LMFDB - Embedded newform 504.3.l.h.181.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(181,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.181"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.14
Character	$\chi$	$=$	504.181
Dual form			504.3.l.h.181.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.172794 - 1.99252i) q^{2} +(-3.94028 + 0.688593i) q^{4} +6.16756 q^{5} +(6.35406 - 2.93700i) q^{7} +(2.05289 + 7.73212i) q^{8} +(-1.06572 - 12.2890i) q^{10} +6.45991i q^{11} +5.92263 q^{13} +(-6.94998 - 12.1531i) q^{14} +(15.0517 - 5.42650i) q^{16} +29.7070i q^{17} -7.53626 q^{19} +(-24.3019 + 4.24694i) q^{20} +(12.8715 - 1.11624i) q^{22} +40.1517 q^{23} +13.0388 q^{25} +(-1.02340 - 11.8010i) q^{26} +(-23.0144 + 15.9480i) q^{28} +19.5496i q^{29} +20.7829i q^{31} +(-13.4133 - 29.0531i) q^{32} +(59.1918 - 5.13320i) q^{34} +(39.1890 - 18.1141i) q^{35} -43.3864i q^{37} +(1.30222 + 15.0162i) q^{38} +(12.6614 + 47.6883i) q^{40} +43.0046i q^{41} -27.7017i q^{43} +(-4.44825 - 25.4539i) q^{44} +(-6.93799 - 80.0032i) q^{46} -75.5771i q^{47} +(31.7481 - 37.3237i) q^{49} +(-2.25303 - 25.9801i) q^{50} +(-23.3368 + 4.07828i) q^{52} -36.6740i q^{53} +39.8419i q^{55} +(35.7534 + 43.1010i) q^{56} +(38.9531 - 3.37807i) q^{58} +21.9834 q^{59} -49.7137 q^{61} +(41.4103 - 3.59116i) q^{62} +(-55.5712 + 31.7464i) q^{64} +36.5282 q^{65} -106.648i q^{67} +(-20.4560 - 117.054i) q^{68} +(-42.8644 - 74.9550i) q^{70} +84.5125 q^{71} +67.2164i q^{73} +(-86.4484 + 7.49693i) q^{74} +(29.6950 - 5.18941i) q^{76} +(18.9728 + 41.0467i) q^{77} +19.2213 q^{79} +(92.8321 - 33.4683i) q^{80} +(85.6876 - 7.43095i) q^{82} -122.024 q^{83} +183.220i q^{85} +(-55.1962 + 4.78669i) q^{86} +(-49.9488 + 13.2615i) q^{88} +43.7186i q^{89} +(37.6327 - 17.3948i) q^{91} +(-158.209 + 27.6482i) q^{92} +(-150.589 + 13.0593i) q^{94} -46.4803 q^{95} -151.843i q^{97} +(-79.8542 - 56.8094i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−0.172794	−	1.99252i	−0.0863972	−	0.996261i
$2$	−0.172794	−	1.99252i	−0.0863972	−	0.996261i
$3$		0			0
$3$		0			0
$4$	−3.94028	+	0.688593i	−0.985071	+	0.172148i
$5$	6.16756			1.23351			0.616756	−	0.787154i	$-0.288447\pi$
$5$	6.16756			1.23351			0.616756	+	0.787154i	$0.288447\pi$
$6$		0			0
$7$	6.35406	−	2.93700i	0.907722	−	0.419571i
$7$	6.35406	−	2.93700i	0.907722	−	0.419571i
$8$	2.05289	+	7.73212i	0.256612	+	0.966515i
$9$		0			0
$10$	−1.06572	−	12.2890i	−0.106572	−	1.22890i
$11$			6.45991i			0.587265i	0.955918	+	0.293632i	$0.0948642\pi$
$11$			6.45991i			0.587265i	−0.955918	+	0.293632i	$0.905136\pi$
$12$		0			0
$13$	5.92263			0.455587			0.227793	−	0.973709i	$-0.426849\pi$
$13$	5.92263			0.455587			0.227793	+	0.973709i	$0.426849\pi$
$14$	−6.94998	−	12.1531i	−0.496427	−	0.868078i
$15$		0			0
$16$	15.0517	−	5.42650i	0.940730	−	0.339156i
$17$			29.7070i			1.74747i	0.486402	+	0.873735i	$0.338309\pi$
$17$			29.7070i			1.74747i	−0.486402	+	0.873735i	$0.661691\pi$
$18$		0			0
$19$	−7.53626			−0.396645			−0.198323	−	0.980137i	$-0.563549\pi$
$19$	−7.53626			−0.396645			−0.198323	+	0.980137i	$0.563549\pi$
$20$	−24.3019	+	4.24694i	−1.21510	+	0.212347i
$21$		0			0
$22$	12.8715	−	1.11624i	0.585069	−	0.0507380i
$23$	40.1517			1.74573			0.872863	−	0.487965i	$-0.162260\pi$
$23$	40.1517			1.74573			0.872863	+	0.487965i	$0.162260\pi$
$24$		0			0
$25$	13.0388			0.521552
$26$	−1.02340	−	11.8010i	−0.0393614	−	0.453883i
$27$		0			0
$28$	−23.0144	+	15.9480i	−0.821943	+	0.569570i
$29$			19.5496i			0.674125i	0.941482	+	0.337063i	$0.109433\pi$
$29$			19.5496i			0.674125i	−0.941482	+	0.337063i	$0.890567\pi$
$30$		0			0
$31$			20.7829i			0.670416i	0.942144	+	0.335208i	$0.108807\pi$
$31$			20.7829i			0.670416i	−0.942144	+	0.335208i	$0.891193\pi$
$32$	−13.4133	−	29.0531i	−0.419165	−	0.907910i
$33$		0			0
$34$	59.1918	−	5.13320i	1.74094	−	0.150977i
$35$	39.1890	−	18.1141i	1.11969	−	0.517546i
$36$		0			0
$37$		−	43.3864i		−	1.17261i	−0.810092	−	0.586303i	$-0.800583\pi$
$37$		−	43.3864i		−	1.17261i	0.810092	−	0.586303i	$-0.199417\pi$
$38$	1.30222	+	15.0162i	0.0342690	+	0.395162i
$39$		0			0
$40$	12.6614	+	47.6883i	0.316534	+	1.19221i
$41$			43.0046i			1.04889i	0.851444	+	0.524446i	$0.175728\pi$
$41$			43.0046i			1.04889i	−0.851444	+	0.524446i	$0.824272\pi$
$42$		0			0
$43$		−	27.7017i		−	0.644225i	−0.946701	−	0.322112i	$-0.895607\pi$
$43$		−	27.7017i		−	0.644225i	0.946701	−	0.322112i	$-0.104393\pi$
$44$	−4.44825	−	25.4539i	−0.101097	−	0.578498i
$45$		0			0
$46$	−6.93799	−	80.0032i	−0.150826	−	1.73920i
$47$		−	75.5771i		−	1.60802i	−0.594613	−	0.804012i	$-0.702695\pi$
$47$		−	75.5771i		−	1.60802i	0.594613	−	0.804012i	$-0.297305\pi$
$48$		0			0
$49$	31.7481	−	37.3237i	0.647920	−	0.761708i
$50$	−2.25303	−	25.9801i	−0.0450606	−	0.519602i
$51$		0			0
$52$	−23.3368	+	4.07828i	−0.448785	+	0.0784285i
$53$		−	36.6740i		−	0.691963i	−0.938241	−	0.345981i	$-0.887546\pi$
$53$		−	36.6740i		−	0.691963i	0.938241	−	0.345981i	$-0.112454\pi$
$54$		0			0
$55$			39.8419i			0.724398i
$56$	35.7534	+	43.1010i	0.638454	+	0.769660i
$57$		0			0
$58$	38.9531	−	3.37807i	0.671604	−	0.0582425i
$59$	21.9834			0.372600			0.186300	−	0.982493i	$-0.440350\pi$
$59$	21.9834			0.372600			0.186300	+	0.982493i	$0.440350\pi$
$60$		0			0
$61$	−49.7137			−0.814978			−0.407489	−	0.913210i	$-0.633596\pi$
$61$	−49.7137			−0.814978			−0.407489	+	0.913210i	$0.633596\pi$
$62$	41.4103	−	3.59116i	0.667909	−	0.0579220i
$63$		0			0
$64$	−55.5712	+	31.7464i	−0.868301	+	0.496038i
$65$	36.5282			0.561972
$66$		0			0
$67$		−	106.648i		−	1.59176i	−0.605457	−	0.795878i	$-0.707010\pi$
$67$		−	106.648i		−	1.59176i	0.605457	−	0.795878i	$-0.292990\pi$
$68$	−20.4560	−	117.054i	−0.300824	−	1.72138i
$69$		0			0
$70$	−42.8644	−	74.9550i	−0.612349	−	1.07079i
$71$	84.5125			1.19032			0.595159	−	0.803608i	$-0.297089\pi$
$71$	84.5125			1.19032			0.595159	+	0.803608i	$0.297089\pi$
$72$		0			0
$73$			67.2164i			0.920773i	0.887719	+	0.460387i	$0.152289\pi$
$73$			67.2164i			0.920773i	−0.887719	+	0.460387i	$0.847711\pi$
$74$	−86.4484	+	7.49693i	−1.16822	+	0.101310i
$75$		0			0
$76$	29.6950	−	5.18941i	0.390724	−	0.0682817i
$77$	18.9728	+	41.0467i	0.246399	+	0.533074i
$78$		0			0
$79$	19.2213			0.243307			0.121654	−	0.992573i	$-0.461180\pi$
$79$	19.2213			0.243307			0.121654	+	0.992573i	$0.461180\pi$
$80$	92.8321	−	33.4683i	1.16040	−	0.418354i
$81$		0			0
$82$	85.6876	−	7.43095i	1.04497	−	0.0906213i
$83$	−122.024			−1.47017			−0.735083	−	0.677977i	$-0.762857\pi$
$83$	−122.024			−1.47017			−0.735083	+	0.677977i	$0.762857\pi$
$84$		0			0
$85$			183.220i			2.15553i
$86$	−55.1962	+	4.78669i	−0.641816	+	0.0556592i
$87$		0			0
$88$	−49.9488	+	13.2615i	−0.567600	+	0.150699i
$89$			43.7186i			0.491221i	0.969369	+	0.245610i	$0.0789884\pi$
$89$			43.7186i			0.491221i	−0.969369	+	0.245610i	$0.921012\pi$
$90$		0			0
$91$	37.6327	−	17.3948i	0.413546	−	0.191151i
$92$	−158.209	+	27.6482i	−1.71966	+	0.300524i
$93$		0			0
$94$	−150.589	+	13.0593i	−1.60201	+	0.138929i
$95$	−46.4803			−0.489266
$96$		0			0
$97$		−	151.843i		−	1.56539i	−0.622403	−	0.782697i	$-0.713843\pi$
$97$		−	151.843i		−	1.56539i	0.622403	−	0.782697i	$-0.286157\pi$
$98$	−79.8542	−	56.8094i	−0.814839	−	0.579688i
$99$		0			0
$100$	−51.3766	+	8.97842i	−0.513766	+	0.0897842i
$101$	−125.953			−1.24706			−0.623530	−	0.781800i	$-0.714302\pi$
$101$	−125.953			−1.24706			−0.623530	+	0.781800i	$0.714302\pi$
$102$		0			0
$103$			78.0095i			0.757373i	0.925525	+	0.378687i	$0.123624\pi$
$103$			78.0095i			0.757373i	−0.925525	+	0.378687i	$0.876376\pi$
$104$	12.1585	+	45.7945i	0.116909	+	0.440331i
$105$		0			0
$106$	−73.0738	+	6.33707i	−0.689376	+	0.0597836i
$107$		−	108.650i		−	1.01542i	−0.861527	−	0.507712i	$-0.830491\pi$
$107$		−	108.650i		−	1.01542i	0.861527	−	0.507712i	$-0.169509\pi$
$108$		0			0
$109$			120.456i			1.10510i	0.833479	+	0.552552i	$0.186346\pi$
$109$			120.456i			1.10510i	−0.833479	+	0.552552i	$0.813654\pi$
$110$	79.3859	−	6.88446i	0.721690	−	0.0625860i
$111$		0			0
$112$	79.7016	−	78.6871i	0.711621	−	0.702563i
$113$	26.1036			0.231005			0.115502	−	0.993307i	$-0.463152\pi$
$113$	26.1036			0.231005			0.115502	+	0.993307i	$0.463152\pi$
$114$		0			0
$115$	247.638			2.15338
$116$	−13.4617	−	77.0311i	−0.116049	−	0.664061i
$117$		0			0
$118$	−3.79860	−	43.8023i	−0.0321915	−	0.371206i
$119$	87.2494	+	188.760i	0.733188	+	1.58622i
$120$		0			0
$121$	79.2695			0.655120
$122$	8.59024	+	99.0555i	0.0704118	+	0.811931i
$123$		0			0
$124$	−14.3109	−	81.8905i	−0.115411	−	0.660407i
$125$	−73.7714			−0.590171
$126$		0			0
$127$	8.22965			0.0648004			0.0324002	−	0.999475i	$-0.489685\pi$
$127$	8.22965			0.0648004			0.0324002	+	0.999475i	$0.489685\pi$
$128$	72.8579	+	105.241i	0.569202	+	0.822198i
$129$		0			0
$130$	−6.31186	−	72.7832i	−0.0485528	−	0.559871i
$131$	124.421			0.949780			0.474890	−	0.880045i	$-0.342488\pi$
$131$	124.421			0.949780			0.474890	+	0.880045i	$0.342488\pi$
$132$		0			0
$133$	−47.8858	+	22.1340i	−0.360044	+	0.166421i
$134$	−212.498	+	18.4281i	−1.58580	+	0.137523i
$135$		0			0
$136$	−229.698	+	60.9853i	−1.68896	+	0.448422i
$137$	−31.1603			−0.227447			−0.113724	−	0.993512i	$-0.536278\pi$
$137$	−31.1603			−0.227447			−0.113724	+	0.993512i	$0.536278\pi$
$138$		0			0
$139$	−91.4021			−0.657569			−0.328784	−	0.944405i	$-0.606639\pi$
$139$	−91.4021			−0.657569			−0.328784	+	0.944405i	$0.606639\pi$
$140$	−141.943	+	98.3600i	−1.01388	+	0.702572i
$141$		0			0
$142$	−14.6033	−	168.393i	−0.102840	−	1.18587i
$143$			38.2597i			0.267550i
$144$		0			0
$145$			120.574i			0.831541i
$146$	133.930	−	11.6146i	0.917330	−	0.0795522i
$147$		0			0
$148$	29.8756	+	170.955i	0.201862	+	1.15510i
$149$			240.341i			1.61303i	0.591216	+	0.806513i	$0.298648\pi$
$149$			240.341i			1.61303i	−0.591216	+	0.806513i	$0.701352\pi$
$150$		0			0
$151$	2.20156			0.0145799			0.00728994	−	0.999973i	$-0.497680\pi$
$151$	2.20156			0.0145799			0.00728994	+	0.999973i	$0.497680\pi$
$152$	−15.4711	−	58.2712i	−0.101784	−	0.383363i
$153$		0			0
$154$	78.5080	−	44.8963i	0.509792	−	0.291534i
$155$			128.180i			0.826966i
$156$		0			0
$157$	177.687			1.13176			0.565882	−	0.824486i	$-0.308536\pi$
$157$	177.687			1.13176			0.565882	+	0.824486i	$0.308536\pi$
$158$	−3.32133	−	38.2988i	−0.0210210	−	0.242397i
$159$		0			0
$160$	−82.7271	−	179.187i	−0.517045	−	1.11992i
$161$	255.126	−	117.926i	1.58464	−	0.732457i
$162$		0			0
$163$			61.2783i			0.375940i	0.982175	+	0.187970i	$0.0601908\pi$
$163$			61.2783i			0.375940i	−0.982175	+	0.187970i	$0.939809\pi$
$164$	−29.6127	−	169.450i	−0.180565	−	1.03323i
$165$		0			0
$166$	21.0850	+	243.135i	0.127018	+	1.46467i
$167$			99.4758i			0.595664i	0.954618	+	0.297832i	$0.0962635\pi$
$167$			99.4758i			0.595664i	−0.954618	+	0.297832i	$0.903737\pi$
$168$		0			0
$169$	−133.922			−0.792441
$170$	365.069	−	31.6593i	2.14747	−	0.186231i
$171$		0			0
$172$	19.0752	+	109.152i	0.110902	+	0.634607i
$173$	95.4661			0.551827			0.275914	−	0.961182i	$-0.411020\pi$
$173$	95.4661			0.551827			0.275914	+	0.961182i	$0.411020\pi$
$174$		0			0
$175$	82.8493	−	38.2949i	0.473424	−	0.218828i
$176$	35.0547	+	97.2326i	0.199175	+	0.552458i
$177$		0			0
$178$	87.1103	−	7.55433i	0.489384	−	0.0424401i
$179$		−	252.000i		−	1.40782i	−0.710289	−	0.703910i	$-0.751436\pi$
$179$		−	252.000i		−	1.40782i	0.710289	−	0.703910i	$-0.248564\pi$
$180$		0			0
$181$	−220.793			−1.21985			−0.609927	−	0.792458i	$-0.708801\pi$
$181$	−220.793			−1.21985			−0.609927	+	0.792458i	$0.708801\pi$
$182$	−41.1621	−	71.9783i	−0.226166	−	0.395485i
$183$		0			0
$184$	82.4273	+	310.458i	0.447974	+	1.68727i
$185$		−	267.588i		−	1.44642i
$186$		0			0
$187$	−191.905			−1.02623
$188$	52.0419	+	297.795i	0.276819	+	1.58402i
$189$		0			0
$190$	8.03153	+	92.6130i	0.0422712	+	0.487437i
$191$	−97.0332			−0.508027			−0.254013	−	0.967201i	$-0.581751\pi$
$191$	−97.0332			−0.508027			−0.254013	+	0.967201i	$0.581751\pi$
$192$		0			0
$193$	−74.1906			−0.384407			−0.192204	−	0.981355i	$-0.561563\pi$
$193$	−74.1906			−0.384407			−0.192204	+	0.981355i	$0.561563\pi$
$194$	−302.551	+	26.2377i	−1.55954	+	0.135246i
$195$		0			0
$196$	−99.3956	+	168.928i	−0.507120	+	0.861875i
$197$			56.4501i			0.286549i	0.989683	+	0.143274i	$0.0457631\pi$
$197$			56.4501i			0.286549i	−0.989683	+	0.143274i	$0.954237\pi$
$198$		0			0
$199$		−	270.199i		−	1.35778i	−0.734238	−	0.678892i	$-0.762460\pi$
$199$		−	270.199i		−	1.35778i	0.734238	−	0.678892i	$-0.237540\pi$
$200$	26.7673	+	100.818i	0.133836	+	0.504088i
$201$		0			0
$202$	21.7640	+	250.964i	0.107742	+	1.24240i
$203$	57.4172	+	124.219i	0.282844	+	0.611919i
$204$		0			0
$205$			265.233i			1.29382i
$206$	155.436	−	13.4796i	0.754541	−	0.0654349i
$207$		0			0
$208$	89.1455	−	32.1392i	0.428584	−	0.154515i
$209$		−	48.6836i		−	0.232936i
$210$		0			0
$211$			52.1555i			0.247183i	0.992333	+	0.123591i	$0.0394412\pi$
$211$			52.1555i			0.247183i	−0.992333	+	0.123591i	$0.960559\pi$
$212$	25.2535	+	144.506i	0.119120	+	0.681633i
$213$		0			0
$214$	−216.488	+	18.7742i	−1.01163	+	0.0877298i
$215$		−	170.852i		−	0.794659i
$216$		0			0
$217$	61.0393	+	132.056i	0.281287	+	0.608551i
$218$	240.012	−	20.8142i	1.10097	−	0.0954778i
$219$		0			0
$220$	−27.4349	−	156.988i	−0.124704	−	0.713584i
$221$			175.944i			0.796125i
$222$		0			0
$223$			133.353i			0.597998i	0.954253	+	0.298999i	$0.0966527\pi$
$223$			133.353i			0.597998i	−0.954253	+	0.298999i	$0.903347\pi$
$224$	−170.558	−	145.210i	−0.761418	−	0.648261i
$225$		0			0
$226$	−4.51055	−	52.0119i	−0.0199582	−	0.230141i
$227$	−359.544			−1.58389			−0.791946	−	0.610591i	$-0.790932\pi$
$227$	−359.544			−1.58389			−0.791946	+	0.610591i	$0.790932\pi$
$228$		0			0
$229$	−392.327			−1.71322			−0.856610	−	0.515965i	$-0.827433\pi$
$229$	−392.327			−1.71322			−0.856610	+	0.515965i	$0.827433\pi$
$230$	−42.7905	−	493.424i	−0.186045	−	2.14532i
$231$		0			0
$232$	−151.160	+	40.1333i	−0.651552	+	0.172989i
$233$	−240.219			−1.03098			−0.515491	−	0.856895i	$-0.672390\pi$
$233$	−240.219			−1.03098			−0.515491	+	0.856895i	$0.672390\pi$
$234$		0			0
$235$		−	466.127i		−	1.98352i
$236$	−86.6207	+	15.1376i	−0.367037	+	0.0641423i
$237$		0			0
$238$	361.032	−	206.463i	1.51694	−	0.867492i
$239$	−132.847			−0.555847			−0.277923	−	0.960603i	$-0.589646\pi$
$239$	−132.847			−0.555847			−0.277923	+	0.960603i	$0.589646\pi$
$240$		0			0
$241$			335.329i			1.39140i	0.718330	+	0.695702i	$0.244907\pi$
$241$			335.329i			1.39140i	−0.718330	+	0.695702i	$0.755093\pi$
$242$	−13.6973	−	157.946i	−0.0566005	−	0.652670i
$243$		0			0
$244$	195.886	−	34.2325i	0.802811	−	0.140297i
$245$	195.808	−	230.196i	0.799217	−	0.939577i
$246$		0			0
$247$	−44.6344			−0.180706
$248$	−160.696	+	42.6651i	−0.647966	+	0.172037i
$249$		0			0
$250$	12.7473	+	146.991i	0.0509891	+	0.587965i
$251$	382.900			1.52550			0.762749	−	0.646694i	$-0.223849\pi$
$251$	382.900			1.52550			0.762749	+	0.646694i	$0.223849\pi$
$252$		0			0
$253$			259.377i			1.02520i
$254$	−1.42204	−	16.3978i	−0.00559857	−	0.0645581i
$255$		0			0
$256$	197.106	−	163.356i	0.769946	−	0.638109i
$257$			426.784i			1.66064i	0.557287	+	0.830320i	$0.311842\pi$
$257$			426.784i			1.66064i	−0.557287	+	0.830320i	$0.688158\pi$
$258$		0			0
$259$	−127.426	−	275.680i	−0.491992	−	1.06440i
$260$	−143.931	+	25.1530i	−0.553582	+	0.0967425i
$261$		0			0
$262$	−21.4993	−	247.912i	−0.0820583	−	0.946228i
$263$	−211.088			−0.802615			−0.401307	−	0.915943i	$-0.631444\pi$
$263$	−211.088			−0.802615			−0.401307	+	0.915943i	$0.631444\pi$
$264$		0			0
$265$		−	226.189i		−	0.853545i
$266$	52.3768	+	91.5889i	0.196905	+	0.344319i
$267$		0			0
$268$	73.4368	+	420.222i	0.274018	+	1.56799i
$269$	32.7632			0.121796			0.0608982	−	0.998144i	$-0.480604\pi$
$269$	32.7632			0.121796			0.0608982	+	0.998144i	$0.480604\pi$
$270$		0			0
$271$		−	429.177i		−	1.58368i	−0.610730	−	0.791839i	$-0.709124\pi$
$271$		−	429.177i		−	1.58368i	0.610730	−	0.791839i	$-0.290876\pi$
$272$	161.205	+	447.140i	0.592666	+	1.64390i
$273$		0			0
$274$	5.38432	+	62.0875i	0.0196508	+	0.226597i
$275$			84.2295i			0.306289i
$276$		0			0
$277$		−	245.879i		−	0.887649i	−0.896114	−	0.443824i	$-0.853621\pi$
$277$		−	245.879i		−	0.887649i	0.896114	−	0.443824i	$-0.146379\pi$
$278$	15.7938	+	182.121i	0.0568121	+	0.655110i
$279$		0			0
$280$	220.511	+	265.828i	0.787541	+	0.949385i
$281$	−50.7953			−0.180766			−0.0903831	−	0.995907i	$-0.528809\pi$
$281$	−50.7953			−0.180766			−0.0903831	+	0.995907i	$0.528809\pi$
$282$		0			0
$283$	101.397			0.358293			0.179147	−	0.983822i	$-0.442666\pi$
$283$	101.397			0.358293			0.179147	+	0.983822i	$0.442666\pi$
$284$	−333.003	+	58.1947i	−1.17255	+	0.204911i
$285$		0			0
$286$	76.2332	−	6.61106i	0.266550	−	0.0231156i
$287$	126.304	+	273.254i	0.440085	+	0.952103i
$288$		0			0
$289$	−593.506			−2.05365
$290$	240.245	−	20.8344i	0.828432	−	0.0718428i
$291$		0			0
$292$	−46.2848	−	264.852i	−0.158509	−	0.907027i
$293$	−218.851			−0.746932			−0.373466	−	0.927644i	$-0.621831\pi$
$293$	−218.851			−0.746932			−0.373466	+	0.927644i	$0.621831\pi$
$294$		0			0
$295$	135.584			0.459606
$296$	335.469	−	89.0678i	1.13334	−	0.300905i
$297$		0			0
$298$	478.884	−	41.5295i	1.60699	−	0.139361i
$299$	237.804			0.795330
$300$		0			0
$301$	−81.3598	−	176.018i	−0.270298	−	0.584777i
$302$	−0.380417	−	4.38666i	−0.00125966	−	0.0145254i
$303$		0			0
$304$	−113.433	+	40.8955i	−0.373136	+	0.134525i
$305$	−306.612			−1.00529
$306$		0			0
$307$	423.419			1.37922			0.689608	−	0.724183i	$-0.257783\pi$
$307$	423.419			1.37922			0.689608	+	0.724183i	$0.257783\pi$
$308$	−103.023	−	148.671i	−0.334489	−	0.482698i
$309$		0			0
$310$	255.401	−	22.1487i	0.823873	−	0.0714475i
$311$			18.7982i			0.0604445i	0.999543	+	0.0302222i	$0.00962150\pi$
$311$			18.7982i			0.0604445i	−0.999543	+	0.0302222i	$0.990378\pi$
$312$		0			0
$313$		−	195.908i		−	0.625905i	−0.949769	−	0.312952i	$-0.898682\pi$
$313$		−	195.908i		−	0.625905i	0.949769	−	0.312952i	$-0.101318\pi$
$314$	−30.7033	−	354.045i	−0.0977812	−	1.12753i
$315$		0			0
$316$	−75.7372	+	13.2356i	−0.239675	+	0.0418849i
$317$		−	343.312i		−	1.08300i	−0.840700	−	0.541501i	$-0.817856\pi$
$317$		−	343.312i		−	1.08300i	0.840700	−	0.541501i	$-0.182144\pi$
$318$		0			0
$319$	−126.289			−0.395890
$320$	−342.739	+	195.798i	−1.07106	+	0.611869i
$321$		0			0
$322$	−279.054	−	487.968i	−0.866626	−	1.51543i
$323$		−	223.880i		−	0.693126i
$324$		0			0
$325$	77.2240			0.237612
$326$	122.098	−	10.5885i	0.374535	−	0.0324802i
$327$		0			0
$328$	−332.517	+	88.2839i	−1.01377	+	0.269158i
$329$	−221.970	−	480.221i	−0.674681	−	1.45964i
$330$		0			0
$331$		−	81.4921i		−	0.246200i	−0.992394	−	0.123100i	$-0.960716\pi$
$331$		−	81.4921i		−	0.246200i	0.992394	−	0.123100i	$-0.0392835\pi$
$332$	480.808	−	84.0247i	1.44822	−	0.253086i
$333$		0			0
$334$	198.208	−	17.1889i	0.593436	−	0.0514636i
$335$		−	657.756i		−	1.96345i
$336$		0			0
$337$	516.227			1.53183			0.765916	−	0.642941i	$-0.222286\pi$
$337$	516.227			1.53183			0.765916	+	0.642941i	$0.222286\pi$
$338$	23.1410	+	266.843i	0.0684646	+	0.789477i
$339$		0			0
$340$	−126.164	−	721.938i	−0.371070	−	2.12335i
$341$	−134.256			−0.393712
$342$		0			0
$343$	92.1094	−	330.401i	0.268541	−	0.963268i
$344$	214.192	−	56.8686i	0.622653	−	0.165316i
$345$		0			0
$346$	−16.4960	−	190.218i	−0.0476763	−	0.549764i
$347$		−	458.680i		−	1.32184i	−0.750455	−	0.660922i	$-0.770165\pi$
$347$		−	458.680i		−	1.32184i	0.750455	−	0.660922i	$-0.229835\pi$
$348$		0			0
$349$	420.639			1.20527			0.602634	−	0.798017i	$-0.294118\pi$
$349$	420.639			1.20527			0.602634	+	0.798017i	$0.294118\pi$
$350$	−90.6194	−	158.462i	−0.258912	−	0.452748i
$351$		0			0
$352$	187.681	−	86.6486i	0.533184	−	0.246161i
$353$		−	93.5372i		−	0.264978i	−0.991184	−	0.132489i	$-0.957703\pi$
$353$		−	93.5372i		−	0.264978i	0.991184	−	0.132489i	$-0.0422969\pi$
$354$		0			0
$355$	521.236			1.46827
$356$	−30.1043	−	172.264i	−0.0845628	−	0.483887i
$357$		0			0
$358$	−502.115	+	43.5441i	−1.40256	+	0.121632i
$359$	−597.696			−1.66489			−0.832446	−	0.554106i	$-0.813060\pi$
$359$	−597.696			−1.66489			−0.832446	+	0.554106i	$0.813060\pi$
$360$		0			0
$361$	−304.205			−0.842673
$362$	38.1519	+	439.936i	0.105392	+	1.21529i
$363$		0			0
$364$	−136.306	+	94.4539i	−0.374466	+	0.259489i
$365$			414.561i			1.13578i
$366$		0			0
$367$			4.47916i			0.0122048i	0.999981	+	0.00610240i	$0.00194247\pi$
$367$			4.47916i			0.0122048i	−0.999981	+	0.00610240i	$0.998058\pi$
$368$	604.351	−	217.883i	1.64226	−	0.592074i
$369$		0			0
$370$	−533.176	+	46.2378i	−1.44102	+	0.124967i
$371$	−107.712	−	233.029i	−0.290328	−	0.628110i
$372$		0			0
$373$		−	121.868i		−	0.326725i	−0.986566	−	0.163363i	$-0.947766\pi$
$373$		−	121.868i		−	0.326725i	0.986566	−	0.163363i	$-0.0522340\pi$
$374$	33.1600	+	382.374i	0.0886632	+	1.02239i
$375$		0			0
$376$	584.371	−	155.152i	1.55418	−	0.412638i
$377$			115.785i			0.307123i
$378$		0			0
$379$			73.1377i			0.192976i	0.995334	+	0.0964878i	$0.0307609\pi$
$379$			73.1377i			0.192976i	−0.995334	+	0.0964878i	$0.969239\pi$
$380$	183.146	−	32.0060i	0.481962	−	0.0842263i
$381$		0			0
$382$	16.7668	+	193.341i	0.0438921	+	0.506127i
$383$		−	263.145i		−	0.687062i	−0.939141	−	0.343531i	$-0.888377\pi$
$383$		−	263.145i		−	0.687062i	0.939141	−	0.343531i	$-0.111623\pi$
$384$		0			0
$385$	117.016	+	253.158i	0.303937	+	0.657553i
$386$	12.8197	+	147.826i	0.0332117	+	0.382970i
$387$		0			0
$388$	104.558	+	598.306i	0.269480	+	1.54202i
$389$		−	8.96716i		−	0.0230518i	−0.999934	−	0.0115259i	$-0.996331\pi$
$389$		−	8.96716i		−	0.0230518i	0.999934	−	0.0115259i	$-0.00366889\pi$
$390$		0			0
$391$			1192.79i			3.05061i
$392$	353.767	+	168.858i	0.902466	+	0.430761i
$393$		0			0
$394$	112.478	−	9.75426i	0.285477	−	0.0247570i
$395$	118.548			0.300122
$396$		0			0
$397$	591.900			1.49093			0.745466	−	0.666544i	$-0.232227\pi$
$397$	591.900			1.49093			0.745466	+	0.666544i	$0.232227\pi$
$398$	−538.378	+	46.6889i	−1.35271	+	0.117309i
$399$		0			0
$400$	196.256	−	70.7551i	0.490640	−	0.176888i
$401$	−433.112			−1.08008			−0.540040	−	0.841640i	$-0.681591\pi$
$401$	−433.112			−1.08008			−0.540040	+	0.841640i	$0.681591\pi$
$402$		0			0
$403$			123.089i			0.305433i
$404$	496.291	−	86.7303i	1.22844	−	0.214679i
$405$		0			0
$406$	237.589	−	135.869i	0.585194	−	0.334654i
$407$	280.273			0.688630
$408$		0			0
$409$		−	200.528i		−	0.490288i	−0.969487	−	0.245144i	$-0.921165\pi$
$409$		−	200.528i		−	0.490288i	0.969487	−	0.245144i	$-0.0788353\pi$
$410$	528.483	−	45.8308i	1.28898	−	0.111783i
$411$		0			0
$412$	−53.7168	−	307.379i	−0.130380	−	0.746067i
$413$	139.684	−	64.5651i	0.338217	−	0.156332i
$414$		0			0
$415$	−752.589			−1.81347
$416$	−79.4418	−	172.071i	−0.190966	−	0.413632i
$417$		0			0
$418$	−97.0031	+	8.41224i	−0.232065	+	0.0201250i
$419$	−324.504			−0.774472			−0.387236	−	0.921981i	$-0.626570\pi$
$419$	−324.504			−0.774472			−0.387236	+	0.921981i	$0.626570\pi$
$420$		0			0
$421$			237.746i			0.564717i	0.959309	+	0.282359i	$0.0911168\pi$
$421$			237.746i			0.564717i	−0.959309	+	0.282359i	$0.908883\pi$
$422$	103.921	−	9.01218i	0.246258	−	0.0213559i
$423$		0			0
$424$	283.568	−	75.2879i	0.668792	−	0.177566i
$425$			387.344i			0.911397i
$426$		0			0
$427$	−315.883	+	146.009i	−0.739774	+	0.341941i
$428$	74.8159	+	428.114i	0.174804	+	1.00027i
$429$		0			0
$430$	−340.426	+	29.5222i	−0.791688	+	0.0686563i
$431$	285.237			0.661804			0.330902	−	0.943665i	$-0.392647\pi$
$431$	285.237			0.661804			0.330902	+	0.943665i	$0.392647\pi$
$432$		0			0
$433$		−	524.457i		−	1.21122i	−0.795763	−	0.605608i	$-0.792930\pi$
$433$		−	524.457i		−	1.21122i	0.795763	−	0.605608i	$-0.207070\pi$
$434$	252.576	−	144.441i	0.581973	−	0.332812i
$435$		0			0
$436$	−82.9453	−	474.632i	−0.190242	−	1.08861i
$437$	−302.594			−0.692434
$438$		0			0
$439$			238.365i			0.542972i	0.962442	+	0.271486i	$0.0875151\pi$
$439$			238.365i			0.542972i	−0.962442	+	0.271486i	$0.912485\pi$
$440$	−308.062	+	81.7913i	−0.700142	+	0.185889i
$441$		0			0
$442$	350.571	−	30.4020i	0.793148	−	0.0687829i
$443$			644.690i			1.45528i	0.685958	+	0.727641i	$0.259383\pi$
$443$			644.690i			1.45528i	−0.685958	+	0.727641i	$0.740617\pi$
$444$		0			0
$445$			269.637i			0.605927i
$446$	265.710	−	23.0427i	0.595762	−	0.0516653i
$447$		0			0
$448$	−259.864	+	364.931i	−0.580053	+	0.814579i
$449$	578.191			1.28773			0.643865	−	0.765139i	$-0.277330\pi$
$449$	578.191			1.28773			0.643865	+	0.765139i	$0.277330\pi$
$450$		0			0
$451$	−277.806			−0.615978
$452$	−102.855	+	17.9747i	−0.227556	+	0.0397671i
$453$		0			0
$454$	62.1271	+	716.399i	0.136844	+	1.57797i
$455$	232.102	−	107.283i	0.510114	−	0.235787i
$456$		0			0
$457$	530.814			1.16152			0.580759	−	0.814075i	$-0.302756\pi$
$457$	530.814			1.16152			0.580759	+	0.814075i	$0.302756\pi$
$458$	67.7919	+	781.720i	0.148017	+	1.70681i
$459$		0			0
$460$	−975.765	+	170.522i	−2.12123	+	0.370700i
$461$	264.540			0.573839			0.286920	−	0.957955i	$-0.407369\pi$
$461$	264.540			0.573839			0.286920	+	0.957955i	$0.407369\pi$
$462$		0			0
$463$	−162.996			−0.352044			−0.176022	−	0.984386i	$-0.556323\pi$
$463$	−162.996			−0.352044			−0.176022	+	0.984386i	$0.556323\pi$
$464$	106.086	+	294.255i	0.228634	+	0.634170i
$465$		0			0
$466$	41.5084	+	478.641i	0.0890739	+	1.02713i
$467$	−451.747			−0.967339			−0.483670	−	0.875251i	$-0.660696\pi$
$467$	−451.747			−0.967339			−0.483670	+	0.875251i	$0.660696\pi$
$468$		0			0
$469$	−313.224	−	677.645i	−0.667855	−	1.44487i
$470$	−928.767	+	80.5440i	−1.97610	+	0.171370i
$471$		0			0
$472$	45.1296	+	169.978i	0.0956135	+	0.360123i
$473$	178.950			0.378331
$474$		0			0
$475$	−98.2637			−0.206871
$476$	−473.766	−	683.689i	−0.995307	−	1.43632i
$477$		0			0
$478$	22.9553	+	264.701i	0.0480236	+	0.553768i
$479$			678.834i			1.41719i	0.705616	+	0.708595i	$0.250670\pi$
$479$			678.834i			1.41719i	−0.705616	+	0.708595i	$0.749330\pi$
$480$		0			0
$481$		−	256.962i		−	0.534224i
$482$	668.149	−	57.9429i	1.38620	−	0.120213i
$483$		0			0
$484$	−312.344	+	54.5844i	−0.645340	+	0.112778i
$485$		−	936.502i		−	1.93093i
$486$		0			0
$487$	186.357			0.382664			0.191332	−	0.981525i	$-0.438719\pi$
$487$	186.357			0.382664			0.191332	+	0.981525i	$0.438719\pi$
$488$	−102.057	−	384.392i	−0.209133	−	0.787688i
$489$		0			0
$490$	−492.506	−	350.375i	−1.00511	−	0.715052i
$491$			196.165i			0.399522i	0.979845	+	0.199761i	$0.0640165\pi$
$491$			196.165i			0.399522i	−0.979845	+	0.199761i	$0.935983\pi$
$492$		0			0
$493$	−580.761			−1.17801
$494$	7.71258	+	88.9351i	0.0156125	+	0.180031i
$495$		0			0
$496$	112.778	+	312.817i	0.227376	+	0.630680i
$497$	536.998	−	248.213i	1.08048	−	0.499423i
$498$		0			0
$499$			486.955i			0.975863i	0.872882	+	0.487931i	$0.162248\pi$
$499$			486.955i			0.975863i	−0.872882	+	0.487931i	$0.837752\pi$
$500$	290.680	−	50.7985i	0.581361	−	0.101597i
$501$		0			0
$502$	−66.1630	−	762.937i	−0.131799	−	1.51979i
$503$		−	192.742i		−	0.383185i	−0.981475	−	0.191593i	$-0.938635\pi$
$503$		−	192.742i		−	0.383185i	0.981475	−	0.191593i	$-0.0613652\pi$
$504$		0			0
$505$	−776.823			−1.53826
$506$	516.814	−	44.8188i	1.02137	−	0.0885747i
$507$		0			0
$508$	−32.4272	+	5.66688i	−0.0638330	+	0.0111553i
$509$	109.782			0.215683			0.107841	−	0.994168i	$-0.465606\pi$
$509$	109.782			0.215683			0.107841	+	0.994168i	$0.465606\pi$
$510$		0			0
$511$	197.415	+	427.097i	0.386330	+	0.835806i
$512$	−359.549	−	364.511i	−0.702244	−	0.711936i
$513$		0			0
$514$	850.377	−	73.7459i	1.65443	−	0.143475i
$515$			481.128i			0.934229i
$516$		0			0
$517$	488.222			0.944336
$518$	−527.279	+	301.535i	−1.01791	+	0.582113i
$519$		0			0
$520$	74.9885	+	282.440i	0.144209	+	0.543154i
$521$		−	7.72697i		−	0.0148310i	−0.999973	−	0.00741552i	$-0.997640\pi$
$521$		−	7.72697i		−	0.0148310i	0.999973	−	0.00741552i	$-0.00236045\pi$
$522$		0			0
$523$	−861.576			−1.64737			−0.823686	−	0.567046i	$-0.808086\pi$
$523$	−861.576			−1.64737			−0.823686	+	0.567046i	$0.808086\pi$
$524$	−490.255	+	85.6755i	−0.935600	+	0.163503i
$525$		0			0
$526$	36.4748	+	420.597i	0.0693436	+	0.799614i
$527$	−617.397			−1.17153
$528$		0			0
$529$	1083.16			2.04756
$530$	−450.687	+	39.0842i	−0.850353	+	0.0737438i
$531$		0			0
$532$	173.442	−	120.188i	0.326019	−	0.225917i
$533$			254.700i			0.477862i
$534$		0			0
$535$		−	670.108i		−	1.25254i
$536$	824.612	−	218.936i	1.53846	−	0.408464i
$537$		0			0
$538$	−5.66130	−	65.2814i	−0.0105229	−	0.121341i
$539$	241.108	+	205.090i	0.447325	+	0.380501i
$540$		0			0
$541$		−	1072.33i		−	1.98212i	−0.133425	−	0.991059i	$-0.542598\pi$
$541$		−	1072.33i		−	1.98212i	0.133425	−	0.991059i	$-0.457402\pi$
$542$	−855.144	+	74.1593i	−1.57776	+	0.136825i
$543$		0			0
$544$	863.081	−	398.468i	1.58655	−	0.732478i
$545$			742.921i			1.36316i
$546$		0			0
$547$			838.104i			1.53218i	0.642732	+	0.766091i	$0.277801\pi$
$547$			838.104i			1.53218i	−0.642732	+	0.766091i	$0.722199\pi$
$548$	122.780	−	21.4567i	0.224052	−	0.0391546i
$549$		0			0
$550$	167.829	−	14.5544i	0.305144	−	0.0264625i
$551$		−	147.331i		−	0.267388i
$552$		0			0
$553$	122.133	−	56.4528i	0.220855	−	0.102085i
$554$	−489.919	+	42.4864i	−0.884329	+	0.0766903i
$555$		0			0
$556$	360.150	−	62.9388i	0.647752	−	0.113199i
$557$		−	150.830i		−	0.270789i	−0.990792	−	0.135395i	$-0.956770\pi$
$557$		−	150.830i		−	0.270789i	0.990792	−	0.135395i	$-0.0432303\pi$
$558$		0			0
$559$		−	164.067i		−	0.293500i
$560$	491.564	−	485.307i	0.877794	−	0.866620i
$561$		0			0
$562$	8.77714	+	101.211i	0.0156177	+	0.180090i
$563$	80.5128			0.143007			0.0715034	−	0.997440i	$-0.477220\pi$
$563$	80.5128			0.143007			0.0715034	+	0.997440i	$0.477220\pi$
$564$		0			0
$565$	160.995			0.284947
$566$	−17.5208	−	202.036i	−0.0309555	−	0.356953i
$567$		0			0
$568$	173.495	+	653.461i	0.305450	+	1.15046i
$569$	−970.937			−1.70639			−0.853196	−	0.521590i	$-0.825339\pi$
$569$	−970.937			−1.70639			−0.853196	+	0.521590i	$0.825339\pi$
$570$		0			0
$571$		−	822.407i		−	1.44029i	−0.693822	−	0.720146i	$-0.744075\pi$
$571$		−	822.407i		−	1.44029i	0.693822	−	0.720146i	$-0.255925\pi$
$572$	−26.3453	−	150.754i	−0.0460583	−	0.263556i
$573$		0			0
$574$	522.639	−	298.881i	0.910521	−	0.520699i
$575$	523.530			0.910487
$576$		0			0
$577$			155.604i			0.269677i	0.990868	+	0.134839i	$0.0430516\pi$
$577$			155.604i			0.269677i	−0.990868	+	0.134839i	$0.956948\pi$
$578$	102.554	+	1182.57i	0.177430	+	2.04597i
$579$		0			0
$580$	−83.0261	−	475.094i	−0.143148	−	0.819127i
$581$	−775.346	+	358.384i	−1.33450	+	0.616839i
$582$		0			0
$583$	236.911			0.406366
$584$	−519.725	+	137.988i	−0.889941	+	0.236281i
$585$		0			0
$586$	37.8162	+	436.065i	0.0645328	+	0.744139i
$587$	45.2760			0.0771313			0.0385656	−	0.999256i	$-0.487721\pi$
$587$	45.2760			0.0771313			0.0385656	+	0.999256i	$0.487721\pi$
$588$		0			0
$589$		−	156.625i		−	0.265917i
$590$	−23.4281	−	270.154i	−0.0397087	−	0.457887i
$591$		0			0
$592$	−235.437	−	653.039i	−0.397697	−	1.10311i
$593$		−	192.741i		−	0.325026i	−0.986706	−	0.162513i	$-0.948040\pi$
$593$		−	192.741i		−	0.325026i	0.986706	−	0.162513i	$-0.0519600\pi$
$594$		0			0
$595$	538.116	+	1164.19i	0.904397	+	1.95662i
$596$	−165.497	−	947.011i	−0.277680	−	1.58895i
$597$		0			0
$598$	−41.0911	−	473.829i	−0.0687143	−	0.792356i
$599$	271.878			0.453886			0.226943	−	0.973908i	$-0.427127\pi$
$599$	271.878			0.453886			0.226943	+	0.973908i	$0.427127\pi$
$600$		0			0
$601$		−	319.614i		−	0.531803i	−0.964000	−	0.265902i	$-0.914330\pi$
$601$		−	319.614i		−	0.531803i	0.964000	−	0.265902i	$-0.0856696\pi$
$602$	−336.661	+	192.526i	−0.559238	+	0.319811i
$603$		0			0
$604$	−8.67478	+	1.51598i	−0.0143622	+	0.00250990i
$605$	488.899			0.808098
$606$		0			0
$607$			305.071i			0.502587i	0.967911	+	0.251294i	$0.0808560\pi$
$607$			305.071i			0.502587i	−0.967911	+	0.251294i	$0.919144\pi$
$608$	101.086	+	218.952i	0.166260	+	0.360118i
$609$		0			0
$610$	52.9808	+	610.931i	0.0868538	+	1.00153i
$611$		−	447.615i		−	0.732595i
$612$		0			0
$613$			870.460i			1.42000i	0.704202	+	0.710000i	$0.251305\pi$
$613$			870.460i			1.42000i	−0.704202	+	0.710000i	$0.748695\pi$
$614$	−73.1644	−	843.672i	−0.119160	−	1.37406i
$615$		0			0
$616$	−278.429	+	230.964i	−0.451994	+	0.374942i
$617$	448.273			0.726537			0.363268	−	0.931685i	$-0.381661\pi$
$617$	448.273			0.726537			0.363268	+	0.931685i	$0.381661\pi$
$618$		0			0
$619$	−879.069			−1.42014			−0.710072	−	0.704129i	$-0.751338\pi$
$619$	−879.069			−1.42014			−0.710072	+	0.704129i	$0.751338\pi$
$620$	−88.2636	−	505.064i	−0.142361	−	0.814620i
$621$		0			0
$622$	37.4559	−	3.24823i	0.0602185	−	0.00522223i
$623$	128.402	+	277.791i	0.206102	+	0.445892i
$624$		0			0
$625$	−780.960			−1.24954
$626$	−390.351	+	33.8518i	−0.623565	+	0.0540764i
$627$		0			0
$628$	−700.137	+	122.354i	−1.11487	+	0.194831i
$629$	1288.88			2.04909
$630$		0			0
$631$	−464.287			−0.735795			−0.367898	−	0.929866i	$-0.619922\pi$
$631$	−464.287			−0.735795			−0.367898	+	0.929866i	$0.619922\pi$
$632$	39.4592	+	148.621i	0.0624355	+	0.235160i
$633$		0			0
$634$	−684.056	+	59.3223i	−1.07895	+	0.0935684i
$635$	50.7569			0.0799321
$636$		0			0
$637$	188.032	−	221.055i	0.295184	−	0.347024i
$638$	21.8220	+	251.633i	0.0342038	+	0.394410i
$639$		0			0
$640$	449.355	+	649.082i	0.702118	+	1.01419i
$641$	83.8113			0.130751			0.0653754	−	0.997861i	$-0.479176\pi$
$641$	83.8113			0.130751			0.0653754	+	0.997861i	$0.479176\pi$
$642$		0			0
$643$	−965.822			−1.50206			−0.751028	−	0.660270i	$-0.770442\pi$
$643$	−965.822			−1.50206			−0.751028	+	0.660270i	$0.770442\pi$
$644$	−924.067	+	640.338i	−1.43489	+	0.994314i
$645$		0			0
$646$	−446.085	+	38.6851i	−0.690534	+	0.0598841i
$647$		−	13.2482i		−	0.0204763i	−0.999948	−	0.0102381i	$-0.996741\pi$
$647$		−	13.2482i		−	0.0204763i	0.999948	−	0.0102381i	$-0.00325896\pi$
$648$		0			0
$649$			142.011i			0.218815i
$650$	−13.3439	−	153.870i	−0.0205290	−	0.236724i
$651$		0			0
$652$	−42.1958	−	241.454i	−0.0647175	−	0.370328i
$653$			504.030i			0.771869i	0.922526	+	0.385934i	$0.126121\pi$
$653$			504.030i			0.771869i	−0.922526	+	0.385934i	$0.873879\pi$
$654$		0			0
$655$	767.375			1.17156
$656$	233.365	+	647.291i	0.355739	+	0.986725i
$657$		0			0
$658$	−918.497	+	525.260i	−1.39589	+	0.798267i
$659$			686.814i			1.04221i	0.853493	+	0.521104i	$0.174479\pi$
$659$			686.814i			1.04221i	−0.853493	+	0.521104i	$0.825521\pi$
$660$		0			0
$661$	−260.765			−0.394500			−0.197250	−	0.980353i	$-0.563201\pi$
$661$	−260.765			−0.394500			−0.197250	+	0.980353i	$0.563201\pi$
$662$	−162.375	+	14.0814i	−0.245279	+	0.0212710i
$663$		0			0
$664$	−250.502	−	943.502i	−0.377262	−	1.42094i
$665$	−295.339	+	136.513i	−0.444118	+	0.205282i
$666$		0			0
$667$			784.951i			1.17684i
$668$	−68.4983	−	391.963i	−0.102542	−	0.586771i
$669$		0			0
$670$	−1310.59	+	113.657i	−1.95611	+	0.169637i
$671$		−	321.146i		−	0.478608i
$672$		0			0
$673$	1162.88			1.72791			0.863953	−	0.503572i	$-0.167981\pi$
$673$	1162.88			1.72791			0.863953	+	0.503572i	$0.167981\pi$
$674$	−89.2011	−	1028.59i	−0.132346	−	1.52610i
$675$		0			0
$676$	527.693	−	92.2180i	0.780610	−	0.136417i
$677$	69.4988			0.102657			0.0513285	−	0.998682i	$-0.483654\pi$
$677$	69.4988			0.102657			0.0513285	+	0.998682i	$0.483654\pi$
$678$		0			0
$679$	−445.963	−	964.821i	−0.656794	−	1.42094i
$680$	−1416.68	+	376.131i	−2.08335	+	0.553134i
$681$		0			0
$682$	23.1986	+	267.507i	0.0340156	+	0.392239i
$683$			576.814i			0.844530i	0.906472	+	0.422265i	$0.138765\pi$
$683$			576.814i			0.844530i	−0.906472	+	0.422265i	$0.861235\pi$
$684$		0			0
$685$	−192.183			−0.280559
$686$	−674.247	−	126.439i	−0.982868	−	0.184313i
$687$		0			0
$688$	−150.323	−	416.957i	−0.218493	−	0.606042i
$689$		−	217.207i		−	0.315249i
$690$		0			0
$691$	941.087			1.36192			0.680960	−	0.732321i	$-0.261563\pi$
$691$	941.087			1.36192			0.680960	+	0.732321i	$0.261563\pi$
$692$	−376.164	+	65.7373i	−0.543589	+	0.0949961i
$693$		0			0
$694$	−913.929	+	79.2573i	−1.31690	+	0.114204i
$695$	−563.728			−0.811119
$696$		0			0
$697$	−1277.54			−1.83291
$698$	−72.6840	−	838.132i	−0.104132	−	1.20076i
$699$		0			0
$700$	−300.080	+	207.942i	−0.428686	+	0.297060i
$701$		−	533.804i		−	0.761489i	−0.924680	−	0.380745i	$-0.875668\pi$
$701$		−	533.804i		−	0.761489i	0.924680	−	0.380745i	$-0.124332\pi$
$702$		0			0
$703$			326.971i			0.465108i
$704$	−205.079	−	358.986i	−0.291306	−	0.509923i
$705$		0			0
$706$	−186.375	+	16.1627i	−0.263987	+	0.0228933i
$707$	−800.313	+	369.924i	−1.13198	+	0.523230i
$708$		0			0
$709$		−	536.848i		−	0.757190i	−0.925562	−	0.378595i	$-0.876407\pi$
$709$		−	536.848i		−	0.757190i	0.925562	−	0.378595i	$-0.123593\pi$
$710$	−90.0667	−	1038.57i	−0.126854	−	1.46278i
$711$		0			0
$712$	−338.038	+	89.7498i	−0.474772	+	0.126053i
$713$			834.468i			1.17036i
$714$		0			0
$715$			235.969i			0.330026i
$716$	173.525	+	992.950i	0.242354	+	1.38680i
$717$		0			0
$718$	103.279	+	1190.92i	0.143842	+	1.65867i
$719$			542.913i			0.755095i	0.925990	+	0.377547i	$0.123232\pi$
$719$			542.913i			0.755095i	−0.925990	+	0.377547i	$0.876768\pi$
$720$		0			0
$721$	229.114	+	495.677i	0.317772	+	0.687485i
$722$	52.5649	+	606.135i	0.0728045	+	0.839522i
$723$		0			0
$724$	869.989	−	152.037i	1.20164	−	0.209996i
$725$			254.904i			0.351591i
$726$		0			0
$727$		−	312.117i		−	0.429322i	−0.976689	−	0.214661i	$-0.931135\pi$
$727$		−	312.117i		−	0.429322i	0.976689	−	0.214661i	$-0.0688646\pi$
$728$	211.754	+	255.271i	0.290871	+	0.350647i
$729$		0			0
$730$	826.023	−	71.6339i	1.13154	−	0.0981286i
$731$	822.933			1.12576
$732$		0			0
$733$	−52.7310			−0.0719386			−0.0359693	−	0.999353i	$-0.511452\pi$
$733$	−52.7310			−0.0719386			−0.0359693	+	0.999353i	$0.511452\pi$
$734$	8.92482	−	0.773973i	0.0121592	−	0.00105446i
$735$		0			0
$736$	−538.566	−	1166.53i	−0.731747	−	1.58496i
$737$	688.935			0.934783
$738$		0			0
$739$		−	783.978i		−	1.06086i	−0.847727	−	0.530432i	$-0.822030\pi$
$739$		−	783.978i		−	1.06086i	0.847727	−	0.530432i	$-0.177970\pi$
$740$	184.259	+	1054.37i	0.248999	+	1.42483i
$741$		0			0
$742$	−445.703	+	254.884i	−0.600678	+	0.343509i
$743$	1098.23			1.47810			0.739051	−	0.673649i	$-0.235274\pi$
$743$	1098.23			1.47810			0.739051	+	0.673649i	$0.235274\pi$
$744$		0			0
$745$			1482.32i			1.98969i
$746$	−242.826	+	21.0582i	−0.325503	+	0.0282281i
$747$		0			0
$748$	756.159	−	132.144i	1.01091	−	0.176663i
$749$	−319.106	−	690.371i	−0.426043	−	0.921724i
$750$		0			0
$751$	−93.6183			−0.124658			−0.0623291	−	0.998056i	$-0.519853\pi$
$751$	−93.6183			−0.124658			−0.0623291	+	0.998056i	$0.519853\pi$
$752$	−410.120	−	1137.56i	−0.545372	−	1.51272i
$753$		0			0
$754$	230.705	−	20.0070i	0.305974	−	0.0265345i
$755$	13.5783			0.0179845
$756$		0			0
$757$		−	380.562i		−	0.502724i	−0.967893	−	0.251362i	$-0.919121\pi$
$757$		−	380.562i		−	0.502724i	0.967893	−	0.251362i	$-0.0808785\pi$
$758$	145.729	−	12.6378i	0.192254	−	0.0166725i
$759$		0			0
$760$	−95.4192	−	359.391i	−0.125552	−	0.472883i
$761$		−	1176.17i		−	1.54556i	−0.634673	−	0.772781i	$-0.718865\pi$
$761$		−	1176.17i		−	1.54556i	0.634673	−	0.772781i	$-0.281135\pi$
$762$		0			0
$763$	353.780	+	765.386i	0.463669	+	1.00313i
$764$	382.338	−	66.8163i	0.500443	−	0.0874559i
$765$		0			0
$766$	−524.322	+	45.4699i	−0.684493	+	0.0593602i
$767$	130.199			0.169751
$768$		0			0
$769$			791.622i			1.02942i	0.857365	+	0.514709i	$0.172100\pi$
$769$			791.622i			1.02942i	−0.857365	+	0.514709i	$0.827900\pi$
$770$	484.203	−	276.900i	0.628835	−	0.359611i
$771$		0			0
$772$	292.332	−	51.0871i	0.378668	−	0.0661750i
$773$	391.607			0.506607			0.253303	−	0.967387i	$-0.418483\pi$
$773$	391.607			0.506607			0.253303	+	0.967387i	$0.418483\pi$
$774$		0			0
$775$			270.984i			0.349657i
$776$	1174.07	−	311.718i	1.51298	−	0.401699i
$777$		0			0
$778$	−17.8673	+	1.54947i	−0.0229656	+	0.00199161i
$779$		−	324.094i		−	0.416038i
$780$		0			0
$781$			545.944i			0.699032i
$782$	2376.65	−	206.107i	3.03920	−	0.263564i
$783$		0			0
$784$	275.325	−	734.066i	0.351179	−	0.936308i
$785$	1095.89			1.39604
$786$		0			0
$787$	427.323			0.542977			0.271489	−	0.962442i	$-0.412484\pi$
$787$	427.323			0.542977			0.271489	+	0.962442i	$0.412484\pi$
$788$	−38.8711	−	222.429i	−0.0493289	−	0.282271i
$789$		0			0
$790$	−20.4845	−	236.210i	−0.0259297	−	0.299000i
$791$	165.863	−	76.6661i	0.209688	−	0.0969230i
$792$		0			0
$793$	−294.436			−0.371293
$794$	−102.277	−	1179.37i	−0.128812	−	1.48536i
$795$		0			0
$796$	186.057	+	1064.66i	0.233740	+	1.33751i
$797$	−1544.99			−1.93851			−0.969255	−	0.246058i	$-0.920864\pi$
$797$	−1544.99			−1.93851			−0.969255	+	0.246058i	$0.920864\pi$
$798$		0			0
$799$	2245.17			2.80998
$800$	−174.893	−	378.818i	−0.218616	−	0.473522i
$801$		0			0
$802$	74.8393	+	862.985i	0.0933158	+	1.07604i
$803$	−434.212			−0.540738
$804$		0			0
$805$	1573.51	−	727.313i	1.95467	−	0.903494i
$806$	245.258	−	21.2691i	0.304290	−	0.0263885i
$807$		0			0
$808$	−258.568	−	973.883i	−0.320010	−	1.20530i
$809$	735.475			0.909116			0.454558	−	0.890717i	$-0.349797\pi$
$809$	735.475			0.909116			0.454558	+	0.890717i	$0.349797\pi$
$810$		0			0
$811$	317.366			0.391327			0.195663	−	0.980671i	$-0.437314\pi$
$811$	317.366			0.391327			0.195663	+	0.980671i	$0.437314\pi$
$812$	−311.777	−	449.923i	−0.383962	−	0.554092i
$813$		0			0
$814$	−48.4295	−	558.449i	−0.0594957	−	0.686056i
$815$			377.938i			0.463727i
$816$		0			0
$817$			208.767i			0.255529i
$818$	−399.556	+	34.6501i	−0.488455	+	0.0423595i
$819$		0			0
$820$	−182.638	−	1045.10i	−0.222729	−	1.27451i
$821$		−	404.042i		−	0.492135i	−0.969253	−	0.246067i	$-0.920862\pi$
$821$		−	404.042i		−	0.492135i	0.969253	−	0.246067i	$-0.0791384\pi$
$822$		0			0
$823$	−744.939			−0.905150			−0.452575	−	0.891726i	$-0.649495\pi$
$823$	−744.939			−0.905150			−0.452575	+	0.891726i	$0.649495\pi$
$824$	−603.178	+	160.145i	−0.732012	+	0.194351i
$825$		0			0
$826$	−152.784	−	267.166i	−0.184968	−	0.323446i
$827$			138.826i			0.167867i	0.996471	+	0.0839334i	$0.0267483\pi$
$827$			138.826i			0.167867i	−0.996471	+	0.0839334i	$0.973252\pi$
$828$		0			0
$829$	37.0766			0.0447245			0.0223623	−	0.999750i	$-0.492881\pi$
$829$	37.0766			0.0447245			0.0223623	+	0.999750i	$0.492881\pi$
$830$	130.043	+	1499.55i	0.156678	+	1.80669i
$831$		0			0
$832$	−329.128	+	188.022i	−0.395586	+	0.225988i
$833$	1108.78	+	943.140i	1.33106	+	1.13222i
$834$		0			0
$835$			613.523i			0.734758i
$836$	33.5232	+	191.827i	0.0400995	+	0.229458i
$837$		0			0
$838$	56.0724	+	646.581i	0.0669122	+	0.771576i
$839$			142.786i			0.170186i	0.996373	+	0.0850931i	$0.0271188\pi$
$839$			142.786i			0.170186i	−0.996373	+	0.0850931i	$0.972881\pi$
$840$		0			0
$841$	458.812			0.545555
$842$	473.714	−	41.0812i	0.562606	−	0.0487900i
$843$		0			0
$844$	−35.9139	−	205.508i	−0.0425521	−	0.243492i
$845$	−825.975			−0.977485
$846$		0			0
$847$	503.683	−	232.814i	0.594667	−	0.274869i
$848$	−199.012	−	552.006i	−0.234684	−	0.650950i
$849$		0			0
$850$	771.790	−	66.9308i	0.907989	−	0.0787421i
$851$		−	1742.04i		−	2.04705i
$852$		0			0
$853$	−978.345			−1.14695			−0.573473	−	0.819224i	$-0.694404\pi$
$853$	−978.345			−1.14695			−0.573473	+	0.819224i	$0.694404\pi$
$854$	345.509	+	604.175i	0.404577	+	0.707465i
$855$		0			0
$856$	840.098	−	223.048i	0.981423	−	0.260570i
$857$		−	816.095i		−	0.952269i	−0.879372	−	0.476135i	$-0.842038\pi$
$857$		−	816.095i		−	0.952269i	0.879372	−	0.476135i	$-0.157962\pi$
$858$		0			0
$859$	−239.289			−0.278567			−0.139284	−	0.990253i	$-0.544480\pi$
$859$	−239.289			−0.278567			−0.139284	+	0.990253i	$0.544480\pi$
$860$	117.647	+	673.204i	0.136799	+	0.782796i
$861$		0			0
$862$	−49.2874	−	568.342i	−0.0571780	−	0.659329i
$863$	694.522			0.804776			0.402388	−	0.915469i	$-0.368180\pi$
$863$	694.522			0.804776			0.402388	+	0.915469i	$0.368180\pi$
$864$		0			0
$865$	588.793			0.680686
$866$	−1044.99	+	90.6232i	−1.20669	+	0.104646i
$867$		0			0
$868$	−331.445	−	478.305i	−0.381849	−	0.551043i
$869$			124.168i			0.142886i
$870$		0			0
$871$		−	631.635i		−	0.725183i
$872$	−931.382	+	247.284i	−1.06810	+	0.283583i
$873$		0			0
$874$	52.2865	+	602.924i	0.0598243	+	0.689845i
$875$	−468.748	+	216.667i	−0.535712	+	0.247619i
$876$		0			0
$877$		−	1245.69i		−	1.42040i	−0.704000	−	0.710200i	$-0.748604\pi$
$877$		−	1245.69i		−	1.42040i	0.704000	−	0.710200i	$-0.251396\pi$
$878$	474.947	−	41.1881i	0.540942	−	0.0469113i
$879$		0			0
$880$	216.202	+	599.688i	0.245684	+	0.681463i
$881$			491.933i			0.558381i	0.960236	+	0.279190i	$0.0900660\pi$
$881$			491.933i			0.558381i	−0.960236	+	0.279190i	$0.909934\pi$
$882$		0			0
$883$		−	1362.09i		−	1.54257i	−0.636489	−	0.771286i	$-0.719614\pi$
$883$		−	1362.09i		−	1.54257i	0.636489	−	0.771286i	$-0.280386\pi$
$884$	−121.153	−	693.268i	−0.137051	−	0.784239i
$885$		0			0
$886$	1284.56	−	111.399i	1.44984	−	0.125732i
$887$			1008.33i			1.13678i	0.822758	+	0.568392i	$0.192434\pi$
$887$			1008.33i			1.13678i	−0.822758	+	0.568392i	$0.807566\pi$
$888$		0			0
$889$	52.2917	−	24.1705i	0.0588208	−	0.0271884i
$890$	537.258	−	46.5918i	0.603661	−	0.0523503i
$891$		0			0
$892$	−91.8263	−	525.451i	−0.102944	−	0.589070i
$893$			569.569i			0.637815i
$894$		0			0
$895$		−	1554.22i		−	1.73656i
$896$	772.037	+	454.726i	0.861648	+	0.507506i
$897$		0			0
$898$	−99.9081	−	1152.06i	−0.111256	−	1.28292i
$899$	−406.298			−0.451944
$900$		0			0
$901$	1089.48			1.20919
$902$	48.0033	+	553.535i	0.0532187	+	0.613675i
$903$		0			0
$904$	53.5879	+	201.836i	0.0592786	+	0.223270i
$905$	−1361.76			−1.50470
$906$		0			0
$907$			213.079i			0.234928i	0.993077	+	0.117464i	$0.0374764\pi$
$907$			213.079i			0.234928i	−0.993077	+	0.117464i	$0.962524\pi$
$908$	1416.70	−	247.579i	1.56025	−	0.272664i
$909$		0			0
$910$	−253.870	−	443.930i	−0.278978	−	0.487836i
$911$	−210.202			−0.230738			−0.115369	−	0.993323i	$-0.536805\pi$
$911$	−210.202			−0.230738			−0.115369	+	0.993323i	$0.536805\pi$
$912$		0			0
$913$		−	788.263i		−	0.863377i
$914$	−91.7216	−	1057.66i	−0.100352	−	1.15718i
$915$		0			0
$916$	1545.88	−	270.154i	1.68764	−	0.294928i
$917$	790.579	−	365.425i	0.862136	−	0.398500i
$918$		0			0
$919$	−743.660			−0.809205			−0.404603	−	0.914493i	$-0.632590\pi$
$919$	−743.660			−0.809205			−0.404603	+	0.914493i	$0.632590\pi$
$920$	508.375	+	1914.77i	0.552582	+	2.08127i
$921$		0			0
$922$	−45.7110	−	527.101i	−0.0495781	−	0.571693i
$923$	500.536			0.542293
$924$		0			0
$925$		−	565.707i		−	0.611575i
$926$	28.1649	+	324.774i	0.0304156	+	0.350728i
$927$		0			0
$928$	567.978	−	262.224i	0.612045	−	0.282569i
$929$		−	987.475i		−	1.06294i	−0.847076	−	0.531472i	$-0.821639\pi$
$929$		−	987.475i		−	1.06294i	0.847076	−	0.531472i	$-0.178361\pi$
$930$		0			0
$931$	−239.262	+	281.281i	−0.256994	+	0.302128i
$932$	946.530	−	165.413i	1.01559	−	0.177482i
$933$		0			0
$934$	78.0594	+	900.117i	0.0835754	+	0.963722i
$935$	−1183.58			−1.26586
$936$		0			0
$937$		−	616.607i		−	0.658065i	−0.944319	−	0.329033i	$-0.893277\pi$
$937$		−	616.607i		−	0.658065i	0.944319	−	0.329033i	$-0.106723\pi$
$938$	−1296.10	+	741.199i	−1.38177	+	0.790191i
$939$		0			0
$940$	320.971	+	1836.67i	0.341459	+	1.95391i
$941$	1331.47			1.41495			0.707475	−	0.706738i	$-0.249834\pi$
$941$	1331.47			1.41495			0.707475	+	0.706738i	$0.249834\pi$
$942$		0			0
$943$			1726.71i			1.83108i
$944$	330.887	−	119.293i	0.350516	−	0.126370i
$945$		0			0
$946$	−30.9216	−	356.563i	−0.0326867	−	0.376916i
$947$			1159.31i			1.22419i	0.790785	+	0.612093i	$0.209672\pi$
$947$			1159.31i			1.22419i	−0.790785	+	0.612093i	$0.790328\pi$
$948$		0			0
$949$			398.098i			0.419492i
$950$	16.9794	+	195.793i	0.0178731	+	0.206097i
$951$		0			0
$952$	−1280.40	+	1062.13i	−1.34496	+	1.11568i
$953$	−1262.64			−1.32491			−0.662456	−	0.749101i	$-0.730486\pi$
$953$	−1262.64			−1.32491			−0.662456	+	0.749101i	$0.730486\pi$
$954$		0			0
$955$	−598.458			−0.626657
$956$	523.456	−	91.4778i	0.547549	−	0.0956880i
$957$		0			0
$958$	1352.59	−	117.299i	1.41189	−	0.122441i
$959$	−197.994	+	91.5177i	−0.206459	+	0.0954303i
$960$		0			0
$961$	529.072			0.550543
$962$	−512.002	+	44.4015i	−0.532226	+	0.0461554i
$963$		0			0
$964$	−230.905	−	1321.29i	−0.239528	−	1.37063i
$965$	−457.575			−0.474171
$966$		0			0
$967$	384.116			0.397224			0.198612	−	0.980078i	$-0.436357\pi$
$967$	384.116			0.397224			0.198612	+	0.980078i	$0.436357\pi$
$968$	162.732	+	612.921i	0.168112	+	0.633183i
$969$		0			0
$970$	−1866.00	+	161.822i	−1.92371	+	0.166827i
$971$	−1655.31			−1.70474			−0.852372	−	0.522937i	$-0.824836\pi$
$971$	−1655.31			−1.70474			−0.852372	+	0.522937i	$0.824836\pi$
$972$		0			0
$973$	−580.774	+	268.448i	−0.596890	+	0.275897i
$974$	−32.2015	−	371.321i	−0.0330611	−	0.381233i
$975$		0			0
$976$	−748.274	+	269.771i	−0.766674	+	0.276405i
$977$	−265.698			−0.271953			−0.135976	−	0.990712i	$-0.543417\pi$
$977$	−265.698			−0.271953			−0.135976	+	0.990712i	$0.543417\pi$
$978$		0			0
$979$	−282.419			−0.288477
$980$	−613.028	+	1041.87i	−0.625539	+	1.06313i
$981$		0			0
$982$	390.863	−	33.8962i	0.398028	−	0.0345175i
$983$		−	297.641i		−	0.302788i	−0.988473	−	0.151394i	$-0.951624\pi$
$983$		−	297.641i		−	0.302788i	0.988473	−	0.151394i	$-0.0483763\pi$
$984$		0			0
$985$			348.159i			0.353461i
$986$	100.352	+	1157.18i	0.101777	+	1.17361i
$987$		0			0
$988$	175.872	−	30.7350i	0.178009	−	0.0311083i
$989$		−	1112.27i		−	1.12464i
$990$		0			0
$991$	−837.488			−0.845093			−0.422547	−	0.906341i	$-0.638864\pi$
$991$	−837.488			−0.845093			−0.422547	+	0.906341i	$0.638864\pi$
$992$	603.808	−	278.766i	0.608677	−	0.281014i
$993$		0			0
$994$	−587.360	−	1027.09i	−0.590906	−	1.03329i
$995$		−	1666.47i		−	1.67484i
$996$		0			0
$997$	1192.10			1.19569			0.597843	−	0.801613i	$-0.296024\pi$
$997$	1192.10			1.19569			0.597843	+	0.801613i	$0.296024\pi$
$998$	970.269	−	84.1431i	0.972214	−	0.0843118i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.l.h.181.14		32
3.2	odd	2		168.3.l.a.13.19	yes	32
4.3	odd	2		2016.3.l.h.433.27		32
7.6	odd	2	inner	504.3.l.h.181.13		32
8.3	odd	2		2016.3.l.h.433.6		32
8.5	even	2	inner	504.3.l.h.181.15		32
12.11	even	2		672.3.l.a.433.22		32
21.20	even	2		168.3.l.a.13.20	yes	32
24.5	odd	2		168.3.l.a.13.18	yes	32
24.11	even	2		672.3.l.a.433.11		32
28.27	even	2		2016.3.l.h.433.5		32
56.13	odd	2	inner	504.3.l.h.181.16		32
56.27	even	2		2016.3.l.h.433.28		32
84.83	odd	2		672.3.l.a.433.6		32
168.83	odd	2		672.3.l.a.433.27		32
168.125	even	2		168.3.l.a.13.17	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.l.a.13.17	✓	32	168.125	even	2
168.3.l.a.13.18	yes	32	24.5	odd	2
168.3.l.a.13.19	yes	32	3.2	odd	2
168.3.l.a.13.20	yes	32	21.20	even	2
504.3.l.h.181.13		32	7.6	odd	2	inner
504.3.l.h.181.14		32	1.1	even	1	trivial
504.3.l.h.181.15		32	8.5	even	2	inner
504.3.l.h.181.16		32	56.13	odd	2	inner
672.3.l.a.433.6		32	84.83	odd	2
672.3.l.a.433.11		32	24.11	even	2
672.3.l.a.433.22		32	12.11	even	2
672.3.l.a.433.27		32	168.83	odd	2
2016.3.l.h.433.5		32	28.27	even	2
2016.3.l.h.433.6		32	8.3	odd	2
2016.3.l.h.433.27		32	4.3	odd	2
2016.3.l.h.433.28		32	56.27	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.172794 - 1.99252i) q^{2} +(-3.94028 + 0.688593i) q^{4} +6.16756 q^{5} +(6.35406 - 2.93700i) q^{7} +(2.05289 + 7.73212i) q^{8} +(-1.06572 - 12.2890i) q^{10} +6.45991i q^{11} +5.92263 q^{13} +(-6.94998 - 12.1531i) q^{14} +(15.0517 - 5.42650i) q^{16} +29.7070i q^{17} -7.53626 q^{19} +(-24.3019 + 4.24694i) q^{20} +(12.8715 - 1.11624i) q^{22} +40.1517 q^{23} +13.0388 q^{25} +(-1.02340 - 11.8010i) q^{26} +(-23.0144 + 15.9480i) q^{28} +19.5496i q^{29} +20.7829i q^{31} +(-13.4133 - 29.0531i) q^{32} +(59.1918 - 5.13320i) q^{34} +(39.1890 - 18.1141i) q^{35} -43.3864i q^{37} +(1.30222 + 15.0162i) q^{38} +(12.6614 + 47.6883i) q^{40} +43.0046i q^{41} -27.7017i q^{43} +(-4.44825 - 25.4539i) q^{44} +(-6.93799 - 80.0032i) q^{46} -75.5771i q^{47} +(31.7481 - 37.3237i) q^{49} +(-2.25303 - 25.9801i) q^{50} +(-23.3368 + 4.07828i) q^{52} -36.6740i q^{53} +39.8419i q^{55} +(35.7534 + 43.1010i) q^{56} +(38.9531 - 3.37807i) q^{58} +21.9834 q^{59} -49.7137 q^{61} +(41.4103 - 3.59116i) q^{62} +(-55.5712 + 31.7464i) q^{64} +36.5282 q^{65} -106.648i q^{67} +(-20.4560 - 117.054i) q^{68} +(-42.8644 - 74.9550i) q^{70} +84.5125 q^{71} +67.2164i q^{73} +(-86.4484 + 7.49693i) q^{74} +(29.6950 - 5.18941i) q^{76} +(18.9728 + 41.0467i) q^{77} +19.2213 q^{79} +(92.8321 - 33.4683i) q^{80} +(85.6876 - 7.43095i) q^{82} -122.024 q^{83} +183.220i q^{85} +(-55.1962 + 4.78669i) q^{86} +(-49.9488 + 13.2615i) q^{88} +43.7186i q^{89} +(37.6327 - 17.3948i) q^{91} +(-158.209 + 27.6482i) q^{92} +(-150.589 + 13.0593i) q^{94} -46.4803 q^{95} -151.843i q^{97} +(-79.8542 - 56.8094i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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