LMFDB - Embedded newform 1740.2.bc.c.1177.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1740,2,Mod(853,1740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1740.853"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1740.bc (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] 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:	$13.8939699517$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1177.3
Character	$\chi$	$=$	1740.1177
Dual form			1740.2.bc.c.853.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{3} +(-1.98303 - 1.03325i) q^{5} +(0.377598 + 0.377598i) q^{7} -1.00000 q^{9} +(-2.83974 + 2.83974i) q^{11} +(-2.93352 - 2.93352i) q^{13} +(-1.03325 + 1.98303i) q^{15} +5.42233 q^{17} +(0.918660 + 0.918660i) q^{19} +(0.377598 - 0.377598i) q^{21} +(-3.74121 + 3.74121i) q^{23} +(2.86479 + 4.09792i) q^{25} +1.00000i q^{27} +(-4.56656 - 2.85422i) q^{29} +(4.45954 - 4.45954i) q^{31} +(2.83974 + 2.83974i) q^{33} +(-0.358634 - 1.13894i) q^{35} +6.53912i q^{37} +(-2.93352 + 2.93352i) q^{39} +(6.74376 + 6.74376i) q^{41} +11.5800i q^{43} +(1.98303 + 1.03325i) q^{45} +5.10275i q^{47} -6.71484i q^{49} -5.42233i q^{51} +(-3.29698 + 3.29698i) q^{53} +(8.56545 - 2.69712i) q^{55} +(0.918660 - 0.918660i) q^{57} +1.80738i q^{59} +(6.15238 - 6.15238i) q^{61} +(-0.377598 - 0.377598i) q^{63} +(2.78618 + 8.84830i) q^{65} +(2.31042 - 2.31042i) q^{67} +(3.74121 + 3.74121i) q^{69} +5.50267i q^{71} +1.79039 q^{73} +(4.09792 - 2.86479i) q^{75} -2.14456 q^{77} +(-0.178306 - 0.178306i) q^{79} +1.00000 q^{81} +(1.51709 - 1.51709i) q^{83} +(-10.7526 - 5.60263i) q^{85} +(-2.85422 + 4.56656i) q^{87} +(10.0729 + 10.0729i) q^{89} -2.21538i q^{91} +(-4.45954 - 4.45954i) q^{93} +(-0.872522 - 2.77093i) q^{95} +3.31231i q^{97} +(2.83974 - 2.83974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 30 q^{9} + 4 q^{11} - 6 q^{13} - 6 q^{15} + 8 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{33} - 16 q^{35} - 6 q^{39} - 10 q^{41} - 6 q^{53} + 4 q^{55} + 8 q^{57} + 30 q^{61} - 2 q^{65} + 4 q^{67} + 12 q^{73}+ \cdots - 4 q^{99}+O(q^{100}) $ 30 * q - 30 * q^9 + 4 * q^11 - 6 * q^13 - 6 * q^15 + 8 * q^19 - 6 * q^25 + 4 * q^29 - 4 * q^33 - 16 * q^35 - 6 * q^39 - 10 * q^41 - 6 * q^53 + 4 * q^55 + 8 * q^57 + 30 * q^61 - 2 * q^65 + 4 * q^67 + 12 * q^73 + 8 * q^75 - 4 * q^77 - 4 * q^79 + 30 * q^81 - 28 * q^83 + 20 * q^85 + 10 * q^87 + 10 * q^89 + 20 * q^95 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1740\mathbb{Z}\right)^\times$.

$n$	$581$	$697$	$871$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		0			0
$5$	−1.98303	−	1.03325i	−0.886836	−	0.462083i
$5$	−1.98303	−	1.03325i	−0.886836	−	0.462083i
$6$		0			0
$7$	0.377598	+	0.377598i	0.142719	+	0.142719i	0.774856	−	0.632138i	$-0.217822\pi$
$7$	0.377598	+	0.377598i	0.142719	+	0.142719i	−0.632138	+	0.774856i	$0.717822\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	−2.83974	+	2.83974i	−0.856214	+	0.856214i	−0.990890	−	0.134675i	$-0.957001\pi$
$11$	−2.83974	+	2.83974i	−0.856214	+	0.856214i	0.134675	+	0.990890i	$0.457001\pi$
$12$		0			0
$13$	−2.93352	−	2.93352i	−0.813611	−	0.813611i	0.171562	−	0.985173i	$-0.445119\pi$
$13$	−2.93352	−	2.93352i	−0.813611	−	0.813611i	−0.985173	+	0.171562i	$0.945119\pi$
$14$		0			0
$15$	−1.03325	+	1.98303i	−0.266784	+	0.512015i
$16$		0			0
$17$	5.42233			1.31511			0.657555	−	0.753407i	$-0.271591\pi$
$17$	5.42233			1.31511			0.657555	+	0.753407i	$0.271591\pi$
$18$		0			0
$19$	0.918660	+	0.918660i	0.210755	+	0.210755i	0.804588	−	0.593833i	$-0.202386\pi$
$19$	0.918660	+	0.918660i	0.210755	+	0.210755i	−0.593833	+	0.804588i	$0.702386\pi$
$20$		0			0
$21$	0.377598	−	0.377598i	0.0823987	−	0.0823987i
$22$		0			0
$23$	−3.74121	+	3.74121i	−0.780095	+	0.780095i	−0.979847	−	0.199751i	$-0.935987\pi$
$23$	−3.74121	+	3.74121i	−0.780095	+	0.780095i	0.199751	+	0.979847i	$0.435987\pi$
$24$		0			0
$25$	2.86479	+	4.09792i	0.572958	+	0.819585i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−4.56656	−	2.85422i	−0.847988	−	0.530015i
$29$	−4.56656	−	2.85422i	−0.847988	−	0.530015i
$30$		0			0
$31$	4.45954	−	4.45954i	0.800957	−	0.800957i	−0.182288	−	0.983245i	$-0.558350\pi$
$31$	4.45954	−	4.45954i	0.800957	−	0.800957i	0.983245	+	0.182288i	$0.0583504\pi$
$32$		0			0
$33$	2.83974	+	2.83974i	0.494336	+	0.494336i
$34$		0			0
$35$	−0.358634	−	1.13894i	−0.0606202	−	0.192516i
$36$		0			0
$37$			6.53912i			1.07502i	0.843256	+	0.537512i	$0.180636\pi$
$37$			6.53912i			1.07502i	−0.843256	+	0.537512i	$0.819364\pi$
$38$		0			0
$39$	−2.93352	+	2.93352i	−0.469739	+	0.469739i
$40$		0			0
$41$	6.74376	+	6.74376i	1.05320	+	1.05320i	0.998503	+	0.0546952i	$0.0174187\pi$
$41$	6.74376	+	6.74376i	1.05320	+	1.05320i	0.0546952	+	0.998503i	$0.482581\pi$
$42$		0			0
$43$			11.5800i			1.76593i	0.469435	+	0.882967i	$0.344458\pi$
$43$			11.5800i			1.76593i	−0.469435	+	0.882967i	$0.655542\pi$
$44$		0			0
$45$	1.98303	+	1.03325i	0.295612	+	0.154028i
$46$		0			0
$47$			5.10275i			0.744313i	0.928170	+	0.372156i	$0.121382\pi$
$47$			5.10275i			0.744313i	−0.928170	+	0.372156i	$0.878618\pi$
$48$		0			0
$49$		−	6.71484i		−	0.959263i
$50$		0			0
$51$		−	5.42233i		−	0.759279i
$52$		0			0
$53$	−3.29698	+	3.29698i	−0.452875	+	0.452875i	−0.896308	−	0.443433i	$-0.853760\pi$
$53$	−3.29698	+	3.29698i	−0.452875	+	0.452875i	0.443433	+	0.896308i	$0.353760\pi$
$54$		0			0
$55$	8.56545	−	2.69712i	1.15496	−	0.363680i
$56$		0			0
$57$	0.918660	−	0.918660i	0.121679	−	0.121679i
$58$		0			0
$59$			1.80738i			0.235301i	0.993055	+	0.117650i	$0.0375362\pi$
$59$			1.80738i			0.235301i	−0.993055	+	0.117650i	$0.962464\pi$
$60$		0			0
$61$	6.15238	−	6.15238i	0.787732	−	0.787732i	−0.193390	−	0.981122i	$-0.561948\pi$
$61$	6.15238	−	6.15238i	0.787732	−	0.787732i	0.981122	+	0.193390i	$0.0619483\pi$
$62$		0			0
$63$	−0.377598	−	0.377598i	−0.0475729	−	0.0475729i
$64$		0			0
$65$	2.78618	+	8.84830i	0.345584	+	1.09750i
$66$		0			0
$67$	2.31042	−	2.31042i	0.282263	−	0.282263i	−0.551748	−	0.834011i	$-0.686039\pi$
$67$	2.31042	−	2.31042i	0.282263	−	0.282263i	0.834011	+	0.551748i	$0.186039\pi$
$68$		0			0
$69$	3.74121	+	3.74121i	0.450388	+	0.450388i
$70$		0			0
$71$			5.50267i			0.653047i	0.945189	+	0.326524i	$0.105877\pi$
$71$			5.50267i			0.653047i	−0.945189	+	0.326524i	$0.894123\pi$
$72$		0			0
$73$	1.79039			0.209549			0.104775	−	0.994496i	$-0.466588\pi$
$73$	1.79039			0.209549			0.104775	+	0.994496i	$0.466588\pi$
$74$		0			0
$75$	4.09792	−	2.86479i	0.473188	−	0.330797i
$76$		0			0
$77$	−2.14456			−0.244396
$78$		0			0
$79$	−0.178306	−	0.178306i	−0.0200609	−	0.0200609i	0.697005	−	0.717066i	$-0.254515\pi$
$79$	−0.178306	−	0.178306i	−0.0200609	−	0.0200609i	−0.717066	+	0.697005i	$0.754515\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	1.51709	−	1.51709i	0.166522	−	0.166522i	−0.618926	−	0.785449i	$-0.712432\pi$
$83$	1.51709	−	1.51709i	0.166522	−	0.166522i	0.785449	+	0.618926i	$0.212432\pi$
$84$		0			0
$85$	−10.7526	−	5.60263i	−1.16629	−	0.607690i
$86$		0			0
$87$	−2.85422	+	4.56656i	−0.306004	+	0.489586i
$88$		0			0
$89$	10.0729	+	10.0729i	1.06772	+	1.06772i	0.997534	+	0.0701904i	$0.0223607\pi$
$89$	10.0729	+	10.0729i	1.06772	+	1.06772i	0.0701904	+	0.997534i	$0.477639\pi$
$90$		0			0
$91$		−	2.21538i		−	0.232235i
$92$		0			0
$93$	−4.45954	−	4.45954i	−0.462433	−	0.462433i
$94$		0			0
$95$	−0.872522	−	2.77093i	−0.0895188	−	0.284292i
$96$		0			0
$97$			3.31231i			0.336314i	0.985760	+	0.168157i	$0.0537816\pi$
$97$			3.31231i			0.336314i	−0.985760	+	0.168157i	$0.946218\pi$
$98$		0			0
$99$	2.83974	−	2.83974i	0.285405	−	0.285405i
$100$		0			0
$101$	−12.1037	+	12.1037i	−1.20436	+	1.20436i	−0.231534	+	0.972827i	$0.574374\pi$
$101$	−12.1037	+	12.1037i	−1.20436	+	1.20436i	−0.972827	+	0.231534i	$0.925626\pi$
$102$		0			0
$103$	7.65353	−	7.65353i	0.754125	−	0.754125i	−0.221122	−	0.975246i	$-0.570972\pi$
$103$	7.65353	−	7.65353i	0.754125	−	0.754125i	0.975246	+	0.221122i	$0.0709717\pi$
$104$		0			0
$105$	−1.13894	+	0.358634i	−0.111149	+	0.0349991i
$106$		0			0
$107$	−1.35592	−	1.35592i	−0.131082	−	0.131082i	0.638522	−	0.769604i	$-0.279546\pi$
$107$	−1.35592	−	1.35592i	−0.131082	−	0.131082i	−0.769604	+	0.638522i	$0.779546\pi$
$108$		0			0
$109$	6.07140			0.581535			0.290768	−	0.956794i	$-0.406089\pi$
$109$	6.07140			0.581535			0.290768	+	0.956794i	$0.406089\pi$
$110$		0			0
$111$	6.53912			0.620666
$112$		0			0
$113$	2.65569			0.249826			0.124913	−	0.992168i	$-0.460135\pi$
$113$	2.65569			0.249826			0.124913	+	0.992168i	$0.460135\pi$
$114$		0			0
$115$	11.2845	−	3.55331i	1.05229	−	0.331348i
$116$		0			0
$117$	2.93352	+	2.93352i	0.271204	+	0.271204i
$118$		0			0
$119$	2.04746	+	2.04746i	0.187691	+	0.187691i
$120$		0			0
$121$		−	5.12827i		−	0.466207i
$122$		0			0
$123$	6.74376	−	6.74376i	0.608064	−	0.608064i
$124$		0			0
$125$	−1.44677	−	11.0863i	−0.129403	−	0.991592i
$126$		0			0
$127$	8.63377			0.766123			0.383062	−	0.923723i	$-0.374870\pi$
$127$	8.63377			0.766123			0.383062	+	0.923723i	$0.374870\pi$
$128$		0			0
$129$	11.5800			1.01956
$130$		0			0
$131$	12.3756	+	12.3756i	1.08126	+	1.08126i	0.996392	+	0.0848723i	$0.0270482\pi$
$131$	12.3756	+	12.3756i	1.08126	+	1.08126i	0.0848723	+	0.996392i	$0.472952\pi$
$132$		0			0
$133$			0.693769i			0.0601574i
$134$		0			0
$135$	1.03325	−	1.98303i	0.0889280	−	0.170672i
$136$		0			0
$137$	−17.2500			−1.47376			−0.736882	−	0.676021i	$-0.763703\pi$
$137$	−17.2500			−1.47376			−0.736882	+	0.676021i	$0.763703\pi$
$138$		0			0
$139$			11.5651i			0.980938i	0.871459	+	0.490469i	$0.163175\pi$
$139$			11.5651i			0.980938i	−0.871459	+	0.490469i	$0.836825\pi$
$140$		0			0
$141$	5.10275			0.429729
$142$		0			0
$143$	16.6609			1.39325
$144$		0			0
$145$	6.10648	+	10.3784i	0.507116	+	0.861878i
$146$		0			0
$147$	−6.71484			−0.553831
$148$		0			0
$149$	−12.2553			−1.00400			−0.501998	−	0.864869i	$-0.667402\pi$
$149$	−12.2553			−1.00400			−0.501998	+	0.864869i	$0.667402\pi$
$150$		0			0
$151$			3.80918i			0.309986i	0.987916	+	0.154993i	$0.0495356\pi$
$151$			3.80918i			0.309986i	−0.987916	+	0.154993i	$0.950464\pi$
$152$		0			0
$153$	−5.42233			−0.438370
$154$		0			0
$155$	−13.4512	+	4.23556i	−1.08043	+	0.340209i
$156$		0			0
$157$			16.9707i			1.35441i	0.735794	+	0.677206i	$0.236809\pi$
$157$			16.9707i			1.35441i	−0.735794	+	0.677206i	$0.763191\pi$
$158$		0			0
$159$	3.29698	+	3.29698i	0.261467	+	0.261467i
$160$		0			0
$161$	−2.82534			−0.222668
$162$		0			0
$163$	−18.1900			−1.42475			−0.712374	−	0.701800i	$-0.752380\pi$
$163$	−18.1900			−1.42475			−0.712374	+	0.701800i	$0.752380\pi$
$164$		0			0
$165$	−2.69712	−	8.56545i	−0.209971	−	0.666819i
$166$		0			0
$167$	−3.83817	+	3.83817i	−0.297007	+	0.297007i	−0.839840	−	0.542834i	$-0.817351\pi$
$167$	−3.83817	+	3.83817i	−0.297007	+	0.297007i	0.542834	+	0.839840i	$0.317351\pi$
$168$		0			0
$169$			4.21103i			0.323926i
$170$		0			0
$171$	−0.918660	−	0.918660i	−0.0702517	−	0.0702517i
$172$		0			0
$173$	−0.514323	−	0.514323i	−0.0391033	−	0.0391033i	0.687285	−	0.726388i	$-0.258802\pi$
$173$	−0.514323	−	0.514323i	−0.0391033	−	0.0391033i	−0.726388	+	0.687285i	$0.758802\pi$
$174$		0			0
$175$	−0.465630	+	2.62911i	−0.0351983	+	0.198742i
$176$		0			0
$177$	1.80738			0.135851
$178$		0			0
$179$	19.1223			1.42927			0.714635	−	0.699498i	$-0.246593\pi$
$179$	19.1223			1.42927			0.714635	+	0.699498i	$0.246593\pi$
$180$		0			0
$181$	−17.5134			−1.30176			−0.650881	−	0.759179i	$-0.725600\pi$
$181$	−17.5134			−1.30176			−0.650881	+	0.759179i	$0.725600\pi$
$182$		0			0
$183$	−6.15238	−	6.15238i	−0.454797	−	0.454797i
$184$		0			0
$185$	6.75654	−	12.9672i	0.496751	−	0.953371i
$186$		0			0
$187$	−15.3980	+	15.3980i	−1.12602	+	1.12602i
$188$		0			0
$189$	−0.377598	+	0.377598i	−0.0274662	+	0.0274662i
$190$		0			0
$191$	−0.499842	+	0.499842i	−0.0361673	+	0.0361673i	−0.724959	−	0.688792i	$-0.758141\pi$
$191$	−0.499842	+	0.499842i	−0.0361673	+	0.0361673i	0.688792	+	0.724959i	$0.258141\pi$
$192$		0			0
$193$		−	21.3077i		−	1.53376i	−0.641790	−	0.766880i	$-0.721808\pi$
$193$		−	21.3077i		−	1.53376i	0.641790	−	0.766880i	$-0.278192\pi$
$194$		0			0
$195$	8.84830	−	2.78618i	0.633640	−	0.199523i
$196$		0			0
$197$	−8.94004	−	8.94004i	−0.636951	−	0.636951i	0.312851	−	0.949802i	$-0.398716\pi$
$197$	−8.94004	−	8.94004i	−0.636951	−	0.636951i	−0.949802	+	0.312851i	$0.898716\pi$
$198$		0			0
$199$		−	0.350184i		−	0.0248239i	−0.999923	−	0.0124119i	$-0.996049\pi$
$199$		−	0.350184i		−	0.0248239i	0.999923	−	0.0124119i	$-0.00395094\pi$
$200$		0			0
$201$	−2.31042	−	2.31042i	−0.162965	−	0.162965i
$202$		0			0
$203$	−0.646576	−	2.80207i	−0.0453807	−	0.196667i
$204$		0			0
$205$	−6.40506	−	20.3410i	−0.447349	−	1.42068i
$206$		0			0
$207$	3.74121	−	3.74121i	0.260032	−	0.260032i
$208$		0			0
$209$	−5.21751			−0.360903
$210$		0			0
$211$	14.0873	+	14.0873i	0.969811	+	0.969811i	0.999557	−	0.0297464i	$-0.00946996\pi$
$211$	14.0873	+	14.0873i	0.969811	+	0.969811i	−0.0297464	+	0.999557i	$0.509470\pi$
$212$		0			0
$213$	5.50267			0.377037
$214$		0			0
$215$	11.9650	−	22.9635i	0.816009	−	1.56609i
$216$		0			0
$217$	3.36783			0.228623
$218$		0			0
$219$		−	1.79039i		−	0.120983i
$220$		0			0
$221$	−15.9065	−	15.9065i	−1.06999	−	1.06999i
$222$		0			0
$223$	−18.0388	+	18.0388i	−1.20797	+	1.20797i	−0.236285	+	0.971684i	$0.575930\pi$
$223$	−18.0388	+	18.0388i	−1.20797	+	1.20797i	−0.971684	+	0.236285i	$0.924070\pi$
$224$		0			0
$225$	−2.86479	−	4.09792i	−0.190986	−	0.273195i
$226$		0			0
$227$	−8.97456	−	8.97456i	−0.595663	−	0.595663i	0.343493	−	0.939155i	$-0.388390\pi$
$227$	−8.97456	−	8.97456i	−0.595663	−	0.595663i	−0.939155	+	0.343493i	$0.888390\pi$
$228$		0			0
$229$	13.3171	−	13.3171i	0.880021	−	0.880021i	−0.113515	−	0.993536i	$-0.536211\pi$
$229$	13.3171	−	13.3171i	0.880021	−	0.880021i	0.993536	+	0.113515i	$0.0362110\pi$
$230$		0			0
$231$			2.14456i			0.141102i
$232$		0			0
$233$	−16.7342	+	16.7342i	−1.09629	+	1.09629i	−0.101451	+	0.994841i	$0.532349\pi$
$233$	−16.7342	+	16.7342i	−1.09629	+	1.09629i	−0.994841	+	0.101451i	$0.967651\pi$
$234$		0			0
$235$	5.27242	−	10.1189i	0.343935	−	0.660084i
$236$		0			0
$237$	−0.178306	+	0.178306i	−0.0115822	+	0.0115822i
$238$		0			0
$239$		−	3.53427i		−	0.228613i	−0.993446	−	0.114306i	$-0.963535\pi$
$239$		−	3.53427i		−	0.228613i	0.993446	−	0.114306i	$-0.0364646\pi$
$240$		0			0
$241$		−	10.4423i		−	0.672647i	−0.941747	−	0.336323i	$-0.890817\pi$
$241$		−	10.4423i		−	0.672647i	0.941747	−	0.336323i	$-0.109183\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$	−6.93811	+	13.3157i	−0.443259	+	0.850709i
$246$		0			0
$247$		−	5.38981i		−	0.342945i
$248$		0			0
$249$	−1.51709	−	1.51709i	−0.0961418	−	0.0961418i
$250$		0			0
$251$	−20.1681	+	20.1681i	−1.27300	+	1.27300i	−0.328495	+	0.944506i	$0.606542\pi$
$251$	−20.1681	+	20.1681i	−1.27300	+	1.27300i	−0.944506	+	0.328495i	$0.893458\pi$
$252$		0			0
$253$		−	21.2481i		−	1.33586i
$254$		0			0
$255$	−5.60263	+	10.7526i	−0.350850	+	0.673356i
$256$		0			0
$257$	−19.2203	−	19.2203i	−1.19893	−	1.19893i	−0.974487	−	0.224444i	$-0.927943\pi$
$257$	−19.2203	−	19.2203i	−1.19893	−	1.19893i	−0.224444	−	0.974487i	$-0.572057\pi$
$258$		0			0
$259$	−2.46916	+	2.46916i	−0.153426	+	0.153426i
$260$		0			0
$261$	4.56656	+	2.85422i	0.282663	+	0.176672i
$262$		0			0
$263$			29.0825i			1.79330i	0.442735	+	0.896652i	$0.354008\pi$
$263$			29.0825i			1.79330i	−0.442735	+	0.896652i	$0.645992\pi$
$264$		0			0
$265$	9.94460	−	3.13139i	0.610892	−	0.192360i
$266$		0			0
$267$	10.0729	−	10.0729i	0.616451	−	0.616451i
$268$		0			0
$269$	6.53556	−	6.53556i	0.398480	−	0.398480i	−0.479217	−	0.877697i	$-0.659079\pi$
$269$	6.53556	−	6.53556i	0.398480	−	0.398480i	0.877697	+	0.479217i	$0.159079\pi$
$270$		0			0
$271$	20.6798	+	20.6798i	1.25621	+	1.25621i	0.952889	+	0.303319i	$0.0980946\pi$
$271$	20.6798	+	20.6798i	1.25621	+	1.25621i	0.303319	+	0.952889i	$0.401905\pi$
$272$		0			0
$273$	−2.21538			−0.134081
$274$		0			0
$275$	−19.7723	−	3.50179i	−1.19232	−	0.211166i
$276$		0			0
$277$	14.0705	+	14.0705i	0.845412	+	0.845412i	0.989557	−	0.144144i	$-0.0460429\pi$
$277$	14.0705	+	14.0705i	0.845412	+	0.845412i	−0.144144	+	0.989557i	$0.546043\pi$
$278$		0			0
$279$	−4.45954	+	4.45954i	−0.266986	+	0.266986i
$280$		0			0
$281$	−14.3473			−0.855889			−0.427944	−	0.903805i	$-0.640762\pi$
$281$	−14.3473			−0.855889			−0.427944	+	0.903805i	$0.640762\pi$
$282$		0			0
$283$	−7.32276	−	7.32276i	−0.435293	−	0.435293i	0.455131	−	0.890424i	$-0.349592\pi$
$283$	−7.32276	−	7.32276i	−0.435293	−	0.435293i	−0.890424	+	0.455131i	$0.849592\pi$
$284$		0			0
$285$	−2.77093	+	0.872522i	−0.164136	+	0.0516837i
$286$		0			0
$287$			5.09286i			0.300622i
$288$		0			0
$289$	12.4017			0.729512
$290$		0			0
$291$	3.31231			0.194171
$292$		0			0
$293$		−	6.12781i		−	0.357990i	−0.983850	−	0.178995i	$-0.942715\pi$
$293$		−	6.12781i		−	0.357990i	0.983850	−	0.178995i	$-0.0572847\pi$
$294$		0			0
$295$	1.86747	−	3.58408i	0.108729	−	0.208673i
$296$		0			0
$297$	−2.83974	−	2.83974i	−0.164779	−	0.164779i
$298$		0			0
$299$	21.9498			1.26939
$300$		0			0
$301$	−4.37259	+	4.37259i	−0.252032	+	0.252032i
$302$		0			0
$303$	12.1037	+	12.1037i	0.695338	+	0.695338i
$304$		0			0
$305$	−18.5573	+	5.84339i	−1.06259	+	0.334591i
$306$		0			0
$307$	−16.0771			−0.917571			−0.458785	−	0.888547i	$-0.651715\pi$
$307$	−16.0771			−0.917571			−0.458785	+	0.888547i	$0.651715\pi$
$308$		0			0
$309$	−7.65353	−	7.65353i	−0.435394	−	0.435394i
$310$		0			0
$311$	18.0492	−	18.0492i	1.02348	−	1.02348i	0.0237608	−	0.999718i	$-0.492436\pi$
$311$	18.0492	−	18.0492i	1.02348	−	1.02348i	0.999718	−	0.0237608i	$-0.00756402\pi$
$312$		0			0
$313$	−5.01014	+	5.01014i	−0.283190	+	0.283190i	−0.834380	−	0.551190i	$-0.814174\pi$
$313$	−5.01014	+	5.01014i	−0.283190	+	0.283190i	0.551190	+	0.834380i	$0.314174\pi$
$314$		0			0
$315$	0.358634	+	1.13894i	0.0202067	+	0.0641720i
$316$		0			0
$317$			23.0626i			1.29533i	0.761926	+	0.647664i	$0.224254\pi$
$317$			23.0626i			1.29533i	−0.761926	+	0.647664i	$0.775746\pi$
$318$		0			0
$319$	21.0731	−	4.86260i	1.17987	−	0.272253i
$320$		0			0
$321$	−1.35592	+	1.35592i	−0.0756803	+	0.0756803i
$322$		0			0
$323$	4.98128	+	4.98128i	0.277166	+	0.277166i
$324$		0			0
$325$	3.61742	−	20.4252i	0.200659	−	1.13299i
$326$		0			0
$327$		−	6.07140i		−	0.335749i
$328$		0			0
$329$	−1.92679	+	1.92679i	−0.106227	+	0.106227i
$330$		0			0
$331$	3.42940	+	3.42940i	0.188497	+	0.188497i	0.795046	−	0.606549i	$-0.207447\pi$
$331$	3.42940	+	3.42940i	0.188497	+	0.188497i	−0.606549	+	0.795046i	$0.707447\pi$
$332$		0			0
$333$		−	6.53912i		−	0.358341i
$334$		0			0
$335$	−6.96888	+	2.19439i	−0.380751	+	0.119892i
$336$		0			0
$337$			11.8940i			0.647909i	0.946073	+	0.323954i	$0.105012\pi$
$337$			11.8940i			0.647909i	−0.946073	+	0.323954i	$0.894988\pi$
$338$		0			0
$339$		−	2.65569i		−	0.144237i
$340$		0			0
$341$			25.3279i			1.37158i
$342$		0			0
$343$	5.17870	−	5.17870i	0.279623	−	0.279623i
$344$		0			0
$345$	−3.55331	−	11.2845i	−0.191304	−	0.607538i
$346$		0			0
$347$	1.11414	−	1.11414i	0.0598104	−	0.0598104i	−0.676569	−	0.736379i	$-0.736534\pi$
$347$	1.11414	−	1.11414i	0.0598104	−	0.0598104i	0.736379	+	0.676569i	$0.236534\pi$
$348$		0			0
$349$		−	22.8551i		−	1.22341i	−0.791088	−	0.611703i	$-0.790485\pi$
$349$		−	22.8551i		−	1.22341i	0.791088	−	0.611703i	$-0.209515\pi$
$350$		0			0
$351$	2.93352	−	2.93352i	0.156580	−	0.156580i
$352$		0			0
$353$	6.88262	+	6.88262i	0.366325	+	0.366325i	0.866135	−	0.499810i	$-0.166597\pi$
$353$	6.88262	+	6.88262i	0.366325	+	0.366325i	−0.499810	+	0.866135i	$0.666597\pi$
$354$		0			0
$355$	5.68564	−	10.9119i	0.301762	−	0.579146i
$356$		0			0
$357$	2.04746	−	2.04746i	0.108363	−	0.108363i
$358$		0			0
$359$	−17.2924	−	17.2924i	−0.912656	−	0.912656i	0.0838245	−	0.996481i	$-0.473286\pi$
$359$	−17.2924	−	17.2924i	−0.912656	−	0.912656i	−0.996481	+	0.0838245i	$0.973286\pi$
$360$		0			0
$361$		−	17.3121i		−	0.911165i
$362$		0			0
$363$	−5.12827			−0.269164
$364$		0			0
$365$	−3.55039	−	1.84992i	−0.185836	−	0.0968292i
$366$		0			0
$367$	−27.0221			−1.41054			−0.705270	−	0.708938i	$-0.749174\pi$
$367$	−27.0221			−1.41054			−0.705270	+	0.708938i	$0.749174\pi$
$368$		0			0
$369$	−6.74376	−	6.74376i	−0.351066	−	0.351066i
$370$		0			0
$371$	−2.48987			−0.129267
$372$		0			0
$373$	−6.05510	+	6.05510i	−0.313521	+	0.313521i	−0.846272	−	0.532751i	$-0.821158\pi$
$373$	−6.05510	+	6.05510i	−0.313521	+	0.313521i	0.532751	+	0.846272i	$0.321158\pi$
$374$		0			0
$375$	−11.0863	+	1.44677i	−0.572496	+	0.0747109i
$376$		0			0
$377$	5.02317	+	21.7690i	0.258706	+	1.12116i
$378$		0			0
$379$	12.9917	+	12.9917i	0.667338	+	0.667338i	0.957099	−	0.289761i	$-0.0935759\pi$
$379$	12.9917	+	12.9917i	0.667338	+	0.667338i	−0.289761	+	0.957099i	$0.593576\pi$
$380$		0			0
$381$		−	8.63377i		−	0.442322i
$382$		0			0
$383$	−3.08675	−	3.08675i	−0.157726	−	0.157726i	0.623833	−	0.781558i	$-0.285575\pi$
$383$	−3.08675	−	3.08675i	−0.157726	−	0.157726i	−0.781558	+	0.623833i	$0.785575\pi$
$384$		0			0
$385$	4.25273	+	2.21587i	0.216739	+	0.112931i
$386$		0			0
$387$		−	11.5800i		−	0.588645i
$388$		0			0
$389$	3.88481	−	3.88481i	0.196968	−	0.196968i	−0.601731	−	0.798699i	$-0.705522\pi$
$389$	3.88481	−	3.88481i	0.196968	−	0.196968i	0.798699	+	0.601731i	$0.205522\pi$
$390$		0			0
$391$	−20.2861	+	20.2861i	−1.02591	+	1.02591i
$392$		0			0
$393$	12.3756	−	12.3756i	0.624268	−	0.624268i
$394$		0			0
$395$	0.169350	+	0.537819i	0.00852094	+	0.0270606i
$396$		0			0
$397$	−15.2769	−	15.2769i	−0.766725	−	0.766725i	0.210803	−	0.977529i	$-0.432392\pi$
$397$	−15.2769	−	15.2769i	−0.766725	−	0.766725i	−0.977529	+	0.210803i	$0.932392\pi$
$398$		0			0
$399$	0.693769			0.0347319
$400$		0			0
$401$	−5.96579			−0.297917			−0.148959	−	0.988843i	$-0.547592\pi$
$401$	−5.96579			−0.297917			−0.148959	+	0.988843i	$0.547592\pi$
$402$		0			0
$403$	−26.1643			−1.30333
$404$		0			0
$405$	−1.98303	−	1.03325i	−0.0985374	−	0.0513426i
$406$		0			0
$407$	−18.5694	−	18.5694i	−0.920451	−	0.920451i
$408$		0			0
$409$	−0.930088	−	0.930088i	−0.0459899	−	0.0459899i	0.683738	−	0.729728i	$-0.260353\pi$
$409$	−0.930088	−	0.930088i	−0.0459899	−	0.0459899i	−0.729728	+	0.683738i	$0.760353\pi$
$410$		0			0
$411$			17.2500i			0.850878i
$412$		0			0
$413$	−0.682463	+	0.682463i	−0.0335818	+	0.0335818i
$414$		0			0
$415$	−4.57597	+	1.44090i	−0.224625	+	0.0707309i
$416$		0			0
$417$	11.5651			0.566345
$418$		0			0
$419$	10.0262			0.489812			0.244906	−	0.969547i	$-0.421243\pi$
$419$	10.0262			0.489812			0.244906	+	0.969547i	$0.421243\pi$
$420$		0			0
$421$	−19.0296	−	19.0296i	−0.927448	−	0.927448i	0.0700926	−	0.997540i	$-0.477671\pi$
$421$	−19.0296	−	19.0296i	−0.927448	−	0.927448i	−0.997540	+	0.0700926i	$0.977671\pi$
$422$		0			0
$423$		−	5.10275i		−	0.248104i
$424$		0			0
$425$	15.5338	+	22.2203i	0.753502	+	1.07784i
$426$		0			0
$427$	4.64626			0.224848
$428$		0			0
$429$		−	16.6609i		−	0.804394i
$430$		0			0
$431$	6.29777			0.303353			0.151676	−	0.988430i	$-0.451533\pi$
$431$	6.29777			0.303353			0.151676	+	0.988430i	$0.451533\pi$
$432$		0			0
$433$	7.41338			0.356265			0.178132	−	0.984007i	$-0.442995\pi$
$433$	7.41338			0.356265			0.178132	+	0.984007i	$0.442995\pi$
$434$		0			0
$435$	10.3784	−	6.10648i	0.497605	−	0.292783i
$436$		0			0
$437$	−6.87379			−0.328818
$438$		0			0
$439$	11.1214			0.530797			0.265398	−	0.964139i	$-0.414497\pi$
$439$	11.1214			0.530797			0.265398	+	0.964139i	$0.414497\pi$
$440$		0			0
$441$			6.71484i			0.319754i
$442$		0			0
$443$	21.3327			1.01355			0.506774	−	0.862079i	$-0.330838\pi$
$443$	21.3327			1.01355			0.506774	+	0.862079i	$0.330838\pi$
$444$		0			0
$445$	−9.56699	−	30.3826i	−0.453519	−	1.44027i
$446$		0			0
$447$			12.2553i			0.579658i
$448$		0			0
$449$	−11.1407	−	11.1407i	−0.525764	−	0.525764i	0.393542	−	0.919307i	$-0.371250\pi$
$449$	−11.1407	−	11.1407i	−0.525764	−	0.525764i	−0.919307	+	0.393542i	$0.871250\pi$
$450$		0			0
$451$	−38.3011			−1.80353
$452$		0			0
$453$	3.80918			0.178971
$454$		0			0
$455$	−2.28904	+	4.39316i	−0.107312	+	0.205954i
$456$		0			0
$457$	−0.0768017	+	0.0768017i	−0.00359263	+	0.00359263i	−0.708901	−	0.705308i	$-0.750809\pi$
$457$	−0.0768017	+	0.0768017i	−0.00359263	+	0.00359263i	0.705308	+	0.708901i	$0.250809\pi$
$458$		0			0
$459$			5.42233i			0.253093i
$460$		0			0
$461$	−15.0059	−	15.0059i	−0.698896	−	0.698896i	0.265276	−	0.964172i	$-0.414537\pi$
$461$	−15.0059	−	15.0059i	−0.698896	−	0.698896i	−0.964172	+	0.265276i	$0.914537\pi$
$462$		0			0
$463$	6.43617	+	6.43617i	0.299114	+	0.299114i	0.840667	−	0.541553i	$-0.182163\pi$
$463$	6.43617	+	6.43617i	0.299114	+	0.299114i	−0.541553	+	0.840667i	$0.682163\pi$
$464$		0			0
$465$	4.23556	+	13.4512i	0.196420	+	0.623785i
$466$		0			0
$467$	−33.7415			−1.56137			−0.780686	−	0.624924i	$-0.785130\pi$
$467$	−33.7415			−1.56137			−0.780686	+	0.624924i	$0.785130\pi$
$468$		0			0
$469$	1.74482			0.0805685
$470$		0			0
$471$	16.9707			0.781970
$472$		0			0
$473$	−32.8842	−	32.8842i	−1.51202	−	1.51202i
$474$		0			0
$475$	−1.13283	+	6.39637i	−0.0519779	+	0.293485i
$476$		0			0
$477$	3.29698	−	3.29698i	0.150958	−	0.150958i
$478$		0			0
$479$	21.3015	−	21.3015i	0.973289	−	0.973289i	−0.0263632	−	0.999652i	$-0.508393\pi$
$479$	21.3015	−	21.3015i	0.973289	−	0.973289i	0.999652	+	0.0263632i	$0.00839263\pi$
$480$		0			0
$481$	19.1826	−	19.1826i	0.874651	−	0.874651i
$482$		0			0
$483$			2.82534i			0.128558i
$484$		0			0
$485$	3.42244	−	6.56840i	0.155405	−	0.298256i
$486$		0			0
$487$	−13.6094	−	13.6094i	−0.616701	−	0.616701i	0.327983	−	0.944684i	$-0.393631\pi$
$487$	−13.6094	−	13.6094i	−0.616701	−	0.616701i	−0.944684	+	0.327983i	$0.893631\pi$
$488$		0			0
$489$			18.1900i			0.822579i
$490$		0			0
$491$	11.1100	+	11.1100i	0.501389	+	0.501389i	0.911869	−	0.410481i	$-0.134639\pi$
$491$	11.1100	+	11.1100i	0.501389	+	0.501389i	−0.410481	+	0.911869i	$0.634639\pi$
$492$		0			0
$493$	−24.7614	−	15.4765i	−1.11520	−	0.697028i
$494$		0			0
$495$	−8.56545	+	2.69712i	−0.384988	+	0.121227i
$496$		0			0
$497$	−2.07780	+	2.07780i	−0.0932021	+	0.0932021i
$498$		0			0
$499$	−0.102509			−0.00458894			−0.00229447	−	0.999997i	$-0.500730\pi$
$499$	−0.102509			−0.00458894			−0.00229447	+	0.999997i	$0.500730\pi$
$500$		0			0
$501$	3.83817	+	3.83817i	0.171477	+	0.171477i
$502$		0			0
$503$	13.0576			0.582212			0.291106	−	0.956691i	$-0.405977\pi$
$503$	13.0576			0.582212			0.291106	+	0.956691i	$0.405977\pi$
$504$		0			0
$505$	36.5080	−	11.4958i	1.62459	−	0.511556i
$506$		0			0
$507$	4.21103			0.187019
$508$		0			0
$509$			24.9607i			1.10636i	0.833061	+	0.553182i	$0.186587\pi$
$509$			24.9607i			1.10636i	−0.833061	+	0.553182i	$0.813413\pi$
$510$		0			0
$511$	0.676048	+	0.676048i	0.0299066	+	0.0299066i
$512$		0			0
$513$	−0.918660	+	0.918660i	−0.0405598	+	0.0405598i
$514$		0			0
$515$	−23.0852	+	7.26914i	−1.01725	+	0.320317i
$516$		0			0
$517$	−14.4905	−	14.4905i	−0.637292	−	0.637292i
$518$		0			0
$519$	−0.514323	+	0.514323i	−0.0225763	+	0.0225763i
$520$		0			0
$521$			32.7477i			1.43470i	0.696712	+	0.717351i	$0.254646\pi$
$521$			32.7477i			1.43470i	−0.696712	+	0.717351i	$0.745354\pi$
$522$		0			0
$523$	25.1643	−	25.1643i	1.10036	−	1.10036i	0.105990	−	0.994367i	$-0.466199\pi$
$523$	25.1643	−	25.1643i	1.10036	−	1.10036i	0.994367	−	0.105990i	$-0.0338011\pi$
$524$		0			0
$525$	2.62911	+	0.465630i	0.114744	+	0.0203218i
$526$		0			0
$527$	24.1811	−	24.1811i	1.05335	−	1.05335i
$528$		0			0
$529$		−	4.99323i		−	0.217097i
$530$		0			0
$531$		−	1.80738i		−	0.0784336i
$532$		0			0
$533$		−	39.5659i		−	1.71379i
$534$		0			0
$535$	1.28783	+	4.08984i	0.0556775	+	0.176819i
$536$		0			0
$537$		−	19.1223i		−	0.825189i
$538$		0			0
$539$	19.0684	+	19.0684i	0.821335	+	0.821335i
$540$		0			0
$541$	−22.1178	+	22.1178i	−0.950916	+	0.950916i	−0.998851	−	0.0479340i	$-0.984736\pi$
$541$	−22.1178	+	22.1178i	−0.950916	+	0.950916i	0.0479340	+	0.998851i	$0.484736\pi$
$542$		0			0
$543$			17.5134i			0.751573i
$544$		0			0
$545$	−12.0398	−	6.27328i	−0.515726	−	0.268718i
$546$		0			0
$547$	30.3510	+	30.3510i	1.29772	+	1.29772i	0.929898	+	0.367817i	$0.119895\pi$
$547$	30.3510	+	30.3510i	1.29772	+	1.29772i	0.367817	+	0.929898i	$0.380105\pi$
$548$		0			0
$549$	−6.15238	+	6.15238i	−0.262577	+	0.262577i
$550$		0			0
$551$	−1.57306	−	6.81717i	−0.0670145	−	0.290421i
$552$		0			0
$553$		−	0.134656i		−	0.00572614i
$554$		0			0
$555$	−12.9672	−	6.75654i	−0.550429	−	0.286799i
$556$		0			0
$557$	5.56912	−	5.56912i	0.235971	−	0.235971i	−0.579208	−	0.815180i	$-0.696638\pi$
$557$	5.56912	−	5.56912i	0.235971	−	0.235971i	0.815180	+	0.579208i	$0.196638\pi$
$558$		0			0
$559$	33.9701	−	33.9701i	1.43678	−	1.43678i
$560$		0			0
$561$	15.3980	+	15.3980i	0.650105	+	0.650105i
$562$		0			0
$563$	3.30354			0.139227			0.0696137	−	0.997574i	$-0.477823\pi$
$563$	3.30354			0.139227			0.0696137	+	0.997574i	$0.477823\pi$
$564$		0			0
$565$	−5.26630	−	2.74399i	−0.221555	−	0.115440i
$566$		0			0
$567$	0.377598	+	0.377598i	0.0158576	+	0.0158576i
$568$		0			0
$569$	25.5065	−	25.5065i	1.06929	−	1.06929i	0.0718735	−	0.997414i	$-0.477102\pi$
$569$	25.5065	−	25.5065i	1.06929	−	1.06929i	0.997414	−	0.0718735i	$-0.0228978\pi$
$570$		0			0
$571$	−14.7988			−0.619309			−0.309654	−	0.950849i	$-0.600213\pi$
$571$	−14.7988			−0.619309			−0.309654	+	0.950849i	$0.600213\pi$
$572$		0			0
$573$	0.499842	+	0.499842i	0.0208812	+	0.0208812i
$574$		0			0
$575$	−26.0489	−	4.61342i	−1.08632	−	0.192393i
$576$		0			0
$577$			16.0430i			0.667878i	0.942595	+	0.333939i	$0.108378\pi$
$577$			16.0430i			0.667878i	−0.942595	+	0.333939i	$0.891622\pi$
$578$		0			0
$579$	−21.3077			−0.885517
$580$		0			0
$581$	1.14570			0.0475317
$582$		0			0
$583$		−	18.7251i		−	0.775516i
$584$		0			0
$585$	−2.78618	−	8.84830i	−0.115195	−	0.365832i
$586$		0			0
$587$	6.86906	+	6.86906i	0.283516	+	0.283516i	0.834510	−	0.550993i	$-0.185751\pi$
$587$	6.86906	+	6.86906i	0.283516	+	0.283516i	−0.550993	+	0.834510i	$0.685751\pi$
$588$		0			0
$589$	8.19360			0.337611
$590$		0			0
$591$	−8.94004	+	8.94004i	−0.367744	+	0.367744i
$592$		0			0
$593$	−33.7607	−	33.7607i	−1.38638	−	1.38638i	−0.832779	−	0.553605i	$-0.813252\pi$
$593$	−33.7607	−	33.7607i	−1.38638	−	1.38638i	−0.553605	−	0.832779i	$-0.686748\pi$
$594$		0			0
$595$	−1.94463	−	6.17572i	−0.0797222	−	0.253180i
$596$		0			0
$597$	−0.350184			−0.0143321
$598$		0			0
$599$	0.0378029	+	0.0378029i	0.00154458	+	0.00154458i	0.707879	−	0.706334i	$-0.249652\pi$
$599$	0.0378029	+	0.0378029i	0.00154458	+	0.00154458i	−0.706334	+	0.707879i	$0.749652\pi$
$600$		0			0
$601$	−1.35035	+	1.35035i	−0.0550820	+	0.0550820i	−0.734111	−	0.679029i	$-0.762401\pi$
$601$	−1.35035	+	1.35035i	−0.0550820	+	0.0550820i	0.679029	+	0.734111i	$0.262401\pi$
$602$		0			0
$603$	−2.31042	+	2.31042i	−0.0940878	+	0.0940878i
$604$		0			0
$605$	−5.29879	+	10.1695i	−0.215426	+	0.413449i
$606$		0			0
$607$			12.0660i			0.489743i	0.969555	+	0.244872i	$0.0787459\pi$
$607$			12.0660i			0.489743i	−0.969555	+	0.244872i	$0.921254\pi$
$608$		0			0
$609$	−2.80207	+	0.646576i	−0.113546	+	0.0262006i
$610$		0			0
$611$	14.9690	−	14.9690i	0.605581	−	0.605581i
$612$		0			0
$613$	16.1190	+	16.1190i	0.651040	+	0.651040i	0.953243	−	0.302204i	$-0.0977223\pi$
$613$	16.1190	+	16.1190i	0.651040	+	0.651040i	−0.302204	+	0.953243i	$0.597722\pi$
$614$		0			0
$615$	−20.3410	+	6.40506i	−0.820230	+	0.258277i
$616$		0			0
$617$			40.3881i			1.62596i	0.582289	+	0.812982i	$0.302157\pi$
$617$			40.3881i			1.62596i	−0.582289	+	0.812982i	$0.697843\pi$
$618$		0			0
$619$	−27.1814	+	27.1814i	−1.09251	+	1.09251i	−0.0972529	+	0.995260i	$0.531006\pi$
$619$	−27.1814	+	27.1814i	−1.09251	+	1.09251i	−0.995260	+	0.0972529i	$0.968994\pi$
$620$		0			0
$621$	−3.74121	−	3.74121i	−0.150129	−	0.150129i
$622$		0			0
$623$			7.60701i			0.304768i
$624$		0			0
$625$	−8.58597	+	23.4794i	−0.343439	+	0.939175i
$626$		0			0
$627$			5.21751i			0.208367i
$628$		0			0
$629$			35.4573i			1.41377i
$630$		0			0
$631$		−	17.9369i		−	0.714056i	−0.934094	−	0.357028i	$-0.883790\pi$
$631$		−	17.9369i		−	0.714056i	0.934094	−	0.357028i	$-0.116210\pi$
$632$		0			0
$633$	14.0873	−	14.0873i	0.559921	−	0.559921i
$634$		0			0
$635$	−17.1210	−	8.92085i	−0.679426	−	0.354013i
$636$		0			0
$637$	−19.6981	+	19.6981i	−0.780467	+	0.780467i
$638$		0			0
$639$		−	5.50267i		−	0.217682i
$640$		0			0
$641$	20.4023	−	20.4023i	0.805843	−	0.805843i	−0.178159	−	0.984002i	$-0.557014\pi$
$641$	20.4023	−	20.4023i	0.805843	−	0.805843i	0.984002	+	0.178159i	$0.0570140\pi$
$642$		0			0
$643$	−23.2686	−	23.2686i	−0.917625	−	0.917625i	0.0792314	−	0.996856i	$-0.474753\pi$
$643$	−23.2686	−	23.2686i	−0.917625	−	0.917625i	−0.996856	+	0.0792314i	$0.974753\pi$
$644$		0			0
$645$	−22.9635	−	11.9650i	−0.904185	−	0.471123i
$646$		0			0
$647$	3.40335	−	3.40335i	0.133799	−	0.133799i	−0.637035	−	0.770835i	$-0.719839\pi$
$647$	3.40335	−	3.40335i	0.133799	−	0.133799i	0.770835	+	0.637035i	$0.219839\pi$
$648$		0			0
$649$	−5.13249	−	5.13249i	−0.201468	−	0.201468i
$650$		0			0
$651$		−	3.36783i		−	0.131996i
$652$		0			0
$653$	0.0401133			0.00156975			0.000784877	−	1.00000i	$-0.499750\pi$
$653$	0.0401133			0.00156975			0.000784877		1.00000i	$0.499750\pi$
$654$		0			0
$655$	−11.7541	−	37.3283i	−0.459270	−	1.45854i
$656$		0			0
$657$	−1.79039			−0.0698497
$658$		0			0
$659$	5.57800	+	5.57800i	0.217288	+	0.217288i	0.807355	−	0.590066i	$-0.200898\pi$
$659$	5.57800	+	5.57800i	0.217288	+	0.217288i	−0.590066	+	0.807355i	$0.700898\pi$
$660$		0			0
$661$	−15.7049			−0.610848			−0.305424	−	0.952216i	$-0.598798\pi$
$661$	−15.7049			−0.610848			−0.305424	+	0.952216i	$0.598798\pi$
$662$		0			0
$663$	−15.9065	+	15.9065i	−0.617757	+	0.617757i
$664$		0			0
$665$	0.716837	−	1.37576i	0.0277977	−	0.0533498i
$666$		0			0
$667$	27.7626	−	6.40621i	1.07497	−	0.248049i
$668$		0			0
$669$	18.0388	+	18.0388i	0.697421	+	0.697421i
$670$		0			0
$671$			34.9424i			1.34893i
$672$		0			0
$673$	19.2758	+	19.2758i	0.743028	+	0.743028i	0.973160	−	0.230132i	$-0.0739156\pi$
$673$	19.2758	+	19.2758i	0.743028	+	0.743028i	−0.230132	+	0.973160i	$0.573916\pi$
$674$		0			0
$675$	−4.09792	+	2.86479i	−0.157729	+	0.110266i
$676$		0			0
$677$		−	19.8901i		−	0.764438i	−0.924072	−	0.382219i	$-0.875160\pi$
$677$		−	19.8901i		−	0.764438i	0.924072	−	0.382219i	$-0.124840\pi$
$678$		0			0
$679$	−1.25072	+	1.25072i	−0.0479983	+	0.0479983i
$680$		0			0
$681$	−8.97456	+	8.97456i	−0.343906	+	0.343906i
$682$		0			0
$683$	4.00643	−	4.00643i	0.153302	−	0.153302i	−0.626289	−	0.779591i	$-0.715427\pi$
$683$	4.00643	−	4.00643i	0.153302	−	0.153302i	0.779591	+	0.626289i	$0.215427\pi$
$684$		0			0
$685$	34.2071	+	17.8235i	1.30699	+	0.681002i
$686$		0			0
$687$	−13.3171	−	13.3171i	−0.508081	−	0.508081i
$688$		0			0
$689$	19.3435			0.736928
$690$		0			0
$691$	35.0459			1.33321			0.666605	−	0.745411i	$-0.267747\pi$
$691$	35.0459			1.33321			0.666605	+	0.745411i	$0.267747\pi$
$692$		0			0
$693$	2.14456			0.0814652
$694$		0			0
$695$	11.9496	−	22.9339i	0.453275	−	0.869932i
$696$		0			0
$697$	36.5669	+	36.5669i	1.38507	+	1.38507i
$698$		0			0
$699$	16.7342	+	16.7342i	0.632944	+	0.632944i
$700$		0			0
$701$			8.32138i			0.314294i	0.987575	+	0.157147i	$0.0502297\pi$
$701$			8.32138i			0.314294i	−0.987575	+	0.157147i	$0.949770\pi$
$702$		0			0
$703$	−6.00722	+	6.00722i	−0.226567	+	0.226567i
$704$		0			0
$705$	−10.1189	−	5.27242i	−0.381100	−	0.198571i
$706$		0			0
$707$	−9.14065			−0.343770
$708$		0			0
$709$	49.8400			1.87178			0.935891	−	0.352290i	$-0.114597\pi$
$709$	49.8400			1.87178			0.935891	+	0.352290i	$0.114597\pi$
$710$		0			0
$711$	0.178306	+	0.178306i	0.00668698	+	0.00668698i
$712$		0			0
$713$			33.3681i			1.24965i
$714$		0			0
$715$	−33.0389	−	17.2148i	−1.23559	−	0.643798i
$716$		0			0
$717$	−3.53427			−0.131990
$718$		0			0
$719$		−	3.66305i		−	0.136609i	−0.997665	−	0.0683043i	$-0.978241\pi$
$719$		−	3.66305i		−	0.136609i	0.997665	−	0.0683043i	$-0.0217589\pi$
$720$		0			0
$721$	5.77992			0.215255
$722$		0			0
$723$	−10.4423			−0.388353
$724$		0			0
$725$	−1.38585	−	26.8901i	−0.0514691	−	0.998675i
$726$		0			0
$727$	11.7765			0.436767			0.218384	−	0.975863i	$-0.429922\pi$
$727$	11.7765			0.436767			0.218384	+	0.975863i	$0.429922\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$			62.7906i			2.32240i
$732$		0			0
$733$	44.8890			1.65801			0.829007	−	0.559239i	$-0.188907\pi$
$733$	44.8890			1.65801			0.829007	+	0.559239i	$0.188907\pi$
$734$		0			0
$735$	13.3157	+	6.93811i	0.491157	+	0.255916i
$736$		0			0
$737$			13.1220i			0.483356i
$738$		0			0
$739$	29.0735	+	29.0735i	1.06949	+	1.06949i	0.997398	+	0.0720891i	$0.0229666\pi$
$739$	29.0735	+	29.0735i	1.06949	+	1.06949i	0.0720891	+	0.997398i	$0.477033\pi$
$740$		0			0
$741$	−5.38981			−0.197999
$742$		0			0
$743$	33.7767			1.23915			0.619574	−	0.784939i	$-0.287306\pi$
$743$	33.7767			1.23915			0.619574	+	0.784939i	$0.287306\pi$
$744$		0			0
$745$	24.3027	+	12.6628i	0.890381	+	0.463930i
$746$		0			0
$747$	−1.51709	+	1.51709i	−0.0555075	+	0.0555075i
$748$		0			0
$749$		−	1.02399i		−	0.0374158i
$750$		0			0
$751$	−25.4756	−	25.4756i	−0.929618	−	0.929618i	0.0680628	−	0.997681i	$-0.478318\pi$
$751$	−25.4756	−	25.4756i	−0.929618	−	0.929618i	−0.997681	+	0.0680628i	$0.978318\pi$
$752$		0			0
$753$	20.1681	+	20.1681i	0.734967	+	0.734967i
$754$		0			0
$755$	3.93583	−	7.55370i	0.143240	−	0.274907i
$756$		0			0
$757$	−10.0465			−0.365146			−0.182573	−	0.983192i	$-0.558443\pi$
$757$	−10.0465			−0.365146			−0.182573	+	0.983192i	$0.558443\pi$
$758$		0			0
$759$	−21.2481			−0.771258
$760$		0			0
$761$	25.0662			0.908648			0.454324	−	0.890837i	$-0.349881\pi$
$761$	25.0662			0.908648			0.454324	+	0.890837i	$0.349881\pi$
$762$		0			0
$763$	2.29255	+	2.29255i	0.0829959	+	0.0829959i
$764$		0			0
$765$	10.7526	+	5.60263i	0.388762	+	0.202563i
$766$		0			0
$767$	5.30198	−	5.30198i	0.191443	−	0.191443i
$768$		0			0
$769$	−11.5564	+	11.5564i	−0.416733	+	0.416733i	−0.884076	−	0.467343i	$-0.845211\pi$
$769$	−11.5564	+	11.5564i	−0.416733	+	0.416733i	0.467343	+	0.884076i	$0.345211\pi$
$770$		0			0
$771$	−19.2203	+	19.2203i	−0.692203	+	0.692203i
$772$		0			0
$773$		−	21.8837i		−	0.787101i	−0.919303	−	0.393550i	$-0.871247\pi$
$773$		−	21.8837i		−	0.787101i	0.919303	−	0.393550i	$-0.128753\pi$
$774$		0			0
$775$	31.0505	+	5.49922i	1.11537	+	0.197538i
$776$		0			0
$777$	2.46916	+	2.46916i	0.0885806	+	0.0885806i
$778$		0			0
$779$			12.3904i			0.443934i
$780$		0			0
$781$	−15.6262	−	15.6262i	−0.559149	−	0.559149i
$782$		0			0
$783$	2.85422	−	4.56656i	0.102001	−	0.163195i
$784$		0			0
$785$	17.5350	−	33.6534i	0.625851	−	1.20114i
$786$		0			0
$787$	−10.8294	+	10.8294i	−0.386027	+	0.386027i	−0.873268	−	0.487241i	$-0.838003\pi$
$787$	−10.8294	+	10.8294i	−0.386027	+	0.386027i	0.487241	+	0.873268i	$0.338003\pi$
$788$		0			0
$789$	29.0825			1.03536
$790$		0			0
$791$	1.00278	+	1.00278i	0.0356548	+	0.0356548i
$792$		0			0
$793$	−36.0962			−1.28181
$794$		0			0
$795$	−3.13139	−	9.94460i	−0.111059	−	0.352698i
$796$		0			0
$797$	19.8698			0.703824			0.351912	−	0.936033i	$-0.385532\pi$
$797$	19.8698			0.703824			0.351912	+	0.936033i	$0.385532\pi$
$798$		0			0
$799$			27.6688i			0.978853i
$800$		0			0
$801$	−10.0729	−	10.0729i	−0.355908	−	0.355908i
$802$		0			0
$803$	−5.08424	+	5.08424i	−0.179419	+	0.179419i
$804$		0			0
$805$	5.60273	+	2.91929i	0.197470	+	0.102891i
$806$		0			0
$807$	−6.53556	−	6.53556i	−0.230062	−	0.230062i
$808$		0			0
$809$	−28.3698	+	28.3698i	−0.997430	+	0.997430i	−0.999997	−	0.00256626i	$-0.999183\pi$
$809$	−28.3698	+	28.3698i	−0.997430	+	0.997430i	0.00256626	+	0.999997i	$0.499183\pi$
$810$		0			0
$811$			37.7726i			1.32638i	0.748453	+	0.663188i	$0.230797\pi$
$811$			37.7726i			1.32638i	−0.748453	+	0.663188i	$0.769203\pi$
$812$		0			0
$813$	20.6798	−	20.6798i	0.725272	−	0.725272i
$814$		0			0
$815$	36.0712	+	18.7948i	1.26352	+	0.658353i
$816$		0			0
$817$	−10.6381	+	10.6381i	−0.372179	+	0.372179i
$818$		0			0
$819$			2.21538i			0.0774117i
$820$		0			0
$821$		−	19.0162i		−	0.663671i	−0.943337	−	0.331836i	$-0.892332\pi$
$821$		−	19.0162i		−	0.663671i	0.943337	−	0.331836i	$-0.107668\pi$
$822$		0			0
$823$			41.3158i			1.44018i	0.693881	+	0.720090i	$0.255899\pi$
$823$			41.3158i			1.44018i	−0.693881	+	0.720090i	$0.744101\pi$
$824$		0			0
$825$	−3.50179	+	19.7723i	−0.121917	+	0.688384i
$826$		0			0
$827$		−	30.9484i		−	1.07618i	−0.842887	−	0.538091i	$-0.819146\pi$
$827$		−	30.9484i		−	1.07618i	0.842887	−	0.538091i	$-0.180854\pi$
$828$		0			0
$829$	−21.3285	−	21.3285i	−0.740769	−	0.740769i	0.231957	−	0.972726i	$-0.425487\pi$
$829$	−21.3285	−	21.3285i	−0.740769	−	0.740769i	−0.972726	+	0.231957i	$0.925487\pi$
$830$		0			0
$831$	14.0705	−	14.0705i	0.488099	−	0.488099i
$832$		0			0
$833$		−	36.4101i		−	1.26154i
$834$		0			0
$835$	11.5770	−	3.64541i	0.400638	−	0.126154i
$836$		0			0
$837$	4.45954	+	4.45954i	0.154144	+	0.154144i
$838$		0			0
$839$	−29.4872	+	29.4872i	−1.01801	+	1.01801i	−0.0181779	+	0.999835i	$0.505787\pi$
$839$	−29.4872	+	29.4872i	−1.01801	+	1.01801i	−0.999835	+	0.0181779i	$0.994213\pi$
$840$		0			0
$841$	12.7069	+	26.0679i	0.438168	+	0.898893i
$842$		0			0
$843$			14.3473i			0.494148i
$844$		0			0
$845$	4.35105	−	8.35059i	0.149681	−	0.287269i
$846$		0			0
$847$	1.93643	−	1.93643i	0.0665364	−	0.0665364i
$848$		0			0
$849$	−7.32276	+	7.32276i	−0.251316	+	0.251316i
$850$		0			0
$851$	−24.4642	−	24.4642i	−0.838621	−	0.838621i
$852$		0			0
$853$	−34.6831			−1.18753			−0.593763	−	0.804640i	$-0.702358\pi$
$853$	−34.6831			−1.18753			−0.593763	+	0.804640i	$0.702358\pi$
$854$		0			0
$855$	0.872522	+	2.77093i	0.0298396	+	0.0947639i
$856$		0			0
$857$	23.8368	+	23.8368i	0.814249	+	0.814249i	0.985268	−	0.171019i	$-0.0547060\pi$
$857$	23.8368	+	23.8368i	0.814249	+	0.814249i	−0.171019	+	0.985268i	$0.554706\pi$
$858$		0			0
$859$	21.5103	−	21.5103i	0.733922	−	0.733922i	−0.237472	−	0.971394i	$-0.576319\pi$
$859$	21.5103	−	21.5103i	0.733922	−	0.733922i	0.971394	+	0.237472i	$0.0763188\pi$
$860$		0			0
$861$	5.09286			0.173564
$862$		0			0
$863$	−1.46109	−	1.46109i	−0.0497360	−	0.0497360i	0.681801	−	0.731537i	$-0.261197\pi$
$863$	−1.46109	−	1.46109i	−0.0497360	−	0.0497360i	−0.731537	+	0.681801i	$0.761197\pi$
$864$		0			0
$865$	0.488492	+	1.55134i	0.0166092	+	0.0527472i
$866$		0			0
$867$		−	12.4017i		−	0.421184i
$868$		0			0
$869$	1.01268			0.0343529
$870$		0			0
$871$	−13.5553			−0.459305
$872$		0			0
$873$		−	3.31231i		−	0.112105i
$874$		0			0
$875$	3.63988	−	4.73248i	0.123051	−	0.159987i
$876$		0			0
$877$	14.7667	+	14.7667i	0.498637	+	0.498637i	0.911013	−	0.412377i	$-0.135301\pi$
$877$	14.7667	+	14.7667i	0.498637	+	0.498637i	−0.412377	+	0.911013i	$0.635301\pi$
$878$		0			0
$879$	−6.12781			−0.206686
$880$		0			0
$881$	39.9760	−	39.9760i	1.34683	−	1.34683i	0.457740	−	0.889086i	$-0.348659\pi$
$881$	39.9760	−	39.9760i	1.34683	−	1.34683i	0.889086	−	0.457740i	$-0.151341\pi$
$882$		0			0
$883$	−6.56378	−	6.56378i	−0.220889	−	0.220889i	0.587984	−	0.808873i	$-0.299922\pi$
$883$	−6.56378	−	6.56378i	−0.220889	−	0.220889i	−0.808873	+	0.587984i	$0.799922\pi$
$884$		0			0
$885$	−3.58408	−	1.86747i	−0.120478	−	0.0627745i
$886$		0			0
$887$	28.4365			0.954805			0.477402	−	0.878685i	$-0.341578\pi$
$887$	28.4365			0.954805			0.477402	+	0.878685i	$0.341578\pi$
$888$		0			0
$889$	3.26010	+	3.26010i	0.109340	+	0.109340i
$890$		0			0
$891$	−2.83974	+	2.83974i	−0.0951349	+	0.0951349i
$892$		0			0
$893$	−4.68769	+	4.68769i	−0.156868	+	0.156868i
$894$		0			0
$895$	−37.9201	−	19.7581i	−1.26753	−	0.660442i
$896$		0			0
$897$		−	21.9498i		−	0.732882i
$898$		0			0
$899$	−33.0932	+	7.63624i	−1.10372	+	0.254683i
$900$		0			0
$901$	−17.8773	+	17.8773i	−0.595580	+	0.595580i
$902$		0			0
$903$	4.37259	+	4.37259i	0.145511	+	0.145511i
$904$		0			0
$905$	34.7296	+	18.0957i	1.15445	+	0.601523i
$906$		0			0
$907$			31.4844i			1.04542i	0.852510	+	0.522711i	$0.175079\pi$
$907$			31.4844i			1.04542i	−0.852510	+	0.522711i	$0.824921\pi$
$908$		0			0
$909$	12.1037	−	12.1037i	0.401454	−	0.401454i
$910$		0			0
$911$	16.4040	+	16.4040i	0.543488	+	0.543488i	0.924550	−	0.381062i	$-0.124441\pi$
$911$	16.4040	+	16.4040i	0.543488	+	0.543488i	−0.381062	+	0.924550i	$0.624441\pi$
$912$		0			0
$913$			8.61630i			0.285158i
$914$		0			0
$915$	5.84339	+	18.5573i	0.193176	+	0.613485i
$916$		0			0
$917$			9.34603i			0.308633i
$918$		0			0
$919$		−	13.3908i		−	0.441721i	−0.975305	−	0.220861i	$-0.929113\pi$
$919$		−	13.3908i		−	0.441721i	0.975305	−	0.220861i	$-0.0708866\pi$
$920$		0			0
$921$			16.0771i			0.529760i
$922$		0			0
$923$	16.1422	−	16.1422i	0.531326	−	0.531326i
$924$		0			0
$925$	−26.7968	+	18.7332i	−0.881074	+	0.615943i
$926$		0			0
$927$	−7.65353	+	7.65353i	−0.251375	+	0.251375i
$928$		0			0
$929$			48.8551i			1.60289i	0.598072	+	0.801443i	$0.295934\pi$
$929$			48.8551i			1.60289i	−0.598072	+	0.801443i	$0.704066\pi$
$930$		0			0
$931$	6.16865	−	6.16865i	0.202169	−	0.202169i
$932$		0			0
$933$	−18.0492	−	18.0492i	−0.590906	−	0.590906i
$934$		0			0
$935$	46.4447	−	14.6247i	1.51890	−	0.478278i
$936$		0			0
$937$	−6.57870	+	6.57870i	−0.214917	+	0.214917i	−0.806352	−	0.591435i	$-0.798561\pi$
$937$	−6.57870	+	6.57870i	−0.214917	+	0.214917i	0.591435	+	0.806352i	$0.298561\pi$
$938$		0			0
$939$	5.01014	+	5.01014i	0.163500	+	0.163500i
$940$		0			0
$941$			33.8776i			1.10438i	0.833719	+	0.552189i	$0.186207\pi$
$941$			33.8776i			1.10438i	−0.833719	+	0.552189i	$0.813793\pi$
$942$		0			0
$943$	−50.4596			−1.64319
$944$		0			0
$945$	1.13894	−	0.358634i	0.0370497	−	0.0116664i
$946$		0			0
$947$	5.74167			0.186579			0.0932896	−	0.995639i	$-0.470262\pi$
$947$	5.74167			0.186579			0.0932896	+	0.995639i	$0.470262\pi$
$948$		0			0
$949$	−5.25214	−	5.25214i	−0.170492	−	0.170492i
$950$		0			0
$951$	23.0626			0.747857
$952$		0			0
$953$	−31.5203	+	31.5203i	−1.02104	+	1.02104i	−0.0212679	+	0.999774i	$0.506770\pi$
$953$	−31.5203	+	31.5203i	−1.02104	+	1.02104i	−0.999774	+	0.0212679i	$0.993230\pi$
$954$		0			0
$955$	1.50766	−	0.474738i	0.0487868	−	0.0153622i
$956$		0			0
$957$	−4.86260	−	21.0731i	−0.157186	−	0.681196i
$958$		0			0
$959$	−6.51356	−	6.51356i	−0.210334	−	0.210334i
$960$		0			0
$961$		−	8.77497i		−	0.283064i
$962$		0			0
$963$	1.35592	+	1.35592i	0.0436941	+	0.0436941i
$964$		0			0
$965$	−22.0162	+	42.2537i	−0.708725	+	1.36019i
$966$		0			0
$967$			49.5135i			1.59225i	0.605135	+	0.796123i	$0.293119\pi$
$967$			49.5135i			1.59225i	−0.605135	+	0.796123i	$0.706881\pi$
$968$		0			0
$969$	4.98128	−	4.98128i	0.160022	−	0.160022i
$970$		0			0
$971$	40.6556	−	40.6556i	1.30470	−	1.30470i	0.379517	−	0.925185i	$-0.376090\pi$
$971$	40.6556	−	40.6556i	1.30470	−	1.30470i	0.925185	−	0.379517i	$-0.123910\pi$
$972$		0			0
$973$	−4.36696	+	4.36696i	−0.139998	+	0.139998i
$974$		0			0
$975$	−20.4252	−	3.61742i	−0.654131	−	0.115850i
$976$		0			0
$977$	24.0951	+	24.0951i	0.770872	+	0.770872i	0.978259	−	0.207387i	$-0.0664960\pi$
$977$	24.0951	+	24.0951i	0.770872	+	0.770872i	−0.207387	+	0.978259i	$0.566496\pi$
$978$		0			0
$979$	−57.2088			−1.82840
$980$		0			0
$981$	−6.07140			−0.193845
$982$		0			0
$983$	−33.2209			−1.05958			−0.529790	−	0.848129i	$-0.677729\pi$
$983$	−33.2209			−1.05958			−0.529790	+	0.848129i	$0.677729\pi$
$984$		0			0
$985$	8.49104	+	26.9656i	0.270547	+	0.859196i
$986$		0			0
$987$	1.92679	+	1.92679i	0.0613304	+	0.0613304i
$988$		0			0
$989$	−43.3232	−	43.3232i	−1.37760	−	1.37760i
$990$		0			0
$991$		−	24.7495i		−	0.786194i	−0.919497	−	0.393097i	$-0.871404\pi$
$991$		−	24.7495i		−	0.786194i	0.919497	−	0.393097i	$-0.128596\pi$
$992$		0			0
$993$	3.42940	−	3.42940i	0.108829	−	0.108829i
$994$		0			0
$995$	−0.361827	+	0.694424i	−0.0114707	+	0.0220147i
$996$		0			0
$997$	−17.8353			−0.564850			−0.282425	−	0.959289i	$-0.591139\pi$
$997$	−17.8353			−0.564850			−0.282425	+	0.959289i	$0.591139\pi$
$998$		0			0
$999$	−6.53912			−0.206889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1740.2.bc.c.1177.3	yes	30
5.3	odd	4		1740.2.bb.c.133.13	✓	30
29.12	odd	4		1740.2.bb.c.157.13	yes	30
145.128	even	4	inner	1740.2.bc.c.853.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1740.2.bb.c.133.13	✓	30	5.3	odd	4
1740.2.bb.c.157.13	yes	30	29.12	odd	4
1740.2.bc.c.853.3	yes	30	145.128	even	4	inner
1740.2.bc.c.1177.3	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1740.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{3} +(-1.98303 - 1.03325i) q^{5} +(0.377598 + 0.377598i) q^{7} -1.00000 q^{9} +(-2.83974 + 2.83974i) q^{11} +(-2.93352 - 2.93352i) q^{13} +(-1.03325 + 1.98303i) q^{15} +5.42233 q^{17} +(0.918660 + 0.918660i) q^{19} +(0.377598 - 0.377598i) q^{21} +(-3.74121 + 3.74121i) q^{23} +(2.86479 + 4.09792i) q^{25} +1.00000i q^{27} +(-4.56656 - 2.85422i) q^{29} +(4.45954 - 4.45954i) q^{31} +(2.83974 + 2.83974i) q^{33} +(-0.358634 - 1.13894i) q^{35} +6.53912i q^{37} +(-2.93352 + 2.93352i) q^{39} +(6.74376 + 6.74376i) q^{41} +11.5800i q^{43} +(1.98303 + 1.03325i) q^{45} +5.10275i q^{47} -6.71484i q^{49} -5.42233i q^{51} +(-3.29698 + 3.29698i) q^{53} +(8.56545 - 2.69712i) q^{55} +(0.918660 - 0.918660i) q^{57} +1.80738i q^{59} +(6.15238 - 6.15238i) q^{61} +(-0.377598 - 0.377598i) q^{63} +(2.78618 + 8.84830i) q^{65} +(2.31042 - 2.31042i) q^{67} +(3.74121 + 3.74121i) q^{69} +5.50267i q^{71} +1.79039 q^{73} +(4.09792 - 2.86479i) q^{75} -2.14456 q^{77} +(-0.178306 - 0.178306i) q^{79} +1.00000 q^{81} +(1.51709 - 1.51709i) q^{83} +(-10.7526 - 5.60263i) q^{85} +(-2.85422 + 4.56656i) q^{87} +(10.0729 + 10.0729i) q^{89} -2.21538i q^{91} +(-4.45954 - 4.45954i) q^{93} +(-0.872522 - 2.77093i) q^{95} +3.31231i q^{97} +(2.83974 - 2.83974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 30 q^{9} + 4 q^{11} - 6 q^{13} - 6 q^{15} + 8 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{33} - 16 q^{35} - 6 q^{39} - 10 q^{41} - 6 q^{53} + 4 q^{55} + 8 q^{57} + 30 q^{61} - 2 q^{65} + 4 q^{67} + 12 q^{73}+ \cdots - 4 q^{99}+O(q^{100}) \) 30 * q - 30 * q^9 + 4 * q^11 - 6 * q^13 - 6 * q^15 + 8 * q^19 - 6 * q^25 + 4 * q^29 - 4 * q^33 - 16 * q^35 - 6 * q^39 - 10 * q^41 - 6 * q^53 + 4 * q^55 + 8 * q^57 + 30 * q^61 - 2 * q^65 + 4 * q^67 + 12 * q^73 + 8 * q^75 - 4 * q^77 - 4 * q^79 + 30 * q^81 - 28 * q^83 + 20 * q^85 + 10 * q^87 + 10 * q^89 + 20 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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