LMFDB - Embedded newform 234.3.bb.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,3,Mod(19,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([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("234.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	234.bb (of order $12$, degree $4$, 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:	$6.37603818603$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.37
Dual form			234.3.bb.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.26795 + 1.26795i) q^{5} +(-2.50000 - 9.33013i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.19615 + 1.26795i) q^{10} +(-9.92820 - 2.66025i) q^{11} +(-11.2583 - 6.50000i) q^{13} +13.6603 q^{14} +(2.00000 + 3.46410i) q^{16} +(-16.3923 - 9.46410i) q^{17} +(31.9545 - 8.56218i) q^{19} +(-0.928203 - 3.46410i) q^{20} +(7.26795 - 12.5885i) q^{22} +(3.58846 - 2.07180i) q^{23} -21.7846i q^{25} +(13.0000 - 13.0000i) q^{26} +(-5.00000 + 18.6603i) q^{28} +(-8.66025 - 15.0000i) q^{29} +(22.1699 + 22.1699i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(18.9282 - 18.9282i) q^{34} +(8.66025 - 15.0000i) q^{35} +(-35.7583 - 9.58142i) q^{37} +46.7846i q^{38} +5.07180 q^{40} +(6.67949 - 24.9282i) q^{41} +(-13.2846 - 7.66987i) q^{43} +(14.5359 + 14.5359i) q^{44} +(1.51666 + 5.66025i) q^{46} +(-7.01924 + 7.01924i) q^{47} +(-38.3660 + 22.1506i) q^{49} +(29.7583 + 7.97372i) q^{50} +(13.0000 + 22.5167i) q^{52} +61.6743 q^{53} +(-9.21539 - 15.9615i) q^{55} +(-23.6603 - 13.6603i) q^{56} +(23.6603 - 6.33975i) q^{58} +(17.1051 + 63.8372i) q^{59} +(3.65064 - 6.32309i) q^{61} +(-38.3993 + 22.1699i) q^{62} -8.00000i q^{64} +(-6.03332 - 22.5167i) q^{65} +(-10.1532 + 37.8923i) q^{67} +(18.9282 + 32.7846i) q^{68} +(17.3205 + 17.3205i) q^{70} +(-103.890 + 27.8372i) q^{71} +(-67.4186 + 67.4186i) q^{73} +(26.1769 - 45.3397i) q^{74} +(-63.9090 - 17.1244i) q^{76} +99.2820i q^{77} +11.8756 q^{79} +(-1.85641 + 6.92820i) q^{80} +(31.6077 + 18.2487i) q^{82} +(-111.033 - 111.033i) q^{83} +(-8.78461 - 32.7846i) q^{85} +(15.3397 - 15.3397i) q^{86} +(-25.1769 + 14.5359i) q^{88} +(-162.067 - 43.4256i) q^{89} +(-32.5000 + 121.292i) q^{91} -8.28719 q^{92} +(-7.01924 - 12.1577i) q^{94} +(51.3731 + 29.6603i) q^{95} +(150.246 - 40.2583i) q^{97} +(-16.2154 - 60.5167i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 12 q^{5} - 10 q^{7} + 8 q^{8} + 12 q^{10} - 12 q^{11} + 20 q^{14} + 8 q^{16} - 24 q^{17} + 62 q^{19} + 24 q^{20} + 36 q^{22} - 48 q^{23} + 52 q^{26} - 20 q^{28} + 106 q^{31} - 8 q^{32} + 48 q^{34}+ \cdots - 148 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 12 * q^5 - 10 * q^7 + 8 * q^8 + 12 * q^10 - 12 * q^11 + 20 * q^14 + 8 * q^16 - 24 * q^17 + 62 * q^19 + 24 * q^20 + 36 * q^22 - 48 * q^23 + 52 * q^26 - 20 * q^28 + 106 * q^31 - 8 * q^32 + 48 * q^34 - 98 * q^37 + 48 * q^40 + 96 * q^41 + 30 * q^43 + 72 * q^44 - 84 * q^46 - 132 * q^47 - 150 * q^49 + 74 * q^50 + 52 * q^52 - 72 * q^53 - 120 * q^55 - 60 * q^56 + 60 * q^58 - 84 * q^59 - 72 * q^61 + 30 * q^62 + 156 * q^65 - 148 * q^67 + 48 * q^68 - 180 * q^71 - 190 * q^73 - 20 * q^74 - 124 * q^76 + 96 * q^79 + 48 * q^80 + 168 * q^82 - 264 * q^83 + 48 * q^85 + 96 * q^86 + 24 * q^88 - 288 * q^89 - 130 * q^91 - 144 * q^92 - 132 * q^94 + 60 * q^95 + 310 * q^97 - 148 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	1.26795	+	1.26795i	0.253590	+	0.253590i	0.822441	−	0.568851i	$-0.192612\pi$
$5$	1.26795	+	1.26795i	0.253590	+	0.253590i	−0.568851	+	0.822441i	$0.692612\pi$
$6$		0			0
$7$	−2.50000	−	9.33013i	−0.357143	−	1.33288i	−0.877766	−	0.479089i	$-0.840967\pi$
$7$	−2.50000	−	9.33013i	−0.357143	−	1.33288i	0.520624	−	0.853786i	$-0.325700\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		0			0
$10$	−2.19615	+	1.26795i	−0.219615	+	0.126795i
$11$	−9.92820	−	2.66025i	−0.902564	−	0.241841i	−0.222447	−	0.974945i	$-0.571404\pi$
$11$	−9.92820	−	2.66025i	−0.902564	−	0.241841i	−0.680117	+	0.733104i	$0.738071\pi$
$12$		0			0
$13$	−11.2583	−	6.50000i	−0.866025	−	0.500000i
$13$	−11.2583	−	6.50000i	−0.866025	−	0.500000i
$14$	13.6603			0.975732
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−16.3923	−	9.46410i	−0.964253	−	0.556712i	−0.0667738	−	0.997768i	$-0.521271\pi$
$17$	−16.3923	−	9.46410i	−0.964253	−	0.556712i	−0.897479	+	0.441056i	$0.854604\pi$
$18$		0			0
$19$	31.9545	−	8.56218i	1.68181	−	0.450641i	0.713558	−	0.700597i	$-0.247083\pi$
$19$	31.9545	−	8.56218i	1.68181	−	0.450641i	0.968257	+	0.249956i	$0.0804160\pi$
$20$	−0.928203	−	3.46410i	−0.0464102	−	0.173205i
$21$		0			0
$22$	7.26795	−	12.5885i	0.330361	−	0.572203i
$23$	3.58846	−	2.07180i	0.156020	−	0.0900781i	−0.419957	−	0.907544i	$-0.637955\pi$
$23$	3.58846	−	2.07180i	0.156020	−	0.0900781i	0.575977	+	0.817466i	$0.304622\pi$
$24$		0			0
$25$		−	21.7846i		−	0.871384i
$26$	13.0000	−	13.0000i	0.500000	−	0.500000i
$27$		0			0
$28$	−5.00000	+	18.6603i	−0.178571	+	0.666438i
$29$	−8.66025	−	15.0000i	−0.298629	−	0.517241i	0.677193	−	0.735805i	$-0.263196\pi$
$29$	−8.66025	−	15.0000i	−0.298629	−	0.517241i	−0.975823	+	0.218564i	$0.929863\pi$
$30$		0			0
$31$	22.1699	+	22.1699i	0.715157	+	0.715157i	0.967609	−	0.252452i	$-0.0812370\pi$
$31$	22.1699	+	22.1699i	0.715157	+	0.715157i	−0.252452	+	0.967609i	$0.581237\pi$
$32$	−5.46410	+	1.46410i	−0.170753	+	0.0457532i
$33$		0			0
$34$	18.9282	−	18.9282i	0.556712	−	0.556712i
$35$	8.66025	−	15.0000i	0.247436	−	0.428571i
$36$		0			0
$37$	−35.7583	−	9.58142i	−0.966441	−	0.258957i	−0.259117	−	0.965846i	$-0.583431\pi$
$37$	−35.7583	−	9.58142i	−0.966441	−	0.258957i	−0.707325	+	0.706889i	$0.750098\pi$
$38$			46.7846i			1.23117i
$39$		0			0
$40$	5.07180			0.126795
$41$	6.67949	−	24.9282i	0.162914	−	0.608005i	−0.835383	−	0.549669i	$-0.814754\pi$
$41$	6.67949	−	24.9282i	0.162914	−	0.608005i	0.998297	−	0.0583360i	$-0.0185795\pi$
$42$		0			0
$43$	−13.2846	−	7.66987i	−0.308944	−	0.178369i	0.337510	−	0.941322i	$-0.390415\pi$
$43$	−13.2846	−	7.66987i	−0.308944	−	0.178369i	−0.646454	+	0.762953i	$0.723749\pi$
$44$	14.5359	+	14.5359i	0.330361	+	0.330361i
$45$		0			0
$46$	1.51666	+	5.66025i	0.0329709	+	0.123049i
$47$	−7.01924	+	7.01924i	−0.149345	+	0.149345i	−0.777826	−	0.628480i	$-0.783677\pi$
$47$	−7.01924	+	7.01924i	−0.149345	+	0.149345i	0.628480	+	0.777826i	$0.283677\pi$
$48$		0			0
$49$	−38.3660	+	22.1506i	−0.782980	+	0.452054i
$50$	29.7583	+	7.97372i	0.595167	+	0.159474i
$51$		0			0
$52$	13.0000	+	22.5167i	0.250000	+	0.433013i
$53$	61.6743			1.16367			0.581833	−	0.813308i	$-0.302336\pi$
$53$	61.6743			1.16367			0.581833	+	0.813308i	$0.302336\pi$
$54$		0			0
$55$	−9.21539	−	15.9615i	−0.167553	−	0.290210i
$56$	−23.6603	−	13.6603i	−0.422505	−	0.243933i
$57$		0			0
$58$	23.6603	−	6.33975i	0.407935	−	0.109306i
$59$	17.1051	+	63.8372i	0.289917	+	1.08199i	0.945171	+	0.326577i	$0.105895\pi$
$59$	17.1051	+	63.8372i	0.289917	+	1.08199i	−0.655253	+	0.755409i	$0.727438\pi$
$60$		0			0
$61$	3.65064	−	6.32309i	0.0598465	−	0.103657i	−0.834550	−	0.550932i	$-0.814272\pi$
$61$	3.65064	−	6.32309i	0.0598465	−	0.103657i	0.894396	+	0.447275i	$0.147606\pi$
$62$	−38.3993	+	22.1699i	−0.619344	+	0.357579i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−6.03332	−	22.5167i	−0.0928203	−	0.346410i
$66$		0			0
$67$	−10.1532	+	37.8923i	−0.151540	+	0.565557i	0.847836	+	0.530258i	$0.177905\pi$
$67$	−10.1532	+	37.8923i	−0.151540	+	0.565557i	−0.999377	+	0.0352988i	$0.988762\pi$
$68$	18.9282	+	32.7846i	0.278356	+	0.482127i
$69$		0			0
$70$	17.3205	+	17.3205i	0.247436	+	0.247436i
$71$	−103.890	+	27.8372i	−1.46324	+	0.392073i	−0.900606	−	0.434636i	$-0.856877\pi$
$71$	−103.890	+	27.8372i	−1.46324	+	0.392073i	−0.562630	+	0.826709i	$0.690210\pi$
$72$		0			0
$73$	−67.4186	+	67.4186i	−0.923542	+	0.923542i	−0.997278	−	0.0737356i	$-0.976508\pi$
$73$	−67.4186	+	67.4186i	−0.923542	+	0.923542i	0.0737356	+	0.997278i	$0.476508\pi$
$74$	26.1769	−	45.3397i	0.353742	−	0.612699i
$75$		0			0
$76$	−63.9090	−	17.1244i	−0.840907	−	0.225320i
$77$			99.2820i			1.28938i
$78$		0			0
$79$	11.8756			0.150325			0.0751623	−	0.997171i	$-0.476053\pi$
$79$	11.8756			0.150325			0.0751623	+	0.997171i	$0.476053\pi$
$80$	−1.85641	+	6.92820i	−0.0232051	+	0.0866025i
$81$		0			0
$82$	31.6077	+	18.2487i	0.385460	+	0.222545i
$83$	−111.033	−	111.033i	−1.33775	−	1.33775i	−0.898235	−	0.439516i	$-0.855150\pi$
$83$	−111.033	−	111.033i	−1.33775	−	1.33775i	−0.439516	−	0.898235i	$-0.644850\pi$
$84$		0			0
$85$	−8.78461	−	32.7846i	−0.103348	−	0.385701i
$86$	15.3397	−	15.3397i	0.178369	−	0.178369i
$87$		0			0
$88$	−25.1769	+	14.5359i	−0.286101	+	0.165181i
$89$	−162.067	−	43.4256i	−1.82097	−	0.487928i	−0.824065	−	0.566496i	$-0.808299\pi$
$89$	−162.067	−	43.4256i	−1.82097	−	0.487928i	−0.996909	+	0.0785673i	$0.974965\pi$
$90$		0			0
$91$	−32.5000	+	121.292i	−0.357143	+	1.33288i
$92$	−8.28719			−0.0900781
$93$		0			0
$94$	−7.01924	−	12.1577i	−0.0746727	−	0.129337i
$95$	51.3731	+	29.6603i	0.540769	+	0.312213i
$96$		0			0
$97$	150.246	−	40.2583i	1.54893	−	0.415034i	0.619791	−	0.784767i	$-0.287217\pi$
$97$	150.246	−	40.2583i	1.54893	−	0.415034i	0.929138	+	0.369733i	$0.120551\pi$
$98$	−16.2154	−	60.5167i	−0.165463	−	0.617517i
$99$		0			0
$100$	−21.7846	+	37.7321i	−0.217846	+	0.377321i
$101$	161.785	−	93.4064i	1.60183	−	0.924816i	0.610706	−	0.791857i	$-0.290886\pi$
$101$	161.785	−	93.4064i	1.60183	−	0.924816i	0.991122	−	0.132958i	$-0.0424477\pi$
$102$		0			0
$103$			83.2628i			0.808377i	0.914676	+	0.404188i	$0.132446\pi$
$103$			83.2628i			0.808377i	−0.914676	+	0.404188i	$0.867554\pi$
$104$	−35.5167	+	9.51666i	−0.341506	+	0.0915064i
$105$		0			0
$106$	−22.5744	+	84.2487i	−0.212966	+	0.794799i
$107$	51.2487	+	88.7654i	0.478960	+	0.829583i	0.999709	−	0.0241269i	$-0.00768059\pi$
$107$	51.2487	+	88.7654i	0.478960	+	0.829583i	−0.520749	+	0.853710i	$0.674347\pi$
$108$		0			0
$109$	48.1891	+	48.1891i	0.442102	+	0.442102i	0.892718	−	0.450616i	$-0.148796\pi$
$109$	48.1891	+	48.1891i	0.442102	+	0.442102i	−0.450616	+	0.892718i	$0.648796\pi$
$110$	25.1769	−	6.74613i	0.228881	−	0.0613285i
$111$		0			0
$112$	27.3205	−	27.3205i	0.243933	−	0.243933i
$113$	−22.6077	+	39.1577i	−0.200068	+	0.346528i	−0.948550	−	0.316627i	$-0.897450\pi$
$113$	−22.6077	+	39.1577i	−0.200068	+	0.346528i	0.748482	+	0.663155i	$0.230783\pi$
$114$		0			0
$115$	7.17691	+	1.92305i	0.0624080	+	0.0167222i
$116$			34.6410i			0.298629i
$117$		0			0
$118$	−93.4641			−0.792069
$119$	−47.3205	+	176.603i	−0.397651	+	1.48405i
$120$		0			0
$121$	−13.2968	−	7.67691i	−0.109891	−	0.0634456i
$122$	7.30127	+	7.30127i	0.0598465	+	0.0598465i
$123$		0			0
$124$	−16.2295	−	60.5692i	−0.130883	−	0.488461i
$125$	59.3205	−	59.3205i	0.474564	−	0.474564i
$126$		0			0
$127$	205.115	−	118.423i	1.61508	−	0.932465i	0.626908	−	0.779093i	$-0.284320\pi$
$127$	205.115	−	118.423i	1.61508	−	0.932465i	0.988169	−	0.153372i	$-0.0490132\pi$
$128$	10.9282	+	2.92820i	0.0853766	+	0.0228766i
$129$		0			0
$130$	32.9667			0.253590
$131$	209.636			1.60027			0.800137	−	0.599817i	$-0.204760\pi$
$131$	209.636			1.60027			0.800137	+	0.599817i	$0.204760\pi$
$132$		0			0
$133$	−159.772	−	276.734i	−1.20130	−	2.08071i
$134$	−48.0455	−	27.7391i	−0.358549	−	0.207008i
$135$		0			0
$136$	−51.7128	+	13.8564i	−0.380241	+	0.101885i
$137$	−29.4782	−	110.014i	−0.215169	−	0.803023i	−0.986107	−	0.166112i	$-0.946879\pi$
$137$	−29.4782	−	110.014i	−0.215169	−	0.803023i	0.770938	−	0.636911i	$-0.219788\pi$
$138$		0			0
$139$	47.8538	−	82.8853i	0.344272	−	0.596297i	−0.640949	−	0.767583i	$-0.721459\pi$
$139$	47.8538	−	82.8853i	0.344272	−	0.596297i	0.985221	+	0.171287i	$0.0547924\pi$
$140$	−30.0000	+	17.3205i	−0.214286	+	0.123718i
$141$		0			0
$142$		−	152.105i		−	1.07116i
$143$	94.4833	+	94.4833i	0.660723	+	0.660723i
$144$		0			0
$145$	8.03848	−	30.0000i	0.0554378	−	0.206897i
$146$	−67.4186	−	116.772i	−0.461771	−	0.799811i
$147$		0			0
$148$	52.3538	+	52.3538i	0.353742	+	0.353742i
$149$	54.9282	−	14.7180i	0.368646	−	0.0987783i	−0.0697402	−	0.997565i	$-0.522217\pi$
$149$	54.9282	−	14.7180i	0.368646	−	0.0987783i	0.438386	+	0.898787i	$0.355550\pi$
$150$		0			0
$151$	−55.0385	+	55.0385i	−0.364493	+	0.364493i	−0.865464	−	0.500971i	$-0.832976\pi$
$151$	−55.0385	+	55.0385i	−0.364493	+	0.364493i	0.500971	+	0.865464i	$0.332976\pi$
$152$	46.7846	−	81.0333i	0.307793	−	0.533114i
$153$		0			0
$154$	−135.622	−	36.3397i	−0.880661	−	0.235972i
$155$			56.2205i			0.362713i
$156$		0			0
$157$	55.4308			0.353062			0.176531	−	0.984295i	$-0.443512\pi$
$157$	55.4308			0.353062			0.176531	+	0.984295i	$0.443512\pi$
$158$	−4.34679	+	16.2224i	−0.0275113	+	0.102674i
$159$		0			0
$160$	−8.78461	−	5.07180i	−0.0549038	−	0.0316987i
$161$	−28.3013	−	28.3013i	−0.175784	−	0.175784i
$162$		0			0
$163$	−52.9468	−	197.600i	−0.324827	−	1.21227i	−0.914486	−	0.404618i	$-0.867405\pi$
$163$	−52.9468	−	197.600i	−0.324827	−	1.21227i	0.589659	−	0.807652i	$-0.299262\pi$
$164$	−36.4974	+	36.4974i	−0.222545	+	0.222545i
$165$		0			0
$166$	192.315	−	111.033i	1.15853	−	0.668875i
$167$	156.315	+	41.8846i	0.936020	+	0.250806i	0.694420	−	0.719570i	$-0.255661\pi$
$167$	156.315	+	41.8846i	0.936020	+	0.250806i	0.241600	+	0.970376i	$0.422328\pi$
$168$		0			0
$169$	84.5000	+	146.358i	0.500000	+	0.866025i
$170$	48.0000			0.282353
$171$		0			0
$172$	15.3397	+	26.5692i	0.0891846	+	0.154472i
$173$	−232.492	−	134.229i	−1.34389	−	0.775893i	−0.356511	−	0.934291i	$-0.616034\pi$
$173$	−232.492	−	134.229i	−1.34389	−	0.775893i	−0.987375	+	0.158398i	$0.949367\pi$
$174$		0			0
$175$	−203.253	+	54.4615i	−1.16145	+	0.311209i
$176$	−10.6410	−	39.7128i	−0.0604603	−	0.225641i
$177$		0			0
$178$	118.641	−	205.492i	0.666523	−	1.15445i
$179$	247.492	−	142.890i	1.38264	−	0.798267i	0.390167	−	0.920744i	$-0.372417\pi$
$179$	247.492	−	142.890i	1.38264	−	0.798267i	0.992471	+	0.122477i	$0.0390839\pi$
$180$		0			0
$181$			177.646i			0.981471i	0.871309	+	0.490735i	$0.163272\pi$
$181$			177.646i			0.981471i	−0.871309	+	0.490735i	$0.836728\pi$
$182$	−153.792	−	88.7917i	−0.845009	−	0.487866i
$183$		0			0
$184$	3.03332	−	11.3205i	0.0164854	−	0.0615245i
$185$	−33.1910	−	57.4885i	−0.179411	−	0.310749i
$186$		0			0
$187$	137.569	+	137.569i	0.735664	+	0.735664i
$188$	19.1769	−	5.13844i	0.102005	−	0.0273321i
$189$		0			0
$190$	−59.3205	+	59.3205i	−0.312213	+	0.312213i
$191$	98.6603	−	170.885i	0.516546	−	0.894684i	−0.483270	−	0.875472i	$-0.660551\pi$
$191$	98.6603	−	170.885i	0.516546	−	0.894684i	0.999815	−	0.0192120i	$-0.00611576\pi$
$192$		0			0
$193$	−20.2846	−	5.43524i	−0.105102	−	0.0281619i	0.205885	−	0.978576i	$-0.433993\pi$
$193$	−20.2846	−	5.43524i	−0.105102	−	0.0281619i	−0.310987	+	0.950414i	$0.600659\pi$
$194$			219.976i			1.13389i
$195$		0			0
$196$	88.6025			0.452054
$197$	−39.1487	+	146.105i	−0.198725	+	0.741650i	0.792547	+	0.609811i	$0.208755\pi$
$197$	−39.1487	+	146.105i	−0.198725	+	0.741650i	−0.991271	+	0.131839i	$0.957912\pi$
$198$		0			0
$199$	19.2391	+	11.1077i	0.0966789	+	0.0558176i	0.547560	−	0.836766i	$-0.315557\pi$
$199$	19.2391	+	11.1077i	0.0966789	+	0.0558176i	−0.450881	+	0.892584i	$0.648890\pi$
$200$	−43.5692	−	43.5692i	−0.217846	−	0.217846i
$201$		0			0
$202$	68.3782	+	255.191i	0.338506	+	1.26332i
$203$	−118.301	+	118.301i	−0.582765	+	0.582765i
$204$		0			0
$205$	40.0770	−	23.1384i	0.195497	−	0.112870i
$206$	−113.739	−	30.4763i	−0.552132	−	0.147943i
$207$		0			0
$208$		−	52.0000i		−	0.250000i
$209$	−340.028			−1.62693
$210$		0			0
$211$	−32.1007	−	55.6000i	−0.152136	−	0.263507i	0.779877	−	0.625933i	$-0.215282\pi$
$211$	−32.1007	−	55.6000i	−0.152136	−	0.263507i	−0.932012	+	0.362426i	$0.881948\pi$
$212$	−106.823	−	61.6743i	−0.503882	−	0.290917i
$213$		0			0
$214$	−140.014	+	37.5167i	−0.654271	+	0.175311i
$215$	−7.11920	−	26.5692i	−0.0331126	−	0.123578i
$216$		0			0
$217$	151.423	−	262.272i	0.697802	−	1.20863i
$218$	−83.4660	+	48.1891i	−0.382872	+	0.221051i
$219$		0			0
$220$			36.8616i			0.167553i
$221$	123.033	+	213.100i	0.556712	+	0.964253i
$222$		0			0
$223$	−56.5622	+	211.093i	−0.253642	+	0.946605i	0.715199	+	0.698921i	$0.246336\pi$
$223$	−56.5622	+	211.093i	−0.253642	+	0.946605i	−0.968841	+	0.247684i	$0.920331\pi$
$224$	27.3205	+	47.3205i	0.121967	+	0.211252i
$225$		0			0
$226$	−45.2154	−	45.2154i	−0.200068	−	0.200068i
$227$	−62.4449	+	16.7321i	−0.275088	+	0.0737095i	−0.393725	−	0.919228i	$-0.628814\pi$
$227$	−62.4449	+	16.7321i	−0.275088	+	0.0737095i	0.118638	+	0.992938i	$0.462147\pi$
$228$		0			0
$229$	58.6846	−	58.6846i	0.256265	−	0.256265i	−0.567268	−	0.823533i	$-0.692000\pi$
$229$	58.6846	−	58.6846i	0.256265	−	0.256265i	0.823533	+	0.567268i	$0.192000\pi$
$230$	−5.25387	+	9.09996i	−0.0228429	+	0.0395651i
$231$		0			0
$232$	−47.3205	−	12.6795i	−0.203968	−	0.0546530i
$233$		−	380.669i		−	1.63377i	−0.576798	−	0.816887i	$-0.695698\pi$
$233$		−	380.669i		−	1.63377i	0.576798	−	0.816887i	$-0.304302\pi$
$234$		0			0
$235$	−17.8001			−0.0757450
$236$	34.2102	−	127.674i	0.144959	−	0.540993i
$237$		0			0
$238$	−223.923	−	129.282i	−0.940853	−	0.543202i
$239$	167.138	+	167.138i	0.699324	+	0.699324i	0.964265	−	0.264941i	$-0.0853524\pi$
$239$	167.138	+	167.138i	0.699324	+	0.699324i	−0.264941	+	0.964265i	$0.585352\pi$
$240$		0			0
$241$	0.796806	+	2.97372i	0.00330625	+	0.0123391i	0.967559	−	0.252644i	$-0.0813002\pi$
$241$	0.796806	+	2.97372i	0.00330625	+	0.0123391i	−0.964253	+	0.264983i	$0.914634\pi$
$242$	15.3538	−	15.3538i	0.0634456	−	0.0634456i
$243$		0			0
$244$	−12.6462	+	7.30127i	−0.0518286	+	0.0299232i
$245$	−76.7321	−	20.5603i	−0.313192	−	0.0839196i
$246$		0			0
$247$	−415.408	−	111.308i	−1.68181	−	0.450641i
$248$	88.6795			0.357579
$249$		0			0
$250$	59.3205	+	102.746i	0.237282	+	0.410985i
$251$	180.746	+	104.354i	0.720104	+	0.415752i	0.814791	−	0.579755i	$-0.196852\pi$
$251$	180.746	+	104.354i	0.720104	+	0.415752i	−0.0946869	+	0.995507i	$0.530185\pi$
$252$		0			0
$253$	−41.1384	+	11.0230i	−0.162603	+	0.0435692i
$254$	86.6917	+	323.538i	0.341306	+	1.27377i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−64.2769	+	37.1103i	−0.250105	+	0.144398i	−0.619812	−	0.784750i	$-0.712791\pi$
$257$	−64.2769	+	37.1103i	−0.250105	+	0.144398i	0.369708	+	0.929148i	$0.379458\pi$
$258$		0			0
$259$			357.583i			1.38063i
$260$	−12.0666	+	45.0333i	−0.0464102	+	0.173205i
$261$		0			0
$262$	−76.7321	+	286.368i	−0.292870	+	1.09301i
$263$	−12.1821	−	21.1000i	−0.0463197	−	0.0802280i	0.841936	−	0.539577i	$-0.181416\pi$
$263$	−12.1821	−	21.1000i	−0.0463197	−	0.0802280i	−0.888256	+	0.459349i	$0.848083\pi$
$264$		0			0
$265$	78.1999	+	78.1999i	0.295094	+	0.295094i
$266$	436.506	−	116.962i	1.64100	−	0.439705i
$267$		0			0
$268$	55.4782	−	55.4782i	0.207008	−	0.207008i
$269$	−87.8705	+	152.196i	−0.326656	+	0.565785i	−0.981846	−	0.189679i	$-0.939255\pi$
$269$	−87.8705	+	152.196i	−0.326656	+	0.565785i	0.655190	+	0.755464i	$0.272589\pi$
$270$		0			0
$271$	269.169	+	72.1237i	0.993244	+	0.266139i	0.718613	−	0.695411i	$-0.244777\pi$
$271$	269.169	+	72.1237i	0.993244	+	0.266139i	0.274632	+	0.961550i	$0.411444\pi$
$272$		−	75.7128i		−	0.278356i
$273$		0			0
$274$	161.072			0.587853
$275$	−57.9526	+	216.282i	−0.210737	+	0.786480i
$276$		0			0
$277$	−387.100	−	223.492i	−1.39747	−	0.806831i	−0.403345	−	0.915048i	$-0.632153\pi$
$277$	−387.100	−	223.492i	−1.39747	−	0.806831i	−0.994127	+	0.108216i	$0.965486\pi$
$278$	95.7077	+	95.7077i	0.344272	+	0.344272i
$279$		0			0
$280$	−12.6795	−	47.3205i	−0.0452839	−	0.169002i
$281$	5.54483	−	5.54483i	0.0197325	−	0.0197325i	−0.697172	−	0.716904i	$-0.745558\pi$
$281$	5.54483	−	5.54483i	0.0197325	−	0.0197325i	0.716904	+	0.697172i	$0.245558\pi$
$282$		0			0
$283$	14.4160	−	8.32309i	0.0509400	−	0.0294102i	−0.474314	−	0.880356i	$-0.657304\pi$
$283$	14.4160	−	8.32309i	0.0509400	−	0.0294102i	0.525254	+	0.850946i	$0.323970\pi$
$284$	207.779	+	55.6743i	0.731618	+	0.196036i
$285$		0			0
$286$	−163.650	+	94.4833i	−0.572203	+	0.330361i
$287$	−249.282			−0.868579
$288$		0			0
$289$	34.6384	+	59.9955i	0.119856	+	0.207597i
$290$	38.0385	+	21.9615i	0.131167	+	0.0757294i
$291$		0			0
$292$	184.191	−	49.3538i	0.630791	−	0.169020i
$293$	−48.4885	−	180.962i	−0.165490	−	0.617616i	−0.997977	−	0.0635723i	$-0.979751\pi$
$293$	−48.4885	−	180.962i	−0.165490	−	0.617616i	0.832487	−	0.554044i	$-0.186916\pi$
$294$		0			0
$295$	−59.2539	+	102.631i	−0.200861	+	0.347901i
$296$	−90.6795	+	52.3538i	−0.306350	+	0.176871i
$297$		0			0
$298$			80.4205i			0.269867i
$299$	−53.8667			−0.180156
$300$		0			0
$301$	−38.3494	+	143.122i	−0.127407	+	0.475488i
$302$	−55.0385	−	95.3294i	−0.182247	−	0.315660i
$303$		0			0
$304$	93.5692	+	93.5692i	0.307793	+	0.307793i
$305$	12.6462	−	3.38853i	0.0414629	−	0.0111099i
$306$		0			0
$307$	375.069	−	375.069i	1.22172	−	1.22172i	0.254702	−	0.967020i	$-0.418023\pi$
$307$	375.069	−	375.069i	1.22172	−	1.22172i	0.967020	−	0.254702i	$-0.0819774\pi$
$308$	99.2820	−	171.962i	0.322344	−	0.558317i
$309$		0			0
$310$	−76.7987	−	20.5781i	−0.247738	−	0.0663811i
$311$			296.238i			0.952535i	0.879300	+	0.476268i	$0.158011\pi$
$311$			296.238i			0.952535i	−0.879300	+	0.476268i	$0.841989\pi$
$312$		0			0
$313$	118.286			0.377910			0.188955	−	0.981986i	$-0.439490\pi$
$313$	118.286			0.377910			0.188955	+	0.981986i	$0.439490\pi$
$314$	−20.2891	+	75.7199i	−0.0646149	+	0.241146i
$315$		0			0
$316$	−20.5692	−	11.8756i	−0.0650925	−	0.0375812i
$317$	280.708	+	280.708i	0.885513	+	0.885513i	0.994088	−	0.108575i	$-0.0346288\pi$
$317$	280.708	+	280.708i	0.885513	+	0.885513i	−0.108575	+	0.994088i	$0.534629\pi$
$318$		0			0
$319$	46.0770	+	171.962i	0.144442	+	0.539064i
$320$	10.1436	−	10.1436i	0.0316987	−	0.0316987i
$321$		0			0
$322$	49.0192	−	28.3013i	0.152234	−	0.0878921i
$323$	−604.841	−	162.067i	−1.87257	−	0.501754i
$324$		0			0
$325$	−141.600	+	245.258i	−0.435692	+	0.754641i
$326$	289.306			0.887443
$327$		0			0
$328$	−36.4974	−	63.2154i	−0.111273	−	0.192730i
$329$	83.0385	+	47.9423i	0.252397	+	0.145721i
$330$		0			0
$331$	−137.454	+	36.8308i	−0.415270	+	0.111271i	−0.460404	−	0.887710i	$-0.652295\pi$
$331$	−137.454	+	36.8308i	−0.415270	+	0.111271i	0.0451334	+	0.998981i	$0.485629\pi$
$332$	81.2820	+	303.349i	0.244825	+	0.913701i
$333$		0			0
$334$	−114.431	+	198.200i	−0.342607	+	0.593413i
$335$	−60.9193	+	35.1718i	−0.181849	+	0.104990i
$336$		0			0
$337$			347.508i			1.03118i	0.856835	+	0.515590i	$0.172427\pi$
$337$			347.508i			1.03118i	−0.856835	+	0.515590i	$0.827573\pi$
$338$	−230.858	+	61.8583i	−0.683013	+	0.183013i
$339$		0			0
$340$	−17.5692	+	65.5692i	−0.0516742	+	0.192851i
$341$	−161.130	−	279.084i	−0.472521	−	0.818430i
$342$		0			0
$343$	−32.0929	−	32.0929i	−0.0935654	−	0.0935654i
$344$	−41.9090	+	11.2295i	−0.121828	+	0.0326438i
$345$		0			0
$346$	268.459	−	268.459i	0.775893	−	0.775893i
$347$	218.851	−	379.061i	0.630695	−	1.09240i	−0.356715	−	0.934213i	$-0.616103\pi$
$347$	218.851	−	379.061i	0.630695	−	1.09240i	0.987410	−	0.158183i	$-0.0505635\pi$
$348$		0			0
$349$	−432.889	−	115.992i	−1.24037	−	0.332356i	−0.421761	−	0.906707i	$-0.638588\pi$
$349$	−432.889	−	115.992i	−1.24037	−	0.332356i	−0.818609	+	0.574351i	$0.805254\pi$
$350$		−	297.583i		−	0.850238i
$351$		0			0
$352$	58.1436			0.165181
$353$	151.914	−	566.951i	0.430352	−	1.60609i	−0.321600	−	0.946876i	$-0.604221\pi$
$353$	151.914	−	566.951i	0.430352	−	1.60609i	0.751951	−	0.659218i	$-0.229113\pi$
$354$		0			0
$355$	−167.023	−	96.4308i	−0.470487	−	0.271636i
$356$	237.282	+	237.282i	0.666523	+	0.666523i
$357$		0			0
$358$	104.603	+	390.382i	0.292186	+	1.09045i
$359$	−64.2769	+	64.2769i	−0.179044	+	0.179044i	−0.790939	−	0.611895i	$-0.790408\pi$
$359$	−64.2769	+	64.2769i	−0.179044	+	0.179044i	0.611895	+	0.790939i	$0.290408\pi$
$360$		0			0
$361$	635.143	−	366.700i	1.75940	−	1.01579i
$362$	−242.669	−	65.0230i	−0.670357	−	0.179622i
$363$		0			0
$364$	177.583	−	177.583i	0.487866	−	0.487866i
$365$	−170.967			−0.468402
$366$		0			0
$367$	108.892	+	188.607i	0.296709	+	0.513916i	0.975381	−	0.220526i	$-0.0707774\pi$
$367$	108.892	+	188.607i	0.296709	+	0.513916i	−0.678672	+	0.734442i	$0.737444\pi$
$368$	14.3538	+	8.28719i	0.0390050	+	0.0225195i
$369$		0			0
$370$	90.6795	−	24.2975i	0.245080	−	0.0656689i
$371$	−154.186	−	575.429i	−0.415595	−	1.55102i
$372$		0			0
$373$	109.803	−	190.185i	0.294378	−	0.509878i	−0.680462	−	0.732784i	$-0.738221\pi$
$373$	109.803	−	190.185i	0.294378	−	0.509878i	0.974840	+	0.222905i	$0.0715541\pi$
$374$	−238.277	+	137.569i	−0.637104	+	0.367832i
$375$		0			0
$376$			28.0770i			0.0746727i
$377$			225.167i			0.597259i
$378$		0			0
$379$	50.1846	−	187.292i	0.132413	−	0.494173i	−0.867582	−	0.497294i	$-0.834327\pi$
$379$	50.1846	−	187.292i	0.132413	−	0.494173i	0.999995	+	0.00312126i	$0.000993528\pi$
$380$	−59.3205	−	102.746i	−0.156107	−	0.270385i
$381$		0			0
$382$	197.321	+	197.321i	0.516546	+	0.516546i
$383$	−188.172	+	50.4205i	−0.491310	+	0.131646i	−0.495964	−	0.868343i	$-0.665185\pi$
$383$	−188.172	+	50.4205i	−0.491310	+	0.131646i	0.00465401	+	0.999989i	$0.498519\pi$
$384$		0			0
$385$	−125.885	+	125.885i	−0.326973	+	0.326973i
$386$	14.8494	−	25.7199i	0.0384699	−	0.0666317i
$387$		0			0
$388$	−300.492	−	80.5167i	−0.774465	−	0.207517i
$389$			17.7513i			0.0456331i	0.999740	+	0.0228166i	$0.00726337\pi$
$389$			17.7513i			0.0456331i	−0.999740	+	0.0228166i	$0.992737\pi$
$390$		0			0
$391$	−78.4308			−0.200590
$392$	−32.4308	+	121.033i	−0.0827316	+	0.308758i
$393$		0			0
$394$	−185.254	−	106.956i	−0.470187	−	0.271463i
$395$	15.0577	+	15.0577i	0.0381208	+	0.0381208i
$396$		0			0
$397$	−87.3494	−	325.992i	−0.220024	−	0.821139i	−0.984337	−	0.176295i	$-0.943589\pi$
$397$	−87.3494	−	325.992i	−0.220024	−	0.821139i	0.764314	−	0.644844i	$-0.223078\pi$
$398$	−22.2154	+	22.2154i	−0.0558176	+	0.0558176i
$399$		0			0
$400$	75.4641	−	43.5692i	0.188660	−	0.108923i
$401$	496.435	+	133.019i	1.23799	+	0.331719i	0.817686	−	0.575664i	$-0.195256\pi$
$401$	496.435	+	133.019i	1.23799	+	0.331719i	0.420305	+	0.907383i	$0.361923\pi$
$402$		0			0
$403$	−105.492	−	393.700i	−0.261766	−	0.976923i
$404$	−373.626			−0.924816
$405$		0			0
$406$	−118.301	−	204.904i	−0.291382	−	0.504689i
$407$	329.527	+	190.252i	0.809649	+	0.467451i
$408$		0			0
$409$	−562.838	+	150.812i	−1.37613	+	0.368734i	−0.869715	−	0.493554i	$-0.835697\pi$
$409$	−562.838	+	150.812i	−1.37613	+	0.368734i	−0.506418	+	0.862288i	$0.669031\pi$
$410$	16.9385	+	63.2154i	0.0413134	+	0.154184i
$411$		0			0
$412$	83.2628	−	144.215i	0.202094	−	0.350037i
$413$	552.846	−	319.186i	1.33861	−	0.772847i
$414$		0			0
$415$		−	281.569i		−	0.678480i
$416$	71.0333	+	19.0333i	0.170753	+	0.0457532i
$417$		0			0
$418$	124.459	−	464.487i	0.297749	−	1.11121i
$419$	−391.177	−	677.538i	−0.933596	−	1.61704i	−0.777118	−	0.629355i	$-0.783319\pi$
$419$	−391.177	−	677.538i	−0.933596	−	1.61704i	−0.156479	−	0.987681i	$-0.550014\pi$
$420$		0			0
$421$	−27.0352	−	27.0352i	−0.0642166	−	0.0642166i	0.674269	−	0.738486i	$-0.264459\pi$
$421$	−27.0352	−	27.0352i	−0.0642166	−	0.0642166i	−0.738486	+	0.674269i	$0.764459\pi$
$422$	87.7006	−	23.4993i	0.207821	−	0.0556856i
$423$		0			0
$424$	123.349	−	123.349i	0.290917	−	0.290917i
$425$	−206.172	+	357.100i	−0.485110	+	0.840235i
$426$		0			0
$427$	−68.1218	−	18.2532i	−0.159536	−	0.0427475i
$428$		−	204.995i		−	0.478960i
$429$		0			0
$430$	38.9000			0.0904652
$431$	−162.995	+	608.305i	−0.378178	+	1.41138i	0.470467	+	0.882418i	$0.344086\pi$
$431$	−162.995	+	608.305i	−0.378178	+	1.41138i	−0.848645	+	0.528963i	$0.822581\pi$
$432$		0			0
$433$	−205.928	−	118.892i	−0.475583	−	0.274578i	0.242991	−	0.970029i	$-0.421872\pi$
$433$	−205.928	−	118.892i	−0.475583	−	0.274578i	−0.718574	+	0.695451i	$0.755205\pi$
$434$	302.846	+	302.846i	0.697802	+	0.697802i
$435$		0			0
$436$	−35.2769	−	131.655i	−0.0809103	−	0.301961i
$437$	96.9282	−	96.9282i	0.221804	−	0.221804i
$438$		0			0
$439$	597.092	−	344.731i	1.36012	−	0.785265i	0.370480	−	0.928841i	$-0.379193\pi$
$439$	597.092	−	344.731i	1.36012	−	0.785265i	0.989639	+	0.143576i	$0.0458600\pi$
$440$	−50.3538	−	13.4923i	−0.114441	−	0.0306642i
$441$		0			0
$442$	−336.133	+	90.0666i	−0.760483	+	0.203771i
$443$	304.028			0.686294			0.343147	−	0.939282i	$-0.388507\pi$
$443$	304.028			0.686294			0.343147	+	0.939282i	$0.388507\pi$
$444$		0			0
$445$	−150.431	−	260.554i	−0.338047	−	0.585514i
$446$	−267.655	−	154.531i	−0.600124	−	0.346481i
$447$		0			0
$448$	−74.6410	+	20.0000i	−0.166609	+	0.0446429i
$449$	73.4589	+	274.153i	0.163606	+	0.610585i	0.998214	+	0.0597407i	$0.0190274\pi$
$449$	73.4589	+	274.153i	0.163606	+	0.610585i	−0.834608	+	0.550844i	$0.814306\pi$
$450$		0			0
$451$	−132.631	+	229.723i	−0.294081	+	0.509364i
$452$	78.3154	−	45.2154i	0.173264	−	0.100034i
$453$		0			0
$454$		−	91.4256i		−	0.201378i
$455$	−195.000	+	112.583i	−0.428571	+	0.247436i
$456$		0			0
$457$	−37.1584	+	138.677i	−0.0813093	+	0.303451i	−0.994590	−	0.103881i	$-0.966874\pi$
$457$	−37.1584	+	138.677i	−0.0813093	+	0.303451i	0.913280	+	0.407331i	$0.133541\pi$
$458$	58.6846	+	101.645i	0.128132	+	0.221932i
$459$		0			0
$460$	−10.5077	−	10.5077i	−0.0228429	−	0.0228429i
$461$	−568.435	+	152.312i	−1.23305	+	0.330394i	−0.815765	−	0.578383i	$-0.803684\pi$
$461$	−568.435	+	152.312i	−1.23305	+	0.330394i	−0.417282	+	0.908777i	$0.637017\pi$
$462$		0			0
$463$	−169.599	+	169.599i	−0.366305	+	0.366305i	−0.866128	−	0.499823i	$-0.833399\pi$
$463$	−169.599	+	169.599i	−0.366305	+	0.366305i	0.499823	+	0.866128i	$0.333399\pi$
$464$	34.6410	−	60.0000i	0.0746574	−	0.129310i
$465$		0			0
$466$	520.004	+	139.335i	1.11589	+	0.299001i
$467$		−	732.649i		−	1.56884i	−0.620230	−	0.784420i	$-0.712961\pi$
$467$		−	732.649i		−	1.56884i	0.620230	−	0.784420i	$-0.287039\pi$
$468$		0			0
$469$	378.923			0.807938
$470$	6.51528	−	24.3154i	0.0138623	−	0.0517348i
$471$		0			0
$472$	161.885	+	93.4641i	0.342976	+	0.198017i
$473$	111.488	+	111.488i	0.235705	+	0.235705i
$474$		0			0
$475$	−186.524	−	696.116i	−0.392681	−	1.46551i
$476$	258.564	−	258.564i	0.543202	−	0.543202i
$477$		0			0
$478$	−289.492	+	167.138i	−0.605632	+	0.349662i
$479$	357.167	+	95.7025i	0.745651	+	0.199796i	0.611588	−	0.791176i	$-0.290531\pi$
$479$	357.167	+	95.7025i	0.745651	+	0.199796i	0.134063	+	0.990973i	$0.457198\pi$
$480$		0			0
$481$	340.300	+	340.300i	0.707484	+	0.707484i
$482$	−4.35383			−0.00903284
$483$		0			0
$484$	15.3538	+	26.5936i	0.0317228	+	0.0549455i
$485$	241.550	+	139.459i	0.498041	+	0.287544i
$486$		0			0
$487$	187.145	−	50.1455i	0.384282	−	0.102968i	−0.0615056	−	0.998107i	$-0.519590\pi$
$487$	187.145	−	50.1455i	0.384282	−	0.102968i	0.445788	+	0.895139i	$0.352924\pi$
$488$	−5.34490	−	19.9474i	−0.0109527	−	0.0408759i
$489$		0			0
$490$	56.1718	−	97.2923i	0.114636	−	0.198556i
$491$	31.9808	−	18.4641i	0.0651339	−	0.0376051i	−0.467079	−	0.884215i	$-0.654694\pi$
$491$	31.9808	−	18.4641i	0.0651339	−	0.0376051i	0.532213	+	0.846610i	$0.321360\pi$
$492$		0			0
$493$			327.846i			0.665002i
$494$	304.100	−	526.717i	0.615587	−	1.06623i
$495$		0			0
$496$	−32.4589	+	121.138i	−0.0654414	+	0.244231i
$497$	519.449	+	899.711i	1.04517	+	1.81028i
$498$		0			0
$499$	462.769	+	462.769i	0.927393	+	0.927393i	0.997537	−	0.0701438i	$-0.0223458\pi$
$499$	462.769	+	462.769i	0.927393	+	0.927393i	−0.0701438	+	0.997537i	$0.522346\pi$
$500$	−162.067	+	43.4256i	−0.324133	+	0.0868513i
$501$		0			0
$502$	−208.708	+	208.708i	−0.415752	+	0.415752i
$503$	−179.378	+	310.692i	−0.356617	+	0.617678i	−0.987393	−	0.158286i	$-0.949403\pi$
$503$	−179.378	+	310.692i	−0.356617	+	0.617678i	0.630777	+	0.775965i	$0.282736\pi$
$504$		0			0
$505$	323.569	+	86.7001i	0.640731	+	0.171683i
$506$		−	60.2309i		−	0.119033i
$507$		0			0
$508$	−473.692			−0.932465
$509$	190.972	−	712.717i	0.375190	−	1.40023i	−0.477876	−	0.878427i	$-0.658593\pi$
$509$	190.972	−	712.717i	0.375190	−	1.40023i	0.853067	−	0.521802i	$-0.174740\pi$
$510$		0			0
$511$	797.570	+	460.477i	1.56080	+	0.901130i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−27.1666	−	101.387i	−0.0528533	−	0.197251i
$515$	−105.573	+	105.573i	−0.204996	+	0.204996i
$516$		0			0
$517$	88.3614	−	51.0155i	0.170912	−	0.0986759i
$518$	−488.468	−	130.885i	−0.942988	−	0.252673i
$519$		0			0
$520$	−57.1000	−	32.9667i	−0.109808	−	0.0633975i
$521$	−156.049			−0.299518			−0.149759	−	0.988723i	$-0.547850\pi$
$521$	−156.049			−0.299518			−0.149759	+	0.988723i	$0.547850\pi$
$522$		0			0
$523$	−20.9615	−	36.3064i	−0.0400794	−	0.0694196i	0.845290	−	0.534308i	$-0.179428\pi$
$523$	−20.9615	−	36.3064i	−0.0400794	−	0.0694196i	−0.885369	+	0.464888i	$0.846094\pi$
$524$	−363.100	−	209.636i	−0.692939	−	0.400068i
$525$		0			0
$526$	33.2820	−	8.91789i	0.0632738	−	0.0169542i
$527$	−153.597	−	573.233i	−0.291456	−	1.08773i
$528$		0			0
$529$	−255.915	+	443.258i	−0.483772	+	0.837917i
$530$	−135.446	+	78.1999i	−0.255559	+	0.147547i
$531$		0			0
$532$			639.090i			1.20130i
$533$	−237.233	+	237.233i	−0.445091	+	0.445091i
$534$		0			0
$535$	−47.5692	+	177.531i	−0.0889144	+	0.331833i
$536$	55.4782	+	96.0910i	0.103504	+	0.179274i
$537$		0			0
$538$	−175.741	−	175.741i	−0.326656	−	0.326656i
$539$	439.832	−	117.853i	0.816015	−	0.218651i
$540$		0			0
$541$	−4.44298	+	4.44298i	−0.00821253	+	0.00821253i	−0.711201	−	0.702989i	$-0.751848\pi$
$541$	−4.44298	+	4.44298i	−0.00821253	+	0.00821253i	0.702989	+	0.711201i	$0.251848\pi$
$542$	−197.046	+	341.293i	−0.363553	+	0.629692i
$543$		0			0
$544$	103.426	+	27.7128i	0.190121	+	0.0509427i
$545$			122.203i			0.224225i
$546$		0			0
$547$	−101.508			−0.185572			−0.0927859	−	0.995686i	$-0.529577\pi$
$547$	−101.508			−0.185572			−0.0927859	+	0.995686i	$0.529577\pi$
$548$	−58.9564	+	220.028i	−0.107585	+	0.401511i
$549$		0			0
$550$	−274.235	−	158.329i	−0.498608	−	0.287872i
$551$	−405.167	−	405.167i	−0.735330	−	0.735330i
$552$		0			0
$553$	−29.6891	−	110.801i	−0.0536874	−	0.200364i
$554$	446.985	−	446.985i	0.806831	−	0.806831i
$555$		0			0
$556$	−165.771	+	95.7077i	−0.298148	+	0.172136i
$557$	636.358	+	170.512i	1.14247	+	0.306125i	0.779945	−	0.625848i	$-0.215247\pi$
$557$	636.358	+	170.512i	1.14247	+	0.306125i	0.362528	+	0.931973i	$0.381914\pi$
$558$		0			0
$559$	99.7083	+	172.700i	0.178369	+	0.308944i
$560$	69.2820			0.123718
$561$		0			0
$562$	5.54483	+	9.60392i	0.00986624	+	0.0170888i
$563$	−76.8385	−	44.3628i	−0.136481	−	0.0787971i	0.430205	−	0.902731i	$-0.358441\pi$
$563$	−76.8385	−	44.3628i	−0.136481	−	0.0787971i	−0.566686	+	0.823934i	$0.691775\pi$
$564$		0			0
$565$	−78.3154	+	20.9845i	−0.138611	+	0.0371408i
$566$	6.09292	+	22.7391i	0.0107649	+	0.0401751i
$567$		0			0
$568$	−152.105	+	263.454i	−0.267791	+	0.463827i
$569$	373.750	−	215.785i	0.656854	−	0.379235i	−0.134223	−	0.990951i	$-0.542854\pi$
$569$	373.750	−	215.785i	0.656854	−	0.379235i	0.791077	+	0.611716i	$0.209521\pi$
$570$		0			0
$571$		−	959.892i		−	1.68107i	−0.541756	−	0.840536i	$-0.682240\pi$
$571$		−	959.892i		−	1.68107i	0.541756	−	0.840536i	$-0.317760\pi$
$572$	−69.1666	−	258.133i	−0.120921	−	0.451282i
$573$		0			0
$574$	91.2436	−	340.526i	0.158961	−	0.593250i
$575$	−45.1333	−	78.1731i	−0.0784927	−	0.135953i
$576$		0			0
$577$	−313.669	−	313.669i	−0.543621	−	0.543621i	0.380968	−	0.924588i	$-0.375591\pi$
$577$	−313.669	−	313.669i	−0.543621	−	0.543621i	−0.924588	+	0.380968i	$0.875591\pi$
$578$	−94.6340	+	25.3571i	−0.163727	+	0.0438704i
$579$		0			0
$580$	−43.9230	+	43.9230i	−0.0757294	+	0.0757294i
$581$	−758.372	+	1313.54i	−1.30529	+	2.26082i
$582$		0			0
$583$	−612.315	−	164.069i	−1.05028	−	0.281423i
$584$			269.674i			0.461771i
$585$		0			0
$586$	264.946			0.452126
$587$	58.5654	−	218.569i	0.0997708	−	0.372350i	−0.897929	−	0.440141i	$-0.854929\pi$
$587$	58.5654	−	218.569i	0.0997708	−	0.372350i	0.997700	+	0.0677912i	$0.0215952\pi$
$588$		0			0
$589$	898.249	+	518.604i	1.52504	+	0.880483i
$590$	−118.508	−	118.508i	−0.200861	−	0.200861i
$591$		0			0
$592$	−38.3257	−	143.033i	−0.0647393	−	0.241610i
$593$	−335.229	+	335.229i	−0.565311	+	0.565311i	−0.930811	−	0.365500i	$-0.880898\pi$
$593$	−335.229	+	335.229i	−0.565311	+	0.565311i	0.365500	+	0.930811i	$0.380898\pi$
$594$		0			0
$595$	−283.923	+	163.923i	−0.477182	+	0.275501i
$596$	−109.856	−	29.4359i	−0.184323	−	0.0493892i
$597$		0			0
$598$	19.7166	−	73.5833i	0.0329709	−	0.123049i
$599$	−136.908			−0.228560			−0.114280	−	0.993449i	$-0.536456\pi$
$599$	−136.908			−0.228560			−0.114280	+	0.993449i	$0.536456\pi$
$600$		0			0
$601$	8.78461	+	15.2154i	0.0146167	+	0.0253168i	0.873241	−	0.487288i	$-0.162014\pi$
$601$	8.78461	+	15.2154i	0.0146167	+	0.0253168i	−0.858625	+	0.512605i	$0.828681\pi$
$602$	−181.471	−	104.772i	−0.301447	−	0.174041i
$603$		0			0
$604$	150.368	−	40.2910i	0.248953	−	0.0667069i
$605$	−7.12574	−	26.5936i	−0.0117781	−	0.0439564i
$606$		0			0
$607$	−422.300	+	731.445i	−0.695716	+	1.20502i	0.274222	+	0.961666i	$0.411580\pi$
$607$	−422.300	+	731.445i	−0.695716	+	1.20502i	−0.969939	+	0.243350i	$0.921754\pi$
$608$	−162.067	+	93.5692i	−0.266557	+	0.153897i
$609$		0			0
$610$			18.5153i			0.0303529i
$611$	124.650	−	33.3999i	0.204010	−	0.0546642i
$612$		0			0
$613$	−163.158	+	608.915i	−0.266164	+	0.993337i	0.695370	+	0.718651i	$0.255240\pi$
$613$	−163.158	+	608.915i	−0.266164	+	0.993337i	−0.961534	+	0.274685i	$0.911426\pi$
$614$	375.069	+	649.638i	0.610861	+	1.05804i
$615$		0			0
$616$	198.564	+	198.564i	0.322344	+	0.322344i
$617$	−107.014	+	28.6743i	−0.173443	+	0.0464738i	−0.344495	−	0.938788i	$-0.611950\pi$
$617$	−107.014	+	28.6743i	−0.173443	+	0.0464738i	0.171053	+	0.985262i	$0.445283\pi$
$618$		0			0
$619$	−111.970	+	111.970i	−0.180888	+	0.180888i	−0.791743	−	0.610854i	$-0.790826\pi$
$619$	−111.970	+	111.970i	−0.180888	+	0.180888i	0.610854	+	0.791743i	$0.290826\pi$
$620$	56.2205	−	97.3768i	0.0906783	−	0.157059i
$621$		0			0
$622$	−404.669	−	108.431i	−0.650594	−	0.174326i
$623$			1620.67i			2.60139i
$624$		0			0
$625$	−394.184			−0.630695
$626$	−43.2956	+	161.581i	−0.0691623	+	0.258117i
$627$		0			0
$628$	−96.0089	−	55.4308i	−0.152880	−	0.0882656i
$629$	495.482	+	495.482i	0.787730	+	0.787730i
$630$		0			0
$631$	283.101	+	1056.55i	0.448654	+	1.67440i	0.706104	+	0.708108i	$0.250451\pi$
$631$	283.101	+	1056.55i	0.448654	+	1.67440i	−0.257450	+	0.966292i	$0.582882\pi$
$632$	23.7513	−	23.7513i	0.0375812	−	0.0375812i
$633$		0			0
$634$	−486.200	+	280.708i	−0.766877	+	0.442757i
$635$	410.229	+	109.921i	0.646031	+	0.173103i
$636$		0			0
$637$	575.917			0.904108
$638$	−251.769			−0.394622
$639$		0			0
$640$	10.1436	+	17.5692i	0.0158494	+	0.0274519i
$641$	353.869	+	204.306i	0.552058	+	0.318731i	0.749952	−	0.661493i	$-0.230077\pi$
$641$	353.869	+	204.306i	0.552058	+	0.318731i	−0.197894	+	0.980223i	$0.563410\pi$
$642$		0			0
$643$	−432.661	+	115.931i	−0.672879	+	0.180297i	−0.579052	−	0.815291i	$-0.696577\pi$
$643$	−432.661	+	115.931i	−0.672879	+	0.180297i	−0.0938279	+	0.995588i	$0.529910\pi$
$644$	20.7180	+	77.3205i	0.0321708	+	0.120063i
$645$		0			0
$646$	442.774	−	766.908i	0.685409	−	1.18716i
$647$	279.588	−	161.420i	0.432131	−	0.249491i	−0.268123	−	0.963385i	$-0.586403\pi$
$647$	279.588	−	161.420i	0.432131	−	0.249491i	0.700254	+	0.713894i	$0.253070\pi$
$648$		0			0
$649$		−	679.292i		−	1.04668i
$650$	−283.200	−	283.200i	−0.435692	−	0.435692i
$651$		0			0
$652$	−105.894	+	395.200i	−0.162413	+	0.606135i
$653$	−510.424	−	884.081i	−0.781660	−	1.35388i	−0.930974	−	0.365086i	$-0.881040\pi$
$653$	−510.424	−	884.081i	−0.781660	−	1.35388i	0.149314	−	0.988790i	$-0.452294\pi$
$654$		0			0
$655$	265.808	+	265.808i	0.405813	+	0.405813i
$656$	99.7128	−	26.7180i	0.152001	−	0.0407286i
$657$		0			0
$658$	−95.8846	+	95.8846i	−0.145721	+	0.145721i
$659$	113.842	−	197.181i	0.172750	−	0.299212i	−0.766630	−	0.642089i	$-0.778068\pi$
$659$	113.842	−	197.181i	0.172750	−	0.299212i	0.939380	+	0.342877i	$0.111401\pi$
$660$		0			0
$661$	146.181	+	39.1692i	0.221152	+	0.0592575i	0.367693	−	0.929947i	$-0.380148\pi$
$661$	146.181	+	39.1692i	0.221152	+	0.0592575i	−0.146542	+	0.989205i	$0.546814\pi$
$662$		−	201.247i		−	0.303999i
$663$		0			0
$664$	−444.133			−0.668875
$665$	148.301	−	553.468i	0.223009	−	0.832283i
$666$		0			0
$667$	−62.1539	−	35.8846i	−0.0931843	−	0.0538000i
$668$	−228.862	−	228.862i	−0.342607	−	0.342607i
$669$		0			0
$670$	−25.7475	−	96.0910i	−0.0384291	−	0.143419i
$671$	−53.0653	+	53.0653i	−0.0790838	+	0.0790838i
$672$		0			0
$673$	−613.138	+	353.996i	−0.911052	+	0.525996i	−0.880770	−	0.473545i	$-0.842974\pi$
$673$	−613.138	+	353.996i	−0.911052	+	0.525996i	−0.0302828	+	0.999541i	$0.509641\pi$
$674$	−474.704	−	127.197i	−0.704309	−	0.188719i
$675$		0			0
$676$		−	338.000i		−	0.500000i
$677$	754.592			1.11461			0.557306	−	0.830307i	$-0.311835\pi$
$677$	754.592			1.11461			0.557306	+	0.830307i	$0.311835\pi$
$678$		0			0
$679$	−751.231	−	1301.17i	−1.10638	−	1.91630i
$680$	−83.1384	−	48.0000i	−0.122262	−	0.0705882i
$681$		0			0
$682$	440.214	−	117.955i	0.645475	−	0.172955i
$683$	37.2168	+	138.895i	0.0544901	+	0.203360i	0.987804	−	0.155701i	$-0.0497636\pi$
$683$	37.2168	+	138.895i	0.0544901	+	0.203360i	−0.933314	+	0.359061i	$0.883097\pi$
$684$		0			0
$685$	102.115	−	176.869i	0.149074	−	0.258203i
$686$	55.5866	−	32.0929i	0.0810300	−	0.0467827i
$687$		0			0
$688$		−	61.3590i		−	0.0891846i
$689$	−694.350	−	400.883i	−1.00776	−	0.581833i
$690$		0			0
$691$	140.931	−	525.961i	0.203952	−	0.761159i	−0.785815	−	0.618462i	$-0.787756\pi$
$691$	140.931	−	525.961i	0.203952	−	0.761159i	0.989766	−	0.142697i	$-0.0455774\pi$
$692$	268.459	+	464.985i	0.387946	+	0.671943i
$693$		0			0
$694$	437.703	+	437.703i	0.630695	+	0.630695i
$695$	165.771	−	44.4181i	0.238519	−	0.0639109i
$696$		0			0
$697$	−345.415	+	345.415i	−0.495574	+	0.495574i
$698$	316.897	−	548.881i	0.454007	−	0.786363i
$699$		0			0
$700$	406.506	+	108.923i	0.580723	+	0.155604i
$701$			568.344i			0.810761i	0.914148	+	0.405381i	$0.132861\pi$
$701$			568.344i			0.810761i	−0.914148	+	0.405381i	$0.867139\pi$
$702$		0			0
$703$	−1224.68			−1.74207
$704$	−21.2820	+	79.4256i	−0.0302302	+	0.112820i
$705$		0			0
$706$	718.865	+	415.037i	1.01822	+	0.587871i
$707$	−1275.95	−	1275.95i	−1.80475	−	1.80475i
$708$		0			0
$709$	94.9538	+	354.372i	0.133926	+	0.499820i	1.00000		9.64632e-5i	$-3.07052e-5\pi$
$709$	94.9538	+	354.372i	0.133926	+	0.499820i	−0.866074	+	0.499916i	$0.833364\pi$
$710$	192.862	−	192.862i	0.271636	−	0.271636i
$711$		0			0
$712$	−410.985	+	237.282i	−0.577225	+	0.333261i
$713$	125.487	+	33.6242i	0.175999	+	0.0471587i
$714$		0			0
$715$			239.600i			0.335105i
$716$	−571.559			−0.798267
$717$		0			0
$718$	−64.2769	−	111.331i	−0.0895221	−	0.155057i
$719$	−228.215	−	131.760i	−0.317407	−	0.183255i	0.332829	−	0.942987i	$-0.391997\pi$
$719$	−228.215	−	131.760i	−0.317407	−	0.183255i	−0.650236	+	0.759732i	$0.725330\pi$
$720$		0			0
$721$	776.852	−	208.157i	1.07747	−	0.288706i
$722$	268.443	+	1001.84i	0.371805	+	1.38759i
$723$		0			0
$724$	177.646	−	307.692i	0.245368	−	0.424989i
$725$	−326.769	+	188.660i	−0.450716	+	0.260221i
$726$		0			0
$727$		−	878.415i		−	1.20827i	−0.796880	−	0.604137i	$-0.793518\pi$
$727$		−	878.415i		−	1.20827i	0.796880	−	0.604137i	$-0.206482\pi$
$728$	177.583	+	307.583i	0.243933	+	0.422505i
$729$		0			0
$730$	62.5781	−	233.545i	0.0857235	−	0.319924i
$731$	145.177	+	251.454i	0.198600	+	0.343986i
$732$		0			0
$733$	−146.627	−	146.627i	−0.200037	−	0.200037i	0.599979	−	0.800016i	$-0.295176\pi$
$733$	−146.627	−	146.627i	−0.200037	−	0.200037i	−0.800016	+	0.599979i	$0.795176\pi$
$734$	−297.499	+	79.7147i	−0.405312	+	0.108603i
$735$		0			0
$736$	−16.5744	+	16.5744i	−0.0225195	+	0.0225195i
$737$	201.606	−	349.192i	0.273550	−	0.473802i
$738$		0			0
$739$	621.762	+	166.601i	0.841356	+	0.225441i	0.653662	−	0.756787i	$-0.273232\pi$
$739$	621.762	+	166.601i	0.841356	+	0.225441i	0.187694	+	0.982227i	$0.439899\pi$
$740$			132.764i			0.179411i
$741$		0			0
$742$	842.487			1.13543
$743$	3.52835	−	13.1680i	0.00474879	−	0.0177227i	−0.963511	−	0.267670i	$-0.913746\pi$
$743$	3.52835	−	13.1680i	0.00474879	−	0.0177227i	0.968260	+	0.249947i	$0.0804131\pi$
$744$		0			0
$745$	88.3078	+	50.9845i	0.118534	+	0.0684356i
$746$	219.606	+	219.606i	0.294378	+	0.294378i
$747$		0			0
$748$	−100.708	−	375.846i	−0.134636	−	0.502468i
$749$	700.070	−	700.070i	0.934673	−	0.934673i
$750$		0			0
$751$	−138.631	+	80.0385i	−0.184595	+	0.106576i	−0.589450	−	0.807805i	$-0.700655\pi$
$751$	−138.631	+	80.0385i	−0.184595	+	0.106576i	0.404855	+	0.914381i	$0.367322\pi$
$752$	−38.3538	−	10.2769i	−0.0510024	−	0.0136661i
$753$		0			0
$754$	−307.583	−	82.4167i	−0.407935	−	0.109306i
$755$	−139.572			−0.184864
$756$		0			0
$757$	733.692	+	1270.79i	0.969210	+	1.67872i	0.697850	+	0.716244i	$0.254140\pi$
$757$	733.692	+	1270.79i	0.969210	+	1.67872i	0.271360	+	0.962478i	$0.412527\pi$
$758$	237.476	+	137.107i	0.313293	+	0.180880i
$759$		0			0
$760$	162.067	−	43.4256i	0.213246	−	0.0571390i
$761$	−47.3514	−	176.718i	−0.0622227	−	0.232218i	0.927811	−	0.373051i	$-0.121688\pi$
$761$	−47.3514	−	176.718i	−0.0622227	−	0.232218i	−0.990033	+	0.140833i	$0.955022\pi$
$762$		0			0
$763$	329.138	−	570.083i	0.431373	−	0.747160i
$764$	−341.769	+	197.321i	−0.447342	+	0.258273i
$765$		0			0
$766$		−	275.503i		−	0.359664i
$767$	222.367	−	829.883i	0.289917	−	1.08199i
$768$		0			0
$769$	351.866	−	1313.18i	0.457563	−	1.70765i	−0.222879	−	0.974846i	$-0.571546\pi$
$769$	351.866	−	1313.18i	0.457563	−	1.70765i	0.680442	−	0.732802i	$-0.261788\pi$
$770$	−125.885	−	218.038i	−0.163486	−	0.283167i
$771$		0			0
$772$	29.6987	+	29.6987i	0.0384699	+	0.0384699i
$773$	−945.606	+	253.374i	−1.22329	+	0.327781i	−0.811965	−	0.583706i	$-0.801602\pi$
$773$	−945.606	+	253.374i	−1.22329	+	0.327781i	−0.411329	+	0.911487i	$0.634935\pi$
$774$		0			0
$775$	482.962	−	482.962i	0.623177	−	0.623177i
$776$	219.976	−	381.009i	0.283474	−	0.490991i
$777$		0			0
$778$	−24.2487	−	6.49742i	−0.0311680	−	0.00835144i
$779$		−	853.759i		−	1.09597i
$780$		0			0
$781$	1105.49			1.41548
$782$	28.7077	−	107.138i	0.0367106	−	0.137006i
$783$		0			0
$784$	−153.464	−	88.6025i	−0.195745	−	0.113013i
$785$	70.2834	+	70.2834i	0.0895330	+	0.0895330i
$786$		0			0
$787$	30.5460	+	113.999i	0.0388132	+	0.144853i	0.982613	−	0.185664i	$-0.0594436\pi$
$787$	30.5460	+	113.999i	0.0388132	+	0.144853i	−0.943800	+	0.330517i	$0.892777\pi$
$788$	213.913	−	213.913i	0.271463	−	0.271463i
$789$		0			0
$790$	−26.0807	+	15.0577i	−0.0330136	+	0.0190604i
$791$	421.865	+	113.038i	0.533332	+	0.142906i
$792$		0			0
$793$	−82.2001	+	47.4583i	−0.103657	+	0.0598465i
$794$	477.286			0.601116
$795$		0			0
$796$	−22.2154	−	38.4782i	−0.0279088	−	0.0483394i
$797$	−491.138	−	283.559i	−0.616234	−	0.355783i	0.159167	−	0.987252i	$-0.449119\pi$
$797$	−491.138	−	283.559i	−0.616234	−	0.355783i	−0.775401	+	0.631469i	$0.782452\pi$
$798$		0			0
$799$	181.492	−	48.6307i	0.227149	−	0.0608645i
$800$	31.8949	+	119.033i	0.0398686	+	0.148792i
$801$		0			0
$802$	−363.415	+	629.454i	−0.453136	+	0.784855i
$803$	848.696	−	489.995i	1.05691	−	0.610205i
$804$		0			0
$805$		−	71.7691i		−	0.0891542i
$806$	576.417			0.715157
$807$		0			0
$808$	136.756	−	510.382i	0.169253	−	0.631661i
$809$	43.7231	+	75.7307i	0.0540459	+	0.0936102i	0.891783	−	0.452464i	$-0.149455\pi$
$809$	43.7231	+	75.7307i	0.0540459	+	0.0936102i	−0.837737	+	0.546074i	$0.816122\pi$
$810$		0			0
$811$	−519.193	−	519.193i	−0.640189	−	0.640189i	0.310413	−	0.950602i	$-0.399533\pi$
$811$	−519.193	−	519.193i	−0.640189	−	0.640189i	−0.950602	+	0.310413i	$0.899533\pi$
$812$	323.205	−	86.6025i	0.398036	−	0.106653i
$813$		0			0
$814$	−380.505	+	380.505i	−0.467451	+	0.467451i
$815$	183.413	−	317.681i	0.225047	−	0.389792i
$816$		0			0
$817$	−490.174	−	131.342i	−0.599968	−	0.160761i
$818$		−	824.053i		−	1.00740i
$819$		0			0
$820$	−92.5538			−0.112870
$821$	−148.881	+	555.631i	−0.181341	+	0.676773i	0.814044	+	0.580804i	$0.197262\pi$
$821$	−148.881	+	555.631i	−0.181341	+	0.676773i	−0.995384	+	0.0959692i	$0.969405\pi$
$822$		0			0
$823$	−285.069	−	164.585i	−0.346378	−	0.199981i	0.316711	−	0.948522i	$-0.397422\pi$
$823$	−285.069	−	164.585i	−0.346378	−	0.199981i	−0.663089	+	0.748541i	$0.730755\pi$
$824$	166.526	+	166.526i	0.202094	+	0.202094i
$825$		0			0
$826$	233.660	+	872.032i	0.282882	+	1.05573i
$827$	−514.410	+	514.410i	−0.622020	+	0.622020i	−0.946048	−	0.324028i	$-0.894963\pi$
$827$	−514.410	+	514.410i	−0.622020	+	0.622020i	0.324028	+	0.946048i	$0.394963\pi$
$828$		0			0
$829$	−816.742	+	471.546i	−0.985213	+	0.568813i	−0.903840	−	0.427871i	$-0.859264\pi$
$829$	−816.742	+	471.546i	−0.985213	+	0.568813i	−0.0813731	+	0.996684i	$0.525931\pi$
$830$	384.631	+	103.061i	0.463410	+	0.124170i
$831$		0			0
$832$	−52.0000	+	90.0666i	−0.0625000	+	0.108253i
$833$	838.543			1.00665
$834$		0			0
$835$	145.092	+	251.307i	0.173763	+	0.300967i
$836$	588.946	+	340.028i	0.704481	+	0.406732i
$837$		0			0
$838$	1068.72	−	286.361i	1.27532	−	0.341720i
$839$	203.536	+	759.606i	0.242593	+	0.905371i	0.974578	+	0.224050i	$0.0719278\pi$
$839$	203.536	+	759.606i	0.242593	+	0.905371i	−0.731984	+	0.681321i	$0.761406\pi$
$840$		0			0
$841$	270.500	−	468.520i	0.321641	−	0.557098i
$842$	46.8264	−	27.0352i	0.0556132	−	0.0321083i
$843$		0			0
$844$			128.403i			0.152136i
$845$	−78.4332	+	292.717i	−0.0928203	+	0.346410i
$846$		0			0
$847$	−38.3846	+	143.253i	−0.0453183	+	0.169130i
$848$	123.349	+	213.646i	0.145458	+	0.251941i
$849$		0			0
$850$	−412.344	−	412.344i	−0.485110	−	0.485110i
$851$	−148.168	+	39.7015i	−0.174110	+	0.0466528i
$852$		0			0
$853$	472.527	−	472.527i	0.553960	−	0.553960i	−0.373622	−	0.927581i	$-0.621884\pi$
$853$	472.527	−	472.527i	0.553960	−	0.553960i	0.927581	+	0.373622i	$0.121884\pi$
$854$	49.8686	−	86.3750i	0.0583941	−	0.101142i
$855$		0			0
$856$	280.028	+	75.0333i	0.327136	+	0.0876557i
$857$			436.543i			0.509386i	0.967022	+	0.254693i	$0.0819743\pi$
$857$			436.543i			0.509386i	−0.967022	+	0.254693i	$0.918026\pi$
$858$		0			0
$859$	−1238.40			−1.44167			−0.720837	−	0.693104i	$-0.756243\pi$
$859$	−1238.40			−1.44167			−0.720837	+	0.693104i	$0.756243\pi$
$860$	−14.2384	+	53.1384i	−0.0165563	+	0.0617889i
$861$		0			0
$862$	−771.300	−	445.310i	−0.894779	−	0.516601i
$863$	−729.373	−	729.373i	−0.845160	−	0.845160i	0.144365	−	0.989525i	$-0.453886\pi$
$863$	−729.373	−	729.373i	−0.845160	−	0.845160i	−0.989525	+	0.144365i	$0.953886\pi$
$864$		0			0
$865$	−124.592	−	464.985i	−0.144037	−	0.537554i
$866$	237.785	−	237.785i	0.274578	−	0.274578i
$867$		0			0
$868$	−524.545	+	302.846i	−0.604314	+	0.348901i
$869$	−117.904	−	31.5922i	−0.135678	−	0.0363547i
$870$		0			0
$871$	360.608	−	360.608i	0.414016	−	0.414016i
$872$	192.756			0.221051
$873$		0			0
$874$	96.9282	+	167.885i	0.110902	+	0.192088i
$875$	−701.769	−	405.167i	−0.802022	−	0.463048i
$876$		0			0
$877$	1314.21	−	352.142i	1.49853	−	0.401530i	0.585923	−	0.810367i	$-0.300732\pi$
$877$	1314.21	−	352.142i	1.49853	−	0.401530i	0.912607	+	0.408837i	$0.134066\pi$
$878$	252.361	+	941.824i	0.287427	+	1.07269i
$879$		0			0
$880$	36.8616	−	63.8461i	0.0418881	−	0.0725524i
$881$	−1354.17	+	781.832i	−1.53709	+	0.887437i	−0.538079	+	0.842895i	$0.680850\pi$
$881$	−1354.17	+	781.832i	−1.53709	+	0.887437i	−0.999007	+	0.0445423i	$0.985817\pi$
$882$		0			0
$883$		−	452.723i		−	0.512710i	−0.966583	−	0.256355i	$-0.917478\pi$
$883$		−	452.723i		−	0.512710i	0.966583	−	0.256355i	$-0.0825216\pi$
$884$		−	492.133i		−	0.556712i
$885$		0			0
$886$	−111.282	+	415.310i	−0.125600	+	0.468747i
$887$	455.469	+	788.896i	0.513494	+	0.889398i	0.999877	+	0.0156524i	$0.00498250\pi$
$887$	455.469	+	788.896i	0.513494	+	0.889398i	−0.486383	+	0.873745i	$0.661684\pi$
$888$		0			0
$889$	−1617.69	−	1617.69i	−1.81967	−	1.81967i
$890$	410.985	−	110.123i	0.461780	−	0.123734i
$891$		0			0
$892$	309.061	−	309.061i	0.346481	−	0.346481i
$893$	−164.196	+	284.396i	−0.183870	+	0.318473i
$894$		0			0
$895$	494.985	+	132.631i	0.553055	+	0.148191i
$896$		−	109.282i		−	0.121967i
$897$		0			0
$898$	−401.387			−0.446979
$899$	140.551	−	524.545i	0.156342	−	0.583476i
$900$		0			0
$901$	−1010.98	−	583.692i	−1.12207	−	0.647827i
$902$	−265.261	−	265.261i	−0.294081	−	0.294081i
$903$		0			0
$904$	33.1000	+	123.531i	0.0366150	+	0.136649i
$905$	−225.246	+	225.246i	−0.248891	+	0.248891i
$906$		0			0
$907$	385.501	−	222.569i	0.425029	−	0.245391i	−0.272198	−	0.962241i	$-0.587750\pi$
$907$	385.501	−	222.569i	0.425029	−	0.245391i	0.697227	+	0.716851i	$0.254417\pi$
$908$	124.890	+	33.4641i	0.137544	+	0.0368547i
$909$		0			0
$910$	−82.4167	−	307.583i	−0.0905678	−	0.338004i
$911$	−717.233			−0.787303			−0.393652	−	0.919260i	$-0.628788\pi$
$911$	−717.233			−0.787303			−0.393652	+	0.919260i	$0.628788\pi$
$912$		0			0
$913$	806.985	+	1397.74i	0.883882	+	1.53093i
$914$	−175.835	−	101.519i	−0.192380	−	0.111071i
$915$		0			0
$916$	−160.329	+	42.9601i	−0.175032	+	0.0468997i
$917$	−524.090	−	1955.93i	−0.571526	−	2.13297i
$918$		0			0
$919$	−371.569	+	643.577i	−0.404319	+	0.700301i	−0.994242	−	0.107158i	$-0.965825\pi$
$919$	−371.569	+	643.577i	−0.404319	+	0.700301i	0.589923	+	0.807460i	$0.299158\pi$
$920$	18.1999	−	10.5077i	0.0197825	−	0.0114214i
$921$		0			0
$922$		−	832.246i		−	0.902653i
$923$	1350.57	+	361.883i	1.46324	+	0.392073i
$924$		0			0
$925$	−208.727	+	778.981i	−0.225651	+	0.842142i
$926$	−169.599	−	293.755i	−0.183153	−	0.317230i
$927$		0			0
$928$	69.2820	+	69.2820i	0.0746574	+	0.0746574i
$929$	−1424.14	+	381.597i	−1.53298	+	0.410761i	−0.923991	−	0.382415i	$-0.875092\pi$
$929$	−1424.14	+	381.597i	−1.53298	+	0.410761i	−0.608992	+	0.793176i	$0.708426\pi$
$930$		0			0
$931$	−1036.31	+	1036.31i	−1.11311	+	1.11311i
$932$	−380.669	+	659.338i	−0.408443	+	0.707445i
$933$		0			0
$934$	1000.82	+	268.168i	1.07154	+	0.287118i
$935$			348.862i			0.373114i
$936$		0			0
$937$	−172.477			−0.184073			−0.0920367	−	0.995756i	$-0.529338\pi$
$937$	−172.477			−0.184073			−0.0920367	+	0.995756i	$0.529338\pi$
$938$	−138.695	+	517.619i	−0.147863	+	0.551832i
$939$		0			0
$940$	30.8306	+	17.8001i	0.0327985	+	0.0189362i
$941$	−145.055	−	145.055i	−0.154150	−	0.154150i	0.625819	−	0.779969i	$-0.284765\pi$
$941$	−145.055	−	145.055i	−0.154150	−	0.154150i	−0.779969	+	0.625819i	$0.784765\pi$
$942$		0			0
$943$	−27.6771	−	103.292i	−0.0293501	−	0.109536i
$944$	−186.928	+	186.928i	−0.198017	+	0.198017i
$945$		0			0
$946$	−193.104	+	111.488i	−0.204127	+	0.117853i
$947$	665.902	+	178.428i	0.703170	+	0.188414i	0.592650	−	0.805460i	$-0.298082\pi$
$947$	665.902	+	178.428i	0.703170	+	0.188414i	0.110520	+	0.993874i	$0.464748\pi$
$948$		0			0
$949$	1197.24	−	320.800i	1.26158	−	0.338040i
$950$	1019.18			1.07283
$951$		0			0
$952$	258.564	+	447.846i	0.271601	+	0.470427i
$953$	1044.96	+	603.309i	1.09650	+	0.633063i	0.935299	−	0.353859i	$-0.115131\pi$
$953$	1044.96	+	603.309i	1.09650	+	0.633063i	0.161198	+	0.986922i	$0.448464\pi$
$954$		0			0
$955$	341.769	−	91.5768i	0.357873	−	0.0958919i
$956$	−122.354	−	456.631i	−0.127985	−	0.477647i
$957$		0			0
$958$	−261.464	+	452.869i	−0.272927	+	0.472723i
$959$	−952.750	+	550.070i	−0.993483	+	0.573588i
$960$		0			0
$961$			22.0065i			0.0228996i
$962$	−589.417	+	340.300i	−0.612699	+	0.353742i
$963$		0			0
$964$	1.59361	−	5.94744i	0.00165312	−	0.00616954i
$965$	−18.8282	−	32.6115i	−0.0195111	−	0.0337943i
$966$		0			0
$967$	−169.831	−	169.831i	−0.175626	−	0.175626i	0.613820	−	0.789446i	$-0.289632\pi$
$967$	−169.831	−	169.831i	−0.175626	−	0.175626i	−0.789446	+	0.613820i	$0.789632\pi$
$968$	−41.9474	+	11.2398i	−0.0433341	+	0.0116113i
$969$		0			0
$970$	−278.918	+	278.918i	−0.287544	+	0.287544i
$971$	373.850	−	647.527i	0.385015	−	0.666866i	−0.606756	−	0.794888i	$-0.707529\pi$
$971$	373.850	−	647.527i	0.385015	−	0.666866i	0.991771	+	0.128022i	$0.0408628\pi$
$972$		0			0
$973$	−892.965	−	239.269i	−0.917744	−	0.245909i
$974$			274.000i			0.281314i
$975$		0			0
$976$	29.2051			0.0299232
$977$	55.9897	−	208.956i	0.0573078	−	0.213876i	−0.931334	−	0.364166i	$-0.881354\pi$
$977$	55.9897	−	208.956i	0.0573078	−	0.213876i	0.988642	+	0.150290i	$0.0480208\pi$
$978$		0			0
$979$	1493.51	+	862.277i	1.52554	+	0.880773i
$980$	112.344	+	112.344i	0.114636	+	0.114636i
$981$		0			0
$982$	13.5167	+	50.4449i	0.0137644	+	0.0513695i
$983$	−1367.93	+	1367.93i	−1.39158	+	1.39158i	−0.569801	+	0.821783i	$0.692980\pi$
$983$	−1367.93	+	1367.93i	−1.39158	+	1.39158i	−0.821783	+	0.569801i	$0.807020\pi$
$984$		0			0
$985$	−234.892	+	135.615i	−0.238470	+	0.137680i
$986$	−447.846	−	120.000i	−0.454205	−	0.121704i
$987$		0			0
$988$	608.200	+	608.200i	0.615587	+	0.615587i
$989$	−63.5617			−0.0642686
$990$		0			0
$991$	935.631	+	1620.56i	0.944128	+	1.63528i	0.757488	+	0.652849i	$0.226426\pi$
$991$	935.631	+	1620.56i	0.944128	+	1.63528i	0.186640	+	0.982428i	$0.440240\pi$
$992$	−153.597	−	88.6795i	−0.154836	−	0.0893946i
$993$		0			0
$994$	−1419.16	+	380.263i	−1.42773	+	0.382558i
$995$	10.3102	+	38.4782i	0.0103620	+	0.0386715i
$996$		0			0
$997$	−768.584	+	1331.23i	−0.770897	+	1.33523i	0.166175	+	0.986096i	$0.446858\pi$
$997$	−768.584	+	1331.23i	−0.770897	+	1.33523i	−0.937072	+	0.349137i	$0.886475\pi$
$998$	−801.540	+	462.769i	−0.803146	+	0.463697i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.3.bb.c.37.1		4
3.2	odd	2		78.3.l.a.37.1	yes	4
13.6	odd	12	inner	234.3.bb.c.19.1		4
39.2	even	12		1014.3.f.e.577.2		4
39.11	even	12		1014.3.f.d.577.2		4
39.23	odd	6		1014.3.f.d.775.2		4
39.29	odd	6		1014.3.f.e.775.2		4
39.32	even	12		78.3.l.a.19.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.a.19.1	✓	4	39.32	even	12
78.3.l.a.37.1	yes	4	3.2	odd	2
234.3.bb.c.19.1		4	13.6	odd	12	inner
234.3.bb.c.37.1		4	1.1	even	1	trivial
1014.3.f.d.577.2		4	39.11	even	12
1014.3.f.d.775.2		4	39.23	odd	6
1014.3.f.e.577.2		4	39.2	even	12
1014.3.f.e.775.2		4	39.29	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	234.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.26795 + 1.26795i) q^{5} +(-2.50000 - 9.33013i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.19615 + 1.26795i) q^{10} +(-9.92820 - 2.66025i) q^{11} +(-11.2583 - 6.50000i) q^{13} +13.6603 q^{14} +(2.00000 + 3.46410i) q^{16} +(-16.3923 - 9.46410i) q^{17} +(31.9545 - 8.56218i) q^{19} +(-0.928203 - 3.46410i) q^{20} +(7.26795 - 12.5885i) q^{22} +(3.58846 - 2.07180i) q^{23} -21.7846i q^{25} +(13.0000 - 13.0000i) q^{26} +(-5.00000 + 18.6603i) q^{28} +(-8.66025 - 15.0000i) q^{29} +(22.1699 + 22.1699i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(18.9282 - 18.9282i) q^{34} +(8.66025 - 15.0000i) q^{35} +(-35.7583 - 9.58142i) q^{37} +46.7846i q^{38} +5.07180 q^{40} +(6.67949 - 24.9282i) q^{41} +(-13.2846 - 7.66987i) q^{43} +(14.5359 + 14.5359i) q^{44} +(1.51666 + 5.66025i) q^{46} +(-7.01924 + 7.01924i) q^{47} +(-38.3660 + 22.1506i) q^{49} +(29.7583 + 7.97372i) q^{50} +(13.0000 + 22.5167i) q^{52} +61.6743 q^{53} +(-9.21539 - 15.9615i) q^{55} +(-23.6603 - 13.6603i) q^{56} +(23.6603 - 6.33975i) q^{58} +(17.1051 + 63.8372i) q^{59} +(3.65064 - 6.32309i) q^{61} +(-38.3993 + 22.1699i) q^{62} -8.00000i q^{64} +(-6.03332 - 22.5167i) q^{65} +(-10.1532 + 37.8923i) q^{67} +(18.9282 + 32.7846i) q^{68} +(17.3205 + 17.3205i) q^{70} +(-103.890 + 27.8372i) q^{71} +(-67.4186 + 67.4186i) q^{73} +(26.1769 - 45.3397i) q^{74} +(-63.9090 - 17.1244i) q^{76} +99.2820i q^{77} +11.8756 q^{79} +(-1.85641 + 6.92820i) q^{80} +(31.6077 + 18.2487i) q^{82} +(-111.033 - 111.033i) q^{83} +(-8.78461 - 32.7846i) q^{85} +(15.3397 - 15.3397i) q^{86} +(-25.1769 + 14.5359i) q^{88} +(-162.067 - 43.4256i) q^{89} +(-32.5000 + 121.292i) q^{91} -8.28719 q^{92} +(-7.01924 - 12.1577i) q^{94} +(51.3731 + 29.6603i) q^{95} +(150.246 - 40.2583i) q^{97} +(-16.2154 - 60.5167i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 12 q^{5} - 10 q^{7} + 8 q^{8} + 12 q^{10} - 12 q^{11} + 20 q^{14} + 8 q^{16} - 24 q^{17} + 62 q^{19} + 24 q^{20} + 36 q^{22} - 48 q^{23} + 52 q^{26} - 20 q^{28} + 106 q^{31} - 8 q^{32} + 48 q^{34}+ \cdots - 148 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 12 * q^5 - 10 * q^7 + 8 * q^8 + 12 * q^10 - 12 * q^11 + 20 * q^14 + 8 * q^16 - 24 * q^17 + 62 * q^19 + 24 * q^20 + 36 * q^22 - 48 * q^23 + 52 * q^26 - 20 * q^28 + 106 * q^31 - 8 * q^32 + 48 * q^34 - 98 * q^37 + 48 * q^40 + 96 * q^41 + 30 * q^43 + 72 * q^44 - 84 * q^46 - 132 * q^47 - 150 * q^49 + 74 * q^50 + 52 * q^52 - 72 * q^53 - 120 * q^55 - 60 * q^56 + 60 * q^58 - 84 * q^59 - 72 * q^61 + 30 * q^62 + 156 * q^65 - 148 * q^67 + 48 * q^68 - 180 * q^71 - 190 * q^73 - 20 * q^74 - 124 * q^76 + 96 * q^79 + 48 * q^80 + 168 * q^82 - 264 * q^83 + 48 * q^85 + 96 * q^86 + 24 * q^88 - 288 * q^89 - 130 * q^91 - 144 * q^92 - 132 * q^94 + 60 * q^95 + 310 * q^97 - 148 * q^98

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