LMFDB - Embedded newform 945.2.k.c.856.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [945,2,Mod(361,945)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(945, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("945.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.k (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.10
Character	$\chi$	$=$	945.856
Dual form			945.2.k.c.361.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0127903 + 0.0221535i) q^{2} +(0.999673 - 1.73148i) q^{4} -1.00000 q^{5} +(0.170066 + 2.64028i) q^{7} +0.102306 q^{8} +(-0.0127903 - 0.0221535i) q^{10} -3.78014 q^{11} +(-2.77025 - 4.79822i) q^{13} +(-0.0563162 + 0.0375376i) q^{14} +(-1.99804 - 3.46070i) q^{16} +(0.271942 + 0.471017i) q^{17} +(3.62126 - 6.27220i) q^{19} +(-0.999673 + 1.73148i) q^{20} +(-0.0483491 - 0.0837432i) q^{22} -7.25591 q^{23} +1.00000 q^{25} +(0.0708649 - 0.122742i) q^{26} +(4.74161 + 2.34495i) q^{28} +(4.04878 - 7.01269i) q^{29} +(-0.870826 + 1.50832i) q^{31} +(0.153417 - 0.265726i) q^{32} +(-0.00695644 + 0.0120489i) q^{34} +(-0.170066 - 2.64028i) q^{35} +(1.67242 - 2.89671i) q^{37} +0.185268 q^{38} -0.102306 q^{40} +(-0.238169 - 0.412522i) q^{41} +(-0.279323 + 0.483802i) q^{43} +(-3.77890 + 6.54524i) q^{44} +(-0.0928054 - 0.160744i) q^{46} +(-4.28862 - 7.42811i) q^{47} +(-6.94215 + 0.898045i) q^{49} +(0.0127903 + 0.0221535i) q^{50} -11.0774 q^{52} +(4.26510 + 7.38738i) q^{53} +3.78014 q^{55} +(0.0173988 + 0.270116i) q^{56} +0.207141 q^{58} +(0.704208 - 1.21972i) q^{59} +(-0.877009 - 1.51902i) q^{61} -0.0445526 q^{62} -7.98430 q^{64} +(2.77025 + 4.79822i) q^{65} +(-6.19157 + 10.7241i) q^{67} +1.08741 q^{68} +(0.0563162 - 0.0375376i) q^{70} -10.3293 q^{71} +(2.91561 + 5.04998i) q^{73} +0.0855629 q^{74} +(-7.24015 - 12.5403i) q^{76} +(-0.642874 - 9.98062i) q^{77} +(-1.48332 - 2.56918i) q^{79} +(1.99804 + 3.46070i) q^{80} +(0.00609253 - 0.0105526i) q^{82} +(3.97711 - 6.88856i) q^{83} +(-0.271942 - 0.471017i) q^{85} -0.0142905 q^{86} -0.386730 q^{88} +(9.02021 - 15.6235i) q^{89} +(12.1975 - 8.13026i) q^{91} +(-7.25354 + 12.5635i) q^{92} +(0.109706 - 0.190016i) q^{94} +(-3.62126 + 6.27220i) q^{95} +(-3.81553 + 6.60869i) q^{97} +(-0.108687 - 0.142307i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 22 q^{4} - 36 q^{5} - q^{7} + 2 q^{11} + 2 q^{13} + 6 q^{14} - 30 q^{16} + 5 q^{17} - 2 q^{19} + 22 q^{20} - 19 q^{22} - 6 q^{23} + 36 q^{25} + 4 q^{26} + 5 q^{28} + 8 q^{29} - 10 q^{32} + 10 q^{34}+ \cdots - 16 q^{98}+O(q^{100}) $ 36 * q - 22 * q^4 - 36 * q^5 - q^7 + 2 * q^11 + 2 * q^13 + 6 * q^14 - 30 * q^16 + 5 * q^17 - 2 * q^19 + 22 * q^20 - 19 * q^22 - 6 * q^23 + 36 * q^25 + 4 * q^26 + 5 * q^28 + 8 * q^29 - 10 * q^32 + 10 * q^34 + q^35 - 15 * q^37 - 44 * q^38 + 4 * q^41 - 29 * q^43 + 7 * q^44 - 24 * q^46 + 23 * q^47 - 7 * q^49 + 14 * q^52 - 2 * q^55 - 33 * q^56 + 40 * q^58 + 5 * q^59 - 3 * q^61 + 12 * q^62 + 128 * q^64 - 2 * q^65 - 35 * q^67 - 34 * q^68 - 6 * q^70 - 24 * q^71 - 10 * q^73 + 44 * q^74 + 10 * q^76 - 5 * q^77 - 28 * q^79 + 30 * q^80 - 8 * q^82 + 22 * q^83 - 5 * q^85 + 38 * q^86 + 100 * q^88 + 4 * q^89 + 7 * q^91 + 50 * q^92 - 2 * q^94 + 2 * q^95 + 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.0127903	+	0.0221535i	0.00904412	+	0.0156649i	0.870512	−	0.492147i	$-0.163788\pi$
$2$	0.0127903	+	0.0221535i	0.00904412	+	0.0156649i	−0.861468	+	0.507812i	$0.830454\pi$
$3$		0			0
$3$		0			0
$4$	0.999673	−	1.73148i	0.499836	−	0.865742i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	0.170066	+	2.64028i	0.0642790	+	0.997932i
$7$	0.170066	+	2.64028i	0.0642790	+	0.997932i
$8$	0.102306			0.0361706
$9$		0			0
$10$	−0.0127903	−	0.0221535i	−0.00404465	−	0.00700555i
$11$	−3.78014			−1.13975			−0.569877	−	0.821730i	$-0.693009\pi$
$11$	−3.78014			−1.13975			−0.569877	+	0.821730i	$0.693009\pi$
$12$		0			0
$13$	−2.77025	−	4.79822i	−0.768330	−	1.33079i	−0.938468	−	0.345367i	$-0.887754\pi$
$13$	−2.77025	−	4.79822i	−0.768330	−	1.33079i	0.170137	−	0.985420i	$-0.445579\pi$
$14$	−0.0563162	+	0.0375376i	−0.0150511	+	0.0100323i
$15$		0			0
$16$	−1.99804	−	3.46070i	−0.499509	−	0.865175i
$17$	0.271942	+	0.471017i	0.0659555	+	0.114238i	0.897117	−	0.441792i	$-0.145657\pi$
$17$	0.271942	+	0.471017i	0.0659555	+	0.114238i	−0.831162	+	0.556030i	$0.812324\pi$
$18$		0			0
$19$	3.62126	−	6.27220i	0.830774	−	1.43894i	−0.0666517	−	0.997776i	$-0.521232\pi$
$19$	3.62126	−	6.27220i	0.830774	−	1.43894i	0.897425	−	0.441166i	$-0.145435\pi$
$20$	−0.999673	+	1.73148i	−0.223534	+	0.387172i
$21$		0			0
$22$	−0.0483491	−	0.0837432i	−0.0103081	−	0.0178541i
$23$	−7.25591			−1.51296			−0.756481	−	0.654016i	$-0.773083\pi$
$23$	−7.25591			−1.51296			−0.756481	+	0.654016i	$0.773083\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	0.0708649	−	0.122742i	0.0138977	−	0.0240716i
$27$		0			0
$28$	4.74161	+	2.34495i	0.896081	+	0.443154i
$29$	4.04878	−	7.01269i	0.751839	−	1.30222i	−0.195092	−	0.980785i	$-0.562500\pi$
$29$	4.04878	−	7.01269i	0.751839	−	1.30222i	0.946931	−	0.321438i	$-0.104166\pi$
$30$		0			0
$31$	−0.870826	+	1.50832i	−0.156405	+	0.270901i	−0.933570	−	0.358396i	$-0.883324\pi$
$31$	−0.870826	+	1.50832i	−0.156405	+	0.270901i	0.777165	+	0.629297i	$0.216657\pi$
$32$	0.153417	−	0.265726i	0.0271205	−	0.0469741i
$33$		0			0
$34$	−0.00695644	+	0.0120489i	−0.00119302	+	0.00206637i
$35$	−0.170066	−	2.64028i	−0.0287465	−	0.446289i
$36$		0			0
$37$	1.67242	−	2.89671i	0.274943	−	0.476216i	−0.695177	−	0.718838i	$-0.744674\pi$
$37$	1.67242	−	2.89671i	0.274943	−	0.476216i	0.970121	+	0.242622i	$0.0780076\pi$
$38$	0.185268			0.0300545
$39$		0			0
$40$	−0.102306			−0.0161760
$41$	−0.238169	−	0.412522i	−0.0371958	−	0.0644250i	0.846828	−	0.531867i	$-0.178509\pi$
$41$	−0.238169	−	0.412522i	−0.0371958	−	0.0644250i	−0.884024	+	0.467441i	$0.845176\pi$
$42$		0			0
$43$	−0.279323	+	0.483802i	−0.0425964	+	0.0737791i	−0.886538	−	0.462657i	$-0.846896\pi$
$43$	−0.279323	+	0.483802i	−0.0425964	+	0.0737791i	0.843941	+	0.536436i	$0.180230\pi$
$44$	−3.77890	+	6.54524i	−0.569690	+	0.986733i
$45$		0			0
$46$	−0.0928054	−	0.160744i	−0.0136834	−	0.0237004i
$47$	−4.28862	−	7.42811i	−0.625560	−	1.08350i	−0.988432	−	0.151663i	$-0.951537\pi$
$47$	−4.28862	−	7.42811i	−0.625560	−	1.08350i	0.362872	−	0.931839i	$-0.381796\pi$
$48$		0			0
$49$	−6.94215	+	0.898045i	−0.991736	+	0.128292i
$50$	0.0127903	+	0.0221535i	0.00180882	+	0.00313298i
$51$		0			0
$52$	−11.0774			−1.53616
$53$	4.26510	+	7.38738i	0.585857	+	1.01473i	0.994768	+	0.102160i	$0.0325754\pi$
$53$	4.26510	+	7.38738i	0.585857	+	1.01473i	−0.408911	+	0.912574i	$0.634091\pi$
$54$		0			0
$55$	3.78014			0.509713
$56$	0.0173988	+	0.270116i	0.00232501	+	0.0360958i
$57$		0			0
$58$	0.207141			0.0271989
$59$	0.704208	−	1.21972i	0.0916801	−	0.158795i	−0.816538	−	0.577292i	$-0.804110\pi$
$59$	0.704208	−	1.21972i	0.0916801	−	0.158795i	0.908218	+	0.418497i	$0.137443\pi$
$60$		0			0
$61$	−0.877009	−	1.51902i	−0.112289	−	0.194491i	0.804404	−	0.594083i	$-0.202485\pi$
$61$	−0.877009	−	1.51902i	−0.112289	−	0.194491i	−0.916693	+	0.399592i	$0.869152\pi$
$62$	−0.0445526			−0.00565818
$63$		0			0
$64$	−7.98430			−0.998037
$65$	2.77025	+	4.79822i	0.343608	+	0.595146i
$66$		0			0
$67$	−6.19157	+	10.7241i	−0.756421	+	1.31016i	0.188244	+	0.982122i	$0.439720\pi$
$67$	−6.19157	+	10.7241i	−0.756421	+	1.31016i	−0.944665	+	0.328037i	$0.893613\pi$
$68$	1.08741			0.131868
$69$		0			0
$70$	0.0563162	−	0.0375376i	0.00673107	−	0.00448660i
$71$	−10.3293			−1.22587			−0.612934	−	0.790134i	$-0.710011\pi$
$71$	−10.3293			−1.22587			−0.612934	+	0.790134i	$0.710011\pi$
$72$		0			0
$73$	2.91561	+	5.04998i	0.341246	+	0.591055i	0.984664	−	0.174459i	$-0.0558178\pi$
$73$	2.91561	+	5.04998i	0.341246	+	0.591055i	−0.643418	+	0.765515i	$0.722484\pi$
$74$	0.0855629			0.00994648
$75$		0			0
$76$	−7.24015	−	12.5403i	−0.830502	−	1.43847i
$77$	−0.642874	−	9.98062i	−0.0732622	−	1.13740i
$78$		0			0
$79$	−1.48332	−	2.56918i	−0.166886	−	0.289056i	0.770437	−	0.637516i	$-0.220038\pi$
$79$	−1.48332	−	2.56918i	−0.166886	−	0.289056i	−0.937324	+	0.348460i	$0.886705\pi$
$80$	1.99804	+	3.46070i	0.223387	+	0.386918i
$81$		0			0
$82$	0.00609253	−	0.0105526i	0.000672807	−	0.00116534i
$83$	3.97711	−	6.88856i	0.436544	−	0.756117i	−0.560876	−	0.827900i	$-0.689535\pi$
$83$	3.97711	−	6.88856i	0.436544	−	0.756117i	0.997420	+	0.0717828i	$0.0228688\pi$
$84$		0			0
$85$	−0.271942	−	0.471017i	−0.0294962	−	0.0510889i
$86$	−0.0142905			−0.00154099
$87$		0			0
$88$	−0.386730			−0.0412255
$89$	9.02021	−	15.6235i	0.956141	−	1.65608i	0.224405	−	0.974496i	$-0.427956\pi$
$89$	9.02021	−	15.6235i	0.956141	−	1.65608i	0.731736	−	0.681588i	$-0.238710\pi$
$90$		0			0
$91$	12.1975	−	8.13026i	1.27865	−	0.852283i
$92$	−7.25354	+	12.5635i	−0.756233	+	1.30983i
$93$		0			0
$94$	0.109706	−	0.190016i	0.0113153	−	0.0195986i
$95$	−3.62126	+	6.27220i	−0.371533	+	0.643515i
$96$		0			0
$97$	−3.81553	+	6.60869i	−0.387408	+	0.671011i	−0.992100	−	0.125449i	$-0.959963\pi$
$97$	−3.81553	+	6.60869i	−0.387408	+	0.671011i	0.604692	+	0.796460i	$0.293296\pi$
$98$	−0.108687	−	0.142307i	−0.0109791	−	0.0143751i
$99$		0			0
$100$	0.999673	−	1.73148i	0.0999673	−	0.173148i
$101$	3.42479			0.340780			0.170390	−	0.985377i	$-0.445497\pi$
$101$	3.42479			0.340780			0.170390	+	0.985377i	$0.445497\pi$
$102$		0			0
$103$	9.43055			0.929219			0.464610	−	0.885516i	$-0.346195\pi$
$103$	9.43055			0.929219			0.464610	+	0.885516i	$0.346195\pi$
$104$	−0.283413	−	0.490886i	−0.0277909	−	0.0481353i
$105$		0			0
$106$	−0.109104	+	0.188974i	−0.0105971	+	0.0183548i
$107$	−0.0944380	+	0.163571i	−0.00912967	+	0.0158131i	−0.870554	−	0.492073i	$-0.836239\pi$
$107$	−0.0944380	+	0.163571i	−0.00912967	+	0.0158131i	0.861424	+	0.507886i	$0.169573\pi$
$108$		0			0
$109$	4.40407	+	7.62807i	0.421833	+	0.730636i	0.996119	−	0.0880186i	$-0.0280535\pi$
$109$	4.40407	+	7.62807i	0.421833	+	0.730636i	−0.574286	+	0.818655i	$0.694720\pi$
$110$	0.0483491	+	0.0837432i	0.00460991	+	0.00798460i
$111$		0			0
$112$	8.79742	−	5.86393i	0.831278	−	0.554089i
$113$	5.83704	+	10.1101i	0.549103	+	0.951074i	0.998336	+	0.0576593i	$0.0183637\pi$
$113$	5.83704	+	10.1101i	0.549103	+	0.951074i	−0.449234	+	0.893414i	$0.648303\pi$
$114$		0			0
$115$	7.25591			0.676617
$116$	−8.09490	−	14.0208i	−0.751593	−	1.30180i
$117$		0			0
$118$	0.0360282			0.00331666
$119$	−1.19737	+	0.798106i	−0.109763	+	0.0731623i
$120$		0			0
$121$	3.28942			0.299039
$122$	0.0224344	−	0.0388576i	0.00203112	−	0.00351800i
$123$		0			0
$124$	1.74108	+	3.01564i	0.156354	+	0.270813i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	1.14668			0.101751			0.0508756	−	0.998705i	$-0.483799\pi$
$127$	1.14668			0.101751			0.0508756	+	0.998705i	$0.483799\pi$
$128$	−0.408955	−	0.708332i	−0.0361469	−	0.0626083i
$129$		0			0
$130$	−0.0708649	+	0.122742i	−0.00621526	+	0.0107651i
$131$	6.36247			0.555891			0.277946	−	0.960597i	$-0.410346\pi$
$131$	6.36247			0.555891			0.277946	+	0.960597i	$0.410346\pi$
$132$		0			0
$133$	17.1762	+	8.49445i	1.48937	+	0.736562i
$134$	−0.316769			−0.0273646
$135$		0			0
$136$	0.0278212	+	0.0481878i	0.00238565	+	0.00413207i
$137$	8.55962			0.731297			0.365649	−	0.930753i	$-0.380847\pi$
$137$	8.55962			0.731297			0.365649	+	0.930753i	$0.380847\pi$
$138$		0			0
$139$	−3.08779	−	5.34821i	−0.261903	−	0.453630i	0.704844	−	0.709362i	$-0.251017\pi$
$139$	−3.08779	−	5.34821i	−0.261903	−	0.453630i	−0.966748	+	0.255732i	$0.917683\pi$
$140$	−4.74161	−	2.34495i	−0.400739	−	0.198184i
$141$		0			0
$142$	−0.132116	−	0.228831i	−0.0110869	−	0.0192031i
$143$	10.4719	+	18.1379i	0.875707	+	1.51677i
$144$		0			0
$145$	−4.04878	+	7.01269i	−0.336233	+	0.582372i
$146$	−0.0745831	+	0.129182i	−0.00617254	+	0.0106912i
$147$		0			0
$148$	−3.34374	−	5.79152i	−0.274853	−	0.476060i
$149$	−4.69295			−0.384461			−0.192231	−	0.981350i	$-0.561572\pi$
$149$	−4.69295			−0.384461			−0.192231	+	0.981350i	$0.561572\pi$
$150$		0			0
$151$	−15.6125			−1.27053			−0.635265	−	0.772294i	$-0.719109\pi$
$151$	−15.6125			−1.27053			−0.635265	+	0.772294i	$0.719109\pi$
$152$	0.370476	−	0.641683i	0.0300496	−	0.0520474i
$153$		0			0
$154$	0.212883	−	0.141897i	0.0171546	−	0.0114344i
$155$	0.870826	−	1.50832i	0.0699464	−	0.121151i
$156$		0			0
$157$	9.28453	−	16.0813i	0.740986	−	1.28343i	−0.211061	−	0.977473i	$-0.567692\pi$
$157$	9.28453	−	16.0813i	0.740986	−	1.28343i	0.952047	−	0.305953i	$-0.0989749\pi$
$158$	0.0379442	−	0.0657213i	0.00301868	−	0.00522851i
$159$		0			0
$160$	−0.153417	+	0.265726i	−0.0121287	+	0.0210075i
$161$	−1.23399	−	19.1576i	−0.0972517	−	1.50983i
$162$		0			0
$163$	−0.655557	+	1.13546i	−0.0513472	+	0.0889359i	−0.890557	−	0.454872i	$-0.849685\pi$
$163$	−0.655557	+	1.13546i	−0.0513472	+	0.0889359i	0.839209	+	0.543808i	$0.183018\pi$
$164$	−0.952366			−0.0743673
$165$		0			0
$166$	0.203474			0.0157926
$167$	−5.56450	−	9.63799i	−0.430594	−	0.745810i	0.566331	−	0.824178i	$-0.308362\pi$
$167$	−5.56450	−	9.63799i	−0.430594	−	0.745810i	−0.996925	+	0.0783678i	$0.975029\pi$
$168$		0			0
$169$	−8.84862	+	15.3263i	−0.680663	+	1.17894i
$170$	0.00695644	−	0.0120489i	0.000533535	−	0.000924109i
$171$		0			0
$172$	0.558463	+	0.967287i	0.0425824	+	0.0737549i
$173$	−0.712352	−	1.23383i	−0.0541592	−	0.0938064i	0.837675	−	0.546169i	$-0.183915\pi$
$173$	−0.712352	−	1.23383i	−0.0541592	−	0.0938064i	−0.891834	+	0.452363i	$0.850581\pi$
$174$		0			0
$175$	0.170066	+	2.64028i	0.0128558	+	0.199586i
$176$	7.55285	+	13.0819i	0.569318	+	0.986087i
$177$		0			0
$178$	0.461486			0.0345898
$179$	6.28599	+	10.8877i	0.469837	+	0.813782i	0.999405	−	0.0344857i	$-0.0109793\pi$
$179$	6.28599	+	10.8877i	0.469837	+	0.813782i	−0.529568	+	0.848267i	$0.677646\pi$
$180$		0			0
$181$	−14.1730			−1.05347			−0.526735	−	0.850029i	$-0.676584\pi$
$181$	−14.1730			−1.05347			−0.526735	+	0.850029i	$0.676584\pi$
$182$	0.336124	+	0.166229i	0.0249152	+	0.0123217i
$183$		0			0
$184$	−0.742322			−0.0547247
$185$	−1.67242	+	2.89671i	−0.122958	+	0.212970i
$186$		0			0
$187$	−1.02798	−	1.78051i	−0.0751731	−	0.130204i
$188$	−17.1489			−1.25071
$189$		0			0
$190$	−0.185268			−0.0134408
$191$	5.09023	+	8.81654i	0.368316	+	0.637942i	0.989302	−	0.145879i	$-0.0466011\pi$
$191$	5.09023	+	8.81654i	0.368316	+	0.637942i	−0.620986	+	0.783821i	$0.713268\pi$
$192$		0			0
$193$	3.42575	−	5.93357i	0.246591	−	0.427108i	−0.715987	−	0.698114i	$-0.754023\pi$
$193$	3.42575	−	5.93357i	0.246591	−	0.427108i	0.962578	+	0.271006i	$0.0873563\pi$
$194$	−0.195207			−0.0140151
$195$		0			0
$196$	−5.38493	+	12.9180i	−0.384638	+	0.922713i
$197$	20.0167			1.42613			0.713065	−	0.701098i	$-0.247307\pi$
$197$	20.0167			1.42613			0.713065	+	0.701098i	$0.247307\pi$
$198$		0			0
$199$	6.47405	+	11.2134i	0.458933	+	0.794896i	0.998905	−	0.0467876i	$-0.0148984\pi$
$199$	6.47405	+	11.2134i	0.458933	+	0.794896i	−0.539972	+	0.841683i	$0.681565\pi$
$200$	0.102306			0.00723411
$201$		0			0
$202$	0.0438042	+	0.0758711i	0.00308205	+	0.00533827i
$203$	19.2040	+	9.49728i	1.34786	+	0.666578i
$204$		0			0
$205$	0.238169	+	0.412522i	0.0166345	+	0.0288118i
$206$	0.120620	+	0.208919i	0.00840397	+	0.0145561i
$207$		0			0
$208$	−11.0701	+	19.1740i	−0.767576	+	1.32948i
$209$	−13.6888	+	23.7098i	−0.946878	+	1.64004i
$210$		0			0
$211$	6.43285	+	11.1420i	0.442856	+	0.767048i	0.997900	−	0.0647723i	$-0.0206321\pi$
$211$	6.43285	+	11.1420i	0.442856	+	0.767048i	−0.555045	+	0.831821i	$0.687299\pi$
$212$	17.0548			1.17133
$213$		0			0
$214$	−0.00483157			−0.000330279
$215$	0.279323	−	0.483802i	0.0190497	−	0.0329950i
$216$		0			0
$217$	−4.13047	−	2.04271i	−0.280395	−	0.138668i
$218$	−0.112659	+	0.195131i	−0.00763022	+	0.0132159i
$219$		0			0
$220$	3.77890	−	6.54524i	0.254773	−	0.441280i
$221$	1.50670	−	2.60967i	0.101351	−	0.175546i
$222$		0			0
$223$	6.20544	−	10.7481i	0.415547	−	0.719749i	−0.579939	−	0.814660i	$-0.696923\pi$
$223$	6.20544	−	10.7481i	0.415547	−	0.719749i	0.995486	+	0.0949115i	$0.0302568\pi$
$224$	0.727682	+	0.359872i	0.0486203	+	0.0240450i
$225$		0			0
$226$	−0.149315	+	0.258622i	−0.00993230	+	0.0172032i
$227$	−8.86221			−0.588206			−0.294103	−	0.955774i	$-0.595021\pi$
$227$	−8.86221			−0.588206			−0.294103	+	0.955774i	$0.595021\pi$
$228$		0			0
$229$	26.3169			1.73907			0.869536	−	0.493869i	$-0.164418\pi$
$229$	26.3169			1.73907			0.869536	+	0.493869i	$0.164418\pi$
$230$	0.0928054	+	0.160744i	0.00611941	+	0.0105991i
$231$		0			0
$232$	0.414213	−	0.717438i	0.0271944	−	0.0471021i
$233$	−13.0236	+	22.5576i	−0.853208	+	1.47780i	0.0250903	+	0.999685i	$0.492013\pi$
$233$	−13.0236	+	22.5576i	−0.853208	+	1.47780i	−0.878298	+	0.478114i	$0.841321\pi$
$234$		0			0
$235$	4.28862	+	7.42811i	0.279759	+	0.484557i
$236$	−1.40796	−	2.43865i	−0.0916501	−	0.158743i
$237$		0			0
$238$	−0.0329955	−	0.0163178i	−0.00213878	−	0.00105773i
$239$	−9.50084	−	16.4559i	−0.614558	−	1.06445i	−0.990462	−	0.137787i	$-0.956001\pi$
$239$	−9.50084	−	16.4559i	−0.614558	−	1.06445i	0.375904	−	0.926659i	$-0.377332\pi$
$240$		0			0
$241$	−14.2829			−0.920042			−0.460021	−	0.887908i	$-0.652158\pi$
$241$	−14.2829			−0.920042			−0.460021	+	0.887908i	$0.652158\pi$
$242$	0.0420728	+	0.0728722i	0.00270454	+	0.00468440i
$243$		0			0
$244$	−3.50689			−0.224505
$245$	6.94215	−	0.898045i	0.443518	−	0.0573740i
$246$		0			0
$247$	−40.1272			−2.55323
$248$	−0.0890906	+	0.154309i	−0.00565726	+	0.00979866i
$249$		0			0
$250$	−0.0127903	−	0.0221535i	−0.000808931	−	0.00140111i
$251$	2.23618			0.141146			0.0705731	−	0.997507i	$-0.477517\pi$
$251$	2.23618			0.141146			0.0705731	+	0.997507i	$0.477517\pi$
$252$		0			0
$253$	27.4283			1.72440
$254$	0.0146664	+	0.0254029i	0.000920250	+	0.00159392i
$255$		0			0
$256$	−7.97384	+	13.8111i	−0.498365	+	0.863193i
$257$	15.7647			0.983377			0.491688	−	0.870771i	$-0.336380\pi$
$257$	15.7647			0.983377			0.491688	+	0.870771i	$0.336380\pi$
$258$		0			0
$259$	7.93254	+	3.92301i	0.492904	+	0.243764i
$260$	11.0774			0.686991
$261$		0			0
$262$	0.0813780	+	0.140951i	0.00502755	+	0.00870797i
$263$	12.7795			0.788015			0.394008	−	0.919107i	$-0.371088\pi$
$263$	12.7795			0.788015			0.394008	+	0.919107i	$0.371088\pi$
$264$		0			0
$265$	−4.26510	−	7.38738i	−0.262003	−	0.453803i
$266$	0.0315079	+	0.489160i	0.00193187	+	0.0299923i
$267$		0			0
$268$	12.3791	+	21.4412i	0.756173	+	1.30973i
$269$	−9.82818	−	17.0229i	−0.599235	−	1.03790i	−0.992934	−	0.118666i	$-0.962138\pi$
$269$	−9.82818	−	17.0229i	−0.599235	−	1.03790i	0.393700	−	0.919239i	$-0.371195\pi$
$270$		0			0
$271$	−1.02524	+	1.77577i	−0.0622791	+	0.107871i	−0.895484	−	0.445094i	$-0.853170\pi$
$271$	−1.02524	+	1.77577i	−0.0622791	+	0.107871i	0.833205	+	0.552965i	$0.186504\pi$
$272$	1.08670	−	1.88222i	0.0658908	−	0.114126i
$273$		0			0
$274$	0.109480	+	0.189625i	0.00661394	+	0.0114557i
$275$	−3.78014			−0.227951
$276$		0			0
$277$	6.42013			0.385748			0.192874	−	0.981224i	$-0.438219\pi$
$277$	6.42013			0.385748			0.192874	+	0.981224i	$0.438219\pi$
$278$	0.0789877	−	0.136811i	0.00473737	−	0.00820536i
$279$		0			0
$280$	−0.0173988	−	0.270116i	−0.00103978	−	0.0161425i
$281$	15.3102	−	26.5180i	0.913327	−	1.58193i	0.103995	−	0.994578i	$-0.466837\pi$
$281$	15.3102	−	26.5180i	0.913327	−	1.58193i	0.809332	−	0.587351i	$-0.199829\pi$
$282$		0			0
$283$	−4.86470	+	8.42590i	−0.289176	+	0.500868i	−0.973613	−	0.228204i	$-0.926715\pi$
$283$	−4.86470	+	8.42590i	−0.289176	+	0.500868i	0.684437	+	0.729072i	$0.260048\pi$
$284$	−10.3260	+	17.8851i	−0.612733	+	1.06129i
$285$		0			0
$286$	−0.267879	+	0.463980i	−0.0158400	+	0.0274357i
$287$	1.04867	−	0.698990i	0.0619009	−	0.0412601i
$288$		0			0
$289$	8.35210	−	14.4663i	0.491300	−	0.850956i
$290$	−0.207141			−0.0121637
$291$		0			0
$292$	11.6586			0.682269
$293$	5.32802	+	9.22840i	0.311266	+	0.539129i	0.978637	−	0.205597i	$-0.0659136\pi$
$293$	5.32802	+	9.22840i	0.311266	+	0.539129i	−0.667371	+	0.744726i	$0.732580\pi$
$294$		0			0
$295$	−0.704208	+	1.21972i	−0.0410006	+	0.0710151i
$296$	0.171098	−	0.296350i	0.00994486	−	0.0172250i
$297$		0			0
$298$	−0.0600243	−	0.103965i	−0.00347712	−	0.00602254i
$299$	20.1007	+	34.8155i	1.16245	+	2.01343i
$300$		0			0
$301$	−1.32488	−	0.655213i	−0.0763646	−	0.0377658i
$302$	−0.199689	−	0.345872i	−0.0114908	−	0.0199027i
$303$		0			0
$304$	−28.9416			−1.65992
$305$	0.877009	+	1.51902i	0.0502174	+	0.0869790i
$306$		0			0
$307$	3.58038			0.204343			0.102171	−	0.994767i	$-0.467421\pi$
$307$	3.58038			0.204343			0.102171	+	0.994767i	$0.467421\pi$
$308$	−17.9239	−	8.86422i	−1.02131	−	0.505086i
$309$		0			0
$310$	0.0445526			0.00253042
$311$	8.15786	−	14.1298i	0.462590	−	0.801229i	−0.536499	−	0.843901i	$-0.680254\pi$
$311$	8.15786	−	14.1298i	0.462590	−	0.801229i	0.999089	+	0.0426715i	$0.0135869\pi$
$312$		0			0
$313$	3.43821	+	5.95516i	0.194339	+	0.336606i	0.946684	−	0.322164i	$-0.104410\pi$
$313$	3.43821	+	5.95516i	0.194339	+	0.336606i	−0.752344	+	0.658770i	$0.771077\pi$
$314$	0.475008			0.0268063
$315$		0			0
$316$	−5.93133			−0.333663
$317$	−9.97368	−	17.2749i	−0.560178	−	0.970256i	−0.997480	−	0.0709419i	$-0.977400\pi$
$317$	−9.97368	−	17.2749i	−0.560178	−	0.970256i	0.437303	−	0.899314i	$-0.355934\pi$
$318$		0			0
$319$	−15.3049	+	26.5089i	−0.856911	+	1.48421i
$320$	7.98430			0.446336
$321$		0			0
$322$	0.408625	−	0.272369i	0.0227718	−	0.0151785i
$323$	3.93908			0.219177
$324$		0			0
$325$	−2.77025	−	4.79822i	−0.153666	−	0.266157i
$326$	−0.0335391			−0.00185756
$327$		0			0
$328$	−0.0243661	−	0.0422033i	−0.00134539	−	0.00233029i
$329$	18.8829	−	12.5864i	1.04105	−	0.693913i
$330$		0			0
$331$	5.43065	+	9.40615i	0.298495	+	0.517009i	0.975792	−	0.218701i	$-0.0701820\pi$
$331$	5.43065	+	9.40615i	0.298495	+	0.517009i	−0.677297	+	0.735710i	$0.736849\pi$
$332$	−7.95162	−	13.7726i	−0.436402	−	0.755870i
$333$		0			0
$334$	0.142343	−	0.246546i	0.00778868	−	0.0134904i
$335$	6.19157	−	10.7241i	0.338282	−	0.585921i
$336$		0			0
$337$	−0.137238	−	0.237703i	−0.00747582	−	0.0129485i	0.862263	−	0.506460i	$-0.169046\pi$
$337$	−0.137238	−	0.237703i	−0.00747582	−	0.0129485i	−0.869739	+	0.493512i	$0.835713\pi$
$338$	−0.452707			−0.0246240
$339$		0			0
$340$	−1.08741			−0.0589731
$341$	3.29184	−	5.70164i	0.178263	−	0.308761i
$342$		0			0
$343$	−3.55172	−	18.1765i	−0.191775	−	0.981439i
$344$	−0.0285764	+	0.0494957i	−0.00154073	+	0.00266863i
$345$		0			0
$346$	0.0182224	−	0.0315622i	0.000979644	−	0.00169679i
$347$	1.89413	−	3.28073i	0.101682	−	0.176119i	−0.810696	−	0.585468i	$-0.800911\pi$
$347$	1.89413	−	3.28073i	0.101682	−	0.176119i	0.912378	+	0.409349i	$0.134244\pi$
$348$		0			0
$349$	14.3243	−	24.8104i	0.766763	−	1.32807i	−0.172547	−	0.985001i	$-0.555200\pi$
$349$	14.3243	−	24.8104i	0.766763	−	1.32807i	0.939310	−	0.343070i	$-0.111467\pi$
$350$	−0.0563162	+	0.0375376i	−0.00301023	+	0.00200647i
$351$		0			0
$352$	−0.579937	+	1.00448i	−0.0309107	+	0.0535389i
$353$	−4.31487			−0.229658			−0.114829	−	0.993385i	$-0.536632\pi$
$353$	−4.31487			−0.229658			−0.114829	+	0.993385i	$0.536632\pi$
$354$		0			0
$355$	10.3293			0.548225
$356$	−18.0345	−	31.2367i	−0.955828	−	1.65554i
$357$		0			0
$358$	−0.160800	+	0.278513i	−0.00849853	+	0.0147199i
$359$	13.5903	−	23.5390i	0.717267	−	1.24234i	−0.244811	−	0.969571i	$-0.578726\pi$
$359$	13.5903	−	23.5390i	0.717267	−	1.24234i	0.962079	−	0.272772i	$-0.0879406\pi$
$360$		0			0
$361$	−16.7270	−	28.9721i	−0.880370	−	1.52485i
$362$	−0.181277	−	0.313981i	−0.00952772	−	0.0165025i
$363$		0			0
$364$	−1.88389	−	29.2474i	−0.0987427	−	1.53298i
$365$	−2.91561	−	5.04998i	−0.152610	−	0.264328i
$366$		0			0
$367$	12.0152			0.627189			0.313595	−	0.949557i	$-0.398467\pi$
$367$	12.0152			0.627189			0.313595	+	0.949557i	$0.398467\pi$
$368$	14.4976	+	25.1105i	0.755738	+	1.30898i
$369$		0			0
$370$	−0.0855629			−0.00444820
$371$	−18.7794	+	12.5174i	−0.974978	+	0.649872i
$372$		0			0
$373$	−8.68386			−0.449633			−0.224816	−	0.974401i	$-0.572178\pi$
$373$	−8.68386			−0.449633			−0.224816	+	0.974401i	$0.572178\pi$
$374$	0.0262963	−	0.0455465i	0.00135975	−	0.00235515i
$375$		0			0
$376$	−0.438751	−	0.759939i	−0.0226269	−	0.0391909i
$377$	−44.8646			−2.31064
$378$		0			0
$379$	12.7019			0.652454			0.326227	−	0.945291i	$-0.394223\pi$
$379$	12.7019			0.652454			0.326227	+	0.945291i	$0.394223\pi$
$380$	7.24015	+	12.5403i	0.371412	+	0.643304i
$381$		0			0
$382$	−0.130211	+	0.225533i	−0.00666219	+	0.0115393i
$383$	−25.1210			−1.28362			−0.641812	−	0.766862i	$-0.721817\pi$
$383$	−25.1210			−1.28362			−0.641812	+	0.766862i	$0.721817\pi$
$384$		0			0
$385$	0.642874	+	9.98062i	0.0327639	+	0.508659i
$386$	0.175266			0.00892079
$387$		0			0
$388$	7.62856	+	13.2131i	0.387282	+	0.670791i
$389$	−19.1424			−0.970559			−0.485280	−	0.874359i	$-0.661282\pi$
$389$	−19.1424			−0.970559			−0.485280	+	0.874359i	$0.661282\pi$
$390$		0			0
$391$	−1.97318	−	3.41766i	−0.0997882	−	0.172838i
$392$	−0.710223	+	0.0918752i	−0.0358717	+	0.00464040i
$393$		0			0
$394$	0.256020	+	0.443439i	0.0128981	+	0.0223401i
$395$	1.48332	+	2.56918i	0.0746338	+	0.129270i
$396$		0			0
$397$	−1.80451	+	3.12551i	−0.0905659	+	0.156865i	−0.907749	−	0.419513i	$-0.862201\pi$
$397$	−1.80451	+	3.12551i	−0.0905659	+	0.156865i	0.817184	+	0.576378i	$0.195534\pi$
$398$	−0.165610	+	0.286845i	−0.00830129	+	0.0143783i
$399$		0			0
$400$	−1.99804	−	3.46070i	−0.0999019	−	0.173035i
$401$	−3.36015			−0.167798			−0.0838989	−	0.996474i	$-0.526737\pi$
$401$	−3.36015			−0.167798			−0.0838989	+	0.996474i	$0.526737\pi$
$402$		0			0
$403$	9.64964			0.480683
$404$	3.42367	−	5.92998i	0.170334	−	0.295027i
$405$		0			0
$406$	0.0352276	+	0.546909i	0.00174832	+	0.0271426i
$407$	−6.32196	+	10.9499i	−0.313368	+	0.542769i
$408$		0			0
$409$	−1.19114	+	2.06311i	−0.0588980	+	0.102014i	−0.893971	−	0.448125i	$-0.852092\pi$
$409$	−1.19114	+	2.06311i	−0.0588980	+	0.102014i	0.835073	+	0.550139i	$0.185425\pi$
$410$	−0.00609253	+	0.0105526i	−0.000300888	+	0.000521154i
$411$		0			0
$412$	9.42746	−	16.3288i	0.464458	−	0.804464i
$413$	3.34017	+	1.65187i	0.164359	+	0.0812833i
$414$		0			0
$415$	−3.97711	+	6.88856i	−0.195229	+	0.338146i
$416$	−1.70002			−0.0833501
$417$		0			0
$418$	−0.700339			−0.0342547
$419$	1.56715	+	2.71438i	0.0765602	+	0.132606i	0.901764	−	0.432229i	$-0.142273\pi$
$419$	1.56715	+	2.71438i	0.0765602	+	0.132606i	−0.825203	+	0.564836i	$0.808940\pi$
$420$		0			0
$421$	6.68047	−	11.5709i	0.325586	−	0.563932i	−0.656044	−	0.754722i	$-0.727772\pi$
$421$	6.68047	−	11.5709i	0.325586	−	0.563932i	0.981631	+	0.190790i	$0.0611050\pi$
$422$	−0.164556	+	0.285020i	−0.00801048	+	0.0138746i
$423$		0			0
$424$	0.436345	+	0.755772i	0.0211908	+	0.0367035i
$425$	0.271942	+	0.471017i	0.0131911	+	0.0228477i
$426$		0			0
$427$	3.86150	−	2.57388i	0.186871	−	0.124559i
$428$	0.188814	+	0.327036i	0.00912668	+	0.0158079i
$429$		0			0
$430$	0.0142905			0.000689150
$431$	11.9751	+	20.7415i	0.576821	+	0.999082i	0.995841	+	0.0911058i	$0.0290401\pi$
$431$	11.9751	+	20.7415i	0.576821	+	0.999082i	−0.419021	+	0.907977i	$0.637627\pi$
$432$		0			0
$433$	−15.3737			−0.738813			−0.369406	−	0.929268i	$-0.620439\pi$
$433$	−15.3737			−0.738813			−0.369406	+	0.929268i	$0.620439\pi$
$434$	−0.00757689	−	0.117631i	−0.000363702	−	0.00564648i
$435$		0			0
$436$	17.6105			0.843390
$437$	−26.2755	+	45.5106i	−1.25693	+	2.17706i
$438$		0			0
$439$	−4.25004	−	7.36128i	−0.202843	−	0.351335i	0.746600	−	0.665273i	$-0.231685\pi$
$439$	−4.25004	−	7.36128i	−0.202843	−	0.351335i	−0.949443	+	0.313938i	$0.898352\pi$
$440$	0.386730			0.0184366
$441$		0			0
$442$	0.0770844			0.00366653
$443$	−15.4662	−	26.7883i	−0.734822	−	1.27275i	−0.954801	−	0.297245i	$-0.903932\pi$
$443$	−15.4662	−	26.7883i	−0.734822	−	1.27275i	0.219979	−	0.975505i	$-0.429401\pi$
$444$		0			0
$445$	−9.02021	+	15.6235i	−0.427599	+	0.740623i
$446$	0.317478			0.0150330
$447$		0			0
$448$	−1.35786	−	21.0808i	−0.0641529	−	0.995973i
$449$	−4.23659			−0.199937			−0.0999686	−	0.994991i	$-0.531874\pi$
$449$	−4.23659			−0.199937			−0.0999686	+	0.994991i	$0.531874\pi$
$450$		0			0
$451$	0.900313	+	1.55939i	0.0423941	+	0.0734287i
$452$	23.3405			1.09785
$453$		0			0
$454$	−0.113350	−	0.196329i	−0.00531980	−	0.00921417i
$455$	−12.1975	+	8.13026i	−0.571829	+	0.381153i
$456$		0			0
$457$	−19.6991	−	34.1198i	−0.921485	−	1.59606i	−0.797119	−	0.603823i	$-0.793644\pi$
$457$	−19.6991	−	34.1198i	−0.921485	−	1.59606i	−0.124366	−	0.992236i	$-0.539690\pi$
$458$	0.336602	+	0.583012i	0.0157284	+	0.0272424i
$459$		0			0
$460$	7.25354	−	12.5635i	0.338198	−	0.585776i
$461$	2.86184	−	4.95686i	0.133289	−	0.230864i	−0.791653	−	0.610971i	$-0.790779\pi$
$461$	2.86184	−	4.95686i	0.133289	−	0.230864i	0.924943	+	0.380107i	$0.124113\pi$
$462$		0			0
$463$	9.45324	+	16.3735i	0.439329	+	0.760941i	0.997638	−	0.0686927i	$-0.0218828\pi$
$463$	9.45324	+	16.3735i	0.439329	+	0.760941i	−0.558309	+	0.829633i	$0.688549\pi$
$464$	−32.3584			−1.50220
$465$		0			0
$466$	−0.666306			−0.0308661
$467$	−11.2057	+	19.4088i	−0.518536	+	0.898131i	0.481232	+	0.876593i	$0.340190\pi$
$467$	−11.2057	+	19.4088i	−0.518536	+	0.898131i	−0.999768	+	0.0215379i	$0.993144\pi$
$468$		0			0
$469$	−29.3676	−	14.5237i	−1.35607	−	0.670641i
$470$	−0.109706	+	0.190016i	−0.00506035	+	0.00876478i
$471$		0			0
$472$	0.0720446	−	0.124785i	0.00331612	−	0.00574369i
$473$	1.05588	−	1.82884i	0.0485494	−	0.0840900i
$474$		0			0
$475$	3.62126	−	6.27220i	0.166155	−	0.287788i
$476$	0.184932	+	2.87107i	0.00847634	+	0.131595i
$477$		0			0
$478$	0.243038	−	0.420953i	0.0111163	−	0.0192540i
$479$	30.1305			1.37670			0.688349	−	0.725380i	$-0.258336\pi$
$479$	30.1305			1.37670			0.688349	+	0.725380i	$0.258336\pi$
$480$		0			0
$481$	−18.5321			−0.844989
$482$	−0.182683	−	0.316416i	−0.00832097	−	0.0144123i
$483$		0			0
$484$	3.28835	−	5.69559i	0.149470	−	0.258890i
$485$	3.81553	−	6.60869i	0.173254	−	0.300085i
$486$		0			0
$487$	−17.0000	−	29.4448i	−0.770343	−	1.33427i	−0.937375	−	0.348322i	$-0.886752\pi$
$487$	−17.0000	−	29.4448i	−0.770343	−	1.33427i	0.167032	−	0.985951i	$-0.446582\pi$
$488$	−0.0897231	−	0.155405i	−0.00406157	−	0.00703485i
$489$		0			0
$490$	0.108687	+	0.142307i	0.00490999	+	0.00642876i
$491$	7.47750	+	12.9514i	0.337455	+	0.584489i	0.983953	−	0.178426i	$-0.0571006\pi$
$491$	7.47750	+	12.9514i	0.337455	+	0.584489i	−0.646498	+	0.762915i	$0.723767\pi$
$492$		0			0
$493$	4.40412			0.198352
$494$	−0.513240	−	0.888958i	−0.0230918	−	0.0399961i
$495$		0			0
$496$	6.95977			0.312503
$497$	−1.75667	−	27.2724i	−0.0787976	−	1.22333i
$498$		0			0
$499$	0.819143			0.0366699			0.0183349	−	0.999832i	$-0.494163\pi$
$499$	0.819143			0.0366699			0.0183349	+	0.999832i	$0.494163\pi$
$500$	−0.999673	+	1.73148i	−0.0447067	+	0.0774343i
$501$		0			0
$502$	0.0286014	+	0.0495391i	0.00127654	+	0.00221104i
$503$	−13.5639			−0.604783			−0.302392	−	0.953184i	$-0.597785\pi$
$503$	−13.5639			−0.604783			−0.302392	+	0.953184i	$0.597785\pi$
$504$		0			0
$505$	−3.42479			−0.152401
$506$	0.350817	+	0.607633i	0.0155957	+	0.0270126i
$507$		0			0
$508$	1.14630	−	1.98545i	0.0508589	−	0.0880903i
$509$	−34.9191			−1.54776			−0.773881	−	0.633330i	$-0.781687\pi$
$509$	−34.9191			−1.54776			−0.773881	+	0.633330i	$0.781687\pi$
$510$		0			0
$511$	−12.8375	+	8.55685i	−0.567898	+	0.378533i
$512$	−2.04377			−0.0903229
$513$		0			0
$514$	0.201636	+	0.349244i	0.00889378	+	0.0154045i
$515$	−9.43055			−0.415560
$516$		0			0
$517$	16.2116	+	28.0793i	0.712984	+	1.23493i
$518$	0.0145514	+	0.225910i	0.000639350	+	0.00992591i
$519$		0			0
$520$	0.283413	+	0.490886i	0.0124285	+	0.0215268i
$521$	−1.55141	−	2.68713i	−0.0679687	−	0.117725i	0.830038	−	0.557706i	$-0.188318\pi$
$521$	−1.55141	−	2.68713i	−0.0679687	−	0.117725i	−0.898007	+	0.439981i	$0.854985\pi$
$522$		0			0
$523$	−5.99060	+	10.3760i	−0.261951	+	0.453712i	−0.966760	−	0.255685i	$-0.917699\pi$
$523$	−5.99060	+	10.3760i	−0.261951	+	0.453712i	0.704810	+	0.709396i	$0.251032\pi$
$524$	6.36039	−	11.0165i	0.277855	−	0.481259i
$525$		0			0
$526$	0.163453	+	0.283110i	0.00712691	+	0.0123442i
$527$	−0.947256			−0.0412631
$528$		0			0
$529$	29.6482			1.28905
$530$	0.109104	−	0.188974i	0.00473918	−	0.00820850i
$531$		0			0
$532$	31.8786	−	21.2487i	1.38211	−	0.921248i
$533$	−1.31958	+	2.28558i	−0.0571574	+	0.0989994i
$534$		0			0
$535$	0.0944380	−	0.163571i	0.00408291	−	0.00707181i
$536$	−0.633434	+	1.09714i	−0.0273602	+	0.0473892i
$537$		0			0
$538$	0.251411	−	0.435457i	0.0108391	−	0.0187739i
$539$	26.2423	−	3.39473i	1.13034	−	0.146221i
$540$		0			0
$541$	0.566880	−	0.981865i	0.0243721	−	0.0422137i	−0.853582	−	0.520958i	$-0.825575\pi$
$541$	0.566880	−	0.981865i	0.0243721	−	0.0422137i	0.877954	+	0.478745i	$0.158908\pi$
$542$	−0.0524527			−0.00225304
$543$		0			0
$544$	0.166882			0.00715500
$545$	−4.40407	−	7.62807i	−0.188650	−	0.326751i
$546$		0			0
$547$	−3.51151	+	6.08211i	−0.150141	+	0.260052i	−0.931279	−	0.364306i	$-0.881306\pi$
$547$	−3.51151	+	6.08211i	−0.150141	+	0.260052i	0.781138	+	0.624358i	$0.214640\pi$
$548$	8.55682	−	14.8208i	0.365529	−	0.633115i
$549$		0			0
$550$	−0.0483491	−	0.0837432i	−0.00206161	−	0.00357082i
$551$	−29.3233	−	50.7895i	−1.24922	−	2.16371i
$552$		0			0
$553$	6.53110	−	4.35331i	0.277731	−	0.185121i
$554$	0.0821155	+	0.142228i	0.00348875	+	0.00604270i
$555$		0			0
$556$	−12.3471			−0.523635
$557$	6.94094	+	12.0221i	0.294097	+	0.509391i	0.974774	−	0.223192i	$-0.0716477\pi$
$557$	6.94094	+	12.0221i	0.294097	+	0.509391i	−0.680677	+	0.732583i	$0.738314\pi$
$558$		0			0
$559$	3.09518			0.130912
$560$	−8.79742	+	5.86393i	−0.371759	+	0.247796i
$561$		0			0
$562$	0.783287			0.0330410
$563$	11.1331	−	19.2831i	0.469204	−	0.812685i	−0.530176	−	0.847887i	$-0.677874\pi$
$563$	11.1331	−	19.2831i	0.469204	−	0.812685i	0.999380	+	0.0352025i	$0.0112076\pi$
$564$		0			0
$565$	−5.83704	−	10.1101i	−0.245566	−	0.425333i
$566$	−0.248884			−0.0104614
$567$		0			0
$568$	−1.05675			−0.0443403
$569$	0.0493845	+	0.0855365i	0.00207031	+	0.00358588i	0.867059	−	0.498206i	$-0.166008\pi$
$569$	0.0493845	+	0.0855365i	0.00207031	+	0.00358588i	−0.864988	+	0.501792i	$0.832674\pi$
$570$		0			0
$571$	−17.4881	+	30.2902i	−0.731852	+	1.26761i	0.224238	+	0.974534i	$0.428011\pi$
$571$	−17.4881	+	30.2902i	−0.731852	+	1.26761i	−0.956091	+	0.293071i	$0.905323\pi$
$572$	41.8740			1.75084
$573$		0			0
$574$	0.0288979	+	0.0142913i	0.00120617	+	0.000596509i
$575$	−7.25591			−0.302592
$576$		0			0
$577$	9.85646	+	17.0719i	0.410330	+	0.710712i	0.994926	−	0.100612i	$-0.0320802\pi$
$577$	9.85646	+	17.0719i	0.410330	+	0.710712i	−0.584596	+	0.811325i	$0.698747\pi$
$578$	0.427304			0.0177735
$579$		0			0
$580$	8.09490	+	14.0208i	0.336123	+	0.582181i
$581$	18.8641	+	9.32917i	0.782614	+	0.387039i
$582$		0			0
$583$	−16.1227	−	27.9253i	−0.667733	−	1.15655i
$584$	0.298283	+	0.516642i	0.0123431	+	0.0213788i
$585$		0			0
$586$	−0.136294	+	0.236068i	−0.00563026	+	0.00975189i
$587$	−13.3822	+	23.1787i	−0.552344	+	0.956687i	0.445761	+	0.895152i	$0.352933\pi$
$587$	−13.3822	+	23.1787i	−0.552344	+	0.956687i	−0.998105	+	0.0615355i	$0.980400\pi$
$588$		0			0
$589$	6.30697	+	10.9240i	0.259874	+	0.450116i
$590$	−0.0360282			−0.00148326
$591$		0			0
$592$	−13.3662			−0.549347
$593$	−2.17116	+	3.76056i	−0.0891589	+	0.154428i	−0.907156	−	0.420795i	$-0.861751\pi$
$593$	−2.17116	+	3.76056i	−0.0891589	+	0.154428i	0.817997	+	0.575223i	$0.195085\pi$
$594$		0			0
$595$	1.19737	−	0.798106i	0.0490873	−	0.0327192i
$596$	−4.69141	+	8.12577i	−0.192168	+	0.332844i
$597$		0			0
$598$	−0.514189	+	0.890602i	−0.0210268	+	0.0364194i
$599$	−19.2922	+	33.4151i	−0.788258	+	1.36530i	0.138775	+	0.990324i	$0.455683\pi$
$599$	−19.2922	+	33.4151i	−0.788258	+	1.36530i	−0.927033	+	0.374979i	$0.877650\pi$
$600$		0			0
$601$	22.6721	−	39.2693i	0.924815	−	1.60183i	0.132957	−	0.991122i	$-0.457553\pi$
$601$	22.6721	−	39.2693i	0.924815	−	1.60183i	0.791858	−	0.610705i	$-0.209114\pi$
$602$	−0.00243034	−	0.0377310i	−9.90531e−5	−	0.00153780i
$603$		0			0
$604$	−15.6074	+	27.0328i	−0.635057	+	1.09995i
$605$	−3.28942			−0.133734
$606$		0			0
$607$	10.7067			0.434572			0.217286	−	0.976108i	$-0.430280\pi$
$607$	10.7067			0.434572			0.217286	+	0.976108i	$0.430280\pi$
$608$	−1.11112	−	1.92452i	−0.0450620	−	0.0780498i
$609$		0			0
$610$	−0.0224344	+	0.0388576i	−0.000908344	+	0.00157330i
$611$	−23.7612	+	41.1555i	−0.961274	+	1.66497i
$612$		0			0
$613$	−14.1382	−	24.4882i	−0.571038	−	0.989067i	−0.996460	−	0.0840720i	$-0.973207\pi$
$613$	−14.1382	−	24.4882i	−0.571038	−	0.989067i	0.425421	−	0.904995i	$-0.360126\pi$
$614$	0.0457942	+	0.0793178i	0.00184810	+	0.00320101i
$615$		0			0
$616$	−0.0657697	−	1.02107i	−0.00264994	−	0.0411403i
$617$	−18.3974	−	31.8653i	−0.740653	−	1.28285i	−0.952198	−	0.305480i	$-0.901183\pi$
$617$	−18.3974	−	31.8653i	−0.740653	−	1.28285i	0.211546	−	0.977368i	$-0.432150\pi$
$618$		0			0
$619$	6.52183			0.262135			0.131067	−	0.991373i	$-0.458160\pi$
$619$	6.52183			0.262135			0.131067	+	0.991373i	$0.458160\pi$
$620$	−1.74108	−	3.01564i	−0.0699236	−	0.121111i
$621$		0			0
$622$	0.417367			0.0167349
$623$	42.7844	+	21.1589i	1.71412	+	0.847712i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−0.0879517	+	0.152337i	−0.00351526	+	0.00608860i
$627$		0			0
$628$	−18.5630	−	32.1520i	−0.740744	−	1.28301i
$629$	1.81920			0.0725362
$630$		0			0
$631$	2.81008			0.111867			0.0559337	−	0.998434i	$-0.482186\pi$
$631$	2.81008			0.111867			0.0559337	+	0.998434i	$0.482186\pi$
$632$	−0.151752	−	0.262842i	−0.00603637	−	0.0104553i
$633$		0			0
$634$	0.255133	−	0.441903i	0.0101326	−	0.0175502i
$635$	−1.14668			−0.0455045
$636$		0			0
$637$	23.5406	+	30.8222i	0.932711	+	1.22122i
$638$	−0.783019			−0.0310000
$639$		0			0
$640$	0.408955	+	0.708332i	0.0161654	+	0.0279993i
$641$	1.71362			0.0676838			0.0338419	−	0.999427i	$-0.489226\pi$
$641$	1.71362			0.0676838			0.0338419	+	0.999427i	$0.489226\pi$
$642$		0			0
$643$	−10.4993	−	18.1854i	−0.414054	−	0.717162i	0.581275	−	0.813707i	$-0.302554\pi$
$643$	−10.4993	−	18.1854i	−0.414054	−	0.717162i	−0.995329	+	0.0965451i	$0.969221\pi$
$644$	−34.4047	−	17.0147i	−1.35574	−	0.670475i
$645$		0			0
$646$	0.0503821	+	0.0872644i	0.00198226	+	0.00343337i
$647$	1.23228	+	2.13437i	0.0484458	+	0.0839105i	0.889231	−	0.457458i	$-0.151240\pi$
$647$	1.23228	+	2.13437i	0.0484458	+	0.0839105i	−0.840786	+	0.541368i	$0.817907\pi$
$648$		0			0
$649$	−2.66200	+	4.61072i	−0.104493	+	0.180987i
$650$	0.0708649	−	0.122742i	0.00277955	−	0.00481432i
$651$		0			0
$652$	1.31068	+	2.27017i	0.0513304	+	0.0889068i
$653$	33.5479			1.31283			0.656416	−	0.754399i	$-0.272072\pi$
$653$	33.5479			1.31283			0.656416	+	0.754399i	$0.272072\pi$
$654$		0			0
$655$	−6.36247			−0.248602
$656$	−0.951743	+	1.64847i	−0.0371593	+	0.0643618i
$657$		0			0
$658$	0.520352	+	0.257338i	0.0202854	+	0.0100321i
$659$	−5.81556	+	10.0728i	−0.226542	+	0.392382i	−0.956781	−	0.290809i	$-0.906075\pi$
$659$	−5.81556	+	10.0728i	−0.226542	+	0.392382i	0.730239	+	0.683192i	$0.239409\pi$
$660$		0			0
$661$	21.0430	−	36.4476i	0.818479	−	1.41765i	−0.0883238	−	0.996092i	$-0.528151\pi$
$661$	21.0430	−	36.4476i	0.818479	−	1.41765i	0.906803	−	0.421555i	$-0.138516\pi$
$662$	−0.138919	+	0.240615i	−0.00539925	+	0.00935178i
$663$		0			0
$664$	0.406881	−	0.704739i	0.0157901	−	0.0273492i
$665$	−17.1762	−	8.49445i	−0.666066	−	0.329401i
$666$		0			0
$667$	−29.3776	+	50.8834i	−1.13750	+	1.97021i
$668$	−22.2507			−0.860906
$669$		0			0
$670$	0.316769			0.0122378
$671$	3.31521	+	5.74211i	0.127982	+	0.221672i
$672$		0			0
$673$	−4.35702	+	7.54659i	−0.167951	+	0.290899i	−0.937699	−	0.347448i	$-0.887048\pi$
$673$	−4.35702	+	7.54659i	−0.167951	+	0.290899i	0.769748	+	0.638347i	$0.220382\pi$
$674$	0.00351063	−	0.00608059i	0.000135224	−	0.000234216i
$675$		0			0
$676$	17.6915	+	30.6425i	0.680440	+	1.17856i
$677$	5.73561	+	9.93437i	0.220437	+	0.381809i	0.954941	−	0.296796i	$-0.0959182\pi$
$677$	5.73561	+	9.93437i	0.220437	+	0.381809i	−0.734503	+	0.678605i	$0.762585\pi$
$678$		0			0
$679$	−18.0977	−	8.95015i	−0.694525	−	0.343475i
$680$	−0.0278212	−	0.0481878i	−0.00106689	−	0.00184792i
$681$		0			0
$682$	0.168415			0.00644893
$683$	−17.5055	−	30.3205i	−0.669831	−	1.16018i	−0.977951	−	0.208834i	$-0.933033\pi$
$683$	−17.5055	−	30.3205i	−0.669831	−	1.16018i	0.308120	−	0.951347i	$-0.400300\pi$
$684$		0			0
$685$	−8.55962			−0.327046
$686$	0.357245	−	0.311166i	0.0136397	−	0.0118804i
$687$		0			0
$688$	2.23239			0.0851091
$689$	23.6309	−	40.9298i	0.900264	−	1.55930i
$690$		0			0
$691$	−1.92339	−	3.33141i	−0.0731692	−	0.126733i	0.827119	−	0.562026i	$-0.189978\pi$
$691$	−1.92339	−	3.33141i	−0.0731692	−	0.126733i	−0.900289	+	0.435293i	$0.856645\pi$
$692$	−2.84848			−0.108283
$693$		0			0
$694$	0.0969062			0.00367851
$695$	3.08779	+	5.34821i	0.117127	+	0.202869i
$696$		0			0
$697$	0.129536	−	0.224364i	0.00490654	−	0.00849838i
$698$	0.732850			0.0277388
$699$		0			0
$700$	4.74161	+	2.34495i	0.179216	+	0.0886307i
$701$	−6.90316			−0.260729			−0.130364	−	0.991466i	$-0.541615\pi$
$701$	−6.90316			−0.260729			−0.130364	+	0.991466i	$0.541615\pi$
$702$		0			0
$703$	−12.1125	−	20.9795i	−0.456832	−	0.791255i
$704$	30.1817			1.13752
$705$		0			0
$706$	−0.0551886	−	0.0955895i	−0.00207705	−	0.00359756i
$707$	0.582442	+	9.04242i	0.0219050	+	0.340075i
$708$		0			0
$709$	−5.27133	−	9.13021i	−0.197969	−	0.342892i	0.749901	−	0.661550i	$-0.230101\pi$
$709$	−5.27133	−	9.13021i	−0.197969	−	0.342892i	−0.947870	+	0.318658i	$0.896768\pi$
$710$	0.132116	+	0.228831i	0.00495821	+	0.00858787i
$711$		0			0
$712$	0.922820	−	1.59837i	0.0345841	−	0.0599015i
$713$	6.31864	−	10.9442i	0.236635	−	0.409863i
$714$		0			0
$715$	−10.4719	−	18.1379i	−0.391628	−	0.678320i
$716$	25.1357			0.939367
$717$		0			0
$718$	0.695296			0.0259482
$719$	17.8806	−	30.9701i	0.666835	−	1.15499i	−0.311950	−	0.950099i	$-0.600982\pi$
$719$	17.8806	−	30.9701i	0.666835	−	1.15499i	0.978784	−	0.204893i	$-0.0656846\pi$
$720$		0			0
$721$	1.60382	+	24.8993i	0.0597293	+	0.927298i
$722$	0.427888	−	0.741124i	0.0159243	−	0.0275818i
$723$		0			0
$724$	−14.1684	+	24.5403i	−0.526563	+	0.912034i
$725$	4.04878	−	7.01269i	0.150368	−	0.260445i
$726$		0			0
$727$	−19.2427	+	33.3294i	−0.713674	+	1.23612i	0.249795	+	0.968299i	$0.419637\pi$
$727$	−19.2427	+	33.3294i	−0.713674	+	1.23612i	−0.963469	+	0.267820i	$0.913697\pi$
$728$	1.24788	−	0.831773i	0.0462494	−	0.0308276i
$729$		0			0
$730$	0.0745831	−	0.129182i	0.00276044	−	0.00478123i
$731$	−0.303838			−0.0112379
$732$		0			0
$733$	41.6428			1.53811			0.769056	−	0.639182i	$-0.220727\pi$
$733$	41.6428			1.53811			0.769056	+	0.639182i	$0.220727\pi$
$734$	0.153678	+	0.266179i	0.00567238	+	0.00982484i
$735$		0			0
$736$	−1.11318	+	1.92808i	−0.0410323	+	0.0710701i
$737$	23.4050	−	40.5386i	0.862133	−	1.49326i
$738$		0			0
$739$	−22.4915	−	38.9565i	−0.827364	−	1.43304i	−0.900099	−	0.435685i	$-0.856506\pi$
$739$	−22.4915	−	38.9565i	−0.827364	−	1.43304i	0.0727349	−	0.997351i	$-0.476827\pi$
$740$	3.34374	+	5.79152i	0.122918	+	0.212901i
$741$		0			0
$742$	−0.517499	−	0.255927i	−0.0189980	−	0.00939539i
$743$	2.24629	+	3.89069i	0.0824083	+	0.142735i	0.904284	−	0.426932i	$-0.140405\pi$
$743$	2.24629	+	3.89069i	0.0824083	+	0.142735i	−0.821876	+	0.569667i	$0.807072\pi$
$744$		0			0
$745$	4.69295			0.171936
$746$	−0.111069	−	0.192378i	−0.00406653	−	0.00704344i
$747$		0			0
$748$	−4.11056			−0.150297
$749$	−0.447935	−	0.221525i	−0.0163672	−	0.00809434i
$750$		0			0
$751$	42.2660			1.54231			0.771154	−	0.636649i	$-0.219680\pi$
$751$	42.2660			1.54231			0.771154	+	0.636649i	$0.219680\pi$
$752$	−17.1377	+	29.6833i	−0.624946	+	1.08244i
$753$		0			0
$754$	−0.573832	−	0.993906i	−0.0208977	−	0.0361959i
$755$	15.6125			0.568198
$756$		0			0
$757$	−25.4479			−0.924918			−0.462459	−	0.886641i	$-0.653033\pi$
$757$	−25.4479			−0.924918			−0.462459	+	0.886641i	$0.653033\pi$
$758$	0.162462	+	0.281392i	0.00590087	+	0.0102206i
$759$		0			0
$760$	−0.370476	+	0.641683i	−0.0134386	+	0.0232763i
$761$	29.8303			1.08135			0.540673	−	0.841233i	$-0.318170\pi$
$761$	29.8303			1.08135			0.540673	+	0.841233i	$0.318170\pi$
$762$		0			0
$763$	−19.3913	+	12.9252i	−0.702010	+	0.467925i
$764$	20.3543			0.736391
$765$		0			0
$766$	−0.321306	−	0.556518i	−0.0116092	−	0.0201078i
$767$	−7.80334			−0.281762
$768$		0			0
$769$	9.71584	+	16.8283i	0.350362	+	0.606845i	0.986313	−	0.164885i	$-0.0527252\pi$
$769$	9.71584	+	16.8283i	0.350362	+	0.606845i	−0.635951	+	0.771730i	$0.719392\pi$
$770$	−0.212883	+	0.141897i	−0.00767176	+	0.00511362i
$771$		0			0
$772$	−6.84926	−	11.8633i	−0.246510	−	0.426968i
$773$	−16.1602	−	27.9902i	−0.581241	−	1.00674i	−0.995333	−	0.0965036i	$-0.969234\pi$
$773$	−16.1602	−	27.9902i	−0.581241	−	1.00674i	0.414092	−	0.910235i	$-0.364099\pi$
$774$		0			0
$775$	−0.870826	+	1.50832i	−0.0312810	+	0.0541803i
$776$	−0.390351	+	0.676107i	−0.0140128	+	0.0242708i
$777$		0			0
$778$	−0.244838	−	0.424071i	−0.00877785	−	0.0152037i
$779$	−3.44989			−0.123605
$780$		0			0
$781$	39.0463			1.39719
$782$	0.0504753	−	0.0874258i	0.00180499	−	0.00312634i
$783$		0			0
$784$	16.9785	+	22.2304i	0.606377	+	0.793943i
$785$	−9.28453	+	16.0813i	−0.331379	+	0.573965i
$786$		0			0
$787$	−13.0951	+	22.6813i	−0.466788	+	0.808501i	−0.999280	−	0.0379339i	$-0.987922\pi$
$787$	−13.0951	+	22.6813i	−0.466788	+	0.808501i	0.532492	+	0.846435i	$0.321256\pi$
$788$	20.0101	−	34.6586i	0.712831	−	1.23466i
$789$		0			0
$790$	−0.0379442	+	0.0657213i	−0.00134999	+	0.00233826i
$791$	−25.7007	+	17.1308i	−0.913811	+	0.609101i
$792$		0			0
$793$	−4.85907	+	8.41616i	−0.172551	+	0.298867i
$794$	−0.0923211			−0.00327635
$795$		0			0
$796$	25.8877			0.917566
$797$	−9.92568	−	17.1918i	−0.351586	−	0.608964i	0.634942	−	0.772560i	$-0.281024\pi$
$797$	−9.92568	−	17.1918i	−0.351586	−	0.608964i	−0.986527	+	0.163596i	$0.947691\pi$
$798$		0			0
$799$	2.33251	−	4.04003i	0.0825183	−	0.142926i
$800$	0.153417	−	0.265726i	0.00542411	−	0.00939483i
$801$		0			0
$802$	−0.0429774	−	0.0744390i	−0.00151758	−	0.00262853i
$803$	−11.0214	−	19.0896i	−0.388936	−	0.673657i
$804$		0			0
$805$	1.23399	+	19.1576i	0.0434923	+	0.675218i
$806$	0.123422	+	0.213773i	0.00434735	+	0.00752984i
$807$		0			0
$808$	0.350376			0.0123262
$809$	1.09725	+	1.90050i	0.0385774	+	0.0668180i	0.884669	−	0.466219i	$-0.154384\pi$
$809$	1.09725	+	1.90050i	0.0385774	+	0.0668180i	−0.846092	+	0.533037i	$0.821051\pi$
$810$		0			0
$811$	−21.8077			−0.765773			−0.382887	−	0.923795i	$-0.625070\pi$
$811$	−21.8077			−0.765773			−0.382887	+	0.923795i	$0.625070\pi$
$812$	35.6421	−	23.7573i	1.25079	−	0.833717i
$813$		0			0
$814$	−0.323439			−0.0113365
$815$	0.655557	−	1.13546i	0.0229632	−	0.0397734i
$816$		0			0
$817$	2.02300	+	3.50394i	0.0707759	+	0.122587i
$818$	−0.0609402			−0.00213072
$819$		0			0
$820$	0.952366			0.0332581
$821$	22.0670	+	38.2212i	0.770144	+	1.33393i	0.937484	+	0.348029i	$0.113149\pi$
$821$	22.0670	+	38.2212i	0.770144	+	1.33393i	−0.167340	+	0.985899i	$0.553518\pi$
$822$		0			0
$823$	−16.7786	+	29.0615i	−0.584867	+	1.01302i	0.410025	+	0.912074i	$0.365520\pi$
$823$	−16.7786	+	29.0615i	−0.584867	+	1.01302i	−0.994892	+	0.100945i	$0.967813\pi$
$824$	0.964800			0.0336104
$825$		0			0
$826$	0.00612718	+	0.0951245i	0.000213192	+	0.00330980i
$827$	4.29754			0.149440			0.0747201	−	0.997205i	$-0.476194\pi$
$827$	4.29754			0.149440			0.0747201	+	0.997205i	$0.476194\pi$
$828$		0			0
$829$	−11.9899	−	20.7671i	−0.416427	−	0.721273i	0.579150	−	0.815221i	$-0.303385\pi$
$829$	−11.9899	−	20.7671i	−0.416427	−	0.721273i	−0.995577	+	0.0939481i	$0.970051\pi$
$830$	−0.203474			−0.00706268
$831$		0			0
$832$	22.1185	+	38.3104i	0.766822	+	1.32818i
$833$	−2.31086	−	3.02566i	−0.0800664	−	0.104833i
$834$		0			0
$835$	5.56450	+	9.63799i	0.192567	+	0.333536i
$836$	27.3687	+	47.4041i	0.946568	+	1.63950i
$837$		0			0
$838$	−0.0400887	+	0.0694356i	−0.00138484	+	0.00239861i
$839$	−24.2851	+	42.0630i	−0.838414	+	1.45218i	0.0528059	+	0.998605i	$0.483184\pi$
$839$	−24.2851	+	42.0630i	−0.838414	+	1.45218i	−0.891220	+	0.453571i	$0.850150\pi$
$840$		0			0
$841$	−18.2852	−	31.6708i	−0.630523	−	1.09210i
$842$	0.341782			0.0117786
$843$		0			0
$844$	25.7230			0.885421
$845$	8.84862	−	15.3263i	0.304402	−	0.527239i
$846$		0			0
$847$	0.559420	+	8.68500i	0.0192219	+	0.298420i
$848$	17.0437	−	29.5205i	0.585282	−	1.01374i
$849$		0			0
$850$	−0.00695644	+	0.0120489i	−0.000238604	+	0.000413274i
$851$	−12.1349	+	21.0183i	−0.415979	+	0.720496i
$852$		0			0
$853$	−8.37813	+	14.5113i	−0.286862	+	0.496859i	−0.973059	−	0.230556i	$-0.925945\pi$
$853$	−8.37813	+	14.5113i	−0.286862	+	0.496859i	0.686197	+	0.727416i	$0.259279\pi$
$854$	0.106410	+	0.0526248i	0.00364128	+	0.00180078i
$855$		0			0
$856$	−0.00966156	+	0.0167343i	−0.000330225	+	0.000571967i
$857$	10.4552			0.357143			0.178571	−	0.983927i	$-0.442852\pi$
$857$	10.4552			0.357143			0.178571	+	0.983927i	$0.442852\pi$
$858$		0			0
$859$	13.4320			0.458295			0.229147	−	0.973392i	$-0.426406\pi$
$859$	13.4320			0.458295			0.229147	+	0.973392i	$0.426406\pi$
$860$	−0.558463	−	0.967287i	−0.0190434	−	0.0329842i
$861$		0			0
$862$	−0.306331	+	0.530581i	−0.0104337	+	0.0180716i
$863$	−15.5326	+	26.9033i	−0.528737	+	0.915799i	0.470702	+	0.882292i	$0.344001\pi$
$863$	−15.5326	+	26.9033i	−0.528737	+	0.915799i	−0.999439	+	0.0335063i	$0.989333\pi$
$864$		0			0
$865$	0.712352	+	1.23383i	0.0242207	+	0.0419515i
$866$	−0.196635	−	0.340581i	−0.00668191	−	0.0115734i
$867$		0			0
$868$	−7.66604	+	5.10980i	−0.260202	+	0.173438i
$869$	5.60714	+	9.71186i	0.190209	+	0.329452i
$870$		0			0
$871$	68.6089			2.32472
$872$	0.450562	+	0.780396i	0.0152579	+	0.0264275i
$873$		0			0
$874$	−1.34429			−0.0454713
$875$	−0.170066	−	2.64028i	−0.00574929	−	0.0892577i
$876$		0			0
$877$	−10.6455			−0.359472			−0.179736	−	0.983715i	$-0.557524\pi$
$877$	−10.6455			−0.359472			−0.179736	+	0.983715i	$0.557524\pi$
$878$	0.108719	−	0.188306i	0.00366908	−	0.00635503i
$879$		0			0
$880$	−7.55285	−	13.0819i	−0.254607	−	0.440991i
$881$	37.4454			1.26157			0.630785	−	0.775958i	$-0.282733\pi$
$881$	37.4454			1.26157			0.630785	+	0.775958i	$0.282733\pi$
$882$		0			0
$883$	−1.93626			−0.0651605			−0.0325802	−	0.999469i	$-0.510372\pi$
$883$	−1.93626			−0.0651605			−0.0325802	+	0.999469i	$0.510372\pi$
$884$	−3.01240	−	5.21764i	−0.101318	−	0.175488i
$885$		0			0
$886$	0.395636	−	0.685261i	0.0132916	−	0.0230218i
$887$	−27.1683			−0.912224			−0.456112	−	0.889922i	$-0.650758\pi$
$887$	−27.1683			−0.912224			−0.456112	+	0.889922i	$0.650758\pi$
$888$		0			0
$889$	0.195011	+	3.02755i	0.00654046	+	0.101541i
$890$	−0.461486			−0.0154690
$891$		0			0
$892$	−12.4068	−	21.4892i	−0.415411	−	0.719513i
$893$	−62.1209			−2.07880
$894$		0			0
$895$	−6.28599	−	10.8877i	−0.210118	−	0.363934i
$896$	1.80064	−	1.20022i	0.0601553	−	0.0400965i
$897$		0			0
$898$	−0.0541874	−	0.0938553i	−0.00180826	−	0.00313199i
$899$	7.05156	+	12.2137i	0.235183	+	0.407348i
$900$		0			0
$901$	−2.31972	+	4.01787i	−0.0772811	+	0.133855i
$902$	−0.0230306	+	0.0398901i	−0.000766834	+	0.00132820i
$903$		0			0
$904$	0.597163	+	1.03432i	0.0198614	+	0.0344009i
$905$	14.1730			0.471127
$906$		0			0
$907$	55.9188			1.85675			0.928376	−	0.371642i	$-0.121205\pi$
$907$	55.9188			1.85675			0.928376	+	0.371642i	$0.121205\pi$
$908$	−8.85931	+	15.3448i	−0.294007	+	0.509234i
$909$		0			0
$910$	−0.336124	−	0.166229i	−0.0111424	−	0.00551043i
$911$	−4.38364	+	7.59269i	−0.145237	+	0.251557i	−0.929461	−	0.368920i	$-0.879728\pi$
$911$	−4.38364	+	7.59269i	−0.145237	+	0.251557i	0.784225	+	0.620477i	$0.213061\pi$
$912$		0			0
$913$	−15.0340	+	26.0397i	−0.497553	+	0.861787i
$914$	0.503916	−	0.872807i	0.0166680	−	0.0288699i
$915$		0			0
$916$	26.3083	−	45.5674i	0.869252	−	1.50559i
$917$	1.08204	+	16.7987i	0.0357322	+	0.554742i
$918$		0			0
$919$	5.14755	−	8.91582i	0.169802	−	0.294106i	−0.768548	−	0.639792i	$-0.779021\pi$
$919$	5.14755	−	8.91582i	0.169802	−	0.294106i	0.938350	+	0.345686i	$0.112354\pi$
$920$	0.742322			0.0244736
$921$		0			0
$922$	0.146416			0.00482194
$923$	28.6149	+	49.5625i	0.941871	+	1.63137i
$924$		0			0
$925$	1.67242	−	2.89671i	0.0549887	−	0.0952432i
$926$	−0.241820	+	0.418844i	−0.00794669	+	0.0137641i
$927$		0			0
$928$	−1.24230	−	2.15173i	−0.0407805	−	0.0706339i
$929$	18.7180	+	32.4206i	0.614119	+	1.06368i	0.990538	+	0.137235i	$0.0438217\pi$
$929$	18.7180	+	32.4206i	0.614119	+	1.06368i	−0.376420	+	0.926449i	$0.622845\pi$
$930$		0			0
$931$	−19.5066	+	46.7947i	−0.639304	+	1.53363i
$932$	26.0388	+	45.1005i	0.852928	+	1.47732i
$933$		0			0
$934$	−0.573296			−0.0187588
$935$	1.02798	+	1.78051i	0.0336184	+	0.0582288i
$936$		0			0
$937$	−20.0462			−0.654882			−0.327441	−	0.944872i	$-0.606186\pi$
$937$	−20.0462			−0.654882			−0.327441	+	0.944872i	$0.606186\pi$
$938$	−0.0538717	−	0.836358i	−0.00175897	−	0.0273081i
$939$		0			0
$940$	17.1489			0.559335
$941$	−4.82903	+	8.36413i	−0.157422	+	0.272663i	−0.933938	−	0.357434i	$-0.883652\pi$
$941$	−4.82903	+	8.36413i	−0.157422	+	0.272663i	0.776516	+	0.630097i	$0.216985\pi$
$942$		0			0
$943$	1.72814	+	2.99322i	0.0562759	+	0.0974726i
$944$	−5.62813			−0.183180
$945$		0			0
$946$	0.0540201			0.00175635
$947$	8.28334	+	14.3472i	0.269172	+	0.466220i	0.968648	−	0.248436i	$-0.0799165\pi$
$947$	8.28334	+	14.3472i	0.269172	+	0.466220i	−0.699476	+	0.714656i	$0.746583\pi$
$948$		0			0
$949$	16.1539	−	27.9795i	0.524379	−	0.908251i
$950$	0.185268			0.00601089
$951$		0			0
$952$	−0.122498	+	0.0816509i	−0.00397017	+	0.00264632i
$953$	−22.6180			−0.732669			−0.366335	−	0.930483i	$-0.619387\pi$
$953$	−22.6180			−0.732669			−0.366335	+	0.930483i	$0.619387\pi$
$954$		0			0
$955$	−5.09023	−	8.81654i	−0.164716	−	0.285296i
$956$	−37.9909			−1.22871
$957$		0			0
$958$	0.385379	+	0.667495i	0.0124510	+	0.0215658i
$959$	1.45570	+	22.5998i	0.0470071	+	0.729785i
$960$		0			0
$961$	13.9833	+	24.2198i	0.451075	+	0.781285i
$962$	−0.237031	−	0.410550i	−0.00764219	−	0.0132367i
$963$		0			0
$964$	−14.2782	+	24.7306i	−0.459871	+	0.796519i
$965$	−3.42575	+	5.93357i	−0.110279	+	0.191009i
$966$		0			0
$967$	−16.1629	−	27.9950i	−0.519764	−	0.900258i	−0.999736	−	0.0229741i	$-0.992686\pi$
$967$	−16.1629	−	27.9950i	−0.519764	−	0.900258i	0.479972	−	0.877284i	$-0.340647\pi$
$968$	0.336527			0.0108164
$969$		0			0
$970$	0.195207			0.00626773
$971$	−19.6527	+	34.0395i	−0.630686	+	1.09238i	0.356726	+	0.934209i	$0.383893\pi$
$971$	−19.6527	+	34.0395i	−0.630686	+	1.09238i	−0.987412	+	0.158171i	$0.949440\pi$
$972$		0			0
$973$	13.5957	−	9.06219i	0.435857	−	0.290520i
$974$	0.434870	−	0.753218i	0.0139341	−	0.0241347i
$975$		0			0
$976$	−3.50459	+	6.07013i	−0.112179	+	0.194300i
$977$	14.9663	−	25.9223i	0.478813	−	0.829328i	−0.520892	−	0.853623i	$-0.674401\pi$
$977$	14.9663	−	25.9223i	0.478813	−	0.829328i	0.999705	+	0.0242942i	$0.00773386\pi$
$978$		0			0
$979$	−34.0976	+	59.0588i	−1.08976	+	1.88753i
$980$	5.38493	−	12.9180i	0.172015	−	0.412650i
$981$		0			0
$982$	−0.191279	+	0.331305i	−0.00610396	+	0.0105724i
$983$	−0.568902			−0.0181451			−0.00907257	−	0.999959i	$-0.502888\pi$
$983$	−0.568902			−0.0181451			−0.00907257	+	0.999959i	$0.502888\pi$
$984$		0			0
$985$	−20.0167			−0.637785
$986$	0.0563301	+	0.0975667i	0.00179392	+	0.00310716i
$987$		0			0
$988$	−40.1141	+	69.4797i	−1.27620	+	2.21044i
$989$	2.02674	−	3.51042i	0.0644467	−	0.111625i
$990$		0			0
$991$	−6.46835	−	11.2035i	−0.205474	−	0.355891i	0.744810	−	0.667277i	$-0.232540\pi$
$991$	−6.46835	−	11.2035i	−0.205474	−	0.355891i	−0.950284	+	0.311386i	$0.899207\pi$
$992$	0.267199	+	0.462802i	0.00848357	+	0.0146940i
$993$		0			0
$994$	0.581709	−	0.387739i	0.0184507	−	0.0122983i
$995$	−6.47405	−	11.2134i	−0.205241	−	0.355488i
$996$		0			0
$997$	10.7662			0.340970			0.170485	−	0.985360i	$-0.445466\pi$
$997$	10.7662			0.340970			0.170485	+	0.985360i	$0.445466\pi$
$998$	0.0104771	+	0.0181469i	0.000331647	+	0.000574429i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.k.c.856.10		36
3.2	odd	2		315.2.k.c.16.9	✓	36
7.4	even	3		945.2.l.c.46.9		36
9.4	even	3		945.2.l.c.226.9		36
9.5	odd	6		315.2.l.c.121.10	yes	36
21.11	odd	6		315.2.l.c.151.10	yes	36
63.4	even	3	inner	945.2.k.c.361.10		36
63.32	odd	6		315.2.k.c.256.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.9	✓	36	3.2	odd	2
315.2.k.c.256.9	yes	36	63.32	odd	6
315.2.l.c.121.10	yes	36	9.5	odd	6
315.2.l.c.151.10	yes	36	21.11	odd	6
945.2.k.c.361.10		36	63.4	even	3	inner
945.2.k.c.856.10		36	1.1	even	1	trivial
945.2.l.c.46.9		36	7.4	even	3
945.2.l.c.226.9		36	9.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.k (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0127903 + 0.0221535i) q^{2} +(0.999673 - 1.73148i) q^{4} -1.00000 q^{5} +(0.170066 + 2.64028i) q^{7} +0.102306 q^{8} +(-0.0127903 - 0.0221535i) q^{10} -3.78014 q^{11} +(-2.77025 - 4.79822i) q^{13} +(-0.0563162 + 0.0375376i) q^{14} +(-1.99804 - 3.46070i) q^{16} +(0.271942 + 0.471017i) q^{17} +(3.62126 - 6.27220i) q^{19} +(-0.999673 + 1.73148i) q^{20} +(-0.0483491 - 0.0837432i) q^{22} -7.25591 q^{23} +1.00000 q^{25} +(0.0708649 - 0.122742i) q^{26} +(4.74161 + 2.34495i) q^{28} +(4.04878 - 7.01269i) q^{29} +(-0.870826 + 1.50832i) q^{31} +(0.153417 - 0.265726i) q^{32} +(-0.00695644 + 0.0120489i) q^{34} +(-0.170066 - 2.64028i) q^{35} +(1.67242 - 2.89671i) q^{37} +0.185268 q^{38} -0.102306 q^{40} +(-0.238169 - 0.412522i) q^{41} +(-0.279323 + 0.483802i) q^{43} +(-3.77890 + 6.54524i) q^{44} +(-0.0928054 - 0.160744i) q^{46} +(-4.28862 - 7.42811i) q^{47} +(-6.94215 + 0.898045i) q^{49} +(0.0127903 + 0.0221535i) q^{50} -11.0774 q^{52} +(4.26510 + 7.38738i) q^{53} +3.78014 q^{55} +(0.0173988 + 0.270116i) q^{56} +0.207141 q^{58} +(0.704208 - 1.21972i) q^{59} +(-0.877009 - 1.51902i) q^{61} -0.0445526 q^{62} -7.98430 q^{64} +(2.77025 + 4.79822i) q^{65} +(-6.19157 + 10.7241i) q^{67} +1.08741 q^{68} +(0.0563162 - 0.0375376i) q^{70} -10.3293 q^{71} +(2.91561 + 5.04998i) q^{73} +0.0855629 q^{74} +(-7.24015 - 12.5403i) q^{76} +(-0.642874 - 9.98062i) q^{77} +(-1.48332 - 2.56918i) q^{79} +(1.99804 + 3.46070i) q^{80} +(0.00609253 - 0.0105526i) q^{82} +(3.97711 - 6.88856i) q^{83} +(-0.271942 - 0.471017i) q^{85} -0.0142905 q^{86} -0.386730 q^{88} +(9.02021 - 15.6235i) q^{89} +(12.1975 - 8.13026i) q^{91} +(-7.25354 + 12.5635i) q^{92} +(0.109706 - 0.190016i) q^{94} +(-3.62126 + 6.27220i) q^{95} +(-3.81553 + 6.60869i) q^{97} +(-0.108687 - 0.142307i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 22 q^{4} - 36 q^{5} - q^{7} + 2 q^{11} + 2 q^{13} + 6 q^{14} - 30 q^{16} + 5 q^{17} - 2 q^{19} + 22 q^{20} - 19 q^{22} - 6 q^{23} + 36 q^{25} + 4 q^{26} + 5 q^{28} + 8 q^{29} - 10 q^{32} + 10 q^{34}+ \cdots - 16 q^{98}+O(q^{100}) \) 36 * q - 22 * q^4 - 36 * q^5 - q^7 + 2 * q^11 + 2 * q^13 + 6 * q^14 - 30 * q^16 + 5 * q^17 - 2 * q^19 + 22 * q^20 - 19 * q^22 - 6 * q^23 + 36 * q^25 + 4 * q^26 + 5 * q^28 + 8 * q^29 - 10 * q^32 + 10 * q^34 + q^35 - 15 * q^37 - 44 * q^38 + 4 * q^41 - 29 * q^43 + 7 * q^44 - 24 * q^46 + 23 * q^47 - 7 * q^49 + 14 * q^52 - 2 * q^55 - 33 * q^56 + 40 * q^58 + 5 * q^59 - 3 * q^61 + 12 * q^62 + 128 * q^64 - 2 * q^65 - 35 * q^67 - 34 * q^68 - 6 * q^70 - 24 * q^71 - 10 * q^73 + 44 * q^74 + 10 * q^76 - 5 * q^77 - 28 * q^79 + 30 * q^80 - 8 * q^82 + 22 * q^83 - 5 * q^85 + 38 * q^86 + 100 * q^88 + 4 * q^89 + 7 * q^91 + 50 * q^92 - 2 * q^94 + 2 * q^95 + 16 * q^97 - 16 * q^98

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