LMFDB - Embedded newform 224.3.o.c.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(79,224)]

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([3, 3, 2]))

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

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

chi := DirichletCharacter("224.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.o (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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2x^{10} - 12x^{9} + 12x^{8} - 12x^{7} + 148x^{6} - 48x^{5} + 192x^{4} - 768x^{3} + 512x^{2} + 4096 $ x^12 + 2x^10 - 12x^9 + 12x^8 - 12x^7 + 148x^6 - 48x^5 + 192x^4 - 768x^3 + 512*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.1
Root			$1.71059 + 1.03628i$ of defining polynomial
Character	$\chi$	$=$	224.79
Dual form			224.3.o.c.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25274 - 3.90186i) q^{3} +(-6.07099 - 3.50509i) q^{5} +(-2.51181 - 6.53382i) q^{7} +(-5.64968 + 9.78553i) q^{9} +O(q^{10})$	\(q+(-2.25274 - 3.90186i) q^{3} +(-6.07099 - 3.50509i) q^{5} +(-2.51181 - 6.53382i) q^{7} +(-5.64968 + 9.78553i) q^{9} +(7.90242 + 13.6874i) q^{11} +2.90039i q^{13} +31.5842i q^{15} +(1.65516 + 2.86682i) q^{17} +(8.10854 - 14.0444i) q^{19} +(-19.8356 + 24.5197i) q^{21} +(-16.4804 - 9.51498i) q^{23} +(12.0713 + 20.9081i) q^{25} +10.3597 q^{27} +21.1392i q^{29} +(-23.6995 + 13.6829i) q^{31} +(35.6042 - 61.6683i) q^{33} +(-7.65245 + 48.4709i) q^{35} +(-15.2932 - 8.82951i) q^{37} +(11.3169 - 6.53382i) q^{39} +1.13482 q^{41} -50.2084 q^{43} +(68.5983 - 39.6053i) q^{45} +(0.657646 + 0.379692i) q^{47} +(-36.3816 + 32.8234i) q^{49} +(7.45728 - 12.9164i) q^{51} +(38.9677 - 22.4980i) q^{53} -110.795i q^{55} -73.0658 q^{57} +(1.19239 + 2.06529i) q^{59} +(-86.1653 - 49.7476i) q^{61} +(78.1278 + 12.3346i) q^{63} +(10.1661 - 17.6082i) q^{65} +(-33.2440 - 57.5804i) q^{67} +85.7391i q^{69} +44.4376i q^{71} +(-0.859703 - 1.48905i) q^{73} +(54.3870 - 94.2011i) q^{75} +(69.5816 - 86.0131i) q^{77} +(62.9171 + 36.3252i) q^{79} +(27.5094 + 47.6476i) q^{81} +102.081 q^{83} -23.2059i q^{85} +(82.4821 - 47.6211i) q^{87} +(30.6865 - 53.1505i) q^{89} +(18.9506 - 7.28522i) q^{91} +(106.778 + 61.6480i) q^{93} +(-98.4538 + 56.8423i) q^{95} -102.826 q^{97} -178.584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 8 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 8 * q^9	$ 12 q - 6 q^{3} - 8 q^{9} + 14 q^{11} - 82 q^{17} + 94 q^{19} + 116 q^{25} + 60 q^{27} + 146 q^{33} - 270 q^{35} + 120 q^{41} - 40 q^{43} - 204 q^{49} + 106 q^{51} - 372 q^{57} - 62 q^{59} - 64 q^{65} + 178 q^{67} + 54 q^{73} - 140 q^{75} + 206 q^{81} + 392 q^{83} - 26 q^{89} + 88 q^{91} - 184 q^{97} - 872 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 - 8 * q^9 + 14 * q^11 - 82 * q^17 + 94 * q^19 + 116 * q^25 + 60 * q^27 + 146 * q^33 - 270 * q^35 + 120 * q^41 - 40 * q^43 - 204 * q^49 + 106 * q^51 - 372 * q^57 - 62 * q^59 - 64 * q^65 + 178 * q^67 + 54 * q^73 - 140 * q^75 + 206 * q^81 + 392 * q^83 - 26 * q^89 + 88 * q^91 - 184 * q^97 - 872 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.25274	−	3.90186i	−0.750913	−	1.30062i	−0.947380	−	0.320110i	$-0.896280\pi$
$3$	−2.25274	−	3.90186i	−0.750913	−	1.30062i	0.196467	−	0.980510i	$-0.437053\pi$
$4$		0			0
$5$	−6.07099	−	3.50509i	−1.21420	−	0.701018i	−0.250528	−	0.968109i	$-0.580604\pi$
$5$	−6.07099	−	3.50509i	−1.21420	−	0.701018i	−0.963671	+	0.267092i	$0.913937\pi$
$6$		0			0
$7$	−2.51181	−	6.53382i	−0.358830	−	0.933403i
$7$	−2.51181	−	6.53382i	−0.358830	−	0.933403i
$8$		0			0
$9$	−5.64968	+	9.78553i	−0.627742	+	1.08728i
$10$		0			0
$11$	7.90242	+	13.6874i	0.718402	+	1.24431i	0.961633	+	0.274340i	$0.0884593\pi$
$11$	7.90242	+	13.6874i	0.718402	+	1.24431i	−0.243231	+	0.969968i	$0.578207\pi$
$12$		0			0
$13$			2.90039i			0.223107i	0.993758	+	0.111553i	$0.0355826\pi$
$13$			2.90039i			0.223107i	−0.993758	+	0.111553i	$0.964417\pi$
$14$		0			0
$15$			31.5842i			2.10562i
$16$		0			0
$17$	1.65516	+	2.86682i	0.0973623	+	0.168636i	0.910592	−	0.413306i	$-0.135626\pi$
$17$	1.65516	+	2.86682i	0.0973623	+	0.168636i	−0.813230	+	0.581943i	$0.802293\pi$
$18$		0			0
$19$	8.10854	−	14.0444i	0.426765	−	0.739179i	−0.569818	−	0.821771i	$-0.692986\pi$
$19$	8.10854	−	14.0444i	0.426765	−	0.739179i	0.996583	+	0.0825915i	$0.0263197\pi$
$20$		0			0
$21$	−19.8356	+	24.5197i	−0.944553	+	1.16761i
$22$		0			0
$23$	−16.4804	−	9.51498i	−0.716540	−	0.413695i	0.0969377	−	0.995290i	$-0.469095\pi$
$23$	−16.4804	−	9.51498i	−0.716540	−	0.413695i	−0.813478	+	0.581596i	$0.802429\pi$
$24$		0			0
$25$	12.0713	+	20.9081i	0.482852	+	0.836325i
$26$		0			0
$27$	10.3597			0.383693
$28$		0			0
$29$			21.1392i			0.728937i	0.931216	+	0.364468i	$0.118749\pi$
$29$			21.1392i			0.728937i	−0.931216	+	0.364468i	$0.881251\pi$
$30$		0			0
$31$	−23.6995	+	13.6829i	−0.764499	+	0.441384i	−0.830909	−	0.556409i	$-0.812179\pi$
$31$	−23.6995	+	13.6829i	−0.764499	+	0.441384i	0.0664095	+	0.997792i	$0.478846\pi$
$32$		0			0
$33$	35.6042	−	61.6683i	1.07891	−	1.86874i
$34$		0			0
$35$	−7.65245	+	48.4709i	−0.218641	+	1.38488i
$36$		0			0
$37$	−15.2932	−	8.82951i	−0.413328	−	0.238635i	0.278890	−	0.960323i	$-0.410033\pi$
$37$	−15.2932	−	8.82951i	−0.413328	−	0.238635i	−0.692219	+	0.721688i	$0.743367\pi$
$38$		0			0
$39$	11.3169	−	6.53382i	0.290177	−	0.167534i
$40$		0			0
$41$	1.13482			0.0276785			0.0138392	−	0.999904i	$-0.495595\pi$
$41$	1.13482			0.0276785			0.0138392	+	0.999904i	$0.495595\pi$
$42$		0			0
$43$	−50.2084			−1.16764			−0.583818	−	0.811884i	$-0.698442\pi$
$43$	−50.2084			−1.16764			−0.583818	+	0.811884i	$0.698442\pi$
$44$		0			0
$45$	68.5983	−	39.6053i	1.52441	−	0.880117i
$46$		0			0
$47$	0.657646	+	0.379692i	0.0139925	+	0.00807855i	0.506980	−	0.861958i	$-0.330762\pi$
$47$	0.657646	+	0.379692i	0.0139925	+	0.00807855i	−0.492987	+	0.870036i	$0.664095\pi$
$48$		0			0
$49$	−36.3816	+	32.8234i	−0.742482	+	0.669866i
$50$		0			0
$51$	7.45728	−	12.9164i	0.146221	−	0.253263i
$52$		0			0
$53$	38.9677	−	22.4980i	0.735240	−	0.424491i	−0.0850958	−	0.996373i	$-0.527120\pi$
$53$	38.9677	−	22.4980i	0.735240	−	0.424491i	0.820336	+	0.571882i	$0.193786\pi$
$54$		0			0
$55$		−	110.795i		−	2.01445i
$56$		0			0
$57$	−73.0658			−1.28186
$58$		0			0
$59$	1.19239	+	2.06529i	0.0202101	+	0.0350048i	0.875954	−	0.482395i	$-0.160233\pi$
$59$	1.19239	+	2.06529i	0.0202101	+	0.0350048i	−0.855743	+	0.517400i	$0.826900\pi$
$60$		0			0
$61$	−86.1653	−	49.7476i	−1.41255	−	0.815534i	−0.416919	−	0.908944i	$-0.636890\pi$
$61$	−86.1653	−	49.7476i	−1.41255	−	0.815534i	−0.995628	+	0.0934097i	$0.970223\pi$
$62$		0			0
$63$	78.1278	+	12.3346i	1.24012	+	0.195787i
$64$		0			0
$65$	10.1661	−	17.6082i	0.156402	−	0.270896i
$66$		0			0
$67$	−33.2440	−	57.5804i	−0.496180	−	0.859408i	0.503811	−	0.863814i	$-0.331931\pi$
$67$	−33.2440	−	57.5804i	−0.496180	−	0.859408i	−0.999990	+	0.00440572i	$0.998598\pi$
$68$		0			0
$69$			85.7391i			1.24260i
$70$		0			0
$71$			44.4376i			0.625882i	0.949773	+	0.312941i	$0.101314\pi$
$71$			44.4376i			0.625882i	−0.949773	+	0.312941i	$0.898686\pi$
$72$		0			0
$73$	−0.859703	−	1.48905i	−0.0117768	−	0.0203979i	0.860077	−	0.510164i	$-0.170415\pi$
$73$	−0.859703	−	1.48905i	−0.0117768	−	0.0203979i	−0.871854	+	0.489766i	$0.837082\pi$
$74$		0			0
$75$	54.3870	−	94.2011i	0.725161	−	1.25602i
$76$		0			0
$77$	69.5816	−	86.0131i	0.903657	−	1.11705i
$78$		0			0
$79$	62.9171	+	36.3252i	0.796418	+	0.459812i	0.842217	−	0.539138i	$-0.181250\pi$
$79$	62.9171	+	36.3252i	0.796418	+	0.459812i	−0.0457989	+	0.998951i	$0.514583\pi$
$80$		0			0
$81$	27.5094	+	47.6476i	0.339622	+	0.588243i
$82$		0			0
$83$	102.081			1.22990			0.614948	−	0.788568i	$-0.289177\pi$
$83$	102.081			1.22990			0.614948	+	0.788568i	$0.289177\pi$
$84$		0			0
$85$		−	23.2059i		−	0.273011i
$86$		0			0
$87$	82.4821	−	47.6211i	0.948070	−	0.547369i
$88$		0			0
$89$	30.6865	−	53.1505i	0.344792	−	0.597197i	−0.640524	−	0.767938i	$-0.721283\pi$
$89$	30.6865	−	53.1505i	0.344792	−	0.597197i	0.985316	+	0.170741i	$0.0546162\pi$
$90$		0			0
$91$	18.9506	−	7.28522i	0.208249	−	0.0800574i
$92$		0			0
$93$	106.778	+	61.6480i	1.14815	+	0.662882i
$94$		0			0
$95$	−98.4538	+	56.8423i	−1.03636	+	0.598340i
$96$		0			0
$97$	−102.826			−1.06006			−0.530030	−	0.847979i	$-0.677819\pi$
$97$	−102.826			−1.06006			−0.530030	+	0.847979i	$0.677819\pi$
$98$		0			0
$99$	−178.584			−1.80388
$100$		0			0
$101$	−157.651	+	91.0197i	−1.56090	+	0.901185i	−0.563731	+	0.825958i	$0.690635\pi$
$101$	−157.651	+	91.0197i	−1.56090	+	0.901185i	−0.997166	+	0.0752264i	$0.976032\pi$
$102$		0			0
$103$	−39.7104	−	22.9268i	−0.385538	−	0.222591i	0.294687	−	0.955594i	$-0.404785\pi$
$103$	−39.7104	−	22.9268i	−0.385538	−	0.222591i	−0.680225	+	0.733003i	$0.738118\pi$
$104$		0			0
$105$	206.366	−	79.3336i	1.96539	−	0.755558i
$106$		0			0
$107$	−36.9463	+	63.9928i	−0.345292	+	0.598064i	−0.985407	−	0.170216i	$-0.945554\pi$
$107$	−36.9463	+	63.9928i	−0.345292	+	0.598064i	0.640115	+	0.768279i	$0.278887\pi$
$108$		0			0
$109$	104.724	−	60.4622i	0.960767	−	0.554699i	0.0643577	−	0.997927i	$-0.479500\pi$
$109$	104.724	−	60.4622i	0.960767	−	0.554699i	0.896409	+	0.443228i	$0.146167\pi$
$110$		0			0
$111$			79.5623i			0.716778i
$112$		0			0
$113$	−97.7663			−0.865188			−0.432594	−	0.901589i	$-0.642402\pi$
$113$	−97.7663			−0.865188			−0.432594	+	0.901589i	$0.642402\pi$
$114$		0			0
$115$	66.7017	+	115.531i	0.580015	+	1.00462i
$116$		0			0
$117$	−28.3818	−	16.3863i	−0.242580	−	0.140053i
$118$		0			0
$119$	14.5738	−	18.0154i	0.122469	−	0.151390i
$120$		0			0
$121$	−64.3964	+	111.538i	−0.532202	+	0.921801i
$122$		0			0
$123$	−2.55645	−	4.42790i	−0.0207841	−	0.0359992i
$124$		0			0
$125$			6.01041i			0.0480833i
$126$		0			0
$127$		−	175.050i		−	1.37835i	−0.724595	−	0.689175i	$-0.757973\pi$
$127$		−	175.050i		−	1.37835i	0.724595	−	0.689175i	$-0.242027\pi$
$128$		0			0
$129$	113.106	+	195.906i	0.876794	+	1.51865i
$130$		0			0
$131$	−4.30993	+	7.46501i	−0.0329002	+	0.0569848i	−0.882007	−	0.471237i	$-0.843808\pi$
$131$	−4.30993	+	7.46501i	−0.0329002	+	0.0569848i	0.849106	+	0.528222i	$0.177141\pi$
$132$		0			0
$133$	−112.131	−	17.7029i	−0.843088	−	0.133104i
$134$		0			0
$135$	−62.8937	−	36.3117i	−0.465879	−	0.268975i
$136$		0			0
$137$	−128.042	−	221.776i	−0.934615	−	1.61880i	−0.775320	−	0.631569i	$-0.782411\pi$
$137$	−128.042	−	221.776i	−0.934615	−	1.61880i	−0.159295	−	0.987231i	$-0.550922\pi$
$138$		0			0
$139$	−218.834			−1.57434			−0.787171	−	0.616735i	$-0.788455\pi$
$139$	−218.834			−1.57434			−0.787171	+	0.616735i	$0.788455\pi$
$140$		0			0
$141$		−	3.42139i		−	0.0242652i
$142$		0			0
$143$	−39.6987	+	22.9201i	−0.277614	+	0.160280i
$144$		0			0
$145$	74.0947	−	128.336i	0.510998	−	0.885074i
$146$		0			0
$147$	210.031	+	68.0134i	1.42878	+	0.462676i
$148$		0			0
$149$	20.6792	+	11.9391i	0.138786	+	0.0801284i	0.567785	−	0.823177i	$-0.307800\pi$
$149$	20.6792	+	11.9391i	0.138786	+	0.0801284i	−0.428999	+	0.903305i	$0.641134\pi$
$150$		0			0
$151$	−158.916	+	91.7504i	−1.05243	+	0.607619i	−0.923328	−	0.384013i	$-0.874542\pi$
$151$	−158.916	+	91.7504i	−1.05243	+	0.607619i	−0.129099	+	0.991632i	$0.541208\pi$
$152$		0			0
$153$	−37.4044			−0.244474
$154$		0			0
$155$	191.839			1.23767
$156$		0			0
$157$	143.703	−	82.9671i	0.915307	−	0.528453i	0.0331720	−	0.999450i	$-0.489439\pi$
$157$	143.703	−	82.9671i	0.915307	−	0.528453i	0.882135	+	0.470997i	$0.156106\pi$
$158$		0			0
$159$	−175.568	−	101.364i	−1.10420	−	0.637512i
$160$		0			0
$161$	−20.7735	+	131.580i	−0.129028	+	0.817267i
$162$		0			0
$163$	−5.05216	+	8.75059i	−0.0309948	+	0.0536846i	−0.881107	−	0.472917i	$-0.843201\pi$
$163$	−5.05216	+	8.75059i	−0.0309948	+	0.0536846i	0.850112	+	0.526602i	$0.176534\pi$
$164$		0			0
$165$	−432.306	+	249.592i	−2.62003	+	1.51268i
$166$		0			0
$167$			285.049i			1.70688i	0.521190	+	0.853441i	$0.325488\pi$
$167$			285.049i			1.70688i	−0.521190	+	0.853441i	$0.674512\pi$
$168$		0			0
$169$	160.588			0.950223
$170$		0			0
$171$	91.6213	+	158.693i	0.535797	+	0.928028i
$172$		0			0
$173$	84.3266	+	48.6860i	0.487437	+	0.281422i	0.723511	−	0.690313i	$-0.242527\pi$
$173$	84.3266	+	48.6860i	0.487437	+	0.281422i	−0.236074	+	0.971735i	$0.575861\pi$
$174$		0			0
$175$	106.289	−	131.389i	0.607366	−	0.750794i
$176$		0			0
$177$	5.37230	−	9.30510i	0.0303520	−	0.0525712i
$178$		0			0
$179$	−150.908	−	261.380i	−0.843061	−	1.46022i	−0.887295	−	0.461203i	$-0.847418\pi$
$179$	−150.908	−	261.380i	−0.843061	−	1.46022i	0.0442343	−	0.999021i	$-0.485915\pi$
$180$		0			0
$181$		−	60.4535i		−	0.333997i	−0.985957	−	0.166999i	$-0.946592\pi$
$181$		−	60.4535i		−	0.333997i	0.985957	−	0.166999i	$-0.0534076\pi$
$182$		0			0
$183$			448.273i			2.44958i
$184$		0			0
$185$	61.8964	+	107.208i	0.334575	+	0.579501i
$186$		0			0
$187$	−26.1595	+	45.3096i	−0.139890	+	0.242297i
$188$		0			0
$189$	−26.0216	−	67.6884i	−0.137680	−	0.358140i
$190$		0			0
$191$	−63.5769	−	36.7062i	−0.332864	−	0.192179i	0.324248	−	0.945972i	$-0.394889\pi$
$191$	−63.5769	−	36.7062i	−0.332864	−	0.192179i	−0.657112	+	0.753793i	$0.728222\pi$
$192$		0			0
$193$	−32.5446	−	56.3690i	−0.168625	−	0.292067i	0.769312	−	0.638874i	$-0.220599\pi$
$193$	−32.5446	−	56.3690i	−0.168625	−	0.292067i	−0.937937	+	0.346807i	$0.887266\pi$
$194$		0			0
$195$	−91.6065			−0.469777
$196$		0			0
$197$			348.324i			1.76814i	0.467355	+	0.884070i	$0.345207\pi$
$197$			348.324i			1.76814i	−0.467355	+	0.884070i	$0.654793\pi$
$198$		0			0
$199$	225.265	−	130.057i	1.13198	−	0.653551i	0.187550	−	0.982255i	$-0.439945\pi$
$199$	225.265	−	130.057i	1.13198	−	0.653551i	0.944433	+	0.328704i	$0.106612\pi$
$200$		0			0
$201$	−149.780	+	259.427i	−0.745176	+	1.29068i
$202$		0			0
$203$	138.120	−	53.0976i	0.680392	−	0.261564i
$204$		0			0
$205$	−6.88946	−	3.97763i	−0.0336071	−	0.0194031i
$206$		0			0
$207$	186.218	−	107.513i	0.899605	−	0.519387i
$208$		0			0
$209$	256.308			1.22636
$210$		0			0
$211$	−4.73025			−0.0224182			−0.0112091	−	0.999937i	$-0.503568\pi$
$211$	−4.73025			−0.0224182			−0.0112091	+	0.999937i	$0.503568\pi$
$212$		0			0
$213$	173.390	−	100.106i	0.814035	−	0.469983i
$214$		0			0
$215$	304.815	+	175.985i	1.41774	+	0.818534i
$216$		0			0
$217$	148.930	+	120.479i	0.686314	+	0.555204i
$218$		0			0
$219$	−3.87337	+	6.70888i	−0.0176866	+	0.0306342i
$220$		0			0
$221$	−8.31489	+	4.80060i	−0.0376239	+	0.0217222i
$222$		0			0
$223$		−	109.315i		−	0.490200i	−0.969498	−	0.245100i	$-0.921179\pi$
$223$		−	109.315i		−	0.490200i	0.969498	−	0.245100i	$-0.0788209\pi$
$224$		0			0
$225$	−272.796			−1.21243
$226$		0			0
$227$	−60.7205	−	105.171i	−0.267491	−	0.463308i	0.700722	−	0.713434i	$-0.252861\pi$
$227$	−60.7205	−	105.171i	−0.267491	−	0.463308i	−0.968213	+	0.250126i	$0.919528\pi$
$228$		0			0
$229$	−124.878	−	72.0983i	−0.545319	−	0.314840i	0.201913	−	0.979403i	$-0.435284\pi$
$229$	−124.878	−	72.0983i	−0.545319	−	0.314840i	−0.747232	+	0.664564i	$0.768617\pi$
$230$		0			0
$231$	−492.360	−	77.7325i	−2.13143	−	0.336504i
$232$		0			0
$233$	−97.1309	+	168.236i	−0.416871	+	0.722042i	−0.995623	−	0.0934621i	$-0.970207\pi$
$233$	−97.1309	+	168.236i	−0.416871	+	0.722042i	0.578752	+	0.815504i	$0.303540\pi$
$234$		0			0
$235$	−2.66171	−	4.61021i	−0.0113264	−	0.0196179i
$236$		0			0
$237$		−	327.325i		−	1.38112i
$238$		0			0
$239$		−	315.567i		−	1.32036i	−0.751106	−	0.660181i	$-0.770479\pi$
$239$		−	315.567i		−	1.32036i	0.751106	−	0.660181i	$-0.229521\pi$
$240$		0			0
$241$	−181.356	−	314.117i	−0.752513	−	1.30339i	−0.946601	−	0.322406i	$-0.895508\pi$
$241$	−181.356	−	314.117i	−0.752513	−	1.30339i	0.194089	−	0.980984i	$-0.437825\pi$
$242$		0			0
$243$	170.562	−	295.421i	0.701900	−	1.21573i
$244$		0			0
$245$	335.922	−	71.7499i	1.37111	−	0.292857i
$246$		0			0
$247$	40.7342	+	23.5179i	0.164916	+	0.0952143i
$248$		0			0
$249$	−229.963	−	398.307i	−0.923545	−	1.59963i
$250$		0			0
$251$	9.04237			0.0360254			0.0180127	−	0.999838i	$-0.494266\pi$
$251$	9.04237			0.0360254			0.0180127	+	0.999838i	$0.494266\pi$
$252$		0			0
$253$		−	300.765i		−	1.18880i
$254$		0			0
$255$	−90.5463	+	52.2769i	−0.355083	+	0.205007i
$256$		0			0
$257$	185.539	−	321.363i	0.721942	−	1.25044i	−0.238279	−	0.971197i	$-0.576583\pi$
$257$	185.539	−	321.363i	0.721942	−	1.25044i	0.960221	−	0.279243i	$-0.0900834\pi$
$258$		0			0
$259$	−19.2769	+	122.101i	−0.0744283	+	0.471432i
$260$		0			0
$261$	−206.858	−	119.430i	−0.792559	−	0.457584i
$262$		0			0
$263$	410.392	−	236.940i	1.56043	−	0.900912i	0.563212	−	0.826313i	$-0.309566\pi$
$263$	410.392	−	236.940i	1.56043	−	0.900912i	0.997214	−	0.0745993i	$-0.0237678\pi$
$264$		0			0
$265$	−315.431			−1.19030
$266$		0			0
$267$	−276.515			−1.03563
$268$		0			0
$269$	81.5026	−	47.0556i	0.302984	−	0.174928i	−0.340799	−	0.940136i	$-0.610697\pi$
$269$	81.5026	−	47.0556i	0.302984	−	0.174928i	0.643782	+	0.765209i	$0.277364\pi$
$270$		0			0
$271$	−137.021	−	79.1093i	−0.505614	−	0.291916i	0.225415	−	0.974263i	$-0.427626\pi$
$271$	−137.021	−	79.1093i	−0.505614	−	0.291916i	−0.731029	+	0.682347i	$0.760959\pi$
$272$		0			0
$273$	−71.1167	−	57.5309i	−0.260501	−	0.210736i
$274$		0			0
$275$	−190.785	+	330.449i	−0.693764	+	1.20163i
$276$		0			0
$277$	205.022	−	118.370i	0.740153	−	0.427328i	−0.0819717	−	0.996635i	$-0.526122\pi$
$277$	205.022	−	118.370i	0.740153	−	0.427328i	0.822125	+	0.569307i	$0.192788\pi$
$278$		0			0
$279$		−	309.216i		−	1.10830i
$280$		0			0
$281$	241.948			0.861025			0.430512	−	0.902585i	$-0.358333\pi$
$281$	241.948			0.861025			0.430512	+	0.902585i	$0.358333\pi$
$282$		0			0
$283$	−116.737	−	202.194i	−0.412498	−	0.714468i	0.582664	−	0.812713i	$-0.302010\pi$
$283$	−116.737	−	202.194i	−0.412498	−	0.714468i	−0.995162	+	0.0982453i	$0.968677\pi$
$284$		0			0
$285$	443.582	+	256.102i	1.55643	+	0.898604i
$286$		0			0
$287$	−2.85044	−	7.41469i	−0.00993186	−	0.0258351i
$288$		0			0
$289$	139.021	−	240.791i	0.481041	−	0.833188i
$290$		0			0
$291$	231.640	+	401.212i	0.796014	+	1.37874i
$292$		0			0
$293$			216.492i			0.738882i	0.929254	+	0.369441i	$0.120451\pi$
$293$			216.492i			0.738882i	−0.929254	+	0.369441i	$0.879549\pi$
$294$		0			0
$295$		−	16.7178i		−	0.0566704i
$296$		0			0
$297$	81.8667	+	141.797i	0.275645	+	0.477432i
$298$		0			0
$299$	27.5971	−	47.7996i	0.0922981	−	0.159865i
$300$		0			0
$301$	126.114	+	328.053i	0.418983	+	1.08988i
$302$		0			0
$303$	710.292	+	410.087i	2.34420	+	1.35342i
$304$		0			0
$305$	348.739	+	604.034i	1.14341	+	1.98044i
$306$		0			0
$307$	−173.487			−0.565106			−0.282553	−	0.959252i	$-0.591181\pi$
$307$	−173.487			−0.565106			−0.282553	+	0.959252i	$0.591181\pi$
$308$		0			0
$309$			206.593i			0.668585i
$310$		0			0
$311$	−100.205	+	57.8536i	−0.322204	+	0.186024i	−0.652374	−	0.757897i	$-0.726227\pi$
$311$	−100.205	+	57.8536i	−0.322204	+	0.186024i	0.330171	+	0.943921i	$0.392894\pi$
$312$		0			0
$313$	−105.261	+	182.317i	−0.336297	+	0.582483i	−0.983733	−	0.179637i	$-0.942508\pi$
$313$	−105.261	+	182.317i	−0.336297	+	0.582483i	0.647436	+	0.762120i	$0.275841\pi$
$314$		0			0
$315$	−431.080	−	348.728i	−1.36851	−	1.10707i
$316$		0			0
$317$	−302.997	−	174.936i	−0.955828	−	0.551847i	−0.0609413	−	0.998141i	$-0.519410\pi$
$317$	−302.997	−	174.936i	−0.955828	−	0.551847i	−0.894886	+	0.446294i	$0.852744\pi$
$318$		0			0
$319$	−289.340	+	167.051i	−0.907022	+	0.523669i
$320$		0			0
$321$	332.921			1.03714
$322$		0			0
$323$	53.6837			0.166203
$324$		0			0
$325$	−60.6417	+	35.0115i	−0.186590	+	0.107728i
$326$		0			0
$327$	−471.830	−	272.411i	−1.44291	−	0.833062i
$328$		0			0
$329$	0.828958	−	5.25065i	0.00251963	−	0.0159594i
$330$		0			0
$331$	107.055	−	185.425i	0.323430	−	0.560196i	−0.657764	−	0.753224i	$-0.728497\pi$
$331$	107.055	−	185.425i	0.323430	−	0.560196i	0.981193	+	0.193028i	$0.0618308\pi$
$332$		0			0
$333$	172.803	−	99.7677i	0.518927	−	0.299603i
$334$		0			0
$335$			466.093i			1.39132i
$336$		0			0
$337$	−437.275			−1.29755			−0.648777	−	0.760979i	$-0.724719\pi$
$337$	−437.275			−1.29755			−0.648777	+	0.760979i	$0.724719\pi$
$338$		0			0
$339$	220.242	+	381.470i	0.649682	+	1.12528i
$340$		0			0
$341$	−374.566	−	216.256i	−1.09844	−	0.634182i
$342$		0			0
$343$	305.846	+	155.265i	0.891680	+	0.452667i
$344$		0			0
$345$	300.523	−	520.522i	0.871082	−	1.50876i
$346$		0			0
$347$	188.694	+	326.827i	0.543786	+	0.941865i	0.998682	+	0.0513208i	$0.0163431\pi$
$347$	188.694	+	326.827i	0.543786	+	0.941865i	−0.454896	+	0.890545i	$0.650324\pi$
$348$		0			0
$349$			211.146i			0.605003i	0.953149	+	0.302502i	$0.0978218\pi$
$349$			211.146i			0.605003i	−0.953149	+	0.302502i	$0.902178\pi$
$350$		0			0
$351$			30.0472i			0.0856044i
$352$		0			0
$353$	−149.375	−	258.725i	−0.423159	−	0.732933i	0.573087	−	0.819494i	$-0.305746\pi$
$353$	−149.375	−	258.725i	−0.423159	−	0.732933i	−0.996247	+	0.0865610i	$0.972412\pi$
$354$		0			0
$355$	155.758	−	269.781i	0.438755	−	0.759946i
$356$		0			0
$357$	−103.125	−	16.2810i	−0.288865	−	0.0456051i
$358$		0			0
$359$	−191.258	−	110.423i	−0.532751	−	0.307584i	0.209385	−	0.977833i	$-0.432854\pi$
$359$	−191.258	−	110.423i	−0.532751	−	0.307584i	−0.742136	+	0.670249i	$0.766187\pi$
$360$		0			0
$361$	49.0031	+	84.8758i	0.135743	+	0.235113i
$362$		0			0
$363$	580.274			1.59855
$364$		0			0
$365$			12.0533i			0.0330229i
$366$		0			0
$367$	−186.496	+	107.674i	−0.508165	+	0.293389i	−0.732079	−	0.681220i	$-0.761450\pi$
$367$	−186.496	+	107.674i	−0.508165	+	0.293389i	0.223914	+	0.974609i	$0.428116\pi$
$368$		0			0
$369$	−6.41135	+	11.1048i	−0.0173749	+	0.0300943i
$370$		0			0
$371$	−244.878	−	198.097i	−0.660048	−	0.533955i
$372$		0			0
$373$	193.884	+	111.939i	0.519796	+	0.300104i	0.736851	−	0.676055i	$-0.236312\pi$
$373$	193.884	+	111.939i	0.519796	+	0.300104i	−0.217055	+	0.976159i	$0.569645\pi$
$374$		0			0
$375$	23.4518	−	13.5399i	0.0625381	−	0.0361064i
$376$		0			0
$377$	−61.3118			−0.162631
$378$		0			0
$379$	507.051			1.33787			0.668933	−	0.743323i	$-0.266751\pi$
$379$	507.051			1.33787			0.668933	+	0.743323i	$0.266751\pi$
$380$		0			0
$381$	−683.023	+	394.343i	−1.79271	+	1.03502i
$382$		0			0
$383$	−128.681	−	74.2939i	−0.335981	−	0.193979i	0.322512	−	0.946565i	$-0.395473\pi$
$383$	−128.681	−	74.2939i	−0.335981	−	0.193979i	−0.658493	+	0.752586i	$0.728806\pi$
$384$		0			0
$385$	−723.913	+	278.295i	−1.88029	+	0.722845i
$386$		0			0
$387$	283.661	−	491.316i	0.732975	−	1.26955i
$388$		0			0
$389$	−137.107	+	79.1586i	−0.352459	+	0.203493i	−0.665768	−	0.746159i	$-0.731896\pi$
$389$	−137.107	+	79.1586i	−0.352459	+	0.203493i	0.313309	+	0.949651i	$0.398563\pi$
$390$		0			0
$391$		−	62.9952i		−	0.161113i
$392$		0			0
$393$	38.8366			0.0988208
$394$		0			0
$395$	−254.646	−	441.060i	−0.644673	−	1.11661i
$396$		0			0
$397$	−240.531	−	138.871i	−0.605872	−	0.349801i	0.165476	−	0.986214i	$-0.447084\pi$
$397$	−240.531	−	138.871i	−0.605872	−	0.349801i	−0.771348	+	0.636413i	$0.780417\pi$
$398$		0			0
$399$	183.527	+	477.399i	0.459968	+	1.19649i
$400$		0			0
$401$	−311.899	+	540.225i	−0.777803	+	1.34719i	0.155402	+	0.987851i	$0.450333\pi$
$401$	−311.899	+	540.225i	−0.777803	+	1.34719i	−0.933205	+	0.359344i	$0.883001\pi$
$402$		0			0
$403$	−39.6857	−	68.7377i	−0.0984757	−	0.170565i
$404$		0			0
$405$		−	385.691i		−	0.952324i
$406$		0			0
$407$		−	279.098i		−	0.685744i
$408$		0			0
$409$	247.569	+	428.801i	0.605302	+	1.04841i	0.992004	+	0.126209i	$0.0402810\pi$
$409$	247.569	+	428.801i	0.605302	+	1.04841i	−0.386701	+	0.922205i	$0.626386\pi$
$410$		0			0
$411$	−576.892	+	999.206i	−1.40363	+	2.43116i
$412$		0			0
$413$	10.4991	−	12.9785i	0.0254217	−	0.0314249i
$414$		0			0
$415$	−619.735	−	357.804i	−1.49334	−	0.862179i
$416$		0			0
$417$	492.975	+	853.858i	1.18219	+	2.04762i
$418$		0			0
$419$	−112.631			−0.268810			−0.134405	−	0.990927i	$-0.542912\pi$
$419$	−112.631			−0.268810			−0.134405	+	0.990927i	$0.542912\pi$
$420$		0			0
$421$		−	821.936i		−	1.95234i	−0.217003	−	0.976171i	$-0.569628\pi$
$421$		−	821.936i		−	1.95234i	0.217003	−	0.976171i	$-0.430372\pi$
$422$		0			0
$423$	−7.43097	+	4.29027i	−0.0175673	+	0.0101425i
$424$		0			0
$425$	−39.9599	+	69.2125i	−0.0940232	+	0.162853i
$426$		0			0
$427$	−108.611	+	687.945i	−0.254358	+	1.61111i
$428$		0			0
$429$	178.862	+	103.266i	0.416928	+	0.240713i
$430$		0			0
$431$	289.087	−	166.904i	0.670735	−	0.387249i	−0.125620	−	0.992078i	$-0.540092\pi$
$431$	289.087	−	166.904i	0.670735	−	0.387249i	0.796355	+	0.604830i	$0.206759\pi$
$432$		0			0
$433$	604.681			1.39649			0.698246	−	0.715858i	$-0.253964\pi$
$433$	604.681			1.39649			0.698246	+	0.715858i	$0.253964\pi$
$434$		0			0
$435$	−667.664			−1.53486
$436$		0			0
$437$	−267.265	+	154.305i	−0.611589	+	0.353101i
$438$		0			0
$439$	416.657	+	240.557i	0.949105	+	0.547966i	0.892803	−	0.450448i	$-0.148736\pi$
$439$	416.657	+	240.557i	0.949105	+	0.547966i	0.0563019	+	0.998414i	$0.482069\pi$
$440$		0			0
$441$	−115.650	−	541.455i	−0.262245	−	1.22779i
$442$		0			0
$443$	92.3599	−	159.972i	0.208487	−	0.361111i	−0.742751	−	0.669568i	$-0.766479\pi$
$443$	92.3599	−	159.972i	0.208487	−	0.361111i	0.951238	+	0.308457i	$0.0998127\pi$
$444$		0			0
$445$	−372.595	+	215.118i	−0.837291	+	0.483410i
$446$		0			0
$447$		−	107.583i		−	0.240678i
$448$		0			0
$449$	115.894			0.258115			0.129057	−	0.991637i	$-0.458805\pi$
$449$	115.894			0.258115			0.129057	+	0.991637i	$0.458805\pi$
$450$		0			0
$451$	8.96779	+	15.5327i	0.0198842	+	0.0344405i
$452$		0			0
$453$	715.995	+	413.380i	1.58056	+	0.912538i
$454$		0			0
$455$	−140.584	−	22.1951i	−0.308977	−	0.0487804i
$456$		0			0
$457$	79.2311	−	137.232i	0.173372	−	0.300290i	−0.766224	−	0.642573i	$-0.777867\pi$
$457$	79.2311	−	137.232i	0.173372	−	0.300290i	0.939597	+	0.342283i	$0.111200\pi$
$458$		0			0
$459$	17.1470	+	29.6994i	0.0373572	+	0.0647046i
$460$		0			0
$461$		−	42.3829i		−	0.0919368i	−0.998943	−	0.0459684i	$-0.985363\pi$
$461$		−	42.3829i		−	0.0919368i	0.998943	−	0.0459684i	$-0.0146374\pi$
$462$		0			0
$463$			390.038i			0.842416i	0.906964	+	0.421208i	$0.138394\pi$
$463$			390.038i			0.842416i	−0.906964	+	0.421208i	$0.861606\pi$
$464$		0			0
$465$	−432.164	−	748.530i	−0.929385	−	1.60974i
$466$		0			0
$467$	19.1723	−	33.2074i	0.0410541	−	0.0711078i	−0.844768	−	0.535132i	$-0.820262\pi$
$467$	19.1723	−	33.2074i	0.0410541	−	0.0711078i	0.885822	+	0.464025i	$0.153595\pi$
$468$		0			0
$469$	−292.717	+	361.841i	−0.624130	+	0.771517i
$470$		0			0
$471$	−647.452	−	373.807i	−1.37463	−	0.793644i
$472$		0			0
$473$	−396.768	−	687.222i	−0.838832	−	1.45290i
$474$		0			0
$475$	391.523			0.824259
$476$		0			0
$477$			508.427i			1.06588i
$478$		0			0
$479$	−561.326	+	324.082i	−1.17187	+	0.676580i	−0.954120	−	0.299424i	$-0.903205\pi$
$479$	−561.326	+	324.082i	−1.17187	+	0.676580i	−0.217751	+	0.976004i	$0.569872\pi$
$480$		0			0
$481$	25.6090	−	44.3561i	0.0532412	−	0.0922164i
$482$		0			0
$483$	560.204	−	215.360i	1.15984	−	0.445881i
$484$		0			0
$485$	624.255	+	360.414i	1.28712	+	0.743121i
$486$		0			0
$487$	−303.304	+	175.113i	−0.622800	+	0.359574i	−0.777959	−	0.628316i	$-0.783745\pi$
$487$	−303.304	+	175.113i	−0.622800	+	0.359574i	0.155158	+	0.987890i	$0.450411\pi$
$488$		0			0
$489$	45.5248			0.0930977
$490$		0			0
$491$	453.547			0.923722			0.461861	−	0.886952i	$-0.347182\pi$
$491$	453.547			0.923722			0.461861	+	0.886952i	$0.347182\pi$
$492$		0			0
$493$	−60.6022	+	34.9887i	−0.122925	+	0.0709710i
$494$		0			0
$495$	1084.19	+	625.955i	2.19027	+	1.26455i
$496$		0			0
$497$	290.348	−	111.619i	0.584200	−	0.224585i
$498$		0			0
$499$	−264.783	+	458.617i	−0.530626	+	0.919072i	0.468735	+	0.883339i	$0.344710\pi$
$499$	−264.783	+	458.617i	−0.530626	+	0.919072i	−0.999361	+	0.0357329i	$0.988623\pi$
$500$		0			0
$501$	1112.22	−	642.142i	2.22000	−	1.28172i
$502$		0			0
$503$		−	321.597i		−	0.639358i	−0.947526	−	0.319679i	$-0.896425\pi$
$503$		−	321.597i		−	0.639358i	0.947526	−	0.319679i	$-0.103575\pi$
$504$		0			0
$505$	1276.13			2.52699
$506$		0			0
$507$	−361.762	−	626.591i	−0.713536	−	1.23588i
$508$		0			0
$509$	−623.464	−	359.957i	−1.22488	−	0.707185i	−0.258926	−	0.965897i	$-0.583369\pi$
$509$	−623.464	−	359.957i	−1.22488	−	0.707185i	−0.965954	+	0.258712i	$0.916702\pi$
$510$		0			0
$511$	−7.56977	+	9.35735i	−0.0148136	+	0.0183118i
$512$		0			0
$513$	84.0021	−	145.496i	0.163747	−	0.283618i
$514$		0			0
$515$	160.721	+	278.377i	0.312080	+	0.540538i
$516$		0			0
$517$			12.0019i			0.0232146i
$518$		0			0
$519$		−	438.708i		−	0.845294i
$520$		0			0
$521$	−206.990	−	358.517i	−0.397294	−	0.688133i	0.596097	−	0.802912i	$-0.296717\pi$
$521$	−206.990	−	358.517i	−0.397294	−	0.688133i	−0.993391	+	0.114779i	$0.963384\pi$
$522$		0			0
$523$	−174.324	+	301.938i	−0.333316	+	0.577320i	−0.983160	−	0.182747i	$-0.941501\pi$
$523$	−174.324	+	301.938i	−0.333316	+	0.577320i	0.649844	+	0.760068i	$0.274834\pi$
$524$		0			0
$525$	−752.103	−	118.740i	−1.43258	−	0.226171i
$526$		0			0
$527$	−78.4528	−	45.2947i	−0.148867	−	0.0859483i
$528$		0			0
$529$	−83.4303	−	144.506i	−0.157713	−	0.273167i
$530$		0			0
$531$	−26.9466			−0.0507468
$532$		0			0
$533$			3.29141i			0.00617525i
$534$		0			0
$535$	448.601	−	259.000i	0.838507	−	0.484112i
$536$		0			0
$537$	−679.912	+	1177.64i	−1.26613	+	2.19300i
$538$		0			0
$539$	−736.770	−	238.585i	−1.36692	−	0.442644i
$540$		0			0
$541$	202.840	+	117.110i	0.374936	+	0.216469i	0.675613	−	0.737257i	$-0.263879\pi$
$541$	202.840	+	117.110i	0.374936	+	0.216469i	−0.300677	+	0.953726i	$0.597213\pi$
$542$		0			0
$543$	−235.881	+	136.186i	−0.434404	+	0.250803i
$544$		0			0
$545$	−847.701			−1.55542
$546$		0			0
$547$	577.082			1.05499			0.527497	−	0.849557i	$-0.323130\pi$
$547$	577.082			1.05499			0.527497	+	0.849557i	$0.323130\pi$
$548$		0			0
$549$	973.613	−	562.116i	1.77343	−	1.02389i
$550$		0			0
$551$	296.887	+	171.408i	0.538815	+	0.311085i
$552$		0			0
$553$	79.3065	−	502.331i	0.143411	−	0.908374i
$554$		0			0
$555$	278.873	−	483.022i	0.502474	−	0.870311i
$556$		0			0
$557$	−36.7252	+	21.2033i	−0.0659339	+	0.0380670i	−0.532605	−	0.846364i	$-0.678787\pi$
$557$	−36.7252	+	21.2033i	−0.0659339	+	0.0380670i	0.466671	+	0.884431i	$0.345453\pi$
$558$		0			0
$559$		−	145.624i		−	0.260508i
$560$		0			0
$561$	235.722			0.420182
$562$		0			0
$563$	−123.648	−	214.165i	−0.219624	−	0.380399i	0.735069	−	0.677992i	$-0.237150\pi$
$563$	−123.648	−	214.165i	−0.219624	−	0.380399i	−0.954693	+	0.297593i	$0.903816\pi$
$564$		0			0
$565$	593.539	+	342.680i	1.05051	+	0.606513i
$566$		0			0
$567$	242.223	−	299.423i	0.427201	−	0.528083i
$568$		0			0
$569$	−312.737	+	541.677i	−0.549626	+	0.951980i	0.448674	+	0.893696i	$0.351896\pi$
$569$	−312.737	+	541.677i	−0.549626	+	0.951980i	−0.998300	+	0.0582847i	$0.981437\pi$
$570$		0			0
$571$	−291.287	−	504.524i	−0.510135	−	0.883579i	−0.999931	−	0.0117423i	$-0.996262\pi$
$571$	−291.287	−	504.524i	−0.510135	−	0.883579i	0.489796	−	0.871837i	$-0.337071\pi$
$572$		0			0
$573$			330.758i			0.577239i
$574$		0			0
$575$		−	459.433i		−	0.799014i
$576$		0			0
$577$	198.380	+	343.605i	0.343814	+	0.595503i	0.985137	−	0.171768i	$-0.0549478\pi$
$577$	198.380	+	343.605i	0.343814	+	0.595503i	−0.641324	+	0.767270i	$0.721615\pi$
$578$		0			0
$579$	−146.629	+	253.969i	−0.253246	+	0.438634i
$580$		0			0
$581$	−256.409	−	666.981i	−0.441324	−	1.14799i
$582$		0			0
$583$	615.879	+	355.578i	1.05640	+	0.609910i
$584$		0			0
$585$	114.871	+	198.962i	0.196360	+	0.340106i
$586$		0			0
$587$	−355.763			−0.606070			−0.303035	−	0.952979i	$-0.598000\pi$
$587$	−355.763			−0.606070			−0.303035	+	0.952979i	$0.598000\pi$
$588$		0			0
$589$			443.794i			0.753470i
$590$		0			0
$591$	1359.11	−	784.682i	2.29968	−	1.32772i
$592$		0			0
$593$	89.8611	−	155.644i	0.151536	−	0.262469i	−0.780256	−	0.625460i	$-0.784911\pi$
$593$	89.8611	−	155.644i	0.151536	−	0.262469i	0.931792	+	0.362991i	$0.118245\pi$
$594$		0			0
$595$	−151.623	+	58.2888i	−0.254829	+	0.0979644i
$596$		0			0
$597$	−1014.93	−	585.967i	−1.70004	−	0.981520i
$598$		0			0
$599$	35.2310	−	20.3406i	0.0588163	−	0.0339576i	−0.470303	−	0.882505i	$-0.655856\pi$
$599$	35.2310	−	20.3406i	0.0588163	−	0.0339576i	0.529120	+	0.848547i	$0.322522\pi$
$600$		0			0
$601$	−1020.79			−1.69849			−0.849245	−	0.527998i	$-0.822943\pi$
$601$	−1020.79			−1.69849			−0.849245	+	0.527998i	$0.822943\pi$
$602$		0			0
$603$	751.272			1.24589
$604$		0			0
$605$	781.901	−	451.431i	1.29240	−	0.746166i
$606$		0			0
$607$	−273.220	−	157.744i	−0.450116	−	0.259874i	0.257763	−	0.966208i	$-0.417014\pi$
$607$	−273.220	−	157.744i	−0.450116	−	0.259874i	−0.707879	+	0.706334i	$0.750348\pi$
$608$		0			0
$609$	−518.327	−	419.308i	−0.851111	−	0.688519i
$610$		0			0
$611$	−1.10125	+	1.90743i	−0.00180238	+	0.00312181i
$612$		0			0
$613$	358.417	−	206.932i	0.584693	−	0.337572i	−0.178303	−	0.983976i	$-0.557061\pi$
$613$	358.417	−	206.932i	0.584693	−	0.337572i	0.762996	+	0.646403i	$0.223728\pi$
$614$		0			0
$615$			35.8423i			0.0582802i
$616$		0			0
$617$	139.167			0.225554			0.112777	−	0.993620i	$-0.464025\pi$
$617$	139.167			0.225554			0.112777	+	0.993620i	$0.464025\pi$
$618$		0			0
$619$	167.006	+	289.264i	0.269800	+	0.467308i	0.968810	−	0.247804i	$-0.0797090\pi$
$619$	167.006	+	289.264i	0.269800	+	0.467308i	−0.699010	+	0.715112i	$0.746376\pi$
$620$		0			0
$621$	−170.732	−	98.5724i	−0.274931	−	0.158732i
$622$		0			0
$623$	−424.354	−	66.9959i	−0.681147	−	0.107538i
$624$		0			0
$625$	322.850	−	559.192i	0.516560	−	0.894707i
$626$		0			0
$627$	−577.396	−	1000.08i	−0.920887	−	1.59502i
$628$		0			0
$629$		−	58.4569i		−	0.0929363i
$630$		0			0
$631$			284.343i			0.450623i	0.974287	+	0.225311i	$0.0723399\pi$
$631$			284.343i			0.450623i	−0.974287	+	0.225311i	$0.927660\pi$
$632$		0			0
$633$	10.6560	+	18.4568i	0.0168342	+	0.0291576i
$634$		0			0
$635$	−613.568	+	1062.73i	−0.966248	+	1.67359i
$636$		0			0
$637$	−95.2007	−	105.521i	−0.149452	−	0.165653i
$638$		0			0
$639$	−434.846	−	251.058i	−0.680510	−	0.392893i
$640$		0			0
$641$	−32.4545	−	56.2128i	−0.0506310	−	0.0876955i	0.839599	−	0.543206i	$-0.182790\pi$
$641$	−32.4545	−	56.2128i	−0.0506310	−	0.0876955i	−0.890230	+	0.455511i	$0.849457\pi$
$642$		0			0
$643$	−683.365			−1.06278			−0.531388	−	0.847128i	$-0.678329\pi$
$643$	−683.365			−1.06278			−0.531388	+	0.847128i	$0.678329\pi$
$644$		0			0
$645$		−	1585.79i		−	2.45859i
$646$		0			0
$647$	−1103.61	+	637.171i	−1.70574	+	0.984808i	−0.766047	+	0.642785i	$0.777779\pi$
$647$	−1103.61	+	637.171i	−1.70574	+	0.984808i	−0.939691	+	0.342024i	$0.888888\pi$
$648$		0			0
$649$	−18.8456	+	32.6415i	−0.0290379	+	0.0502951i
$650$		0			0
$651$	134.592	−	852.514i	0.206747	−	1.30954i
$652$		0			0
$653$	−472.891	−	273.024i	−0.724182	−	0.418107i	0.0921079	−	0.995749i	$-0.470640\pi$
$653$	−472.891	−	273.024i	−0.724182	−	0.418107i	−0.816290	+	0.577642i	$0.803973\pi$
$654$		0			0
$655$	52.3311	−	30.2134i	0.0798948	−	0.0461273i
$656$		0			0
$657$	19.4282			0.0295710
$658$		0			0
$659$	398.883			0.605285			0.302642	−	0.953104i	$-0.402131\pi$
$659$	398.883			0.605285			0.302642	+	0.953104i	$0.402131\pi$
$660$		0			0
$661$	−718.146	+	414.622i	−1.08645	+	0.627264i	−0.932630	−	0.360834i	$-0.882492\pi$
$661$	−718.146	+	414.622i	−1.08645	+	0.627264i	−0.153824	+	0.988098i	$0.549159\pi$
$662$		0			0
$663$	37.4626	+	21.6290i	0.0565046	+	0.0326230i
$664$		0			0
$665$	618.695	+	500.502i	0.930368	+	0.752635i
$666$		0			0
$667$	201.139	−	348.383i	0.301557	−	0.522313i
$668$		0			0
$669$	−426.531	+	246.258i	−0.637565	+	0.368098i
$670$		0			0
$671$		−	1572.50i		−	2.34352i
$672$		0			0
$673$	946.218			1.40597			0.702985	−	0.711205i	$-0.251850\pi$
$673$	946.218			1.40597			0.702985	+	0.711205i	$0.251850\pi$
$674$		0			0
$675$	125.055	+	216.602i	0.185267	+	0.320892i
$676$		0			0
$677$	987.793	+	570.303i	1.45907	+	0.842397i	0.998966	−	0.0454660i	$-0.0144773\pi$
$677$	987.793	+	570.303i	1.45907	+	0.842397i	0.460108	+	0.887863i	$0.347811\pi$
$678$		0			0
$679$	258.279	+	671.846i	0.380381	+	0.989463i
$680$		0			0
$681$	−273.575	+	473.846i	−0.401725	+	0.695809i
$682$		0			0
$683$	58.7041	+	101.678i	0.0859504	+	0.148870i	0.905796	−	0.423715i	$-0.139274\pi$
$683$	58.7041	+	101.678i	0.0859504	+	0.148870i	−0.819845	+	0.572585i	$0.805941\pi$
$684$		0			0
$685$			1795.20i			2.62073i
$686$		0			0
$687$			649.675i			0.945670i
$688$		0			0
$689$	65.2530	+	113.022i	0.0947069	+	0.164037i
$690$		0			0
$691$	477.961	−	827.853i	0.691695	−	1.19805i	−0.279588	−	0.960120i	$-0.590198\pi$
$691$	477.961	−	827.853i	0.691695	−	1.19805i	0.971282	−	0.237930i	$-0.0764690\pi$
$692$		0			0
$693$	448.570	+	1166.84i	0.647287	+	1.68375i
$694$		0			0
$695$	1328.54	+	767.031i	1.91156	+	1.10364i
$696$		0			0
$697$	1.87830	+	3.25331i	0.00269484	+	0.00466759i
$698$		0			0
$699$	875.243			1.25214
$700$		0			0
$701$		−	824.950i		−	1.17682i	−0.808563	−	0.588410i	$-0.799754\pi$
$701$		−	824.950i		−	1.17682i	0.808563	−	0.588410i	$-0.200246\pi$
$702$		0			0
$703$	−248.010	+	143.189i	−0.352789	+	0.203683i
$704$		0			0
$705$	−11.9923	+	20.7712i	−0.0170103	+	0.0294627i
$706$		0			0
$707$	990.695	+	801.437i	1.40127	+	1.13357i
$708$		0			0
$709$	−112.576	−	64.9959i	−0.158782	−	0.0916726i	0.418504	−	0.908215i	$-0.362555\pi$
$709$	−112.576	−	64.9959i	−0.158782	−	0.0916726i	−0.577285	+	0.816542i	$0.695888\pi$
$710$		0			0
$711$	−710.922	+	410.451i	−0.999890	+	0.577287i
$712$		0			0
$713$	520.770			0.730393
$714$		0			0
$715$	321.348			0.449437
$716$		0			0
$717$	−1231.30	+	710.890i	−1.71729	+	0.991478i
$718$		0			0
$719$	438.623	+	253.239i	0.610046	+	0.352210i	0.772984	−	0.634426i	$-0.218763\pi$
$719$	438.623	+	253.239i	0.610046	+	0.352210i	−0.162937	+	0.986636i	$0.552097\pi$
$720$		0			0
$721$	−50.0547	+	317.049i	−0.0694240	+	0.439735i
$722$		0			0
$723$	−817.094	+	1415.25i	−1.13014	+	1.95747i
$724$		0			0
$725$	−441.980	+	255.177i	−0.609628	+	0.351969i
$726$		0			0
$727$			1272.41i			1.75022i	0.483924	+	0.875110i	$0.339211\pi$
$727$			1272.41i			1.75022i	−0.483924	+	0.875110i	$0.660789\pi$
$728$		0			0
$729$	−1041.76			−1.42902
$730$		0			0
$731$	−83.1028	−	143.938i	−0.113684	−	0.196906i
$732$		0			0
$733$	615.475	+	355.345i	0.839666	+	0.484781i	0.857151	−	0.515066i	$-0.172233\pi$
$733$	615.475	+	355.345i	0.839666	+	0.484781i	−0.0174847	+	0.999847i	$0.505566\pi$
$734$		0			0
$735$	−1036.70	−	1149.09i	−1.41048	−	1.56338i
$736$		0			0
$737$	525.417	−	910.048i	0.712913	−	1.23480i
$738$		0			0
$739$	−105.509	−	182.748i	−0.142773	−	0.247291i	0.785767	−	0.618523i	$-0.212269\pi$
$739$	−105.509	−	182.748i	−0.142773	−	0.247291i	−0.928540	+	0.371232i	$0.878935\pi$
$740$		0			0
$741$		−	211.919i		−	0.285991i
$742$		0			0
$743$		−	244.355i		−	0.328876i	−0.986387	−	0.164438i	$-0.947419\pi$
$743$		−	244.355i		−	0.328876i	0.986387	−	0.164438i	$-0.0525811\pi$
$744$		0			0
$745$	−83.6954	−	144.965i	−0.112343	−	0.194583i
$746$		0			0
$747$	−576.727	+	998.920i	−0.772057	+	1.33724i
$748$		0			0
$749$	510.919	+	80.6625i	0.682136	+	0.107694i
$750$		0			0
$751$	−262.737	−	151.692i	−0.349850	−	0.201986i	0.314769	−	0.949168i	$-0.398073\pi$
$751$	−262.737	−	151.692i	−0.349850	−	0.201986i	−0.664619	+	0.747182i	$0.731406\pi$
$752$		0			0
$753$	−20.3701	−	35.2821i	−0.0270519	−	0.0468553i
$754$		0			0
$755$	1286.37			1.70381
$756$		0			0
$757$			668.225i			0.882728i	0.897328	+	0.441364i	$0.145505\pi$
$757$			668.225i			0.882728i	−0.897328	+	0.441364i	$0.854495\pi$
$758$		0			0
$759$	−1173.54	+	677.546i	−1.54617	+	0.892683i
$760$		0			0
$761$	−45.4152	+	78.6615i	−0.0596784	+	0.103366i	−0.894321	−	0.447426i	$-0.852341\pi$
$761$	−45.4152	+	78.6615i	−0.0596784	+	0.103366i	0.834643	+	0.550792i	$0.185674\pi$
$762$		0			0
$763$	−658.095	−	532.375i	−0.862509	−	0.697740i
$764$		0			0
$765$	227.082	+	131.106i	0.296839	+	0.171380i
$766$		0			0
$767$	−5.99013	+	3.45840i	−0.00780982	+	0.00450900i
$768$		0			0
$769$	421.091			0.547582			0.273791	−	0.961789i	$-0.411722\pi$
$769$	421.091			0.547582			0.273791	+	0.961789i	$0.411722\pi$
$770$		0			0
$771$	−1671.88			−2.16846
$772$		0			0
$773$	508.100	−	293.352i	0.657309	−	0.379498i	−0.133942	−	0.990989i	$-0.542763\pi$
$773$	508.100	−	293.352i	0.657309	−	0.379498i	0.791251	+	0.611492i	$0.209430\pi$
$774$		0			0
$775$	−572.167	−	330.341i	−0.738281	−	0.426247i
$776$		0			0
$777$	519.846	−	199.845i	0.669043	−	0.257201i
$778$		0			0
$779$	9.20171	−	15.9378i	0.0118122	−	0.0204593i
$780$		0			0
$781$	−608.235	+	351.165i	−0.778791	+	0.449635i
$782$		0			0
$783$			218.996i			0.279688i
$784$		0			0
$785$	−1163.23			−1.48182
$786$		0			0
$787$	681.137	+	1179.76i	0.865485	+	1.49906i	0.866565	+	0.499065i	$0.166323\pi$
$787$	681.137	+	1179.76i	0.865485	+	1.49906i	−0.00107958	+	0.999999i	$0.500344\pi$
$788$		0			0
$789$	−1849.01	−	1067.53i	−2.34349	−	1.35301i
$790$		0			0
$791$	245.570	+	638.787i	0.310456	+	0.807569i
$792$		0			0
$793$	144.287	−	249.913i	0.181951	−	0.315149i
$794$		0			0
$795$	710.583	+	1230.77i	0.893815	+	1.54813i
$796$		0			0
$797$		−	874.598i		−	1.09736i	−0.836032	−	0.548681i	$-0.815130\pi$
$797$		−	874.598i		−	1.09736i	0.836032	−	0.548681i	$-0.184870\pi$
$798$		0			0
$799$			2.51380i			0.00314618i
$800$		0			0
$801$	346.737	+	600.567i	0.432880	+	0.749771i
$802$		0			0
$803$	13.5875	−	23.5342i	0.0169209	−	0.0293078i
$804$		0			0
$805$	587.315	−	726.008i	0.729584	−	0.901874i
$806$		0			0
$807$	−367.208	−	212.008i	−0.455029	−	0.262711i
$808$		0			0
$809$	27.9415	+	48.3961i	0.0345383	+	0.0598222i	0.882778	−	0.469791i	$-0.155671\pi$
$809$	27.9415	+	48.3961i	0.0345383	+	0.0598222i	−0.848240	+	0.529613i	$0.822337\pi$
$810$		0			0
$811$	−917.924			−1.13184			−0.565921	−	0.824459i	$-0.691479\pi$
$811$	−917.924			−1.13184			−0.565921	+	0.824459i	$0.691479\pi$
$812$		0			0
$813$			712.850i			0.876815i
$814$		0			0
$815$	61.3432	−	35.4165i	0.0752677	−	0.0434559i
$816$		0			0
$817$	−407.117	+	705.147i	−0.498307	+	0.863093i
$818$		0			0
$819$	−35.7751	+	226.601i	−0.0436815	+	0.276680i
$820$		0			0
$821$	1178.10	+	680.176i	1.43496	+	0.828472i	0.997493	−	0.0707646i	$-0.0225439\pi$
$821$	1178.10	+	680.176i	1.43496	+	0.828472i	0.437463	+	0.899237i	$0.355877\pi$
$822$		0			0
$823$	488.057	−	281.780i	0.593022	−	0.342382i	−0.173269	−	0.984874i	$-0.555433\pi$
$823$	488.057	−	281.780i	0.593022	−	0.342382i	0.766292	+	0.642493i	$0.222100\pi$
$824$		0			0
$825$	1719.16			2.08383
$826$		0			0
$827$	−63.4180			−0.0766844			−0.0383422	−	0.999265i	$-0.512208\pi$
$827$	−63.4180			−0.0766844			−0.0383422	+	0.999265i	$0.512208\pi$
$828$		0			0
$829$	252.620	−	145.850i	0.304728	−	0.175935i	−0.339837	−	0.940484i	$-0.610372\pi$
$829$	252.620	−	145.850i	0.304728	−	0.175935i	0.644565	+	0.764549i	$0.277038\pi$
$830$		0			0
$831$	−923.725	−	533.313i	−1.11158	−	0.641772i
$832$		0			0
$833$	−154.316	−	49.9715i	−0.185254	−	0.0599899i
$834$		0			0
$835$	999.123	−	1730.53i	1.19655	−	2.07249i
$836$		0			0
$837$	−245.520	+	141.751i	−0.293333	+	0.169356i
$838$		0			0
$839$		−	463.917i		−	0.552940i	−0.961023	−	0.276470i	$-0.910835\pi$
$839$		−	463.917i		−	0.552940i	0.961023	−	0.276470i	$-0.0891646\pi$
$840$		0			0
$841$	394.135			0.468651
$842$		0			0
$843$	−545.046	−	944.047i	−0.646555	−	1.11987i
$844$		0			0
$845$	−974.927	−	562.874i	−1.15376	−	0.666124i
$846$		0			0
$847$	890.520	+	140.593i	1.05138	+	0.165989i
$848$		0			0
$849$	−525.956	+	910.983i	−0.619501	+	1.07301i
$850$		0			0
$851$	168.025	+	291.028i	0.197444	+	0.341984i
$852$		0			0
$853$		−	649.909i		−	0.761909i	−0.924594	−	0.380955i	$-0.875595\pi$
$853$		−	649.909i		−	0.761909i	0.924594	−	0.380955i	$-0.124405\pi$
$854$		0			0
$855$		−	1284.56i		−	1.50241i
$856$		0			0
$857$	−584.140	−	1011.76i	−0.681610	−	1.18058i	−0.974489	−	0.224433i	$-0.927947\pi$
$857$	−584.140	−	1011.76i	−0.681610	−	1.18058i	0.292880	−	0.956149i	$-0.405386\pi$
$858$		0			0
$859$	733.208	−	1269.95i	0.853560	−	1.47841i	−0.0244139	−	0.999702i	$-0.507772\pi$
$859$	733.208	−	1269.95i	0.853560	−	1.47841i	0.877974	−	0.478708i	$-0.158895\pi$
$860$		0			0
$861$	−22.5098	+	27.8254i	−0.0261438	+	0.0323175i
$862$		0			0
$863$	−36.9921	−	21.3574i	−0.0428646	−	0.0247479i	0.478415	−	0.878134i	$-0.341212\pi$
$863$	−36.9921	−	21.3574i	−0.0428646	−	0.0247479i	−0.521279	+	0.853386i	$0.674545\pi$
$864$		0			0
$865$	−341.298	−	591.145i	−0.394564	−	0.683404i
$866$		0			0
$867$	−1252.71			−1.44488
$868$		0			0
$869$			1148.23i			1.32132i
$870$		0			0
$871$	167.005	−	96.4206i	0.191740	−	0.110701i
$872$		0			0
$873$	580.933	−	1006.21i	0.665444	−	1.15258i
$874$		0			0
$875$	39.2709	−	15.0970i	0.0448811	−	0.0172537i
$876$		0			0
$877$	−842.217	−	486.254i	−0.960338	−	0.554452i	−0.0640612	−	0.997946i	$-0.520405\pi$
$877$	−842.217	−	486.254i	−0.960338	−	0.554452i	−0.896277	+	0.443494i	$0.853739\pi$
$878$		0			0
$879$	844.723	−	487.701i	0.961005	−	0.554836i
$880$		0			0
$881$	−110.722			−0.125678			−0.0628390	−	0.998024i	$-0.520015\pi$
$881$	−110.722			−0.125678			−0.0628390	+	0.998024i	$0.520015\pi$
$882$		0			0
$883$	−1283.66			−1.45375			−0.726874	−	0.686770i	$-0.759028\pi$
$883$	−1283.66			−1.45375			−0.726874	+	0.686770i	$0.759028\pi$
$884$		0			0
$885$	−65.2305	+	37.6608i	−0.0737067	+	0.0425546i
$886$		0			0
$887$	−429.755	−	248.119i	−0.484504	−	0.279729i	0.237788	−	0.971317i	$-0.423578\pi$
$887$	−429.755	−	248.119i	−0.484504	−	0.279729i	−0.722292	+	0.691589i	$0.756911\pi$
$888$		0			0
$889$	−1143.75	+	439.693i	−1.28656	+	0.494593i
$890$		0			0
$891$	−434.781	+	753.063i	−0.487970	+	0.845189i
$892$		0			0
$893$	10.6651	−	6.15750i	0.0119430	−	0.00689529i
$894$		0			0
$895$			2115.78i			2.36400i
$896$		0			0
$897$	−248.677			−0.277232
$898$		0			0
$899$	−289.245	−	500.987i	−0.321741	−	0.557272i
$900$		0			0
$901$	128.996	+	74.4756i	0.143169	+	0.0826589i
$902$		0			0
$903$	995.914	−	1231.10i	1.10289	−	1.36334i
$904$		0			0
$905$	−211.895	+	367.013i	−0.234138	+	0.405539i
$906$		0			0
$907$	796.131	+	1378.94i	0.877763	+	1.52033i	0.853790	+	0.520617i	$0.174298\pi$
$907$	796.131	+	1378.94i	0.877763	+	1.52033i	0.0239725	+	0.999713i	$0.492369\pi$
$908$		0			0
$909$		−	2056.93i		−	2.26285i
$910$		0			0
$911$			663.197i			0.727988i	0.931401	+	0.363994i	$0.118587\pi$
$911$			663.197i			0.727988i	−0.931401	+	0.363994i	$0.881413\pi$
$912$		0			0
$913$	806.690	+	1397.23i	0.883559	+	1.53037i
$914$		0			0
$915$	1571.24	−	2721.47i	1.71720	−	2.97428i
$916$		0			0
$917$	59.6008	+	9.40960i	0.0649954	+	0.0102613i
$918$		0			0
$919$	441.371	+	254.826i	0.480273	+	0.277286i	0.720530	−	0.693424i	$-0.243898\pi$
$919$	441.371	+	254.826i	0.480273	+	0.277286i	−0.240257	+	0.970709i	$0.577232\pi$
$920$		0			0
$921$	390.822	+	676.924i	0.424345	+	0.734988i
$922$		0			0
$923$	−128.886			−0.139639
$924$		0			0
$925$		−	426.335i		−	0.460902i
$926$		0			0
$927$	448.702	−	259.058i	0.484037	−	0.279459i
$928$		0			0
$929$	161.143	−	279.108i	0.173459	−	0.300439i	−0.766168	−	0.642640i	$-0.777839\pi$
$929$	161.143	−	279.108i	0.173459	−	0.300439i	0.939627	+	0.342201i	$0.111172\pi$
$930$		0			0
$931$	165.984	+	777.109i	0.178285	+	0.834703i
$932$		0			0
$933$	451.473	+	260.658i	0.483894	+	0.279376i
$934$		0			0
$935$	317.628	−	183.383i	0.339710	−	0.196131i
$936$		0			0
$937$	−1077.79			−1.15026			−0.575130	−	0.818062i	$-0.695048\pi$
$937$	−1077.79			−1.15026			−0.575130	+	0.818062i	$0.695048\pi$
$938$		0			0
$939$	948.502			1.01012
$940$		0			0
$941$	−63.5953	+	36.7168i	−0.0675827	+	0.0390189i	−0.533411	−	0.845856i	$-0.679090\pi$
$941$	−63.5953	+	36.7168i	−0.0675827	+	0.0390189i	0.465828	+	0.884875i	$0.345757\pi$
$942$		0			0
$943$	−18.7023	−	10.7978i	−0.0198327	−	0.0114504i
$944$		0			0
$945$	−79.2771	+	502.144i	−0.0838911	+	0.531369i
$946$		0			0
$947$	38.4077	−	66.5241i	0.0405572	−	0.0702472i	−0.845034	−	0.534712i	$-0.820420\pi$
$947$	38.4077	−	66.5241i	0.0405572	−	0.0702472i	0.885591	+	0.464465i	$0.153753\pi$
$948$		0			0
$949$	4.31882	−	2.49347i	0.00455092	−	0.00262747i
$950$		0			0
$951$			1576.34i			1.65756i
$952$		0			0
$953$	−1329.39			−1.39495			−0.697477	−	0.716607i	$-0.745694\pi$
$953$	−1329.39			−1.39495			−0.697477	+	0.716607i	$0.745694\pi$
$954$		0			0
$955$	257.317	+	445.686i	0.269442	+	0.466687i
$956$		0			0
$957$	1303.62	+	752.643i	1.36219	+	0.786461i
$958$		0			0
$959$	−1127.42	+	1393.66i	−1.17563	+	1.45325i
$960$		0			0
$961$	−106.056	+	183.695i	−0.110360	+	0.191150i
$962$		0			0
$963$	−417.469	−	723.077i	−0.433509	−	0.750859i
$964$		0			0
$965$			456.288i			0.472837i
$966$		0			0
$967$		−	601.743i		−	0.622279i	−0.950364	−	0.311139i	$-0.899289\pi$
$967$		−	601.743i		−	0.622279i	0.950364	−	0.311139i	$-0.100711\pi$
$968$		0			0
$969$	−120.935	−	209.466i	−0.124804	−	0.216167i
$970$		0			0
$971$	213.139	−	369.168i	0.219505	−	0.380193i	−0.735152	−	0.677902i	$-0.762889\pi$
$971$	213.139	−	369.168i	0.219505	−	0.380193i	0.954657	+	0.297709i	$0.0962225\pi$
$972$		0			0
$973$	549.668	+	1429.82i	0.564921	+	1.46950i
$974$		0			0
$975$	273.220	+	157.744i	0.280225	+	0.161788i
$976$		0			0
$977$	−109.928	−	190.401i	−0.112516	−	0.194884i	0.804268	−	0.594267i	$-0.202558\pi$
$977$	−109.928	−	190.401i	−0.112516	−	0.194884i	−0.916784	+	0.399383i	$0.869224\pi$
$978$		0			0
$979$	969.989			0.990796
$980$		0			0
$981$			1366.37i			1.39283i
$982$		0			0
$983$	1444.72	−	834.112i	1.46971	−	0.848537i	0.470286	−	0.882514i	$-0.344151\pi$
$983$	1444.72	−	834.112i	1.46971	−	0.848537i	0.999423	+	0.0339771i	$0.0108173\pi$
$984$		0			0
$985$	1220.91	−	2114.67i	1.23950	−	2.14687i
$986$		0			0
$987$	−22.3547	+	8.59388i	−0.0226492	+	0.00870707i
$988$		0			0
$989$	827.456	+	477.732i	0.836659	+	0.483045i
$990$		0			0
$991$	1184.20	−	683.697i	1.19495	−	0.689906i	0.235527	−	0.971868i	$-0.424318\pi$
$991$	1184.20	−	683.697i	1.19495	−	0.689906i	0.959426	+	0.281962i	$0.0909851\pi$
$992$		0			0
$993$	−964.670			−0.971471
$994$		0			0
$995$	−1823.44			−1.83260
$996$		0			0
$997$	803.308	−	463.790i	0.805725	−	0.465186i	−0.0397440	−	0.999210i	$-0.512654\pi$
$997$	803.308	−	463.790i	0.805725	−	0.465186i	0.845469	+	0.534024i	$0.179321\pi$
$998$		0			0
$999$	−158.433	−	91.4711i	−0.158591	−	0.0915626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.o.c.79.1		12
4.3	odd	2		56.3.k.c.51.5	yes	12
7.2	even	3		1568.3.g.k.687.6		6
7.4	even	3	inner	224.3.o.c.207.2		12
7.5	odd	6		1568.3.g.i.687.1		6
8.3	odd	2	inner	224.3.o.c.79.2		12
8.5	even	2		56.3.k.c.51.4	yes	12
28.3	even	6		392.3.k.k.67.4		12
28.11	odd	6		56.3.k.c.11.4	✓	12
28.19	even	6		392.3.g.l.99.1		6
28.23	odd	6		392.3.g.k.99.1		6
28.27	even	2		392.3.k.k.275.5		12
56.5	odd	6		392.3.g.l.99.2		6
56.11	odd	6	inner	224.3.o.c.207.1		12
56.13	odd	2		392.3.k.k.275.4		12
56.19	even	6		1568.3.g.i.687.2		6
56.37	even	6		392.3.g.k.99.2		6
56.45	odd	6		392.3.k.k.67.5		12
56.51	odd	6		1568.3.g.k.687.5		6
56.53	even	6		56.3.k.c.11.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.c.11.4	✓	12	28.11	odd	6
56.3.k.c.11.5	yes	12	56.53	even	6
56.3.k.c.51.4	yes	12	8.5	even	2
56.3.k.c.51.5	yes	12	4.3	odd	2
224.3.o.c.79.1		12	1.1	even	1	trivial
224.3.o.c.79.2		12	8.3	odd	2	inner
224.3.o.c.207.1		12	56.11	odd	6	inner
224.3.o.c.207.2		12	7.4	even	3	inner
392.3.g.k.99.1		6	28.23	odd	6
392.3.g.k.99.2		6	56.37	even	6
392.3.g.l.99.1		6	28.19	even	6
392.3.g.l.99.2		6	56.5	odd	6
392.3.k.k.67.4		12	28.3	even	6
392.3.k.k.67.5		12	56.45	odd	6
392.3.k.k.275.4		12	56.13	odd	2
392.3.k.k.275.5		12	28.27	even	2
1568.3.g.i.687.1		6	7.5	odd	6
1568.3.g.i.687.2		6	56.19	even	6
1568.3.g.k.687.5		6	56.51	odd	6
1568.3.g.k.687.6		6	7.2	even	3

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.25274 - 3.90186i) q^{3} +(-6.07099 - 3.50509i) q^{5} +(-2.51181 - 6.53382i) q^{7} +(-5.64968 + 9.78553i) q^{9} +O(q^{10})\)	\(q+(-2.25274 - 3.90186i) q^{3} +(-6.07099 - 3.50509i) q^{5} +(-2.51181 - 6.53382i) q^{7} +(-5.64968 + 9.78553i) q^{9} +(7.90242 + 13.6874i) q^{11} +2.90039i q^{13} +31.5842i q^{15} +(1.65516 + 2.86682i) q^{17} +(8.10854 - 14.0444i) q^{19} +(-19.8356 + 24.5197i) q^{21} +(-16.4804 - 9.51498i) q^{23} +(12.0713 + 20.9081i) q^{25} +10.3597 q^{27} +21.1392i q^{29} +(-23.6995 + 13.6829i) q^{31} +(35.6042 - 61.6683i) q^{33} +(-7.65245 + 48.4709i) q^{35} +(-15.2932 - 8.82951i) q^{37} +(11.3169 - 6.53382i) q^{39} +1.13482 q^{41} -50.2084 q^{43} +(68.5983 - 39.6053i) q^{45} +(0.657646 + 0.379692i) q^{47} +(-36.3816 + 32.8234i) q^{49} +(7.45728 - 12.9164i) q^{51} +(38.9677 - 22.4980i) q^{53} -110.795i q^{55} -73.0658 q^{57} +(1.19239 + 2.06529i) q^{59} +(-86.1653 - 49.7476i) q^{61} +(78.1278 + 12.3346i) q^{63} +(10.1661 - 17.6082i) q^{65} +(-33.2440 - 57.5804i) q^{67} +85.7391i q^{69} +44.4376i q^{71} +(-0.859703 - 1.48905i) q^{73} +(54.3870 - 94.2011i) q^{75} +(69.5816 - 86.0131i) q^{77} +(62.9171 + 36.3252i) q^{79} +(27.5094 + 47.6476i) q^{81} +102.081 q^{83} -23.2059i q^{85} +(82.4821 - 47.6211i) q^{87} +(30.6865 - 53.1505i) q^{89} +(18.9506 - 7.28522i) q^{91} +(106.778 + 61.6480i) q^{93} +(-98.4538 + 56.8423i) q^{95} -102.826 q^{97} -178.584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 8 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 8 * q^9	\( 12 q - 6 q^{3} - 8 q^{9} + 14 q^{11} - 82 q^{17} + 94 q^{19} + 116 q^{25} + 60 q^{27} + 146 q^{33} - 270 q^{35} + 120 q^{41} - 40 q^{43} - 204 q^{49} + 106 q^{51} - 372 q^{57} - 62 q^{59} - 64 q^{65} + 178 q^{67} + 54 q^{73} - 140 q^{75} + 206 q^{81} + 392 q^{83} - 26 q^{89} + 88 q^{91} - 184 q^{97} - 872 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 - 8 * q^9 + 14 * q^11 - 82 * q^17 + 94 * q^19 + 116 * q^25 + 60 * q^27 + 146 * q^33 - 270 * q^35 + 120 * q^41 - 40 * q^43 - 204 * q^49 + 106 * q^51 - 372 * q^57 - 62 * q^59 - 64 * q^65 + 178 * q^67 + 54 * q^73 - 140 * q^75 + 206 * q^81 + 392 * q^83 - 26 * q^89 + 88 * q^91 - 184 * q^97 - 872 * q^99

Introduction

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