LMFDB - Embedded newform 176.5.n.c.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,5,Mod(17,176)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("176.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	176.n (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.1931135028$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 $ x^16 - 4x^15 + 138x^14 - 428x^13 + 7783x^12 - 18620x^11 + 235604x^10 - 425164x^9 + 4199998x^8 - 5446172x^7 + 45313276x^6 - 38408204x^5 + 290282498x^4 - 132888724x^3 + 1016893202x^2 - 153602264*x + 1499670491
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			145.3
Root			$0.809017 + 5.77971i$ of defining polynomial
Character	$\chi$	$=$	176.145
Dual form			176.5.n.c.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.20187 - 2.32629i) q^{3} +(13.3838 + 41.1910i) q^{5} +(7.80030 - 10.7362i) q^{7} +(-20.1901 + 62.1386i) q^{9} +O(q^{10})$	\(q+(3.20187 - 2.32629i) q^{3} +(13.3838 + 41.1910i) q^{5} +(7.80030 - 10.7362i) q^{7} +(-20.1901 + 62.1386i) q^{9} +(-90.5882 + 80.2170i) q^{11} +(-170.407 - 55.3685i) q^{13} +(138.675 + 100.754i) q^{15} +(167.901 - 54.5543i) q^{17} +(-213.240 - 293.500i) q^{19} -52.5217i q^{21} -564.946 q^{23} +(-1011.94 + 735.215i) q^{25} +(178.970 + 550.813i) q^{27} +(505.658 - 695.978i) q^{29} +(-276.141 + 849.875i) q^{31} +(-103.443 + 467.579i) q^{33} +(546.632 + 177.611i) q^{35} +(-164.418 - 119.457i) q^{37} +(-674.423 + 219.133i) q^{39} +(1540.12 + 2119.80i) q^{41} +2603.62i q^{43} -2829.77 q^{45} +(1250.87 - 908.812i) q^{47} +(687.529 + 2116.00i) q^{49} +(410.687 - 565.262i) q^{51} +(-454.551 + 1398.97i) q^{53} +(-4516.63 - 2657.81i) q^{55} +(-1365.53 - 443.689i) q^{57} +(-3977.33 - 2889.70i) q^{59} +(-1508.75 + 490.221i) q^{61} +(509.644 + 701.464i) q^{63} -7760.26i q^{65} +3004.99 q^{67} +(-1808.88 + 1314.23i) q^{69} +(2625.89 + 8081.67i) q^{71} +(2674.58 - 3681.24i) q^{73} +(-1529.76 + 4708.12i) q^{75} +(154.610 + 1598.29i) q^{77} +(-2009.88 - 653.050i) q^{79} +(-2427.13 - 1763.41i) q^{81} +(8994.67 - 2922.55i) q^{83} +(4494.29 + 6185.86i) q^{85} -3404.74i q^{87} +14557.2 q^{89} +(-1923.67 + 1397.63i) q^{91} +(1092.89 + 3363.57i) q^{93} +(9235.60 - 12711.7i) q^{95} +(2097.12 - 6454.28i) q^{97} +(-3155.59 - 7248.61i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} + 30 q^{5} - 150 q^{7} + 110 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 + 30 * q^5 - 150 * q^7 + 110 * q^9	$ 16 q + 2 q^{3} + 30 q^{5} - 150 q^{7} + 110 q^{9} + 30 q^{11} - 510 q^{13} + 1398 q^{15} + 1770 q^{17} - 1020 q^{19} + 2424 q^{23} - 858 q^{25} - 2224 q^{27} + 4890 q^{29} - 602 q^{31} - 2648 q^{33} + 8670 q^{35} - 4518 q^{37} + 1130 q^{39} + 1290 q^{41} + 12152 q^{45} - 642 q^{47} + 9534 q^{49} + 1500 q^{51} + 2598 q^{53} - 2582 q^{55} + 9140 q^{57} - 6660 q^{59} - 27410 q^{61} + 27260 q^{63} - 21524 q^{67} + 11416 q^{69} + 5562 q^{71} - 7790 q^{73} - 3576 q^{75} - 1110 q^{77} + 2770 q^{79} - 25464 q^{81} + 36900 q^{83} - 24750 q^{85} + 46596 q^{89} - 32370 q^{91} + 20722 q^{93} - 74250 q^{95} - 3732 q^{97} - 45802 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 + 30 * q^5 - 150 * q^7 + 110 * q^9 + 30 * q^11 - 510 * q^13 + 1398 * q^15 + 1770 * q^17 - 1020 * q^19 + 2424 * q^23 - 858 * q^25 - 2224 * q^27 + 4890 * q^29 - 602 * q^31 - 2648 * q^33 + 8670 * q^35 - 4518 * q^37 + 1130 * q^39 + 1290 * q^41 + 12152 * q^45 - 642 * q^47 + 9534 * q^49 + 1500 * q^51 + 2598 * q^53 - 2582 * q^55 + 9140 * q^57 - 6660 * q^59 - 27410 * q^61 + 27260 * q^63 - 21524 * q^67 + 11416 * q^69 + 5562 * q^71 - 7790 * q^73 - 3576 * q^75 - 1110 * q^77 + 2770 * q^79 - 25464 * q^81 + 36900 * q^83 - 24750 * q^85 + 46596 * q^89 - 32370 * q^91 + 20722 * q^93 - 74250 * q^95 - 3732 * q^97 - 45802 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{10}\right)$

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
$3$	3.20187	−	2.32629i	0.355763	−	0.258477i	−0.395520	−	0.918458i	$-0.629435\pi$
$3$	3.20187	−	2.32629i	0.355763	−	0.258477i	0.751283	+	0.659980i	$0.229435\pi$
$4$		0			0
$5$	13.3838	+	41.1910i	0.535350	+	1.64764i	0.742891	+	0.669413i	$0.233454\pi$
$5$	13.3838	+	41.1910i	0.535350	+	1.64764i	−0.207540	+	0.978226i	$0.566546\pi$
$6$		0			0
$7$	7.80030	−	10.7362i	0.159190	−	0.219106i	−0.721970	−	0.691924i	$-0.756763\pi$
$7$	7.80030	−	10.7362i	0.159190	−	0.219106i	0.881160	+	0.472818i	$0.156763\pi$
$8$		0			0
$9$	−20.1901	+	62.1386i	−0.249260	+	0.767143i
$10$		0			0
$11$	−90.5882	+	80.2170i	−0.748663	+	0.662951i
$11$	−90.5882	+	80.2170i	−0.748663	+	0.662951i
$12$		0			0
$13$	−170.407	−	55.3685i	−1.00832	−	0.327624i	−0.242137	−	0.970242i	$-0.577848\pi$
$13$	−170.407	−	55.3685i	−1.00832	−	0.327624i	−0.766187	+	0.642618i	$0.777848\pi$
$14$		0			0
$15$	138.675	+	100.754i	0.616335	+	0.447794i
$16$		0			0
$17$	167.901	−	54.5543i	0.580972	−	0.188769i	−0.00376408	−	0.999993i	$-0.501198\pi$
$17$	167.901	−	54.5543i	0.580972	−	0.188769i	0.584736	+	0.811224i	$0.301198\pi$
$18$		0			0
$19$	−213.240	−	293.500i	−0.590693	−	0.813019i	0.404123	−	0.914704i	$-0.367577\pi$
$19$	−213.240	−	293.500i	−0.590693	−	0.813019i	−0.994817	+	0.101685i	$0.967577\pi$
$20$		0			0
$21$		−	52.5217i		−	0.119097i
$22$		0			0
$23$	−564.946			−1.06795			−0.533975	−	0.845500i	$-0.679302\pi$
$23$	−564.946			−1.06795			−0.533975	+	0.845500i	$0.679302\pi$
$24$		0			0
$25$	−1011.94	+	735.215i	−1.61910	+	1.17634i
$26$		0			0
$27$	178.970	+	550.813i	0.245501	+	0.755574i
$28$		0			0
$29$	505.658	−	695.978i	0.601258	−	0.827560i	−0.394565	−	0.918868i	$-0.629105\pi$
$29$	505.658	−	695.978i	0.601258	−	0.827560i	0.995823	+	0.0913079i	$0.0291048\pi$
$30$		0			0
$31$	−276.141	+	849.875i	−0.287348	+	0.884365i	0.698338	+	0.715769i	$0.253923\pi$
$31$	−276.141	+	849.875i	−0.287348	+	0.884365i	−0.985685	+	0.168596i	$0.946077\pi$
$32$		0			0
$33$	−103.443	+	467.579i	−0.0949893	+	0.429366i
$34$		0			0
$35$	546.632	+	177.611i	0.446230	+	0.144989i
$36$		0			0
$37$	−164.418	−	119.457i	−0.120101	−	0.0872585i	0.526113	−	0.850415i	$-0.323649\pi$
$37$	−164.418	−	119.457i	−0.120101	−	0.0872585i	−0.646214	+	0.763156i	$0.723649\pi$
$38$		0			0
$39$	−674.423	+	219.133i	−0.443408	+	0.144072i
$40$		0			0
$41$	1540.12	+	2119.80i	0.916196	+	1.26103i	0.965006	+	0.262227i	$0.0844569\pi$
$41$	1540.12	+	2119.80i	0.916196	+	1.26103i	−0.0488107	+	0.998808i	$0.515543\pi$
$42$		0			0
$43$			2603.62i			1.40812i	0.710140	+	0.704061i	$0.248632\pi$
$43$			2603.62i			1.40812i	−0.710140	+	0.704061i	$0.751368\pi$
$44$		0			0
$45$	−2829.77			−1.39742
$46$		0			0
$47$	1250.87	−	908.812i	0.566262	−	0.411413i	−0.267484	−	0.963562i	$-0.586192\pi$
$47$	1250.87	−	908.812i	0.566262	−	0.411413i	0.833745	+	0.552149i	$0.186192\pi$
$48$		0			0
$49$	687.529	+	2116.00i	0.286351	+	0.881298i
$50$		0			0
$51$	410.687	−	565.262i	0.157896	−	0.217325i
$52$		0			0
$53$	−454.551	+	1398.97i	−0.161820	+	0.498030i	−0.998788	−	0.0492218i	$-0.984326\pi$
$53$	−454.551	+	1398.97i	−0.161820	+	0.498030i	0.836968	+	0.547251i	$0.184326\pi$
$54$		0			0
$55$	−4516.63	−	2657.81i	−1.49310	−	0.878616i
$56$		0			0
$57$	−1365.53	−	443.689i	−0.420294	−	0.136562i
$58$		0			0
$59$	−3977.33	−	2889.70i	−1.14258	−	0.830135i	−0.155106	−	0.987898i	$-0.549572\pi$
$59$	−3977.33	−	2889.70i	−1.14258	−	0.830135i	−0.987477	+	0.157762i	$0.949572\pi$
$60$		0			0
$61$	−1508.75	+	490.221i	−0.405468	+	0.131745i	−0.504648	−	0.863325i	$-0.668378\pi$
$61$	−1508.75	+	490.221i	−0.405468	+	0.131745i	0.0991805	+	0.995069i	$0.468378\pi$
$62$		0			0
$63$	509.644	+	701.464i	0.128406	+	0.176736i
$64$		0			0
$65$		−	7760.26i		−	1.83675i
$66$		0			0
$67$	3004.99			0.669413			0.334706	−	0.942323i	$-0.391363\pi$
$67$	3004.99			0.669413			0.334706	+	0.942323i	$0.391363\pi$
$68$		0			0
$69$	−1808.88	+	1314.23i	−0.379937	+	0.276041i
$70$		0			0
$71$	2625.89	+	8081.67i	0.520907	+	1.60319i	0.772270	+	0.635295i	$0.219121\pi$
$71$	2625.89	+	8081.67i	0.520907	+	1.60319i	−0.251362	+	0.967893i	$0.580879\pi$
$72$		0			0
$73$	2674.58	−	3681.24i	0.501891	−	0.690793i	−0.480635	−	0.876921i	$-0.659594\pi$
$73$	2674.58	−	3681.24i	0.501891	−	0.690793i	0.982526	+	0.186127i	$0.0595937\pi$
$74$		0			0
$75$	−1529.76	+	4708.12i	−0.271958	+	0.836999i
$76$		0			0
$77$	154.610	+	1598.29i	0.0260769	+	0.269572i
$78$		0			0
$79$	−2009.88	−	653.050i	−0.322045	−	0.104639i	0.143533	−	0.989645i	$-0.454154\pi$
$79$	−2009.88	−	653.050i	−0.322045	−	0.104639i	−0.465578	+	0.885007i	$0.654154\pi$
$80$		0			0
$81$	−2427.13	−	1763.41i	−0.369932	−	0.268772i
$82$		0			0
$83$	8994.67	−	2922.55i	1.30566	−	0.424234i	0.428111	−	0.903726i	$-0.359179\pi$
$83$	8994.67	−	2922.55i	1.30566	−	0.424234i	0.877546	+	0.479493i	$0.159179\pi$
$84$		0			0
$85$	4494.29	+	6185.86i	0.622047	+	0.856174i
$86$		0			0
$87$		−	3404.74i		−	0.449827i
$88$		0			0
$89$	14557.2			1.83779			0.918896	−	0.394499i	$-0.129082\pi$
$89$	14557.2			1.83779			0.918896	+	0.394499i	$0.129082\pi$
$90$		0			0
$91$	−1923.67	+	1397.63i	−0.232299	+	0.168775i
$92$		0			0
$93$	1092.89	+	3363.57i	0.126360	+	0.388897i
$94$		0			0
$95$	9235.60	−	12711.7i	1.02333	−	1.40850i
$96$		0			0
$97$	2097.12	−	6454.28i	0.222885	−	0.685969i	−0.775614	−	0.631207i	$-0.782560\pi$
$97$	2097.12	−	6454.28i	0.222885	−	0.685969i	0.998499	−	0.0547624i	$-0.0174401\pi$
$98$		0			0
$99$	−3155.59	−	7248.61i	−0.321966	−	0.739579i
$100$		0			0
$101$	−12997.2	−	4223.06i	−1.27411	−	0.413985i	−0.407611	−	0.913156i	$-0.633638\pi$
$101$	−12997.2	−	4223.06i	−1.27411	−	0.413985i	−0.866504	+	0.499171i	$0.833638\pi$
$102$		0			0
$103$	995.164	+	723.029i	0.0938038	+	0.0681524i	0.633699	−	0.773580i	$-0.281536\pi$
$103$	995.164	+	723.029i	0.0938038	+	0.0681524i	−0.539895	+	0.841733i	$0.681536\pi$
$104$		0			0
$105$	2163.42	−	702.937i	0.196228	−	0.0637585i
$106$		0			0
$107$	4974.60	+	6846.95i	0.434501	+	0.598040i	0.968979	−	0.247143i	$-0.0794917\pi$
$107$	4974.60	+	6846.95i	0.434501	+	0.598040i	−0.534478	+	0.845182i	$0.679492\pi$
$108$		0			0
$109$			7648.65i			0.643771i	0.946779	+	0.321886i	$0.104317\pi$
$109$			7648.65i			0.643771i	−0.946779	+	0.321886i	$0.895683\pi$
$110$		0			0
$111$	−804.338			−0.0652819
$112$		0			0
$113$	7345.60	−	5336.89i	0.575269	−	0.417957i	−0.261747	−	0.965137i	$-0.584298\pi$
$113$	7345.60	−	5336.89i	0.575269	−	0.417957i	0.837015	+	0.547180i	$0.184298\pi$
$114$		0			0
$115$	−7561.10	−	23270.7i	−0.571728	−	1.75960i
$116$		0			0
$117$	6881.04	−	9470.94i	0.502670	−	0.691865i
$118$		0			0
$119$	723.972	−	2228.16i	0.0511243	−	0.157345i
$120$		0			0
$121$	1771.46	−	14533.4i	0.120993	−	0.992653i
$122$		0			0
$123$	9862.55	+	3204.54i	0.651897	+	0.211814i
$124$		0			0
$125$	−21928.3	−	15931.8i	−1.40341	−	1.01964i
$126$		0			0
$127$	6550.78	−	2128.48i	0.406149	−	0.131966i	−0.0988156	−	0.995106i	$-0.531505\pi$
$127$	6550.78	−	2128.48i	0.406149	−	0.131966i	0.504965	+	0.863140i	$0.331505\pi$
$128$		0			0
$129$	6056.78	+	8336.44i	0.363967	+	0.500958i
$130$		0			0
$131$			1471.01i			0.0857182i	0.999081	+	0.0428591i	$0.0136467\pi$
$131$			1471.01i			0.0857182i	−0.999081	+	0.0428591i	$0.986353\pi$
$132$		0			0
$133$	−4814.41			−0.272170
$134$		0			0
$135$	−20293.3	+	14743.9i	−1.11348	+	0.808994i
$136$		0			0
$137$	5600.55	+	17236.7i	0.298394	+	0.918361i	0.982060	+	0.188567i	$0.0603841\pi$
$137$	5600.55	+	17236.7i	0.298394	+	0.918361i	−0.683667	+	0.729794i	$0.739616\pi$
$138$		0			0
$139$	−5984.50	+	8236.96i	−0.309741	+	0.426322i	−0.935300	−	0.353855i	$-0.884871\pi$
$139$	−5984.50	+	8236.96i	−0.309741	+	0.426322i	0.625559	+	0.780176i	$0.284871\pi$
$140$		0			0
$141$	1890.97	−	5819.79i	0.0951142	−	0.292731i
$142$		0			0
$143$	19878.3	−	8653.78i	0.972094	−	0.423189i
$144$		0			0
$145$	35435.6	+	11513.7i	1.68540	+	0.547621i
$146$		0			0
$147$	7123.80	+	5175.75i	0.329668	+	0.239518i
$148$		0			0
$149$	−25251.0	+	8204.56i	−1.13738	+	0.369558i	−0.816377	−	0.577519i	$-0.804021\pi$
$149$	−25251.0	+	8204.56i	−1.13738	+	0.369558i	−0.321006	+	0.947077i	$0.604021\pi$
$150$		0			0
$151$	11161.2	+	15362.0i	0.489503	+	0.673744i	0.980296	−	0.197533i	$-0.0632928\pi$
$151$	11161.2	+	15362.0i	0.489503	+	0.673744i	−0.490793	+	0.871276i	$0.663293\pi$
$152$		0			0
$153$			11534.6i			0.492741i
$154$		0			0
$155$	−38703.0			−1.61095
$156$		0			0
$157$	2755.25	−	2001.81i	0.111779	−	0.0812124i	−0.530491	−	0.847690i	$-0.677993\pi$
$157$	2755.25	−	2001.81i	0.111779	−	0.0812124i	0.642271	+	0.766478i	$0.277993\pi$
$158$		0			0
$159$	1798.99	+	5536.72i	0.0711598	+	0.219007i
$160$		0			0
$161$	−4406.74	+	6065.36i	−0.170007	+	0.233994i
$162$		0			0
$163$	−2632.77	+	8102.84i	−0.0990918	+	0.304973i	−0.988298	−	0.152533i	$-0.951257\pi$
$163$	−2632.77	+	8102.84i	−0.0990918	+	0.304973i	0.889207	+	0.457506i	$0.151257\pi$
$164$		0			0
$165$	−20644.5	+	1997.04i	−0.758292	+	0.0733530i
$166$		0			0
$167$	−12611.3	−	4097.65i	−0.452196	−	0.146927i	0.0740598	−	0.997254i	$-0.476404\pi$
$167$	−12611.3	−	4097.65i	−0.452196	−	0.146927i	−0.526255	+	0.850327i	$0.676404\pi$
$168$		0			0
$169$	2866.45	+	2082.59i	0.100362	+	0.0729174i
$170$		0			0
$171$	22543.0	−	7324.67i	0.770939	−	0.250493i
$172$		0			0
$173$	−12984.4	−	17871.4i	−0.433839	−	0.597128i	0.534990	−	0.844858i	$-0.320315\pi$
$173$	−12984.4	−	17871.4i	−0.433839	−	0.597128i	−0.968829	+	0.247730i	$0.920315\pi$
$174$		0			0
$175$			16599.2i			0.542016i
$176$		0			0
$177$	−19457.2			−0.621060
$178$		0			0
$179$	−6760.86	+	4912.05i	−0.211006	+	0.153305i	−0.688269	−	0.725456i	$-0.741629\pi$
$179$	−6760.86	+	4912.05i	−0.211006	+	0.153305i	0.477263	+	0.878761i	$0.341629\pi$
$180$		0			0
$181$	3111.80	+	9577.13i	0.0949848	+	0.292333i	0.987250	−	0.159179i	$-0.0508847\pi$
$181$	3111.80	+	9577.13i	0.0949848	+	0.292333i	−0.892265	+	0.451512i	$0.850885\pi$
$182$		0			0
$183$	−3690.41	+	5079.41i	−0.110198	+	0.151674i
$184$		0			0
$185$	2720.01	−	8371.34i	0.0794744	−	0.244597i
$186$		0			0
$187$	−10833.7	+	18410.5i	−0.309808	+	0.526480i
$188$		0			0
$189$	7309.66	+	2375.05i	0.204632	+	0.0664890i
$190$		0			0
$191$	−28569.5	−	20757.0i	−0.783134	−	0.568980i	0.122784	−	0.992433i	$-0.460818\pi$
$191$	−28569.5	−	20757.0i	−0.783134	−	0.568980i	−0.905918	+	0.423453i	$0.860818\pi$
$192$		0			0
$193$	−7441.19	+	2417.79i	−0.199769	+	0.0649088i	−0.407192	−	0.913342i	$-0.633492\pi$
$193$	−7441.19	+	2417.79i	−0.199769	+	0.0649088i	0.207424	+	0.978251i	$0.433492\pi$
$194$		0			0
$195$	−18052.6	−	24847.3i	−0.474757	−	0.653447i
$196$		0			0
$197$		−	1473.23i		−	0.0379610i	−0.999820	−	0.0189805i	$-0.993958\pi$
$197$		−	1473.23i		−	0.0379610i	0.999820	−	0.0189805i	$-0.00604205\pi$
$198$		0			0
$199$	26096.6			0.658987			0.329494	−	0.944158i	$-0.393122\pi$
$199$	26096.6			0.658987			0.329494	+	0.944158i	$0.393122\pi$
$200$		0			0
$201$	9621.59	−	6990.49i	0.238152	−	0.173028i
$202$		0			0
$203$	−3527.87	−	10857.7i	−0.0856093	−	0.263478i
$204$		0			0
$205$	−66704.0	+	91810.1i	−1.58725	+	2.18466i
$206$		0			0
$207$	11406.3	−	35104.9i	0.266197	−	0.819271i
$208$		0			0
$209$	42860.8	+	9482.15i	0.981222	+	0.217077i
$210$		0			0
$211$	68859.0	+	22373.6i	1.54666	+	0.502541i	0.953205	−	0.302323i	$-0.0977622\pi$
$211$	68859.0	+	22373.6i	1.54666	+	0.502541i	0.593458	+	0.804865i	$0.297762\pi$
$212$		0			0
$213$	27208.1	+	19767.8i	0.599707	+	0.435713i
$214$		0			0
$215$	−107246.	+	34846.2i	−2.32008	+	0.753839i
$216$		0			0
$217$	6970.43	+	9593.98i	0.148027	+	0.203741i
$218$		0			0
$219$		−	18008.7i		−	0.375486i
$220$		0			0
$221$	−31632.0			−0.647653
$222$		0			0
$223$	22887.6	−	16628.8i	0.460246	−	0.334388i	−0.333382	−	0.942792i	$-0.608190\pi$
$223$	22887.6	−	16628.8i	0.460246	−	0.334388i	0.793628	+	0.608404i	$0.208190\pi$
$224$		0			0
$225$	−25254.2	−	77724.3i	−0.498848	−	1.53530i
$226$		0			0
$227$	−42352.4	+	58293.1i	−0.821913	+	1.13127i	0.167461	+	0.985879i	$0.446443\pi$
$227$	−42352.4	+	58293.1i	−0.821913	+	1.13127i	−0.989375	+	0.145388i	$0.953557\pi$
$228$		0			0
$229$	2762.09	−	8500.84i	0.0526704	−	0.162103i	−0.921261	−	0.388944i	$-0.872840\pi$
$229$	2762.09	−	8500.84i	0.0526704	−	0.162103i	0.973932	+	0.226841i	$0.0728399\pi$
$230$		0			0
$231$	4213.13	+	4757.84i	0.0789552	+	0.0891633i
$232$		0			0
$233$	46046.9	+	14961.6i	0.848182	+	0.275591i	0.700684	−	0.713472i	$-0.252878\pi$
$233$	46046.9	+	14961.6i	0.848182	+	0.275591i	0.147497	+	0.989062i	$0.452878\pi$
$234$		0			0
$235$	54176.2	+	39361.3i	0.981009	+	0.712745i
$236$		0			0
$237$	−7954.57	+	2584.59i	−0.141618	+	0.0460146i
$238$		0			0
$239$	31831.6	+	43812.5i	0.557266	+	0.767011i	0.990976	−	0.134041i	$-0.0427955\pi$
$239$	31831.6	+	43812.5i	0.557266	+	0.767011i	−0.433709	+	0.901053i	$0.642796\pi$
$240$		0			0
$241$		−	54166.9i		−	0.932610i	−0.884624	−	0.466305i	$-0.845585\pi$
$241$		−	54166.9i		−	0.932610i	0.884624	−	0.466305i	$-0.154415\pi$
$242$		0			0
$243$	−58785.5			−0.995537
$244$		0			0
$245$	−77958.2	+	56640.0i	−1.29876	+	0.943606i
$246$		0			0
$247$	20086.9	+	61821.2i	0.329245	+	1.01331i
$248$		0			0
$249$	22001.0	−	30281.8i	0.354850	−	0.488409i
$250$		0			0
$251$	−4416.42	+	13592.3i	−0.0701008	+	0.215748i	−0.979969	−	0.199149i	$-0.936182\pi$
$251$	−4416.42	+	13592.3i	−0.0701008	+	0.215748i	0.909868	+	0.414897i	$0.136182\pi$
$252$		0			0
$253$	51177.4	−	45318.2i	0.799535	−	0.707998i
$254$		0			0
$255$	28780.2	+	9351.27i	0.442603	+	0.143810i
$256$		0			0
$257$	31133.7	+	22619.9i	0.471372	+	0.342472i	0.797976	−	0.602689i	$-0.205904\pi$
$257$	31133.7	+	22619.9i	0.471372	+	0.342472i	−0.326604	+	0.945161i	$0.605904\pi$
$258$		0			0
$259$	−2565.02	+	833.427i	−0.0382377	+	0.0124242i
$260$		0			0
$261$	33037.8	+	45472.7i	0.484988	+	0.667528i
$262$		0			0
$263$		−	130054.i		−	1.88024i	−0.340841	−	0.940121i	$-0.610712\pi$
$263$		−	130054.i		−	1.88024i	0.340841	−	0.940121i	$-0.389288\pi$
$264$		0			0
$265$	−63708.4			−0.907203
$266$		0			0
$267$	46610.1	−	33864.2i	0.653819	−	0.475027i
$268$		0			0
$269$	−21831.7	−	67190.9i	−0.301705	−	0.928552i	−0.980886	−	0.194582i	$-0.937665\pi$
$269$	−21831.7	−	67190.9i	−0.301705	−	0.928552i	0.679182	−	0.733970i	$-0.262335\pi$
$270$		0			0
$271$	−46867.1	+	64507.0i	−0.638160	+	0.878352i	−0.998516	−	0.0544632i	$-0.982655\pi$
$271$	−46867.1	+	64507.0i	−0.638160	+	0.878352i	0.360356	+	0.932815i	$0.382655\pi$
$272$		0			0
$273$	−2908.05	+	8950.04i	−0.0390190	+	0.120088i
$274$		0			0
$275$	32692.8	−	147776.i	0.432301	−	1.95407i
$276$		0			0
$277$	42143.0	+	13693.1i	0.549245	+	0.178461i	0.570476	−	0.821314i	$-0.306759\pi$
$277$	42143.0	+	13693.1i	0.549245	+	0.178461i	−0.0212312	+	0.999775i	$0.506759\pi$
$278$		0			0
$279$	−47234.7	−	34318.0i	−0.606810	−	0.440874i
$280$		0			0
$281$	74439.7	−	24186.9i	0.942740	−	0.306315i	0.202978	−	0.979183i	$-0.434938\pi$
$281$	74439.7	−	24186.9i	0.942740	−	0.306315i	0.739762	+	0.672868i	$0.234938\pi$
$282$		0			0
$283$	−52782.1	−	72648.4i	−0.659043	−	0.907095i	0.340406	−	0.940279i	$-0.389436\pi$
$283$	−52782.1	−	72648.4i	−0.659043	−	0.907095i	−0.999449	+	0.0331832i	$0.989436\pi$
$284$		0			0
$285$		−	62185.9i		−	0.765601i
$286$		0			0
$287$	34772.0			0.422149
$288$		0			0
$289$	−42355.4	+	30773.0i	−0.507123	+	0.368446i
$290$		0			0
$291$	−8299.84	−	25544.3i	−0.0980131	−	0.301653i
$292$		0			0
$293$	12058.9	−	16597.6i	0.140466	−	0.193335i	−0.732988	−	0.680242i	$-0.761875\pi$
$293$	12058.9	−	16597.6i	0.140466	−	0.193335i	0.873454	+	0.486907i	$0.161875\pi$
$294$		0			0
$295$	65798.0	−	202505.i	0.756081	−	2.32698i
$296$		0			0
$297$	−60397.2	−	35540.8i	−0.684706	−	0.402915i
$298$		0			0
$299$	96270.5	+	31280.2i	1.07684	+	0.349886i
$300$		0			0
$301$	27952.9	+	20309.0i	0.308528	+	0.224159i
$302$		0			0
$303$	−51439.5	+	16713.7i	−0.560289	+	0.182049i
$304$		0			0
$305$	−40385.4	−	55585.7i	−0.434135	−	0.597535i
$306$		0			0
$307$			133825.i			1.41991i	0.704248	+	0.709954i	$0.251284\pi$
$307$			133825.i			1.41991i	−0.704248	+	0.709954i	$0.748716\pi$
$308$		0			0
$309$	4868.36			0.0509878
$310$		0			0
$311$	34207.5	−	24853.2i	0.353672	−	0.256958i	−0.396736	−	0.917933i	$-0.629857\pi$
$311$	34207.5	−	24853.2i	0.353672	−	0.256958i	0.750408	+	0.660975i	$0.229857\pi$
$312$		0			0
$313$	53394.1	+	164330.i	0.545011	+	1.67737i	0.720965	+	0.692972i	$0.243699\pi$
$313$	53394.1	+	164330.i	0.545011	+	1.67737i	−0.175954	+	0.984398i	$0.556301\pi$
$314$		0			0
$315$	−22073.0	+	30380.9i	−0.222455	+	0.306182i
$316$		0			0
$317$	26059.8	−	80203.7i	0.259329	−	0.798134i	−0.733616	−	0.679564i	$-0.762169\pi$
$317$	26059.8	−	80203.7i	0.259329	−	0.798134i	0.992946	−	0.118570i	$-0.0378310\pi$
$318$		0			0
$319$	10022.6	+	103610.i	0.0984920	+	1.01817i
$320$		0			0
$321$	31856.1	+	10350.7i	0.309159	+	0.100452i
$322$		0			0
$323$	−51814.9	−	37645.7i	−0.496649	−	0.360837i
$324$		0			0
$325$	213149.	−	69256.1i	2.01797	−	0.655679i
$326$		0			0
$327$	17793.0	+	24490.0i	0.166400	+	0.229030i
$328$		0			0
$329$		−	20518.6i		−	0.189564i
$330$		0			0
$331$	130067.			1.18717			0.593583	−	0.804773i	$-0.297713\pi$
$331$	130067.			1.18717			0.593583	+	0.804773i	$0.297713\pi$
$332$		0			0
$333$	10742.5	−	7804.89i	0.0968762	−	0.0703847i
$334$		0			0
$335$	40218.1	+	123779.i	0.358370	+	1.10295i
$336$		0			0
$337$	−48084.9	+	66183.1i	−0.423398	+	0.582757i	−0.966422	−	0.256960i	$-0.917279\pi$
$337$	−48084.9	+	66183.1i	−0.423398	+	0.582757i	0.543024	+	0.839717i	$0.317279\pi$
$338$		0			0
$339$	11104.5	−	34176.1i	0.0966270	−	0.297387i
$340$		0			0
$341$	−43159.3	−	99139.9i	−0.371164	−	0.852589i
$342$		0			0
$343$	58384.0	+	18970.1i	0.496256	+	0.161243i
$344$		0			0
$345$	−78344.0	−	56920.3i	−0.658215	−	0.478221i
$346$		0			0
$347$	219762.	−	71404.9i	1.82513	−	0.593019i	0.825537	−	0.564348i	$-0.190872\pi$
$347$	219762.	−	71404.9i	1.82513	−	0.593019i	0.999589	−	0.0286715i	$-0.00912768\pi$
$348$		0			0
$349$	−7604.61	−	10466.9i	−0.0624347	−	0.0859340i	0.776658	−	0.629923i	$-0.216913\pi$
$349$	−7604.61	−	10466.9i	−0.0624347	−	0.0859340i	−0.839093	+	0.543989i	$0.816913\pi$
$350$		0			0
$351$		−	103772.i		−	0.842295i
$352$		0			0
$353$	59097.3			0.474262			0.237131	−	0.971478i	$-0.423793\pi$
$353$	59097.3			0.474262			0.237131	+	0.971478i	$0.423793\pi$
$354$		0			0
$355$	−297748.	+	216326.i	−2.36261	+	1.71654i
$356$		0			0
$357$	−2865.28	−	8818.43i	−0.0224818	−	0.0691918i
$358$		0			0
$359$	32828.5	−	45184.6i	0.254720	−	0.350591i	−0.662438	−	0.749117i	$-0.730478\pi$
$359$	32828.5	−	45184.6i	0.254720	−	0.350591i	0.917157	+	0.398526i	$0.130478\pi$
$360$		0			0
$361$	−399.455	+	1229.40i	−0.00306517	+	0.00943361i
$362$		0			0
$363$	−28137.1	−	50655.1i	−0.213533	−	0.384423i
$364$		0			0
$365$	187430.	+	60899.6i	1.40687	+	0.457118i
$366$		0			0
$367$	−128062.	−	93042.3i	−0.950796	−	0.690793i	0.000199318	−	1.00000i	$-0.499937\pi$
$367$	−128062.	−	93042.3i	−0.950796	−	0.690793i	−0.950995	+	0.309207i	$0.899937\pi$
$368$		0			0
$369$	−162817.	+	52902.3i	−1.19577	+	0.388528i
$370$		0			0
$371$	11473.9	+	15792.5i	0.0833612	+	0.114737i
$372$		0			0
$373$			133744.i			0.961297i	0.876913	+	0.480649i	$0.159599\pi$
$373$			133744.i			0.961297i	−0.876913	+	0.480649i	$0.840401\pi$
$374$		0			0
$375$	−107274.			−0.762834
$376$		0			0
$377$	−124703.	+	90601.8i	−0.877391	+	0.637462i
$378$		0			0
$379$	16655.2	+	51259.4i	0.115950	+	0.356858i	0.992144	−	0.125101i	$-0.0399255\pi$
$379$	16655.2	+	51259.4i	0.115950	+	0.356858i	−0.876194	+	0.481959i	$0.839925\pi$
$380$		0			0
$381$	16023.3	−	22054.1i	0.110383	−	0.151929i
$382$		0			0
$383$	−15091.9	+	46448.1i	−0.102884	+	0.316643i	−0.989228	−	0.146383i	$-0.953237\pi$
$383$	−15091.9	+	46448.1i	−0.102884	+	0.316643i	0.886344	+	0.463027i	$0.153237\pi$
$384$		0			0
$385$	−63765.9	+	27759.7i	−0.430196	+	0.187281i
$386$		0			0
$387$	−161785.	−	52567.2i	−1.08023	−	0.350988i
$388$		0			0
$389$	−221746.	−	161108.i	−1.46540	−	1.06468i	−0.981914	−	0.189329i	$-0.939369\pi$
$389$	−221746.	−	161108.i	−1.46540	−	1.06468i	−0.483491	−	0.875349i	$-0.660631\pi$
$390$		0			0
$391$	−94854.8	+	30820.2i	−0.620449	+	0.201596i
$392$		0			0
$393$	3422.00	+	4709.98i	0.0221562	+	0.0304954i
$394$		0			0
$395$		−	91529.3i		−	0.586632i
$396$		0			0
$397$	49313.3			0.312884			0.156442	−	0.987687i	$-0.449998\pi$
$397$	49313.3			0.312884			0.156442	+	0.987687i	$0.449998\pi$
$398$		0			0
$399$	−15415.1	+	11199.7i	−0.0968280	+	0.0703496i
$400$		0			0
$401$	2341.63	+	7206.79i	0.0145623	+	0.0448181i	0.958074	−	0.286522i	$-0.0924992\pi$
$401$	2341.63	+	7206.79i	0.0145623	+	0.0448181i	−0.943511	+	0.331340i	$0.892499\pi$
$402$		0			0
$403$	94112.6	−	129535.i	0.579479	−	0.797584i
$404$		0			0
$405$	40152.5	−	123577.i	0.244795	−	0.753402i
$406$		0			0
$407$	24476.8	−	2367.76i	0.147763	−	0.0142938i
$408$		0			0
$409$	−13724.0	−	4459.20i	−0.0820417	−	0.0266570i	0.267709	−	0.963500i	$-0.413734\pi$
$409$	−13724.0	−	4459.20i	−0.0820417	−	0.0266570i	−0.349750	+	0.936843i	$0.613734\pi$
$410$		0			0
$411$	58029.9	+	42161.2i	0.343533	+	0.249591i
$412$		0			0
$413$	−62048.8	+	20160.9i	−0.363775	+	0.118198i
$414$		0			0
$415$	240765.	+	331385.i	1.39797	+	1.92414i
$416$		0			0
$417$			40295.4i			0.231731i
$418$		0			0
$419$	−229500.			−1.30724			−0.653619	−	0.756824i	$-0.726750\pi$
$419$	−229500.			−1.30724			−0.653619	+	0.756824i	$0.726750\pi$
$420$		0			0
$421$	−9854.14	+	7159.45i	−0.0555974	+	0.0403939i	−0.615237	−	0.788342i	$-0.710940\pi$
$421$	−9854.14	+	7159.45i	−0.0555974	+	0.0403939i	0.559639	+	0.828736i	$0.310940\pi$
$422$		0			0
$423$	31217.1	+	96076.4i	0.174467	+	0.536953i
$424$		0			0
$425$	−129796.	+	178649.i	−0.718593	+	0.989058i
$426$		0			0
$427$	−6505.56	+	20022.1i	−0.0356803	+	0.109813i
$428$		0			0
$429$	43516.6	−	73951.1i	0.236451	−	0.401819i
$430$		0			0
$431$	40180.7	+	13055.5i	0.216303	+	0.0702813i	0.415164	−	0.909747i	$-0.363724\pi$
$431$	40180.7	+	13055.5i	0.216303	+	0.0702813i	−0.198861	+	0.980028i	$0.563724\pi$
$432$		0			0
$433$	−53631.9	−	38965.8i	−0.286053	−	0.207830i	0.435500	−	0.900189i	$-0.356572\pi$
$433$	−53631.9	−	38965.8i	−0.286053	−	0.207830i	−0.721553	+	0.692359i	$0.756572\pi$
$434$		0			0
$435$	140244.	−	45568.2i	0.741152	−	0.240815i
$436$		0			0
$437$	120469.	+	165812.i	0.630831	+	0.868264i
$438$		0			0
$439$		−	212489.i		−	1.10257i	−0.834316	−	0.551287i	$-0.814137\pi$
$439$		−	212489.i		−	1.10257i	0.834316	−	0.551287i	$-0.185863\pi$
$440$		0			0
$441$	−145366.			−0.747457
$442$		0			0
$443$	−289268.	+	210166.i	−1.47399	+	1.07091i	−0.494553	+	0.869148i	$0.664668\pi$
$443$	−289268.	+	210166.i	−1.47399	+	1.07091i	−0.979434	+	0.201766i	$0.935332\pi$
$444$		0			0
$445$	194829.	+	599624.i	0.983863	+	3.02802i
$446$		0			0
$447$	−61764.3	+	85011.3i	−0.309117	+	0.425463i
$448$		0			0
$449$	11170.1	−	34378.0i	0.0554069	−	0.170525i	−0.919523	−	0.393035i	$-0.871425\pi$
$449$	11170.1	−	34378.0i	0.0554069	−	0.170525i	0.974930	+	0.222510i	$0.0714251\pi$
$450$		0			0
$451$	−309561.	−	68484.7i	−1.52193	−	0.336698i
$452$		0			0
$453$	71473.2	+	23223.0i	0.348295	+	0.113168i
$454$		0			0
$455$	−83315.6	−	60532.3i	−0.402442	−	0.292391i
$456$		0			0
$457$	23357.6	−	7589.34i	0.111840	−	0.0363389i	−0.252563	−	0.967581i	$-0.581273\pi$
$457$	23357.6	−	7589.34i	0.111840	−	0.0363389i	0.364402	+	0.931242i	$0.381273\pi$
$458$		0			0
$459$	60098.5	+	82718.4i	0.285258	+	0.392624i
$460$		0			0
$461$		−	41038.8i		−	0.193105i	−0.995328	−	0.0965523i	$-0.969218\pi$
$461$		−	41038.8i		−	0.193105i	0.995328	−	0.0965523i	$-0.0307815\pi$
$462$		0			0
$463$	263948.			1.23128			0.615640	−	0.788027i	$-0.288897\pi$
$463$	263948.			1.23128			0.615640	+	0.788027i	$0.288897\pi$
$464$		0			0
$465$	−123922.	+	90034.5i	−0.573115	+	0.416393i
$466$		0			0
$467$	7002.66	+	21552.0i	0.0321092	+	0.0988219i	0.965827	−	0.259189i	$-0.0834552\pi$
$467$	7002.66	+	21552.0i	0.0321092	+	0.0988219i	−0.933718	+	0.358011i	$0.883455\pi$
$468$		0			0
$469$	23439.8	−	32262.2i	0.106564	−	0.146672i
$470$		0			0
$471$	4165.16	−	12819.0i	0.0187754	−	0.0577848i
$472$		0			0
$473$	−208854.	−	235857.i	−0.933515	−	1.05421i
$474$		0			0
$475$	431571.	+	140226.i	1.91278	+	0.621500i
$476$		0			0
$477$	−77752.3	−	56490.4i	−0.341725	−	0.248278i
$478$		0			0
$479$	−63206.4	+	20537.0i	−0.275480	+	0.0895089i	−0.443499	−	0.896275i	$-0.646263\pi$
$479$	−63206.4	+	20537.0i	−0.275480	+	0.0895089i	0.168019	+	0.985784i	$0.446263\pi$
$480$		0			0
$481$	21403.8	+	29459.9i	0.0925127	+	0.127333i
$482$		0			0
$483$			29671.9i			0.127189i
$484$		0			0
$485$	293926.			1.24955
$486$		0			0
$487$	−329613.	+	239478.i	−1.38978	+	1.00973i	−0.393890	+	0.919158i	$0.628871\pi$
$487$	−329613.	+	239478.i	−1.38978	+	1.00973i	−0.995890	+	0.0905764i	$0.971129\pi$
$488$		0			0
$489$	10419.8	+	32068.8i	0.0435754	+	0.134111i
$490$		0			0
$491$	−20767.7	+	28584.3i	−0.0861442	+	0.118567i	−0.849914	−	0.526921i	$-0.823346\pi$
$491$	−20767.7	+	28584.3i	−0.0861442	+	0.118567i	0.763770	+	0.645489i	$0.223346\pi$
$492$		0			0
$493$	46931.8	−	144441.i	0.193096	−	0.594288i
$494$		0			0
$495$	256344.	−	226996.i	1.04619	−	0.926418i
$496$		0			0
$497$	107249.	+	34847.4i	0.434191	+	0.141077i
$498$		0			0
$499$	24801.7	+	18019.5i	0.0996046	+	0.0723670i	0.636473	−	0.771299i	$-0.280393\pi$
$499$	24801.7	+	18019.5i	0.0996046	+	0.0723670i	−0.536868	+	0.843666i	$0.680393\pi$
$500$		0			0
$501$	−49912.0	+	16217.4i	−0.198852	+	0.0646109i
$502$		0			0
$503$	−164396.	−	226272.i	−0.649764	−	0.894323i	0.349325	−	0.937002i	$-0.386411\pi$
$503$	−164396.	−	226272.i	−0.649764	−	0.894323i	−0.999089	+	0.0426785i	$0.986411\pi$
$504$		0			0
$505$		−	591890.i		−	2.32091i
$506$		0			0
$507$	14022.7			0.0545527
$508$		0			0
$509$	−122810.	+	89227.0i	−0.474024	+	0.344398i	−0.799007	−	0.601321i	$-0.794641\pi$
$509$	−122810.	+	89227.0i	−0.474024	+	0.344398i	0.324984	+	0.945720i	$0.394641\pi$
$510$		0			0
$511$	−18660.0	−	57429.5i	−0.0714611	−	0.219935i
$512$		0			0
$513$	123500.	−	169983.i	0.469281	−	0.645909i
$514$		0			0
$515$	−16463.2	+	50668.6i	−0.0620727	+	0.191040i
$516$		0			0
$517$	−40412.1	+	182669.i	−0.151193	+	0.683414i
$518$		0			0
$519$	−83148.4	−	27016.6i	−0.308688	−	0.100299i
$520$		0			0
$521$	1689.60	+	1227.57i	0.00622455	+	0.00452240i	0.590893	−	0.806750i	$-0.298775\pi$
$521$	1689.60	+	1227.57i	0.00622455	+	0.00452240i	−0.584669	+	0.811272i	$0.698775\pi$
$522$		0			0
$523$	290679.	−	94447.4i	1.06270	−	0.345292i	0.275060	−	0.961427i	$-0.411302\pi$
$523$	290679.	−	94447.4i	1.06270	−	0.345292i	0.787641	+	0.616135i	$0.211302\pi$
$524$		0			0
$525$	38614.7	+	53148.6i	0.140099	+	0.192829i
$526$		0			0
$527$			157759.i			0.568033i
$528$		0			0
$529$	39322.4			0.140517
$530$		0			0
$531$	259865.	−	188803.i	0.921633	−	0.669606i
$532$		0			0
$533$	−145077.	−	446503.i	−0.510676	−	1.57170i
$534$		0			0
$535$	−215454.	+	296547.i	−0.752743	+	1.03606i
$536$		0			0
$537$	−10220.5	+	31455.5i	−0.0354424	+	0.109081i
$538$		0			0
$539$	−232021.	−	136533.i	−0.798637	−	0.469959i
$540$		0			0
$541$	−120348.	−	39103.4i	−0.411192	−	0.133604i	0.0961142	−	0.995370i	$-0.469359\pi$
$541$	−120348.	−	39103.4i	−0.411192	−	0.133604i	−0.507306	+	0.861766i	$0.669359\pi$
$542$		0			0
$543$	32242.8	+	23425.8i	0.109354	+	0.0794500i
$544$		0			0
$545$	−315055.	+	102368.i	−1.06070	+	0.344643i
$546$		0			0
$547$	−208238.	−	286615.i	−0.695961	−	0.957908i	−0.999986	−	0.00524442i	$-0.998331\pi$
$547$	−208238.	−	286615.i	−0.695961	−	0.957908i	0.304025	−	0.952664i	$-0.401669\pi$
$548$		0			0
$549$		−	103649.i		−	0.343891i
$550$		0			0
$551$	−312096.			−1.02798
$552$		0			0
$553$	−22689.0	+	16484.5i	−0.0741932	+	0.0539045i
$554$		0			0
$555$	−10765.1	−	33131.5i	−0.0349487	−	0.107561i
$556$		0			0
$557$	18181.9	−	25025.2i	0.0586042	−	0.0806618i	−0.778709	−	0.627385i	$-0.784125\pi$
$557$	18181.9	−	25025.2i	0.0586042	−	0.0806618i	0.837313	+	0.546724i	$0.184125\pi$
$558$		0			0
$559$	144158.	−	443674.i	0.461335	−	1.41984i
$560$		0			0
$561$	8140.23	+	84150.2i	0.0258649	+	0.267380i
$562$		0			0
$563$	338262.	+	109908.i	1.06718	+	0.346747i	0.789387	−	0.613896i	$-0.210398\pi$
$563$	338262.	+	109908.i	1.06718	+	0.346747i	0.277789	+	0.960642i	$0.410398\pi$
$564$		0			0
$565$	318144.	+	231145.i	0.996613	+	0.724082i
$566$		0			0
$567$	−37864.6	+	12303.0i	−0.117779	+	0.0382687i
$568$		0			0
$569$	257141.	+	353925.i	0.794232	+	1.09317i	0.993568	+	0.113235i	$0.0361213\pi$
$569$	257141.	+	353925.i	0.794232	+	1.09317i	−0.199337	+	0.979931i	$0.563879\pi$
$570$		0			0
$571$			1830.95i			0.00561570i	0.999996	+	0.00280785i	$0.000893767\pi$
$571$			1830.95i			0.00561570i	−0.999996	+	0.00280785i	$0.999106\pi$
$572$		0			0
$573$	−139763.			−0.425679
$574$		0			0
$575$	571689.	−	415356.i	1.72912	−	1.25628i
$576$		0			0
$577$	71653.2	+	220526.i	0.215221	+	0.662381i	0.999138	+	0.0415155i	$0.0132186\pi$
$577$	71653.2	+	220526.i	0.215221	+	0.662381i	−0.783917	+	0.620865i	$0.786781\pi$
$578$		0			0
$579$	−18201.2	+	25051.8i	−0.0542930	+	0.0747278i
$580$		0			0
$581$	38784.1	−	119365.i	0.114895	−	0.353611i
$582$		0			0
$583$	−71043.8	−	163193.i	−0.209021	−	0.480135i
$584$		0			0
$585$	482212.	+	156680.i	1.40905	+	0.457828i
$586$		0			0
$587$	41941.6	+	30472.3i	0.121722	+	0.0884361i	0.646981	−	0.762506i	$-0.276031\pi$
$587$	41941.6	+	30472.3i	0.121722	+	0.0884361i	−0.525259	+	0.850943i	$0.676031\pi$
$588$		0			0
$589$	308323.	−	100180.i	0.888740	−	0.288769i
$590$		0			0
$591$	−3427.16	−	4717.09i	−0.00981205	−	0.0135051i
$592$		0			0
$593$			94653.9i			0.269171i	0.990902	+	0.134586i	$0.0429704\pi$
$593$			94653.9i			0.269171i	−0.990902	+	0.134586i	$0.957030\pi$
$594$		0			0
$595$	101469.			0.286616
$596$		0			0
$597$	83557.7	−	60708.2i	0.234443	−	0.170333i
$598$		0			0
$599$	−35391.5	−	108924.i	−0.0986382	−	0.303577i	0.889547	−	0.456844i	$-0.151020\pi$
$599$	−35391.5	−	108924.i	−0.0986382	−	0.303577i	−0.988185	+	0.153267i	$0.951020\pi$
$600$		0			0
$601$	−190529.	+	262240.i	−0.527486	+	0.726023i	−0.986745	−	0.162280i	$-0.948115\pi$
$601$	−190529.	+	262240.i	−0.527486	+	0.726023i	0.459258	+	0.888303i	$0.348115\pi$
$602$		0			0
$603$	−60671.0	+	186726.i	−0.166858	+	0.513535i
$604$		0			0
$605$	622355.	−	121544.i	1.70031	−	0.332064i
$606$		0			0
$607$	666226.	+	216470.i	1.80819	+	0.587517i	0.999999	−	0.00140328i	$-0.000446679\pi$
$607$	666226.	+	216470.i	1.80819	+	0.587517i	0.808191	+	0.588920i	$0.200447\pi$
$608$		0			0
$609$	−36553.9	−	26558.0i	−0.0985597	−	0.0716078i
$610$		0			0
$611$	−263477.	+	85608.7i	−0.705764	+	0.229317i
$612$		0			0
$613$	−351341.	−	483580.i	−0.934992	−	1.28691i	−0.957880	−	0.287168i	$-0.907286\pi$
$613$	−351341.	−	483580.i	−0.934992	−	1.28691i	0.0228878	−	0.999738i	$-0.492714\pi$
$614$		0			0
$615$			449137.i			1.18749i
$616$		0			0
$617$	−704195.			−1.84979			−0.924896	−	0.380221i	$-0.875848\pi$
$617$	−704195.			−1.84979			−0.924896	+	0.380221i	$0.875848\pi$
$618$		0			0
$619$	31537.5	−	22913.3i	0.0823087	−	0.0598008i	−0.545870	−	0.837870i	$-0.683801\pi$
$619$	31537.5	−	22913.3i	0.0823087	−	0.0598008i	0.628179	+	0.778069i	$0.283801\pi$
$620$		0			0
$621$	−101108.	−	311180.i	−0.262183	−	0.806915i
$622$		0			0
$623$	113550.	−	156288.i	0.292558	−	0.402671i
$624$		0			0
$625$	121186.	−	372973.i	0.310237	−	0.954811i
$626$		0			0
$627$	159293.	−	69346.1i	0.405192	−	0.176395i
$628$		0			0
$629$	−34122.9	−	11087.2i	−0.0862471	−	0.0280234i
$630$		0			0
$631$	−15476.7	−	11244.5i	−0.0388706	−	0.0282411i	0.568180	−	0.822904i	$-0.307648\pi$
$631$	−15476.7	−	11244.5i	−0.0388706	−	0.0282411i	−0.607051	+	0.794663i	$0.707648\pi$
$632$		0			0
$633$	272525.	−	88548.8i	0.680141	−	0.220991i
$634$		0			0
$635$	175348.	+	241346.i	0.434864	+	0.598540i
$636$		0			0
$637$		−	398647.i		−	0.982449i
$638$		0			0
$639$	−555201.			−1.35972
$640$		0			0
$641$	277946.	−	201939.i	0.676462	−	0.491479i	−0.195720	−	0.980660i	$-0.562704\pi$
$641$	277946.	−	201939.i	0.676462	−	0.491479i	0.872182	+	0.489181i	$0.162704\pi$
$642$		0			0
$643$	22016.3	+	67759.1i	0.0532503	+	0.163887i	0.974145	−	0.225924i	$-0.0725401\pi$
$643$	22016.3	+	67759.1i	0.0532503	+	0.163887i	−0.920895	+	0.389812i	$0.872540\pi$
$644$		0			0
$645$	−262324.	+	361058.i	−0.630548	+	0.867875i
$646$		0			0
$647$	−42270.7	+	130096.i	−0.100979	+	0.310781i	−0.988766	−	0.149474i	$-0.952242\pi$
$647$	−42270.7	+	130096.i	−0.100979	+	0.310781i	0.887787	+	0.460255i	$0.152242\pi$
$648$		0			0
$649$	592103.	−	57276.8i	1.40575	−	0.135984i
$650$		0			0
$651$	44636.8	+	14503.4i	0.105325	+	0.0342222i
$652$		0			0
$653$	−439262.	−	319143.i	−1.03014	−	0.748443i	−0.0618056	−	0.998088i	$-0.519686\pi$
$653$	−439262.	−	319143.i	−1.03014	−	0.748443i	−0.968337	+	0.249646i	$0.919686\pi$
$654$		0			0
$655$	−60592.4	+	19687.7i	−0.141233	+	0.0458893i
$656$		0			0
$657$	174747.	+	240519.i	0.404836	+	0.557209i
$658$		0			0
$659$		−	702060.i		−	1.61660i	−0.588768	−	0.808302i	$-0.700387\pi$
$659$		−	702060.i		−	1.61660i	0.588768	−	0.808302i	$-0.299613\pi$
$660$		0			0
$661$	−226372.			−0.518108			−0.259054	−	0.965863i	$-0.583411\pi$
$661$	−226372.			−0.518108			−0.259054	+	0.965863i	$0.583411\pi$
$662$		0			0
$663$	−101282.	+	73585.4i	−0.230411	+	0.167403i
$664$		0			0
$665$	−64434.9	−	198310.i	−0.145706	−	0.448438i
$666$		0			0
$667$	−285669.	+	393190.i	−0.642113	+	0.883793i
$668$		0			0
$669$	34599.5	−	106486.i	0.0773069	−	0.237926i
$670$		0			0
$671$	97350.6	−	165435.i	0.216219	−	0.367437i
$672$		0			0
$673$	−41554.0	−	13501.7i	−0.0917450	−	0.0298097i	0.262785	−	0.964854i	$-0.415359\pi$
$673$	−41554.0	−	13501.7i	−0.0917450	−	0.0298097i	−0.354530	+	0.935045i	$0.615359\pi$
$674$		0			0
$675$	−586073.	−	425807.i	−1.28630	−	0.934555i
$676$		0			0
$677$	−488471.	+	158714.i	−1.06577	+	0.346288i	−0.788837	−	0.614602i	$-0.789317\pi$
$677$	−488471.	+	158714.i	−1.06577	+	0.346288i	−0.276929	+	0.960891i	$0.589317\pi$
$678$		0			0
$679$	−52936.2	−	72860.5i	−0.114819	−	0.158035i
$680$		0			0
$681$			285171.i			0.614909i
$682$		0			0
$683$	289751.			0.621131			0.310566	−	0.950552i	$-0.399482\pi$
$683$	289751.			0.621131			0.310566	+	0.950552i	$0.399482\pi$
$684$		0			0
$685$	−635041.	+	461384.i	−1.35338	+	0.983290i
$686$		0			0
$687$	−10931.6	−	33644.0i	−0.0231617	−	0.0712844i
$688$		0			0
$689$	154917.	−	213225.i	0.326333	−	0.449159i
$690$		0			0
$691$	148192.	−	456087.i	0.310361	−	0.955194i	−0.667261	−	0.744824i	$-0.732533\pi$
$691$	148192.	−	456087.i	0.310361	−	0.955194i	0.977622	−	0.210370i	$-0.0674667\pi$
$692$		0			0
$693$	−102437.	−	22662.3i	−0.213300	−	0.0471887i
$694$		0			0
$695$	−419384.	−	136266.i	−0.868245	−	0.282110i
$696$		0			0
$697$	374232.	+	271896.i	0.770328	+	0.559676i
$698$		0			0
$699$	182241.	−	59213.7i	0.372986	−	0.121190i
$700$		0			0
$701$	397842.	+	547582.i	0.809607	+	1.11433i	0.991384	+	0.130989i	$0.0418152\pi$
$701$	397842.	+	547582.i	0.809607	+	1.11433i	−0.181777	+	0.983340i	$0.558185\pi$
$702$		0			0
$703$			73729.8i			0.149188i
$704$		0			0
$705$	265031.			0.533235
$706$		0			0
$707$	−146722.	+	106600.i	−0.293533	+	0.213264i
$708$		0			0
$709$	−69762.5	−	214707.i	−0.138781	−	0.427124i	0.857378	−	0.514687i	$-0.172092\pi$
$709$	−69762.5	−	214707.i	−0.138781	−	0.427124i	−0.996159	+	0.0875635i	$0.972092\pi$
$710$		0			0
$711$	81159.3	−	111706.i	0.160546	−	0.220972i
$712$		0			0
$713$	156005.	−	480133.i	0.306873	−	0.944457i
$714$		0			0
$715$	622505.	+	702988.i	1.21767	+	1.37511i
$716$		0			0
$717$	203841.	+	66232.0i	0.396510	+	0.128834i
$718$		0			0
$719$	752504.	+	546726.i	1.45563	+	1.05758i	0.984475	+	0.175527i	$0.0561629\pi$
$719$	752504.	+	546726.i	1.45563	+	1.05758i	0.471155	+	0.882050i	$0.343837\pi$
$720$		0			0
$721$	15525.2	−	5044.43i	0.0298652	−	0.00970379i
$722$		0			0
$723$	−126008.	−	173435.i	−0.241058	−	0.331788i
$724$		0			0
$725$			1.07605e6i			2.04719i
$726$		0			0
$727$	−141940.			−0.268556			−0.134278	−	0.990944i	$-0.542872\pi$
$727$	−141940.			−0.268556			−0.134278	+	0.990944i	$0.542872\pi$
$728$		0			0
$729$	8373.95	−	6084.03i	0.0157571	−	0.0114482i
$730$		0			0
$731$	142039.	+	437150.i	0.265810	+	0.818079i
$732$		0			0
$733$	−599214.	+	824747.i	−1.11525	+	1.53502i	−0.301813	+	0.953367i	$0.597592\pi$
$733$	−599214.	+	824747.i	−1.11525	+	1.53502i	−0.813441	+	0.581648i	$0.802408\pi$
$734$		0			0
$735$	−117851.	+	362707.i	−0.218151	+	0.671401i
$736$		0			0
$737$	−272217.	+	241052.i	−0.501165	+	0.443787i
$738$		0			0
$739$	−902735.	−	293316.i	−1.65299	−	0.537091i	−0.673609	−	0.739088i	$-0.735257\pi$
$739$	−902735.	−	293316.i	−1.65299	−	0.537091i	−0.979386	+	0.201997i	$0.935257\pi$
$740$		0			0
$741$	208130.	+	151215.i	0.379051	+	0.275397i
$742$		0			0
$743$	−432128.	+	140407.i	−0.782771	+	0.254338i	−0.673023	−	0.739622i	$-0.735004\pi$
$743$	−432128.	+	140407.i	−0.782771	+	0.254338i	−0.109748	+	0.993959i	$0.535004\pi$
$744$		0			0
$745$	−675908.	−	930308.i	−1.21780	−	1.67615i
$746$		0			0
$747$			617923.i			1.10737i
$748$		0			0
$749$	112314.			0.200202
$750$		0			0
$751$	−337489.	+	245200.i	−0.598383	+	0.434751i	−0.845305	−	0.534285i	$-0.820581\pi$
$751$	−337489.	+	245200.i	−0.598383	+	0.434751i	0.246921	+	0.969036i	$0.420581\pi$
$752$		0			0
$753$	17479.0	+	53794.8i	0.0308266	+	0.0948747i
$754$		0			0
$755$	−483399.	+	665341.i	−0.848031	+	1.16721i
$756$		0			0
$757$	−344073.	+	1.05895e6i	−0.600425	+	1.84792i	−0.0748048	+	0.997198i	$0.523833\pi$
$757$	−344073.	+	1.05895e6i	−0.600425	+	1.84792i	−0.525620	+	0.850719i	$0.676167\pi$
$758$		0			0
$759$	58439.8	−	264157.i	0.101444	−	0.458541i
$760$		0			0
$761$	230550.	+	74910.2i	0.398103	+	0.129352i	0.501225	−	0.865317i	$-0.332883\pi$
$761$	230550.	+	74910.2i	0.398103	+	0.129352i	−0.103121	+	0.994669i	$0.532883\pi$
$762$		0			0
$763$	82117.3	+	59661.7i	0.141054	+	0.102482i
$764$		0			0
$765$	−475121.	+	154376.i	−0.811860	+	0.263789i
$766$		0			0
$767$	517766.	+	712643.i	0.880121	+	1.21138i
$768$		0			0
$769$		−	502205.i		−	0.849235i	−0.905373	−	0.424618i	$-0.860409\pi$
$769$		−	502205.i		−	0.849235i	0.905373	−	0.424618i	$-0.139591\pi$
$770$		0			0
$771$	152306.			0.256218
$772$		0			0
$773$	514266.	−	373636.i	0.860654	−	0.625302i	−0.0674085	−	0.997725i	$-0.521473\pi$
$773$	514266.	−	373636.i	0.860654	−	0.625302i	0.928063	+	0.372423i	$0.121473\pi$
$774$		0			0
$775$	−345403.	−	1.06304e6i	−0.575073	−	1.76989i
$776$		0			0
$777$	−6274.08	+	8635.52i	−0.0103922	+	0.0143036i
$778$		0			0
$779$	293745.	−	904053.i	0.484055	−	1.48977i
$780$		0			0
$781$	−886163.	−	521463.i	−1.45282	−	0.854912i
$782$		0			0
$783$	473852.	+	153964.i	0.772892	+	0.251128i
$784$		0			0
$785$	119332.	+	86699.7i	0.193650	+	0.140695i
$786$		0			0
$787$	−573732.	+	186417.i	−0.926317	+	0.300979i	−0.733056	−	0.680168i	$-0.761907\pi$
$787$	−573732.	+	186417.i	−0.926317	+	0.300979i	−0.193262	+	0.981147i	$0.561907\pi$
$788$		0			0
$789$	−302545.	−	416417.i	−0.485999	−	0.668921i
$790$		0			0
$791$		−	120493.i		−	0.192579i
$792$		0			0
$793$	284243.			0.452006
$794$		0			0
$795$	−203986.	+	148204.i	−0.322750	+	0.234491i
$796$		0			0
$797$	268673.	+	826889.i	0.422967	+	1.30176i	0.904927	+	0.425566i	$0.139925\pi$
$797$	268673.	+	826889.i	0.422967	+	1.30176i	−0.481960	+	0.876193i	$0.660075\pi$
$798$		0			0
$799$	160443.	−	220831.i	0.251320	−	0.345912i
$800$		0			0
$801$	−293910.	+	904561.i	−0.458088	+	1.40985i
$802$		0			0
$803$	53012.8	+	548023.i	0.0822147	+	0.849900i
$804$		0			0
$805$	−308817.	−	100341.i	−0.476551	−	0.154841i
$806$		0			0
$807$	−226208.	−	164350.i	−0.347345	−	0.252361i
$808$		0			0
$809$	344281.	−	111864.i	0.526036	−	0.170920i	−0.0339467	−	0.999424i	$-0.510808\pi$
$809$	344281.	−	111864.i	0.526036	−	0.170920i	0.559983	+	0.828504i	$0.310808\pi$
$810$		0			0
$811$	−332769.	−	458018.i	−0.505943	−	0.696371i	0.477285	−	0.878748i	$-0.341621\pi$
$811$	−332769.	−	458018.i	−0.505943	−	0.696371i	−0.983229	+	0.182377i	$0.941621\pi$
$812$		0			0
$813$			315570.i			0.477435i
$814$		0			0
$815$	−369000.			−0.555535
$816$		0			0
$817$	764162.	−	555196.i	1.14483	−	0.831768i
$818$		0			0
$819$	−48007.7	−	147752.i	−0.0715719	−	0.220276i
$820$		0			0
$821$	426408.	−	586901.i	0.632615	−	0.870720i	−0.365580	−	0.930780i	$-0.619129\pi$
$821$	426408.	−	586901.i	0.632615	−	0.870720i	0.998195	+	0.0600604i	$0.0191293\pi$
$822$		0			0
$823$	−291256.	+	896394.i	−0.430007	+	1.32343i	0.468110	+	0.883670i	$0.344935\pi$
$823$	−291256.	+	896394.i	−0.430007	+	1.32343i	−0.898118	+	0.439756i	$0.855065\pi$
$824$		0			0
$825$	−239093.	−	549213.i	−0.351285	−	0.806925i
$826$		0			0
$827$	−303169.	−	98505.6i	−0.443276	−	0.144029i	0.0788708	−	0.996885i	$-0.474869\pi$
$827$	−303169.	−	98505.6i	−0.443276	−	0.144029i	−0.522146	+	0.852856i	$0.674869\pi$
$828$		0			0
$829$	−793128.	−	576241.i	−1.15408	−	0.838485i	−0.165058	−	0.986284i	$-0.552781\pi$
$829$	−793128.	−	576241.i	−1.15408	−	0.838485i	−0.989017	+	0.147799i	$0.952781\pi$
$830$		0			0
$831$	166791.	−	54193.6i	0.241529	−	0.0784776i
$832$		0			0
$833$	230873.	+	317770.i	0.332724	+	0.457955i
$834$		0			0
$835$		−	574313.i		−	0.823713i
$836$		0			0
$837$	−517543.			−0.738747
$838$		0			0
$839$	423441.	−	307648.i	0.601546	−	0.437048i	−0.244882	−	0.969553i	$-0.578749\pi$
$839$	423441.	−	307648.i	0.601546	−	0.437048i	0.846427	+	0.532505i	$0.178749\pi$
$840$		0			0
$841$	−10133.9	−	31188.9i	−0.0143280	−	0.0440969i
$842$		0			0
$843$	182080.	−	250612.i	0.256217	−	0.352652i
$844$		0			0
$845$	−47420.3	+	145945.i	−0.0664127	+	0.204397i
$846$		0			0
$847$	−142216.	−	132384.i	−0.198235	−	0.184531i
$848$		0			0
$849$	−338003.	−	109824.i	−0.468927	−	0.152364i
$850$		0			0
$851$	92887.4	+	67486.7i	0.128262	+	0.0931877i
$852$		0			0
$853$	328116.	−	106611.i	0.450951	−	0.146523i	−0.0747314	−	0.997204i	$-0.523810\pi$
$853$	328116.	−	106611.i	0.450951	−	0.146523i	0.525683	+	0.850681i	$0.323810\pi$
$854$		0			0
$855$	603421.	+	830537.i	0.825445	+	1.13613i
$856$		0			0
$857$			652071.i			0.887837i	0.896067	+	0.443919i	$0.146412\pi$
$857$			652071.i			0.887837i	−0.896067	+	0.443919i	$0.853588\pi$
$858$		0			0
$859$	559418.			0.758142			0.379071	−	0.925368i	$-0.376244\pi$
$859$	559418.			0.758142			0.379071	+	0.925368i	$0.376244\pi$
$860$		0			0
$861$	111335.	−	80889.9i	0.150185	−	0.109116i
$862$		0			0
$863$	116919.	+	359840.i	0.156987	+	0.483157i	0.998357	−	0.0573033i	$-0.0182502\pi$
$863$	116919.	+	359840.i	0.156987	+	0.483157i	−0.841370	+	0.540460i	$0.818250\pi$
$864$		0			0
$865$	562363.	−	774026.i	0.751596	−	1.03448i
$866$		0			0
$867$	−64029.4	+	197062.i	−0.0851806	+	0.262159i
$868$		0			0
$869$	234457.	−	102068.i	0.310474	−	0.135161i
$870$		0			0
$871$	−512071.	−	166382.i	−0.674985	−	0.219316i
$872$		0			0
$873$	358719.	+	260625.i	0.470680	+	0.341969i
$874$		0			0
$875$	−342094.	+	111153.i	−0.446817	+	0.145180i
$876$		0			0
$877$	133607.	+	183894.i	0.173712	+	0.239094i	0.886992	−	0.461785i	$-0.152791\pi$
$877$	133607.	+	183894.i	0.173712	+	0.239094i	−0.713280	+	0.700880i	$0.752791\pi$
$878$		0			0
$879$		−	81196.0i		−	0.105089i
$880$		0			0
$881$	721351.			0.929383			0.464692	−	0.885473i	$-0.346165\pi$
$881$	721351.			0.929383			0.464692	+	0.885473i	$0.346165\pi$
$882$		0			0
$883$	173179.	−	125822.i	0.222113	−	0.161374i	−0.471165	−	0.882045i	$-0.656166\pi$
$883$	173179.	−	125822.i	0.222113	−	0.161374i	0.693277	+	0.720671i	$0.256166\pi$
$884$		0			0
$885$	−260410.	−	801461.i	−0.332485	−	1.02328i
$886$		0			0
$887$	720290.	−	991394.i	0.915504	−	1.26008i	−0.0497477	−	0.998762i	$-0.515842\pi$
$887$	720290.	−	991394.i	0.915504	−	1.26008i	0.965252	−	0.261322i	$-0.0841583\pi$
$888$		0			0
$889$	28246.3	−	86933.2i	0.0357403	−	0.109997i
$890$		0			0
$891$	361325.	−	34952.6i	0.455137	−	0.0440275i
$892$		0			0
$893$	−533473.	−	173336.i	−0.668974	−	0.217363i
$894$		0			0
$895$	−292818.	−	212745.i	−0.365554	−	0.265591i
$896$		0			0
$897$	381012.	−	123798.i	0.473537	−	0.153862i
$898$		0			0
$899$	451861.	+	621934.i	0.559095	+	0.769528i
$900$		0			0
$901$			259685.i			0.319888i
$902$		0			0
$903$	136746.			0.167703
$904$		0			0
$905$	−352844.	+	256356.i	−0.430810	+	0.313001i
$906$		0			0
$907$	313569.	+	965067.i	0.381170	+	1.17312i	0.939221	+	0.343314i	$0.111550\pi$
$907$	313569.	+	965067.i	0.381170	+	1.17312i	−0.558050	+	0.829807i	$0.688450\pi$
$908$		0			0
$909$	524830.	−	722367.i	0.635172	−	0.874239i
$910$		0			0
$911$	−369150.	+	1.13613e6i	−0.444802	+	1.36896i	0.437899	+	0.899024i	$0.355723\pi$
$911$	−369150.	+	1.13613e6i	−0.444802	+	1.36896i	−0.882701	+	0.469935i	$0.844277\pi$
$912$		0			0
$913$	−580373.	+	986274.i	−0.696251	+	1.18319i
$914$		0			0
$915$	−258617.	−	84029.9i	−0.308898	−	0.100367i
$916$		0			0
$917$	15793.0	+	11474.3i	0.0187814	+	0.0136455i
$918$		0			0
$919$	1.42102e6	−	461717.i	1.68255	−	0.546695i	0.697150	−	0.716925i	$-0.254451\pi$
$919$	1.42102e6	−	461717.i	1.68255	−	0.546695i	0.985404	+	0.170230i	$0.0544512\pi$
$920$		0			0
$921$	311316.	+	428490.i	0.367014	+	0.505151i
$922$		0			0
$923$		−	1.52256e6i		−	1.78719i
$924$		0			0
$925$	254207.			0.297101
$926$		0			0
$927$	−65020.5	+	47240.1i	−0.0756642	+	0.0549733i
$928$		0			0
$929$	−147042.	−	452547.i	−0.170376	−	0.524364i	0.829016	−	0.559225i	$-0.188901\pi$
$929$	−147042.	−	452547.i	−0.170376	−	0.524364i	−0.999392	+	0.0348610i	$0.988901\pi$
$930$		0			0
$931$	474436.	−	653005.i	0.547367	−	0.753385i
$932$		0			0
$933$	51712.0	−	159153.i	0.0594057	−	0.182832i
$934$		0			0
$935$	−903341.	−	199848.i	−1.03330	−	0.228600i
$936$		0			0
$937$	869952.	+	282665.i	0.990869	+	0.321953i	0.759211	−	0.650845i	$-0.225585\pi$
$937$	869952.	+	282665.i	0.990869	+	0.321953i	0.231658	+	0.972797i	$0.425585\pi$
$938$		0			0
$939$	553241.	+	401953.i	0.627456	+	0.455874i
$940$		0			0
$941$	790180.	−	256745.i	0.892374	−	0.289950i	0.173288	−	0.984871i	$-0.444561\pi$
$941$	790180.	−	256745.i	0.892374	−	0.289950i	0.719086	+	0.694921i	$0.244561\pi$
$942$		0			0
$943$	−870087.	−	1.19757e6i	−0.978451	−	1.34672i
$944$		0			0
$945$			332879.i			0.372755i
$946$		0			0
$947$	322279.			0.359362			0.179681	−	0.983725i	$-0.442494\pi$
$947$	322279.			0.359362			0.179681	+	0.983725i	$0.442494\pi$
$948$		0			0
$949$	−659590.	+	479220.i	−0.732389	+	0.532112i
$950$		0			0
$951$	−103137.	−	317424.i	−0.114039	−	0.350977i
$952$		0			0
$953$	−182953.	+	251813.i	−0.201444	+	0.277263i	−0.897772	−	0.440459i	$-0.854816\pi$
$953$	−182953.	+	251813.i	−0.201444	+	0.277263i	0.696329	+	0.717723i	$0.254816\pi$
$954$		0			0
$955$	472632.	−	1.45461e6i	0.518223	−	1.59493i
$956$		0			0
$957$	273118.	+	308429.i	0.298213	+	0.336769i
$958$		0			0
$959$	228743.	+	74323.0i	0.248720	+	0.0808139i
$960$		0			0
$961$	101111.	+	73461.5i	0.109484	+	0.0795450i
$962$		0			0
$963$	−525898.	+	170875.i	−0.567086	+	0.184257i
$964$		0			0
$965$	−199182.	−	274151.i	−0.213893	−	0.294398i
$966$		0			0
$967$			852868.i			0.912072i	0.889961	+	0.456036i	$0.150731\pi$
$967$			852868.i			0.912072i	−0.889961	+	0.456036i	$0.849269\pi$
$968$		0			0
$969$	−253480.			−0.269957
$970$		0			0
$971$	372880.	−	270914.i	0.395486	−	0.287337i	−0.372214	−	0.928147i	$-0.621401\pi$
$971$	372880.	−	270914.i	0.395486	−	0.287337i	0.767700	+	0.640810i	$0.221401\pi$
$972$		0			0
$973$	41752.7	+	128502.i	0.0441021	+	0.135732i
$974$		0			0
$975$	521363.	−	717595.i	0.548443	−	0.754867i
$976$		0			0
$977$	−252268.	+	776402.i	−0.264285	+	0.813387i	0.727572	+	0.686032i	$0.240649\pi$
$977$	−252268.	+	776402.i	−0.264285	+	0.813387i	−0.991857	+	0.127355i	$0.959351\pi$
$978$		0			0
$979$	−1.31871e6	+	1.16773e6i	−1.37589	+	1.21837i
$980$		0			0
$981$	−475276.	−	154427.i	−0.493865	−	0.160466i
$982$		0			0
$983$	−1.31752e6	−	957232.i	−1.36348	−	0.990627i	−0.998215	−	0.0597245i	$-0.980978\pi$
$983$	−1.31752e6	−	957232.i	−1.36348	−	0.990627i	−0.365267	−	0.930903i	$-0.619022\pi$
$984$		0			0
$985$	60683.8	−	19717.4i	0.0625461	−	0.0203225i
$986$		0			0
$987$	−47732.3	−	65697.9i	−0.0489980	−	0.0674399i
$988$		0			0
$989$		−	1.47090e6i		−	1.50380i
$990$		0			0
$991$	552727.			0.562812			0.281406	−	0.959589i	$-0.409199\pi$
$991$	552727.			0.562812			0.281406	+	0.959589i	$0.409199\pi$
$992$		0			0
$993$	416457.	−	302574.i	0.422350	−	0.306855i
$994$		0			0
$995$	349270.	+	1.07494e6i	0.352789	+	1.08577i
$996$		0			0
$997$	701494.	−	965524.i	0.705722	−	0.971344i	−0.294156	−	0.955757i	$-0.595039\pi$
$997$	701494.	−	965524.i	0.705722	−	0.971344i	0.999879	−	0.0155861i	$-0.00496143\pi$
$998$		0			0
$999$	36372.5	−	111943.i	0.0364454	−	0.112167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.5.n.c.145.3		16
4.3	odd	2		22.5.d.a.13.1	✓	16
11.6	odd	10	inner	176.5.n.c.17.3		16
12.11	even	2		198.5.j.a.145.3		16
44.7	even	10		242.5.b.e.241.13		16
44.15	odd	10		242.5.b.e.241.5		16
44.39	even	10		22.5.d.a.17.1	yes	16
132.83	odd	10		198.5.j.a.127.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.13.1	✓	16	4.3	odd	2
22.5.d.a.17.1	yes	16	44.39	even	10
176.5.n.c.17.3		16	11.6	odd	10	inner
176.5.n.c.145.3		16	1.1	even	1	trivial
198.5.j.a.127.3		16	132.83	odd	10
198.5.j.a.145.3		16	12.11	even	2
242.5.b.e.241.5		16	44.15	odd	10
242.5.b.e.241.13		16	44.7	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	176.n (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.20187 - 2.32629i) q^{3} +(13.3838 + 41.1910i) q^{5} +(7.80030 - 10.7362i) q^{7} +(-20.1901 + 62.1386i) q^{9} +O(q^{10})\)	\(q+(3.20187 - 2.32629i) q^{3} +(13.3838 + 41.1910i) q^{5} +(7.80030 - 10.7362i) q^{7} +(-20.1901 + 62.1386i) q^{9} +(-90.5882 + 80.2170i) q^{11} +(-170.407 - 55.3685i) q^{13} +(138.675 + 100.754i) q^{15} +(167.901 - 54.5543i) q^{17} +(-213.240 - 293.500i) q^{19} -52.5217i q^{21} -564.946 q^{23} +(-1011.94 + 735.215i) q^{25} +(178.970 + 550.813i) q^{27} +(505.658 - 695.978i) q^{29} +(-276.141 + 849.875i) q^{31} +(-103.443 + 467.579i) q^{33} +(546.632 + 177.611i) q^{35} +(-164.418 - 119.457i) q^{37} +(-674.423 + 219.133i) q^{39} +(1540.12 + 2119.80i) q^{41} +2603.62i q^{43} -2829.77 q^{45} +(1250.87 - 908.812i) q^{47} +(687.529 + 2116.00i) q^{49} +(410.687 - 565.262i) q^{51} +(-454.551 + 1398.97i) q^{53} +(-4516.63 - 2657.81i) q^{55} +(-1365.53 - 443.689i) q^{57} +(-3977.33 - 2889.70i) q^{59} +(-1508.75 + 490.221i) q^{61} +(509.644 + 701.464i) q^{63} -7760.26i q^{65} +3004.99 q^{67} +(-1808.88 + 1314.23i) q^{69} +(2625.89 + 8081.67i) q^{71} +(2674.58 - 3681.24i) q^{73} +(-1529.76 + 4708.12i) q^{75} +(154.610 + 1598.29i) q^{77} +(-2009.88 - 653.050i) q^{79} +(-2427.13 - 1763.41i) q^{81} +(8994.67 - 2922.55i) q^{83} +(4494.29 + 6185.86i) q^{85} -3404.74i q^{87} +14557.2 q^{89} +(-1923.67 + 1397.63i) q^{91} +(1092.89 + 3363.57i) q^{93} +(9235.60 - 12711.7i) q^{95} +(2097.12 - 6454.28i) q^{97} +(-3155.59 - 7248.61i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} + 30 q^{5} - 150 q^{7} + 110 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 + 30 * q^5 - 150 * q^7 + 110 * q^9	\( 16 q + 2 q^{3} + 30 q^{5} - 150 q^{7} + 110 q^{9} + 30 q^{11} - 510 q^{13} + 1398 q^{15} + 1770 q^{17} - 1020 q^{19} + 2424 q^{23} - 858 q^{25} - 2224 q^{27} + 4890 q^{29} - 602 q^{31} - 2648 q^{33} + 8670 q^{35} - 4518 q^{37} + 1130 q^{39} + 1290 q^{41} + 12152 q^{45} - 642 q^{47} + 9534 q^{49} + 1500 q^{51} + 2598 q^{53} - 2582 q^{55} + 9140 q^{57} - 6660 q^{59} - 27410 q^{61} + 27260 q^{63} - 21524 q^{67} + 11416 q^{69} + 5562 q^{71} - 7790 q^{73} - 3576 q^{75} - 1110 q^{77} + 2770 q^{79} - 25464 q^{81} + 36900 q^{83} - 24750 q^{85} + 46596 q^{89} - 32370 q^{91} + 20722 q^{93} - 74250 q^{95} - 3732 q^{97} - 45802 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 + 30 * q^5 - 150 * q^7 + 110 * q^9 + 30 * q^11 - 510 * q^13 + 1398 * q^15 + 1770 * q^17 - 1020 * q^19 + 2424 * q^23 - 858 * q^25 - 2224 * q^27 + 4890 * q^29 - 602 * q^31 - 2648 * q^33 + 8670 * q^35 - 4518 * q^37 + 1130 * q^39 + 1290 * q^41 + 12152 * q^45 - 642 * q^47 + 9534 * q^49 + 1500 * q^51 + 2598 * q^53 - 2582 * q^55 + 9140 * q^57 - 6660 * q^59 - 27410 * q^61 + 27260 * q^63 - 21524 * q^67 + 11416 * q^69 + 5562 * q^71 - 7790 * q^73 - 3576 * q^75 - 1110 * q^77 + 2770 * q^79 - 25464 * q^81 + 36900 * q^83 - 24750 * q^85 + 46596 * q^89 - 32370 * q^91 + 20722 * q^93 - 74250 * q^95 - 3732 * q^97 - 45802 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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