LMFDB - Embedded newform 792.2.k.a.683.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(683,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.683"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.k (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			683.18
Character	$\chi$	$=$	792.683
Dual form			792.2.k.a.683.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.313193 + 1.37910i) q^{2} +(-1.80382 - 0.863848i) q^{4} -1.89382 q^{5} +3.03135i q^{7} +(1.75627 - 2.21709i) q^{8} +(0.593133 - 2.61177i) q^{10} -1.00000i q^{11} +5.44282i q^{13} +(-4.18052 - 0.949397i) q^{14} +(2.50753 + 3.11645i) q^{16} -6.40451i q^{17} -5.86923 q^{19} +(3.41612 + 1.63598i) q^{20} +(1.37910 + 0.313193i) q^{22} -2.92580 q^{23} -1.41343 q^{25} +(-7.50618 - 1.70465i) q^{26} +(2.61862 - 5.46801i) q^{28} +0.600643 q^{29} -10.8348i q^{31} +(-5.08323 + 2.48208i) q^{32} +(8.83245 + 2.00585i) q^{34} -5.74084i q^{35} +1.96238i q^{37} +(1.83820 - 8.09424i) q^{38} +(-3.32608 + 4.19879i) q^{40} -8.98233i q^{41} +2.80132 q^{43} +(-0.863848 + 1.80382i) q^{44} +(0.916341 - 4.03497i) q^{46} -0.286711 q^{47} -2.18907 q^{49} +(0.442676 - 1.94925i) q^{50} +(4.70177 - 9.81787i) q^{52} -10.9248 q^{53} +1.89382i q^{55} +(6.72078 + 5.32388i) q^{56} +(-0.188117 + 0.828346i) q^{58} +6.10246i q^{59} -14.1808i q^{61} +(14.9423 + 3.39339i) q^{62} +(-1.83100 - 7.78765i) q^{64} -10.3078i q^{65} -12.2822 q^{67} +(-5.53252 + 11.5526i) q^{68} +(7.91718 + 1.79799i) q^{70} -9.74776 q^{71} +7.25976 q^{73} +(-2.70631 - 0.614604i) q^{74} +(10.5870 + 5.07012i) q^{76} +3.03135 q^{77} +3.48834i q^{79} +(-4.74883 - 5.90201i) q^{80} +(12.3875 + 2.81320i) q^{82} +9.17926i q^{83} +12.1290i q^{85} +(-0.877355 + 3.86330i) q^{86} +(-2.21709 - 1.75627i) q^{88} +9.80721i q^{89} -16.4991 q^{91} +(5.27762 + 2.52745i) q^{92} +(0.0897961 - 0.395403i) q^{94} +11.1153 q^{95} +4.90282 q^{97} +(0.685601 - 3.01894i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} + 8 q^{10} - 8 q^{16} + 32 q^{19} + 40 q^{25} - 32 q^{28} + 32 q^{34} + 16 q^{40} - 24 q^{46} - 8 q^{49} + 40 q^{52} - 8 q^{58} + 16 q^{64} + 72 q^{70} + 32 q^{73} - 8 q^{76} - 64 q^{82}+ \cdots - 32 q^{97}+O(q^{100}) $ 40 * q - 8 * q^4 + 8 * q^10 - 8 * q^16 + 32 * q^19 + 40 * q^25 - 32 * q^28 + 32 * q^34 + 16 * q^40 - 24 * q^46 - 8 * q^49 + 40 * q^52 - 8 * q^58 + 16 * q^64 + 72 * q^70 + 32 * q^73 - 8 * q^76 - 64 * q^82 - 24 * q^88 - 56 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−0.313193	+	1.37910i	−0.221461	+	0.975169i
$2$	−0.313193	+	1.37910i	−0.221461	+	0.975169i
$3$		0			0
$3$		0			0
$4$	−1.80382	−	0.863848i	−0.901910	−	0.431924i
$5$	−1.89382			−0.846944			−0.423472	−	0.905909i	$-0.639189\pi$
$5$	−1.89382			−0.846944			−0.423472	+	0.905909i	$0.639189\pi$
$6$		0			0
$7$			3.03135i			1.14574i	0.819646	+	0.572871i	$0.194170\pi$
$7$			3.03135i			1.14574i	−0.819646	+	0.572871i	$0.805830\pi$
$8$	1.75627	−	2.21709i	0.620937	−	0.783861i
$9$		0			0
$10$	0.593133	−	2.61177i	0.187565	−	0.825914i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$		0			0
$13$			5.44282i			1.50957i	0.655974	+	0.754784i	$0.272258\pi$
$13$			5.44282i			1.50957i	−0.655974	+	0.754784i	$0.727742\pi$
$14$	−4.18052	−	0.949397i	−1.11729	−	0.253737i
$15$		0			0
$16$	2.50753	+	3.11645i	0.626883	+	0.779113i
$17$		−	6.40451i		−	1.55332i	−0.629919	−	0.776661i	$-0.716912\pi$
$17$		−	6.40451i		−	1.55332i	0.629919	−	0.776661i	$-0.283088\pi$
$18$		0			0
$19$	−5.86923			−1.34649			−0.673247	−	0.739418i	$-0.735101\pi$
$19$	−5.86923			−1.34649			−0.673247	+	0.739418i	$0.735101\pi$
$20$	3.41612	+	1.63598i	0.763868	+	0.365815i
$21$		0			0
$22$	1.37910	+	0.313193i	0.294025	+	0.0667730i
$23$	−2.92580			−0.610072			−0.305036	−	0.952341i	$-0.598668\pi$
$23$	−2.92580			−0.610072			−0.305036	+	0.952341i	$0.598668\pi$
$24$		0			0
$25$	−1.41343			−0.282685
$26$	−7.50618	−	1.70465i	−1.47208	−	0.334310i
$27$		0			0
$28$	2.61862	−	5.46801i	0.494873	−	1.03336i
$29$	0.600643			0.111537			0.0557683	−	0.998444i	$-0.482239\pi$
$29$	0.600643			0.111537			0.0557683	+	0.998444i	$0.482239\pi$
$30$		0			0
$31$		−	10.8348i		−	1.94599i	−0.230823	−	0.972996i	$-0.574142\pi$
$31$		−	10.8348i		−	1.94599i	0.230823	−	0.972996i	$-0.425858\pi$
$32$	−5.08323	+	2.48208i	−0.898597	+	0.438774i
$33$		0			0
$34$	8.83245	+	2.00585i	1.51475	+	0.344000i
$35$		−	5.74084i		−	0.970379i
$36$		0			0
$37$			1.96238i			0.322613i	0.986904	+	0.161307i	$0.0515708\pi$
$37$			1.96238i			0.322613i	−0.986904	+	0.161307i	$0.948429\pi$
$38$	1.83820	−	8.09424i	0.298196	−	1.31306i
$39$		0			0
$40$	−3.32608	+	4.19879i	−0.525899	+	0.663886i
$41$		−	8.98233i		−	1.40280i	−0.712766	−	0.701402i	$-0.752558\pi$
$41$		−	8.98233i		−	1.40280i	0.712766	−	0.701402i	$-0.247442\pi$
$42$		0			0
$43$	2.80132			0.427198			0.213599	−	0.976921i	$-0.431481\pi$
$43$	2.80132			0.427198			0.213599	+	0.976921i	$0.431481\pi$
$44$	−0.863848	+	1.80382i	−0.130230	+	0.271936i
$45$		0			0
$46$	0.916341	−	4.03497i	0.135107	−	0.594923i
$47$	−0.286711			−0.0418212			−0.0209106	−	0.999781i	$-0.506657\pi$
$47$	−0.286711			−0.0418212			−0.0209106	+	0.999781i	$0.506657\pi$
$48$		0			0
$49$	−2.18907			−0.312724
$50$	0.442676	−	1.94925i	0.0626038	−	0.275666i
$51$		0			0
$52$	4.70177	−	9.81787i	0.652018	−	1.36149i
$53$	−10.9248			−1.50063			−0.750316	−	0.661080i	$-0.770098\pi$
$53$	−10.9248			−1.50063			−0.750316	+	0.661080i	$0.770098\pi$
$54$		0			0
$55$			1.89382i			0.255363i
$56$	6.72078	+	5.32388i	0.898102	+	0.711433i
$57$		0			0
$58$	−0.188117	+	0.828346i	−0.0247010	+	0.108767i
$59$			6.10246i			0.794473i	0.917716	+	0.397237i	$0.130031\pi$
$59$			6.10246i			0.794473i	−0.917716	+	0.397237i	$0.869969\pi$
$60$		0			0
$61$		−	14.1808i		−	1.81567i	−0.419328	−	0.907835i	$-0.637734\pi$
$61$		−	14.1808i		−	1.81567i	0.419328	−	0.907835i	$-0.362266\pi$
$62$	14.9423	+	3.39339i	1.89767	+	0.430961i
$63$		0			0
$64$	−1.83100	−	7.78765i	−0.228875	−	0.973456i
$65$		−	10.3078i		−	1.27852i
$66$		0			0
$67$	−12.2822			−1.50051			−0.750256	−	0.661147i	$-0.770070\pi$
$67$	−12.2822			−1.50051			−0.750256	+	0.661147i	$0.770070\pi$
$68$	−5.53252	+	11.5526i	−0.670917	+	1.40096i
$69$		0			0
$70$	7.91718	+	1.79799i	0.946284	+	0.214901i
$71$	−9.74776			−1.15685			−0.578423	−	0.815737i	$-0.696332\pi$
$71$	−9.74776			−1.15685			−0.578423	+	0.815737i	$0.696332\pi$
$72$		0			0
$73$	7.25976			0.849690			0.424845	−	0.905266i	$-0.360329\pi$
$73$	7.25976			0.849690			0.424845	+	0.905266i	$0.360329\pi$
$74$	−2.70631	−	0.614604i	−0.314602	−	0.0714462i
$75$		0			0
$76$	10.5870	+	5.07012i	1.21442	+	0.581583i
$77$	3.03135			0.345454
$78$		0			0
$79$			3.48834i			0.392469i	0.980557	+	0.196234i	$0.0628713\pi$
$79$			3.48834i			0.392469i	−0.980557	+	0.196234i	$0.937129\pi$
$80$	−4.74883	−	5.90201i	−0.530935	−	0.659865i
$81$		0			0
$82$	12.3875	+	2.81320i	1.36797	+	0.310666i
$83$			9.17926i			1.00755i	0.863834	+	0.503777i	$0.168057\pi$
$83$			9.17926i			1.00755i	−0.863834	+	0.503777i	$0.831943\pi$
$84$		0			0
$85$			12.1290i			1.31558i
$86$	−0.877355	+	3.86330i	−0.0946076	+	0.416590i
$87$		0			0
$88$	−2.21709	−	1.75627i	−0.236343	−	0.187220i
$89$			9.80721i			1.03956i	0.854299	+	0.519781i	$0.173986\pi$
$89$			9.80721i			1.03956i	−0.854299	+	0.519781i	$0.826014\pi$
$90$		0			0
$91$	−16.4991			−1.72957
$92$	5.27762	+	2.52745i	0.550230	+	0.263505i
$93$		0			0
$94$	0.0897961	−	0.395403i	0.00926176	−	0.0407827i
$95$	11.1153			1.14040
$96$		0			0
$97$	4.90282			0.497806			0.248903	−	0.968528i	$-0.419930\pi$
$97$	4.90282			0.497806			0.248903	+	0.968528i	$0.419930\pi$
$98$	0.685601	−	3.01894i	0.0692562	−	0.304959i
$99$		0			0
$100$	2.54957	+	1.22099i	0.254957	+	0.122099i
$101$	−8.89361			−0.884947			−0.442474	−	0.896782i	$-0.645899\pi$
$101$	−8.89361			−0.884947			−0.442474	+	0.896782i	$0.645899\pi$
$102$		0			0
$103$			18.9666i			1.86883i	0.356181	+	0.934417i	$0.384079\pi$
$103$			18.9666i			1.86883i	−0.356181	+	0.934417i	$0.615921\pi$
$104$	12.0672	+	9.55909i	1.18329	+	0.937346i
$105$		0			0
$106$	3.42156	−	15.0663i	0.332331	−	1.46337i
$107$			3.57243i			0.345360i	0.984978	+	0.172680i	$0.0552427\pi$
$107$			3.57243i			0.345360i	−0.984978	+	0.172680i	$0.944757\pi$
$108$		0			0
$109$		−	7.99636i		−	0.765912i	−0.923767	−	0.382956i	$-0.874906\pi$
$109$		−	7.99636i		−	0.765912i	0.923767	−	0.382956i	$-0.125094\pi$
$110$	−2.61177	−	0.593133i	−0.249022	−	0.0565530i
$111$		0			0
$112$	−9.44705	+	7.60121i	−0.892662	+	0.718247i
$113$		−	16.1728i		−	1.52141i	−0.649100	−	0.760703i	$-0.724854\pi$
$113$		−	16.1728i		−	1.52141i	0.649100	−	0.760703i	$-0.275146\pi$
$114$		0			0
$115$	5.54096			0.516697
$116$	−1.08345	−	0.518865i	−0.100596	−	0.0481754i
$117$		0			0
$118$	−8.41589	−	1.91125i	−0.774746	−	0.175945i
$119$	19.4143			1.77971
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	19.5568	+	4.44134i	1.77059	+	0.402100i
$123$		0			0
$124$	−9.35964	+	19.5441i	−0.840520	+	1.75511i
$125$	12.1459			1.08636
$126$		0			0
$127$			12.9725i			1.15113i	0.817757	+	0.575563i	$0.195217\pi$
$127$			12.9725i			1.15113i	−0.817757	+	0.575563i	$0.804783\pi$
$128$	11.3134	−	0.0860886i	0.999971	−	0.00760922i
$129$		0			0
$130$	14.2154	+	3.22832i	1.24677	+	0.283142i
$131$		−	2.79197i		−	0.243936i	−0.992534	−	0.121968i	$-0.961080\pi$
$131$		−	2.79197i		−	0.243936i	0.992534	−	0.121968i	$-0.0389205\pi$
$132$		0			0
$133$		−	17.7917i		−	1.54273i
$134$	3.84671	−	16.9384i	0.332305	−	1.46325i
$135$		0			0
$136$	−14.1994	−	11.2481i	−1.21759	−	0.964515i
$137$			1.92047i			0.164077i	0.996629	+	0.0820386i	$0.0261431\pi$
$137$			1.92047i			0.164077i	−0.996629	+	0.0820386i	$0.973857\pi$
$138$		0			0
$139$	−5.27856			−0.447722			−0.223861	−	0.974621i	$-0.571866\pi$
$139$	−5.27856			−0.447722			−0.223861	+	0.974621i	$0.571866\pi$
$140$	−4.95921	+	10.3554i	−0.419130	+	0.875195i
$141$		0			0
$142$	3.05293	−	13.4431i	0.256196	−	1.12812i
$143$	5.44282			0.455152
$144$		0			0
$145$	−1.13751			−0.0944654
$146$	−2.27371	+	10.0119i	−0.188173	+	0.828592i
$147$		0			0
$148$	1.69520	−	3.53978i	0.139344	−	0.290968i
$149$	−6.86168			−0.562131			−0.281065	−	0.959689i	$-0.590688\pi$
$149$	−6.86168			−0.562131			−0.281065	+	0.959689i	$0.590688\pi$
$150$		0			0
$151$		−	3.42172i		−	0.278456i	−0.990260	−	0.139228i	$-0.955538\pi$
$151$		−	3.42172i		−	0.278456i	0.990260	−	0.139228i	$-0.0444621\pi$
$152$	−10.3080	+	13.0126i	−0.836087	+	1.05546i
$153$		0			0
$154$	−0.949397	+	4.18052i	−0.0765046	+	0.336876i
$155$			20.5193i			1.64815i
$156$		0			0
$157$			11.0872i			0.884852i	0.896805	+	0.442426i	$0.145882\pi$
$157$			11.0872i			0.884852i	−0.896805	+	0.442426i	$0.854118\pi$
$158$	−4.81076	−	1.09252i	−0.382723	−	0.0869165i
$159$		0			0
$160$	9.62676	−	4.70063i	0.761062	−	0.371617i
$161$		−	8.86912i		−	0.698985i
$162$		0			0
$163$	4.41416			0.345744			0.172872	−	0.984944i	$-0.444695\pi$
$163$	4.41416			0.345744			0.172872	+	0.984944i	$0.444695\pi$
$164$	−7.75937	+	16.2025i	−0.605905	+	1.26520i
$165$		0			0
$166$	−12.6591	−	2.87488i	−0.982536	−	0.223134i
$167$	−10.3233			−0.798839			−0.399419	−	0.916768i	$-0.630788\pi$
$167$	−10.3233			−0.798839			−0.399419	+	0.916768i	$0.630788\pi$
$168$		0			0
$169$	−16.6243			−1.27879
$170$	−16.7271	−	3.79873i	−1.28291	−	0.291349i
$171$		0			0
$172$	−5.05308	−	2.41992i	−0.385294	−	0.184517i
$173$	−11.3286			−0.861301			−0.430650	−	0.902519i	$-0.641716\pi$
$173$	−11.3286			−0.861301			−0.430650	+	0.902519i	$0.641716\pi$
$174$		0			0
$175$		−	4.28459i		−	0.323885i
$176$	3.11645	−	2.50753i	0.234911	−	0.189012i
$177$		0			0
$178$	−13.5251	−	3.07155i	−1.01375	−	0.230222i
$179$			5.71663i			0.427281i	0.976912	+	0.213640i	$0.0685321\pi$
$179$			5.71663i			0.427281i	−0.976912	+	0.213640i	$0.931468\pi$
$180$		0			0
$181$			5.36910i			0.399082i	0.979889	+	0.199541i	$0.0639451\pi$
$181$			5.36910i			0.399082i	−0.979889	+	0.199541i	$0.936055\pi$
$182$	5.16740	−	22.7538i	0.383033	−	1.68663i
$183$		0			0
$184$	−5.13851	+	6.48677i	−0.378816	+	0.478211i
$185$		−	3.71640i		−	0.273235i
$186$		0			0
$187$	−6.40451			−0.468344
$188$	0.517176	+	0.247675i	0.0377189	+	0.0180636i
$189$		0			0
$190$	−3.48123	+	15.3291i	−0.252555	+	1.11209i
$191$	−9.76090			−0.706274			−0.353137	−	0.935572i	$-0.614885\pi$
$191$	−9.76090			−0.706274			−0.353137	+	0.935572i	$0.614885\pi$
$192$		0			0
$193$	−13.7187			−0.987492			−0.493746	−	0.869606i	$-0.664373\pi$
$193$	−13.7187			−0.987492			−0.493746	+	0.869606i	$0.664373\pi$
$194$	−1.53553	+	6.76146i	−0.110245	+	0.485445i
$195$		0			0
$196$	3.94869	+	1.89102i	0.282049	+	0.135073i
$197$	16.5373			1.17823			0.589116	−	0.808048i	$-0.299476\pi$
$197$	16.5373			1.17823			0.589116	+	0.808048i	$0.299476\pi$
$198$		0			0
$199$			16.6620i			1.18114i	0.806986	+	0.590570i	$0.201097\pi$
$199$			16.6620i			1.18114i	−0.806986	+	0.590570i	$0.798903\pi$
$200$	−2.48237	+	3.13370i	−0.175530	+	0.221586i
$201$		0			0
$202$	2.78542	−	12.2652i	0.195981	−	0.862973i
$203$			1.82076i			0.127792i
$204$		0			0
$205$			17.0110i			1.18810i
$206$	−26.1568	−	5.94021i	−1.82243	−	0.413874i
$207$		0			0
$208$	−16.9623	+	13.6481i	−1.17612	+	0.946323i
$209$			5.86923i			0.405983i
$210$		0			0
$211$	−13.5380			−0.931997			−0.465998	−	0.884786i	$-0.654305\pi$
$211$	−13.5380			−0.931997			−0.465998	+	0.884786i	$0.654305\pi$
$212$	19.7063	+	9.43733i	1.35343	+	0.648159i
$213$		0			0
$214$	−4.92674	−	1.11886i	−0.336785	−	0.0764838i
$215$	−5.30521			−0.361812
$216$		0			0
$217$	32.8441			2.22960
$218$	11.0278	+	2.50441i	0.746894	+	0.169620i
$219$		0			0
$220$	1.63598	−	3.41612i	0.110298	−	0.230315i
$221$	34.8586			2.34484
$222$		0			0
$223$		−	7.44081i		−	0.498274i	−0.968468	−	0.249137i	$-0.919853\pi$
$223$		−	7.44081i		−	0.498274i	0.968468	−	0.249137i	$-0.0801469\pi$
$224$	−7.52405	−	15.4090i	−0.502722	−	1.02956i
$225$		0			0
$226$	22.3038	+	5.06520i	1.48363	+	0.336932i
$227$			17.8423i			1.18424i	0.805851	+	0.592118i	$0.201708\pi$
$227$			17.8423i			1.18424i	−0.805851	+	0.592118i	$0.798292\pi$
$228$		0			0
$229$		−	1.69896i		−	0.112271i	−0.998423	−	0.0561353i	$-0.982122\pi$
$229$		−	1.69896i		−	0.112271i	0.998423	−	0.0561353i	$-0.0178778\pi$
$230$	−1.73539	+	7.64152i	−0.114428	+	0.503867i
$231$		0			0
$232$	1.05489	−	1.33168i	0.0692572	−	0.0874292i
$233$		−	20.6370i		−	1.35197i	−0.736914	−	0.675986i	$-0.763718\pi$
$233$		−	20.6370i		−	1.35197i	0.736914	−	0.675986i	$-0.236282\pi$
$234$		0			0
$235$	0.542981			0.0354202
$236$	5.27160	−	11.0077i	0.343152	−	0.716543i
$237$		0			0
$238$	−6.08043	+	26.7742i	−0.394135	+	1.73551i
$239$	−11.1366			−0.720369			−0.360185	−	0.932881i	$-0.617286\pi$
$239$	−11.1366			−0.720369			−0.360185	+	0.932881i	$0.617286\pi$
$240$		0			0
$241$	21.8983			1.41059			0.705297	−	0.708912i	$-0.250814\pi$
$241$	21.8983			1.41059			0.705297	+	0.708912i	$0.250814\pi$
$242$	0.313193	−	1.37910i	0.0201328	−	0.0886517i
$243$		0			0
$244$	−12.2501	+	25.5797i	−0.784231	+	1.63757i
$245$	4.14571			0.264860
$246$		0			0
$247$		−	31.9452i		−	2.03262i
$248$	−24.0218	−	19.0289i	−1.52539	−	1.20834i
$249$		0			0
$250$	−3.80402	+	16.7504i	−0.240587	+	1.05939i
$251$			4.82931i			0.304823i	0.988317	+	0.152412i	$0.0487040\pi$
$251$			4.82931i			0.304823i	−0.988317	+	0.152412i	$0.951296\pi$
$252$		0			0
$253$			2.92580i			0.183944i
$254$	−17.8904	−	4.06291i	−1.12254	−	0.254930i
$255$		0			0
$256$	−3.42455	+	15.6292i	−0.214034	+	0.976826i
$257$		−	4.67491i		−	0.291613i	−0.989313	−	0.145806i	$-0.953422\pi$
$257$		−	4.67491i		−	0.291613i	0.989313	−	0.145806i	$-0.0465776\pi$
$258$		0			0
$259$	−5.94865			−0.369631
$260$	−8.90433	+	18.5933i	−0.552223	+	1.15311i
$261$		0			0
$262$	3.85040	+	0.874426i	0.237879	+	0.0540222i
$263$	6.52091			0.402096			0.201048	−	0.979581i	$-0.435565\pi$
$263$	6.52091			0.402096			0.201048	+	0.979581i	$0.435565\pi$
$264$		0			0
$265$	20.6896			1.27095
$266$	24.5364	+	5.57223i	1.50443	+	0.341655i
$267$		0			0
$268$	22.1549	+	10.6100i	1.35333	+	0.648107i
$269$	−4.26314			−0.259928			−0.129964	−	0.991519i	$-0.541486\pi$
$269$	−4.26314			−0.259928			−0.129964	+	0.991519i	$0.541486\pi$
$270$		0			0
$271$		−	2.03841i		−	0.123824i	−0.998082	−	0.0619122i	$-0.980280\pi$
$271$		−	2.03841i		−	0.123824i	0.998082	−	0.0619122i	$-0.0197199\pi$
$272$	19.9594	−	16.0595i	1.21021	−	0.973752i
$273$		0			0
$274$	−2.64852	−	0.601479i	−0.160003	−	0.0363367i
$275$			1.41343i			0.0852329i
$276$		0			0
$277$		−	13.8227i		−	0.830526i	−0.909701	−	0.415263i	$-0.863690\pi$
$277$		−	13.8227i		−	0.830526i	0.909701	−	0.415263i	$-0.136310\pi$
$278$	1.65321	−	7.27966i	0.0991530	−	0.436605i
$279$		0			0
$280$	−12.7280	−	10.0825i	−0.760642	−	0.602544i
$281$			15.3473i			0.915543i	0.889070	+	0.457772i	$0.151352\pi$
$281$			15.3473i			0.915543i	−0.889070	+	0.457772i	$0.848648\pi$
$282$		0			0
$283$	−6.72089			−0.399516			−0.199758	−	0.979845i	$-0.564016\pi$
$283$	−6.72089			−0.399516			−0.199758	+	0.979845i	$0.564016\pi$
$284$	17.5832	+	8.42058i	1.04337	+	0.499670i
$285$		0			0
$286$	−1.70465	+	7.50618i	−0.100798	+	0.443850i
$287$	27.2286			1.60725
$288$		0			0
$289$	−24.0178			−1.41281
$290$	0.356261	−	1.56874i	0.0209204	−	0.0921197i
$291$		0			0
$292$	−13.0953	−	6.27133i	−0.766344	−	0.367002i
$293$	−28.4865			−1.66420			−0.832098	−	0.554628i	$-0.812861\pi$
$293$	−28.4865			−1.66420			−0.832098	+	0.554628i	$0.812861\pi$
$294$		0			0
$295$		−	11.5570i		−	0.672874i
$296$	4.35078	+	3.44648i	0.252884	+	0.200322i
$297$		0			0
$298$	2.14903	−	9.46293i	0.124490	−	0.548173i
$299$		−	15.9246i		−	0.920944i
$300$		0			0
$301$			8.49178i			0.489458i
$302$	4.71889	+	1.07166i	0.271542	+	0.0616671i
$303$		0			0
$304$	−14.7173	−	18.2912i	−0.844094	−	1.04907i
$305$			26.8560i			1.53777i
$306$		0			0
$307$	12.0385			0.687071			0.343536	−	0.939140i	$-0.388375\pi$
$307$	12.0385			0.687071			0.343536	+	0.939140i	$0.388375\pi$
$308$	−5.46801	−	2.61862i	−0.311569	−	0.149210i
$309$		0			0
$310$	−28.2981	−	6.42649i	−1.60722	−	0.365000i
$311$	−18.0967			−1.02617			−0.513084	−	0.858338i	$-0.671497\pi$
$311$	−18.0967			−1.02617			−0.513084	+	0.858338i	$0.671497\pi$
$312$		0			0
$313$	29.1782			1.64925			0.824625	−	0.565680i	$-0.191386\pi$
$313$	29.1782			1.64925			0.824625	+	0.565680i	$0.191386\pi$
$314$	−15.2903	−	3.47242i	−0.862880	−	0.195960i
$315$		0			0
$316$	3.01339	−	6.29233i	0.169517	−	0.353971i
$317$	−5.26052			−0.295460			−0.147730	−	0.989028i	$-0.547197\pi$
$317$	−5.26052			−0.295460			−0.147730	+	0.989028i	$0.547197\pi$
$318$		0			0
$319$		−	0.600643i		−	0.0336296i
$320$	3.46759	+	14.7484i	0.193844	+	0.824463i
$321$		0			0
$322$	12.2314	+	2.77775i	0.681628	+	0.154798i
$323$			37.5895i			2.09154i
$324$		0			0
$325$		−	7.69303i		−	0.426733i
$326$	−1.38249	+	6.08756i	−0.0765688	+	0.337159i
$327$		0			0
$328$	−19.9147	−	15.7754i	−1.09960	−	0.871053i
$329$		−	0.869122i		−	0.0479162i
$330$		0			0
$331$	24.3562			1.33874			0.669369	−	0.742930i	$-0.266565\pi$
$331$	24.3562			1.33874			0.669369	+	0.742930i	$0.266565\pi$
$332$	7.92948	−	16.5577i	0.435187	−	0.908724i
$333$		0			0
$334$	3.23318	−	14.2368i	0.176912	−	0.779003i
$335$	23.2604			1.27085
$336$		0			0
$337$	−11.1496			−0.607359			−0.303680	−	0.952774i	$-0.598215\pi$
$337$	−11.1496			−0.607359			−0.303680	+	0.952774i	$0.598215\pi$
$338$	5.20662	−	22.9265i	0.283203	−	1.24704i
$339$		0			0
$340$	10.4776	−	21.8786i	0.568229	−	1.18653i
$341$	−10.8348			−0.586739
$342$		0			0
$343$			14.5836i			0.787441i
$344$	4.91989	−	6.21079i	0.265263	−	0.334863i
$345$		0			0
$346$	3.54805	−	15.6233i	0.190745	−	0.839914i
$347$		−	7.87537i		−	0.422772i	−0.977403	−	0.211386i	$-0.932202\pi$
$347$		−	7.87537i		−	0.422772i	0.977403	−	0.211386i	$-0.0677977\pi$
$348$		0			0
$349$		−	5.06335i		−	0.271035i	−0.990775	−	0.135517i	$-0.956730\pi$
$349$		−	5.06335i		−	0.271035i	0.990775	−	0.135517i	$-0.0432696\pi$
$350$	5.90887	+	1.34190i	0.315842	+	0.0717278i
$351$		0			0
$352$	2.48208	+	5.08323i	0.132295	+	0.270937i
$353$			24.4608i			1.30192i	0.759114	+	0.650958i	$0.225633\pi$
$353$			24.4608i			1.30192i	−0.759114	+	0.650958i	$0.774367\pi$
$354$		0			0
$355$	18.4605			0.979784
$356$	8.47194	−	17.6904i	0.449012	−	0.937592i
$357$		0			0
$358$	−7.88379	−	1.79041i	−0.416671	−	0.0946261i
$359$	−5.36867			−0.283348			−0.141674	−	0.989913i	$-0.545248\pi$
$359$	−5.36867			−0.283348			−0.141674	+	0.989913i	$0.545248\pi$
$360$		0			0
$361$	15.4478			0.813044
$362$	−7.40451	−	1.68156i	−0.389172	−	0.0883811i
$363$		0			0
$364$	29.7614	+	14.2527i	1.55992	+	0.747044i
$365$	−13.7487			−0.719640
$366$		0			0
$367$		−	28.9008i		−	1.50861i	−0.656525	−	0.754304i	$-0.727974\pi$
$367$		−	28.9008i		−	1.50861i	0.656525	−	0.754304i	$-0.272026\pi$
$368$	−7.33655	−	9.11812i	−0.382444	−	0.475315i
$369$		0			0
$370$	5.12528	+	1.16395i	0.266451	+	0.0605110i
$371$		−	33.1167i		−	1.71934i
$372$		0			0
$373$		−	32.3825i		−	1.67670i	−0.545130	−	0.838352i	$-0.683520\pi$
$373$		−	32.3825i		−	1.67670i	0.545130	−	0.838352i	$-0.316480\pi$
$374$	2.00585	−	8.83245i	0.103720	−	0.456715i
$375$		0			0
$376$	−0.503544	+	0.635666i	−0.0259683	+	0.0327820i
$377$			3.26920i			0.168372i
$378$		0			0
$379$	−16.7643			−0.861123			−0.430562	−	0.902561i	$-0.641685\pi$
$379$	−16.7643			−0.861123			−0.430562	+	0.902561i	$0.641685\pi$
$380$	−20.0500	−	9.60192i	−1.02854	−	0.492568i
$381$		0			0
$382$	3.05705	−	13.4612i	0.156412	−	0.688737i
$383$	11.2458			0.574634			0.287317	−	0.957836i	$-0.407237\pi$
$383$	11.2458			0.574634			0.287317	+	0.957836i	$0.407237\pi$
$384$		0			0
$385$	−5.74084			−0.292580
$386$	4.29660	−	18.9194i	0.218691	−	0.962972i
$387$		0			0
$388$	−8.84380	−	4.23529i	−0.448976	−	0.215014i
$389$	15.3472			0.778136			0.389068	−	0.921209i	$-0.372797\pi$
$389$	15.3472			0.778136			0.389068	+	0.921209i	$0.372797\pi$
$390$		0			0
$391$			18.7383i			0.947638i
$392$	−3.84461	+	4.85337i	−0.194182	+	0.245132i
$393$		0			0
$394$	−5.17937	+	22.8065i	−0.260933	+	1.14898i
$395$		−	6.60630i		−	0.332399i
$396$		0			0
$397$			13.8736i			0.696297i	0.937439	+	0.348148i	$0.113189\pi$
$397$			13.8736i			0.696297i	−0.937439	+	0.348148i	$0.886811\pi$
$398$	−22.9786	−	5.21843i	−1.15181	−	0.261576i
$399$		0			0
$400$	−3.54422	−	4.40488i	−0.177211	−	0.220244i
$401$		−	8.36307i		−	0.417632i	−0.977955	−	0.208816i	$-0.933039\pi$
$401$		−	8.36307i		−	0.417632i	0.977955	−	0.208816i	$-0.0669609\pi$
$402$		0			0
$403$	58.9720			2.93761
$404$	16.0425	+	7.68273i	0.798143	+	0.382230i
$405$		0			0
$406$	−2.51100	−	0.570249i	−0.124619	−	0.0283010i
$407$	1.96238			0.0972715
$408$		0			0
$409$	20.6740			1.02226			0.511132	−	0.859502i	$-0.329226\pi$
$409$	20.6740			1.02226			0.511132	+	0.859502i	$0.329226\pi$
$410$	−23.4598	−	5.32772i	−1.15860	−	0.263117i
$411$		0			0
$412$	16.3843	−	34.2123i	0.807194	−	1.68552i
$413$	−18.4987			−0.910261
$414$		0			0
$415$		−	17.3839i		−	0.853343i
$416$	−13.5095	−	27.6671i	−0.662359	−	1.35649i
$417$		0			0
$418$	−8.09424	−	1.83820i	−0.395902	−	0.0899094i
$419$		−	4.14867i		−	0.202676i	−0.994852	−	0.101338i	$-0.967688\pi$
$419$		−	4.14867i		−	0.202676i	0.994852	−	0.101338i	$-0.0323123\pi$
$420$		0			0
$421$			17.8077i			0.867896i	0.900938	+	0.433948i	$0.142880\pi$
$421$			17.8077i			0.867896i	−0.900938	+	0.433948i	$0.857120\pi$
$422$	4.24002	−	18.6703i	0.206401	−	0.908855i
$423$		0			0
$424$	−19.1869	+	24.2212i	−0.931797	+	1.17629i
$425$			9.05231i			0.439102i
$426$		0			0
$427$	42.9870			2.08029
$428$	3.08604	−	6.44403i	0.149169	−	0.311484i
$429$		0			0
$430$	1.66156	−	7.31641i	0.0801274	−	0.352828i
$431$	−29.5960			−1.42559			−0.712796	−	0.701372i	$-0.752571\pi$
$431$	−29.5960			−1.42559			−0.712796	+	0.701372i	$0.752571\pi$
$432$		0			0
$433$	−13.0944			−0.629278			−0.314639	−	0.949211i	$-0.601883\pi$
$433$	−13.0944			−0.629278			−0.314639	+	0.949211i	$0.601883\pi$
$434$	−10.2866	+	45.2952i	−0.493770	+	2.17424i
$435$		0			0
$436$	−6.90764	+	14.4240i	−0.330816	+	0.690784i
$437$	17.1722			0.821457
$438$		0			0
$439$		−	2.26583i		−	0.108142i	−0.998537	−	0.0540710i	$-0.982780\pi$
$439$		−	2.26583i		−	0.108142i	0.998537	−	0.0540710i	$-0.0172197\pi$
$440$	4.19879	+	3.32608i	0.200169	+	0.158564i
$441$		0			0
$442$	−10.9175	+	48.0734i	−0.519292	+	2.28662i
$443$		−	0.704612i		−	0.0334771i	−0.999860	−	0.0167386i	$-0.994672\pi$
$443$		−	0.704612i		−	0.0334771i	0.999860	−	0.0167386i	$-0.00532830\pi$
$444$		0			0
$445$		−	18.5731i		−	0.880451i
$446$	10.2616	+	2.33041i	0.485901	+	0.110348i
$447$		0			0
$448$	23.6071	−	5.55039i	1.11533	−	0.262232i
$449$		−	28.1301i		−	1.32754i	−0.747935	−	0.663771i	$-0.768955\pi$
$449$		−	28.1301i		−	1.32754i	0.747935	−	0.663771i	$-0.231045\pi$
$450$		0			0
$451$	−8.98233			−0.422961
$452$	−13.9708	+	29.1728i	−0.657132	+	1.37217i
$453$		0			0
$454$	−24.6063	−	5.58809i	−1.15483	−	0.262262i
$455$	31.2464			1.46485
$456$		0			0
$457$	−1.92294			−0.0899512			−0.0449756	−	0.998988i	$-0.514321\pi$
$457$	−1.92294			−0.0899512			−0.0449756	+	0.998988i	$0.514321\pi$
$458$	2.34304	+	0.532104i	0.109483	+	0.0248636i
$459$		0			0
$460$	−9.99489	−	4.78654i	−0.466014	−	0.223174i
$461$	−21.1590			−0.985474			−0.492737	−	0.870178i	$-0.664003\pi$
$461$	−21.1590			−0.985474			−0.492737	+	0.870178i	$0.664003\pi$
$462$		0			0
$463$		−	9.13809i		−	0.424683i	−0.977195	−	0.212342i	$-0.931891\pi$
$463$		−	9.13809i		−	0.424683i	0.977195	−	0.212342i	$-0.0681090\pi$
$464$	1.50613	+	1.87188i	0.0699205	+	0.0868997i
$465$		0			0
$466$	28.4604	+	6.46335i	1.31840	+	0.299409i
$467$			28.4368i			1.31590i	0.753063	+	0.657949i	$0.228576\pi$
$467$			28.4368i			1.31590i	−0.753063	+	0.657949i	$0.771424\pi$
$468$		0			0
$469$		−	37.2317i		−	1.71920i
$470$	−0.170058	+	0.748824i	−0.00784419	+	0.0345407i
$471$		0			0
$472$	13.5297	+	10.7176i	0.622756	+	0.493318i
$473$		−	2.80132i		−	0.128805i
$474$		0			0
$475$	8.29573			0.380634
$476$	−35.0199	−	16.7710i	−1.60513	−	0.768698i
$477$		0			0
$478$	3.48792	−	15.3585i	0.159534	−	0.702482i
$479$	30.6250			1.39929			0.699646	−	0.714490i	$-0.253341\pi$
$479$	30.6250			1.39929			0.699646	+	0.714490i	$0.253341\pi$
$480$		0			0
$481$	−10.6809			−0.487006
$482$	−6.85840	+	30.1999i	−0.312392	+	1.37557i
$483$		0			0
$484$	1.80382	+	0.863848i	0.0819918	+	0.0392658i
$485$	−9.28508			−0.421614
$486$		0			0
$487$		−	12.3155i		−	0.558067i	−0.960281	−	0.279033i	$-0.909986\pi$
$487$		−	12.3155i		−	0.558067i	0.960281	−	0.279033i	$-0.0900140\pi$
$488$	−31.4402	−	24.9054i	−1.42323	−	1.12742i
$489$		0			0
$490$	−1.29841	+	5.71734i	−0.0586561	+	0.258283i
$491$		−	34.9081i		−	1.57538i	−0.616072	−	0.787690i	$-0.711277\pi$
$491$		−	34.9081i		−	1.57538i	0.616072	−	0.787690i	$-0.288723\pi$
$492$		0			0
$493$		−	3.84683i		−	0.173252i
$494$	44.0555	+	10.0050i	1.98215	+	0.450147i
$495$		0			0
$496$	33.7662	−	27.1687i	1.51615	−	1.21991i
$497$		−	29.5488i		−	1.32545i
$498$		0			0
$499$	−3.73964			−0.167409			−0.0837047	−	0.996491i	$-0.526675\pi$
$499$	−3.73964			−0.167409			−0.0837047	+	0.996491i	$0.526675\pi$
$500$	−21.9090	−	10.4922i	−0.979802	−	0.469226i
$501$		0			0
$502$	−6.66009	−	1.51251i	−0.297254	−	0.0675065i
$503$	8.50418			0.379182			0.189591	−	0.981863i	$-0.439284\pi$
$503$	8.50418			0.379182			0.189591	+	0.981863i	$0.439284\pi$
$504$		0			0
$505$	16.8429			0.749501
$506$	−4.03497	−	0.916341i	−0.179376	−	0.0407363i
$507$		0			0
$508$	11.2063	−	23.4001i	0.497199	−	1.03821i
$509$	13.2510			0.587342			0.293671	−	0.955907i	$-0.405123\pi$
$509$	13.2510			0.587342			0.293671	+	0.955907i	$0.405123\pi$
$510$		0			0
$511$			22.0068i			0.973526i
$512$	−20.4817	−	9.61775i	−0.905171	−	0.425049i
$513$		0			0
$514$	6.44715	+	1.46415i	0.284372	+	0.0645808i
$515$		−	35.9194i		−	1.58280i
$516$		0			0
$517$			0.286711i			0.0126096i
$518$	1.86308	−	8.20377i	0.0818589	−	0.360453i
$519$		0			0
$520$	−22.8532	−	18.1032i	−1.00218	−	0.793880i
$521$			37.2904i			1.63372i	0.576836	+	0.816860i	$0.304287\pi$
$521$			37.2904i			1.63372i	−0.576836	+	0.816860i	$0.695713\pi$
$522$		0			0
$523$	−20.1065			−0.879196			−0.439598	−	0.898195i	$-0.644879\pi$
$523$	−20.1065			−0.879196			−0.439598	+	0.898195i	$0.644879\pi$
$524$	−2.41184	+	5.03621i	−0.105362	+	0.220008i
$525$		0			0
$526$	−2.04230	+	8.99297i	−0.0890487	+	0.392112i
$527$	−69.3917			−3.02275
$528$		0			0
$529$	−14.4397			−0.627812
$530$	−6.47984	+	28.5330i	−0.281466	+	1.23939i
$531$		0			0
$532$	−15.3693	+	32.0930i	−0.666343	+	1.39141i
$533$	48.8892			2.11763
$534$		0			0
$535$		−	6.76557i		−	0.292501i
$536$	−21.5710	+	27.2308i	−0.931723	+	1.17619i
$537$		0			0
$538$	1.33519	−	5.87928i	0.0575639	−	0.253474i
$539$			2.18907i			0.0942899i
$540$		0			0
$541$		−	2.44647i		−	0.105182i	−0.998616	−	0.0525911i	$-0.983252\pi$
$541$		−	2.44647i		−	0.105182i	0.998616	−	0.0525911i	$-0.0167480\pi$
$542$	2.81116	+	0.638415i	0.120750	+	0.0274223i
$543$		0			0
$544$	15.8965	+	32.5556i	0.681558	+	1.39581i
$545$			15.1437i			0.648685i
$546$		0			0
$547$	−43.2279			−1.84829			−0.924147	−	0.382038i	$-0.875223\pi$
$547$	−43.2279			−1.84829			−0.924147	+	0.382038i	$0.875223\pi$
$548$	1.65900	−	3.46419i	0.0708689	−	0.147983i
$549$		0			0
$550$	−1.94925	−	0.442676i	−0.0831165	−	0.0188758i
$551$	−3.52531			−0.150183
$552$		0			0
$553$	−10.5744			−0.449668
$554$	19.0629	+	4.32918i	0.809903	+	0.183929i
$555$		0			0
$556$	9.52158	+	4.55988i	0.403805	+	0.193382i
$557$	42.3302			1.79359			0.896795	−	0.442447i	$-0.145890\pi$
$557$	42.3302			1.79359			0.896795	+	0.442447i	$0.145890\pi$
$558$		0			0
$559$			15.2471i			0.644883i
$560$	17.8911	−	14.3954i	0.756035	−	0.608315i
$561$		0			0
$562$	−21.1654	−	4.80667i	−0.892810	−	0.202757i
$563$		−	46.1269i		−	1.94402i	−0.234942	−	0.972009i	$-0.575490\pi$
$563$		−	46.1269i		−	1.94402i	0.234942	−	0.972009i	$-0.424510\pi$
$564$		0			0
$565$			30.6284i			1.28855i
$566$	2.10494	−	9.26877i	0.0884772	−	0.389595i
$567$		0			0
$568$	−17.1197	+	21.6117i	−0.718328	+	0.906806i
$569$			28.6718i			1.20198i	0.799255	+	0.600992i	$0.205228\pi$
$569$			28.6718i			1.20198i	−0.799255	+	0.600992i	$0.794772\pi$
$570$		0			0
$571$	8.59888			0.359852			0.179926	−	0.983680i	$-0.442414\pi$
$571$	8.59888			0.359852			0.179926	+	0.983680i	$0.442414\pi$
$572$	−9.81787	−	4.70177i	−0.410506	−	0.196591i
$573$		0			0
$574$	−8.52780	+	37.5509i	−0.355944	+	1.56734i
$575$	4.13541			0.172458
$576$		0			0
$577$	0.581402			0.0242041			0.0121020	−	0.999927i	$-0.496148\pi$
$577$	0.581402			0.0242041			0.0121020	+	0.999927i	$0.496148\pi$
$578$	7.52220	−	33.1228i	0.312882	−	1.37773i
$579$		0			0
$580$	2.05187	+	0.982639i	0.0851993	+	0.0408019i
$581$	−27.8255			−1.15440
$582$		0			0
$583$			10.9248i			0.452457i
$584$	12.7501	−	16.0956i	0.527604	−	0.666039i
$585$		0			0
$586$	8.92177	−	39.2856i	0.368555	−	1.62287i
$587$			44.5638i			1.83934i	0.392686	+	0.919672i	$0.371546\pi$
$587$			44.5638i			1.83934i	−0.392686	+	0.919672i	$0.628454\pi$
$588$		0			0
$589$			63.5920i			2.62026i
$590$	15.9382	+	3.61957i	0.656166	+	0.149015i
$591$		0			0
$592$	−6.11566	+	4.92073i	−0.251352	+	0.202241i
$593$			28.3669i			1.16489i	0.812870	+	0.582445i	$0.197904\pi$
$593$			28.3669i			1.16489i	−0.812870	+	0.582445i	$0.802096\pi$
$594$		0			0
$595$	−36.7673			−1.50731
$596$	12.3772	+	5.92745i	0.506991	+	0.242798i
$597$		0			0
$598$	21.9616	+	4.98748i	0.898077	+	0.203953i
$599$	−20.6490			−0.843696			−0.421848	−	0.906667i	$-0.638618\pi$
$599$	−20.6490			−0.843696			−0.421848	+	0.906667i	$0.638618\pi$
$600$		0			0
$601$	−38.2236			−1.55917			−0.779587	−	0.626295i	$-0.784571\pi$
$601$	−38.2236			−1.55917			−0.779587	+	0.626295i	$0.784571\pi$
$602$	−11.7110	−	2.65957i	−0.477304	−	0.108396i
$603$		0			0
$604$	−2.95585	+	6.17217i	−0.120272	+	0.251142i
$605$	1.89382			0.0769949
$606$		0			0
$607$			40.4873i			1.64333i	0.569971	+	0.821665i	$0.306954\pi$
$607$			40.4873i			1.64333i	−0.569971	+	0.821665i	$0.693046\pi$
$608$	29.8347	−	14.5679i	1.20996	−	0.590807i
$609$		0			0
$610$	−37.0371	−	8.41112i	−1.49959	−	0.340556i
$611$		−	1.56052i		−	0.0631318i
$612$		0			0
$613$			3.43337i			0.138673i	0.997593	+	0.0693363i	$0.0220882\pi$
$613$			3.43337i			0.138673i	−0.997593	+	0.0693363i	$0.977912\pi$
$614$	−3.77037	+	16.6022i	−0.152160	+	0.670011i
$615$		0			0
$616$	5.32388	−	6.72078i	0.214505	−	0.270788i
$617$			26.0661i			1.04938i	0.851293	+	0.524690i	$0.175819\pi$
$617$			26.0661i			1.04938i	−0.851293	+	0.524690i	$0.824181\pi$
$618$		0			0
$619$	37.0540			1.48933			0.744664	−	0.667440i	$-0.232610\pi$
$619$	37.0540			1.48933			0.744664	+	0.667440i	$0.232610\pi$
$620$	17.7255	−	37.0130i	0.711874	−	1.48648i
$621$		0			0
$622$	5.66775	−	24.9571i	0.227256	−	1.00069i
$623$	−29.7291			−1.19107
$624$		0			0
$625$	−15.9351			−0.637403
$626$	−9.13842	+	40.2396i	−0.365245	+	1.60830i
$627$		0			0
$628$	9.57762	−	19.9992i	0.382189	−	0.798057i
$629$	12.5681			0.501122
$630$		0			0
$631$		−	19.3001i		−	0.768325i	−0.923266	−	0.384162i	$-0.874490\pi$
$631$		−	19.3001i		−	0.768325i	0.923266	−	0.384162i	$-0.125510\pi$
$632$	7.73396	+	6.12648i	0.307641	+	0.243698i
$633$		0			0
$634$	1.64756	−	7.25477i	0.0654329	−	0.288124i
$635$		−	24.5677i		−	0.974940i
$636$		0			0
$637$		−	11.9147i		−	0.472078i
$638$	0.828346	+	0.188117i	0.0327945	+	0.00744764i
$639$		0			0
$640$	−21.4256	+	0.163037i	−0.846920	+	0.00644459i
$641$		−	26.9766i		−	1.06551i	−0.846269	−	0.532757i	$-0.821156\pi$
$641$		−	26.9766i		−	1.06551i	0.846269	−	0.532757i	$-0.178844\pi$
$642$		0			0
$643$	29.2484			1.15345			0.576723	−	0.816940i	$-0.304331\pi$
$643$	29.2484			1.15345			0.576723	+	0.816940i	$0.304331\pi$
$644$	−7.66157	+	15.9983i	−0.301908	+	0.630421i
$645$		0			0
$646$	−51.8396	−	11.7728i	−2.03960	−	0.463194i
$647$	−27.7125			−1.08949			−0.544746	−	0.838601i	$-0.683374\pi$
$647$	−27.7125			−1.08949			−0.544746	+	0.838601i	$0.683374\pi$
$648$		0			0
$649$	6.10246			0.239543
$650$	10.6094	+	2.40941i	0.416137	+	0.0945047i
$651$		0			0
$652$	−7.96235	−	3.81316i	−0.311830	−	0.149335i
$653$	−33.4035			−1.30718			−0.653590	−	0.756849i	$-0.726738\pi$
$653$	−33.4035			−1.30718			−0.653590	+	0.756849i	$0.726738\pi$
$654$		0			0
$655$			5.28750i			0.206600i
$656$	27.9930	−	22.5235i	1.09294	−	0.879395i
$657$		0			0
$658$	1.19860	+	0.272203i	0.0467264	+	0.0106116i
$659$			7.79075i			0.303485i	0.988420	+	0.151742i	$0.0484884\pi$
$659$			7.79075i			0.303485i	−0.988420	+	0.151742i	$0.951512\pi$
$660$		0			0
$661$		−	9.59043i		−	0.373024i	−0.982453	−	0.186512i	$-0.940282\pi$
$661$		−	9.59043i		−	0.373024i	0.982453	−	0.186512i	$-0.0597184\pi$
$662$	−7.62819	+	33.5896i	−0.296478	+	1.30550i
$663$		0			0
$664$	20.3513	+	16.1213i	0.789782	+	0.625628i
$665$			33.6943i			1.30661i
$666$		0			0
$667$	−1.75736			−0.0680454
$668$	18.6213	+	8.91774i	0.720481	+	0.345038i
$669$		0			0
$670$	−7.28499	+	32.0783i	−0.281444	+	1.23929i
$671$	−14.1808			−0.547445
$672$		0			0
$673$	−17.3398			−0.668399			−0.334199	−	0.942502i	$-0.608466\pi$
$673$	−17.3398			−0.668399			−0.334199	+	0.942502i	$0.608466\pi$
$674$	3.49199	−	15.3764i	0.134506	−	0.592278i
$675$		0			0
$676$	29.9873	+	14.3609i	1.15336	+	0.552341i
$677$	19.5740			0.752290			0.376145	−	0.926561i	$-0.377249\pi$
$677$	19.5740			0.752290			0.376145	+	0.926561i	$0.377249\pi$
$678$		0			0
$679$			14.8621i			0.570357i
$680$	26.8912	+	21.3019i	1.03123	+	0.816890i
$681$		0			0
$682$	3.39339	−	14.9423i	0.129940	−	0.572169i
$683$		−	29.6643i		−	1.13507i	−0.823348	−	0.567537i	$-0.807897\pi$
$683$		−	29.6643i		−	1.13507i	0.823348	−	0.567537i	$-0.192103\pi$
$684$		0			0
$685$		−	3.63704i		−	0.138964i
$686$	−20.1122	−	4.56749i	−0.767888	−	0.174387i
$687$		0			0
$688$	7.02441	+	8.73018i	0.267803	+	0.332835i
$689$		−	59.4615i		−	2.26530i
$690$		0			0
$691$	17.6568			0.671695			0.335848	−	0.941916i	$-0.390977\pi$
$691$	17.6568			0.671695			0.335848	+	0.941916i	$0.390977\pi$
$692$	20.4348	+	9.78623i	0.776816	+	0.372016i
$693$		0			0
$694$	10.8609	+	2.46651i	0.412274	+	0.0936276i
$695$	9.99668			0.379196
$696$		0			0
$697$	−57.5274			−2.17901
$698$	6.98285	+	1.58581i	0.264305	+	0.0600236i
$699$		0			0
$700$	−3.70123	+	7.72863i	−0.139893	+	0.292115i
$701$	23.0321			0.869909			0.434955	−	0.900452i	$-0.356764\pi$
$701$	23.0321			0.869909			0.434955	+	0.900452i	$0.356764\pi$
$702$		0			0
$703$		−	11.5177i		−	0.434396i
$704$	−7.78765	+	1.83100i	−0.293508	+	0.0690084i
$705$		0			0
$706$	−33.7338	−	7.66095i	−1.26959	−	0.288324i
$707$		−	26.9596i		−	1.01392i
$708$		0			0
$709$			34.3471i			1.28993i	0.764211	+	0.644966i	$0.223128\pi$
$709$			34.3471i			1.28993i	−0.764211	+	0.644966i	$0.776872\pi$
$710$	−5.78172	+	25.4589i	−0.216984	+	0.955455i
$711$		0			0
$712$	21.7435	+	17.2242i	0.814872	+	0.645502i
$713$			31.7005i			1.18719i
$714$		0			0
$715$	−10.3078			−0.385488
$716$	4.93830	−	10.3118i	0.184553	−	0.385369i
$717$		0			0
$718$	1.68143	−	7.40392i	0.0627504	−	0.276312i
$719$	26.4769			0.987422			0.493711	−	0.869626i	$-0.335640\pi$
$719$	26.4769			0.987422			0.493711	+	0.869626i	$0.335640\pi$
$720$		0			0
$721$	−57.4943			−2.14120
$722$	−4.83816	+	21.3041i	−0.180057	+	0.792855i
$723$		0			0
$724$	4.63808	−	9.68489i	0.172373	−	0.359936i
$725$	−0.848966			−0.0315298
$726$		0			0
$727$		−	40.9300i		−	1.51801i	−0.651085	−	0.759005i	$-0.725686\pi$
$727$		−	40.9300i		−	1.51801i	0.651085	−	0.759005i	$-0.274314\pi$
$728$	−28.9769	+	36.5800i	−1.07396	+	1.35575i
$729$		0			0
$730$	4.30600	−	18.9608i	0.159372	−	0.701771i
$731$		−	17.9411i		−	0.663575i
$732$		0			0
$733$		−	22.4662i		−	0.829808i	−0.909865	−	0.414904i	$-0.863815\pi$
$733$		−	22.4662i		−	0.829808i	0.909865	−	0.414904i	$-0.136185\pi$
$734$	39.8570	+	9.05153i	1.47115	+	0.334098i
$735$		0			0
$736$	14.8725	−	7.26208i	0.548209	−	0.267684i
$737$			12.2822i			0.452422i
$738$		0			0
$739$	−27.2642			−1.00293			−0.501465	−	0.865178i	$-0.667206\pi$
$739$	−27.2642			−1.00293			−0.501465	+	0.865178i	$0.667206\pi$
$740$	−3.21041	+	6.70372i	−0.118017	+	0.246434i
$741$		0			0
$742$	45.6712	+	10.3719i	1.67664	+	0.380766i
$743$	15.4473			0.566706			0.283353	−	0.959016i	$-0.408553\pi$
$743$	15.4473			0.566706			0.283353	+	0.959016i	$0.408553\pi$
$744$		0			0
$745$	12.9948			0.476093
$746$	44.6587	+	10.1420i	1.63507	+	0.371324i
$747$		0			0
$748$	11.5526	+	5.53252i	0.422404	+	0.202289i
$749$	−10.8293			−0.395694
$750$		0			0
$751$			44.7392i			1.63256i	0.577658	+	0.816279i	$0.303967\pi$
$751$			44.7392i			1.63256i	−0.577658	+	0.816279i	$0.696033\pi$
$752$	−0.718939	−	0.893522i	−0.0262170	−	0.0325834i
$753$		0			0
$754$	−4.50854	−	1.02389i	−0.164191	−	0.0372879i
$755$			6.48014i			0.235837i
$756$		0			0
$757$		−	22.6158i		−	0.821985i	−0.911639	−	0.410992i	$-0.865182\pi$
$757$		−	22.6158i		−	0.821985i	0.911639	−	0.410992i	$-0.134818\pi$
$758$	5.25046	−	23.1196i	0.190705	−	0.839741i
$759$		0			0
$760$	19.5215	−	24.6436i	0.708119	−	0.893918i
$761$			4.47443i			0.162198i	0.996706	+	0.0810990i	$0.0258430\pi$
$761$			4.47443i			0.162198i	−0.996706	+	0.0810990i	$0.974157\pi$
$762$		0			0
$763$	24.2397			0.877538
$764$	17.6069	+	8.43193i	0.636996	+	0.305057i
$765$		0			0
$766$	−3.52211	+	15.5091i	−0.127259	+	0.560365i
$767$	−33.2146			−1.19931
$768$		0			0
$769$	−37.5456			−1.35393			−0.676965	−	0.736016i	$-0.736705\pi$
$769$	−37.5456			−1.35393			−0.676965	+	0.736016i	$0.736705\pi$
$770$	1.79799	−	7.91718i	0.0647951	−	0.285315i
$771$		0			0
$772$	24.7460	+	11.8509i	0.890629	+	0.426521i
$773$	−8.97430			−0.322783			−0.161392	−	0.986890i	$-0.551598\pi$
$773$	−8.97430			−0.322783			−0.161392	+	0.986890i	$0.551598\pi$
$774$		0			0
$775$			15.3142i			0.550104i
$776$	8.61069	−	10.8700i	0.309106	−	0.390210i
$777$		0			0
$778$	−4.80665	+	21.1653i	−0.172327	+	0.758814i
$779$			52.7193i			1.88887i
$780$		0			0
$781$			9.74776i			0.348802i
$782$	−25.8420	−	5.86872i	−0.924107	−	0.209865i
$783$		0			0
$784$	−5.48916	−	6.82213i	−0.196042	−	0.243647i
$785$		−	20.9971i		−	0.749420i
$786$		0			0
$787$	−6.21327			−0.221479			−0.110740	−	0.993849i	$-0.535322\pi$
$787$	−6.21327			−0.221479			−0.110740	+	0.993849i	$0.535322\pi$
$788$	−29.8303	−	14.2857i	−1.06266	−	0.508907i
$789$		0			0
$790$	9.11073	+	2.06905i	0.324145	+	0.0736134i
$791$	49.0253			1.74314
$792$		0			0
$793$	77.1838			2.74088
$794$	−19.1331	−	4.34512i	−0.679007	−	0.154203i
$795$		0			0
$796$	14.3935	−	30.0553i	0.510163	−	1.06528i
$797$	−23.4519			−0.830708			−0.415354	−	0.909660i	$-0.636342\pi$
$797$	−23.4519			−0.830708			−0.415354	+	0.909660i	$0.636342\pi$
$798$		0			0
$799$			1.83625i			0.0649617i
$800$	7.18478	−	3.50824i	0.254020	−	0.124035i
$801$		0			0
$802$	11.5335	+	2.61926i	0.407262	+	0.0924891i
$803$		−	7.25976i		−	0.256191i
$804$		0			0
$805$			16.7966i			0.592001i
$806$	−18.4696	+	81.3282i	−0.650565	+	2.86466i
$807$		0			0
$808$	−15.6196	+	19.7180i	−0.549496	+	0.693675i
$809$			38.3475i			1.34823i	0.738628	+	0.674113i	$0.235474\pi$
$809$			38.3475i			1.34823i	−0.738628	+	0.674113i	$0.764526\pi$
$810$		0			0
$811$	−20.3661			−0.715152			−0.357576	−	0.933884i	$-0.616397\pi$
$811$	−20.3661			−0.715152			−0.357576	+	0.933884i	$0.616397\pi$
$812$	1.57286	−	3.28432i	0.0551965	−	0.115257i
$813$		0			0
$814$	−0.614604	+	2.70631i	−0.0215419	+	0.0948562i
$815$	−8.35965			−0.292826
$816$		0			0
$817$	−16.4416			−0.575219
$818$	−6.47496	+	28.5115i	−0.226392	+	0.996880i
$819$		0			0
$820$	14.6949	−	30.6847i	0.513168	−	1.07156i
$821$	−30.2233			−1.05480			−0.527401	−	0.849617i	$-0.676833\pi$
$821$	−30.2233			−1.05480			−0.527401	+	0.849617i	$0.676833\pi$
$822$		0			0
$823$		−	6.31287i		−	0.220053i	−0.993929	−	0.110026i	$-0.964906\pi$
$823$		−	6.31287i		−	0.220053i	0.993929	−	0.110026i	$-0.0350935\pi$
$824$	42.0507	+	33.3105i	1.46491	+	1.16043i
$825$		0			0
$826$	5.79366	−	25.5115i	0.201587	−	0.887659i
$827$		−	39.5499i		−	1.37528i	−0.726050	−	0.687642i	$-0.758646\pi$
$827$		−	39.5499i		−	1.37528i	0.726050	−	0.687642i	$-0.241354\pi$
$828$		0			0
$829$			11.5153i			0.399944i	0.979802	+	0.199972i	$0.0640851\pi$
$829$			11.5153i			0.399944i	−0.979802	+	0.199972i	$0.935915\pi$
$830$	23.9741	+	5.44452i	0.832154	+	0.188982i
$831$		0			0
$832$	42.3868	−	9.96580i	1.46950	−	0.345502i
$833$			14.0199i			0.485761i
$834$		0			0
$835$	19.5505			0.676572
$836$	5.07012	−	10.5870i	0.175354	−	0.366160i
$837$		0			0
$838$	5.72142	+	1.29934i	0.197643	+	0.0448848i
$839$	−13.8630			−0.478603			−0.239301	−	0.970945i	$-0.576918\pi$
$839$	−13.8630			−0.478603			−0.239301	+	0.970945i	$0.576918\pi$
$840$		0			0
$841$	−28.6392			−0.987560
$842$	−24.5586	−	5.57726i	−0.846346	−	0.192205i
$843$		0			0
$844$	24.4202	+	11.6948i	0.840577	+	0.402552i
$845$	31.4835			1.08307
$846$		0			0
$847$		−	3.03135i		−	0.104158i
$848$	−27.3942	−	34.0465i	−0.940721	−	1.16916i
$849$		0			0
$850$	−12.4840	−	2.83512i	−0.428198	−	0.0972439i
$851$		−	5.74153i		−	0.196817i
$852$		0			0
$853$			13.8053i			0.472683i	0.971670	+	0.236341i	$0.0759484\pi$
$853$			13.8053i			0.472683i	−0.971670	+	0.236341i	$0.924052\pi$
$854$	−13.4632	+	59.2833i	−0.460703	+	2.02863i
$855$		0			0
$856$	7.92042	+	6.27418i	0.270714	+	0.214447i
$857$		−	14.3186i		−	0.489114i	−0.969635	−	0.244557i	$-0.921357\pi$
$857$		−	14.3186i		−	0.489114i	0.969635	−	0.244557i	$-0.0786425\pi$
$858$		0			0
$859$	−50.8997			−1.73667			−0.868337	−	0.495974i	$-0.834811\pi$
$859$	−50.8997			−1.73667			−0.868337	+	0.495974i	$0.834811\pi$
$860$	9.56965	+	4.58290i	0.326322	+	0.156275i
$861$		0			0
$862$	9.26928	−	40.8158i	0.315713	−	1.39019i
$863$	25.0310			0.852066			0.426033	−	0.904708i	$-0.359911\pi$
$863$	25.0310			0.852066			0.426033	+	0.904708i	$0.359911\pi$
$864$		0			0
$865$	21.4545			0.729474
$866$	4.10108	−	18.0585i	0.139361	−	0.613652i
$867$		0			0
$868$	−59.2449	−	28.3723i	−2.01090	−	0.963019i
$869$	3.48834			0.118334
$870$		0			0
$871$		−	66.8500i		−	2.26512i
$872$	−17.7287	−	14.0438i	−0.600368	−	0.475583i
$873$		0			0
$874$	−5.37821	+	23.6821i	−0.181921	+	0.801060i
$875$			36.8185i			1.24469i
$876$		0			0
$877$		−	51.9131i		−	1.75298i	−0.481420	−	0.876490i	$-0.659879\pi$
$877$		−	51.9131i		−	1.75298i	0.481420	−	0.876490i	$-0.340121\pi$
$878$	3.12480	+	0.709641i	0.105457	+	0.0239492i
$879$		0			0
$880$	−5.90201	+	4.74883i	−0.198957	+	0.160083i
$881$			40.2674i			1.35664i	0.734765	+	0.678322i	$0.237292\pi$
$881$			40.2674i			1.35664i	−0.734765	+	0.678322i	$0.762708\pi$
$882$		0			0
$883$	−14.7777			−0.497309			−0.248655	−	0.968592i	$-0.579988\pi$
$883$	−14.7777			−0.497309			−0.248655	+	0.968592i	$0.579988\pi$
$884$	−62.8787	−	30.1125i	−2.11484	−	1.01279i
$885$		0			0
$886$	0.971728	+	0.220680i	0.0326459	+	0.00741388i
$887$	38.9704			1.30850			0.654249	−	0.756279i	$-0.272985\pi$
$887$	38.9704			1.30850			0.654249	+	0.756279i	$0.272985\pi$
$888$		0			0
$889$	−39.3243			−1.31889
$890$	25.6142	+	5.81698i	0.858589	+	0.194986i
$891$		0			0
$892$	−6.42773	+	13.4219i	−0.215216	+	0.449398i
$893$	1.68277			0.0563119
$894$		0			0
$895$		−	10.8263i		−	0.361883i
$896$	0.260964	+	34.2948i	0.00871821	+	1.14571i
$897$		0			0
$898$	38.7942	+	8.81016i	1.29458	+	0.293999i
$899$		−	6.50787i		−	0.217049i
$900$		0			0
$901$			69.9677i			2.33096i
$902$	2.81320	−	12.3875i	0.0936695	−	0.412459i
$903$		0			0
$904$	−35.8565	−	28.4038i	−1.19257	−	0.944697i
$905$		−	10.1681i		−	0.338000i
$906$		0			0
$907$	−13.4008			−0.444967			−0.222484	−	0.974936i	$-0.571416\pi$
$907$	−13.4008			−0.444967			−0.222484	+	0.974936i	$0.571416\pi$
$908$	15.4130	−	32.1843i	0.511500	−	1.06807i
$909$		0			0
$910$	−9.78615	+	43.0918i	−0.324408	+	1.42848i
$911$	−41.8465			−1.38644			−0.693218	−	0.720728i	$-0.743808\pi$
$911$	−41.8465			−1.38644			−0.693218	+	0.720728i	$0.743808\pi$
$912$		0			0
$913$	9.17926			0.303789
$914$	0.602251	−	2.65192i	0.0199207	−	0.0877177i
$915$		0			0
$916$	−1.46765	+	3.06462i	−0.0484924	+	0.101258i
$917$	8.46344			0.279487
$918$		0			0
$919$		−	9.95866i		−	0.328506i	−0.986418	−	0.164253i	$-0.947479\pi$
$919$		−	9.95866i		−	0.328506i	0.986418	−	0.164253i	$-0.0525213\pi$
$920$	9.73144	−	12.2848i	0.320836	−	0.405018i
$921$		0			0
$922$	6.62686	−	29.1803i	0.218244	−	0.961003i
$923$		−	53.0553i		−	1.74634i
$924$		0			0
$925$		−	2.77368i		−	0.0911981i
$926$	12.6023	+	2.86199i	0.414138	+	0.0940508i
$927$		0			0
$928$	−3.05321	+	1.49085i	−0.100227	+	0.0489394i
$929$			2.24932i			0.0737976i	0.999319	+	0.0368988i	$0.0117479\pi$
$929$			2.24932i			0.0737976i	−0.999319	+	0.0368988i	$0.988252\pi$
$930$		0			0
$931$	12.8481			0.421081
$932$	−17.8272	+	37.2254i	−0.583949	+	1.21936i
$933$		0			0
$934$	−39.2171	−	8.90620i	−1.28322	−	0.291420i
$935$	12.1290			0.396661
$936$		0			0
$937$	53.8032			1.75767			0.878837	−	0.477123i	$-0.158320\pi$
$937$	53.8032			1.75767			0.878837	+	0.477123i	$0.158320\pi$
$938$	51.3461	+	11.6607i	1.67651	+	0.380736i
$939$		0			0
$940$	−0.979440	−	0.469053i	−0.0319458	−	0.0152988i
$941$	51.7764			1.68786			0.843931	−	0.536451i	$-0.180235\pi$
$941$	51.7764			1.68786			0.843931	+	0.536451i	$0.180235\pi$
$942$		0			0
$943$			26.2805i			0.855811i
$944$	−19.0180	+	15.3021i	−0.618984	+	0.498042i
$945$		0			0
$946$	3.86330	+	0.877355i	0.125607	+	0.0285253i
$947$		−	15.6828i		−	0.509622i	−0.966991	−	0.254811i	$-0.917987\pi$
$947$		−	15.6828i		−	0.509622i	0.966991	−	0.254811i	$-0.0820132\pi$
$948$		0			0
$949$			39.5136i			1.28266i
$950$	−2.59816	+	11.4406i	−0.0842956	+	0.371183i
$951$		0			0
$952$	34.0968	−	43.0433i	1.10508	−	1.39504i
$953$		−	21.4309i		−	0.694215i	−0.937825	−	0.347107i	$-0.887164\pi$
$953$		−	21.4309i		−	0.694215i	0.937825	−	0.347107i	$-0.112836\pi$
$954$		0			0
$955$	18.4854			0.598175
$956$	20.0885	+	9.62036i	0.649708	+	0.311145i
$957$		0			0
$958$	−9.59154	+	42.2348i	−0.309889	+	1.36455i
$959$	−5.82162			−0.187990
$960$		0			0
$961$	−86.3934			−2.78688
$962$	3.34518	−	14.7300i	0.107853	−	0.474914i
$963$		0			0
$964$	−39.5006	−	18.9168i	−1.27223	−	0.609269i
$965$	25.9808			0.836351
$966$		0			0
$967$			20.8025i			0.668963i	0.942402	+	0.334481i	$0.108561\pi$
$967$			20.8025i			0.668963i	−0.942402	+	0.334481i	$0.891439\pi$
$968$	−1.75627	+	2.21709i	−0.0564488	+	0.0712601i
$969$		0			0
$970$	2.90802	−	12.8050i	0.0933710	−	0.411145i
$971$			10.5120i			0.337346i	0.985672	+	0.168673i	$0.0539481\pi$
$971$			10.5120i			0.337346i	−0.985672	+	0.168673i	$0.946052\pi$
$972$		0			0
$973$		−	16.0012i		−	0.512974i
$974$	16.9842	+	3.85712i	0.544209	+	0.123590i
$975$		0			0
$976$	44.1939	−	35.5589i	1.41461	−	1.13821i
$977$		−	57.0894i		−	1.82645i	−0.407453	−	0.913226i	$-0.633583\pi$
$977$		−	57.0894i		−	1.82645i	0.407453	−	0.913226i	$-0.366417\pi$
$978$		0			0
$979$	9.80721			0.313440
$980$	−7.47812	−	3.58127i	−0.238880	−	0.114399i
$981$		0			0
$982$	48.1417	+	10.9330i	1.53626	+	0.348885i
$983$	−17.1034			−0.545514			−0.272757	−	0.962083i	$-0.587936\pi$
$983$	−17.1034			−0.545514			−0.272757	+	0.962083i	$0.587936\pi$
$984$		0			0
$985$	−31.3187			−0.997898
$986$	5.30515	+	1.20480i	0.168950	+	0.0383687i
$987$		0			0
$988$	−27.5958	+	57.6233i	−0.877938	+	1.83324i
$989$	−8.19611			−0.260621
$990$		0			0
$991$			40.9703i			1.30147i	0.759307	+	0.650733i	$0.225538\pi$
$991$			40.9703i			1.30147i	−0.759307	+	0.650733i	$0.774462\pi$
$992$	26.8929	+	55.0759i	0.853851	+	1.74866i
$993$		0			0
$994$	40.7507	+	9.25450i	1.29254	+	0.293535i
$995$		−	31.5550i		−	1.00036i
$996$		0			0
$997$			21.1608i			0.670168i	0.942188	+	0.335084i	$0.108765\pi$
$997$			21.1608i			0.670168i	−0.942188	+	0.335084i	$0.891235\pi$
$998$	1.17123	−	5.15733i	0.0370747	−	0.163253i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.k.a.683.18	yes	40
3.2	odd	2	inner	792.2.k.a.683.23	yes	40
4.3	odd	2		3168.2.k.a.1871.12		40
8.3	odd	2	inner	792.2.k.a.683.24	yes	40
8.5	even	2		3168.2.k.a.1871.29		40
12.11	even	2		3168.2.k.a.1871.30		40
24.5	odd	2		3168.2.k.a.1871.11		40
24.11	even	2	inner	792.2.k.a.683.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.k.a.683.17	✓	40	24.11	even	2	inner
792.2.k.a.683.18	yes	40	1.1	even	1	trivial
792.2.k.a.683.23	yes	40	3.2	odd	2	inner
792.2.k.a.683.24	yes	40	8.3	odd	2	inner
3168.2.k.a.1871.11		40	24.5	odd	2
3168.2.k.a.1871.12		40	4.3	odd	2
3168.2.k.a.1871.29		40	8.5	even	2
3168.2.k.a.1871.30		40	12.11	even	2

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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.313193 + 1.37910i) q^{2} +(-1.80382 - 0.863848i) q^{4} -1.89382 q^{5} +3.03135i q^{7} +(1.75627 - 2.21709i) q^{8} +(0.593133 - 2.61177i) q^{10} -1.00000i q^{11} +5.44282i q^{13} +(-4.18052 - 0.949397i) q^{14} +(2.50753 + 3.11645i) q^{16} -6.40451i q^{17} -5.86923 q^{19} +(3.41612 + 1.63598i) q^{20} +(1.37910 + 0.313193i) q^{22} -2.92580 q^{23} -1.41343 q^{25} +(-7.50618 - 1.70465i) q^{26} +(2.61862 - 5.46801i) q^{28} +0.600643 q^{29} -10.8348i q^{31} +(-5.08323 + 2.48208i) q^{32} +(8.83245 + 2.00585i) q^{34} -5.74084i q^{35} +1.96238i q^{37} +(1.83820 - 8.09424i) q^{38} +(-3.32608 + 4.19879i) q^{40} -8.98233i q^{41} +2.80132 q^{43} +(-0.863848 + 1.80382i) q^{44} +(0.916341 - 4.03497i) q^{46} -0.286711 q^{47} -2.18907 q^{49} +(0.442676 - 1.94925i) q^{50} +(4.70177 - 9.81787i) q^{52} -10.9248 q^{53} +1.89382i q^{55} +(6.72078 + 5.32388i) q^{56} +(-0.188117 + 0.828346i) q^{58} +6.10246i q^{59} -14.1808i q^{61} +(14.9423 + 3.39339i) q^{62} +(-1.83100 - 7.78765i) q^{64} -10.3078i q^{65} -12.2822 q^{67} +(-5.53252 + 11.5526i) q^{68} +(7.91718 + 1.79799i) q^{70} -9.74776 q^{71} +7.25976 q^{73} +(-2.70631 - 0.614604i) q^{74} +(10.5870 + 5.07012i) q^{76} +3.03135 q^{77} +3.48834i q^{79} +(-4.74883 - 5.90201i) q^{80} +(12.3875 + 2.81320i) q^{82} +9.17926i q^{83} +12.1290i q^{85} +(-0.877355 + 3.86330i) q^{86} +(-2.21709 - 1.75627i) q^{88} +9.80721i q^{89} -16.4991 q^{91} +(5.27762 + 2.52745i) q^{92} +(0.0897961 - 0.395403i) q^{94} +11.1153 q^{95} +4.90282 q^{97} +(0.685601 - 3.01894i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} + 8 q^{10} - 8 q^{16} + 32 q^{19} + 40 q^{25} - 32 q^{28} + 32 q^{34} + 16 q^{40} - 24 q^{46} - 8 q^{49} + 40 q^{52} - 8 q^{58} + 16 q^{64} + 72 q^{70} + 32 q^{73} - 8 q^{76} - 64 q^{82}+ \cdots - 32 q^{97}+O(q^{100}) \) 40 * q - 8 * q^4 + 8 * q^10 - 8 * q^16 + 32 * q^19 + 40 * q^25 - 32 * q^28 + 32 * q^34 + 16 * q^40 - 24 * q^46 - 8 * q^49 + 40 * q^52 - 8 * q^58 + 16 * q^64 + 72 * q^70 + 32 * q^73 - 8 * q^76 - 64 * q^82 - 24 * q^88 - 56 * q^94 - 32 * q^97

Introduction

L-functions

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Representations

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Database

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