LMFDB - Embedded newform 380.3.h.a.39.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(39,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("380.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.h (of order $2$, degree $1$, 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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$108$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.4
Character	$\chi$	$=$	380.39
Dual form			380.3.h.a.39.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99455 + 0.147607i) q^{2} -0.578687 q^{3} +(3.95642 - 0.588817i) q^{4} +(-3.52665 + 3.54440i) q^{5} +(1.15422 - 0.0854181i) q^{6} +11.0384 q^{7} +(-7.80436 + 1.75842i) q^{8} -8.66512 q^{9} +O(q^{10})$	\(q+(-1.99455 + 0.147607i) q^{2} -0.578687 q^{3} +(3.95642 - 0.588817i) q^{4} +(-3.52665 + 3.54440i) q^{5} +(1.15422 - 0.0854181i) q^{6} +11.0384 q^{7} +(-7.80436 + 1.75842i) q^{8} -8.66512 q^{9} +(6.51089 - 7.59002i) q^{10} -19.3643i q^{11} +(-2.28953 + 0.340740i) q^{12} -4.94590i q^{13} +(-22.0165 + 1.62934i) q^{14} +(2.04082 - 2.05110i) q^{15} +(15.3066 - 4.65922i) q^{16} +20.8304i q^{17} +(17.2830 - 1.27903i) q^{18} +4.35890i q^{19} +(-11.8659 + 16.0997i) q^{20} -6.38775 q^{21} +(2.85831 + 38.6230i) q^{22} -7.14491 q^{23} +(4.51628 - 1.01757i) q^{24} +(-0.125495 - 24.9997i) q^{25} +(0.730047 + 9.86481i) q^{26} +10.2226 q^{27} +(43.6724 - 6.49957i) q^{28} +34.0400 q^{29} +(-3.76776 + 4.39224i) q^{30} -23.8062i q^{31} +(-29.8420 + 11.5524i) q^{32} +11.2059i q^{33} +(-3.07471 - 41.5472i) q^{34} +(-38.9284 + 39.1243i) q^{35} +(-34.2829 + 5.10217i) q^{36} -67.7450i q^{37} +(-0.643403 - 8.69402i) q^{38} +2.86212i q^{39} +(21.2907 - 33.8631i) q^{40} +20.9967 q^{41} +(12.7407 - 0.942875i) q^{42} +47.7631 q^{43} +(-11.4020 - 76.6135i) q^{44} +(30.5588 - 30.7126i) q^{45} +(14.2509 - 1.05464i) q^{46} +23.3276 q^{47} +(-8.85772 + 2.69623i) q^{48} +72.8454 q^{49} +(3.94043 + 49.8445i) q^{50} -12.0543i q^{51} +(-2.91223 - 19.5681i) q^{52} +12.8768i q^{53} +(-20.3894 + 1.50892i) q^{54} +(68.6349 + 68.2912i) q^{55} +(-86.1473 + 19.4100i) q^{56} -2.52244i q^{57} +(-67.8944 + 5.02453i) q^{58} -76.9352i q^{59} +(6.86665 - 9.31667i) q^{60} +55.2257 q^{61} +(3.51396 + 47.4826i) q^{62} -95.6487 q^{63} +(57.8159 - 27.4466i) q^{64} +(17.5302 + 17.4424i) q^{65} +(-1.65406 - 22.3506i) q^{66} +51.0598 q^{67} +(12.2653 + 82.4140i) q^{68} +4.13467 q^{69} +(71.8695 - 83.7813i) q^{70} -129.596i q^{71} +(67.6257 - 15.2369i) q^{72} +64.4246i q^{73} +(9.99961 + 135.120i) q^{74} +(0.0726220 + 14.4670i) q^{75} +(2.56659 + 17.2457i) q^{76} -213.750i q^{77} +(-0.422469 - 5.70864i) q^{78} +27.9745i q^{79} +(-37.4669 + 70.6841i) q^{80} +72.0704 q^{81} +(-41.8789 + 3.09925i) q^{82} +82.5330 q^{83} +(-25.2727 + 3.76122i) q^{84} +(-73.8313 - 73.4616i) q^{85} +(-95.2657 + 7.05016i) q^{86} -19.6985 q^{87} +(34.0506 + 151.126i) q^{88} -104.970 q^{89} +(-56.4176 + 65.7684i) q^{90} -54.5946i q^{91} +(-28.2683 + 4.20705i) q^{92} +13.7763i q^{93} +(-46.5280 + 3.44331i) q^{94} +(-15.4497 - 15.3723i) q^{95} +(17.2691 - 6.68521i) q^{96} -14.4820i q^{97} +(-145.293 + 10.7525i) q^{98} +167.794i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) $ 108 * q + 4 * q^5 + 324 * q^9	$ 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) $ 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.99455	+	0.147607i	−0.997273	+	0.0738034i
$2$	−1.99455	+	0.147607i	−0.997273	+	0.0738034i
$3$	−0.578687			−0.192896			−0.0964478	−	0.995338i	$-0.530748\pi$
$3$	−0.578687			−0.192896			−0.0964478	+	0.995338i	$0.530748\pi$
$4$	3.95642	−	0.588817i	0.989106	−	0.147204i
$5$	−3.52665	+	3.54440i	−0.705330	+	0.708879i
$5$	−3.52665	+	3.54440i	−0.705330	+	0.708879i
$6$	1.15422	−	0.0854181i	0.192369	−	0.0142363i
$7$	11.0384			1.57691			0.788454	−	0.615093i	$-0.210882\pi$
$7$	11.0384			1.57691			0.788454	+	0.615093i	$0.210882\pi$
$8$	−7.80436	+	1.75842i	−0.975544	+	0.219802i
$9$	−8.66512			−0.962791
$10$	6.51089	−	7.59002i	0.651089	−	0.759002i
$11$		−	19.3643i		−	1.76039i	−0.474609	−	0.880197i	$-0.657411\pi$
$11$		−	19.3643i		−	1.76039i	0.474609	−	0.880197i	$-0.342589\pi$
$12$	−2.28953	+	0.340740i	−0.190794	+	0.0283950i
$13$		−	4.94590i		−	0.380453i	−0.981740	−	0.190227i	$-0.939078\pi$
$13$		−	4.94590i		−	0.380453i	0.981740	−	0.190227i	$-0.0609223\pi$
$14$	−22.0165	+	1.62934i	−1.57261	+	0.116381i
$15$	2.04082	−	2.05110i	0.136055	−	0.136740i
$16$	15.3066	−	4.65922i	0.956662	−	0.291201i
$17$			20.8304i			1.22532i	0.790347	+	0.612660i	$0.209900\pi$
$17$			20.8304i			1.22532i	−0.790347	+	0.612660i	$0.790100\pi$
$18$	17.2830	−	1.27903i	0.960166	−	0.0710572i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−11.8659	+	16.0997i	−0.593296	+	0.804984i
$21$	−6.38775			−0.304179
$22$	2.85831	+	38.6230i	0.129923	+	1.75559i
$23$	−7.14491			−0.310648			−0.155324	−	0.987864i	$-0.549642\pi$
$23$	−7.14491			−0.310648			−0.155324	+	0.987864i	$0.549642\pi$
$24$	4.51628	−	1.01757i	0.188178	−	0.0423988i
$25$	−0.125495	−	24.9997i	−0.00501978	−	0.999987i
$26$	0.730047	+	9.86481i	0.0280787	+	0.379416i
$27$	10.2226			0.378614
$28$	43.6724	−	6.49957i	1.55973	−	0.232128i
$29$	34.0400			1.17379			0.586897	−	0.809662i	$-0.300349\pi$
$29$	34.0400			1.17379			0.586897	+	0.809662i	$0.300349\pi$
$30$	−3.76776	+	4.39224i	−0.125592	+	0.146408i
$31$		−	23.8062i		−	0.767942i	−0.923345	−	0.383971i	$-0.874556\pi$
$31$		−	23.8062i		−	0.767942i	0.923345	−	0.383971i	$-0.125444\pi$
$32$	−29.8420	+	11.5524i	−0.932561	+	0.361012i
$33$			11.2059i			0.339572i
$34$	−3.07471	−	41.5472i	−0.0904327	−	1.22198i
$35$	−38.9284	+	39.1243i	−1.11224	+	1.11784i
$36$	−34.2829	+	5.10217i	−0.952303	+	0.141727i
$37$		−	67.7450i		−	1.83095i	−0.402380	−	0.915473i	$-0.631817\pi$
$37$		−	67.7450i		−	1.83095i	0.402380	−	0.915473i	$-0.368183\pi$
$38$	−0.643403	−	8.69402i	−0.0169317	−	0.228790i
$39$			2.86212i			0.0733878i
$40$	21.2907	−	33.8631i	0.532267	−	0.846576i
$41$	20.9967			0.512115			0.256057	−	0.966662i	$-0.417576\pi$
$41$	20.9967			0.512115			0.256057	+	0.966662i	$0.417576\pi$
$42$	12.7407	−	0.942875i	0.303349	−	0.0224494i
$43$	47.7631			1.11077			0.555385	−	0.831593i	$-0.312571\pi$
$43$	47.7631			1.11077			0.555385	+	0.831593i	$0.312571\pi$
$44$	−11.4020	−	76.6135i	−0.259137	−	1.74122i
$45$	30.5588	−	30.7126i	0.679085	−	0.682503i
$46$	14.2509	−	1.05464i	0.309801	−	0.0229269i
$47$	23.3276			0.496332			0.248166	−	0.968718i	$-0.420172\pi$
$47$	23.3276			0.496332			0.248166	+	0.968718i	$0.420172\pi$
$48$	−8.85772	+	2.69623i	−0.184536	+	0.0561714i
$49$	72.8454			1.48664
$50$	3.94043	+	49.8445i	0.0788085	+	0.996890i
$51$		−	12.0543i		−	0.236359i
$52$	−2.91223	−	19.5681i	−0.0560043	−	0.376309i
$53$			12.8768i			0.242958i	0.992594	+	0.121479i	$0.0387638\pi$
$53$			12.8768i			0.242958i	−0.992594	+	0.121479i	$0.961236\pi$
$54$	−20.3894	+	1.50892i	−0.377581	+	0.0279430i
$55$	68.6349	+	68.2912i	1.24791	+	1.24166i
$56$	−86.1473	+	19.4100i	−1.53834	+	0.346608i
$57$		−	2.52244i		−	0.0442533i
$58$	−67.8944	+	5.02453i	−1.17059	+	0.0866299i
$59$		−	76.9352i		−	1.30399i	−0.758225	−	0.651993i	$-0.773933\pi$
$59$		−	76.9352i		−	1.30399i	0.758225	−	0.651993i	$-0.226067\pi$
$60$	6.86665	−	9.31667i	0.114444	−	0.155278i
$61$	55.2257			0.905339			0.452670	−	0.891678i	$-0.350472\pi$
$61$	55.2257			0.905339			0.452670	+	0.891678i	$0.350472\pi$
$62$	3.51396	+	47.4826i	0.0566767	+	0.765848i
$63$	−95.6487			−1.51823
$64$	57.8159	−	27.4466i	0.903374	−	0.428853i
$65$	17.5302	+	17.4424i	0.269696	+	0.268345i
$66$	−1.65406	−	22.3506i	−0.0250616	−	0.338646i
$67$	51.0598			0.762087			0.381044	−	0.924557i	$-0.375565\pi$
$67$	51.0598			0.762087			0.381044	+	0.924557i	$0.375565\pi$
$68$	12.2653	+	82.4140i	0.180372	+	1.21197i
$69$	4.13467			0.0599227
$70$	71.8695	−	83.7813i	1.02671	−	1.19688i
$71$		−	129.596i		−	1.82529i	−0.408754	−	0.912644i	$-0.634037\pi$
$71$		−	129.596i		−	1.82529i	0.408754	−	0.912644i	$-0.365963\pi$
$72$	67.6257	−	15.2369i	0.939246	−	0.211624i
$73$			64.4246i			0.882529i	0.897377	+	0.441265i	$0.145470\pi$
$73$			64.4246i			0.882529i	−0.897377	+	0.441265i	$0.854530\pi$
$74$	9.99961	+	135.120i	0.135130	+	1.82595i
$75$	0.0726220	+	14.4670i	0.000968294	+	0.192893i
$76$	2.56659	+	17.2457i	0.0337710	+	0.226917i
$77$		−	213.750i		−	2.77598i
$78$	−0.422469	−	5.70864i	−0.00541627	−	0.0731876i
$79$			27.9745i			0.354108i	0.984201	+	0.177054i	$0.0566567\pi$
$79$			27.9745i			0.354108i	−0.984201	+	0.177054i	$0.943343\pi$
$80$	−37.4669	+	70.6841i	−0.468336	+	0.883551i
$81$	72.0704			0.889758
$82$	−41.8789	+	3.09925i	−0.510718	+	0.0377958i
$83$	82.5330			0.994373			0.497187	−	0.867644i	$-0.334366\pi$
$83$	82.5330			0.994373			0.497187	+	0.867644i	$0.334366\pi$
$84$	−25.2727	+	3.76122i	−0.300865	+	0.0447764i
$85$	−73.8313	−	73.4616i	−0.868603	−	0.864254i
$86$	−95.2657	+	7.05016i	−1.10774	+	0.0819786i
$87$	−19.6985			−0.226420
$88$	34.0506	+	151.126i	0.386938	+	1.71734i
$89$	−104.970			−1.17943			−0.589717	−	0.807610i	$-0.700761\pi$
$89$	−104.970			−1.17943			−0.589717	+	0.807610i	$0.700761\pi$
$90$	−56.4176	+	65.7684i	−0.626862	+	0.730760i
$91$		−	54.5946i		−	0.599940i
$92$	−28.2683	+	4.20705i	−0.307264	+	0.0457288i
$93$			13.7763i			0.148133i
$94$	−46.5280	+	3.44331i	−0.494978	+	0.0366310i
$95$	−15.4497	−	15.3723i	−0.162628	−	0.161814i
$96$	17.2691	−	6.68521i	0.179887	−	0.0696376i
$97$		−	14.4820i		−	0.149299i	−0.997210	−	0.0746494i	$-0.976216\pi$
$97$		−	14.4820i		−	0.149299i	0.997210	−	0.0746494i	$-0.0237838\pi$
$98$	−145.293	+	10.7525i	−1.48259	+	0.109719i
$99$			167.794i			1.69489i
$100$	−15.2167	−	98.8355i	−0.152167	−	0.988355i
$101$	131.494			1.30192			0.650962	−	0.759110i	$-0.274366\pi$
$101$	131.494			1.30192			0.650962	+	0.759110i	$0.274366\pi$
$102$	1.77929	+	24.0428i	0.0174441	+	0.235714i
$103$	−39.5837			−0.384308			−0.192154	−	0.981365i	$-0.561547\pi$
$103$	−39.5837			−0.384308			−0.192154	+	0.981365i	$0.561547\pi$
$104$	8.69695	+	38.5995i	0.0836245	+	0.371149i
$105$	22.5274	−	22.6407i	0.214546	−	0.215626i
$106$	−1.90070	−	25.6834i	−0.0179311	−	0.242296i
$107$	−94.9922			−0.887777			−0.443889	−	0.896082i	$-0.646401\pi$
$107$	−94.9922			−0.887777			−0.443889	+	0.896082i	$0.646401\pi$
$108$	40.4448	−	6.01922i	0.374489	−	0.0557335i
$109$	52.7543			0.483985			0.241992	−	0.970278i	$-0.422199\pi$
$109$	52.7543			0.483985			0.241992	+	0.970278i	$0.422199\pi$
$110$	−146.976	−	126.079i	−1.33614	−	1.14617i
$111$			39.2031i			0.353181i
$112$	168.960	−	51.4301i	1.50857	−	0.459198i
$113$			51.0064i			0.451384i	0.974199	+	0.225692i	$0.0724643\pi$
$113$			51.0064i			0.451384i	−0.974199	+	0.225692i	$0.927536\pi$
$114$	0.372329	+	5.03112i	0.00326604	+	0.0441326i
$115$	25.1976	−	25.3244i	0.219110	−	0.220212i
$116$	134.677	−	20.0433i	1.16101	−	0.172787i
$117$			42.8568i			0.366297i
$118$	11.3561	+	153.451i	0.0962385	+	1.30043i
$119$			229.934i			1.93222i
$120$	−12.3206	+	19.5961i	−0.102672	+	0.163301i
$121$	−253.977			−2.09898
$122$	−110.150	+	8.15169i	−0.902870	+	0.0668171i
$123$	−12.1505			−0.0987846
$124$	−14.0175	−	94.1874i	−0.113044	−	0.759576i
$125$	89.0514	+	87.7203i	0.712411	+	0.701762i
$126$	190.776	−	14.1184i	1.51409	−	0.112051i
$127$	−220.114			−1.73318			−0.866590	−	0.499022i	$-0.833693\pi$
$127$	−220.114			−1.73318			−0.866590	+	0.499022i	$0.833693\pi$
$128$	−111.265	+	63.2776i	−0.869260	+	0.494356i
$129$	−27.6399			−0.214263
$130$	−37.5394	−	32.2022i	−0.288765	−	0.247709i
$131$			113.031i			0.862831i	0.902153	+	0.431415i	$0.141986\pi$
$131$			113.031i			0.862831i	−0.902153	+	0.431415i	$0.858014\pi$
$132$	6.59821	+	44.3352i	0.0499864	+	0.335873i
$133$			48.1151i			0.361768i
$134$	−101.841	+	7.53678i	−0.760009	+	0.0562446i
$135$	−36.0514	+	36.2328i	−0.267048	+	0.268391i
$136$	−36.6286	−	162.568i	−0.269328	−	1.19535i
$137$		−	167.463i		−	1.22236i	−0.791492	−	0.611180i	$-0.790695\pi$
$137$		−	167.463i		−	1.22236i	0.791492	−	0.611180i	$-0.209305\pi$
$138$	−8.24678	+	0.610305i	−0.0597593	+	0.00442250i
$139$		−	61.9412i		−	0.445620i	−0.974862	−	0.222810i	$-0.928477\pi$
$139$		−	61.9412i		−	0.445620i	0.974862	−	0.222810i	$-0.0715230\pi$
$140$	−130.980	+	177.714i	−0.935573	+	1.26939i
$141$	−13.4994			−0.0957402
$142$	19.1292	+	258.484i	0.134712	+	1.82031i
$143$	−95.7739			−0.669748
$144$	−132.633	+	40.3727i	−0.921066	+	0.280366i
$145$	−120.047	+	120.651i	−0.827911	+	0.832078i
$146$	−9.50951	−	128.498i	−0.0651336	−	0.880122i
$147$	−42.1546			−0.286766
$148$	−39.8894	−	268.028i	−0.269523	−	1.81100i
$149$	−186.675			−1.25285			−0.626427	−	0.779480i	$-0.715483\pi$
$149$	−186.675			−1.25285			−0.626427	+	0.779480i	$0.715483\pi$
$150$	−2.28027	−	28.8443i	−0.0152018	−	0.192296i
$151$		−	14.9893i		−	0.0992670i	−0.998767	−	0.0496335i	$-0.984195\pi$
$151$		−	14.9893i		−	0.0992670i	0.998767	−	0.0496335i	$-0.0158053\pi$
$152$	−7.66476	−	34.0184i	−0.0504261	−	0.223805i
$153$		−	180.498i		−	1.17973i
$154$	31.5510	+	426.335i	0.204877	+	2.76841i
$155$	84.3786	+	83.9561i	0.544378	+	0.541652i
$156$	1.68527	+	11.3238i	0.0108030	+	0.0725883i
$157$			197.930i			1.26070i	0.776310	+	0.630351i	$0.217089\pi$
$157$			197.930i			1.26070i	−0.776310	+	0.630351i	$0.782911\pi$
$158$	−4.12923	−	55.7965i	−0.0261344	−	0.353142i
$159$		−	7.45163i		−	0.0468656i
$160$	64.2959	−	146.513i	0.401849	−	0.915706i
$161$	−78.8681			−0.489864
$162$	−143.748	+	10.6381i	−0.887332	+	0.0656672i
$163$	−27.9812			−0.171664			−0.0858320	−	0.996310i	$-0.527355\pi$
$163$	−27.9812			−0.171664			−0.0858320	+	0.996310i	$0.527355\pi$
$164$	83.0719	−	12.3632i	0.506536	−	0.0753854i
$165$	−39.7181	−	39.5192i	−0.240716	−	0.239510i
$166$	−164.616	+	12.1824i	−0.991662	+	0.0733881i
$167$	−63.7638			−0.381819			−0.190909	−	0.981608i	$-0.561144\pi$
$167$	−63.7638			−0.381819			−0.190909	+	0.981608i	$0.561144\pi$
$168$	49.8523	−	11.2323i	0.296740	−	0.0668591i
$169$	144.538			0.855255
$170$	158.103	+	135.625i	0.930019	+	0.797791i
$171$		−	37.7704i		−	0.220879i
$172$	188.971	−	28.1237i	1.09867	−	0.163510i
$173$			141.416i			0.817436i	0.912661	+	0.408718i	$0.134024\pi$
$173$			141.416i			0.817436i	−0.912661	+	0.408718i	$0.865976\pi$
$174$	39.2896	−	2.90763i	0.225802	−	0.0167105i
$175$	−1.38525	−	275.956i	−0.00791574	−	1.57689i
$176$	−90.2226	−	296.402i	−0.512629	−	1.68410i
$177$			44.5214i			0.251533i
$178$	209.367	−	15.4942i	1.17622	−	0.0870462i
$179$		−	141.081i		−	0.788165i	−0.919075	−	0.394082i	$-0.871063\pi$
$179$		−	141.081i		−	0.788165i	0.919075	−	0.394082i	$-0.128937\pi$
$180$	102.820	−	139.506i	0.571220	−	0.775032i
$181$	188.269			1.04016			0.520081	−	0.854117i	$-0.325902\pi$
$181$	188.269			1.04016			0.520081	+	0.854117i	$0.325902\pi$
$182$	8.05853	+	108.891i	0.0442776	+	0.598304i
$183$	−31.9584			−0.174636
$184$	55.7615	−	12.5637i	0.303051	−	0.0682812i
$185$	240.115	+	238.913i	1.29792	+	1.29142i
$186$	−2.03348	−	27.4775i	−0.0109327	−	0.147729i
$187$	403.367			2.15704
$188$	92.2939	−	13.7357i	0.490925	−	0.0730622i
$189$	112.840			0.597039
$190$	33.0841	+	28.3803i	0.174127	+	0.149370i
$191$		−	189.571i		−	0.992517i	−0.868175	−	0.496258i	$-0.834707\pi$
$191$		−	189.571i		−	0.992517i	0.868175	−	0.496258i	$-0.165293\pi$
$192$	−33.4573	+	15.8830i	−0.174257	+	0.0827239i
$193$		−	51.1699i		−	0.265129i	−0.991174	−	0.132565i	$-0.957679\pi$
$193$		−	51.1699i		−	0.265129i	0.991174	−	0.132565i	$-0.0423212\pi$
$194$	2.13764	+	28.8850i	0.0110188	+	0.148892i
$195$	−10.1445	−	10.0937i	−0.0520231	−	0.0517626i
$196$	288.207	−	42.8926i	1.47045	−	0.218840i
$197$		−	238.263i		−	1.20946i	−0.796432	−	0.604728i	$-0.793282\pi$
$197$		−	238.263i		−	1.20946i	0.796432	−	0.604728i	$-0.206718\pi$
$198$	−24.7676	−	334.673i	−0.125089	−	1.69027i
$199$			135.291i			0.679853i	0.940452	+	0.339926i	$0.110402\pi$
$199$			135.291i			0.679853i	−0.940452	+	0.339926i	$0.889598\pi$
$200$	44.9393	+	194.886i	0.224696	+	0.974429i
$201$	−29.5476			−0.147003
$202$	−262.272	+	19.4095i	−1.29837	+	0.0960864i
$203$	375.746			1.85096
$204$	−7.09777	−	47.6919i	−0.0347930	−	0.233784i
$205$	−74.0480	+	74.4206i	−0.361210	+	0.363027i
$206$	78.9515	−	5.84282i	0.383260	−	0.0283632i
$207$	61.9116			0.299090
$208$	−23.0440	−	75.7048i	−0.110788	−	0.363965i
$209$	84.4071			0.403862
$210$	−41.5899	+	48.4831i	−0.198047	+	0.230872i
$211$		−	96.5118i		−	0.457402i	−0.973497	−	0.228701i	$-0.926552\pi$
$211$		−	96.5118i		−	0.457402i	0.973497	−	0.228701i	$-0.0734478\pi$
$212$	7.58207	+	50.9461i	0.0357645	+	0.240312i
$213$			74.9952i			0.352090i
$214$	189.466	−	14.0215i	0.885356	−	0.0655210i
$215$	−168.444	+	169.291i	−0.783459	+	0.787402i
$216$	−79.7806	+	17.9755i	−0.369355	+	0.0832201i
$217$		−	262.781i		−	1.21097i
$218$	−105.221	+	7.78690i	−0.482665	+	0.0357197i
$219$		−	37.2817i		−	0.170236i
$220$	311.760	+	229.776i	1.41709	+	1.04443i
$221$	103.025			0.466177
$222$	−5.78664	−	78.1924i	−0.0260660	−	0.352218i
$223$	−136.510			−0.612151			−0.306075	−	0.952007i	$-0.599016\pi$
$223$	−136.510			−0.612151			−0.306075	+	0.952007i	$0.599016\pi$
$224$	−329.406	+	127.519i	−1.47056	+	0.569283i
$225$	1.08743	+	216.625i	0.00483300	+	0.962779i
$226$	−7.52889	−	101.735i	−0.0333137	−	0.450153i
$227$	179.438			0.790475			0.395237	−	0.918579i	$-0.370662\pi$
$227$	179.438			0.790475			0.395237	+	0.918579i	$0.370662\pi$
$228$	−1.48525	−	9.97983i	−0.00651427	−	0.0437712i
$229$	−251.825			−1.09967			−0.549836	−	0.835273i	$-0.685310\pi$
$229$	−251.825			−1.09967			−0.549836	+	0.835273i	$0.685310\pi$
$230$	−46.5197	+	54.2300i	−0.202260	+	0.235783i
$231$			123.695i			0.535474i
$232$	−265.660	+	59.8565i	−1.14509	+	0.258002i
$233$		−	130.654i		−	0.560748i	−0.959891	−	0.280374i	$-0.909541\pi$
$233$		−	130.654i		−	0.560748i	0.959891	−	0.280374i	$-0.0904585\pi$
$234$	−6.32595	−	85.4798i	−0.0270340	−	0.365298i
$235$	−82.2683	+	82.6823i	−0.350078	+	0.351840i
$236$	−45.3007	−	304.388i	−0.191952	−	1.28978i
$237$		−	16.1885i		−	0.0683058i
$238$	−33.9398	−	458.613i	−0.142604	−	1.92695i
$239$			448.680i			1.87732i	0.344839	+	0.938662i	$0.387934\pi$
$239$			448.680i			1.87732i	−0.344839	+	0.938662i	$0.612066\pi$
$240$	21.6816	−	40.9039i	0.0903399	−	0.170433i
$241$	−396.151			−1.64378			−0.821891	−	0.569645i	$-0.807081\pi$
$241$	−396.151			−1.64378			−0.821891	+	0.569645i	$0.807081\pi$
$242$	506.569	−	37.4887i	2.09326	−	0.154912i
$243$	−133.709			−0.550244
$244$	218.496	−	32.5178i	0.895477	−	0.133270i
$245$	−256.900	+	258.193i	−1.04857	+	1.05385i
$246$	24.2347	−	1.79350i	0.0985152	−	0.00729064i
$247$	21.5587			0.0872820
$248$	41.8612	+	185.792i	0.168795	+	0.749162i
$249$	−47.7607			−0.191810
$250$	−190.565	−	161.818i	−0.762261	−	0.647270i
$251$		−	367.150i		−	1.46275i	−0.681976	−	0.731374i	$-0.738879\pi$
$251$		−	367.150i		−	1.46275i	0.681976	−	0.731374i	$-0.261121\pi$
$252$	−378.427	+	56.3196i	−1.50169	+	0.223490i
$253$			138.356i			0.546864i
$254$	439.027	−	32.4903i	1.72845	−	0.127914i
$255$	42.7252	+	42.5112i	0.167550	+	0.166711i
$256$	212.583	−	142.633i	0.830404	−	0.557162i
$257$			73.4399i			0.285758i	0.989740	+	0.142879i	$0.0456360\pi$
$257$			73.4399i			0.285758i	−0.989740	+	0.142879i	$0.954364\pi$
$258$	55.1290	−	4.07983i	0.213678	−	0.0158133i
$259$		−	747.793i		−	2.88723i
$260$	79.6274	+	58.6876i	0.306259	+	0.225722i
$261$	−294.961			−1.13012
$262$	−16.6841	−	225.445i	−0.0636798	−	0.860478i
$263$	47.4233			0.180317			0.0901583	−	0.995927i	$-0.471263\pi$
$263$	47.4233			0.180317			0.0901583	+	0.995927i	$0.471263\pi$
$264$	−19.7046	−	87.4547i	−0.0746387	−	0.331268i
$265$	−45.6405	−	45.4119i	−0.172228	−	0.171366i
$266$	−7.10211	−	95.9677i	−0.0266997	−	0.360781i
$267$	60.7445			0.227508
$268$	202.014	−	30.0649i	0.753785	−	0.112182i
$269$	−255.400			−0.949442			−0.474721	−	0.880136i	$-0.657451\pi$
$269$	−255.400			−0.949442			−0.474721	+	0.880136i	$0.657451\pi$
$270$	66.5580	−	77.5895i	0.246511	−	0.287368i
$271$			165.726i			0.611533i	0.952106	+	0.305767i	$0.0989127\pi$
$271$			165.726i			0.611533i	−0.952106	+	0.305767i	$0.901087\pi$
$272$	97.0535	+	318.843i	0.356814	+	1.17222i
$273$			31.5931i			0.115726i
$274$	24.7187	+	334.013i	0.0902143	+	1.21903i
$275$	−484.102	+	2.43012i	−1.76037	+	0.00883679i
$276$	16.3585	−	2.43456i	0.0592699	−	0.00882087i
$277$			180.434i			0.651385i	0.945476	+	0.325693i	$0.105597\pi$
$277$			180.434i			0.651385i	−0.945476	+	0.325693i	$0.894403\pi$
$278$	9.14294	+	123.545i	0.0328883	+	0.444405i
$279$			206.284i			0.739368i
$280$	235.014	−	373.793i	0.839337	−	1.33497i
$281$	170.152			0.605522			0.302761	−	0.953067i	$-0.402092\pi$
$281$	170.152			0.605522			0.302761	+	0.953067i	$0.402092\pi$
$282$	26.9251	−	1.99260i	0.0954791	−	0.00706595i
$283$	30.9553			0.109383			0.0546913	−	0.998503i	$-0.482583\pi$
$283$	30.9553			0.109383			0.0546913	+	0.998503i	$0.482583\pi$
$284$	−76.3080	−	512.735i	−0.268690	−	1.80540i
$285$	8.94052	+	8.89575i	0.0313702	+	0.0312132i
$286$	191.025	−	14.1369i	0.667921	−	0.0494296i
$287$	231.769			0.807558
$288$	258.584	−	100.103i	0.897862	−	0.347579i
$289$	−144.907			−0.501407
$290$	221.631	−	258.364i	0.764243	−	0.890911i
$291$			8.38053i			0.0287991i
$292$	37.9343	+	254.891i	0.129912	+	0.872915i
$293$			485.683i			1.65762i	0.559530	+	0.828810i	$0.310982\pi$
$293$			485.683i			1.65762i	−0.559530	+	0.828810i	$0.689018\pi$
$294$	84.0794	−	6.22231i	0.285984	−	0.0211643i
$295$	272.689	+	271.323i	0.924369	+	0.919740i
$296$	119.124	+	528.706i	0.402446	+	1.78617i
$297$		−	197.953i		−	0.666509i
$298$	372.332	−	27.5545i	1.24944	−	0.0924649i
$299$			35.3380i			0.118187i
$300$	8.80573	+	57.1948i	0.0293524	+	0.190649i
$301$	527.226			1.75158
$302$	2.21252	+	29.8969i	0.00732624	+	0.0989962i
$303$	−76.0940			−0.251135
$304$	20.3091	+	66.7199i	0.0668061	+	0.219473i
$305$	−194.762	+	195.742i	−0.638563	+	0.641776i
$306$	26.6427	+	360.012i	0.0870678	+	1.17651i
$307$	−260.020			−0.846969			−0.423485	−	0.905903i	$-0.639193\pi$
$307$	−260.020			−0.846969			−0.423485	+	0.905903i	$0.639193\pi$
$308$	−125.860	−	845.687i	−0.408636	−	2.74574i
$309$	22.9066			0.0741313
$310$	−180.689	−	154.999i	−0.582869	−	0.499998i
$311$		−	229.473i		−	0.737856i	−0.929458	−	0.368928i	$-0.879725\pi$
$311$		−	229.473i		−	0.737856i	0.929458	−	0.368928i	$-0.120275\pi$
$312$	−5.03281	−	22.3370i	−0.0161308	−	0.0715931i
$313$			89.8947i			0.287203i	0.989636	+	0.143602i	$0.0458684\pi$
$313$			89.8947i			0.287203i	−0.989636	+	0.143602i	$0.954132\pi$
$314$	−29.2158	−	394.781i	−0.0930441	−	1.25726i
$315$	337.319	−	339.017i	1.07086	−	1.07624i
$316$	16.4719	+	110.679i	0.0521262	+	0.350250i
$317$		−	606.821i		−	1.91426i	−0.289655	−	0.957131i	$-0.593541\pi$
$317$		−	606.821i		−	1.91426i	0.289655	−	0.957131i	$-0.406459\pi$
$318$	1.09991	+	14.8626i	0.00345884	+	0.0467378i
$319$		−	659.162i		−	2.06634i
$320$	−106.615	+	301.717i	−0.333171	+	0.942866i
$321$	54.9707			0.171248
$322$	157.306	−	11.6415i	0.488528	−	0.0361536i
$323$	−90.7977			−0.281107
$324$	285.141	−	42.4363i	0.880065	−	0.130976i
$325$	−123.646	+	0.620683i	−0.380449	+	0.00190979i
$326$	55.8098	−	4.13022i	0.171196	−	0.0126694i
$327$	−30.5282			−0.0933585
$328$	−163.866	+	36.9210i	−0.499591	+	0.112564i
$329$	257.498			0.782670
$330$	85.0528	+	72.9602i	0.257736	+	0.221091i
$331$		−	224.002i		−	0.676744i	−0.941012	−	0.338372i	$-0.890124\pi$
$331$		−	224.002i		−	0.676744i	0.941012	−	0.338372i	$-0.109876\pi$
$332$	326.536	−	48.5968i	0.983541	−	0.146376i
$333$			587.018i			1.76282i
$334$	127.180	−	9.41196i	0.380778	−	0.0281795i
$335$	−180.070	+	180.976i	−0.537523	+	0.540228i
$336$	−97.7747	+	29.7619i	−0.290996	+	0.0885772i
$337$			54.9691i			0.163113i	0.996669	+	0.0815565i	$0.0259891\pi$
$337$			54.9691i			0.163113i	−0.996669	+	0.0815565i	$0.974011\pi$
$338$	−288.288	+	21.3348i	−0.852923	+	0.0631207i
$339$		−	29.5167i		−	0.0870700i
$340$	−335.363	−	247.172i	−0.986363	−	0.726977i
$341$	−460.991			−1.35188
$342$	5.57516	+	75.3348i	0.0163016	+	0.220277i
$343$	263.214			0.767387
$344$	−372.760	+	83.9875i	−1.08361	+	0.244150i
$345$	−14.5815	+	14.6549i	−0.0422653	+	0.0424780i
$346$	−20.8740	−	282.061i	−0.0603295	−	0.815206i
$347$	77.4158			0.223100			0.111550	−	0.993759i	$-0.464418\pi$
$347$	77.4158			0.223100			0.111550	+	0.993759i	$0.464418\pi$
$348$	−77.9356	+	11.5988i	−0.223953	+	0.0333299i
$349$	−163.821			−0.469401			−0.234701	−	0.972068i	$-0.575411\pi$
$349$	−163.821			−0.469401			−0.234701	+	0.972068i	$0.575411\pi$
$350$	43.4958	+	550.201i	0.124274	+	1.57200i
$351$		−	50.5598i		−	0.144045i
$352$	223.704	+	577.869i	0.635523	+	1.64167i
$353$			152.192i			0.431138i	0.976489	+	0.215569i	$0.0691607\pi$
$353$			152.192i			0.431138i	−0.976489	+	0.215569i	$0.930839\pi$
$354$	−6.57165	−	88.7999i	−0.0185640	−	0.250847i
$355$	459.338	+	457.038i	1.29391	+	1.28743i
$356$	−415.304	+	61.8079i	−1.16659	+	0.173618i
$357$		−	133.060i		−	0.372716i
$358$	20.8246	+	281.393i	0.0581692	+	0.786015i
$359$			17.9083i			0.0498839i	0.999689	+	0.0249420i	$0.00794010\pi$
$359$			17.9083i			0.0498839i	−0.999689	+	0.0249420i	$0.992060\pi$
$360$	−184.486	+	293.427i	−0.512462	+	0.815076i
$361$	−19.0000			−0.0526316
$362$	−375.511	+	27.7898i	−1.03732	+	0.0767674i
$363$	146.973			0.404885
$364$	−32.1462	−	215.999i	−0.0883137	−	0.593405i
$365$	−228.346	−	227.203i	−0.625607	−	0.622474i
$366$	63.7425	−	4.71727i	0.174160	−	0.0128887i
$367$	318.002			0.866491			0.433246	−	0.901276i	$-0.357368\pi$
$367$	318.002			0.866491			0.433246	+	0.901276i	$0.357368\pi$
$368$	−109.364	+	33.2897i	−0.297186	+	0.0904612i
$369$	−181.939			−0.493060
$370$	−514.186	−	441.080i	−1.38969	−	1.19211i
$371$			142.139i			0.383123i
$372$	8.11173	+	54.5050i	0.0218057	+	0.146519i
$373$		−	139.096i		−	0.372912i	−0.982463	−	0.186456i	$-0.940300\pi$
$373$		−	139.096i		−	0.372912i	0.982463	−	0.186456i	$-0.0597001\pi$
$374$	−804.534	+	59.5397i	−2.15116	+	0.159197i
$375$	−51.5328	−	50.7626i	−0.137421	−	0.135367i
$376$	−182.057	+	41.0197i	−0.484194	+	0.109095i
$377$		−	168.358i		−	0.446574i
$378$	−225.065	+	16.6560i	−0.595411	+	0.0440635i
$379$			343.111i			0.905306i	0.891687	+	0.452653i	$0.149522\pi$
$379$			343.111i			0.905306i	−0.891687	+	0.452653i	$0.850478\pi$
$380$	−70.1769	−	51.7223i	−0.184676	−	0.136111i
$381$	127.377			0.334323
$382$	27.9819	+	378.107i	0.0732511	+	0.989810i
$383$	326.461			0.852378			0.426189	−	0.904634i	$-0.359856\pi$
$383$	326.461			0.852378			0.426189	+	0.904634i	$0.359856\pi$
$384$	64.3877	−	36.6179i	0.167676	−	0.0953591i
$385$	757.616	+	753.823i	1.96783	+	1.95798i
$386$	7.55303	+	102.061i	0.0195674	+	0.264406i
$387$	−413.873			−1.06944
$388$	−8.52724	−	57.2969i	−0.0219774	−	0.147672i
$389$	281.415			0.723433			0.361716	−	0.932288i	$-0.382191\pi$
$389$	281.415			0.723433			0.361716	+	0.932288i	$0.382191\pi$
$390$	21.7236	+	18.6350i	0.0557015	+	0.0477819i
$391$		−	148.832i		−	0.380644i
$392$	−568.511	+	128.093i	−1.45028	+	0.326767i
$393$		−	65.4094i		−	0.166436i
$394$	35.1692	+	475.226i	0.0892619	+	1.20616i
$395$	−99.1528	−	98.6563i	−0.251020	−	0.249763i
$396$	98.8001	+	663.865i	0.249495	+	1.67643i
$397$		−	227.035i		−	0.571877i	−0.958248	−	0.285938i	$-0.907695\pi$
$397$		−	227.035i		−	0.571877i	0.958248	−	0.285938i	$-0.0923053\pi$
$398$	−19.9698	−	269.843i	−0.0501754	−	0.677998i
$399$		−	27.8436i		−	0.0697834i
$400$	−118.400	−	382.075i	−0.296000	−	0.955188i
$401$	443.796			1.10672			0.553361	−	0.832941i	$-0.313345\pi$
$401$	443.796			1.10672			0.553361	+	0.832941i	$0.313345\pi$
$402$	58.9341	−	4.36143i	0.146602	−	0.0108493i
$403$	−117.743			−0.292166
$404$	520.248	−	77.4261i	1.28774	−	0.191649i
$405$	−254.167	+	255.446i	−0.627573	+	0.630731i
$406$	−749.442	+	55.4626i	−1.84592	+	0.136607i
$407$	−1311.84			−3.22318
$408$	21.1965	+	94.0760i	0.0519521	+	0.230578i
$409$	−69.9527			−0.171034			−0.0855168	−	0.996337i	$-0.527254\pi$
$409$	−69.9527			−0.171034			−0.0855168	+	0.996337i	$0.527254\pi$
$410$	136.707	−	159.365i	0.333432	−	0.388696i
$411$			96.9088i			0.235788i
$412$	−156.610	+	23.3076i	−0.380121	+	0.0565717i
$413$		−	849.238i		−	2.05627i
$414$	−123.485	+	9.13856i	−0.298274	+	0.0220738i
$415$	−291.065	+	292.530i	−0.701361	+	0.704891i
$416$	57.1369	+	147.595i	0.137348	+	0.354796i
$417$			35.8445i			0.0859581i
$418$	−168.354	+	12.4591i	−0.402761	+	0.0298064i
$419$			345.690i			0.825035i	0.910950	+	0.412517i	$0.135350\pi$
$419$			345.690i			0.825035i	−0.910950	+	0.412517i	$0.864650\pi$
$420$	75.7965	−	102.841i	0.180468	−	0.244859i
$421$	−208.409			−0.495034			−0.247517	−	0.968884i	$-0.579615\pi$
$421$	−208.409			−0.495034			−0.247517	+	0.968884i	$0.579615\pi$
$422$	14.2458	+	192.497i	0.0337578	+	0.456154i
$423$	−202.137			−0.477864
$424$	−22.6428	−	100.495i	−0.0534028	−	0.237017i
$425$	520.754	−	2.61410i	1.22530	−	0.00615083i
$426$	−11.0698	−	149.581i	−0.0259854	−	0.351130i
$427$	609.601			1.42764
$428$	−375.829	+	55.9330i	−0.878106	+	0.130685i
$429$	55.4231			0.129191
$430$	310.980	−	362.523i	0.723210	−	0.843077i
$431$			526.613i			1.22184i	0.791692	+	0.610920i	$0.209201\pi$
$431$			526.613i			1.22184i	−0.791692	+	0.610920i	$0.790799\pi$
$432$	156.473	−	47.6292i	0.362205	−	0.110253i
$433$		−	824.618i		−	1.90443i	−0.305428	−	0.952215i	$-0.598800\pi$
$433$		−	824.618i		−	1.90443i	0.305428	−	0.952215i	$-0.401200\pi$
$434$	38.7883	+	524.129i	0.0893740	+	1.20767i
$435$	69.4697	−	69.8193i	0.159700	−	0.160504i
$436$	208.719	−	31.0626i	0.478712	−	0.0712446i
$437$		−	31.1440i		−	0.0712676i
$438$	5.50303	+	74.3600i	0.0125640	+	0.169772i
$439$			175.750i			0.400342i	0.979761	+	0.200171i	$0.0641498\pi$
$439$			175.750i			0.400342i	−0.979761	+	0.200171i	$0.935850\pi$
$440$	−655.735	−	412.280i	−1.49031	−	0.937000i
$441$	−631.214			−1.43132
$442$	−205.488	+	15.2072i	−0.464906	+	0.0344054i
$443$	−628.957			−1.41977			−0.709884	−	0.704319i	$-0.751252\pi$
$443$	−628.957			−1.41977			−0.709884	+	0.704319i	$0.751252\pi$
$444$	23.0834	+	155.104i	0.0519898	+	0.349334i
$445$	370.191	−	372.054i	0.831890	−	0.836076i
$446$	272.275	−	20.1497i	0.610481	−	0.0451788i
$447$	108.027			0.241670
$448$	638.193	−	302.966i	1.42454	−	0.676263i
$449$	774.826			1.72567			0.862835	−	0.505486i	$-0.168687\pi$
$449$	774.826			1.72567			0.862835	+	0.505486i	$0.168687\pi$
$450$	−34.1443	−	431.909i	−0.0758762	−	0.959797i
$451$		−	406.587i		−	0.901523i
$452$	30.0334	+	201.803i	0.0664456	+	0.446467i
$453$			8.67411i			0.0191482i
$454$	−357.897	+	26.4862i	−0.788319	+	0.0583397i
$455$	193.505	+	192.536i	0.425285	+	0.423156i
$456$	4.43550	+	19.6860i	0.00972696	+	0.0431710i
$457$			783.996i			1.71553i	0.514044	+	0.857764i	$0.328147\pi$
$457$			783.996i			1.71553i	−0.514044	+	0.857764i	$0.671853\pi$
$458$	502.276	−	37.1711i	1.09667	−	0.0811595i
$459$			212.940i			0.463923i
$460$	84.7810	−	115.031i	0.184306	−	0.250067i
$461$	−81.7725			−0.177381			−0.0886903	−	0.996059i	$-0.528268\pi$
$461$	−81.7725			−0.177381			−0.0886903	+	0.996059i	$0.528268\pi$
$462$	−18.2581	−	246.714i	−0.0395198	−	0.534014i
$463$	−183.913			−0.397220			−0.198610	−	0.980079i	$-0.563643\pi$
$463$	−183.913			−0.397220			−0.198610	+	0.980079i	$0.563643\pi$
$464$	521.036	−	158.600i	1.12292	−	0.341810i
$465$	−48.8288	−	48.5843i	−0.105008	−	0.104482i
$466$	19.2855	+	260.596i	0.0413851	+	0.559219i
$467$	−592.245			−1.26819			−0.634095	−	0.773255i	$-0.718627\pi$
$467$	−592.245			−1.26819			−0.634095	+	0.773255i	$0.718627\pi$
$468$	25.2348	+	169.560i	0.0539205	+	0.362307i
$469$	563.617			1.20174
$470$	151.883	−	177.057i	0.323156	−	0.376717i
$471$		−	114.540i		−	0.243184i
$472$	135.284	+	600.429i	0.286619	+	1.27210i
$473$		−	924.901i		−	1.95539i
$474$	2.38953	+	32.2887i	0.00504120	+	0.0681196i
$475$	108.971	−	0.547018i	0.229413	−	0.00115162i
$476$	135.389	+	909.715i	0.284430	+	1.91117i
$477$		−	111.579i		−	0.233918i
$478$	−66.2282	−	894.913i	−0.138553	−	1.87220i
$479$			474.433i			0.990465i	0.868761	+	0.495232i	$0.164917\pi$
$479$			474.433i			0.990465i	−0.868761	+	0.495232i	$0.835083\pi$
$480$	−37.2072	+	84.7851i	−0.0775150	+	0.176636i
$481$	−335.060			−0.696589
$482$	790.142	−	58.4746i	1.63930	−	0.121317i
$483$	45.6399			0.0944926
$484$	−1004.84	+	149.546i	−2.07612	+	0.308979i
$485$	51.3299	+	51.0729i	0.105835	+	0.105305i
$486$	266.689	−	19.7364i	0.548744	−	0.0406099i
$487$	−435.322			−0.893884			−0.446942	−	0.894563i	$-0.647487\pi$
$487$	−435.322			−0.893884			−0.446942	+	0.894563i	$0.647487\pi$
$488$	−431.001	+	97.1098i	−0.883199	+	0.198996i
$489$	16.1924			0.0331132
$490$	474.288	−	552.898i	0.967934	−	1.12836i
$491$			472.001i			0.961306i	0.876911	+	0.480653i	$0.159600\pi$
$491$			472.001i			0.961306i	−0.876911	+	0.480653i	$0.840400\pi$
$492$	−48.0726	+	7.15442i	−0.0977085	+	0.0145415i
$493$			709.068i			1.43827i
$494$	−42.9997	+	3.18220i	−0.0870440	+	0.00644171i
$495$	−594.729	−	591.751i	−1.20147	−	1.19546i
$496$	−110.918	−	364.392i	−0.223626	−	0.734661i
$497$		−	1430.52i		−	2.87831i
$498$	95.2610	−	7.04981i	0.191287	−	0.0141562i
$499$			54.4889i			0.109196i	0.998508	+	0.0545981i	$0.0173878\pi$
$499$			54.4889i			0.109196i	−0.998508	+	0.0545981i	$0.982612\pi$
$500$	403.976	+	294.624i	0.807952	+	0.589248i
$501$	36.8992			0.0736512
$502$	54.1938	+	732.297i	0.107956	+	1.45876i
$503$	103.945			0.206649			0.103325	−	0.994648i	$-0.467052\pi$
$503$	103.945			0.206649			0.103325	+	0.994648i	$0.467052\pi$
$504$	746.477	−	168.190i	1.48110	−	0.333711i
$505$	−463.735	+	466.068i	−0.918286	+	0.922907i
$506$	−20.4223	−	275.958i	−0.0403604	−	0.545372i
$507$	−83.6423			−0.164975
$508$	−870.863	+	129.607i	−1.71430	+	0.255131i
$509$	−455.340			−0.894578			−0.447289	−	0.894389i	$-0.647610\pi$
$509$	−455.340			−0.894578			−0.447289	+	0.894389i	$0.647610\pi$
$510$	−91.4923	−	78.4841i	−0.179397	−	0.153890i
$511$			711.142i			1.39167i
$512$	−402.954	+	315.868i	−0.787019	+	0.616929i
$513$			44.5592i			0.0868599i
$514$	−10.8402	−	146.479i	−0.0210899	−	0.284979i
$515$	139.598	−	140.300i	0.271064	−	0.272428i
$516$	−109.355	+	16.2748i	−0.211928	+	0.0315404i
$517$		−	451.723i		−	0.873740i
$518$	110.379	+	1491.51i	0.213088	+	2.87936i
$519$		−	81.8358i		−	0.157680i
$520$	−167.483	−	105.302i	−0.322083	−	0.202503i
$521$	802.316			1.53995			0.769977	−	0.638071i	$-0.220267\pi$
$521$	802.316			1.53995			0.769977	+	0.638071i	$0.220267\pi$
$522$	588.313	−	43.5382i	1.12704	−	0.0834065i
$523$	580.678			1.11028			0.555141	−	0.831756i	$-0.312664\pi$
$523$	580.678			1.11028			0.555141	+	0.831756i	$0.312664\pi$
$524$	66.5544	+	447.198i	0.127012	+	0.853431i
$525$	0.801628	+	159.692i	0.00152691	+	0.304175i
$526$	−94.5879	+	6.99999i	−0.179825	+	0.0133080i
$527$	495.893			0.940974
$528$	52.2106	+	171.524i	0.0988838	+	0.324856i
$529$	−477.950			−0.903498
$530$	97.7351	+	83.8393i	0.184406	+	0.158187i
$531$			666.653i			1.25547i
$532$	28.3310	+	190.364i	0.0532537	+	0.357827i
$533$		−	103.847i		−	0.194836i
$534$	−121.158	+	8.96630i	−0.226887	+	0.0167908i
$535$	335.004	−	336.690i	0.626176	−	0.629327i
$536$	−398.489	+	89.7845i	−0.743450	+	0.167508i
$537$			81.6420i			0.152033i
$538$	509.407	−	37.6987i	0.946852	−	0.0700720i
$539$		−	1410.60i		−	2.61707i
$540$	−121.300	+	164.580i	−0.224630	+	0.304778i
$541$	938.838			1.73537			0.867687	−	0.497110i	$-0.165606\pi$
$541$	938.838			1.73537			0.867687	+	0.497110i	$0.165606\pi$
$542$	−24.4622	−	330.547i	−0.0451332	−	0.609866i
$543$	−108.949			−0.200642
$544$	−240.641	−	621.621i	−0.442355	−	1.14269i
$545$	−186.046	+	186.982i	−0.341369	+	0.343087i
$546$	−4.66336	−	63.0140i	−0.00854096	−	0.115410i
$547$	412.786			0.754636			0.377318	−	0.926084i	$-0.376846\pi$
$547$	412.786			0.754636			0.377318	+	0.926084i	$0.376846\pi$
$548$	−98.6052	−	662.556i	−0.179937	−	1.20904i
$549$	−478.537			−0.871653
$550$	965.205	−	76.3037i	1.75492	−	0.138734i
$551$			148.377i			0.269287i
$552$	−32.2684	+	7.27047i	−0.0584573	+	0.0131711i
$553$			308.793i			0.558396i
$554$	−26.6332	−	359.883i	−0.0480744	−	0.649609i
$555$	−138.951	−	138.256i	−0.250363	−	0.249109i
$556$	−36.4720	−	245.066i	−0.0655971	−	0.440766i
$557$		−	715.975i		−	1.28541i	−0.766112	−	0.642707i	$-0.777811\pi$
$557$		−	715.975i		−	1.28541i	0.766112	−	0.642707i	$-0.222189\pi$
$558$	−30.4489	−	411.442i	−0.0545678	−	0.737351i
$559$		−	236.231i		−	0.422596i
$560$	−413.573	+	780.236i	−0.738522	+	1.39328i
$561$	−233.423			−0.416084
$562$	−339.375	+	25.1155i	−0.603870	+	0.0446895i
$563$	710.197			1.26145			0.630725	−	0.776006i	$-0.282758\pi$
$563$	710.197			1.26145			0.630725	+	0.776006i	$0.282758\pi$
$564$	−53.4093	+	7.94866i	−0.0946973	+	0.0140934i
$565$	−180.787	−	179.882i	−0.319977	−	0.318375i
$566$	−61.7417	+	4.56921i	−0.109084	+	0.00807281i
$567$	795.539			1.40307
$568$	227.883	+	1011.41i	0.401202	+	1.78065i
$569$	799.602			1.40528			0.702638	−	0.711547i	$-0.252005\pi$
$569$	799.602			1.40528			0.702638	+	0.711547i	$0.252005\pi$
$570$	−19.1453	−	16.4233i	−0.0335883	−	0.0288128i
$571$			334.419i			0.585672i	0.956163	+	0.292836i	$0.0945990\pi$
$571$			334.419i			0.585672i	−0.956163	+	0.292836i	$0.905401\pi$
$572$	−378.922	+	56.3933i	−0.662452	+	0.0985897i
$573$			109.702i			0.191452i
$574$	−462.274	+	34.2107i	−0.805356	+	0.0596005i
$575$	0.896648	+	178.621i	0.00155939	+	0.310645i
$576$	−500.982	+	237.828i	−0.869761	+	0.412896i
$577$			73.3119i			0.127057i	0.997980	+	0.0635285i	$0.0202354\pi$
$577$			73.3119i			0.127057i	−0.997980	+	0.0635285i	$0.979765\pi$
$578$	289.023	−	21.3892i	0.500039	−	0.0370055i
$579$			29.6114i			0.0511423i
$580$	−403.916	+	548.034i	−0.696407	+	0.944885i
$581$	911.029			1.56804
$582$	−1.23702	−	16.7154i	−0.00212547	−	0.0287205i
$583$	249.350			0.427702
$584$	−113.285	−	502.793i	−0.193982	−	0.860946i
$585$	−151.901	−	151.141i	−0.259661	−	0.258360i
$586$	−71.6900	−	968.716i	−0.122338	−	1.65310i
$587$	942.478			1.60559			0.802793	−	0.596258i	$-0.203347\pi$
$587$	942.478			1.60559			0.802793	+	0.596258i	$0.203347\pi$
$588$	−166.782	+	24.8214i	−0.283642	+	0.0422132i
$589$	103.769			0.176178
$590$	−583.939	−	500.916i	−0.989728	−	0.849010i
$591$			137.880i			0.233299i
$592$	−315.639	−	1036.94i	−0.533173	−	1.75160i
$593$			389.667i			0.657111i	0.944485	+	0.328555i	$0.106562\pi$
$593$			389.667i			0.657111i	−0.944485	+	0.328555i	$0.893438\pi$
$594$	29.2192	+	394.827i	0.0491906	+	0.664691i
$595$	−814.976	−	810.895i	−1.36971	−	1.36285i
$596$	−738.567	+	109.918i	−1.23921	+	0.184425i
$597$		−	78.2909i		−	0.131141i
$598$	−5.21613	−	70.4833i	−0.00872262	−	0.117865i
$599$			518.140i			0.865009i	0.901632	+	0.432504i	$0.142370\pi$
$599$			518.140i			0.865009i	−0.901632	+	0.432504i	$0.857630\pi$
$600$	−26.0058	−	112.778i	−0.0433429	−	0.187963i
$601$	482.924			0.803535			0.401767	−	0.915742i	$-0.368396\pi$
$601$	482.924			0.803535			0.401767	+	0.915742i	$0.368396\pi$
$602$	−1051.58	+	77.8222i	−1.74681	+	0.129273i
$603$	−442.440			−0.733731
$604$	−8.82596	−	59.3041i	−0.0146125	−	0.0981856i
$605$	895.688	−	900.196i	1.48048	−	1.48793i
$606$	151.773	−	11.2320i	0.250451	−	0.0185346i
$607$	15.6176			0.0257292			0.0128646	−	0.999917i	$-0.495905\pi$
$607$	15.6176			0.0257292			0.0128646	+	0.999917i	$0.495905\pi$
$608$	−50.3557	−	130.078i	−0.0828218	−	0.213944i
$609$	−217.439			−0.357043
$610$	359.568	−	419.164i	0.589456	−	0.687154i
$611$		−	115.376i		−	0.188831i
$612$	−106.280	−	714.127i	−0.173661	−	1.16687i
$613$		−	295.218i		−	0.481596i	−0.970575	−	0.240798i	$-0.922591\pi$
$613$		−	295.218i		−	0.481596i	0.970575	−	0.240798i	$-0.0774091\pi$
$614$	518.621	−	38.3806i	0.844660	−	0.0625092i
$615$	42.8506	−	43.0662i	0.0696757	−	0.0700264i
$616$	375.862	+	1668.18i	0.610166	+	2.70809i
$617$			2.29497i			0.00371956i	0.999998	+	0.00185978i	$0.000591987\pi$
$617$			2.29497i			0.00371956i	−0.999998	+	0.00185978i	$0.999408\pi$
$618$	−45.6882	+	3.38116i	−0.0739291	+	0.00547114i
$619$		−	1103.05i		−	1.78198i	−0.454023	−	0.890990i	$-0.650012\pi$
$619$		−	1103.05i		−	1.78198i	0.454023	−	0.890990i	$-0.349988\pi$
$620$	383.272	+	282.482i	0.618181	+	0.455617i
$621$	−73.0394			−0.117616
$622$	33.8718	+	457.695i	0.0544563	+	0.735844i
$623$	−1158.69			−1.85986
$624$	13.3353	+	43.8094i	0.0213706	+	0.0702073i
$625$	−624.969	+	6.27465i	−0.999950	+	0.0100394i
$626$	−13.2691	−	179.299i	−0.0211966	−	0.286420i
$627$	−48.8453			−0.0779032
$628$	116.545	+	783.096i	0.185581	+	1.24697i
$629$	1411.16			2.24349
$630$	−622.758	+	725.976i	−0.988505	+	1.15234i
$631$			667.384i			1.05766i	0.848727	+	0.528831i	$0.177369\pi$
$631$			667.384i			1.05766i	−0.848727	+	0.528831i	$0.822631\pi$
$632$	−49.1909	−	218.323i	−0.0778337	−	0.345448i
$633$			55.8501i			0.0882308i
$634$	89.5709	+	1210.33i	0.141279	+	1.90904i
$635$	776.264	−	780.170i	1.22246	−	1.22861i
$636$	−4.38764	−	29.4818i	−0.00689881	−	0.0463550i
$637$		−	360.286i		−	0.565597i
$638$	97.2967	+	1314.73i	0.152503	+	2.06070i
$639$			1122.96i			1.75737i
$640$	168.113	−	617.526i	0.262676	−	0.964884i
$641$	−741.488			−1.15677			−0.578384	−	0.815765i	$-0.696316\pi$
$641$	−741.488			−1.15677			−0.578384	+	0.815765i	$0.696316\pi$
$642$	−109.642	+	8.11405i	−0.170781	+	0.0126387i
$643$	−949.013			−1.47591			−0.737957	−	0.674848i	$-0.764209\pi$
$643$	−949.013			−1.47591			−0.737957	+	0.674848i	$0.764209\pi$
$644$	−312.036	+	46.4389i	−0.484528	+	0.0721101i
$645$	97.4762	−	97.9667i	0.151126	−	0.151886i
$646$	181.100	−	13.4024i	0.280341	−	0.0207467i
$647$	−140.612			−0.217329			−0.108665	−	0.994078i	$-0.534657\pi$
$647$	−140.612			−0.217329			−0.108665	+	0.994078i	$0.534657\pi$
$648$	−562.463	+	126.730i	−0.867999	+	0.195571i
$649$	−1489.80			−2.29553
$650$	246.526	−	19.4889i	0.379270	−	0.0299830i
$651$			152.068i			0.233592i
$652$	−110.706	+	16.4758i	−0.169794	+	0.0252697i
$653$			514.787i			0.788341i	0.919037	+	0.394171i	$0.128968\pi$
$653$			514.787i			0.788341i	−0.919037	+	0.394171i	$0.871032\pi$
$654$	60.8900	−	4.50617i	0.0931039	−	0.00689017i
$655$	−400.626	−	398.620i	−0.611643	−	0.608580i
$656$	321.388	−	97.8282i	0.489921	−	0.149128i
$657$		−	558.247i		−	0.849691i
$658$	−513.592	+	38.0085i	−0.780536	+	0.0577637i
$659$		−	759.986i		−	1.15324i	−0.817012	−	0.576621i	$-0.804371\pi$
$659$		−	759.986i		−	1.15324i	0.817012	−	0.576621i	$-0.195629\pi$
$660$	−180.411	−	132.968i	−0.273350	−	0.201467i
$661$	−399.587			−0.604519			−0.302259	−	0.953226i	$-0.597741\pi$
$661$	−399.587			−0.604519			−0.302259	+	0.953226i	$0.597741\pi$
$662$	33.0643	+	446.783i	0.0499460	+	0.674899i
$663$	−59.6193			−0.0899235
$664$	−644.117	+	145.127i	−0.970055	+	0.218565i
$665$	−170.539	−	169.685i	−0.256450	−	0.255165i
$666$	−86.6479	−	1170.83i	−0.130102	−	1.75801i
$667$	−243.213			−0.364637
$668$	−252.277	+	37.5452i	−0.377659	+	0.0562053i
$669$	78.9963			0.118081
$670$	332.445	−	387.545i	0.496186	−	0.578426i
$671$		−	1069.41i		−	1.59375i
$672$	190.623	−	73.7937i	0.283665	−	0.109812i
$673$			784.566i			1.16577i	0.812553	+	0.582887i	$0.198077\pi$
$673$			784.566i			1.16577i	−0.812553	+	0.582887i	$0.801923\pi$
$674$	−8.11380	−	109.638i	−0.0120383	−	0.162668i
$675$	−1.28288	−	255.561i	−0.00190056	−	0.378609i
$676$	571.854	−	85.1065i	0.845938	−	0.125897i
$677$			1249.77i			1.84604i	0.384757	+	0.923018i	$0.374285\pi$
$677$			1249.77i			1.84604i	−0.384757	+	0.923018i	$0.625715\pi$
$678$	4.35687	+	58.8724i	0.00642606	+	0.0868325i
$679$		−	159.857i		−	0.235431i
$680$	705.382	+	443.494i	1.03733	+	0.652197i
$681$	−103.838			−0.152479
$682$	919.468	−	68.0454i	1.34819	−	0.0997733i
$683$	958.737			1.40371			0.701857	−	0.712317i	$-0.252354\pi$
$683$	958.737			1.40371			0.701857	+	0.712317i	$0.252354\pi$
$684$	−22.2398	−	149.436i	−0.0325144	−	0.218473i
$685$	593.556	+	590.584i	0.866506	+	0.862167i
$686$	−524.992	+	38.8521i	−0.765294	+	0.0566358i
$687$	145.728			0.212122
$688$	731.090	−	222.539i	1.06263	−	0.323458i
$689$	63.6873			0.0924344
$690$	26.9203	−	31.3822i	0.0390150	−	0.0454814i
$691$			550.362i			0.796472i	0.917283	+	0.398236i	$0.130378\pi$
$691$			550.362i			0.796472i	−0.917283	+	0.398236i	$0.869622\pi$
$692$	83.2683	+	559.503i	0.120330	+	0.808531i
$693$			1852.17i			2.67269i
$694$	−154.409	+	11.4271i	−0.222492	+	0.0164656i
$695$	219.544	+	218.445i	0.315891	+	0.314309i
$696$	153.734	−	34.6382i	0.220882	−	0.0497675i
$697$			437.370i			0.627504i
$698$	326.749	−	24.1811i	0.468121	−	0.0346434i
$699$			75.6079i			0.108166i
$700$	−167.968	−	1090.98i	−0.239954	−	1.55854i
$701$	−683.968			−0.975704			−0.487852	−	0.872926i	$-0.662219\pi$
$701$	−683.968			−0.975704			−0.487852	+	0.872926i	$0.662219\pi$
$702$	7.46296	+	100.844i	0.0106310	+	0.143652i
$703$	295.293			0.420048
$704$	−531.485	−	1119.57i	−0.754951	−	1.59029i
$705$	47.6076	−	47.8471i	0.0675284	−	0.0678683i
$706$	−22.4645	−	303.554i	−0.0318195	−	0.429963i
$707$	1451.48			2.05302
$708$	26.2149	+	176.145i	0.0370267	+	0.248793i
$709$	737.353			1.03999			0.519995	−	0.854169i	$-0.325934\pi$
$709$	737.353			1.03999			0.519995	+	0.854169i	$0.325934\pi$
$710$	−983.632	−	843.782i	−1.38540	−	1.18842i
$711$		−	242.403i		−	0.340932i
$712$	819.220	−	184.580i	1.15059	−	0.259242i
$713$			170.093i			0.238560i
$714$	19.6405	+	265.393i	0.0275077	+	0.371699i
$715$	337.761	−	339.461i	0.472393	−	0.474770i
$716$	−83.0711	−	558.178i	−0.116021	−	0.779578i
$717$		−	259.645i		−	0.362127i
$718$	−2.64339	−	35.7190i	−0.00368160	−	0.0497479i
$719$		−	531.159i		−	0.738748i	−0.929281	−	0.369374i	$-0.879572\pi$
$719$		−	531.159i		−	0.738748i	0.929281	−	0.369374i	$-0.120428\pi$
$720$	324.655	−	612.486i	0.450909	−	0.850675i
$721$	−436.939			−0.606019
$722$	37.8964	−	2.80453i	0.0524880	−	0.00388439i
$723$	229.248			0.317078
$724$	744.873	−	110.856i	1.02883	−	0.153116i
$725$	−4.27184	−	850.989i	−0.00589219	−	1.17378i
$726$	−293.145	+	21.6942i	−0.403781	+	0.0298819i
$727$	−216.462			−0.297747			−0.148874	−	0.988856i	$-0.547565\pi$
$727$	−216.462			−0.297747			−0.148874	+	0.988856i	$0.547565\pi$
$728$	96.0000	+	426.075i	0.131868	+	0.585268i
$729$	−571.258			−0.783619
$730$	488.984	+	419.461i	0.669841	+	0.574605i
$731$			994.926i			1.36105i
$732$	−126.441	+	18.8176i	−0.172734	+	0.0257071i
$733$		−	102.292i		−	0.139553i	−0.997563	−	0.0697765i	$-0.977771\pi$
$733$		−	102.292i		−	0.139553i	0.997563	−	0.0697765i	$-0.0222286\pi$
$734$	−634.270	+	46.9393i	−0.864128	+	0.0639500i
$735$	148.665	−	149.413i	0.202265	−	0.203283i
$736$	213.218	−	82.5408i	0.289699	−	0.112148i
$737$		−	988.739i		−	1.34157i
$738$	362.886	−	26.8554i	0.491715	−	0.0363895i
$739$		−	50.7719i		−	0.0687035i	−0.999410	−	0.0343517i	$-0.989063\pi$
$739$		−	50.7719i		−	0.0687035i	0.999410	−	0.0343517i	$-0.0109367\pi$
$740$	1090.67	+	803.856i	1.47388	+	1.08629i
$741$	−12.4757			−0.0168363
$742$	−20.9806	−	283.502i	−0.0282758	−	0.382078i
$743$	−992.730			−1.33611			−0.668055	−	0.744112i	$-0.732873\pi$
$743$	−992.730			−1.33611			−0.668055	+	0.744112i	$0.732873\pi$
$744$	−24.2245	−	107.515i	−0.0325599	−	0.144510i
$745$	658.338	−	661.651i	0.883676	−	0.888123i
$746$	20.5315	+	277.433i	0.0275221	+	0.371895i
$747$	−715.158			−0.957374
$748$	1595.89	−	237.509i	2.13355	−	0.317526i
$749$	−1048.56			−1.39994
$750$	110.278	+	93.6417i	0.147037	+	0.124856i
$751$			778.282i			1.03633i	0.855282	+	0.518164i	$0.173384\pi$
$751$			778.282i			1.03633i	−0.855282	+	0.518164i	$0.826616\pi$
$752$	357.066	−	108.688i	0.474822	−	0.144532i
$753$			212.465i			0.282158i
$754$	24.8508	+	335.798i	0.0329587	+	0.445356i
$755$	53.1281	+	52.8620i	0.0703683	+	0.0700159i
$756$	446.445	−	66.4423i	0.590535	−	0.0878867i
$757$			1120.66i			1.48040i	0.672386	+	0.740201i	$0.265270\pi$
$757$			1120.66i			1.48040i	−0.672386	+	0.740201i	$0.734730\pi$
$758$	−50.6455	−	684.351i	−0.0668146	−	0.902837i
$759$		−	80.0650i		−	0.105488i
$760$	147.606	+	92.8040i	0.194218	+	0.122111i
$761$	1163.34			1.52870			0.764348	−	0.644804i	$-0.223061\pi$
$761$	1163.34			1.52870			0.764348	+	0.644804i	$0.223061\pi$
$762$	−254.059	+	18.8017i	−0.333411	+	0.0246741i
$763$	582.321			0.763200
$764$	−111.622	−	750.022i	−0.146103	−	0.981704i
$765$	639.757	+	636.554i	0.836284	+	0.832096i
$766$	−651.141	+	48.1878i	−0.850054	+	0.0629084i
$767$	−380.513			−0.496106
$768$	−123.019	+	82.5401i	−0.160181	+	0.107474i
$769$	794.584			1.03327			0.516635	−	0.856206i	$-0.327184\pi$
$769$	794.584			1.03327			0.516635	+	0.856206i	$0.327184\pi$
$770$	−1622.37	−	1391.70i	−2.10697	−	1.80741i
$771$		−	42.4987i		−	0.0551215i
$772$	−30.1297	−	202.450i	−0.0390281	−	0.262241i
$773$		−	524.845i		−	0.678972i	−0.940611	−	0.339486i	$-0.889747\pi$
$773$		−	524.845i		−	0.678972i	0.940611	−	0.339486i	$-0.110253\pi$
$774$	825.489	−	61.0905i	1.06652	−	0.0789283i
$775$	−595.148	+	2.98755i	−0.767932	+	0.00385490i
$776$	25.4654	+	113.023i	0.0328162	+	0.145648i
$777$			432.738i			0.556934i
$778$	−561.296	+	41.5388i	−0.721460	+	0.0533918i
$779$			91.5225i			0.117487i
$780$	−46.0793	−	33.9617i	−0.0590760	−	0.0435407i
$781$	−2509.53			−3.21323
$782$	21.9685	+	296.851i	0.0280928	+	0.379605i
$783$	347.976			0.444414
$784$	1115.01	−	339.402i	1.42221	−	0.432911i
$785$	−701.543	−	698.031i	−0.893686	−	0.889211i
$786$	9.65487	+	130.462i	0.0122836	+	0.165982i
$787$	44.4290			0.0564536			0.0282268	−	0.999602i	$-0.491014\pi$
$787$	44.4290			0.0564536			0.0282268	+	0.999602i	$0.491014\pi$
$788$	−140.293	−	942.669i	−0.178037	−	1.19628i
$789$	−27.4432			−0.0347823
$790$	212.327	+	182.139i	0.268769	+	0.230556i
$791$			563.027i			0.711791i
$792$	−295.052	−	1309.53i	−0.372541	−	1.65344i
$793$		−	273.141i		−	0.344440i
$794$	33.5119	+	452.832i	0.0422064	+	0.570317i
$795$	26.4115	+	26.2793i	0.0332220	+	0.0330557i
$796$	79.6614	+	535.267i	0.100077	+	0.672446i
$797$		−	916.910i		−	1.15045i	−0.817995	−	0.575226i	$-0.804914\pi$
$797$		−	916.910i		−	1.15045i	0.817995	−	0.575226i	$-0.195086\pi$
$798$	4.10990	+	55.5353i	0.00515025	+	0.0695931i
$799$			485.924i			0.608165i
$800$	292.551	+	744.590i	0.365689	+	0.930737i
$801$	909.575			1.13555
$802$	−885.171	+	65.5072i	−1.10370	+	0.0816799i
$803$	1247.54			1.55360
$804$	−116.903	+	17.3982i	−0.145402	+	0.0216395i
$805$	278.140	−	279.540i	0.345516	−	0.347255i
$806$	234.844	−	17.3797i	0.291369	−	0.0215628i
$807$	147.796			0.183143
$808$	−1026.23	+	231.222i	−1.27009	+	0.286166i
$809$	477.015			0.589635			0.294817	−	0.955554i	$-0.404741\pi$
$809$	477.015			0.589635			0.294817	+	0.955554i	$0.404741\pi$
$810$	469.242	−	547.016i	0.579311	−	0.675328i
$811$		−	783.018i		−	0.965496i	−0.875759	−	0.482748i	$-0.839639\pi$
$811$		−	783.018i		−	0.965496i	0.875759	−	0.482748i	$-0.160361\pi$
$812$	1486.61	−	221.245i	1.83080	−	0.272470i
$813$		−	95.9032i		−	0.117962i
$814$	2616.52	−	193.636i	3.21439	−	0.237882i
$815$	98.6800	−	99.1766i	0.121080	−	0.121689i
$816$	−56.1636	−	184.510i	−0.0688279	−	0.226115i
$817$			208.195i			0.254828i
$818$	139.524	−	10.3255i	0.170567	−	0.0126228i
$819$			473.069i			0.577617i
$820$	−249.145	+	338.040i	−0.303836	+	0.412244i
$821$	−1312.80			−1.59903			−0.799515	−	0.600647i	$-0.794910\pi$
$821$	−1312.80			−1.59903			−0.799515	+	0.600647i	$0.794910\pi$
$822$	−14.3044	−	193.289i	−0.0174019	−	0.235145i
$823$	535.460			0.650620			0.325310	−	0.945607i	$-0.394531\pi$
$823$	535.460			0.650620			0.325310	+	0.945607i	$0.394531\pi$
$824$	308.925	−	69.6047i	0.374910	−	0.0844717i
$825$	280.143	−	1.40628i	0.339568	−	0.00170458i
$826$	125.353	+	1693.84i	0.151759	+	2.05066i
$827$	876.215			1.05951			0.529755	−	0.848151i	$-0.322284\pi$
$827$	876.215			1.05951			0.529755	+	0.848151i	$0.322284\pi$
$828$	244.948	−	36.4546i	0.295831	−	0.0440273i
$829$	463.464			0.559064			0.279532	−	0.960136i	$-0.409821\pi$
$829$	463.464			0.559064			0.279532	+	0.960136i	$0.409821\pi$
$830$	537.363	−	626.427i	0.647425	−	0.754731i
$831$		−	104.415i		−	0.125649i
$832$	−135.748	−	285.952i	−0.163159	−	0.343692i
$833$			1517.40i			1.82161i
$834$	−5.29090	−	71.4936i	−0.00634400	−	0.0857237i
$835$	224.872	−	226.004i	0.269308	−	0.270664i
$836$	333.950	−	49.7003i	0.399462	−	0.0594502i
$837$		−	243.361i		−	0.290753i
$838$	−51.0261	−	689.494i	−0.0608903	−	0.822785i
$839$			257.776i			0.307242i	0.988130	+	0.153621i	$0.0490935\pi$
$839$			257.776i			0.307242i	−0.988130	+	0.153621i	$0.950906\pi$
$840$	−136.000	+	216.309i	−0.161904	+	0.257510i
$841$	317.722			0.377791
$842$	415.682	−	30.7626i	0.493684	−	0.0365352i
$843$	−98.4644			−0.116802
$844$	−56.8278	−	381.842i	−0.0673315	−	0.452419i
$845$	−509.735	+	512.300i	−0.603237	+	0.606273i
$846$	403.171	−	29.8367i	0.476561	−	0.0352680i
$847$	−2803.49			−3.30991
$848$	59.9958	+	197.100i	0.0707498	+	0.232429i
$849$	−17.9134			−0.0210994
$850$	−1038.28	+	82.0808i	−1.22151	+	0.0965656i
$851$			484.032i			0.568780i
$852$	44.1584	+	296.713i	0.0518291	+	0.348254i
$853$		−	1516.41i		−	1.77774i	−0.458157	−	0.888871i	$-0.651490\pi$
$853$		−	1516.41i		−	1.77774i	0.458157	−	0.888871i	$-0.348510\pi$
$854$	−1215.88	+	89.9813i	−1.42374	+	0.105364i
$855$	133.873	+	133.203i	0.156577	+	0.155793i
$856$	741.353	−	167.036i	0.866066	−	0.195135i
$857$			501.628i			0.585330i	0.956215	+	0.292665i	$0.0945420\pi$
$857$			501.628i			0.585330i	−0.956215	+	0.292665i	$0.905458\pi$
$858$	−110.544	+	8.18082i	−0.128839	+	0.00953476i
$859$		−	1137.54i		−	1.32426i	−0.749390	−	0.662129i	$-0.769653\pi$
$859$		−	1137.54i		−	1.32426i	0.749390	−	0.662129i	$-0.230347\pi$
$860$	−566.753	+	768.971i	−0.659015	+	0.894153i
$861$	−134.122			−0.155774
$862$	−77.7317	−	1050.35i	−0.0901760	−	1.21851i
$863$	−794.989			−0.921192			−0.460596	−	0.887610i	$-0.652364\pi$
$863$	−794.989			−0.921192			−0.460596	+	0.887610i	$0.652364\pi$
$864$	−305.062	+	118.095i	−0.353080	+	0.136684i
$865$	−501.236	−	498.726i	−0.579463	−	0.576562i
$866$	121.719	+	1644.74i	0.140553	+	1.89924i
$867$	83.8555			0.0967192
$868$	−154.730	−	1039.67i	−0.178260	−	1.19778i
$869$	541.708			0.623369
$870$	−128.255	+	149.512i	−0.147419	+	0.171853i
$871$		−	252.537i		−	0.289939i
$872$	−411.714	+	92.7641i	−0.472149	+	0.106381i
$873$			125.488i			0.143744i
$874$	4.59706	+	62.1181i	0.00525979	+	0.0710733i
$875$	982.981	+	968.288i	1.12341	+	1.10662i
$876$	−21.9521	−	147.502i	−0.0250594	−	0.168381i
$877$			1101.89i			1.25643i	0.778041	+	0.628213i	$0.216213\pi$
$877$			1101.89i			1.25643i	−0.778041	+	0.628213i	$0.783787\pi$
$878$	−25.9419	−	350.542i	−0.0295466	−	0.399250i
$879$		−	281.058i		−	0.319748i
$880$	1368.75	+	725.520i	1.55540	+	0.824455i
$881$	833.420			0.945994			0.472997	−	0.881064i	$-0.343172\pi$
$881$	833.420			0.945994			0.472997	+	0.881064i	$0.343172\pi$
$882$	1258.99	−	93.1714i	1.42742	−	0.105637i
$883$	−1121.97			−1.27063			−0.635315	−	0.772253i	$-0.719130\pi$
$883$	−1121.97			−1.27063			−0.635315	+	0.772253i	$0.719130\pi$
$884$	407.611	−	60.6629i	0.461098	−	0.0686232i
$885$	−157.801	−	157.011i	−0.178307	−	0.177414i
$886$	1254.48	−	92.8383i	1.41590	−	0.104784i
$887$	−695.421			−0.784015			−0.392007	−	0.919962i	$-0.628219\pi$
$887$	−695.421			−0.784015			−0.392007	+	0.919962i	$0.628219\pi$
$888$	−68.9354	−	305.955i	−0.0776300	−	0.344544i
$889$	−2429.69			−2.73306
$890$	−683.445	+	796.721i	−0.767916	+	0.895192i
$891$		−	1395.60i		−	1.56632i
$892$	−540.090	+	80.3791i	−0.605482	+	0.0901112i
$893$			101.683i			0.113866i
$894$	−215.464	+	15.9454i	−0.241011	+	0.0178361i
$895$	500.049	+	497.545i	0.558714	+	0.555916i
$896$	−1228.19	+	698.480i	−1.37074	+	0.779554i
$897$		−	20.4496i		−	0.0227978i
$898$	−1545.43	+	114.369i	−1.72096	+	0.127360i
$899$		−	810.363i		−	0.901405i
$900$	131.855	+	856.421i	0.146505	+	0.951579i
$901$	−268.229			−0.297702
$902$	60.0150	+	810.956i	0.0665355	+	0.899065i
$903$	−305.099			−0.337873
$904$	−89.6905	−	398.072i	−0.0992151	−	0.440345i
$905$	−663.959	+	667.301i	−0.733657	+	0.737349i
$906$	−1.28036	−	17.3009i	−0.00141320	−	0.0190959i
$907$	−1447.27			−1.59567			−0.797834	−	0.602878i	$-0.794021\pi$
$907$	−1447.27			−1.59567			−0.797834	+	0.602878i	$0.794021\pi$
$908$	709.932	−	105.656i	0.781864	−	0.116361i
$909$	−1139.41			−1.25348
$910$	−414.374	−	355.459i	−0.455356	−	0.390614i
$911$		−	907.227i		−	0.995859i	−0.867218	−	0.497929i	$-0.834094\pi$
$911$		−	907.227i		−	0.995859i	0.867218	−	0.497929i	$-0.165906\pi$
$912$	−11.7526	−	38.6099i	−0.0128866	−	0.0423354i
$913$		−	1598.20i		−	1.75049i
$914$	−115.723	−	1563.72i	−0.126612	−	1.71085i
$915$	112.706	−	113.273i	0.123176	−	0.123796i
$916$	−996.326	+	148.279i	−1.08769	+	0.161876i
$917$			1247.67i			1.36060i
$918$	−31.4315	−	424.720i	−0.0342391	−	0.462657i
$919$			1252.77i			1.36319i	0.731732	+	0.681593i	$0.238712\pi$
$919$			1252.77i			1.36319i	−0.731732	+	0.681593i	$0.761288\pi$
$920$	−152.120	+	241.949i	−0.165348	+	0.262988i
$921$	150.470			0.163377
$922$	163.099	−	12.0702i	0.176897	−	0.0130913i
$923$	−640.966			−0.694438
$924$	72.8334	+	489.388i	0.0788240	+	0.529641i
$925$	−1693.60	+	8.50162i	−1.83092	+	0.00919095i
$926$	366.823	−	27.1468i	0.396137	−	0.0293162i
$927$	342.998			0.370008
$928$	−1015.82	+	393.243i	−1.09463	+	0.423753i
$929$	12.2979			0.0132378			0.00661889	−	0.999978i	$-0.497893\pi$
$929$	12.2979			0.0132378			0.00661889	+	0.999978i	$0.497893\pi$
$930$	104.563	+	89.6961i	0.112433	+	0.0964474i
$931$			317.526i			0.341059i
$932$	−76.9315	−	516.924i	−0.0825445	−	0.554640i
$933$			132.793i			0.142329i
$934$	1181.26	−	87.4193i	1.26473	−	0.0935967i
$935$	−1422.53	+	1429.69i	−1.52143	+	1.52908i
$936$	−75.3601	−	334.470i	−0.0805129	−	0.357339i
$937$			1665.88i			1.77789i	0.458019	+	0.888943i	$0.348559\pi$
$937$			1665.88i			1.77789i	−0.458019	+	0.888943i	$0.651441\pi$
$938$	−1124.16	+	83.1936i	−1.19846	+	0.0886926i
$939$		−	52.0209i		−	0.0554003i
$940$	−276.803	+	375.567i	−0.294472	+	0.399540i
$941$	1308.95			1.39102			0.695509	−	0.718517i	$-0.255179\pi$
$941$	1308.95			1.39102			0.695509	+	0.718517i	$0.255179\pi$
$942$	16.9068	+	228.454i	0.0179478	+	0.242521i
$943$	−150.020			−0.159088
$944$	−358.458	−	1177.61i	−0.379722	−	1.24747i
$945$	−397.948	+	399.951i	−0.421110	+	0.423229i
$946$	136.522	+	1844.76i	0.144315	+	1.95006i
$947$	713.615			0.753554			0.376777	−	0.926304i	$-0.377032\pi$
$947$	713.615			0.753554			0.376777	+	0.926304i	$0.377032\pi$
$948$	−9.53205	−	64.0485i	−0.0100549	−	0.0675617i
$949$	318.637			0.335761
$950$	−217.267	+	17.1759i	−0.228702	+	0.0180799i
$951$			351.159i			0.369253i
$952$	−404.319	−	1794.48i	−0.424705	−	1.88496i
$953$			656.924i			0.689322i	0.938727	+	0.344661i	$0.112006\pi$
$953$			656.924i			0.689322i	−0.938727	+	0.344661i	$0.887994\pi$
$954$	16.4698	+	222.549i	0.0172640	+	0.233280i
$955$	671.914	+	668.549i	0.703574	+	0.700052i
$956$	264.191	+	1775.17i	0.276350	+	1.85687i
$957$			381.448i			0.398587i
$958$	−70.0294	−	946.277i	−0.0730996	−	0.987763i
$959$		−	1848.52i		−	1.92755i
$960$	61.6966	−	174.600i	0.0642673	−	0.181875i
$961$	394.265			0.410265
$962$	668.292	−	49.4570i	0.694690	−	0.0514106i
$963$	823.119			0.854744
$964$	−1567.34	+	233.261i	−1.62587	+	0.241972i
$965$	181.367	+	180.458i	0.187945	+	0.187004i
$966$	−91.0309	+	6.73676i	−0.0942349	+	0.00697387i
$967$	−38.8421			−0.0401676			−0.0200838	−	0.999798i	$-0.506393\pi$
$967$	−38.8421			−0.0401676			−0.0200838	+	0.999798i	$0.506393\pi$
$968$	1982.13	−	446.598i	2.04765	−	0.461361i
$969$	52.5434			0.0542244
$970$	−109.919	−	94.2906i	−0.113318	−	0.0972068i
$971$		−	297.009i		−	0.305879i	−0.988236	−	0.152940i	$-0.951126\pi$
$971$		−	297.009i		−	0.305879i	0.988236	−	0.152940i	$-0.0488740\pi$
$972$	−529.011	+	78.7303i	−0.544250	+	0.0809982i
$973$		−	683.729i		−	0.702702i
$974$	868.269	−	64.2564i	0.891446	−	0.0659717i
$975$	71.5522	−	0.359181i	0.0733869	−	0.000368391i
$976$	845.317	−	257.309i	0.866104	−	0.263636i
$977$			107.297i			0.109823i	0.998491	+	0.0549113i	$0.0174876\pi$
$977$			107.297i			0.109823i	−0.998491	+	0.0549113i	$0.982512\pi$
$978$	−32.2964	+	2.39010i	−0.0330229	+	0.00244387i
$979$			2032.67i			2.07627i
$980$	−864.377	+	1172.79i	−0.882018	+	1.19672i
$981$	−457.123			−0.465976
$982$	−69.6706	−	941.428i	−0.0709476	−	0.958684i
$983$	674.148			0.685807			0.342904	−	0.939371i	$-0.388590\pi$
$983$	674.148			0.685807			0.342904	+	0.939371i	$0.388590\pi$
$984$	94.8269	−	21.3657i	0.0963688	−	0.0217131i
$985$	844.498	+	840.269i	0.857358	+	0.853065i
$986$	−104.663	−	1414.27i	−0.106149	−	1.43435i
$987$	−149.011			−0.150974
$988$	85.2952	−	12.6941i	0.0863312	−	0.0128483i
$989$	−341.263			−0.345059
$990$	1273.56	+	1092.49i	1.28643	+	1.10352i
$991$			1576.28i			1.59059i	0.606220	+	0.795297i	$0.292685\pi$
$991$			1576.28i			1.59059i	−0.606220	+	0.795297i	$0.707315\pi$
$992$	275.018	+	710.424i	0.277236	+	0.716153i
$993$			129.627i			0.130541i
$994$	211.155	+	2853.24i	0.212429	+	2.87046i
$995$	−479.524	−	477.123i	−0.481933	−	0.479520i
$996$	−188.962	+	28.1223i	−0.189721	+	0.0282353i
$997$			834.220i			0.836730i	0.908279	+	0.418365i	$0.137397\pi$
$997$			834.220i			0.836730i	−0.908279	+	0.418365i	$0.862603\pi$
$998$	−8.04293	−	108.681i	−0.00805905	−	0.108898i
$999$		−	692.528i		−	0.693221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.h.a.39.4	yes	108
4.3	odd	2	inner	380.3.h.a.39.106	yes	108
5.4	even	2	inner	380.3.h.a.39.105	yes	108
20.19	odd	2	inner	380.3.h.a.39.3	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.h.a.39.3	✓	108	20.19	odd	2	inner
380.3.h.a.39.4	yes	108	1.1	even	1	trivial
380.3.h.a.39.105	yes	108	5.4	even	2	inner
380.3.h.a.39.106	yes	108	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99455 + 0.147607i) q^{2} -0.578687 q^{3} +(3.95642 - 0.588817i) q^{4} +(-3.52665 + 3.54440i) q^{5} +(1.15422 - 0.0854181i) q^{6} +11.0384 q^{7} +(-7.80436 + 1.75842i) q^{8} -8.66512 q^{9} +O(q^{10})\)	\(q+(-1.99455 + 0.147607i) q^{2} -0.578687 q^{3} +(3.95642 - 0.588817i) q^{4} +(-3.52665 + 3.54440i) q^{5} +(1.15422 - 0.0854181i) q^{6} +11.0384 q^{7} +(-7.80436 + 1.75842i) q^{8} -8.66512 q^{9} +(6.51089 - 7.59002i) q^{10} -19.3643i q^{11} +(-2.28953 + 0.340740i) q^{12} -4.94590i q^{13} +(-22.0165 + 1.62934i) q^{14} +(2.04082 - 2.05110i) q^{15} +(15.3066 - 4.65922i) q^{16} +20.8304i q^{17} +(17.2830 - 1.27903i) q^{18} +4.35890i q^{19} +(-11.8659 + 16.0997i) q^{20} -6.38775 q^{21} +(2.85831 + 38.6230i) q^{22} -7.14491 q^{23} +(4.51628 - 1.01757i) q^{24} +(-0.125495 - 24.9997i) q^{25} +(0.730047 + 9.86481i) q^{26} +10.2226 q^{27} +(43.6724 - 6.49957i) q^{28} +34.0400 q^{29} +(-3.76776 + 4.39224i) q^{30} -23.8062i q^{31} +(-29.8420 + 11.5524i) q^{32} +11.2059i q^{33} +(-3.07471 - 41.5472i) q^{34} +(-38.9284 + 39.1243i) q^{35} +(-34.2829 + 5.10217i) q^{36} -67.7450i q^{37} +(-0.643403 - 8.69402i) q^{38} +2.86212i q^{39} +(21.2907 - 33.8631i) q^{40} +20.9967 q^{41} +(12.7407 - 0.942875i) q^{42} +47.7631 q^{43} +(-11.4020 - 76.6135i) q^{44} +(30.5588 - 30.7126i) q^{45} +(14.2509 - 1.05464i) q^{46} +23.3276 q^{47} +(-8.85772 + 2.69623i) q^{48} +72.8454 q^{49} +(3.94043 + 49.8445i) q^{50} -12.0543i q^{51} +(-2.91223 - 19.5681i) q^{52} +12.8768i q^{53} +(-20.3894 + 1.50892i) q^{54} +(68.6349 + 68.2912i) q^{55} +(-86.1473 + 19.4100i) q^{56} -2.52244i q^{57} +(-67.8944 + 5.02453i) q^{58} -76.9352i q^{59} +(6.86665 - 9.31667i) q^{60} +55.2257 q^{61} +(3.51396 + 47.4826i) q^{62} -95.6487 q^{63} +(57.8159 - 27.4466i) q^{64} +(17.5302 + 17.4424i) q^{65} +(-1.65406 - 22.3506i) q^{66} +51.0598 q^{67} +(12.2653 + 82.4140i) q^{68} +4.13467 q^{69} +(71.8695 - 83.7813i) q^{70} -129.596i q^{71} +(67.6257 - 15.2369i) q^{72} +64.4246i q^{73} +(9.99961 + 135.120i) q^{74} +(0.0726220 + 14.4670i) q^{75} +(2.56659 + 17.2457i) q^{76} -213.750i q^{77} +(-0.422469 - 5.70864i) q^{78} +27.9745i q^{79} +(-37.4669 + 70.6841i) q^{80} +72.0704 q^{81} +(-41.8789 + 3.09925i) q^{82} +82.5330 q^{83} +(-25.2727 + 3.76122i) q^{84} +(-73.8313 - 73.4616i) q^{85} +(-95.2657 + 7.05016i) q^{86} -19.6985 q^{87} +(34.0506 + 151.126i) q^{88} -104.970 q^{89} +(-56.4176 + 65.7684i) q^{90} -54.5946i q^{91} +(-28.2683 + 4.20705i) q^{92} +13.7763i q^{93} +(-46.5280 + 3.44331i) q^{94} +(-15.4497 - 15.3723i) q^{95} +(17.2691 - 6.68521i) q^{96} -14.4820i q^{97} +(-145.293 + 10.7525i) q^{98} +167.794i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) \) 108 * q + 4 * q^5 + 324 * q^9	\( 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) \) 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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