\pi$
$710$	−152.877	+	152.877i	−0.215320	+	0.215320i
$711$	18.6959	−	18.6959i	0.0262953	−	0.0262953i
$712$	626.039	+	626.039i	0.879268	+	0.879268i
$713$			429.407i			0.602254i
$714$	−3.71896	−	253.645i	−0.00520862	−	0.355245i
$715$	−117.259			−0.163999
$716$	226.670	−	226.670i	0.316578	−	0.316578i
$717$	−1072.65			−1.49603
$718$		−	524.519i		−	0.730528i
$719$	390.459	+	390.459i	0.543059	+	0.543059i	0.924424	−	0.381365i	$-0.124546\pi$
$719$	390.459	+	390.459i	0.543059	+	0.543059i	−0.381365	+	0.924424i	$0.624546\pi$
$720$		−	65.1268i		−	0.0904539i
$721$	−529.166	+	7.75866i	−0.733933	+	0.0107610i
$722$	6.84727			0.00948375
$723$	−39.8848	+	39.8848i	−0.0551657	+	0.0551657i
$724$	289.442	+	289.442i	0.399781	+	0.399781i
$725$	−603.906	−	603.906i	−0.832974	−	0.832974i
$726$	375.283	−	375.283i	0.516919	−	0.516919i
$727$	588.279	−	588.279i	0.809187	−	0.809187i	−0.175324	−	0.984511i	$-0.556097\pi$
$727$	588.279	−	588.279i	0.809187	−	0.809187i	0.984511	+	0.175324i	$0.0560973\pi$
$728$	171.534	+	166.577i	0.235624	+	0.228814i
$729$			627.907i			0.861326i
$730$			564.544i			0.773348i
$731$	67.5633	−	67.5633i	0.0924259	−	0.0924259i
$732$	113.422	−	113.422i	0.154949	−	0.154949i
$733$	−642.566			−0.876624			−0.438312	−	0.898823i	$-0.644424\pi$
$733$	−642.566			−0.876624			−0.438312	+	0.898823i	$0.644424\pi$
$734$			368.260i			0.501716i
$735$	707.101	−	749.833i	0.962042	−	1.02018i
$736$			752.572i			1.02252i
$737$	155.199			0.210583
$738$	−67.6905	−	17.9974i	−0.0917215	−	0.0243867i
$739$	−327.099			−0.442624			−0.221312	−	0.975203i	$-0.571034\pi$
$739$	−327.099			−0.442624			−0.221312	+	0.975203i	$0.571034\pi$
$740$	103.630			0.140040
$741$	−167.890	+	167.890i	−0.226572	+	0.226572i
$742$	−71.8452	+	73.9834i	−0.0968265	+	0.0997081i
$743$			585.868i			0.788516i	0.919000	+	0.394258i	$0.128998\pi$
$743$			585.868i			0.788516i	−0.919000	+	0.394258i	$0.871002\pi$
$744$	210.629	−	210.629i	0.283104	−	0.283104i
$745$	−555.048	+	555.048i	−0.745031	+	0.745031i
$746$			466.835i			0.625784i
$747$	−47.5207			−0.0636154
$748$			38.1688i			0.0510278i
$749$	1369.96	−	20.0864i	1.82905	−	0.0268176i
$750$	145.410	+	145.410i	0.193880	+	0.193880i
$751$	−20.5349	−	20.5349i	−0.0273434	−	0.0273434i	0.693303	−	0.720646i	$-0.256155\pi$
$751$	−20.5349	−	20.5349i	−0.0273434	−	0.0273434i	−0.720646	+	0.693303i	$0.756155\pi$
$752$	−196.581	−	196.581i	−0.261411	−	0.261411i
$753$	−566.112	+	566.112i	−0.751809	+	0.751809i
$754$		−	291.521i		−	0.386633i
$755$	−733.385	−	733.385i	−0.971371	−	0.971371i
$756$	−156.348	−	151.829i	−0.206809	−	0.200833i
$757$	−78.8076	+	78.8076i	−0.104105	+	0.104105i	−0.757241	−	0.653136i	$-0.773453\pi$
$757$	−78.8076	+	78.8076i	−0.104105	+	0.104105i	0.653136	+	0.757241i	$0.273453\pi$
$758$			617.765i			0.814993i
$759$	−566.038			−0.745769
$760$	781.243	−	781.243i	1.02795	−	1.02795i
$761$			26.8137i			0.0352348i	0.999845	+	0.0176174i	$0.00560808\pi$
$761$			26.8137i			0.0352348i	−0.999845	+	0.0176174i	$0.994392\pi$
$762$	398.890	+	398.890i	0.523478	+	0.523478i
$763$	486.989	−	501.482i	0.638255	−	0.657250i
$764$	131.529	−	131.529i	0.172158	−	0.172158i
$765$	33.1893	−	33.1893i	0.0433848	−	0.0433848i
$766$	−536.734	+	536.734i	−0.700697	+	0.700697i
$767$	45.1453	+	45.1453i	0.0588596	+	0.0588596i
$768$	474.585	−	474.585i	0.617949	−	0.617949i
$769$		−	1492.47i		−	1.94079i	−0.241528	−	0.970394i	$-0.577649\pi$
$769$		−	1492.47i		−	1.94079i	0.241528	−	0.970394i	$-0.422351\pi$
$770$	242.394	−	249.608i	0.314798	−	0.324166i
$771$		−	75.9308i		−	0.0984836i
$772$	−236.039	−	236.039i	−0.305750	−	0.305750i
$773$	531.207	+	531.207i	0.687202	+	0.687202i	0.961613	−	0.274411i	$-0.0884829\pi$
$773$	531.207	+	531.207i	0.687202	+	0.687202i	−0.274411	+	0.961613i	$0.588483\pi$
$774$		−	23.7248i		−	0.0306522i
$775$		−	206.649i		−	0.266644i
$776$	−407.676	+	407.676i	−0.525356	+	0.525356i
$777$	195.359	−	201.173i	0.251428	−	0.258910i
$778$	818.362			1.05188
$779$	−393.025	−	677.711i	−0.504526	−	0.869975i
$780$			101.784i			0.130493i
$781$		−	88.0279i		−	0.112712i
$782$	321.552	−	321.552i	0.411192	−	0.411192i
$783$			1127.58i			1.44008i
$784$	−467.578	+	13.7143i	−0.596401	+	0.0174927i
$785$	316.729	−	316.729i	0.403476	−	0.403476i
$786$	−377.636	−	377.636i	−0.480454	−	0.480454i
$787$	−808.732			−1.02761			−0.513807	−	0.857906i	$-0.671765\pi$
$787$	−808.732			−1.02761			−0.513807	+	0.857906i	$0.671765\pi$
$788$			323.529i			0.410570i
$789$		−	76.8018i		−	0.0973407i
$790$	−201.132	+	201.132i	−0.254597	+	0.254597i
$791$	−399.191	+	5.85296i	−0.504667	+	0.00739945i
$792$	28.4386	+	28.4386i	0.0359073	+	0.0359073i
$793$	113.978	−	113.978i	0.143730	−	0.143730i
$794$	652.662	+	652.662i	0.821993	+	0.821993i
$795$	−186.295			−0.234334
$796$	194.132	+	194.132i	0.243884	+	0.243884i
$797$		−	603.159i		−	0.756787i	−0.925645	−	0.378394i	$-0.876477\pi$
$797$		−	603.159i		−	0.756787i	0.925645	−	0.378394i	$-0.123523\pi$
$798$	−10.3285	−	704.439i	−0.0129430	−	0.882756i
$799$		−	200.359i		−	0.250763i
$800$		−	362.169i		−	0.452711i
$801$	73.8637	+	73.8637i	0.0922143	+	0.0922143i
$802$	−1179.22			−1.47034
$803$	−162.534	−	162.534i	−0.202409	−	0.202409i
$804$		−	134.717i		−	0.167559i
$805$	1847.39	−	27.0865i	2.29490	−	0.0336479i
$806$	49.8774	−	49.8774i	0.0618826	−	0.0618826i
$807$	1123.09	+	1123.09i	1.39169	+	1.39169i
$808$	−255.392	+	255.392i	−0.316079	+	0.316079i
$809$	−750.564	−	750.564i	−0.927768	−	0.927768i	0.0697935	−	0.997561i	$-0.477766\pi$
$809$	−750.564	−	750.564i	−0.927768	−	0.927768i	−0.997561	+	0.0697935i	$0.977766\pi$
$810$			985.436i			1.21659i
$811$	−169.224			−0.208661			−0.104330	−	0.994543i	$-0.533270\pi$
$811$	−169.224			−0.208661			−0.104330	+	0.994543i	$0.533270\pi$
$812$	−276.585	−	268.592i	−0.340622	−	0.330778i
$813$	556.342	+	556.342i	0.684308	+	0.684308i
$814$	66.9396	−	66.9396i	0.0822354	−	0.0822354i
$815$	1659.32			2.03597
$816$	−207.984			−0.254882
$817$	187.641	−	187.641i	0.229671	−	0.229671i
$818$	349.634			0.427425
$819$	20.2386	+	19.6537i	0.0247113	+	0.0239972i
$820$	−324.571	−	86.2963i	−0.395818	−	0.105239i
$821$	−258.388			−0.314724			−0.157362	−	0.987541i	$-0.550299\pi$
$821$	−258.388			−0.314724			−0.157362	+	0.987541i	$0.550299\pi$
$822$	−1432.09			−1.74220
$823$	112.888	+	112.888i	0.137167	+	0.137167i	0.772356	−	0.635189i	$-0.219078\pi$
$823$	112.888	+	112.888i	0.137167	+	0.137167i	−0.635189	+	0.772356i	$0.719078\pi$
$824$			658.107i			0.798674i
$825$	272.401			0.330183
$826$	−189.423	+	2.77733i	−0.229326	+	0.00336238i
$827$	81.2789	+	81.2789i	0.0982816	+	0.0982816i	0.754538	−	0.656256i	$-0.227861\pi$
$827$	81.2789	+	81.2789i	0.0982816	+	0.0982816i	−0.656256	+	0.754538i	$0.727861\pi$
$828$			50.3260i			0.0607802i
$829$	99.9547			0.120573			0.0602863	−	0.998181i	$-0.480799\pi$
$829$	99.9547			0.120573			0.0602863	+	0.998181i	$0.480799\pi$
$830$	511.230			0.615940
$831$	201.030	−	201.030i	0.241913	−	0.241913i
$832$	193.370	−	193.370i	0.232416	−	0.232416i
$833$	−245.272	−	231.294i	−0.294444	−	0.277664i
$834$	314.862	−	314.862i	0.377532	−	0.377532i
$835$	1250.95	−	1250.95i	1.49814	−	1.49814i
$836$			106.005i			0.126800i
$837$	−192.922	+	192.922i	−0.230493	+	0.230493i
$838$		−	98.8249i		−	0.117929i
$839$	−116.188	−	116.188i	−0.138484	−	0.138484i	0.634467	−	0.772950i	$-0.281220\pi$
$839$	−116.188	−	116.188i	−0.138484	−	0.138484i	−0.772950	+	0.634467i	$0.781220\pi$
$840$	−919.453	−	892.881i	−1.09459	−	1.06295i
$841$			1153.74i			1.37187i
$842$	−260.673	+	260.673i	−0.309587	+	0.309587i
$843$			1072.00i			1.27165i
$844$	−5.36603	+	5.36603i	−0.00635786	+	0.00635786i
$845$		−	1020.29i		−	1.20745i
$846$	−35.1781	−	35.1781i	−0.0415816	−	0.0415816i
$847$	−10.3406	−	705.260i	−0.0122085	−	0.832656i
$848$	59.7883	+	59.7883i	0.0705051	+	0.0705051i
$849$	1053.67	+	1053.67i	1.24107	+	1.24107i
$850$	−154.744	+	154.744i	−0.182052	+	0.182052i
$851$	502.695			0.590711
$852$	−76.4105			−0.0896837
$853$	−307.409			−0.360386			−0.180193	−	0.983631i	$-0.557672\pi$
$853$	−307.409			−0.360386			−0.180193	+	0.983631i	$0.557672\pi$
$854$	7.01190	+	478.234i	0.00821066	+	0.559993i
$855$	92.1756	−	92.1756i	0.107808	−	0.107808i
$856$		−	1703.77i		−	1.99039i
$857$		−	1460.96i		−	1.70474i	−0.522943	−	0.852368i	$-0.675166\pi$
$857$		−	1460.96i		−	1.70474i	0.522943	−	0.852368i	$-0.324834\pi$
$858$	65.7476	+	65.7476i	0.0766289	+	0.0766289i
$859$	1286.91			1.49815			0.749076	−	0.662485i	$-0.230498\pi$
$859$	1286.91			1.49815			0.749076	+	0.662485i	$0.230498\pi$
$860$		−	113.759i		−	0.132278i
$861$	−779.395	+	467.397i	−0.905221	+	0.542854i
$862$	−391.711			−0.454421
$863$			1236.40i			1.43268i	0.697753	+	0.716339i	$0.254184\pi$
$863$			1236.40i			1.43268i	−0.697753	+	0.716339i	$0.745816\pi$
$864$	−338.112	+	338.112i	−0.391334	+	0.391334i
$865$	1412.54			1.63300
$866$	556.375			0.642465
$867$	541.106	+	541.106i	0.624113	+	0.624113i
$868$	−1.36762	−	93.2763i	−0.00157560	−	0.107461i
$869$		−	115.813i		−	0.133272i
$870$			1562.60i			1.79610i
$871$		−	135.377i		−	0.155427i
$872$	−614.665	−	614.665i	−0.704891	−	0.704891i
$873$	−48.1000	+	48.1000i	−0.0550973	+	0.0550973i
$874$	893.036	−	893.036i	1.02178	−	1.02178i
$875$	273.265	−	4.00663i	0.312303	−	0.00457900i
$876$	−141.084	+	141.084i	−0.161055	+	0.161055i
$877$	739.991			0.843775			0.421887	−	0.906648i	$-0.361368\pi$
$877$	739.991			0.843775			0.421887	+	0.906648i	$0.361368\pi$
$878$	−523.333	−	523.333i	−0.596051	−	0.596051i
$879$	−1194.85			−1.35932
$880$	−201.716	−	201.716i	−0.229223	−	0.229223i
$881$	−1054.54			−1.19698			−0.598489	−	0.801131i	$-0.704232\pi$
$881$	−1054.54			−1.19698			−0.598489	+	0.801131i	$0.704232\pi$
$882$	−83.6730	+	2.45416i	−0.0948673	+	0.00278250i
$883$	375.264	−	375.264i	0.424987	−	0.424987i	−0.461930	−	0.886917i	$-0.652843\pi$
$883$	375.264	−	375.264i	0.424987	−	0.424987i	0.886917	+	0.461930i	$0.152843\pi$
$884$	33.2938			0.0376627
$885$	−241.987	−	241.987i	−0.273431	−	0.273431i
$886$	−640.080			−0.722438
$887$	361.346	+	361.346i	0.407380	+	0.407380i	0.880824	−	0.473444i	$-0.156989\pi$
$887$	361.346	+	361.346i	0.407380	+	0.407380i	−0.473444	+	0.880824i	$0.656989\pi$
$888$	−246.578	−	246.578i	−0.277678	−	0.277678i
$889$	749.623	−	10.9910i	0.843221	−	0.0123634i
$890$	−794.629	−	794.629i	−0.892842	−	0.892842i
$891$	−283.711	−	283.711i	−0.318418	−	0.318418i
$892$		−	82.7184i		−	0.0927336i
$893$		−	556.451i		−	0.623125i
$894$	622.433			0.696234
$895$	−1220.94	+	1220.94i	−1.36418	+	1.36418i
$896$	4.12153	+	281.102i	0.00459992	+	0.313730i
$897$			493.743i			0.550438i
$898$	−451.438			−0.502715
$899$	−341.287	+	341.287i	−0.379629	+	0.379629i
$900$		−	24.2190i		−	0.0269099i
$901$			60.9375i			0.0676332i
$902$	−265.400	+	153.913i	−0.294235	+	0.170636i
$903$	−220.837	−	214.455i	−0.244559	−	0.237491i
$904$			496.462i			0.549183i
$905$	−1559.06	−	1559.06i	−1.72271	−	1.72271i
$906$			822.421i			0.907750i
$907$		−	1291.18i		−	1.42357i	−0.702397	−	0.711786i	$-0.747887\pi$
$907$		−	1291.18i		−	1.42357i	0.702397	−	0.711786i	$-0.252113\pi$
$908$	209.176	+	209.176i	0.230370	+	0.230370i
$909$	−30.1326	+	30.1326i	−0.0331491	+	0.0331491i
$910$	−217.728	−	211.435i	−0.239261	−	0.232347i
$911$			1218.98i			1.33807i	0.743230	+	0.669037i	$0.233293\pi$
$911$			1218.98i			1.33807i	−0.743230	+	0.669037i	$0.766707\pi$
$912$	−577.626			−0.633362
$913$	−147.185	+	147.185i	−0.161210	+	0.161210i
$914$	−583.112	−	583.112i	−0.637978	−	0.637978i
$915$	−610.942	+	610.942i	−0.667696	+	0.667696i
$916$	−303.908	−	303.908i	−0.331778	−	0.331778i
$917$	−709.682	+	10.4054i	−0.773917	+	0.0113472i
$918$	288.931			0.314740
$919$	381.625	−	381.625i	0.415261	−	0.415261i	−0.468306	−	0.883567i	$-0.655135\pi$
$919$	381.625	−	381.625i	0.415261	−	0.415261i	0.883567	+	0.468306i	$0.155135\pi$
$920$		−	2297.54i		−	2.49733i
$921$	−880.593	+	880.593i	−0.956127	+	0.956127i
$922$	625.251			0.678147
$923$	−76.7848			−0.0831905
$924$	122.955	−	1.80278i	0.133069	−	0.00195106i
$925$	−241.918			−0.261533
$926$	−976.163	+	976.163i	−1.05417	+	1.05417i
$927$			77.6473i			0.0837619i
$928$	−598.133	+	598.133i	−0.644540	+	0.644540i
$929$	138.548	+	138.548i	0.149136	+	0.149136i	0.777732	−	0.628596i	$-0.216370\pi$
$929$	138.548	+	138.548i	0.149136	+	0.149136i	−0.628596	+	0.777732i	$0.716370\pi$
$930$	−267.351	+	267.351i	−0.287474	+	0.287474i
$931$	−681.185	−	642.364i	−0.731670	−	0.689973i
$932$	−242.180	−	242.180i	−0.259850	−	0.259850i
$933$	−291.211			−0.312123
$934$	237.962			0.254777
$935$		−	205.594i		−	0.219886i
$936$	24.8064	−	24.8064i	0.0265026	−	0.0265026i
$937$	−136.385	−	136.385i	−0.145555	−	0.145555i	0.630574	−	0.776129i	$-0.282819\pi$
$937$	−136.385	−	136.385i	−0.145555	−	0.145555i	−0.776129	+	0.630574i	$0.782819\pi$
$938$	288.175	+	279.847i	0.307223	+	0.298344i
$939$	9.95162			0.0105981
$940$	−168.676	−	168.676i	−0.179443	−	0.179443i
$941$	631.698			0.671305			0.335652	−	0.941986i	$-0.391043\pi$
$941$	631.698			0.671305			0.335652	+	0.941986i	$0.391043\pi$
$942$	−355.181			−0.377050
$943$	−1574.45	−	418.613i	−1.66962	−	0.443916i
$944$			155.323i			0.164537i
$945$	842.157	+	817.819i	0.891172	+	0.865417i
$946$	−73.4825	−	73.4825i	−0.0776771	−	0.0776771i
$947$	1678.47			1.77240			0.886202	−	0.463299i	$-0.153334\pi$
$947$	1678.47			1.77240			0.886202	+	0.463299i	$0.153334\pi$
$948$	−100.529			−0.106043
$949$	−141.775	+	141.775i	−0.149394	+	0.149394i
$950$	−429.766	+	429.766i	−0.452385	+	0.452385i
$951$	1690.33			1.77743
$952$	−292.063	+	300.755i	−0.306789	+	0.315919i
$953$	−758.655			−0.796071			−0.398035	−	0.917370i	$-0.630308\pi$
$953$	−758.655			−0.796071			−0.398035	+	0.917370i	$0.630308\pi$
$954$	10.6991	+	10.6991i	0.0112150	+	0.0112150i
$955$	−708.470	+	708.470i	−0.741853	+	0.741853i
$956$	295.383	+	295.383i	0.308978	+	0.308978i
$957$	−449.879	−	449.879i	−0.470093	−	0.470093i
$958$	876.782	+	876.782i	0.915221	+	0.915221i
$959$	−1325.91	+	1365.37i	−1.38260	+	1.42375i
$960$	−1036.50	+	1036.50i	−1.07969	+	1.07969i
$961$	844.216			0.878477
$962$	−58.3900	−	58.3900i	−0.0606964	−	0.0606964i
$963$		−	201.021i		−	0.208744i
$964$	21.9667			0.0227870
$965$	1271.41	+	1271.41i	1.31752	+	1.31752i
$966$	−1051.02	−	1020.65i	−1.08802	−	1.05657i
$967$	−33.5592	+	33.5592i	−0.0347045	+	0.0347045i	−0.724246	−	0.689542i	$-0.757812\pi$
$967$	−33.5592	+	33.5592i	−0.0347045	+	0.0347045i	0.689542	+	0.724246i	$0.257812\pi$
$968$	−877.110			−0.906105
$969$	−294.365	−	294.365i	−0.303782	−	0.303782i
$970$	517.462	−	517.462i	0.533466	−	0.533466i
$971$	−1153.07	+	1153.07i	−1.18751	+	1.18751i	−0.209754	+	0.977754i	$0.567266\pi$
$971$	−1153.07	+	1153.07i	−1.18751	+	1.18751i	−0.977754	+	0.209754i	$0.932734\pi$
$972$	−48.1330	+	48.1330i	−0.0495196	+	0.0495196i
$973$	−8.67571	−	591.711i	−0.00891645	−	0.608131i
$974$	−407.481			−0.418359
$975$		−	237.610i		−	0.243702i
$976$	392.143			0.401786
$977$	414.202	+	414.202i	0.423953	+	0.423953i	0.886562	−	0.462609i	$-0.153087\pi$
$977$	414.202	+	414.202i	0.423953	+	0.423953i	−0.462609	+	0.886562i	$0.653087\pi$
$978$	−930.381	−	930.381i	−0.951310	−	0.951310i
$979$	457.553			0.467368
$980$	−401.206	+	11.7675i	−0.409393	+	0.0120077i
$981$	−72.5217	−	72.5217i	−0.0739263	−	0.0739263i
$982$			407.526i			0.414996i
$983$		−	323.740i		−	0.329339i	−0.986349	−	0.164670i	$-0.947344\pi$
$983$		−	323.740i		−	0.329339i	0.986349	−	0.164670i	$-0.0526558\pi$
$984$	566.953	+	977.622i	0.576172	+	0.993519i
$985$		−	1742.67i		−	1.76920i
$986$	511.130			0.518388
$987$	−645.430	+	9.46332i	−0.653931	+	0.00958797i
$988$	92.4657			0.0935888
$989$		−	551.830i		−	0.557968i
$990$	−36.0970	−	36.0970i	−0.0364617	−	0.0364617i
$991$	397.828	+	397.828i	0.401441	+	0.401441i	0.878741	−	0.477299i	$-0.158384\pi$
$991$	397.828	+	397.828i	0.401441	+	0.401441i	−0.477299	+	0.878741i	$0.658384\pi$
$992$	−204.673			−0.206324
$993$	−1510.27			−1.52092
$994$	158.727	−	163.451i	0.159685	−	0.164437i
$995$	−1045.68	−	1045.68i	−1.05093	−	1.05093i
$996$	127.761	+	127.761i	0.128274	+	0.128274i
$997$	−442.253	+	442.253i	−0.443584	+	0.443584i	−0.893215	−	0.449631i	$-0.851556\pi$
$997$	−442.253	+	442.253i	−0.443584	+	0.443584i	0.449631	+	0.893215i	$0.351556\pi$
$998$	663.374	−	663.374i	0.664703	−	0.664703i
$999$	225.849	+	225.849i	0.226075	+	0.226075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.17	✓	108
7.6	odd	2	inner	287.3.g.a.132.18	yes	108
41.32	even	4	inner	287.3.g.a.237.38	yes	108
287.237	odd	4	inner	287.3.g.a.237.37	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.17	✓	108	1.1	even	1	trivial
287.3.g.a.132.18	yes	108	7.6	odd	2	inner
287.3.g.a.237.37	yes	108	287.237	odd	4	inner
287.3.g.a.237.38	yes	108	41.32	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.66337i q^{2} +(-2.23909 + 2.23909i) q^{3} +1.23319 q^{4} -6.64247 q^{5} +(3.72444 + 3.72444i) q^{6} +(6.99925 - 0.102623i) q^{7} -8.70475i q^{8} -1.02704i q^{9} +O(q^{10})\)	\(q-1.66337i q^{2} +(-2.23909 + 2.23909i) q^{3} +1.23319 q^{4} -6.64247 q^{5} +(3.72444 + 3.72444i) q^{6} +(6.99925 - 0.102623i) q^{7} -8.70475i q^{8} -1.02704i q^{9} +11.0489i q^{10} +(-3.18102 - 3.18102i) q^{11} +(-2.76121 + 2.76121i) q^{12} +(-2.77474 + 2.77474i) q^{13} +(-0.170701 - 11.6424i) q^{14} +(14.8731 - 14.8731i) q^{15} -9.54651 q^{16} +(-4.86501 - 4.86501i) q^{17} -1.70835 q^{18} +(-13.5114 - 13.5114i) q^{19} -8.19139 q^{20} +(-15.4422 + 15.9017i) q^{21} +(-5.29123 + 5.29123i) q^{22} -39.7354 q^{23} +(19.4907 + 19.4907i) q^{24} +19.1224 q^{25} +(4.61543 + 4.61543i) q^{26} +(-17.8522 - 17.8522i) q^{27} +(8.63137 - 0.126554i) q^{28} +(-31.5812 - 31.5812i) q^{29} +(-24.7395 - 24.7395i) q^{30} -10.8067i q^{31} -18.9396i q^{32} +14.2452 q^{33} +(-8.09233 + 8.09233i) q^{34} +(-46.4923 + 0.681672i) q^{35} -1.26653i q^{36} -12.6510 q^{37} +(-22.4745 + 22.4745i) q^{38} -12.4258i q^{39} +57.8210i q^{40} +(39.6234 + 10.5350i) q^{41} +(26.4505 + 25.6861i) q^{42} +13.8876i q^{43} +(-3.92279 - 3.92279i) q^{44} +6.82205i q^{45} +66.0949i q^{46} +(20.5919 + 20.5919i) q^{47} +(21.3755 - 21.3755i) q^{48} +(48.9789 - 1.43657i) q^{49} -31.8076i q^{50} +21.7864 q^{51} +(-3.42176 + 3.42176i) q^{52} +(-6.26284 - 6.26284i) q^{53} +(-29.6948 + 29.6948i) q^{54} +(21.1298 + 21.1298i) q^{55} +(-0.893310 - 60.9267i) q^{56} +60.5065 q^{57} +(-52.5313 + 52.5313i) q^{58} -16.2701i q^{59} +(18.3413 - 18.3413i) q^{60} -41.0771 q^{61} -17.9755 q^{62} +(-0.105398 - 7.18848i) q^{63} -69.6896 q^{64} +(18.4311 - 18.4311i) q^{65} -23.6951i q^{66} +(-24.3946 + 24.3946i) q^{67} +(-5.99946 - 5.99946i) q^{68} +(88.9712 - 88.9712i) q^{69} +(1.13388 + 77.3340i) q^{70} +(13.8364 + 13.8364i) q^{71} -8.94009 q^{72} +51.0950 q^{73} +21.0434i q^{74} +(-42.8166 + 42.8166i) q^{75} +(-16.6621 - 16.6621i) q^{76} +(-22.5912 - 21.9383i) q^{77} -20.6687 q^{78} +(18.2038 + 18.2038i) q^{79} +63.4124 q^{80} +89.1885 q^{81} +(17.5236 - 65.9086i) q^{82} -46.2697i q^{83} +(-19.0430 + 19.6098i) q^{84} +(32.3157 + 32.3157i) q^{85} +23.1003 q^{86} +141.426 q^{87} +(-27.6900 + 27.6900i) q^{88} +(-71.9192 + 71.9192i) q^{89} +11.3476 q^{90} +(-19.1363 + 19.7058i) q^{91} -49.0012 q^{92} +(24.1971 + 24.1971i) q^{93} +(34.2520 - 34.2520i) q^{94} +(89.7491 + 89.7491i) q^{95} +(42.4074 + 42.4074i) q^{96} +(-46.8338 - 46.8338i) q^{97} +(-2.38956 - 81.4703i) q^{98} +(-3.26702 + 3.26702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \) 108 * q - 216 * q^4 - 2 * q^7	\( 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) \) 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more