LMFDB - Embedded newform 448.3.o.b.95.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,3,Mod(95,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.95"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,6] 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:	$12.2071158433$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 34 x^{18} + 755 x^{16} - 9698 x^{14} + 89921 x^{12} - 522048 x^{10} + 2189920 x^{8} + \cdots + 7311616 $ x^20 - 34x^18 + 755x^16 - 9698x^14 + 89921x^12 - 522048x^10 + 2189920x^8 - 5640416x^6 + 10423552x^4 - 10729472*x^2 + 7311616
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.7
Root			$-3.26468 + 1.88486i$ of defining polynomial
Character	$\chi$	$=$	448.95
Dual form			448.3.o.b.415.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.565829 - 0.980045i) q^{3} +(3.20158 - 1.84843i) q^{5} +(2.72101 + 6.44951i) q^{7} +(3.85967 + 6.68515i) q^{9} +(-3.28683 + 5.69296i) q^{11} -1.88929i q^{13} -4.18359i q^{15} +(-0.399585 + 0.692102i) q^{17} +(14.6135 + 25.3113i) q^{19} +(7.86043 + 0.982611i) q^{21} +(-22.4205 + 12.9445i) q^{23} +(-5.66658 + 9.81480i) q^{25} +18.9206 q^{27} -38.2608i q^{29} +(-6.26083 - 3.61469i) q^{31} +(3.71957 + 6.44249i) q^{33} +(20.6330 + 15.6190i) q^{35} +(56.7282 - 32.7520i) q^{37} +(-1.85159 - 1.06901i) q^{39} +55.0502 q^{41} +22.3313 q^{43} +(24.7141 + 14.2687i) q^{45} +(-16.3276 + 9.42672i) q^{47} +(-34.1923 + 35.0983i) q^{49} +(0.452194 + 0.783223i) q^{51} +(0.264740 + 0.152848i) q^{53} +24.3020i q^{55} +33.0750 q^{57} +(-27.0974 + 46.9340i) q^{59} +(28.4960 - 16.4522i) q^{61} +(-32.6137 + 43.0833i) q^{63} +(-3.49223 - 6.04871i) q^{65} +(-4.74132 + 8.21221i) q^{67} +29.2974i q^{69} -33.4413i q^{71} +(47.2993 - 81.9248i) q^{73} +(6.41263 + 11.1070i) q^{75} +(-45.6603 - 5.70787i) q^{77} +(-7.35280 + 4.24514i) q^{79} +(-24.0313 + 41.6234i) q^{81} +77.8103 q^{83} +2.95443i q^{85} +(-37.4973 - 21.6491i) q^{87} +(23.8785 + 41.3588i) q^{89} +(12.1850 - 5.14076i) q^{91} +(-7.08512 + 4.09060i) q^{93} +(93.5727 + 54.0242i) q^{95} -125.723 q^{97} -50.7444 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{5} - 28 q^{9} + 46 q^{17} - 114 q^{21} + 36 q^{25} + 94 q^{33} + 114 q^{37} - 160 q^{41} - 708 q^{45} - 92 q^{49} - 6 q^{53} + 308 q^{57} + 90 q^{61} + 212 q^{65} + 314 q^{73} - 198 q^{77} - 322 q^{81}+ \cdots - 224 q^{97}+O(q^{100}) $ 20 * q + 6 * q^5 - 28 * q^9 + 46 * q^17 - 114 * q^21 + 36 * q^25 + 94 * q^33 + 114 * q^37 - 160 * q^41 - 708 * q^45 - 92 * q^49 - 6 * q^53 + 308 * q^57 + 90 * q^61 + 212 * q^65 + 314 * q^73 - 198 * q^77 - 322 * q^81 - 206 * q^89 + 1530 * q^93 - 224 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.565829	−	0.980045i	0.188610	−	0.326682i	−0.756177	−	0.654367i	$-0.772935\pi$
$3$	0.565829	−	0.980045i	0.188610	−	0.326682i	0.944787	+	0.327685i	$0.106269\pi$
$4$		0			0
$5$	3.20158	−	1.84843i	0.640317	−	0.369687i	−0.144420	−	0.989516i	$-0.546132\pi$
$5$	3.20158	−	1.84843i	0.640317	−	0.369687i	0.784736	+	0.619830i	$0.212798\pi$
$6$		0			0
$7$	2.72101	+	6.44951i	0.388715	+	0.921358i
$7$	2.72101	+	6.44951i	0.388715	+	0.921358i
$8$		0			0
$9$	3.85967	+	6.68515i	0.428853	+	0.742795i
$10$		0			0
$11$	−3.28683	+	5.69296i	−0.298803	+	0.517542i	−0.975862	−	0.218386i	$-0.929921\pi$
$11$	−3.28683	+	5.69296i	−0.298803	+	0.517542i	0.677059	+	0.735928i	$0.263254\pi$
$12$		0			0
$13$		−	1.88929i		−	0.145330i	−0.997356	−	0.0726650i	$-0.976850\pi$
$13$		−	1.88929i		−	0.145330i	0.997356	−	0.0726650i	$-0.0231504\pi$
$14$		0			0
$15$		−	4.18359i		−	0.278906i
$16$		0			0
$17$	−0.399585	+	0.692102i	−0.0235050	+	0.0407119i	−0.877539	−	0.479506i	$-0.840816\pi$
$17$	−0.399585	+	0.692102i	−0.0235050	+	0.0407119i	0.854034	+	0.520218i	$0.174149\pi$
$18$		0			0
$19$	14.6135	+	25.3113i	0.769132	+	1.33218i	0.938034	+	0.346542i	$0.112644\pi$
$19$	14.6135	+	25.3113i	0.769132	+	1.33218i	−0.168903	+	0.985633i	$0.554022\pi$
$20$		0			0
$21$	7.86043	+	0.982611i	0.374306	+	0.0467910i
$22$		0			0
$23$	−22.4205	+	12.9445i	−0.974803	+	0.562803i	−0.900697	−	0.434447i	$-0.856944\pi$
$23$	−22.4205	+	12.9445i	−0.974803	+	0.562803i	−0.0741061	+	0.997250i	$0.523610\pi$
$24$		0			0
$25$	−5.66658	+	9.81480i	−0.226663	+	0.392592i
$26$		0			0
$27$	18.9206			0.700763
$28$		0			0
$29$		−	38.2608i		−	1.31934i	−0.751557	−	0.659669i	$-0.770697\pi$
$29$		−	38.2608i		−	1.31934i	0.751557	−	0.659669i	$-0.229303\pi$
$30$		0			0
$31$	−6.26083	−	3.61469i	−0.201962	−	0.116603i	0.395608	−	0.918419i	$-0.370534\pi$
$31$	−6.26083	−	3.61469i	−0.201962	−	0.116603i	−0.597570	+	0.801816i	$0.703867\pi$
$32$		0			0
$33$	3.71957	+	6.44249i	0.112714	+	0.195227i
$34$		0			0
$35$	20.6330	+	15.6190i	0.589515	+	0.446258i
$36$		0			0
$37$	56.7282	−	32.7520i	1.53319	−	0.885190i	0.533983	−	0.845495i	$-0.320695\pi$
$37$	56.7282	−	32.7520i	1.53319	−	0.885190i	0.999212	−	0.0396949i	$-0.0126386\pi$
$38$		0			0
$39$	−1.85159	−	1.06901i	−0.0474766	−	0.0274106i
$40$		0			0
$41$	55.0502			1.34269			0.671344	−	0.741146i	$-0.265717\pi$
$41$	55.0502			1.34269			0.671344	+	0.741146i	$0.265717\pi$
$42$		0			0
$43$	22.3313			0.519332			0.259666	−	0.965699i	$-0.416388\pi$
$43$	22.3313			0.519332			0.259666	+	0.965699i	$0.416388\pi$
$44$		0			0
$45$	24.7141	+	14.2687i	0.549203	+	0.317083i
$46$		0			0
$47$	−16.3276	+	9.42672i	−0.347395	+	0.200569i	−0.663537	−	0.748143i	$-0.730946\pi$
$47$	−16.3276	+	9.42672i	−0.347395	+	0.200569i	0.316142	+	0.948712i	$0.397612\pi$
$48$		0			0
$49$	−34.1923	+	35.0983i	−0.697801	+	0.716291i
$50$		0			0
$51$	0.452194	+	0.783223i	0.00886655	+	0.0153573i
$52$		0			0
$53$	0.264740	+	0.152848i	0.00499510	+	0.00288392i	0.502495	−	0.864580i	$-0.332415\pi$
$53$	0.264740	+	0.152848i	0.00499510	+	0.00288392i	−0.497500	+	0.867464i	$0.665749\pi$
$54$		0			0
$55$			24.3020i			0.441854i
$56$		0			0
$57$	33.0750			0.580263
$58$		0			0
$59$	−27.0974	+	46.9340i	−0.459277	+	0.795491i	−0.998923	−	0.0464009i	$-0.985225\pi$
$59$	−27.0974	+	46.9340i	−0.459277	+	0.795491i	0.539646	+	0.841892i	$0.318558\pi$
$60$		0			0
$61$	28.4960	−	16.4522i	0.467148	−	0.269708i	−0.247897	−	0.968786i	$-0.579739\pi$
$61$	28.4960	−	16.4522i	0.467148	−	0.269708i	0.715045	+	0.699078i	$0.246406\pi$
$62$		0			0
$63$	−32.6137	+	43.0833i	−0.517678	+	0.683862i
$64$		0			0
$65$	−3.49223	−	6.04871i	−0.0537266	−	0.0930571i
$66$		0			0
$67$	−4.74132	+	8.21221i	−0.0707660	+	0.122570i	−0.899237	−	0.437461i	$-0.855878\pi$
$67$	−4.74132	+	8.21221i	−0.0707660	+	0.122570i	0.828471	+	0.560032i	$0.189211\pi$
$68$		0			0
$69$			29.2974i			0.424600i
$70$		0			0
$71$		−	33.4413i		−	0.471004i	−0.971874	−	0.235502i	$-0.924327\pi$
$71$		−	33.4413i		−	0.471004i	0.971874	−	0.235502i	$-0.0756733\pi$
$72$		0			0
$73$	47.2993	−	81.9248i	0.647936	−	1.12226i	−0.335679	−	0.941976i	$-0.608966\pi$
$73$	47.2993	−	81.9248i	0.647936	−	1.12226i	0.983615	−	0.180281i	$-0.0577008\pi$
$74$		0			0
$75$	6.41263	+	11.1070i	0.0855017	+	0.148093i
$76$		0			0
$77$	−45.6603	−	5.70787i	−0.592991	−	0.0741282i
$78$		0			0
$79$	−7.35280	+	4.24514i	−0.0930734	+	0.0537359i	−0.545814	−	0.837906i	$-0.683780\pi$
$79$	−7.35280	+	4.24514i	−0.0930734	+	0.0537359i	0.452741	+	0.891642i	$0.350446\pi$
$80$		0			0
$81$	−24.0313	+	41.6234i	−0.296682	+	0.513869i
$82$		0			0
$83$	77.8103			0.937473			0.468737	−	0.883338i	$-0.344709\pi$
$83$	77.8103			0.937473			0.468737	+	0.883338i	$0.344709\pi$
$84$		0			0
$85$			2.95443i			0.0347580i
$86$		0			0
$87$	−37.4973	−	21.6491i	−0.431003	−	0.248840i
$88$		0			0
$89$	23.8785	+	41.3588i	0.268298	+	0.464705i	0.968422	−	0.249315i	$-0.0802055\pi$
$89$	23.8785	+	41.3588i	0.268298	+	0.464705i	−0.700125	+	0.714021i	$0.746872\pi$
$90$		0			0
$91$	12.1850	−	5.14076i	0.133901	−	0.0564919i
$92$		0			0
$93$	−7.08512	+	4.09060i	−0.0761841	+	0.0439849i
$94$		0			0
$95$	93.5727	+	54.0242i	0.984975	+	0.568676i
$96$		0			0
$97$	−125.723			−1.29611			−0.648057	−	0.761592i	$-0.724418\pi$
$97$	−125.723			−1.29611			−0.648057	+	0.761592i	$0.724418\pi$
$98$		0			0
$99$	−50.7444			−0.512570
$100$		0			0
$101$	−136.597	−	78.8646i	−1.35245	−	0.780837i	−0.363858	−	0.931454i	$-0.618541\pi$
$101$	−136.597	−	78.8646i	−1.35245	−	0.780837i	−0.988592	+	0.150617i	$0.951874\pi$
$102$		0			0
$103$	99.3139	−	57.3389i	0.964212	−	0.556688i	0.0667453	−	0.997770i	$-0.478739\pi$
$103$	99.3139	−	57.3389i	0.964212	−	0.556688i	0.897467	+	0.441082i	$0.145405\pi$
$104$		0			0
$105$	26.9821	−	11.3836i	0.256972	−	0.108415i
$106$		0			0
$107$	−91.3564	−	158.234i	−0.853798	−	1.47882i	−0.877755	−	0.479109i	$-0.840960\pi$
$107$	−91.3564	−	158.234i	−0.853798	−	1.47882i	0.0239572	−	0.999713i	$-0.492373\pi$
$108$		0			0
$109$	62.0689	+	35.8355i	0.569440	+	0.328766i	0.756926	−	0.653501i	$-0.226701\pi$
$109$	62.0689	+	35.8355i	0.569440	+	0.328766i	−0.187486	+	0.982267i	$0.560034\pi$
$110$		0			0
$111$		−	74.1282i		−	0.667822i
$112$		0			0
$113$	−141.669			−1.25371			−0.626855	−	0.779136i	$-0.715658\pi$
$113$	−141.669			−1.25371			−0.626855	+	0.779136i	$0.715658\pi$
$114$		0			0
$115$	−47.8540	+	82.8856i	−0.416122	+	0.720744i
$116$		0			0
$117$	12.6302	−	7.29204i	0.107950	−	0.0623251i
$118$		0			0
$119$	−5.55099	−	0.693915i	−0.0466470	−	0.00583122i
$120$		0			0
$121$	38.8934	+	67.3654i	0.321433	+	0.556739i
$122$		0			0
$123$	31.1490	−	53.9517i	0.253244	−	0.438631i
$124$		0			0
$125$			134.319i			1.07455i
$126$		0			0
$127$		−	71.8695i		−	0.565902i	−0.959134	−	0.282951i	$-0.908687\pi$
$127$		−	71.8695i		−	0.565902i	0.959134	−	0.282951i	$-0.0913133\pi$
$128$		0			0
$129$	12.6357	−	21.8856i	0.0979510	−	0.169656i
$130$		0			0
$131$	−120.270	−	208.313i	−0.918089	−	1.59018i	−0.802315	−	0.596900i	$-0.796399\pi$
$131$	−120.270	−	208.313i	−0.918089	−	1.59018i	−0.115773	−	0.993276i	$-0.536935\pi$
$132$		0			0
$133$	−123.482	+	163.122i	−0.928437	+	1.22648i
$134$		0			0
$135$	60.5758	−	34.9735i	0.448710	−	0.259063i
$136$		0			0
$137$	67.8806	−	117.573i	0.495479	−	0.858195i	−0.504507	−	0.863407i	$-0.668326\pi$
$137$	67.8806	−	117.573i	0.495479	−	0.858195i	0.999986	+	0.00521241i	$0.00165917\pi$
$138$		0			0
$139$	−37.1158			−0.267020			−0.133510	−	0.991047i	$-0.542625\pi$
$139$	−37.1158			−0.267020			−0.133510	+	0.991047i	$0.542625\pi$
$140$		0			0
$141$			21.3357i			0.151317i
$142$		0			0
$143$	10.7557	+	6.20978i	0.0752144	+	0.0434250i
$144$		0			0
$145$	−70.7225	−	122.495i	−0.487742	−	0.844793i
$146$		0			0
$147$	15.0509	+	53.3696i	0.102387	+	0.363058i
$148$		0			0
$149$	−31.3945	+	18.1256i	−0.210701	+	0.121648i	−0.601637	−	0.798769i	$-0.705485\pi$
$149$	−31.3945	+	18.1256i	−0.210701	+	0.121648i	0.390936	+	0.920418i	$0.372151\pi$
$150$		0			0
$151$	−12.8838	−	7.43844i	−0.0853229	−	0.0492612i	0.456732	−	0.889605i	$-0.349020\pi$
$151$	−12.8838	−	7.43844i	−0.0853229	−	0.0492612i	−0.542054	+	0.840343i	$0.682353\pi$
$152$		0			0
$153$	−6.16908			−0.0403208
$154$		0			0
$155$	−26.7261			−0.172426
$156$		0			0
$157$	−174.780	−	100.909i	−1.11325	−	0.642734i	−0.173579	−	0.984820i	$-0.555533\pi$
$157$	−174.780	−	100.909i	−1.11325	−	0.642734i	−0.939669	+	0.342086i	$0.888867\pi$
$158$		0			0
$159$	0.299595	−	0.172971i	0.00188425	−	0.00108787i
$160$		0			0
$161$	−144.492	−	109.379i	−0.897464	−	0.679373i
$162$		0			0
$163$	−66.1378	−	114.554i	−0.405753	−	0.702786i	0.588655	−	0.808384i	$-0.299657\pi$
$163$	−66.1378	−	114.554i	−0.405753	−	0.702786i	−0.994409	+	0.105599i	$0.966324\pi$
$164$		0			0
$165$	23.8170	+	13.7508i	0.144346	+	0.0833380i
$166$		0			0
$167$			239.413i			1.43361i	0.697274	+	0.716805i	$0.254396\pi$
$167$			239.413i			1.43361i	−0.697274	+	0.716805i	$0.745604\pi$
$168$		0			0
$169$	165.431			0.978879
$170$		0			0
$171$	−112.807	+	195.387i	−0.659688	+	1.14261i
$172$		0			0
$173$	−139.852	+	80.7433i	−0.808390	+	0.466724i	−0.846397	−	0.532553i	$-0.821233\pi$
$173$	−139.852	+	80.7433i	−0.808390	+	0.466724i	0.0380063	+	0.999277i	$0.487899\pi$
$174$		0			0
$175$	−78.7194	−	9.84050i	−0.449825	−	0.0562315i
$176$		0			0
$177$	30.6649	+	53.1132i	0.173248	+	0.300075i
$178$		0			0
$179$	124.034	−	214.834i	0.692929	−	1.20019i	−0.277945	−	0.960597i	$-0.589653\pi$
$179$	124.034	−	214.834i	0.692929	−	1.20019i	0.970874	−	0.239591i	$-0.0770133\pi$
$180$		0			0
$181$			184.486i			1.01926i	0.860393	+	0.509631i	$0.170218\pi$
$181$			184.486i			1.01926i	−0.860393	+	0.509631i	$0.829782\pi$
$182$		0			0
$183$		−	37.2365i		−	0.203478i
$184$		0			0
$185$	121.080	−	209.717i	0.654487	−	1.13360i
$186$		0			0
$187$	−2.62674	−	4.54965i	−0.0140468	−	0.0243297i
$188$		0			0
$189$	51.4830	+	122.028i	0.272397	+	0.645653i
$190$		0			0
$191$	321.742	−	185.758i	1.68452	−	0.972555i	0.725922	−	0.687777i	$-0.241413\pi$
$191$	321.742	−	185.758i	1.68452	−	0.972555i	0.958593	−	0.284778i	$-0.0919200\pi$
$192$		0			0
$193$	−107.615	+	186.395i	−0.557592	+	0.965778i	0.440105	+	0.897946i	$0.354941\pi$
$193$	−107.615	+	186.395i	−0.557592	+	0.965778i	−0.997697	+	0.0678314i	$0.978392\pi$
$194$		0			0
$195$	−7.90401			−0.0405334
$196$		0			0
$197$		−	181.962i		−	0.923663i	−0.886968	−	0.461831i	$-0.847193\pi$
$197$		−	181.962i		−	0.923663i	0.886968	−	0.461831i	$-0.152807\pi$
$198$		0			0
$199$	−149.053	−	86.0558i	−0.749010	−	0.432441i	0.0763259	−	0.997083i	$-0.475681\pi$
$199$	−149.053	−	86.0558i	−0.749010	−	0.432441i	−0.825336	+	0.564642i	$0.809014\pi$
$200$		0			0
$201$	5.36556	+	9.29342i	0.0266943	+	0.0462359i
$202$		0			0
$203$	246.763	−	104.108i	1.21558	−	0.512846i
$204$		0			0
$205$	176.248	−	101.757i	0.859745	−	0.496374i
$206$		0			0
$207$	−173.071	−	99.9229i	−0.836094	−	0.482719i
$208$		0			0
$209$	−192.129			−0.919276
$210$		0			0
$211$	−350.415			−1.66073			−0.830367	−	0.557217i	$-0.811869\pi$
$211$	−350.415			−1.66073			−0.830367	+	0.557217i	$0.811869\pi$
$212$		0			0
$213$	−32.7739	−	18.9220i	−0.153868	−	0.0888358i
$214$		0			0
$215$	71.4954	−	41.2779i	0.332537	−	0.191990i
$216$		0			0
$217$	6.27723	−	50.2149i	0.0289273	−	0.231405i
$218$		0			0
$219$	−53.5266	−	92.7109i	−0.244414	−	0.423337i
$220$		0			0
$221$	1.30758	+	0.754932i	0.00591666	+	0.00341598i
$222$		0			0
$223$			188.995i			0.847510i	0.905777	+	0.423755i	$0.139288\pi$
$223$			188.995i			0.847510i	−0.905777	+	0.423755i	$0.860712\pi$
$224$		0			0
$225$	−87.4846			−0.388820
$226$		0			0
$227$	−13.9566	+	24.1736i	−0.0614829	+	0.106491i	−0.895128	−	0.445808i	$-0.852916\pi$
$227$	−13.9566	+	24.1736i	−0.0614829	+	0.106491i	0.833646	+	0.552300i	$0.186250\pi$
$228$		0			0
$229$	200.369	−	115.683i	0.874976	−	0.505167i	0.00597712	−	0.999982i	$-0.498097\pi$
$229$	200.369	−	115.683i	0.874976	−	0.505167i	0.868998	+	0.494815i	$0.164764\pi$
$230$		0			0
$231$	−31.4299	+	41.5195i	−0.136060	+	0.179738i
$232$		0			0
$233$	109.501	+	189.661i	0.469960	+	0.813994i	0.999410	−	0.0343468i	$-0.0109351\pi$
$233$	109.501	+	189.661i	0.469960	+	0.813994i	−0.529450	+	0.848341i	$0.677602\pi$
$234$		0			0
$235$	−34.8494	+	60.3609i	−0.148295	+	0.256855i
$236$		0			0
$237$			9.60809i			0.0405405i
$238$		0			0
$239$		−	108.752i		−	0.455030i	−0.973775	−	0.227515i	$-0.926940\pi$
$239$		−	108.752i		−	0.455030i	0.973775	−	0.227515i	$-0.0730601\pi$
$240$		0			0
$241$	−74.3039	+	128.698i	−0.308315	+	0.534017i	−0.977994	−	0.208634i	$-0.933098\pi$
$241$	−74.3039	+	128.698i	−0.308315	+	0.534017i	0.669679	+	0.742651i	$0.266432\pi$
$242$		0			0
$243$	112.338	+	194.575i	0.462296	+	0.800719i
$244$		0			0
$245$	−44.5925	+	175.572i	−0.182010	+	0.716621i
$246$		0			0
$247$	47.8204	−	27.6091i	0.193605	−	0.111778i
$248$		0			0
$249$	44.0273	−	76.2575i	0.176817	−	0.306255i
$250$		0			0
$251$	303.364			1.20862			0.604310	−	0.796749i	$-0.293449\pi$
$251$	303.364			1.20862			0.604310	+	0.796749i	$0.293449\pi$
$252$		0			0
$253$		−	170.185i		−	0.672669i
$254$		0			0
$255$	2.89547	+	1.67170i	0.0113548	+	0.00655570i
$256$		0			0
$257$	43.9898	+	76.1925i	0.171166	+	0.296469i	0.938828	−	0.344387i	$-0.111913\pi$
$257$	43.9898	+	76.1925i	0.171166	+	0.296469i	−0.767661	+	0.640856i	$0.778580\pi$
$258$		0			0
$259$	365.592	+	276.750i	1.41155	+	1.06853i
$260$		0			0
$261$	255.779	−	147.674i	0.979997	−	0.565801i
$262$		0			0
$263$	109.743	+	63.3603i	0.417275	+	0.240914i	0.693911	−	0.720061i	$-0.255886\pi$
$263$	109.743	+	63.3603i	0.417275	+	0.240914i	−0.276636	+	0.960975i	$0.589220\pi$
$264$		0			0
$265$	1.13012			0.00426459
$266$		0			0
$267$	54.0446			0.202414
$268$		0			0
$269$	−430.764	−	248.702i	−1.60135	−	0.924542i	−0.991217	−	0.132245i	$-0.957781\pi$
$269$	−430.764	−	248.702i	−1.60135	−	0.924542i	−0.610136	−	0.792297i	$-0.708885\pi$
$270$		0			0
$271$	−360.736	+	208.271i	−1.33113	+	0.768528i	−0.985473	−	0.169833i	$-0.945677\pi$
$271$	−360.736	+	208.271i	−1.33113	+	0.768528i	−0.345656	+	0.938361i	$0.612344\pi$
$272$		0			0
$273$	1.85644	−	14.8506i	0.00680013	−	0.0543979i
$274$		0			0
$275$	−37.2502	−	64.5193i	−0.135455	−	0.234615i
$276$		0			0
$277$	137.732	+	79.5197i	0.497228	+	0.287075i	0.727568	−	0.686035i	$-0.240650\pi$
$277$	137.732	+	79.5197i	0.497228	+	0.287075i	−0.230340	+	0.973110i	$0.573984\pi$
$278$		0			0
$279$		−	55.8062i		−	0.200022i
$280$		0			0
$281$	349.562			1.24399			0.621997	−	0.783020i	$-0.286322\pi$
$281$	349.562			1.24399			0.621997	+	0.783020i	$0.286322\pi$
$282$		0			0
$283$	−243.870	+	422.396i	−0.861732	+	1.49256i	0.00852309	+	0.999964i	$0.497287\pi$
$283$	−243.870	+	422.396i	−0.861732	+	1.49256i	−0.870255	+	0.492601i	$0.836046\pi$
$284$		0			0
$285$	105.892	−	61.1369i	0.371552	−	0.214516i
$286$		0			0
$287$	149.792	+	355.047i	0.521923	+	1.23710i
$288$		0			0
$289$	144.181	+	249.728i	0.498895	+	0.864112i
$290$		0			0
$291$	−71.1378	+	123.214i	−0.244460	+	0.423417i
$292$		0			0
$293$		−	124.718i		−	0.425658i	−0.977089	−	0.212829i	$-0.931732\pi$
$293$		−	124.718i		−	0.425658i	0.977089	−	0.212829i	$-0.0682678\pi$
$294$		0			0
$295$			200.351i			0.679155i
$296$		0			0
$297$	−62.1888	+	107.714i	−0.209390	+	0.362674i
$298$		0			0
$299$	24.4558	+	42.3588i	0.0817921	+	0.141668i
$300$		0			0
$301$	60.7635	+	144.026i	0.201872	+	0.478490i
$302$		0			0
$303$	−154.582	+	89.2478i	−0.510170	+	0.294547i
$304$		0			0
$305$	60.8216	−	105.346i	0.199415	−	0.345397i
$306$		0			0
$307$	429.152			1.39789			0.698945	−	0.715176i	$-0.253653\pi$
$307$	429.152			1.39789			0.698945	+	0.715176i	$0.253653\pi$
$308$		0			0
$309$		−	129.776i		−	0.419987i
$310$		0			0
$311$	−281.671	−	162.623i	−0.905693	−	0.522902i	−0.0266502	−	0.999645i	$-0.508484\pi$
$311$	−281.671	−	162.623i	−0.905693	−	0.522902i	−0.879043	+	0.476743i	$0.841817\pi$
$312$		0			0
$313$	51.3765	+	88.9867i	0.164142	+	0.284303i	0.936350	−	0.351067i	$-0.114181\pi$
$313$	51.3765	+	88.9867i	0.164142	+	0.284303i	−0.772208	+	0.635370i	$0.780848\pi$
$314$		0			0
$315$	−24.7789	+	198.219i	−0.0786630	+	0.629267i
$316$		0			0
$317$	345.808	−	199.652i	1.09088	−	0.629818i	0.157067	−	0.987588i	$-0.449796\pi$
$317$	345.808	−	199.652i	1.09088	−	0.629818i	0.933810	+	0.357770i	$0.116463\pi$
$318$		0			0
$319$	217.817	+	125.757i	0.682813	+	0.394222i
$320$		0			0
$321$	−206.768			−0.644139
$322$		0			0
$323$	−23.3574			−0.0723138
$324$		0			0
$325$	18.5430	+	10.7058i	0.0570554	+	0.0329409i
$326$		0			0
$327$	70.2408	−	40.5536i	0.214804	−	0.124017i
$328$		0			0
$329$	−105.225	−	79.6546i	−0.319833	−	0.242111i
$330$		0			0
$331$	−28.7333	−	49.7675i	−0.0868075	−	0.150355i	0.819352	−	0.573290i	$-0.194333\pi$
$331$	−28.7333	−	49.7675i	−0.0868075	−	0.150355i	−0.906160	+	0.422935i	$0.861000\pi$
$332$		0			0
$333$	437.905	+	252.824i	1.31503	+	0.759233i
$334$		0			0
$335$			35.0561i			0.104645i
$336$		0			0
$337$	354.086			1.05070			0.525350	−	0.850886i	$-0.323934\pi$
$337$	354.086			1.05070			0.525350	+	0.850886i	$0.323934\pi$
$338$		0			0
$339$	−80.1606	+	138.842i	−0.236462	+	0.409564i
$340$		0			0
$341$	41.1566	−	23.7618i	0.120694	−	0.0696827i
$342$		0			0
$343$	−319.404	−	125.021i	−0.931207	−	0.364491i
$344$		0			0
$345$	54.1544	+	93.7981i	0.156969	+	0.271879i
$346$		0			0
$347$	159.542	−	276.336i	0.459776	−	0.796356i	−0.539172	−	0.842195i	$-0.681263\pi$
$347$	159.542	−	276.336i	0.459776	−	0.796356i	0.998949	+	0.0458393i	$0.0145962\pi$
$348$		0			0
$349$			151.395i			0.433796i	0.976194	+	0.216898i	$0.0695938\pi$
$349$			151.395i			0.433796i	−0.976194	+	0.216898i	$0.930406\pi$
$350$		0			0
$351$		−	35.7465i		−	0.101842i
$352$		0			0
$353$	269.802	−	467.311i	0.764311	−	1.32383i	−0.176298	−	0.984337i	$-0.556412\pi$
$353$	269.802	−	467.311i	0.764311	−	1.32383i	0.940610	−	0.339489i	$-0.110254\pi$
$354$		0			0
$355$	−61.8140	−	107.065i	−0.174124	−	0.301591i
$356$		0			0
$357$	−3.82098	+	5.04758i	−0.0107030	+	0.0141389i
$358$		0			0
$359$	99.2112	−	57.2796i	0.276354	−	0.159553i	−0.355417	−	0.934708i	$-0.615661\pi$
$359$	99.2112	−	57.2796i	0.276354	−	0.159553i	0.631772	+	0.775154i	$0.282328\pi$
$360$		0			0
$361$	−246.609	+	427.139i	−0.683127	+	1.18321i
$362$		0			0
$363$	88.0282			0.242502
$364$		0			0
$365$		−	349.719i		−	0.958133i
$366$		0			0
$367$	−462.804	−	267.200i	−1.26105	−	0.728065i	−0.287769	−	0.957700i	$-0.592913\pi$
$367$	−462.804	−	267.200i	−1.26105	−	0.728065i	−0.973277	+	0.229635i	$0.926247\pi$
$368$		0			0
$369$	212.476	+	368.019i	0.575816	+	0.997342i
$370$		0			0
$371$	−0.265433	+	2.12334i	−0.000715454	+	0.00572330i
$372$		0			0
$373$	446.370	−	257.712i	1.19670	−	0.690916i	0.236883	−	0.971538i	$-0.423874\pi$
$373$	446.370	−	257.712i	1.19670	−	0.690916i	0.959818	+	0.280622i	$0.0905407\pi$
$374$		0			0
$375$	131.639	+	76.0016i	0.351036	+	0.202671i
$376$		0			0
$377$	−72.2856			−0.191739
$378$		0			0
$379$	127.845			0.337323			0.168661	−	0.985674i	$-0.446056\pi$
$379$	127.845			0.337323			0.168661	+	0.985674i	$0.446056\pi$
$380$		0			0
$381$	−70.4353	−	40.6659i	−0.184870	−	0.106735i
$382$		0			0
$383$	196.198	−	113.275i	0.512265	−	0.295756i	−0.221499	−	0.975161i	$-0.571095\pi$
$383$	196.198	−	113.275i	0.512265	−	0.295756i	0.733764	+	0.679404i	$0.237762\pi$
$384$		0			0
$385$	−156.736	+	66.1259i	−0.407106	+	0.171755i
$386$		0			0
$387$	86.1914	+	149.288i	0.222717	+	0.385757i
$388$		0			0
$389$	−477.391	−	275.622i	−1.22722	−	0.708539i	−0.260776	−	0.965399i	$-0.583979\pi$
$389$	−477.391	−	275.622i	−1.22722	−	0.708539i	−0.966448	+	0.256861i	$0.917312\pi$
$390$		0			0
$391$		−	20.6897i		−	0.0529148i
$392$		0			0
$393$	−272.208			−0.692642
$394$		0			0
$395$	−15.6937	+	27.1823i	−0.0397309	+	0.0688160i
$396$		0			0
$397$	200.760	−	115.909i	0.505692	−	0.291962i	−0.225369	−	0.974273i	$-0.572359\pi$
$397$	200.760	−	115.909i	0.505692	−	0.291962i	0.731061	+	0.682312i	$0.239025\pi$
$398$		0			0
$399$	89.9972	+	213.317i	0.225557	+	0.534630i
$400$		0			0
$401$	−271.319	−	469.939i	−0.676607	−	1.17192i	−0.975996	−	0.217786i	$-0.930116\pi$
$401$	−271.319	−	469.939i	−0.676607	−	1.17192i	0.299390	−	0.954131i	$-0.403217\pi$
$402$		0			0
$403$	−6.82920	+	11.8285i	−0.0169459	+	0.0293512i
$404$		0			0
$405$			177.681i			0.438718i
$406$		0			0
$407$			430.602i			1.05799i
$408$		0			0
$409$	105.418	−	182.589i	0.257745	−	0.446428i	−0.707892	−	0.706320i	$-0.750354\pi$
$409$	105.418	−	182.589i	0.257745	−	0.446428i	0.965638	+	0.259893i	$0.0836872\pi$
$410$		0			0
$411$	−76.8177	−	133.052i	−0.186904	−	0.323728i
$412$		0			0
$413$	−376.433	−	47.0569i	−0.911460	−	0.113939i
$414$		0			0
$415$	249.116	−	143.827i	0.600280	−	0.346572i
$416$		0			0
$417$	−21.0012	+	36.3751i	−0.0503626	+	0.0872305i
$418$		0			0
$419$	369.614			0.882133			0.441066	−	0.897474i	$-0.354600\pi$
$419$	369.614			0.882133			0.441066	+	0.897474i	$0.354600\pi$
$420$		0			0
$421$			710.526i			1.68771i	0.536572	+	0.843855i	$0.319719\pi$
$421$			710.526i			1.68771i	−0.536572	+	0.843855i	$0.680281\pi$
$422$		0			0
$423$	−126.038	−	72.7682i	−0.297963	−	0.172029i
$424$		0			0
$425$	−4.52856	−	7.84370i	−0.0106554	−	0.0184558i
$426$		0			0
$427$	183.646	+	139.019i	0.430085	+	0.325571i
$428$		0			0
$429$	12.1717	−	7.02735i	0.0283723	−	0.0163808i
$430$		0			0
$431$	−549.117	−	317.033i	−1.27405	−	0.735575i	−0.298305	−	0.954471i	$-0.596421\pi$
$431$	−549.117	−	317.033i	−1.27405	−	0.735575i	−0.975748	+	0.218896i	$0.929755\pi$
$432$		0			0
$433$	389.086			0.898581			0.449291	−	0.893386i	$-0.351677\pi$
$433$	389.086			0.898581			0.449291	+	0.893386i	$0.351677\pi$
$434$		0			0
$435$	−160.067			−0.367971
$436$		0			0
$437$	−655.283	−	378.328i	−1.49950	−	0.865739i
$438$		0			0
$439$	93.9735	−	54.2556i	0.214063	−	0.123589i	−0.389135	−	0.921181i	$-0.627226\pi$
$439$	93.9735	−	54.2556i	0.214063	−	0.123589i	0.603198	+	0.797591i	$0.293893\pi$
$440$		0			0
$441$	−366.608	−	93.1125i	−0.831312	−	0.211140i
$442$		0			0
$443$	−259.449	−	449.380i	−0.585665	−	1.01440i	−0.994792	−	0.101924i	$-0.967500\pi$
$443$	−259.449	−	449.380i	−0.585665	−	1.01440i	0.409128	−	0.912477i	$-0.365833\pi$
$444$		0			0
$445$	152.898	+	88.2757i	0.343591	+	0.198372i
$446$		0			0
$447$			41.0240i			0.0917763i
$448$		0			0
$449$	357.190			0.795524			0.397762	−	0.917489i	$-0.369787\pi$
$449$	357.190			0.795524			0.397762	+	0.917489i	$0.369787\pi$
$450$		0			0
$451$	−180.941	+	313.399i	−0.401199	+	0.694898i
$452$		0			0
$453$	−14.5800	+	8.41777i	−0.0321854	+	0.0185823i
$454$		0			0
$455$	29.5089	−	38.9817i	0.0648546	−	0.0856741i
$456$		0			0
$457$	−222.274	−	384.991i	−0.486377	−	0.842430i	0.513500	−	0.858090i	$-0.328349\pi$
$457$	−222.274	−	384.991i	−0.486377	−	0.842430i	−0.999877	+	0.0156592i	$0.995015\pi$
$458$		0			0
$459$	−7.56039	+	13.0950i	−0.0164714	+	0.0285294i
$460$		0			0
$461$			876.733i			1.90181i	0.309487	+	0.950904i	$0.399843\pi$
$461$			876.733i			1.90181i	−0.309487	+	0.950904i	$0.600157\pi$
$462$		0			0
$463$		−	794.872i		−	1.71679i	−0.512993	−	0.858393i	$-0.671463\pi$
$463$		−	794.872i		−	1.71679i	0.512993	−	0.858393i	$-0.328537\pi$
$464$		0			0
$465$	−15.1224	+	26.1928i	−0.0325213	+	0.0563285i
$466$		0			0
$467$	−198.249	−	343.378i	−0.424517	−	0.735285i	0.571858	−	0.820353i	$-0.306223\pi$
$467$	−198.249	−	343.378i	−0.424517	−	0.735285i	−0.996375	+	0.0850674i	$0.972889\pi$
$468$		0			0
$469$	−65.8659	−	8.23372i	−0.140439	−	0.0175559i
$470$		0			0
$471$	−197.791	+	114.195i	−0.419939	+	0.242452i
$472$		0			0
$473$	−73.3991	+	127.131i	−0.155178	+	0.268776i
$474$		0			0
$475$	−331.234			−0.697335
$476$		0			0
$477$			2.35977i			0.00494711i
$478$		0			0
$479$	697.779	+	402.863i	1.45674	+	0.841049i	0.998849	−	0.0479591i	$-0.0152717\pi$
$479$	697.779	+	402.863i	1.45674	+	0.841049i	0.457891	+	0.889008i	$0.348605\pi$
$480$		0			0
$481$	−61.8781	−	107.176i	−0.128645	−	0.222819i
$482$		0			0
$483$	−188.954	+	79.7185i	−0.391209	+	0.165049i
$484$		0			0
$485$	−402.513	+	232.391i	−0.829923	+	0.479157i
$486$		0			0
$487$	693.543	+	400.417i	1.42411	+	0.822212i	0.996647	−	0.0818195i	$-0.0260731\pi$
$487$	693.543	+	400.417i	1.42411	+	0.822212i	0.427466	+	0.904032i	$0.359406\pi$
$488$		0			0
$489$	−149.691			−0.306116
$490$		0			0
$491$	−627.714			−1.27844			−0.639220	−	0.769024i	$-0.720743\pi$
$491$	−627.714			−1.27844			−0.639220	+	0.769024i	$0.720743\pi$
$492$		0			0
$493$	26.4804	+	15.2884i	0.0537127	+	0.0310111i
$494$		0			0
$495$	−162.463	+	93.7978i	−0.328207	+	0.189491i
$496$		0			0
$497$	215.680	−	90.9938i	0.433963	−	0.183086i
$498$		0			0
$499$	−330.214	−	571.948i	−0.661752	−	1.14619i	−0.980155	−	0.198233i	$-0.936480\pi$
$499$	−330.214	−	571.948i	−0.661752	−	1.14619i	0.318402	−	0.947956i	$-0.396854\pi$
$500$		0			0
$501$	234.635	+	135.467i	0.468334	+	0.270393i
$502$		0			0
$503$		−	178.302i		−	0.354477i	−0.984168	−	0.177239i	$-0.943284\pi$
$503$		−	178.302i		−	0.354477i	0.984168	−	0.177239i	$-0.0567164\pi$
$504$		0			0
$505$	−583.104			−1.15466
$506$		0			0
$507$	93.6054	−	162.129i	0.184626	−	0.319782i
$508$		0			0
$509$	−356.288	+	205.703i	−0.699976	+	0.404131i	−0.807339	−	0.590089i	$-0.799093\pi$
$509$	−356.288	+	205.703i	−0.699976	+	0.404131i	0.107362	+	0.994220i	$0.465759\pi$
$510$		0			0
$511$	657.076	+	82.1393i	1.28586	+	0.160742i
$512$		0			0
$513$	276.496	+	478.905i	0.538979	+	0.933538i
$514$		0			0
$515$	211.974	−	367.150i	0.411601	−	0.712913i
$516$		0			0
$517$		−	123.936i		−	0.239722i
$518$		0			0
$519$			182.748i			0.352115i
$520$		0			0
$521$	−112.479	+	194.820i	−0.215891	+	0.373934i	−0.953548	−	0.301242i	$-0.902599\pi$
$521$	−112.479	+	194.820i	−0.215891	+	0.373934i	0.737657	+	0.675176i	$0.235932\pi$
$522$		0			0
$523$	−0.861075	−	1.49143i	−0.00164641	−	0.00285167i	0.865201	−	0.501425i	$-0.167191\pi$
$523$	−0.861075	−	1.49143i	−0.00164641	−	0.00285167i	−0.866847	+	0.498573i	$0.833857\pi$
$524$		0			0
$525$	−54.1859	+	71.5805i	−0.103211	+	0.136344i
$526$		0			0
$527$	5.00347	−	2.88876i	0.00949426	−	0.00548151i
$528$		0			0
$529$	70.6185	−	122.315i	0.133494	−	0.231219i
$530$		0			0
$531$	−418.348			−0.787849
$532$		0			0
$533$		−	104.006i		−	0.195133i
$534$		0			0
$535$	−584.970	−	337.733i	−1.09340	−	0.631276i
$536$		0			0
$537$	−140.364	−	243.118i	−0.261386	−	0.452734i
$538$		0			0
$539$	−87.4290	−	310.018i	−0.162206	−	0.575172i
$540$		0			0
$541$	−302.222	+	174.488i	−0.558636	+	0.322529i	−0.752598	−	0.658480i	$-0.771200\pi$
$541$	−302.222	+	174.488i	−0.558636	+	0.322529i	0.193962	+	0.981009i	$0.437866\pi$
$542$		0			0
$543$	180.805	+	104.388i	0.332974	+	0.192243i
$544$		0			0
$545$	264.958			0.486162
$546$		0			0
$547$	269.286			0.492296			0.246148	−	0.969232i	$-0.420835\pi$
$547$	269.286			0.492296			0.246148	+	0.969232i	$0.420835\pi$
$548$		0			0
$549$	219.971	+	127.000i	0.400675	+	0.231330i
$550$		0			0
$551$	968.431	−	559.124i	1.75759	−	1.01474i
$552$		0			0
$553$	−47.3860	−	35.8709i	−0.0856890	−	0.0648659i
$554$		0			0
$555$	−137.021	−	237.328i	−0.246885	−	0.427617i
$556$		0			0
$557$	−523.095	−	302.009i	−0.939128	−	0.542206i	−0.0494415	−	0.998777i	$-0.515744\pi$
$557$	−523.095	−	302.009i	−0.939128	−	0.542206i	−0.889687	+	0.456571i	$0.849077\pi$
$558$		0			0
$559$		−	42.1902i		−	0.0754744i
$560$		0			0
$561$	−5.94515			−0.0105974
$562$		0			0
$563$	140.572	−	243.477i	0.249683	−	0.432464i	−0.713755	−	0.700396i	$-0.753007\pi$
$563$	140.572	−	243.477i	0.249683	−	0.432464i	0.963438	+	0.267932i	$0.0863401\pi$
$564$		0			0
$565$	−453.566	+	261.866i	−0.802771	+	0.463480i
$566$		0			0
$567$	−333.839	−	41.7324i	−0.588782	−	0.0736020i
$568$		0			0
$569$	−40.9170	−	70.8703i	−0.0719104	−	0.124552i	0.827828	−	0.560982i	$-0.189576\pi$
$569$	−40.9170	−	70.8703i	−0.0719104	−	0.124552i	−0.899739	+	0.436429i	$0.856243\pi$
$570$		0			0
$571$	−154.965	+	268.407i	−0.271392	+	0.470065i	−0.969219	−	0.246202i	$-0.920817\pi$
$571$	−154.965	+	268.407i	−0.271392	+	0.470065i	0.697826	+	0.716267i	$0.254151\pi$
$572$		0			0
$573$		−	420.429i		−	0.733734i
$574$		0			0
$575$		−	293.403i		−	0.510267i
$576$		0			0
$577$	177.870	−	308.079i	0.308266	−	0.533933i	−0.669717	−	0.742616i	$-0.733585\pi$
$577$	177.870	−	308.079i	0.308266	−	0.533933i	0.977983	+	0.208684i	$0.0669179\pi$
$578$		0			0
$579$	121.784	+	210.936i	0.210335	+	0.364310i
$580$		0			0
$581$	211.722	+	501.838i	0.364410	+	0.863748i
$582$		0			0
$583$	−1.74031	+	1.00477i	−0.00298510	+	0.00172345i
$584$		0			0
$585$	26.9577	−	46.6921i	0.0460816	−	0.0798156i
$586$		0			0
$587$	363.215			0.618764			0.309382	−	0.950938i	$-0.399878\pi$
$587$	363.215			0.618764			0.309382	+	0.950938i	$0.399878\pi$
$588$		0			0
$589$		−	211.293i		−	0.358732i
$590$		0			0
$591$	−178.330	−	102.959i	−0.301744	−	0.174212i
$592$		0			0
$593$	−238.107	−	412.414i	−0.401530	−	0.695471i	0.592381	−	0.805658i	$-0.298188\pi$
$593$	−238.107	−	412.414i	−0.401530	−	0.695471i	−0.993911	+	0.110187i	$0.964855\pi$
$594$		0			0
$595$	−19.0546	+	8.03902i	−0.0320246	+	0.0135110i
$596$		0			0
$597$	−168.677	+	97.3858i	−0.282541	+	0.163125i
$598$		0			0
$599$	−102.017	−	58.8994i	−0.170312	−	0.0983295i	0.412421	−	0.910993i	$-0.364683\pi$
$599$	−102.017	−	58.8994i	−0.170312	−	0.0983295i	−0.582733	+	0.812664i	$0.698017\pi$
$600$		0			0
$601$	−1117.79			−1.85989			−0.929945	−	0.367699i	$-0.880146\pi$
$601$	−1117.79			−1.85989			−0.929945	+	0.367699i	$0.880146\pi$
$602$		0			0
$603$	−73.1999			−0.121393
$604$		0			0
$605$	249.041	+	143.784i	0.411638	+	0.237659i
$606$		0			0
$607$	−523.639	+	302.323i	−0.862668	+	0.498061i	−0.864905	−	0.501936i	$-0.832621\pi$
$607$	−523.639	+	302.323i	−0.862668	+	0.498061i	0.00223707	+	0.999997i	$0.499288\pi$
$608$		0			0
$609$	37.5955	−	300.746i	0.0617331	−	0.493836i
$610$		0			0
$611$	17.8098	+	30.8475i	0.0291486	+	0.0504869i
$612$		0			0
$613$	−229.518	−	132.512i	−0.374418	−	0.216170i	0.300969	−	0.953634i	$-0.402690\pi$
$613$	−229.518	−	132.512i	−0.374418	−	0.216170i	−0.675387	+	0.737464i	$0.736023\pi$
$614$		0			0
$615$		−	230.308i		−	0.374484i
$616$		0			0
$617$	−255.786			−0.414564			−0.207282	−	0.978281i	$-0.566462\pi$
$617$	−255.786			−0.414564			−0.207282	+	0.978281i	$0.566462\pi$
$618$		0			0
$619$	233.792	−	404.940i	0.377693	−	0.654184i	−0.613033	−	0.790057i	$-0.710051\pi$
$619$	233.792	−	404.940i	0.377693	−	0.654184i	0.990726	+	0.135873i	$0.0433840\pi$
$620$		0			0
$621$	−424.209	+	244.917i	−0.683106	+	0.394391i
$622$		0			0
$623$	−201.770	+	266.542i	−0.323869	+	0.427836i
$624$		0			0
$625$	106.615	+	184.663i	0.170584	+	0.295461i
$626$		0			0
$627$	−108.712	+	188.295i	−0.173384	+	0.300310i
$628$		0			0
$629$			52.3490i			0.0832257i
$630$		0			0
$631$		−	95.0377i		−	0.150614i	−0.997160	−	0.0753072i	$-0.976006\pi$
$631$		−	95.0377i		−	0.150614i	0.997160	−	0.0753072i	$-0.0239937\pi$
$632$		0			0
$633$	−198.275	+	343.422i	−0.313230	+	0.542531i
$634$		0			0
$635$	−132.846	−	230.096i	−0.209206	−	0.362356i
$636$		0			0
$637$	66.3108	+	64.5991i	0.104099	+	0.101411i
$638$		0			0
$639$	223.560	−	129.072i	0.349859	−	0.201991i
$640$		0			0
$641$	277.514	−	480.669i	0.432940	−	0.749873i	−0.564185	−	0.825648i	$-0.690810\pi$
$641$	277.514	−	480.669i	0.432940	−	0.749873i	0.997125	+	0.0757747i	$0.0241430\pi$
$642$		0			0
$643$	−830.144			−1.29105			−0.645524	−	0.763740i	$-0.723361\pi$
$643$	−830.144			−1.29105			−0.645524	+	0.763740i	$0.723361\pi$
$644$		0			0
$645$		−	93.4249i		−	0.144845i
$646$		0			0
$647$	390.816	+	225.637i	0.604043	+	0.348744i	0.770630	−	0.637282i	$-0.219942\pi$
$647$	390.816	+	225.637i	0.604043	+	0.348744i	−0.166588	+	0.986027i	$0.553275\pi$
$648$		0			0
$649$	−178.129	−	308.528i	−0.274467	−	0.475391i
$650$		0			0
$651$	−45.6610	−	34.5650i	−0.0701398	−	0.0530952i
$652$		0			0
$653$	−199.901	+	115.413i	−0.306127	+	0.176743i	−0.645192	−	0.764020i	$-0.723223\pi$
$653$	−199.901	+	115.413i	−0.306127	+	0.176743i	0.339065	+	0.940763i	$0.389889\pi$
$654$		0			0
$655$	−770.106	−	444.621i	−1.17573	−	0.678811i
$656$		0			0
$657$	730.240			1.11148
$658$		0			0
$659$	300.628			0.456189			0.228094	−	0.973639i	$-0.426751\pi$
$659$	300.628			0.456189			0.228094	+	0.973639i	$0.426751\pi$
$660$		0			0
$661$	573.915	+	331.350i	0.868253	+	0.501286i	0.866767	−	0.498713i	$-0.166194\pi$
$661$	573.915	+	331.350i	0.868253	+	0.501286i	0.00148565	+	0.999999i	$0.499527\pi$
$662$		0			0
$663$	1.47973	−	0.854325i	0.00223188	−	0.00128858i
$664$		0			0
$665$	−93.8177	+	750.498i	−0.141079	+	1.12857i
$666$		0			0
$667$	495.265	+	857.825i	0.742527	+	1.28609i
$668$		0			0
$669$	185.223	+	106.939i	0.276866	+	0.159849i
$670$		0			0
$671$			216.302i			0.322358i
$672$		0			0
$673$	590.494			0.877405			0.438703	−	0.898632i	$-0.355438\pi$
$673$	590.494			0.877405			0.438703	+	0.898632i	$0.355438\pi$
$674$		0			0
$675$	−107.215	+	185.702i	−0.158837	+	0.275114i
$676$		0			0
$677$	750.444	−	433.269i	1.10848	−	0.639984i	0.170048	−	0.985436i	$-0.445608\pi$
$677$	750.444	−	433.269i	1.10848	−	0.639984i	0.938437	+	0.345452i	$0.112274\pi$
$678$		0			0
$679$	−342.093	−	810.852i	−0.503819	−	1.19419i
$680$		0			0
$681$	15.7941	+	27.3562i	0.0231925	+	0.0401707i
$682$		0			0
$683$	−8.89548	+	15.4074i	−0.0130241	+	0.0225585i	−0.872464	−	0.488678i	$-0.837479\pi$
$683$	−8.89548	+	15.4074i	−0.0130241	+	0.0225585i	0.859440	+	0.511237i	$0.170812\pi$
$684$		0			0
$685$		−	501.892i		−	0.732689i
$686$		0			0
$687$		−	261.828i		−	0.381118i
$688$		0			0
$689$	0.288774	−	0.500171i	0.000419120	−	0.000725937i
$690$		0			0
$691$	176.728	+	306.101i	0.255756	+	0.442983i	0.965101	−	0.261879i	$-0.0843422\pi$
$691$	176.728	+	306.101i	0.255756	+	0.442983i	−0.709344	+	0.704862i	$0.751009\pi$
$692$		0			0
$693$	−138.076	−	327.277i	−0.199244	−	0.472261i
$694$		0			0
$695$	−118.829	+	68.6061i	−0.170977	+	0.0987138i
$696$		0			0
$697$	−21.9973	+	38.1004i	−0.0315599	+	0.0546634i
$698$		0			0
$699$	247.835			0.354556
$700$		0			0
$701$			441.991i			0.630516i	0.949006	+	0.315258i	$0.102091\pi$
$701$			441.991i			0.630516i	−0.949006	+	0.315258i	$0.897909\pi$
$702$		0			0
$703$	1658.00	+	957.244i	2.35846	+	1.36166i
$704$		0			0
$705$	39.4376	+	68.3079i	0.0559398	+	0.0968906i
$706$		0			0
$707$	136.955	−	1095.58i	0.193713	−	1.54961i
$708$		0			0
$709$	385.131	−	222.355i	0.543202	−	0.313618i	−0.203173	−	0.979143i	$-0.565126\pi$
$709$	385.131	−	222.355i	0.543202	−	0.313618i	0.746376	+	0.665525i	$0.231792\pi$
$710$		0			0
$711$	−56.7588	−	32.7697i	−0.0798295	−	0.0460896i
$712$		0			0
$713$	187.161			0.262498
$714$		0			0
$715$	45.9135			0.0642147
$716$		0			0
$717$	−106.582	−	61.5352i	−0.148650	−	0.0858232i
$718$		0			0
$719$	−1231.69	+	711.118i	−1.71306	+	0.989037i	−0.782698	+	0.622401i	$0.786157\pi$
$719$	−1231.69	+	711.118i	−1.71306	+	0.989037i	−0.930365	+	0.366636i	$0.880510\pi$
$720$		0			0
$721$	640.041	+	484.506i	0.887713	+	0.671992i
$722$		0			0
$723$	84.0866	+	145.642i	0.116302	+	0.201442i
$724$		0			0
$725$	375.522	+	216.808i	0.517961	+	0.299045i
$726$		0			0
$727$			778.491i			1.07083i	0.844590	+	0.535413i	$0.179844\pi$
$727$			778.491i			1.07083i	−0.844590	+	0.535413i	$0.820156\pi$
$728$		0			0
$729$	−178.307			−0.244591
$730$		0			0
$731$	−8.92324	+	15.4555i	−0.0122069	+	0.0211430i
$732$		0			0
$733$	261.732	−	151.111i	0.357070	−	0.206154i	−0.310725	−	0.950500i	$-0.600572\pi$
$733$	261.732	−	151.111i	0.357070	−	0.206154i	0.667795	+	0.744346i	$0.267238\pi$
$734$		0			0
$735$	146.837	+	143.046i	0.199778	+	0.194621i
$736$		0			0
$737$	−31.1679	−	53.9844i	−0.0422902	−	0.0732488i
$738$		0			0
$739$	−11.6714	+	20.2155i	−0.0157935	+	0.0273551i	−0.873814	−	0.486260i	$-0.838361\pi$
$739$	−11.6714	+	20.2155i	−0.0157935	+	0.0273551i	0.858021	+	0.513615i	$0.171694\pi$
$740$		0			0
$741$		−	62.4882i		−	0.0843295i
$742$		0			0
$743$			946.890i			1.27442i	0.770692	+	0.637208i	$0.219911\pi$
$743$			946.890i			1.27442i	−0.770692	+	0.637208i	$0.780089\pi$
$744$		0			0
$745$	−67.0080	+	116.061i	−0.0899437	+	0.155787i
$746$		0			0
$747$	300.322	+	520.174i	0.402038	+	0.696350i
$748$		0			0
$749$	771.950	−	1019.76i	1.03064	−	1.36149i
$750$		0			0
$751$	−63.4721	+	36.6456i	−0.0845167	+	0.0487958i	−0.541663	−	0.840596i	$-0.682205\pi$
$751$	−63.4721	+	36.6456i	−0.0845167	+	0.0487958i	0.457146	+	0.889392i	$0.348872\pi$
$752$		0			0
$753$	171.652	−	297.310i	0.227957	−	0.394834i
$754$		0			0
$755$	−54.9979			−0.0728449
$756$		0			0
$757$		−	817.472i		−	1.07988i	−0.841702	−	0.539942i	$-0.818446\pi$
$757$		−	817.472i		−	1.07988i	0.841702	−	0.539942i	$-0.181554\pi$
$758$		0			0
$759$	−166.789	−	96.2958i	−0.219749	−	0.126872i
$760$		0			0
$761$	484.282	+	838.801i	0.636376	+	1.10224i	0.986222	+	0.165428i	$0.0529007\pi$
$761$	484.282	+	838.801i	0.636376	+	1.10224i	−0.349846	+	0.936807i	$0.613766\pi$
$762$		0			0
$763$	−62.2315	+	497.823i	−0.0815616	+	0.652454i
$764$		0			0
$765$	−19.7508	+	11.4031i	−0.0258181	+	0.0149061i
$766$		0			0
$767$	88.6719	+	51.1947i	0.115609	+	0.0667467i
$768$		0			0
$769$	512.038			0.665849			0.332925	−	0.942953i	$-0.391965\pi$
$769$	512.038			0.665849			0.332925	+	0.942953i	$0.391965\pi$
$770$		0			0
$771$	99.5628			0.129135
$772$		0			0
$773$	537.444	+	310.294i	0.695271	+	0.401415i	0.805584	−	0.592482i	$-0.201852\pi$
$773$	537.444	+	310.294i	0.695271	+	0.401415i	−0.110313	+	0.993897i	$0.535185\pi$
$774$		0			0
$775$	70.9550	−	40.9659i	0.0915548	−	0.0528592i
$776$		0			0
$777$	478.090	−	201.703i	0.615303	−	0.259592i
$778$		0			0
$779$	804.476	+	1393.39i	1.03270	+	1.78870i
$780$		0			0
$781$	190.380	+	109.916i	0.243764	+	0.140737i
$782$		0			0
$783$		−	723.916i		−	0.924542i
$784$		0			0
$785$	−746.096			−0.950441
$786$		0			0
$787$	254.651	−	441.068i	0.323572	−	0.560442i	−0.657651	−	0.753323i	$-0.728450\pi$
$787$	254.651	−	441.068i	0.323572	−	0.560442i	0.981222	+	0.192881i	$0.0617830\pi$
$788$		0			0
$789$	124.192	−	71.7022i	0.157404	−	0.0908774i
$790$		0			0
$791$	−385.483	−	913.697i	−0.487336	−	1.15512i
$792$		0			0
$793$	−31.0829	−	53.8372i	−0.0391966	−	0.0678906i
$794$		0			0
$795$	0.639453	−	1.10756i	0.000804343	−	0.00139316i
$796$		0			0
$797$		−	739.232i		−	0.927519i	−0.885961	−	0.463759i	$-0.846500\pi$
$797$		−	739.232i		−	0.927519i	0.885961	−	0.463759i	$-0.153500\pi$
$798$		0			0
$799$		−	15.0671i		−	0.0188575i
$800$		0			0
$801$	−184.327	+	319.263i	−0.230121	+	0.398580i
$802$		0			0
$803$	310.930	+	538.546i	0.387210	+	0.670668i
$804$		0			0
$805$	−664.782	−	83.1026i	−0.825816	−	0.103233i
$806$		0			0
$807$	−487.478	+	281.445i	−0.604061	+	0.348755i
$808$		0			0
$809$	64.1469	−	111.106i	0.0792915	−	0.137337i	−0.823653	−	0.567094i	$-0.808068\pi$
$809$	64.1469	−	111.106i	0.0792915	−	0.137337i	0.902944	+	0.429757i	$0.141401\pi$
$810$		0			0
$811$	−791.144			−0.975517			−0.487759	−	0.872979i	$-0.662185\pi$
$811$	−791.144			−0.975517			−0.487759	+	0.872979i	$0.662185\pi$
$812$		0			0
$813$			471.383i			0.579807i
$814$		0			0
$815$	−423.491	−	244.503i	−0.519621	−	0.300003i
$816$		0			0
$817$	326.338	+	565.234i	0.399434	+	0.691841i
$818$		0			0
$819$	81.3969	+	61.6168i	0.0993857	+	0.0752342i
$820$		0			0
$821$	−794.776	+	458.864i	−0.968058	+	0.558909i	−0.898644	−	0.438679i	$-0.855446\pi$
$821$	−794.776	+	458.864i	−0.968058	+	0.558909i	−0.0694147	+	0.997588i	$0.522113\pi$
$822$		0			0
$823$	−60.6374	−	35.0090i	−0.0736785	−	0.0425383i	0.462708	−	0.886511i	$-0.346878\pi$
$823$	−60.6374	−	35.0090i	−0.0736785	−	0.0425383i	−0.536387	+	0.843972i	$0.680211\pi$
$824$		0			0
$825$	−84.3090			−0.102193
$826$		0			0
$827$	1014.27			1.22644			0.613221	−	0.789911i	$-0.289873\pi$
$827$	1014.27			1.22644			0.613221	+	0.789911i	$0.289873\pi$
$828$		0			0
$829$	564.615	+	325.981i	0.681080	+	0.393222i	0.800262	−	0.599651i	$-0.204694\pi$
$829$	564.615	+	325.981i	0.681080	+	0.393222i	−0.119182	+	0.992872i	$0.538027\pi$
$830$		0			0
$831$	155.866	−	89.9892i	0.187564	−	0.108290i
$832$		0			0
$833$	−10.6289	−	37.6893i	−0.0127598	−	0.0452453i
$834$		0			0
$835$	442.539	+	766.500i	0.529987	+	0.917964i
$836$		0			0
$837$	−118.459	−	68.3921i	−0.141528	−	0.0817110i
$838$		0			0
$839$			905.246i			1.07896i	0.841999	+	0.539479i	$0.181379\pi$
$839$			905.246i			1.07896i	−0.841999	+	0.539479i	$0.818621\pi$
$840$		0			0
$841$	−622.887			−0.740650
$842$		0			0
$843$	197.792	−	342.587i	0.234629	−	0.406390i
$844$		0			0
$845$	529.640	−	305.788i	0.626793	−	0.361879i
$846$		0			0
$847$	−328.644	+	434.145i	−0.388010	+	0.512568i
$848$		0			0
$849$	275.978	+	478.008i	0.325062	+	0.563024i
$850$		0			0
$851$	−847.915	+	1468.63i	−0.996375	+	1.72577i
$852$		0			0
$853$		−	956.190i		−	1.12097i	−0.828164	−	0.560486i	$-0.810614\pi$
$853$		−	956.190i		−	1.12097i	0.828164	−	0.560486i	$-0.189386\pi$
$854$		0			0
$855$			834.063i			0.975513i
$856$		0			0
$857$	−270.837	+	469.103i	−0.316029	+	0.547378i	−0.979656	−	0.200686i	$-0.935683\pi$
$857$	−270.837	+	469.103i	−0.316029	+	0.547378i	0.663627	+	0.748064i	$0.269016\pi$
$858$		0			0
$859$	−20.0712	−	34.7644i	−0.0233658	−	0.0404708i	0.854106	−	0.520099i	$-0.174105\pi$
$859$	−20.0712	−	34.7644i	−0.0233658	−	0.0404708i	−0.877472	+	0.479628i	$0.840772\pi$
$860$		0			0
$861$	432.718	+	54.0930i	0.502576	+	0.0628257i
$862$		0			0
$863$	−24.6998	+	14.2604i	−0.0286209	+	0.0165243i	−0.514242	−	0.857645i	$-0.671927\pi$
$863$	−24.6998	+	14.2604i	−0.0286209	+	0.0165243i	0.485621	+	0.874169i	$0.338593\pi$
$864$		0			0
$865$	−298.497	+	517.013i	−0.345084	+	0.597703i
$866$		0			0
$867$	326.326			0.376386
$868$		0			0
$869$		−	55.8123i		−	0.0642259i
$870$		0			0
$871$	15.5152	+	8.95773i	0.0178131	+	0.0102844i
$872$		0			0
$873$	−485.250	−	840.478i	−0.555842	−	0.962747i
$874$		0			0
$875$	−866.291	+	365.483i	−0.990047	+	0.417694i
$876$		0			0
$877$	−448.601	+	259.000i	−0.511518	+	0.295325i	−0.733457	−	0.679736i	$-0.762095\pi$
$877$	−448.601	+	259.000i	−0.511518	+	0.295325i	0.221940	+	0.975060i	$0.428761\pi$
$878$		0			0
$879$	−122.229	−	70.5690i	−0.139055	−	0.0802833i
$880$		0			0
$881$	−958.207			−1.08764			−0.543818	−	0.839203i	$-0.683022\pi$
$881$	−958.207			−1.08764			−0.543818	+	0.839203i	$0.683022\pi$
$882$		0			0
$883$	1650.96			1.86972			0.934859	−	0.355019i	$-0.115525\pi$
$883$	1650.96			1.86972			0.934859	+	0.355019i	$0.115525\pi$
$884$		0			0
$885$	196.353	+	113.364i	0.221867	+	0.128095i
$886$		0			0
$887$	1274.68	−	735.939i	1.43707	−	0.829694i	0.439427	−	0.898278i	$-0.355181\pi$
$887$	1274.68	−	735.939i	1.43707	−	0.829694i	0.997645	+	0.0685839i	$0.0218481\pi$
$888$		0			0
$889$	463.523	−	195.557i	0.521398	−	0.219975i
$890$		0			0
$891$	−157.974	−	273.618i	−0.177299	−	0.307091i
$892$		0			0
$893$	−477.206	−	275.515i	−0.534385	−	0.308527i
$894$		0			0
$895$		−	917.077i		−	1.02467i
$896$		0			0
$897$	55.3513			0.0617071
$898$		0			0
$899$	−138.301	+	239.544i	−0.153839	+	0.266456i
$900$		0			0
$901$	−0.211573	+	0.122151i	−0.000234820	+	0.000135573i
$902$		0			0
$903$	175.533	+	21.9429i	0.194389	+	0.0243000i
$904$		0			0
$905$	341.011	+	590.648i	0.376808	+	0.652650i
$906$		0			0
$907$	463.777	−	803.285i	0.511331	−	0.885651i	−0.488583	−	0.872517i	$-0.662486\pi$
$907$	463.777	−	803.285i	0.511331	−	0.885651i	0.999914	−	0.0131332i	$-0.00418056\pi$
$908$		0			0
$909$		−	1217.57i		−	1.33946i
$910$		0			0
$911$		−	1168.02i		−	1.28213i	−0.767488	−	0.641063i	$-0.778494\pi$
$911$		−	1168.02i		−	1.28213i	0.767488	−	0.641063i	$-0.221506\pi$
$912$		0			0
$913$	−255.749	+	442.971i	−0.280120	+	0.485182i
$914$		0			0
$915$	−68.8293	−	119.216i	−0.0752232	−	0.130290i
$916$		0			0
$917$	1016.26	−	1342.50i	1.10825	−	1.46401i
$918$		0			0
$919$	−1286.49	+	742.755i	−1.39988	+	0.808221i	−0.994380	−	0.105874i	$-0.966236\pi$
$919$	−1286.49	+	742.755i	−1.39988	+	0.808221i	−0.405501	+	0.914095i	$0.632903\pi$
$920$		0			0
$921$	242.827	−	420.588i	0.263656	−	0.456665i
$922$		0			0
$923$	−63.1802			−0.0684509
$924$		0			0
$925$			742.368i			0.802560i
$926$		0			0
$927$	766.638	+	442.619i	0.827010	+	0.477475i
$928$		0			0
$929$	−57.3779	−	99.3815i	−0.0617631	−	0.106977i	0.833490	−	0.552534i	$-0.186339\pi$
$929$	−57.3779	−	99.3815i	−0.0617631	−	0.106977i	−0.895254	+	0.445557i	$0.853006\pi$
$930$		0			0
$931$	−1388.05	−	352.543i	−1.49093	−	0.378671i
$932$		0			0
$933$	−318.755	+	184.033i	−0.341645	+	0.197249i
$934$		0			0
$935$	−16.8195	−	9.71072i	−0.0179887	−	0.0103858i
$936$		0			0
$937$	1712.72			1.82787			0.913936	−	0.405858i	$-0.133027\pi$
$937$	1712.72			1.82787			0.913936	+	0.405858i	$0.133027\pi$
$938$		0			0
$939$	116.281			0.123835
$940$		0			0
$941$	1267.32	+	731.690i	1.34678	+	0.777566i	0.987793	−	0.155774i	$-0.0497873\pi$
$941$	1267.32	+	731.690i	1.34678	+	0.777566i	0.358992	+	0.933341i	$0.383121\pi$
$942$		0			0
$943$	−1234.25	+	712.596i	−1.30886	+	0.755669i
$944$		0			0
$945$	390.389	+	295.521i	0.413110	+	0.312721i
$946$		0			0
$947$	340.899	+	590.454i	0.359978	+	0.623500i	0.987957	−	0.154731i	$-0.0494510\pi$
$947$	340.899	+	590.454i	0.359978	+	0.623500i	−0.627979	+	0.778230i	$0.716118\pi$
$948$		0			0
$949$	−154.780	−	89.3620i	−0.163098	−	0.0941644i
$950$		0			0
$951$		−	451.876i		−	0.475159i
$952$		0			0
$953$	817.928			0.858266			0.429133	−	0.903241i	$-0.358819\pi$
$953$	817.928			0.858266			0.429133	+	0.903241i	$0.358819\pi$
$954$		0			0
$955$	686.723	−	1189.44i	0.719082	−	1.24549i
$956$		0			0
$957$	246.495	−	142.314i	0.257570	−	0.148708i
$958$		0			0
$959$	942.990	+	117.881i	0.983305	+	0.122920i
$960$		0			0
$961$	−454.368	−	786.988i	−0.472807	−	0.818927i
$962$		0			0
$963$	705.212	−	1221.46i	0.732307	−	1.26839i
$964$		0			0
$965$			795.679i			0.824538i
$966$		0			0
$967$			1096.98i			1.13442i	0.823573	+	0.567210i	$0.191977\pi$
$967$			1096.98i			1.13442i	−0.823573	+	0.567210i	$0.808023\pi$
$968$		0			0
$969$	−13.2163	+	22.8913i	−0.0136391	+	0.0236236i
$970$		0			0
$971$	−349.701	−	605.700i	−0.360145	−	0.623790i	0.627839	−	0.778343i	$-0.283940\pi$
$971$	−349.701	−	605.700i	−0.360145	−	0.623790i	−0.987984	+	0.154553i	$0.950606\pi$
$972$		0			0
$973$	−100.992	−	239.378i	−0.103795	−	0.246021i
$974$		0			0
$975$	20.9843	−	12.1153i	0.0215224	−	0.0124260i
$976$		0			0
$977$	288.393	−	499.511i	0.295182	−	0.511270i	−0.679845	−	0.733356i	$-0.737953\pi$
$977$	288.393	−	499.511i	0.295182	−	0.511270i	0.975027	+	0.222085i	$0.0712864\pi$
$978$		0			0
$979$	−313.939			−0.320673
$980$		0			0
$981$			553.254i			0.563969i
$982$		0			0
$983$	−706.812	−	408.078i	−0.719036	−	0.415135i	0.0953621	−	0.995443i	$-0.469599\pi$
$983$	−706.812	−	408.078i	−0.719036	−	0.415135i	−0.814398	+	0.580307i	$0.802932\pi$
$984$		0			0
$985$	−336.344	−	582.565i	−0.341466	−	0.591436i
$986$		0			0
$987$	−137.604	+	58.0544i	−0.139417	+	0.0588191i
$988$		0			0
$989$	−500.677	+	289.066i	−0.506246	+	0.292281i
$990$		0			0
$991$	−110.376	−	63.7255i	−0.111378	−	0.0643042i	0.443276	−	0.896385i	$-0.353816\pi$
$991$	−110.376	−	63.7255i	−0.111378	−	0.0643042i	−0.554654	+	0.832081i	$0.687149\pi$
$992$		0			0
$993$	−65.0325			−0.0654909
$994$		0			0
$995$	−636.274			−0.639472
$996$		0			0
$997$	−92.1637	−	53.2107i	−0.0924410	−	0.0533708i	0.453067	−	0.891477i	$-0.350330\pi$
$997$	−92.1637	−	53.2107i	−0.0924410	−	0.0533708i	−0.545508	+	0.838106i	$0.683663\pi$
$998$		0			0
$999$	1073.33	−	619.688i	1.07441	−	0.620308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.3.o.b.95.7	yes	20
4.3	odd	2	inner	448.3.o.b.95.4	yes	20
7.2	even	3		448.3.o.a.415.7	yes	20
8.3	odd	2		448.3.o.a.95.7	yes	20
8.5	even	2		448.3.o.a.95.4	✓	20
28.23	odd	6		448.3.o.a.415.4	yes	20
56.37	even	6	inner	448.3.o.b.415.4	yes	20
56.51	odd	6	inner	448.3.o.b.415.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.3.o.a.95.4	✓	20	8.5	even	2
448.3.o.a.95.7	yes	20	8.3	odd	2
448.3.o.a.415.4	yes	20	28.23	odd	6
448.3.o.a.415.7	yes	20	7.2	even	3
448.3.o.b.95.4	yes	20	4.3	odd	2	inner
448.3.o.b.95.7	yes	20	1.1	even	1	trivial
448.3.o.b.415.4	yes	20	56.37	even	6	inner
448.3.o.b.415.7	yes	20	56.51	odd	6	inner

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.565829 - 0.980045i) q^{3} +(3.20158 - 1.84843i) q^{5} +(2.72101 + 6.44951i) q^{7} +(3.85967 + 6.68515i) q^{9} +(-3.28683 + 5.69296i) q^{11} -1.88929i q^{13} -4.18359i q^{15} +(-0.399585 + 0.692102i) q^{17} +(14.6135 + 25.3113i) q^{19} +(7.86043 + 0.982611i) q^{21} +(-22.4205 + 12.9445i) q^{23} +(-5.66658 + 9.81480i) q^{25} +18.9206 q^{27} -38.2608i q^{29} +(-6.26083 - 3.61469i) q^{31} +(3.71957 + 6.44249i) q^{33} +(20.6330 + 15.6190i) q^{35} +(56.7282 - 32.7520i) q^{37} +(-1.85159 - 1.06901i) q^{39} +55.0502 q^{41} +22.3313 q^{43} +(24.7141 + 14.2687i) q^{45} +(-16.3276 + 9.42672i) q^{47} +(-34.1923 + 35.0983i) q^{49} +(0.452194 + 0.783223i) q^{51} +(0.264740 + 0.152848i) q^{53} +24.3020i q^{55} +33.0750 q^{57} +(-27.0974 + 46.9340i) q^{59} +(28.4960 - 16.4522i) q^{61} +(-32.6137 + 43.0833i) q^{63} +(-3.49223 - 6.04871i) q^{65} +(-4.74132 + 8.21221i) q^{67} +29.2974i q^{69} -33.4413i q^{71} +(47.2993 - 81.9248i) q^{73} +(6.41263 + 11.1070i) q^{75} +(-45.6603 - 5.70787i) q^{77} +(-7.35280 + 4.24514i) q^{79} +(-24.0313 + 41.6234i) q^{81} +77.8103 q^{83} +2.95443i q^{85} +(-37.4973 - 21.6491i) q^{87} +(23.8785 + 41.3588i) q^{89} +(12.1850 - 5.14076i) q^{91} +(-7.08512 + 4.09060i) q^{93} +(93.5727 + 54.0242i) q^{95} -125.723 q^{97} -50.7444 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5} - 28 q^{9} + 46 q^{17} - 114 q^{21} + 36 q^{25} + 94 q^{33} + 114 q^{37} - 160 q^{41} - 708 q^{45} - 92 q^{49} - 6 q^{53} + 308 q^{57} + 90 q^{61} + 212 q^{65} + 314 q^{73} - 198 q^{77} - 322 q^{81}+ \cdots - 224 q^{97}+O(q^{100}) \) 20 * q + 6 * q^5 - 28 * q^9 + 46 * q^17 - 114 * q^21 + 36 * q^25 + 94 * q^33 + 114 * q^37 - 160 * q^41 - 708 * q^45 - 92 * q^49 - 6 * q^53 + 308 * q^57 + 90 * q^61 + 212 * q^65 + 314 * q^73 - 198 * q^77 - 322 * q^81 - 206 * q^89 + 1530 * q^93 - 224 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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