LMFDB - Embedded newform 448.3.s.h.129.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,3,Mod(129,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("448.129");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.2071158433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} + \cdots + 208849 $ x^16 - 26x^14 - 16x^13 + 469x^12 + 144x^11 - 4526x^10 + 4440x^9 + 32608x^8 - 33728x^7 - 49760x^6 + 203528x^5 + 27401x^4 - 156928x^3 + 114964x^2 - 248608x + 208849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 7 $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.6
Root			$-1.90990 + 0.286185i$ of defining polynomial
Character	$\chi$	$=$	448.129
Dual form			448.3.s.h.257.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20101 + 1.27075i) q^{3} +(-3.56697 + 2.05939i) q^{5} +(-6.98814 - 0.407289i) q^{7} +(-1.27038 - 2.20036i) q^{9} +O(q^{10})$	\(q+(2.20101 + 1.27075i) q^{3} +(-3.56697 + 2.05939i) q^{5} +(-6.98814 - 0.407289i) q^{7} +(-1.27038 - 2.20036i) q^{9} +(1.63392 - 2.83003i) q^{11} -5.88759i q^{13} -10.4679 q^{15} +(-12.0204 - 6.93999i) q^{17} +(13.7058 - 7.91304i) q^{19} +(-14.8634 - 9.77664i) q^{21} +(-18.2518 - 31.6131i) q^{23} +(-4.01784 + 6.95910i) q^{25} -29.3309i q^{27} +28.4655 q^{29} +(-36.2014 - 20.9009i) q^{31} +(7.19253 - 4.15261i) q^{33} +(25.7652 - 12.9385i) q^{35} +(7.14285 + 12.3718i) q^{37} +(7.48167 - 12.9586i) q^{39} +21.3515i q^{41} -55.3992 q^{43} +(9.06280 + 5.23241i) q^{45} +(29.3178 - 16.9266i) q^{47} +(48.6682 + 5.69238i) q^{49} +(-17.6380 - 30.5499i) q^{51} +(-42.4271 + 73.4859i) q^{53} +13.4595i q^{55} +40.2220 q^{57} +(-58.5062 - 33.7786i) q^{59} +(25.6135 - 14.7879i) q^{61} +(7.98140 + 15.8938i) q^{63} +(12.1248 + 21.0008i) q^{65} +(-27.4789 + 47.5949i) q^{67} -92.7741i q^{69} +83.8102 q^{71} +(-108.784 - 62.8065i) q^{73} +(-17.6866 + 10.2113i) q^{75} +(-12.5707 + 19.1112i) q^{77} +(-35.1955 - 60.9604i) q^{79} +(25.8389 - 44.7542i) q^{81} -27.1264i q^{83} +57.1685 q^{85} +(62.6527 + 36.1726i) q^{87} +(-126.553 + 73.0654i) q^{89} +(-2.39795 + 41.1433i) q^{91} +(-53.1196 - 92.0059i) q^{93} +(-32.5920 + 56.4511i) q^{95} -11.3574i q^{97} -8.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{9}+O(q^{10}) $ 16 * q + 40 * q^9	$ 16 q + 40 q^{9} - 48 q^{17} + 136 q^{21} + 80 q^{25} + 16 q^{29} - 264 q^{33} - 72 q^{37} - 312 q^{45} + 128 q^{49} - 40 q^{53} + 368 q^{57} - 216 q^{61} - 168 q^{65} - 312 q^{73} - 64 q^{77} - 384 q^{81} + 1072 q^{85} + 24 q^{89} + 168 q^{93}+O(q^{100}) $ 16 * q + 40 * q^9 - 48 * q^17 + 136 * q^21 + 80 * q^25 + 16 * q^29 - 264 * q^33 - 72 * q^37 - 312 * q^45 + 128 * q^49 - 40 * q^53 + 368 * q^57 - 216 * q^61 - 168 * q^65 - 312 * q^73 - 64 * q^77 - 384 * q^81 + 1072 * q^85 + 24 * q^89 + 168 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	2.20101	+	1.27075i	0.733669	+	0.423584i	0.819763	−	0.572703i	$-0.194105\pi$
$3$	2.20101	+	1.27075i	0.733669	+	0.423584i	−0.0860939	+	0.996287i	$0.527439\pi$
$4$		0			0
$5$	−3.56697	+	2.05939i	−0.713393	+	0.411878i	−0.812316	−	0.583217i	$-0.801794\pi$
$5$	−3.56697	+	2.05939i	−0.713393	+	0.411878i	0.0989230	+	0.995095i	$0.468460\pi$
$6$		0			0
$7$	−6.98814	−	0.407289i	−0.998306	−	0.0581841i
$7$	−6.98814	−	0.407289i	−0.998306	−	0.0581841i
$8$		0			0
$9$	−1.27038	−	2.20036i	−0.141153	−	0.244485i
$10$		0			0
$11$	1.63392	−	2.83003i	0.148538	−	0.257275i	−0.782149	−	0.623091i	$-0.785877\pi$
$11$	1.63392	−	2.83003i	0.148538	−	0.257275i	0.930687	+	0.365816i	$0.119210\pi$
$12$		0			0
$13$		−	5.88759i		−	0.452892i	−0.974024	−	0.226446i	$-0.927289\pi$
$13$		−	5.88759i		−	0.452892i	0.974024	−	0.226446i	$-0.0727107\pi$
$14$		0			0
$15$	−10.4679			−0.697859
$16$		0			0
$17$	−12.0204	−	6.93999i	−0.707083	−	0.408234i	0.102897	−	0.994692i	$-0.467189\pi$
$17$	−12.0204	−	6.93999i	−0.707083	−	0.408234i	−0.809980	+	0.586458i	$0.800522\pi$
$18$		0			0
$19$	13.7058	−	7.91304i	0.721357	−	0.416476i	−0.0938951	−	0.995582i	$-0.529932\pi$
$19$	13.7058	−	7.91304i	0.721357	−	0.416476i	0.815252	+	0.579107i	$0.196598\pi$
$20$		0			0
$21$	−14.8634	−	9.77664i	−0.707780	−	0.465554i
$22$		0			0
$23$	−18.2518	−	31.6131i	−0.793557	−	1.37448i	−0.923751	−	0.382993i	$-0.874894\pi$
$23$	−18.2518	−	31.6131i	−0.793557	−	1.37448i	0.130194	−	0.991488i	$-0.458440\pi$
$24$		0			0
$25$	−4.01784	+	6.95910i	−0.160713	+	0.278364i
$26$		0			0
$27$		−	29.3309i		−	1.08633i
$28$		0			0
$29$	28.4655			0.981568			0.490784	−	0.871281i	$-0.336710\pi$
$29$	28.4655			0.981568			0.490784	+	0.871281i	$0.336710\pi$
$30$		0			0
$31$	−36.2014	−	20.9009i	−1.16779	−	0.674222i	−0.214629	−	0.976696i	$-0.568854\pi$
$31$	−36.2014	−	20.9009i	−1.16779	−	0.674222i	−0.953158	+	0.302474i	$0.902187\pi$
$32$		0			0
$33$	7.19253	−	4.15261i	0.217955	−	0.125837i
$34$		0			0
$35$	25.7652	−	12.9385i	0.736149	−	0.369672i
$36$		0			0
$37$	7.14285	+	12.3718i	0.193050	+	0.334372i	0.946260	−	0.323408i	$-0.104829\pi$
$37$	7.14285	+	12.3718i	0.193050	+	0.334372i	−0.753210	+	0.657781i	$0.771495\pi$
$38$		0			0
$39$	7.48167	−	12.9586i	0.191838	−	0.332273i
$40$		0			0
$41$			21.3515i			0.520769i	0.965505	+	0.260385i	$0.0838493\pi$
$41$			21.3515i			0.520769i	−0.965505	+	0.260385i	$0.916151\pi$
$42$		0			0
$43$	−55.3992			−1.28835			−0.644177	−	0.764877i	$-0.722800\pi$
$43$	−55.3992			−1.28835			−0.644177	+	0.764877i	$0.722800\pi$
$44$		0			0
$45$	9.06280	+	5.23241i	0.201395	+	0.116276i
$46$		0			0
$47$	29.3178	−	16.9266i	0.623783	−	0.360141i	−0.154558	−	0.987984i	$-0.549395\pi$
$47$	29.3178	−	16.9266i	0.623783	−	0.360141i	0.778340	+	0.627843i	$0.216062\pi$
$48$		0			0
$49$	48.6682	+	5.69238i	0.993229	+	0.116171i
$50$		0			0
$51$	−17.6380	−	30.5499i	−0.345843	−	0.599018i
$52$		0			0
$53$	−42.4271	+	73.4859i	−0.800512	+	1.38653i	0.118768	+	0.992922i	$0.462106\pi$
$53$	−42.4271	+	73.4859i	−0.800512	+	1.38653i	−0.919280	+	0.393605i	$0.871228\pi$
$54$		0			0
$55$			13.4595i			0.244718i
$56$		0			0
$57$	40.2220			0.705649
$58$		0			0
$59$	−58.5062	−	33.7786i	−0.991631	−	0.572518i	−0.0858695	−	0.996306i	$-0.527367\pi$
$59$	−58.5062	−	33.7786i	−0.991631	−	0.572518i	−0.905761	+	0.423788i	$0.860700\pi$
$60$		0			0
$61$	25.6135	−	14.7879i	0.419893	−	0.242425i	−0.275139	−	0.961405i	$-0.588724\pi$
$61$	25.6135	−	14.7879i	0.419893	−	0.242425i	0.695032	+	0.718979i	$0.255390\pi$
$62$		0			0
$63$	7.98140	+	15.8938i	0.126689	+	0.252283i
$64$		0			0
$65$	12.1248	+	21.0008i	0.186536	+	0.323090i
$66$		0			0
$67$	−27.4789	+	47.5949i	−0.410133	+	0.710371i	−0.994904	−	0.100827i	$-0.967851\pi$
$67$	−27.4789	+	47.5949i	−0.410133	+	0.710371i	0.584771	+	0.811198i	$0.301184\pi$
$68$		0			0
$69$		−	92.7741i		−	1.34455i
$70$		0			0
$71$	83.8102			1.18043			0.590213	−	0.807248i	$-0.299044\pi$
$71$	83.8102			1.18043			0.590213	+	0.807248i	$0.299044\pi$
$72$		0			0
$73$	−108.784	−	62.8065i	−1.49019	−	0.860363i	−0.490255	−	0.871579i	$-0.663096\pi$
$73$	−108.784	−	62.8065i	−1.49019	−	0.860363i	−0.999937	+	0.0112159i	$0.996430\pi$
$74$		0			0
$75$	−17.6866	+	10.2113i	−0.235821	+	0.136151i
$76$		0			0
$77$	−12.5707	+	19.1112i	−0.163256	+	0.248197i
$78$		0			0
$79$	−35.1955	−	60.9604i	−0.445512	−	0.771650i	0.552575	−	0.833463i	$-0.313645\pi$
$79$	−35.1955	−	60.9604i	−0.445512	−	0.771650i	−0.998088	+	0.0618128i	$0.980312\pi$
$80$		0			0
$81$	25.8389	−	44.7542i	0.318998	−	0.552521i
$82$		0			0
$83$		−	27.1264i		−	0.326824i	−0.986558	−	0.163412i	$-0.947750\pi$
$83$		−	27.1264i		−	0.326824i	0.986558	−	0.163412i	$-0.0522500\pi$
$84$		0			0
$85$	57.1685			0.672571
$86$		0			0
$87$	62.6527	+	36.1726i	0.720146	+	0.415777i
$88$		0			0
$89$	−126.553	+	73.0654i	−1.42194	+	0.820959i	−0.996465	−	0.0840094i	$-0.973227\pi$
$89$	−126.553	+	73.0654i	−1.42194	+	0.820959i	−0.425478	+	0.904969i	$0.639894\pi$
$90$		0			0
$91$	−2.39795	+	41.1433i	−0.0263511	+	0.452125i
$92$		0			0
$93$	−53.1196	−	92.0059i	−0.571179	−	0.989311i
$94$		0			0
$95$	−32.5920	+	56.4511i	−0.343074	+	0.594222i
$96$		0			0
$97$		−	11.3574i		−	0.117086i	−0.998285	−	0.0585431i	$-0.981354\pi$
$97$		−	11.3574i		−	0.117086i	0.998285	−	0.0585431i	$-0.0186455\pi$
$98$		0			0
$99$	−8.30278			−0.0838664
$100$		0			0
$101$	36.2851	+	20.9492i	0.359258	+	0.207418i	0.668755	−	0.743482i	$-0.266827\pi$
$101$	36.2851	+	20.9492i	0.359258	+	0.207418i	−0.309497	+	0.950900i	$0.600161\pi$
$102$		0			0
$103$	84.1601	−	48.5899i	0.817089	−	0.471746i	−0.0323227	−	0.999477i	$-0.510290\pi$
$103$	84.1601	−	48.5899i	0.817089	−	0.471746i	0.849412	+	0.527731i	$0.176957\pi$
$104$		0			0
$105$	73.1511	+	4.26345i	0.696677	+	0.0406043i
$106$		0			0
$107$	−41.7218	−	72.2643i	−0.389924	−	0.675368i	0.602515	−	0.798107i	$-0.294165\pi$
$107$	−41.7218	−	72.2643i	−0.389924	−	0.675368i	−0.992439	+	0.122740i	$0.960832\pi$
$108$		0			0
$109$	−80.9965	+	140.290i	−0.743088	+	1.28707i	0.207995	+	0.978130i	$0.433306\pi$
$109$	−80.9965	+	140.290i	−0.743088	+	1.28707i	−0.951083	+	0.308936i	$0.900027\pi$
$110$		0			0
$111$			36.3072i			0.327092i
$112$		0			0
$113$	27.2503			0.241153			0.120576	−	0.992704i	$-0.461526\pi$
$113$	27.2503			0.241153			0.120576	+	0.992704i	$0.461526\pi$
$114$		0			0
$115$	130.207	+	75.1751i	1.13224	+	0.653697i
$116$		0			0
$117$	−12.9548	+	7.47948i	−0.110725	+	0.0639271i
$118$		0			0
$119$	81.1737	+	53.3934i	0.682132	+	0.448684i
$120$		0			0
$121$	55.1606	+	95.5410i	0.455873	+	0.789595i
$122$		0			0
$123$	−27.1325	+	46.9949i	−0.220589	+	0.382072i
$124$		0			0
$125$		−	136.067i		−	1.08853i
$126$		0			0
$127$	−232.457			−1.83037			−0.915183	−	0.403038i	$-0.867954\pi$
$127$	−232.457			−1.83037			−0.915183	+	0.403038i	$0.867954\pi$
$128$		0			0
$129$	−121.934	−	70.3986i	−0.945225	−	0.545726i
$130$		0			0
$131$	152.509	−	88.0512i	1.16419	−	0.672146i	0.211887	−	0.977294i	$-0.432039\pi$
$131$	152.509	−	88.0512i	1.16419	−	0.672146i	0.952305	+	0.305148i	$0.0987058\pi$
$132$		0			0
$133$	−99.0008	+	49.7152i	−0.744367	+	0.373798i
$134$		0			0
$135$	60.4037	+	104.622i	0.447435	+	0.774980i
$136$		0			0
$137$	132.462	−	229.432i	0.966879	−	1.67468i	0.262400	−	0.964959i	$-0.415486\pi$
$137$	132.462	−	229.432i	0.966879	−	1.67468i	0.704479	−	0.709725i	$-0.251181\pi$
$138$		0			0
$139$			267.680i			1.92576i	0.269935	+	0.962878i	$0.412998\pi$
$139$			267.680i			1.92576i	−0.269935	+	0.962878i	$0.587002\pi$
$140$		0			0
$141$	86.0382			0.610200
$142$		0			0
$143$	−16.6621	−	9.61984i	−0.116518	−	0.0672716i
$144$		0			0
$145$	−101.535	+	58.6215i	−0.700244	+	0.404286i
$146$		0			0
$147$	99.8855	+	74.3742i	0.679493	+	0.505947i
$148$		0			0
$149$	−0.972701	−	1.68477i	−0.00652820	−	0.0113072i	0.862743	−	0.505643i	$-0.168745\pi$
$149$	−0.972701	−	1.68477i	−0.00652820	−	0.0113072i	−0.869271	+	0.494336i	$0.835411\pi$
$150$		0			0
$151$	−50.1524	+	86.8665i	−0.332135	+	0.575275i	−0.982930	−	0.183978i	$-0.941102\pi$
$151$	−50.1524	+	86.8665i	−0.332135	+	0.575275i	0.650795	+	0.759253i	$0.274436\pi$
$152$		0			0
$153$			35.2656i			0.230494i
$154$		0			0
$155$	172.172			1.11079
$156$		0			0
$157$	117.153	+	67.6386i	0.746200	+	0.430819i	0.824319	−	0.566125i	$-0.191558\pi$
$157$	117.153	+	67.6386i	0.746200	+	0.430819i	−0.0781191	+	0.996944i	$0.524891\pi$
$158$		0			0
$159$	−186.765	+	107.829i	−1.17462	+	0.678168i
$160$		0			0
$161$	114.671	+	228.350i	0.712240	+	1.41832i
$162$		0			0
$163$	127.353	+	220.582i	0.781307	+	1.35326i	0.931180	+	0.364559i	$0.118780\pi$
$163$	127.353	+	220.582i	0.781307	+	1.35326i	−0.149873	+	0.988705i	$0.547886\pi$
$164$		0			0
$165$	−17.1037	+	29.6244i	−0.103659	+	0.179542i
$166$		0			0
$167$			50.9246i			0.304938i	0.988308	+	0.152469i	$0.0487224\pi$
$167$			50.9246i			0.304938i	−0.988308	+	0.152469i	$0.951278\pi$
$168$		0			0
$169$	134.336			0.794889
$170$		0			0
$171$	−34.8231	−	20.1051i	−0.203644	−	0.117574i
$172$		0			0
$173$	−60.9855	+	35.2100i	−0.352517	+	0.203526i	−0.665793	−	0.746136i	$-0.731907\pi$
$173$	−60.9855	+	35.2100i	−0.352517	+	0.203526i	0.313276	+	0.949662i	$0.398573\pi$
$174$		0			0
$175$	30.9116	−	46.9947i	0.176638	−	0.268541i
$176$		0			0
$177$	−85.8484	−	148.694i	−0.485019	−	0.840078i
$178$		0			0
$179$	73.7202	−	127.687i	0.411845	−	0.713336i	−0.583247	−	0.812295i	$-0.698218\pi$
$179$	73.7202	−	127.687i	0.411845	−	0.713336i	0.995092	+	0.0989591i	$0.0315513\pi$
$180$		0			0
$181$		−	294.491i		−	1.62702i	−0.581550	−	0.813511i	$-0.697553\pi$
$181$		−	294.491i		−	1.62702i	0.581550	−	0.813511i	$-0.302447\pi$
$182$		0			0
$183$	75.1672			0.410750
$184$		0			0
$185$	−50.9566	−	29.4198i	−0.275441	−	0.159026i
$186$		0			0
$187$	−39.2807	+	22.6787i	−0.210057	+	0.121277i
$188$		0			0
$189$	−11.9461	+	204.968i	−0.0632071	+	1.08449i
$190$		0			0
$191$	56.2595	+	97.4444i	0.294553	+	0.510180i	0.974881	−	0.222728i	$-0.0714961\pi$
$191$	56.2595	+	97.4444i	0.294553	+	0.510180i	−0.680328	+	0.732908i	$0.738163\pi$
$192$		0			0
$193$	−63.7435	+	110.407i	−0.330277	+	0.572057i	−0.982566	−	0.185914i	$-0.940475\pi$
$193$	−63.7435	+	110.407i	−0.330277	+	0.572057i	0.652289	+	0.757970i	$0.273809\pi$
$194$		0			0
$195$			61.6307i			0.316055i
$196$		0			0
$197$	293.140			1.48802			0.744011	−	0.668167i	$-0.232921\pi$
$197$	293.140			1.48802			0.744011	+	0.668167i	$0.232921\pi$
$198$		0			0
$199$	−8.43677	−	4.87097i	−0.0423958	−	0.0244772i	0.478652	−	0.878005i	$-0.341125\pi$
$199$	−8.43677	−	4.87097i	−0.0423958	−	0.0244772i	−0.521048	+	0.853527i	$0.674459\pi$
$200$		0			0
$201$	−120.963	+	69.8378i	−0.601804	+	0.347452i
$202$		0			0
$203$	−198.921	−	11.5937i	−0.979905	−	0.0571117i
$204$		0			0
$205$	−43.9711	−	76.1602i	−0.214493	−	0.371513i
$206$		0			0
$207$	−46.3734	+	80.3211i	−0.224026	+	0.388025i
$208$		0			0
$209$		−	51.7170i		−	0.247450i
$210$		0			0
$211$	139.516			0.661214			0.330607	−	0.943769i	$-0.392747\pi$
$211$	139.516			0.661214			0.330607	+	0.943769i	$0.392747\pi$
$212$		0			0
$213$	184.467	+	106.502i	0.866042	+	0.500009i
$214$		0			0
$215$	197.607	−	114.088i	0.919102	−	0.530644i
$216$		0			0
$217$	244.468	+	160.803i	1.12658	+	0.741026i
$218$		0			0
$219$	−159.623	−	276.475i	−0.728872	−	1.26244i
$220$		0			0
$221$	−40.8598	+	70.7713i	−0.184886	+	0.320232i
$222$		0			0
$223$		−	273.426i		−	1.22612i	−0.790035	−	0.613062i	$-0.789938\pi$
$223$		−	273.426i		−	1.22612i	0.790035	−	0.613062i	$-0.210062\pi$
$224$		0			0
$225$	20.4167			0.0907409
$226$		0			0
$227$	−58.4952	−	33.7722i	−0.257688	−	0.148776i	0.365591	−	0.930775i	$-0.380867\pi$
$227$	−58.4952	−	33.7722i	−0.257688	−	0.148776i	−0.623279	+	0.781999i	$0.714200\pi$
$228$		0			0
$229$	−166.765	+	96.2816i	−0.728230	+	0.420444i	−0.817774	−	0.575539i	$-0.804792\pi$
$229$	−166.765	+	96.2816i	−0.728230	+	0.420444i	0.0895442	+	0.995983i	$0.471459\pi$
$230$		0			0
$231$	−51.9537	+	26.0896i	−0.224908	+	0.112942i
$232$		0			0
$233$	−40.7024	−	70.4987i	−0.174689	−	0.302569i	0.765365	−	0.643597i	$-0.222559\pi$
$233$	−40.7024	−	70.4987i	−0.174689	−	0.302569i	−0.940053	+	0.341027i	$0.889225\pi$
$234$		0			0
$235$	−69.7170	+	120.753i	−0.296668	+	0.513844i
$236$		0			0
$237$		−	178.899i		−	0.754848i
$238$		0			0
$239$	22.6152			0.0946244			0.0473122	−	0.998880i	$-0.484934\pi$
$239$	22.6152			0.0946244			0.0473122	+	0.998880i	$0.484934\pi$
$240$		0			0
$241$	−81.5504	−	47.0832i	−0.338384	−	0.195366i	0.321173	−	0.947020i	$-0.395923\pi$
$241$	−81.5504	−	47.0832i	−0.338384	−	0.195366i	−0.659557	+	0.751655i	$0.729256\pi$
$242$		0			0
$243$	−114.869	+	66.3194i	−0.472710	+	0.272919i
$244$		0			0
$245$	−185.321	+	79.9223i	−0.756411	+	0.326213i
$246$		0			0
$247$	−46.5887	−	80.6941i	−0.188618	−	0.326697i
$248$		0			0
$249$	34.4710	−	59.7054i	0.138438	−	0.239781i
$250$		0			0
$251$		−	316.694i		−	1.26173i	−0.775892	−	0.630865i	$-0.782700\pi$
$251$		−	316.694i		−	1.26173i	0.775892	−	0.630865i	$-0.217300\pi$
$252$		0			0
$253$	−119.288			−0.471493
$254$		0			0
$255$	125.828	+	72.6470i	0.493444	+	0.284890i
$256$		0			0
$257$	40.7550	−	23.5299i	0.158580	−	0.0915560i	−0.418610	−	0.908166i	$-0.637483\pi$
$257$	40.7550	−	23.5299i	0.158580	−	0.0915560i	0.577190	+	0.816610i	$0.304149\pi$
$258$		0			0
$259$	−44.8764	−	89.3649i	−0.173268	−	0.345038i
$260$		0			0
$261$	−36.1619	−	62.6343i	−0.138551	−	0.239978i
$262$		0			0
$263$	203.252	−	352.043i	0.772822	−	1.33857i	−0.163189	−	0.986595i	$-0.552178\pi$
$263$	203.252	−	352.043i	0.772822	−	1.33857i	0.936011	−	0.351972i	$-0.114489\pi$
$264$		0			0
$265$		−	349.496i		−	1.31885i
$266$		0			0
$267$	−371.392			−1.39098
$268$		0			0
$269$	−287.957	−	166.252i	−1.07047	−	0.618038i	−0.142162	−	0.989843i	$-0.545405\pi$
$269$	−287.957	−	166.252i	−1.07047	−	0.618038i	−0.928311	+	0.371806i	$0.878739\pi$
$270$		0			0
$271$	−61.7686	+	35.6621i	−0.227928	+	0.131595i	−0.609616	−	0.792697i	$-0.708676\pi$
$271$	−61.7686	+	35.6621i	−0.227928	+	0.131595i	0.381688	+	0.924291i	$0.375343\pi$
$272$		0			0
$273$	−57.5609	+	87.5096i	−0.210846	+	0.320548i
$274$		0			0
$275$	13.1296	+	22.7412i	0.0477441	+	0.0826952i
$276$		0			0
$277$	−14.8574	+	25.7337i	−0.0536367	+	0.0929015i	−0.891597	−	0.452829i	$-0.850415\pi$
$277$	−14.8574	+	25.7337i	−0.0536367	+	0.0929015i	0.837960	+	0.545731i	$0.183748\pi$
$278$		0			0
$279$			106.208i			0.380674i
$280$		0			0
$281$	9.06447			0.0322579			0.0161289	−	0.999870i	$-0.494866\pi$
$281$	9.06447			0.0322579			0.0161289	+	0.999870i	$0.494866\pi$
$282$		0			0
$283$	−159.988	−	92.3689i	−0.565327	−	0.326392i	0.189954	−	0.981793i	$-0.439166\pi$
$283$	−159.988	−	92.3689i	−0.565327	−	0.326392i	−0.755281	+	0.655401i	$0.772500\pi$
$284$		0			0
$285$	−143.471	+	82.8328i	−0.503406	+	0.290641i
$286$		0			0
$287$	8.69624	−	149.208i	0.0303005	−	0.519887i
$288$		0			0
$289$	−48.1732	−	83.4384i	−0.166689	−	0.288714i
$290$		0			0
$291$	14.4324	−	24.9976i	0.0495959	−	0.0859026i
$292$		0			0
$293$		−	300.389i		−	1.02522i	−0.858622	−	0.512609i	$-0.828679\pi$
$293$		−	300.389i		−	1.02522i	0.858622	−	0.512609i	$-0.171321\pi$
$294$		0			0
$295$	278.253			0.943230
$296$		0			0
$297$	−83.0072	−	47.9242i	−0.279486	−	0.161361i
$298$		0			0
$299$	−186.125	+	107.459i	−0.622491	+	0.359395i
$300$		0			0
$301$	387.137	+	22.5635i	1.28617	+	0.0749617i
$302$		0			0
$303$	53.2425	+	92.2187i	0.175718	+	0.304352i
$304$		0			0
$305$	−60.9083	+	105.496i	−0.199699	+	0.345889i
$306$		0			0
$307$		−	390.385i		−	1.27161i	−0.771848	−	0.635807i	$-0.780667\pi$
$307$		−	390.385i		−	1.27161i	0.771848	−	0.635807i	$-0.219333\pi$
$308$		0			0
$309$	246.983			0.799297
$310$		0			0
$311$	−83.2050	−	48.0384i	−0.267540	−	0.154464i	0.360229	−	0.932864i	$-0.382699\pi$
$311$	−83.2050	−	48.0384i	−0.267540	−	0.154464i	−0.627769	+	0.778400i	$0.716032\pi$
$312$		0			0
$313$	−419.921	+	242.442i	−1.34160	+	0.774574i	−0.987042	−	0.160460i	$-0.948702\pi$
$313$	−419.921	+	242.442i	−1.34160	+	0.774574i	−0.354559	+	0.935034i	$0.615369\pi$
$314$		0			0
$315$	−61.2010	−	40.2560i	−0.194289	−	0.127797i
$316$		0			0
$317$	33.9714	+	58.8401i	0.107165	+	0.185616i	0.914621	−	0.404313i	$-0.132489\pi$
$317$	33.9714	+	58.8401i	0.107165	+	0.185616i	−0.807456	+	0.589928i	$0.799156\pi$
$318$		0			0
$319$	46.5102	−	80.5581i	0.145800	−	0.252533i
$320$		0			0
$321$		−	212.072i		−	0.660662i
$322$		0			0
$323$	−219.665			−0.680079
$324$		0			0
$325$	40.9723	+	23.6554i	0.126069	+	0.0727858i
$326$		0			0
$327$	−356.548	+	205.853i	−1.09036	+	0.629520i
$328$		0			0
$329$	−211.771	+	106.345i	−0.643680	+	0.323237i
$330$		0			0
$331$	132.634	+	229.729i	0.400707	+	0.694046i	0.993811	−	0.111080i	$-0.0354311\pi$
$331$	132.634	+	229.729i	0.400707	+	0.694046i	−0.593104	+	0.805126i	$0.702098\pi$
$332$		0			0
$333$	18.1483	−	31.4337i	0.0544993	−	0.0943955i
$334$		0			0
$335$		−	226.359i		−	0.675699i
$336$		0			0
$337$	549.980			1.63199			0.815993	−	0.578061i	$-0.196191\pi$
$337$	549.980			1.63199			0.815993	+	0.578061i	$0.196191\pi$
$338$		0			0
$339$	59.9780	+	34.6283i	0.176926	+	0.102148i
$340$		0			0
$341$	−118.300	+	68.3006i	−0.346921	+	0.200295i
$342$		0			0
$343$	−337.782	−	59.6012i	−0.984787	−	0.173764i
$344$		0			0
$345$	191.058	+	330.922i	0.553791	+	0.959194i
$346$		0			0
$347$	339.375	−	587.815i	0.978026	−	1.69399i	0.308463	−	0.951236i	$-0.400185\pi$
$347$	339.375	−	587.815i	0.978026	−	1.69399i	0.669563	−	0.742755i	$-0.266481\pi$
$348$		0			0
$349$			170.081i			0.487339i	0.969858	+	0.243669i	$0.0783511\pi$
$349$			170.081i			0.487339i	−0.969858	+	0.243669i	$0.921649\pi$
$350$		0			0
$351$	−172.688			−0.491990
$352$		0			0
$353$	204.423	+	118.024i	0.579102	+	0.334345i	0.760776	−	0.649014i	$-0.224818\pi$
$353$	204.423	+	118.024i	0.579102	+	0.334345i	−0.181675	+	0.983359i	$0.558152\pi$
$354$		0			0
$355$	−298.948	+	172.598i	−0.842108	+	0.486191i
$356$		0			0
$357$	110.814	+	220.671i	0.310404	+	0.618126i
$358$		0			0
$359$	−229.058	−	396.740i	−0.638044	−	1.10512i	−0.985861	−	0.167562i	$-0.946410\pi$
$359$	−229.058	−	396.740i	−0.638044	−	1.10512i	0.347818	−	0.937562i	$-0.386923\pi$
$360$		0			0
$361$	−55.2677	+	95.7266i	−0.153096	+	0.265170i
$362$		0			0
$363$			280.382i			0.772402i
$364$		0			0
$365$	517.372			1.41746
$366$		0			0
$367$	−356.315	−	205.718i	−0.970885	−	0.560541i	−0.0713791	−	0.997449i	$-0.522740\pi$
$367$	−356.315	−	205.718i	−0.970885	−	0.560541i	−0.899506	+	0.436909i	$0.856073\pi$
$368$		0			0
$369$	46.9811	−	27.1245i	0.127320	−	0.0735082i
$370$		0			0
$371$	326.417	−	496.250i	0.879829	−	1.33760i
$372$		0			0
$373$	7.89853	+	13.6807i	0.0211757	+	0.0366774i	0.876419	−	0.481549i	$-0.159926\pi$
$373$	7.89853	+	13.6807i	0.0211757	+	0.0366774i	−0.855243	+	0.518227i	$0.826592\pi$
$374$		0			0
$375$	172.907	−	299.483i	0.461085	−	0.798623i
$376$		0			0
$377$		−	167.593i		−	0.444544i
$378$		0			0
$379$	455.384			1.20154			0.600770	−	0.799422i	$-0.294861\pi$
$379$	455.384			1.20154			0.600770	+	0.799422i	$0.294861\pi$
$380$		0			0
$381$	−511.639	−	295.395i	−1.34288	−	0.775314i
$382$		0			0
$383$	158.732	−	91.6439i	0.414443	−	0.239279i	−0.278254	−	0.960508i	$-0.589756\pi$
$383$	158.732	−	91.6439i	0.414443	−	0.239279i	0.692697	+	0.721229i	$0.256422\pi$
$384$		0			0
$385$	5.48190	−	94.0568i	0.0142387	−	0.244303i
$386$		0			0
$387$	70.3780	+	121.898i	0.181855	+	0.314982i
$388$		0			0
$389$	−92.7471	+	160.643i	−0.238424	+	0.412963i	−0.960262	−	0.279099i	$-0.909964\pi$
$389$	−92.7471	+	160.643i	−0.238424	+	0.412963i	0.721838	+	0.692062i	$0.243298\pi$
$390$		0			0
$391$			506.669i			1.29583i
$392$		0			0
$393$	447.565			1.13884
$394$		0			0
$395$	251.082	+	144.962i	0.635651	+	0.366993i
$396$		0			0
$397$	39.5520	−	22.8353i	0.0996271	−	0.0575197i	−0.449359	−	0.893351i	$-0.648347\pi$
$397$	39.5520	−	22.8353i	0.0996271	−	0.0575197i	0.548986	+	0.835832i	$0.315014\pi$
$398$		0			0
$399$	−281.077	−	16.3820i	−0.704454	−	0.0410576i
$400$		0			0
$401$	−19.2312	−	33.3094i	−0.0479580	−	0.0830657i	0.841050	−	0.540958i	$-0.181938\pi$
$401$	−19.2312	−	33.3094i	−0.0479580	−	0.0830657i	−0.889008	+	0.457892i	$0.848605\pi$
$402$		0			0
$403$	−123.056	+	213.139i	−0.305349	+	0.528881i
$404$		0			0
$405$			212.849i			0.525553i
$406$		0			0
$407$	46.6833			0.114701
$408$		0			0
$409$	−145.264	−	83.8684i	−0.355169	−	0.205057i	0.311790	−	0.950151i	$-0.399071\pi$
$409$	−145.264	−	83.8684i	−0.355169	−	0.205057i	−0.666960	+	0.745094i	$0.732405\pi$
$410$		0			0
$411$	583.102	−	336.654i	1.41874	−	0.819109i
$412$		0			0
$413$	395.092	+	259.878i	0.956640	+	0.629246i
$414$		0			0
$415$	55.8639	+	96.7590i	0.134612	+	0.233154i
$416$		0			0
$417$	−340.155	+	589.166i	−0.815720	+	1.41287i
$418$		0			0
$419$		−	300.318i		−	0.716751i	−0.933578	−	0.358375i	$-0.883331\pi$
$419$		−	300.318i		−	0.716751i	0.933578	−	0.358375i	$-0.116669\pi$
$420$		0			0
$421$	−280.567			−0.666430			−0.333215	−	0.942851i	$-0.608133\pi$
$421$	−280.567			−0.666430			−0.333215	+	0.942851i	$0.608133\pi$
$422$		0			0
$423$	−74.4894	−	43.0065i	−0.176098	−	0.101670i
$424$		0			0
$425$	96.5920	−	55.7674i	0.227275	−	0.131218i
$426$		0			0
$427$	−185.014	+	92.9082i	−0.433287	+	0.217584i
$428$		0			0
$429$	−24.4489	−	42.3467i	−0.0569904	−	0.0987102i
$430$		0			0
$431$	−112.382	+	194.651i	−0.260747	+	0.451627i	−0.966441	−	0.256890i	$-0.917302\pi$
$431$	−112.382	+	194.651i	−0.260747	+	0.451627i	0.705693	+	0.708517i	$0.250636\pi$
$432$		0			0
$433$		−	731.236i		−	1.68877i	−0.535739	−	0.844383i	$-0.679967\pi$
$433$		−	731.236i		−	1.68877i	0.535739	−	0.844383i	$-0.320033\pi$
$434$		0			0
$435$	−297.973			−0.684996
$436$		0			0
$437$	−500.311	−	288.854i	−1.14488	−	0.660994i
$438$		0			0
$439$	−259.322	+	149.720i	−0.590711	+	0.341047i	−0.765379	−	0.643580i	$-0.777448\pi$
$439$	−259.322	+	149.720i	−0.590711	+	0.341047i	0.174668	+	0.984627i	$0.444115\pi$
$440$		0			0
$441$	−49.3018	−	114.319i	−0.111795	−	0.259227i
$442$		0			0
$443$	198.077	+	343.080i	0.447127	+	0.774447i	0.998198	−	0.0600116i	$-0.0191138\pi$
$443$	198.077	+	343.080i	0.447127	+	0.774447i	−0.551070	+	0.834459i	$0.685780\pi$
$444$		0			0
$445$	300.940	−	521.243i	0.676270	−	1.17133i
$446$		0			0
$447$		−	4.94425i		−	0.0110610i
$448$		0			0
$449$	128.183			0.285486			0.142743	−	0.989760i	$-0.454408\pi$
$449$	128.183			0.285486			0.142743	+	0.989760i	$0.454408\pi$
$450$		0			0
$451$	60.4254	+	34.8866i	0.133981	+	0.0773540i
$452$		0			0
$453$	−220.772	+	127.463i	−0.487354	+	0.281374i
$454$		0			0
$455$	−76.1767	−	151.695i	−0.167421	−	0.333396i
$456$		0			0
$457$	−202.574	−	350.868i	−0.443268	−	0.767763i	0.554661	−	0.832076i	$-0.312848\pi$
$457$	−202.574	−	350.868i	−0.443268	−	0.767763i	−0.997930	+	0.0643128i	$0.979514\pi$
$458$		0			0
$459$	−203.556	+	352.569i	−0.443477	+	0.768124i
$460$		0			0
$461$			312.620i			0.678134i	0.940762	+	0.339067i	$0.110111\pi$
$461$			312.620i			0.678134i	−0.940762	+	0.339067i	$0.889889\pi$
$462$		0			0
$463$	246.396			0.532173			0.266087	−	0.963949i	$-0.414269\pi$
$463$	246.396			0.532173			0.266087	+	0.963949i	$0.414269\pi$
$464$		0			0
$465$	378.952	+	218.788i	0.814950	+	0.470512i
$466$		0			0
$467$	−18.8539	+	10.8853i	−0.0403723	+	0.0233090i	−0.520050	−	0.854136i	$-0.674087\pi$
$467$	−18.8539	+	10.8853i	−0.0403723	+	0.0233090i	0.479678	+	0.877445i	$0.340753\pi$
$468$		0			0
$469$	211.411	−	321.408i	0.450770	−	0.685304i
$470$		0			0
$471$	171.904	+	297.746i	0.364976	+	0.632157i
$472$		0			0
$473$	−90.5177	+	156.781i	−0.191369	+	0.331461i
$474$		0			0
$475$			127.173i			0.267733i
$476$		0			0
$477$	215.594			0.451979
$478$		0			0
$479$	452.490	+	261.245i	0.944656	+	0.545397i	0.891417	−	0.453185i	$-0.149712\pi$
$479$	452.490	+	261.245i	0.944656	+	0.545397i	0.0532389	+	0.998582i	$0.483046\pi$
$480$		0			0
$481$	72.8400	−	42.0542i	0.151435	−	0.0874308i
$482$		0			0
$483$	−37.7858	+	648.318i	−0.0782316	+	1.34227i
$484$		0			0
$485$	23.3892	+	40.5113i	0.0482252	+	0.0835285i
$486$		0			0
$487$	−409.067	+	708.525i	−0.839974	+	1.45488i	0.0499421	+	0.998752i	$0.484096\pi$
$487$	−409.067	+	708.525i	−0.839974	+	1.45488i	−0.889916	+	0.456125i	$0.849237\pi$
$488$		0			0
$489$			647.337i			1.32380i
$490$		0			0
$491$	762.002			1.55194			0.775969	−	0.630771i	$-0.217261\pi$
$491$	762.002			1.55194			0.775969	+	0.630771i	$0.217261\pi$
$492$		0			0
$493$	−342.167	−	197.550i	−0.694050	−	0.400710i
$494$		0			0
$495$	29.6157	−	17.0986i	0.0598297	−	0.0345427i
$496$		0			0
$497$	−585.678	−	34.1350i	−1.17843	−	0.0686820i
$498$		0			0
$499$	−25.4935	−	44.1560i	−0.0510891	−	0.0884889i	0.839350	−	0.543592i	$-0.182936\pi$
$499$	−25.4935	−	44.1560i	−0.0510891	−	0.0884889i	−0.890439	+	0.455103i	$0.849603\pi$
$500$		0			0
$501$	−64.7126	+	112.086i	−0.129167	+	0.223724i
$502$		0			0
$503$		−	305.233i		−	0.606825i	−0.952859	−	0.303413i	$-0.901874\pi$
$503$		−	305.233i		−	0.606825i	0.952859	−	0.303413i	$-0.0981260\pi$
$504$		0			0
$505$	−172.570			−0.341723
$506$		0			0
$507$	295.675	+	170.708i	0.583185	+	0.336702i
$508$		0			0
$509$	−156.536	+	90.3761i	−0.307536	+	0.177556i	−0.645823	−	0.763487i	$-0.723486\pi$
$509$	−156.536	+	90.3761i	−0.307536	+	0.177556i	0.338287	+	0.941043i	$0.390152\pi$
$510$		0			0
$511$	734.618	+	483.207i	1.43761	+	0.945611i
$512$		0			0
$513$	−232.096	−	402.003i	−0.452429	−	0.783631i
$514$		0			0
$515$	−200.131	+	346.637i	−0.388604	+	0.673081i
$516$		0			0
$517$		−	110.627i		−	0.213978i
$518$		0			0
$519$	−178.973			−0.344841
$520$		0			0
$521$	−312.767	−	180.576i	−0.600321	−	0.346595i	0.168847	−	0.985642i	$-0.445996\pi$
$521$	−312.767	−	180.576i	−0.600321	−	0.346595i	−0.769168	+	0.639047i	$0.779329\pi$
$522$		0			0
$523$	−566.506	+	327.072i	−1.08318	+	0.625377i	−0.931754	−	0.363091i	$-0.881721\pi$
$523$	−566.506	+	327.072i	−1.08318	+	0.625377i	−0.151431	+	0.988468i	$0.548388\pi$
$524$		0			0
$525$	127.755	−	64.1548i	0.243343	−	0.122200i
$526$		0			0
$527$	290.103	+	502.474i	0.550481	+	0.953461i
$528$		0			0
$529$	−401.757	+	695.864i	−0.759465	+	1.31543i
$530$		0			0
$531$			171.646i			0.323251i
$532$		0			0
$533$	125.709			0.235852
$534$		0			0
$535$	297.641	+	171.843i	0.556338	+	0.321202i
$536$		0			0
$537$	324.517	−	187.360i	0.604315	−	0.348902i
$538$		0			0
$539$	95.6295	−	128.432i	0.177420	−	0.238277i
$540$		0			0
$541$	301.642	+	522.459i	0.557564	+	0.965729i	0.997699	+	0.0677973i	$0.0215971\pi$
$541$	301.642	+	522.459i	0.557564	+	0.965729i	−0.440135	+	0.897931i	$0.645070\pi$
$542$		0			0
$543$	374.225	−	648.177i	0.689180	−	1.19370i
$544$		0			0
$545$		−	667.214i		−	1.22424i
$546$		0			0
$547$	−686.167			−1.25442			−0.627209	−	0.778851i	$-0.715803\pi$
$547$	−686.167			−1.25442			−0.627209	+	0.778851i	$0.715803\pi$
$548$		0			0
$549$	−65.0776	−	37.5726i	−0.118538	−	0.0684382i
$550$		0			0
$551$	390.142	−	225.248i	0.708061	−	0.408799i
$552$		0			0
$553$	221.123	+	440.334i	0.399860	+	0.796265i
$554$		0			0
$555$	−74.7706	−	129.506i	−0.134722	−	0.233345i
$556$		0			0
$557$	392.661	−	680.108i	0.704956	−	1.22102i	−0.261751	−	0.965135i	$-0.584300\pi$
$557$	392.661	−	680.108i	0.704956	−	1.22102i	0.966707	−	0.255885i	$-0.0823668\pi$
$558$		0			0
$559$			326.168i			0.583485i
$560$		0			0
$561$	−115.276			−0.205483
$562$		0			0
$563$	−393.226	−	227.029i	−0.698447	−	0.403249i	0.108321	−	0.994116i	$-0.465452\pi$
$563$	−393.226	−	227.029i	−0.698447	−	0.403249i	−0.806769	+	0.590867i	$0.798786\pi$
$564$		0			0
$565$	−97.2007	+	56.1189i	−0.172037	+	0.0993254i
$566$		0			0
$567$	−198.794	+	302.225i	−0.350606	+	0.533025i
$568$		0			0
$569$	35.7137	+	61.8580i	0.0627658	+	0.108713i	0.895701	−	0.444657i	$-0.146675\pi$
$569$	35.7137	+	61.8580i	0.0627658	+	0.108713i	−0.832935	+	0.553371i	$0.813341\pi$
$570$		0			0
$571$	359.033	−	621.864i	0.628780	−	1.08908i	−0.359017	−	0.933331i	$-0.616888\pi$
$571$	359.033	−	621.864i	0.628780	−	1.08908i	0.987797	−	0.155748i	$-0.0497787\pi$
$572$		0			0
$573$			285.968i			0.499071i
$574$		0			0
$575$	293.331			0.510141
$576$		0			0
$577$	786.338	+	453.993i	1.36280	+	0.786815i	0.989996	−	0.141093i	$-0.0450617\pi$
$577$	786.338	+	453.993i	1.36280	+	0.786815i	0.372808	+	0.927909i	$0.378395\pi$
$578$		0			0
$579$	−280.600	+	162.004i	−0.484628	+	0.279800i
$580$		0			0
$581$	−11.0483	+	189.563i	−0.0190160	+	0.326271i
$582$		0			0
$583$	138.645	+	240.140i	0.237813	+	0.411904i
$584$		0			0
$585$	30.8063	−	53.3581i	0.0526603	−	0.0912104i
$586$		0			0
$587$			862.870i			1.46997i	0.678086	+	0.734983i	$0.262810\pi$
$587$			862.870i			1.46997i	−0.678086	+	0.734983i	$0.737190\pi$
$588$		0			0
$589$	−661.557			−1.12319
$590$		0			0
$591$	645.204	+	372.509i	1.09172	+	0.630302i
$592$		0			0
$593$	470.127	−	271.428i	0.792794	−	0.457720i	−0.0481510	−	0.998840i	$-0.515333\pi$
$593$	470.127	−	271.428i	0.792794	−	0.457720i	0.840945	+	0.541120i	$0.182000\pi$
$594$		0			0
$595$	−399.502	−	23.2841i	−0.671431	−	0.0391329i
$596$		0			0
$597$	−12.3796	−	21.4421i	−0.0207363	−	0.0359164i
$598$		0			0
$599$	−39.3074	+	68.0824i	−0.0656216	+	0.113660i	−0.896970	−	0.442092i	$-0.854236\pi$
$599$	−39.3074	+	68.0824i	−0.0656216	+	0.113660i	0.831348	+	0.555752i	$0.187570\pi$
$600$		0			0
$601$		−	851.603i		−	1.41698i	−0.705722	−	0.708489i	$-0.749377\pi$
$601$		−	851.603i		−	1.41698i	0.705722	−	0.708489i	$-0.250623\pi$
$602$		0			0
$603$	139.635			0.231566
$604$		0			0
$605$	−393.512	−	227.194i	−0.650433	−	0.375528i
$606$		0			0
$607$	202.282	−	116.788i	0.333249	−	0.192401i	−0.324034	−	0.946045i	$-0.605039\pi$
$607$	202.282	−	116.788i	0.333249	−	0.192401i	0.657282	+	0.753644i	$0.271706\pi$
$608$		0			0
$609$	−423.093	−	278.297i	−0.694734	−	0.456973i
$610$		0			0
$611$	−99.6571	−	172.611i	−0.163105	−	0.282506i
$612$		0			0
$613$	40.5620	−	70.2555i	0.0661697	−	0.114609i	−0.831043	−	0.556209i	$-0.812255\pi$
$613$	40.5620	−	70.2555i	0.0661697	−	0.114609i	0.897212	+	0.441600i	$0.145589\pi$
$614$		0			0
$615$		−	223.505i		−	0.363424i
$616$		0			0
$617$	47.2962			0.0766552			0.0383276	−	0.999265i	$-0.487797\pi$
$617$	47.2962			0.0766552			0.0383276	+	0.999265i	$0.487797\pi$
$618$		0			0
$619$	−569.331	−	328.703i	−0.919759	−	0.531023i	−0.0362006	−	0.999345i	$-0.511526\pi$
$619$	−569.331	−	328.703i	−0.919759	−	0.531023i	−0.883558	+	0.468322i	$0.844859\pi$
$620$		0			0
$621$	−927.239	+	535.342i	−1.49314	+	0.862064i
$622$		0			0
$623$	914.129	−	459.048i	1.46730	−	0.736834i
$624$		0			0
$625$	179.768	+	311.367i	0.287629	+	0.498188i
$626$		0			0
$627$	65.7194	−	113.829i	0.104816	−	0.181546i
$628$		0			0
$629$		−	198.285i		−	0.315239i
$630$		0			0
$631$	−270.276			−0.428330			−0.214165	−	0.976797i	$-0.568703\pi$
$631$	−270.276			−0.428330			−0.214165	+	0.976797i	$0.568703\pi$
$632$		0			0
$633$	307.076	+	177.290i	0.485112	+	0.280079i
$634$		0			0
$635$	829.165	−	478.718i	1.30577	−	0.753887i
$636$		0			0
$637$	33.5144	−	286.539i	0.0526129	−	0.449825i
$638$		0			0
$639$	−106.471	−	184.413i	−0.166621	−	0.288596i
$640$		0			0
$641$	−122.305	+	211.838i	−0.190803	+	0.330481i	−0.945517	−	0.325574i	$-0.894443\pi$
$641$	−122.305	+	211.838i	−0.190803	+	0.330481i	0.754713	+	0.656055i	$0.227776\pi$
$642$		0			0
$643$			358.233i			0.557128i	0.960418	+	0.278564i	$0.0898584\pi$
$643$			358.233i			0.557128i	−0.960418	+	0.278564i	$0.910142\pi$
$644$		0			0
$645$	579.913			0.899089
$646$		0			0
$647$	−1024.30	−	591.377i	−1.58315	−	0.914030i	−0.994397	−	0.105715i	$-0.966287\pi$
$647$	−1024.30	−	591.377i	−1.58315	−	0.914030i	−0.588750	−	0.808315i	$-0.700380\pi$
$648$		0			0
$649$	−191.189	+	110.383i	−0.294590	+	0.170081i
$650$		0			0
$651$	333.735	+	664.585i	0.512649	+	1.02087i
$652$		0			0
$653$	107.647	+	186.451i	0.164850	+	0.285529i	0.936602	−	0.350395i	$-0.113953\pi$
$653$	107.647	+	186.451i	0.164850	+	0.285529i	−0.771752	+	0.635924i	$0.780619\pi$
$654$		0			0
$655$	−362.663	+	628.151i	−0.553684	+	0.959009i
$656$		0			0
$657$			319.152i			0.485772i
$658$		0			0
$659$	254.983			0.386925			0.193462	−	0.981108i	$-0.438028\pi$
$659$	254.983			0.386925			0.193462	+	0.981108i	$0.438028\pi$
$660$		0			0
$661$	1077.04	+	621.830i	1.62941	+	0.940741i	0.984269	+	0.176679i	$0.0565353\pi$
$661$	1077.04	+	621.830i	1.62941	+	0.940741i	0.645142	+	0.764062i	$0.276798\pi$
$662$		0			0
$663$	−179.865	+	103.845i	−0.271290	+	0.156630i
$664$		0			0
$665$	250.750	−	381.214i	0.377067	−	0.573253i
$666$		0			0
$667$	−519.546	−	899.881i	−0.778930	−	1.34915i
$668$		0			0
$669$	347.456	−	601.812i	0.519367	−	0.899569i
$670$		0			0
$671$		−	96.6491i		−	0.144037i
$672$		0			0
$673$	−63.0354			−0.0936633			−0.0468317	−	0.998903i	$-0.514912\pi$
$673$	−63.0354			−0.0936633			−0.0468317	+	0.998903i	$0.514912\pi$
$674$		0			0
$675$	204.116	+	117.847i	0.302395	+	0.174588i
$676$		0			0
$677$	855.162	−	493.728i	1.26316	−	0.729288i	0.289479	−	0.957184i	$-0.406518\pi$
$677$	855.162	−	493.728i	1.26316	−	0.729288i	0.973685	+	0.227896i	$0.0731847\pi$
$678$		0			0
$679$	−4.62573	+	79.3669i	−0.00681256	+	0.116888i
$680$		0			0
$681$	−85.8322	−	148.666i	−0.126038	−	0.218305i
$682$		0			0
$683$	−467.447	+	809.642i	−0.684403	+	1.18542i	0.289221	+	0.957262i	$0.406604\pi$
$683$	−467.447	+	809.642i	−0.684403	+	1.18542i	−0.973624	+	0.228159i	$0.926730\pi$
$684$		0			0
$685$			1091.17i			1.59294i
$686$		0			0
$687$	−489.400			−0.712373
$688$		0			0
$689$	432.655	+	249.794i	0.627947	+	0.362545i
$690$		0			0
$691$	842.192	−	486.240i	1.21880	−	0.703676i	0.254140	−	0.967167i	$-0.418207\pi$
$691$	842.192	−	486.240i	1.21880	−	0.703676i	0.964662	+	0.263492i	$0.0848741\pi$
$692$		0			0
$693$	58.0210	+	3.38163i	0.0837243	+	0.00487969i
$694$		0			0
$695$	−551.258	−	954.806i	−0.793176	−	1.37382i
$696$		0			0
$697$	148.179	−	256.654i	0.212596	−	0.368227i
$698$		0			0
$699$		−	206.891i		−	0.295981i
$700$		0			0
$701$	−695.549			−0.992224			−0.496112	−	0.868259i	$-0.665239\pi$
$701$	−695.549			−0.992224			−0.496112	+	0.868259i	$0.665239\pi$
$702$		0			0
$703$	195.797	+	113.043i	0.278516	+	0.160801i
$704$		0			0
$705$	−306.895	+	177.186i	−0.435312	+	0.251328i
$706$		0			0
$707$	−245.033	−	161.175i	−0.346581	−	0.227970i
$708$		0			0
$709$	−78.6320	−	136.195i	−0.110905	−	0.192094i	0.805230	−	0.592962i	$-0.202042\pi$
$709$	−78.6320	−	136.195i	−0.110905	−	0.192094i	−0.916136	+	0.400869i	$0.868708\pi$
$710$		0			0
$711$	−89.4232	+	154.886i	−0.125771	+	0.217842i
$712$		0			0
$713$			1525.91i			2.14013i
$714$		0			0
$715$	79.2440			0.110831
$716$		0			0
$717$	49.7763	+	28.7384i	0.0694230	+	0.0400814i
$718$		0			0
$719$	183.553	−	105.975i	0.255290	−	0.147392i	−0.366894	−	0.930263i	$-0.619579\pi$
$719$	183.553	−	105.975i	0.255290	−	0.147392i	0.622184	+	0.782871i	$0.286246\pi$
$720$		0			0
$721$	−607.913	+	305.275i	−0.843153	+	0.423406i
$722$		0			0
$723$	−119.662	−	207.261i	−0.165508	−	0.286668i
$724$		0			0
$725$	−114.370	+	198.094i	−0.157751	+	0.273233i
$726$		0			0
$727$			271.507i			0.373462i	0.982411	+	0.186731i	$0.0597893\pi$
$727$			271.507i			0.373462i	−0.982411	+	0.186731i	$0.940211\pi$
$728$		0			0
$729$	−802.202			−1.10041
$730$		0			0
$731$	665.921	+	384.470i	0.910972	+	0.525950i
$732$		0			0
$733$	442.045	−	255.215i	0.603062	−	0.348178i	−0.167183	−	0.985926i	$-0.553467\pi$
$733$	442.045	−	255.215i	0.603062	−	0.348178i	0.770245	+	0.637748i	$0.220134\pi$
$734$		0			0
$735$	−509.454	−	59.5872i	−0.693134	−	0.0810711i
$736$		0			0
$737$	89.7965	+	155.532i	0.121841	+	0.211034i
$738$		0			0
$739$	−187.084	+	324.039i	−0.253158	+	0.438483i	−0.964394	−	0.264471i	$-0.914803\pi$
$739$	−187.084	+	324.039i	−0.253158	+	0.438483i	0.711235	+	0.702954i	$0.248136\pi$
$740$		0			0
$741$		−	236.811i		−	0.319583i
$742$		0			0
$743$	−792.307			−1.06636			−0.533181	−	0.846001i	$-0.679004\pi$
$743$	−792.307			−1.06636			−0.533181	+	0.846001i	$0.679004\pi$
$744$		0			0
$745$	6.93919	+	4.00634i	0.00931434	+	0.00537764i
$746$		0			0
$747$	−59.6879	+	34.4608i	−0.0799035	+	0.0461323i
$748$		0			0
$749$	262.126	+	521.986i	0.349967	+	0.696911i
$750$		0			0
$751$	13.1482	+	22.7733i	0.0175076	+	0.0303240i	0.874646	−	0.484761i	$-0.161094\pi$
$751$	13.1482	+	22.7733i	0.0175076	+	0.0303240i	−0.857139	+	0.515085i	$0.827760\pi$
$752$		0			0
$753$	402.440	−	697.046i	0.534449	−	0.925692i
$754$		0			0
$755$		−	413.133i		−	0.547196i
$756$		0			0
$757$	−1287.30			−1.70053			−0.850264	−	0.526356i	$-0.823558\pi$
$757$	−1287.30			−1.70053			−0.850264	+	0.526356i	$0.823558\pi$
$758$		0			0
$759$	−262.553	−	151.585i	−0.345920	−	0.199717i
$760$		0			0
$761$	839.569	−	484.726i	1.10324	−	0.636959i	0.166174	−	0.986097i	$-0.446859\pi$
$761$	839.569	−	484.726i	1.10324	−	0.636959i	0.937071	+	0.349138i	$0.113525\pi$
$762$		0			0
$763$	623.154	−	947.378i	0.816715	−	1.24165i
$764$		0			0
$765$	−72.6257	−	125.791i	−0.0949355	−	0.164433i
$766$		0			0
$767$	−198.875	+	344.461i	−0.259289	+	0.449102i
$768$		0			0
$769$		−	499.204i		−	0.649160i	−0.945858	−	0.324580i	$-0.894777\pi$
$769$		−	499.204i		−	0.649160i	0.945858	−	0.324580i	$-0.105223\pi$
$770$		0			0
$771$	119.603			0.155127
$772$		0			0
$773$	125.870	+	72.6713i	0.162834	+	0.0940120i	0.579202	−	0.815184i	$-0.303364\pi$
$773$	125.870	+	72.6713i	0.162834	+	0.0940120i	−0.416369	+	0.909196i	$0.636697\pi$
$774$		0			0
$775$	290.902	−	167.953i	0.375358	−	0.216713i
$776$		0			0
$777$	14.7875	−	253.720i	0.0190315	−	0.326537i
$778$		0			0
$779$	168.955	+	292.639i	0.216888	+	0.375660i
$780$		0			0
$781$	136.939	−	237.185i	0.175338	−	0.303694i
$782$		0			0
$783$		−	834.918i		−	1.06631i
$784$		0			0
$785$	−557.176			−0.709779
$786$		0			0
$787$	−333.132	−	192.334i	−0.423294	−	0.244389i	0.273192	−	0.961960i	$-0.411921\pi$
$787$	−333.132	−	192.334i	−0.423294	−	0.244389i	−0.696486	+	0.717571i	$0.745254\pi$
$788$		0			0
$789$	894.719	−	516.566i	1.13399	−	0.654710i
$790$		0			0
$791$	−190.429	−	11.0987i	−0.240744	−	0.0140313i
$792$		0			0
$793$	−87.0654	−	150.802i	−0.109792	−	0.190166i
$794$		0			0
$795$	444.122	−	769.243i	0.558645	−	0.967601i
$796$		0			0
$797$		−	9.29571i		−	0.0116634i	−0.999983	−	0.00583169i	$-0.998144\pi$
$797$		−	9.29571i		−	0.0116634i	0.999983	−	0.00583169i	$-0.00185629\pi$
$798$		0			0
$799$	−469.882			−0.588088
$800$		0			0
$801$	321.540	+	185.641i	0.401424	+	0.231762i
$802$		0			0
$803$	−355.488	+	205.241i	−0.442700	+	0.255593i
$804$		0			0
$805$	−879.288	−	578.366i	−1.09228	−	0.718468i
$806$		0			0
$807$	−422.530	−	731.844i	−0.523582	−	0.906870i
$808$		0			0
$809$	407.696	−	706.149i	0.503950	−	0.872867i	−0.496040	−	0.868300i	$-0.665213\pi$
$809$	407.696	−	706.149i	0.503950	−	0.872867i	0.999990	−	0.00456703i	$-0.00145374\pi$
$810$		0			0
$811$		−	762.398i		−	0.940071i	−0.882647	−	0.470036i	$-0.844241\pi$
$811$		−	762.398i		−	0.940071i	0.882647	−	0.470036i	$-0.155759\pi$
$812$		0			0
$813$	−181.271			−0.222965
$814$		0			0
$815$	−908.528	−	524.539i	−1.11476	−	0.643606i
$816$		0			0
$817$	−759.289	+	438.376i	−0.929362	+	0.536568i
$818$		0			0
$819$	93.5765	−	46.9913i	0.114257	−	0.0573764i
$820$		0			0
$821$	−561.968	−	973.358i	−0.684493	−	1.18558i	−0.973596	−	0.228278i	$-0.926690\pi$
$821$	−561.968	−	973.358i	−0.684493	−	1.18558i	0.289103	−	0.957298i	$-0.406643\pi$
$822$		0			0
$823$	166.411	−	288.232i	0.202200	−	0.350221i	−0.747037	−	0.664783i	$-0.768524\pi$
$823$	166.411	−	288.232i	0.202200	−	0.350221i	0.949237	+	0.314561i	$0.101857\pi$
$824$		0			0
$825$			66.7380i			0.0808945i
$826$		0			0
$827$	−451.741			−0.546241			−0.273120	−	0.961980i	$-0.588056\pi$
$827$	−451.741			−0.546241			−0.273120	+	0.961980i	$0.588056\pi$
$828$		0			0
$829$	−396.030	−	228.648i	−0.477720	−	0.275812i	0.241746	−	0.970340i	$-0.422280\pi$
$829$	−396.030	−	228.648i	−0.477720	−	0.275812i	−0.719466	+	0.694528i	$0.755613\pi$
$830$		0			0
$831$	−65.4024	+	37.7601i	−0.0787032	+	0.0454393i
$832$		0			0
$833$	−545.507	−	406.182i	−0.654870	−	0.487613i
$834$		0			0
$835$	−104.874	−	181.646i	−0.125597	−	0.217541i
$836$		0			0
$837$	−613.041	+	1061.82i	−0.732426	+	1.26860i
$838$		0			0
$839$		−	97.6089i		−	0.116340i	−0.998307	−	0.0581698i	$-0.981474\pi$
$839$		−	97.6089i		−	0.116340i	0.998307	−	0.0581698i	$-0.0185265\pi$
$840$		0			0
$841$	−30.7167			−0.0365240
$842$		0			0
$843$	19.9510	+	11.5187i	0.0236666	+	0.0136639i
$844$		0			0
$845$	−479.173	+	276.651i	−0.567068	+	0.327397i
$846$		0			0
$847$	−346.557	−	690.120i	−0.409159	−	0.814782i
$848$		0			0
$849$	−234.756	−	406.609i	−0.276509	−	0.478927i
$850$		0			0
$851$	260.740	−	451.615i	0.306392	−	0.530687i
$852$		0			0
$853$			832.329i			0.975766i	0.872909	+	0.487883i	$0.162231\pi$
$853$			832.329i			0.975766i	−0.872909	+	0.487883i	$0.837769\pi$
$854$		0			0
$855$	165.617			0.193704
$856$		0			0
$857$	−846.076	−	488.482i	−0.987253	−	0.569991i	−0.0828008	−	0.996566i	$-0.526387\pi$
$857$	−846.076	−	488.482i	−0.987253	−	0.569991i	−0.904452	+	0.426575i	$0.859720\pi$
$858$		0			0
$859$	604.432	−	348.969i	0.703646	−	0.406250i	−0.105058	−	0.994466i	$-0.533503\pi$
$859$	604.432	−	348.969i	0.703646	−	0.406250i	0.808704	+	0.588216i	$0.200169\pi$
$860$		0			0
$861$	208.746	−	317.356i	0.242446	−	0.368590i
$862$		0			0
$863$	−421.518	−	730.091i	−0.488434	−	0.845992i	0.511478	−	0.859296i	$-0.329098\pi$
$863$	−421.518	−	730.091i	−0.488434	−	0.845992i	−0.999911	+	0.0133047i	$0.995765\pi$
$864$		0			0
$865$	145.022	−	251.186i	0.167656	−	0.290388i
$866$		0			0
$867$		−	244.865i		−	0.282428i
$868$		0			0
$869$	−230.026			−0.264702
$870$		0			0
$871$	280.219	+	161.785i	0.321721	+	0.185746i
$872$		0			0
$873$	−24.9903	+	14.4282i	−0.0286258	+	0.0165271i
$874$		0			0
$875$	−55.4184	+	950.852i	−0.0633353	+	1.08669i
$876$		0			0
$877$	29.0573	+	50.3287i	0.0331326	+	0.0573873i	0.882116	−	0.471032i	$-0.156118\pi$
$877$	29.0573	+	50.3287i	0.0331326	+	0.0573873i	−0.848984	+	0.528419i	$0.822785\pi$
$878$		0			0
$879$	381.720	−	661.158i	0.434266	−	0.752171i
$880$		0			0
$881$			1034.35i			1.17406i	0.809565	+	0.587030i	$0.199703\pi$
$881$			1034.35i			1.17406i	−0.809565	+	0.587030i	$0.800297\pi$
$882$		0			0
$883$	−483.067			−0.547075			−0.273538	−	0.961861i	$-0.588194\pi$
$883$	−483.067			−0.547075			−0.273538	+	0.961861i	$0.588194\pi$
$884$		0			0
$885$	612.437	+	353.590i	0.692019	+	0.399537i
$886$		0			0
$887$	−381.611	+	220.323i	−0.430227	+	0.248392i	−0.699443	−	0.714688i	$-0.746569\pi$
$887$	−381.611	+	220.323i	−0.430227	+	0.248392i	0.269216	+	0.963080i	$0.413235\pi$
$888$		0			0
$889$	1624.44	+	94.6770i	1.82727	+	0.106498i
$890$		0			0
$891$	−84.4371	−	146.249i	−0.0947667	−	0.164141i
$892$		0			0
$893$	267.882	−	463.985i	0.299980	−	0.519580i
$894$		0			0
$895$			607.274i			0.678519i
$896$		0			0
$897$	−546.216			−0.608937
$898$		0			0
$899$	−1030.49	−	594.953i	−1.14626	−	0.661795i
$900$		0			0
$901$	1019.98	−	588.887i	1.13206	−	0.653593i
$902$		0			0
$903$	823.419	+	541.618i	0.911871	+	0.599798i
$904$		0			0
$905$	606.471	+	1050.44i	0.670134	+	1.16071i
$906$		0			0
$907$	−229.774	+	397.981i	−0.253334	+	0.438788i	−0.964442	−	0.264295i	$-0.914861\pi$
$907$	−229.774	+	397.981i	−0.253334	+	0.438788i	0.711107	+	0.703083i	$0.248194\pi$
$908$		0			0
$909$		−	106.454i		−	0.117111i
$910$		0			0
$911$	1515.03			1.66304			0.831518	−	0.555498i	$-0.187472\pi$
$911$	1515.03			1.66304			0.831518	+	0.555498i	$0.187472\pi$
$912$		0			0
$913$	−76.7685	−	44.3223i	−0.0840838	−	0.0485458i
$914$		0			0
$915$	−268.119	+	154.799i	−0.293026	+	0.169179i
$916$		0			0
$917$	−1101.62	+	553.199i	−1.20133	+	0.603270i
$918$		0			0
$919$	51.6821	+	89.5160i	0.0562373	+	0.0974058i	0.892773	−	0.450506i	$-0.148756\pi$
$919$	51.6821	+	89.5160i	0.0562373	+	0.0974058i	−0.836536	+	0.547912i	$0.815423\pi$
$920$		0			0
$921$	496.083	−	859.241i	0.538635	−	0.932944i
$922$		0			0
$923$		−	493.441i		−	0.534605i
$924$		0			0
$925$	−114.795			−0.124103
$926$		0			0
$927$	−213.831	−	123.455i	−0.230669	−	0.133177i
$928$		0			0
$929$	1171.77	−	676.521i	1.26132	−	0.728225i	0.287992	−	0.957633i	$-0.407012\pi$
$929$	1171.77	−	676.521i	1.26132	−	0.728225i	0.973330	+	0.229408i	$0.0736791\pi$
$930$		0			0
$931$	712.080	−	307.095i	0.764855	−	0.329855i
$932$		0			0
$933$	−122.090	−	211.466i	−0.130857	−	0.226651i
$934$		0			0
$935$	93.4086	−	161.788i	0.0999023	−	0.173036i
$936$		0			0
$937$			1443.67i			1.54074i	0.637600	+	0.770368i	$0.279927\pi$
$937$			1443.67i			1.54074i	−0.637600	+	0.770368i	$0.720073\pi$
$938$		0			0
$939$	−1232.33			−1.31239
$940$		0			0
$941$	1097.89	+	633.869i	1.16673	+	0.673612i	0.952908	−	0.303261i	$-0.0980753\pi$
$941$	1097.89	+	633.869i	1.16673	+	0.673612i	0.213822	+	0.976873i	$0.431409\pi$
$942$		0			0
$943$	674.987	−	389.704i	0.715787	−	0.413260i
$944$		0			0
$945$	−379.498	−	755.717i	−0.401585	−	0.799700i
$946$		0			0
$947$	−200.712	−	347.643i	−0.211945	−	0.367099i	0.740378	−	0.672190i	$-0.234646\pi$
$947$	−200.712	−	347.643i	−0.211945	−	0.367099i	−0.952323	+	0.305091i	$0.901313\pi$
$948$		0			0
$949$	−369.779	+	640.476i	−0.389651	+	0.674896i
$950$		0			0
$951$			172.677i			0.181574i
$952$		0			0
$953$	−1544.95			−1.62115			−0.810573	−	0.585637i	$-0.800844\pi$
$953$	−1544.95			−1.62115			−0.810573	+	0.585637i	$0.800844\pi$
$954$		0			0
$955$	−401.352	−	231.721i	−0.420264	−	0.242639i
$956$		0			0
$957$	204.739	−	118.206i	0.213938	−	0.123517i
$958$		0			0
$959$	−1019.11	+	1549.35i	−1.06268	+	1.61559i
$960$		0			0
$961$	393.193	+	681.030i	0.409150	+	0.708668i
$962$		0			0
$963$	−106.005	+	183.606i	−0.110078	+	0.190661i
$964$		0			0
$965$		−	525.090i		−	0.544135i
$966$		0			0
$967$	1272.03			1.31544			0.657718	−	0.753264i	$-0.271522\pi$
$967$	1272.03			1.31544			0.657718	+	0.753264i	$0.271522\pi$
$968$		0			0
$969$	−483.485	−	279.140i	−0.498953	−	0.288070i
$970$		0			0
$971$	−916.173	+	528.953i	−0.943536	+	0.544751i	−0.891067	−	0.453872i	$-0.850042\pi$
$971$	−916.173	+	528.953i	−0.943536	+	0.544751i	−0.0524687	+	0.998623i	$0.516709\pi$
$972$		0			0
$973$	109.023	−	1870.59i	0.112048	−	1.92249i
$974$		0			0
$975$	60.1203	+	104.131i	0.0616618	+	0.106801i
$976$		0			0
$977$	−227.645	+	394.293i	−0.233004	+	0.403575i	−0.958691	−	0.284450i	$-0.908189\pi$
$977$	−227.645	+	394.293i	−0.233004	+	0.403575i	0.725687	+	0.688025i	$0.241522\pi$
$978$		0			0
$979$			477.531i			0.487774i
$980$		0			0
$981$	411.585			0.419557
$982$		0			0
$983$	938.128	+	541.628i	0.954352	+	0.550995i	0.894430	−	0.447208i	$-0.147582\pi$
$983$	938.128	+	541.628i	0.954352	+	0.550995i	0.0599216	+	0.998203i	$0.480915\pi$
$984$		0			0
$985$	−1045.62	+	603.690i	−1.06154	+	0.612883i
$986$		0			0
$987$	−601.247	−	35.0424i	−0.609166	−	0.0355039i
$988$		0			0
$989$	1011.14	+	1751.34i	1.02238	+	1.77082i
$990$		0			0
$991$	555.040	−	961.358i	0.560081	−	0.970088i	−0.437408	−	0.899263i	$-0.644103\pi$
$991$	555.040	−	961.358i	0.560081	−	0.970088i	0.997489	−	0.0708253i	$-0.0225633\pi$
$992$		0			0
$993$			674.180i			0.678933i
$994$		0			0
$995$	40.1249			0.0403265
$996$		0			0
$997$	1332.56	+	769.353i	1.33657	+	0.771668i	0.986297	−	0.164980i	$-0.0527559\pi$
$997$	1332.56	+	769.353i	1.33657	+	0.771668i	0.350272	+	0.936648i	$0.386089\pi$
$998$		0			0
$999$	362.875	−	209.506i	0.363238	−	0.209716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.3.s.h.129.6		16
4.3	odd	2	inner	448.3.s.h.129.3		16
7.5	odd	6	inner	448.3.s.h.257.6		16
8.3	odd	2		224.3.s.b.129.6	yes	16
8.5	even	2		224.3.s.b.129.3	yes	16
28.19	even	6	inner	448.3.s.h.257.3		16
56.3	even	6		1568.3.c.g.97.11		16
56.5	odd	6		224.3.s.b.33.3	✓	16
56.11	odd	6		1568.3.c.g.97.6		16
56.19	even	6		224.3.s.b.33.6	yes	16
56.45	odd	6		1568.3.c.g.97.5		16
56.53	even	6		1568.3.c.g.97.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.b.33.3	✓	16	56.5	odd	6
224.3.s.b.33.6	yes	16	56.19	even	6
224.3.s.b.129.3	yes	16	8.5	even	2
224.3.s.b.129.6	yes	16	8.3	odd	2
448.3.s.h.129.3		16	4.3	odd	2	inner
448.3.s.h.129.6		16	1.1	even	1	trivial
448.3.s.h.257.3		16	28.19	even	6	inner
448.3.s.h.257.6		16	7.5	odd	6	inner
1568.3.c.g.97.5		16	56.45	odd	6
1568.3.c.g.97.6		16	56.11	odd	6
1568.3.c.g.97.11		16	56.3	even	6
1568.3.c.g.97.12		16	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.20101 + 1.27075i) q^{3} +(-3.56697 + 2.05939i) q^{5} +(-6.98814 - 0.407289i) q^{7} +(-1.27038 - 2.20036i) q^{9} +O(q^{10})\)	\(q+(2.20101 + 1.27075i) q^{3} +(-3.56697 + 2.05939i) q^{5} +(-6.98814 - 0.407289i) q^{7} +(-1.27038 - 2.20036i) q^{9} +(1.63392 - 2.83003i) q^{11} -5.88759i q^{13} -10.4679 q^{15} +(-12.0204 - 6.93999i) q^{17} +(13.7058 - 7.91304i) q^{19} +(-14.8634 - 9.77664i) q^{21} +(-18.2518 - 31.6131i) q^{23} +(-4.01784 + 6.95910i) q^{25} -29.3309i q^{27} +28.4655 q^{29} +(-36.2014 - 20.9009i) q^{31} +(7.19253 - 4.15261i) q^{33} +(25.7652 - 12.9385i) q^{35} +(7.14285 + 12.3718i) q^{37} +(7.48167 - 12.9586i) q^{39} +21.3515i q^{41} -55.3992 q^{43} +(9.06280 + 5.23241i) q^{45} +(29.3178 - 16.9266i) q^{47} +(48.6682 + 5.69238i) q^{49} +(-17.6380 - 30.5499i) q^{51} +(-42.4271 + 73.4859i) q^{53} +13.4595i q^{55} +40.2220 q^{57} +(-58.5062 - 33.7786i) q^{59} +(25.6135 - 14.7879i) q^{61} +(7.98140 + 15.8938i) q^{63} +(12.1248 + 21.0008i) q^{65} +(-27.4789 + 47.5949i) q^{67} -92.7741i q^{69} +83.8102 q^{71} +(-108.784 - 62.8065i) q^{73} +(-17.6866 + 10.2113i) q^{75} +(-12.5707 + 19.1112i) q^{77} +(-35.1955 - 60.9604i) q^{79} +(25.8389 - 44.7542i) q^{81} -27.1264i q^{83} +57.1685 q^{85} +(62.6527 + 36.1726i) q^{87} +(-126.553 + 73.0654i) q^{89} +(-2.39795 + 41.1433i) q^{91} +(-53.1196 - 92.0059i) q^{93} +(-32.5920 + 56.4511i) q^{95} -11.3574i q^{97} -8.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{9}+O(q^{10}) \) 16 * q + 40 * q^9	\( 16 q + 40 q^{9} - 48 q^{17} + 136 q^{21} + 80 q^{25} + 16 q^{29} - 264 q^{33} - 72 q^{37} - 312 q^{45} + 128 q^{49} - 40 q^{53} + 368 q^{57} - 216 q^{61} - 168 q^{65} - 312 q^{73} - 64 q^{77} - 384 q^{81} + 1072 q^{85} + 24 q^{89} + 168 q^{93}+O(q^{100}) \) 16 * q + 40 * q^9 - 48 * q^17 + 136 * q^21 + 80 * q^25 + 16 * q^29 - 264 * q^33 - 72 * q^37 - 312 * q^45 + 128 * q^49 - 40 * q^53 + 368 * q^57 - 216 * q^61 - 168 * q^65 - 312 * q^73 - 64 * q^77 - 384 * q^81 + 1072 * q^85 + 24 * q^89 + 168 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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