LMFDB - Embedded newform 483.2.d.c.461.6

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:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.6
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	483.461
Dual form			483.2.d.c.461.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.382683 - 1.68925i) q^{3} +1.00000 q^{4} -2.93015 q^{5} +(1.68925 - 0.382683i) q^{6} +(0.414214 + 2.61313i) q^{7} +3.00000i q^{8} +(-2.70711 + 1.29289i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.382683 - 1.68925i) q^{3} +1.00000 q^{4} -2.93015 q^{5} +(1.68925 - 0.382683i) q^{6} +(0.414214 + 2.61313i) q^{7} +3.00000i q^{8} +(-2.70711 + 1.29289i) q^{9} -2.93015i q^{10} +0.585786i q^{11} +(-0.382683 - 1.68925i) q^{12} +1.53073i q^{13} +(-2.61313 + 0.414214i) q^{14} +(1.12132 + 4.94975i) q^{15} -1.00000 q^{16} -0.317025 q^{17} +(-1.29289 - 2.70711i) q^{18} +2.16478i q^{19} -2.93015 q^{20} +(4.25570 - 1.69971i) q^{21} -0.585786 q^{22} +1.00000i q^{23} +(5.06774 - 1.14805i) q^{24} +3.58579 q^{25} -1.53073 q^{26} +(3.21998 + 4.07820i) q^{27} +(0.414214 + 2.61313i) q^{28} +4.24264i q^{29} +(-4.94975 + 1.12132i) q^{30} +6.62567i q^{31} +5.00000i q^{32} +(0.989538 - 0.224171i) q^{33} -0.317025i q^{34} +(-1.21371 - 7.65685i) q^{35} +(-2.70711 + 1.29289i) q^{36} -6.48528 q^{37} -2.16478 q^{38} +(2.58579 - 0.585786i) q^{39} -8.79045i q^{40} +9.55582 q^{41} +(1.69971 + 4.25570i) q^{42} +1.65685 q^{43} +0.585786i q^{44} +(7.93223 - 3.78837i) q^{45} -1.00000 q^{46} +4.01254 q^{47} +(0.382683 + 1.68925i) q^{48} +(-6.65685 + 2.16478i) q^{49} +3.58579i q^{50} +(0.121320 + 0.535534i) q^{51} +1.53073i q^{52} -4.82843i q^{53} +(-4.07820 + 3.21998i) q^{54} -1.71644i q^{55} +(-7.83938 + 1.24264i) q^{56} +(3.65685 - 0.828427i) q^{57} -4.24264 q^{58} -5.09494 q^{59} +(1.12132 + 4.94975i) q^{60} -13.8310i q^{61} -6.62567 q^{62} +(-4.49981 - 6.53848i) q^{63} -7.00000 q^{64} -4.48528i q^{65} +(0.224171 + 0.989538i) q^{66} -10.7279 q^{67} -0.317025 q^{68} +(1.68925 - 0.382683i) q^{69} +(7.65685 - 1.21371i) q^{70} -9.65685i q^{71} +(-3.87868 - 8.12132i) q^{72} +5.86030i q^{73} -6.48528i q^{74} +(-1.37222 - 6.05728i) q^{75} +2.16478i q^{76} +(-1.53073 + 0.242641i) q^{77} +(0.585786 + 2.58579i) q^{78} +14.7279 q^{79} +2.93015 q^{80} +(5.65685 - 7.00000i) q^{81} +9.55582i q^{82} -8.92177 q^{83} +(4.25570 - 1.69971i) q^{84} +0.928932 q^{85} +1.65685i q^{86} +(7.16687 - 1.62359i) q^{87} -1.75736 q^{88} -10.1355 q^{89} +(3.78837 + 7.93223i) q^{90} +(-4.00000 + 0.634051i) q^{91} +1.00000i q^{92} +(11.1924 - 2.53553i) q^{93} +4.01254i q^{94} -6.34315i q^{95} +(8.44623 - 1.91342i) q^{96} +2.74444i q^{97} +(-2.16478 - 6.65685i) q^{98} +(-0.757359 - 1.58579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 8 * q^7 - 16 * q^9	$ 8 q + 8 q^{4} - 8 q^{7} - 16 q^{9} - 8 q^{15} - 8 q^{16} - 16 q^{18} + 24 q^{21} - 16 q^{22} + 40 q^{25} - 8 q^{28} - 16 q^{36} + 16 q^{37} + 32 q^{39} + 8 q^{42} - 32 q^{43} - 8 q^{46} - 8 q^{49} - 16 q^{51} - 16 q^{57} - 8 q^{60} + 8 q^{63} - 56 q^{64} + 16 q^{67} + 16 q^{70} - 48 q^{72} + 16 q^{78} + 16 q^{79} + 24 q^{84} + 64 q^{85} - 48 q^{88} - 32 q^{91} + 16 q^{93} - 40 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^7 - 16 * q^9 - 8 * q^15 - 8 * q^16 - 16 * q^18 + 24 * q^21 - 16 * q^22 + 40 * q^25 - 8 * q^28 - 16 * q^36 + 16 * q^37 + 32 * q^39 + 8 * q^42 - 32 * q^43 - 8 * q^46 - 8 * q^49 - 16 * q^51 - 16 * q^57 - 8 * q^60 + 8 * q^63 - 56 * q^64 + 16 * q^67 + 16 * q^70 - 48 * q^72 + 16 * q^78 + 16 * q^79 + 24 * q^84 + 64 * q^85 - 48 * q^88 - 32 * q^91 + 16 * q^93 - 40 * 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 $

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$	−0.382683	−	1.68925i	−0.220942	−	0.975287i
$3$	−0.382683	−	1.68925i	−0.220942	−	0.975287i
$4$	1.00000			0.500000
$5$	−2.93015			−1.31040			−0.655202	−	0.755454i	$-0.727416\pi$
$5$	−2.93015			−1.31040			−0.655202	+	0.755454i	$0.727416\pi$
$6$	1.68925	−	0.382683i	0.689632	−	0.156230i
$7$	0.414214	+	2.61313i	0.156558	+	0.987669i
$7$	0.414214	+	2.61313i	0.156558	+	0.987669i
$8$			3.00000i			1.06066i
$9$	−2.70711	+	1.29289i	−0.902369	+	0.430964i
$10$		−	2.93015i		−	0.926595i
$11$			0.585786i			0.176621i	0.996093	+	0.0883106i	$0.0281468\pi$
$11$			0.585786i			0.176621i	−0.996093	+	0.0883106i	$0.971853\pi$
$12$	−0.382683	−	1.68925i	−0.110471	−	0.487643i
$13$			1.53073i			0.424549i	0.977210	+	0.212275i	$0.0680871\pi$
$13$			1.53073i			0.424549i	−0.977210	+	0.212275i	$0.931913\pi$
$14$	−2.61313	+	0.414214i	−0.698387	+	0.110703i
$15$	1.12132	+	4.94975i	0.289524	+	1.27802i
$16$	−1.00000			−0.250000
$17$	−0.317025			−0.0768899			−0.0384450	−	0.999261i	$-0.512240\pi$
$17$	−0.317025			−0.0768899			−0.0384450	+	0.999261i	$0.512240\pi$
$18$	−1.29289	−	2.70711i	−0.304738	−	0.638071i
$19$			2.16478i			0.496636i	0.968679	+	0.248318i	$0.0798777\pi$
$19$			2.16478i			0.496636i	−0.968679	+	0.248318i	$0.920122\pi$
$20$	−2.93015			−0.655202
$21$	4.25570	−	1.69971i	0.928670	−	0.370907i
$22$	−0.585786			−0.124890
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	5.06774	−	1.14805i	1.03445	−	0.234345i
$25$	3.58579			0.717157
$26$	−1.53073			−0.300202
$27$	3.21998	+	4.07820i	0.619685	+	0.784850i
$28$	0.414214	+	2.61313i	0.0782790	+	0.493834i
$29$			4.24264i			0.787839i	0.919145	+	0.393919i	$0.128881\pi$
$29$			4.24264i			0.787839i	−0.919145	+	0.393919i	$0.871119\pi$
$30$	−4.94975	+	1.12132i	−0.903696	+	0.204724i
$31$			6.62567i			1.19001i	0.803724	+	0.595003i	$0.202849\pi$
$31$			6.62567i			1.19001i	−0.803724	+	0.595003i	$0.797151\pi$
$32$			5.00000i			0.883883i
$33$	0.989538	−	0.224171i	0.172256	−	0.0390231i
$34$		−	0.317025i		−	0.0543694i
$35$	−1.21371	−	7.65685i	−0.205154	−	1.29424i
$36$	−2.70711	+	1.29289i	−0.451184	+	0.215482i
$37$	−6.48528			−1.06617			−0.533087	−	0.846061i	$-0.678968\pi$
$37$	−6.48528			−1.06617			−0.533087	+	0.846061i	$0.678968\pi$
$38$	−2.16478			−0.351174
$39$	2.58579	−	0.585786i	0.414057	−	0.0938009i
$40$		−	8.79045i		−	1.38989i
$41$	9.55582			1.49237			0.746184	−	0.665740i	$-0.231884\pi$
$41$	9.55582			1.49237			0.746184	+	0.665740i	$0.231884\pi$
$42$	1.69971	+	4.25570i	0.262271	+	0.656669i
$43$	1.65685			0.252668			0.126334	−	0.991988i	$-0.459679\pi$
$43$	1.65685			0.252668			0.126334	+	0.991988i	$0.459679\pi$
$44$			0.585786i			0.0883106i
$45$	7.93223	−	3.78837i	1.18247	−	0.564737i
$46$	−1.00000			−0.147442
$47$	4.01254			0.585290			0.292645	−	0.956221i	$-0.405465\pi$
$47$	4.01254			0.585290			0.292645	+	0.956221i	$0.405465\pi$
$48$	0.382683	+	1.68925i	0.0552356	+	0.243822i
$49$	−6.65685	+	2.16478i	−0.950979	+	0.309255i
$50$			3.58579i			0.507107i
$51$	0.121320	+	0.535534i	0.0169882	+	0.0749897i
$52$			1.53073i			0.212275i
$53$		−	4.82843i		−	0.663235i	−0.943414	−	0.331618i	$-0.892406\pi$
$53$		−	4.82843i		−	0.663235i	0.943414	−	0.331618i	$-0.107594\pi$
$54$	−4.07820	+	3.21998i	−0.554973	+	0.438184i
$55$		−	1.71644i		−	0.231445i
$56$	−7.83938	+	1.24264i	−1.04758	+	0.166055i
$57$	3.65685	−	0.828427i	0.484362	−	0.109728i
$58$	−4.24264			−0.557086
$59$	−5.09494			−0.663304			−0.331652	−	0.943402i	$-0.607606\pi$
$59$	−5.09494			−0.663304			−0.331652	+	0.943402i	$0.607606\pi$
$60$	1.12132	+	4.94975i	0.144762	+	0.639010i
$61$		−	13.8310i		−	1.77088i	−0.464756	−	0.885439i	$-0.653858\pi$
$61$		−	13.8310i		−	1.77088i	0.464756	−	0.885439i	$-0.346142\pi$
$62$	−6.62567			−0.841461
$63$	−4.49981	−	6.53848i	−0.566923	−	0.823771i
$64$	−7.00000			−0.875000
$65$		−	4.48528i		−	0.556331i
$66$	0.224171	+	0.989538i	0.0275935	+	0.121804i
$67$	−10.7279			−1.31062			−0.655312	−	0.755358i	$-0.727463\pi$
$67$	−10.7279			−1.31062			−0.655312	+	0.755358i	$0.727463\pi$
$68$	−0.317025			−0.0384450
$69$	1.68925	−	0.382683i	0.203361	−	0.0460697i
$70$	7.65685	−	1.21371i	0.915169	−	0.145066i
$71$		−	9.65685i		−	1.14606i	−0.819535	−	0.573029i	$-0.805768\pi$
$71$		−	9.65685i		−	1.14606i	0.819535	−	0.573029i	$-0.194232\pi$
$72$	−3.87868	−	8.12132i	−0.457107	−	0.957107i
$73$			5.86030i			0.685897i	0.939354	+	0.342948i	$0.111426\pi$
$73$			5.86030i			0.685897i	−0.939354	+	0.342948i	$0.888574\pi$
$74$		−	6.48528i		−	0.753899i
$75$	−1.37222	−	6.05728i	−0.158450	−	0.699434i
$76$			2.16478i			0.248318i
$77$	−1.53073	+	0.242641i	−0.174443	+	0.0276515i
$78$	0.585786	+	2.58579i	0.0663273	+	0.292783i
$79$	14.7279			1.65702			0.828510	−	0.559974i	$-0.189189\pi$
$79$	14.7279			1.65702			0.828510	+	0.559974i	$0.189189\pi$
$80$	2.93015			0.327601
$81$	5.65685	−	7.00000i	0.628539	−	0.777778i
$82$			9.55582i			1.05526i
$83$	−8.92177			−0.979291			−0.489646	−	0.871921i	$-0.662874\pi$
$83$	−8.92177			−0.979291			−0.489646	+	0.871921i	$0.662874\pi$
$84$	4.25570	−	1.69971i	0.464335	−	0.185453i
$85$	0.928932			0.100757
$86$			1.65685i			0.178663i
$87$	7.16687	−	1.62359i	0.768369	−	0.174067i
$88$	−1.75736			−0.187335
$89$	−10.1355			−1.07436			−0.537179	−	0.843468i	$-0.680510\pi$
$89$	−10.1355			−1.07436			−0.537179	+	0.843468i	$0.680510\pi$
$90$	3.78837	+	7.93223i	0.399330	+	0.836131i
$91$	−4.00000	+	0.634051i	−0.419314	+	0.0664666i
$92$			1.00000i			0.104257i
$93$	11.1924	−	2.53553i	1.16060	−	0.262923i
$94$			4.01254i			0.413862i
$95$		−	6.34315i		−	0.650793i
$96$	8.44623	−	1.91342i	0.862040	−	0.195287i
$97$			2.74444i			0.278656i	0.990246	+	0.139328i	$0.0444942\pi$
$97$			2.74444i			0.278656i	−0.990246	+	0.139328i	$0.955506\pi$
$98$	−2.16478	−	6.65685i	−0.218676	−	0.672444i
$99$	−0.757359	−	1.58579i	−0.0761175	−	0.159378i
$100$	3.58579			0.358579
$101$	16.3128			1.62318			0.811592	−	0.584224i	$-0.198601\pi$
$101$	16.3128			1.62318			0.811592	+	0.584224i	$0.198601\pi$
$102$	−0.535534	+	0.121320i	−0.0530258	+	0.0120125i
$103$		−	3.06147i		−	0.301655i	−0.988560	−	0.150828i	$-0.951806\pi$
$103$		−	3.06147i		−	0.301655i	0.988560	−	0.150828i	$-0.0481939\pi$
$104$	−4.59220			−0.450302
$105$	−12.4698	+	4.98040i	−1.21693	+	0.486038i
$106$	4.82843			0.468978
$107$		−	0.828427i		−	0.0800871i	−0.999198	−	0.0400435i	$-0.987250\pi$
$107$		−	0.828427i		−	0.0800871i	0.999198	−	0.0400435i	$-0.0127497\pi$
$108$	3.21998	+	4.07820i	0.309843	+	0.392425i
$109$	3.65685			0.350263			0.175132	−	0.984545i	$-0.443965\pi$
$109$	3.65685			0.350263			0.175132	+	0.984545i	$0.443965\pi$
$110$	1.71644			0.163656
$111$	2.48181	+	10.9552i	0.235563	+	1.03983i
$112$	−0.414214	−	2.61313i	−0.0391395	−	0.246917i
$113$		−	3.17157i		−	0.298356i	−0.988810	−	0.149178i	$-0.952337\pi$
$113$		−	3.17157i		−	0.298356i	0.988810	−	0.149178i	$-0.0476628\pi$
$114$	0.828427	+	3.65685i	0.0775893	+	0.342496i
$115$		−	2.93015i		−	0.273238i
$116$			4.24264i			0.393919i
$117$	−1.97908	−	4.14386i	−0.182966	−	0.383100i
$118$		−	5.09494i		−	0.469027i
$119$	−0.131316	−	0.828427i	−0.0120377	−	0.0759418i
$120$	−14.8492	+	3.36396i	−1.35554	+	0.307086i
$121$	10.6569			0.968805
$122$	13.8310			1.25220
$123$	−3.65685	−	16.1421i	−0.329727	−	1.45549i
$124$			6.62567i			0.595003i
$125$	4.14386			0.370638
$126$	6.53848	−	4.49981i	0.582494	−	0.400875i
$127$	1.17157			0.103960			0.0519801	−	0.998648i	$-0.483447\pi$
$127$	1.17157			0.103960			0.0519801	+	0.998648i	$0.483447\pi$
$128$			3.00000i			0.265165i
$129$	−0.634051	−	2.79884i	−0.0558250	−	0.246424i
$130$	4.48528			0.393385
$131$	−14.4650			−1.26382			−0.631909	−	0.775043i	$-0.717728\pi$
$131$	−14.4650			−1.26382			−0.631909	+	0.775043i	$0.717728\pi$
$132$	0.989538	−	0.224171i	0.0861282	−	0.0195116i
$133$	−5.65685	+	0.896683i	−0.490511	+	0.0777523i
$134$		−	10.7279i		−	0.926751i
$135$	−9.43503	−	11.9497i	−0.812038	−	1.02847i
$136$		−	0.951076i		−	0.0815541i
$137$			7.65685i			0.654169i	0.944995	+	0.327085i	$0.106066\pi$
$137$			7.65685i			0.654169i	−0.944995	+	0.327085i	$0.893934\pi$
$138$	0.382683	+	1.68925i	0.0325762	+	0.143798i
$139$		−	5.80591i		−	0.492451i	−0.969213	−	0.246225i	$-0.920810\pi$
$139$		−	5.80591i		−	0.492451i	0.969213	−	0.246225i	$-0.0791904\pi$
$140$	−1.21371	−	7.65685i	−0.102577	−	0.647122i
$141$	−1.53553	−	6.77817i	−0.129315	−	0.570825i
$142$	9.65685			0.810385
$143$	−0.896683			−0.0749844
$144$	2.70711	−	1.29289i	0.225592	−	0.107741i
$145$		−	12.4316i		−	1.03239i
$146$	−5.86030			−0.485002
$147$	6.20432	+	10.4166i	0.511724	+	0.859150i
$148$	−6.48528			−0.533087
$149$			22.4853i			1.84207i	0.389485	+	0.921033i	$0.372653\pi$
$149$			22.4853i			1.84207i	−0.389485	+	0.921033i	$0.627347\pi$
$150$	6.05728	−	1.37222i	0.494575	−	0.112041i
$151$	10.8284			0.881205			0.440602	−	0.897702i	$-0.354765\pi$
$151$	10.8284			0.881205			0.440602	+	0.897702i	$0.354765\pi$
$152$	−6.49435			−0.526762
$153$	0.858221	−	0.409880i	0.0693831	−	0.0331368i
$154$	−0.242641	−	1.53073i	−0.0195525	−	0.123350i
$155$		−	19.4142i		−	1.55939i
$156$	2.58579	−	0.585786i	0.207029	−	0.0469005i
$157$			16.4441i			1.31238i	0.754594	+	0.656192i	$0.227834\pi$
$157$			16.4441i			1.31238i	−0.754594	+	0.656192i	$0.772166\pi$
$158$			14.7279i			1.17169i
$159$	−8.15640	+	1.84776i	−0.646845	+	0.146537i
$160$		−	14.6508i		−	1.15824i
$161$	−2.61313	+	0.414214i	−0.205943	+	0.0326446i
$162$	7.00000	+	5.65685i	0.549972	+	0.444444i
$163$	14.1421			1.10770			0.553849	−	0.832617i	$-0.313159\pi$
$163$	14.1421			1.10770			0.553849	+	0.832617i	$0.313159\pi$
$164$	9.55582			0.746184
$165$	−2.89949	+	0.656854i	−0.225725	+	0.0511360i
$166$		−	8.92177i		−	0.692464i
$167$	24.2835			1.87911			0.939557	−	0.342393i	$-0.111237\pi$
$167$	24.2835			1.87911			0.939557	+	0.342393i	$0.111237\pi$
$168$	5.09913	+	12.7671i	0.393406	+	0.985003i
$169$	10.6569			0.819758
$170$			0.928932i			0.0712458i
$171$	−2.79884	−	5.86030i	−0.214032	−	0.448149i
$172$	1.65685			0.126334
$173$	−10.4525			−0.794689			−0.397345	−	0.917669i	$-0.630068\pi$
$173$	−10.4525			−0.794689			−0.397345	+	0.917669i	$0.630068\pi$
$174$	1.62359	+	7.16687i	0.123084	+	0.543319i
$175$	1.48528	+	9.37011i	0.112277	+	0.708314i
$176$		−	0.585786i		−	0.0441553i
$177$	1.94975	+	8.60660i	0.146552	+	0.646912i
$178$		−	10.1355i		−	0.759686i
$179$		−	15.7990i		−	1.18087i	−0.807084	−	0.590436i	$-0.798956\pi$
$179$		−	15.7990i		−	1.18087i	0.807084	−	0.590436i	$-0.201044\pi$
$180$	7.93223	−	3.78837i	0.591234	−	0.282369i
$181$		−	9.05309i		−	0.672911i	−0.941699	−	0.336455i	$-0.890772\pi$
$181$		−	9.05309i		−	0.672911i	0.941699	−	0.336455i	$-0.109228\pi$
$182$	−0.634051	−	4.00000i	−0.0469990	−	0.296500i
$183$	−23.3640	+	5.29289i	−1.72711	+	0.391262i
$184$	−3.00000			−0.221163
$185$	19.0029			1.39712
$186$	2.53553	+	11.1924i	0.185914	+	0.820666i
$187$		−	0.185709i		−	0.0135804i
$188$	4.01254			0.292645
$189$	−9.32309	+	10.1035i	−0.678155	+	0.734919i
$190$	6.34315			0.460180
$191$		−	5.51472i		−	0.399031i	−0.979895	−	0.199516i	$-0.936063\pi$
$191$		−	5.51472i		−	0.399031i	0.979895	−	0.199516i	$-0.0639368\pi$
$192$	2.67878	+	11.8247i	0.193325	+	0.853376i
$193$	−25.6569			−1.84682			−0.923410	−	0.383814i	$-0.874610\pi$
$193$	−25.6569			−1.84682			−0.923410	+	0.383814i	$0.874610\pi$
$194$	−2.74444			−0.197039
$195$	−7.57675	+	1.71644i	−0.542582	+	0.122917i
$196$	−6.65685	+	2.16478i	−0.475490	+	0.154627i
$197$			23.3137i			1.66103i	0.556994	+	0.830516i	$0.311955\pi$
$197$			23.3137i			1.66103i	−0.556994	+	0.830516i	$0.688045\pi$
$198$	1.58579	−	0.757359i	0.112697	−	0.0538232i
$199$		−	8.28772i		−	0.587501i	−0.955882	−	0.293750i	$-0.905097\pi$
$199$		−	8.28772i		−	0.587501i	0.955882	−	0.293750i	$-0.0949035\pi$
$200$			10.7574i			0.760660i
$201$	4.10540	+	18.1221i	0.289572	+	1.27823i
$202$			16.3128i			1.14777i
$203$	−11.0866	+	1.75736i	−0.778124	+	0.123342i
$204$	0.121320	+	0.535534i	0.00849412	+	0.0374949i
$205$	−28.0000			−1.95560
$206$	3.06147			0.213303
$207$	−1.29289	−	2.70711i	−0.0898623	−	0.188157i
$208$		−	1.53073i		−	0.106137i
$209$	−1.26810			−0.0877164
$210$	−4.98040	−	12.4698i	−0.343681	−	0.860501i
$211$	20.4853			1.41026			0.705132	−	0.709076i	$-0.250888\pi$
$211$	20.4853			1.41026			0.705132	+	0.709076i	$0.250888\pi$
$212$		−	4.82843i		−	0.331618i
$213$	−16.3128	+	3.69552i	−1.11774	+	0.253213i
$214$	0.828427			0.0566301
$215$	−4.85483			−0.331097
$216$	−12.2346	+	9.65994i	−0.832459	+	0.657276i
$217$	−17.3137	+	2.74444i	−1.17533	+	0.186305i
$218$			3.65685i			0.247673i
$219$	9.89949	−	2.24264i	0.668946	−	0.151544i
$220$		−	1.71644i		−	0.115723i
$221$		−	0.485281i		−	0.0326436i
$222$	−10.9552	+	2.48181i	−0.735267	+	0.166568i
$223$			13.1969i			0.883733i	0.897081	+	0.441866i	$0.145683\pi$
$223$			13.1969i			0.883733i	−0.897081	+	0.441866i	$0.854317\pi$
$224$	−13.0656	+	2.07107i	−0.872984	+	0.138379i
$225$	−9.70711	+	4.63604i	−0.647140	+	0.309069i
$226$	3.17157			0.210970
$227$	11.7206			0.777924			0.388962	−	0.921254i	$-0.372834\pi$
$227$	11.7206			0.777924			0.388962	+	0.921254i	$0.372834\pi$
$228$	3.65685	−	0.828427i	0.242181	−	0.0548639i
$229$		−	4.19825i		−	0.277428i	−0.990332	−	0.138714i	$-0.955703\pi$
$229$		−	4.19825i		−	0.277428i	0.990332	−	0.138714i	$-0.0442969\pi$
$230$	2.93015			0.193208
$231$	0.995666	+	2.49293i	0.0655100	+	0.164023i
$232$	−12.7279			−0.835629
$233$			17.2132i			1.12767i	0.825886	+	0.563837i	$0.190675\pi$
$233$			17.2132i			1.12767i	−0.825886	+	0.563837i	$0.809325\pi$
$234$	4.14386	−	1.97908i	0.270893	−	0.129376i
$235$	−11.7574			−0.766966
$236$	−5.09494			−0.331652
$237$	−5.63613	−	24.8791i	−0.366106	−	1.61607i
$238$	0.828427	−	0.131316i	0.0536990	−	0.00851196i
$239$		−	17.1716i		−	1.11074i	−0.831604	−	0.555368i	$-0.812577\pi$
$239$		−	17.1716i		−	1.11074i	0.831604	−	0.555368i	$-0.187423\pi$
$240$	−1.12132	−	4.94975i	−0.0723809	−	0.319505i
$241$			19.2430i			1.23955i	0.784780	+	0.619774i	$0.212776\pi$
$241$			19.2430i			1.23955i	−0.784780	+	0.619774i	$0.787224\pi$
$242$			10.6569i			0.685049i
$243$	−13.9895	−	6.87704i	−0.897427	−	0.441162i
$244$		−	13.8310i		−	0.885439i
$245$	19.5056	−	6.34315i	1.24617	−	0.405249i
$246$	16.1421	−	3.65685i	1.02918	−	0.233153i
$247$	−3.31371			−0.210846
$248$	−19.8770			−1.26219
$249$	3.41421	+	15.0711i	0.216367	+	0.955090i
$250$			4.14386i			0.262081i
$251$	−14.4107			−0.909592			−0.454796	−	0.890596i	$-0.650288\pi$
$251$	−14.4107			−0.909592			−0.454796	+	0.890596i	$0.650288\pi$
$252$	−4.49981	−	6.53848i	−0.283462	−	0.411885i
$253$	−0.585786			−0.0368281
$254$			1.17157i			0.0735110i
$255$	−0.355487	−	1.56920i	−0.0222615	−	0.0982668i
$256$	−17.0000			−1.06250
$257$	−4.32957			−0.270071			−0.135036	−	0.990841i	$-0.543115\pi$
$257$	−4.32957			−0.270071			−0.135036	+	0.990841i	$0.543115\pi$
$258$	2.79884	−	0.634051i	0.174248	−	0.0394743i
$259$	−2.68629	−	16.9469i	−0.166918	−	1.05303i
$260$		−	4.48528i		−	0.278165i
$261$	−5.48528	−	11.4853i	−0.339530	−	0.710921i
$262$		−	14.4650i		−	0.893654i
$263$			25.0711i			1.54595i	0.634438	+	0.772974i	$0.281232\pi$
$263$			25.0711i			1.54595i	−0.634438	+	0.772974i	$0.718768\pi$
$264$	0.672512	+	2.96861i	0.0413903	+	0.182705i
$265$			14.1480i			0.869106i
$266$	−0.896683	−	5.65685i	−0.0549792	−	0.346844i
$267$	3.87868	+	17.1213i	0.237371	+	1.04781i
$268$	−10.7279			−0.655312
$269$	7.01962			0.427994			0.213997	−	0.976834i	$-0.431352\pi$
$269$	7.01962			0.427994			0.213997	+	0.976834i	$0.431352\pi$
$270$	11.9497	−	9.43503i	0.727238	−	0.574198i
$271$			4.01254i			0.243745i	0.992546	+	0.121872i	$0.0388898\pi$
$271$			4.01254i			0.243745i	−0.992546	+	0.121872i	$0.961110\pi$
$272$	0.317025			0.0192225
$273$	2.60180	+	6.51434i	0.157468	+	0.394266i
$274$	−7.65685			−0.462567
$275$			2.10051i			0.126665i
$276$	1.68925	−	0.382683i	0.101681	−	0.0230348i
$277$	17.4142			1.04632			0.523159	−	0.852235i	$-0.324753\pi$
$277$	17.4142			1.04632			0.523159	+	0.852235i	$0.324753\pi$
$278$	5.80591			0.348215
$279$	−8.56628	−	17.9364i	−0.512850	−	1.07382i
$280$	22.9706	−	3.64113i	1.37275	−	0.217599i
$281$		−	22.4853i		−	1.34136i	−0.741747	−	0.670680i	$-0.766003\pi$
$281$		−	22.4853i		−	1.34136i	0.741747	−	0.670680i	$-0.233997\pi$
$282$	6.77817	−	1.53553i	0.403634	−	0.0914397i
$283$		−	13.8854i		−	0.825401i	−0.910867	−	0.412700i	$-0.864586\pi$
$283$		−	13.8854i		−	0.825401i	0.910867	−	0.412700i	$-0.135414\pi$
$284$		−	9.65685i		−	0.573029i
$285$	−10.7151	+	2.42742i	−0.634710	+	0.143788i
$286$		−	0.896683i		−	0.0530220i
$287$	3.95815	+	24.9706i	0.233642	+	1.47397i
$288$	−6.46447	−	13.5355i	−0.380922	−	0.797589i
$289$	−16.8995			−0.994088
$290$	12.4316			0.730007
$291$	4.63604	−	1.05025i	0.271769	−	0.0615669i
$292$			5.86030i			0.342948i
$293$	29.6955			1.73483			0.867414	−	0.497588i	$-0.165781\pi$
$293$	29.6955			1.73483			0.867414	+	0.497588i	$0.165781\pi$
$294$	−10.4166	+	6.20432i	−0.607511	+	0.361843i
$295$	14.9289			0.869196
$296$		−	19.4558i		−	1.13085i
$297$	−2.38896	+	1.88622i	−0.138621	+	0.109450i
$298$	−22.4853			−1.30254
$299$	−1.53073			−0.0885246
$300$	−1.37222	−	6.05728i	−0.0792252	−	0.349717i
$301$	0.686292	+	4.32957i	0.0395572	+	0.249552i
$302$			10.8284i			0.623106i
$303$	−6.24264	−	27.5563i	−0.358630	−	1.58307i
$304$		−	2.16478i		−	0.124159i
$305$			40.5269i			2.32056i
$306$	0.409880	+	0.858221i	0.0234313	+	0.0490613i
$307$		−	17.3408i		−	0.989692i	−0.868981	−	0.494846i	$-0.835224\pi$
$307$		−	17.3408i		−	0.989692i	0.868981	−	0.494846i	$-0.164776\pi$
$308$	−1.53073	+	0.242641i	−0.0872216	+	0.0138257i
$309$	−5.17157	+	1.17157i	−0.294201	+	0.0666485i
$310$	19.4142			1.10265
$311$	18.6089			1.05521			0.527607	−	0.849488i	$-0.323089\pi$
$311$	18.6089			1.05521			0.527607	+	0.849488i	$0.323089\pi$
$312$	1.75736	+	7.75736i	0.0994909	+	0.439174i
$313$			5.99162i			0.338666i	0.985559	+	0.169333i	$0.0541614\pi$
$313$			5.99162i			0.338666i	−0.985559	+	0.169333i	$0.945839\pi$
$314$	−16.4441			−0.927996
$315$	13.1851	+	19.1587i	0.742898	+	1.07947i
$316$	14.7279			0.828510
$317$			29.2132i			1.64078i	0.571807	+	0.820388i	$0.306243\pi$
$317$			29.2132i			1.64078i	−0.571807	+	0.820388i	$0.693757\pi$
$318$	−1.84776	−	8.15640i	−0.103617	−	0.457388i
$319$	−2.48528			−0.139149
$320$	20.5111			1.14660
$321$	−1.39942	+	0.317025i	−0.0781079	+	0.0176946i
$322$	−0.414214	−	2.61313i	−0.0230832	−	0.145624i
$323$		−	0.686292i		−	0.0381863i
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$			5.48888i			0.304469i
$326$			14.1421i			0.783260i
$327$	−1.39942	−	6.17733i	−0.0773880	−	0.341607i
$328$			28.6675i			1.58290i
$329$	1.66205	+	10.4853i	0.0916318	+	0.578072i
$330$	−0.656854	−	2.89949i	−0.0361586	−	0.159612i
$331$	−16.9706			−0.932786			−0.466393	−	0.884577i	$-0.654447\pi$
$331$	−16.9706			−0.932786			−0.466393	+	0.884577i	$0.654447\pi$
$332$	−8.92177			−0.489646
$333$	17.5563	−	8.38478i	0.962082	−	0.459483i
$334$			24.2835i			1.32873i
$335$	31.4344			1.71745
$336$	−4.25570	+	1.69971i	−0.232168	+	0.0927267i
$337$	18.9706			1.03339			0.516696	−	0.856169i	$-0.327162\pi$
$337$	18.9706			1.03339			0.516696	+	0.856169i	$0.327162\pi$
$338$			10.6569i			0.579656i
$339$	−5.35757	+	1.21371i	−0.290983	+	0.0659196i
$340$	0.928932			0.0503784
$341$	−3.88123			−0.210180
$342$	5.86030	−	2.79884i	0.316889	−	0.151344i
$343$	−8.41421	−	16.4985i	−0.454325	−	0.890836i
$344$			4.97056i			0.267995i
$345$	−4.94975	+	1.12132i	−0.266485	+	0.0603699i
$346$		−	10.4525i		−	0.561930i
$347$		−	14.8284i		−	0.796032i	−0.917379	−	0.398016i	$-0.869699\pi$
$347$		−	14.8284i		−	0.796032i	0.917379	−	0.398016i	$-0.130301\pi$
$348$	7.16687	−	1.62359i	0.384184	−	0.0870335i
$349$		−	20.9050i		−	1.11902i	−0.828824	−	0.559510i	$-0.810989\pi$
$349$		−	20.9050i		−	1.11902i	0.828824	−	0.559510i	$-0.189011\pi$
$350$	−9.37011	+	1.48528i	−0.500854	+	0.0793916i
$351$	−6.24264	+	4.92893i	−0.333208	+	0.263087i
$352$	−2.92893			−0.156113
$353$	22.8072			1.21390			0.606951	−	0.794739i	$-0.292392\pi$
$353$	22.8072			1.21390			0.606951	+	0.794739i	$0.292392\pi$
$354$	−8.60660	+	1.94975i	−0.457436	+	0.103628i
$355$			28.2960i			1.50180i
$356$	−10.1355			−0.537179
$357$	−1.34917	+	0.538851i	−0.0714054	+	0.0285190i
$358$	15.7990			0.835003
$359$			12.5858i			0.664252i	0.943235	+	0.332126i	$0.107766\pi$
$359$			12.5858i			0.664252i	−0.943235	+	0.332126i	$0.892234\pi$
$360$	11.3651	+	23.7967i	0.598994	+	1.25420i
$361$	14.3137			0.753353
$362$	9.05309			0.475820
$363$	−4.07820	−	18.0021i	−0.214050	−	0.944863i
$364$	−4.00000	+	0.634051i	−0.209657	+	0.0332333i
$365$		−	17.1716i		−	0.898801i
$366$	−5.29289	−	23.3640i	−0.276664	−	1.22125i
$367$			29.8268i			1.55695i	0.627679	+	0.778473i	$0.284005\pi$
$367$			29.8268i			1.55695i	−0.627679	+	0.778473i	$0.715995\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	−25.8686	+	12.3547i	−1.34667	+	0.643158i
$370$			19.0029i			0.987911i
$371$	12.6173	−	2.00000i	0.655057	−	0.103835i
$372$	11.1924	−	2.53553i	0.580298	−	0.131461i
$373$	−22.9706			−1.18937			−0.594685	−	0.803959i	$-0.702723\pi$
$373$	−22.9706			−1.18937			−0.594685	+	0.803959i	$0.702723\pi$
$374$	0.185709			0.00960279
$375$	−1.58579	−	7.00000i	−0.0818897	−	0.361478i
$376$			12.0376i			0.620793i
$377$	−6.49435			−0.334476
$378$	−10.1035	−	9.32309i	−0.519666	−	0.479528i
$379$	10.9289			0.561382			0.280691	−	0.959798i	$-0.409436\pi$
$379$	10.9289			0.561382			0.280691	+	0.959798i	$0.409436\pi$
$380$		−	6.34315i		−	0.325397i
$381$	−0.448342	−	1.97908i	−0.0229692	−	0.101391i
$382$	5.51472			0.282158
$383$	34.1563			1.74531			0.872654	−	0.488339i	$-0.162397\pi$
$383$	34.1563			1.74531			0.872654	+	0.488339i	$0.162397\pi$
$384$	5.06774	−	1.14805i	0.258612	−	0.0585862i
$385$	4.48528	−	0.710974i	0.228591	−	0.0362346i
$386$		−	25.6569i		−	1.30590i
$387$	−4.48528	+	2.14214i	−0.228000	+	0.108891i
$388$			2.74444i			0.139328i
$389$		−	12.8284i		−	0.650427i	−0.945641	−	0.325214i	$-0.894564\pi$
$389$		−	12.8284i		−	0.650427i	0.945641	−	0.325214i	$-0.105436\pi$
$390$	−1.71644	−	7.57675i	−0.0869155	−	0.383663i
$391$		−	0.317025i		−	0.0160327i
$392$	−6.49435	−	19.9706i	−0.328014	−	1.00867i
$393$	5.53553	+	24.4350i	0.279231	+	1.23258i
$394$	−23.3137			−1.17453
$395$	−43.1550			−2.17137
$396$	−0.757359	−	1.58579i	−0.0380587	−	0.0796888i
$397$		−	2.42742i		−	0.121829i	−0.998143	−	0.0609143i	$-0.980598\pi$
$397$		−	2.42742i		−	0.121829i	0.998143	−	0.0609143i	$-0.0194016\pi$
$398$	8.28772			0.415426
$399$	3.67950	+	9.21267i	0.184206	+	0.461211i
$400$	−3.58579			−0.179289
$401$			23.1716i			1.15713i	0.815635	+	0.578567i	$0.196388\pi$
$401$			23.1716i			1.15713i	−0.815635	+	0.578567i	$0.803612\pi$
$402$	−18.1221	+	4.10540i	−0.903848	+	0.204759i
$403$	−10.1421			−0.505216
$404$	16.3128			0.811592
$405$	−16.5754	+	20.5111i	−0.823640	+	1.01920i
$406$	−1.75736	−	11.0866i	−0.0872163	−	0.550216i
$407$		−	3.79899i		−	0.188309i
$408$	−1.60660	+	0.363961i	−0.0795386	+	0.0180188i
$409$			5.48888i			0.271408i	0.990749	+	0.135704i	$0.0433296\pi$
$409$			5.48888i			0.271408i	−0.990749	+	0.135704i	$0.956670\pi$
$410$		−	28.0000i		−	1.38282i
$411$	12.9343	−	2.93015i	0.638003	−	0.144534i
$412$		−	3.06147i		−	0.150828i
$413$	−2.11039	−	13.3137i	−0.103846	−	0.655125i
$414$	2.70711	−	1.29289i	0.133047	−	0.0635422i
$415$	26.1421			1.28327
$416$	−7.65367			−0.375252
$417$	−9.80761	+	2.22183i	−0.480281	+	0.108803i
$418$		−	1.26810i		−	0.0620249i
$419$	18.7402			0.915520			0.457760	−	0.889076i	$-0.348652\pi$
$419$	18.7402			0.915520			0.457760	+	0.889076i	$0.348652\pi$
$420$	−12.4698	+	4.98040i	−0.608466	+	0.243019i
$421$	23.6569			1.15296			0.576482	−	0.817110i	$-0.304425\pi$
$421$	23.6569			1.15296			0.576482	+	0.817110i	$0.304425\pi$
$422$			20.4853i			0.997208i
$423$	−10.8624	+	5.18779i	−0.528147	+	0.252239i
$424$	14.4853			0.703467
$425$	−1.13679			−0.0551422
$426$	−3.69552	−	16.3128i	−0.179048	−	0.790358i
$427$	36.1421	−	5.72899i	1.74904	−	0.277245i
$428$		−	0.828427i		−	0.0400435i
$429$	0.343146	+	1.51472i	0.0165672	+	0.0731313i
$430$		−	4.85483i		−	0.234121i
$431$		−	39.5980i		−	1.90737i	−0.300811	−	0.953684i	$-0.597257\pi$
$431$		−	39.5980i		−	1.90737i	0.300811	−	0.953684i	$-0.402743\pi$
$432$	−3.21998	−	4.07820i	−0.154921	−	0.196213i
$433$		−	3.37849i		−	0.162360i	−0.996699	−	0.0811800i	$-0.974131\pi$
$433$		−	3.37849i		−	0.162360i	0.996699	−	0.0811800i	$-0.0258689\pi$
$434$	−2.74444	−	17.3137i	−0.131737	−	0.831085i
$435$	−21.0000	+	4.75736i	−1.00687	+	0.228098i
$436$	3.65685			0.175132
$437$	−2.16478			−0.103556
$438$	2.24264	+	9.89949i	0.107158	+	0.473016i
$439$			3.37849i			0.161247i	0.996745	+	0.0806233i	$0.0256911\pi$
$439$			3.37849i			0.161247i	−0.996745	+	0.0806233i	$0.974309\pi$
$440$	5.14933			0.245485
$441$	15.2220	−	14.4669i	0.724856	−	0.688900i
$442$	0.485281			0.0230825
$443$		−	23.7990i		−	1.13072i	−0.824843	−	0.565362i	$-0.808736\pi$
$443$		−	23.7990i		−	1.13072i	0.824843	−	0.565362i	$-0.191264\pi$
$444$	2.48181	+	10.9552i	0.117781	+	0.519913i
$445$	29.6985			1.40784
$446$	−13.1969			−0.624893
$447$	37.9832	−	8.60474i	1.79654	−	0.406990i
$448$	−2.89949	−	18.2919i	−0.136988	−	0.864210i
$449$		−	3.07107i		−	0.144933i	−0.997371	−	0.0724663i	$-0.976913\pi$
$449$		−	3.07107i		−	0.144933i	0.997371	−	0.0724663i	$-0.0230870\pi$
$450$	−4.63604	−	9.70711i	−0.218545	−	0.457597i
$451$			5.59767i			0.263584i
$452$		−	3.17157i		−	0.149178i
$453$	−4.14386	−	18.2919i	−0.194696	−	0.859428i
$454$			11.7206i			0.550075i
$455$	11.7206	−	1.85786i	0.549470	−	0.0870980i
$456$	2.48528	+	10.9706i	0.116384	+	0.513744i
$457$	−13.5147			−0.632192			−0.316096	−	0.948727i	$-0.602372\pi$
$457$	−13.5147			−0.632192			−0.316096	+	0.948727i	$0.602372\pi$
$458$	4.19825			0.196171
$459$	−1.02082	−	1.29289i	−0.0476476	−	0.0603471i
$460$		−	2.93015i		−	0.136619i
$461$	−20.0083			−0.931881			−0.465940	−	0.884816i	$-0.654284\pi$
$461$	−20.0083			−0.931881			−0.465940	+	0.884816i	$0.654284\pi$
$462$	−2.49293	+	0.995666i	−0.115982	+	0.0463226i
$463$	−18.6274			−0.865689			−0.432845	−	0.901468i	$-0.642490\pi$
$463$	−18.6274			−0.865689			−0.432845	+	0.901468i	$0.642490\pi$
$464$		−	4.24264i		−	0.196960i
$465$	−32.7954	+	7.42950i	−1.52085	+	0.344535i
$466$	−17.2132			−0.797386
$467$	−23.9665			−1.10904			−0.554518	−	0.832172i	$-0.687097\pi$
$467$	−23.9665			−1.10904			−0.554518	+	0.832172i	$0.687097\pi$
$468$	−1.97908	−	4.14386i	−0.0914828	−	0.191550i
$469$	−4.44365	−	28.0334i	−0.205189	−	1.29446i
$470$		−	11.7574i		−	0.542327i
$471$	27.7782	−	6.29289i	1.27995	−	0.289961i
$472$		−	15.2848i		−	0.703540i
$473$			0.970563i			0.0446265i
$474$	24.8791	−	5.63613i	1.14273	−	0.258876i
$475$			7.76245i			0.356166i
$476$	−0.131316	−	0.828427i	−0.00601887	−	0.0379709i
$477$	6.24264	+	13.0711i	0.285831	+	0.598483i
$478$	17.1716			0.785409
$479$	−16.9469			−0.774322			−0.387161	−	0.922012i	$-0.626544\pi$
$479$	−16.9469			−0.774322			−0.387161	+	0.922012i	$0.626544\pi$
$480$	−24.7487	+	5.60660i	−1.12962	+	0.255905i
$481$		−	9.92724i		−	0.452643i
$482$	−19.2430			−0.876493
$483$	1.69971	+	4.25570i	0.0773394	+	0.193641i
$484$	10.6569			0.484402
$485$		−	8.04163i		−	0.365152i
$486$	6.87704	−	13.9895i	0.311949	−	0.634577i
$487$	−15.3137			−0.693930			−0.346965	−	0.937878i	$-0.612788\pi$
$487$	−15.3137			−0.693930			−0.346965	+	0.937878i	$0.612788\pi$
$488$	41.4930			1.87830
$489$	−5.41196	−	23.8896i	−0.244737	−	1.08032i
$490$	6.34315	+	19.5056i	0.286554	+	0.881173i
$491$			3.31371i			0.149546i	0.997201	+	0.0747728i	$0.0238232\pi$
$491$			3.31371i			0.149546i	−0.997201	+	0.0747728i	$0.976177\pi$
$492$	−3.65685	−	16.1421i	−0.164864	−	0.727744i
$493$		−	1.34502i		−	0.0605769i
$494$		−	3.31371i		−	0.149091i
$495$	2.21918	+	4.64659i	0.0997446	+	0.208849i
$496$		−	6.62567i		−	0.297501i
$497$	25.2346	−	4.00000i	1.13193	−	0.179425i
$498$	−15.0711	+	3.41421i	−0.675351	+	0.152995i
$499$	13.6569			0.611365			0.305682	−	0.952134i	$-0.401115\pi$
$499$	13.6569			0.611365			0.305682	+	0.952134i	$0.401115\pi$
$500$	4.14386			0.185319
$501$	−9.29289	−	41.0208i	−0.415176	−	1.83267i
$502$		−	14.4107i		−	0.643179i
$503$	1.26810			0.0565418			0.0282709	−	0.999600i	$-0.491000\pi$
$503$	1.26810			0.0565418			0.0282709	+	0.999600i	$0.491000\pi$
$504$	19.6154	−	13.4994i	0.873741	−	0.601313i
$505$	−47.7990			−2.12703
$506$		−	0.585786i		−	0.0260414i
$507$	−4.07820	−	18.0021i	−0.181119	−	0.799499i
$508$	1.17157			0.0519801
$509$	8.65914			0.383810			0.191905	−	0.981414i	$-0.438534\pi$
$509$	8.65914			0.383810			0.191905	+	0.981414i	$0.438534\pi$
$510$	1.56920	−	0.355487i	0.0694851	−	0.0157412i
$511$	−15.3137	+	2.42742i	−0.677439	+	0.107383i
$512$		−	11.0000i		−	0.486136i
$513$	−8.82843	+	6.97056i	−0.389785	+	0.307758i
$514$		−	4.32957i		−	0.190969i
$515$			8.97056i			0.395290i
$516$	−0.634051	−	2.79884i	−0.0279125	−	0.123212i
$517$			2.35049i			0.103375i
$518$	16.9469	−	2.68629i	0.744602	−	0.118029i
$519$	4.00000	+	17.6569i	0.175581	+	0.775050i
$520$	13.4558			0.590078
$521$	−23.8352			−1.04424			−0.522119	−	0.852873i	$-0.674858\pi$
$521$	−23.8352			−1.04424			−0.522119	+	0.852873i	$0.674858\pi$
$522$	11.4853	−	5.48528i	0.502697	−	0.240084i
$523$		−	3.06147i		−	0.133869i	−0.997757	−	0.0669343i	$-0.978678\pi$
$523$		−	3.06147i		−	0.133869i	0.997757	−	0.0669343i	$-0.0213218\pi$
$524$	−14.4650			−0.631909
$525$	15.2600	−	6.09479i	0.666003	−	0.265999i
$526$	−25.0711			−1.09315
$527$		−	2.10051i		−	0.0914994i
$528$	−0.989538	+	0.224171i	−0.0430641	+	0.00975578i
$529$	−1.00000			−0.0434783
$530$	−14.1480			−0.614551
$531$	13.7925	−	6.58721i	0.598545	−	0.285860i
$532$	−5.65685	+	0.896683i	−0.245256	+	0.0388761i
$533$			14.6274i			0.633584i
$534$	−17.1213	+	3.87868i	−0.740912	+	0.167847i
$535$			2.42742i			0.104946i
$536$		−	32.1838i		−	1.39013i
$537$	−26.6884	+	6.04601i	−1.15169	+	0.260905i
$538$			7.01962i			0.302637i
$539$	−1.26810	−	3.89949i	−0.0546210	−	0.167963i
$540$	−9.43503	−	11.9497i	−0.406019	−	0.514235i
$541$	25.8995			1.11351			0.556753	−	0.830678i	$-0.312047\pi$
$541$	25.8995			1.11351			0.556753	+	0.830678i	$0.312047\pi$
$542$	−4.01254			−0.172353
$543$	−15.2929	+	3.46447i	−0.656281	+	0.148674i
$544$		−	1.58513i		−	0.0679617i
$545$	−10.7151			−0.458986
$546$	−6.51434	+	2.60180i	−0.278788	+	0.111347i
$547$	−34.8284			−1.48916			−0.744578	−	0.667535i	$-0.767349\pi$
$547$	−34.8284			−1.48916			−0.744578	+	0.667535i	$0.767349\pi$
$548$			7.65685i			0.327085i
$549$	17.8820	+	37.4420i	0.763185	+	1.59798i
$550$	−2.10051			−0.0895658
$551$	−9.18440			−0.391269
$552$	1.14805	+	5.06774i	0.0488643	+	0.215697i
$553$	6.10051	+	38.4859i	0.259420	+	1.63659i
$554$			17.4142i			0.739859i
$555$	−7.27208	−	32.1005i	−0.308683	−	1.36259i
$556$		−	5.80591i		−	0.246225i
$557$			9.51472i			0.403152i	0.979473	+	0.201576i	$0.0646062\pi$
$557$			9.51472i			0.403152i	−0.979473	+	0.201576i	$0.935394\pi$
$558$	17.9364	−	8.56628i	0.759308	−	0.362640i
$559$			2.53620i			0.107270i
$560$	1.21371	+	7.65685i	0.0512885	+	0.323561i
$561$	−0.313708	+	0.0710678i	−0.0132448	+	0.00300049i
$562$	22.4853			0.948484
$563$	−14.4107			−0.607337			−0.303668	−	0.952778i	$-0.598211\pi$
$563$	−14.4107			−0.607337			−0.303668	+	0.952778i	$0.598211\pi$
$564$	−1.53553	−	6.77817i	−0.0646576	−	0.285413i
$565$			9.29319i			0.390967i
$566$	13.8854			0.583646
$567$	20.6350	+	11.8826i	0.866590	+	0.499021i
$568$	28.9706			1.21558
$569$			36.3431i			1.52358i	0.647822	+	0.761792i	$0.275680\pi$
$569$			36.3431i			1.52358i	−0.647822	+	0.761792i	$0.724320\pi$
$570$	−2.42742	−	10.7151i	−0.101673	−	0.448808i
$571$	−1.65685			−0.0693372			−0.0346686	−	0.999399i	$-0.511038\pi$
$571$	−1.65685			−0.0693372			−0.0346686	+	0.999399i	$0.511038\pi$
$572$	−0.896683			−0.0374922
$573$	−9.31572	+	2.11039i	−0.389170	+	0.0881629i
$574$	−24.9706	+	3.95815i	−1.04225	+	0.165210i
$575$			3.58579i			0.149538i
$576$	18.9497	−	9.05025i	0.789573	−	0.377094i
$577$		−	18.1062i		−	0.753770i	−0.926260	−	0.376885i	$-0.876995\pi$
$577$		−	18.1062i		−	0.753770i	0.926260	−	0.376885i	$-0.123005\pi$
$578$		−	16.8995i		−	0.702926i
$579$	9.81845	+	43.3407i	0.408041	+	1.80118i
$580$		−	12.4316i		−	0.516193i
$581$	−3.69552	−	23.3137i	−0.153316	−	0.967216i
$582$	1.05025	+	4.63604i	0.0435344	+	0.192170i
$583$	2.82843			0.117141
$584$	−17.5809			−0.727503
$585$	5.79899	+	12.1421i	0.239759	+	0.502016i
$586$			29.6955i			1.22671i
$587$	19.8770			0.820412			0.410206	−	0.911993i	$-0.365457\pi$
$587$	19.8770			0.820412			0.410206	+	0.911993i	$0.365457\pi$
$588$	6.20432	+	10.4166i	0.255862	+	0.429575i
$589$	−14.3431			−0.590999
$590$			14.9289i			0.614614i
$591$	39.3826	−	8.92177i	1.61998	−	0.366993i
$592$	6.48528			0.266543
$593$	−20.3797			−0.836896			−0.418448	−	0.908241i	$-0.637426\pi$
$593$	−20.3797			−0.836896			−0.418448	+	0.908241i	$0.637426\pi$
$594$	−1.88622	−	2.38896i	−0.0773926	−	0.0980200i
$595$	0.384776	+	2.42742i	0.0157743	+	0.0995144i
$596$			22.4853i			0.921033i
$597$	−14.0000	+	3.17157i	−0.572982	+	0.129804i
$598$		−	1.53073i		−	0.0625964i
$599$			27.1127i			1.10779i	0.832585	+	0.553897i	$0.186860\pi$
$599$			27.1127i			1.10779i	−0.832585	+	0.553897i	$0.813140\pi$
$600$	18.1718	−	4.11666i	0.741862	−	0.168062i
$601$			26.7653i			1.09178i	0.837857	+	0.545890i	$0.183808\pi$
$601$			26.7653i			1.09178i	−0.837857	+	0.545890i	$0.816192\pi$
$602$	−4.32957	+	0.686292i	−0.176460	+	0.0279712i
$603$	29.0416	−	13.8701i	1.18267	−	0.564832i
$604$	10.8284			0.440602
$605$	−31.2262			−1.26953
$606$	27.5563	−	6.24264i	1.11940	−	0.253590i
$607$		−	27.5307i		−	1.11744i	−0.829358	−	0.558718i	$-0.811293\pi$
$607$		−	27.5307i		−	1.11744i	0.829358	−	0.558718i	$-0.188707\pi$
$608$	−10.8239			−0.438968
$609$	7.21125	+	18.0554i	0.292215	+	0.731642i
$610$	−40.5269			−1.64089
$611$			6.14214i			0.248484i
$612$	0.858221	−	0.409880i	0.0346915	−	0.0165684i
$613$	12.3431			0.498535			0.249267	−	0.968435i	$-0.419810\pi$
$613$	12.3431			0.498535			0.249267	+	0.968435i	$0.419810\pi$
$614$	17.3408			0.699818
$615$	10.7151	+	47.2989i	0.432076	+	1.90728i
$616$	−0.727922	−	4.59220i	−0.0293288	−	0.185025i
$617$			10.0000i			0.402585i	0.979531	+	0.201292i	$0.0645141\pi$
$617$			10.0000i			0.402585i	−0.979531	+	0.201292i	$0.935486\pi$
$618$	−1.17157	−	5.17157i	−0.0471276	−	0.208031i
$619$		−	15.9414i		−	0.640738i	−0.947293	−	0.320369i	$-0.896193\pi$
$619$		−	15.9414i		−	0.640738i	0.947293	−	0.320369i	$-0.103807\pi$
$620$		−	19.4142i		−	0.779694i
$621$	−4.07820	+	3.21998i	−0.163653	+	0.129213i
$622$			18.6089i			0.746149i
$623$	−4.19825	−	26.4853i	−0.168199	−	1.06111i
$624$	−2.58579	+	0.585786i	−0.103514	+	0.0234502i
$625$	−30.0711			−1.20284
$626$	−5.99162			−0.239473
$627$	0.485281	+	2.14214i	0.0193803	+	0.0855487i
$628$			16.4441i			0.656192i
$629$	2.05600			0.0819780
$630$	−19.1587	+	13.1851i	−0.763302	+	0.525308i
$631$	−34.0416			−1.35518			−0.677588	−	0.735442i	$-0.736975\pi$
$631$	−34.0416			−1.35518			−0.677588	+	0.735442i	$0.736975\pi$
$632$			44.1838i			1.75754i
$633$	−7.83938	−	34.6047i	−0.311587	−	1.37541i
$634$	−29.2132			−1.16020
$635$	−3.43289			−0.136230
$636$	−8.15640	+	1.84776i	−0.323422	+	0.0732684i
$637$	−3.31371	−	10.1899i	−0.131294	−	0.403737i
$638$		−	2.48528i		−	0.0983932i
$639$	12.4853	+	26.1421i	0.493910	+	1.03417i
$640$		−	8.79045i		−	0.347473i
$641$			50.2843i			1.98611i	0.117654	+	0.993055i	$0.462463\pi$
$641$			50.2843i			1.98611i	−0.117654	+	0.993055i	$0.537537\pi$
$642$	−0.317025	−	1.39942i	−0.0125120	−	0.0552306i
$643$			5.75152i			0.226818i	0.993548	+	0.113409i	$0.0361770\pi$
$643$			5.75152i			0.226818i	−0.993548	+	0.113409i	$0.963823\pi$
$644$	−2.61313	+	0.414214i	−0.102972	+	0.0163223i
$645$	1.85786	+	8.20101i	0.0731533	+	0.322914i
$646$	0.686292			0.0270018
$647$	−42.7611			−1.68111			−0.840556	−	0.541725i	$-0.817772\pi$
$647$	−42.7611			−1.68111			−0.840556	+	0.541725i	$0.817772\pi$
$648$	21.0000	+	16.9706i	0.824958	+	0.666667i
$649$		−	2.98454i		−	0.117154i
$650$	−5.48888			−0.215292
$651$	11.2617	+	28.1969i	0.441381	+	1.10512i
$652$	14.1421			0.553849
$653$		−	19.3137i		−	0.755804i	−0.925846	−	0.377902i	$-0.876646\pi$
$653$		−	19.3137i		−	0.755804i	0.925846	−	0.377902i	$-0.123354\pi$
$654$	6.17733	−	1.39942i	0.241553	−	0.0547216i
$655$	42.3848			1.65611
$656$	−9.55582			−0.373092
$657$	−7.57675	−	15.8645i	−0.295597	−	0.618932i
$658$	−10.4853	+	1.66205i	−0.408759	+	0.0647935i
$659$			28.0000i			1.09073i	0.838200	+	0.545363i	$0.183608\pi$
$659$			28.0000i			1.09073i	−0.838200	+	0.545363i	$0.816392\pi$
$660$	−2.89949	+	0.656854i	−0.112863	+	0.0255680i
$661$		−	29.7724i		−	1.15801i	−0.815323	−	0.579006i	$-0.803441\pi$
$661$		−	29.7724i		−	1.15801i	0.815323	−	0.579006i	$-0.196559\pi$
$662$		−	16.9706i		−	0.659580i
$663$	−0.819760	+	0.185709i	−0.0318368	+	0.00721235i
$664$		−	26.7653i		−	1.03870i
$665$	16.5754	−	2.62742i	0.642768	−	0.101887i
$666$	8.38478	+	17.5563i	0.324903	+	0.680295i
$667$	−4.24264			−0.164276
$668$	24.2835			0.939557
$669$	22.2929	−	5.05025i	0.861893	−	0.195254i
$670$			31.4344i			1.21442i
$671$	8.10201			0.312775
$672$	8.49854	+	21.2785i	0.327838	+	0.820836i
$673$	2.58579			0.0996747			0.0498374	−	0.998757i	$-0.484130\pi$
$673$	2.58579			0.0996747			0.0498374	+	0.998757i	$0.484130\pi$
$674$			18.9706i			0.730719i
$675$	11.5462	+	14.6236i	0.444412	+	0.562861i
$676$	10.6569			0.409879
$677$	18.7177			0.719379			0.359690	−	0.933072i	$-0.382883\pi$
$677$	18.7177			0.719379			0.359690	+	0.933072i	$0.382883\pi$
$678$	−1.21371	−	5.35757i	−0.0466122	−	0.205756i
$679$	−7.17157	+	1.13679i	−0.275220	+	0.0436258i
$680$			2.78680i			0.106869i
$681$	−4.48528	−	19.7990i	−0.171876	−	0.758699i
$682$		−	3.88123i		−	0.148620i
$683$		−	7.79899i		−	0.298420i	−0.988806	−	0.149210i	$-0.952327\pi$
$683$		−	7.79899i		−	0.298420i	0.988806	−	0.149210i	$-0.0476731\pi$
$684$	−2.79884	−	5.86030i	−0.107016	−	0.224074i
$685$		−	22.4357i		−	0.857226i
$686$	16.4985	−	8.41421i	0.629916	−	0.321256i
$687$	−7.09188	+	1.60660i	−0.270572	+	0.0612957i
$688$	−1.65685			−0.0631670
$689$	7.39104			0.281576
$690$	−1.12132	−	4.94975i	−0.0426879	−	0.188434i
$691$		−	4.08947i		−	0.155571i	−0.996970	−	0.0777853i	$-0.975215\pi$
$691$		−	4.08947i		−	0.155571i	0.996970	−	0.0777853i	$-0.0247849\pi$
$692$	−10.4525			−0.397345
$693$	3.83015	−	2.63593i	0.145495	−	0.100131i
$694$	14.8284			0.562879
$695$			17.0122i			0.645309i
$696$	4.87076	+	21.5006i	0.184626	+	0.814978i
$697$	−3.02944			−0.114748
$698$	20.9050			0.791266
$699$	29.0773	−	6.58721i	1.09981	−	0.249151i
$700$	1.48528	+	9.37011i	0.0561384	+	0.354157i
$701$		−	38.9706i		−	1.47190i	−0.677037	−	0.735949i	$-0.736736\pi$
$701$		−	38.9706i		−	1.47190i	0.677037	−	0.735949i	$-0.263264\pi$
$702$	−4.92893	−	6.24264i	−0.186031	−	0.235613i
$703$		−	14.0392i		−	0.529500i
$704$		−	4.10051i		−	0.154544i
$705$	4.49935	+	19.8611i	0.169455	+	0.748011i
$706$			22.8072i			0.858359i
$707$	6.75699	+	42.6274i	0.254123	+	1.60317i
$708$	1.94975	+	8.60660i	0.0732760	+	0.323456i
$709$	22.2843			0.836903			0.418452	−	0.908239i	$-0.362573\pi$
$709$	22.2843			0.836903			0.418452	+	0.908239i	$0.362573\pi$
$710$	−28.2960			−1.06193
$711$	−39.8701	+	19.0416i	−1.49524	+	0.714117i
$712$		−	30.4064i		−	1.13953i
$713$	−6.62567			−0.248133
$714$	−0.538851	−	1.34917i	−0.0201660	−	0.0504912i
$715$	2.62742			0.0982598
$716$		−	15.7990i		−	0.590436i
$717$	−29.0070	+	6.57128i	−1.08329	+	0.245409i
$718$	−12.5858			−0.469697
$719$	2.74444			0.102350			0.0511752	−	0.998690i	$-0.483703\pi$
$719$	2.74444			0.102350			0.0511752	+	0.998690i	$0.483703\pi$
$720$	−7.93223	+	3.78837i	−0.295617	+	0.141184i
$721$	8.00000	−	1.26810i	0.297936	−	0.0472266i
$722$			14.3137i			0.532701i
$723$	32.5061	−	7.36396i	1.20891	−	0.273869i
$724$		−	9.05309i		−	0.336455i
$725$			15.2132i			0.565004i
$726$	18.0021	−	4.07820i	0.668119	−	0.151356i
$727$		−	30.8322i		−	1.14350i	−0.820426	−	0.571752i	$-0.806264\pi$
$727$		−	30.8322i		−	1.14350i	0.820426	−	0.571752i	$-0.193736\pi$
$728$	−1.90215	−	12.0000i	−0.0704984	−	0.444750i
$729$	−6.26346	+	26.2635i	−0.231980	+	0.972721i
$730$	17.1716			0.635548
$731$	−0.525265			−0.0194276
$732$	−23.3640	+	5.29289i	−0.863557	+	0.195631i
$733$		−	48.8840i		−	1.80557i	−0.430089	−	0.902786i	$-0.641518\pi$
$733$		−	48.8840i		−	1.80557i	0.430089	−	0.902786i	$-0.358482\pi$
$734$	−29.8268			−1.10093
$735$	−18.1796	−	30.5223i	−0.670565	−	1.12583i
$736$	−5.00000			−0.184302
$737$		−	6.28427i		−	0.231484i
$738$	−12.3547	−	25.8686i	−0.454781	−	0.952237i
$739$	−12.9706			−0.477130			−0.238565	−	0.971127i	$-0.576677\pi$
$739$	−12.9706			−0.477130			−0.238565	+	0.971127i	$0.576677\pi$
$740$	19.0029			0.698559
$741$	1.26810	+	5.59767i	0.0465849	+	0.205636i
$742$	2.00000	+	12.6173i	0.0734223	+	0.463195i
$743$			2.44365i			0.0896489i	0.998995	+	0.0448244i	$0.0142728\pi$
$743$			2.44365i			0.0896489i	−0.998995	+	0.0448244i	$0.985727\pi$
$744$	7.60660	+	33.5772i	0.278872	+	1.23100i
$745$		−	65.8853i		−	2.41385i
$746$		−	22.9706i		−	0.841012i
$747$	24.1522	−	11.5349i	0.883682	−	0.422040i
$748$		−	0.185709i		−	0.00679020i
$749$	2.16478	−	0.343146i	0.0790995	−	0.0125383i
$750$	7.00000	−	1.58579i	0.255604	−	0.0579047i
$751$	49.8406			1.81871			0.909355	−	0.416021i	$-0.136576\pi$
$751$	49.8406			1.81871			0.909355	+	0.416021i	$0.136576\pi$
$752$	−4.01254			−0.146322
$753$	5.51472	+	24.3431i	0.200968	+	0.887114i
$754$		−	6.49435i		−	0.236510i
$755$	−31.7289			−1.15473
$756$	−9.32309	+	10.1035i	−0.339078	+	0.367459i
$757$	−1.51472			−0.0550534			−0.0275267	−	0.999621i	$-0.508763\pi$
$757$	−1.51472			−0.0550534			−0.0275267	+	0.999621i	$0.508763\pi$
$758$			10.9289i			0.396957i
$759$	0.224171	+	0.989538i	0.00813688	+	0.0359179i
$760$	19.0294			0.690270
$761$	2.79884			0.101458			0.0507288	−	0.998712i	$-0.483846\pi$
$761$	2.79884			0.101458			0.0507288	+	0.998712i	$0.483846\pi$
$762$	1.97908	−	0.448342i	0.0716943	−	0.0162417i
$763$	1.51472	+	9.55582i	0.0548365	+	0.345944i
$764$		−	5.51472i		−	0.199516i
$765$	−2.51472	+	1.20101i	−0.0909198	+	0.0434226i
$766$			34.1563i			1.23412i
$767$		−	7.79899i		−	0.281605i
$768$	6.50562	+	28.7172i	0.234751	+	1.03624i
$769$		−	19.2430i		−	0.693919i	−0.937880	−	0.346959i	$-0.887214\pi$
$769$		−	19.2430i		−	0.693919i	0.937880	−	0.346959i	$-0.112786\pi$
$770$	0.710974	+	4.48528i	0.0256217	+	0.161638i
$771$	1.65685	+	7.31371i	0.0596701	+	0.263397i
$772$	−25.6569			−0.923410
$773$	−9.50143			−0.341743			−0.170871	−	0.985293i	$-0.554658\pi$
$773$	−9.50143			−0.341743			−0.170871	+	0.985293i	$0.554658\pi$
$774$	−2.14214	−	4.48528i	−0.0769975	−	0.161220i
$775$			23.7582i			0.853421i
$776$	−8.23333			−0.295559
$777$	−27.5994	+	11.0231i	−0.990124	+	0.395451i
$778$	12.8284			0.459921
$779$			20.6863i			0.741163i
$780$	−7.57675	+	1.71644i	−0.271291	+	0.0614585i
$781$	5.65685			0.202418
$782$	0.317025			0.0113368
$783$	−17.3023	+	13.6612i	−0.618335	+	0.488212i
$784$	6.65685	−	2.16478i	0.237745	−	0.0773137i
$785$		−	48.1838i		−	1.71975i
$786$	−24.4350	+	5.53553i	−0.871569	+	0.197446i
$787$			30.1982i			1.07645i	0.842801	+	0.538225i	$0.180905\pi$
$787$			30.1982i			1.07645i	−0.842801	+	0.538225i	$0.819095\pi$
$788$			23.3137i			0.830516i
$789$	42.3512	−	9.59428i	1.50774	−	0.341565i
$790$		−	43.1550i		−	1.53539i
$791$	8.28772	−	1.31371i	0.294677	−	0.0467101i
$792$	4.75736	−	2.27208i	0.169045	−	0.0807348i
$793$	21.1716			0.751825
$794$	2.42742			0.0861458
$795$	23.8995	−	5.41421i	0.847628	−	0.192022i
$796$		−	8.28772i		−	0.293750i
$797$	−46.4566			−1.64558			−0.822789	−	0.568347i	$-0.807583\pi$
$797$	−46.4566			−1.64558			−0.822789	+	0.568347i	$0.807583\pi$
$798$	−9.21267	+	3.67950i	−0.326125	+	0.130253i
$799$	−1.27208			−0.0450029
$800$			17.9289i			0.633883i
$801$	27.4378	−	13.1041i	0.969468	−	0.463010i
$802$	−23.1716			−0.818217
$803$	−3.43289			−0.121144
$804$	4.10540	+	18.1221i	0.144786	+	0.639117i
$805$	7.65685	−	1.21371i	0.269869	−	0.0427776i
$806$		−	10.1421i		−	0.357241i
$807$	−2.68629	−	11.8579i	−0.0945619	−	0.417417i
$808$			48.9384i			1.72165i
$809$			29.3137i			1.03062i	0.857005	+	0.515308i	$0.172322\pi$
$809$			29.3137i			1.03062i	−0.857005	+	0.515308i	$0.827678\pi$
$810$	−20.5111	−	16.5754i	−0.720685	−	0.582402i
$811$			14.5420i			0.510638i	0.966857	+	0.255319i	$0.0821804\pi$
$811$			14.5420i			0.510638i	−0.966857	+	0.255319i	$0.917820\pi$
$812$	−11.0866	+	1.75736i	−0.389062	+	0.0616712i
$813$	6.77817	−	1.53553i	0.237721	−	0.0538535i
$814$	3.79899			0.133155
$815$	−41.4386			−1.45153
$816$	−0.121320	−	0.535534i	−0.00424706	−	0.0187474i
$817$			3.58673i			0.125484i
$818$	−5.48888			−0.191914
$819$	10.0087	−	6.88802i	0.349731	−	0.240687i
$820$	−28.0000			−0.977802
$821$		−	48.2426i		−	1.68368i	−0.539727	−	0.841840i	$-0.681473\pi$
$821$		−	48.2426i		−	1.68368i	0.539727	−	0.841840i	$-0.318527\pi$
$822$	2.93015	+	12.9343i	0.102201	+	0.451136i
$823$	27.1127			0.945089			0.472545	−	0.881307i	$-0.343336\pi$
$823$	27.1127			0.945089			0.472545	+	0.881307i	$0.343336\pi$
$824$	9.18440			0.319954
$825$	3.54827	−	0.803828i	0.123535	−	0.0279857i
$826$	13.3137	−	2.11039i	0.463243	−	0.0734299i
$827$		−	34.6274i		−	1.20411i	−0.798453	−	0.602057i	$-0.794348\pi$
$827$		−	34.6274i		−	1.20411i	0.798453	−	0.602057i	$-0.205652\pi$
$828$	−1.29289	−	2.70711i	−0.0449311	−	0.0940785i
$829$			45.7682i			1.58959i	0.606875	+	0.794797i	$0.292423\pi$
$829$			45.7682i			1.58959i	−0.606875	+	0.794797i	$0.707577\pi$
$830$			26.1421i			0.907407i
$831$	−6.66413	−	29.4169i	−0.231176	−	1.02046i
$832$		−	10.7151i		−	0.371481i
$833$	2.11039	−	0.686292i	0.0731207	−	0.0237786i
$834$	−2.22183	−	9.80761i	−0.0769355	−	0.339610i
$835$	−71.1543			−2.46240
$836$	−1.26810			−0.0438582
$837$	−27.0208	+	21.3345i	−0.933976	+	0.737429i
$838$			18.7402i			0.647370i
$839$	3.69552			0.127583			0.0637917	−	0.997963i	$-0.479681\pi$
$839$	3.69552			0.127583			0.0637917	+	0.997963i	$0.479681\pi$
$840$	−14.9412	−	37.4095i	−0.515521	−	1.29075i
$841$	11.0000			0.379310
$842$			23.6569i			0.815269i
$843$	−37.9832	+	8.60474i	−1.30821	+	0.296363i
$844$	20.4853			0.705132
$845$	−31.2262			−1.07421
$846$	−5.18779	−	10.8624i	−0.178360	−	0.373456i
$847$	4.41421	+	27.8477i	0.151674	+	0.956858i
$848$			4.82843i			0.165809i
$849$	−23.4558	+	5.31371i	−0.805002	+	0.182366i
$850$		−	1.13679i		−	0.0389914i
$851$		−	6.48528i		−	0.222313i
$852$	−16.3128	+	3.69552i	−0.558868	+	0.126606i
$853$			51.4746i			1.76246i	0.472690	+	0.881229i	$0.343283\pi$
$853$			51.4746i			1.76246i	−0.472690	+	0.881229i	$0.656717\pi$
$854$	5.72899	+	36.1421i	0.196042	+	1.23676i
$855$	8.20101	+	17.1716i	0.280469	+	0.587255i
$856$	2.48528			0.0849452
$857$	14.4107			0.492259			0.246129	−	0.969237i	$-0.420841\pi$
$857$	14.4107			0.492259			0.246129	+	0.969237i	$0.420841\pi$
$858$	−1.51472	+	0.343146i	−0.0517116	+	0.0117148i
$859$		−	48.3588i		−	1.64998i	−0.565148	−	0.824990i	$-0.691181\pi$
$859$		−	48.3588i		−	1.64998i	0.565148	−	0.824990i	$-0.308819\pi$
$860$	−4.85483			−0.165548
$861$	40.6667	−	16.2421i	1.38592	−	0.553530i
$862$	39.5980			1.34871
$863$		−	22.6274i		−	0.770246i	−0.922865	−	0.385123i	$-0.874159\pi$
$863$		−	22.6274i		−	0.770246i	0.922865	−	0.385123i	$-0.125841\pi$
$864$	−20.3910	+	16.0999i	−0.693716	+	0.547730i
$865$	30.6274			1.04136
$866$	3.37849			0.114806
$867$	6.46716	+	28.5474i	0.219636	+	0.969521i
$868$	−17.3137	+	2.74444i	−0.587666	+	0.0931524i
$869$			8.62742i			0.292665i
$870$	−4.75736	−	21.0000i	−0.161290	−	0.711967i
$871$		−	16.4216i		−	0.556424i
$872$			10.9706i			0.371510i
$873$	−3.54827	−	7.42950i	−0.120091	−	0.251450i
$874$		−	2.16478i		−	0.0732249i
$875$	1.71644	+	10.8284i	0.0580264	+	0.366068i
$876$	9.89949	−	2.24264i	0.334473	−	0.0757718i
$877$	−50.8701			−1.71776			−0.858880	−	0.512177i	$-0.828839\pi$
$877$	−50.8701			−1.71776			−0.858880	+	0.512177i	$0.828839\pi$
$878$	−3.37849			−0.114019
$879$	−11.3640	−	50.1630i	−0.383297	−	1.69195i
$880$			1.71644i			0.0578613i
$881$	−21.7473			−0.732685			−0.366343	−	0.930480i	$-0.619390\pi$
$881$	−21.7473			−0.732685			−0.366343	+	0.930480i	$0.619390\pi$
$882$	14.4669	+	15.2220i	0.487126	+	0.512551i
$883$	−23.5147			−0.791333			−0.395667	−	0.918394i	$-0.629486\pi$
$883$	−23.5147			−0.791333			−0.395667	+	0.918394i	$0.629486\pi$
$884$		−	0.485281i		−	0.0163218i
$885$	−5.71306	−	25.2186i	−0.192042	−	0.847715i
$886$	23.7990			0.799543
$887$	−28.5361			−0.958150			−0.479075	−	0.877774i	$-0.659028\pi$
$887$	−28.5361			−0.958150			−0.479075	+	0.877774i	$0.659028\pi$
$888$	−32.8657	+	7.44543i	−1.10290	+	0.249852i
$889$	0.485281	+	3.06147i	0.0162758	+	0.102678i
$890$			29.6985i			0.995495i
$891$	4.10051	+	3.31371i	0.137372	+	0.111013i
$892$			13.1969i			0.441866i
$893$			8.68629i			0.290676i
$894$	8.60474	+	37.9832i	0.287786	+	1.27035i
$895$			46.2934i			1.54742i
$896$	−7.83938	+	1.24264i	−0.261895	+	0.0415137i
$897$	0.585786	+	2.58579i	0.0195588	+	0.0863369i
$898$	3.07107			0.102483
$899$	−28.1103			−0.937532
$900$	−9.70711	+	4.63604i	−0.323570	+	0.154535i
$901$			1.53073i			0.0509961i
$902$	−5.59767			−0.186382
$903$	7.05108	−	2.81617i	0.234645	−	0.0937163i
$904$	9.51472			0.316455
$905$			26.5269i			0.881784i
$906$	18.2919	−	4.14386i	0.607707	−	0.137671i
$907$	−13.1127			−0.435400			−0.217700	−	0.976016i	$-0.569855\pi$
$907$	−13.1127			−0.435400			−0.217700	+	0.976016i	$0.569855\pi$
$908$	11.7206			0.388962
$909$	−44.1605	+	21.0907i	−1.46471	+	0.699535i
$910$	1.85786	+	11.7206i	0.0615876	+	0.388534i
$911$		−	25.2721i		−	0.837301i	−0.908147	−	0.418651i	$-0.862503\pi$
$911$		−	25.2721i		−	0.837301i	0.908147	−	0.418651i	$-0.137497\pi$
$912$	−3.65685	+	0.828427i	−0.121091	+	0.0274320i
$913$		−	5.22625i		−	0.172964i
$914$		−	13.5147i		−	0.447027i
$915$	68.4599	−	15.5090i	2.26322	−	0.512711i
$916$		−	4.19825i		−	0.138714i
$917$	−5.99162	−	37.7990i	−0.197861	−	1.24823i
$918$	1.29289	−	1.02082i	0.0426718	−	0.0336919i
$919$	2.44365			0.0806086			0.0403043	−	0.999187i	$-0.487167\pi$
$919$	2.44365			0.0806086			0.0403043	+	0.999187i	$0.487167\pi$
$920$	8.79045			0.289813
$921$	−29.2929	+	6.63604i	−0.965234	+	0.218665i
$922$		−	20.0083i		−	0.658939i
$923$	14.7821			0.486558
$924$	0.995666	+	2.49293i	0.0327550	+	0.0820114i
$925$	−23.2548			−0.764614
$926$		−	18.6274i		−	0.612135i
$927$	3.95815	+	8.28772i	0.130003	+	0.272204i
$928$	−21.2132			−0.696358
$929$	48.3044			1.58481			0.792407	−	0.609992i	$-0.208827\pi$
$929$	48.3044			1.58481			0.792407	+	0.609992i	$0.208827\pi$
$930$	−7.42950	−	32.7954i	−0.243623	−	1.07540i
$931$	−4.68629	−	14.4107i	−0.153587	−	0.472290i
$932$			17.2132i			0.563837i
$933$	−7.12132	−	31.4350i	−0.233142	−	1.02914i
$934$		−	23.9665i		−	0.784207i
$935$			0.544156i			0.0177958i
$936$	12.4316	−	5.93723i	0.406339	−	0.194064i
$937$		−	6.73446i		−	0.220005i	−0.993931	−	0.110003i	$-0.964914\pi$
$937$		−	6.73446i		−	0.220005i	0.993931	−	0.110003i	$-0.0350859\pi$
$938$	28.0334	−	4.44365i	0.915323	−	0.145090i
$939$	10.1213	−	2.29289i	0.330297	−	0.0748257i
$940$	−11.7574			−0.383483
$941$	27.9790			0.912090			0.456045	−	0.889957i	$-0.349266\pi$
$941$	27.9790			0.912090			0.456045	+	0.889957i	$0.349266\pi$
$942$	6.29289	+	27.7782i	0.205034	+	0.905062i
$943$			9.55582i			0.311180i
$944$	5.09494			0.165826
$945$	27.3181	−	29.6047i	0.888657	−	0.963040i
$946$	−0.970563			−0.0315557
$947$		−	48.2843i		−	1.56903i	−0.620111	−	0.784514i	$-0.712912\pi$
$947$		−	48.2843i		−	1.56903i	0.620111	−	0.784514i	$-0.287088\pi$
$948$	−5.63613	−	24.8791i	−0.183053	−	0.808035i
$949$	−8.97056			−0.291197
$950$	−7.76245			−0.251847
$951$	49.3483	−	11.1794i	1.60023	−	0.362517i
$952$	2.48528	−	0.393949i	0.0805484	−	0.0127679i
$953$		−	27.6569i		−	0.895893i	−0.894060	−	0.447947i	$-0.852155\pi$
$953$		−	27.6569i		−	0.895893i	0.894060	−	0.447947i	$-0.147845\pi$
$954$	−13.0711	+	6.24264i	−0.423191	+	0.202113i
$955$			16.1590i			0.522892i
$956$		−	17.1716i		−	0.555368i
$957$	0.951076	+	4.19825i	0.0307439	+	0.135710i
$958$		−	16.9469i		−	0.547528i
$959$	−20.0083	+	3.17157i	−0.646102	+	0.102415i
$960$	−7.84924	−	34.6482i	−0.253333	−	1.11827i
$961$	−12.8995			−0.416113
$962$	9.92724			0.320067
$963$	1.07107	+	2.24264i	0.0345147	+	0.0722681i
$964$			19.2430i			0.619774i
$965$	75.1785			2.42008
$966$	−4.25570	+	1.69971i	−0.136925	+	0.0546872i
$967$	2.82843			0.0909561			0.0454780	−	0.998965i	$-0.485519\pi$
$967$	2.82843			0.0909561			0.0454780	+	0.998965i	$0.485519\pi$
$968$			31.9706i			1.02757i
$969$	−1.15932	+	0.262632i	−0.0372426	+	0.00843697i
$970$	8.04163			0.258201
$971$	52.7427			1.69259			0.846297	−	0.532711i	$-0.178827\pi$
$971$	52.7427			1.69259			0.846297	+	0.532711i	$0.178827\pi$
$972$	−13.9895	−	6.87704i	−0.448714	−	0.220581i
$973$	15.1716	−	2.40489i	0.486378	−	0.0770971i
$974$		−	15.3137i		−	0.490683i
$975$	9.27208	−	2.10051i	0.296944	−	0.0672700i
$976$			13.8310i			0.442719i
$977$		−	40.4264i		−	1.29336i	−0.762763	−	0.646678i	$-0.776158\pi$
$977$		−	40.4264i		−	1.29336i	0.762763	−	0.646678i	$-0.223842\pi$
$978$	23.8896	−	5.41196i	0.763904	−	0.173055i
$979$		−	5.93723i		−	0.189755i
$980$	19.5056	−	6.34315i	0.623083	−	0.202624i
$981$	−9.89949	+	4.72792i	−0.316067	+	0.150951i
$982$	−3.31371			−0.105745
$983$	−18.8490			−0.601190			−0.300595	−	0.953752i	$-0.597185\pi$
$983$	−18.8490			−0.601190			−0.300595	+	0.953752i	$0.597185\pi$
$984$	48.4264	−	10.9706i	1.54378	−	0.349729i
$985$		−	68.3127i		−	2.17662i
$986$	1.34502			0.0428343
$987$	17.0762	−	6.82016i	0.543541	−	0.217088i
$988$	−3.31371			−0.105423
$989$			1.65685i			0.0526849i
$990$	−4.64659	+	2.21918i	−0.147678	+	0.0705301i
$991$	−33.9411			−1.07818			−0.539088	−	0.842250i	$-0.681231\pi$
$991$	−33.9411			−1.07818			−0.539088	+	0.842250i	$0.681231\pi$
$992$	−33.1283			−1.05183
$993$	6.49435	+	28.6675i	0.206092	+	0.909734i
$994$	4.00000	+	25.2346i	0.126872	+	0.800392i
$995$			24.2843i			0.769863i
$996$	3.41421	+	15.0711i	0.108183	+	0.477545i
$997$			1.79337i			0.0567965i	0.999597	+	0.0283982i	$0.00904066\pi$
$997$			1.79337i			0.0567965i	−0.999597	+	0.0283982i	$0.990959\pi$
$998$			13.6569i			0.432300i
$999$	−20.8825	−	26.4483i	−0.660692	−	0.836787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.c.461.6	yes	8
3.2	odd	2	inner	483.2.d.c.461.3	yes	8
7.6	odd	2	inner	483.2.d.c.461.7	yes	8
21.20	even	2	inner	483.2.d.c.461.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.c.461.2	✓	8	21.20	even	2	inner
483.2.d.c.461.3	yes	8	3.2	odd	2	inner
483.2.d.c.461.6	yes	8	1.1	even	1	trivial
483.2.d.c.461.7	yes	8	7.6	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.382683 - 1.68925i) q^{3} +1.00000 q^{4} -2.93015 q^{5} +(1.68925 - 0.382683i) q^{6} +(0.414214 + 2.61313i) q^{7} +3.00000i q^{8} +(-2.70711 + 1.29289i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.382683 - 1.68925i) q^{3} +1.00000 q^{4} -2.93015 q^{5} +(1.68925 - 0.382683i) q^{6} +(0.414214 + 2.61313i) q^{7} +3.00000i q^{8} +(-2.70711 + 1.29289i) q^{9} -2.93015i q^{10} +0.585786i q^{11} +(-0.382683 - 1.68925i) q^{12} +1.53073i q^{13} +(-2.61313 + 0.414214i) q^{14} +(1.12132 + 4.94975i) q^{15} -1.00000 q^{16} -0.317025 q^{17} +(-1.29289 - 2.70711i) q^{18} +2.16478i q^{19} -2.93015 q^{20} +(4.25570 - 1.69971i) q^{21} -0.585786 q^{22} +1.00000i q^{23} +(5.06774 - 1.14805i) q^{24} +3.58579 q^{25} -1.53073 q^{26} +(3.21998 + 4.07820i) q^{27} +(0.414214 + 2.61313i) q^{28} +4.24264i q^{29} +(-4.94975 + 1.12132i) q^{30} +6.62567i q^{31} +5.00000i q^{32} +(0.989538 - 0.224171i) q^{33} -0.317025i q^{34} +(-1.21371 - 7.65685i) q^{35} +(-2.70711 + 1.29289i) q^{36} -6.48528 q^{37} -2.16478 q^{38} +(2.58579 - 0.585786i) q^{39} -8.79045i q^{40} +9.55582 q^{41} +(1.69971 + 4.25570i) q^{42} +1.65685 q^{43} +0.585786i q^{44} +(7.93223 - 3.78837i) q^{45} -1.00000 q^{46} +4.01254 q^{47} +(0.382683 + 1.68925i) q^{48} +(-6.65685 + 2.16478i) q^{49} +3.58579i q^{50} +(0.121320 + 0.535534i) q^{51} +1.53073i q^{52} -4.82843i q^{53} +(-4.07820 + 3.21998i) q^{54} -1.71644i q^{55} +(-7.83938 + 1.24264i) q^{56} +(3.65685 - 0.828427i) q^{57} -4.24264 q^{58} -5.09494 q^{59} +(1.12132 + 4.94975i) q^{60} -13.8310i q^{61} -6.62567 q^{62} +(-4.49981 - 6.53848i) q^{63} -7.00000 q^{64} -4.48528i q^{65} +(0.224171 + 0.989538i) q^{66} -10.7279 q^{67} -0.317025 q^{68} +(1.68925 - 0.382683i) q^{69} +(7.65685 - 1.21371i) q^{70} -9.65685i q^{71} +(-3.87868 - 8.12132i) q^{72} +5.86030i q^{73} -6.48528i q^{74} +(-1.37222 - 6.05728i) q^{75} +2.16478i q^{76} +(-1.53073 + 0.242641i) q^{77} +(0.585786 + 2.58579i) q^{78} +14.7279 q^{79} +2.93015 q^{80} +(5.65685 - 7.00000i) q^{81} +9.55582i q^{82} -8.92177 q^{83} +(4.25570 - 1.69971i) q^{84} +0.928932 q^{85} +1.65685i q^{86} +(7.16687 - 1.62359i) q^{87} -1.75736 q^{88} -10.1355 q^{89} +(3.78837 + 7.93223i) q^{90} +(-4.00000 + 0.634051i) q^{91} +1.00000i q^{92} +(11.1924 - 2.53553i) q^{93} +4.01254i q^{94} -6.34315i q^{95} +(8.44623 - 1.91342i) q^{96} +2.74444i q^{97} +(-2.16478 - 6.65685i) q^{98} +(-0.757359 - 1.58579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 8 * q^7 - 16 * q^9	\( 8 q + 8 q^{4} - 8 q^{7} - 16 q^{9} - 8 q^{15} - 8 q^{16} - 16 q^{18} + 24 q^{21} - 16 q^{22} + 40 q^{25} - 8 q^{28} - 16 q^{36} + 16 q^{37} + 32 q^{39} + 8 q^{42} - 32 q^{43} - 8 q^{46} - 8 q^{49} - 16 q^{51} - 16 q^{57} - 8 q^{60} + 8 q^{63} - 56 q^{64} + 16 q^{67} + 16 q^{70} - 48 q^{72} + 16 q^{78} + 16 q^{79} + 24 q^{84} + 64 q^{85} - 48 q^{88} - 32 q^{91} + 16 q^{93} - 40 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^7 - 16 * q^9 - 8 * q^15 - 8 * q^16 - 16 * q^18 + 24 * q^21 - 16 * q^22 + 40 * q^25 - 8 * q^28 - 16 * q^36 + 16 * q^37 + 32 * q^39 + 8 * q^42 - 32 * q^43 - 8 * q^46 - 8 * q^49 - 16 * q^51 - 16 * q^57 - 8 * q^60 + 8 * q^63 - 56 * q^64 + 16 * q^67 + 16 * q^70 - 48 * q^72 + 16 * q^78 + 16 * q^79 + 24 * q^84 + 64 * q^85 - 48 * q^88 - 32 * q^91 + 16 * q^93 - 40 * q^99

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