LMFDB - Embedded newform 483.2.e.a.344.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(344,483)]

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, 0, 1]))

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

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

chi := DirichletCharacter("483.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.e (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			344.9
Character	$\chi$	$=$	483.344
Dual form			483.2.e.a.344.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98227i q^{2} +(0.949942 + 1.44831i) q^{3} -1.92939 q^{4} -4.16373 q^{5} +(2.87095 - 1.88304i) q^{6} -1.00000i q^{7} -0.139961i q^{8} +(-1.19522 + 2.75163i) q^{9} +O(q^{10})$	\(q-1.98227i q^{2} +(0.949942 + 1.44831i) q^{3} -1.92939 q^{4} -4.16373 q^{5} +(2.87095 - 1.88304i) q^{6} -1.00000i q^{7} -0.139961i q^{8} +(-1.19522 + 2.75163i) q^{9} +8.25364i q^{10} +0.579030 q^{11} +(-1.83281 - 2.79436i) q^{12} -3.14753 q^{13} -1.98227 q^{14} +(-3.95531 - 6.03039i) q^{15} -4.13623 q^{16} -6.11094 q^{17} +(5.45447 + 2.36925i) q^{18} +1.67193i q^{19} +8.03348 q^{20} +(1.44831 - 0.949942i) q^{21} -1.14779i q^{22} +(-0.215042 + 4.79101i) q^{23} +(0.202708 - 0.132955i) q^{24} +12.3367 q^{25} +6.23926i q^{26} +(-5.12061 + 0.882837i) q^{27} +1.92939i q^{28} -4.32062i q^{29} +(-11.9539 + 7.84049i) q^{30} -9.63196 q^{31} +7.91920i q^{32} +(0.550045 + 0.838616i) q^{33} +12.1135i q^{34} +4.16373i q^{35} +(2.30605 - 5.30897i) q^{36} -5.13864i q^{37} +3.31421 q^{38} +(-2.98997 - 4.55861i) q^{39} +0.582762i q^{40} -6.82316i q^{41} +(-1.88304 - 2.87095i) q^{42} +11.2876i q^{43} -1.11718 q^{44} +(4.97657 - 11.4570i) q^{45} +(9.49707 + 0.426271i) q^{46} -6.65641i q^{47} +(-3.92918 - 5.99055i) q^{48} -1.00000 q^{49} -24.4546i q^{50} +(-5.80505 - 8.85056i) q^{51} +6.07283 q^{52} +9.21609 q^{53} +(1.75002 + 10.1504i) q^{54} -2.41093 q^{55} -0.139961 q^{56} +(-2.42147 + 1.58823i) q^{57} -8.56464 q^{58} +0.0193612i q^{59} +(7.63134 + 11.6350i) q^{60} -8.32013i q^{61} +19.0931i q^{62} +(2.75163 + 1.19522i) q^{63} +7.42553 q^{64} +13.1055 q^{65} +(1.66236 - 1.09034i) q^{66} -4.78951i q^{67} +11.7904 q^{68} +(-7.14315 + 4.23973i) q^{69} +8.25364 q^{70} +1.09749i q^{71} +(0.385121 + 0.167284i) q^{72} +5.90547 q^{73} -10.1862 q^{74} +(11.7191 + 17.8674i) q^{75} -3.22580i q^{76} -0.579030i q^{77} +(-9.03640 + 5.92694i) q^{78} +1.77940i q^{79} +17.2222 q^{80} +(-6.14290 - 6.57759i) q^{81} -13.5253 q^{82} +16.1674 q^{83} +(-2.79436 + 1.83281i) q^{84} +25.4443 q^{85} +22.3751 q^{86} +(6.25761 - 4.10434i) q^{87} -0.0810418i q^{88} -6.78948 q^{89} +(-22.7109 - 9.86491i) q^{90} +3.14753i q^{91} +(0.414901 - 9.24374i) q^{92} +(-9.14981 - 13.9501i) q^{93} -13.1948 q^{94} -6.96146i q^{95} +(-11.4695 + 7.52278i) q^{96} +7.76547i q^{97} +1.98227i q^{98} +(-0.692067 + 1.59327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

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 $

$2$		−	1.98227i		−	1.40168i	−0.713320	−	0.700838i	$-0.752809\pi$
$2$		−	1.98227i		−	1.40168i	0.713320	−	0.700838i	$-0.247191\pi$
$3$	0.949942	+	1.44831i	0.548449	+	0.836184i
$3$	0.949942	+	1.44831i	0.548449	+	0.836184i
$4$	−1.92939			−0.964697
$5$	−4.16373			−1.86208			−0.931039	−	0.364919i	$-0.881097\pi$
$5$	−4.16373			−1.86208			−0.931039	+	0.364919i	$0.881097\pi$
$6$	2.87095	−	1.88304i	1.17206	−	0.768749i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	0.139961i		−	0.0494838i
$9$	−1.19522	+	2.75163i	−0.398406	+	0.917209i
$10$			8.25364i			2.61003i
$11$	0.579030			0.174584			0.0872920	−	0.996183i	$-0.472179\pi$
$11$	0.579030			0.174584			0.0872920	+	0.996183i	$0.472179\pi$
$12$	−1.83281	−	2.79436i	−0.529087	−	0.806664i
$13$	−3.14753			−0.872969			−0.436484	−	0.899712i	$-0.643777\pi$
$13$	−3.14753			−0.872969			−0.436484	+	0.899712i	$0.643777\pi$
$14$	−1.98227			−0.529784
$15$	−3.95531	−	6.03039i	−1.02126	−	1.55704i
$16$	−4.13623			−1.03406
$17$	−6.11094			−1.48212			−0.741061	−	0.671438i	$-0.765677\pi$
$17$	−6.11094			−1.48212			−0.741061	+	0.671438i	$0.765677\pi$
$18$	5.45447	+	2.36925i	1.28563	+	0.558437i
$19$			1.67193i			0.383566i	0.981437	+	0.191783i	$0.0614270\pi$
$19$			1.67193i			0.383566i	−0.981437	+	0.191783i	$0.938573\pi$
$20$	8.03348			1.79634
$21$	1.44831	−	0.949942i	0.316048	−	0.207294i
$22$		−	1.14779i		−	0.244710i
$23$	−0.215042	+	4.79101i	−0.0448394	+	0.998994i
$23$	−0.215042	+	4.79101i	−0.0448394	+	0.998994i
$24$	0.202708	−	0.132955i	0.0413775	−	0.0271394i
$25$	12.3367			2.46734
$26$			6.23926i			1.22362i
$27$	−5.12061	+	0.882837i	−0.985461	+	0.169902i
$28$			1.92939i			0.364621i
$29$		−	4.32062i		−	0.802320i	−0.916008	−	0.401160i	$-0.868607\pi$
$29$		−	4.32062i		−	0.802320i	0.916008	−	0.401160i	$-0.131393\pi$
$30$	−11.9539	+	7.84049i	−2.18247	+	1.43147i
$31$	−9.63196			−1.72995			−0.864975	−	0.501814i	$-0.832666\pi$
$31$	−9.63196			−1.72995			−0.864975	+	0.501814i	$0.832666\pi$
$32$			7.91920i			1.39993i
$33$	0.550045	+	0.838616i	0.0957506	+	0.145984i
$34$			12.1135i			2.07746i
$35$			4.16373i			0.703799i
$36$	2.30605	−	5.30897i	0.384341	−	0.884829i
$37$		−	5.13864i		−	0.844787i	−0.906413	−	0.422393i	$-0.861190\pi$
$37$		−	5.13864i		−	0.844787i	0.906413	−	0.422393i	$-0.138810\pi$
$38$	3.31421			0.537636
$39$	−2.98997	−	4.55861i	−0.478779	−	0.729962i
$40$			0.582762i			0.0921427i
$41$		−	6.82316i		−	1.06560i	−0.846242	−	0.532799i	$-0.821140\pi$
$41$		−	6.82316i		−	1.06560i	0.846242	−	0.532799i	$-0.178860\pi$
$42$	−1.88304	−	2.87095i	−0.290560	−	0.442997i
$43$			11.2876i			1.72135i	0.509157	+	0.860674i	$0.329957\pi$
$43$			11.2876i			1.72135i	−0.509157	+	0.860674i	$0.670043\pi$
$44$	−1.11718			−0.168421
$45$	4.97657	−	11.4570i	0.741864	−	1.70791i
$46$	9.49707	+	0.426271i	1.40027	+	0.0628503i
$47$		−	6.65641i		−	0.970937i	−0.874254	−	0.485469i	$-0.838649\pi$
$47$		−	6.65641i		−	0.970937i	0.874254	−	0.485469i	$-0.161351\pi$
$48$	−3.92918	−	5.99055i	−0.567128	−	0.864662i
$49$	−1.00000			−0.142857
$50$		−	24.4546i		−	3.45841i
$51$	−5.80505	−	8.85056i	−0.812869	−	1.23933i
$52$	6.07283			0.842150
$53$	9.21609			1.26593			0.632964	−	0.774181i	$-0.281838\pi$
$53$	9.21609			1.26593			0.632964	+	0.774181i	$0.281838\pi$
$54$	1.75002	+	10.1504i	0.238148	+	1.38130i
$55$	−2.41093			−0.325089
$56$	−0.139961			−0.0187031
$57$	−2.42147	+	1.58823i	−0.320732	+	0.210367i
$58$	−8.56464			−1.12459
$59$			0.0193612i			0.00252062i	0.999999	+	0.00126031i	$0.000401168\pi$
$59$			0.0193612i			0.00252062i	−0.999999	+	0.00126031i	$0.999599\pi$
$60$	7.63134	+	11.6350i	0.985202	+	1.50207i
$61$		−	8.32013i		−	1.06528i	−0.846341	−	0.532642i	$-0.821199\pi$
$61$		−	8.32013i		−	1.06528i	0.846341	−	0.532642i	$-0.178801\pi$
$62$			19.0931i			2.42483i
$63$	2.75163	+	1.19522i	0.346672	+	0.150583i
$64$	7.42553			0.928191
$65$	13.1055			1.62554
$66$	1.66236	−	1.09034i	0.204623	−	0.134211i
$67$		−	4.78951i		−	0.585132i	−0.956245	−	0.292566i	$-0.905491\pi$
$67$		−	4.78951i		−	0.585132i	0.956245	−	0.292566i	$-0.0945091\pi$
$68$	11.7904			1.42980
$69$	−7.14315	+	4.23973i	−0.859935	+	0.510404i
$70$	8.25364			0.986499
$71$			1.09749i			0.130248i	0.997877	+	0.0651239i	$0.0207443\pi$
$71$			1.09749i			0.130248i	−0.997877	+	0.0651239i	$0.979256\pi$
$72$	0.385121	+	0.167284i	0.0453870	+	0.0197147i
$73$	5.90547			0.691183			0.345592	−	0.938385i	$-0.387678\pi$
$73$	5.90547			0.691183			0.345592	+	0.938385i	$0.387678\pi$
$74$	−10.1862			−1.18412
$75$	11.7191	+	17.8674i	1.35321	+	2.06315i
$76$		−	3.22580i		−	0.370025i
$77$		−	0.579030i		−	0.0659866i
$78$	−9.03640	+	5.92694i	−1.02317	+	0.671093i
$79$			1.77940i			0.200198i	0.994977	+	0.100099i	$0.0319160\pi$
$79$			1.77940i			0.200198i	−0.994977	+	0.100099i	$0.968084\pi$
$80$	17.2222			1.92549
$81$	−6.14290	−	6.57759i	−0.682545	−	0.730844i
$82$	−13.5253			−1.49362
$83$	16.1674			1.77460			0.887299	−	0.461194i	$-0.152579\pi$
$83$	16.1674			1.77460			0.887299	+	0.461194i	$0.152579\pi$
$84$	−2.79436	+	1.83281i	−0.304890	+	0.199976i
$85$	25.4443			2.75983
$86$	22.3751			2.41277
$87$	6.25761	−	4.10434i	0.670887	−	0.440032i
$88$		−	0.0810418i		−	0.00863908i
$89$	−6.78948			−0.719684			−0.359842	−	0.933013i	$-0.617169\pi$
$89$	−6.78948			−0.719684			−0.359842	+	0.933013i	$0.617169\pi$
$90$	−22.7109	−	9.86491i	−2.39394	−	1.03985i
$91$			3.14753i			0.329951i
$92$	0.414901	−	9.24374i	0.0432564	−	0.963726i
$93$	−9.14981	−	13.9501i	−0.948791	−	1.44656i
$94$	−13.1948			−1.36094
$95$		−	6.96146i		−	0.714230i
$96$	−11.4695	+	7.52278i	−1.17060	+	0.767791i
$97$			7.76547i			0.788464i	0.919011	+	0.394232i	$0.128989\pi$
$97$			7.76547i			0.788464i	−0.919011	+	0.394232i	$0.871011\pi$
$98$			1.98227i			0.200239i
$99$	−0.692067	+	1.59327i	−0.0695554	+	0.160130i
$100$	−23.8023			−2.38023
$101$			3.66070i			0.364253i	0.983275	+	0.182127i	$0.0582981\pi$
$101$			3.66070i			0.364253i	−0.983275	+	0.182127i	$0.941702\pi$
$102$	−17.5442	+	11.5072i	−1.73713	+	1.13938i
$103$		−	4.23932i		−	0.417713i	−0.977946	−	0.208856i	$-0.933026\pi$
$103$		−	4.23932i		−	0.417713i	0.977946	−	0.208856i	$-0.0669742\pi$
$104$			0.440533i			0.0431978i
$105$	−6.03039	+	3.95531i	−0.588506	+	0.385998i
$106$		−	18.2688i		−	1.77442i
$107$	−11.9893			−1.15905			−0.579523	−	0.814956i	$-0.696761\pi$
$107$	−11.9893			−1.15905			−0.579523	+	0.814956i	$0.696761\pi$
$108$	9.87966	−	1.70334i	0.950671	−	0.163904i
$109$		−	9.31287i		−	0.892011i	−0.895030	−	0.446005i	$-0.852846\pi$
$109$		−	9.31287i		−	0.892011i	0.895030	−	0.446005i	$-0.147154\pi$
$110$			4.77911i			0.455670i
$111$	7.44235	−	4.88141i	0.706397	−	0.463323i
$112$			4.13623i			0.390837i
$113$	0.716417			0.0673949			0.0336974	−	0.999432i	$-0.489272\pi$
$113$	0.716417			0.0673949			0.0336974	+	0.999432i	$0.489272\pi$
$114$	3.14831	+	4.80001i	0.294866	+	0.449562i
$115$	0.895378	−	19.9485i	0.0834944	−	1.86021i
$116$			8.33618i			0.773995i
$117$	3.76199	−	8.66084i	0.347796	−	0.800695i
$118$	0.0383791			0.00353309
$119$			6.11094i			0.560189i
$120$	−0.844021	+	0.553590i	−0.0770482	+	0.0505356i
$121$	−10.6647			−0.969520
$122$	−16.4927			−1.49318
$123$	9.88206	−	6.48161i	0.891036	−	0.584427i
$124$	18.5838			1.66888
$125$	−30.5480			−2.73229
$126$	2.36925	−	5.45447i	0.211069	−	0.485923i
$127$	−6.41223			−0.568993			−0.284497	−	0.958677i	$-0.591826\pi$
$127$	−6.41223			−0.568993			−0.284497	+	0.958677i	$0.591826\pi$
$128$			1.11899i			0.0989059i
$129$	−16.3480	+	10.7226i	−1.43936	+	0.944072i
$130$		−	25.9786i		−	2.27848i
$131$			13.7688i			1.20298i	0.798879	+	0.601491i	$0.205427\pi$
$131$			13.7688i			1.20298i	−0.798879	+	0.601491i	$0.794573\pi$
$132$	−1.06125	−	1.61802i	−0.0923702	−	0.140831i
$133$	1.67193			0.144974
$134$	−9.49410			−0.820166
$135$	21.3208	−	3.67590i	1.83501	−	0.316371i
$136$			0.855296i			0.0733410i
$137$	−4.33891			−0.370698			−0.185349	−	0.982673i	$-0.559342\pi$
$137$	−4.33891			−0.370698			−0.185349	+	0.982673i	$0.559342\pi$
$138$	8.40430	+	14.1597i	0.715421	+	1.20535i
$139$	−2.17725			−0.184672			−0.0923361	−	0.995728i	$-0.529433\pi$
$139$	−2.17725			−0.184672			−0.0923361	+	0.995728i	$0.529433\pi$
$140$		−	8.03348i		−	0.678953i
$141$	9.64056	−	6.32321i	0.811882	−	0.532510i
$142$	2.17552			0.182565
$143$	−1.82252			−0.152406
$144$	4.94370	−	11.3814i	0.411975	−	0.948446i
$145$			17.9899i			1.49398i
$146$		−	11.7062i		−	0.968815i
$147$	−0.949942	−	1.44831i	−0.0783499	−	0.119455i
$148$			9.91445i			0.814963i
$149$	−15.0808			−1.23547			−0.617734	−	0.786387i	$-0.711949\pi$
$149$	−15.0808			−1.23547			−0.617734	+	0.786387i	$0.711949\pi$
$150$	35.4179	−	23.2305i	2.89186	−	1.89676i
$151$	−0.768746			−0.0625597			−0.0312798	−	0.999511i	$-0.509958\pi$
$151$	−0.768746			−0.0625597			−0.0312798	+	0.999511i	$0.509958\pi$
$152$	0.234005			0.0189803
$153$	7.30392	−	16.8150i	0.590487	−	1.35942i
$154$	−1.14779			−0.0924918
$155$	40.1049			3.22130
$156$	5.76884	+	8.79536i	0.461877	+	0.704192i
$157$			5.53736i			0.441930i	0.975282	+	0.220965i	$0.0709206\pi$
$157$			5.53736i			0.441930i	−0.975282	+	0.220965i	$0.929079\pi$
$158$	3.52725			0.280613
$159$	8.75476	+	13.3478i	0.694297	+	1.05855i
$160$		−	32.9734i		−	2.60678i
$161$	4.79101	+	0.215042i	0.377584	+	0.0169477i
$162$	−13.0386	+	12.1769i	−1.02441	+	0.956707i
$163$	−16.7725			−1.31372			−0.656861	−	0.754011i	$-0.728116\pi$
$163$	−16.7725			−1.31372			−0.656861	+	0.754011i	$0.728116\pi$
$164$			13.1646i			1.02798i
$165$	−2.29024	−	3.49177i	−0.178295	−	0.271834i
$166$		−	32.0481i		−	2.48741i
$167$			9.57186i			0.740693i	0.928894	+	0.370346i	$0.120761\pi$
$167$			9.57186i			0.740693i	−0.928894	+	0.370346i	$0.879239\pi$
$168$	−0.132955	−	0.202708i	−0.0102577	−	0.0156392i
$169$	−3.09304			−0.237926
$170$		−	50.4376i		−	3.86838i
$171$	−4.60052	−	1.99832i	−0.351810	−	0.152815i
$172$		−	21.7783i		−	1.66058i
$173$			6.77510i			0.515101i	0.966265	+	0.257551i	$0.0829154\pi$
$173$			6.77510i			0.515101i	−0.966265	+	0.257551i	$0.917085\pi$
$174$	−8.13591	−	12.4043i	−0.616782	−	0.940366i
$175$		−	12.3367i		−	0.932565i
$176$	−2.39500			−0.180530
$177$	−0.0280411	+	0.0183920i	−0.00210770	+	0.00138243i
$178$			13.4586i			1.00876i
$179$		−	0.228288i		−	0.0170630i	−0.999964	−	0.00853152i	$-0.997284\pi$
$179$		−	0.228288i		−	0.0170630i	0.999964	−	0.00853152i	$-0.00271570\pi$
$180$	−9.60177	+	22.1051i	−0.715673	+	1.64762i
$181$			7.53346i			0.559958i	0.960006	+	0.279979i	$0.0903275\pi$
$181$			7.53346i			0.559958i	−0.960006	+	0.279979i	$0.909673\pi$
$182$	6.23926			0.462485
$183$	12.0501	−	7.90364i	0.890772	−	0.584254i
$184$	0.670556	+	0.0300976i	0.0494340	+	0.00221882i
$185$			21.3959i			1.57306i
$186$	−27.6528	+	18.1374i	−2.02760	+	1.32990i
$187$	−3.53842			−0.258755
$188$			12.8428i			0.936660i
$189$	0.882837	+	5.12061i	0.0642169	+	0.372469i
$190$	−13.7995			−1.00112
$191$	−17.3704			−1.25687			−0.628437	−	0.777860i	$-0.716305\pi$
$191$	−17.3704			−1.25687			−0.628437	+	0.777860i	$0.716305\pi$
$192$	7.05382	+	10.7545i	0.509066	+	0.776138i
$193$	−6.97175			−0.501838			−0.250919	−	0.968008i	$-0.580733\pi$
$193$	−6.97175			−0.501838			−0.250919	+	0.968008i	$0.580733\pi$
$194$	15.3933			1.10517
$195$	12.4495	+	18.9808i	0.891524	+	1.35925i
$196$	1.92939			0.137814
$197$			3.29714i			0.234911i	0.993078	+	0.117456i	$0.0374738\pi$
$197$			3.29714i			0.234911i	−0.993078	+	0.117456i	$0.962526\pi$
$198$	3.15830	+	1.37186i	0.224451	+	0.0974942i
$199$			8.13107i			0.576396i	0.957571	+	0.288198i	$0.0930562\pi$
$199$			8.13107i			0.576396i	−0.957571	+	0.288198i	$0.906944\pi$
$200$		−	1.72666i		−	0.122093i
$201$	6.93671	−	4.54976i	0.489278	−	0.320915i
$202$	7.25650			0.510565
$203$	−4.32062			−0.303248
$204$	11.2002	+	17.0762i	0.784172	+	1.19557i
$205$			28.4098i			1.98423i
$206$	−8.40348			−0.585498
$207$	−12.9260	−	6.31802i	−0.898422	−	0.439133i
$208$	13.0189			0.902699
$209$			0.968095i			0.0669646i
$210$	7.84049	+	11.9539i	0.541045	+	0.824894i
$211$	3.69474			0.254357			0.127178	−	0.991880i	$-0.459408\pi$
$211$	3.69474			0.254357			0.127178	+	0.991880i	$0.459408\pi$
$212$	−17.7815			−1.22124
$213$	−1.58951	+	1.04255i	−0.108911	+	0.0714344i
$214$			23.7660i			1.62461i
$215$		−	46.9987i		−	3.20528i
$216$	0.123563	+	0.716687i	0.00840739	+	0.0487643i
$217$			9.63196i			0.653860i
$218$	−18.4606			−1.25031
$219$	5.60986	+	8.55297i	0.379079	+	0.577956i
$220$	4.65163			0.313613
$221$	19.2344			1.29385
$222$	−9.67627	−	14.7527i	−0.649429	−	0.990140i
$223$	10.9651			0.734280			0.367140	−	0.930166i	$-0.380337\pi$
$223$	10.9651			0.734280			0.367140	+	0.930166i	$0.380337\pi$
$224$	7.91920			0.529124
$225$	−14.7450	+	33.9459i	−0.983002	+	2.26306i
$226$		−	1.42013i		−	0.0944658i
$227$	15.7877			1.04787			0.523934	−	0.851759i	$-0.324464\pi$
$227$	15.7877			1.04787			0.523934	+	0.851759i	$0.324464\pi$
$228$	4.67197	−	3.06433i	0.309409	−	0.202940i
$229$		−	18.8645i		−	1.24660i	−0.781982	−	0.623300i	$-0.785791\pi$
$229$		−	18.8645i		−	1.24660i	0.781982	−	0.623300i	$-0.214209\pi$
$230$	−39.5433	−	1.77488i	−2.60741	−	0.117032i
$231$	0.838616	−	0.550045i	0.0551769	−	0.0361903i
$232$	−0.604720			−0.0397018
$233$		−	9.43800i		−	0.618304i	−0.951013	−	0.309152i	$-0.899955\pi$
$233$		−	9.43800i		−	0.618304i	0.951013	−	0.309152i	$-0.100045\pi$
$234$	−17.1681	−	7.45728i	−1.12231	−	0.487498i
$235$			27.7155i			1.80796i
$236$		−	0.0373554i		−	0.00243163i
$237$	−2.57713	+	1.69033i	−0.167402	+	0.109799i
$238$	12.1135			0.785204
$239$			21.1107i			1.36554i	0.730635	+	0.682768i	$0.239224\pi$
$239$			21.1107i			1.36554i	−0.730635	+	0.682768i	$0.760776\pi$
$240$	16.3601	+	24.9431i	1.05604	+	1.61007i
$241$		−	1.43388i		−	0.0923642i	−0.998933	−	0.0461821i	$-0.985295\pi$
$241$		−	1.43388i		−	0.0923642i	0.998933	−	0.0461821i	$-0.0147055\pi$
$242$			21.1404i			1.35895i
$243$	3.69101	−	15.1452i	0.236778	−	0.971564i
$244$			16.0528i			1.02768i
$245$	4.16373			0.266011
$246$	−12.8483	−	19.5889i	−0.819177	−	1.24894i
$247$		−	5.26244i		−	0.334841i
$248$			1.34810i			0.0856045i
$249$	15.3581	+	23.4154i	0.973278	+	1.48389i
$250$			60.5543i			3.82979i
$251$	0.139399			0.00879882			0.00439941	−	0.999990i	$-0.498600\pi$
$251$	0.139399			0.00879882			0.00439941	+	0.999990i	$0.498600\pi$
$252$	−5.30897	−	2.30605i	−0.334434	−	0.145267i
$253$	−0.124516	+	2.77414i	−0.00782824	+	0.174408i
$254$			12.7108i			0.797544i
$255$	24.1707	+	36.8514i	1.51363	+	2.30772i
$256$	17.0692			1.06683
$257$		−	11.1455i		−	0.695239i	−0.937636	−	0.347620i	$-0.886990\pi$
$257$		−	11.1455i		−	0.695239i	0.937636	−	0.347620i	$-0.113010\pi$
$258$	21.2551	+	32.4062i	1.32328	+	2.01752i
$259$	−5.13864			−0.319299
$260$	−25.2856			−1.56815
$261$	11.8887	+	5.16409i	0.735895	+	0.319649i
$262$	27.2934			1.68619
$263$	−19.7454			−1.21755			−0.608776	−	0.793342i	$-0.708339\pi$
$263$	−19.7454			−1.21755			−0.608776	+	0.793342i	$0.708339\pi$
$264$	0.117374	−	0.0769850i	0.00722386	−	0.00473810i
$265$	−38.3733			−2.35726
$266$		−	3.31421i		−	0.203207i
$267$	−6.44962	−	9.83329i	−0.394710	−	0.601788i
$268$			9.24085i			0.564475i
$269$		−	20.0368i		−	1.22166i	−0.791760	−	0.610832i	$-0.790835\pi$
$269$		−	20.0368i		−	1.22166i	0.791760	−	0.610832i	$-0.209165\pi$
$270$	−7.28662	−	42.2636i	−0.443449	−	2.57208i
$271$	−10.2763			−0.624244			−0.312122	−	0.950042i	$-0.601040\pi$
$271$	−10.2763			−0.624244			−0.312122	+	0.950042i	$0.601040\pi$
$272$	25.2763			1.53260
$273$	−4.55861	+	2.98997i	−0.275900	+	0.180962i
$274$			8.60088i			0.519598i
$275$	7.14330			0.430757
$276$	13.7820	−	8.18011i	0.829576	−	0.492385i
$277$	17.9468			1.07832			0.539159	−	0.842204i	$-0.318742\pi$
$277$	17.9468			1.07832			0.539159	+	0.842204i	$0.318742\pi$
$278$			4.31590i			0.258851i
$279$	11.5123	−	26.5036i	0.689223	−	1.58673i
$280$	0.582762			0.0348267
$281$	−18.7854			−1.12064			−0.560322	−	0.828275i	$-0.689323\pi$
$281$	−18.7854			−1.12064			−0.560322	+	0.828275i	$0.689323\pi$
$282$	−12.5343	−	19.1102i	−0.746407	−	1.13800i
$283$			7.53749i			0.448057i	0.974583	+	0.224029i	$0.0719209\pi$
$283$			7.53749i			0.448057i	−0.974583	+	0.224029i	$0.928079\pi$
$284$		−	2.11749i		−	0.125650i
$285$	10.0824	−	6.61298i	0.597228	−	0.391719i
$286$			3.61272i			0.213624i
$287$	−6.82316			−0.402758
$288$	−21.7907	−	9.46517i	−1.28403	−	0.557741i
$289$	20.3436			1.19669
$290$	35.6609			2.09408
$291$	−11.2468	+	7.37675i	−0.659301	+	0.432433i
$292$	−11.3940			−0.666782
$293$	−5.44228			−0.317941			−0.158971	−	0.987283i	$-0.550818\pi$
$293$	−5.44228			−0.317941			−0.158971	+	0.987283i	$0.550818\pi$
$294$	−2.87095	+	1.88304i	−0.167437	+	0.109821i
$295$		−	0.0806149i		−	0.00469358i
$296$	−0.719210			−0.0418032
$297$	−2.96498	+	0.511189i	−0.172046	+	0.0296622i
$298$			29.8943i			1.73173i
$299$	0.676852	−	15.0799i	0.0391433	−	0.872091i
$300$	−22.6108	−	34.4732i	−1.30544	−	1.99031i
$301$	11.2876			0.650608
$302$			1.52386i			0.0876884i
$303$	−5.30184	+	3.47746i	−0.304583	+	0.199775i
$304$		−	6.91547i		−	0.396629i
$305$			34.6428i			1.98364i
$306$	−33.3319	−	14.4783i	−1.90546	−	0.827671i
$307$	17.0891			0.975326			0.487663	−	0.873032i	$-0.337850\pi$
$307$	17.0891			0.975326			0.487663	+	0.873032i	$0.337850\pi$
$308$			1.11718i			0.0636570i
$309$	6.13987	−	4.02711i	0.349285	−	0.229094i
$310$		−	79.4987i		−	4.51523i
$311$		−	4.36850i		−	0.247715i	−0.992300	−	0.123857i	$-0.960473\pi$
$311$		−	4.36850i		−	0.247715i	0.992300	−	0.123857i	$-0.0395265\pi$
$312$	−0.638029	+	0.418481i	−0.0361213	+	0.0236918i
$313$		−	19.7910i		−	1.11865i	−0.828948	−	0.559326i	$-0.811060\pi$
$313$		−	19.7910i		−	1.11865i	0.828948	−	0.559326i	$-0.188940\pi$
$314$	10.9765			0.619442
$315$	−11.4570	−	4.97657i	−0.645531	−	0.280398i
$316$		−	3.43316i		−	0.193130i
$317$		−	21.5965i		−	1.21298i	−0.795091	−	0.606490i	$-0.792577\pi$
$317$		−	21.5965i		−	1.21298i	0.795091	−	0.606490i	$-0.207423\pi$
$318$	26.4589	−	17.3543i	1.48374	−	0.973180i
$319$		−	2.50177i		−	0.140072i
$320$	−30.9179			−1.72836
$321$	−11.3891	−	17.3642i	−0.635678	−	0.969175i
$322$	0.426271	−	9.49707i	0.0237552	−	0.529251i
$323$		−	10.2170i		−	0.568492i
$324$	11.8521	+	12.6908i	0.658449	+	0.705043i
$325$	−38.8301			−2.15391
$326$			33.2476i			1.84141i
$327$	13.4879	−	8.84669i	0.745885	−	0.489223i
$328$	−0.954978			−0.0527298
$329$	−6.65641			−0.366980
$330$	−6.92164	+	4.53988i	−0.381024	+	0.249912i
$331$	8.32855			0.457778			0.228889	−	0.973452i	$-0.426491\pi$
$331$	8.32855			0.457778			0.228889	+	0.973452i	$0.426491\pi$
$332$	−31.1932			−1.71195
$333$	14.1396	+	6.14180i	0.774846	+	0.336568i
$334$	18.9740			1.03821
$335$			19.9422i			1.08956i
$336$	−5.99055	+	3.92918i	−0.326811	+	0.214354i
$337$			25.5472i			1.39165i	0.718213	+	0.695823i	$0.244960\pi$
$337$			25.5472i			1.39165i	−0.718213	+	0.695823i	$0.755040\pi$
$338$			6.13123i			0.333495i
$339$	0.680555	+	1.03760i	0.0369627	+	0.0563545i
$340$	−49.0922			−2.66240
$341$	−5.57719			−0.302022
$342$	−3.96121	+	9.11947i	−0.214197	+	0.493124i
$343$			1.00000i			0.0539949i
$344$	1.57983			0.0851788
$345$	29.7422	−	17.6531i	1.60127	−	0.950412i
$346$	13.4301			0.722005
$347$		−	16.2579i		−	0.872767i	−0.899761	−	0.436384i	$-0.856259\pi$
$347$		−	16.2579i		−	0.872767i	0.899761	−	0.436384i	$-0.143741\pi$
$348$	−12.0734	+	7.91889i	−0.647202	+	0.424497i
$349$	−3.48227			−0.186401			−0.0932007	−	0.995647i	$-0.529710\pi$
$349$	−3.48227			−0.186401			−0.0932007	+	0.995647i	$0.529710\pi$
$350$	−24.4546			−1.30715
$351$	16.1173	−	2.77876i	0.860276	−	0.148319i
$352$			4.58545i			0.244405i
$353$			34.3329i			1.82735i	0.406441	+	0.913677i	$0.366770\pi$
$353$			34.3329i			1.82735i	−0.406441	+	0.913677i	$0.633230\pi$
$354$	0.0364580	+	0.0555850i	0.00193772	+	0.00295431i
$355$		−	4.56965i		−	0.242532i
$356$	13.0996			0.694277
$357$	−8.85056	+	5.80505i	−0.468421	+	0.307236i
$358$	−0.452528			−0.0239168
$359$	−22.3933			−1.18188			−0.590938	−	0.806717i	$-0.701242\pi$
$359$	−22.3933			−1.18188			−0.590938	+	0.806717i	$0.701242\pi$
$360$	−1.60354	−	0.696528i	−0.0845141	−	0.0367102i
$361$	16.2047			0.852877
$362$	14.9334			0.784880
$363$	−10.1309	−	15.4459i	−0.531733	−	0.810697i
$364$		−	6.07283i		−	0.318303i
$365$	−24.5888			−1.28704
$366$	−15.6671	−	23.8866i	−0.818935	−	1.24857i
$367$		−	20.1499i		−	1.05182i	−0.850541	−	0.525908i	$-0.823725\pi$
$367$		−	20.1499i		−	1.05182i	0.850541	−	0.525908i	$-0.176275\pi$
$368$	0.889463	−	19.8167i	0.0463664	−	1.03302i
$369$	18.7748	+	8.15517i	0.977376	+	0.424541i
$370$	42.4125			2.20492
$371$		−	9.21609i		−	0.478476i
$372$	17.6536	+	26.9152i	0.915295	+	1.39549i
$373$			26.6915i			1.38204i	0.722838	+	0.691018i	$0.242837\pi$
$373$			26.6915i			1.38204i	−0.722838	+	0.691018i	$0.757163\pi$
$374$			7.01410i			0.362691i
$375$	−29.0188	−	44.2430i	−1.49852	−	2.28470i
$376$	−0.931640			−0.0480457
$377$			13.5993i			0.700400i
$378$	10.1504	−	1.75002i	0.522081	−	0.0900113i
$379$		−	12.0170i		−	0.617272i	−0.951180	−	0.308636i	$-0.900128\pi$
$379$		−	12.0170i		−	0.617272i	0.951180	−	0.308636i	$-0.0998725\pi$
$380$			13.4314i			0.689016i
$381$	−6.09125	−	9.28691i	−0.312064	−	0.475783i
$382$			34.4327i			1.76173i
$383$	27.4752			1.40392			0.701959	−	0.712217i	$-0.252309\pi$
$383$	27.4752			1.40392			0.701959	+	0.712217i	$0.252309\pi$
$384$	−1.62065	+	1.06298i	−0.0827035	+	0.0542449i
$385$			2.41093i			0.122872i
$386$			13.8199i			0.703414i
$387$	−31.0594	−	13.4912i	−1.57884	−	0.685796i
$388$		−	14.9826i		−	0.760629i
$389$	−34.0199			−1.72488			−0.862438	−	0.506163i	$-0.831063\pi$
$389$	−34.0199			−1.72488			−0.862438	+	0.506163i	$0.831063\pi$
$390$	37.6252	−	24.6782i	1.90522	−	1.24963i
$391$	1.31411	−	29.2776i	0.0664574	−	1.48063i
$392$			0.139961i			0.00706911i
$393$	−19.9415	+	13.0795i	−1.00591	+	0.659775i
$394$	6.53581			0.329269
$395$		−	7.40895i		−	0.372784i
$396$	1.33527	−	3.07405i	0.0670999	−	0.154477i
$397$	10.8159			0.542835			0.271418	−	0.962462i	$-0.412508\pi$
$397$	10.8159			0.542835			0.271418	+	0.962462i	$0.412508\pi$
$398$	16.1180			0.807921
$399$	1.58823	+	2.42147i	0.0795111	+	0.121225i
$400$	−51.0273			−2.55137
$401$	−0.358946			−0.0179249			−0.00896245	−	0.999960i	$-0.502853\pi$
$401$	−0.358946			−0.0179249			−0.00896245	+	0.999960i	$0.502853\pi$
$402$	−9.01885	−	13.7504i	−0.449819	−	0.685809i
$403$	30.3169			1.51019
$404$		−	7.06293i		−	0.351394i
$405$	25.5774	+	27.3873i	1.27095	+	1.36089i
$406$			8.56464i			0.425056i
$407$		−	2.97542i		−	0.147486i
$408$	−1.23874	+	0.812482i	−0.0613266	+	0.0402238i
$409$	−11.8041			−0.583676			−0.291838	−	0.956468i	$-0.594267\pi$
$409$	−11.8041			−0.583676			−0.291838	+	0.956468i	$0.594267\pi$
$410$	56.3159			2.78124
$411$	−4.12171	−	6.28409i	−0.203309	−	0.309971i
$412$			8.17932i			0.402966i
$413$	0.0193612			0.000952703
$414$	−12.5240	+	25.6229i	−0.615522	+	1.25930i
$415$	−67.3166			−3.30444
$416$		−	24.9259i		−	1.22209i
$417$	−2.06826	−	3.15334i	−0.101283	−	0.154420i
$418$	1.91903			0.0938626
$419$	28.2455			1.37988			0.689942	−	0.723864i	$-0.257636\pi$
$419$	28.2455			1.37988			0.689942	+	0.723864i	$0.257636\pi$
$420$	11.6350	−	7.63134i	0.567729	−	0.372371i
$421$		−	37.1258i		−	1.80940i	−0.426048	−	0.904701i	$-0.640094\pi$
$421$		−	37.1258i		−	1.80940i	0.426048	−	0.904701i	$-0.359906\pi$
$422$		−	7.32398i		−	0.356526i
$423$	18.3160	+	7.95587i	0.890552	+	0.386828i
$424$		−	1.28990i		−	0.0626429i
$425$	−75.3887			−3.65689
$426$	2.06662	+	3.15083i	0.100128	+	0.152658i
$427$	−8.32013			−0.402639
$428$	23.1320			1.11813
$429$	−1.73128	−	2.63957i	−0.0835872	−	0.127440i
$430$	−93.1641			−4.49277
$431$	−1.87270			−0.0902048			−0.0451024	−	0.998982i	$-0.514361\pi$
$431$	−1.87270			−0.0902048			−0.0451024	+	0.998982i	$0.514361\pi$
$432$	21.1800	−	3.65161i	1.01902	−	0.175688i
$433$			32.6296i			1.56808i	0.620712	+	0.784038i	$0.286843\pi$
$433$			32.6296i			1.56808i	−0.620712	+	0.784038i	$0.713157\pi$
$434$	19.0931			0.916500
$435$	−26.0550	+	17.0894i	−1.24924	+	0.819374i
$436$			17.9682i			0.860520i
$437$	−8.01021	−	0.359534i	−0.383180	−	0.0171989i
$438$	16.9543	−	11.1203i	0.810107	−	0.531346i
$439$	1.74530			0.0832988			0.0416494	−	0.999132i	$-0.486739\pi$
$439$	1.74530			0.0832988			0.0416494	+	0.999132i	$0.486739\pi$
$440$			0.337436i			0.0160866i
$441$	1.19522	−	2.75163i	0.0569152	−	0.131030i
$442$		−	38.1278i		−	1.81355i
$443$		−	34.8056i		−	1.65366i	−0.562450	−	0.826832i	$-0.690141\pi$
$443$		−	34.8056i		−	1.65366i	0.562450	−	0.826832i	$-0.309859\pi$
$444$	−14.3592	+	9.41816i	−0.681459	+	0.446966i
$445$	28.2696			1.34011
$446$		−	21.7359i		−	1.02922i
$447$	−14.3259	−	21.8417i	−0.677592	−	1.03308i
$448$		−	7.42553i		−	0.350823i
$449$		−	14.1189i		−	0.666314i	−0.942871	−	0.333157i	$-0.891886\pi$
$449$		−	14.1189i		−	0.666314i	0.942871	−	0.333157i	$-0.108114\pi$
$450$	67.2900	+	29.2286i	3.17208	+	1.37785i
$451$		−	3.95081i		−	0.186036i
$452$	−1.38225			−0.0650156
$453$	−0.730264	−	1.11338i	−0.0343108	−	0.0523114i
$454$		−	31.2955i		−	1.46877i
$455$		−	13.1055i		−	0.614395i
$456$	0.222291	+	0.338912i	0.0104097	+	0.0158710i
$457$			24.8794i			1.16381i	0.813258	+	0.581904i	$0.197692\pi$
$457$			24.8794i			1.16381i	−0.813258	+	0.581904i	$0.802308\pi$
$458$	−37.3945			−1.74733
$459$	31.2917	−	5.39497i	1.46057	−	0.251815i
$460$	−1.72754	+	38.4885i	−0.0805468	+	1.79453i
$461$		−	17.4239i		−	0.811513i	−0.913981	−	0.405757i	$-0.867008\pi$
$461$		−	17.4239i		−	0.811513i	0.913981	−	0.405757i	$-0.132992\pi$
$462$	−1.09034	−	1.66236i	−0.0507271	−	0.0773402i
$463$	13.9472			0.648179			0.324090	−	0.946026i	$-0.394942\pi$
$463$	13.9472			0.648179			0.324090	+	0.946026i	$0.394942\pi$
$464$			17.8711i			0.829644i
$465$	38.0974	+	58.0844i	1.76672	+	2.69360i
$466$	−18.7087			−0.866662
$467$	15.5857			0.721220			0.360610	−	0.932717i	$-0.382569\pi$
$467$	15.5857			0.721220			0.360610	+	0.932717i	$0.382569\pi$
$468$	−7.25836	+	16.7102i	−0.335518	+	0.772427i
$469$	−4.78951			−0.221159
$470$	54.9396			2.53418
$471$	−8.01983	+	5.26018i	−0.369534	+	0.242376i
$472$	0.00270982			0.000124730
$473$			6.53588i			0.300520i
$474$	3.35068	+	5.10856i	0.153902	+	0.234644i
$475$			20.6260i			0.946386i
$476$		−	11.7904i		−	0.540413i
$477$	−11.0152	+	25.3592i	−0.504353	+	1.16112i
$478$	41.8471			1.91404
$479$	−3.59019			−0.164040			−0.0820199	−	0.996631i	$-0.526137\pi$
$479$	−3.59019			−0.164040			−0.0820199	+	0.996631i	$0.526137\pi$
$480$	47.7558	−	31.3229i	2.17975	−	1.42969i
$481$			16.1740i			0.737472i
$482$	−2.84233			−0.129465
$483$	4.23973	+	7.14315i	0.192915	+	0.325025i
$484$	20.5764			0.935293
$485$		−	32.3333i		−	1.46818i
$486$	−30.0218	−	7.31657i	−1.36182	−	0.331886i
$487$	8.45021			0.382916			0.191458	−	0.981501i	$-0.438678\pi$
$487$	8.45021			0.382916			0.191458	+	0.981501i	$0.438678\pi$
$488$	−1.16450			−0.0527142
$489$	−15.9329	−	24.2918i	−0.720510	−	1.09851i
$490$		−	8.25364i		−	0.372862i
$491$			30.1103i			1.35886i	0.733741	+	0.679430i	$0.237773\pi$
$491$			30.1103i			1.35886i	−0.733741	+	0.679430i	$0.762227\pi$
$492$	−19.0664	+	12.5056i	−0.859579	+	0.563795i
$493$			26.4031i			1.18914i
$494$	−10.4316			−0.469339
$495$	2.88158	−	6.63397i	0.129518	−	0.298175i
$496$	39.8400			1.78887
$497$	1.09749			0.0492291
$498$	46.4156	−	30.4438i	2.07993	−	1.36422i
$499$	19.6750			0.880774			0.440387	−	0.897808i	$-0.354841\pi$
$499$	19.6750			0.880774			0.440387	+	0.897808i	$0.354841\pi$
$500$	58.9390			2.63583
$501$	−13.8630	+	9.09272i	−0.619355	+	0.406233i
$502$		−	0.276327i		−	0.0123331i
$503$	−34.3183			−1.53018			−0.765088	−	0.643925i	$-0.777305\pi$
$503$	−34.3183			−1.53018			−0.765088	+	0.643925i	$0.777305\pi$
$504$	0.167284	−	0.385121i	0.00745144	−	0.0171547i
$505$		−	15.2422i		−	0.678268i
$506$	5.49909	+	0.246824i	0.244464	+	0.0109727i
$507$	−2.93821	−	4.47968i	−0.130490	−	0.198950i
$508$	12.3717			0.548906
$509$			24.9543i			1.10608i	0.833155	+	0.553039i	$0.186532\pi$
$509$			24.9543i			1.10608i	−0.833155	+	0.553039i	$0.813468\pi$
$510$	73.0493	−	47.9128i	3.23468	−	2.12161i
$511$		−	5.90547i		−	0.261243i
$512$		−	31.5978i		−	1.39644i
$513$	−1.47604	−	8.56128i	−0.0651687	−	0.377990i
$514$	−22.0934			−0.974500
$515$			17.6514i			0.777814i
$516$	31.5418	−	20.6881i	1.38855	−	0.910744i
$517$		−	3.85426i		−	0.169510i
$518$			10.1862i			0.447554i
$519$	−9.81246	+	6.43595i	−0.430719	+	0.282507i
$520$		−	1.83426i		−	0.0804377i
$521$	−18.2868			−0.801161			−0.400580	−	0.916262i	$-0.631191\pi$
$521$	−18.2868			−0.801161			−0.400580	+	0.916262i	$0.631191\pi$
$522$	10.2366	−	23.5667i	0.448045	−	1.03149i
$523$			21.6760i			0.947826i	0.880572	+	0.473913i	$0.157159\pi$
$523$			21.6760i			0.947826i	−0.880572	+	0.473913i	$0.842841\pi$
$524$		−	26.5654i		−	1.16051i
$525$	17.8674	−	11.7191i	0.779796	−	0.511465i
$526$			39.1407i			1.70661i
$527$	58.8604			2.56400
$528$	−2.27511	−	3.46871i	−0.0990115	−	0.150956i
$529$	−22.9075	−	2.06054i	−0.995979	−	0.0895885i
$530$			76.0663i			3.30411i
$531$	−0.0532748	−	0.0231409i	−0.00231193	−	0.00100423i
$532$	−3.22580			−0.139856
$533$			21.4761i			0.930234i
$534$	−19.4922	+	12.7849i	−0.843512	+	0.553256i
$535$	49.9201			2.15823
$536$	−0.670346			−0.0289545
$537$	0.330632	−	0.216860i	0.0142678	−	0.00935821i
$538$	−39.7183			−1.71238
$539$	−0.579030			−0.0249406
$540$	−41.1363	+	7.09225i	−1.77022	+	0.305202i
$541$	5.03442			0.216446			0.108223	−	0.994127i	$-0.465484\pi$
$541$	5.03442			0.216446			0.108223	+	0.994127i	$0.465484\pi$
$542$			20.3705i			0.874987i
$543$	−10.9108	+	7.15636i	−0.468228	+	0.307109i
$544$		−	48.3938i		−	2.07487i
$545$			38.7763i			1.66099i
$546$	5.92694	+	9.03640i	0.253649	+	0.386722i
$547$	−2.62173			−0.112097			−0.0560485	−	0.998428i	$-0.517850\pi$
$547$	−2.62173			−0.112097			−0.0560485	+	0.998428i	$0.517850\pi$
$548$	8.37146			0.357611
$549$	22.8939	+	9.94437i	0.977087	+	0.424415i
$550$		−	14.1600i		−	0.603783i
$551$	7.22376			0.307743
$552$	0.593399	+	0.999765i	0.0252567	+	0.0425528i
$553$	1.77940			0.0756678
$554$		−	35.5754i		−	1.51145i
$555$	−30.9880	+	20.3249i	−1.31537	+	0.862743i
$556$	4.20078			0.178153
$557$	18.5001			0.783873			0.391937	−	0.919992i	$-0.371805\pi$
$557$	18.5001			0.783873			0.391937	+	0.919992i	$0.371805\pi$
$558$	−52.5372	−	22.8205i	−2.22408	−	0.966068i
$559$		−	35.5282i		−	1.50268i
$560$		−	17.2222i		−	0.727769i
$561$	−3.36129	−	5.12474i	−0.141914	−	0.216367i
$562$			37.2378i			1.57078i
$563$	−36.2418			−1.52741			−0.763704	−	0.645566i	$-0.776621\pi$
$563$	−36.2418			−1.52741			−0.763704	+	0.645566i	$0.776621\pi$
$564$	−18.6004	+	12.2000i	−0.783220	+	0.513711i
$565$	−2.98297			−0.125495
$566$	14.9413			0.628031
$567$	−6.57759	+	6.14290i	−0.276233	+	0.257978i
$568$	0.153606			0.00644516
$569$	12.6583			0.530664			0.265332	−	0.964157i	$-0.414518\pi$
$569$	12.6583			0.530664			0.265332	+	0.964157i	$0.414518\pi$
$570$	−13.1087	−	19.9860i	−0.549064	−	0.837120i
$571$		−	34.6058i		−	1.44821i	−0.689691	−	0.724104i	$-0.742254\pi$
$571$		−	34.6058i		−	1.44821i	0.689691	−	0.724104i	$-0.257746\pi$
$572$	3.51635			0.147026
$573$	−16.5008	−	25.1577i	−0.689332	−	1.05098i
$574$			13.5253i			0.564537i
$575$	−2.65290	+	59.1051i	−0.110634	+	2.46485i
$576$	−8.87513	+	20.4323i	−0.369797	+	0.851345i
$577$	−27.6061			−1.14926			−0.574628	−	0.818415i	$-0.694853\pi$
$577$	−27.6061			−1.14926			−0.574628	+	0.818415i	$0.694853\pi$
$578$		−	40.3266i		−	1.67737i
$579$	−6.62277	−	10.0973i	−0.275233	−	0.419629i
$580$		−	34.7096i		−	1.44124i
$581$		−	16.1674i		−	0.670735i
$582$	14.6227	+	22.2942i	0.606131	+	0.924126i
$583$	5.33639			0.221011
$584$		−	0.826537i		−	0.0342024i
$585$	−15.6639	+	36.0614i	−0.647624	+	1.49096i
$586$			10.7881i			0.445651i
$587$			30.2582i			1.24889i	0.781069	+	0.624445i	$0.214675\pi$
$587$			30.2582i			1.24889i	−0.781069	+	0.624445i	$0.785325\pi$
$588$	1.83281	+	2.79436i	0.0755839	+	0.115238i
$589$		−	16.1039i		−	0.663551i
$590$	−0.159801			−0.00657888
$591$	−4.77528	+	3.13209i	−0.196429	+	0.128837i
$592$			21.2546i			0.873558i
$593$		−	10.3700i		−	0.425845i	−0.977069	−	0.212922i	$-0.931702\pi$
$593$		−	10.3700i		−	0.425845i	0.977069	−	0.212922i	$-0.0682982\pi$
$594$	1.01331	+	5.87740i	0.0415768	+	0.241153i
$595$		−	25.4443i		−	1.04312i
$596$	29.0968			1.19185
$597$	−11.7763	+	7.72405i	−0.481973	+	0.316124i
$598$	−29.8923	−	1.34170i	−1.22239	−	0.0548663i
$599$		−	25.8760i		−	1.05726i	−0.848851	−	0.528632i	$-0.822705\pi$
$599$		−	25.8760i		−	1.05726i	0.848851	−	0.528632i	$-0.177295\pi$
$600$	2.50074	−	1.64022i	0.102092	−	0.0669619i
$601$	−28.9975			−1.18283			−0.591416	−	0.806366i	$-0.701431\pi$
$601$	−28.9975			−1.18283			−0.591416	+	0.806366i	$0.701431\pi$
$602$		−	22.3751i		−	0.911942i
$603$	13.1789	+	5.72451i	0.536688	+	0.233120i
$604$	1.48321			0.0603511
$605$	44.4051			1.80532
$606$	6.89326	+	10.5097i	0.280019	+	0.426926i
$607$	−21.8206			−0.885671			−0.442836	−	0.896603i	$-0.646027\pi$
$607$	−21.8206			−0.885671			−0.442836	+	0.896603i	$0.646027\pi$
$608$	−13.2403			−0.536966
$609$	−4.10434	−	6.25761i	−0.166316	−	0.253571i
$610$	68.6714			2.78042
$611$			20.9513i			0.847598i
$612$	−14.0921	+	32.4428i	−0.569641	+	1.31142i
$613$			9.12971i			0.368745i	0.982856	+	0.184373i	$0.0590253\pi$
$613$			9.12971i			0.368745i	−0.982856	+	0.184373i	$0.940975\pi$
$614$		−	33.8752i		−	1.36709i
$615$	−41.1463	+	26.9877i	−1.65918	+	1.08825i
$616$	−0.0810418			−0.00326527
$617$	−6.65027			−0.267730			−0.133865	−	0.991000i	$-0.542739\pi$
$617$	−6.65027			−0.267730			−0.133865	+	0.991000i	$0.542739\pi$
$618$	−7.98282	−	12.1709i	−0.321116	−	0.489584i
$619$		−	11.3595i		−	0.456577i	−0.973594	−	0.228288i	$-0.926687\pi$
$619$		−	11.3595i		−	0.456577i	0.973594	−	0.228288i	$-0.0733129\pi$
$620$	−77.3781			−3.10758
$621$	−3.12853	−	24.7227i	−0.125544	−	0.992088i
$622$	−8.65954			−0.347216
$623$			6.78948i			0.272015i
$624$	12.3672	+	18.8555i	0.495085	+	0.754822i
$625$	65.5102			2.62041
$626$	−39.2311			−1.56799
$627$	−1.40210	+	0.919635i	−0.0559947	+	0.0367267i
$628$		−	10.6838i		−	0.426328i
$629$			31.4019i			1.25208i
$630$	−9.86491	+	22.7109i	−0.393027	+	0.904826i
$631$			16.1474i			0.642818i	0.946941	+	0.321409i	$0.104156\pi$
$631$			16.1474i			0.642818i	−0.946941	+	0.321409i	$0.895844\pi$
$632$	0.249047			0.00990656
$633$	3.50979	+	5.35114i	0.139502	+	0.212689i
$634$	−42.8101			−1.70021
$635$	26.6988			1.05951
$636$	−16.8914	−	25.7531i	−0.669786	−	1.02118i
$637$	3.14753			0.124710
$638$	−4.95918			−0.196336
$639$	−3.01988	−	1.31174i	−0.119464	−	0.0518916i
$640$		−	4.65919i		−	0.184171i
$641$	−26.5563			−1.04891			−0.524456	−	0.851438i	$-0.675731\pi$
$641$	−26.5563			−1.04891			−0.524456	+	0.851438i	$0.675731\pi$
$642$	−34.4205	+	22.5763i	−1.35847	+	0.891015i
$643$			10.8674i			0.428568i	0.976771	+	0.214284i	$0.0687418\pi$
$643$			10.8674i			0.428568i	−0.976771	+	0.214284i	$0.931258\pi$
$644$	−9.24374	−	0.414901i	−0.364254	−	0.0163494i
$645$	68.0688	−	44.6461i	2.68021	−	1.75794i
$646$	−20.2529			−0.796842
$647$			25.8975i			1.01813i	0.860727	+	0.509067i	$0.170010\pi$
$647$			25.8975i			1.01813i	−0.860727	+	0.509067i	$0.829990\pi$
$648$	−0.920609	+	0.859769i	−0.0361649	+	0.0337749i
$649$			0.0112107i			0.000440059i
$650$			76.9717i			3.01908i
$651$	−13.9501	+	9.14981i	−0.546747	+	0.358609i
$652$	32.3607			1.26734
$653$		−	18.8629i		−	0.738161i	−0.929397	−	0.369081i	$-0.879673\pi$
$653$		−	18.8629i		−	0.738161i	0.929397	−	0.369081i	$-0.120327\pi$
$654$	−17.5365	−	26.7367i	−0.685732	−	1.04549i
$655$		−	57.3295i		−	2.24005i
$656$			28.2221i			1.10189i
$657$	−7.05833	+	16.2497i	−0.275372	+	0.633959i
$658$			13.1948i			0.514387i
$659$	−34.9890			−1.36298			−0.681488	−	0.731829i	$-0.738667\pi$
$659$	−34.9890			−1.36298			−0.681488	+	0.731829i	$0.738667\pi$
$660$	4.41878	+	6.73701i	0.172001	+	0.262238i
$661$		−	47.6703i		−	1.85416i	−0.374863	−	0.927080i	$-0.622310\pi$
$661$		−	47.6703i		−	1.85416i	0.374863	−	0.927080i	$-0.377690\pi$
$662$		−	16.5094i		−	0.641657i
$663$	18.2716	+	27.8574i	0.709609	+	1.08189i
$664$		−	2.26281i		−	0.0878139i
$665$	−6.96146			−0.269954
$666$	12.1747	−	28.0285i	0.471760	−	1.08608i
$667$	20.7001	+	0.929115i	0.801513	+	0.0359755i
$668$		−	18.4679i		−	0.714544i
$669$	10.4163	+	15.8810i	0.402716	+	0.613993i
$670$	39.5309			1.52721
$671$		−	4.81760i		−	0.185981i
$672$	7.52278	+	11.4695i	0.290198	+	0.442445i
$673$	−1.11165			−0.0428509			−0.0214255	−	0.999770i	$-0.506820\pi$
$673$	−1.11165			−0.0428509			−0.0214255	+	0.999770i	$0.506820\pi$
$674$	50.6415			1.95064
$675$	−63.1713	+	10.8913i	−2.43146	+	0.419205i
$676$	5.96768			0.229526
$677$	22.5092			0.865098			0.432549	−	0.901611i	$-0.357614\pi$
$677$	22.5092			0.865098			0.432549	+	0.901611i	$0.357614\pi$
$678$	2.05680	−	1.34904i	0.0789908	−	0.0518097i
$679$	7.76547			0.298011
$680$		−	3.56122i		−	0.136567i
$681$	14.9974	+	22.8656i	0.574703	+	0.876210i
$682$			11.0555i			0.423337i
$683$			0.613557i			0.0234771i	0.999931	+	0.0117386i	$0.00373658\pi$
$683$			0.613557i			0.0234771i	−0.999931	+	0.0117386i	$0.996263\pi$
$684$	8.87621	+	3.85554i	0.339390	+	0.147420i
$685$	18.0661			0.690268
$686$	1.98227			0.0756834
$687$	27.3217	−	17.9202i	1.04239	−	0.683698i
$688$		−	46.6882i		−	1.77997i
$689$	−29.0079			−1.10511
$690$	−34.9932	−	58.9570i	−1.33217	−	2.24446i
$691$	−52.1300			−1.98312			−0.991560	−	0.129650i	$-0.958615\pi$
$691$	−52.1300			−1.98312			−0.991560	+	0.129650i	$0.958615\pi$
$692$		−	13.0718i		−	0.496916i
$693$	1.59327	+	0.692067i	0.0605235	+	0.0262895i
$694$	−32.2274			−1.22334
$695$	9.06550			0.343874
$696$	−0.574449	−	0.875824i	−0.0217744	−	0.0331980i
$697$			41.6959i			1.57935i
$698$			6.90279i			0.261275i
$699$	13.6692	−	8.96556i	0.517016	−	0.339109i
$700$			23.8023i			0.899642i
$701$	−5.80840			−0.219380			−0.109690	−	0.993966i	$-0.534986\pi$
$701$	−5.80840			−0.219380			−0.109690	+	0.993966i	$0.534986\pi$
$702$	−5.50825	−	31.9488i	−0.207895	−	1.20583i
$703$	8.59142			0.324032
$704$	4.29960			0.162047
$705$	−40.1407	+	26.3281i	−1.51179	+	0.991575i
$706$	68.0570			2.56136
$707$	3.66070			0.137675
$708$	0.0541023	−	0.0354855i	0.00203329	−	0.00133363i
$709$		−	51.8777i		−	1.94831i	−0.225883	−	0.974154i	$-0.572527\pi$
$709$		−	51.8777i		−	1.94831i	0.225883	−	0.974154i	$-0.427473\pi$
$710$	−9.05827			−0.339951
$711$	−4.89624	−	2.12677i	−0.183623	−	0.0797602i
$712$			0.950265i			0.0356127i
$713$	2.07128	−	46.1468i	0.0775699	−	1.72821i
$714$	11.5072	+	17.5442i	0.430645	+	0.656575i
$715$	7.58847			0.283793
$716$			0.440457i			0.0164606i
$717$	−30.5749	+	20.0539i	−1.14184	+	0.748928i
$718$			44.3896i			1.65661i
$719$		−	9.85672i		−	0.367594i	−0.982964	−	0.183797i	$-0.941161\pi$
$719$		−	9.85672i		−	0.367594i	0.982964	−	0.183797i	$-0.0588388\pi$
$720$	−20.5842	+	47.3889i	−0.767129	+	1.76608i
$721$	−4.23932			−0.157881
$722$		−	32.1220i		−	1.19546i
$723$	2.07670	−	1.36210i	0.0772335	−	0.0506571i
$724$		−	14.5350i		−	0.540190i
$725$		−	53.3021i		−	1.97959i
$726$	−30.6179	+	20.0821i	−1.13634	+	0.745318i
$727$		−	7.79470i		−	0.289089i	−0.989498	−	0.144545i	$-0.953828\pi$
$727$		−	7.79470i		−	0.289089i	0.989498	−	0.144545i	$-0.0461717\pi$
$728$	0.440533			0.0163272
$729$	25.4412	−	9.04132i	0.942267	−	0.334864i
$730$			48.7416i			1.80401i
$731$		−	68.9781i		−	2.55125i
$732$	−23.2495	+	15.2492i	−0.859325	+	0.563628i
$733$			12.2829i			0.453680i	0.973932	+	0.226840i	$0.0728394\pi$
$733$			12.2829i			0.453680i	−0.973932	+	0.226840i	$0.927161\pi$
$734$	−39.9426			−1.47431
$735$	3.95531	+	6.03039i	0.145894	+	0.222434i
$736$	−37.9409	−	1.70296i	−1.39852	−	0.0627719i
$737$		−	2.77327i		−	0.102155i
$738$	16.1657	−	37.2167i	0.595069	−	1.36997i
$739$	2.90928			0.107019			0.0535097	−	0.998567i	$-0.482959\pi$
$739$	2.90928			0.107019			0.0535097	+	0.998567i	$0.482959\pi$
$740$		−	41.2811i		−	1.51752i
$741$	7.62166	−	4.99902i	0.279989	−	0.183644i
$742$	−18.2688			−0.670668
$743$	−9.69774			−0.355775			−0.177888	−	0.984051i	$-0.556926\pi$
$743$	−9.69774			−0.355775			−0.177888	+	0.984051i	$0.556926\pi$
$744$	−1.95247	+	1.28062i	−0.0715811	+	0.0469498i
$745$	62.7925			2.30054
$746$	52.9098			1.93717
$747$	−19.3235	+	44.4866i	−0.707011	+	1.62768i
$748$	6.82700			0.249620
$749$			11.9893i			0.438078i
$750$	−87.7016	+	57.5231i	−3.20241	+	2.10045i
$751$		−	15.5639i		−	0.567934i	−0.958834	−	0.283967i	$-0.908349\pi$
$751$		−	15.5639i		−	0.567934i	0.958834	−	0.283967i	$-0.0916507\pi$
$752$			27.5324i			1.00400i
$753$	0.132421	+	0.201894i	0.00482571	+	0.00735743i
$754$	26.9575			0.981734
$755$	3.20085			0.116491
$756$	−1.70334	−	9.87966i	−0.0619498	−	0.359320i
$757$			29.2993i			1.06490i	0.846461	+	0.532451i	$0.178729\pi$
$757$			29.2993i			1.06490i	−0.846461	+	0.532451i	$0.821271\pi$
$758$	−23.8209			−0.865215
$759$	−4.13610	+	2.45493i	−0.150131	+	0.0891084i
$760$	−0.974334			−0.0353428
$761$		−	0.843121i		−	0.0305631i	−0.999883	−	0.0152816i	$-0.995136\pi$
$761$		−	0.843121i		−	0.0305631i	0.999883	−	0.0152816i	$-0.00486446\pi$
$762$	−18.4092	+	12.0745i	−0.666893	+	0.437413i
$763$	−9.31287			−0.337148
$764$	33.5142			1.21250
$765$	−30.4116	+	70.0133i	−1.09953	+	2.53134i
$766$		−	54.4633i		−	1.96784i
$767$		−	0.0609400i		−	0.00220042i
$768$	16.2148	+	24.7215i	0.585100	+	0.892062i
$769$			4.60300i			0.165988i	0.996550	+	0.0829942i	$0.0264483\pi$
$769$			4.60300i			0.165988i	−0.996550	+	0.0829942i	$0.973552\pi$
$770$	4.77911			0.172227
$771$	16.1422	−	10.5876i	0.581348	−	0.381304i
$772$	13.4513			0.484121
$773$	34.7078			1.24835			0.624177	−	0.781283i	$-0.285434\pi$
$773$	34.7078			1.24835			0.624177	+	0.781283i	$0.285434\pi$
$774$	−26.7432	+	61.5680i	−0.961264	+	2.21302i
$775$	−118.826			−4.26837
$776$	1.08687			0.0390162
$777$	−4.88141	−	7.44235i	−0.175120	−	0.266993i
$778$			67.4365i			2.41772i
$779$	11.4078			0.408727
$780$	−24.0199	−	36.6215i	−0.860051	−	1.31126i
$781$			0.635478i			0.0227392i
$782$	−58.0361	−	2.60492i	−2.07537	−	0.0931518i
$783$	3.81440	+	22.1242i	0.136316	+	0.790655i
$784$	4.13623			0.147722
$785$		−	23.0561i		−	0.822908i
$786$	25.9272	+	39.5294i	0.924791	+	1.40997i
$787$			8.78017i			0.312979i	0.987680	+	0.156490i	$0.0500178\pi$
$787$			8.78017i			0.312979i	−0.987680	+	0.156490i	$0.949982\pi$
$788$		−	6.36147i		−	0.226618i
$789$	−18.7570	−	28.5975i	−0.667766	−	1.01810i
$790$	−14.6865			−0.522523
$791$		−	0.716417i		−	0.0254729i
$792$	0.222997	+	0.0968627i	0.00792384	+	0.00344187i
$793$			26.1879i			0.929959i
$794$		−	21.4401i		−	0.760880i
$795$	−36.4525	−	55.5766i	−1.29284	−	1.97110i
$796$		−	15.6880i		−	0.556048i
$797$	26.5263			0.939610			0.469805	−	0.882770i	$-0.344324\pi$
$797$	26.5263			0.939610			0.469805	+	0.882770i	$0.344324\pi$
$798$	4.80001	−	3.14831i	0.169919	−	0.111449i
$799$			40.6770i			1.43905i
$800$			97.6966i			3.45410i
$801$	8.11492	−	18.6821i	0.286727	−	0.660100i
$802$			0.711528i			0.0251249i
$803$	3.41944			0.120670
$804$	−13.3836	+	8.77828i	−0.472005	+	0.309586i
$805$	−19.9485	−	0.895378i	−0.703092	−	0.0315579i
$806$		−	60.0963i		−	2.11680i
$807$	29.0195	−	19.0338i	1.02154	−	0.670021i
$808$	0.512357			0.0180246
$809$		−	18.8618i		−	0.663145i	−0.943430	−	0.331573i	$-0.892421\pi$
$809$		−	18.8618i		−	0.663145i	0.943430	−	0.331573i	$-0.107579\pi$
$810$	54.2891	−	50.7013i	1.90752	−	1.78146i
$811$	19.2882			0.677302			0.338651	−	0.940912i	$-0.390029\pi$
$811$	19.2882			0.677302			0.338651	+	0.940912i	$0.390029\pi$
$812$	8.33618			0.292543
$813$	−9.76194	−	14.8834i	−0.342366	−	0.521982i
$814$	−5.89809			−0.206728
$815$	69.8362			2.44625
$816$	24.0110	+	36.6079i	0.840553	+	1.28153i
$817$	−18.8721			−0.660251
$818$			23.3989i			0.818124i
$819$	−8.66084	−	3.76199i	−0.302634	−	0.131455i
$820$		−	54.8137i		−	1.91418i
$821$			42.1055i			1.46949i	0.678342	+	0.734746i	$0.262699\pi$
$821$			42.1055i			1.46949i	−0.678342	+	0.734746i	$0.737301\pi$
$822$	−12.4568	+	8.17034i	−0.434480	+	0.284973i
$823$	−16.1363			−0.562475			−0.281237	−	0.959638i	$-0.590745\pi$
$823$	−16.1363			−0.562475			−0.281237	+	0.959638i	$0.590745\pi$
$824$	−0.593341			−0.0206700
$825$	6.78573	+	10.3457i	0.236249	+	0.360192i
$826$		−	0.0383791i		−	0.00133538i
$827$	21.3600			0.742761			0.371381	−	0.928481i	$-0.378885\pi$
$827$	21.3600			0.742761			0.371381	+	0.928481i	$0.378885\pi$
$828$	24.9394	+	12.1899i	0.866705	+	0.423630i
$829$	34.7879			1.20823			0.604117	−	0.796895i	$-0.293526\pi$
$829$	34.7879			1.20823			0.604117	+	0.796895i	$0.293526\pi$
$830$			133.440i			4.63176i
$831$	17.0484	+	25.9926i	0.591403	+	0.901672i
$832$	−23.3721			−0.810282
$833$	6.11094			0.211732
$834$	−6.25078	+	4.09986i	−0.216447	+	0.141966i
$835$		−	39.8547i		−	1.37923i
$836$		−	1.86784i		−	0.0646005i
$837$	49.3215	−	8.50345i	1.70480	−	0.293922i
$838$		−	55.9903i		−	1.93415i
$839$	−15.8214			−0.546214			−0.273107	−	0.961984i	$-0.588051\pi$
$839$	−15.8214			−0.546214			−0.273107	+	0.961984i	$0.588051\pi$
$840$	0.553590	+	0.844021i	0.0191007	+	0.0291215i
$841$	10.3322			0.356283
$842$	−73.5934			−2.53620
$843$	−17.8451	−	27.2072i	−0.614617	−	0.937064i
$844$	−7.12861			−0.245377
$845$	12.8786			0.443037
$846$	15.7707	−	36.3072i	0.542207	−	1.24827i
$847$			10.6647i			0.366444i
$848$	−38.1199			−1.30904
$849$	−10.9166	+	7.16018i	−0.374658	+	0.245737i
$850$			149.441i			5.12578i
$851$	24.6192	+	1.10502i	0.843937	+	0.0378797i
$852$	3.06678	−	2.01149i	0.105066	−	0.0689125i
$853$	−17.7723			−0.608511			−0.304256	−	0.952590i	$-0.598408\pi$
$853$	−17.7723			−0.608511			−0.304256	+	0.952590i	$0.598408\pi$
$854$			16.4927i			0.564370i
$855$	19.1553	+	8.32046i	0.655098	+	0.284554i
$856$			1.67803i			0.0573540i
$857$		−	25.5281i		−	0.872024i	−0.899941	−	0.436012i	$-0.856391\pi$
$857$		−	25.5281i		−	0.872024i	0.899941	−	0.436012i	$-0.143609\pi$
$858$	−5.23234	+	3.43187i	−0.178629	+	0.117162i
$859$	49.7209			1.69646			0.848228	−	0.529631i	$-0.177670\pi$
$859$	49.7209			1.69646			0.848228	+	0.529631i	$0.177670\pi$
$860$			90.6790i			3.09213i
$861$	−6.48161	−	9.88206i	−0.220893	−	0.336780i
$862$			3.71220i			0.126438i
$863$			11.5375i			0.392741i	0.980530	+	0.196370i	$0.0629155\pi$
$863$			11.5375i			0.392741i	−0.980530	+	0.196370i	$0.937084\pi$
$864$	−6.99136	−	40.5511i	−0.237851	−	1.37958i
$865$		−	28.2097i		−	0.959158i
$866$	64.6806			2.19794
$867$	19.3253	+	29.4640i	0.656321	+	1.00065i
$868$		−	18.5838i		−	0.630777i
$869$			1.03033i			0.0349514i
$870$	33.8758	+	51.6481i	1.14850	+	1.75103i
$871$			15.0751i			0.510802i
$872$	−1.30344			−0.0441401
$873$	−21.3677	−	9.28144i	−0.723186	−	0.314129i
$874$	−0.712694	+	15.8784i	−0.0241072	+	0.537095i
$875$			30.5480i			1.03271i
$876$	−10.8236	−	16.5020i	−0.365696	−	0.557552i
$877$	−8.15966			−0.275532			−0.137766	−	0.990465i	$-0.543992\pi$
$877$	−8.15966			−0.275532			−0.137766	+	0.990465i	$0.543992\pi$
$878$		−	3.45966i		−	0.116758i
$879$	−5.16985	−	7.88212i	−0.174375	−	0.265857i
$880$	9.97214			0.336161
$881$	−3.38436			−0.114022			−0.0570111	−	0.998374i	$-0.518157\pi$
$881$	−3.38436			−0.114022			−0.0570111	+	0.998374i	$0.518157\pi$
$882$	−5.45447	−	2.36925i	−0.183661	−	0.0797767i
$883$	−0.559185			−0.0188181			−0.00940904	−	0.999956i	$-0.502995\pi$
$883$	−0.559185			−0.0188181			−0.00940904	+	0.999956i	$0.502995\pi$
$884$	−37.1107			−1.24817
$885$	0.116756	−	0.0765795i	0.00392470	−	0.00257419i
$886$	−68.9941			−2.31790
$887$		−	27.4079i		−	0.920268i	−0.887850	−	0.460134i	$-0.847801\pi$
$887$		−	27.4079i		−	0.920268i	0.887850	−	0.460134i	$-0.152199\pi$
$888$	−0.683208	−	1.04164i	−0.0229270	−	0.0349552i
$889$			6.41223i			0.215059i
$890$		−	56.0380i		−	1.87840i
$891$	−3.55692	−	3.80862i	−0.119161	−	0.127594i
$892$	−21.1561			−0.708358
$893$	11.1290			0.372419
$894$	−43.2962	+	28.3978i	−1.44804	+	0.949765i
$895$			0.950529i			0.0317727i
$896$	1.11899			0.0373829
$897$	22.4833	−	13.3447i	0.750696	−	0.445567i
$898$	−27.9876			−0.933957
$899$			41.6161i			1.38797i
$900$	28.4490	−	65.4951i	0.948299	−	2.18317i
$901$	−56.3190			−1.87626
$902$	−7.83158			−0.260763
$903$	10.7226	+	16.3480i	0.356826	+	0.544028i
$904$		−	0.100271i		−	0.00333495i
$905$		−	31.3673i		−	1.04269i
$906$	−2.20703	+	1.44758i	−0.0733236	+	0.0480927i
$907$		−	38.9028i		−	1.29175i	−0.763444	−	0.645874i	$-0.776493\pi$
$907$		−	38.9028i		−	1.29175i	0.763444	−	0.645874i	$-0.223507\pi$
$908$	−30.4607			−1.01088
$909$	−10.0729	−	4.37534i	−0.334097	−	0.145121i
$910$	−25.9786			−0.861183
$911$	45.1624			1.49630			0.748149	−	0.663531i	$-0.230943\pi$
$911$	45.1624			1.49630			0.748149	+	0.663531i	$0.230943\pi$
$912$	10.0158	−	6.56930i	0.331655	−	0.217531i
$913$	9.36139			0.309817
$914$	49.3176			1.63128
$915$	−50.1736	+	32.9087i	−1.65869	+	1.08793i
$916$			36.3970i			1.20259i
$917$	13.7688			0.454685
$918$	−10.6943	−	62.0287i	−0.352964	−	2.04725i
$919$			36.0987i			1.19079i	0.803435	+	0.595393i	$0.203004\pi$
$919$			36.0987i			1.19079i	−0.803435	+	0.595393i	$0.796996\pi$
$920$	−2.79202	−	0.125318i	−0.0920500	−	0.00413162i
$921$	16.2337	+	24.7503i	0.534917	+	0.815552i
$922$	−34.5389			−1.13748
$923$		−	3.45438i		−	0.113702i
$924$	−1.61802	+	1.06125i	−0.0532290	+	0.0349127i
$925$		−	63.3937i		−	2.08437i
$926$		−	27.6470i		−	0.908537i
$927$	11.6650	+	5.06692i	0.383130	+	0.166419i
$928$	34.2159			1.12319
$929$		−	6.04502i		−	0.198331i	−0.995071	−	0.0991653i	$-0.968383\pi$
$929$		−	6.04502i		−	0.198331i	0.995071	−	0.0991653i	$-0.0316173\pi$
$930$	115.139	−	75.5192i	3.77556	−	2.47637i
$931$		−	1.67193i		−	0.0547952i
$932$			18.2096i			0.596476i
$933$	6.32695	−	4.14982i	0.207135	−	0.135859i
$934$		−	30.8950i		−	1.01092i
$935$	14.7330			0.481822
$936$	−1.21218	−	0.526533i	−0.0396214	−	0.0172103i
$937$			27.6832i			0.904371i	0.891924	+	0.452185i	$0.149355\pi$
$937$			27.6832i			0.904371i	−0.891924	+	0.452185i	$0.850645\pi$
$938$			9.49410i			0.309993i
$939$	28.6635	−	18.8003i	0.935399	−	0.613525i
$940$		−	53.4741i		−	1.74413i
$941$	47.9835			1.56422			0.782109	−	0.623142i	$-0.214144\pi$
$941$	47.9835			1.56422			0.782109	+	0.623142i	$0.214144\pi$
$942$	10.4271	+	15.8975i	0.339733	+	0.517968i
$943$	32.6898	+	1.46727i	1.06453	+	0.0477807i
$944$		−	0.0800824i		−	0.00260646i
$945$	−3.67590	−	21.3208i	−0.119577	−	0.693567i
$946$	12.9559			0.421232
$947$			23.5416i			0.765001i	0.923955	+	0.382500i	$0.124937\pi$
$947$			23.5416i			0.765001i	−0.923955	+	0.382500i	$0.875063\pi$
$948$	4.97229	−	3.26131i	0.161493	−	0.105922i
$949$	−18.5877			−0.603381
$950$	40.8863			1.32653
$951$	31.2785	−	20.5154i	1.01427	−	0.665259i
$952$	0.855296			0.0277203
$953$	−16.5133			−0.534917			−0.267459	−	0.963569i	$-0.586184\pi$
$953$	−16.5133			−0.534917			−0.267459	+	0.963569i	$0.586184\pi$
$954$	50.2689	+	21.8352i	1.62751	+	0.706940i
$955$	72.3255			2.34040
$956$		−	40.7308i		−	1.31733i
$957$	3.62334	−	2.37654i	0.117126	−	0.0768225i
$958$			7.11672i			0.229931i
$959$			4.33891i			0.140111i
$960$	−29.3702	−	44.7788i	−0.947921	−	1.44523i
$961$	61.7746			1.99273
$962$	32.0613			1.03370
$963$	14.3298	−	32.9900i	0.461771	−	1.06309i
$964$			2.76652i			0.0891035i
$965$	29.0285			0.934461
$966$	14.1597	−	8.40430i	0.455580	−	0.270404i
$967$	1.26050			0.0405349			0.0202675	−	0.999795i	$-0.493548\pi$
$967$	1.26050			0.0405349			0.0202675	+	0.999795i	$0.493548\pi$
$968$			1.49265i			0.0479755i
$969$	14.7975	−	9.70561i	0.475364	−	0.311789i
$970$	−64.0934			−2.05792
$971$	26.2003			0.840808			0.420404	−	0.907337i	$-0.361888\pi$
$971$	26.2003			0.840808			0.420404	+	0.907337i	$0.361888\pi$
$972$	−7.12140	+	29.2210i	−0.228419	+	0.937264i
$973$			2.17725i			0.0697995i
$974$		−	16.7506i		−	0.536724i
$975$	−36.8864	−	56.2381i	−1.18131	−	1.80106i
$976$			34.4139i			1.10156i
$977$	15.4629			0.494702			0.247351	−	0.968926i	$-0.420440\pi$
$977$	15.4629			0.494702			0.247351	+	0.968926i	$0.420440\pi$
$978$	−48.1529	+	31.5833i	−1.53976	+	1.00992i
$979$	−3.93131			−0.125645
$980$	−8.03348			−0.256620
$981$	25.6255	+	11.1309i	0.818160	+	0.355383i
$982$	59.6868			1.90468
$983$	−42.8558			−1.36689			−0.683443	−	0.730004i	$-0.739518\pi$
$983$	−42.8558			−1.36689			−0.683443	+	0.730004i	$0.739518\pi$
$984$	−0.907174	−	1.38311i	−0.0289197	−	0.0440918i
$985$		−	13.7284i		−	0.437423i
$986$	52.3380			1.66678
$987$	−6.32321	−	9.64056i	−0.201270	−	0.306863i
$988$			10.1533i			0.323020i
$989$	−54.0791	−	2.42732i	−1.71962	−	0.0771841i
$990$	−13.1503	−	5.71208i	−0.417945	−	0.181542i
$991$	−27.6179			−0.877312			−0.438656	−	0.898655i	$-0.644545\pi$
$991$	−27.6179			−0.877312			−0.438656	+	0.898655i	$0.644545\pi$
$992$		−	76.2774i		−	2.42181i
$993$	7.91164	+	12.0623i	0.251068	+	0.382787i
$994$		−	2.17552i		−	0.0690032i
$995$		−	33.8556i		−	1.07329i
$996$	−29.6318	−	45.1775i	−0.938918	−	1.43150i
$997$	−24.3419			−0.770916			−0.385458	−	0.922725i	$-0.625957\pi$
$997$	−24.3419			−0.770916			−0.385458	+	0.922725i	$0.625957\pi$
$998$		−	39.0012i		−	1.23456i
$999$	4.53658	+	26.3129i	0.143531	+	0.832504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.e.a.344.9	✓	48
3.2	odd	2	inner	483.2.e.a.344.40	yes	48
23.22	odd	2	inner	483.2.e.a.344.10	yes	48
69.68	even	2	inner	483.2.e.a.344.39	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.e.a.344.9	✓	48	1.1	even	1	trivial
483.2.e.a.344.10	yes	48	23.22	odd	2	inner
483.2.e.a.344.39	yes	48	69.68	even	2	inner
483.2.e.a.344.40	yes	48	3.2	odd	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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.98227i q^{2} +(0.949942 + 1.44831i) q^{3} -1.92939 q^{4} -4.16373 q^{5} +(2.87095 - 1.88304i) q^{6} -1.00000i q^{7} -0.139961i q^{8} +(-1.19522 + 2.75163i) q^{9} +O(q^{10})\)	\(q-1.98227i q^{2} +(0.949942 + 1.44831i) q^{3} -1.92939 q^{4} -4.16373 q^{5} +(2.87095 - 1.88304i) q^{6} -1.00000i q^{7} -0.139961i q^{8} +(-1.19522 + 2.75163i) q^{9} +8.25364i q^{10} +0.579030 q^{11} +(-1.83281 - 2.79436i) q^{12} -3.14753 q^{13} -1.98227 q^{14} +(-3.95531 - 6.03039i) q^{15} -4.13623 q^{16} -6.11094 q^{17} +(5.45447 + 2.36925i) q^{18} +1.67193i q^{19} +8.03348 q^{20} +(1.44831 - 0.949942i) q^{21} -1.14779i q^{22} +(-0.215042 + 4.79101i) q^{23} +(0.202708 - 0.132955i) q^{24} +12.3367 q^{25} +6.23926i q^{26} +(-5.12061 + 0.882837i) q^{27} +1.92939i q^{28} -4.32062i q^{29} +(-11.9539 + 7.84049i) q^{30} -9.63196 q^{31} +7.91920i q^{32} +(0.550045 + 0.838616i) q^{33} +12.1135i q^{34} +4.16373i q^{35} +(2.30605 - 5.30897i) q^{36} -5.13864i q^{37} +3.31421 q^{38} +(-2.98997 - 4.55861i) q^{39} +0.582762i q^{40} -6.82316i q^{41} +(-1.88304 - 2.87095i) q^{42} +11.2876i q^{43} -1.11718 q^{44} +(4.97657 - 11.4570i) q^{45} +(9.49707 + 0.426271i) q^{46} -6.65641i q^{47} +(-3.92918 - 5.99055i) q^{48} -1.00000 q^{49} -24.4546i q^{50} +(-5.80505 - 8.85056i) q^{51} +6.07283 q^{52} +9.21609 q^{53} +(1.75002 + 10.1504i) q^{54} -2.41093 q^{55} -0.139961 q^{56} +(-2.42147 + 1.58823i) q^{57} -8.56464 q^{58} +0.0193612i q^{59} +(7.63134 + 11.6350i) q^{60} -8.32013i q^{61} +19.0931i q^{62} +(2.75163 + 1.19522i) q^{63} +7.42553 q^{64} +13.1055 q^{65} +(1.66236 - 1.09034i) q^{66} -4.78951i q^{67} +11.7904 q^{68} +(-7.14315 + 4.23973i) q^{69} +8.25364 q^{70} +1.09749i q^{71} +(0.385121 + 0.167284i) q^{72} +5.90547 q^{73} -10.1862 q^{74} +(11.7191 + 17.8674i) q^{75} -3.22580i q^{76} -0.579030i q^{77} +(-9.03640 + 5.92694i) q^{78} +1.77940i q^{79} +17.2222 q^{80} +(-6.14290 - 6.57759i) q^{81} -13.5253 q^{82} +16.1674 q^{83} +(-2.79436 + 1.83281i) q^{84} +25.4443 q^{85} +22.3751 q^{86} +(6.25761 - 4.10434i) q^{87} -0.0810418i q^{88} -6.78948 q^{89} +(-22.7109 - 9.86491i) q^{90} +3.14753i q^{91} +(0.414901 - 9.24374i) q^{92} +(-9.14981 - 13.9501i) q^{93} -13.1948 q^{94} -6.96146i q^{95} +(-11.4695 + 7.52278i) q^{96} +7.76547i q^{97} +1.98227i q^{98} +(-0.692067 + 1.59327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more