LMFDB - Embedded newform 882.2.bl.a.395.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(17,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("882.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bl (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.5
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(0.432474 + 0.294856i) q^{5} +(-1.64529 - 2.07196i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})$	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(0.432474 + 0.294856i) q^{5} +(-1.64529 - 2.07196i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.294856 - 0.432474i) q^{10} +(0.320403 + 2.12573i) q^{11} +(2.39364 - 1.90887i) q^{13} +(0.774586 + 2.52983i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-4.61725 - 1.42423i) q^{17} +(4.76929 - 2.75355i) q^{19} +(0.116473 + 0.510302i) q^{20} +(0.478363 - 2.09584i) q^{22} +(0.0351218 + 0.113862i) q^{23} +(-1.72661 - 4.39933i) q^{25} +(-2.92557 + 0.902418i) q^{26} +(0.203207 - 2.63794i) q^{28} +(-4.76446 + 1.08746i) q^{29} +(-1.23724 - 0.714321i) q^{31} +(0.294755 - 0.955573i) q^{32} +(3.77774 + 3.01265i) q^{34} +(-0.100616 - 1.38119i) q^{35} +(5.24515 - 4.86679i) q^{37} +(-5.44560 + 0.820792i) q^{38} +(0.0780125 - 0.517579i) q^{40} +(0.904889 - 0.435771i) q^{41} +(-3.78354 - 1.82206i) q^{43} +(-1.21099 + 1.77620i) q^{44} +(0.00890452 - 0.118823i) q^{46} +(4.33440 - 11.0439i) q^{47} +(-1.58603 + 6.81795i) q^{49} +4.72603i q^{50} +(3.05302 + 0.228792i) q^{52} +(-0.364637 + 0.392985i) q^{53} +(-0.488219 + 1.01380i) q^{55} +(-1.15291 + 2.38135i) q^{56} +(4.83240 + 0.728367i) q^{58} +(9.74959 - 6.64716i) q^{59} +(-0.182617 - 0.196814i) q^{61} +(0.890744 + 1.11696i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(1.59803 - 0.119756i) q^{65} +(6.72968 - 11.6562i) q^{67} +(-2.41596 - 4.18456i) q^{68} +(-0.410945 + 1.32248i) q^{70} +(-2.17664 - 0.496803i) q^{71} +(-7.27960 + 2.85703i) q^{73} +(-6.66061 + 2.61410i) q^{74} +(5.36903 + 1.22545i) q^{76} +(3.87728 - 4.16131i) q^{77} +(-4.67750 - 8.10167i) q^{79} +(-0.261713 + 0.453299i) q^{80} +(-1.00154 + 0.0750552i) q^{82} +(-0.0574893 + 0.0720893i) q^{83} +(-1.57690 - 1.97737i) q^{85} +(2.85632 + 3.07838i) q^{86} +(1.77620 - 1.21099i) q^{88} +(-10.7099 - 1.61426i) q^{89} +(-7.89333 - 1.81889i) q^{91} +(-0.0516997 + 0.107356i) q^{92} +(-8.06956 + 8.69692i) q^{94} +(2.87450 + 0.215414i) q^{95} +11.6182i q^{97} +(3.96728 - 5.76721i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) $ 240 * q - 20 * q^4 - 4 * q^7	$ 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64} - 32 q^{67} - 16 q^{70} - 24 q^{73} - 28 q^{79} - 48 q^{82} - 112 q^{85} + 4 q^{88} + 80 q^{91} + 80 q^{94}+O(q^{100}) $ 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$3$		0			0
$3$		0			0
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	0.432474	+	0.294856i	0.193408	+	0.131864i	0.656153	−	0.754628i	$-0.272183\pi$
$5$	0.432474	+	0.294856i	0.193408	+	0.131864i	−0.462744	+	0.886492i	$0.653135\pi$
$6$		0			0
$7$	−1.64529	−	2.07196i	−0.621862	−	0.783127i
$7$	−1.64529	−	2.07196i	−0.621862	−	0.783127i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$		0			0
$10$	−0.294856	−	0.432474i	−0.0932416	−	0.136760i
$11$	0.320403	+	2.12573i	0.0966050	+	0.640932i	0.983764	+	0.179468i	$0.0574377\pi$
$11$	0.320403	+	2.12573i	0.0966050	+	0.640932i	−0.887159	+	0.461464i	$0.847324\pi$
$12$		0			0
$13$	2.39364	−	1.90887i	0.663877	−	0.529424i	−0.232568	−	0.972580i	$-0.574713\pi$
$13$	2.39364	−	1.90887i	0.663877	−	0.529424i	0.896444	+	0.443156i	$0.146141\pi$
$14$	0.774586	+	2.52983i	0.207017	+	0.676124i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−4.61725	−	1.42423i	−1.11985	−	0.345427i	−0.321071	−	0.947055i	$-0.604043\pi$
$17$	−4.61725	−	1.42423i	−1.11985	−	0.345427i	−0.798776	+	0.601628i	$0.794519\pi$
$18$		0			0
$19$	4.76929	−	2.75355i	1.09415	−	0.631709i	0.159473	−	0.987202i	$-0.449021\pi$
$19$	4.76929	−	2.75355i	1.09415	−	0.631709i	0.934679	+	0.355494i	$0.115687\pi$
$20$	0.116473	+	0.510302i	0.0260442	+	0.114107i
$21$		0			0
$22$	0.478363	−	2.09584i	0.101987	−	0.446836i
$23$	0.0351218	+	0.113862i	0.00732340	+	0.0237419i	0.959161	−	0.282861i	$-0.0912837\pi$
$23$	0.0351218	+	0.113862i	0.00732340	+	0.0237419i	−0.951837	+	0.306603i	$0.900807\pi$
$24$		0			0
$25$	−1.72661	−	4.39933i	−0.345322	−	0.879867i
$26$	−2.92557	+	0.902418i	−0.573751	+	0.176979i
$27$		0			0
$28$	0.203207	−	2.63794i	0.0384025	−	0.498523i
$29$	−4.76446	+	1.08746i	−0.884738	+	0.201936i	−0.640664	−	0.767821i	$-0.721341\pi$
$29$	−4.76446	+	1.08746i	−0.884738	+	0.201936i	−0.244073	+	0.969757i	$0.578484\pi$
$30$		0			0
$31$	−1.23724	−	0.714321i	−0.222215	−	0.128296i	0.384761	−	0.923016i	$-0.374284\pi$
$31$	−1.23724	−	0.714321i	−0.222215	−	0.128296i	−0.606975	+	0.794721i	$0.707617\pi$
$32$	0.294755	−	0.955573i	0.0521058	−	0.168923i
$33$		0			0
$34$	3.77774	+	3.01265i	0.647878	+	0.516665i
$35$	−0.100616	−	1.38119i	−0.0170073	−	0.233464i
$36$		0			0
$37$	5.24515	−	4.86679i	0.862298	−	0.800095i	−0.118939	−	0.992902i	$-0.537949\pi$
$37$	5.24515	−	4.86679i	0.862298	−	0.800095i	0.981237	+	0.192806i	$0.0617588\pi$
$38$	−5.44560	+	0.820792i	−0.883393	+	0.133150i
$39$		0			0
$40$	0.0780125	−	0.517579i	0.0123349	−	0.0818364i
$41$	0.904889	−	0.435771i	0.141320	−	0.0680561i	−0.361887	−	0.932222i	$-0.617868\pi$
$41$	0.904889	−	0.435771i	0.141320	−	0.0680561i	0.503207	+	0.864166i	$0.332153\pi$
$42$		0			0
$43$	−3.78354	−	1.82206i	−0.576984	−	0.277861i	0.122547	−	0.992463i	$-0.460894\pi$
$43$	−3.78354	−	1.82206i	−0.576984	−	0.277861i	−0.699531	+	0.714602i	$0.746608\pi$
$44$	−1.21099	+	1.77620i	−0.182564	+	0.267772i
$45$		0			0
$46$	0.00890452	−	0.118823i	0.00131290	−	0.0175194i
$47$	4.33440	−	11.0439i	0.632237	−	1.61091i	−0.150534	−	0.988605i	$-0.548099\pi$
$47$	4.33440	−	11.0439i	0.632237	−	1.61091i	0.782771	−	0.622310i	$-0.213806\pi$
$48$		0			0
$49$	−1.58603	+	6.81795i	−0.226576	+	0.973993i
$50$			4.72603i			0.668361i
$51$		0			0
$52$	3.05302	+	0.228792i	0.423378	+	0.0317278i
$53$	−0.364637	+	0.392985i	−0.0500868	+	0.0539807i	−0.757598	−	0.652721i	$-0.773627\pi$
$53$	−0.364637	+	0.392985i	−0.0500868	+	0.0539807i	0.707511	+	0.706702i	$0.249818\pi$
$54$		0			0
$55$	−0.488219	+	1.01380i	−0.0658314	+	0.136700i
$56$	−1.15291	+	2.38135i	−0.154064	+	0.318221i
$57$		0			0
$58$	4.83240	+	0.728367i	0.634525	+	0.0956393i
$59$	9.74959	−	6.64716i	1.26929	−	0.865386i	0.273942	−	0.961746i	$-0.411672\pi$
$59$	9.74959	−	6.64716i	1.26929	−	0.865386i	0.995347	+	0.0963599i	$0.0307200\pi$
$60$		0			0
$61$	−0.182617	−	0.196814i	−0.0233817	−	0.0251995i	0.721253	−	0.692672i	$-0.243567\pi$
$61$	−0.182617	−	0.196814i	−0.0233817	−	0.0251995i	−0.744634	+	0.667473i	$0.767376\pi$
$62$	0.890744	+	1.11696i	0.113125	+	0.141854i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	1.59803	−	0.119756i	0.198211	−	0.0148539i
$66$		0			0
$67$	6.72968	−	11.6562i	0.822162	−	1.42403i	−0.0819075	−	0.996640i	$-0.526101\pi$
$67$	6.72968	−	11.6562i	0.822162	−	1.42403i	0.904069	−	0.427386i	$-0.140565\pi$
$68$	−2.41596	−	4.18456i	−0.292978	−	0.507453i
$69$		0			0
$70$	−0.410945	+	1.32248i	−0.0491174	+	0.158066i
$71$	−2.17664	−	0.496803i	−0.258319	−	0.0589596i	0.0914000	−	0.995814i	$-0.470866\pi$
$71$	−2.17664	−	0.496803i	−0.258319	−	0.0589596i	−0.349719	+	0.936855i	$0.613723\pi$
$72$		0			0
$73$	−7.27960	+	2.85703i	−0.852013	+	0.334390i	−0.750845	−	0.660479i	$-0.770353\pi$
$73$	−7.27960	+	2.85703i	−0.852013	+	0.334390i	−0.101168	+	0.994869i	$0.532258\pi$
$74$	−6.66061	+	2.61410i	−0.774281	+	0.303883i
$75$		0			0
$76$	5.36903	+	1.22545i	0.615870	+	0.140568i
$77$	3.87728	−	4.16131i	0.441857	−	0.474225i
$78$		0			0
$79$	−4.67750	−	8.10167i	−0.526260	−	0.911509i	−0.999532	−	0.0305925i	$-0.990261\pi$
$79$	−4.67750	−	8.10167i	−0.526260	−	0.911509i	0.473272	−	0.880916i	$-0.343073\pi$
$80$	−0.261713	+	0.453299i	−0.0292604	+	0.0506804i
$81$		0			0
$82$	−1.00154	+	0.0750552i	−0.110602	+	0.00828846i
$83$	−0.0574893	+	0.0720893i	−0.00631027	+	0.00791282i	−0.784977	−	0.619525i	$-0.787325\pi$
$83$	−0.0574893	+	0.0720893i	−0.00631027	+	0.00791282i	0.778666	+	0.627438i	$0.215897\pi$
$84$		0			0
$85$	−1.57690	−	1.97737i	−0.171038	−	0.214475i
$86$	2.85632	+	3.07838i	0.308005	+	0.331951i
$87$		0			0
$88$	1.77620	−	1.21099i	0.189344	−	0.129092i
$89$	−10.7099	−	1.61426i	−1.13525	−	0.171111i	−0.445583	−	0.895241i	$-0.647003\pi$
$89$	−10.7099	−	1.61426i	−1.13525	−	0.171111i	−0.689664	+	0.724130i	$0.742242\pi$
$90$		0			0
$91$	−7.89333	−	1.81889i	−0.827446	−	0.190672i
$92$	−0.0516997	+	0.107356i	−0.00539007	+	0.0111926i
$93$		0			0
$94$	−8.06956	+	8.69692i	−0.832312	+	0.897019i
$95$	2.87450	+	0.215414i	0.294917	+	0.0221010i
$96$		0			0
$97$			11.6182i			1.17965i	0.807532	+	0.589824i	$0.200803\pi$
$97$			11.6182i			1.17965i	−0.807532	+	0.589824i	$0.799197\pi$
$98$	3.96728	−	5.76721i	0.400755	−	0.582576i
$99$		0			0
$100$	1.72661	−	4.39933i	0.172661	−	0.439933i
$101$	−0.140699	+	1.87750i	−0.0140001	+	0.186818i	0.985819	+	0.167810i	$0.0536697\pi$
$101$	−0.140699	+	1.87750i	−0.0140001	+	0.186818i	−0.999819	+	0.0190074i	$0.993949\pi$
$102$		0			0
$103$	1.95928	−	2.87373i	0.193053	−	0.283157i	−0.717492	−	0.696567i	$-0.754710\pi$
$103$	1.95928	−	2.87373i	0.193053	−	0.283157i	0.910545	+	0.413410i	$0.135662\pi$
$104$	−2.75839	−	1.32837i	−0.270483	−	0.130258i
$105$		0			0
$106$	0.483005	−	0.232603i	0.0469136	−	0.0225924i
$107$	2.14837	−	14.2535i	0.207691	−	1.37794i	−0.605454	−	0.795880i	$-0.707008\pi$
$107$	2.14837	−	14.2535i	0.207691	−	1.37794i	0.813145	−	0.582061i	$-0.197754\pi$
$108$		0			0
$109$	−8.29194	+	1.24981i	−0.794223	+	0.119710i	−0.533607	−	0.845733i	$-0.679164\pi$
$109$	−8.29194	+	1.24981i	−0.794223	+	0.119710i	−0.260616	+	0.965442i	$0.583926\pi$
$110$	0.824852	−	0.765350i	0.0786465	−	0.0729733i
$111$		0			0
$112$	1.94321	−	1.79553i	0.183616	−	0.169661i
$113$	−11.3002	−	9.01161i	−1.06303	−	0.847741i	−0.0742710	−	0.997238i	$-0.523663\pi$
$113$	−11.3002	−	9.01161i	−1.06303	−	0.847741i	−0.988762	+	0.149497i	$0.952234\pi$
$114$		0			0
$115$	−0.0183836	+	0.0595982i	−0.00171428	+	0.00555756i
$116$	−4.23225	−	2.44349i	−0.392955	−	0.226873i
$117$		0			0
$118$	−11.5041	+	2.62574i	−1.05904	+	0.241719i
$119$	4.64576	+	11.9100i	0.425876	+	1.09179i
$120$		0			0
$121$	6.09522	−	1.88013i	0.554111	−	0.170921i
$122$	0.0980890	+	0.249927i	0.00888056	+	0.0226273i
$123$		0			0
$124$	−0.421100	−	1.36517i	−0.0378159	−	0.122596i
$125$	1.13282	−	4.96321i	0.101322	−	0.443923i
$126$		0			0
$127$	−2.40232	−	10.5252i	−0.213171	−	0.933963i	−0.962397	−	0.271648i	$-0.912431\pi$
$127$	−2.40232	−	10.5252i	−0.213171	−	0.933963i	0.749225	−	0.662315i	$-0.230426\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.53131	−	0.472348i	−0.134305	−	0.0414277i
$131$	−0.187419	−	2.50093i	−0.0163749	−	0.218508i	−0.999388	−	0.0349735i	$-0.988865\pi$
$131$	−0.187419	−	2.50093i	−0.0163749	−	0.218508i	0.983013	−	0.183534i	$-0.0587537\pi$
$132$		0			0
$133$	−13.5521	−	5.35139i	−1.17512	−	0.464024i
$134$	−10.5230	+	8.39178i	−0.909045	+	0.724939i
$135$		0			0
$136$	0.720160	+	4.77795i	0.0617532	+	0.409706i
$137$	8.24453	+	12.0925i	0.704377	+	1.03313i	0.997038	+	0.0769154i	$0.0245071\pi$
$137$	8.24453	+	12.0925i	0.704377	+	1.03313i	−0.292660	+	0.956216i	$0.594540\pi$
$138$		0			0
$139$	5.43530	+	11.2865i	0.461016	+	0.957310i	0.993813	+	0.111067i	$0.0354267\pi$
$139$	5.43530	+	11.2865i	0.461016	+	0.957310i	−0.532797	+	0.846243i	$0.678859\pi$
$140$	0.865693	−	1.08092i	0.0731644	−	0.0913546i
$141$		0			0
$142$	1.84467	+	1.25767i	0.154801	+	0.105542i
$143$	4.82467	+	4.47664i	0.403459	+	0.374355i
$144$		0			0
$145$	−2.38115	−	0.934532i	−0.197744	−	0.0776086i
$146$	7.82018			0.647203
$147$		0			0
$148$	7.15523			0.588156
$149$	18.1900	+	7.13906i	1.49019	+	0.584855i	0.964091	−	0.265571i	$-0.0855606\pi$
$149$	18.1900	+	7.13906i	1.49019	+	0.584855i	0.526095	+	0.850426i	$0.323656\pi$
$150$		0			0
$151$	−0.447086	−	0.414836i	−0.0363834	−	0.0337588i	0.661772	−	0.749706i	$-0.269805\pi$
$151$	−0.447086	−	0.414836i	−0.0363834	−	0.0337588i	−0.698155	+	0.715947i	$0.745995\pi$
$152$	−4.55019	−	3.10226i	−0.369069	−	0.251627i
$153$		0			0
$154$	−5.12955	+	2.45713i	−0.413351	+	0.198001i
$155$	−0.324453	−	0.673733i	−0.0260607	−	0.0541155i
$156$		0			0
$157$	5.68628	+	8.34024i	0.453814	+	0.665624i	0.983152	−	0.182787i	$-0.0585120\pi$
$157$	5.68628	+	8.34024i	0.453814	+	0.665624i	−0.529338	+	0.848411i	$0.677560\pi$
$158$	1.39429	+	9.25051i	0.110924	+	0.735931i
$159$		0			0
$160$	0.409230	−	0.326350i	0.0323525	−	0.0258002i
$161$	0.178132	−	0.260107i	0.0140388	−	0.0204993i
$162$		0			0
$163$	1.61648	+	21.5705i	0.126613	+	1.68953i	0.593201	+	0.805054i	$0.297864\pi$
$163$	1.61648	+	21.5705i	0.126613	+	1.68953i	−0.466589	+	0.884474i	$0.654517\pi$
$164$	0.959730	+	0.296038i	0.0749423	+	0.0231166i
$165$		0			0
$166$	0.0798524	−	0.0461028i	0.00619775	−	0.00357827i
$167$	3.18917	+	13.9727i	0.246785	+	1.08124i	0.934698	+	0.355443i	$0.115670\pi$
$167$	3.18917	+	13.9727i	0.246785	+	1.08124i	−0.687913	+	0.725793i	$0.741473\pi$
$168$		0			0
$169$	−0.807018	+	3.53578i	−0.0620783	+	0.271983i
$170$	0.745479	+	2.41678i	0.0571756	+	0.185359i
$171$		0			0
$172$	−1.53422	−	3.90912i	−0.116983	−	0.298068i
$173$	3.28522	−	1.01336i	0.249771	−	0.0770440i	−0.167342	−	0.985899i	$-0.553518\pi$
$173$	3.28522	−	1.01336i	0.249771	−	0.0770440i	0.417112	+	0.908855i	$0.363042\pi$
$174$		0			0
$175$	−6.27446	+	10.8157i	−0.474305	+	0.817587i
$176$	−2.09584	+	0.478363i	−0.157980	+	0.0360580i
$177$		0			0
$178$	9.37980	+	5.41543i	0.703046	+	0.405904i
$179$	−3.39802	+	11.0161i	−0.253980	+	0.823383i	0.735349	+	0.677688i	$0.237018\pi$
$179$	−3.39802	+	11.0161i	−0.253980	+	0.823383i	−0.989330	+	0.145695i	$0.953458\pi$
$180$		0			0
$181$	14.3897	+	11.4754i	1.06958	+	0.852959i	0.989601	−	0.143838i	$-0.0459444\pi$
$181$	14.3897	+	11.4754i	1.06958	+	0.852959i	0.0799753	+	0.996797i	$0.474516\pi$
$182$	6.68318	+	4.57692i	0.495390	+	0.339264i
$183$		0			0
$184$	0.0873473	−	0.0810465i	0.00643933	−	0.00597483i
$185$	3.70339	−	0.558197i	0.272279	−	0.0410395i
$186$		0			0
$187$	1.54816	−	10.2714i	0.113213	−	0.751116i
$188$	10.6891	−	5.14759i	0.779582	−	0.375427i
$189$		0			0
$190$	−2.59710	−	1.25070i	−0.188413	−	0.0907350i
$191$	8.88345	−	13.0296i	0.642784	−	0.942791i	−0.357178	−	0.934036i	$-0.616261\pi$
$191$	8.88345	−	13.0296i	0.642784	−	0.942791i	0.999962	−	0.00875455i	$-0.00278669\pi$
$192$		0			0
$193$	−0.499707	+	6.66812i	−0.0359697	+	0.479982i	0.949910	+	0.312525i	$0.101175\pi$
$193$	−0.499707	+	6.66812i	−0.0359697	+	0.479982i	−0.985879	+	0.167457i	$0.946444\pi$
$194$	4.24460	−	10.8151i	0.304745	−	0.776477i
$195$		0			0
$196$	−5.80003	+	3.91914i	−0.414288	+	0.279938i
$197$		−	12.5893i		−	0.896952i	−0.893795	−	0.448476i	$-0.851967\pi$
$197$		−	12.5893i		−	0.896952i	0.893795	−	0.448476i	$-0.148033\pi$
$198$		0			0
$199$	−14.3817	−	1.07776i	−1.01949	−	0.0764006i	−0.445519	−	0.895273i	$-0.646981\pi$
$199$	−14.3817	−	1.07776i	−1.01949	−	0.0764006i	−0.573976	+	0.818872i	$0.694600\pi$
$200$	−3.21451	+	3.46442i	−0.227300	+	0.244972i
$201$		0			0
$202$	0.816899	−	1.69631i	0.0574768	−	0.119352i
$203$	10.0921	+	8.08258i	0.708326	+	0.567286i
$204$		0			0
$205$	0.519831	+	0.0783519i	0.0363066	+	0.00547233i
$206$	−2.87373	+	1.95928i	−0.200223	+	0.136509i
$207$		0			0
$208$	2.08241	+	2.24430i	0.144389	+	0.155614i
$209$	7.38141	+	9.25600i	0.510583	+	0.640251i
$210$		0			0
$211$	−4.50845	+	5.65342i	−0.310375	+	0.389198i	−0.912414	−	0.409269i	$-0.865784\pi$
$211$	−4.50845	+	5.65342i	−0.310375	+	0.389198i	0.602039	+	0.798467i	$0.294355\pi$
$212$	−0.534596	+	0.0400624i	−0.0367162	+	0.00275150i
$213$		0			0
$214$	−7.20727	+	12.4834i	−0.492679	+	0.853344i
$215$	−1.09904	−	1.90359i	−0.0749538	−	0.129824i
$216$		0			0
$217$	0.555576	+	3.73878i	0.0377149	+	0.253805i
$218$	8.17535	+	1.86597i	0.553705	+	0.126379i
$219$		0			0
$220$	−1.04745	+	0.411093i	−0.0706188	+	0.0277159i
$221$	−13.7707	+	5.40460i	−0.926318	+	0.363553i
$222$		0			0
$223$	18.1541	+	4.14355i	1.21569	+	0.277472i	0.781820	−	0.623505i	$-0.214292\pi$
$223$	18.1541	+	4.14355i	1.21569	+	0.277472i	0.433867	+	0.900977i	$0.357149\pi$
$224$	−2.46487	+	0.961474i	−0.164691	+	0.0642412i
$225$		0			0
$226$	7.22675	+	12.5171i	0.480716	+	0.832625i
$227$	−1.41681	+	2.45399i	−0.0940372	+	0.162877i	−0.909206	−	0.416346i	$-0.863311\pi$
$227$	−1.41681	+	2.45399i	−0.0940372	+	0.162877i	0.815169	+	0.579223i	$0.196644\pi$
$228$		0			0
$229$	15.8495	−	1.18776i	1.04737	−	0.0784892i	0.460087	−	0.887874i	$-0.347818\pi$
$229$	15.8495	−	1.18776i	1.04737	−	0.0784892i	0.587279	+	0.809385i	$0.300199\pi$
$230$	0.0388865	−	0.0487621i	0.00256410	−	0.00321528i
$231$		0			0
$232$	3.04699	+	3.82080i	0.200044	+	0.250848i
$233$	−12.5072	−	13.4796i	−0.819377	−	0.883078i	0.175468	−	0.984485i	$-0.443856\pi$
$233$	−12.5072	−	13.4796i	−0.819377	−	0.883078i	−0.994845	+	0.101407i	$0.967666\pi$
$234$		0			0
$235$	5.13087	−	3.49817i	0.334701	−	0.228195i
$236$	11.6682	+	1.75869i	0.759533	+	0.114481i
$237$		0			0
$238$	0.0266021	−	12.7840i	0.00172436	−	0.828665i
$239$	−4.37080	+	9.07606i	−0.282723	+	0.587081i	−0.993171	−	0.116669i	$-0.962778\pi$
$239$	−4.37080	+	9.07606i	−0.282723	+	0.587081i	0.710447	+	0.703750i	$0.248493\pi$
$240$		0			0
$241$	−17.7554	+	19.1357i	−1.14372	+	1.23264i	−0.174981	+	0.984572i	$0.555987\pi$
$241$	−17.7554	+	19.1357i	−1.14372	+	1.23264i	−0.968742	+	0.248069i	$0.920204\pi$
$242$	−6.36077	−	0.476674i	−0.408886	−	0.0306417i
$243$		0			0
$244$		−	0.268486i		−	0.0171881i
$245$	−2.69623	+	2.48094i	−0.172256	+	0.158501i
$246$		0			0
$247$	6.15982	−	15.6950i	0.391940	−	0.998647i
$248$	−0.106763	+	1.42465i	−0.00677943	+	0.0904652i
$249$		0			0
$250$	−2.86778	+	4.20625i	−0.181374	+	0.266027i
$251$	2.67668	+	1.28902i	0.168950	+	0.0813622i	0.516448	−	0.856319i	$-0.327254\pi$
$251$	2.67668	+	1.28902i	0.168950	+	0.0813622i	−0.347497	+	0.937681i	$0.612968\pi$
$252$		0			0
$253$	−0.230787	+	0.111141i	−0.0145095	+	0.00698738i
$254$	−1.60905	+	10.6753i	−0.100961	+	0.669830i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	−10.3855	+	9.63632i	−0.647829	+	0.601097i	−0.934083	−	0.357057i	$-0.883780\pi$
$257$	−10.3855	+	9.63632i	−0.647829	+	0.601097i	0.286254	+	0.958154i	$0.407590\pi$
$258$		0			0
$259$	−18.7136	−	2.86046i	−1.16281	−	0.177740i
$260$	1.25289	+	0.999148i	0.0777011	+	0.0619646i
$261$		0			0
$262$	−0.739230	+	2.39652i	−0.0456698	+	0.148058i
$263$	22.1294	+	12.7764i	1.36456	+	0.787827i	0.990226	−	0.139469i	$-0.0445397\pi$
$263$	22.1294	+	12.7764i	1.36456	+	0.787827i	0.374329	+	0.927296i	$0.377873\pi$
$264$		0			0
$265$	−0.273570	+	0.0624406i	−0.0168053	+	0.00383570i
$266$	10.6602	+	9.93262i	0.653621	+	0.609008i
$267$		0			0
$268$	12.8614	−	3.96722i	0.785635	−	0.242336i
$269$	0.375421	+	0.956557i	0.0228898	+	0.0583223i	0.941862	−	0.336001i	$-0.109074\pi$
$269$	0.375421	+	0.956557i	0.0228898	+	0.0583223i	−0.918972	+	0.394323i	$0.870979\pi$
$270$		0			0
$271$	1.16737	+	3.78454i	0.0709130	+	0.229894i	0.984091	−	0.177668i	$-0.0568552\pi$
$271$	1.16737	+	3.78454i	0.0709130	+	0.229894i	−0.913178	+	0.407562i	$0.866379\pi$
$272$	1.07520	−	4.71077i	0.0651937	−	0.285632i
$273$		0			0
$274$	−3.25673	−	14.2687i	−0.196746	−	0.862001i
$275$	8.79860	−	5.07987i	0.530575	−	0.306328i
$276$		0			0
$277$	−24.5384	−	7.56911i	−1.47437	−	0.454784i	−0.549640	−	0.835402i	$-0.685235\pi$
$277$	−24.5384	−	7.56911i	−1.47437	−	0.454784i	−0.924732	+	0.380618i	$0.875711\pi$
$278$	−0.936151	−	12.4921i	−0.0561466	−	0.749224i
$279$		0			0
$280$	−1.20076	+	0.689929i	−0.0717589	+	0.0412312i
$281$	−13.7567	+	10.9706i	−0.820654	+	0.654450i	−0.941047	−	0.338277i	$-0.890156\pi$
$281$	−13.7567	+	10.9706i	−0.820654	+	0.654450i	0.120393	+	0.992726i	$0.461585\pi$
$282$		0			0
$283$	2.40135	+	15.9319i	0.142745	+	0.947052i	0.939451	+	0.342685i	$0.111336\pi$
$283$	2.40135	+	15.9319i	0.142745	+	0.947052i	−0.796705	+	0.604368i	$0.793426\pi$
$284$	−1.25767	−	1.84467i	−0.0746293	−	0.109461i
$285$		0			0
$286$	−2.85566	−	5.92983i	−0.168859	−	0.350638i
$287$	−2.39171	−	1.15792i	−0.141178	−	0.0683500i
$288$		0			0
$289$	5.24448	+	3.57563i	0.308499	+	0.210331i
$290$	1.87513	+	1.73986i	0.110111	+	0.102168i
$291$		0			0
$292$	−7.27960	−	2.85703i	−0.426006	−	0.167195i
$293$	−21.0672			−1.23076			−0.615379	−	0.788232i	$-0.710997\pi$
$293$	−21.0672			−1.23076			−0.615379	+	0.788232i	$0.710997\pi$
$294$		0			0
$295$	6.17640			0.359604
$296$	−6.66061	−	2.61410i	−0.387140	−	0.151941i
$297$		0			0
$298$	−14.3244	−	13.2911i	−0.829792	−	0.769935i
$299$	0.301416	+	0.205502i	0.0174314	+	0.0118845i
$300$		0			0
$301$	2.44979	+	10.8371i	0.141204	+	0.624643i
$302$	0.264625	+	0.549498i	0.0152274	+	0.0316201i
$303$		0			0
$304$	3.10226	+	4.55019i	0.177927	+	0.260971i
$305$	−0.0209453	−	0.138963i	−0.00119932	−	0.00795698i
$306$		0			0
$307$	−4.16239	+	3.31940i	−0.237560	+	0.189448i	−0.735032	−	0.678032i	$-0.762833\pi$
$307$	−4.16239	+	3.31940i	−0.237560	+	0.189448i	0.497472	+	0.867480i	$0.334262\pi$
$308$	5.67265	−	0.413238i	0.323229	−	0.0235464i
$309$		0			0
$310$	0.0558822	+	0.745696i	0.00317390	+	0.0423527i
$311$	28.4205	+	8.76656i	1.61158	+	0.497106i	0.964225	−	0.265085i	$-0.0854001\pi$
$311$	28.4205	+	8.76656i	1.61158	+	0.497106i	0.647352	+	0.762191i	$0.275876\pi$
$312$		0			0
$313$	16.4716	−	9.50986i	0.931027	−	0.537529i	0.0438911	−	0.999036i	$-0.486025\pi$
$313$	16.4716	−	9.50986i	0.931027	−	0.537529i	0.887136	+	0.461507i	$0.152691\pi$
$314$	−2.24618	−	9.84114i	−0.126759	−	0.555368i
$315$		0			0
$316$	2.08168	−	9.12045i	0.117104	−	0.513065i
$317$	−5.05296	−	16.3813i	−0.283803	−	0.920065i	−0.979451	−	0.201683i	$-0.935359\pi$
$317$	−5.05296	−	16.3813i	−0.283803	−	0.920065i	0.695648	−	0.718383i	$-0.255117\pi$
$318$		0			0
$319$	−3.83819	−	9.77954i	−0.214897	−	0.547549i
$320$	−0.500171	+	0.154282i	−0.0279604	+	0.00862464i
$321$		0			0
$322$	−0.260846	+	0.177048i	−0.0145364	+	0.00986649i
$323$	−25.9427	+	5.92126i	−1.44349	+	0.329467i
$324$		0			0
$325$	−12.5306	−	7.23456i	−0.695074	−	0.401301i
$326$	6.37583	−	20.6699i	0.353125	−	1.14480i
$327$		0			0
$328$	−0.785233	−	0.626202i	−0.0433572	−	0.0345762i
$329$	−30.0138	+	9.18968i	−1.65472	+	0.506644i
$330$		0			0
$331$	15.1477	−	14.0550i	0.832592	−	0.772532i	−0.143555	−	0.989642i	$-0.545854\pi$
$331$	15.1477	−	14.0550i	0.832592	−	0.772532i	0.976147	+	0.217110i	$0.0696630\pi$
$332$	−0.0911758	+	0.0137425i	−0.00500392	+	0.000754220i
$333$		0			0
$334$	2.13607	−	14.1719i	0.116881	−	0.775452i
$335$	6.34730	−	3.05670i	0.346790	−	0.167005i
$336$		0			0
$337$	13.8055	+	6.64839i	0.752034	+	0.362161i	0.770308	−	0.637672i	$-0.220103\pi$
$337$	13.8055	+	6.64839i	0.752034	+	0.362161i	−0.0182733	+	0.999833i	$0.505817\pi$
$338$	2.04300	−	2.99652i	0.111124	−	0.162989i
$339$		0			0
$340$	0.189003	−	2.52207i	0.0102501	−	0.136779i
$341$	1.12204	−	2.85891i	0.0607619	−	0.154819i
$342$		0			0
$343$	16.7360	−	7.93132i	0.903660	−	0.428251i
$344$			4.19941i			0.226417i
$345$		0			0
$346$	−3.42834	−	0.256919i	−0.184309	−	0.0138120i
$347$	−8.56654	+	9.23253i	−0.459876	+	0.495628i	−0.919831	−	0.392314i	$-0.871675\pi$
$347$	−8.56654	+	9.23253i	−0.459876	+	0.495628i	0.459956	+	0.887942i	$0.347865\pi$
$348$		0			0
$349$	−4.77584	+	9.91713i	−0.255645	+	0.530852i	−0.988807	−	0.149202i	$-0.952329\pi$
$349$	−4.77584	+	9.91713i	−0.255645	+	0.530852i	0.733162	+	0.680054i	$0.238044\pi$
$350$	9.79214	−	7.77569i	0.523412	−	0.415628i
$351$		0			0
$352$	2.12573	+	0.320403i	0.113302	+	0.0170775i
$353$	19.7065	−	13.4357i	1.04887	−	0.715110i	0.0891391	−	0.996019i	$-0.471588\pi$
$353$	19.7065	−	13.4357i	1.04887	−	0.715110i	0.959734	+	0.280909i	$0.0906361\pi$
$354$		0			0
$355$	−0.794853	−	0.856648i	−0.0421864	−	0.0454662i
$356$	−6.75293	−	8.46791i	−0.357905	−	0.448798i
$357$		0			0
$358$	7.18777	−	9.01318i	0.379885	−	0.476361i
$359$	7.95144	−	0.595878i	0.419661	−	0.0314493i	0.136774	−	0.990602i	$-0.456327\pi$
$359$	7.95144	−	0.595878i	0.419661	−	0.0314493i	0.282888	+	0.959153i	$0.408708\pi$
$360$		0			0
$361$	5.66412	−	9.81054i	0.298111	−	0.516344i
$362$	−9.20255	−	15.9393i	−0.483675	−	0.837750i
$363$		0			0
$364$	−4.54906	−	6.70217i	−0.238436	−	0.351289i
$365$	−3.99065	−	0.910840i	−0.208880	−	0.0476756i
$366$		0			0
$367$	13.8483	−	5.43505i	0.722875	−	0.283707i	0.0247602	−	0.999693i	$-0.492118\pi$
$367$	13.8483	−	5.43505i	0.722875	−	0.283707i	0.698115	+	0.715986i	$0.254023\pi$
$368$	−0.110919	+	0.0435325i	−0.00578205	+	0.00226929i
$369$		0			0
$370$	−3.65132	−	0.833391i	−0.189823	−	0.0433259i
$371$	1.41418	+	0.108938i	0.0734208	+	0.00565579i
$372$		0			0
$373$	17.2158	+	29.8187i	0.891403	+	1.54395i	0.838194	+	0.545371i	$0.183611\pi$
$373$	17.2158	+	29.8187i	0.891403	+	1.54395i	0.0532083	+	0.998583i	$0.483055\pi$
$374$	−5.19369	+	8.99573i	−0.268559	+	0.465158i
$375$		0			0
$376$	−11.8308	+	0.886597i	−0.610128	+	0.0457227i
$377$	−9.32860	+	11.6977i	−0.480447	+	0.602462i
$378$		0			0
$379$	−11.3913	−	14.2842i	−0.585129	−	0.733729i	0.397849	−	0.917451i	$-0.369757\pi$
$379$	−11.3913	−	14.2842i	−0.585129	−	0.733729i	−0.982978	+	0.183722i	$0.941185\pi$
$380$	1.96064	+	2.11306i	0.100579	+	0.108398i
$381$		0			0
$382$	−13.0296	+	8.88345i	−0.666654	+	0.454517i
$383$	−4.89584	−	0.737929i	−0.250166	−	0.0377064i	0.0227621	−	0.999741i	$-0.492754\pi$
$383$	−4.89584	−	0.737929i	−0.250166	−	0.0377064i	−0.272928	+	0.962034i	$0.587992\pi$
$384$		0			0
$385$	2.90381	−	0.656421i	0.147992	−	0.0334543i
$386$	2.90130	−	6.02462i	0.147672	−	0.306645i
$387$		0			0
$388$	−7.90238	+	8.51674i	−0.401182	+	0.432372i
$389$	−15.8967	−	1.19129i	−0.805993	−	0.0604008i	−0.334640	−	0.942346i	$-0.608615\pi$
$389$	−15.8967	−	1.19129i	−0.805993	−	0.0604008i	−0.471352	+	0.881945i	$0.656234\pi$
$390$		0			0
$391$		−	0.575751i		−	0.0291170i
$392$	6.83092	−	1.52923i	0.345014	−	0.0772378i
$393$		0			0
$394$	−4.59940	+	11.7191i	−0.231714	+	0.590398i
$395$	0.365926	−	4.88295i	0.0184118	−	0.245688i
$396$		0			0
$397$	4.31382	−	6.32721i	0.216504	−	0.317554i	−0.702587	−	0.711598i	$-0.747972\pi$
$397$	4.31382	−	6.32721i	0.216504	−	0.317554i	0.919092	+	0.394044i	$0.128924\pi$
$398$	12.9938	+	6.25750i	0.651322	+	0.313660i
$399$		0			0
$400$	4.25800	−	2.05055i	0.212900	−	0.102527i
$401$	0.289227	−	1.91890i	0.0144433	−	0.0958250i	−0.980448	−	0.196780i	$-0.936952\pi$
$401$	0.289227	−	1.91890i	0.0144433	−	0.0958250i	0.994891	+	0.100955i	$0.0321897\pi$
$402$		0			0
$403$	−4.32505	+	0.651897i	−0.215446	+	0.0324733i
$404$	−1.38016	+	1.28060i	−0.0686656	+	0.0637124i
$405$		0			0
$406$	−6.44156	−	11.2109i	−0.319689	−	0.556389i
$407$	12.0261	+	9.59046i	0.596109	+	0.475381i
$408$		0			0
$409$	−1.75976	+	5.70499i	−0.0870144	+	0.282094i	−0.988613	−	0.150480i	$-0.951918\pi$
$409$	−1.75976	+	5.70499i	−0.0870144	+	0.282094i	0.901599	+	0.432573i	$0.142394\pi$
$410$	−0.455272	−	0.262851i	−0.0224843	−	0.0129813i
$411$		0			0
$412$	3.39089	−	0.773948i	0.167057	−	0.0381297i
$413$	−29.8136	−	9.26425i	−1.46703	−	0.455864i
$414$		0			0
$415$	−0.0461186	+	0.0142257i	−0.00226387	+	0.000698312i
$416$	−1.11852	−	2.84995i	−0.0548401	−	0.139730i
$417$		0			0
$418$	−3.48957	−	11.3129i	−0.170680	−	0.553332i
$419$	4.83750	−	21.1945i	0.236328	−	1.03542i	−0.707948	−	0.706264i	$-0.750379\pi$
$419$	4.83750	−	21.1945i	0.236328	−	1.03542i	0.944276	−	0.329155i	$-0.106764\pi$
$420$		0			0
$421$	−7.25112	−	31.7693i	−0.353398	−	1.54834i	−0.769275	−	0.638918i	$-0.779382\pi$
$421$	−7.25112	−	31.7693i	−0.353398	−	1.54834i	0.415877	−	0.909421i	$-0.363475\pi$
$422$	6.26223	−	3.61550i	0.304841	−	0.176000i
$423$		0			0
$424$	0.512278	+	0.158017i	0.0248784	+	0.00767397i
$425$	1.70652	+	22.7719i	0.0827783	+	1.10460i
$426$		0			0
$427$	−0.107333	+	0.702192i	−0.00519422	+	0.0339814i
$428$	11.2697	−	8.98732i	0.544743	−	0.434418i
$429$		0			0
$430$	0.327606	+	2.17353i	0.0157986	+	0.104817i
$431$	−1.12032	−	1.64321i	−0.0539640	−	0.0791507i	0.798308	−	0.602249i	$-0.205729\pi$
$431$	−1.12032	−	1.64321i	−0.0539640	−	0.0791507i	−0.852272	+	0.523098i	$0.824776\pi$
$432$		0			0
$433$	10.7762	+	22.3771i	0.517872	+	1.07537i	0.981873	+	0.189538i	$0.0606990\pi$
$433$	10.7762	+	22.3771i	0.517872	+	1.07537i	−0.464001	+	0.885835i	$0.653587\pi$
$434$	0.848758	−	3.68330i	0.0407417	−	0.176804i
$435$		0			0
$436$	−6.92850	−	4.72377i	−0.331815	−	0.226228i
$437$	0.481031	+	0.446332i	0.0230108	+	0.0213509i
$438$		0			0
$439$	4.23898	+	1.66368i	0.202316	+	0.0794030i	0.464335	−	0.885660i	$-0.346293\pi$
$439$	4.23898	+	1.66368i	0.202316	+	0.0794030i	−0.262020	+	0.965063i	$0.584389\pi$
$440$	1.12523			0.0536432
$441$		0			0
$442$	14.7933			0.703646
$443$	−22.5228	−	8.83956i	−1.07009	−	0.419980i	−0.236084	−	0.971733i	$-0.575864\pi$
$443$	−22.5228	−	8.83956i	−1.07009	−	0.419980i	−0.834008	+	0.551752i	$0.813959\pi$
$444$		0			0
$445$	−4.15578	−	3.85600i	−0.197003	−	0.182792i
$446$	−15.3853	−	10.4895i	−0.728517	−	0.496694i
$447$		0			0
$448$	2.64575	+	0.00550551i	0.125000	+	0.000260111i
$449$	−13.4046	−	27.8350i	−0.632603	−	1.31361i	−0.933026	−	0.359808i	$-0.882842\pi$
$449$	−13.4046	−	27.8350i	−0.632603	−	1.31361i	0.300423	−	0.953806i	$-0.402872\pi$
$450$		0			0
$451$	1.21626	+	1.78393i	0.0572715	+	0.0840019i
$452$	−2.15418	−	14.2921i	−0.101324	−	0.672242i
$453$		0			0
$454$	2.21542	−	1.76674i	0.103975	−	0.0829171i
$455$	−2.87735	−	3.11402i	−0.134892	−	0.145987i
$456$		0			0
$457$	−1.07945	−	14.4042i	−0.0504944	−	0.673800i	−0.963817	−	0.266564i	$-0.914112\pi$
$457$	−1.07945	−	14.4042i	−0.0504944	−	0.673800i	0.913323	−	0.407236i	$-0.133507\pi$
$458$	−15.1878	−	4.68483i	−0.709681	−	0.218908i
$459$		0			0
$460$	−0.0540132	+	0.0311846i	−0.00251838	+	0.00145399i
$461$	3.70821	+	16.2467i	0.172708	+	0.756685i	0.984876	+	0.173261i	$0.0554303\pi$
$461$	3.70821	+	16.2467i	0.172708	+	0.756685i	−0.812168	+	0.583424i	$0.801713\pi$
$462$		0			0
$463$	3.48220	−	15.2565i	0.161831	−	0.709030i	−0.827271	−	0.561803i	$-0.810108\pi$
$463$	3.48220	−	15.2565i	0.161831	−	0.709030i	0.989103	−	0.147227i	$-0.0470348\pi$
$464$	−1.44046	−	4.66987i	−0.0668719	−	0.216793i
$465$		0			0
$466$	6.71801	+	17.1172i	0.311206	+	0.792940i
$467$	−7.08699	+	2.18605i	−0.327947	+	0.101158i	−0.454356	−	0.890820i	$-0.650131\pi$
$467$	−7.08699	+	2.18605i	−0.327947	+	0.101158i	0.126410	+	0.991978i	$0.459655\pi$
$468$		0			0
$469$	−35.2234	+	5.23413i	−1.62646	+	0.241690i
$470$	−6.05421	+	1.38183i	−0.279260	+	0.0637393i
$471$		0			0
$472$	−10.2191	−	5.89998i	−0.470371	−	0.271569i
$473$	2.66095	−	8.62658i	0.122350	−	0.396651i
$474$		0			0
$475$	−20.3485	−	16.2274i	−0.933654	−	0.744564i
$476$	−4.69529	+	11.8906i	−0.215208	+	0.545004i
$477$		0			0
$478$	7.38452	−	6.85183i	0.337760	−	0.313395i
$479$	6.51158	−	0.981463i	0.297522	−	0.0448442i	0.00141482	−	0.999999i	$-0.499550\pi$
$479$	6.51158	−	0.981463i	0.297522	−	0.0448442i	0.296107	+	0.955155i	$0.404312\pi$
$480$		0			0
$481$	3.26497	−	21.6617i	0.148870	−	0.987686i
$482$	23.5191	−	11.3262i	1.07126	−	0.515894i
$483$		0			0
$484$	5.74692	+	2.76757i	0.261224	+	0.125799i
$485$	−3.42569	+	5.02457i	−0.155553	+	0.228154i
$486$		0			0
$487$	1.33718	−	17.8435i	0.0605935	−	0.808564i	−0.881280	−	0.472595i	$-0.843317\pi$
$487$	1.33718	−	17.8435i	0.0605935	−	0.808564i	0.941873	−	0.335969i	$-0.109064\pi$
$488$	−0.0980890	+	0.249927i	−0.00444028	+	0.0113137i
$489$		0			0
$490$	3.41624	−	1.32439i	0.154330	−	0.0598300i
$491$		−	41.0109i		−	1.85080i	−0.378994	−	0.925399i	$-0.623730\pi$
$491$		−	41.0109i		−	1.85080i	0.378994	−	0.925399i	$-0.376270\pi$
$492$		0			0
$493$	23.5475	+	1.76464i	1.06052	+	0.0794754i
$494$	−11.4680	+	12.3596i	−0.515971	+	0.556085i
$495$		0			0
$496$	0.619865	−	1.28716i	0.0278327	−	0.0577953i
$497$	2.55184	+	5.32729i	0.114466	+	0.238961i
$498$		0			0
$499$	−20.9199	−	3.15317i	−0.936505	−	0.141155i	−0.336980	−	0.941512i	$-0.609406\pi$
$499$	−20.9199	−	3.15317i	−0.936505	−	0.141155i	−0.599525	+	0.800356i	$0.704644\pi$
$500$	4.20625	−	2.86778i	0.188109	−	0.128251i
$501$		0			0
$502$	−2.02072	−	2.17781i	−0.0901889	−	0.0972006i
$503$	−19.3671	−	24.2855i	−0.863534	−	1.08284i	−0.995794	−	0.0916226i	$-0.970795\pi$
$503$	−19.3671	−	24.2855i	−0.863534	−	1.08284i	0.132260	−	0.991215i	$-0.457777\pi$
$504$		0			0
$505$	−0.614439	+	0.770483i	−0.0273422	+	0.0342860i
$506$	0.255438	−	0.0191424i	0.0113556	−	0.000850985i
$507$		0			0
$508$	5.39795	−	9.34953i	0.239496	−	0.414818i
$509$	11.0974	+	19.2213i	0.491886	+	0.851971i	0.999956	−	0.00934436i	$-0.00297445\pi$
$509$	11.0974	+	19.2213i	0.491886	+	0.851971i	−0.508071	+	0.861315i	$0.669641\pi$
$510$		0			0
$511$	17.8967	+	10.3824i	0.791704	+	0.459290i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$		0			0
$514$	13.1881	−	5.17596i	0.581703	−	0.228302i
$515$	1.69467	−	0.665111i	0.0746763	−	0.0293083i
$516$		0			0
$517$	24.8651	+	5.67529i	1.09356	+	0.249599i
$518$	16.3750	+	9.49957i	0.719474	+	0.417387i
$519$		0			0
$520$	−0.801255	−	1.38781i	−0.0351373	−	0.0608597i
$521$	−14.7848	+	25.6080i	−0.647732	+	1.12190i	0.335931	+	0.941887i	$0.390949\pi$
$521$	−14.7848	+	25.6080i	−0.647732	+	1.12190i	−0.983663	+	0.180018i	$0.942384\pi$
$522$		0			0
$523$	40.0836	−	3.00385i	1.75273	−	0.131349i	0.840709	−	0.541488i	$-0.182139\pi$
$523$	40.0836	−	3.00385i	1.75273	−	0.131349i	0.912023	+	0.410138i	$0.134520\pi$
$524$	1.56368	−	1.96079i	0.0683096	−	0.0856576i
$525$		0			0
$526$	−15.9319	−	19.9780i	−0.694664	−	0.871081i
$527$	4.69529	+	5.06031i	0.204530	+	0.220431i
$528$		0			0
$529$	18.9918	−	12.9484i	0.825729	−	0.562972i
$530$	0.277471	+	0.0418221i	0.0120526	+	0.00181663i
$531$		0			0
$532$	−6.29455	−	13.1406i	−0.272903	−	0.569719i
$533$	1.33415	−	2.77039i	0.0577885	−	0.119999i
$534$		0			0
$535$	5.13186	−	5.53082i	0.221869	−	0.239118i
$536$	−13.4217	−	1.00582i	−0.579731	−	0.0434448i
$537$		0			0
$538$		−	1.02759i		−	0.0443026i
$539$	−15.0013	−	1.18700i	−0.646152	−	0.0511275i
$540$		0			0
$541$	−5.91317	+	15.0665i	−0.254227	+	0.647760i	−0.999826	−	0.0186346i	$-0.994068\pi$
$541$	−5.91317	+	15.0665i	−0.254227	+	0.647760i	0.745599	+	0.666395i	$0.232163\pi$
$542$	0.295968	−	3.94942i	0.0127129	−	0.169642i
$543$		0			0
$544$	−2.72192	+	3.99232i	−0.116701	+	0.171169i
$545$	−3.95456	−	1.90442i	−0.169395	−	0.0815762i
$546$		0			0
$547$	−13.5780	+	6.53880i	−0.580551	+	0.279579i	−0.701024	−	0.713138i	$-0.747273\pi$
$547$	−13.5780	+	6.53880i	−0.580551	+	0.279579i	0.120473	+	0.992717i	$0.461559\pi$
$548$	−2.18132	+	14.4721i	−0.0931815	+	0.618219i
$549$		0			0
$550$	−10.0463	+	1.51423i	−0.428374	+	0.0645670i
$551$	−19.7287	+	18.3056i	−0.840472	+	0.779845i
$552$		0			0
$553$	−9.09048	+	23.0212i	−0.386567	+	0.978961i
$554$	20.0769	+	16.0108i	0.852985	+	0.680233i
$555$		0			0
$556$	−3.69242	+	11.9705i	−0.156594	+	0.507664i
$557$	4.12163	+	2.37963i	0.174639	+	0.100828i	0.584772	−	0.811198i	$-0.301184\pi$
$557$	4.12163	+	2.37963i	0.174639	+	0.100828i	−0.410132	+	0.912026i	$0.634517\pi$
$558$		0			0
$559$	−12.5345	+	2.86092i	−0.530153	+	0.121004i
$560$	1.36981	−	0.203552i	0.0578851	−	0.00860162i
$561$		0			0
$562$	16.8137	−	5.18635i	0.709244	−	0.218773i
$563$	4.32544	+	11.0211i	0.182296	+	0.464482i	0.992586	−	0.121547i	$-0.0387856\pi$
$563$	4.32544	+	11.0211i	0.182296	+	0.464482i	−0.810290	+	0.586029i	$0.800690\pi$
$564$		0			0
$565$	−2.22992	−	7.22922i	−0.0938133	−	0.304135i
$566$	3.58522	−	15.7079i	0.150698	−	0.660252i
$567$		0			0
$568$	0.496803	+	2.17664i	0.0208454	+	0.0913296i
$569$	−8.85832	+	5.11436i	−0.371360	+	0.214405i	−0.674053	−	0.738683i	$-0.735448\pi$
$569$	−8.85832	+	5.11436i	−0.371360	+	0.214405i	0.302692	+	0.953088i	$0.402115\pi$
$570$		0			0
$571$	−16.1603	−	4.98480i	−0.676289	−	0.208607i	−0.0624609	−	0.998047i	$-0.519895\pi$
$571$	−16.1603	−	4.98480i	−0.676289	−	0.208607i	−0.613828	+	0.789440i	$0.710371\pi$
$572$	0.491845	+	6.56321i	0.0205651	+	0.274422i
$573$		0			0
$574$	1.80334	+	1.95167i	0.0752700	+	0.0814610i
$575$	0.440275	−	0.351108i	0.0183607	−	0.0146422i
$576$		0			0
$577$	−1.95598	−	12.9771i	−0.0814286	−	0.540243i	−0.991935	−	0.126748i	$-0.959546\pi$
$577$	−1.95598	−	12.9771i	−0.0814286	−	0.540243i	0.910506	−	0.413495i	$-0.135692\pi$
$578$	−3.57563	−	5.24448i	−0.148726	−	0.218142i
$579$		0			0
$580$	−1.10986	−	2.30465i	−0.0460845	−	0.0956955i
$581$	0.243953		0.000507639i	0.0101209		2.10604e-5i
$582$		0			0
$583$	−0.952212	−	0.649207i	−0.0394366	−	0.0268874i
$584$	5.73260	+	5.31907i	0.237217	+	0.220105i
$585$		0			0
$586$	19.6109	+	7.69670i	0.810118	+	0.317948i
$587$	42.6484			1.76029			0.880144	−	0.474708i	$-0.157446\pi$
$587$	42.6484			1.76029			0.880144	+	0.474708i	$0.157446\pi$
$588$		0			0
$589$	−7.86768			−0.324182
$590$	−5.74945	−	2.25649i	−0.236701	−	0.0928983i
$591$		0			0
$592$	5.24515	+	4.86679i	0.215574	+	0.200024i
$593$	−36.2935	−	24.7445i	−1.49040	−	1.01614i	−0.988502	−	0.151206i	$-0.951684\pi$
$593$	−36.2935	−	24.7445i	−1.49040	−	1.01614i	−0.501894	−	0.864929i	$-0.667363\pi$
$594$		0			0
$595$	−1.50257	+	6.52061i	−0.0615993	+	0.267319i
$596$	8.47844	+	17.6057i	0.347291	+	0.721156i
$597$		0			0
$598$	−0.205502	−	0.301416i	−0.00840361	−	0.0123258i
$599$	4.96345	+	32.9303i	0.202801	+	1.34550i	0.826104	+	0.563517i	$0.190552\pi$
$599$	4.96345	+	32.9303i	0.202801	+	1.34550i	−0.623303	+	0.781980i	$0.714210\pi$
$600$		0			0
$601$	19.4018	−	15.4724i	0.791417	−	0.631134i	−0.142024	−	0.989863i	$-0.545361\pi$
$601$	19.4018	−	15.4724i	0.791417	−	0.631134i	0.933442	+	0.358729i	$0.116790\pi$
$602$	1.67881	−	10.9830i	0.0684230	−	0.447635i
$603$		0			0
$604$	−0.0455777	−	0.608192i	−0.00185453	−	0.0247470i
$605$	3.19039	+	0.984105i	0.129708	+	0.0400096i
$606$		0			0
$607$	−3.09948	+	1.78949i	−0.125804	+	0.0726330i	−0.561581	−	0.827421i	$-0.689807\pi$
$607$	−3.09948	+	1.78949i	−0.125804	+	0.0726330i	0.435777	+	0.900055i	$0.356474\pi$
$608$	−1.22545	−	5.36903i	−0.0496984	−	0.217743i
$609$		0			0
$610$	−0.0312714	+	0.137009i	−0.00126614	+	0.00554733i
$611$	−10.7063	−	34.7089i	−0.433129	−	1.40417i
$612$		0			0
$613$	7.76749	+	19.7912i	0.313726	+	0.799361i	0.997566	+	0.0697288i	$0.0222134\pi$
$613$	7.76749	+	19.7912i	0.313726	+	0.799361i	−0.683840	+	0.729632i	$0.739691\pi$
$614$	5.08737	−	1.56925i	0.205310	−	0.0633297i
$615$		0			0
$616$	−5.43150	−	1.68778i	−0.218841	−	0.0680026i
$617$	18.2851	−	4.17345i	0.736130	−	0.168017i	0.162011	−	0.986789i	$-0.448202\pi$
$617$	18.2851	−	4.17345i	0.736130	−	0.168017i	0.574119	+	0.818772i	$0.305345\pi$
$618$		0			0
$619$	−27.1418	−	15.6703i	−1.09092	−	0.629844i	−0.157100	−	0.987583i	$-0.550214\pi$
$619$	−27.1418	−	15.6703i	−1.09092	−	0.629844i	−0.933822	+	0.357739i	$0.883548\pi$
$620$	0.220414	−	0.714565i	0.00885204	−	0.0286976i
$621$		0			0
$622$	−23.2531	−	18.5437i	−0.932364	−	0.743536i
$623$	14.2762	+	24.8464i	0.571964	+	0.995449i
$624$		0			0
$625$	−15.3688	+	14.2601i	−0.614751	+	0.570405i
$626$	−18.8073	+	2.83474i	−0.751690	+	0.113299i
$627$		0			0
$628$	−1.50447	+	9.98148i	−0.0600347	+	0.398304i
$629$	−31.1496	+	15.0009i	−1.24202	+	0.598124i
$630$		0			0
$631$	21.0475	+	10.1360i	0.837888	+	0.403506i	0.803068	−	0.595888i	$-0.203200\pi$
$631$	21.0475	+	10.1360i	0.837888	+	0.403506i	0.0348207	+	0.999394i	$0.488914\pi$
$632$	−5.26986	+	7.72946i	−0.209624	+	0.307462i
$633$		0			0
$634$	−1.28109	+	17.0950i	−0.0508786	+	0.678928i
$635$	2.06449	−	5.26023i	0.0819267	−	0.208746i
$636$		0			0
$637$	9.21816	+	19.3473i	0.365237	+	0.766567i
$638$			10.5058i			0.415927i
$639$		0			0
$640$	0.521961	+	0.0391156i	0.0206323	+	0.00154618i
$641$	16.9843	−	18.3047i	0.670838	−	0.722991i	−0.302300	−	0.953213i	$-0.597755\pi$
$641$	16.9843	−	18.3047i	0.670838	−	0.722991i	0.973138	+	0.230222i	$0.0739451\pi$
$642$		0			0
$643$	−4.72201	+	9.80535i	−0.186218	+	0.386685i	−0.973088	−	0.230433i	$-0.925986\pi$
$643$	−4.72201	+	9.80535i	−0.186218	+	0.386685i	0.786870	+	0.617118i	$0.211700\pi$
$644$	0.307498	−	0.0695114i	0.0121171	−	0.00273913i
$645$		0			0
$646$	26.3127	+	3.96600i	1.03526	+	0.156040i
$647$	35.8213	−	24.4225i	1.40828	−	0.960149i	0.409423	−	0.912345i	$-0.365730\pi$
$647$	35.8213	−	24.4225i	1.40828	−	0.960149i	0.998857	−	0.0478042i	$-0.0152223\pi$
$648$		0			0
$649$	17.2539	+	18.5953i	0.677274	+	0.729928i
$650$	9.02135	+	11.3124i	0.353847	+	0.443709i
$651$		0			0
$652$	−13.4867	+	16.9118i	−0.528179	+	0.662315i
$653$	0.423423	−	0.0317311i	0.0165698	−	0.00124174i	−0.0664426	−	0.997790i	$-0.521165\pi$
$653$	0.423423	−	0.0317311i	0.0165698	−	0.00124174i	0.0830124	+	0.996549i	$0.473546\pi$
$654$		0			0
$655$	0.656361	−	1.13685i	0.0256461	−	0.0444204i
$656$	0.502175	+	0.869793i	0.0196067	+	0.0339597i
$657$		0			0
$658$	31.2964	+	2.41084i	1.22006	+	0.0939845i
$659$	−31.9057	−	7.28226i	−1.24287	−	0.283677i	−0.449977	−	0.893040i	$-0.648568\pi$
$659$	−31.9057	−	7.28226i	−1.24287	−	0.283677i	−0.792891	+	0.609363i	$0.791425\pi$
$660$		0			0
$661$	36.8279	−	14.4539i	1.43244	−	0.562191i	0.482855	−	0.875700i	$-0.339600\pi$
$661$	36.8279	−	14.4539i	1.43244	−	0.562191i	0.949585	+	0.313509i	$0.101505\pi$
$662$	−19.2354	+	7.54936i	−0.747607	+	0.293414i
$663$		0			0
$664$	0.0898938	+	0.0205177i	0.00348856	+	0.000796241i
$665$	−4.28306	−	6.31026i	−0.166090	−	0.244701i
$666$		0			0
$667$	−0.291156	−	0.504297i	−0.0112736	−	0.0195265i
$668$	−7.16599	+	12.4119i	−0.277261	+	0.480229i
$669$		0			0
$670$	−7.02527	+	0.526471i	−0.271410	+	0.0203394i
$671$	0.359864	−	0.451255i	0.0138924	−	0.0174205i
$672$		0			0
$673$	−24.6623	−	30.9256i	−0.950662	−	1.19209i	−0.981285	−	0.192561i	$-0.938321\pi$
$673$	−24.6623	−	30.9256i	−0.950662	−	1.19209i	0.0306229	−	0.999531i	$-0.490251\pi$
$674$	−10.4223	−	11.2325i	−0.401451	−	0.432661i
$675$		0			0
$676$	−2.99652	+	2.04300i	−0.115251	+	0.0785768i
$677$	46.6507	+	7.03145i	1.79293	+	0.270241i	0.959363	−	0.282176i	$-0.0910564\pi$
$677$	46.6507	+	7.03145i	1.79293	+	0.270241i	0.833568	+	0.552417i	$0.186294\pi$
$678$		0			0
$679$	24.0724	−	19.1153i	0.923815	−	0.733578i
$680$	−1.09736	+	2.27868i	−0.0420817	+	0.0873835i
$681$		0			0
$682$	−2.08896	+	2.25136i	−0.0799902	+	0.0862090i
$683$	−15.1269	−	1.13361i	−0.578816	−	0.0433762i	−0.217894	−	0.975972i	$-0.569919\pi$
$683$	−15.1269	−	1.13361i	−0.578816	−	0.0433762i	−0.360922	+	0.932596i	$0.617538\pi$
$684$		0			0
$685$			7.66064i			0.292698i
$686$	−18.4768	+	1.26870i	−0.705446	+	0.0484393i
$687$		0			0
$688$	1.53422	−	3.90912i	0.0584915	−	0.149034i
$689$	−0.122654	+	1.63671i	−0.00467276	+	0.0623537i
$690$		0			0
$691$	−17.5400	+	25.7265i	−0.667255	+	0.978683i	0.332117	+	0.943238i	$0.392237\pi$
$691$	−17.5400	+	25.7265i	−0.667255	+	0.978683i	−0.999372	+	0.0354447i	$0.988715\pi$
$692$	3.09749	+	1.49167i	0.117749	+	0.0567049i
$693$		0			0
$694$	11.3474	−	5.46461i	0.430741	−	0.207434i
$695$	−0.977269	+	6.48376i	−0.0370699	+	0.245943i
$696$		0			0
$697$	−4.79873	+	0.723293i	−0.181765	+	0.0273967i
$698$	8.06884	−	7.48679i	0.305410	−	0.283379i
$699$		0			0
$700$	−11.9560	+	3.66072i	−0.451895	+	0.138362i
$701$	31.6227	+	25.2182i	1.19437	+	0.952479i	0.999598	−	0.0283690i	$-0.00903135\pi$
$701$	31.6227	+	25.2182i	1.19437	+	0.952479i	0.194774	+	0.980848i	$0.437603\pi$
$702$		0			0
$703$	11.6147	−	37.6540i	0.438057	−	1.42015i
$704$	−1.86173	−	1.07487i	−0.0701667	−	0.0405107i
$705$		0			0
$706$	−23.2529	+	5.30733i	−0.875135	+	0.199744i
$707$	4.12159	−	2.79751i	0.155008	−	0.105211i
$708$		0			0
$709$	−4.17457	+	1.28769i	−0.156779	+	0.0483600i	−0.372151	−	0.928172i	$-0.621380\pi$
$709$	−4.17457	+	1.28769i	−0.156779	+	0.0483600i	0.215372	+	0.976532i	$0.430904\pi$
$710$	0.426939	+	1.08782i	0.0160227	+	0.0408253i
$711$		0			0
$712$	3.19245	+	10.3497i	0.119642	+	0.387871i
$713$	0.0378799	−	0.165963i	0.00141861	−	0.00621536i
$714$		0			0
$715$	0.766581	+	3.35861i	0.0286685	+	0.125605i
$716$	−9.98379	+	5.76414i	−0.373112	+	0.215416i
$717$		0			0
$718$	−7.61949	−	2.35030i	−0.284357	−	0.0877125i
$719$	3.74296	+	49.9463i	0.139589	+	1.86268i	0.426191	+	0.904633i	$0.359855\pi$
$719$	3.74296	+	49.9463i	0.139589	+	1.86268i	−0.286603	+	0.958050i	$0.592526\pi$
$720$		0			0
$721$	−9.17784	+	0.668582i	−0.341801	+	0.0248993i
$722$	−8.85677	+	7.06304i	−0.329615	+	0.262859i
$723$		0			0
$724$	2.74314	+	18.1995i	0.101948	+	0.676380i
$725$	13.0105	+	19.0828i	0.483196	+	0.708718i
$726$		0			0
$727$	−2.91743	−	6.05810i	−0.108201	−	0.224683i	0.839837	−	0.542839i	$-0.182651\pi$
$727$	−2.91743	−	6.05810i	−0.108201	−	0.224683i	−0.948038	+	0.318156i	$0.896936\pi$
$728$	1.78602	+	7.90083i	0.0661945	+	0.292824i
$729$		0			0
$730$	3.38203	+	2.30583i	0.125174	+	0.0853425i
$731$	14.8745	+	13.8015i	0.550153	+	0.510468i
$732$		0			0
$733$	4.71332	+	1.84984i	0.174091	+	0.0683255i	0.450786	−	0.892632i	$-0.351144\pi$
$733$	4.71332	+	1.84984i	0.174091	+	0.0683255i	−0.276695	+	0.960958i	$0.589239\pi$
$734$	−14.8767			−0.549107
$735$		0			0
$736$	0.119156			0.00439214
$737$	26.9341	+	10.5708i	0.992129	+	0.389382i
$738$		0			0
$739$	−9.46109	−	8.77861i	−0.348032	−	0.322926i	0.486714	−	0.873561i	$-0.338195\pi$
$739$	−9.46109	−	8.77861i	−0.348032	−	0.322926i	−0.834746	+	0.550635i	$0.814386\pi$
$740$	3.09445	+	2.10976i	0.113754	+	0.0775563i
$741$		0			0
$742$	−1.27663	−	0.618067i	−0.0468665	−	0.0226900i
$743$	7.93682	+	16.4810i	0.291174	+	0.604628i	0.994322	−	0.106415i	$-0.0339372\pi$
$743$	7.93682	+	16.4810i	0.291174	+	0.604628i	−0.703148	+	0.711043i	$0.748223\pi$
$744$		0			0
$745$	5.76172	+	8.45090i	0.211093	+	0.309617i
$746$	−5.13178	−	34.0471i	−0.187888	−	1.24655i
$747$		0			0
$748$	8.12118	−	6.47642i	0.296940	−	0.236802i
$749$	−33.0675	+	18.9999i	−1.20826	+	0.694240i
$750$		0			0
$751$	−0.0447101	−	0.596615i	−0.00163149	−	0.0217708i	0.996329	−	0.0856110i	$-0.0272842\pi$
$751$	−0.0447101	−	0.596615i	−0.00163149	−	0.0217708i	−0.997960	+	0.0638402i	$0.979665\pi$
$752$	11.3369	+	3.49697i	0.413414	+	0.127521i
$753$		0			0
$754$	12.9574	−	7.48096i	0.471881	−	0.272440i
$755$	−0.0710366	−	0.311232i	−0.00258529	−	0.0113269i
$756$		0			0
$757$	−7.98913	+	35.0027i	−0.290370	+	1.27219i	0.593642	+	0.804729i	$0.297689\pi$
$757$	−7.98913	+	35.0027i	−0.290370	+	1.27219i	−0.884012	+	0.467464i	$0.845168\pi$
$758$	5.38522	+	17.4585i	0.195600	+	0.634120i
$759$		0			0
$760$	−1.05312	−	2.68330i	−0.0382006	−	0.0973334i
$761$	20.5458	−	6.33754i	0.744784	−	0.229736i	0.100940	−	0.994892i	$-0.467815\pi$
$761$	20.5458	−	6.33754i	0.744784	−	0.229736i	0.643844	+	0.765157i	$0.277339\pi$
$762$		0			0
$763$	16.2322	+	15.1243i	0.587645	+	0.547535i
$764$	15.3744	−	3.50911i	0.556227	−	0.126955i
$765$		0			0
$766$	4.28781	+	2.47557i	0.154925	+	0.0894460i
$767$	10.6485	−	34.5216i	0.384495	−	1.24650i
$768$		0			0
$769$	−23.3196	−	18.5967i	−0.840926	−	0.670616i	0.105187	−	0.994452i	$-0.466456\pi$
$769$	−23.3196	−	18.5967i	−0.840926	−	0.670616i	−0.946113	+	0.323837i	$0.895027\pi$
$770$	−2.94290	−	0.449835i	−0.106055	−	0.0162109i
$771$		0			0
$772$	−4.90179	+	4.54819i	−0.176419	+	0.163693i
$773$	−11.4780	+	1.73002i	−0.412834	+	0.0622246i	−0.352176	−	0.935934i	$-0.614558\pi$
$773$	−11.4780	+	1.73002i	−0.412834	+	0.0622246i	−0.0606580	+	0.998159i	$0.519320\pi$
$774$		0			0
$775$	−1.00630	+	6.67639i	−0.0361475	+	0.239823i
$776$	10.4676	−	5.04094i	0.375766	−	0.180959i
$777$		0			0
$778$	14.3626	+	6.91664i	0.514923	+	0.247974i
$779$	3.11576	−	4.56998i	0.111634	−	0.163737i
$780$		0			0
$781$	0.358670	−	4.78612i	0.0128342	−	0.171261i
$782$	−0.210345	+	0.535951i	−0.00752193	+	0.0191656i
$783$		0			0
$784$	−6.91741	−	1.07209i	−0.247050	−	0.0382891i
$785$			5.28357i			0.188579i
$786$		0			0
$787$	−19.0760	−	1.42955i	−0.679988	−	0.0509580i	−0.269741	−	0.962933i	$-0.586938\pi$
$787$	−19.0760	−	1.42955i	−0.679988	−	0.0509580i	−0.410246	+	0.911975i	$0.634557\pi$
$788$	8.56291	−	9.22863i	0.305041	−	0.328756i
$789$		0			0
$790$	−2.12457	+	4.41172i	−0.0755889	+	0.156962i
$791$	−0.0795738	+	38.2403i	−0.00282932	+	1.35967i
$792$		0			0
$793$	−0.812812	−	0.122512i	−0.0288638	−	0.00435052i
$794$	−6.32721	+	4.31382i	−0.224544	+	0.153092i
$795$		0			0
$796$	−9.80950	−	10.5721i	−0.347688	−	0.374719i
$797$	−17.6588	−	22.1434i	−0.625506	−	0.784360i	0.363602	−	0.931555i	$-0.381547\pi$
$797$	−17.6588	−	22.1434i	−0.625506	−	0.784360i	−0.989108	+	0.147195i	$0.952976\pi$
$798$		0			0
$799$	−35.7420	+	44.8191i	−1.26446	+	1.58559i
$800$	−4.71281	+	0.353176i	−0.166623	+	0.0124867i
$801$		0			0
$802$	−0.970285	+	1.68058i	−0.0342619	+	0.0593434i
$803$	−8.40569	−	14.5591i	−0.296630	−	0.513779i
$804$		0			0
$805$	0.153732	−	0.0599663i	0.00541832	−	0.00211353i
$806$	4.26424	+	0.973286i	0.150202	+	0.0342825i
$807$		0			0
$808$	1.75261	−	0.687850i	0.0616567	−	0.0241985i
$809$	12.8508	−	5.04356i	0.451810	−	0.177322i	−0.128515	−	0.991708i	$-0.541021\pi$
$809$	12.8508	−	5.04356i	0.451810	−	0.177322i	0.580325	+	0.814385i	$0.302926\pi$
$810$		0			0
$811$	17.2952	+	3.94752i	0.607318	+	0.138616i	0.515111	−	0.857124i	$-0.327751\pi$
$811$	17.2952	+	3.94752i	0.607318	+	0.138616i	0.0922069	+	0.995740i	$0.470608\pi$
$812$	1.90047	+	12.7893i	0.0666934	+	0.448817i
$813$		0			0
$814$	−7.69095	−	13.3211i	−0.269568	−	0.466905i
$815$	−5.66109	+	9.80529i	−0.198299	+	0.343464i
$816$		0			0
$817$	−23.0619	+	1.72825i	−0.806835	+	0.0604639i
$818$	3.72238	−	4.66771i	0.130150	−	0.163203i
$819$		0			0
$820$	0.327770	+	0.411011i	0.0114462	+	0.0143531i
$821$	−10.0823	−	10.8661i	−0.351874	−	0.379230i	0.532167	−	0.846639i	$-0.321378\pi$
$821$	−10.0823	−	10.8661i	−0.351874	−	0.379230i	−0.884041	+	0.467410i	$0.845187\pi$
$822$		0			0
$823$	−1.77901	+	1.21291i	−0.0620123	+	0.0422793i	−0.593929	−	0.804517i	$-0.702424\pi$
$823$	−1.77901	+	1.21291i	−0.0620123	+	0.0422793i	0.531917	+	0.846796i	$0.321472\pi$
$824$	−3.43924	−	0.518383i	−0.119812	−	0.0180587i
$825$		0			0
$826$	24.3680	+	19.5160i	0.847873	+	0.679047i
$827$	13.5374	−	28.1108i	0.470742	−	0.977507i	−0.521507	−	0.853247i	$-0.674630\pi$
$827$	13.5374	−	28.1108i	0.470742	−	0.977507i	0.992250	−	0.124260i	$-0.0396557\pi$
$828$		0			0
$829$	−37.3176	+	40.2188i	−1.29610	+	1.39686i	−0.425423	+	0.904995i	$0.639875\pi$
$829$	−37.3176	+	40.2188i	−1.29610	+	1.39686i	−0.870672	+	0.491864i	$0.836316\pi$
$830$	0.0481278	+	0.00360668i	0.00167054	+	0.000125190i
$831$		0			0
$832$			3.06158i			0.106141i
$833$	17.0335	−	29.2213i	0.590175	−	1.01246i
$834$		0			0
$835$	−2.74069	+	6.98316i	−0.0948454	+	0.241662i
$836$	−0.884720	+	11.8058i	−0.0305987	+	0.408311i
$837$		0			0
$838$	−12.2463	+	17.9621i	−0.423042	+	0.620489i
$839$	34.3133	+	16.5244i	1.18463	+	0.570487i	0.919256	−	0.393659i	$-0.128791\pi$
$839$	34.3133	+	16.5244i	1.18463	+	0.570487i	0.265372	+	0.964146i	$0.414505\pi$
$840$		0			0
$841$	−4.61059	+	2.22034i	−0.158986	+	0.0765636i
$842$	−4.85673	+	32.2223i	−0.167374	+	1.11045i
$843$		0			0
$844$	−7.15024	+	1.07772i	−0.246121	+	0.0370968i
$845$	−1.39156	+	1.29118i	−0.0478711	+	0.0444179i
$846$		0			0
$847$	−13.9240	−	9.53570i	−0.478433	−	0.327650i
$848$	−0.419136	−	0.334250i	−0.0143932	−	0.0114782i
$849$		0			0
$850$	6.73096	−	21.8212i	0.230870	−	0.748462i
$851$	0.738362	+	0.426293i	0.0253107	+	0.0146131i
$852$		0			0
$853$	3.23721	−	0.738872i	0.110840	−	0.0252985i	−0.166741	−	0.986001i	$-0.553324\pi$
$853$	3.23721	−	0.738872i	0.110840	−	0.0252985i	0.277581	+	0.960702i	$0.410467\pi$
$854$	0.356453	−	0.614439i	0.0121976	−	0.0210257i
$855$		0			0
$856$	−13.7741	+	4.24876i	−0.470790	+	0.145220i
$857$	−10.0776	−	25.6774i	−0.344246	−	0.877124i	−0.993213	−	0.116308i	$-0.962894\pi$
$857$	−10.0776	−	25.6774i	−0.344246	−	0.877124i	0.648967	−	0.760816i	$-0.275201\pi$
$858$		0			0
$859$	8.00237	+	25.9431i	0.273037	+	0.885166i	0.983419	+	0.181349i	$0.0580462\pi$
$859$	8.00237	+	25.9431i	0.273037	+	0.885166i	−0.710381	+	0.703817i	$0.751478\pi$
$860$	0.489118	−	2.14297i	0.0166788	−	0.0730745i
$861$		0			0
$862$	0.442546	+	1.93892i	0.0150732	+	0.0660400i
$863$	18.5603	−	10.7158i	0.631802	−	0.364771i	−0.149648	−	0.988739i	$-0.547814\pi$
$863$	18.5603	−	10.7158i	0.631802	−	0.364771i	0.781449	+	0.623969i	$0.214481\pi$
$864$		0			0
$865$	1.71957	+	0.530416i	0.0584670	+	0.0180347i
$866$	−1.85605	−	24.7672i	−0.0630710	−	0.841624i
$867$		0			0
$868$	−2.13575	+	3.11861i	−0.0724920	+	0.105852i
$869$	15.7233	−	12.5389i	0.533376	−	0.425353i
$870$		0			0
$871$	−6.14158	−	40.7467i	−0.208100	−	1.38065i
$872$	4.72377	+	6.92850i	0.159967	+	0.234629i
$873$		0			0
$874$	−0.284716	−	0.591219i	−0.00963066	−	0.0199983i
$875$	−12.1474	+	5.81876i	−0.410657	+	0.196710i
$876$		0			0
$877$	−39.2384	−	26.7523i	−1.32499	−	0.903360i	−0.325871	−	0.945414i	$-0.605657\pi$
$877$	−39.2384	−	26.7523i	−1.32499	−	0.903360i	−0.999115	+	0.0420542i	$0.986610\pi$
$878$	−3.33815	−	3.09735i	−0.112657	−	0.104530i
$879$		0			0
$880$	−1.04745	−	0.411093i	−0.0353094	−	0.0138579i
$881$	30.2755			1.02001			0.510003	−	0.860173i	$-0.329644\pi$
$881$	30.2755			1.02001			0.510003	+	0.860173i	$0.329644\pi$
$882$		0			0
$883$	54.7945			1.84398			0.921992	−	0.387210i	$-0.126561\pi$
$883$	54.7945			1.84398			0.921992	+	0.387210i	$0.126561\pi$
$884$	−13.7707	−	5.40460i	−0.463159	−	0.181777i
$885$		0			0
$886$	17.7365	+	16.4570i	0.595868	+	0.552885i
$887$	18.3823	+	12.5328i	0.617217	+	0.420812i	0.831159	−	0.556035i	$-0.187678\pi$
$887$	18.3823	+	12.5328i	0.617217	+	0.420812i	−0.213942	+	0.976846i	$0.568630\pi$
$888$		0			0
$889$	−17.8554	+	22.2946i	−0.598849	+	0.747736i
$890$	2.45975	+	5.10772i	0.0824510	+	0.171211i
$891$		0			0
$892$	10.4895	+	15.3853i	0.351216	+	0.515139i
$893$	−9.73786	−	64.6065i	−0.325865	−	2.16197i
$894$		0			0
$895$	−4.71772	+	3.76226i	−0.157696	+	0.125758i
$896$	−2.46084	−	0.971724i	−0.0822110	−	0.0324630i
$897$		0			0
$898$	2.30875	+	30.8081i	0.0770440	+	1.02808i
$899$	6.67157	+	2.05791i	0.222509	+	0.0686351i
$900$		0			0
$901$	2.24332	−	1.29518i	0.0747359	−	0.0431488i
$902$	−0.480444	−	2.10496i	−0.0159970	−	0.0700876i
$903$		0			0
$904$	−3.21621	+	14.0911i	−0.106969	+	0.468664i
$905$	2.83958	+	9.20569i	0.0943908	+	0.306007i
$906$		0			0
$907$	19.4728	+	49.6158i	0.646583	+	1.64747i	0.756869	+	0.653566i	$0.226728\pi$
$907$	19.4728	+	49.6158i	0.646583	+	1.64747i	−0.110287	+	0.993900i	$0.535177\pi$
$908$	−2.70774	+	0.835226i	−0.0898594	+	0.0277180i
$909$		0			0
$910$	1.54077	+	3.94997i	0.0510761	+	0.130940i
$911$	−13.5084	+	3.08320i	−0.447553	+	0.102151i	−0.440357	−	0.897823i	$-0.645148\pi$
$911$	−13.5084	+	3.08320i	−0.447553	+	0.102151i	−0.00719671	+	0.999974i	$0.502291\pi$
$912$		0			0
$913$	−0.171662	−	0.0991092i	−0.00568119	−	0.00328004i
$914$	−4.25762	+	13.8029i	−0.140830	+	0.456558i
$915$		0			0
$916$	12.4264	+	9.90972i	0.410580	+	0.327426i
$917$	−4.87347	+	4.50309i	−0.160936	+	0.148705i
$918$		0			0
$919$	−9.99646	+	9.27536i	−0.329753	+	0.305966i	−0.827622	−	0.561286i	$-0.810307\pi$
$919$	−9.99646	+	9.27536i	−0.329753	+	0.305966i	0.497869	+	0.867252i	$0.334116\pi$
$920$	0.0616725	−	0.00929563i	0.00203328	−	0.000306468i
$921$		0			0
$922$	2.48372	−	16.4784i	0.0817969	−	0.542687i
$923$	−6.15842	+	2.96574i	−0.202707	+	0.0976184i
$924$		0			0
$925$	−30.4670	−	14.6721i	−1.00175	−	0.482416i
$926$	−8.81531	+	12.9297i	−0.289689	+	0.424896i
$927$		0			0
$928$	−0.365205	+	4.87332i	−0.0119884	+	0.159975i
$929$	4.99690	−	12.7319i	0.163943	−	0.417720i	−0.825169	−	0.564886i	$-0.808920\pi$
$929$	4.99690	−	12.7319i	0.163943	−	0.417720i	0.989112	+	0.147166i	$0.0470152\pi$
$930$		0			0
$931$	11.2093	+	36.8841i	0.367371	+	1.20883i
$932$		−	18.3883i		−	0.602330i
$933$		0			0
$934$	7.39574	+	0.554234i	0.241996	+	0.0181351i
$935$	3.69811	−	3.98561i	0.120941	−	0.130344i
$936$		0			0
$937$	−16.6372	+	34.5475i	−0.543513	+	1.12862i	0.430597	+	0.902544i	$0.358303\pi$
$937$	−16.6372	+	34.5475i	−0.543513	+	1.12862i	−0.974110	+	0.226073i	$0.927411\pi$
$938$	34.7008	+	7.99623i	1.13302	+	0.261086i
$939$		0			0
$940$	6.14055	+	0.925539i	0.200283	+	0.0301878i
$941$	18.6331	−	12.7038i	0.607421	−	0.414132i	−0.220172	−	0.975461i	$-0.570662\pi$
$941$	18.6331	−	12.7038i	0.607421	−	0.414132i	0.827593	+	0.561329i	$0.189710\pi$
$942$		0			0
$943$	0.0813991	+	0.0877274i	0.00265072	+	0.00285680i
$944$	7.35716	+	9.22559i	0.239455	+	0.300267i
$945$		0			0
$946$	−5.62865	+	7.05810i	−0.183003	+	0.229479i
$947$	−18.0326	+	1.35136i	−0.585982	+	0.0439133i	−0.364423	−	0.931234i	$-0.618734\pi$
$947$	−18.0326	+	1.35136i	−0.585982	+	0.0439133i	−0.221559	+	0.975147i	$0.571115\pi$
$948$		0			0
$949$	−11.9711	+	20.7345i	−0.388597	+	0.673070i
$950$	13.0134	+	22.5398i	0.422209	+	0.731288i
$951$		0			0
$952$	8.71484	−	9.35326i	0.282450	−	0.303141i
$953$	55.8525	+	12.7480i	1.80924	+	0.412947i	0.987591	−	0.157049i	$-0.0501980\pi$
$953$	55.8525	+	12.7480i	1.80924	+	0.412947i	0.821648	+	0.569996i	$0.193055\pi$
$954$		0			0
$955$	7.68373	−	3.01564i	0.248640	−	0.0975838i
$956$	−9.37731	+	3.68032i	−0.303284	+	0.119030i
$957$		0			0
$958$	−6.42003	−	1.46533i	−0.207422	−	0.0473426i
$959$	11.4905	−	36.9780i	0.371048	−	1.19408i
$960$		0			0
$961$	−14.4795	−	25.0792i	−0.467080	−	0.809007i
$962$	−10.9532	+	18.9714i	−0.353144	+	0.611664i
$963$		0			0
$964$	−26.0312	+	1.95077i	−0.838409	+	0.0628300i
$965$	−2.18225	+	2.73645i	−0.0702490	+	0.0880894i
$966$		0			0
$967$	−6.70283	−	8.40509i	−0.215549	−	0.270289i	0.662288	−	0.749249i	$-0.269585\pi$
$967$	−6.70283	−	8.40509i	−0.215549	−	0.270289i	−0.877837	+	0.478960i	$0.841014\pi$
$968$	−4.33855	−	4.67585i	−0.139446	−	0.150287i
$969$		0			0
$970$	5.02457	−	3.42569i	0.161329	−	0.109992i
$971$	6.19017	+	0.933018i	0.198652	+	0.0299420i	0.247614	−	0.968859i	$-0.420353\pi$
$971$	6.19017	+	0.933018i	0.198652	+	0.0299420i	−0.0489625	+	0.998801i	$0.515591\pi$
$972$		0			0
$973$	14.4426	−	29.8313i	0.463007	−	0.956349i
$974$	−7.76369	+	16.1215i	−0.248765	+	0.516565i
$975$		0			0
$976$	0.182617	−	0.196814i	0.00584543	−	0.00629987i
$977$	27.2398	+	2.04134i	0.871478	+	0.0653083i	0.502957	−	0.864311i	$-0.332245\pi$
$977$	27.2398	+	2.04134i	0.871478	+	0.0653083i	0.368521	+	0.929619i	$0.379864\pi$
$978$		0			0
$979$		−	23.2836i		−	0.744146i
$980$	−3.66394	−	0.0152486i	−0.117040	−	0.000487098i
$981$		0			0
$982$	−14.9830	+	38.1760i	−0.478126	+	1.21825i
$983$	4.06113	−	54.1920i	0.129530	−	1.72846i	−0.432754	−	0.901512i	$-0.642458\pi$
$983$	4.06113	−	54.1920i	0.129530	−	1.72846i	0.562284	−	0.826944i	$-0.309923\pi$
$984$		0			0
$985$	3.71204	−	5.44456i	0.118275	−	0.173478i
$986$	−21.2750	−	10.2455i	−0.677535	−	0.326284i
$987$		0			0
$988$	15.1908	−	7.31548i	0.483282	−	0.232737i
$989$	0.0745783	−	0.494795i	0.00237145	−	0.0157336i
$990$		0			0
$991$	53.2603	−	8.02770i	1.69187	−	0.255008i	0.768757	−	0.639540i	$-0.220875\pi$
$991$	53.2603	−	8.02770i	1.69187	−	0.255008i	0.923112	+	0.384532i	$0.125637\pi$
$992$	−1.04727	+	0.971723i	−0.0332508	+	0.0308522i
$993$		0			0
$994$	−0.429168	−	5.89132i	−0.0136124	−	0.186861i
$995$	−5.90195	−	4.70665i	−0.187104	−	0.149211i
$996$		0			0
$997$	16.2210	−	52.5871i	0.513723	−	1.66545i	−0.211847	−	0.977303i	$-0.567948\pi$
$997$	16.2210	−	52.5871i	0.513723	−	1.66545i	0.725571	−	0.688147i	$-0.241576\pi$
$998$	18.3218	+	10.5781i	0.579968	+	0.334845i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.395.5	✓	240
3.2	odd	2	inner	882.2.bl.a.395.16	yes	240
49.33	odd	42	inner	882.2.bl.a.719.16	yes	240
147.131	even	42	inner	882.2.bl.a.719.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.5	✓	240	1.1	even	1	trivial
882.2.bl.a.395.16	yes	240	3.2	odd	2	inner
882.2.bl.a.719.5	yes	240	147.131	even	42	inner
882.2.bl.a.719.16	yes	240	49.33	odd	42	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bl (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(0.432474 + 0.294856i) q^{5} +(-1.64529 - 2.07196i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(0.432474 + 0.294856i) q^{5} +(-1.64529 - 2.07196i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.294856 - 0.432474i) q^{10} +(0.320403 + 2.12573i) q^{11} +(2.39364 - 1.90887i) q^{13} +(0.774586 + 2.52983i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-4.61725 - 1.42423i) q^{17} +(4.76929 - 2.75355i) q^{19} +(0.116473 + 0.510302i) q^{20} +(0.478363 - 2.09584i) q^{22} +(0.0351218 + 0.113862i) q^{23} +(-1.72661 - 4.39933i) q^{25} +(-2.92557 + 0.902418i) q^{26} +(0.203207 - 2.63794i) q^{28} +(-4.76446 + 1.08746i) q^{29} +(-1.23724 - 0.714321i) q^{31} +(0.294755 - 0.955573i) q^{32} +(3.77774 + 3.01265i) q^{34} +(-0.100616 - 1.38119i) q^{35} +(5.24515 - 4.86679i) q^{37} +(-5.44560 + 0.820792i) q^{38} +(0.0780125 - 0.517579i) q^{40} +(0.904889 - 0.435771i) q^{41} +(-3.78354 - 1.82206i) q^{43} +(-1.21099 + 1.77620i) q^{44} +(0.00890452 - 0.118823i) q^{46} +(4.33440 - 11.0439i) q^{47} +(-1.58603 + 6.81795i) q^{49} +4.72603i q^{50} +(3.05302 + 0.228792i) q^{52} +(-0.364637 + 0.392985i) q^{53} +(-0.488219 + 1.01380i) q^{55} +(-1.15291 + 2.38135i) q^{56} +(4.83240 + 0.728367i) q^{58} +(9.74959 - 6.64716i) q^{59} +(-0.182617 - 0.196814i) q^{61} +(0.890744 + 1.11696i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(1.59803 - 0.119756i) q^{65} +(6.72968 - 11.6562i) q^{67} +(-2.41596 - 4.18456i) q^{68} +(-0.410945 + 1.32248i) q^{70} +(-2.17664 - 0.496803i) q^{71} +(-7.27960 + 2.85703i) q^{73} +(-6.66061 + 2.61410i) q^{74} +(5.36903 + 1.22545i) q^{76} +(3.87728 - 4.16131i) q^{77} +(-4.67750 - 8.10167i) q^{79} +(-0.261713 + 0.453299i) q^{80} +(-1.00154 + 0.0750552i) q^{82} +(-0.0574893 + 0.0720893i) q^{83} +(-1.57690 - 1.97737i) q^{85} +(2.85632 + 3.07838i) q^{86} +(1.77620 - 1.21099i) q^{88} +(-10.7099 - 1.61426i) q^{89} +(-7.89333 - 1.81889i) q^{91} +(-0.0516997 + 0.107356i) q^{92} +(-8.06956 + 8.69692i) q^{94} +(2.87450 + 0.215414i) q^{95} +11.6182i q^{97} +(3.96728 - 5.76721i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7}+O(q^{10}) \) 240 * q - 20 * q^4 - 4 * q^7	\( 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64} - 32 q^{67} - 16 q^{70} - 24 q^{73} - 28 q^{79} - 48 q^{82} - 112 q^{85} + 4 q^{88} + 80 q^{91} + 80 q^{94}+O(q^{100}) \) 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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