LMFDB - Embedded newform 224.3.s.b.33.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(33,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("224.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.s (of order $6$, degree $2$, 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:	$6.10355792167$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			33.3
Root			$1.20279 + 1.51093i$ of defining polynomial
Character	$\chi$	$=$	224.33
Dual form			224.3.s.b.129.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.20101 + 1.27075i) q^{3} +(3.56697 + 2.05939i) q^{5} +(-6.98814 + 0.407289i) q^{7} +(-1.27038 + 2.20036i) q^{9} +O(q^{10})$	\(q+(-2.20101 + 1.27075i) q^{3} +(3.56697 + 2.05939i) q^{5} +(-6.98814 + 0.407289i) q^{7} +(-1.27038 + 2.20036i) q^{9} +(-1.63392 - 2.83003i) q^{11} -5.88759i q^{13} -10.4679 q^{15} +(-12.0204 + 6.93999i) q^{17} +(-13.7058 - 7.91304i) q^{19} +(14.8634 - 9.77664i) q^{21} +(-18.2518 + 31.6131i) q^{23} +(-4.01784 - 6.95910i) q^{25} -29.3309i q^{27} -28.4655 q^{29} +(-36.2014 + 20.9009i) q^{31} +(7.19253 + 4.15261i) q^{33} +(-25.7652 - 12.9385i) q^{35} +(-7.14285 + 12.3718i) q^{37} +(7.48167 + 12.9586i) q^{39} -21.3515i q^{41} +55.3992 q^{43} +(-9.06280 + 5.23241i) q^{45} +(29.3178 + 16.9266i) q^{47} +(48.6682 - 5.69238i) q^{49} +(17.6380 - 30.5499i) q^{51} +(42.4271 + 73.4859i) q^{53} -13.4595i q^{55} +40.2220 q^{57} +(58.5062 - 33.7786i) q^{59} +(-25.6135 - 14.7879i) q^{61} +(7.98140 - 15.8938i) q^{63} +(12.1248 - 21.0008i) q^{65} +(27.4789 + 47.5949i) q^{67} -92.7741i q^{69} +83.8102 q^{71} +(-108.784 + 62.8065i) q^{73} +(17.6866 + 10.2113i) q^{75} +(12.5707 + 19.1112i) q^{77} +(-35.1955 + 60.9604i) q^{79} +(25.8389 + 44.7542i) q^{81} -27.1264i q^{83} -57.1685 q^{85} +(62.6527 - 36.1726i) q^{87} +(-126.553 - 73.0654i) q^{89} +(2.39795 + 41.1433i) q^{91} +(53.1196 - 92.0059i) q^{93} +(-32.5920 - 56.4511i) q^{95} +11.3574i q^{97} +8.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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	$-0.805895\pi$
$3$	−2.20101	+	1.27075i	−0.733669	+	0.423584i	0.0860939	+	0.996287i	$0.472561\pi$
$4$		0			0
$5$	3.56697	+	2.05939i	0.713393	+	0.411878i	0.812316	−	0.583217i	$-0.198206\pi$
$5$	3.56697	+	2.05939i	0.713393	+	0.411878i	−0.0989230	+	0.995095i	$0.531540\pi$
$6$		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	$-0.214123\pi$
$11$	−1.63392	−	2.83003i	−0.148538	−	0.257275i	−0.930687	+	0.365816i	$0.880790\pi$
$12$		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	−0.809980	−	0.586458i	$-0.800522\pi$
$17$	−12.0204	+	6.93999i	−0.707083	+	0.408234i	0.102897	+	0.994692i	$0.467189\pi$
$18$		0			0
$19$	−13.7058	−	7.91304i	−0.721357	−	0.416476i	0.0938951	−	0.995582i	$-0.470068\pi$
$19$	−13.7058	−	7.91304i	−0.721357	−	0.416476i	−0.815252	+	0.579107i	$0.803402\pi$
$20$		0			0
$21$	14.8634	−	9.77664i	0.707780	−	0.465554i
$22$		0			0
$23$	−18.2518	+	31.6131i	−0.793557	+	1.37448i	0.130194	+	0.991488i	$0.458440\pi$
$23$	−18.2518	+	31.6131i	−0.793557	+	1.37448i	−0.923751	+	0.382993i	$0.874894\pi$
$24$		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	$-0.663290\pi$
$29$	−28.4655			−0.981568			−0.490784	+	0.871281i	$0.663290\pi$
$30$		0			0
$31$	−36.2014	+	20.9009i	−1.16779	+	0.674222i	−0.953158	−	0.302474i	$-0.902187\pi$
$31$	−36.2014	+	20.9009i	−1.16779	+	0.674222i	−0.214629	+	0.976696i	$0.568854\pi$
$32$		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	$-0.895171\pi$
$37$	−7.14285	+	12.3718i	−0.193050	+	0.334372i	0.753210	+	0.657781i	$0.228505\pi$
$38$		0			0
$39$	7.48167	+	12.9586i	0.191838	+	0.332273i
$40$		0			0
$41$		−	21.3515i		−	0.520769i	−0.965505	−	0.260385i	$-0.916151\pi$
$41$		−	21.3515i		−	0.520769i	0.965505	−	0.260385i	$-0.0838493\pi$
$42$		0			0
$43$	55.3992			1.28835			0.644177	−	0.764877i	$-0.277200\pi$
$43$	55.3992			1.28835			0.644177	+	0.764877i	$0.277200\pi$
$44$		0			0
$45$	−9.06280	+	5.23241i	−0.201395	+	0.116276i
$46$		0			0
$47$	29.3178	+	16.9266i	0.623783	+	0.360141i	0.778340	−	0.627843i	$-0.216062\pi$
$47$	29.3178	+	16.9266i	0.623783	+	0.360141i	−0.154558	+	0.987984i	$0.549395\pi$
$48$		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	0.919280	+	0.393605i	$0.128772\pi$
$53$	42.4271	+	73.4859i	0.800512	+	1.38653i	−0.118768	+	0.992922i	$0.537894\pi$
$54$		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	$-0.472633\pi$
$59$	58.5062	−	33.7786i	0.991631	−	0.572518i	0.905761	+	0.423788i	$0.139300\pi$
$60$		0			0
$61$	−25.6135	−	14.7879i	−0.419893	−	0.242425i	0.275139	−	0.961405i	$-0.411276\pi$
$61$	−25.6135	−	14.7879i	−0.419893	−	0.242425i	−0.695032	+	0.718979i	$0.744610\pi$
$62$		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	$-0.0321489\pi$
$67$	27.4789	+	47.5949i	0.410133	+	0.710371i	−0.584771	+	0.811198i	$0.698816\pi$
$68$		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	−0.999937	−	0.0112159i	$-0.996430\pi$
$73$	−108.784	+	62.8065i	−1.49019	+	0.860363i	−0.490255	+	0.871579i	$0.663096\pi$
$74$		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	−0.998088	−	0.0618128i	$-0.980312\pi$
$79$	−35.1955	+	60.9604i	−0.445512	+	0.771650i	0.552575	+	0.833463i	$0.313645\pi$
$80$		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	−0.425478	−	0.904969i	$-0.639894\pi$
$89$	−126.553	−	73.0654i	−1.42194	−	0.820959i	−0.996465	+	0.0840094i	$0.973227\pi$
$90$		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	$0.0186455\pi$
$97$			11.3574i			0.117086i	−0.998285	+	0.0585431i	$0.981354\pi$
$98$		0			0
$99$	8.30278			0.0838664
$100$		0			0
$101$	−36.2851	+	20.9492i	−0.359258	+	0.207418i	−0.668755	−	0.743482i	$-0.733173\pi$
$101$	−36.2851	+	20.9492i	−0.359258	+	0.207418i	0.309497	+	0.950900i	$0.399839\pi$
$102$		0			0
$103$	84.1601	+	48.5899i	0.817089	+	0.471746i	0.849412	−	0.527731i	$-0.176957\pi$
$103$	84.1601	+	48.5899i	0.817089	+	0.471746i	−0.0323227	+	0.999477i	$0.510290\pi$
$104$		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	$-0.705835\pi$
$107$	41.7218	−	72.2643i	0.389924	−	0.675368i	0.992439	+	0.122740i	$0.0391680\pi$
$108$		0			0
$109$	80.9965	+	140.290i	0.743088	+	1.28707i	0.951083	+	0.308936i	$0.0999728\pi$
$109$	80.9965	+	140.290i	0.743088	+	1.28707i	−0.207995	+	0.978130i	$0.566694\pi$
$110$		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	$-0.567961\pi$
$131$	−152.509	−	88.0512i	−1.16419	−	0.672146i	−0.952305	+	0.305148i	$0.901294\pi$
$132$		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	0.704479	+	0.709725i	$0.251181\pi$
$137$	132.462	+	229.432i	0.966879	+	1.67468i	0.262400	+	0.964959i	$0.415486\pi$
$138$		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	$-0.831255\pi$
$149$	0.972701	−	1.68477i	0.00652820	−	0.0113072i	0.869271	+	0.494336i	$0.164589\pi$
$150$		0			0
$151$	−50.1524	−	86.8665i	−0.332135	−	0.575275i	0.650795	−	0.759253i	$-0.274436\pi$
$151$	−50.1524	−	86.8665i	−0.332135	−	0.575275i	−0.982930	+	0.183978i	$0.941102\pi$
$152$		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	$-0.808442\pi$
$157$	−117.153	+	67.6386i	−0.746200	+	0.430819i	0.0781191	+	0.996944i	$0.475109\pi$
$158$		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	0.149873	+	0.988705i	$0.452114\pi$
$163$	−127.353	+	220.582i	−0.781307	+	1.35326i	−0.931180	+	0.364559i	$0.881220\pi$
$164$		0			0
$165$	17.1037	+	29.6244i	0.103659	+	0.179542i
$166$		0			0
$167$		−	50.9246i		−	0.304938i	−0.988308	−	0.152469i	$-0.951278\pi$
$167$		−	50.9246i		−	0.304938i	0.988308	−	0.152469i	$-0.0487224\pi$
$168$		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	$-0.268093\pi$
$173$	60.9855	+	35.2100i	0.352517	+	0.203526i	−0.313276	+	0.949662i	$0.601427\pi$
$174$		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	$-0.301782\pi$
$179$	−73.7202	−	127.687i	−0.411845	−	0.713336i	−0.995092	+	0.0989591i	$0.968449\pi$
$180$		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	−0.680328	−	0.732908i	$-0.738163\pi$
$191$	56.2595	−	97.4444i	0.294553	−	0.510180i	0.974881	+	0.222728i	$0.0714961\pi$
$192$		0			0
$193$	−63.7435	−	110.407i	−0.330277	−	0.572057i	0.652289	−	0.757970i	$-0.273809\pi$
$193$	−63.7435	−	110.407i	−0.330277	−	0.572057i	−0.982566	+	0.185914i	$0.940475\pi$
$194$		0			0
$195$			61.6307i			0.316055i
$196$		0			0
$197$	−293.140			−1.48802			−0.744011	−	0.668167i	$-0.767079\pi$
$197$	−293.140			−1.48802			−0.744011	+	0.668167i	$0.767079\pi$
$198$		0			0
$199$	−8.43677	+	4.87097i	−0.0423958	+	0.0244772i	−0.521048	−	0.853527i	$-0.674459\pi$
$199$	−8.43677	+	4.87097i	−0.0423958	+	0.0244772i	0.478652	+	0.878005i	$0.341125\pi$
$200$		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	$-0.607253\pi$
$211$	−139.516			−0.661214			−0.330607	+	0.943769i	$0.607253\pi$
$212$		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	$0.210062\pi$
$223$			273.426i			1.22612i	−0.790035	+	0.613062i	$0.789938\pi$
$224$		0			0
$225$	20.4167			0.0907409
$226$		0			0
$227$	58.4952	−	33.7722i	0.257688	−	0.148776i	−0.365591	−	0.930775i	$-0.619133\pi$
$227$	58.4952	−	33.7722i	0.257688	−	0.148776i	0.623279	+	0.781999i	$0.285800\pi$
$228$		0			0
$229$	166.765	+	96.2816i	0.728230	+	0.420444i	0.817774	−	0.575539i	$-0.195208\pi$
$229$	166.765	+	96.2816i	0.728230	+	0.420444i	−0.0895442	+	0.995983i	$0.528541\pi$
$230$		0			0
$231$	−51.9537	−	26.0896i	−0.224908	−	0.112942i
$232$		0			0
$233$	−40.7024	+	70.4987i	−0.174689	+	0.302569i	−0.940053	−	0.341027i	$-0.889225\pi$
$233$	−40.7024	+	70.4987i	−0.174689	+	0.302569i	0.765365	+	0.643597i	$0.222559\pi$
$234$		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	−0.659557	−	0.751655i	$-0.729256\pi$
$241$	−81.5504	+	47.0832i	−0.338384	+	0.195366i	0.321173	+	0.947020i	$0.395923\pi$
$242$		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	0.577190	−	0.816610i	$-0.304149\pi$
$257$	40.7550	+	23.5299i	0.158580	+	0.0915560i	−0.418610	+	0.908166i	$0.637483\pi$
$258$		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	0.936011	+	0.351972i	$0.114489\pi$
$263$	203.252	+	352.043i	0.772822	+	1.33857i	−0.163189	+	0.986595i	$0.552178\pi$
$264$		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	$-0.454595\pi$
$269$	287.957	−	166.252i	1.07047	−	0.618038i	0.928311	+	0.371806i	$0.121261\pi$
$270$		0			0
$271$	−61.7686	−	35.6621i	−0.227928	−	0.131595i	0.381688	−	0.924291i	$-0.375343\pi$
$271$	−61.7686	−	35.6621i	−0.227928	−	0.131595i	−0.609616	+	0.792697i	$0.708676\pi$
$272$		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	$-0.149585\pi$
$277$	14.8574	+	25.7337i	0.0536367	+	0.0929015i	−0.837960	+	0.545731i	$0.816252\pi$
$278$		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	$-0.560834\pi$
$283$	159.988	−	92.3689i	0.565327	−	0.326392i	0.755281	+	0.655401i	$0.227500\pi$
$284$		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	−0.627769	−	0.778400i	$-0.716032\pi$
$311$	−83.2050	+	48.0384i	−0.267540	+	0.154464i	0.360229	+	0.932864i	$0.382699\pi$
$312$		0			0
$313$	−419.921	−	242.442i	−1.34160	−	0.774574i	−0.354559	−	0.935034i	$-0.615369\pi$
$313$	−419.921	−	242.442i	−1.34160	−	0.774574i	−0.987042	+	0.160460i	$0.948702\pi$
$314$		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	$-0.867511\pi$
$317$	−33.9714	+	58.8401i	−0.107165	+	0.185616i	0.807456	+	0.589928i	$0.200844\pi$
$318$		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	$-0.964569\pi$
$331$	−132.634	+	229.729i	−0.400707	+	0.694046i	0.593104	+	0.805126i	$0.297902\pi$
$332$		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	−0.669563	−	0.742755i	$-0.733519\pi$
$347$	−339.375	−	587.815i	−0.978026	−	1.69399i	−0.308463	−	0.951236i	$-0.599815\pi$
$348$		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	−0.181675	−	0.983359i	$-0.558152\pi$
$353$	204.423	−	118.024i	0.579102	−	0.334345i	0.760776	+	0.649014i	$0.224818\pi$
$354$		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	0.347818	+	0.937562i	$0.386923\pi$
$359$	−229.058	+	396.740i	−0.638044	+	1.10512i	−0.985861	+	0.167562i	$0.946410\pi$
$360$		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	−0.899506	−	0.436909i	$-0.856073\pi$
$367$	−356.315	+	205.718i	−0.970885	+	0.560541i	−0.0713791	+	0.997449i	$0.522740\pi$
$368$		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	$-0.840074\pi$
$373$	−7.89853	+	13.6807i	−0.0211757	+	0.0366774i	0.855243	+	0.518227i	$0.173408\pi$
$374$		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	$-0.705139\pi$
$379$	−455.384			−1.20154			−0.600770	+	0.799422i	$0.705139\pi$
$380$		0			0
$381$	511.639	−	295.395i	1.34288	−	0.775314i
$382$		0			0
$383$	158.732	+	91.6439i	0.414443	+	0.239279i	0.692697	−	0.721229i	$-0.256422\pi$
$383$	158.732	+	91.6439i	0.414443	+	0.239279i	−0.278254	+	0.960508i	$0.589756\pi$
$384$		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	$-0.0900357\pi$
$389$	92.7471	+	160.643i	0.238424	+	0.412963i	−0.721838	+	0.692062i	$0.756702\pi$
$390$		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	$-0.351653\pi$
$397$	−39.5520	−	22.8353i	−0.0996271	−	0.0575197i	−0.548986	+	0.835832i	$0.684986\pi$
$398$		0			0
$399$	−281.077	+	16.3820i	−0.704454	+	0.0410576i
$400$		0			0
$401$	−19.2312	+	33.3094i	−0.0479580	+	0.0830657i	−0.889008	−	0.457892i	$-0.848605\pi$
$401$	−19.2312	+	33.3094i	−0.0479580	+	0.0830657i	0.841050	+	0.540958i	$0.181938\pi$
$402$		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	−0.666960	−	0.745094i	$-0.732405\pi$
$409$	−145.264	+	83.8684i	−0.355169	+	0.205057i	0.311790	+	0.950151i	$0.399071\pi$
$410$		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	$-0.391867\pi$
$421$	280.567			0.666430			0.333215	+	0.942851i	$0.391867\pi$
$422$		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	0.705693	−	0.708517i	$-0.250636\pi$
$431$	−112.382	−	194.651i	−0.260747	−	0.451627i	−0.966441	+	0.256890i	$0.917302\pi$
$432$		0			0
$433$			731.236i			1.68877i	0.535739	+	0.844383i	$0.320033\pi$
$433$			731.236i			1.68877i	−0.535739	+	0.844383i	$0.679967\pi$
$434$		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	0.174668	−	0.984627i	$-0.444115\pi$
$439$	−259.322	−	149.720i	−0.590711	−	0.341047i	−0.765379	+	0.643580i	$0.777448\pi$
$440$		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	$-0.980886\pi$
$443$	−198.077	+	343.080i	−0.447127	+	0.774447i	0.551070	+	0.834459i	$0.314220\pi$
$444$		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	−0.997930	−	0.0643128i	$-0.979514\pi$
$457$	−202.574	+	350.868i	−0.443268	+	0.767763i	0.554661	+	0.832076i	$0.312848\pi$
$458$		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	$-0.325913\pi$
$467$	18.8539	+	10.8853i	0.0403723	+	0.0233090i	−0.479678	+	0.877445i	$0.659247\pi$
$468$		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	0.0532389	−	0.998582i	$-0.483046\pi$
$479$	452.490	−	261.245i	0.944656	−	0.545397i	0.891417	+	0.453185i	$0.149712\pi$
$480$		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	−0.889916	−	0.456125i	$-0.849237\pi$
$487$	−409.067	−	708.525i	−0.839974	−	1.45488i	0.0499421	−	0.998752i	$-0.484096\pi$
$488$		0			0
$489$		−	647.337i		−	1.32380i
$490$		0			0
$491$	−762.002			−1.55194			−0.775969	−	0.630771i	$-0.782739\pi$
$491$	−762.002			−1.55194			−0.775969	+	0.630771i	$0.782739\pi$
$492$		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	$-0.817064\pi$
$499$	25.4935	−	44.1560i	0.0510891	−	0.0884889i	0.890439	+	0.455103i	$0.150397\pi$
$500$		0			0
$501$	64.7126	+	112.086i	0.129167	+	0.223724i
$502$		0			0
$503$			305.233i			0.606825i	0.952859	+	0.303413i	$0.0981260\pi$
$503$			305.233i			0.606825i	−0.952859	+	0.303413i	$0.901874\pi$
$504$		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	$-0.276514\pi$
$509$	156.536	+	90.3761i	0.307536	+	0.177556i	−0.338287	+	0.941043i	$0.609848\pi$
$510$		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	−0.769168	−	0.639047i	$-0.779329\pi$
$521$	−312.767	+	180.576i	−0.600321	+	0.346595i	0.168847	+	0.985642i	$0.445996\pi$
$522$		0			0
$523$	566.506	+	327.072i	1.08318	+	0.625377i	0.931754	−	0.363091i	$-0.118279\pi$
$523$	566.506	+	327.072i	1.08318	+	0.625377i	0.151431	+	0.988468i	$0.451612\pi$
$524$		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	0.440135	+	0.897931i	$0.354930\pi$
$541$	−301.642	+	522.459i	−0.557564	+	0.965729i	−0.997699	+	0.0677973i	$0.978403\pi$
$542$		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	$-0.284197\pi$
$547$	686.167			1.25442			0.627209	+	0.778851i	$0.284197\pi$
$548$		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	−0.966707	−	0.255885i	$-0.917633\pi$
$557$	−392.661	−	680.108i	−0.704956	−	1.22102i	0.261751	−	0.965135i	$-0.415700\pi$
$558$		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	$-0.534548\pi$
$563$	393.226	−	227.029i	0.698447	−	0.403249i	0.806769	+	0.590867i	$0.201214\pi$
$564$		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	−0.832935	−	0.553371i	$-0.813341\pi$
$569$	35.7137	−	61.8580i	0.0627658	−	0.108713i	0.895701	+	0.444657i	$0.146675\pi$
$570$		0			0
$571$	−359.033	−	621.864i	−0.628780	−	1.08908i	−0.987797	−	0.155748i	$-0.950221\pi$
$571$	−359.033	−	621.864i	−0.628780	−	1.08908i	0.359017	−	0.933331i	$-0.383112\pi$
$572$		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	0.372808	−	0.927909i	$-0.378395\pi$
$577$	786.338	−	453.993i	1.36280	−	0.786815i	0.989996	+	0.141093i	$0.0450617\pi$
$578$		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	0.840945	−	0.541120i	$-0.182000\pi$
$593$	470.127	+	271.428i	0.792794	+	0.457720i	−0.0481510	+	0.998840i	$0.515333\pi$
$594$		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	0.831348	−	0.555752i	$-0.187570\pi$
$599$	−39.3074	−	68.0824i	−0.0656216	−	0.113660i	−0.896970	+	0.442092i	$0.854236\pi$
$600$		0			0
$601$			851.603i			1.41698i	0.705722	+	0.708489i	$0.250623\pi$
$601$			851.603i			1.41698i	−0.705722	+	0.708489i	$0.749377\pi$
$602$		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	0.657282	−	0.753644i	$-0.271706\pi$
$607$	202.282	+	116.788i	0.333249	+	0.192401i	−0.324034	+	0.946045i	$0.605039\pi$
$608$		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	$-0.187745\pi$
$613$	−40.5620	−	70.2555i	−0.0661697	−	0.114609i	−0.897212	+	0.441600i	$0.854411\pi$
$614$		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	$-0.488474\pi$
$619$	569.331	−	328.703i	0.919759	−	0.531023i	0.883558	+	0.468322i	$0.155141\pi$
$620$		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	0.754713	−	0.656055i	$-0.227776\pi$
$641$	−122.305	−	211.838i	−0.190803	−	0.330481i	−0.945517	+	0.325574i	$0.894443\pi$
$642$		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	−0.588750	+	0.808315i	$0.700380\pi$
$647$	−1024.30	+	591.377i	−1.58315	+	0.914030i	−0.994397	+	0.105715i	$0.966287\pi$
$648$		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	$-0.886047\pi$
$653$	−107.647	+	186.451i	−0.164850	+	0.285529i	0.771752	+	0.635924i	$0.219381\pi$
$654$		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	$-0.561972\pi$
$659$	−254.983			−0.386925			−0.193462	+	0.981108i	$0.561972\pi$
$660$		0			0
$661$	−1077.04	+	621.830i	−1.62941	+	0.940741i	−0.645142	+	0.764062i	$0.723202\pi$
$661$	−1077.04	+	621.830i	−1.62941	+	0.940741i	−0.984269	+	0.176679i	$0.943465\pi$
$662$		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	$-0.593482\pi$
$677$	−855.162	−	493.728i	−1.26316	−	0.729288i	−0.973685	+	0.227896i	$0.926815\pi$
$678$		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	0.973624	+	0.228159i	$0.0732705\pi$
$683$	467.447	+	809.642i	0.684403	+	1.18542i	−0.289221	+	0.957262i	$0.593396\pi$
$684$		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	$-0.581793\pi$
$691$	−842.192	−	486.240i	−1.21880	−	0.703676i	−0.964662	+	0.263492i	$0.915126\pi$
$692$		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	$-0.334761\pi$
$701$	695.549			0.992224			0.496112	+	0.868259i	$0.334761\pi$
$702$		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	$-0.797958\pi$
$709$	78.6320	−	136.195i	0.110905	−	0.192094i	0.916136	+	0.400869i	$0.131292\pi$
$710$		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	0.622184	−	0.782871i	$-0.286246\pi$
$719$	183.553	+	105.975i	0.255290	+	0.147392i	−0.366894	+	0.930263i	$0.619579\pi$
$720$		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	$-0.940211\pi$
$727$		−	271.507i		−	0.373462i	0.982411	−	0.186731i	$-0.0597893\pi$
$728$		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	$-0.446533\pi$
$733$	−442.045	−	255.215i	−0.603062	−	0.348178i	−0.770245	+	0.637748i	$0.779866\pi$
$734$		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	$-0.0851973\pi$
$739$	187.084	+	324.039i	0.253158	+	0.438483i	−0.711235	+	0.702954i	$0.751864\pi$
$740$		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	−0.857139	−	0.515085i	$-0.827760\pi$
$751$	13.1482	−	22.7733i	0.0175076	−	0.0303240i	0.874646	+	0.484761i	$0.161094\pi$
$752$		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	$-0.176442\pi$
$757$	1287.30			1.70053			0.850264	+	0.526356i	$0.176442\pi$
$758$		0			0
$759$	−262.553	+	151.585i	−0.345920	+	0.199717i
$760$		0			0
$761$	839.569	+	484.726i	1.10324	+	0.636959i	0.937071	−	0.349138i	$-0.113525\pi$
$761$	839.569	+	484.726i	1.10324	+	0.636959i	0.166174	+	0.986097i	$0.446859\pi$
$762$		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	$0.105223\pi$
$769$			499.204i			0.649160i	−0.945858	+	0.324580i	$0.894777\pi$
$770$		0			0
$771$	−119.603			−0.155127
$772$		0			0
$773$	−125.870	+	72.6713i	−0.162834	+	0.0940120i	−0.579202	−	0.815184i	$-0.696636\pi$
$773$	−125.870	+	72.6713i	−0.162834	+	0.0940120i	0.416369	+	0.909196i	$0.363303\pi$
$774$		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	$-0.588079\pi$
$787$	333.132	−	192.334i	0.423294	−	0.244389i	0.696486	+	0.717571i	$0.254746\pi$
$788$		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	0.999990	+	0.00456703i	$0.00145374\pi$
$809$	407.696	+	706.149i	0.503950	+	0.872867i	−0.496040	+	0.868300i	$0.665213\pi$
$810$		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	−0.289103	−	0.957298i	$-0.593357\pi$
$821$	561.968	−	973.358i	0.684493	−	1.18558i	0.973596	−	0.228278i	$-0.0733095\pi$
$822$		0			0
$823$	166.411	+	288.232i	0.202200	+	0.350221i	0.949237	−	0.314561i	$-0.101857\pi$
$823$	166.411	+	288.232i	0.202200	+	0.350221i	−0.747037	+	0.664783i	$0.768524\pi$
$824$		0			0
$825$		−	66.7380i		−	0.0808945i
$826$		0			0
$827$	451.741			0.546241			0.273120	−	0.961980i	$-0.411944\pi$
$827$	451.741			0.546241			0.273120	+	0.961980i	$0.411944\pi$
$828$		0			0
$829$	396.030	−	228.648i	0.477720	−	0.275812i	−0.241746	−	0.970340i	$-0.577720\pi$
$829$	396.030	−	228.648i	0.477720	−	0.275812i	0.719466	+	0.694528i	$0.244387\pi$
$830$		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	$0.0185265\pi$
$839$			97.6089i			0.116340i	−0.998307	+	0.0581698i	$0.981474\pi$
$840$		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	−0.904452	−	0.426575i	$-0.859720\pi$
$857$	−846.076	+	488.482i	−0.987253	+	0.569991i	−0.0828008	+	0.996566i	$0.526387\pi$
$858$		0			0
$859$	−604.432	−	348.969i	−0.703646	−	0.406250i	0.105058	−	0.994466i	$-0.466497\pi$
$859$	−604.432	−	348.969i	−0.703646	−	0.406250i	−0.808704	+	0.588216i	$0.799831\pi$
$860$		0			0
$861$	−208.746	−	317.356i	−0.242446	−	0.368590i
$862$		0			0
$863$	−421.518	+	730.091i	−0.488434	+	0.845992i	−0.999911	−	0.0133047i	$-0.995765\pi$
$863$	−421.518	+	730.091i	−0.488434	+	0.845992i	0.511478	+	0.859296i	$0.329098\pi$
$864$		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	$-0.843882\pi$
$877$	−29.0573	+	50.3287i	−0.0331326	+	0.0573873i	0.848984	+	0.528419i	$0.177215\pi$
$878$		0			0
$879$	381.720	+	661.158i	0.434266	+	0.752171i
$880$		0			0
$881$		−	1034.35i		−	1.17406i	−0.809565	−	0.587030i	$-0.800297\pi$
$881$		−	1034.35i		−	1.17406i	0.809565	−	0.587030i	$-0.199703\pi$
$882$		0			0
$883$	483.067			0.547075			0.273538	−	0.961861i	$-0.411806\pi$
$883$	483.067			0.547075			0.273538	+	0.961861i	$0.411806\pi$
$884$		0			0
$885$	−612.437	+	353.590i	−0.692019	+	0.399537i
$886$		0			0
$887$	−381.611	−	220.323i	−0.430227	−	0.248392i	0.269216	−	0.963080i	$-0.413235\pi$
$887$	−381.611	−	220.323i	−0.430227	−	0.248392i	−0.699443	+	0.714688i	$0.746569\pi$
$888$		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	$-0.0851393\pi$
$907$	229.774	+	397.981i	0.253334	+	0.438788i	−0.711107	+	0.703083i	$0.751806\pi$
$908$		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	−0.836536	−	0.547912i	$-0.815423\pi$
$919$	51.6821	−	89.5160i	0.0562373	−	0.0974058i	0.892773	+	0.450506i	$0.148756\pi$
$920$		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	0.973330	−	0.229408i	$-0.0736791\pi$
$929$	1171.77	+	676.521i	1.26132	+	0.728225i	0.287992	+	0.957633i	$0.407012\pi$
$930$		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	$-0.720073\pi$
$937$		−	1443.67i		−	1.54074i	0.637600	−	0.770368i	$-0.279927\pi$
$938$		0			0
$939$	1232.33			1.31239
$940$		0			0
$941$	−1097.89	+	633.869i	−1.16673	+	0.673612i	−0.952908	−	0.303261i	$-0.901925\pi$
$941$	−1097.89	+	633.869i	−1.16673	+	0.673612i	−0.213822	+	0.976873i	$0.568591\pi$
$942$		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	$-0.765354\pi$
$947$	200.712	−	347.643i	0.211945	−	0.367099i	0.952323	+	0.305091i	$0.0986869\pi$
$948$		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	$-0.149958\pi$
$971$	916.173	+	528.953i	0.943536	+	0.544751i	0.0524687	+	0.998623i	$0.483291\pi$
$972$		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	0.725687	−	0.688025i	$-0.241522\pi$
$977$	−227.645	−	394.293i	−0.233004	−	0.403575i	−0.958691	+	0.284450i	$0.908189\pi$
$978$		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	0.0599216	−	0.998203i	$-0.480915\pi$
$983$	938.128	−	541.628i	0.954352	−	0.550995i	0.894430	+	0.447208i	$0.147582\pi$
$984$		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	0.997489	+	0.0708253i	$0.0225633\pi$
$991$	555.040	+	961.358i	0.560081	+	0.970088i	−0.437408	+	0.899263i	$0.644103\pi$
$992$		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	$-0.947244\pi$
$997$	−1332.56	+	769.353i	−1.33657	+	0.771668i	−0.350272	+	0.936648i	$0.613911\pi$
$998$		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	224.3.s.b.33.3	✓	16
4.3	odd	2	inner	224.3.s.b.33.6	yes	16
7.2	even	3		1568.3.c.g.97.5		16
7.3	odd	6	inner	224.3.s.b.129.3	yes	16
7.5	odd	6		1568.3.c.g.97.12		16
8.3	odd	2		448.3.s.h.257.3		16
8.5	even	2		448.3.s.h.257.6		16
28.3	even	6	inner	224.3.s.b.129.6	yes	16
28.19	even	6		1568.3.c.g.97.6		16
28.23	odd	6		1568.3.c.g.97.11		16
56.3	even	6		448.3.s.h.129.3		16
56.45	odd	6		448.3.s.h.129.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.b.33.3	✓	16	1.1	even	1	trivial
224.3.s.b.33.6	yes	16	4.3	odd	2	inner
224.3.s.b.129.3	yes	16	7.3	odd	6	inner
224.3.s.b.129.6	yes	16	28.3	even	6	inner
448.3.s.h.129.3		16	56.3	even	6
448.3.s.h.129.6		16	56.45	odd	6
448.3.s.h.257.3		16	8.3	odd	2
448.3.s.h.257.6		16	8.5	even	2
1568.3.c.g.97.5		16	7.2	even	3
1568.3.c.g.97.6		16	28.19	even	6
1568.3.c.g.97.11		16	28.23	odd	6
1568.3.c.g.97.12		16	7.5	odd	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.s (of order \(6\), degree \(2\), 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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