LMFDB - Embedded newform 639.2.z.a.35.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			35.14
Character	$\chi$	$=$	639.35
Dual form			639.2.z.a.566.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.106529 - 0.00478422i) q^{2} +(-1.98062 + 0.178259i) q^{4} +(-0.619962 - 0.201438i) q^{5} +(-0.0215270 - 0.0780015i) q^{7} +(-0.421483 + 0.0570938i) q^{8} +O(q^{10})$	\(q+(0.106529 - 0.00478422i) q^{2} +(-1.98062 + 0.178259i) q^{4} +(-0.619962 - 0.201438i) q^{5} +(-0.0215270 - 0.0780015i) q^{7} +(-0.421483 + 0.0570938i) q^{8} +(-0.0670076 - 0.0184929i) q^{10} +(1.23013 + 2.28596i) q^{11} +(-1.92504 - 1.03591i) q^{13} +(-0.00266643 - 0.00820642i) q^{14} +(3.86871 - 0.702068i) q^{16} +(5.32011 - 3.86529i) q^{17} +(2.21898 - 5.19156i) q^{19} +(1.26382 + 0.288459i) q^{20} +(0.141981 + 0.237635i) q^{22} +(3.47891 - 4.36242i) q^{23} +(-3.70131 - 2.68916i) q^{25} +(-0.210029 - 0.101144i) q^{26} +(0.0565415 + 0.150654i) q^{28} +(-4.65531 + 7.79167i) q^{29} +(1.90992 - 10.5245i) q^{31} +(1.23811 - 0.282590i) q^{32} +(0.548253 - 0.437218i) q^{34} +(-0.00236651 + 0.0526944i) q^{35} +(-1.73938 - 2.18111i) q^{37} +(0.211548 - 0.563667i) q^{38} +(0.272804 + 0.0495067i) q^{40} +(6.96427 - 3.35381i) q^{41} +(-6.71268 + 2.51931i) q^{43} +(-2.84391 - 4.30834i) q^{44} +(0.349734 - 0.481367i) q^{46} +(6.19842 + 5.41539i) q^{47} +(6.00352 - 3.58694i) q^{49} +(-0.407162 - 0.268765i) q^{50} +(3.99744 + 1.70859i) q^{52} +(8.21087 + 0.738992i) q^{53} +(-0.302153 - 1.66500i) q^{55} +(0.0135267 + 0.0316472i) q^{56} +(-0.458648 + 0.852310i) q^{58} +(-0.998534 + 1.04438i) q^{59} +(1.42392 - 5.15947i) q^{61} +(0.153110 - 1.13030i) q^{62} +(-7.44987 + 2.05603i) q^{64} +(0.984782 + 1.03000i) q^{65} +(-0.365764 - 4.06397i) q^{67} +(-9.84812 + 8.60404i) q^{68} +0.00562479i q^{70} +(-7.68706 - 3.45095i) q^{71} +(0.592849 + 13.2008i) q^{73} +(-0.195729 - 0.224030i) q^{74} +(-3.46952 + 10.6781i) q^{76} +(0.151827 - 0.145162i) q^{77} +(1.39388 + 10.2900i) q^{79} +(-2.53988 - 0.344050i) q^{80} +(0.725850 - 0.390597i) q^{82} +(-4.96061 - 4.74283i) q^{83} +(-4.07689 + 1.32466i) q^{85} +(-0.703041 + 0.300494i) q^{86} +(-0.648992 - 0.893260i) q^{88} +(1.14491 - 12.7210i) q^{89} +(-0.0393620 + 0.172456i) q^{91} +(-6.11277 + 9.26046i) q^{92} +(0.686219 + 0.547241i) q^{94} +(-2.42146 + 2.77159i) q^{95} +(7.16402 - 14.8762i) q^{97} +(0.622388 - 0.410834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{29}{70}\right)$	$-1$

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 $

$2$	0.106529	−	0.00478422i	0.0753273	−	0.00338295i	−0.00716929	−	0.999974i	$-0.502282\pi$
$2$	0.106529	−	0.00478422i	0.0753273	−	0.00338295i	0.0824966	+	0.996591i	$0.473711\pi$
$3$		0			0
$3$		0			0
$4$	−1.98062	+	0.178259i	−0.990312	+	0.0891297i
$5$	−0.619962	−	0.201438i	−0.277256	−	0.0900858i	0.167089	−	0.985942i	$-0.446563\pi$
$5$	−0.619962	−	0.201438i	−0.277256	−	0.0900858i	−0.444344	+	0.895856i	$0.646563\pi$
$6$		0			0
$7$	−0.0215270	−	0.0780015i	−0.00813646	−	0.0294818i	0.959782	−	0.280747i	$-0.0905821\pi$
$7$	−0.0215270	−	0.0780015i	−0.00813646	−	0.0294818i	−0.967918	+	0.251265i	$0.919153\pi$
$8$	−0.421483	+	0.0570938i	−0.149017	+	0.0201857i
$9$		0			0
$10$	−0.0670076	−	0.0184929i	−0.0211897	−	0.00584798i
$11$	1.23013	+	2.28596i	0.370897	+	0.689242i	0.995809	−	0.0914525i	$-0.0291510\pi$
$11$	1.23013	+	2.28596i	0.370897	+	0.689242i	−0.624912	+	0.780695i	$0.714865\pi$
$12$		0			0
$13$	−1.92504	−	1.03591i	−0.533910	−	0.287309i	0.184614	−	0.982811i	$-0.440896\pi$
$13$	−1.92504	−	1.03591i	−0.533910	−	0.287309i	−0.718525	+	0.695502i	$0.755182\pi$
$14$	−0.00266643	−	0.00820642i	−0.000712633	−	0.00219326i
$15$		0			0
$16$	3.86871	−	0.702068i	0.967179	−	0.175517i
$17$	5.32011	−	3.86529i	1.29032	−	0.937470i	0.290506	−	0.956873i	$-0.406177\pi$
$17$	5.32011	−	3.86529i	1.29032	−	0.937470i	0.999812	+	0.0194030i	$0.00617654\pi$
$18$		0			0
$19$	2.21898	−	5.19156i	0.509069	−	1.19103i	−0.446105	−	0.894981i	$-0.647189\pi$
$19$	2.21898	−	5.19156i	0.509069	−	1.19103i	0.955174	−	0.296045i	$-0.0956679\pi$
$20$	1.26382	+	0.288459i	0.282599	+	0.0645013i
$21$		0			0
$22$	0.141981	+	0.237635i	0.0302704	+	0.0506640i
$23$	3.47891	−	4.36242i	0.725403	−	0.909627i	−0.273227	−	0.961950i	$-0.588091\pi$
$23$	3.47891	−	4.36242i	0.725403	−	0.909627i	0.998630	+	0.0523225i	$0.0166624\pi$
$24$		0			0
$25$	−3.70131	−	2.68916i	−0.740262	−	0.537832i
$26$	−0.210029	−	0.101144i	−0.0411900	−	0.0198360i
$27$		0			0
$28$	0.0565415	+	0.150654i	0.0106853	+	0.0284710i
$29$	−4.65531	+	7.79167i	−0.864469	+	1.44688i	0.0299026	+	0.999553i	$0.490480\pi$
$29$	−4.65531	+	7.79167i	−0.864469	+	1.44688i	−0.894372	+	0.447325i	$0.852377\pi$
$30$		0			0
$31$	1.90992	−	10.5245i	0.343031	−	1.89026i	−0.102071	−	0.994777i	$-0.532547\pi$
$31$	1.90992	−	10.5245i	0.343031	−	1.89026i	0.445102	−	0.895480i	$-0.353167\pi$
$32$	1.23811	−	0.282590i	0.218869	−	0.0499553i
$33$		0			0
$34$	0.548253	−	0.437218i	0.0940247	−	0.0749822i
$35$	−0.00236651	+	0.0526944i	−0.000400013	+	0.00890697i
$36$		0			0
$37$	−1.73938	−	2.18111i	−0.285952	−	0.358573i	0.618021	−	0.786161i	$-0.287935\pi$
$37$	−1.73938	−	2.18111i	−0.285952	−	0.358573i	−0.903973	+	0.427589i	$0.859363\pi$
$38$	0.211548	−	0.563667i	0.0343176	−	0.0914389i
$39$		0			0
$40$	0.272804	+	0.0495067i	0.0431342	+	0.00782770i
$41$	6.96427	−	3.35381i	1.08764	−	0.523778i	0.197885	−	0.980225i	$-0.436593\pi$
$41$	6.96427	−	3.35381i	1.08764	−	0.523778i	0.889750	+	0.456447i	$0.150878\pi$
$42$		0			0
$43$	−6.71268	+	2.51931i	−1.02367	+	0.384191i	−0.806054	−	0.591842i	$-0.798401\pi$
$43$	−6.71268	+	2.51931i	−1.02367	+	0.384191i	−0.217620	+	0.976034i	$0.569829\pi$
$44$	−2.84391	−	4.30834i	−0.428736	−	0.649507i
$45$		0			0
$46$	0.349734	−	0.481367i	0.0515654	−	0.0709738i
$47$	6.19842	+	5.41539i	0.904132	+	0.789916i	0.978271	−	0.207332i	$-0.0664780\pi$
$47$	6.19842	+	5.41539i	0.904132	+	0.789916i	−0.0741389	+	0.997248i	$0.523621\pi$
$48$		0			0
$49$	6.00352	−	3.58694i	0.857646	−	0.512420i
$50$	−0.407162	−	0.268765i	−0.0575814	−	0.0380091i
$51$		0			0
$52$	3.99744	+	1.70859i	0.554345	+	0.236939i
$53$	8.21087	+	0.738992i	1.12785	+	0.101508i	0.637812	−	0.770192i	$-0.279840\pi$
$53$	8.21087	+	0.738992i	1.12785	+	0.101508i	0.490039	+	0.871701i	$0.336983\pi$
$54$		0			0
$55$	−0.302153	−	1.66500i	−0.0407424	−	0.224509i
$56$	0.0135267	+	0.0316472i	0.00180758	+	0.00422904i
$57$		0			0
$58$	−0.458648	+	0.852310i	−0.0602234	+	0.111914i
$59$	−0.998534	+	1.04438i	−0.129998	+	0.135967i	−0.784590	−	0.620015i	$-0.787126\pi$
$59$	−0.998534	+	1.04438i	−0.129998	+	0.135967i	0.654592	+	0.755983i	$0.272841\pi$
$60$		0			0
$61$	1.42392	−	5.15947i	0.182315	−	0.660602i	−0.814450	−	0.580233i	$-0.802961\pi$
$61$	1.42392	−	5.15947i	0.182315	−	0.660602i	0.996765	−	0.0803693i	$-0.0256100\pi$
$62$	0.153110	−	1.13030i	0.0194449	−	0.143548i
$63$		0			0
$64$	−7.44987	+	2.05603i	−0.931234	+	0.257004i
$65$	0.984782	+	1.03000i	0.122147	+	0.127756i
$66$		0			0
$67$	−0.365764	−	4.06397i	−0.0446852	−	0.496493i	−0.986883	−	0.161436i	$-0.948387\pi$
$67$	−0.365764	−	4.06397i	−0.0446852	−	0.496493i	0.942198	−	0.335057i	$-0.108756\pi$
$68$	−9.84812	+	8.60404i	−1.19426	+	1.04339i
$69$		0			0
$70$			0.00562479i			0.000672291i
$71$	−7.68706	−	3.45095i	−0.912286	−	0.409553i
$71$	−7.68706	−	3.45095i	−0.912286	−	0.409553i
$72$		0			0
$73$	0.592849	+	13.2008i	0.0693877	+	1.54504i	0.668099	+	0.744073i	$0.267108\pi$
$73$	0.592849	+	13.2008i	0.0693877	+	1.54504i	−0.598711	+	0.800965i	$0.704320\pi$
$74$	−0.195729	−	0.224030i	−0.0227530	−	0.0260429i
$75$		0			0
$76$	−3.46952	+	10.6781i	−0.397981	+	1.22486i
$77$	0.151827	−	0.145162i	0.0173023	−	0.0165427i
$78$		0			0
$79$	1.39388	+	10.2900i	0.156823	+	1.15772i	0.882715	+	0.469908i	$0.155713\pi$
$79$	1.39388	+	10.2900i	0.156823	+	1.15772i	−0.725892	+	0.687809i	$0.758573\pi$
$80$	−2.53988	−	0.344050i	−0.283967	−	0.0384660i
$81$		0			0
$82$	0.725850	−	0.390597i	0.0801567	−	0.0431342i
$83$	−4.96061	−	4.74283i	−0.544497	−	0.520593i	0.367918	−	0.929858i	$-0.380071\pi$
$83$	−4.96061	−	4.74283i	−0.544497	−	0.520593i	−0.912415	+	0.409265i	$0.865785\pi$
$84$		0			0
$85$	−4.07689	+	1.32466i	−0.442200	+	0.143680i
$86$	−0.703041	+	0.300494i	−0.0758109	+	0.0324031i
$87$		0			0
$88$	−0.648992	−	0.893260i	−0.0691827	−	0.0952219i
$89$	1.14491	−	12.7210i	0.121360	−	1.34843i	−0.672397	−	0.740191i	$-0.734735\pi$
$89$	1.14491	−	12.7210i	0.121360	−	1.34843i	0.793757	−	0.608234i	$-0.208122\pi$
$90$		0			0
$91$	−0.0393620	+	0.172456i	−0.00412626	+	0.0180783i
$92$	−6.11277	+	9.26046i	−0.637301	+	0.965469i
$93$		0			0
$94$	0.686219	+	0.547241i	0.0707780	+	0.0564436i
$95$	−2.42146	+	2.77159i	−0.248437	+	0.284359i
$96$		0			0
$97$	7.16402	−	14.8762i	0.727396	−	1.51045i	−0.127604	−	0.991825i	$-0.540729\pi$
$97$	7.16402	−	14.8762i	0.727396	−	1.51045i	0.855000	−	0.518628i	$-0.173557\pi$
$98$	0.622388	−	0.410834i	0.0628706	−	0.0415005i
$99$		0			0
$100$	7.81027	+	4.66642i	0.781027	+	0.466642i
$101$	4.02253	+	8.35288i	0.400257	+	0.831142i	0.999532	+	0.0305989i	$0.00974147\pi$
$101$	4.02253	+	8.35288i	0.400257	+	0.831142i	−0.599275	+	0.800544i	$0.704544\pi$
$102$		0			0
$103$	3.57667	+	15.6704i	0.352420	+	1.54405i	0.771576	+	0.636137i	$0.219469\pi$
$103$	3.57667	+	15.6704i	0.352420	+	1.54405i	−0.419157	+	0.907914i	$0.637674\pi$
$104$	0.870516	+	0.326710i	0.0853611	+	0.0320366i
$105$		0			0
$106$	0.878231	+	0.0394414i	0.0853013	+	0.00383089i
$107$	−14.5618	−	0.653969i	−1.40774	−	0.0632216i	−0.672032	−	0.740522i	$-0.734578\pi$
$107$	−14.5618	−	0.653969i	−1.40774	−	0.0632216i	−0.735706	+	0.677301i	$0.763150\pi$
$108$		0			0
$109$	−10.5542	−	3.96105i	−1.01091	−	0.379400i	−0.209687	−	0.977769i	$-0.567244\pi$
$109$	−10.5542	−	3.96105i	−1.01091	−	0.379400i	−0.801221	+	0.598369i	$0.795816\pi$
$110$	−0.0401538	−	0.175925i	−0.00382851	−	0.0167738i
$111$		0			0
$112$	−0.138044	−	0.286652i	−0.0130440	−	0.0270861i
$113$	1.59999	+	0.955947i	0.150514	+	0.0899280i	0.586182	−	0.810180i	$-0.300631\pi$
$113$	1.59999	+	0.955947i	0.150514	+	0.0899280i	−0.435668	+	0.900108i	$0.643488\pi$
$114$		0			0
$115$	−3.03555	+	2.00375i	−0.283067	+	0.186851i
$116$	7.83147	−	16.2622i	0.727134	−	1.50991i
$117$		0			0
$118$	−0.101376	+	0.116034i	−0.00933243	+	0.0106818i
$119$	−0.416025	−	0.331769i	−0.0381369	−	0.0304132i
$120$		0			0
$121$	2.34747	−	3.55627i	0.213407	−	0.323297i
$122$	0.127005	−	0.556445i	0.0114985	−	0.0503781i
$123$		0			0
$124$	−1.90673	+	21.1855i	−0.171230	+	1.90252i
$125$	3.66876	+	5.04962i	0.328144	+	0.451652i
$126$		0			0
$127$	0.772230	−	0.330067i	0.0685243	−	0.0292887i	−0.358490	−	0.933534i	$-0.616708\pi$
$127$	0.772230	−	0.330067i	0.0685243	−	0.0292887i	0.427014	+	0.904245i	$0.359565\pi$
$128$	−3.19937	+	1.03954i	−0.282787	+	0.0918832i
$129$		0			0
$130$	0.109835	+	0.105013i	0.00963321	+	0.00921029i
$131$	−2.38000	+	1.28074i	−0.207942	+	0.111898i	−0.574525	−	0.818487i	$-0.694813\pi$
$131$	−2.38000	+	1.28074i	−0.207942	+	0.111898i	0.366583	+	0.930385i	$0.380528\pi$
$132$		0			0
$133$	−0.452718	−	0.0613248i	−0.0392556	−	0.00531753i
$134$	−0.0584074	−	0.431181i	−0.00504563	−	0.0372483i
$135$		0			0
$136$	−2.02165	+	1.93290i	−0.173355	+	0.165745i
$137$	−0.557394	+	1.71548i	−0.0476213	+	0.146563i	−0.972040	−	0.234817i	$-0.924551\pi$
$137$	−0.557394	+	1.71548i	−0.0476213	+	0.146563i	0.924418	+	0.381380i	$0.124551\pi$
$138$		0			0
$139$	0.240881	+	0.275711i	0.0204313	+	0.0233855i	0.763196	−	0.646167i	$-0.223629\pi$
$139$	0.240881	+	0.275711i	0.0204313	+	0.0233855i	−0.742765	+	0.669552i	$0.766486\pi$
$140$	−0.00470610	−	0.104789i	−0.000397738	−	0.00885633i
$141$		0			0
$142$	−0.835404	−	0.330850i	−0.0701056	−	0.0277643i
$143$		−	5.67486i		−	0.474556i
$144$		0			0
$145$	4.45565	−	3.89279i	0.370022	−	0.323278i
$146$	0.126311	+	1.40343i	0.0104536	+	0.116149i
$147$		0			0
$148$	3.83386	+	4.00990i	0.315141	+	0.329612i
$149$	−7.47638	+	2.06335i	−0.612489	+	0.169036i	−0.558499	−	0.829505i	$-0.688623\pi$
$149$	−7.47638	+	2.06335i	−0.612489	+	0.169036i	−0.0539902	+	0.998541i	$0.517194\pi$
$150$		0			0
$151$	−0.763847	+	5.63894i	−0.0621610	+	0.458891i	0.932940	+	0.360031i	$0.117234\pi$
$151$	−0.763847	+	5.63894i	−0.0621610	+	0.458891i	−0.995101	+	0.0988599i	$0.968480\pi$
$152$	−0.638857	+	2.31485i	−0.0518181	+	0.187759i
$153$		0			0
$154$	0.0154795	−	0.0161903i	0.00124737	−	0.00130465i
$155$	−3.30411	+	6.14007i	−0.265393	+	0.493182i
$156$		0			0
$157$	0.0946927	+	0.221545i	0.00755730	+	0.0176812i	0.923264	−	0.384166i	$-0.125511\pi$
$157$	0.0946927	+	0.221545i	0.00755730	+	0.0176812i	−0.915707	+	0.401847i	$0.868368\pi$
$158$	0.197718	+	1.08952i	0.0157296	+	0.0866772i
$159$		0			0
$160$	−0.824505	−	0.0742068i	−0.0651828	−	0.00586656i
$161$	−0.415166	−	0.177450i	−0.0327197	−	0.0139851i
$162$		0			0
$163$	−1.23322	−	0.814042i	−0.0965933	−	0.0637607i	0.501677	−	0.865055i	$-0.332717\pi$
$163$	−1.23322	−	0.814042i	−0.0965933	−	0.0637607i	−0.598270	+	0.801294i	$0.704145\pi$
$164$	−13.1957	+	7.88409i	−1.03041	+	0.615644i
$165$		0			0
$166$	−0.551139	−	0.481515i	−0.0427767	−	0.0373728i
$167$	5.85693	−	8.06138i	0.453223	−	0.623808i	−0.519863	−	0.854250i	$-0.674017\pi$
$167$	5.85693	−	8.06138i	0.453223	−	0.623808i	0.973086	+	0.230442i	$0.0740171\pi$
$168$		0			0
$169$	−4.52898	−	6.86112i	−0.348383	−	0.527778i
$170$	−0.427969	+	0.160619i	−0.0328237	+	0.0123189i
$171$		0			0
$172$	12.8462	−	6.18640i	0.979513	−	0.471709i
$173$	−15.2360	−	2.76492i	−1.15837	−	0.210213i	−0.434840	−	0.900508i	$-0.643195\pi$
$173$	−15.2360	−	2.76492i	−1.15837	−	0.210213i	−0.723528	+	0.690295i	$0.757481\pi$
$174$		0			0
$175$	−0.130080	+	0.346597i	−0.00983313	+	0.0262003i
$176$	6.36391	+	7.98009i	0.479698	+	0.601522i
$177$		0			0
$178$	0.0611061	−	1.36063i	0.00458010	−	0.101984i
$179$	15.9548	−	12.7235i	1.19252	−	0.951000i	0.192973	−	0.981204i	$-0.438187\pi$
$179$	15.9548	−	12.7235i	1.19252	−	0.951000i	0.999544	+	0.0302038i	$0.00961562\pi$
$180$		0			0
$181$	−1.07973	+	0.246442i	−0.0802559	+	0.0183179i	−0.262460	−	0.964943i	$-0.584534\pi$
$181$	−1.07973	+	0.246442i	−0.0802559	+	0.0183179i	0.182204	+	0.983261i	$0.441677\pi$
$182$	−0.00336812	+	0.0185599i	−0.000249662	+	0.00137575i
$183$		0			0
$184$	−1.21724	+	2.03731i	−0.0897358	+	0.150192i
$185$	0.638991	+	1.70258i	0.0469795	+	0.125177i
$186$		0			0
$187$	15.3803	+	7.40677i	1.12472	+	0.541636i
$188$	−13.2421	−	9.62093i	−0.965777	−	0.701678i
$189$		0			0
$190$	−0.244696	+	0.306839i	−0.0177521	+	0.0222604i
$191$	1.25896	+	2.10714i	0.0910951	+	0.152468i	0.900605	−	0.434639i	$-0.143124\pi$
$191$	1.25896	+	2.10714i	0.0910951	+	0.152468i	−0.809510	+	0.587107i	$0.800267\pi$
$192$		0			0
$193$	−17.3114	−	3.95122i	−1.24610	−	0.284415i	−0.451901	−	0.892068i	$-0.649254\pi$
$193$	−17.3114	−	3.95122i	−1.24610	−	0.284415i	−0.794203	+	0.607653i	$0.792111\pi$
$194$	0.692004	−	1.61902i	0.0496830	−	0.116239i
$195$		0			0
$196$	−11.2513	+	8.17455i	−0.803665	+	0.583897i
$197$	15.6375	−	2.83779i	1.11413	−	0.202184i	0.409880	−	0.912140i	$-0.365571\pi$
$197$	15.6375	−	2.83779i	1.11413	−	0.202184i	0.704247	+	0.709955i	$0.251285\pi$
$198$		0			0
$199$	5.18093	+	15.9453i	0.367267	+	1.13033i	0.948549	+	0.316629i	$0.102551\pi$
$199$	5.18093	+	15.9453i	0.367267	+	1.13033i	−0.581283	+	0.813702i	$0.697449\pi$
$200$	1.71357	+	0.922113i	0.121168	+	0.0652032i
$201$		0			0
$202$	0.468478	+	0.870578i	0.0329620	+	0.0612537i
$203$	0.707977	+	0.195389i	0.0496903	+	0.0137136i
$204$		0			0
$205$	−4.99317	+	0.676371i	−0.348738	+	0.0472398i
$206$	0.455989	+	1.65224i	0.0317703	+	0.115117i
$207$		0			0
$208$	−8.17471	−	2.65613i	−0.566814	−	0.184169i
$209$	14.5973	−	1.31378i	1.00972	−	0.0908763i
$210$		0			0
$211$	26.2712	−	1.17984i	1.80858	−	0.0812235i	0.885224	−	0.465165i	$-0.154005\pi$
$211$	26.2712	−	1.17984i	1.80858	−	0.0812235i	0.923357	+	0.383941i	$0.125434\pi$
$212$	−16.3944			−1.12597
$213$		0			0
$214$	−1.55438			−0.106255
$215$	4.66909	−	0.209689i	0.318429	−	0.0143007i
$216$		0			0
$217$	−0.862042	+	0.0775852i	−0.0585192	+	0.00526682i
$218$	−1.14328	−	0.371473i	−0.0774324	−	0.0251593i
$219$		0			0
$220$	0.895254	+	3.24388i	0.0603580	+	0.218702i
$221$	−14.2455	+	1.92969i	−0.958258	+	0.129805i
$222$		0			0
$223$	−10.2470	−	2.82800i	−0.686193	−	0.189377i	−0.0944809	−	0.995527i	$-0.530119\pi$
$223$	−10.2470	−	2.82800i	−0.686193	−	0.189377i	−0.591712	+	0.806149i	$0.701548\pi$
$224$	−0.0486952	−	0.0904909i	−0.00325359	−	0.00604618i
$225$		0			0
$226$	0.175018	+	0.0941813i	0.0116420	+	0.00626485i
$227$	7.64107	+	23.5168i	0.507156	+	1.56086i	0.797116	+	0.603826i	$0.206358\pi$
$227$	7.64107	+	23.5168i	0.507156	+	1.56086i	−0.289961	+	0.957039i	$0.593642\pi$
$228$		0			0
$229$	−9.68111	+	1.75686i	−0.639746	+	0.116097i	−0.488731	−	0.872435i	$-0.662540\pi$
$229$	−9.68111	+	1.75686i	−0.639746	+	0.116097i	−0.151015	+	0.988531i	$0.548254\pi$
$230$	−0.313788	+	0.227980i	−0.0206905	+	0.0150326i
$231$		0			0
$232$	1.51728	−	3.54985i	0.0996142	−	0.233059i
$233$	−18.5528	−	4.23455i	−1.21543	−	0.277414i	−0.433716	−	0.901050i	$-0.642798\pi$
$233$	−18.5528	−	4.23455i	−1.21543	−	0.277414i	−0.781715	+	0.623635i	$0.785655\pi$
$234$		0			0
$235$	−2.75192	−	4.60594i	−0.179515	−	0.300458i
$236$	1.79155	−	2.24653i	0.116620	−	0.146237i
$237$		0			0
$238$	−0.0459059	−	0.0333526i	−0.00297564	−	0.00216193i
$239$	−0.779229	−	0.375257i	−0.0504041	−	0.0242733i	0.408512	−	0.912753i	$-0.366048\pi$
$239$	−0.779229	−	0.375257i	−0.0504041	−	0.0242733i	−0.458916	+	0.888480i	$0.651762\pi$
$240$		0			0
$241$	−4.19816	−	11.1859i	−0.270427	−	0.720550i	−0.999353	−	0.0359581i	$-0.988552\pi$
$241$	−4.19816	−	11.1859i	−0.270427	−	0.720550i	0.728926	−	0.684592i	$-0.240020\pi$
$242$	0.233060	−	0.390076i	0.0149816	−	0.0250750i
$243$		0			0
$244$	−1.90053	+	10.4728i	−0.121669	+	0.670452i
$245$	−4.44450	+	1.01443i	−0.283949	+	0.0648095i
$246$		0			0
$247$	−9.64961	+	7.69531i	−0.613990	+	0.489641i
$248$	−0.204114	+	4.54494i	−0.0129612	+	0.288604i
$249$		0			0
$250$	0.414988	+	0.520378i	0.0262461	+	0.0329116i
$251$	−3.29257	+	8.77303i	−0.207825	+	0.553749i	−0.998271	−	0.0587839i	$-0.981278\pi$
$251$	−3.29257	+	8.77303i	−0.207825	+	0.553749i	0.790445	+	0.612532i	$0.209849\pi$
$252$		0			0
$253$	14.2518	+	2.58632i	0.896004	+	0.162601i
$254$	0.0806857	−	0.0388562i	0.00506267	−	0.00243805i
$255$		0			0
$256$	14.1353	−	5.30507i	0.883457	−	0.331567i
$257$	6.61686	+	10.0241i	0.412749	+	0.625288i	0.980174	−	0.198137i	$-0.0634891\pi$
$257$	6.61686	+	10.0241i	0.412749	+	0.625288i	−0.567426	+	0.823425i	$0.692061\pi$
$258$		0			0
$259$	−0.132686	+	0.182627i	−0.00824473	+	0.0113479i
$260$	−2.13409	−	1.86450i	−0.132351	−	0.115631i
$261$		0			0
$262$	−0.247412	+	0.147822i	−0.0152852	+	0.00913246i
$263$	−0.502766	−	0.331873i	−0.0310019	−	0.0204642i	0.535301	−	0.844661i	$-0.320198\pi$
$263$	−0.502766	−	0.331873i	−0.0310019	−	0.0204642i	−0.566303	+	0.824197i	$0.691627\pi$
$264$		0			0
$265$	−4.94157	−	2.11213i	−0.303558	−	0.129747i
$266$	−0.0485209	−	0.00436696i	−0.00297501	−	0.000267755i
$267$		0			0
$268$	1.44888	+	7.98400i	0.0885046	+	0.487700i
$269$	−7.26977	−	17.0085i	−0.443246	−	1.03702i	−0.981015	−	0.193933i	$-0.937876\pi$
$269$	−7.26977	−	17.0085i	−0.443246	−	1.03702i	0.537769	−	0.843092i	$-0.319267\pi$
$270$		0			0
$271$	−4.18327	+	7.77381i	−0.254115	+	0.472225i	−0.975409	−	0.220404i	$-0.929262\pi$
$271$	−4.18327	+	7.77381i	−0.254115	+	0.472225i	0.721293	+	0.692630i	$0.243548\pi$
$272$	17.8683	−	18.6888i	1.08343	−	1.13317i
$273$		0			0
$274$	−0.0511713	+	0.185415i	−0.00309137	+	0.0112013i
$275$	1.59423	−	11.7690i	0.0961354	−	0.709700i
$276$		0			0
$277$	21.9729	−	6.06413i	1.32022	−	0.364358i	0.466239	−	0.884659i	$-0.345609\pi$
$277$	21.9729	−	6.06413i	1.32022	−	0.364358i	0.853983	+	0.520301i	$0.174180\pi$
$278$	0.0269799	+	0.0282187i	0.00161814	+	0.00169245i
$279$		0			0
$280$	−0.00201108	−	0.0223449i	−0.000120185	−	0.00133536i
$281$	15.6179	−	13.6450i	0.931688	−	0.813991i	−0.0511065	−	0.998693i	$-0.516275\pi$
$281$	15.6179	−	13.6450i	0.931688	−	0.813991i	0.982795	+	0.184702i	$0.0591319\pi$
$282$		0			0
$283$		−	5.85346i		−	0.347952i	−0.984750	−	0.173976i	$-0.944338\pi$
$283$		−	5.85346i		−	0.347952i	0.984750	−	0.173976i	$-0.0556615\pi$
$284$	15.8403	+	5.46475i	0.939951	+	0.324273i
$285$		0			0
$286$	−0.0271498	−	0.604537i	−0.00160540	−	0.0357470i
$287$	−0.411523	−	0.471026i	−0.0242914	−	0.0278038i
$288$		0			0
$289$	8.10987	−	24.9596i	0.477051	−	1.46821i
$290$	0.456032	−	0.436011i	0.0267791	−	0.0256035i
$291$		0			0
$292$	−3.52738	−	26.0401i	−0.206424	−	1.52388i
$293$	21.9312	+	2.97078i	1.28123	+	0.173555i	0.743029	−	0.669259i	$-0.233388\pi$
$293$	21.9312	+	2.97078i	1.28123	+	0.173555i	0.538205	+	0.842814i	$0.319103\pi$
$294$		0			0
$295$	0.829432	−	0.446336i	0.0482914	−	0.0259867i
$296$	0.857647	+	0.819994i	0.0498497	+	0.0476612i
$297$		0			0
$298$	−0.786579	+	0.255575i	−0.0455653	+	0.0148051i
$299$	−11.2161	+	4.79400i	−0.648645	+	0.277244i
$300$		0			0
$301$	0.341014	+	0.469366i	0.0196557	+	0.0270538i
$302$	−0.0543938	+	0.604365i	−0.00313001	+	0.0347773i
$303$		0			0
$304$	4.93977	−	21.6425i	0.283315	−	1.24129i
$305$	−1.92209	+	2.91184i	−0.110059	+	0.166732i
$306$		0			0
$307$	−10.8892	−	8.68384i	−0.621479	−	0.495613i	0.261390	−	0.965233i	$-0.415819\pi$
$307$	−10.8892	−	8.68384i	−0.621479	−	0.495613i	−0.882868	+	0.469621i	$0.844391\pi$
$308$	−0.274836	+	0.314575i	−0.0156602	+	0.0179246i
$309$		0			0
$310$	−0.322608	+	0.669902i	−0.0183229	+	0.0380479i
$311$	−24.0549	+	15.8785i	−1.36403	+	0.900388i	−0.999525	−	0.0308130i	$-0.990190\pi$
$311$	−24.0549	+	15.8785i	−1.36403	+	0.900388i	−0.364505	+	0.931201i	$0.618762\pi$
$312$		0			0
$313$	−15.6158	−	9.33004i	−0.882660	−	0.527365i	−0.00140127	−	0.999999i	$-0.500446\pi$
$313$	−15.6158	−	9.33004i	−0.882660	−	0.527365i	−0.881259	+	0.472634i	$0.843303\pi$
$314$	0.0111474	+	0.0231479i	0.000629086	+	0.00130631i
$315$		0			0
$316$	−4.59504	−	20.1322i	−0.258491	−	1.13252i
$317$	27.2118	+	10.2128i	1.52837	+	0.573606i	0.967182	−	0.254085i	$-0.0817743\pi$
$317$	27.2118	+	10.2128i	1.52837	+	0.573606i	0.561185	+	0.827691i	$0.310346\pi$
$318$		0			0
$319$	−23.5381	−	1.05710i	−1.31788	−	0.0591860i
$320$	5.03280	+	0.226023i	0.281342	+	0.0126351i
$321$		0			0
$322$	−0.0450761	−	0.0169173i	−0.00251199	−	0.000942767i
$323$	−8.26166	−	36.1967i	−0.459691	−	2.01404i
$324$		0			0
$325$	4.33945	+	9.01096i	0.240709	+	0.499838i
$326$	−0.135268	−	0.0808189i	−0.00749181	−	0.00447615i
$327$		0			0
$328$	−2.74384	+	1.81119i	−0.151503	+	0.100006i
$329$	0.288975	−	0.600063i	0.0159317	−	0.0330825i
$330$		0			0
$331$	−0.605544	+	0.693101i	−0.0332837	+	0.0380963i	−0.769472	−	0.638680i	$-0.779481\pi$
$331$	−0.605544	+	0.693101i	−0.0332837	+	0.0380963i	0.736189	+	0.676776i	$0.236624\pi$
$332$	10.6705	+	8.50948i	0.585622	+	0.467018i
$333$		0			0
$334$	0.585365	−	0.886790i	0.0320298	−	0.0485230i
$335$	−0.591878	+	2.59319i	−0.0323378	+	0.141681i
$336$		0			0
$337$	0.330743	−	3.67486i	0.0180167	−	0.200182i	−0.981924	−	0.189277i	$-0.939386\pi$
$337$	0.330743	−	3.67486i	0.0180167	−	0.200182i	0.999941	−	0.0109057i	$-0.00347145\pi$
$338$	−0.515293	−	0.709239i	−0.0280282	−	0.0385775i
$339$		0			0
$340$	7.83864	−	3.35040i	0.425110	−	0.181701i
$341$	26.4080	−	8.58049i	1.43007	−	0.464659i
$342$		0			0
$343$	−0.818432	−	0.782501i	−0.0441912	−	0.0422511i
$344$	2.68544	−	1.44510i	0.144789	−	0.0779145i
$345$		0			0
$346$	−1.63630	−	0.221651i	−0.0879679	−	0.0119161i
$347$	4.54550	+	33.5562i	0.244015	+	1.80139i	0.535199	+	0.844726i	$0.320237\pi$
$347$	4.54550	+	33.5562i	0.244015	+	1.80139i	−0.291183	+	0.956667i	$0.594049\pi$
$348$		0			0
$349$	19.6757	−	18.8119i	1.05322	−	1.00698i	0.0532537	−	0.998581i	$-0.483041\pi$
$349$	19.6757	−	18.8119i	1.05322	−	1.00698i	0.999965	−	0.00839896i	$-0.00267350\pi$
$350$	−0.0121991	+	0.0375449i	−0.000652069	+	0.00200686i
$351$		0			0
$352$	2.16902	+	2.48264i	0.115609	+	0.132325i
$353$	−0.387479	−	8.62789i	−0.0206234	−	0.459217i	−0.982560	−	0.185945i	$-0.940466\pi$
$353$	−0.387479	−	8.62789i	−0.0206234	−	0.459217i	0.961937	−	0.273272i	$-0.0881059\pi$
$354$		0			0
$355$	4.07054	+	3.68793i	0.216042	+	0.195735i
$356$			25.3996i			1.34618i
$357$		0			0
$358$	1.63877	−	1.43175i	0.0866119	−	0.0756705i
$359$	2.42745	+	26.9712i	0.128116	+	1.42348i	0.760756	+	0.649038i	$0.224829\pi$
$359$	2.42745	+	26.9712i	0.128116	+	1.42348i	−0.632640	+	0.774446i	$0.718029\pi$
$360$		0			0
$361$	−8.89825	−	9.30684i	−0.468329	−	0.489834i
$362$	−0.113844	+	0.0314189i	−0.00598349	+	0.00165134i
$363$		0			0
$364$	0.0472194	−	0.348587i	0.00247497	−	0.0182709i
$365$	2.29160	−	8.30343i	0.119948	−	0.434621i
$366$		0			0
$367$	7.09151	−	7.41714i	0.370174	−	0.387171i	−0.511302	−	0.859401i	$-0.670837\pi$
$367$	7.09151	−	7.41714i	0.370174	−	0.387171i	0.881475	+	0.472230i	$0.156551\pi$
$368$	10.3962	−	19.3194i	0.541940	−	1.00709i
$369$		0			0
$370$	0.0762165	+	0.178317i	0.00396231	+	0.00927028i
$371$	−0.119113	−	0.656369i	−0.00618406	−	0.0340770i
$372$		0			0
$373$	18.4397	+	1.65960i	0.954772	+	0.0859310i	0.556057	−	0.831144i	$-0.312314\pi$
$373$	18.4397	+	1.65960i	0.954772	+	0.0859310i	0.398715	+	0.917075i	$0.369456\pi$
$374$	1.67388	+	0.715452i	0.0865544	+	0.0369951i
$375$		0			0
$376$	−2.92171	−	1.92861i	−0.150676	−	0.0994602i
$377$	17.0331	−	10.1768i	0.877251	−	0.524133i
$378$		0			0
$379$	4.29223	+	3.75001i	0.220477	+	0.192625i	0.761090	−	0.648647i	$-0.224665\pi$
$379$	4.29223	+	3.75001i	0.220477	+	0.192625i	−0.540613	+	0.841272i	$0.681807\pi$
$380$	4.30194	−	5.92112i	0.220685	−	0.303747i
$381$		0			0
$382$	0.144197	+	0.218448i	0.00737774	+	0.0111768i
$383$	−11.3349	+	4.25408i	−0.579189	+	0.217373i	−0.623737	−	0.781634i	$-0.714386\pi$
$383$	−11.3349	+	4.25408i	−0.579189	+	0.217373i	0.0445486	+	0.999007i	$0.485815\pi$
$384$		0			0
$385$	−0.123368	+	0.0594110i	−0.00628743	+	0.00302786i
$386$	−1.86307	−	0.338097i	−0.0948278	−	0.0172087i
$387$		0			0
$388$	−11.5374	+	30.7413i	−0.585722	+	1.56065i
$389$	−8.92268	−	11.1887i	−0.452398	−	0.567289i	0.502366	−	0.864655i	$-0.332463\pi$
$389$	−8.92268	−	11.1887i	−0.452398	−	0.567289i	−0.954763	+	0.297367i	$0.903892\pi$
$390$		0			0
$391$	1.64620	−	36.6556i	0.0832521	−	1.85375i
$392$	−2.32559	+	1.85460i	−0.117460	+	0.0936713i
$393$		0			0
$394$	1.65227	−	0.377120i	0.0832401	−	0.0189990i
$395$	1.20865	−	6.66020i	0.0608137	−	0.335111i
$396$		0			0
$397$	−5.68220	+	9.51040i	−0.285181	+	0.477313i	−0.967198	−	0.254023i	$-0.918246\pi$
$397$	−5.68220	+	9.51040i	−0.285181	+	0.477313i	0.682017	+	0.731337i	$0.261103\pi$
$398$	0.628205	+	1.67385i	0.0314891	+	0.0839023i
$399$		0			0
$400$	−16.2073	−	7.80501i	−0.810364	−	0.390251i
$401$	31.3494	+	22.7767i	1.56551	+	1.13741i	0.931298	+	0.364258i	$0.118677\pi$
$401$	31.3494	+	22.7767i	1.56551	+	1.13741i	0.634217	+	0.773155i	$0.281323\pi$
$402$		0			0
$403$	−14.5791	+	18.2816i	−0.726236	+	0.910672i
$404$	−9.45610	−	15.8268i	−0.470459	−	0.787415i
$405$		0			0
$406$	0.0763548	+	0.0174275i	0.00378943	+	0.000864912i
$407$	2.84628	−	6.65919i	0.141085	−	0.330084i
$408$		0			0
$409$	0.0836187	−	0.0607526i	0.00413468	−	0.00300402i	−0.585716	−	0.810516i	$-0.699187\pi$
$409$	0.0836187	−	0.0607526i	0.00413468	−	0.00300402i	0.589851	+	0.807512i	$0.299187\pi$
$410$	−0.528681	+	0.0959414i	−0.0261097	+	0.00473821i
$411$		0			0
$412$	−9.87743	−	30.3996i	−0.486626	−	1.49768i
$413$	0.102959	+	0.0554046i	0.00506628	+	0.00272628i
$414$		0			0
$415$	2.12000	+	3.93963i	0.104067	+	0.193389i
$416$	−2.67615	−	0.738569i	−0.131209	−	0.0362113i
$417$		0			0
$418$	1.54875	−	0.209793i	0.0757519	−	0.0102613i
$419$	−2.23452	−	8.09659i	−0.109163	−	0.395544i	0.888875	−	0.458150i	$-0.151488\pi$
$419$	−2.23452	−	8.09659i	−0.109163	−	0.395544i	−0.998038	+	0.0626053i	$0.980059\pi$
$420$		0			0
$421$	−9.86441	−	3.20514i	−0.480762	−	0.156209i	0.0586025	−	0.998281i	$-0.481336\pi$
$421$	−9.86441	−	3.20514i	−0.480762	−	0.156209i	−0.539365	+	0.842072i	$0.681336\pi$
$422$	2.79299	−	0.251374i	0.135961	−	0.0122367i
$423$		0			0
$424$	−3.50294	+	0.157317i	−0.170118	+	0.00763999i
$425$	−30.0858			−1.45937
$426$		0			0
$427$	−0.433099			−0.0209591
$428$	28.9579	−	1.30050i	1.39973	−	0.0628621i
$429$		0			0
$430$	0.496390	−	0.0446759i	0.0239380	−	0.00215446i
$431$	1.24951	+	0.405991i	0.0601869	+	0.0195559i	0.338956	−	0.940802i	$-0.389926\pi$
$431$	1.24951	+	0.405991i	0.0601869	+	0.0195559i	−0.278769	+	0.960358i	$0.589926\pi$
$432$		0			0
$433$	−7.47532	−	27.0862i	−0.359241	−	1.30168i	−0.890698	−	0.454595i	$-0.849784\pi$
$433$	−7.47532	−	27.0862i	−0.359241	−	1.30168i	0.531458	−	0.847085i	$-0.321644\pi$
$434$	−0.0914612	+	0.0123893i	−0.00439028	+	0.000594703i
$435$		0			0
$436$	21.6100	+	5.96397i	1.03493	+	0.285622i
$437$	−14.9281	−	27.7411i	−0.714109	−	1.32704i
$438$		0			0
$439$	17.9150	+	9.64047i	0.855036	+	0.460114i	0.841795	−	0.539798i	$-0.181499\pi$
$439$	17.9150	+	9.64047i	0.855036	+	0.460114i	0.0132412	+	0.999912i	$0.495785\pi$
$440$	0.222414	+	0.684519i	0.0106032	+	0.0326332i
$441$		0			0
$442$	−1.50833	+	0.273721i	−0.0717438	+	0.0130196i
$443$	−26.0910	+	18.9562i	−1.23962	+	0.900637i	−0.997573	−	0.0696270i	$-0.977819\pi$
$443$	−26.0910	+	18.9562i	−1.23962	+	0.900637i	−0.242048	+	0.970264i	$0.577819\pi$
$444$		0			0
$445$	−3.27230	+	7.65592i	−0.155122	+	0.362926i
$446$	−1.10514	−	0.252240i	−0.0523297	−	0.0119439i
$447$		0			0
$448$	0.320747	+	0.536841i	0.0151539	+	0.0253633i
$449$	−10.4472	+	13.1004i	−0.493036	+	0.618247i	−0.964642	−	0.263562i	$-0.915103\pi$
$449$	−10.4472	+	13.1004i	−0.493036	+	0.618247i	0.471607	+	0.881809i	$0.343674\pi$
$450$		0			0
$451$	16.2336	+	11.7944i	0.764411	+	0.555377i
$452$	−3.33938	−	1.60816i	−0.157071	−	0.0756414i
$453$		0			0
$454$	0.926504	+	2.46866i	0.0434830	+	0.115860i
$455$	0.0591422	−	0.0989873i	0.00277263	−	0.00464060i
$456$		0			0
$457$	−0.890187	+	4.90533i	−0.0416412	+	0.229462i	−0.998038	−	0.0626079i	$-0.980058\pi$
$457$	−0.890187	+	4.90533i	−0.0416412	+	0.229462i	0.956397	+	0.292070i	$0.0943440\pi$
$458$	−1.02291	+	0.233473i	−0.0477976	+	0.0109095i
$459$		0			0
$460$	5.65510	−	4.50979i	0.263670	−	0.210270i
$461$	−0.435935	+	9.70685i	−0.0203035	+	0.452093i	0.962931	+	0.269748i	$0.0869403\pi$
$461$	−0.435935	+	9.70685i	−0.0203035	+	0.452093i	−0.983235	+	0.182345i	$0.941631\pi$
$462$		0			0
$463$	18.0420	+	22.6239i	0.838481	+	1.05142i	0.997936	+	0.0642165i	$0.0204548\pi$
$463$	18.0420	+	22.6239i	0.838481	+	1.05142i	−0.159455	+	0.987205i	$0.550974\pi$
$464$	−12.5398	+	33.4121i	−0.582144	+	1.55112i
$465$		0			0
$466$	−1.99666	−	0.362341i	−0.0924937	−	0.0167851i
$467$	8.14988	−	3.92478i	0.377132	−	0.181617i	−0.235709	−	0.971824i	$-0.575741\pi$
$467$	8.14988	−	3.92478i	0.377132	−	0.181617i	0.612840	+	0.790207i	$0.290027\pi$
$468$		0			0
$469$	−0.309122	+	0.116015i	−0.0142739	+	0.00535710i
$470$	−0.315195	−	0.477499i	−0.0145388	−	0.0220254i
$471$		0			0
$472$	0.361237	−	0.497200i	0.0166273	−	0.0228855i
$473$	−14.0165	−	12.2458i	−0.644479	−	0.563064i
$474$		0			0
$475$	−22.1741	+	13.2484i	−1.01742	+	0.607878i
$476$	0.883129	+	0.582948i	0.0404781	+	0.0267194i
$477$		0			0
$478$	−0.0848057	−	0.0362477i	−0.00387892	−	0.00165793i
$479$	7.36624	+	0.662974i	0.336572	+	0.0302920i	0.256637	−	0.966508i	$-0.417386\pi$
$479$	7.36624	+	0.662974i	0.336572	+	0.0302920i	0.0799356	+	0.996800i	$0.474529\pi$
$480$		0			0
$481$	1.08894	+	6.00057i	0.0496515	+	0.273602i
$482$	−0.500741	−	1.17154i	−0.0228081	−	0.0533623i
$483$		0			0
$484$	−4.01552	+	7.46208i	−0.182524	+	0.339186i
$485$	−7.43806	+	7.77960i	−0.337745	+	0.353254i
$486$		0			0
$487$	0.658903	−	2.38748i	0.0298577	−	0.108187i	−0.947515	−	0.319711i	$-0.896414\pi$
$487$	0.658903	−	2.38748i	0.0298577	−	0.108187i	0.977373	+	0.211524i	$0.0678427\pi$
$488$	−0.305586	+	2.25593i	−0.0138332	+	0.102121i
$489$		0			0
$490$	−0.468615	+	0.129329i	−0.0211698	+	0.00584251i
$491$	−22.4409	−	23.4713i	−1.01274	−	1.05925i	−0.998237	−	0.0593518i	$-0.981097\pi$
$491$	−22.4409	−	23.4713i	−1.01274	−	1.05925i	−0.0145063	−	0.999895i	$-0.504618\pi$
$492$		0			0
$493$	5.35030	+	59.4467i	0.240965	+	2.67735i
$494$	−0.991146	+	0.865939i	−0.0445938	+	0.0389604i
$495$		0			0
$496$		−	42.0572i		−	1.88842i
$497$	−0.103700	+	0.673891i	−0.00465157	+	0.0302281i
$498$		0			0
$499$	1.65015	+	36.7435i	0.0738710	+	1.64487i	0.604026	+	0.796965i	$0.293562\pi$
$499$	1.65015	+	36.7435i	0.0738710	+	1.64487i	−0.530155	+	0.847901i	$0.677866\pi$
$500$	−8.16658	−	9.34740i	−0.365220	−	0.418028i
$501$		0			0
$502$	−0.308782	+	0.950333i	−0.0137816	+	0.0424154i
$503$	−7.07625	+	6.76559i	−0.315514	+	0.301663i	−0.832159	−	0.554537i	$-0.812895\pi$
$503$	−7.07625	+	6.76559i	−0.315514	+	0.301663i	0.516644	+	0.856200i	$0.327181\pi$
$504$		0			0
$505$	−0.811233	−	5.98876i	−0.0360994	−	0.266496i
$506$	1.53060	+	0.207334i	0.0680436	+	0.00921713i
$507$		0			0
$508$	−1.47066	+	0.791395i	−0.0652499	+	0.0351125i
$509$	12.9695	+	12.4001i	0.574862	+	0.549625i	0.921502	−	0.388374i	$-0.126963\pi$
$509$	12.9695	+	12.4001i	0.574862	+	0.549625i	−0.346640	+	0.937998i	$0.612677\pi$
$510$		0			0
$511$	1.01692	−	0.330417i	0.0449859	−	0.0146168i
$512$	7.66706	−	3.27706i	0.338839	−	0.144827i
$513$		0			0
$514$	0.752845	+	1.03620i	0.0332066	+	0.0457049i
$515$	0.939215	−	10.4355i	0.0413868	−	0.459845i
$516$		0			0
$517$	−4.75453	+	20.8309i	−0.209104	+	0.916144i
$518$	−0.0132612	+	0.0200899i	−0.000582664	+	0.000882698i
$519$		0			0
$520$	−0.473875	−	0.377903i	−0.0207808	−	0.0165721i
$521$	17.8345	−	20.4132i	0.781344	−	0.894320i	−0.215269	−	0.976555i	$-0.569063\pi$
$521$	17.8345	−	20.4132i	0.781344	−	0.894320i	0.996613	+	0.0822350i	$0.0262058\pi$
$522$		0			0
$523$	−15.3498	+	31.8743i	−0.671201	+	1.39376i	0.235451	+	0.971886i	$0.424343\pi$
$523$	−15.3498	+	31.8743i	−0.671201	+	1.39376i	−0.906653	+	0.421878i	$0.861371\pi$
$524$	4.48559	−	2.96091i	0.195954	−	0.129348i
$525$		0			0
$526$	−0.0551468	−	0.0329487i	−0.00240452	−	0.00143663i
$527$	−30.5193	−	63.3739i	−1.32944	−	2.76061i
$528$		0			0
$529$	−1.80988	−	7.92960i	−0.0786904	−	0.344765i
$530$	−0.536525	−	0.201361i	−0.0233052	−	0.00874657i
$531$		0			0
$532$	0.907595	+	0.0407601i	0.0393492	+	0.00176718i
$533$	−16.8807	−	0.758115i	−0.731186	−	0.0328376i
$534$		0			0
$535$	8.89601	+	3.33873i	0.384608	+	0.144346i
$536$	0.386191	+	1.69201i	0.0166809	+	0.0730838i
$537$		0			0
$538$	−0.855812	−	1.77711i	−0.0368967	−	0.0766168i
$539$	15.5847	+	9.31141i	0.671280	+	0.401071i
$540$		0			0
$541$	16.6493	−	10.9901i	0.715808	−	0.472501i	−0.139764	−	0.990185i	$-0.544634\pi$
$541$	16.6493	−	10.9901i	0.715808	−	0.472501i	0.855572	+	0.517684i	$0.173206\pi$
$542$	−0.408447	+	0.848149i	−0.0175443	+	0.0364311i
$543$		0			0
$544$	5.49458	−	6.28906i	0.235578	−	0.269641i
$545$	5.74529	+	4.58172i	0.246101	+	0.196259i
$546$		0			0
$547$	−13.3545	+	20.2312i	−0.570996	+	0.865022i	−0.999253	−	0.0386347i	$-0.987699\pi$
$547$	−13.3545	+	20.2312i	−0.570996	+	0.865022i	0.428257	+	0.903657i	$0.359128\pi$
$548$	0.798186	−	3.49708i	0.0340968	−	0.149388i
$549$		0			0
$550$	0.113525	−	1.26137i	0.00484074	−	0.0537850i
$551$	30.1209	+	41.4579i	1.28319	+	1.76617i
$552$		0			0
$553$	0.772631	−	0.330238i	0.0328556	−	0.0140432i
$554$	2.31173	−	0.751128i	0.0982162	−	0.0319124i
$555$		0			0
$556$	−0.526243	−	0.503140i	−0.0223177	−	0.0213379i
$557$	−39.2646	+	21.1292i	−1.66369	+	0.895272i	−0.676369	+	0.736563i	$0.736447\pi$
$557$	−39.2646	+	21.1292i	−1.66369	+	0.895272i	−0.987325	+	0.158709i	$0.949267\pi$
$558$		0			0
$559$	15.5320	+	2.10395i	0.656932	+	0.0889875i
$560$	0.0278397	+	0.205521i	0.00117644	+	0.00868484i
$561$		0			0
$562$	1.59848	−	1.52830i	0.0674278	−	0.0644676i
$563$	1.27519	−	3.92463i	0.0537429	−	0.165404i	−0.920582	−	0.390548i	$-0.872285\pi$
$563$	1.27519	−	3.92463i	0.0537429	−	0.165404i	0.974325	+	0.225145i	$0.0722855\pi$
$564$		0			0
$565$	−0.799367	−	0.914949i	−0.0336296	−	0.0384922i
$566$	−0.0280042	−	0.623562i	−0.00117711	−	0.0262103i
$567$		0			0
$568$	3.43699	+	1.01563i	0.144213	+	0.0426151i
$569$			24.8862i			1.04328i	0.853165	+	0.521641i	$0.174680\pi$
$569$			24.8862i			1.04328i	−0.853165	+	0.521641i	$0.825320\pi$
$570$		0			0
$571$	10.5183	−	9.18955i	0.440176	−	0.384571i	−0.409125	−	0.912478i	$-0.634166\pi$
$571$	10.5183	−	9.18955i	0.440176	−	0.384571i	0.849302	+	0.527908i	$0.177023\pi$
$572$	1.01160	+	11.2398i	0.0422970	+	0.469958i
$573$		0			0
$574$	−0.0460925	−	0.0482090i	−0.00192387	−	0.00201221i
$575$	−24.6078	+	6.79131i	−1.02621	+	0.283217i
$576$		0			0
$577$	−0.771399	+	5.69469i	−0.0321137	+	0.237073i	−0.999891	−	0.0147328i	$-0.995310\pi$
$577$	−0.771399	+	5.69469i	−0.0321137	+	0.237073i	0.967778	+	0.251806i	$0.0810245\pi$
$578$	0.744523	−	2.69772i	0.0309681	−	0.112210i
$579$		0			0
$580$	−8.13105	+	8.50441i	−0.337623	+	0.353126i
$581$	−0.263160	+	0.489034i	−0.0109177	+	0.0202885i
$582$		0			0
$583$	8.41111	+	19.6788i	0.348353	+	0.815011i
$584$	−1.00356	−	5.53007i	−0.0415276	−	0.228836i
$585$		0			0
$586$	2.35052	+	0.211551i	0.0970991	+	0.00873907i
$587$	−24.9521	−	10.6651i	−1.02989	−	0.440194i	−0.189326	−	0.981914i	$-0.560630\pi$
$587$	−24.9521	−	10.6651i	−1.02989	−	0.440194i	−0.840559	+	0.541720i	$0.817773\pi$
$588$		0			0
$589$	−50.4006	−	33.2691i	−2.07672	−	1.37083i
$590$	0.0862231	−	0.0515159i	0.00354975	−	0.00212088i
$591$		0			0
$592$	−8.26045	−	7.21694i	−0.339502	−	0.296614i
$593$	−10.8782	+	14.9725i	−0.446714	+	0.614848i	−0.971687	−	0.236270i	$-0.924075\pi$
$593$	−10.8782	+	14.9725i	−0.446714	+	0.614848i	0.524974	+	0.851118i	$0.324075\pi$
$594$		0			0
$595$	0.191089	+	0.289487i	0.00783388	+	0.0118678i
$596$	14.4401	−	5.41945i	0.591489	−	0.221990i
$597$		0			0
$598$	−1.17191	+	0.564360i	−0.0479228	+	0.0230784i
$599$	−7.34269	−	1.33250i	−0.300014	−	0.0544445i	0.0264625	−	0.999650i	$-0.491576\pi$
$599$	−7.34269	−	1.33250i	−0.300014	−	0.0544445i	−0.326477	+	0.945205i	$0.605861\pi$
$600$		0			0
$601$	2.78128	−	7.41071i	0.113451	−	0.302289i	−0.867229	−	0.497910i	$-0.834101\pi$
$601$	2.78128	−	7.41071i	0.113451	−	0.302289i	0.980680	+	0.195621i	$0.0626723\pi$
$602$	0.0385734	+	0.0483695i	0.00157213	+	0.00197139i
$603$		0			0
$604$	0.507699	−	11.3048i	0.0206580	−	0.459985i
$605$	−2.17171	+	1.73188i	−0.0882926	+	0.0704110i
$606$		0			0
$607$	18.7438	−	4.27816i	0.760789	−	0.173645i	0.175511	−	0.984478i	$-0.443842\pi$
$607$	18.7438	−	4.27816i	0.760789	−	0.173645i	0.585278	+	0.810832i	$0.300985\pi$
$608$	1.28025	−	7.05478i	0.0519211	−	0.286109i
$609$		0			0
$610$	−0.190827	+	0.319391i	−0.00772637	+	0.0129318i
$611$	−6.32235	−	16.8458i	−0.255775	−	0.681510i
$612$		0			0
$613$	2.59676	+	1.25054i	0.104882	+	0.0505087i	0.485589	−	0.874187i	$-0.338605\pi$
$613$	2.59676	+	1.25054i	0.104882	+	0.0505087i	−0.380707	+	0.924696i	$0.624319\pi$
$614$	−1.20156	−	0.872983i	−0.0484909	−	0.0352307i
$615$		0			0
$616$	−0.0557048	+	0.0698516i	−0.00224441	+	0.00281440i
$617$	19.2661	+	32.2461i	0.775626	+	1.29818i	0.949611	+	0.313430i	$0.101478\pi$
$617$	19.2661	+	32.2461i	0.775626	+	1.29818i	−0.173986	+	0.984748i	$0.555665\pi$
$618$		0			0
$619$	22.3744	+	5.10681i	0.899303	+	0.205260i	0.647092	−	0.762412i	$-0.275985\pi$
$619$	22.3744	+	5.10681i	0.899303	+	0.205260i	0.252211	+	0.967672i	$0.418842\pi$
$620$	5.44967	−	12.7501i	0.218864	−	0.512058i
$621$		0			0
$622$	−2.48658	+	1.80661i	−0.0997027	+	0.0724383i
$623$	−1.01690	+	0.184541i	−0.0407414	+	0.00739348i
$624$		0			0
$625$	5.81156	+	17.8861i	0.232462	+	0.715446i
$626$	−1.70818	−	0.919209i	−0.0682724	−	0.0367390i
$627$		0			0
$628$	−0.227043	−	0.421917i	−0.00906000	−	0.0168363i
$629$	−17.6843	−	4.88056i	−0.705120	−	0.194601i
$630$		0			0
$631$	−5.65197	+	0.765612i	−0.225002	+	0.0304785i	−0.245866	−	0.969304i	$-0.579072\pi$
$631$	−5.65197	+	0.765612i	−0.225002	+	0.0304785i	0.0208646	+	0.999782i	$0.493358\pi$
$632$	−1.17499	−	4.25749i	−0.0467387	−	0.169354i
$633$		0			0
$634$	2.94770	+	0.957766i	0.117068	+	0.0380378i
$635$	−0.545241	+	0.0490726i	−0.0216372	+	0.00194739i
$636$		0			0
$637$	−15.2728	+	0.685901i	−0.605129	+	0.0271764i
$638$	−2.51254			−0.0994724
$639$		0			0
$640$	2.19289			0.0866818
$641$	41.6033	−	1.86840i	1.64323	−	0.0737975i	0.796094	−	0.605173i	$-0.206896\pi$
$641$	41.6033	−	1.86840i	1.64323	−	0.0737975i	0.847136	+	0.531376i	$0.178325\pi$
$642$		0			0
$643$	−46.0128	+	4.14122i	−1.81457	+	0.163314i	−0.944261	−	0.329198i	$-0.893222\pi$
$643$	−46.0128	+	4.14122i	−1.81457	+	0.163314i	−0.870306	+	0.492512i	$0.836079\pi$
$644$	0.853919	+	0.277455i	0.0336491	+	0.0109333i
$645$		0			0
$646$	−1.05328	−	3.81647i	−0.0414407	−	0.150157i
$647$	−48.2070	+	6.53009i	−1.89521	+	0.256724i	−0.986872	−	0.161504i	$-0.948365\pi$
$647$	−48.2070	+	6.53009i	−1.89521	+	0.256724i	−0.908342	+	0.418228i	$0.862651\pi$
$648$		0			0
$649$	−3.61574	−	0.997881i	−0.141930	−	0.0391703i
$650$	0.505387	+	0.939167i	0.0198229	+	0.0368371i
$651$		0			0
$652$	2.58766	+	1.39248i	0.101340	+	0.0545336i
$653$	−7.38424	−	22.7264i	−0.288968	−	0.889351i	−0.985181	−	0.171517i	$-0.945133\pi$
$653$	−7.38424	−	22.7264i	−0.288968	−	0.889351i	0.696213	−	0.717835i	$-0.254867\pi$
$654$		0			0
$655$	1.73350	−	0.314584i	0.0677335	−	0.0122918i
$656$	24.5882	−	17.8643i	0.960006	−	0.697485i
$657$		0			0
$658$	0.0279134	−	0.0653066i	0.00108818	−	0.00254591i
$659$	17.2367	+	3.93418i	0.671448	+	0.153254i	0.544635	−	0.838673i	$-0.316668\pi$
$659$	17.2367	+	3.93418i	0.671448	+	0.153254i	0.126813	+	0.991927i	$0.459525\pi$
$660$		0			0
$661$	16.1140	+	26.9704i	0.626763	+	1.04903i	0.992956	+	0.118486i	$0.0378040\pi$
$661$	16.1140	+	26.9704i	0.626763	+	1.04903i	−0.366192	+	0.930539i	$0.619339\pi$
$662$	−0.0611920	+	0.0767323i	−0.00237829	+	0.00298229i
$663$		0			0
$664$	2.36160	+	1.71580i	0.0916478	+	0.0665860i
$665$	0.268315	+	0.129214i	0.0104048	+	0.00501069i
$666$		0			0
$667$	17.7951	+	47.4150i	0.689030	+	1.83591i
$668$	−10.1634	+	17.0106i	−0.393232	+	0.658160i
$669$		0			0
$670$	−0.0506458	+	0.279081i	−0.00195662	+	0.0107818i
$671$	13.5459	−	3.09177i	0.522935	−	0.119357i
$672$		0			0
$673$	−5.07238	+	4.04509i	−0.195526	+	0.155927i	−0.716359	−	0.697732i	$-0.754193\pi$
$673$	−5.07238	+	4.04509i	−0.195526	+	0.155927i	0.520833	+	0.853658i	$0.325621\pi$
$674$	0.0176524	−	0.393061i	0.000679945	−	0.0151401i
$675$		0			0
$676$	10.1933	+	12.7820i	0.392049	+	0.491614i
$677$	−12.3670	+	32.9519i	−0.475304	+	1.26644i	0.451961	+	0.892038i	$0.350725\pi$
$677$	−12.3670	+	32.9519i	−0.475304	+	1.26644i	−0.927265	+	0.374405i	$0.877847\pi$
$678$		0			0
$679$	−1.31459	−	0.238563i	−0.0504493	−	0.00915520i
$680$	1.64271	−	0.791087i	0.0629950	−	0.0303368i
$681$		0			0
$682$	2.77217	−	1.04041i	0.106152	−	0.0398394i
$683$	7.80047	+	11.8172i	0.298477	+	0.452173i	0.952605	−	0.304211i	$-0.0983928\pi$
$683$	7.80047	+	11.8172i	0.298477	+	0.452173i	−0.654128	+	0.756384i	$0.726964\pi$
$684$		0			0
$685$	0.691126	−	0.951253i	0.0264066	−	0.0363455i
$686$	−0.0909303	−	0.0794434i	−0.00347173	−	0.00303316i
$687$		0			0
$688$	−24.2007	+	14.4592i	−0.922643	+	0.551254i
$689$	−15.0407	−	9.92831i	−0.573007	−	0.378238i
$690$		0			0
$691$	30.3867	+	12.9879i	1.15597	+	0.494083i	0.883661	−	0.468128i	$-0.155071\pi$
$691$	30.3867	+	12.9879i	1.15597	+	0.494083i	0.272304	+	0.962211i	$0.412214\pi$
$692$	30.6695	+	2.76031i	1.16588	+	0.104931i
$693$		0			0
$694$	0.644768	+	3.55296i	0.0244750	+	0.134869i
$695$	−0.0937986	−	0.219453i	−0.00355798	−	0.00832432i
$696$		0			0
$697$	24.0872	−	44.7616i	0.912369	−	1.69547i
$698$	2.00603	−	2.09815i	0.0759295	−	0.0794161i
$699$		0			0
$700$	0.195856	−	0.709667i	0.00740264	−	0.0268229i
$701$	−1.40581	+	10.3781i	−0.0530969	+	0.391977i	0.944827	+	0.327570i	$0.106230\pi$
$701$	−1.40581	+	10.3781i	−0.0530969	+	0.391977i	−0.997924	+	0.0644067i	$0.979484\pi$
$702$		0			0
$703$	−15.1830	+	4.19025i	−0.572639	+	0.158038i
$704$	−13.8643	−	14.5009i	−0.522530	−	0.546524i
$705$		0			0
$706$	−0.0825554	−	0.917266i	−0.00310702	−	0.0345218i
$707$	0.564944	−	0.493576i	0.0212469	−	0.0185629i
$708$		0			0
$709$		−	20.5147i		−	0.770447i	−0.922823	−	0.385223i	$-0.874124\pi$
$709$		−	20.5147i		−	0.770447i	0.922823	−	0.385223i	$-0.125876\pi$
$710$	0.451273	+	0.373396i	0.0169360	+	0.0140133i
$711$		0			0
$712$	0.243730	+	5.42706i	0.00913415	+	0.203388i
$713$	−39.2679	−	44.9457i	−1.47059	−	1.68323i
$714$		0			0
$715$	−1.14313	+	3.51820i	−0.0427508	+	0.131573i
$716$	−29.3323	+	28.0446i	−1.09620	+	1.04808i
$717$		0			0
$718$	0.387630	+	2.86160i	0.0144662	+	0.106794i
$719$	−9.23224	−	1.25059i	−0.344304	−	0.0466392i	−0.0399600	−	0.999201i	$-0.512723\pi$
$719$	−9.23224	−	1.25059i	−0.344304	−	0.0466392i	−0.304344	+	0.952562i	$0.598437\pi$
$720$		0			0
$721$	1.14532	−	0.616323i	0.0426539	−	0.0229531i
$722$	−0.992447	−	0.948876i	−0.0369350	−	0.0353135i
$723$		0			0
$724$	2.09461	−	0.680581i	0.0778457	−	0.0252936i
$725$	38.1838	−	16.3205i	1.41811	−	0.606129i
$726$		0			0
$727$	−16.4852	−	22.6900i	−0.611403	−	0.841524i	0.385289	−	0.922796i	$-0.374102\pi$
$727$	−16.4852	−	22.6900i	−0.611403	−	0.841524i	−0.996692	+	0.0812720i	$0.974102\pi$
$728$	0.00674424	−	0.0749347i	0.000249958	−	0.00277726i
$729$		0			0
$730$	0.204396	−	0.895518i	0.00756504	−	0.0331446i
$731$	−25.9744	+	39.3495i	−0.960696	+	1.45539i
$732$		0			0
$733$	7.33740	+	5.85138i	0.271013	+	0.216126i	0.749560	−	0.661936i	$-0.230265\pi$
$733$	7.33740	+	5.85138i	0.271013	+	0.216126i	−0.478547	+	0.878062i	$0.658836\pi$
$734$	0.719965	−	0.824067i	0.0265744	−	0.0304169i
$735$		0			0
$736$	3.07449	−	6.38425i	0.113327	−	0.235327i
$737$	8.84014	−	5.83532i	0.325631	−	0.214947i
$738$		0			0
$739$	−27.1456	−	16.2187i	−0.998567	−	0.596616i	−0.0820570	−	0.996628i	$-0.526149\pi$
$739$	−27.1456	−	16.2187i	−0.998567	−	0.596616i	−0.916510	+	0.400012i	$0.869006\pi$
$740$	−1.56910	−	3.25827i	−0.0576813	−	0.119776i
$741$		0			0
$742$	−0.0158292	−	0.0693524i	−0.000581109	−	0.00254601i
$743$	10.9360	+	4.10436i	0.401204	+	0.150574i	0.543817	−	0.839204i	$-0.316979\pi$
$743$	10.9360	+	4.10436i	0.401204	+	0.150574i	−0.142612	+	0.989779i	$0.545550\pi$
$744$		0			0
$745$	5.05071	+	0.226828i	0.185044	+	0.00831033i
$746$	1.97230	+	0.0885762i	0.0722111	+	0.00324300i
$747$		0			0
$748$	−31.7829	−	11.9283i	−1.16210	−	0.436143i
$749$	0.262461	+	1.14992i	0.00959012	+	0.0420170i
$750$		0			0
$751$	12.5261	+	26.0108i	0.457086	+	0.949148i	0.994392	+	0.105761i	$0.0337278\pi$
$751$	12.5261	+	26.0108i	0.457086	+	0.949148i	−0.537306	+	0.843387i	$0.680558\pi$
$752$	27.7819	+	16.5989i	1.01310	+	0.605299i
$753$		0			0
$754$	1.76583	−	1.16562i	0.0643078	−	0.0424492i
$755$	1.60945	−	3.34207i	0.0585740	−	0.121630i
$756$		0			0
$757$	−19.0503	+	21.8049i	−0.692396	+	0.792511i	−0.986587	−	0.163235i	$-0.947807\pi$
$757$	−19.0503	+	21.8049i	−0.692396	+	0.792511i	0.294191	+	0.955747i	$0.404950\pi$
$758$	0.475188	+	0.378950i	0.0172596	+	0.0137641i
$759$		0			0
$760$	0.862365	−	1.30643i	0.0312813	−	0.0473891i
$761$	1.18883	−	5.20860i	0.0430950	−	0.188812i	−0.948799	−	0.315881i	$-0.897700\pi$
$761$	1.18883	−	5.20860i	0.0430950	−	0.188812i	0.991894	+	0.127069i	$0.0405571\pi$
$762$		0			0
$763$	−0.0817676	+	0.908512i	−0.00296019	+	0.0328904i
$764$	−2.86914	−	3.94903i	−0.103802	−	0.142871i
$765$		0			0
$766$	−1.18715	+	0.507411i	−0.0428934	+	0.0183335i
$767$	3.00411	−	0.976093i	0.108472	−	0.0352447i
$768$		0			0
$769$	20.4658	+	19.5673i	0.738016	+	0.705615i	0.963225	−	0.268695i	$-0.0865924\pi$
$769$	20.4658	+	19.5673i	0.738016	+	0.705615i	−0.225210	+	0.974310i	$0.572307\pi$
$770$	−0.0128580	+	0.00691921i	−0.000463372	+	0.000249351i
$771$		0			0
$772$	34.9917	+	4.73995i	1.25938	+	0.170595i
$773$	3.41341	+	25.1988i	0.122772	+	0.906339i	0.942646	+	0.333795i	$0.108329\pi$
$773$	3.41341	+	25.1988i	0.122772	+	0.906339i	−0.819874	+	0.572544i	$0.805956\pi$
$774$		0			0
$775$	−35.3712	+	33.8184i	−1.27057	+	1.21479i
$776$	−2.17017	+	6.67910i	−0.0779046	+	0.239766i
$777$		0			0
$778$	−1.00405	−	1.14923i	−0.0359970	−	0.0412019i
$779$	−1.95796	−	43.5975i	−0.0701514	−	1.56204i
$780$		0			0
$781$	−1.56733	−	21.8174i	−0.0560833	−	0.780689i
$782$		−	3.91275i		−	0.139920i
$783$		0			0
$784$	20.7076	−	18.0917i	0.739558	−	0.646133i
$785$	−0.0140784	−	0.156424i	−0.000502480	−	0.00558301i
$786$		0			0
$787$	−11.4161	−	11.9403i	−0.406940	−	0.425625i	0.487286	−	0.873243i	$-0.337987\pi$
$787$	−11.4161	−	11.9403i	−0.406940	−	0.425625i	−0.894225	+	0.447617i	$0.852273\pi$
$788$	−30.4661	+	8.40812i	−1.08531	+	0.299527i
$789$		0			0
$790$	0.0968921	−	0.715286i	0.00344727	−	0.0254487i
$791$	0.0401223	−	0.145380i	0.00142659	−	0.00516912i
$792$		0			0
$793$	−8.08585	+	8.45714i	−0.287137	+	0.300322i
$794$	−0.559819	+	1.04032i	−0.0198672	+	0.0369195i
$795$		0			0
$796$	−13.1039	−	30.6580i	−0.464454	−	1.08665i
$797$	−1.86737	−	10.2900i	−0.0661455	−	0.364492i	−0.999977	−	0.00677873i	$-0.997842\pi$
$797$	−1.86737	−	10.2900i	−0.0661455	−	0.364492i	0.933831	−	0.357713i	$-0.116443\pi$
$798$		0			0
$799$	53.9083	+	4.85184i	1.90714	+	0.171646i
$800$	−5.34255	−	2.28351i	−0.188888	−	0.0807344i
$801$		0			0
$802$	3.44859	+	2.27639i	0.121774	+	0.0803822i
$803$	−29.4472	+	17.5939i	−1.03917	+	0.620875i
$804$		0			0
$805$	0.221642	+	0.193643i	0.00781185	+	0.00682501i
$806$	−1.46563	+	2.01727i	−0.0516247	+	0.0710553i
$807$		0			0
$808$	−2.17233	−	3.29094i	−0.0764222	−	0.115775i
$809$	25.3629	−	9.51885i	0.891711	−	0.334665i	0.136883	−	0.990587i	$-0.456292\pi$
$809$	25.3629	−	9.51885i	0.891711	−	0.334665i	0.754828	+	0.655922i	$0.227720\pi$
$810$		0			0
$811$	10.8495	−	5.22485i	0.380978	−	0.183469i	−0.233586	−	0.972336i	$-0.575046\pi$
$811$	10.8495	−	5.22485i	0.380978	−	0.183469i	0.614564	+	0.788867i	$0.289332\pi$
$812$	−1.43707	−	0.260789i	−0.0504311	−	0.00915190i
$813$		0			0
$814$	0.271352	−	0.723014i	0.00951087	−	0.0253416i
$815$	0.600571	+	0.753093i	0.0210371	+	0.0263797i
$816$		0			0
$817$	−1.81614	+	40.4396i	−0.0635388	+	1.41480i
$818$	0.00861715	−	0.00687195i	0.000301292	−	0.000240272i
$819$		0			0
$820$	9.76902	−	2.22971i	0.341149	−	0.0778650i
$821$	4.96091	−	27.3369i	0.173137	−	0.954064i	−0.773988	−	0.633200i	$-0.781741\pi$
$821$	4.96091	−	27.3369i	0.173137	−	0.954064i	0.947125	−	0.320864i	$-0.103973\pi$
$822$		0			0
$823$	4.05145	−	6.78099i	0.141225	−	0.236371i	−0.779662	−	0.626201i	$-0.784609\pi$
$823$	4.05145	−	6.78099i	0.141225	−	0.236371i	0.920887	+	0.389830i	$0.127466\pi$
$824$	−2.40219	−	6.40061i	−0.0836842	−	0.222976i
$825$		0			0
$826$	0.0112332	+	0.00540961i	0.000390852	+	0.000188224i
$827$	−9.79614	−	7.11731i	−0.340645	−	0.247493i	0.404289	−	0.914631i	$-0.367519\pi$
$827$	−9.79614	−	7.11731i	−0.340645	−	0.247493i	−0.744934	+	0.667138i	$0.767519\pi$
$828$		0			0
$829$	4.01621	−	5.03617i	0.139489	−	0.174913i	−0.707180	−	0.707033i	$-0.750033\pi$
$829$	4.01621	−	5.03617i	0.139489	−	0.174913i	0.846669	+	0.532120i	$0.178604\pi$
$830$	0.244690	+	0.409542i	0.00849330	+	0.0142154i
$831$		0			0
$832$	16.4712	+	3.75944i	0.571035	+	0.130335i
$833$	18.0749	−	42.2883i	0.626257	−	1.46520i
$834$		0			0
$835$	−5.25494	+	3.81794i	−0.181855	+	0.132125i
$836$	−28.6776	+	5.20422i	−0.991836	+	0.179992i
$837$		0			0
$838$	−0.276776	−	0.851830i	−0.00956108	−	0.0294260i
$839$	15.3113	+	8.23935i	0.528604	+	0.284454i	0.716323	−	0.697769i	$-0.245824\pi$
$839$	15.3113	+	8.23935i	0.528604	+	0.284454i	−0.187719	+	0.982223i	$0.560109\pi$
$840$		0			0
$841$	−25.2961	−	47.0080i	−0.872279	−	1.62097i
$842$	−1.06618	−	0.294247i	−0.0367430	−	0.0101404i
$843$		0			0
$844$	−51.8230	+	7.01990i	−1.78382	+	0.241635i
$845$	1.42571	+	5.16594i	0.0490459	+	0.177714i
$846$		0			0
$847$	−0.327928	−	0.106550i	−0.0112678	−	0.00366111i
$848$	32.2843	−	2.90564i	1.10865	−	0.0997802i
$849$		0			0
$850$	−3.20500	+	0.143937i	−0.109931	+	0.00493699i
$851$	−15.5661			−0.533598
$852$		0			0
$853$	−32.0024			−1.09574			−0.547870	−	0.836563i	$-0.684561\pi$
$853$	−32.0024			−1.09574			−0.547870	+	0.836563i	$0.684561\pi$
$854$	−0.0461376	+	0.00207204i	−0.00157879	+	7.09038e-5i
$855$		0			0
$856$	6.17487	−	0.555748i	0.211053	−	0.0189951i
$857$	−11.2579	−	3.65792i	−0.384563	−	0.124952i	0.110354	−	0.993892i	$-0.464802\pi$
$857$	−11.2579	−	3.65792i	−0.384563	−	0.124952i	−0.494917	+	0.868940i	$0.664802\pi$
$858$		0			0
$859$	−0.101130	−	0.366438i	−0.00345052	−	0.0125027i	0.962217	−	0.272283i	$-0.0877786\pi$
$859$	−0.101130	−	0.366438i	−0.00345052	−	0.0125027i	−0.965668	+	0.259780i	$0.916350\pi$
$860$	−9.21033	+	1.24762i	−0.314070	+	0.0425436i
$861$		0			0
$862$	0.135051	+	0.0372718i	0.00459987	+	0.00126948i
$863$	18.4137	+	34.2183i	0.626809	+	1.16481i	0.973901	+	0.226975i	$0.0728835\pi$
$863$	18.4137	+	34.2183i	0.626809	+	1.16481i	−0.347092	+	0.937831i	$0.612831\pi$
$864$		0			0
$865$	8.88876	+	4.78324i	0.302227	+	0.162635i
$866$	−0.925923	−	2.84970i	−0.0314642	−	0.0968367i
$867$		0			0
$868$	1.69355	−	0.307334i	0.0574828	−	0.0104316i
$869$	−21.8079	+	15.8444i	−0.739783	+	0.537484i
$870$		0			0
$871$	−3.50579	+	8.20221i	−0.118789	+	0.277921i
$872$	4.67456	+	1.06694i	0.158301	+	0.0361311i
$873$		0			0
$874$	−1.72300	−	2.88381i	−0.0582812	−	0.0975463i
$875$	0.314900	−	0.394872i	0.0106456	−	0.0133491i
$876$		0			0
$877$	5.31122	+	3.85883i	0.179347	+	0.130303i	0.673837	−	0.738880i	$-0.264645\pi$
$877$	5.31122	+	3.85883i	0.179347	+	0.130303i	−0.494490	+	0.869183i	$0.664645\pi$
$878$	1.95459	+	0.941279i	0.0659641	+	0.0317666i
$879$		0			0
$880$	−2.33789	−	6.22929i	−0.0788103	−	0.209989i
$881$	−5.09792	+	8.53248i	−0.171753	+	0.287467i	−0.932207	−	0.361926i	$-0.882119\pi$
$881$	−5.09792	+	8.53248i	−0.171753	+	0.287467i	0.760454	+	0.649392i	$0.224977\pi$
$882$		0			0
$883$	9.03348	−	49.7786i	0.304001	−	1.67518i	−0.364292	−	0.931285i	$-0.618689\pi$
$883$	9.03348	−	49.7786i	0.304001	−	1.67518i	0.668293	−	0.743898i	$-0.267025\pi$
$884$	27.8710	−	6.36138i	0.937404	−	0.213956i
$885$		0			0
$886$	−2.68875	+	2.14421i	−0.0903305	+	0.0720361i
$887$	−0.376153	+	8.37571i	−0.0126300	+	0.281229i	0.982732	+	0.185033i	$0.0592391\pi$
$887$	−0.376153	+	8.37571i	−0.0126300	+	0.281229i	−0.995362	+	0.0961962i	$0.969332\pi$
$888$		0			0
$889$	−0.0423695	−	0.0531297i	−0.00142103	−	0.00178191i
$890$	−0.311967	+	0.831232i	−0.0104571	+	0.0278630i
$891$		0			0
$892$	20.7997	+	3.77458i	0.696424	+	0.126382i
$893$	41.8685	−	20.1628i	1.40108	−	0.674723i
$894$		0			0
$895$	−12.4544	+	4.67420i	−0.416304	+	0.156241i
$896$	0.149959	+	0.227178i	0.00500977	+	0.00758948i
$897$		0			0
$898$	−1.05026	+	1.44555i	−0.0350475	+	0.0482388i
$899$	73.1123	+	63.8763i	2.43843	+	2.13039i
$900$		0			0
$901$	46.5392	−	27.8059i	1.55045	−	0.926348i
$902$	1.78578	+	1.17878i	0.0594598	+	0.0392491i
$903$		0			0
$904$	−0.728946	−	0.311566i	−0.0242444	−	0.0103625i
$905$	0.719037	+	0.0647145i	0.0239016	+	0.00215118i
$906$		0			0
$907$	−4.63053	−	25.5163i	−0.153754	−	0.847256i	−0.964941	−	0.262468i	$-0.915463\pi$
$907$	−4.63053	−	25.5163i	−0.153754	−	0.847256i	0.811186	−	0.584788i	$-0.198822\pi$
$908$	−19.3262	−	45.2158i	−0.641361	−	1.50054i
$909$		0			0
$910$	0.00582677	−	0.0108280i	0.000193156	−	0.000358943i
$911$	12.6566	−	13.2378i	0.419332	−	0.438587i	−0.479059	−	0.877783i	$-0.659022\pi$
$911$	12.6566	−	13.2378i	0.419332	−	0.438587i	0.898392	+	0.439195i	$0.144736\pi$
$912$		0			0
$913$	4.73973	−	17.1740i	0.156862	−	0.568377i
$914$	−0.0713624	+	0.526819i	−0.00236046	+	0.0174256i
$915$		0			0
$916$	18.8615	−	5.20543i	0.623200	−	0.171992i
$917$	0.151134	+	0.158073i	0.00499087	+	0.00522005i
$918$		0			0
$919$	−1.36086	−	15.1204i	−0.0448906	−	0.498776i	−0.986691	−	0.162604i	$-0.948011\pi$
$919$	−1.36086	−	15.1204i	−0.0448906	−	0.498776i	0.941801	−	0.336172i	$-0.109132\pi$
$920$	1.16503	−	1.01786i	0.0384100	−	0.0335578i
$921$		0			0
$922$			1.03615i			0.0341236i
$923$	11.2230	+	14.6063i	0.369411	+	0.480773i
$924$		0			0
$925$	0.572623	+	12.7504i	0.0188277	+	0.419232i
$926$	2.03023	+	2.32378i	0.0667174	+	0.0763642i
$927$		0			0
$928$	−3.56192	+	10.9625i	−0.116926	+	0.359861i
$929$	19.4296	−	18.5766i	0.637464	−	0.609478i	−0.301511	−	0.953463i	$-0.597491\pi$
$929$	19.4296	−	18.5766i	0.637464	−	0.609478i	0.938975	+	0.343984i	$0.111777\pi$
$930$		0			0
$931$	−5.30011	−	39.1270i	−0.173704	−	1.28234i
$932$	37.5009	+	5.07984i	1.22838	+	0.166396i
$933$		0			0
$934$	0.849421	−	0.457093i	0.0277939	−	0.0149565i
$935$	−8.04321	−	7.69009i	−0.263041	−	0.251493i
$936$		0			0
$937$	3.18019	−	1.03331i	0.103892	−	0.0337567i	−0.256610	−	0.966515i	$-0.582605\pi$
$937$	3.18019	−	1.03331i	0.103892	−	0.0337567i	0.360502	+	0.932758i	$0.382605\pi$
$938$	−0.0323754	+	0.0138379i	−0.00105709	+	0.000451824i
$939$		0			0
$940$	6.27156	+	8.63207i	0.204556	+	0.281547i
$941$	2.41798	−	26.8659i	0.0788238	−	0.875804i	−0.855131	−	0.518412i	$-0.826523\pi$
$941$	2.41798	−	26.8659i	0.0788238	−	0.875804i	0.933955	−	0.357392i	$-0.116334\pi$
$942$		0			0
$943$	9.59734	−	42.0487i	0.312532	−	1.36929i
$944$	−3.12981	+	4.74146i	−0.101867	+	0.154321i
$945$		0			0
$946$	−1.55175	−	1.23748i	−0.0504516	−	0.0402338i
$947$	−14.1646	+	16.2127i	−0.460289	+	0.526843i	−0.935641	−	0.352952i	$-0.885178\pi$
$947$	−14.1646	+	16.2127i	−0.460289	+	0.526843i	0.475352	+	0.879796i	$0.342321\pi$
$948$		0			0
$949$	12.5336	−	26.0262i	0.406857	−	0.844847i
$950$	−2.29879	+	1.51742i	−0.0745828	+	0.0492316i
$951$		0			0
$952$	0.194289	+	0.116082i	0.00629695	+	0.00376225i
$953$	21.6173	+	44.8888i	0.700253	+	1.45409i	0.882245	+	0.470791i	$0.156031\pi$
$953$	21.6173	+	44.8888i	0.700253	+	1.45409i	−0.181992	+	0.983300i	$0.558254\pi$
$954$		0			0
$955$	−0.356049	−	1.55995i	−0.0115215	−	0.0504788i
$956$	1.61025	+	0.604337i	0.0520793	+	0.0195457i
$957$		0			0
$958$	0.787889	+	0.0353841i	0.0254555	+	0.00114321i
$959$	0.145809	+	0.00654829i	0.00470842	+	0.000211455i
$960$		0			0
$961$	−78.0941	−	29.3092i	−2.51917	−	0.945459i
$962$	0.144712	+	0.634024i	0.00466570	+	0.0204418i
$963$		0			0
$964$	10.3090	+	21.4068i	0.332029	+	0.689466i
$965$	9.93650	+	5.93678i	0.319867	+	0.191112i
$966$		0			0
$967$	−43.7006	+	28.8465i	−1.40532	+	0.927642i	−0.405409	+	0.914136i	$0.632871\pi$
$967$	−43.7006	+	28.8465i	−1.40532	+	0.927642i	−0.999909	+	0.0135062i	$0.995701\pi$
$968$	−0.786379	+	1.63293i	−0.0252752	+	0.0524844i
$969$		0			0
$970$	−0.755149	+	0.864338i	−0.0242464	+	0.0277522i
$971$	22.0534	+	17.5870i	0.707727	+	0.564393i	0.909835	−	0.414970i	$-0.136208\pi$
$971$	22.0534	+	17.5870i	0.707727	+	0.564393i	−0.202108	+	0.979363i	$0.564779\pi$
$972$		0			0
$973$	0.0163204	−	0.0247243i	0.000523207	−	0.000792625i
$974$	0.0587699	−	0.257488i	0.00188311	−	0.00825044i
$975$		0			0
$976$	1.88645	−	20.9602i	0.0603839	−	0.670920i
$977$	3.92860	+	5.40726i	0.125687	+	0.172993i	0.867223	−	0.497919i	$-0.165902\pi$
$977$	3.92860	+	5.40726i	0.125687	+	0.172993i	−0.741536	+	0.670913i	$0.765902\pi$
$978$		0			0
$979$	30.4881	−	13.0312i	0.974404	−	0.416480i
$980$	8.62205	−	2.80147i	0.275421	−	0.0894898i
$981$		0			0
$982$	−2.50290	−	2.39301i	−0.0798706	−	0.0763641i
$983$	−19.5893	+	10.5414i	−0.624800	+	0.336219i	−0.755447	−	0.655210i	$-0.772580\pi$
$983$	−19.5893	+	10.5414i	−0.624800	+	0.336219i	0.130647	+	0.991429i	$0.458295\pi$
$984$		0			0
$985$	−10.2663	−	1.39067i	−0.327112	−	0.0443103i
$986$	0.854367	+	6.30719i	0.0272086	+	0.200862i
$987$		0			0
$988$	17.7405	−	16.9616i	0.564400	−	0.539622i
$989$	−12.3625	+	38.0480i	−0.393106	+	1.20986i
$990$		0			0
$991$	−10.5739	−	12.1028i	−0.335892	−	0.384460i	0.560178	−	0.828372i	$-0.310733\pi$
$991$	−10.5739	−	12.1028i	−0.335892	−	0.384460i	−0.896070	+	0.443913i	$0.853590\pi$
$992$	−0.609438	−	13.5702i	−0.0193497	−	0.430854i
$993$		0			0
$994$	−0.00782298	+	0.0722850i	−0.000248130	+	0.00229274i
$995$		−	10.9291i		−	0.346476i
$996$		0			0
$997$	2.78442	−	2.43267i	0.0881834	−	0.0770435i	−0.612718	−	0.790301i	$-0.709924\pi$
$997$	2.78442	−	2.43267i	0.0881834	−	0.0770435i	0.700902	+	0.713258i	$0.252781\pi$
$998$	0.351578	+	3.90635i	0.0111290	+	0.123653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.35.14	yes	576
3.2	odd	2	inner	639.2.z.a.35.11	✓	576
71.69	odd	70	inner	639.2.z.a.566.11	yes	576
213.140	even	70	inner	639.2.z.a.566.14	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.35.11	✓	576	3.2	odd	2	inner
639.2.z.a.35.14	yes	576	1.1	even	1	trivial
639.2.z.a.566.11	yes	576	71.69	odd	70	inner
639.2.z.a.566.14	yes	576	213.140	even	70	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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.106529 - 0.00478422i) q^{2} +(-1.98062 + 0.178259i) q^{4} +(-0.619962 - 0.201438i) q^{5} +(-0.0215270 - 0.0780015i) q^{7} +(-0.421483 + 0.0570938i) q^{8} +O(q^{10})\)	\(q+(0.106529 - 0.00478422i) q^{2} +(-1.98062 + 0.178259i) q^{4} +(-0.619962 - 0.201438i) q^{5} +(-0.0215270 - 0.0780015i) q^{7} +(-0.421483 + 0.0570938i) q^{8} +(-0.0670076 - 0.0184929i) q^{10} +(1.23013 + 2.28596i) q^{11} +(-1.92504 - 1.03591i) q^{13} +(-0.00266643 - 0.00820642i) q^{14} +(3.86871 - 0.702068i) q^{16} +(5.32011 - 3.86529i) q^{17} +(2.21898 - 5.19156i) q^{19} +(1.26382 + 0.288459i) q^{20} +(0.141981 + 0.237635i) q^{22} +(3.47891 - 4.36242i) q^{23} +(-3.70131 - 2.68916i) q^{25} +(-0.210029 - 0.101144i) q^{26} +(0.0565415 + 0.150654i) q^{28} +(-4.65531 + 7.79167i) q^{29} +(1.90992 - 10.5245i) q^{31} +(1.23811 - 0.282590i) q^{32} +(0.548253 - 0.437218i) q^{34} +(-0.00236651 + 0.0526944i) q^{35} +(-1.73938 - 2.18111i) q^{37} +(0.211548 - 0.563667i) q^{38} +(0.272804 + 0.0495067i) q^{40} +(6.96427 - 3.35381i) q^{41} +(-6.71268 + 2.51931i) q^{43} +(-2.84391 - 4.30834i) q^{44} +(0.349734 - 0.481367i) q^{46} +(6.19842 + 5.41539i) q^{47} +(6.00352 - 3.58694i) q^{49} +(-0.407162 - 0.268765i) q^{50} +(3.99744 + 1.70859i) q^{52} +(8.21087 + 0.738992i) q^{53} +(-0.302153 - 1.66500i) q^{55} +(0.0135267 + 0.0316472i) q^{56} +(-0.458648 + 0.852310i) q^{58} +(-0.998534 + 1.04438i) q^{59} +(1.42392 - 5.15947i) q^{61} +(0.153110 - 1.13030i) q^{62} +(-7.44987 + 2.05603i) q^{64} +(0.984782 + 1.03000i) q^{65} +(-0.365764 - 4.06397i) q^{67} +(-9.84812 + 8.60404i) q^{68} +0.00562479i q^{70} +(-7.68706 - 3.45095i) q^{71} +(0.592849 + 13.2008i) q^{73} +(-0.195729 - 0.224030i) q^{74} +(-3.46952 + 10.6781i) q^{76} +(0.151827 - 0.145162i) q^{77} +(1.39388 + 10.2900i) q^{79} +(-2.53988 - 0.344050i) q^{80} +(0.725850 - 0.390597i) q^{82} +(-4.96061 - 4.74283i) q^{83} +(-4.07689 + 1.32466i) q^{85} +(-0.703041 + 0.300494i) q^{86} +(-0.648992 - 0.893260i) q^{88} +(1.14491 - 12.7210i) q^{89} +(-0.0393620 + 0.172456i) q^{91} +(-6.11277 + 9.26046i) q^{92} +(0.686219 + 0.547241i) q^{94} +(-2.42146 + 2.77159i) q^{95} +(7.16402 - 14.8762i) q^{97} +(0.622388 - 0.410834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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