LMFDB - Embedded newform 588.3.g.d.295.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(295,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.295"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0,2,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.489494783471841.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 11 x^{9} + 18 x^{8} - 22 x^{7} + 33 x^{6} - 44 x^{5} + 72 x^{4} + \cdots + 64 $ x^12 - 3x^11 + 7x^10 - 11x^9 + 18x^8 - 22x^7 + 33x^6 - 44x^5 + 72x^4 - 88x^3 + 112x^2 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.10
Root			$-1.15503 + 0.816025i$ of defining polynomial
Character	$\chi$	$=$	588.295
Dual form			588.3.g.d.295.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42562 + 1.40272i) q^{2} -1.73205i q^{3} +(0.0647610 + 3.99948i) q^{4} -1.94731 q^{5} +(2.42958 - 2.46924i) q^{6} +(-5.51781 + 5.79256i) q^{8} -3.00000 q^{9} +(-2.77611 - 2.73152i) q^{10} -1.01531i q^{11} +(6.92730 - 0.112169i) q^{12} -3.44342 q^{13} +3.37283i q^{15} +(-15.9916 + 0.518020i) q^{16} -26.4211 q^{17} +(-4.27685 - 4.20816i) q^{18} +33.7546i q^{19} +(-0.126110 - 7.78820i) q^{20} +(1.42420 - 1.44744i) q^{22} +2.98330i q^{23} +(10.0330 + 9.55714i) q^{24} -21.2080 q^{25} +(-4.90899 - 4.83015i) q^{26} +5.19615i q^{27} +30.3904 q^{29} +(-4.73114 + 4.80836i) q^{30} +0.713577i q^{31} +(-23.5245 - 21.6932i) q^{32} -1.75857 q^{33} +(-37.6663 - 37.0613i) q^{34} +(-0.194283 - 11.9984i) q^{36} -60.0588 q^{37} +(-47.3482 + 48.1210i) q^{38} +5.96418i q^{39} +(10.7449 - 11.2799i) q^{40} -2.67381 q^{41} +6.69857i q^{43} +(4.06071 - 0.0657526i) q^{44} +5.84192 q^{45} +(-4.18473 + 4.25304i) q^{46} -24.3012i q^{47} +(0.897237 + 27.6983i) q^{48} +(-30.2345 - 29.7489i) q^{50} +45.7626i q^{51} +(-0.222999 - 13.7719i) q^{52} -65.8324 q^{53} +(-7.28874 + 7.40772i) q^{54} +1.97712i q^{55} +58.4646 q^{57} +(43.3250 + 42.6291i) q^{58} -33.7709i q^{59} +(-13.4896 + 0.218428i) q^{60} +81.7452 q^{61} +(-1.00095 + 1.01729i) q^{62} +(-3.10744 - 63.9245i) q^{64} +6.70539 q^{65} +(-2.50705 - 2.46678i) q^{66} +62.6486i q^{67} +(-1.71106 - 105.670i) q^{68} +5.16722 q^{69} +132.221i q^{71} +(16.5534 - 17.3777i) q^{72} -100.072 q^{73} +(-85.6207 - 84.2455i) q^{74} +36.7333i q^{75} +(-135.001 + 2.18598i) q^{76} +(-8.36606 + 8.50263i) q^{78} -97.5751i q^{79} +(31.1406 - 1.00874i) q^{80} +9.00000 q^{81} +(-3.81183 - 3.75061i) q^{82} +87.9287i q^{83} +51.4499 q^{85} +(-9.39621 + 9.54958i) q^{86} -52.6377i q^{87} +(5.88125 + 5.60230i) q^{88} +110.387 q^{89} +(8.32833 + 8.19457i) q^{90} +(-11.9316 + 0.193201i) q^{92} +1.23595 q^{93} +(34.0878 - 34.6442i) q^{94} -65.7305i q^{95} +(-37.5738 + 40.7457i) q^{96} -35.6839 q^{97} +3.04593i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{4} - 8 q^{5} + 12 q^{6} - 10 q^{8} - 36 q^{9} - 28 q^{10} - 24 q^{12} + 24 q^{13} - 14 q^{16} + 40 q^{17} - 6 q^{18} + 20 q^{20} - 88 q^{22} + 36 q^{24} + 180 q^{25} - 100 q^{26} + 72 q^{29}+ \cdots + 264 q^{97}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^4 - 8 * q^5 + 12 * q^6 - 10 * q^8 - 36 * q^9 - 28 * q^10 - 24 * q^12 + 24 * q^13 - 14 * q^16 + 40 * q^17 - 6 * q^18 + 20 * q^20 - 88 * q^22 + 36 * q^24 + 180 * q^25 - 100 * q^26 + 72 * q^29 + 72 * q^30 + 142 * q^32 + 100 * q^34 - 6 * q^36 - 88 * q^37 - 128 * q^38 + 28 * q^40 + 200 * q^41 - 40 * q^44 + 24 * q^45 - 24 * q^46 - 48 * q^48 - 346 * q^50 + 364 * q^52 + 104 * q^53 - 36 * q^54 + 148 * q^58 + 96 * q^60 - 104 * q^61 - 64 * q^62 - 70 * q^64 + 176 * q^65 - 24 * q^66 - 188 * q^68 + 192 * q^69 + 30 * q^72 - 312 * q^73 + 4 * q^74 - 432 * q^76 + 48 * q^78 + 564 * q^80 + 108 * q^81 - 332 * q^82 + 352 * q^85 + 160 * q^86 + 328 * q^88 + 552 * q^89 + 84 * q^90 + 232 * q^92 - 48 * q^93 + 144 * q^94 + 108 * q^96 + 264 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.42562	+	1.40272i	0.712808	+	0.701359i
$2$	1.42562	+	1.40272i	0.712808	+	0.701359i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	0.0647610	+	3.99948i	0.0161903	+	0.999869i
$5$	−1.94731			−0.389461			−0.194731	−	0.980857i	$-0.562383\pi$
$5$	−1.94731			−0.389461			−0.194731	+	0.980857i	$0.562383\pi$
$6$	2.42958	−	2.46924i	0.404930	−	0.411540i
$7$		0			0
$7$		0			0
$8$	−5.51781	+	5.79256i	−0.689727	+	0.724070i
$9$	−3.00000			−0.333333
$10$	−2.77611	−	2.73152i	−0.277611	−	0.273152i
$11$		−	1.01531i		−	0.0923010i	−0.998934	−	0.0461505i	$-0.985305\pi$
$11$		−	1.01531i		−	0.0923010i	0.998934	−	0.0461505i	$-0.0146954\pi$
$12$	6.92730	−	0.112169i	0.577275	−	0.00934745i
$13$	−3.44342			−0.264878			−0.132439	−	0.991191i	$-0.542281\pi$
$13$	−3.44342			−0.264878			−0.132439	+	0.991191i	$0.542281\pi$
$14$		0			0
$15$			3.37283i			0.224856i
$16$	−15.9916	+	0.518020i	−0.999476	+	0.0323763i
$17$	−26.4211			−1.55418			−0.777090	−	0.629389i	$-0.783305\pi$
$17$	−26.4211			−1.55418			−0.777090	+	0.629389i	$0.783305\pi$
$18$	−4.27685	−	4.20816i	−0.237603	−	0.233786i
$19$			33.7546i			1.77656i	0.459306	+	0.888278i	$0.348098\pi$
$19$			33.7546i			1.77656i	−0.459306	+	0.888278i	$0.651902\pi$
$20$	−0.126110	−	7.78820i	−0.00630548	−	0.389410i
$21$		0			0
$22$	1.42420	−	1.44744i	0.0647362	−	0.0657929i
$23$			2.98330i			0.129709i	0.997895	+	0.0648543i	$0.0206583\pi$
$23$			2.98330i			0.129709i	−0.997895	+	0.0648543i	$0.979342\pi$
$24$	10.0330	+	9.55714i	0.418042	+	0.398214i
$25$	−21.2080			−0.848320
$26$	−4.90899	−	4.83015i	−0.188807	−	0.185775i
$27$			5.19615i			0.192450i
$28$		0			0
$29$	30.3904			1.04794			0.523972	−	0.851736i	$-0.324450\pi$
$29$	30.3904			1.04794			0.523972	+	0.851736i	$0.324450\pi$
$30$	−4.73114	+	4.80836i	−0.157705	+	0.160279i
$31$			0.713577i			0.0230186i	0.999934	+	0.0115093i	$0.00366361\pi$
$31$			0.713577i			0.0230186i	−0.999934	+	0.0115093i	$0.996336\pi$
$32$	−23.5245	−	21.6932i	−0.735142	−	0.677914i
$33$	−1.75857			−0.0532900
$34$	−37.6663	−	37.0613i	−1.10783	−	1.09004i
$35$		0			0
$36$	−0.194283	−	11.9984i	−0.00539675	−	0.333290i
$37$	−60.0588			−1.62321			−0.811605	−	0.584207i	$-0.801406\pi$
$37$	−60.0588			−1.62321			−0.811605	+	0.584207i	$0.801406\pi$
$38$	−47.3482	+	48.1210i	−1.24600	+	1.26634i
$39$			5.96418i			0.152928i
$40$	10.7449	−	11.2799i	0.268622	−	0.281997i
$41$	−2.67381			−0.0652149			−0.0326075	−	0.999468i	$-0.510381\pi$
$41$	−2.67381			−0.0652149			−0.0326075	+	0.999468i	$0.510381\pi$
$42$		0			0
$43$			6.69857i			0.155781i	0.996962	+	0.0778903i	$0.0248184\pi$
$43$			6.69857i			0.155781i	−0.996962	+	0.0778903i	$0.975182\pi$
$44$	4.06071	−	0.0657526i	0.0922889	−	0.00149438i
$45$	5.84192			0.129820
$46$	−4.18473	+	4.25304i	−0.0909723	+	0.0924573i
$47$		−	24.3012i		−	0.517048i	−0.966005	−	0.258524i	$-0.916764\pi$
$47$		−	24.3012i		−	0.517048i	0.966005	−	0.258524i	$-0.0832361\pi$
$48$	0.897237	+	27.6983i	0.0186924	+	0.577048i
$49$		0			0
$50$	−30.2345	−	29.7489i	−0.604689	−	0.594977i
$51$			45.7626i			0.897307i
$52$	−0.222999	−	13.7719i	−0.00428845	−	0.264844i
$53$	−65.8324			−1.24212			−0.621061	−	0.783763i	$-0.713298\pi$
$53$	−65.8324			−1.24212			−0.621061	+	0.783763i	$0.713298\pi$
$54$	−7.28874	+	7.40772i	−0.134977	+	0.137180i
$55$			1.97712i			0.0359477i
$56$		0			0
$57$	58.4646			1.02570
$58$	43.3250	+	42.6291i	0.746983	+	0.734985i
$59$		−	33.7709i		−	0.572388i	−0.958172	−	0.286194i	$-0.907610\pi$
$59$		−	33.7709i		−	0.572388i	0.958172	−	0.286194i	$-0.0923901\pi$
$60$	−13.4896	+	0.218428i	−0.224826	+	0.00364047i
$61$	81.7452			1.34009			0.670043	−	0.742323i	$-0.266276\pi$
$61$	81.7452			1.34009			0.670043	+	0.742323i	$0.266276\pi$
$62$	−1.00095	+	1.01729i	−0.0161443	+	0.0164079i
$63$		0			0
$64$	−3.10744	−	63.9245i	−0.0485538	−	0.998821i
$65$	6.70539			0.103160
$66$	−2.50705	−	2.46678i	−0.0379855	−	0.0373754i
$67$			62.6486i			0.935054i	0.883979	+	0.467527i	$0.154855\pi$
$67$			62.6486i			0.935054i	−0.883979	+	0.467527i	$0.845145\pi$
$68$	−1.71106	−	105.670i	−0.0251626	−	1.55398i
$69$	5.16722			0.0748873
$70$		0			0
$71$			132.221i			1.86226i	0.364682	+	0.931132i	$0.381178\pi$
$71$			132.221i			1.86226i	−0.364682	+	0.931132i	$0.618822\pi$
$72$	16.5534	−	17.3777i	0.229909	−	0.241357i
$73$	−100.072			−1.37084			−0.685422	−	0.728146i	$-0.740382\pi$
$73$	−100.072			−1.37084			−0.685422	+	0.728146i	$0.740382\pi$
$74$	−85.6207	−	84.2455i	−1.15704	−	1.13845i
$75$			36.7333i			0.489778i
$76$	−135.001	+	2.18598i	−1.77632	+	0.0287629i
$77$		0			0
$78$	−8.36606	+	8.50263i	−0.107257	+	0.109008i
$79$		−	97.5751i		−	1.23513i	−0.786521	−	0.617564i	$-0.788120\pi$
$79$		−	97.5751i		−	1.23513i	0.786521	−	0.617564i	$-0.211880\pi$
$80$	31.1406	−	1.00874i	0.389257	−	0.0126093i
$81$	9.00000			0.111111
$82$	−3.81183	−	3.75061i	−0.0464857	−	0.0457391i
$83$			87.9287i			1.05938i	0.848191	+	0.529691i	$0.177692\pi$
$83$			87.9287i			1.05938i	−0.848191	+	0.529691i	$0.822308\pi$
$84$		0			0
$85$	51.4499			0.605293
$86$	−9.39621	+	9.54958i	−0.109258	+	0.111042i
$87$		−	52.6377i		−	0.605031i
$88$	5.88125	+	5.60230i	0.0668323	+	0.0636625i
$89$	110.387			1.24031			0.620154	−	0.784480i	$-0.287070\pi$
$89$	110.387			1.24031			0.620154	+	0.784480i	$0.287070\pi$
$90$	8.32833	+	8.19457i	0.0925370	+	0.0910507i
$91$		0			0
$92$	−11.9316	+	0.193201i	−0.129692	+	0.00210002i
$93$	1.23595			0.0132898
$94$	34.0878	−	34.6442i	0.362636	−	0.368556i
$95$		−	65.7305i		−	0.691900i
$96$	−37.5738	+	40.7457i	−0.391394	+	0.424434i
$97$	−35.6839			−0.367876			−0.183938	−	0.982938i	$-0.558884\pi$
$97$	−35.6839			−0.367876			−0.183938	+	0.982938i	$0.558884\pi$
$98$		0			0
$99$			3.04593i			0.0307670i
$100$	−1.37345	−	84.8209i	−0.0137345	−	0.848209i
$101$	56.6957			0.561344			0.280672	−	0.959804i	$-0.409443\pi$
$101$	56.6957			0.561344			0.280672	+	0.959804i	$0.409443\pi$
$102$	−64.1921	+	65.2399i	−0.629334	+	0.639607i
$103$			143.694i			1.39509i	0.716541	+	0.697545i	$0.245724\pi$
$103$			143.694i			1.39509i	−0.716541	+	0.697545i	$0.754276\pi$
$104$	19.0001	−	19.9462i	0.182694	−	0.191790i
$105$		0			0
$106$	−93.8518	−	92.3444i	−0.885394	−	0.871173i
$107$		−	170.939i		−	1.59756i	−0.601625	−	0.798779i	$-0.705480\pi$
$107$		−	170.939i		−	1.59756i	0.601625	−	0.798779i	$-0.294520\pi$
$108$	−20.7819	+	0.336508i	−0.192425	+	0.00311582i
$109$	7.83710			0.0719000			0.0359500	−	0.999354i	$-0.488554\pi$
$109$	7.83710			0.0719000			0.0359500	+	0.999354i	$0.488554\pi$
$110$	−2.77334	+	2.81861i	−0.0252122	+	0.0256238i
$111$			104.025i			0.937160i
$112$		0			0
$113$	179.807			1.59121			0.795607	−	0.605813i	$-0.207152\pi$
$113$	179.807			1.59121			0.795607	+	0.605813i	$0.207152\pi$
$114$	83.3481	+	82.0094i	0.731124	+	0.719381i
$115$		−	5.80939i		−	0.0505165i
$116$	1.96811	+	121.546i	0.0169665	+	1.04781i
$117$	10.3303			0.0882928
$118$	47.3710	−	48.1443i	0.401449	−	0.408002i
$119$		0			0
$120$	−19.5373	−	18.6107i	−0.162811	−	0.155089i
$121$	119.969			0.991481
$122$	116.537	+	114.666i	0.955223	+	0.939881i
$123$			4.63118i			0.0376519i
$124$	−2.85393	+	0.0462120i	−0.0230156	+	0.000372677i
$125$	89.9811			0.719849
$126$		0			0
$127$			130.862i			1.03041i	0.857068	+	0.515204i	$0.172284\pi$
$127$			130.862i			1.03041i	−0.857068	+	0.515204i	$0.827716\pi$
$128$	85.2381	−	95.4907i	0.665923	−	0.746021i
$129$	11.6023			0.0899400
$130$	9.55931	+	9.40578i	0.0735332	+	0.0723521i
$131$		−	190.151i		−	1.45154i	−0.687939	−	0.725768i	$-0.741485\pi$
$131$		−	190.151i		−	1.45154i	0.687939	−	0.725768i	$-0.258515\pi$
$132$	−0.113887	−	7.03336i	−0.000862779	−	0.0532830i
$133$		0			0
$134$	−87.8784	+	89.3128i	−0.655809	+	0.666514i
$135$		−	10.1185i		−	0.0749518i
$136$	145.787	−	153.046i	1.07196	−	1.12534i
$137$	248.425			1.81332			0.906662	−	0.421859i	$-0.138622\pi$
$137$	248.425			1.81332			0.906662	+	0.421859i	$0.138622\pi$
$138$	7.36648	+	7.24816i	0.0533803	+	0.0525229i
$139$		−	88.3746i		−	0.635789i	−0.948126	−	0.317894i	$-0.897024\pi$
$139$		−	88.3746i		−	0.635789i	0.948126	−	0.317894i	$-0.102976\pi$
$140$		0			0
$141$	−42.0910			−0.298518
$142$	−185.469	+	188.496i	−1.30612	+	1.32744i
$143$			3.49614i			0.0244485i
$144$	47.9748	−	1.55406i	0.333159	−	0.0107921i
$145$	−59.1794			−0.408133
$146$	−142.664	−	140.372i	−0.977148	−	0.961454i
$147$		0			0
$148$	−3.88947	−	240.204i	−0.0262802	−	1.62300i
$149$	−89.3854			−0.599902			−0.299951	−	0.953955i	$-0.596970\pi$
$149$	−89.3854			−0.599902			−0.299951	+	0.953955i	$0.596970\pi$
$150$	−51.5265	+	52.3676i	−0.343510	+	0.349117i
$151$			197.560i			1.30834i	0.756346	+	0.654172i	$0.226983\pi$
$151$			197.560i			1.30834i	−0.756346	+	0.654172i	$0.773017\pi$
$152$	−195.525	−	186.251i	−1.28635	−	1.22534i
$153$	79.2632			0.518060
$154$		0			0
$155$		−	1.38955i		−	0.00896486i
$156$	−23.8536	+	0.386246i	−0.152908	+	0.00247594i
$157$	−195.026			−1.24220			−0.621101	−	0.783731i	$-0.713314\pi$
$157$	−195.026			−1.24220			−0.621101	+	0.783731i	$0.713314\pi$
$158$	136.870	−	139.105i	0.866268	−	0.880409i
$159$			114.025i			0.717139i
$160$	45.8095	+	42.2434i	0.286309	+	0.264021i
$161$		0			0
$162$	12.8305	+	12.6245i	0.0792009	+	0.0779288i
$163$			119.613i			0.733823i	0.930256	+	0.366911i	$0.119585\pi$
$163$			119.613i			0.733823i	−0.930256	+	0.366911i	$0.880415\pi$
$164$	−0.173159	−	10.6938i	−0.00105585	−	0.0652064i
$165$	3.42447			0.0207544
$166$	−123.339	+	125.353i	−0.743007	+	0.755136i
$167$		−	72.7649i		−	0.435718i	−0.975980	−	0.217859i	$-0.930093\pi$
$167$		−	72.7649i		−	0.435718i	0.975980	−	0.217859i	$-0.0699073\pi$
$168$		0			0
$169$	−157.143			−0.929839
$170$	73.3478	+	72.1697i	0.431458	+	0.424528i
$171$		−	101.264i		−	0.592185i
$172$	−26.7908	+	0.433806i	−0.155760	+	0.00252213i
$173$	−9.89253			−0.0571822			−0.0285911	−	0.999591i	$-0.509102\pi$
$173$	−9.89253			−0.0571822			−0.0285911	+	0.999591i	$0.509102\pi$
$174$	73.8358	−	75.0411i	0.424344	−	0.431271i
$175$		0			0
$176$	0.525952	+	16.2365i	0.00298836	+	0.0922526i
$177$	−58.4929			−0.330468
$178$	157.370	+	154.842i	0.884101	+	0.869901i
$179$		−	251.994i		−	1.40779i	−0.710305	−	0.703895i	$-0.751443\pi$
$179$		−	251.994i		−	1.40779i	0.710305	−	0.703895i	$-0.248557\pi$
$180$	0.378329	+	23.3646i	0.00210183	+	0.129803i
$181$	299.047			1.65219			0.826097	−	0.563528i	$-0.190556\pi$
$181$	299.047			1.65219			0.826097	+	0.563528i	$0.190556\pi$
$182$		0			0
$183$		−	141.587i		−	0.773699i
$184$	−17.2809	−	16.4613i	−0.0939181	−	0.0894635i
$185$	116.953			0.632177
$186$	1.76199	+	1.73369i	0.00947308	+	0.00932093i
$187$			26.8256i			0.143452i
$188$	97.1923	−	1.57377i	0.516980	−	0.00837114i
$189$		0			0
$190$	92.2014	−	93.7064i	0.485270	−	0.493192i
$191$			121.179i			0.634444i	0.948351	+	0.317222i	$0.102750\pi$
$191$			121.179i			0.634444i	−0.948351	+	0.317222i	$0.897250\pi$
$192$	−110.721	+	5.38225i	−0.576669	+	0.0280325i
$193$	110.062			0.570270			0.285135	−	0.958487i	$-0.407962\pi$
$193$	110.062			0.570270			0.285135	+	0.958487i	$0.407962\pi$
$194$	−50.8716	−	50.0545i	−0.262225	−	0.258013i
$195$		−	11.6141i		−	0.0595594i
$196$		0			0
$197$	−78.6134			−0.399053			−0.199527	−	0.979892i	$-0.563940\pi$
$197$	−78.6134			−0.399053			−0.199527	+	0.979892i	$0.563940\pi$
$198$	−4.27259	+	4.34233i	−0.0215787	+	0.0219310i
$199$			89.9183i			0.451851i	0.974145	+	0.225925i	$0.0725405\pi$
$199$			89.9183i			0.451851i	−0.974145	+	0.225925i	$0.927459\pi$
$200$	117.022	−	122.849i	0.585109	−	0.614243i
$201$	108.511			0.539854
$202$	80.8263	+	79.5281i	0.400130	+	0.393704i
$203$		0			0
$204$	−183.027	+	2.96363i	−0.897189	+	0.0145276i
$205$	5.20673			0.0253987
$206$	−201.563	+	204.853i	−0.978460	+	0.994432i
$207$		−	8.94989i		−	0.0432362i
$208$	55.0658	−	1.78376i	0.264740	−	0.00857577i
$209$	34.2714			0.163978
$210$		0			0
$211$			146.363i			0.693663i	0.937927	+	0.346832i	$0.112742\pi$
$211$			146.363i			0.693663i	−0.937927	+	0.346832i	$0.887258\pi$
$212$	−4.26337	−	263.295i	−0.0201103	−	1.24196i
$213$	229.013			1.07518
$214$	239.779	−	243.693i	1.12046	−	1.13875i
$215$		−	13.0442i		−	0.0606705i
$216$	−30.0990	−	28.6714i	−0.139347	−	0.132738i
$217$		0			0
$218$	11.1727	+	10.9932i	0.0512509	+	0.0504277i
$219$			173.329i			0.791457i
$220$	−7.90745	+	0.128040i	−0.0359429	+	0.000582002i
$221$	90.9788			0.411669
$222$	−145.918	+	148.299i	−0.657286	+	0.668015i
$223$			137.385i			0.616074i	0.951374	+	0.308037i	$0.0996721\pi$
$223$			137.385i			0.616074i	−0.951374	+	0.308037i	$0.900328\pi$
$224$		0			0
$225$	63.6240			0.282773
$226$	256.336	+	252.219i	1.13423	+	1.11601i
$227$			61.6479i			0.271577i	0.990738	+	0.135788i	$0.0433567\pi$
$227$			61.6479i			0.271577i	−0.990738	+	0.135788i	$0.956643\pi$
$228$	3.78623	+	233.828i	0.0166063	+	1.02556i
$229$	−313.417			−1.36863			−0.684316	−	0.729186i	$-0.739899\pi$
$229$	−313.417			−1.36863			−0.684316	+	0.729186i	$0.739899\pi$
$230$	8.14894	−	8.28196i	0.0354302	−	0.0360085i
$231$		0			0
$232$	−167.688	+	176.038i	−0.722795	+	0.758784i
$233$	−142.259			−0.610554			−0.305277	−	0.952264i	$-0.598749\pi$
$233$	−142.259			−0.610554			−0.305277	+	0.952264i	$0.598749\pi$
$234$	14.7270	+	14.4904i	0.0629358	+	0.0619250i
$235$			47.3220i			0.201370i
$236$	135.066	−	2.18704i	0.572313	−	0.00926710i
$237$	−169.005			−0.713101
$238$		0			0
$239$			164.416i			0.687933i	0.938982	+	0.343966i	$0.111771\pi$
$239$			164.416i			0.687933i	−0.938982	+	0.343966i	$0.888229\pi$
$240$	−1.74720	−	53.9370i	−0.00727998	−	0.224738i
$241$	−69.0501			−0.286515			−0.143257	−	0.989685i	$-0.545758\pi$
$241$	−69.0501			−0.286515			−0.143257	+	0.989685i	$0.545758\pi$
$242$	171.030	+	168.283i	0.706735	+	0.695384i
$243$		−	15.5885i		−	0.0641500i
$244$	5.29390	+	326.938i	0.0216963	+	1.33991i
$245$		0			0
$246$	−6.49624	+	6.60228i	−0.0264075	+	0.0268385i
$247$		−	116.231i		−	0.470571i
$248$	−4.13344	−	3.93739i	−0.0166671	−	0.0158766i
$249$	152.297			0.611634
$250$	128.278	+	126.218i	0.513114	+	0.504873i
$251$		−	41.8933i		−	0.166906i	−0.996512	−	0.0834528i	$-0.973405\pi$
$251$		−	41.8933i		−	0.166906i	0.996512	−	0.0834528i	$-0.0265948\pi$
$252$		0			0
$253$	3.02897			0.0119722
$254$	−183.562	+	186.559i	−0.722686	+	0.734483i
$255$		−	89.1139i		−	0.349466i
$256$	255.463	−	16.5680i	0.997904	−	0.0647186i
$257$	−215.796			−0.839671			−0.419836	−	0.907600i	$-0.637912\pi$
$257$	−215.796			−0.839671			−0.419836	+	0.907600i	$0.637912\pi$
$258$	16.5404	+	16.2747i	0.0641099	+	0.0630803i
$259$		0			0
$260$	0.434248	+	26.8180i	0.00167018	+	0.103146i
$261$	−91.1711			−0.349315
$262$	266.729	−	271.083i	1.01805	−	1.03467i
$263$			111.918i			0.425543i	0.977102	+	0.212772i	$0.0682490\pi$
$263$			111.918i			0.425543i	−0.977102	+	0.212772i	$0.931751\pi$
$264$	9.70346	−	10.1866i	0.0367555	−	0.0385857i
$265$	128.196			0.483758
$266$		0			0
$267$		−	191.196i		−	0.716092i
$268$	−250.562	+	4.05719i	−0.934931	+	0.0151388i
$269$	131.483			0.488784			0.244392	−	0.969677i	$-0.421412\pi$
$269$	131.483			0.488784			0.244392	+	0.969677i	$0.421412\pi$
$270$	14.1934	−	14.4251i	0.0525682	−	0.0534263i
$271$			143.088i			0.528000i	0.964523	+	0.264000i	$0.0850418\pi$
$271$			143.088i			0.528000i	−0.964523	+	0.264000i	$0.914958\pi$
$272$	422.516	−	13.6866i	1.55337	−	0.0503186i
$273$		0			0
$274$	354.159	+	348.471i	1.29255	+	1.27179i
$275$			21.5327i			0.0783008i
$276$	0.334635	+	20.6662i	0.00121244	+	0.0748775i
$277$	−282.748			−1.02075			−0.510375	−	0.859952i	$-0.670493\pi$
$277$	−282.748			−1.02075			−0.510375	+	0.859952i	$0.670493\pi$
$278$	123.965	−	125.988i	0.445916	−	0.453195i
$279$		−	2.14073i		−	0.00767287i
$280$		0			0
$281$	−258.526			−0.920021			−0.460010	−	0.887913i	$-0.652154\pi$
$281$	−258.526			−0.920021			−0.460010	+	0.887913i	$0.652154\pi$
$282$	−60.0056	−	59.0418i	−0.212786	−	0.209368i
$283$			471.840i			1.66728i	0.552309	+	0.833640i	$0.313747\pi$
$283$			471.840i			1.66728i	−0.552309	+	0.833640i	$0.686253\pi$
$284$	−528.814	+	8.56275i	−1.86202	+	0.0301505i
$285$	−113.849			−0.399468
$286$	−4.90410	+	4.98415i	−0.0171472	+	0.0174271i
$287$		0			0
$288$	70.5736	+	65.0797i	0.245047	+	0.225971i
$289$	409.073			1.41548
$290$	−84.3670	−	83.0120i	−0.290921	−	0.286248i
$291$			61.8064i			0.212393i
$292$	−6.48074	−	400.234i	−0.0221943	−	1.37066i
$293$	−348.535			−1.18954			−0.594770	−	0.803896i	$-0.702757\pi$
$293$	−348.535			−1.18954			−0.594770	+	0.803896i	$0.702757\pi$
$294$		0			0
$295$			65.7622i			0.222923i
$296$	331.393	−	347.894i	1.11957	−	1.17532i
$297$	5.27571			0.0177633
$298$	−127.429	−	125.383i	−0.427615	−	0.420747i
$299$		−	10.2727i		−	0.0343570i
$300$	−146.914	+	2.37889i	−0.489714	+	0.00792963i
$301$		0			0
$302$	−277.121	+	281.644i	−0.917619	+	0.932598i
$303$		−	98.1999i		−	0.324092i
$304$	−17.4855	−	539.790i	−0.0575183	−	1.77562i
$305$	−159.183			−0.521911
$306$	112.999	+	111.184i	0.369277	+	0.363346i
$307$		−	24.1654i		−	0.0787148i	−0.999225	−	0.0393574i	$-0.987469\pi$
$307$		−	24.1654i		−	0.0787148i	0.999225	−	0.0393574i	$-0.0125311\pi$
$308$		0			0
$309$	248.886			0.805456
$310$	1.94915	−	1.98097i	0.00628759	−	0.00639022i
$311$		−	351.843i		−	1.13133i	−0.824635	−	0.565665i	$-0.808620\pi$
$311$		−	351.843i		−	1.13133i	0.824635	−	0.565665i	$-0.191380\pi$
$312$	−34.5478	−	32.9092i	−0.110730	−	0.105478i
$313$	178.717			0.570982			0.285491	−	0.958381i	$-0.407843\pi$
$313$	178.717			0.570982			0.285491	+	0.958381i	$0.407843\pi$
$314$	−278.032	−	273.566i	−0.885451	−	0.871229i
$315$		0			0
$316$	390.249	−	6.31906i	1.23497	−	0.0199970i
$317$	101.728			0.320910			0.160455	−	0.987043i	$-0.448704\pi$
$317$	101.728			0.320910			0.160455	+	0.987043i	$0.448704\pi$
$318$	−159.945	+	162.556i	−0.502972	+	0.511182i
$319$		−	30.8557i		−	0.0967263i
$320$	6.05114	+	124.481i	0.0189098	+	0.389002i
$321$	−296.074			−0.922350
$322$		0			0
$323$		−	891.832i		−	2.76109i
$324$	0.582849	+	35.9953i	0.00179892	+	0.111097i
$325$	73.0280			0.224702
$326$	−167.784	+	170.522i	−0.514674	+	0.523075i
$327$		−	13.5743i		−	0.0415115i
$328$	14.7536	−	15.4882i	0.0449805	−	0.0472201i
$329$		0			0
$330$	4.88198	+	4.80357i	0.0147939	+	0.0145563i
$331$			2.78294i			0.00840768i	0.999991	+	0.00420384i	$0.00133813\pi$
$331$			2.78294i			0.00840768i	−0.999991	+	0.00420384i	$0.998662\pi$
$332$	−351.669	+	5.69435i	−1.05924	+	0.0171517i
$333$	180.176			0.541070
$334$	102.069	−	103.735i	0.305595	−	0.310583i
$335$		−	121.996i		−	0.364167i
$336$		0			0
$337$	−303.217			−0.899755			−0.449877	−	0.893090i	$-0.648532\pi$
$337$	−303.217			−0.899755			−0.449877	+	0.893090i	$0.648532\pi$
$338$	−224.025	−	220.427i	−0.662797	−	0.652152i
$339$		−	311.435i		−	0.918688i
$340$	3.33195	+	205.773i	0.00979985	+	0.605214i
$341$	0.724503			0.00212464
$342$	142.044	−	144.363i	0.415335	−	0.422114i
$343$		0			0
$344$	−38.8018	−	36.9615i	−0.112796	−	0.107446i
$345$	−10.0622			−0.0291657
$346$	−14.1029	−	13.8764i	−0.0407600	−	0.0401053i
$347$		−	166.421i		−	0.479600i	−0.970822	−	0.239800i	$-0.922918\pi$
$347$		−	166.421i		−	0.479600i	0.970822	−	0.239800i	$-0.0770819\pi$
$348$	210.523	−	3.40887i	0.604951	−	0.00979560i
$349$	−327.232			−0.937629			−0.468814	−	0.883297i	$-0.655319\pi$
$349$	−327.232			−0.937629			−0.468814	+	0.883297i	$0.655319\pi$
$350$		0			0
$351$		−	17.8925i		−	0.0509759i
$352$	−22.0254	+	23.8847i	−0.0625721	+	0.0678543i
$353$	−43.6810			−0.123742			−0.0618711	−	0.998084i	$-0.519707\pi$
$353$	−43.6810			−0.123742			−0.0618711	+	0.998084i	$0.519707\pi$
$354$	−83.3883	−	82.0490i	−0.235560	−	0.231777i
$355$		−	257.474i		−	0.725280i
$356$	7.14880	+	441.491i	0.0200809	+	1.24014i
$357$		0			0
$358$	353.477	−	359.247i	0.987366	−	1.00348i
$359$		−	72.4245i		−	0.201740i	−0.994900	−	0.100870i	$-0.967837\pi$
$359$		−	72.4245i		−	0.201740i	0.994900	−	0.100870i	$-0.0321625\pi$
$360$	−32.2346	+	33.8396i	−0.0895406	+	0.0939990i
$361$	−778.371			−2.15615
$362$	426.326	+	419.479i	1.17770	+	1.15878i
$363$		−	207.793i		−	0.572432i
$364$		0			0
$365$	194.870			0.533890
$366$	198.606	−	201.848i	0.542641	−	0.551498i
$367$			508.952i			1.38679i	0.720558	+	0.693395i	$0.243886\pi$
$367$			508.952i			1.38679i	−0.720558	+	0.693395i	$0.756114\pi$
$368$	−1.54541	−	47.7077i	−0.00419948	−	0.129641i
$369$	8.02144			0.0217383
$370$	166.730	+	164.052i	0.450621	+	0.443383i
$371$		0			0
$372$	0.0800415	+	4.94316i	0.000215165	+	0.0132881i
$373$	124.672			0.334242			0.167121	−	0.985936i	$-0.446553\pi$
$373$	124.672			0.334242			0.167121	+	0.985936i	$0.446553\pi$
$374$	−37.6288	+	38.2430i	−0.100612	+	0.102254i
$375$		−	155.852i		−	0.415605i
$376$	140.766	+	134.090i	0.374379	+	0.356622i
$377$	−104.647			−0.277578
$378$		0			0
$379$		−	539.605i		−	1.42376i	−0.702301	−	0.711880i	$-0.747844\pi$
$379$		−	539.605i		−	1.42376i	0.702301	−	0.711880i	$-0.252156\pi$
$380$	262.887	−	4.25677i	0.691809	−	0.0112020i
$381$	226.659			0.594906
$382$	−169.980	+	172.754i	−0.444973	+	0.452237i
$383$		−	563.542i		−	1.47139i	−0.677313	−	0.735695i	$-0.736856\pi$
$383$		−	563.542i		−	1.47139i	0.677313	−	0.735695i	$-0.263144\pi$
$384$	−165.395	−	147.637i	−0.430715	−	0.384471i
$385$		0			0
$386$	156.906	+	154.386i	0.406493	+	0.399964i
$387$		−	20.0957i		−	0.0519269i
$388$	−2.31093	−	142.717i	−0.00595600	−	0.367827i
$389$	−211.324			−0.543248			−0.271624	−	0.962403i	$-0.587561\pi$
$389$	−211.324			−0.543248			−0.271624	+	0.962403i	$0.587561\pi$
$390$	16.2913	−	16.5572i	0.0417725	−	0.0424544i
$391$		−	78.8219i		−	0.201591i
$392$		0			0
$393$	−329.352			−0.838045
$394$	−112.073	−	110.273i	−0.284448	−	0.279880i
$395$			190.009i			0.481034i
$396$	−12.1821	+	0.197258i	−0.0307630	+	0.000498125i
$397$	−271.257			−0.683266			−0.341633	−	0.939833i	$-0.610980\pi$
$397$	−271.257			−0.683266			−0.341633	+	0.939833i	$0.610980\pi$
$398$	−126.130	+	128.189i	−0.316910	+	0.322083i
$399$		0			0
$400$	339.150	−	10.9862i	0.847875	−	0.0274654i
$401$	143.015			0.356647			0.178323	−	0.983972i	$-0.442933\pi$
$401$	143.015			0.356647			0.178323	+	0.983972i	$0.442933\pi$
$402$	154.694	+	152.210i	0.384812	+	0.378631i
$403$		−	2.45715i		−	0.00609714i
$404$	3.67167	+	226.753i	0.00908830	+	0.561270i
$405$	−17.5258			−0.0432735
$406$		0			0
$407$			60.9783i			0.149824i
$408$	−265.083	−	252.510i	−0.649713	−	0.618896i
$409$	−223.590			−0.546676			−0.273338	−	0.961918i	$-0.588128\pi$
$409$	−223.590			−0.546676			−0.273338	+	0.961918i	$0.588128\pi$
$410$	7.42280	+	7.30358i	0.0181044	+	0.0178136i
$411$		−	430.285i		−	1.04692i
$412$	−574.702	+	9.30579i	−1.39491	+	0.0225869i
$413$		0			0
$414$	12.5542	−	12.7591i	0.0303241	−	0.0308191i
$415$		−	171.224i		−	0.412588i
$416$	81.0048	+	74.6989i	0.194723	+	0.179565i
$417$	−153.069			−0.367073
$418$	48.8578	+	48.0731i	0.116885	+	0.115007i
$419$		−	293.605i		−	0.700729i	−0.936614	−	0.350364i	$-0.886058\pi$
$419$		−	293.605i		−	0.700729i	0.936614	−	0.350364i	$-0.113942\pi$
$420$		0			0
$421$	−603.329			−1.43309			−0.716543	−	0.697543i	$-0.754277\pi$
$421$	−603.329			−1.43309			−0.716543	+	0.697543i	$0.754277\pi$
$422$	−205.306	+	208.657i	−0.486507	+	0.494449i
$423$			72.9037i			0.172349i
$424$	363.251	−	381.338i	0.856724	−	0.899382i
$425$	560.338			1.31844
$426$	326.485	+	321.241i	0.766396	+	0.754087i
$427$		0			0
$428$	683.665	−	11.0702i	1.59735	−	0.0258649i
$429$	6.05549			0.0141154
$430$	18.2973	−	18.5960i	0.0425518	−	0.0432464i
$431$			285.866i			0.663262i	0.943409	+	0.331631i	$0.107599\pi$
$431$			285.866i			0.663262i	−0.943409	+	0.331631i	$0.892401\pi$
$432$	−2.69171	−	83.0949i	−0.00623081	−	0.192349i
$433$	232.262			0.536403			0.268201	−	0.963363i	$-0.413571\pi$
$433$	232.262			0.536403			0.268201	+	0.963363i	$0.413571\pi$
$434$		0			0
$435$			102.502i			0.235636i
$436$	0.507539	+	31.3443i	0.00116408	+	0.0718906i
$437$	−100.700			−0.230435
$438$	−243.132	+	247.101i	−0.555096	+	0.564157i
$439$		−	30.1779i		−	0.0687423i	−0.999409	−	0.0343711i	$-0.989057\pi$
$439$		−	30.1779i		−	0.0687423i	0.999409	−	0.0343711i	$-0.0109428\pi$
$440$	−11.4526	−	10.9094i	−0.0260286	−	0.0247941i
$441$		0			0
$442$	129.701	+	127.618i	0.293441	+	0.288728i
$443$			708.628i			1.59961i	0.600258	+	0.799806i	$0.295064\pi$
$443$			708.628i			1.59961i	−0.600258	+	0.799806i	$0.704936\pi$
$444$	−416.045	+	6.73675i	−0.937038	+	0.0151729i
$445$	−214.958			−0.483051
$446$	−192.712	+	195.858i	−0.432090	+	0.439143i
$447$			154.820i			0.346354i
$448$		0			0
$449$	−69.7117			−0.155260			−0.0776299	−	0.996982i	$-0.524735\pi$
$449$	−69.7117			−0.155260			−0.0776299	+	0.996982i	$0.524735\pi$
$450$	90.7034	+	89.2466i	0.201563	+	0.198326i
$451$			2.71475i			0.00601940i
$452$	11.6445	+	719.135i	0.0257622	+	1.59101i
$453$	342.184			0.755372
$454$	−86.4747	+	87.8863i	−0.190473	+	0.193582i
$455$		0			0
$456$	−322.597	+	338.660i	−0.707450	+	0.742675i
$457$	−356.679			−0.780480			−0.390240	−	0.920713i	$-0.627608\pi$
$457$	−356.679			−0.780480			−0.390240	+	0.920713i	$0.627608\pi$
$458$	−446.812	−	439.636i	−0.975572	−	0.959903i
$459$		−	137.288i		−	0.299102i
$460$	23.2345	−	0.376222i	0.0505098	−	0.000817874i
$461$	−597.234			−1.29552			−0.647759	−	0.761845i	$-0.724294\pi$
$461$	−597.234			−1.29552			−0.647759	+	0.761845i	$0.724294\pi$
$462$		0			0
$463$			518.054i			1.11891i	0.828862	+	0.559453i	$0.188989\pi$
$463$			518.054i			1.11891i	−0.828862	+	0.559453i	$0.811011\pi$
$464$	−485.991	+	15.7428i	−1.04739	+	0.0339285i
$465$	−2.40678			−0.00517586
$466$	−202.807	−	199.549i	−0.435208	−	0.428218i
$467$			546.318i			1.16985i	0.811089	+	0.584923i	$0.198875\pi$
$467$			546.318i			1.16985i	−0.811089	+	0.584923i	$0.801125\pi$
$468$	0.668998	+	41.3156i	0.00142948	+	0.0882812i
$469$		0			0
$470$	−66.3794	+	67.4629i	−0.141233	+	0.143538i
$471$			337.794i			0.717185i
$472$	195.620	+	186.341i	0.414448	+	0.394791i
$473$	6.80113			0.0143787
$474$	−240.936	−	237.067i	−0.508304	−	0.500140i
$475$		−	715.867i		−	1.50709i
$476$		0			0
$477$	197.497			0.414040
$478$	−230.629	+	234.394i	−0.482488	+	0.490364i
$479$		−	674.246i		−	1.40761i	−0.710392	−	0.703806i	$-0.751483\pi$
$479$		−	674.246i		−	1.40761i	0.710392	−	0.703806i	$-0.248517\pi$
$480$	73.1676	−	79.3443i	0.152433	−	0.165301i
$481$	206.807			0.429953
$482$	−98.4389	−	96.8579i	−0.204230	−	0.200950i
$483$		0			0
$484$	7.76932	+	479.814i	0.0160523	+	0.991351i
$485$	69.4875			0.143273
$486$	21.8662	−	22.2232i	0.0449922	−	0.0457266i
$487$		−	251.723i		−	0.516886i	−0.966027	−	0.258443i	$-0.916791\pi$
$487$		−	251.723i		−	0.516886i	0.966027	−	0.258443i	$-0.0832094\pi$
$488$	−451.055	+	473.514i	−0.924293	+	0.970315i
$489$	207.176			0.423673
$490$		0			0
$491$		−	181.391i		−	0.369433i	−0.982792	−	0.184716i	$-0.940863\pi$
$491$		−	181.391i		−	0.369433i	0.982792	−	0.184716i	$-0.0591366\pi$
$492$	−18.5223	+	0.299920i	−0.0376469	+	0.000609593i
$493$	−802.946			−1.62869
$494$	163.040	−	165.701i	0.330040	−	0.335427i
$495$		−	5.93136i		−	0.0119826i
$496$	−0.369647	−	11.4113i	−0.000745257	−	0.0230066i
$497$		0			0
$498$	217.117	+	213.630i	0.435978	+	0.428975i
$499$		−	230.573i		−	0.462069i	−0.972946	−	0.231035i	$-0.925789\pi$
$499$		−	230.573i		−	0.462069i	0.972946	−	0.231035i	$-0.0742111\pi$
$500$	5.82727	+	359.877i	0.0116545	+	0.719755i
$501$	−126.033			−0.251562
$502$	58.7645	−	59.7237i	0.117061	−	0.118972i
$503$			761.117i			1.51316i	0.653903	+	0.756578i	$0.273130\pi$
$503$			761.117i			1.51316i	−0.653903	+	0.756578i	$0.726870\pi$
$504$		0			0
$505$	−110.404			−0.218622
$506$	4.31815	+	4.24880i	0.00853390	+	0.00839684i
$507$			272.179i			0.536843i
$508$	−523.379	+	8.47475i	−1.03027	+	0.0166826i
$509$	−685.349			−1.34646			−0.673231	−	0.739432i	$-0.735094\pi$
$509$	−685.349			−1.34646			−0.673231	+	0.739432i	$0.735094\pi$
$510$	125.002	−	127.042i	0.245101	−	0.249102i
$511$		0			0
$512$	387.433	+	334.724i	0.756705	+	0.653757i
$513$	−175.394			−0.341898
$514$	−307.642	−	302.700i	−0.598524	−	0.588911i
$515$		−	279.817i		−	0.543334i
$516$	0.751374	+	46.4030i	0.00145615	+	0.0899282i
$517$	−24.6733			−0.0477240
$518$		0			0
$519$			17.1344i			0.0330142i
$520$	−36.9991	+	38.8414i	−0.0711521	+	0.0746949i
$521$	1027.31			1.97181			0.985906	−	0.167298i	$-0.0535043\pi$
$521$	1027.31			1.97181			0.985906	+	0.167298i	$0.0535043\pi$
$522$	−129.975	−	127.887i	−0.248994	−	0.244995i
$523$		−	874.410i		−	1.67191i	−0.548797	−	0.835956i	$-0.684914\pi$
$523$		−	874.410i		−	1.67191i	0.548797	−	0.835956i	$-0.315086\pi$
$524$	760.505	−	12.3144i	1.45135	−	0.0235007i
$525$		0			0
$526$	−156.989	+	159.552i	−0.298459	+	0.303331i
$527$		−	18.8535i		−	0.0357751i
$528$	28.1224	−	0.910975i	0.0532621	−	0.00172533i
$529$	520.100			0.983176
$530$	182.758	+	179.823i	0.344827	+	0.339288i
$531$			101.313i			0.190796i
$532$		0			0
$533$	9.20705			0.0172740
$534$	268.195	−	272.573i	0.502238	−	0.510436i
$535$			332.870i			0.622186i
$536$	−362.896	−	345.683i	−0.677044	−	0.644932i
$537$	−436.467			−0.812787
$538$	187.444	+	184.433i	0.348409	+	0.342813i
$539$		0			0
$540$	40.4687	−	0.655284i	0.0749420	−	0.00121349i
$541$	182.995			0.338253			0.169127	−	0.985594i	$-0.445905\pi$
$541$	182.995			0.338253			0.169127	+	0.985594i	$0.445905\pi$
$542$	−200.712	+	203.988i	−0.370317	+	0.376362i
$543$		−	517.965i		−	0.953895i
$544$	621.543	+	573.158i	1.14254	+	1.05360i
$545$	−15.2612			−0.0280023
$546$		0			0
$547$			91.9279i			0.168058i	0.996463	+	0.0840291i	$0.0267789\pi$
$547$			91.9279i			0.168058i	−0.996463	+	0.0840291i	$0.973221\pi$
$548$	16.0883	+	993.571i	0.0293582	+	1.81309i
$549$	−245.236			−0.446695
$550$	−30.2043	+	30.6974i	−0.0549170	+	0.0558134i
$551$			1025.81i			1.86173i
$552$	−28.5118	+	29.9314i	−0.0516518	+	0.0542236i
$553$		0			0
$554$	−403.090	−	396.615i	−0.727598	−	0.715912i
$555$		−	202.568i		−	0.364988i
$556$	353.452	−	5.72323i	0.635705	−	0.0102936i
$557$	204.578			0.367285			0.183643	−	0.982993i	$-0.441211\pi$
$557$	204.578			0.367285			0.183643	+	0.982993i	$0.441211\pi$
$558$	3.00284	−	3.05186i	0.00538144	−	0.00546929i
$559$		−	23.0660i		−	0.0412629i
$560$		0			0
$561$	46.4633			0.0828223
$562$	−368.559	−	362.639i	−0.655798	−	0.645265i
$563$			681.311i			1.21014i	0.796171	+	0.605072i	$0.206856\pi$
$563$			681.311i			1.21014i	−0.796171	+	0.605072i	$0.793144\pi$
$564$	−2.72586	−	168.342i	−0.00483308	−	0.298479i
$565$	−350.140			−0.619716
$566$	−661.859	+	672.663i	−1.16936	+	1.18845i
$567$		0			0
$568$	−765.896	−	729.570i	−1.34841	−	1.28445i
$569$	−436.176			−0.766566			−0.383283	−	0.923631i	$-0.625207\pi$
$569$	−436.176			−0.766566			−0.383283	+	0.923631i	$0.625207\pi$
$570$	−162.304	−	159.697i	−0.284744	−	0.280171i
$571$			235.145i			0.411813i	0.978572	+	0.205906i	$0.0660143\pi$
$571$			235.145i			0.411813i	−0.978572	+	0.205906i	$0.933986\pi$
$572$	−13.9827	+	0.226414i	−0.0244453	+	0.000395828i
$573$	209.888			0.366296
$574$		0			0
$575$		−	63.2698i		−	0.110034i
$576$	9.32233	+	191.774i	0.0161846	+	0.332940i
$577$	−380.151			−0.658840			−0.329420	−	0.944183i	$-0.606853\pi$
$577$	−380.151			−0.658840			−0.329420	+	0.944183i	$0.606853\pi$
$578$	583.181	+	573.814i	1.00896	+	0.992758i
$579$		−	190.633i		−	0.329246i
$580$	−3.83251	−	236.686i	−0.00660778	−	0.408080i
$581$		0			0
$582$	−86.6970	+	88.1122i	−0.148964	+	0.151395i
$583$			66.8404i			0.114649i
$584$	552.176	−	579.670i	0.945507	−	0.992586i
$585$	−20.1162			−0.0343866
$586$	−496.877	−	488.897i	−0.847913	−	0.834295i
$587$			364.304i			0.620620i	0.950635	+	0.310310i	$0.100433\pi$
$587$			364.304i			0.620620i	−0.950635	+	0.310310i	$0.899567\pi$
$588$		0			0
$589$	−24.0865			−0.0408939
$590$	−92.2459	+	93.7516i	−0.156349	+	0.158901i
$591$			136.162i			0.230393i
$592$	960.436	−	31.1116i	1.62236	−	0.0525535i
$593$	57.6374			0.0971963			0.0485982	−	0.998818i	$-0.484525\pi$
$593$	57.6374			0.0971963			0.0485982	+	0.998818i	$0.484525\pi$
$594$	7.52114	+	7.40034i	0.0126618	+	0.0124585i
$595$		0			0
$596$	−5.78869	−	357.495i	−0.00971257	−	0.599824i
$597$	155.743			0.260876
$598$	14.4098	−	14.6450i	0.0240966	−	0.0244899i
$599$			496.778i			0.829346i	0.909970	+	0.414673i	$0.136104\pi$
$599$			496.778i			0.829346i	−0.909970	+	0.414673i	$0.863896\pi$
$600$	−212.780	−	202.688i	−0.354633	−	0.337813i
$601$	−467.713			−0.778224			−0.389112	−	0.921190i	$-0.627218\pi$
$601$	−467.713			−0.778224			−0.389112	+	0.921190i	$0.627218\pi$
$602$		0			0
$603$		−	187.946i		−	0.311685i
$604$	−790.136	+	12.7942i	−1.30817	+	0.0211824i
$605$	−233.617			−0.386143
$606$	137.747	−	139.995i	0.227305	−	0.231015i
$607$			750.168i			1.23586i	0.786233	+	0.617930i	$0.212029\pi$
$607$			750.168i			1.23586i	−0.786233	+	0.617930i	$0.787971\pi$
$608$	732.246	−	794.060i	1.20435	−	1.30602i
$609$		0			0
$610$	−226.934	−	223.289i	−0.372022	−	0.366047i
$611$			83.6794i			0.136955i
$612$	5.13317	+	317.011i	0.00838753	+	0.517992i
$613$	854.291			1.39362			0.696811	−	0.717255i	$-0.254602\pi$
$613$	854.291			1.39362			0.696811	+	0.717255i	$0.254602\pi$
$614$	33.8973	−	34.4506i	0.0552073	−	0.0561085i
$615$		−	9.01832i		−	0.0146639i
$616$		0			0
$617$	272.107			0.441015			0.220508	−	0.975385i	$-0.429229\pi$
$617$	272.107			0.441015			0.220508	+	0.975385i	$0.429229\pi$
$618$	354.816	+	349.117i	0.574135	+	0.564914i
$619$			414.506i			0.669639i	0.942282	+	0.334819i	$0.108675\pi$
$619$			414.506i			0.669639i	−0.942282	+	0.334819i	$0.891325\pi$
$620$	5.55748	−	0.0899889i	0.00896368	−	0.000145143i
$621$	−15.5017			−0.0249624
$622$	493.537	−	501.594i	0.793469	−	0.806421i
$623$		0			0
$624$	−3.08956	−	95.3768i	−0.00495122	−	0.152847i
$625$	354.979			0.567967
$626$	254.782	+	250.690i	0.407000	+	0.400463i
$627$		−	59.3598i		−	0.0946727i
$628$	−12.6301	−	780.000i	−0.0201116	−	1.24204i
$629$	1586.82			2.52276
$630$		0			0
$631$			303.910i			0.481632i	0.970571	+	0.240816i	$0.0774150\pi$
$631$			303.910i			0.481632i	−0.970571	+	0.240816i	$0.922585\pi$
$632$	565.209	+	538.401i	0.894319	+	0.851901i
$633$	253.508			0.400487
$634$	145.026	+	142.696i	0.228747	+	0.225073i
$635$		−	254.828i		−	0.401304i
$636$	−456.041	+	7.38438i	−0.717045	+	0.0116107i
$637$		0			0
$638$	43.2818	−	43.9883i	0.0678399	−	0.0689472i
$639$		−	396.662i		−	0.620755i
$640$	−165.985	+	185.950i	−0.259351	+	0.290546i
$641$	532.633			0.830941			0.415471	−	0.909607i	$-0.363617\pi$
$641$	532.633			0.830941			0.415471	+	0.909607i	$0.363617\pi$
$642$	−422.088	−	415.309i	−0.657458	−	0.646899i
$643$		−	844.547i		−	1.31345i	−0.754131	−	0.656724i	$-0.771942\pi$
$643$		−	844.547i		−	1.31345i	0.754131	−	0.656724i	$-0.228058\pi$
$644$		0			0
$645$	−22.5931			−0.0350281
$646$	1250.99	−	1271.41i	1.93652	−	1.96813i
$647$		−	606.314i		−	0.937116i	−0.883433	−	0.468558i	$-0.844774\pi$
$647$		−	606.314i		−	0.937116i	0.883433	−	0.468558i	$-0.155226\pi$
$648$	−49.6603	+	52.1330i	−0.0766363	+	0.0804522i
$649$	−34.2879			−0.0528319
$650$	104.110	+	102.438i	0.160169	+	0.157597i
$651$		0			0
$652$	−478.390	+	7.74627i	−0.733727	+	0.0118808i
$653$	−16.8535			−0.0258094			−0.0129047	−	0.999917i	$-0.504108\pi$
$653$	−16.8535			−0.0258094			−0.0129047	+	0.999917i	$0.504108\pi$
$654$	19.0409	−	19.3517i	0.0291145	−	0.0295897i
$655$			370.283i			0.565317i
$656$	42.7586	−	1.38509i	0.0651807	−	0.00211142i
$657$	300.215			0.456948
$658$		0			0
$659$		−	761.139i		−	1.15499i	−0.816394	−	0.577495i	$-0.804030\pi$
$659$		−	761.139i		−	1.15499i	0.816394	−	0.577495i	$-0.195970\pi$
$660$	0.221772	+	13.6961i	0.000336019	+	0.0207517i
$661$	982.016			1.48565			0.742826	−	0.669485i	$-0.233485\pi$
$661$	982.016			1.48565			0.742826	+	0.669485i	$0.233485\pi$
$662$	−3.90369	+	3.96741i	−0.00589681	+	0.00599306i
$663$		−	157.580i		−	0.237677i
$664$	−509.332	−	485.174i	−0.767066	−	0.730684i
$665$		0			0
$666$	256.862	+	252.737i	0.385679	+	0.379484i
$667$			90.6635i			0.135927i
$668$	291.022	−	4.71233i	0.435661	−	0.00705439i
$669$	237.957			0.355691
$670$	171.126	−	173.919i	0.255412	−	0.259581i
$671$		−	82.9968i		−	0.123691i
$672$		0			0
$673$	700.065			1.04022			0.520108	−	0.854101i	$-0.325892\pi$
$673$	700.065			1.04022			0.520108	+	0.854101i	$0.325892\pi$
$674$	−432.272	−	425.329i	−0.641352	−	0.631052i
$675$		−	110.200i		−	0.163259i
$676$	−10.1767	−	628.489i	−0.0150543	−	0.929718i
$677$	712.131			1.05189			0.525946	−	0.850518i	$-0.323711\pi$
$677$	712.131			1.05189			0.525946	+	0.850518i	$0.323711\pi$
$678$	436.856	−	443.987i	0.644331	−	0.654848i
$679$		0			0
$680$	−283.891	+	298.027i	−0.417487	+	0.438274i
$681$	106.777			0.156795
$682$	1.03286	+	1.01627i	0.00151446	+	0.00149014i
$683$			480.992i			0.704235i	0.935956	+	0.352117i	$0.114538\pi$
$683$			480.992i			0.704235i	−0.935956	+	0.352117i	$0.885462\pi$
$684$	405.002	−	6.55794i	0.592108	−	0.00958763i
$685$	−483.760			−0.706219
$686$		0			0
$687$			542.854i			0.790180i
$688$	−3.46999	−	107.121i	−0.00504360	−	0.155699i
$689$	226.689			0.329011
$690$	−14.3448	−	14.1144i	−0.0207895	−	0.0204556i
$691$			47.0484i			0.0680874i	0.999420	+	0.0340437i	$0.0108385\pi$
$691$			47.0484i			0.0680874i	−0.999420	+	0.0340437i	$0.989161\pi$
$692$	−0.640650	−	39.5649i	−0.000925795	−	0.0571747i
$693$		0			0
$694$	233.442	−	237.253i	0.336372	−	0.341863i
$695$			172.092i			0.247615i
$696$	304.907	+	290.445i	0.438084	+	0.417306i
$697$	70.6450			0.101356
$698$	−466.508	−	459.015i	−0.668349	−	0.657615i
$699$			246.400i			0.352503i
$700$		0			0
$701$	−95.2081			−0.135818			−0.0679088	−	0.997692i	$-0.521633\pi$
$701$	−95.2081			−0.135818			−0.0679088	+	0.997692i	$0.521633\pi$
$702$	25.0982	−	25.5079i	0.0357524	−	0.0363360i
$703$		−	2027.26i		−	2.88372i
$704$	−64.9033	+	3.15502i	−0.0921921	+	0.00448156i
$705$	81.9640			0.116261
$706$	−62.2723	−	61.2721i	−0.0882044	−	0.0867877i
$707$		0			0
$708$	−3.78806	−	233.941i	−0.00535036	−	0.330425i
$709$	−408.681			−0.576419			−0.288210	−	0.957567i	$-0.593060\pi$
$709$	−408.681			−0.576419			−0.288210	+	0.957567i	$0.593060\pi$
$710$	361.164	−	367.059i	0.508682	−	0.516985i
$711$			292.725i			0.411709i
$712$	−609.097	+	639.425i	−0.855473	+	0.898069i
$713$	−2.12881			−0.00298571
$714$		0			0
$715$		−	6.80806i		−	0.00952176i
$716$	1007.84	−	16.3194i	1.40760	−	0.0227925i
$717$	284.777			0.397178
$718$	101.591	−	103.250i	0.141492	−	0.143802i
$719$			800.605i			1.11350i	0.830681	+	0.556749i	$0.187952\pi$
$719$			800.605i			1.11350i	−0.830681	+	0.556749i	$0.812048\pi$
$720$	−93.4217	+	3.02623i	−0.129752	+	0.00420310i
$721$		0			0
$722$	−1109.66	−	1091.84i	−1.53692	−	1.51224i
$723$			119.598i			0.165419i
$724$	19.3666	+	1196.03i	0.0267494	+	1.65198i
$725$	−644.519			−0.888992
$726$	291.475	−	296.232i	0.401480	−	0.408034i
$727$			751.732i			1.03402i	0.855980	+	0.517009i	$0.172955\pi$
$727$			751.732i			1.03402i	−0.855980	+	0.517009i	$0.827045\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	277.810	+	273.348i	0.380561	+	0.374449i
$731$		−	176.983i		−	0.242111i
$732$	566.273	−	9.16931i	0.773597	−	0.0125264i
$733$	389.015			0.530716			0.265358	−	0.964150i	$-0.414510\pi$
$733$	389.015			0.530716			0.265358	+	0.964150i	$0.414510\pi$
$734$	−713.916	+	725.570i	−0.972638	+	0.988515i
$735$		0			0
$736$	64.7174	−	70.1807i	0.0879312	−	0.0953542i
$737$	63.6078			0.0863064
$738$	11.4355	+	11.2518i	0.0154952	+	0.0152464i
$739$		−	95.5532i		−	0.129301i	−0.997908	−	0.0646503i	$-0.979407\pi$
$739$		−	95.5532i		−	0.129301i	0.997908	−	0.0646503i	$-0.0205932\pi$
$740$	7.57398	+	467.750i	0.0102351	+	0.632094i
$741$	−201.318			−0.271685
$742$		0			0
$743$			1204.73i			1.62144i	0.585433	+	0.810721i	$0.300925\pi$
$743$			1204.73i			1.62144i	−0.585433	+	0.810721i	$0.699075\pi$
$744$	−6.81975	+	7.15932i	−0.00916634	+	0.00962275i
$745$	174.061			0.233639
$746$	177.735	+	174.880i	0.238251	+	0.234424i
$747$		−	263.786i		−	0.353127i
$748$	−107.288	+	1.73725i	−0.143434	+	0.00232253i
$749$		0			0
$750$	218.616	−	222.185i	0.291488	−	0.296246i
$751$		−	1162.57i		−	1.54804i	−0.633164	−	0.774018i	$-0.718244\pi$
$751$		−	1162.57i		−	1.54804i	0.633164	−	0.774018i	$-0.281756\pi$
$752$	12.5885	+	388.616i	0.0167401	+	0.516777i
$753$	−72.5613			−0.0963630
$754$	−149.186	−	146.790i	−0.197860	−	0.194682i
$755$		−	384.709i		−	0.509549i
$756$		0			0
$757$	379.147			0.500855			0.250428	−	0.968135i	$-0.419429\pi$
$757$	379.147			0.500855			0.250428	+	0.968135i	$0.419429\pi$
$758$	756.914	−	769.270i	0.998568	−	1.01487i
$759$		−	5.24634i		−	0.00691217i
$760$	380.748	+	362.689i	0.500984	+	0.477222i
$761$	−814.146			−1.06984			−0.534918	−	0.844904i	$-0.679658\pi$
$761$	−814.146			−1.06984			−0.534918	+	0.844904i	$0.679658\pi$
$762$	323.129	+	317.939i	0.424054	+	0.417243i
$763$		0			0
$764$	−484.652	+	7.84766i	−0.634361	+	0.0102718i
$765$	−154.350			−0.201764
$766$	790.491	−	803.394i	1.03197	−	1.04882i
$767$			116.287i			0.151613i
$768$	−28.6965	−	442.475i	−0.0373653	−	0.576140i
$769$	973.923			1.26648			0.633240	−	0.773956i	$-0.281725\pi$
$769$	973.923			1.26648			0.633240	+	0.773956i	$0.281725\pi$
$770$		0			0
$771$			373.769i			0.484785i
$772$	7.12774	+	440.191i	0.00923282	+	0.570196i
$773$	−757.451			−0.979885			−0.489943	−	0.871755i	$-0.662982\pi$
$773$	−757.451			−0.979885			−0.489943	+	0.871755i	$0.662982\pi$
$774$	28.1886	−	28.6488i	0.0364194	−	0.0370139i
$775$		−	15.1335i		−	0.0195272i
$776$	196.897	−	206.701i	0.253734	−	0.266368i
$777$		0			0
$778$	−301.266	−	296.428i	−0.387232	−	0.381012i
$779$		−	90.2534i		−	0.115858i
$780$	46.4502	−	0.752139i	0.0595516	−	0.000964281i
$781$	134.245			0.171889
$782$	110.565	−	112.370i	0.141387	−	0.143695i
$783$			157.913i			0.201677i
$784$		0			0
$785$	379.774			0.483789
$786$	−469.529	−	461.988i	−0.597365	−	0.587771i
$787$			113.131i			0.143750i	0.997414	+	0.0718749i	$0.0228982\pi$
$787$			113.131i			0.143750i	−0.997414	+	0.0718749i	$0.977102\pi$
$788$	−5.09109	−	314.413i	−0.00646077	−	0.399001i
$789$	193.847			0.245688
$790$	−266.529	+	270.879i	−0.337378	+	0.342885i
$791$		0			0
$792$	−17.6437	−	16.8069i	−0.0222774	−	0.0212208i
$793$	−281.483			−0.354960
$794$	−386.708	−	380.497i	−0.487038	−	0.479215i
$795$		−	222.042i		−	0.279298i
$796$	−359.626	+	5.82320i	−0.451791	+	0.00731558i
$797$	421.650			0.529047			0.264523	−	0.964379i	$-0.414785\pi$
$797$	421.650			0.529047			0.264523	+	0.964379i	$0.414785\pi$
$798$		0			0
$799$			642.065i			0.803586i
$800$	498.908	+	460.070i	0.623635	+	0.575088i
$801$	−331.162			−0.413436
$802$	203.885	+	200.610i	0.254221	+	0.250138i
$803$			101.604i			0.126530i
$804$	7.02725	+	433.985i	0.00874037	+	0.539783i
$805$		0			0
$806$	3.44668	−	3.50295i	0.00427628	−	0.00434609i
$807$		−	227.735i		−	0.282199i
$808$	−312.837	+	328.413i	−0.387174	+	0.406452i
$809$	241.212			0.298161			0.149081	−	0.988825i	$-0.452369\pi$
$809$	241.212			0.298161			0.149081	+	0.988825i	$0.452369\pi$
$810$	−24.9850	−	24.5837i	−0.0308457	−	0.0303502i
$811$			1343.28i			1.65632i	0.560491	+	0.828160i	$0.310612\pi$
$811$			1343.28i			1.65632i	−0.560491	+	0.828160i	$0.689388\pi$
$812$		0			0
$813$	247.836			0.304841
$814$	−85.5354	+	86.9316i	−0.105080	+	0.106796i
$815$		−	232.923i		−	0.285796i
$816$	−23.7060	−	731.818i	−0.0290514	−	0.896836i
$817$	−226.107			−0.276753
$818$	−318.754	−	313.634i	−0.389675	−	0.383416i
$819$		0			0
$820$	0.337193	+	20.8242i	0.000411211	+	0.0253953i
$821$	1046.03			1.27409			0.637047	−	0.770825i	$-0.280156\pi$
$821$	1046.03			1.27409			0.637047	+	0.770825i	$0.280156\pi$
$822$	603.569	−	613.421i	0.734269	−	0.746255i
$823$			410.187i			0.498404i	0.968452	+	0.249202i	$0.0801683\pi$
$823$			410.187i			0.498404i	−0.968452	+	0.249202i	$0.919832\pi$
$824$	−832.358	−	792.879i	−1.01014	−	0.962231i
$825$	37.2958			0.0452070
$826$		0			0
$827$			438.443i			0.530161i	0.964226	+	0.265080i	$0.0853985\pi$
$827$			438.443i			0.530161i	−0.964226	+	0.265080i	$0.914601\pi$
$828$	35.7949	−	0.579604i	0.0432305	−	0.000700005i
$829$	830.325			1.00160			0.500799	−	0.865563i	$-0.333039\pi$
$829$	830.325			1.00160			0.500799	+	0.865563i	$0.333039\pi$
$830$	240.179	−	244.100i	0.289372	−	0.294096i
$831$			489.733i			0.589330i
$832$	10.7002	+	220.119i	0.0128608	+	0.264566i
$833$		0			0
$834$	−218.218	−	214.713i	−0.261652	−	0.257450i
$835$			141.696i			0.169695i
$836$	2.21945	+	137.068i	0.00265484	+	0.163956i
$837$	−3.70786			−0.00442994
$838$	411.846	−	418.568i	0.491462	−	0.499485i
$839$			1492.60i			1.77903i	0.456910	+	0.889513i	$0.348956\pi$
$839$			1492.60i			1.77903i	−0.456910	+	0.889513i	$0.651044\pi$
$840$		0			0
$841$	82.5748			0.0981864
$842$	−860.116	−	846.301i	−1.02152	−	1.00511i
$843$			447.780i			0.531174i
$844$	−585.375	+	9.47861i	−0.693572	+	0.0112306i
$845$	306.005			0.362136
$846$	−102.263	+	103.933i	−0.120879	+	0.122852i
$847$		0			0
$848$	1052.77	−	34.1025i	1.24147	−	0.0402152i
$849$	817.251			0.962604
$850$	798.827	+	785.997i	0.939796	+	0.924702i
$851$		−	179.173i		−	0.210544i
$852$	14.8311	+	915.932i	0.0174074	+	1.07504i
$853$	861.696			1.01020			0.505098	−	0.863062i	$-0.331457\pi$
$853$	861.696			1.01020			0.505098	+	0.863062i	$0.331457\pi$
$854$		0			0
$855$			197.191i			0.230633i
$856$	990.172	+	943.208i	1.15674	+	1.10188i
$857$	−1354.69			−1.58074			−0.790369	−	0.612630i	$-0.790111\pi$
$857$	−1354.69			−1.58074			−0.790369	+	0.612630i	$0.790111\pi$
$858$	8.63281	+	8.49415i	0.0100615	+	0.00989995i
$859$			35.9658i			0.0418694i	0.999781	+	0.0209347i	$0.00666421\pi$
$859$			35.9658i			0.0418694i	−0.999781	+	0.0209347i	$0.993336\pi$
$860$	52.1698	−	0.844753i	0.0606626	−	0.000982271i
$861$		0			0
$862$	−400.990	+	407.535i	−0.465185	+	0.472779i
$863$		−	160.407i		−	0.185871i	−0.995672	−	0.0929355i	$-0.970375\pi$
$863$		−	160.407i		−	0.185871i	0.995672	−	0.0929355i	$-0.0296250\pi$
$864$	112.721	−	122.237i	0.130465	−	0.141478i
$865$	19.2638			0.0222703
$866$	331.117	+	325.799i	0.382352	+	0.376211i
$867$		−	708.535i		−	0.817226i
$868$		0			0
$869$	−99.0691			−0.114004
$870$	−143.781	+	146.128i	−0.165265	+	0.167963i
$871$		−	215.725i		−	0.247676i
$872$	−43.2437	+	45.3969i	−0.0495914	+	0.0520606i
$873$	107.052			0.122625
$874$	−143.559	−	141.254i	−0.164256	−	0.161617i
$875$		0			0
$876$	−693.225	+	11.2250i	−0.791353	+	0.0128139i
$877$	−1496.48			−1.70636			−0.853182	−	0.521613i	$-0.825330\pi$
$877$	−1496.48			−1.70636			−0.853182	+	0.521613i	$0.825330\pi$
$878$	42.3310	−	43.0220i	0.0482130	−	0.0490000i
$879$			603.681i			0.686781i
$880$	−1.02419	−	31.6173i	−0.00116385	−	0.0359288i
$881$	−627.408			−0.712154			−0.356077	−	0.934457i	$-0.615886\pi$
$881$	−627.408			−0.712154			−0.356077	+	0.934457i	$0.615886\pi$
$882$		0			0
$883$		−	1501.32i		−	1.70025i	−0.526579	−	0.850126i	$-0.676526\pi$
$883$		−	1501.32i		−	1.70025i	0.526579	−	0.850126i	$-0.323474\pi$
$884$	5.89188	+	363.868i	0.00666502	+	0.411615i
$885$	113.903			0.128704
$886$	−994.006	+	1010.23i	−1.12190	+	1.14022i
$887$			655.427i			0.738925i	0.929246	+	0.369463i	$0.120458\pi$
$887$			655.427i			0.738925i	−0.929246	+	0.369463i	$0.879542\pi$
$888$	−602.570	−	573.990i	−0.678569	−	0.646385i
$889$		0			0
$890$	−306.447	−	301.525i	−0.344323	−	0.338793i
$891$		−	9.13780i		−	0.0102557i
$892$	−549.466	+	8.89717i	−0.615994	+	0.00997440i
$893$	820.278			0.918565
$894$	−217.169	+	220.714i	−0.242918	+	0.246884i
$895$			490.710i			0.548279i
$896$		0			0
$897$	−17.7929			−0.0198360
$898$	−99.3821	−	97.7858i	−0.110670	−	0.108893i
$899$			21.6859i			0.0241222i
$900$	4.12035	+	254.463i	0.00457817	+	0.282736i
$901$	1739.36			1.93048
$902$	−3.80803	+	3.87019i	−0.00422176	+	0.00429068i
$903$		0			0
$904$	−992.143	+	1041.54i	−1.09750	+	1.15215i
$905$	−582.336			−0.643465
$906$	487.822	+	479.987i	0.538435	+	0.529787i
$907$		−	1187.82i		−	1.30962i	−0.755794	−	0.654809i	$-0.772749\pi$
$907$		−	1187.82i		−	1.30962i	0.755794	−	0.654809i	$-0.227251\pi$
$908$	−246.559	+	3.99238i	−0.271541	+	0.00439690i
$909$	−170.087			−0.187115
$910$		0			0
$911$			1557.23i			1.70937i	0.519150	+	0.854683i	$0.326248\pi$
$911$			1557.23i			1.70937i	−0.519150	+	0.854683i	$0.673752\pi$
$912$	−934.944	+	30.2859i	−1.02516	+	0.0332082i
$913$	89.2749			0.0977820
$914$	−508.488	−	500.321i	−0.556332	−	0.547397i
$915$			275.713i			0.301326i
$916$	−20.2972	−	1253.50i	−0.0221585	−	1.36845i
$917$		0			0
$918$	192.576	−	195.720i	0.209778	−	0.213202i
$919$			813.603i			0.885313i	0.896691	+	0.442657i	$0.145964\pi$
$919$			813.603i			0.885313i	−0.896691	+	0.442657i	$0.854036\pi$
$920$	33.6512	+	32.0552i	0.0365774	+	0.0348426i
$921$	−41.8558			−0.0454460
$922$	−851.426	−	837.751i	−0.923456	−	0.908624i
$923$		−	455.292i		−	0.493274i
$924$		0			0
$925$	1273.73			1.37700
$926$	−726.684	+	738.546i	−0.784756	+	0.797566i
$927$		−	431.083i		−	0.465030i
$928$	−714.919	−	659.265i	−0.770387	−	0.710415i
$929$	−231.239			−0.248911			−0.124456	−	0.992225i	$-0.539718\pi$
$929$	−231.239			−0.248911			−0.124456	+	0.992225i	$0.539718\pi$
$930$	−3.43114	−	3.37603i	−0.00368940	−	0.00363014i
$931$		0			0
$932$	−9.21284	−	568.962i	−0.00988502	−	0.610474i
$933$	−609.411			−0.653173
$934$	−766.330	+	778.839i	−0.820482	+	0.833875i
$935$		−	52.2377i		−	0.0558691i
$936$	−57.0004	+	59.8386i	−0.0608979	+	0.0639301i
$937$	−595.601			−0.635647			−0.317823	−	0.948150i	$-0.602952\pi$
$937$	−595.601			−0.635647			−0.317823	+	0.948150i	$0.602952\pi$
$938$		0			0
$939$		−	309.548i		−	0.329657i
$940$	−189.263	+	3.06462i	−0.201344	+	0.00326023i
$941$	−847.831			−0.900990			−0.450495	−	0.892779i	$-0.648752\pi$
$941$	−847.831			−0.900990			−0.450495	+	0.892779i	$0.648752\pi$
$942$	−473.830	+	481.565i	−0.503005	+	0.511215i
$943$		−	7.97678i		−	0.00845894i
$944$	17.4940	+	540.051i	0.0185318	+	0.572087i
$945$		0			0
$946$	9.69580	+	9.54007i	0.0102493	+	0.0100846i
$947$		−	193.623i		−	0.204459i	−0.994761	−	0.102230i	$-0.967402\pi$
$947$		−	193.623i		−	0.204459i	0.994761	−	0.102230i	$-0.0325976\pi$
$948$	−10.9449	−	675.932i	−0.0115453	−	0.713008i
$949$	344.588			0.363107
$950$	1004.16	−	1020.55i	1.05701	−	1.07426i
$951$		−	176.199i		−	0.185277i
$952$		0			0
$953$	1097.59			1.15172			0.575858	−	0.817550i	$-0.304668\pi$
$953$	1097.59			1.15172			0.575858	+	0.817550i	$0.304668\pi$
$954$	281.555	+	277.033i	0.295131	+	0.290391i
$955$		−	235.972i		−	0.247091i
$956$	−657.577	+	10.6477i	−0.687842	+	0.0111378i
$957$	−53.4436			−0.0558449
$958$	945.777	−	961.216i	0.987241	−	1.00336i
$959$		0			0
$960$	215.607	−	10.4809i	0.224590	−	0.0109176i
$961$	960.491			0.999470
$962$	294.828	+	290.093i	0.306474	+	0.301552i
$963$			512.816i			0.532519i
$964$	−4.47175	−	276.164i	−0.00463875	−	0.286477i
$965$	−214.325			−0.222098
$966$		0			0
$967$			1111.07i			1.14899i	0.818507	+	0.574496i	$0.194802\pi$
$967$			1111.07i			1.14899i	−0.818507	+	0.574496i	$0.805198\pi$
$968$	−661.968	+	694.928i	−0.683851	+	0.717901i
$969$	−1544.70			−1.59412
$970$	99.0625	+	97.4714i	0.102126	+	0.100486i
$971$		−	1113.58i		−	1.14683i	−0.819263	−	0.573417i	$-0.805617\pi$
$971$		−	1113.58i		−	1.14683i	0.819263	−	0.573417i	$-0.194383\pi$
$972$	62.3457	−	1.00952i	0.0641416	−	0.00103861i
$973$		0			0
$974$	353.097	−	358.861i	0.362523	−	0.368440i
$975$		−	126.488i		−	0.129732i
$976$	−1307.24	+	42.3457i	−1.33938	+	0.0433869i
$977$	−630.333			−0.645172			−0.322586	−	0.946540i	$-0.604552\pi$
$977$	−630.333			−0.645172			−0.322586	+	0.946540i	$0.604552\pi$
$978$	295.353	+	290.610i	0.301997	+	0.297147i
$979$		−	112.077i		−	0.114482i
$980$		0			0
$981$	−23.5113			−0.0239667
$982$	254.441	−	258.594i	0.259105	−	0.263334i
$983$			1659.64i			1.68834i	0.536078	+	0.844168i	$0.319905\pi$
$983$			1659.64i			1.68834i	−0.536078	+	0.844168i	$0.680095\pi$
$984$	−26.8264	−	25.5540i	−0.0272626	−	0.0259695i
$985$	153.084			0.155416
$986$	−1144.69	−	1126.31i	−1.16095	−	1.14230i
$987$		0			0
$988$	464.864	−	7.52725i	0.470510	−	0.00761867i
$989$	−19.9838			−0.0202061
$990$	8.32003	−	8.45584i	0.00840407	−	0.00854126i
$991$		−	1945.49i		−	1.96316i	−0.191053	−	0.981580i	$-0.561190\pi$
$991$		−	1945.49i		−	1.96316i	0.191053	−	0.981580i	$-0.438810\pi$
$992$	15.4798	−	16.7866i	0.0156046	−	0.0169219i
$993$	4.82020			0.00485418
$994$		0			0
$995$		−	175.098i		−	0.175978i
$996$	9.86290	+	609.108i	0.00990251	+	0.611554i
$997$	142.870			0.143300			0.0716499	−	0.997430i	$-0.477174\pi$
$997$	142.870			0.143300			0.0716499	+	0.997430i	$0.477174\pi$
$998$	323.428	−	328.708i	0.324077	−	0.329367i
$999$		−	312.074i		−	0.312387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.d.295.10		12
4.3	odd	2	inner	588.3.g.d.295.9		12
7.6	odd	2		84.3.g.a.43.10	yes	12
21.20	even	2		252.3.g.b.127.3		12
28.27	even	2		84.3.g.a.43.9	✓	12
56.13	odd	2		1344.3.m.e.127.3		12
56.27	even	2		1344.3.m.e.127.9		12
84.83	odd	2		252.3.g.b.127.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.g.a.43.9	✓	12	28.27	even	2
84.3.g.a.43.10	yes	12	7.6	odd	2
252.3.g.b.127.3		12	21.20	even	2
252.3.g.b.127.4		12	84.83	odd	2
588.3.g.d.295.9		12	4.3	odd	2	inner
588.3.g.d.295.10		12	1.1	even	1	trivial
1344.3.m.e.127.3		12	56.13	odd	2
1344.3.m.e.127.9		12	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42562 + 1.40272i) q^{2} -1.73205i q^{3} +(0.0647610 + 3.99948i) q^{4} -1.94731 q^{5} +(2.42958 - 2.46924i) q^{6} +(-5.51781 + 5.79256i) q^{8} -3.00000 q^{9} +(-2.77611 - 2.73152i) q^{10} -1.01531i q^{11} +(6.92730 - 0.112169i) q^{12} -3.44342 q^{13} +3.37283i q^{15} +(-15.9916 + 0.518020i) q^{16} -26.4211 q^{17} +(-4.27685 - 4.20816i) q^{18} +33.7546i q^{19} +(-0.126110 - 7.78820i) q^{20} +(1.42420 - 1.44744i) q^{22} +2.98330i q^{23} +(10.0330 + 9.55714i) q^{24} -21.2080 q^{25} +(-4.90899 - 4.83015i) q^{26} +5.19615i q^{27} +30.3904 q^{29} +(-4.73114 + 4.80836i) q^{30} +0.713577i q^{31} +(-23.5245 - 21.6932i) q^{32} -1.75857 q^{33} +(-37.6663 - 37.0613i) q^{34} +(-0.194283 - 11.9984i) q^{36} -60.0588 q^{37} +(-47.3482 + 48.1210i) q^{38} +5.96418i q^{39} +(10.7449 - 11.2799i) q^{40} -2.67381 q^{41} +6.69857i q^{43} +(4.06071 - 0.0657526i) q^{44} +5.84192 q^{45} +(-4.18473 + 4.25304i) q^{46} -24.3012i q^{47} +(0.897237 + 27.6983i) q^{48} +(-30.2345 - 29.7489i) q^{50} +45.7626i q^{51} +(-0.222999 - 13.7719i) q^{52} -65.8324 q^{53} +(-7.28874 + 7.40772i) q^{54} +1.97712i q^{55} +58.4646 q^{57} +(43.3250 + 42.6291i) q^{58} -33.7709i q^{59} +(-13.4896 + 0.218428i) q^{60} +81.7452 q^{61} +(-1.00095 + 1.01729i) q^{62} +(-3.10744 - 63.9245i) q^{64} +6.70539 q^{65} +(-2.50705 - 2.46678i) q^{66} +62.6486i q^{67} +(-1.71106 - 105.670i) q^{68} +5.16722 q^{69} +132.221i q^{71} +(16.5534 - 17.3777i) q^{72} -100.072 q^{73} +(-85.6207 - 84.2455i) q^{74} +36.7333i q^{75} +(-135.001 + 2.18598i) q^{76} +(-8.36606 + 8.50263i) q^{78} -97.5751i q^{79} +(31.1406 - 1.00874i) q^{80} +9.00000 q^{81} +(-3.81183 - 3.75061i) q^{82} +87.9287i q^{83} +51.4499 q^{85} +(-9.39621 + 9.54958i) q^{86} -52.6377i q^{87} +(5.88125 + 5.60230i) q^{88} +110.387 q^{89} +(8.32833 + 8.19457i) q^{90} +(-11.9316 + 0.193201i) q^{92} +1.23595 q^{93} +(34.0878 - 34.6442i) q^{94} -65.7305i q^{95} +(-37.5738 + 40.7457i) q^{96} -35.6839 q^{97} +3.04593i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{4} - 8 q^{5} + 12 q^{6} - 10 q^{8} - 36 q^{9} - 28 q^{10} - 24 q^{12} + 24 q^{13} - 14 q^{16} + 40 q^{17} - 6 q^{18} + 20 q^{20} - 88 q^{22} + 36 q^{24} + 180 q^{25} - 100 q^{26} + 72 q^{29}+ \cdots + 264 q^{97}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^4 - 8 * q^5 + 12 * q^6 - 10 * q^8 - 36 * q^9 - 28 * q^10 - 24 * q^12 + 24 * q^13 - 14 * q^16 + 40 * q^17 - 6 * q^18 + 20 * q^20 - 88 * q^22 + 36 * q^24 + 180 * q^25 - 100 * q^26 + 72 * q^29 + 72 * q^30 + 142 * q^32 + 100 * q^34 - 6 * q^36 - 88 * q^37 - 128 * q^38 + 28 * q^40 + 200 * q^41 - 40 * q^44 + 24 * q^45 - 24 * q^46 - 48 * q^48 - 346 * q^50 + 364 * q^52 + 104 * q^53 - 36 * q^54 + 148 * q^58 + 96 * q^60 - 104 * q^61 - 64 * q^62 - 70 * q^64 + 176 * q^65 - 24 * q^66 - 188 * q^68 + 192 * q^69 + 30 * q^72 - 312 * q^73 + 4 * q^74 - 432 * q^76 + 48 * q^78 + 564 * q^80 + 108 * q^81 - 332 * q^82 + 352 * q^85 + 160 * q^86 + 328 * q^88 + 552 * q^89 + 84 * q^90 + 232 * q^92 - 48 * q^93 + 144 * q^94 + 108 * q^96 + 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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