LMFDB - Embedded newform 483.2.d.d.461.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(461,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("483.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.d (of order $2$, degree $1$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.10
Character	$\chi$	$=$	483.461
Dual form			483.2.d.d.461.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16117i q^{2} +(1.71298 - 0.256312i) q^{3} -2.67065 q^{4} -0.517542 q^{5} +(-0.553932 - 3.70204i) q^{6} +(1.45986 + 2.20654i) q^{7} +1.44938i q^{8} +(2.86861 - 0.878114i) q^{9} +O(q^{10})$	\(q-2.16117i q^{2} +(1.71298 - 0.256312i) q^{3} -2.67065 q^{4} -0.517542 q^{5} +(-0.553932 - 3.70204i) q^{6} +(1.45986 + 2.20654i) q^{7} +1.44938i q^{8} +(2.86861 - 0.878114i) q^{9} +1.11850i q^{10} -4.77836i q^{11} +(-4.57477 + 0.684518i) q^{12} -1.14450i q^{13} +(4.76870 - 3.15501i) q^{14} +(-0.886540 + 0.132652i) q^{15} -2.20894 q^{16} +1.79484 q^{17} +(-1.89775 - 6.19955i) q^{18} -3.65708i q^{19} +1.38217 q^{20} +(3.06628 + 3.40558i) q^{21} -10.3268 q^{22} -1.00000i q^{23} +(0.371493 + 2.48276i) q^{24} -4.73215 q^{25} -2.47346 q^{26} +(4.68880 - 2.23945i) q^{27} +(-3.89878 - 5.89288i) q^{28} +2.33033i q^{29} +(0.286683 + 1.91596i) q^{30} +10.1644i q^{31} +7.67265i q^{32} +(-1.22475 - 8.18523i) q^{33} -3.87896i q^{34} +(-0.755540 - 1.14198i) q^{35} +(-7.66104 + 2.34513i) q^{36} -2.59233 q^{37} -7.90357 q^{38} +(-0.293349 - 1.96051i) q^{39} -0.750116i q^{40} +9.39090 q^{41} +(7.36002 - 6.62674i) q^{42} +10.0548 q^{43} +12.7613i q^{44} +(-1.48463 + 0.454461i) q^{45} -2.16117 q^{46} -2.16757 q^{47} +(-3.78387 + 0.566176i) q^{48} +(-2.73761 + 6.44248i) q^{49} +10.2270i q^{50} +(3.07453 - 0.460039i) q^{51} +3.05657i q^{52} +0.121842i q^{53} +(-4.83983 - 10.1333i) q^{54} +2.47300i q^{55} +(-3.19811 + 2.11590i) q^{56} +(-0.937352 - 6.26451i) q^{57} +5.03623 q^{58} -1.52547 q^{59} +(2.36764 - 0.354267i) q^{60} +9.95652i q^{61} +21.9669 q^{62} +(6.12536 + 5.04777i) q^{63} +12.1640 q^{64} +0.592329i q^{65} +(-17.6897 + 2.64689i) q^{66} +4.00092 q^{67} -4.79339 q^{68} +(-0.256312 - 1.71298i) q^{69} +(-2.46800 + 1.63285i) q^{70} +8.01899i q^{71} +(1.27272 + 4.15771i) q^{72} +3.71123i q^{73} +5.60246i q^{74} +(-8.10608 + 1.21290i) q^{75} +9.76677i q^{76} +(10.5436 - 6.97574i) q^{77} +(-4.23700 + 0.633978i) q^{78} -14.9783 q^{79} +1.14322 q^{80} +(7.45783 - 5.03793i) q^{81} -20.2953i q^{82} -15.5515 q^{83} +(-8.18894 - 9.09509i) q^{84} -0.928907 q^{85} -21.7302i q^{86} +(0.597290 + 3.99181i) q^{87} +6.92566 q^{88} -9.95125 q^{89} +(0.982166 + 3.20853i) q^{90} +(2.52539 - 1.67082i) q^{91} +2.67065i q^{92} +(2.60524 + 17.4113i) q^{93} +4.68449i q^{94} +1.89269i q^{95} +(1.96659 + 13.1431i) q^{96} -3.44422i q^{97} +(13.9233 + 5.91643i) q^{98} +(-4.19594 - 13.7072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.16117i		−	1.52818i	−0.645112	−	0.764088i	$-0.723189\pi$
$2$		−	2.16117i		−	1.52818i	0.645112	−	0.764088i	$-0.276811\pi$
$3$	1.71298	−	0.256312i	0.988990	−	0.147982i
$3$	1.71298	−	0.256312i	0.988990	−	0.147982i
$4$	−2.67065			−1.33532
$5$	−0.517542			−0.231452			−0.115726	−	0.993281i	$-0.536919\pi$
$5$	−0.517542			−0.231452			−0.115726	+	0.993281i	$0.536919\pi$
$6$	−0.553932	−	3.70204i	−0.226142	−	1.51135i
$7$	1.45986	+	2.20654i	0.551776	+	0.833992i
$7$	1.45986	+	2.20654i	0.551776	+	0.833992i
$8$			1.44938i			0.512434i
$9$	2.86861	−	0.878114i	0.956203	−	0.292705i
$10$			1.11850i			0.353699i
$11$		−	4.77836i		−	1.44073i	−0.693596	−	0.720364i	$-0.743975\pi$
$11$		−	4.77836i		−	1.44073i	0.693596	−	0.720364i	$-0.256025\pi$
$12$	−4.57477	+	0.684518i	−1.32062	+	0.197603i
$13$		−	1.14450i		−	0.317428i	−0.987325	−	0.158714i	$-0.949265\pi$
$13$		−	1.14450i		−	0.317428i	0.987325	−	0.158714i	$-0.0507348\pi$
$14$	4.76870	−	3.15501i	1.27449	−	0.843211i
$15$	−0.886540	+	0.132652i	−0.228904	+	0.0342506i
$16$	−2.20894			−0.552234
$17$	1.79484			0.435313			0.217657	−	0.976025i	$-0.430159\pi$
$17$	1.79484			0.435313			0.217657	+	0.976025i	$0.430159\pi$
$18$	−1.89775	−	6.19955i	−0.447304	−	1.46125i
$19$		−	3.65708i		−	0.838992i	−0.907757	−	0.419496i	$-0.862207\pi$
$19$		−	3.65708i		−	0.838992i	0.907757	−	0.419496i	$-0.137793\pi$
$20$	1.38217			0.309063
$21$	3.06628	+	3.40558i	0.669116	+	0.743158i
$22$	−10.3268			−2.20169
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	0.371493	+	2.48276i	0.0758307	+	0.506792i
$25$	−4.73215			−0.946430
$26$	−2.47346			−0.485086
$27$	4.68880	−	2.23945i	0.902360	−	0.430982i
$28$	−3.89878	−	5.89288i	−0.736799	−	1.11365i
$29$			2.33033i			0.432731i	0.976312	+	0.216366i	$0.0694203\pi$
$29$			2.33033i			0.432731i	−0.976312	+	0.216366i	$0.930580\pi$
$30$	0.286683	+	1.91596i	0.0523410	+	0.349805i
$31$			10.1644i			1.82557i	0.408438	+	0.912786i	$0.366074\pi$
$31$			10.1644i			1.82557i	−0.408438	+	0.912786i	$0.633926\pi$
$32$			7.67265i			1.35635i
$33$	−1.22475	−	8.18523i	−0.213201	−	1.42487i
$34$		−	3.87896i		−	0.665236i
$35$	−0.755540	−	1.14198i	−0.127710	−	0.193029i
$36$	−7.66104	+	2.34513i	−1.27684	+	0.390855i
$37$	−2.59233			−0.426176			−0.213088	−	0.977033i	$-0.568352\pi$
$37$	−2.59233			−0.426176			−0.213088	+	0.977033i	$0.568352\pi$
$38$	−7.90357			−1.28213
$39$	−0.293349	−	1.96051i	−0.0469735	−	0.313933i
$40$		−	0.750116i		−	0.118604i
$41$	9.39090			1.46661			0.733306	−	0.679899i	$-0.237976\pi$
$41$	9.39090			1.46661			0.733306	+	0.679899i	$0.237976\pi$
$42$	7.36002	−	6.62674i	1.13568	−	1.02253i
$43$	10.0548			1.53335			0.766674	−	0.642036i	$-0.221910\pi$
$43$	10.0548			1.53335			0.766674	+	0.642036i	$0.221910\pi$
$44$			12.7613i			1.92384i
$45$	−1.48463	+	0.454461i	−0.221315	+	0.0677470i
$46$	−2.16117			−0.318647
$47$	−2.16757			−0.316173			−0.158086	−	0.987425i	$-0.550532\pi$
$47$	−2.16757			−0.316173			−0.158086	+	0.987425i	$0.550532\pi$
$48$	−3.78387	+	0.566176i	−0.546154	+	0.0817205i
$49$	−2.73761	+	6.44248i	−0.391087	+	0.920354i
$50$			10.2270i			1.44631i
$51$	3.07453	−	0.460039i	0.430521	−	0.0644184i
$52$			3.05657i			0.423869i
$53$			0.121842i			0.0167363i	0.999965	+	0.00836815i	$0.00266369\pi$
$53$			0.121842i			0.0167363i	−0.999965	+	0.00836815i	$0.997336\pi$
$54$	−4.83983	−	10.1333i	−0.658617	−	1.37897i
$55$			2.47300i			0.333459i
$56$	−3.19811	+	2.11590i	−0.427366	+	0.282749i
$57$	−0.937352	−	6.26451i	−0.124155	−	0.829755i
$58$	5.03623			0.661290
$59$	−1.52547			−0.198599			−0.0992994	−	0.995058i	$-0.531660\pi$
$59$	−1.52547			−0.198599			−0.0992994	+	0.995058i	$0.531660\pi$
$60$	2.36764	−	0.354267i	0.305660	−	0.0457357i
$61$			9.95652i			1.27480i	0.770532	+	0.637401i	$0.219990\pi$
$61$			9.95652i			1.27480i	−0.770532	+	0.637401i	$0.780010\pi$
$62$	21.9669			2.78980
$63$	6.12536	+	5.04777i	0.771723	+	0.635959i
$64$	12.1640			1.52050
$65$			0.592329i			0.0734694i
$66$	−17.6897	+	2.64689i	−2.17745	+	0.325809i
$67$	4.00092			0.488790			0.244395	−	0.969676i	$-0.421411\pi$
$67$	4.00092			0.488790			0.244395	+	0.969676i	$0.421411\pi$
$68$	−4.79339			−0.581284
$69$	−0.256312	−	1.71298i	−0.0308563	−	0.206219i
$70$	−2.46800	+	1.63285i	−0.294983	+	0.195163i
$71$			8.01899i			0.951678i	0.879532	+	0.475839i	$0.157856\pi$
$71$			8.01899i			0.951678i	−0.879532	+	0.475839i	$0.842144\pi$
$72$	1.27272	+	4.15771i	0.149992	+	0.489991i
$73$			3.71123i			0.434367i	0.976131	+	0.217183i	$0.0696870\pi$
$73$			3.71123i			0.434367i	−0.976131	+	0.217183i	$0.930313\pi$
$74$			5.60246i			0.651273i
$75$	−8.10608	+	1.21290i	−0.936010	+	0.140054i
$76$			9.76677i			1.12033i
$77$	10.5436	−	6.97574i	1.20156	−	0.794959i
$78$	−4.23700	+	0.633978i	−0.479746	+	0.0717838i
$79$	−14.9783			−1.68519			−0.842597	−	0.538545i	$-0.818974\pi$
$79$	−14.9783			−1.68519			−0.842597	+	0.538545i	$0.818974\pi$
$80$	1.14322			0.127816
$81$	7.45783	−	5.03793i	0.828648	−	0.559770i
$82$		−	20.2953i		−	2.24124i
$83$	−15.5515			−1.70700			−0.853498	−	0.521095i	$-0.825524\pi$
$83$	−15.5515			−1.70700			−0.853498	+	0.521095i	$0.825524\pi$
$84$	−8.18894	−	9.09509i	−0.893487	−	0.992356i
$85$	−0.928907			−0.100754
$86$		−	21.7302i		−	2.34323i
$87$	0.597290	+	3.99181i	0.0640362	+	0.427967i
$88$	6.92566			0.738278
$89$	−9.95125			−1.05483			−0.527415	−	0.849608i	$-0.676839\pi$
$89$	−9.95125			−1.05483			−0.527415	+	0.849608i	$0.676839\pi$
$90$	0.982166	+	3.20853i	0.103529	+	0.338208i
$91$	2.52539	−	1.67082i	0.264733	−	0.175149i
$92$			2.67065i			0.278434i
$93$	2.60524	+	17.4113i	0.270151	+	1.80547i
$94$			4.68449i			0.483168i
$95$			1.89269i			0.194186i
$96$	1.96659	+	13.1431i	0.200714	+	1.34141i
$97$		−	3.44422i		−	0.349707i	−0.984594	−	0.174854i	$-0.944055\pi$
$97$		−	3.44422i		−	0.349707i	0.984594	−	0.174854i	$-0.0559453\pi$
$98$	13.9233	+	5.91643i	1.40646	+	0.597650i
$99$	−4.19594	−	13.7072i	−0.421708	−	1.37763i
$100$	12.6379			1.26379
$101$	1.09394			0.108851			0.0544257	−	0.998518i	$-0.482667\pi$
$101$	1.09394			0.108851			0.0544257	+	0.998518i	$0.482667\pi$
$102$	−0.994222	−	6.64458i	−0.0984426	−	0.657912i
$103$		−	3.97467i		−	0.391636i	−0.980640	−	0.195818i	$-0.937264\pi$
$103$		−	3.97467i		−	0.391636i	0.980640	−	0.195818i	$-0.0627362\pi$
$104$	1.65882			0.162661
$105$	−1.58693	−	1.76253i	−0.154868	−	0.172005i
$106$	0.263321			0.0255760
$107$		−	6.22278i		−	0.601579i	−0.953691	−	0.300789i	$-0.902750\pi$
$107$		−	6.22278i		−	0.601579i	0.953691	−	0.300789i	$-0.0972501\pi$
$108$	−12.5221	+	5.98078i	−1.20494	+	0.575501i
$109$	13.2007			1.26440			0.632201	−	0.774804i	$-0.282152\pi$
$109$	13.2007			1.26440			0.632201	+	0.774804i	$0.282152\pi$
$110$	5.34457			0.509585
$111$	−4.44061	+	0.664444i	−0.421484	+	0.0630662i
$112$	−3.22474	−	4.87410i	−0.304710	−	0.460559i
$113$			9.09363i			0.855457i	0.903907	+	0.427728i	$0.140686\pi$
$113$			9.09363i			0.855457i	−0.903907	+	0.427728i	$0.859314\pi$
$114$	−13.5387	+	2.02578i	−1.26801	+	0.189731i
$115$			0.517542i			0.0482611i
$116$		−	6.22349i		−	0.577836i
$117$	−1.00500	−	3.28313i	−0.0929127	−	0.303526i
$118$			3.29679i			0.303494i
$119$	2.62022	+	3.96039i	0.240195	+	0.363048i
$120$	−0.192263	−	1.28494i	−0.0175512	−	0.117298i
$121$	−11.8327			−1.07570
$122$	21.5177			1.94812
$123$	16.0864	−	2.40700i	1.45046	−	0.217031i
$124$		−	27.1454i		−	2.43773i
$125$	5.03680			0.450505
$126$	10.9091	−	13.2379i	0.971857	−	1.17933i
$127$	16.5926			1.47236			0.736180	−	0.676786i	$-0.236628\pi$
$127$	16.5926			1.47236			0.736180	+	0.676786i	$0.236628\pi$
$128$		−	10.9432i		−	0.967249i
$129$	17.2238	−	2.57717i	1.51647	−	0.226907i
$130$	1.28012			0.112274
$131$	9.73168			0.850261			0.425130	−	0.905132i	$-0.360228\pi$
$131$	9.73168			0.850261			0.425130	+	0.905132i	$0.360228\pi$
$132$	3.27087	+	21.8599i	0.284693	+	1.90266i
$133$	8.06948	−	5.33883i	0.699713	−	0.462935i
$134$		−	8.64666i		−	0.746957i
$135$	−2.42665	+	1.15901i	−0.208853	+	0.0997517i
$136$			2.60141i			0.223069i
$137$		−	2.79623i		−	0.238898i	−0.992840	−	0.119449i	$-0.961887\pi$
$137$		−	2.79623i		−	0.238898i	0.992840	−	0.119449i	$-0.0381128\pi$
$138$	−3.70204	+	0.553932i	−0.315139	+	0.0471538i
$139$			19.3067i			1.63757i	0.574100	+	0.818785i	$0.305352\pi$
$139$			19.3067i			1.63757i	−0.574100	+	0.818785i	$0.694648\pi$
$140$	2.01778	+	3.04982i	0.170534	+	0.257756i
$141$	−3.71301	+	0.555574i	−0.312692	+	0.0467878i
$142$	17.3304			1.45433
$143$	−5.46885			−0.457328
$144$	−6.33658	+	1.93970i	−0.528048	+	0.161641i
$145$		−	1.20604i		−	0.100156i
$146$	8.02060			0.663789
$147$	−3.03819	+	11.7375i	−0.250586	+	0.968094i
$148$	6.92320			0.569083
$149$		−	19.0855i		−	1.56355i	−0.623563	−	0.781773i	$-0.714315\pi$
$149$		−	19.0855i		−	1.56355i	0.623563	−	0.781773i	$-0.285685\pi$
$150$	2.62129	+	17.5186i	0.214027	+	1.43039i
$151$	−3.51180			−0.285786			−0.142893	−	0.989738i	$-0.545640\pi$
$151$	−3.51180			−0.285786			−0.142893	+	0.989738i	$0.545640\pi$
$152$	5.30051			0.429928
$153$	5.14870	−	1.57608i	0.416248	−	0.127418i
$154$	−15.0757	−	22.7865i	−1.21484	−	1.83619i
$155$		−	5.26048i		−	0.422532i
$156$	0.783433	+	5.23584i	0.0627248	+	0.419203i
$157$			2.00307i			0.159862i	0.996800	+	0.0799312i	$0.0254701\pi$
$157$			2.00307i			0.159862i	−0.996800	+	0.0799312i	$0.974530\pi$
$158$			32.3707i			2.57527i
$159$	0.0312295	+	0.208713i	0.00247666	+	0.0165520i
$160$		−	3.97092i		−	0.313929i
$161$	2.20654	−	1.45986i	0.173899	−	0.115053i
$162$	−10.8878	−	16.1176i	−0.855427	−	1.26632i
$163$	18.5855			1.45573			0.727866	−	0.685719i	$-0.240512\pi$
$163$	18.5855			1.45573			0.727866	+	0.685719i	$0.240512\pi$
$164$	−25.0798			−1.95840
$165$	0.633859	+	4.23620i	0.0493458	+	0.329788i
$166$			33.6094i			2.60859i
$167$	−18.1559			−1.40495			−0.702473	−	0.711711i	$-0.747921\pi$
$167$	−18.1559			−1.40495			−0.702473	+	0.711711i	$0.747921\pi$
$168$	−4.93598	+	4.44420i	−0.380819	+	0.342878i
$169$	11.6901			0.899239
$170$			2.00752i			0.153970i
$171$	−3.21133	−	10.4907i	−0.245577	−	0.802246i
$172$	−26.8529			−2.04752
$173$	−21.1070			−1.60473			−0.802367	−	0.596831i	$-0.796426\pi$
$173$	−21.1070			−1.60473			−0.802367	+	0.596831i	$0.796426\pi$
$174$	8.62697	−	1.29084i	0.654009	−	0.0978587i
$175$	−6.90828	−	10.4417i	−0.522217	−	0.789316i
$176$			10.5551i			0.795620i
$177$	−2.61309	+	0.390995i	−0.196412	+	0.0293889i
$178$			21.5063i			1.61197i
$179$		−	7.68889i		−	0.574694i	−0.957827	−	0.287347i	$-0.907227\pi$
$179$		−	7.68889i		−	0.574694i	0.957827	−	0.287347i	$-0.0927733\pi$
$180$	3.96491	−	1.21370i	0.295527	−	0.0904642i
$181$			7.90034i			0.587228i	0.955924	+	0.293614i	$0.0948580\pi$
$181$			7.90034i			0.587228i	−0.955924	+	0.293614i	$0.905142\pi$
$182$	−3.61092	−	5.45779i	−0.267659	−	0.404558i
$183$	2.55197	+	17.0553i	0.188647	+	1.26077i
$184$	1.44938			0.106850
$185$	1.34164			0.0986393
$186$	37.6288	−	5.63036i	2.75908	−	0.412838i
$187$		−	8.57640i		−	0.627169i
$188$	5.78882			0.422193
$189$	11.7864	+	7.07673i	0.857337	+	0.514756i
$190$	4.09043			0.296751
$191$			1.83575i			0.132830i	0.997792	+	0.0664150i	$0.0211561\pi$
$191$			1.83575i			0.132830i	−0.997792	+	0.0664150i	$0.978844\pi$
$192$	20.8367	−	3.11778i	1.50376	−	0.225006i
$193$	−21.9972			−1.58339			−0.791696	−	0.610916i	$-0.790801\pi$
$193$	−21.9972			−1.58339			−0.791696	+	0.610916i	$0.790801\pi$
$194$	−7.44354			−0.534415
$195$	0.151821	+	1.01465i	0.0108721	+	0.0726605i
$196$	7.31119	−	17.2056i	0.522228	−	1.22897i
$197$			7.02679i			0.500638i	0.968163	+	0.250319i	$0.0805355\pi$
$197$			7.02679i			0.500638i	−0.968163	+	0.250319i	$0.919465\pi$
$198$	−29.6236	+	9.06813i	−2.10526	+	0.644444i
$199$		−	10.0977i		−	0.715807i	−0.933758	−	0.357904i	$-0.883492\pi$
$199$		−	10.0977i		−	0.715807i	0.933758	−	0.357904i	$-0.116508\pi$
$200$		−	6.85869i		−	0.484983i
$201$	6.85350	−	1.02548i	0.483408	−	0.0723319i
$202$		−	2.36419i		−	0.166344i
$203$	−5.14196	+	3.40196i	−0.360895	+	0.238771i
$204$	−8.21099	+	1.22860i	−0.574885	+	0.0860194i
$205$	−4.86019			−0.339450
$206$	−8.58993			−0.598489
$207$	−0.878114	−	2.86861i	−0.0610331	−	0.199382i
$208$			2.52814i			0.175295i
$209$	−17.4748			−1.20876
$210$	−3.80912	+	3.42962i	−0.262854	+	0.236666i
$211$	6.86867			0.472859			0.236429	−	0.971649i	$-0.424023\pi$
$211$	6.86867			0.472859			0.236429	+	0.971649i	$0.424023\pi$
$212$		−	0.325397i		−	0.0223484i
$213$	2.05536	+	13.7364i	0.140831	+	0.941201i
$214$	−13.4485			−0.919319
$215$	−5.20381			−0.354897
$216$	3.24582	+	6.79586i	0.220850	+	0.462400i
$217$	−22.4280	+	14.8386i	−1.52251	+	1.00731i
$218$		−	28.5290i		−	1.93223i
$219$	0.951232	+	6.35727i	0.0642783	+	0.429585i
$220$		−	6.60451i		−	0.445276i
$221$		−	2.05420i		−	0.138181i
$222$	1.43597	+	9.59691i	0.0963763	+	0.644102i
$223$		−	0.933115i		−	0.0624860i	−0.999512	−	0.0312430i	$-0.990053\pi$
$223$		−	0.933115i		−	0.0624860i	0.999512	−	0.0312430i	$-0.00994657\pi$
$224$	−16.9300	+	11.2010i	−1.13118	+	0.748399i
$225$	−13.5747	+	4.15537i	−0.904979	+	0.277024i
$226$	19.6529			1.30729
$227$	13.7544			0.912912			0.456456	−	0.889746i	$-0.349119\pi$
$227$	13.7544			0.912912			0.456456	+	0.889746i	$0.349119\pi$
$228$	2.50334	+	16.7303i	0.165788	+	1.10799i
$229$		−	16.0238i		−	1.05888i	−0.848347	−	0.529441i	$-0.822402\pi$
$229$		−	16.0238i		−	1.05888i	0.848347	−	0.529441i	$-0.177598\pi$
$230$	1.11850			0.0737514
$231$	16.2731	−	14.6518i	1.07069	−	0.964015i
$232$	−3.37754			−0.221746
$233$			15.7412i			1.03124i	0.856817	+	0.515621i	$0.172439\pi$
$233$			15.7412i			1.03124i	−0.856817	+	0.515621i	$0.827561\pi$
$234$	−7.09540	+	2.17198i	−0.463841	+	0.141987i
$235$	1.12181			0.0731788
$236$	4.07398			0.265194
$237$	−25.6576	+	3.83912i	−1.66664	+	0.249377i
$238$	8.55906	−	5.66274i	0.554802	−	0.367061i
$239$		−	3.84950i		−	0.249003i	−0.992219	−	0.124502i	$-0.960267\pi$
$239$		−	3.84950i		−	0.249003i	0.992219	−	0.124502i	$-0.0397332\pi$
$240$	1.95831	−	0.293020i	0.126408	−	0.0189144i
$241$		−	19.2949i		−	1.24289i	−0.783457	−	0.621446i	$-0.786546\pi$
$241$		−	19.2949i		−	1.24289i	0.783457	−	0.621446i	$-0.213454\pi$
$242$			25.5724i			1.64386i
$243$	11.4838	−	10.5414i	0.736689	−	0.676232i
$244$		−	26.5904i		−	1.70227i
$245$	1.41683	−	3.33425i	0.0905178	−	0.213018i
$246$	−5.20192	−	34.7655i	−0.331662	−	2.21657i
$247$	−4.18554			−0.266320
$248$	−14.7320			−0.935485
$249$	−26.6394	+	3.98602i	−1.68820	+	0.252604i
$250$		−	10.8854i		−	0.688451i
$251$	−18.9174			−1.19406			−0.597028	−	0.802220i	$-0.703652\pi$
$251$	−18.9174			−1.19406			−0.597028	+	0.802220i	$0.703652\pi$
$252$	−16.3587	−	13.4808i	−1.03050	−	0.849211i
$253$	−4.77836			−0.300413
$254$		−	35.8595i		−	2.25003i
$255$	−1.59120	+	0.238090i	−0.0996449	+	0.0149098i
$256$	0.677988			0.0423742
$257$	−17.0925			−1.06620			−0.533101	−	0.846051i	$-0.678973\pi$
$257$	−17.0925			−1.06620			−0.533101	+	0.846051i	$0.678973\pi$
$258$	−5.56970	−	37.2234i	−0.346754	−	2.31743i
$259$	−3.78444	−	5.72007i	−0.235154	−	0.355428i
$260$		−	1.58190i		−	0.0981054i
$261$	2.04629	+	6.68480i	0.126662	+	0.413779i
$262$		−	21.0318i		−	1.29935i
$263$			17.3180i			1.06787i	0.845525	+	0.533936i	$0.179288\pi$
$263$			17.3180i			1.06787i	−0.845525	+	0.533936i	$0.820712\pi$
$264$	11.8635	−	1.77513i	0.730150	−	0.109252i
$265$		−	0.0630584i		−	0.00387365i
$266$	−11.5381	−	17.4395i	−0.707447	−	1.06928i
$267$	−17.0463	+	2.55062i	−1.04322	+	0.156095i
$268$	−10.6850			−0.652693
$269$	7.85603			0.478991			0.239495	−	0.970898i	$-0.423018\pi$
$269$	7.85603			0.478991			0.239495	+	0.970898i	$0.423018\pi$
$270$	2.50481	+	5.24441i	0.152438	+	0.319164i
$271$			5.21797i			0.316969i	0.987361	+	0.158485i	$0.0506608\pi$
$271$			5.21797i			0.316969i	−0.987361	+	0.158485i	$0.949339\pi$
$272$	−3.96470			−0.240395
$273$	3.89769	−	3.50936i	0.235899	−	0.212396i
$274$	−6.04312			−0.365078
$275$			22.6119i			1.36355i
$276$	0.684518	+	4.57477i	0.0412031	+	0.275369i
$277$	−14.9590			−0.898799			−0.449400	−	0.893331i	$-0.648362\pi$
$277$	−14.9590			−0.898799			−0.449400	+	0.893331i	$0.648362\pi$
$278$	41.7250			2.50250
$279$	8.92546	+	29.1576i	0.534353	+	1.74562i
$280$	1.65516	−	1.09507i	0.0989147	−	0.0654427i
$281$		−	21.4450i		−	1.27930i	−0.768667	−	0.639649i	$-0.779080\pi$
$281$		−	21.4450i		−	1.27930i	0.768667	−	0.639649i	$-0.220920\pi$
$282$	1.20069	+	8.02444i	0.0714999	+	0.477848i
$283$			13.8274i			0.821954i	0.911646	+	0.410977i	$0.134812\pi$
$283$			13.8274i			0.821954i	−0.911646	+	0.410977i	$0.865188\pi$
$284$		−	21.4159i		−	1.27080i
$285$	0.485119	+	3.24215i	0.0287360	+	0.192048i
$286$			11.8191i			0.698878i
$287$	13.7094	+	20.7214i	0.809241	+	1.22314i
$288$	6.73746	+	22.0098i	0.397008	+	1.29694i
$289$	−13.7785			−0.810502
$290$	−2.60646			−0.153057
$291$	−0.882793	−	5.89988i	−0.0517502	−	0.345857i
$292$		−	9.91140i		−	0.580021i
$293$	−0.0554835			−0.00324138			−0.00162069	−	0.999999i	$-0.500516\pi$
$293$	−0.0554835			−0.00324138			−0.00162069	+	0.999999i	$0.500516\pi$
$294$	25.3668	+	6.56604i	1.47942	+	0.382939i
$295$	0.789493			0.0459661
$296$		−	3.75727i		−	0.218387i
$297$	−10.7009	−	22.4048i	−0.620929	−	1.30006i
$298$	−41.2470			−2.38937
$299$	−1.14450			−0.0661884
$300$	21.6485	−	3.23924i	1.24988	−	0.187018i
$301$	14.6787	+	22.1864i	0.846065	+	1.27880i
$302$			7.58958i			0.436731i
$303$	1.87390	−	0.280390i	0.107653	−	0.0161080i
$304$			8.07826i			0.463320i
$305$		−	5.15292i		−	0.295055i
$306$	−3.40617	−	11.1272i	−0.194718	−	0.636100i
$307$			23.6395i			1.34918i	0.738193	+	0.674590i	$0.235679\pi$
$307$			23.6395i			1.34918i	−0.738193	+	0.674590i	$0.764321\pi$
$308$	−28.1583	+	18.6297i	−1.60447	+	1.06153i
$309$	−1.01875	−	6.80854i	−0.0579549	−	0.387324i
$310$	−11.3688			−0.645704
$311$	8.25876			0.468311			0.234156	−	0.972199i	$-0.424767\pi$
$311$	8.25876			0.468311			0.234156	+	0.972199i	$0.424767\pi$
$312$	2.84153	−	0.425175i	0.160870	−	0.0240708i
$313$		−	6.59544i		−	0.372797i	−0.982474	−	0.186398i	$-0.940319\pi$
$313$		−	6.59544i		−	0.372797i	0.982474	−	0.186398i	$-0.0596815\pi$
$314$	4.32897			0.244298
$315$	−3.17013	−	2.61243i	−0.178617	−	0.147194i
$316$	40.0018			2.25028
$317$			12.0172i			0.674952i	0.941334	+	0.337476i	$0.109573\pi$
$317$			12.0172i			0.674952i	−0.941334	+	0.337476i	$0.890427\pi$
$318$	0.451064	−	0.0674922i	0.0252944	−	0.00378478i
$319$	11.1351			0.623448
$320$	−6.29539			−0.351923
$321$	−1.59497	−	10.6595i	−0.0890226	−	0.594955i
$322$	−3.15501	−	4.76870i	−0.175822	−	0.265749i
$323$		−	6.56389i		−	0.365224i
$324$	−19.9172	+	13.4545i	−1.10651	+	0.747474i
$325$			5.41596i			0.300424i
$326$		−	40.1665i		−	2.22462i
$327$	22.6126	−	3.38350i	1.25048	−	0.187108i
$328$			13.6110i			0.751542i
$329$	−3.16436	−	4.78283i	−0.174457	−	0.263686i
$330$	9.15515	−	1.36988i	0.503974	−	0.0754092i
$331$	12.9844			0.713689			0.356845	−	0.934164i	$-0.383853\pi$
$331$	12.9844			0.713689			0.356845	+	0.934164i	$0.383853\pi$
$332$	41.5325			2.27939
$333$	−7.43638	+	2.27636i	−0.407511	+	0.124744i
$334$			39.2379i			2.14700i
$335$	−2.07064			−0.113131
$336$	−6.77321	−	7.52270i	−0.369509	−	0.410397i
$337$	−17.5304			−0.954940			−0.477470	−	0.878648i	$-0.658446\pi$
$337$	−17.5304			−0.954940			−0.477470	+	0.878648i	$0.658446\pi$
$338$		−	25.2643i		−	1.37420i
$339$	2.33080	+	15.5772i	0.126592	+	0.846039i
$340$	2.48078			0.134539
$341$	48.5689			2.63015
$342$	−22.6722	+	6.94023i	−1.22597	+	0.375285i
$343$	−18.2121	+	3.36449i	−0.983360	+	0.181665i
$344$			14.5733i			0.785740i
$345$	0.132652	+	0.886540i	0.00714175	+	0.0477297i
$346$			45.6157i			2.45232i
$347$		−	14.5056i		−	0.778702i	−0.921090	−	0.389351i	$-0.872699\pi$
$347$		−	14.5056i		−	0.778702i	0.921090	−	0.389351i	$-0.127301\pi$
$348$	−1.59515	−	10.6607i	−0.0855091	−	0.571474i
$349$		−	27.2440i		−	1.45834i	−0.684334	−	0.729169i	$-0.739907\pi$
$349$		−	27.2440i		−	1.45834i	0.684334	−	0.729169i	$-0.260093\pi$
$350$	−22.5662	+	14.9300i	−1.20621	+	0.798040i
$351$	−2.56306	−	5.36635i	−0.136806	−	0.286435i
$352$	36.6626			1.95413
$353$	−26.6866			−1.42038			−0.710192	−	0.704008i	$-0.751392\pi$
$353$	−26.6866			−1.42038			−0.710192	+	0.704008i	$0.751392\pi$
$354$	0.845005	+	5.64734i	0.0449115	+	0.300153i
$355$		−	4.15016i		−	0.220268i
$356$	26.5763			1.40854
$357$	5.50349	+	6.11248i	0.291275	+	0.323507i
$358$	−16.6170			−0.878234
$359$		−	30.0130i		−	1.58402i	−0.610506	−	0.792012i	$-0.709034\pi$
$359$		−	30.0130i		−	1.58402i	0.610506	−	0.792012i	$-0.290966\pi$
$360$	−0.658687	−	2.15179i	−0.0347159	−	0.113409i
$361$	5.62576			0.296093
$362$	17.0740			0.897388
$363$	−20.2692	+	3.03285i	−1.06386	+	0.159184i
$364$	−6.74442	+	4.46216i	−0.353504	+	0.233881i
$365$		−	1.92072i		−	0.100535i
$366$	36.8594	−	5.51524i	1.92667	−	0.288286i
$367$			28.4565i			1.48542i	0.669614	+	0.742709i	$0.266459\pi$
$367$			28.4565i			1.48542i	−0.669614	+	0.742709i	$0.733541\pi$
$368$			2.20894i			0.115149i
$369$	26.9388	−	8.24627i	1.40238	−	0.429284i
$370$		−	2.89951i		−	0.150738i
$371$	−0.268849	+	0.177872i	−0.0139579	+	0.00923468i
$372$	−6.95768	−	46.4996i	−0.360739	−	2.41089i
$373$	−3.36308			−0.174134			−0.0870669	−	0.996202i	$-0.527749\pi$
$373$	−3.36308			−0.174134			−0.0870669	+	0.996202i	$0.527749\pi$
$374$	−18.5350			−0.958424
$375$	8.62794	−	1.29099i	0.445545	−	0.0666664i
$376$		−	3.14164i		−	0.162018i
$377$	2.66707			0.137361
$378$	15.2940	−	25.4725i	0.786638	−	1.31016i
$379$	−6.68815			−0.343547			−0.171774	−	0.985136i	$-0.554950\pi$
$379$	−6.68815			−0.343547			−0.171774	+	0.985136i	$0.554950\pi$
$380$		−	5.05472i		−	0.259302i
$381$	28.4229	−	4.25289i	1.45615	−	0.217882i
$382$	3.96736			0.202988
$383$	33.8423			1.72926			0.864631	−	0.502407i	$-0.167552\pi$
$383$	33.8423			1.72926			0.864631	+	0.502407i	$0.167552\pi$
$384$	−2.80486	−	18.7454i	−0.143135	−	0.956599i
$385$	−5.45677	+	3.61024i	−0.278103	+	0.183995i
$386$			47.5396i			2.41970i
$387$	28.8434	−	8.82929i	1.46619	−	0.448818i
$388$			9.19830i			0.466973i
$389$		−	16.5292i		−	0.838065i	−0.907971	−	0.419032i	$-0.862369\pi$
$389$		−	16.5292i		−	0.838065i	0.907971	−	0.419032i	$-0.137631\pi$
$390$	2.19283	−	0.328110i	0.111038	−	0.0166145i
$391$		−	1.79484i		−	0.0907691i
$392$	−9.33761	−	3.96784i	−0.471620	−	0.200406i
$393$	16.6702	−	2.49434i	0.840899	−	0.125823i
$394$	15.1861			0.765063
$395$	7.75192			0.390041
$396$	11.2059	+	36.6072i	0.563116	+	1.83958i
$397$		−	33.6576i		−	1.68922i	−0.535378	−	0.844612i	$-0.679831\pi$
$397$		−	33.6576i		−	1.68922i	0.535378	−	0.844612i	$-0.320169\pi$
$398$	−21.8228			−1.09388
$399$	12.4545	−	11.2136i	0.623503	−	0.561383i
$400$	10.4530			0.522651
$401$		−	1.11172i		−	0.0555164i	−0.999615	−	0.0277582i	$-0.991163\pi$
$401$		−	1.11172i		−	0.0555164i	0.999615	−	0.0277582i	$-0.00883685\pi$
$402$	−2.21624	−	14.8116i	−0.110536	−	0.738733i
$403$	11.6331			0.579488
$404$	−2.92153			−0.145352
$405$	−3.85974	+	2.60734i	−0.191792	+	0.129560i
$406$	7.35220	+	11.1126i	0.364884	+	0.551511i
$407$			12.3871i			0.614004i
$408$	0.666772	+	4.45617i	0.0330101	+	0.220613i
$409$		−	21.6912i		−	1.07256i	−0.844040	−	0.536280i	$-0.819829\pi$
$409$		−	21.6912i		−	1.07256i	0.844040	−	0.536280i	$-0.180171\pi$
$410$			10.5037i			0.518740i
$411$	−0.716706	−	4.78989i	−0.0353525	−	0.236268i
$412$			10.6149i			0.522961i
$413$	−2.22697	−	3.36600i	−0.109582	−	0.165630i
$414$	−6.19955	+	1.89775i	−0.304691	+	0.0932694i
$415$	8.04855			0.395088
$416$	8.78137			0.430542
$417$	4.94852	+	33.0720i	0.242330	+	1.61954i
$418$			37.7661i			1.84720i
$419$	−33.3792			−1.63068			−0.815340	−	0.578982i	$-0.803450\pi$
$419$	−33.3792			−1.63068			−0.815340	+	0.578982i	$0.803450\pi$
$420$	4.23812	+	4.70710i	0.206799	+	0.229683i
$421$	−5.93366			−0.289189			−0.144594	−	0.989491i	$-0.546188\pi$
$421$	−5.93366			−0.289189			−0.144594	+	0.989491i	$0.546188\pi$
$422$		−	14.8444i		−	0.722612i
$423$	−6.21792	+	1.90337i	−0.302325	+	0.0925452i
$424$	−0.176596			−0.00857624
$425$	−8.49347			−0.411994
$426$	29.6866	−	4.44198i	1.43832	−	0.215214i
$427$	−21.9694	+	14.5351i	−1.06318	+	0.703405i
$428$			16.6188i			0.803302i
$429$	−9.36803	+	1.40173i	−0.452293	+	0.0676761i
$430$			11.2463i			0.542345i
$431$		−	0.167957i		−	0.00809022i	−0.999992	−	0.00404511i	$-0.998712\pi$
$431$		−	0.167957i		−	0.00809022i	0.999992	−	0.00404511i	$-0.00128760\pi$
$432$	−10.3573	+	4.94680i	−0.498314	+	0.238003i
$433$		−	25.0548i		−	1.20406i	−0.798474	−	0.602029i	$-0.794359\pi$
$433$		−	25.0548i		−	1.20406i	0.798474	−	0.602029i	$-0.205641\pi$
$434$	32.0686	+	48.4707i	1.53934	+	2.32667i
$435$	−0.309123	−	2.06593i	−0.0148213	−	0.0990537i
$436$	−35.2545			−1.68839
$437$	−3.65708			−0.174942
$438$	13.7391	−	2.05577i	0.656481	−	0.0982286i
$439$			19.5453i			0.932845i	0.884562	+	0.466423i	$0.154457\pi$
$439$			19.5453i			0.932845i	−0.884562	+	0.466423i	$0.845543\pi$
$440$	−3.58432			−0.170876
$441$	−2.19590	+	20.8849i	−0.104567	+	0.994518i
$442$	−4.43948			−0.211165
$443$		−	24.2202i		−	1.15074i	−0.817894	−	0.575369i	$-0.804858\pi$
$443$		−	24.2202i		−	1.15074i	0.817894	−	0.575369i	$-0.195142\pi$
$444$	11.8593	−	1.77450i	0.562818	−	0.0842138i
$445$	5.15019			0.244142
$446$	−2.01662			−0.0954896
$447$	−4.89184	−	32.6931i	−0.231376	−	1.54633i
$448$	17.7578	+	26.8403i	0.838976	+	1.26809i
$449$		−	20.1385i		−	0.950392i	−0.879880	−	0.475196i	$-0.842377\pi$
$449$		−	20.1385i		−	0.950392i	0.879880	−	0.475196i	$-0.157623\pi$
$450$	8.98044	+	29.3372i	0.423342	+	1.38297i
$451$		−	44.8731i		−	2.11299i
$452$		−	24.2859i		−	1.14231i
$453$	−6.01564	+	0.900114i	−0.282640	+	0.0422910i
$454$		−	29.7256i		−	1.39509i
$455$	−1.30700	+	0.864718i	−0.0612729	+	0.0405386i
$456$	9.07967	−	1.35858i	0.425194	−	0.0636214i
$457$	−5.51652			−0.258052			−0.129026	−	0.991641i	$-0.541185\pi$
$457$	−5.51652			−0.258052			−0.129026	+	0.991641i	$0.541185\pi$
$458$	−34.6301			−1.61816
$459$	8.41567	−	4.01946i	0.392810	−	0.187612i
$460$		−	1.38217i		−	0.0644441i
$461$	−22.5064			−1.04823			−0.524113	−	0.851649i	$-0.675603\pi$
$461$	−22.5064			−1.04823			−0.524113	+	0.851649i	$0.675603\pi$
$462$	−31.6649	−	35.1688i	−1.47319	−	1.63620i
$463$	0.990379			0.0460268			0.0230134	−	0.999735i	$-0.492674\pi$
$463$	0.990379			0.0460268			0.0230134	+	0.999735i	$0.492674\pi$
$464$		−	5.14755i		−	0.238969i
$465$	−1.34832	−	9.01111i	−0.0625270	−	0.417880i
$466$	34.0194			1.57592
$467$	8.45963			0.391465			0.195732	−	0.980657i	$-0.437292\pi$
$467$	8.45963			0.391465			0.195732	+	0.980657i	$0.437292\pi$
$468$	2.68401	+	8.76809i	0.124068	+	0.405305i
$469$	5.84079	+	8.82817i	0.269702	+	0.407647i
$470$		−	2.42442i		−	0.111830i
$471$	0.513410	+	3.43122i	0.0236567	+	0.158102i
$472$		−	2.21098i		−	0.101769i
$473$		−	48.0456i		−	2.20914i
$474$	8.29698	+	55.4504i	0.381093	+	2.54692i
$475$			17.3059i			0.794047i
$476$	−6.99769	−	10.5768i	−0.320739	−	0.484787i
$477$	0.106991	+	0.349517i	0.00489879	+	0.0160033i
$478$	−8.31941			−0.380521
$479$	29.9537			1.36862			0.684310	−	0.729191i	$-0.260104\pi$
$479$	29.9537			1.36862			0.684310	+	0.729191i	$0.260104\pi$
$480$	−1.01779	−	6.80211i	−0.0464557	−	0.310472i
$481$			2.96693i			0.135280i
$482$	−41.6995			−1.89936
$483$	3.40558	−	3.06628i	0.154959	−	0.139520i
$484$	31.6009			1.43641
$485$			1.78253i			0.0809405i
$486$	−22.7818	−	24.8185i	−1.03340	−	1.12579i
$487$	18.5837			0.842109			0.421054	−	0.907035i	$-0.361660\pi$
$487$	18.5837			0.842109			0.421054	+	0.907035i	$0.361660\pi$
$488$	−14.4308			−0.653252
$489$	31.8367	−	4.76369i	1.43971	−	0.215422i
$490$	−7.20588	−	3.06200i	−0.325529	−	0.138327i
$491$			36.7513i			1.65856i	0.558831	+	0.829282i	$0.311250\pi$
$491$			36.7513i			1.65856i	−0.558831	+	0.829282i	$0.688750\pi$
$492$	−42.9612	+	6.42824i	−1.93684	+	0.289807i
$493$			4.18258i			0.188374i
$494$			9.04566i			0.406983i
$495$	2.17158	+	7.09407i	0.0976051	+	0.318855i
$496$		−	22.4524i		−	1.00814i
$497$	−17.6942	+	11.7066i	−0.793693	+	0.525113i
$498$	8.61447	+	57.5722i	0.386024	+	2.57987i
$499$	−5.48660			−0.245614			−0.122807	−	0.992431i	$-0.539190\pi$
$499$	−5.48660			−0.245614			−0.122807	+	0.992431i	$0.539190\pi$
$500$	−13.4515			−0.601570
$501$	−31.1007	+	4.65357i	−1.38948	+	0.207906i
$502$			40.8837i			1.82473i
$503$	−9.47339			−0.422397			−0.211199	−	0.977443i	$-0.567737\pi$
$503$	−9.47339			−0.422397			−0.211199	+	0.977443i	$0.567737\pi$
$504$	−7.31614	+	8.87799i	−0.325887	+	0.395457i
$505$	−0.566161			−0.0251938
$506$			10.3268i			0.459084i
$507$	20.0249	−	2.99631i	0.889339	−	0.133071i
$508$	−44.3131			−1.96608
$509$	−37.0096			−1.64042			−0.820211	−	0.572062i	$-0.806144\pi$
$509$	−37.0096			−1.64042			−0.820211	+	0.572062i	$0.806144\pi$
$510$	0.514552	+	3.43885i	0.0227847	+	0.152275i
$511$	−8.18897	+	5.41789i	−0.362259	+	0.239673i
$512$		−	23.3516i		−	1.03200i
$513$	−8.18985	−	17.1473i	−0.361591	−	0.757073i
$514$			36.9398i			1.62935i
$515$			2.05706i			0.0906449i
$516$	−45.9986	+	6.88272i	−2.02497	+	0.302995i
$517$			10.3574i			0.455519i
$518$	−12.3620	+	8.17881i	−0.543156	+	0.359356i
$519$	−36.1559	+	5.40996i	−1.58707	+	0.237471i
$520$	−0.858511			−0.0376482
$521$	10.3670			0.454188			0.227094	−	0.973873i	$-0.427078\pi$
$521$	10.3670			0.454188			0.227094	+	0.973873i	$0.427078\pi$
$522$	14.4470	−	4.42238i	0.632327	−	0.193562i
$523$		−	30.7876i		−	1.34625i	−0.739529	−	0.673124i	$-0.764952\pi$
$523$		−	30.7876i		−	1.34625i	0.739529	−	0.673124i	$-0.235048\pi$
$524$	−25.9899			−1.13537
$525$	−14.5101	−	16.1157i	−0.633272	−	0.703347i
$526$	37.4270			1.63190
$527$			18.2434i			0.794696i
$528$	2.70539	+	18.0807i	0.117737	+	0.786860i
$529$	−1.00000			−0.0434783
$530$	−0.136280			−0.00591962
$531$	−4.37596	+	1.33953i	−0.189901	+	0.0581308i
$532$	−21.5507	+	14.2581i	−0.934343	+	0.618169i
$533$		−	10.7479i		−	0.465544i
$534$	5.51232	+	36.8399i	0.238541	+	1.59422i
$535$			3.22055i			0.139237i
$536$			5.79886i			0.250472i
$537$	−1.97075	−	13.1709i	−0.0850441	−	0.568367i
$538$		−	16.9782i		−	0.731982i
$539$	30.7844	+	13.0813i	1.32598	+	0.563450i
$540$	6.48073	−	3.09531i	0.278886	−	0.133201i
$541$	−1.06671			−0.0458613			−0.0229306	−	0.999737i	$-0.507300\pi$
$541$	−1.06671			−0.0458613			−0.0229306	+	0.999737i	$0.507300\pi$
$542$	11.2769			0.484385
$543$	2.02495	+	13.5331i	0.0868989	+	0.580763i
$544$			13.7712i			0.590435i
$545$	−6.83195			−0.292648
$546$	−7.58433	−	8.42357i	−0.324579	−	0.360496i
$547$	2.45394			0.104923			0.0524613	−	0.998623i	$-0.483293\pi$
$547$	2.45394			0.104923			0.0524613	+	0.998623i	$0.483293\pi$
$548$			7.46774i			0.319006i
$549$	8.74296	+	28.5614i	0.373140	+	1.21897i
$550$	48.8681			2.08374
$551$	8.52220			0.363058
$552$	2.48276	−	0.371493i	0.105673	−	0.0158118i
$553$	−21.8663	−	33.0502i	−0.929849	−	1.40544i
$554$			32.3289i			1.37352i
$555$	2.29820	−	0.343878i	0.0975533	−	0.0145968i
$556$		−	51.5613i		−	2.18669i
$557$			33.9926i			1.44031i	0.693812	+	0.720156i	$0.255930\pi$
$557$			33.9926i			1.44031i	−0.693812	+	0.720156i	$0.744070\pi$
$558$	63.0144	−	19.2894i	2.66761	−	0.816586i
$559$		−	11.5078i		−	0.486728i
$560$	1.66894	+	2.52255i	0.0705256	+	0.106597i
$561$	−2.19823	−	14.6912i	−0.0928094	−	0.620264i
$562$	−46.3462			−1.95499
$563$	−23.8691			−1.00596			−0.502981	−	0.864297i	$-0.667764\pi$
$563$	−23.8691			−1.00596			−0.502981	+	0.864297i	$0.667764\pi$
$564$	9.91614	−	1.48374i	0.417545	−	0.0624768i
$565$		−	4.70634i		−	0.197997i
$566$	29.8833			1.25609
$567$	22.0038	+	9.10130i	0.924072	+	0.382219i
$568$	−11.6226			−0.487672
$569$			39.3479i			1.64955i	0.565462	+	0.824775i	$0.308698\pi$
$569$			39.3479i			1.64955i	−0.565462	+	0.824775i	$0.691302\pi$
$570$	7.00683	−	1.04842i	0.293484	−	0.0439137i
$571$	7.34434			0.307351			0.153676	−	0.988121i	$-0.450889\pi$
$571$	7.34434			0.307351			0.153676	+	0.988121i	$0.450889\pi$
$572$	14.6054			0.610681
$573$	0.470523	+	3.14460i	0.0196564	+	0.131368i
$574$	44.7823	−	29.6283i	1.86918	−	1.23666i
$575$			4.73215i			0.197344i
$576$	34.8938	−	10.6814i	1.45391	−	0.445058i
$577$			6.06831i			0.252627i	0.991990	+	0.126313i	$0.0403145\pi$
$577$			6.06831i			0.252627i	−0.991990	+	0.126313i	$0.959685\pi$
$578$			29.7777i			1.23859i
$579$	−37.6807	+	5.63813i	−1.56596	+	0.234313i
$580$			3.22092i			0.133741i
$581$	−22.7030	−	34.3149i	−0.941880	−	1.42362i
$582$	−12.7506	+	1.90786i	−0.528531	+	0.0790835i
$583$	0.582205			0.0241125
$584$	−5.37899			−0.222584
$585$	0.520132	+	1.69916i	0.0215048	+	0.0702516i
$586$			0.119909i			0.00495340i
$587$	35.6479			1.47135			0.735674	−	0.677336i	$-0.236866\pi$
$587$	35.6479			1.47135			0.735674	+	0.677336i	$0.236866\pi$
$588$	8.11394	−	31.3468i	0.334613	−	1.29272i
$589$	37.1719			1.53164
$590$		−	1.70623i		−	0.0702443i
$591$	1.80105	+	12.0368i	0.0740851	+	0.495126i
$592$	5.72629			0.235349
$593$	−19.6534			−0.807068			−0.403534	−	0.914965i	$-0.632218\pi$
$593$	−19.6534			−0.807068			−0.403534	+	0.914965i	$0.632218\pi$
$594$	−48.4205	+	23.1264i	−1.98672	+	0.948888i
$595$	−1.35608	−	2.04967i	−0.0555937	−	0.0840282i
$596$			50.9707i			2.08784i
$597$	−2.58816	−	17.2972i	−0.105926	−	0.707927i
$598$			2.47346i			0.101147i
$599$		−	45.6452i		−	1.86501i	−0.361153	−	0.932507i	$-0.617617\pi$
$599$		−	45.6452i		−	1.86501i	0.361153	−	0.932507i	$-0.382383\pi$
$600$	−1.75796	−	11.7488i	−0.0717685	−	0.479643i
$601$		−	5.70423i		−	0.232680i	−0.993209	−	0.116340i	$-0.962884\pi$
$601$		−	5.70423i		−	0.232680i	0.993209	−	0.116340i	$-0.0371163\pi$
$602$	47.9485	−	31.7231i	1.95423	−	1.29294i
$603$	11.4771	−	3.51326i	0.467382	−	0.143071i
$604$	9.37877			0.381617
$605$	6.12392			0.248973
$606$	−0.605970	−	4.04982i	−0.0246158	−	0.164513i
$607$			23.2838i			0.945061i	0.881314	+	0.472530i	$0.156659\pi$
$607$			23.2838i			0.945061i	−0.881314	+	0.472530i	$0.843341\pi$
$608$	28.0595			1.13796
$609$	−7.93611	+	7.14543i	−0.321587	+	0.289547i
$610$	−11.1363			−0.450897
$611$			2.48079i			0.100362i
$612$	−13.7504	+	4.20914i	−0.555826	+	0.170145i
$613$	40.5101			1.63619			0.818095	−	0.575084i	$-0.195031\pi$
$613$	40.5101			1.63619			0.818095	+	0.575084i	$0.195031\pi$
$614$	51.0890			2.06178
$615$	−8.32541	+	1.24572i	−0.335713	+	0.0502323i
$616$	10.1105	+	15.2817i	0.407364	+	0.615718i
$617$		−	9.80961i		−	0.394920i	−0.980311	−	0.197460i	$-0.936731\pi$
$617$		−	9.80961i		−	0.394920i	0.980311	−	0.197460i	$-0.0632692\pi$
$618$	−14.7144	+	2.20170i	−0.591900	+	0.0885653i
$619$		−	19.4726i		−	0.782670i	−0.920248	−	0.391335i	$-0.872013\pi$
$619$		−	19.4726i		−	0.782670i	0.920248	−	0.391335i	$-0.127987\pi$
$620$			14.0489i			0.564217i
$621$	−2.23945	−	4.68880i	−0.0898660	−	0.188155i
$622$		−	17.8486i		−	0.715663i
$623$	−14.5274	−	21.9578i	−0.582030	−	0.879720i
$624$	0.647991	+	4.33065i	0.0259404	+	0.173365i
$625$	21.0540			0.842160
$626$	−14.2539			−0.569699
$627$	−29.9341	+	4.47900i	−1.19545	+	0.178874i
$628$		−	5.34949i		−	0.213468i
$629$	−4.65282			−0.185520
$630$	−5.64591	+	6.85119i	−0.224938	+	0.272958i
$631$	4.26468			0.169774			0.0848870	−	0.996391i	$-0.472947\pi$
$631$	4.26468			0.169774			0.0848870	+	0.996391i	$0.472947\pi$
$632$		−	21.7093i		−	0.863550i
$633$	11.7659	−	1.76052i	0.467653	−	0.0699744i
$634$	25.9711			1.03145
$635$	−8.58740			−0.340780
$636$	−0.0834030	−	0.557399i	−0.00330715	−	0.0221023i
$637$	7.37344	+	3.13320i	0.292146	+	0.124142i
$638$		−	24.0649i		−	0.952739i
$639$	7.04158	+	23.0033i	0.278561	+	0.909998i
$640$			5.66355i			0.223872i
$641$		−	9.54021i		−	0.376816i	−0.982091	−	0.188408i	$-0.939667\pi$
$641$		−	9.54021i		−	0.376816i	0.982091	−	0.188408i	$-0.0603327\pi$
$642$	−23.0370	+	3.44700i	−0.909197	+	0.136042i
$643$		−	5.50331i		−	0.217029i	−0.994095	−	0.108515i	$-0.965391\pi$
$643$		−	5.50331i		−	0.217029i	0.994095	−	0.108515i	$-0.0346095\pi$
$644$	−5.89288	+	3.89878i	−0.232212	+	0.153633i
$645$	−8.91402	+	1.33380i	−0.350989	+	0.0525181i
$646$	−14.1857			−0.558127
$647$	27.5664			1.08375			0.541874	−	0.840460i	$-0.317715\pi$
$647$	27.5664			1.08375			0.541874	+	0.840460i	$0.317715\pi$
$648$	7.30188	+	10.8092i	0.286845	+	0.424627i
$649$			7.28922i			0.286127i
$650$	11.7048			0.459100
$651$	−34.6155	+	31.1667i	−1.35669	+	1.22152i
$652$	−49.6354			−1.94387
$653$		−	6.31477i		−	0.247116i	−0.992337	−	0.123558i	$-0.960570\pi$
$653$		−	6.31477i		−	0.247116i	0.992337	−	0.123558i	$-0.0394305\pi$
$654$	−7.31232	−	48.8697i	−0.285934	−	1.91096i
$655$	−5.03655			−0.196794
$656$	−20.7439			−0.809913
$657$	3.25888	+	10.6461i	0.127141	+	0.415343i
$658$	−10.3365	+	6.83870i	−0.402959	+	0.266600i
$659$		−	2.31820i		−	0.0903044i	−0.998980	−	0.0451522i	$-0.985623\pi$
$659$		−	2.31820i		−	0.0903044i	0.998980	−	0.0451522i	$-0.0143773\pi$
$660$	−1.69281	−	11.3134i	−0.0658927	−	0.440374i
$661$		−	10.4523i		−	0.406547i	−0.979122	−	0.203274i	$-0.934842\pi$
$661$		−	10.4523i		−	0.406547i	0.979122	−	0.203274i	$-0.0651581\pi$
$662$		−	28.0615i		−	1.09064i
$663$	−0.526516	−	3.51881i	−0.0204482	−	0.136659i
$664$		−	22.5400i		−	0.874723i
$665$	−4.17630	+	2.76307i	−0.161950	+	0.107147i
$666$	4.91960	+	16.0713i	0.190630	+	0.622749i
$667$	2.33033			0.0902307
$668$	48.4880			1.87606
$669$	−0.239168	−	1.59841i	−0.00924677	−	0.0617980i
$670$			4.47501i			0.172885i
$671$	47.5758			1.83664
$672$	−26.1298	+	23.5265i	−1.00798	+	0.907553i
$673$	−34.2996			−1.32215			−0.661076	−	0.750319i	$-0.729900\pi$
$673$	−34.2996			−1.32215			−0.661076	+	0.750319i	$0.729900\pi$
$674$			37.8861i			1.45932i
$675$	−22.1881	+	10.5974i	−0.854021	+	0.407895i
$676$	−31.2202			−1.20078
$677$	−25.1862			−0.967986			−0.483993	−	0.875072i	$-0.660814\pi$
$677$	−25.1862			−0.967986			−0.483993	+	0.875072i	$0.660814\pi$
$678$	33.6650	−	5.03726i	1.29290	−	0.193455i
$679$	7.59980	−	5.02808i	0.291653	−	0.192960i
$680$		−	1.34634i		−	0.0516298i
$681$	23.5610	−	3.52541i	0.902861	−	0.135094i
$682$		−	104.966i		−	4.01934i
$683$			23.1934i			0.887471i	0.896158	+	0.443735i	$0.146347\pi$
$683$			23.1934i			0.887471i	−0.896158	+	0.443735i	$0.853653\pi$
$684$	8.57634	+	28.0171i	0.327924	+	1.07126i
$685$			1.44717i			0.0552934i
$686$	7.27123	+	39.3594i	0.277617	+	1.50275i
$687$	−4.10708	−	27.4484i	−0.156695	−	1.04722i
$688$	−22.2105			−0.846768
$689$	0.139449			0.00531257
$690$	1.91596	−	0.286683i	0.0729394	−	0.0109138i
$691$			32.1610i			1.22346i	0.791065	+	0.611732i	$0.209527\pi$
$691$			32.1610i			1.22346i	−0.791065	+	0.611732i	$0.790473\pi$
$692$	56.3693			2.14284
$693$	24.1200	−	29.2692i	0.916244	−	1.11184i
$694$	−31.3490			−1.18999
$695$		−	9.99202i		−	0.379019i
$696$	−5.78566	+	0.865701i	−0.219305	+	0.0328143i
$697$	16.8552			0.638436
$698$	−58.8788			−2.22860
$699$	4.03466	+	26.9644i	0.152605	+	1.01989i
$700$	18.4496	+	27.8860i	0.697329	+	1.05399i
$701$		−	32.7177i		−	1.23573i	−0.786284	−	0.617865i	$-0.787998\pi$
$701$		−	32.7177i		−	1.23573i	0.786284	−	0.617865i	$-0.212002\pi$
$702$	−11.5976	+	5.53920i	−0.437723	+	0.209064i
$703$			9.48036i			0.357558i
$704$		−	58.1240i		−	2.19063i
$705$	1.92164	−	0.287533i	0.0723731	−	0.0108291i
$706$			57.6742i			2.17060i
$707$	1.59700	+	2.41382i	0.0600615	+	0.0907812i
$708$	6.97865	−	1.04421i	0.262274	−	0.0392438i
$709$	−42.9544			−1.61319			−0.806594	−	0.591106i	$-0.798691\pi$
$709$	−42.9544			−1.61319			−0.806594	+	0.591106i	$0.798691\pi$
$710$	−8.96920			−0.336608
$711$	−42.9670	+	13.1527i	−1.61139	+	0.493264i
$712$		−	14.4232i		−	0.540531i
$713$	10.1644			0.380658
$714$	13.2101	−	11.8940i	0.494375	−	0.445120i
$715$	2.83036			0.105849
$716$			20.5343i			0.767403i
$717$	−0.986671	−	6.59412i	−0.0368479	−	0.246262i
$718$	−64.8630			−2.42067
$719$	−4.03136			−0.150344			−0.0751721	−	0.997171i	$-0.523951\pi$
$719$	−4.03136			−0.150344			−0.0751721	+	0.997171i	$0.523951\pi$
$720$	3.27945	−	1.00388i	0.122218	−	0.0374122i
$721$	8.77026	−	5.80247i	0.326621	−	0.216095i
$722$		−	12.1582i		−	0.452482i
$723$	−4.94550	−	33.0518i	−0.183925	−	1.22921i
$724$		−	21.0990i		−	0.784139i
$725$		−	11.0275i		−	0.409550i
$726$	6.55451	+	43.8051i	0.243261	+	1.62576i
$727$			26.8106i			0.994350i	0.867650	+	0.497175i	$0.165629\pi$
$727$			26.8106i			0.994350i	−0.867650	+	0.497175i	$0.834371\pi$
$728$	2.42165	+	3.66025i	0.0897524	+	0.135658i
$729$	16.9697	−	21.0007i	0.628509	−	0.777803i
$730$	−4.15100			−0.153635
$731$	18.0469			0.667487
$732$	−6.81541	−	45.5488i	−0.251905	−	1.68353i
$733$		−	38.0221i		−	1.40438i	−0.711990	−	0.702189i	$-0.752206\pi$
$733$		−	38.0221i		−	1.40438i	0.711990	−	0.702189i	$-0.247794\pi$
$734$	61.4993			2.26998
$735$	1.57239	−	6.07466i	0.0579986	−	0.224067i
$736$	7.67265			0.282818
$737$		−	19.1178i		−	0.704214i
$738$	−17.8216	−	58.2193i	−0.656022	−	2.14308i
$739$	−11.5044			−0.423197			−0.211598	−	0.977357i	$-0.567867\pi$
$739$	−11.5044			−0.423197			−0.211598	+	0.977357i	$0.567867\pi$
$740$	−3.58305			−0.131715
$741$	−7.16975	+	1.07280i	−0.263388	+	0.0394104i
$742$	0.384412	+	0.581028i	0.0141122	+	0.0213302i
$743$			30.8860i			1.13310i	0.824028	+	0.566549i	$0.191722\pi$
$743$			30.8860i			1.13310i	−0.824028	+	0.566549i	$0.808278\pi$
$744$	−25.2357	+	3.77599i	−0.925185	+	0.138434i
$745$			9.87756i			0.361886i
$746$			7.26818i			0.266107i
$747$	−44.6111	+	13.6560i	−1.63224	+	0.499646i
$748$			22.9045i			0.837473i
$749$	13.7308	−	9.08440i	0.501712	−	0.331937i
$750$	−2.79005	−	18.6464i	−0.101878	−	0.680871i
$751$	6.35605			0.231936			0.115968	−	0.993253i	$-0.463003\pi$
$751$	6.35605			0.231936			0.115968	+	0.993253i	$0.463003\pi$
$752$	4.78803			0.174602
$753$	−32.4052	+	4.84875i	−1.18091	+	0.176698i
$754$		−	5.76399i		−	0.209912i
$755$	1.81750			0.0661457
$756$	−31.4774	−	18.8994i	−1.14482	−	0.687366i
$757$	−41.4589			−1.50685			−0.753424	−	0.657535i	$-0.771599\pi$
$757$	−41.4589			−1.50685			−0.753424	+	0.657535i	$0.771599\pi$
$758$			14.4542i			0.525001i
$759$	−8.18523	+	1.22475i	−0.297105	+	0.0444555i
$760$	−2.74324			−0.0995076
$761$	47.8324			1.73392			0.866961	−	0.498376i	$-0.166070\pi$
$761$	47.8324			1.73392			0.866961	+	0.498376i	$0.166070\pi$
$762$	−9.19120	−	61.4266i	−0.332962	−	2.22525i
$763$	19.2713	+	29.1279i	0.697667	+	1.05450i
$764$		−	4.90263i		−	0.177371i
$765$	−2.66467	+	0.815686i	−0.0963414	+	0.0294912i
$766$		−	73.1390i		−	2.64262i
$767$			1.74590i			0.0630408i
$768$	1.16138	−	0.173776i	0.0419077	−	0.00627060i
$769$		−	9.55963i		−	0.344729i	−0.985033	−	0.172365i	$-0.944859\pi$
$769$		−	9.55963i		−	0.344729i	0.985033	−	0.172365i	$-0.0551407\pi$
$770$	7.80233	+	11.7930i	0.281177	+	0.424990i
$771$	−29.2792	+	4.38101i	−1.05446	+	0.157778i
$772$	58.7467			2.11434
$773$	27.7088			0.996617			0.498308	−	0.867000i	$-0.333955\pi$
$773$	27.7088			0.996617			0.498308	+	0.867000i	$0.333955\pi$
$774$	−19.0816	−	62.3354i	−0.685873	−	2.24060i
$775$		−	48.0993i		−	1.72778i
$776$	4.99199			0.179202
$777$	−7.94880	−	8.82837i	−0.285161	−	0.316716i
$778$	−35.7224			−1.28071
$779$		−	34.3433i		−	1.23048i
$780$	−0.405460	−	2.70977i	−0.0145178	−	0.0970253i
$781$	38.3176			1.37111
$782$	−3.87896			−0.138711
$783$	5.21865	+	10.9264i	0.186499	+	0.390479i
$784$	6.04721	−	14.2310i	0.215972	−	0.508251i
$785$		−	1.03667i		−	0.0370005i
$786$	−5.39069	−	36.0271i	−0.192280	−	1.28504i
$787$		−	46.5036i		−	1.65767i	−0.559491	−	0.828836i	$-0.689003\pi$
$787$		−	46.5036i		−	1.65767i	0.559491	−	0.828836i	$-0.310997\pi$
$788$		−	18.7661i		−	0.668514i
$789$	4.43880	+	29.6654i	0.158025	+	1.05611i
$790$		−	16.7532i		−	0.596052i
$791$	−20.0654	+	13.2754i	−0.713445	+	0.472020i
$792$	19.8670	−	6.08152i	0.705944	−	0.216097i
$793$	11.3953			0.404658
$794$	−72.7396			−2.58143
$795$	−0.0161626	−	0.108018i	−0.000573228	−	0.00383100i
$796$			26.9674i			0.955835i
$797$	−39.3876			−1.39518			−0.697590	−	0.716497i	$-0.745744\pi$
$797$	−39.3876			−1.39518			−0.697590	+	0.716497i	$0.745744\pi$
$798$	−24.2345	−	26.9162i	−0.857893	−	0.952823i
$799$	−3.89045			−0.137634
$800$		−	36.3081i		−	1.28369i
$801$	−28.5462	+	8.73832i	−1.00863	+	0.308754i
$802$	−2.40260			−0.0848389
$803$	17.7336			0.625805
$804$	−18.3033	+	2.73870i	−0.645507	+	0.0965865i
$805$	−1.14198	+	0.755540i	−0.0402494	+	0.0266293i
$806$		−	25.1412i		−	0.885560i
$807$	13.4572	−	2.01359i	0.473717	−	0.0708818i
$808$			1.58554i			0.0557791i
$809$			36.5898i			1.28643i	0.765686	+	0.643215i	$0.222400\pi$
$809$			36.5898i			1.28643i	−0.765686	+	0.643215i	$0.777600\pi$
$810$	5.63490	+	8.34155i	0.197990	+	0.293092i
$811$			18.3947i			0.645925i	0.946412	+	0.322963i	$0.104679\pi$
$811$			18.3947i			0.645925i	−0.946412	+	0.322963i	$0.895321\pi$
$812$	13.7324	−	9.08543i	0.481911	−	0.318836i
$813$	1.33743	+	8.93829i	0.0469056	+	0.313479i
$814$	26.7705			0.938307
$815$	−9.61881			−0.336932
$816$	−6.79145	+	1.01620i	−0.237748	+	0.0355740i
$817$		−	36.7714i		−	1.28647i
$818$	−46.8783			−1.63906
$819$	5.77719	−	7.01050i	0.201871	−	0.244967i
$820$	12.9798			0.453276
$821$			35.3657i			1.23427i	0.786857	+	0.617136i	$0.211707\pi$
$821$			35.3657i			1.23427i	−0.786857	+	0.617136i	$0.788293\pi$
$822$	−10.3518	+	1.54892i	−0.361059	+	0.0540248i
$823$	−0.0597619			−0.00208317			−0.00104159	−	0.999999i	$-0.500332\pi$
$823$	−0.0597619			−0.00208317			−0.00104159	+	0.999999i	$0.500332\pi$
$824$	5.76082			0.200688
$825$	5.79569	+	38.7338i	0.201780	+	1.34854i
$826$	−7.27448	+	4.81285i	−0.253112	+	0.167461i
$827$			48.5632i			1.68871i	0.535785	+	0.844355i	$0.320016\pi$
$827$			48.5632i			1.68871i	−0.535785	+	0.844355i	$0.679984\pi$
$828$	2.34513	+	7.66104i	0.0814990	+	0.266240i
$829$		−	37.6855i		−	1.30887i	−0.756118	−	0.654435i	$-0.772907\pi$
$829$		−	37.6855i		−	1.30887i	0.756118	−	0.654435i	$-0.227093\pi$
$830$		−	17.3943i		−	0.603764i
$831$	−25.6245	+	3.83417i	−0.888904	+	0.133006i
$832$		−	13.9218i		−	0.482650i
$833$	−4.91358	+	11.5632i	−0.170245	+	0.400642i
$834$	71.4741	−	10.6946i	2.47495	−	0.370323i
$835$	9.39644			0.325177
$836$	46.6691			1.61409
$837$	22.7626	+	47.6586i	0.786789	+	1.64732i
$838$			72.1381i			2.49197i
$839$	52.7968			1.82275			0.911375	−	0.411578i	$-0.135022\pi$
$839$	52.7968			1.82275			0.911375	+	0.411578i	$0.135022\pi$
$840$	2.55458	−	2.30006i	0.0881413	−	0.0793597i
$841$	23.5696			0.812744
$842$			12.8236i			0.441931i
$843$	−5.49659	−	36.7348i	−0.189313	−	1.26521i
$844$	−18.3438			−0.631420
$845$	−6.05013			−0.208131
$846$	4.11351	+	13.4380i	0.141425	+	0.462007i
$847$	−17.2741	−	26.1093i	−0.593545	−	0.897125i
$848$		−	0.269141i		−	0.00924235i
$849$	3.54412	+	23.6861i	0.121634	+	0.812904i
$850$			18.3558i			0.629599i
$851$			2.59233i			0.0888639i
$852$	−5.48914	−	36.6850i	−0.188055	−	1.25681i
$853$			13.8140i			0.472981i	0.971634	+	0.236490i	$0.0759972\pi$
$853$			13.8140i			0.472981i	−0.971634	+	0.236490i	$0.924003\pi$
$854$	31.4129	+	47.4796i	1.07493	+	1.62472i
$855$	1.66200	+	5.42940i	0.0568392	+	0.185681i
$856$	9.01918			0.308269
$857$	−7.99518			−0.273110			−0.136555	−	0.990632i	$-0.543603\pi$
$857$	−7.99518			−0.273110			−0.136555	+	0.990632i	$0.543603\pi$
$858$	3.02937	+	20.2459i	0.103421	+	0.691183i
$859$		−	37.0861i		−	1.26536i	−0.774413	−	0.632680i	$-0.781955\pi$
$859$		−	37.0861i		−	1.26536i	0.774413	−	0.632680i	$-0.218045\pi$
$860$	13.8975			0.473902
$861$	28.7951	+	31.9814i	0.981334	+	1.08992i
$862$	−0.362984			−0.0123633
$863$		−	12.9341i		−	0.440283i	−0.975468	−	0.220142i	$-0.929348\pi$
$863$		−	12.9341i		−	0.440283i	0.975468	−	0.220142i	$-0.0706520\pi$
$864$	17.1825	+	35.9755i	0.584561	+	1.22391i
$865$	10.9238			0.371419
$866$	−54.1477			−1.84001
$867$	−23.6024	+	3.53160i	−0.801579	+	0.119939i
$868$	59.8973	−	39.6285i	2.03305	−	1.34508i
$869$			71.5718i			2.42791i
$870$	−4.46482	+	0.668066i	−0.151372	+	0.0226496i
$871$		−	4.57906i		−	0.155156i
$872$			19.1329i			0.647923i
$873$	−3.02442	−	9.88012i	−0.102361	−	0.334391i
$874$			7.90357i			0.267342i
$875$	7.35303	+	11.1139i	0.248578	+	0.375718i
$876$	−2.54040	−	16.9780i	−0.0858323	−	0.573635i
$877$	44.0835			1.48859			0.744297	−	0.667849i	$-0.232785\pi$
$877$	44.0835			1.48859			0.744297	+	0.667849i	$0.232785\pi$
$878$	42.2406			1.42555
$879$	−0.0950422	+	0.0142211i	−0.00320569	+	0.000479665i
$880$		−	5.46270i		−	0.184148i
$881$	10.6450			0.358639			0.179320	−	0.983791i	$-0.442610\pi$
$881$	10.6450			0.358639			0.179320	+	0.983791i	$0.442610\pi$
$882$	45.1357	+	4.74571i	1.51980	+	0.159796i
$883$	35.4935			1.19445			0.597225	−	0.802074i	$-0.296270\pi$
$883$	35.4935			1.19445			0.597225	+	0.802074i	$0.296270\pi$
$884$			5.48606i			0.184516i
$885$	1.35239	−	0.202356i	0.0454600	−	0.00680213i
$886$	−52.3440			−1.75853
$887$	−38.5780			−1.29532			−0.647661	−	0.761929i	$-0.724253\pi$
$887$	−38.5780			−1.29532			−0.647661	+	0.761929i	$0.724253\pi$
$888$	−0.963033	−	6.43614i	−0.0323173	−	0.215983i
$889$	24.2230	+	36.6123i	0.812412	+	1.22794i
$890$		−	11.1304i		−	0.373093i
$891$	−24.0730	−	35.6362i	−0.806477	−	1.19386i
$892$			2.49202i			0.0834390i
$893$			7.92699i			0.265266i
$894$	−70.6553	+	10.5721i	−2.36307	+	0.353583i
$895$			3.97932i			0.133014i
$896$	24.1465	−	15.9755i	0.806678	−	0.533704i
$897$	−1.96051	+	0.293349i	−0.0654596	+	0.00979465i
$898$	−43.5226			−1.45237
$899$	−23.6863			−0.789982
$900$	36.2532	−	11.0975i	1.20844	−	0.369917i
$901$			0.218687i			0.00728553i
$902$	−96.9782			−3.22902
$903$	30.8309	+	34.2425i	1.02599	+	1.13952i
$904$	−13.1801			−0.438365
$905$		−	4.08876i		−	0.135915i
$906$	1.94530	+	13.0008i	0.0646282	+	0.431923i
$907$	−41.6025			−1.38139			−0.690693	−	0.723148i	$-0.742695\pi$
$907$	−41.6025			−1.38139			−0.690693	+	0.723148i	$0.742695\pi$
$908$	−36.7332			−1.21903
$909$	3.13809	−	0.960605i	0.104084	−	0.0318613i
$910$	1.86880	+	2.82464i	0.0619502	+	0.0936358i
$911$			28.5596i			0.946221i	0.881003	+	0.473110i	$0.156869\pi$
$911$			28.5596i			0.946221i	−0.881003	+	0.473110i	$0.843131\pi$
$912$	2.07055	+	13.8379i	0.0685628	+	0.458219i
$913$			74.3105i			2.45932i
$914$			11.9221i			0.394349i
$915$	−1.32075	−	8.82685i	−0.0436627	−	0.291807i
$916$			42.7939i			1.41395i
$917$	14.2069	+	21.4733i	0.469153	+	0.709111i
$918$	−8.68673	−	18.1877i	−0.286705	−	0.600283i
$919$	34.7764			1.14717			0.573583	−	0.819147i	$-0.305553\pi$
$919$	34.7764			1.14717			0.573583	+	0.819147i	$0.305553\pi$
$920$	−0.750116			−0.0247306
$921$	6.05909	+	40.4941i	0.199654	+	1.33433i
$922$			48.6401i			1.60187i
$923$	9.17776			0.302090
$924$	−43.4596	+	39.1297i	−1.42972	+	1.28727i
$925$	12.2673			0.403346
$926$		−	2.14038i		−	0.0703371i
$927$	−3.49021	−	11.4018i	−0.114634	−	0.374483i
$928$	−17.8798			−0.586933
$929$	−17.7634			−0.582797			−0.291399	−	0.956602i	$-0.594121\pi$
$929$	−17.7634			−0.582797			−0.291399	+	0.956602i	$0.594121\pi$
$930$	−19.4745	+	2.91395i	−0.638595	+	0.0955522i
$931$	23.5607	+	10.0117i	0.772169	+	0.328119i
$932$		−	42.0393i		−	1.37704i
$933$	14.1471	−	2.11682i	0.463155	−	0.0693014i
$934$		−	18.2827i		−	0.598227i
$935$			4.43865i			0.145159i
$936$	4.75851	−	1.45663i	0.155537	−	0.0476116i
$937$		−	20.6332i		−	0.674059i	−0.941494	−	0.337029i	$-0.890578\pi$
$937$		−	20.6332i		−	0.674059i	0.941494	−	0.337029i	$-0.109422\pi$
$938$	19.0792	−	12.6229i	0.622957	−	0.412153i
$939$	−1.69049	−	11.2979i	−0.0551670	−	0.368692i
$940$	−2.99596			−0.0977174
$941$	−47.7850			−1.55775			−0.778873	−	0.627181i	$-0.784209\pi$
$941$	−47.7850			−1.55775			−0.778873	+	0.627181i	$0.784209\pi$
$942$	7.41545	−	1.10957i	0.241608	−	0.0361516i
$943$		−	9.39090i		−	0.305810i
$944$	3.36966			0.109673
$945$	−6.09998	−	3.66251i	−0.198432	−	0.119141i
$946$	−103.835			−3.37596
$947$			32.9461i			1.07060i	0.844661	+	0.535302i	$0.179802\pi$
$947$			32.9461i			1.07060i	−0.844661	+	0.535302i	$0.820198\pi$
$948$	68.5224	−	10.2529i	2.22550	−	0.333000i
$949$	4.24752			0.137880
$950$	37.4009			1.21344
$951$	3.08014	+	20.5852i	0.0998804	+	0.667521i
$952$	−5.74011	+	3.79770i	−0.186038	+	0.123084i
$953$		−	12.7522i		−	0.413085i	−0.978438	−	0.206542i	$-0.933779\pi$
$953$		−	12.7522i		−	0.413085i	0.978438	−	0.206542i	$-0.0662211\pi$
$954$	0.755365	−	0.231226i	0.0244559	−	0.00748621i
$955$		−	0.950077i		−	0.0307438i
$956$			10.2807i			0.332500i
$957$	19.0743	−	2.85406i	0.616584	−	0.0922588i
$958$		−	64.7350i		−	2.09149i
$959$	6.16998	−	4.08211i	0.199239	−	0.131818i
$960$	−10.7839	+	1.61358i	−0.348048	+	0.0520781i
$961$	−72.3141			−2.33271
$962$	6.41203			0.206732
$963$	−5.46431	−	17.8507i	−0.176085	−	0.575231i
$964$			51.5298i			1.65966i
$965$	11.3845			0.366479
$966$	−6.62674	−	7.36002i	−0.213212	−	0.236805i
$967$	8.90190			0.286266			0.143133	−	0.989703i	$-0.454282\pi$
$967$	8.90190			0.286266			0.143133	+	0.989703i	$0.454282\pi$
$968$		−	17.1501i		−	0.551225i
$969$	−1.68240	−	11.2438i	−0.0540465	−	0.361203i
$970$	3.85234			0.123691
$971$	19.8965			0.638508			0.319254	−	0.947669i	$-0.396568\pi$
$971$	19.8965			0.638508			0.319254	+	0.947669i	$0.396568\pi$
$972$	−30.6693	+	28.1524i	−0.983719	+	0.902988i
$973$	−42.6009	+	28.1851i	−1.36572	+	0.903572i
$974$		−	40.1625i		−	1.28689i
$975$	1.38817	+	9.27744i	0.0444571	+	0.297116i
$976$		−	21.9933i		−	0.703989i
$977$			4.25193i			0.136031i	0.997684	+	0.0680157i	$0.0216668\pi$
$977$			4.25193i			0.136031i	−0.997684	+	0.0680157i	$0.978333\pi$
$978$	−10.2951	−	68.8044i	−0.329202	−	2.20012i
$979$			47.5506i			1.51972i
$980$	−3.78385	+	8.90462i	−0.120871	+	0.284448i
$981$	37.8678	−	11.5918i	1.20903	−	0.370096i
$982$	79.4258			2.53458
$983$	14.3131			0.456516			0.228258	−	0.973601i	$-0.426697\pi$
$983$	14.3131			0.456516			0.228258	+	0.973601i	$0.426697\pi$
$984$	3.48866	+	23.3154i	0.111214	+	0.743267i
$985$		−	3.63666i		−	0.115874i
$986$	9.03925			0.287868
$987$	−6.64638	−	7.38183i	−0.211556	−	0.234966i
$988$	11.1781			0.355623
$989$		−	10.0548i		−	0.319725i
$990$	15.3315	−	4.69314i	0.487267	−	0.149158i
$991$	52.1349			1.65612			0.828061	−	0.560639i	$-0.189444\pi$
$991$	52.1349			1.65612			0.828061	+	0.560639i	$0.189444\pi$
$992$	−77.9875			−2.47611
$993$	22.2421	−	3.32806i	0.705831	−	0.105613i
$994$	25.2999	+	38.2401i	0.802466	+	1.21290i
$995$			5.22599i			0.165675i
$996$	71.1444	−	10.6453i	2.25430	−	0.337308i
$997$			36.9505i			1.17024i	0.810949	+	0.585118i	$0.198952\pi$
$997$			36.9505i			1.17024i	−0.810949	+	0.585118i	$0.801048\pi$
$998$			11.8575i			0.375341i
$999$	−12.1549	+	5.80539i	−0.384565	+	0.183674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.d.461.10	yes	44
3.2	odd	2	inner	483.2.d.d.461.35	yes	44
7.6	odd	2	inner	483.2.d.d.461.9	✓	44
21.20	even	2	inner	483.2.d.d.461.36	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.d.461.9	✓	44	7.6	odd	2	inner
483.2.d.d.461.10	yes	44	1.1	even	1	trivial
483.2.d.d.461.35	yes	44	3.2	odd	2	inner
483.2.d.d.461.36	yes	44	21.20	even	2	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.16117i q^{2} +(1.71298 - 0.256312i) q^{3} -2.67065 q^{4} -0.517542 q^{5} +(-0.553932 - 3.70204i) q^{6} +(1.45986 + 2.20654i) q^{7} +1.44938i q^{8} +(2.86861 - 0.878114i) q^{9} +O(q^{10})\)	\(q-2.16117i q^{2} +(1.71298 - 0.256312i) q^{3} -2.67065 q^{4} -0.517542 q^{5} +(-0.553932 - 3.70204i) q^{6} +(1.45986 + 2.20654i) q^{7} +1.44938i q^{8} +(2.86861 - 0.878114i) q^{9} +1.11850i q^{10} -4.77836i q^{11} +(-4.57477 + 0.684518i) q^{12} -1.14450i q^{13} +(4.76870 - 3.15501i) q^{14} +(-0.886540 + 0.132652i) q^{15} -2.20894 q^{16} +1.79484 q^{17} +(-1.89775 - 6.19955i) q^{18} -3.65708i q^{19} +1.38217 q^{20} +(3.06628 + 3.40558i) q^{21} -10.3268 q^{22} -1.00000i q^{23} +(0.371493 + 2.48276i) q^{24} -4.73215 q^{25} -2.47346 q^{26} +(4.68880 - 2.23945i) q^{27} +(-3.89878 - 5.89288i) q^{28} +2.33033i q^{29} +(0.286683 + 1.91596i) q^{30} +10.1644i q^{31} +7.67265i q^{32} +(-1.22475 - 8.18523i) q^{33} -3.87896i q^{34} +(-0.755540 - 1.14198i) q^{35} +(-7.66104 + 2.34513i) q^{36} -2.59233 q^{37} -7.90357 q^{38} +(-0.293349 - 1.96051i) q^{39} -0.750116i q^{40} +9.39090 q^{41} +(7.36002 - 6.62674i) q^{42} +10.0548 q^{43} +12.7613i q^{44} +(-1.48463 + 0.454461i) q^{45} -2.16117 q^{46} -2.16757 q^{47} +(-3.78387 + 0.566176i) q^{48} +(-2.73761 + 6.44248i) q^{49} +10.2270i q^{50} +(3.07453 - 0.460039i) q^{51} +3.05657i q^{52} +0.121842i q^{53} +(-4.83983 - 10.1333i) q^{54} +2.47300i q^{55} +(-3.19811 + 2.11590i) q^{56} +(-0.937352 - 6.26451i) q^{57} +5.03623 q^{58} -1.52547 q^{59} +(2.36764 - 0.354267i) q^{60} +9.95652i q^{61} +21.9669 q^{62} +(6.12536 + 5.04777i) q^{63} +12.1640 q^{64} +0.592329i q^{65} +(-17.6897 + 2.64689i) q^{66} +4.00092 q^{67} -4.79339 q^{68} +(-0.256312 - 1.71298i) q^{69} +(-2.46800 + 1.63285i) q^{70} +8.01899i q^{71} +(1.27272 + 4.15771i) q^{72} +3.71123i q^{73} +5.60246i q^{74} +(-8.10608 + 1.21290i) q^{75} +9.76677i q^{76} +(10.5436 - 6.97574i) q^{77} +(-4.23700 + 0.633978i) q^{78} -14.9783 q^{79} +1.14322 q^{80} +(7.45783 - 5.03793i) q^{81} -20.2953i q^{82} -15.5515 q^{83} +(-8.18894 - 9.09509i) q^{84} -0.928907 q^{85} -21.7302i q^{86} +(0.597290 + 3.99181i) q^{87} +6.92566 q^{88} -9.95125 q^{89} +(0.982166 + 3.20853i) q^{90} +(2.52539 - 1.67082i) q^{91} +2.67065i q^{92} +(2.60524 + 17.4113i) q^{93} +4.68449i q^{94} +1.89269i q^{95} +(1.96659 + 13.1431i) q^{96} -3.44422i q^{97} +(13.9233 + 5.91643i) q^{98} +(-4.19594 - 13.7072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

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