LMFDB - Embedded newform 882.2.bl.a.395.16

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			395.16
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.16

$q$-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	0.462744	−	0.886492i	$-0.346865\pi$
$5$	−0.432474	−	0.294856i	−0.193408	−	0.131864i	−0.656153	+	0.754628i	$0.727817\pi$
$6$		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	$-0.942562\pi$
$11$	−0.320403	−	2.12573i	−0.0966050	−	0.640932i	0.887159	−	0.461464i	$-0.152676\pi$
$12$		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	0.798776	−	0.601628i	$-0.205481\pi$
$17$	4.61725	+	1.42423i	1.11985	+	0.345427i	0.321071	+	0.947055i	$0.395957\pi$
$18$		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	0.951837	−	0.306603i	$-0.0991925\pi$
$23$	−0.0351218	−	0.113862i	−0.00732340	−	0.0237419i	−0.959161	+	0.282861i	$0.908716\pi$
$24$		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	0.244073	−	0.969757i	$-0.421516\pi$
$29$	4.76446	−	1.08746i	0.884738	−	0.201936i	0.640664	+	0.767821i	$0.278659\pi$
$30$		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	−0.503207	−	0.864166i	$-0.667847\pi$
$41$	−0.904889	+	0.435771i	−0.141320	+	0.0680561i	0.361887	+	0.932222i	$0.382132\pi$
$42$		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	$0.451901\pi$
$47$	−4.33440	+	11.0439i	−0.632237	+	1.61091i	−0.782771	+	0.622310i	$0.786194\pi$
$48$		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	−0.707511	−	0.706702i	$-0.750182\pi$
$53$	0.364637	−	0.392985i	0.0500868	−	0.0539807i	0.757598	+	0.652721i	$0.226373\pi$
$54$		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	−0.995347	−	0.0963599i	$-0.969280\pi$
$59$	−9.74959	+	6.64716i	−1.26929	+	0.865386i	−0.273942	+	0.961746i	$0.588328\pi$
$60$		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	0.349719	−	0.936855i	$-0.386277\pi$
$71$	2.17664	+	0.496803i	0.258319	+	0.0589596i	−0.0914000	+	0.995814i	$0.529134\pi$
$72$		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	−0.778666	−	0.627438i	$-0.784103\pi$
$83$	0.0574893	−	0.0720893i	0.00631027	−	0.00791282i	0.784977	+	0.619525i	$0.212675\pi$
$84$		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	0.689664	−	0.724130i	$-0.257758\pi$
$89$	10.7099	+	1.61426i	1.13525	+	0.171111i	0.445583	+	0.895241i	$0.352997\pi$
$90$		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	$-0.946330\pi$
$101$	0.140699	−	1.87750i	0.0140001	−	0.186818i	0.999819	−	0.0190074i	$-0.00605061\pi$
$102$		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	$0.292992\pi$
$107$	−2.14837	+	14.2535i	−0.207691	+	1.37794i	−0.813145	+	0.582061i	$0.802246\pi$
$108$		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	0.988762	−	0.149497i	$-0.0477656\pi$
$113$	11.3002	+	9.01161i	1.06303	+	0.847741i	0.0742710	+	0.997238i	$0.476337\pi$
$114$		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	$0.0111347\pi$
$131$	0.187419	+	2.50093i	0.0163749	+	0.218508i	−0.983013	+	0.183534i	$0.941246\pi$
$132$		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	$-0.975493\pi$
$137$	−8.24453	−	12.0925i	−0.704377	−	1.03313i	0.292660	−	0.956216i	$-0.405460\pi$
$138$		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	−0.526095	−	0.850426i	$-0.676344\pi$
$149$	−18.1900	−	7.13906i	−1.49019	−	0.584855i	−0.964091	+	0.265571i	$0.914439\pi$
$150$		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	$-0.884330\pi$
$167$	−3.18917	−	13.9727i	−0.246785	−	1.08124i	0.687913	−	0.725793i	$-0.258527\pi$
$168$		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	−0.417112	−	0.908855i	$-0.636958\pi$
$173$	−3.28522	+	1.01336i	−0.249771	+	0.0770440i	0.167342	+	0.985899i	$0.446482\pi$
$174$		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	$-0.762982\pi$
$179$	3.39802	−	11.0161i	0.253980	−	0.823383i	0.989330	−	0.145695i	$-0.0465418\pi$
$180$		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	$0.383739\pi$
$191$	−8.88345	+	13.0296i	−0.642784	+	0.942791i	−0.999962	+	0.00875455i	$0.997213\pi$
$192$		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	$0.148033\pi$
$197$			12.5893i			0.896952i	−0.893795	+	0.448476i	$0.851967\pi$
$198$		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	−0.815169	−	0.579223i	$-0.803356\pi$
$227$	1.41681	−	2.45399i	0.0940372	−	0.162877i	0.909206	+	0.416346i	$0.136689\pi$
$228$		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	0.994845	−	0.101407i	$-0.0323344\pi$
$233$	12.5072	+	13.4796i	0.819377	+	0.883078i	−0.175468	+	0.984485i	$0.556144\pi$
$234$		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	−0.710447	−	0.703750i	$-0.751507\pi$
$239$	4.37080	−	9.07606i	0.282723	−	0.587081i	0.993171	+	0.116669i	$0.0372217\pi$
$240$		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	0.347497	−	0.937681i	$-0.387032\pi$
$251$	−2.67668	−	1.28902i	−0.168950	−	0.0813622i	−0.516448	+	0.856319i	$0.672746\pi$
$252$		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	−0.286254	−	0.958154i	$-0.592410\pi$
$257$	10.3855	−	9.63632i	0.647829	−	0.601097i	0.934083	+	0.357057i	$0.116220\pi$
$258$		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	−0.374329	−	0.927296i	$-0.622127\pi$
$263$	−22.1294	−	12.7764i	−1.36456	−	0.787827i	−0.990226	+	0.139469i	$0.955460\pi$
$264$		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	0.918972	−	0.394323i	$-0.129021\pi$
$269$	−0.375421	−	0.956557i	−0.0228898	−	0.0583223i	−0.941862	+	0.336001i	$0.890926\pi$
$270$		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	−0.120393	−	0.992726i	$-0.538415\pi$
$281$	13.7567	−	10.9706i	0.820654	−	0.654450i	0.941047	+	0.338277i	$0.109844\pi$
$282$		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	$-0.289003\pi$
$293$	21.0672			1.23076			0.615379	+	0.788232i	$0.289003\pi$
$294$		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	−0.647352	−	0.762191i	$-0.724124\pi$
$311$	−28.4205	−	8.76656i	−1.61158	−	0.497106i	−0.964225	+	0.265085i	$0.914600\pi$
$312$		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	$0.0646410\pi$
$317$	5.05296	+	16.3813i	0.283803	+	0.920065i	−0.695648	+	0.718383i	$0.744883\pi$
$318$		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	−0.459956	−	0.887942i	$-0.652135\pi$
$347$	8.56654	−	9.23253i	0.459876	−	0.495628i	0.919831	+	0.392314i	$0.128325\pi$
$348$		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	−0.959734	−	0.280909i	$-0.909364\pi$
$353$	−19.7065	+	13.4357i	−1.04887	+	0.715110i	−0.0891391	+	0.996019i	$0.528412\pi$
$354$		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	−0.282888	−	0.959153i	$-0.591292\pi$
$359$	−7.95144	+	0.595878i	−0.419661	+	0.0314493i	−0.136774	+	0.990602i	$0.543673\pi$
$360$		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	0.272928	−	0.962034i	$-0.412008\pi$
$383$	4.89584	+	0.737929i	0.250166	+	0.0377064i	−0.0227621	+	0.999741i	$0.507246\pi$
$384$		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	0.471352	−	0.881945i	$-0.343766\pi$
$389$	15.8967	+	1.19129i	0.805993	+	0.0604008i	0.334640	+	0.942346i	$0.391385\pi$
$390$		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	−0.994891	−	0.100955i	$-0.967810\pi$
$401$	−0.289227	+	1.91890i	−0.0144433	+	0.0958250i	0.980448	+	0.196780i	$0.0630484\pi$
$402$		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	$0.249621\pi$
$419$	−4.83750	+	21.1945i	−0.236328	+	1.03542i	−0.944276	+	0.329155i	$0.893236\pi$
$420$		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	0.852272	−	0.523098i	$-0.175224\pi$
$431$	1.12032	+	1.64321i	0.0539640	+	0.0791507i	−0.798308	+	0.602249i	$0.794271\pi$
$432$		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	0.834008	−	0.551752i	$-0.186041\pi$
$443$	22.5228	+	8.83956i	1.07009	+	0.419980i	0.236084	+	0.971733i	$0.424136\pi$
$444$		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	$0.117158\pi$
$449$	13.4046	+	27.8350i	0.632603	+	1.31361i	−0.300423	+	0.953806i	$0.597128\pi$
$450$		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	$-0.944570\pi$
$461$	−3.70821	−	16.2467i	−0.172708	−	0.756685i	0.812168	−	0.583424i	$-0.198287\pi$
$462$		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	−0.126410	−	0.991978i	$-0.540345\pi$
$467$	7.08699	−	2.18605i	0.327947	−	0.101158i	0.454356	+	0.890820i	$0.349869\pi$
$468$		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	−0.296107	−	0.955155i	$-0.595688\pi$
$479$	−6.51158	+	0.981463i	−0.297522	+	0.0448442i	−0.00141482	+	0.999999i	$0.500450\pi$
$480$		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	$0.376270\pi$
$491$			41.0109i			1.85080i	−0.378994	+	0.925399i	$0.623730\pi$
$492$		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	$0.0292053\pi$
$503$	19.3671	+	24.2855i	0.863534	+	1.08284i	−0.132260	+	0.991215i	$0.542223\pi$
$504$		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	0.508071	−	0.861315i	$-0.330359\pi$
$509$	−11.0974	−	19.2213i	−0.491886	−	0.851971i	−0.999956	+	0.00934436i	$0.997026\pi$
$510$		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	$-0.609051\pi$
$521$	14.7848	−	25.6080i	0.647732	−	1.12190i	0.983663	−	0.180018i	$-0.0576157\pi$
$522$		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	0.410132	−	0.912026i	$-0.365483\pi$
$557$	−4.12163	−	2.37963i	−0.174639	−	0.100828i	−0.584772	+	0.811198i	$0.698816\pi$
$558$		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	0.810290	−	0.586029i	$-0.199310\pi$
$563$	−4.32544	−	11.0211i	−0.182296	−	0.464482i	−0.992586	+	0.121547i	$0.961214\pi$
$564$		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	−0.302692	−	0.953088i	$-0.597885\pi$
$569$	8.85832	−	5.11436i	0.371360	−	0.214405i	0.674053	+	0.738683i	$0.264552\pi$
$570$		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	$-0.842554\pi$
$587$	−42.6484			−1.76029			−0.880144	+	0.474708i	$0.842554\pi$
$588$		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	$0.0483158\pi$
$593$	36.2935	+	24.7445i	1.49040	+	1.01614i	0.501894	+	0.864929i	$0.332637\pi$
$594$		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	$-0.809448\pi$
$599$	−4.96345	−	32.9303i	−0.202801	−	1.34550i	0.623303	−	0.781980i	$-0.285790\pi$
$600$		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	−0.574119	−	0.818772i	$-0.694655\pi$
$617$	−18.2851	+	4.17345i	−0.736130	+	0.168017i	−0.162011	+	0.986789i	$0.551798\pi$
$618$		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	−0.973138	−	0.230222i	$-0.926055\pi$
$641$	−16.9843	+	18.3047i	−0.670838	+	0.722991i	0.302300	+	0.953213i	$0.402245\pi$
$642$		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	$0.634270\pi$
$647$	−35.8213	+	24.4225i	−1.40828	+	0.960149i	−0.998857	+	0.0478042i	$0.984778\pi$
$648$		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	−0.0830124	−	0.996549i	$-0.526454\pi$
$653$	−0.423423	+	0.0317311i	−0.0165698	+	0.00124174i	0.0664426	+	0.997790i	$0.478835\pi$
$654$		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	0.792891	−	0.609363i	$-0.208575\pi$
$659$	31.9057	+	7.28226i	1.24287	+	0.283677i	0.449977	+	0.893040i	$0.351432\pi$
$660$		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	−0.833568	−	0.552417i	$-0.813706\pi$
$677$	−46.6507	−	7.03145i	−1.79293	−	0.270241i	−0.959363	+	0.282176i	$0.908944\pi$
$678$		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	0.360922	−	0.932596i	$-0.382462\pi$
$683$	15.1269	+	1.13361i	0.578816	+	0.0433762i	0.217894	+	0.975972i	$0.430081\pi$
$684$		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	−0.194774	−	0.980848i	$-0.562397\pi$
$701$	−31.6227	−	25.2182i	−1.19437	−	0.952479i	−0.999598	+	0.0283690i	$0.990969\pi$
$702$		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	$-0.640145\pi$
$719$	−3.74296	−	49.9463i	−0.139589	−	1.86268i	0.286603	−	0.958050i	$-0.407474\pi$
$720$		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	0.703148	−	0.711043i	$-0.251777\pi$
$743$	−7.93682	−	16.4810i	−0.291174	−	0.604628i	−0.994322	+	0.106415i	$0.966063\pi$
$744$		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	−0.643844	−	0.765157i	$-0.722661\pi$
$761$	−20.5458	+	6.33754i	−0.744784	+	0.229736i	−0.100940	+	0.994892i	$0.532185\pi$
$762$		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	0.0606580	−	0.998159i	$-0.480680\pi$
$773$	11.4780	−	1.73002i	0.412834	−	0.0622246i	0.352176	+	0.935934i	$0.385442\pi$
$774$		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	0.989108	−	0.147195i	$-0.0470244\pi$
$797$	17.6588	+	22.1434i	0.625506	+	0.784360i	−0.363602	+	0.931555i	$0.618453\pi$
$798$		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	−0.580325	−	0.814385i	$-0.697074\pi$
$809$	−12.8508	+	5.04356i	−0.451810	+	0.177322i	0.128515	+	0.991708i	$0.458979\pi$
$810$		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	0.884041	−	0.467410i	$-0.154813\pi$
$821$	10.0823	+	10.8661i	0.351874	+	0.379230i	−0.532167	+	0.846639i	$0.678622\pi$
$822$		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	$0.325370\pi$
$827$	−13.5374	+	28.1108i	−0.470742	+	0.977507i	−0.992250	+	0.124260i	$0.960344\pi$
$828$		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	−0.265372	−	0.964146i	$-0.585495\pi$
$839$	−34.3133	−	16.5244i	−1.18463	−	0.570487i	−0.919256	+	0.393659i	$0.871209\pi$
$840$		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	$0.0371060\pi$
$857$	10.0776	+	25.6774i	0.344246	+	0.877124i	−0.648967	+	0.760816i	$0.724799\pi$
$858$		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	−0.781449	−	0.623969i	$-0.785519\pi$
$863$	−18.5603	+	10.7158i	−0.631802	+	0.364771i	0.149648	+	0.988739i	$0.452186\pi$
$864$		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	$-0.670356\pi$
$881$	−30.2755			−1.02001			−0.510003	+	0.860173i	$0.670356\pi$
$882$		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	0.213942	−	0.976846i	$-0.431370\pi$
$887$	−18.3823	−	12.5328i	−0.617217	−	0.420812i	−0.831159	+	0.556035i	$0.812322\pi$
$888$		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	0.00719671	−	0.999974i	$-0.497709\pi$
$911$	13.5084	−	3.08320i	0.447553	−	0.102151i	0.440357	+	0.897823i	$0.354852\pi$
$912$		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	−0.989112	−	0.147166i	$-0.952985\pi$
$929$	−4.99690	+	12.7319i	−0.163943	+	0.417720i	0.825169	+	0.564886i	$0.191080\pi$
$930$		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	−0.827593	−	0.561329i	$-0.810290\pi$
$941$	−18.6331	+	12.7038i	−0.607421	+	0.414132i	0.220172	+	0.975461i	$0.429338\pi$
$942$		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	0.221559	−	0.975147i	$-0.428885\pi$
$947$	18.0326	−	1.35136i	0.585982	−	0.0439133i	0.364423	+	0.931234i	$0.381266\pi$
$948$		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	−0.821648	−	0.569996i	$-0.806945\pi$
$953$	−55.8525	−	12.7480i	−1.80924	−	0.412947i	−0.987591	+	0.157049i	$0.949802\pi$
$954$		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	0.0489625	−	0.998801i	$-0.484409\pi$
$971$	−6.19017	−	0.933018i	−0.198652	−	0.0299420i	−0.247614	+	0.968859i	$0.579647\pi$
$972$		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	−0.368521	−	0.929619i	$-0.620136\pi$
$977$	−27.2398	−	2.04134i	−0.871478	−	0.0653083i	−0.502957	+	0.864311i	$0.667755\pi$
$978$		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	$0.357542\pi$
$983$	−4.06113	+	54.1920i	−0.129530	+	1.72846i	−0.562284	+	0.826944i	$0.690077\pi$
$984$		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.395.16	yes	240
3.2	odd	2	inner	882.2.bl.a.395.5	✓	240
49.33	odd	42	inner	882.2.bl.a.719.5	yes	240
147.131	even	42	inner	882.2.bl.a.719.16	yes	240

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