LMFDB - Embedded newform 961.2.d.k.374.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			374.1
Root			$1.14412 + 0.831254i$ of defining polynomial
Character	$\chi$	$=$	961.374
Dual form			961.2.d.k.388.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{2} +(-2.28825 + 1.66251i) q^{3} +(-0.309017 - 0.951057i) q^{4} -2.82843 q^{6} +(1.23607 + 3.80423i) q^{7} +(0.927051 - 2.85317i) q^{8} +(1.54508 - 4.75528i) q^{9} +(0.874032 + 2.68999i) q^{11} +(2.28825 + 1.66251i) q^{12} +(-1.14412 + 0.831254i) q^{13} +(-1.23607 + 3.80423i) q^{14} +(0.809017 - 0.587785i) q^{16} +(0.437016 - 1.34500i) q^{17} +(4.04508 - 2.93893i) q^{18} +(3.23607 + 2.35114i) q^{19} +(-9.15298 - 6.65003i) q^{21} +(-0.874032 + 2.68999i) q^{22} +(-1.74806 + 5.37999i) q^{23} +(2.62210 + 8.06998i) q^{24} -5.00000 q^{25} -1.41421 q^{26} +(1.74806 + 5.37999i) q^{27} +(3.23607 - 2.35114i) q^{28} +(1.14412 + 0.831254i) q^{29} -5.00000 q^{32} +(-6.47214 - 4.70228i) q^{33} +(1.14412 - 0.831254i) q^{34} -5.00000 q^{36} -4.24264 q^{37} +(1.23607 + 3.80423i) q^{38} +(1.23607 - 3.80423i) q^{39} +(1.61803 + 1.17557i) q^{41} +(-3.49613 - 10.7600i) q^{42} +(-6.86474 - 4.98752i) q^{43} +(2.28825 - 1.66251i) q^{44} +(-4.57649 + 3.32502i) q^{46} +(-9.70820 + 7.05342i) q^{47} +(-0.874032 + 2.68999i) q^{48} +(-7.28115 + 5.29007i) q^{49} +(-4.04508 - 2.93893i) q^{50} +(1.23607 + 3.80423i) q^{51} +(1.14412 + 0.831254i) q^{52} +(1.31105 - 4.03499i) q^{53} +(-1.74806 + 5.37999i) q^{54} +12.0000 q^{56} -11.3137 q^{57} +(0.437016 + 1.34500i) q^{58} +(-6.47214 + 4.70228i) q^{59} +1.41421 q^{61} +20.0000 q^{63} +(-5.66312 - 4.11450i) q^{64} +(-2.47214 - 7.60845i) q^{66} -4.00000 q^{67} -1.41421 q^{68} +(-4.94427 - 15.2169i) q^{69} +(2.47214 - 7.60845i) q^{71} +(-12.1353 - 8.81678i) q^{72} +(-1.31105 - 4.03499i) q^{73} +(-3.43237 - 2.49376i) q^{74} +(11.4412 - 8.31254i) q^{75} +(1.23607 - 3.80423i) q^{76} +(-9.15298 + 6.65003i) q^{77} +(3.23607 - 2.35114i) q^{78} +(-3.49613 + 10.7600i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.618034 + 1.90211i) q^{82} +(11.4412 + 8.31254i) q^{83} +(-3.49613 + 10.7600i) q^{84} +(-2.62210 - 8.06998i) q^{86} -4.00000 q^{87} +8.48528 q^{88} +(-2.18508 - 6.72499i) q^{89} +(-4.57649 - 3.32502i) q^{91} +5.65685 q^{92} -12.0000 q^{94} +(11.4412 - 8.31254i) q^{96} +(2.47214 + 7.60845i) q^{97} -9.00000 q^{98} +14.1421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{4} - 8 q^{7} - 6 q^{8} - 10 q^{9} + 8 q^{14} + 2 q^{16} + 10 q^{18} + 8 q^{19} - 40 q^{25} + 8 q^{28} - 40 q^{32} - 16 q^{33} - 40 q^{36} - 8 q^{38} - 8 q^{39} + 4 q^{41} - 24 q^{47}+ \cdots - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^4 - 8 * q^7 - 6 * q^8 - 10 * q^9 + 8 * q^14 + 2 * q^16 + 10 * q^18 + 8 * q^19 - 40 * q^25 + 8 * q^28 - 40 * q^32 - 16 * q^33 - 40 * q^36 - 8 * q^38 - 8 * q^39 + 4 * q^41 - 24 * q^47 - 18 * q^49 - 10 * q^50 - 8 * q^51 + 96 * q^56 - 16 * q^59 + 160 * q^63 - 14 * q^64 + 16 * q^66 - 32 * q^67 + 32 * q^69 - 16 * q^71 - 30 * q^72 - 8 * q^76 + 8 * q^78 - 2 * q^81 - 4 * q^82 - 32 * q^87 - 96 * q^94 - 16 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i	0.835853	−	0.548953i	$-0.184973\pi$
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i	−0.263792	+	0.964580i	$0.584973\pi$
$3$	−2.28825	+	1.66251i	−1.32112	+	0.959849i	−0.321202	+	0.947011i	$0.604087\pi$
$3$	−2.28825	+	1.66251i	−1.32112	+	0.959849i	−0.999918	+	0.0128385i	$0.995913\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$	−2.82843			−1.15470
$7$	1.23607	+	3.80423i	0.467190	+	1.43786i	0.856208	+	0.516632i	$0.172814\pi$
$7$	1.23607	+	3.80423i	0.467190	+	1.43786i	−0.389018	+	0.921230i	$0.627186\pi$
$8$	0.927051	−	2.85317i	0.327762	−	1.00875i
$9$	1.54508	−	4.75528i	0.515028	−	1.58509i
$10$		0			0
$11$	0.874032	+	2.68999i	0.263531	+	0.811064i	0.992028	+	0.126015i	$0.0402189\pi$
$11$	0.874032	+	2.68999i	0.263531	+	0.811064i	−0.728498	+	0.685048i	$0.759781\pi$
$12$	2.28825	+	1.66251i	0.660560	+	0.479925i
$13$	−1.14412	+	0.831254i	−0.317323	+	0.230548i	−0.735032	−	0.678032i	$-0.762833\pi$
$13$	−1.14412	+	0.831254i	−0.317323	+	0.230548i	0.417710	+	0.908581i	$0.362833\pi$
$14$	−1.23607	+	3.80423i	−0.330353	+	1.01672i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	0.437016	−	1.34500i	0.105992	−	0.326210i	−0.883970	−	0.467544i	$-0.845139\pi$
$17$	0.437016	−	1.34500i	0.105992	−	0.326210i	0.989962	+	0.141334i	$0.0451391\pi$
$18$	4.04508	−	2.93893i	0.953436	−	0.692712i
$19$	3.23607	+	2.35114i	0.742405	+	0.539389i	0.893463	−	0.449136i	$-0.148268\pi$
$19$	3.23607	+	2.35114i	0.742405	+	0.539389i	−0.151058	+	0.988525i	$0.548268\pi$
$20$		0			0
$21$	−9.15298	−	6.65003i	−1.99734	−	1.45116i
$22$	−0.874032	+	2.68999i	−0.186344	+	0.573509i
$23$	−1.74806	+	5.37999i	−0.364497	+	1.12181i	0.585799	+	0.810456i	$0.300781\pi$
$23$	−1.74806	+	5.37999i	−0.364497	+	1.12181i	−0.950296	+	0.311349i	$0.899219\pi$
$24$	2.62210	+	8.06998i	0.535233	+	1.64728i
$25$	−5.00000			−1.00000
$26$	−1.41421			−0.277350
$27$	1.74806	+	5.37999i	0.336415	+	1.03538i
$28$	3.23607	−	2.35114i	0.611559	−	0.444324i
$29$	1.14412	+	0.831254i	0.212458	+	0.154360i	0.688925	−	0.724832i	$-0.258083\pi$
$29$	1.14412	+	0.831254i	0.212458	+	0.154360i	−0.476467	+	0.879192i	$0.658083\pi$
$30$		0			0
$31$		0			0
$31$		0			0
$32$	−5.00000			−0.883883
$33$	−6.47214	−	4.70228i	−1.12665	−	0.818562i
$34$	1.14412	−	0.831254i	0.196215	−	0.142559i
$35$		0			0
$36$	−5.00000			−0.833333
$37$	−4.24264			−0.697486			−0.348743	−	0.937218i	$-0.613391\pi$
$37$	−4.24264			−0.697486			−0.348743	+	0.937218i	$0.613391\pi$
$38$	1.23607	+	3.80423i	0.200517	+	0.617127i
$39$	1.23607	−	3.80423i	0.197929	−	0.609164i
$40$		0			0
$41$	1.61803	+	1.17557i	0.252694	+	0.183593i	0.706920	−	0.707293i	$-0.250084\pi$
$41$	1.61803	+	1.17557i	0.252694	+	0.183593i	−0.454226	+	0.890887i	$0.650084\pi$
$42$	−3.49613	−	10.7600i	−0.539464	−	1.66030i
$43$	−6.86474	−	4.98752i	−1.04686	−	0.760590i	−0.0752492	−	0.997165i	$-0.523975\pi$
$43$	−6.86474	−	4.98752i	−1.04686	−	0.760590i	−0.971613	+	0.236575i	$0.923975\pi$
$44$	2.28825	−	1.66251i	0.344966	−	0.250632i
$45$		0			0
$46$	−4.57649	+	3.32502i	−0.674767	+	0.490247i
$47$	−9.70820	+	7.05342i	−1.41609	+	1.02885i	−0.423685	+	0.905810i	$0.639264\pi$
$47$	−9.70820	+	7.05342i	−1.41609	+	1.02885i	−0.992402	+	0.123038i	$0.960736\pi$
$48$	−0.874032	+	2.68999i	−0.126156	+	0.388267i
$49$	−7.28115	+	5.29007i	−1.04016	+	0.755724i
$50$	−4.04508	−	2.93893i	−0.572061	−	0.415627i
$51$	1.23607	+	3.80423i	0.173084	+	0.532698i
$52$	1.14412	+	0.831254i	0.158661	+	0.115274i
$53$	1.31105	−	4.03499i	0.180086	−	0.554249i	−0.819743	−	0.572732i	$-0.805884\pi$
$53$	1.31105	−	4.03499i	0.180086	−	0.554249i	0.999829	+	0.0184831i	$0.00588368\pi$
$54$	−1.74806	+	5.37999i	−0.237881	+	0.732124i
$55$		0			0
$56$	12.0000			1.60357
$57$	−11.3137			−1.49854
$58$	0.437016	+	1.34500i	0.0573830	+	0.176607i
$59$	−6.47214	+	4.70228i	−0.842600	+	0.612185i	−0.923096	−	0.384570i	$-0.874350\pi$
$59$	−6.47214	+	4.70228i	−0.842600	+	0.612185i	0.0804955	+	0.996755i	$0.474350\pi$
$60$		0			0
$61$	1.41421			0.181071			0.0905357	−	0.995893i	$-0.471142\pi$
$61$	1.41421			0.181071			0.0905357	+	0.995893i	$0.471142\pi$
$62$		0			0
$63$	20.0000			2.51976
$64$	−5.66312	−	4.11450i	−0.707890	−	0.514312i
$65$		0			0
$66$	−2.47214	−	7.60845i	−0.304299	−	0.936536i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.41421			−0.171499
$69$	−4.94427	−	15.2169i	−0.595220	−	1.83190i
$70$		0			0
$71$	2.47214	−	7.60845i	0.293389	−	0.902957i	−0.690369	−	0.723457i	$-0.742552\pi$
$71$	2.47214	−	7.60845i	0.293389	−	0.902957i	0.983758	−	0.179500i	$-0.0574480\pi$
$72$	−12.1353	−	8.81678i	−1.43015	−	1.03907i
$73$	−1.31105	−	4.03499i	−0.153447	−	0.472260i	0.844554	−	0.535471i	$-0.179866\pi$
$73$	−1.31105	−	4.03499i	−0.153447	−	0.472260i	−0.998000	+	0.0632110i	$0.979866\pi$
$74$	−3.43237	−	2.49376i	−0.399005	−	0.289894i
$75$	11.4412	−	8.31254i	1.32112	−	0.959849i
$76$	1.23607	−	3.80423i	0.141787	−	0.436375i
$77$	−9.15298	+	6.65003i	−1.04308	+	0.757841i
$78$	3.23607	−	2.35114i	0.366413	−	0.266214i
$79$	−3.49613	+	10.7600i	−0.393345	+	1.21059i	0.536898	+	0.843647i	$0.319596\pi$
$79$	−3.49613	+	10.7600i	−0.393345	+	1.21059i	−0.930243	+	0.366945i	$0.880404\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.618034	+	1.90211i	0.0682504	+	0.210053i
$83$	11.4412	+	8.31254i	1.25584	+	0.912420i	0.998546	−	0.0539139i	$-0.0171697\pi$
$83$	11.4412	+	8.31254i	1.25584	+	0.912420i	0.257292	+	0.966334i	$0.417170\pi$
$84$	−3.49613	+	10.7600i	−0.381459	+	1.17401i
$85$		0			0
$86$	−2.62210	−	8.06998i	−0.282748	−	0.870209i
$87$	−4.00000			−0.428845
$88$	8.48528			0.904534
$89$	−2.18508	−	6.72499i	−0.231618	−	0.712847i	−0.997552	−	0.0699278i	$-0.977723\pi$
$89$	−2.18508	−	6.72499i	−0.231618	−	0.712847i	0.765934	−	0.642919i	$-0.222277\pi$
$90$		0			0
$91$	−4.57649	−	3.32502i	−0.479747	−	0.348556i
$92$	5.65685			0.589768
$93$		0			0
$94$	−12.0000			−1.23771
$95$		0			0
$96$	11.4412	−	8.31254i	1.16772	−	0.848395i
$97$	2.47214	+	7.60845i	0.251007	+	0.772521i	0.994590	+	0.103877i	$0.0331249\pi$
$97$	2.47214	+	7.60845i	0.251007	+	0.772521i	−0.743583	+	0.668644i	$0.766875\pi$
$98$	−9.00000			−0.909137
$99$	14.1421			1.42134
$100$	1.54508	+	4.75528i	0.154508	+	0.475528i
$101$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$101$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$102$	−1.23607	+	3.80423i	−0.122389	+	0.376675i
$103$	12.9443	+	9.40456i	1.27544	+	0.926659i	0.999405	−	0.0344892i	$-0.0109804\pi$
$103$	12.9443	+	9.40456i	1.27544	+	0.926659i	0.276032	+	0.961148i	$0.410980\pi$
$104$	1.31105	+	4.03499i	0.128559	+	0.395663i
$105$		0			0
$106$	3.43237	−	2.49376i	0.333381	−	0.242216i
$107$	−2.47214	+	7.60845i	−0.238990	+	0.735537i	0.757577	+	0.652746i	$0.226383\pi$
$107$	−2.47214	+	7.60845i	−0.238990	+	0.735537i	−0.996567	+	0.0827905i	$0.973617\pi$
$108$	4.57649	−	3.32502i	0.440373	−	0.319950i
$109$	−1.61803	+	1.17557i	−0.154980	+	0.112599i	−0.662573	−	0.748998i	$-0.730535\pi$
$109$	−1.61803	+	1.17557i	−0.154980	+	0.112599i	0.507593	+	0.861597i	$0.330535\pi$
$110$		0			0
$111$	9.70820	−	7.05342i	0.921462	−	0.669481i
$112$	3.23607	+	2.35114i	0.305780	+	0.222162i
$113$	2.47214	+	7.60845i	0.232559	+	0.715743i	0.997436	+	0.0715664i	$0.0227998\pi$
$113$	2.47214	+	7.60845i	0.232559	+	0.715743i	−0.764877	+	0.644177i	$0.777200\pi$
$114$	−9.15298	−	6.65003i	−0.857255	−	0.622832i
$115$		0			0
$116$	0.437016	−	1.34500i	0.0405759	−	0.124880i
$117$	2.18508	+	6.72499i	0.202011	+	0.621725i
$118$	−8.00000			−0.736460
$119$	5.65685			0.518563
$120$		0			0
$121$	2.42705	−	1.76336i	0.220641	−	0.160305i
$122$	1.14412	+	0.831254i	0.103584	+	0.0752582i
$123$	−5.65685			−0.510061
$124$		0			0
$125$		0			0
$126$	16.1803	+	11.7557i	1.44146	+	1.04728i
$127$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$127$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$128$	0.927051	+	2.85317i	0.0819405	+	0.252187i
$129$	24.0000			2.11308
$130$		0			0
$131$	1.23607	+	3.80423i	0.107996	+	0.332377i	0.990422	−	0.138074i	$-0.0440912\pi$
$131$	1.23607	+	3.80423i	0.107996	+	0.332377i	−0.882426	+	0.470451i	$0.844091\pi$
$132$	−2.47214	+	7.60845i	−0.215172	+	0.662231i
$133$	−4.94427	+	15.2169i	−0.428723	+	1.31947i
$134$	−3.23607	−	2.35114i	−0.279554	−	0.203108i
$135$		0			0
$136$	−3.43237	−	2.49376i	−0.294323	−	0.213838i
$137$	−12.5854	+	9.14379i	−1.07524	+	0.781207i	−0.976847	−	0.213941i	$-0.931370\pi$
$137$	−12.5854	+	9.14379i	−1.07524	+	0.781207i	−0.0983925	+	0.995148i	$0.531370\pi$
$138$	4.94427	−	15.2169i	0.420884	−	1.29535i
$139$	16.0177	−	11.6376i	1.35861	−	0.987084i	0.360073	−	0.932924i	$-0.382752\pi$
$139$	16.0177	−	11.6376i	1.35861	−	0.987084i	0.998532	−	0.0541603i	$-0.0172482\pi$
$140$		0			0
$141$	10.4884	−	32.2799i	0.883281	−	2.71846i
$142$	6.47214	−	4.70228i	0.543130	−	0.394607i
$143$	−3.23607	−	2.35114i	−0.270614	−	0.196612i
$144$	−1.54508	−	4.75528i	−0.128757	−	0.396274i
$145$		0			0
$146$	1.31105	−	4.03499i	0.108503	−	0.333938i
$147$	7.86629	−	24.2099i	0.648801	−	1.99680i
$148$	1.31105	+	4.03499i	0.107767	+	0.331674i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	14.1421			1.15470
$151$	−3.49613	−	10.7600i	−0.284511	−	0.875634i	−0.986545	−	0.163491i	$-0.947725\pi$
$151$	−3.49613	−	10.7600i	−0.284511	−	0.875634i	0.702034	−	0.712143i	$-0.252275\pi$
$152$	9.70820	−	7.05342i	0.787439	−	0.572108i
$153$	−5.72061	−	4.15627i	−0.462484	−	0.336014i
$154$	−11.3137			−0.911685
$155$		0			0
$156$	−4.00000			−0.320256
$157$	−1.61803	−	1.17557i	−0.129133	−	0.0938207i	0.521344	−	0.853347i	$-0.325431\pi$
$157$	−1.61803	−	1.17557i	−0.129133	−	0.0938207i	−0.650477	+	0.759526i	$0.725431\pi$
$158$	−9.15298	+	6.65003i	−0.728172	+	0.529048i
$159$	3.70820	+	11.4127i	0.294080	+	0.905084i
$160$		0			0
$161$	−22.6274			−1.78329
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	4.94427	−	15.2169i	0.387265	−	1.19188i	−0.547558	−	0.836768i	$-0.684443\pi$
$163$	4.94427	−	15.2169i	0.387265	−	1.19188i	0.934824	−	0.355112i	$-0.115557\pi$
$164$	0.618034	−	1.90211i	0.0482603	−	0.148530i
$165$		0			0
$166$	4.37016	+	13.4500i	0.339190	+	1.04392i
$167$	13.7295	+	9.97505i	1.06242	+	0.771892i	0.974534	−	0.224238i	$-0.0719894\pi$
$167$	13.7295	+	9.97505i	1.06242	+	0.771892i	0.0878843	+	0.996131i	$0.471989\pi$
$168$	−27.4589	+	19.9501i	−2.11850	+	1.53918i
$169$	−3.39919	+	10.4616i	−0.261476	+	0.804740i
$170$		0			0
$171$	16.1803	−	11.7557i	1.23734	−	0.898981i
$172$	−2.62210	+	8.06998i	−0.199933	+	0.615330i
$173$	−14.5623	+	10.5801i	−1.10715	+	0.804393i	−0.982213	−	0.187772i	$-0.939873\pi$
$173$	−14.5623	+	10.5801i	−1.10715	+	0.804393i	−0.124939	+	0.992164i	$0.539873\pi$
$174$	−3.23607	−	2.35114i	−0.245326	−	0.178240i
$175$	−6.18034	−	19.0211i	−0.467190	−	1.43786i
$176$	2.28825	+	1.66251i	0.172483	+	0.125316i
$177$	6.99226	−	21.5200i	0.525570	−	1.61754i
$178$	2.18508	−	6.72499i	0.163779	−	0.504059i
$179$	−7.86629	−	24.2099i	−0.587954	−	1.80954i	−0.587069	−	0.809537i	$-0.699718\pi$
$179$	−7.86629	−	24.2099i	−0.587954	−	1.80954i	−0.000884795	−	1.00000i	$-0.500282\pi$
$180$		0			0
$181$	4.24264			0.315353			0.157676	−	0.987491i	$-0.449600\pi$
$181$	4.24264			0.315353			0.157676	+	0.987491i	$0.449600\pi$
$182$	−1.74806	−	5.37999i	−0.129575	−	0.398791i
$183$	−3.23607	+	2.35114i	−0.239217	+	0.173801i
$184$	13.7295	+	9.97505i	1.01215	+	0.735370i
$185$		0			0
$186$		0			0
$187$	4.00000			0.292509
$188$	9.70820	+	7.05342i	0.708044	+	0.514424i
$189$	−18.3060	+	13.3001i	−1.33156	+	0.967437i
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	19.7990			1.42887
$193$	4.94427	+	15.2169i	0.355896	+	1.09534i	0.955488	+	0.295030i	$0.0953298\pi$
$193$	4.94427	+	15.2169i	0.355896	+	1.09534i	−0.599591	+	0.800306i	$0.704670\pi$
$194$	−2.47214	+	7.60845i	−0.177489	+	0.546255i
$195$		0			0
$196$	7.28115	+	5.29007i	0.520082	+	0.377862i
$197$	5.68121	+	17.4850i	0.404769	+	1.24575i	0.921088	+	0.389355i	$0.127302\pi$
$197$	5.68121	+	17.4850i	0.404769	+	1.24575i	−0.516318	+	0.856397i	$0.672698\pi$
$198$	11.4412	+	8.31254i	0.813093	+	0.590746i
$199$	9.15298	−	6.65003i	0.648838	−	0.471408i	−0.214037	−	0.976825i	$-0.568661\pi$
$199$	9.15298	−	6.65003i	0.648838	−	0.471408i	0.862875	+	0.505417i	$0.168661\pi$
$200$	−4.63525	+	14.2658i	−0.327762	+	1.00875i
$201$	9.15298	−	6.65003i	0.645602	−	0.469057i
$202$		0			0
$203$	−1.74806	+	5.37999i	−0.122690	+	0.377601i
$204$	3.23607	−	2.35114i	0.226570	−	0.164613i
$205$		0			0
$206$	4.94427	+	15.2169i	0.344484	+	1.06021i
$207$	22.8825	+	16.6251i	1.59044	+	1.15552i
$208$	−0.437016	+	1.34500i	−0.0303016	+	0.0932588i
$209$	−3.49613	+	10.7600i	−0.241832	+	0.744283i
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	−4.24264			−0.291386
$213$	6.99226	+	21.5200i	0.479102	+	1.47452i
$214$	−6.47214	+	4.70228i	−0.442426	+	0.321441i
$215$		0			0
$216$	16.9706			1.15470
$217$		0			0
$218$	−2.00000			−0.135457
$219$	9.70820	+	7.05342i	0.656020	+	0.476626i
$220$		0			0
$221$	0.618034	+	1.90211i	0.0415735	+	0.127950i
$222$	12.0000			0.805387
$223$	16.9706			1.13643			0.568216	−	0.822879i	$-0.307634\pi$
$223$	16.9706			1.13643			0.568216	+	0.822879i	$0.307634\pi$
$224$	−6.18034	−	19.0211i	−0.412941	−	1.27090i
$225$	−7.72542	+	23.7764i	−0.515028	+	1.58509i
$226$	−2.47214	+	7.60845i	−0.164444	+	0.506107i
$227$	−19.4164	−	14.1068i	−1.28871	−	0.936304i	−0.288934	−	0.957349i	$-0.593301\pi$
$227$	−19.4164	−	14.1068i	−1.28871	−	0.936304i	−0.999779	+	0.0210448i	$0.993301\pi$
$228$	3.49613	+	10.7600i	0.231537	+	0.712597i
$229$	14.8736	+	10.8063i	0.982875	+	0.714100i	0.958349	−	0.285599i	$-0.0921925\pi$
$229$	14.8736	+	10.8063i	0.982875	+	0.714100i	0.0245256	+	0.999699i	$0.492192\pi$
$230$		0			0
$231$	9.88854	−	30.4338i	0.650618	−	2.00240i
$232$	3.43237	−	2.49376i	0.225346	−	0.163723i
$233$	19.4164	−	14.1068i	1.27201	−	0.924170i	0.272730	−	0.962090i	$-0.412073\pi$
$233$	19.4164	−	14.1068i	1.27201	−	0.924170i	0.999281	+	0.0379203i	$0.0120733\pi$
$234$	−2.18508	+	6.72499i	−0.142843	+	0.439626i
$235$		0			0
$236$	6.47214	+	4.70228i	0.421300	+	0.306092i
$237$	−9.88854	−	30.4338i	−0.642330	−	1.97689i
$238$	4.57649	+	3.32502i	0.296650	+	0.215529i
$239$	−6.99226	+	21.5200i	−0.452291	+	1.39201i	0.421994	+	0.906598i	$0.361330\pi$
$239$	−6.99226	+	21.5200i	−0.452291	+	1.39201i	−0.874286	+	0.485412i	$0.838670\pi$
$240$		0			0
$241$	−3.05911	−	9.41498i	−0.197055	−	0.606472i	−0.999946	−	0.0103472i	$-0.996706\pi$
$241$	−3.05911	−	9.41498i	−0.197055	−	0.606472i	0.802892	−	0.596125i	$-0.203294\pi$
$242$	3.00000			0.192847
$243$	−14.1421			−0.907218
$244$	−0.437016	−	1.34500i	−0.0279771	−	0.0861046i
$245$		0			0
$246$	−4.57649	−	3.32502i	−0.291786	−	0.211995i
$247$	−5.65685			−0.359937
$248$		0			0
$249$	−40.0000			−2.53490
$250$		0			0
$251$	−2.28825	+	1.66251i	−0.144433	+	0.104937i	−0.657655	−	0.753319i	$-0.728452\pi$
$251$	−2.28825	+	1.66251i	−0.144433	+	0.104937i	0.513222	+	0.858256i	$0.328452\pi$
$252$	−6.18034	−	19.0211i	−0.389325	−	1.19822i
$253$	−16.0000			−1.00591
$254$		0			0
$255$		0			0
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$257$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$258$	19.4164	+	14.1068i	1.20881	+	0.878254i
$259$	−5.24419	−	16.1400i	−0.325858	−	1.00289i
$260$		0			0
$261$	5.72061	−	4.15627i	0.354097	−	0.257267i
$262$	−1.23607	+	3.80423i	−0.0763645	+	0.235026i
$263$	−22.8825	+	16.6251i	−1.41099	+	1.02515i	−0.417815	+	0.908532i	$0.637204\pi$
$263$	−22.8825	+	16.6251i	−1.41099	+	1.02515i	−0.993177	+	0.116614i	$0.962796\pi$
$264$	−19.4164	+	14.1068i	−1.19500	+	0.868216i
$265$		0			0
$266$	−12.9443	+	9.40456i	−0.793664	+	0.576631i
$267$	16.1803	+	11.7557i	0.990221	+	0.719437i
$268$	1.23607	+	3.80423i	0.0755049	+	0.232380i
$269$	1.14412	+	0.831254i	0.0697584	+	0.0506824i	0.622118	−	0.782924i	$-0.286272\pi$
$269$	1.14412	+	0.831254i	0.0697584	+	0.0506824i	−0.552360	+	0.833606i	$0.686272\pi$
$270$		0			0
$271$	1.74806	−	5.37999i	0.106187	−	0.326811i	−0.883820	−	0.467827i	$-0.845037\pi$
$271$	1.74806	−	5.37999i	0.106187	−	0.326811i	0.990007	+	0.141016i	$0.0450370\pi$
$272$	−0.437016	−	1.34500i	−0.0264980	−	0.0815524i
$273$	16.0000			0.968364
$274$	−15.5563			−0.939793
$275$	−4.37016	−	13.4500i	−0.263531	−	0.811064i
$276$	−12.9443	+	9.40456i	−0.779154	+	0.566088i
$277$	3.43237	+	2.49376i	0.206231	+	0.149836i	0.686107	−	0.727501i	$-0.259318\pi$
$277$	3.43237	+	2.49376i	0.206231	+	0.149836i	−0.479876	+	0.877336i	$0.659318\pi$
$278$	19.7990			1.18746
$279$		0			0
$280$		0			0
$281$	−12.9443	−	9.40456i	−0.772191	−	0.561029i	0.130435	−	0.991457i	$-0.458363\pi$
$281$	−12.9443	−	9.40456i	−0.772191	−	0.561029i	−0.902625	+	0.430428i	$0.858363\pi$
$282$	27.4589	−	19.9501i	1.63516	−	1.18801i
$283$	−4.94427	−	15.2169i	−0.293906	−	0.904551i	−0.983587	−	0.180437i	$-0.942249\pi$
$283$	−4.94427	−	15.2169i	−0.293906	−	0.904551i	0.689680	−	0.724114i	$-0.257751\pi$
$284$	−8.00000			−0.474713
$285$		0			0
$286$	−1.23607	−	3.80423i	−0.0730902	−	0.224949i
$287$	−2.47214	+	7.60845i	−0.145926	+	0.449113i
$288$	−7.72542	+	23.7764i	−0.455225	+	1.40104i
$289$	12.1353	+	8.81678i	0.713839	+	0.518634i
$290$		0			0
$291$	−18.3060	−	13.3001i	−1.07311	−	0.779663i
$292$	−3.43237	+	2.49376i	−0.200864	+	0.145936i
$293$	8.03444	−	24.7275i	0.469377	−	1.44459i	−0.384016	−	0.923326i	$-0.625459\pi$
$293$	8.03444	−	24.7275i	0.469377	−	1.44459i	0.853393	−	0.521268i	$-0.174541\pi$
$294$	20.5942	−	14.9626i	1.20108	−	0.872635i
$295$		0			0
$296$	−3.93314	+	12.1050i	−0.228609	+	0.703587i
$297$	−12.9443	+	9.40456i	−0.751103	+	0.545708i
$298$		0			0
$299$	−2.47214	−	7.60845i	−0.142967	−	0.440008i
$300$	−11.4412	−	8.31254i	−0.660560	−	0.479925i
$301$	10.4884	−	32.2799i	0.604540	−	1.86058i
$302$	3.49613	−	10.7600i	0.201180	−	0.619167i
$303$		0			0
$304$	4.00000			0.229416
$305$		0			0
$306$	−2.18508	−	6.72499i	−0.124913	−	0.384442i
$307$	12.9443	−	9.40456i	0.738769	−	0.536747i	−0.153557	−	0.988140i	$-0.549073\pi$
$307$	12.9443	−	9.40456i	0.738769	−	0.536747i	0.892325	+	0.451393i	$0.149073\pi$
$308$	9.15298	+	6.65003i	0.521540	+	0.378921i
$309$	−45.2548			−2.57446
$310$		0			0
$311$	16.0000			0.907277			0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000			0.907277			0.453638	+	0.891186i	$0.350126\pi$
$312$	−9.70820	−	7.05342i	−0.549619	−	0.399321i
$313$	24.0266	−	17.4563i	1.35806	−	0.986690i	0.359497	−	0.933146i	$-0.382948\pi$
$313$	24.0266	−	17.4563i	1.35806	−	0.986690i	0.998565	−	0.0535440i	$-0.0170517\pi$
$314$	−0.618034	−	1.90211i	−0.0348777	−	0.107342i
$315$		0			0
$316$	11.3137			0.636446
$317$	−4.94427	−	15.2169i	−0.277698	−	0.854666i	−0.988493	−	0.151267i	$-0.951665\pi$
$317$	−4.94427	−	15.2169i	−0.277698	−	0.854666i	0.710795	−	0.703399i	$-0.248335\pi$
$318$	−3.70820	+	11.4127i	−0.207946	+	0.639991i
$319$	−1.23607	+	3.80423i	−0.0692065	+	0.212996i
$320$		0			0
$321$	−6.99226	−	21.5200i	−0.390270	−	1.20113i
$322$	−18.3060	−	13.3001i	−1.02015	−	0.741183i
$323$	4.57649	−	3.32502i	0.254643	−	0.185009i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	5.72061	−	4.15627i	0.317323	−	0.230548i
$326$	12.9443	−	9.40456i	0.716917	−	0.520871i
$327$	1.74806	−	5.37999i	0.0966682	−	0.297514i
$328$	4.85410	−	3.52671i	0.268023	−	0.194730i
$329$	−38.8328	−	28.2137i	−2.14092	−	1.55547i
$330$		0			0
$331$	2.28825	+	1.66251i	0.125773	+	0.0913797i	0.648893	−	0.760879i	$-0.275232\pi$
$331$	2.28825	+	1.66251i	0.125773	+	0.0913797i	−0.523120	+	0.852259i	$0.675232\pi$
$332$	4.37016	−	13.4500i	0.239844	−	0.738163i
$333$	−6.55524	+	20.1750i	−0.359225	+	1.10558i
$334$	5.24419	+	16.1400i	0.286949	+	0.883140i
$335$		0			0
$336$	−11.3137			−0.617213
$337$	10.9254	+	33.6249i	0.595144	+	1.83167i	0.554006	+	0.832513i	$0.313099\pi$
$337$	10.9254	+	33.6249i	0.595144	+	1.83167i	0.0411389	+	0.999153i	$0.486901\pi$
$338$	−8.89919	+	6.46564i	−0.484052	+	0.351684i
$339$	−18.3060	−	13.3001i	−0.994244	−	0.722360i
$340$		0			0
$341$		0			0
$342$	20.0000			1.08148
$343$	−6.47214	−	4.70228i	−0.349462	−	0.253899i
$344$	−20.5942	+	14.9626i	−1.11037	+	0.806728i
$345$		0			0
$346$	−18.0000			−0.967686
$347$	−19.7990			−1.06287			−0.531433	−	0.847100i	$-0.678346\pi$
$347$	−19.7990			−1.06287			−0.531433	+	0.847100i	$0.678346\pi$
$348$	1.23607	+	3.80423i	0.0662602	+	0.203928i
$349$	4.94427	−	15.2169i	0.264661	−	0.814542i	−0.727111	−	0.686520i	$-0.759137\pi$
$349$	4.94427	−	15.2169i	0.264661	−	0.814542i	0.991771	−	0.128022i	$-0.0408628\pi$
$350$	6.18034	−	19.0211i	0.330353	−	1.01672i
$351$	−6.47214	−	4.70228i	−0.345457	−	0.250989i
$352$	−4.37016	−	13.4500i	−0.232930	−	0.716886i
$353$	10.2971	+	7.48128i	0.548060	+	0.398189i	0.827070	−	0.562100i	$-0.190006\pi$
$353$	10.2971	+	7.48128i	0.548060	+	0.398189i	−0.279010	+	0.960288i	$0.590006\pi$
$354$	18.3060	−	13.3001i	0.972951	−	0.706890i
$355$		0			0
$356$	−5.72061	+	4.15627i	−0.303192	+	0.220282i
$357$	−12.9443	+	9.40456i	−0.685084	+	0.497742i
$358$	7.86629	−	24.2099i	0.415746	−	1.27954i
$359$	−9.70820	+	7.05342i	−0.512379	+	0.372265i	−0.813725	−	0.581249i	$-0.802564\pi$
$359$	−9.70820	+	7.05342i	−0.512379	+	0.372265i	0.301346	+	0.953515i	$0.402564\pi$
$360$		0			0
$361$	−0.927051	−	2.85317i	−0.0487922	−	0.150167i
$362$	3.43237	+	2.49376i	0.180401	+	0.131069i
$363$	−2.62210	+	8.06998i	−0.137624	+	0.423564i
$364$	−1.74806	+	5.37999i	−0.0916235	+	0.281988i
$365$		0			0
$366$	−4.00000			−0.209083
$367$	16.9706			0.885856			0.442928	−	0.896557i	$-0.353940\pi$
$367$	16.9706			0.885856			0.442928	+	0.896557i	$0.353940\pi$
$368$	1.74806	+	5.37999i	0.0911241	+	0.280451i
$369$	8.09017	−	5.87785i	0.421157	−	0.305989i
$370$		0			0
$371$	16.9706			0.881068
$372$		0			0
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$	3.23607	+	2.35114i	0.167333	+	0.121575i
$375$		0			0
$376$	11.1246	+	34.2380i	0.573708	+	1.76569i
$377$	−2.00000			−0.103005
$378$	−22.6274			−1.16383
$379$	−4.94427	−	15.2169i	−0.253970	−	0.781640i	−0.994031	−	0.109100i	$-0.965203\pi$
$379$	−4.94427	−	15.2169i	−0.253970	−	0.781640i	0.740061	−	0.672540i	$-0.234797\pi$
$380$		0			0
$381$		0			0
$382$	9.70820	+	7.05342i	0.496715	+	0.360885i
$383$	1.74806	+	5.37999i	0.0893219	+	0.274905i	0.985732	−	0.168320i	$-0.0538343\pi$
$383$	1.74806	+	5.37999i	0.0893219	+	0.274905i	−0.896410	+	0.443225i	$0.853834\pi$
$384$	−6.86474	−	4.98752i	−0.350315	−	0.254518i
$385$		0			0
$386$	−4.94427	+	15.2169i	−0.251657	+	0.774520i
$387$	−34.3237	+	24.9376i	−1.74477	+	1.26765i
$388$	6.47214	−	4.70228i	0.328573	−	0.238722i
$389$	−4.80718	+	14.7950i	−0.243734	+	0.750135i	0.752109	+	0.659039i	$0.229037\pi$
$389$	−4.80718	+	14.7950i	−0.243734	+	0.750135i	−0.995842	+	0.0910955i	$0.970963\pi$
$390$		0			0
$391$	6.47214	+	4.70228i	0.327310	+	0.237805i
$392$	8.34346	+	25.6785i	0.421408	+	1.29696i
$393$	−9.15298	−	6.65003i	−0.461707	−	0.335450i
$394$	−5.68121	+	17.4850i	−0.286215	+	0.880880i
$395$		0			0
$396$	−4.37016	−	13.4500i	−0.219609	−	0.675886i
$397$	−32.0000			−1.60603			−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000			−1.60603			−0.803017	+	0.595956i	$0.796773\pi$
$398$	11.3137			0.567105
$399$	−13.9845	−	43.0399i	−0.700101	−	2.15469i
$400$	−4.04508	+	2.93893i	−0.202254	+	0.146946i
$401$	1.14412	+	0.831254i	0.0571348	+	0.0415108i	0.615986	−	0.787757i	$-0.288758\pi$
$401$	1.14412	+	0.831254i	0.0571348	+	0.0415108i	−0.558851	+	0.829268i	$0.688758\pi$
$402$	11.3137			0.564276
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−4.57649	+	3.32502i	−0.227127	+	0.165018i
$407$	−3.70820	−	11.4127i	−0.183809	−	0.565705i
$408$	12.0000			0.594089
$409$	4.24264			0.209785			0.104893	−	0.994484i	$-0.466550\pi$
$409$	4.24264			0.209785			0.104893	+	0.994484i	$0.466550\pi$
$410$		0			0
$411$	13.5967	−	41.8465i	0.670678	−	2.06413i
$412$	4.94427	−	15.2169i	0.243587	−	0.749683i
$413$	−25.8885	−	18.8091i	−1.27389	−	0.925537i
$414$	8.74032	+	26.8999i	0.429563	+	1.32206i
$415$		0			0
$416$	5.72061	−	4.15627i	0.280476	−	0.203778i
$417$	−17.3050	+	53.2592i	−0.847427	+	2.60811i
$418$	−9.15298	+	6.65003i	−0.447687	+	0.325264i
$419$	−12.9443	+	9.40456i	−0.632369	+	0.459443i	−0.857220	−	0.514950i	$-0.827810\pi$
$419$	−12.9443	+	9.40456i	−0.632369	+	0.459443i	0.224851	+	0.974393i	$0.427810\pi$
$420$		0			0
$421$	25.8885	−	18.8091i	1.26173	−	0.916701i	0.262889	−	0.964826i	$-0.415325\pi$
$421$	25.8885	−	18.8091i	1.26173	−	0.916701i	0.998841	+	0.0481252i	$0.0153247\pi$
$422$		0			0
$423$	18.5410	+	57.0634i	0.901495	+	2.77452i
$424$	−10.2971	−	7.48128i	−0.500072	−	0.363323i
$425$	−2.18508	+	6.72499i	−0.105992	+	0.326210i
$426$	−6.99226	+	21.5200i	−0.338776	+	1.04265i
$427$	1.74806	+	5.37999i	0.0845948	+	0.260356i
$428$	8.00000			0.386695
$429$	11.3137			0.546231
$430$		0			0
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	−0.796516	−	0.604617i	$-0.793326\pi$
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	0.328888	+	0.944369i	$0.393326\pi$
$432$	4.57649	+	3.32502i	0.220187	+	0.159975i
$433$	12.7279			0.611665			0.305832	−	0.952085i	$-0.401065\pi$
$433$	12.7279			0.611665			0.305832	+	0.952085i	$0.401065\pi$
$434$		0			0
$435$		0			0
$436$	1.61803	+	1.17557i	0.0774898	+	0.0562996i
$437$	−18.3060	+	13.3001i	−0.875693	+	0.636228i
$438$	3.70820	+	11.4127i	0.177185	+	0.545319i
$439$	20.0000			0.954548			0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000			0.954548			0.477274	+	0.878755i	$0.341625\pi$
$440$		0			0
$441$	13.9058	+	42.7975i	0.662179	+	2.03798i
$442$	−0.618034	+	1.90211i	−0.0293969	+	0.0904743i
$443$	6.18034	−	19.0211i	0.293637	−	0.903721i	−0.690039	−	0.723772i	$-0.742407\pi$
$443$	6.18034	−	19.0211i	0.293637	−	0.903721i	0.983676	−	0.179949i	$-0.0575933\pi$
$444$	−9.70820	−	7.05342i	−0.460731	−	0.334741i
$445$		0			0
$446$	13.7295	+	9.97505i	0.650109	+	0.472332i
$447$		0			0
$448$	8.65248	−	26.6296i	0.408791	−	1.25813i
$449$	19.4501	−	14.1313i	0.917906	−	0.666898i	−0.0250956	−	0.999685i	$-0.507989\pi$
$449$	19.4501	−	14.1313i	0.917906	−	0.666898i	0.943002	+	0.332787i	$0.107989\pi$
$450$	−20.2254	+	14.6946i	−0.953436	+	0.692712i
$451$	−1.74806	+	5.37999i	−0.0823131	+	0.253334i
$452$	6.47214	−	4.70228i	0.304424	−	0.221177i
$453$	25.8885	+	18.8091i	1.21635	+	0.883730i
$454$	−7.41641	−	22.8254i	−0.348069	−	1.07125i
$455$		0			0
$456$	−10.4884	+	32.2799i	−0.491164	+	1.51165i
$457$	−1.31105	+	4.03499i	−0.0613282	+	0.188749i	−0.977027	−	0.213117i	$-0.931638\pi$
$457$	−1.31105	+	4.03499i	−0.0613282	+	0.188749i	0.915698	+	0.401866i	$0.131638\pi$
$458$	5.68121	+	17.4850i	0.265465	+	0.817019i
$459$	8.00000			0.373408
$460$		0			0
$461$	7.42927	+	22.8649i	0.346016	+	1.06493i	0.961038	+	0.276417i	$0.0891471\pi$
$461$	7.42927	+	22.8649i	0.346016	+	1.06493i	−0.615022	+	0.788510i	$0.710853\pi$
$462$	25.8885	−	18.8091i	1.20444	−	0.875080i
$463$	−18.3060	−	13.3001i	−0.850750	−	0.618106i	0.0746025	−	0.997213i	$-0.476231\pi$
$463$	−18.3060	−	13.3001i	−0.850750	−	0.618106i	−0.925353	+	0.379107i	$0.876231\pi$
$464$	1.41421			0.0656532
$465$		0			0
$466$	24.0000			1.11178
$467$	32.3607	+	23.5114i	1.49747	+	1.08798i	0.971374	+	0.237555i	$0.0763461\pi$
$467$	32.3607	+	23.5114i	1.49747	+	1.08798i	0.526100	+	0.850423i	$0.323654\pi$
$468$	5.72061	−	4.15627i	0.264435	−	0.192124i
$469$	−4.94427	−	15.2169i	−0.228305	−	0.702651i
$470$		0			0
$471$	5.65685			0.260654
$472$	7.41641	+	22.8254i	0.341368	+	1.05062i
$473$	7.41641	−	22.8254i	0.341007	−	1.04951i
$474$	9.88854	−	30.4338i	0.454196	−	1.39787i
$475$	−16.1803	−	11.7557i	−0.742405	−	0.539389i
$476$	−1.74806	−	5.37999i	−0.0801224	−	0.246591i
$477$	−17.1618	−	12.4688i	−0.785787	−	0.570908i
$478$	−18.3060	+	13.3001i	−0.837295	+	0.608331i
$479$	−7.41641	+	22.8254i	−0.338864	+	1.04292i	0.625923	+	0.779885i	$0.284723\pi$
$479$	−7.41641	+	22.8254i	−0.338864	+	1.04292i	−0.964787	+	0.263032i	$0.915277\pi$
$480$		0			0
$481$	4.85410	−	3.52671i	0.221328	−	0.160804i
$482$	3.05911	−	9.41498i	0.139339	−	0.428841i
$483$	51.7771	−	37.6183i	2.35594	−	1.71169i
$484$	−2.42705	−	1.76336i	−0.110320	−	0.0801525i
$485$		0			0
$486$	−11.4412	−	8.31254i	−0.518985	−	0.377064i
$487$	−10.4884	+	32.2799i	−0.475274	+	1.46274i	0.370314	+	0.928907i	$0.379250\pi$
$487$	−10.4884	+	32.2799i	−0.475274	+	1.46274i	−0.845588	+	0.533836i	$0.820750\pi$
$488$	1.31105	−	4.03499i	0.0593484	−	0.182655i
$489$	13.9845	+	43.0399i	0.632402	+	1.94633i
$490$		0			0
$491$	19.7990			0.893516			0.446758	−	0.894655i	$-0.352579\pi$
$491$	19.7990			0.893516			0.446758	+	0.894655i	$0.352579\pi$
$492$	1.74806	+	5.37999i	0.0788088	+	0.242549i
$493$	1.61803	−	1.17557i	0.0728726	−	0.0529450i
$494$	−4.57649	−	3.32502i	−0.205906	−	0.149600i
$495$		0			0
$496$		0			0
$497$	32.0000			1.43540
$498$	−32.3607	−	23.5114i	−1.45012	−	1.05357i
$499$	−2.28825	+	1.66251i	−0.102436	+	0.0744241i	−0.637824	−	0.770182i	$-0.720165\pi$
$499$	−2.28825	+	1.66251i	−0.102436	+	0.0744241i	0.535388	+	0.844606i	$0.320165\pi$
$500$		0			0
$501$	−48.0000			−2.14448
$502$	−2.82843			−0.126239
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$	18.5410	−	57.0634i	0.825883	−	2.54181i
$505$		0			0
$506$	−12.9443	−	9.40456i	−0.575443	−	0.418084i
$507$	−9.61435	−	29.5899i	−0.426988	−	1.31414i
$508$		0			0
$509$	−8.00886	+	5.81878i	−0.354986	+	0.257913i	−0.750958	−	0.660350i	$-0.770408\pi$
$509$	−8.00886	+	5.81878i	−0.354986	+	0.257913i	0.395971	+	0.918263i	$0.370408\pi$
$510$		0			0
$511$	13.7295	−	9.97505i	0.607356	−	0.441270i
$512$	−8.89919	+	6.46564i	−0.393292	+	0.285744i
$513$	−6.99226	+	21.5200i	−0.308716	+	0.950129i
$514$		0			0
$515$		0			0
$516$	−7.41641	−	22.8254i	−0.326489	−	1.00483i
$517$	−27.4589	−	19.9501i	−1.20764	−	0.877404i
$518$	5.24419	−	16.1400i	0.230417	−	0.709149i
$519$	15.7326	−	48.4199i	0.690583	−	2.12540i
$520$		0			0
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$	7.07107			0.309492
$523$	−7.86629	−	24.2099i	−0.343969	−	1.05863i	−0.962134	−	0.272578i	$-0.912124\pi$
$523$	−7.86629	−	24.2099i	−0.343969	−	1.05863i	0.618165	−	0.786049i	$-0.287876\pi$
$524$	3.23607	−	2.35114i	0.141368	−	0.102710i
$525$	45.7649	+	33.2502i	1.99734	+	1.45116i
$526$	−28.2843			−1.23325
$527$		0			0
$528$	−8.00000			−0.348155
$529$	−7.28115	−	5.29007i	−0.316572	−	0.230003i
$530$		0			0
$531$	12.3607	+	38.0423i	0.536408	+	1.65089i
$532$	16.0000			0.693688
$533$	−2.82843			−0.122513
$534$	6.18034	+	19.0211i	0.267449	+	0.823125i
$535$		0			0
$536$	−3.70820	+	11.4127i	−0.160170	+	0.492953i
$537$	58.2492	+	42.3205i	2.51364	+	1.82627i
$538$	0.437016	+	1.34500i	0.0188411	+	0.0579869i
$539$	−20.5942	−	14.9626i	−0.887055	−	0.644484i
$540$		0			0
$541$	4.32624	−	13.3148i	0.185999	−	0.572448i	−0.813965	−	0.580914i	$-0.802695\pi$
$541$	4.32624	−	13.3148i	0.185999	−	0.572448i	0.999964	+	0.00846681i	$0.00269510\pi$
$542$	4.57649	−	3.32502i	0.196577	−	0.142822i
$543$	−9.70820	+	7.05342i	−0.416619	+	0.302691i
$544$	−2.18508	+	6.72499i	−0.0936845	+	0.288331i
$545$		0			0
$546$	12.9443	+	9.40456i	0.553964	+	0.402478i
$547$	7.41641	+	22.8254i	0.317103	+	0.975942i	0.974880	+	0.222730i	$0.0714967\pi$
$547$	7.41641	+	22.8254i	0.317103	+	0.975942i	−0.657778	+	0.753212i	$0.728503\pi$
$548$	12.5854	+	9.14379i	0.537620	+	0.390603i
$549$	2.18508	−	6.72499i	0.0932569	−	0.287015i
$550$	4.37016	−	13.4500i	0.186344	−	0.573509i
$551$	1.74806	+	5.37999i	0.0744700	+	0.229195i
$552$	−48.0000			−2.04302
$553$	−45.2548			−1.92443
$554$	1.31105	+	4.03499i	0.0557011	+	0.171430i
$555$		0			0
$556$	−16.0177	−	11.6376i	−0.679303	−	0.493542i
$557$	9.89949			0.419455			0.209728	−	0.977760i	$-0.432742\pi$
$557$	9.89949			0.419455			0.209728	+	0.977760i	$0.432742\pi$
$558$		0			0
$559$	12.0000			0.507546
$560$		0			0
$561$	−9.15298	+	6.65003i	−0.386439	+	0.280765i
$562$	−4.94427	−	15.2169i	−0.208562	−	0.641886i
$563$	12.0000			0.505740			0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000			0.505740			0.252870	+	0.967500i	$0.418626\pi$
$564$	−33.9411			−1.42918
$565$		0			0
$566$	4.94427	−	15.2169i	0.207823	−	0.639614i
$567$	1.23607	−	3.80423i	0.0519100	−	0.159762i
$568$	−19.4164	−	14.1068i	−0.814694	−	0.591910i
$569$	2.18508	+	6.72499i	0.0916033	+	0.281926i	0.986354	−	0.164641i	$-0.0526465\pi$
$569$	2.18508	+	6.72499i	0.0916033	+	0.281926i	−0.894750	+	0.446567i	$0.852646\pi$
$570$		0			0
$571$	−6.86474	+	4.98752i	−0.287280	+	0.208721i	−0.722087	−	0.691803i	$-0.756817\pi$
$571$	−6.86474	+	4.98752i	−0.287280	+	0.208721i	0.434806	+	0.900524i	$0.356817\pi$
$572$	−1.23607	+	3.80423i	−0.0516826	+	0.159063i
$573$	−27.4589	+	19.9501i	−1.14711	+	0.833427i
$574$	−6.47214	+	4.70228i	−0.270142	+	0.196269i
$575$	8.74032	−	26.8999i	0.364497	−	1.12181i
$576$	−28.3156	+	20.5725i	−1.17982	+	0.857187i
$577$	8.09017	+	5.87785i	0.336798	+	0.244698i	0.743310	−	0.668947i	$-0.233255\pi$
$577$	8.09017	+	5.87785i	0.336798	+	0.244698i	−0.406512	+	0.913646i	$0.633255\pi$
$578$	4.63525	+	14.2658i	0.192801	+	0.593381i
$579$	−36.6119	−	26.6001i	−1.52154	−	1.10546i
$580$		0			0
$581$	−17.4806	+	53.7999i	−0.725219	+	2.23200i
$582$	−6.99226	−	21.5200i	−0.289838	−	0.892031i
$583$	12.0000			0.496989
$584$	−12.7279			−0.526685
$585$		0			0
$586$	21.0344	−	15.2824i	0.868925	−	0.631311i
$587$	16.0177	+	11.6376i	0.661122	+	0.480333i	0.867042	−	0.498236i	$-0.166019\pi$
$587$	16.0177	+	11.6376i	0.661122	+	0.480333i	−0.205920	+	0.978569i	$0.566019\pi$
$588$	−25.4558			−1.04978
$589$		0			0
$590$		0			0
$591$	−42.0689	−	30.5648i	−1.73048	−	1.25727i
$592$	−3.43237	+	2.49376i	−0.141069	+	0.102493i
$593$	−1.85410	−	5.70634i	−0.0761388	−	0.234331i	0.905742	−	0.423829i	$-0.139314\pi$
$593$	−1.85410	−	5.70634i	−0.0761388	−	0.234331i	−0.981881	+	0.189497i	$0.939314\pi$
$594$	−16.0000			−0.656488
$595$		0			0
$596$		0			0
$597$	−9.88854	+	30.4338i	−0.404711	+	1.24557i
$598$	2.47214	−	7.60845i	0.101093	−	0.311133i
$599$	−16.1803	−	11.7557i	−0.661111	−	0.480325i	0.205927	−	0.978567i	$-0.433979\pi$
$599$	−16.1803	−	11.7557i	−0.661111	−	0.480325i	−0.867038	+	0.498242i	$0.833979\pi$
$600$	−13.1105	−	40.3499i	−0.535233	−	1.64728i
$601$	−3.43237	−	2.49376i	−0.140009	−	0.101723i	0.515576	−	0.856844i	$-0.327578\pi$
$601$	−3.43237	−	2.49376i	−0.140009	−	0.101723i	−0.655585	+	0.755121i	$0.727578\pi$
$602$	27.4589	−	19.9501i	1.11914	−	0.813105i
$603$	−6.18034	+	19.0211i	−0.251683	+	0.774600i
$604$	−9.15298	+	6.65003i	−0.372430	+	0.270586i
$605$		0			0
$606$		0			0
$607$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$607$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$608$	−16.1803	−	11.7557i	−0.656199	−	0.476757i
$609$	−4.94427	−	15.2169i	−0.200352	−	0.616620i
$610$		0			0
$611$	5.24419	−	16.1400i	0.212157	−	0.652953i
$612$	−2.18508	+	6.72499i	−0.0883266	+	0.271841i
$613$	1.31105	+	4.03499i	0.0529527	+	0.162972i	0.974036	−	0.226395i	$-0.0726939\pi$
$613$	1.31105	+	4.03499i	0.0529527	+	0.162972i	−0.921083	+	0.389367i	$0.872694\pi$
$614$	16.0000			0.645707
$615$		0			0
$616$	10.4884	+	32.2799i	0.422589	+	1.30060i
$617$	−30.7426	+	22.3358i	−1.23765	+	0.899207i	−0.997440	−	0.0715132i	$-0.977217\pi$
$617$	−30.7426	+	22.3358i	−1.23765	+	0.899207i	−0.240213	+	0.970720i	$0.577217\pi$
$618$	−36.6119	−	26.6001i	−1.47275	−	1.07001i
$619$	8.48528			0.341052			0.170526	−	0.985353i	$-0.445453\pi$
$619$	8.48528			0.341052			0.170526	+	0.985353i	$0.445453\pi$
$620$		0			0
$621$	−32.0000			−1.28412
$622$	12.9443	+	9.40456i	0.519018	+	0.377089i
$623$	22.8825	−	16.6251i	0.916766	−	0.666070i
$624$	−1.23607	−	3.80423i	−0.0494823	−	0.152291i
$625$	25.0000			1.00000
$626$	29.6985			1.18699
$627$	−9.88854	−	30.4338i	−0.394910	−	1.21541i
$628$	−0.618034	+	1.90211i	−0.0246622	+	0.0759026i
$629$	−1.85410	+	5.70634i	−0.0739279	+	0.227527i
$630$		0			0
$631$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$631$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$632$	27.4589	+	19.9501i	1.09226	+	0.793572i
$633$		0			0
$634$	4.94427	−	15.2169i	0.196362	−	0.604340i
$635$		0			0
$636$	9.70820	−	7.05342i	0.384955	−	0.279686i
$637$	3.93314	−	12.1050i	0.155837	−	0.479617i
$638$	−3.23607	+	2.35114i	−0.128117	+	0.0930826i
$639$	−32.3607	−	23.5114i	−1.28017	−	0.930097i
$640$		0			0
$641$	10.2971	+	7.48128i	0.406711	+	0.295493i	0.772269	−	0.635296i	$-0.219122\pi$
$641$	10.2971	+	7.48128i	0.406711	+	0.295493i	−0.365558	+	0.930789i	$0.619122\pi$
$642$	6.99226	−	21.5200i	0.275962	−	0.849325i
$643$	−13.1105	+	40.3499i	−0.517027	+	1.59125i	0.262537	+	0.964922i	$0.415441\pi$
$643$	−13.1105	+	40.3499i	−0.517027	+	1.59125i	−0.779564	+	0.626323i	$0.784559\pi$
$644$	6.99226	+	21.5200i	0.275534	+	0.848005i
$645$		0			0
$646$	5.65685			0.222566
$647$	13.9845	+	43.0399i	0.549788	+	1.69207i	0.709325	+	0.704881i	$0.249000\pi$
$647$	13.9845	+	43.0399i	0.549788	+	1.69207i	−0.159537	+	0.987192i	$0.551000\pi$
$648$	−2.42705	+	1.76336i	−0.0953436	+	0.0692712i
$649$	−18.3060	−	13.3001i	−0.718572	−	0.522073i
$650$	7.07107			0.277350
$651$		0			0
$652$	−16.0000			−0.626608
$653$	12.9443	+	9.40456i	0.506549	+	0.368029i	0.811513	−	0.584335i	$-0.198644\pi$
$653$	12.9443	+	9.40456i	0.506549	+	0.368029i	−0.304964	+	0.952364i	$0.598644\pi$
$654$	4.57649	−	3.32502i	0.178955	−	0.130018i
$655$		0			0
$656$	2.00000			0.0780869
$657$	−21.2132			−0.827606
$658$	−14.8328	−	45.6507i	−0.578243	−	1.77965i
$659$	−13.5967	+	41.8465i	−0.529654	+	1.63011i	0.225271	+	0.974296i	$0.427673\pi$
$659$	−13.5967	+	41.8465i	−0.529654	+	1.63011i	−0.754925	+	0.655811i	$0.772327\pi$
$660$		0			0
$661$	−4.85410	−	3.52671i	−0.188803	−	0.137173i	0.489369	−	0.872077i	$-0.337227\pi$
$661$	−4.85410	−	3.52671i	−0.188803	−	0.137173i	−0.678171	+	0.734904i	$0.737227\pi$
$662$	0.874032	+	2.68999i	0.0339702	+	0.104550i
$663$	−4.57649	−	3.32502i	−0.177736	−	0.129133i
$664$	34.3237	−	24.9376i	1.33202	−	0.967767i
$665$		0			0
$666$	−17.1618	+	12.4688i	−0.665008	+	0.483157i
$667$	−6.47214	+	4.70228i	−0.250602	+	0.182073i
$668$	5.24419	−	16.1400i	0.202904	−	0.624474i
$669$	−38.8328	+	28.2137i	−1.50136	+	1.09080i
$670$		0			0
$671$	1.23607	+	3.80423i	0.0477179	+	0.146861i
$672$	45.7649	+	33.2502i	1.76542	+	1.28265i
$673$	−3.93314	+	12.1050i	−0.151612	+	0.466612i	−0.997802	−	0.0662685i	$-0.978891\pi$
$673$	−3.93314	+	12.1050i	−0.151612	+	0.466612i	0.846190	+	0.532881i	$0.178891\pi$
$674$	−10.9254	+	33.6249i	−0.420831	+	1.29518i
$675$	−8.74032	−	26.8999i	−0.336415	−	1.03538i
$676$	11.0000			0.423077
$677$	7.07107			0.271763			0.135882	−	0.990725i	$-0.456613\pi$
$677$	7.07107			0.271763			0.135882	+	0.990725i	$0.456613\pi$
$678$	−6.99226	−	21.5200i	−0.268536	−	0.826469i
$679$	−25.8885	+	18.8091i	−0.993511	+	0.721828i
$680$		0			0
$681$	67.8823			2.60125
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$	−16.1803	−	11.7557i	−0.618671	−	0.449491i
$685$		0			0
$686$	−2.47214	−	7.60845i	−0.0943866	−	0.290492i
$687$	−52.0000			−1.98392
$688$	−8.48528			−0.323498
$689$	1.85410	+	5.70634i	0.0706357	+	0.217394i
$690$		0			0
$691$	−6.18034	+	19.0211i	−0.235111	+	0.723598i	0.761995	+	0.647582i	$0.224220\pi$
$691$	−6.18034	+	19.0211i	−0.235111	+	0.723598i	−0.997107	+	0.0760155i	$0.975780\pi$
$692$	14.5623	+	10.5801i	0.553576	+	0.402196i
$693$	17.4806	+	53.7999i	0.664035	+	2.04369i
$694$	−16.0177	−	11.6376i	−0.608024	−	0.441756i
$695$		0			0
$696$	−3.70820	+	11.4127i	−0.140559	+	0.432596i
$697$	2.28825	−	1.66251i	0.0866735	−	0.0629720i
$698$	12.9443	−	9.40456i	0.489948	−	0.355968i
$699$	−20.9768	+	64.5599i	−0.793414	+	2.44188i
$700$	−16.1803	+	11.7557i	−0.611559	+	0.444324i
$701$	14.5623	+	10.5801i	0.550011	+	0.399606i	0.827789	−	0.561039i	$-0.189598\pi$
$701$	14.5623	+	10.5801i	0.550011	+	0.399606i	−0.277779	+	0.960645i	$0.589598\pi$
$702$	−2.47214	−	7.60845i	−0.0933048	−	0.287163i
$703$	−13.7295	−	9.97505i	−0.517817	−	0.376216i
$704$	6.11822	−	18.8300i	0.230589	−	0.709681i
$705$		0			0
$706$	3.93314	+	12.1050i	0.148026	+	0.455577i
$707$		0			0
$708$	−22.6274			−0.850390
$709$	−9.17734	−	28.2449i	−0.344662	−	1.06076i	−0.961764	−	0.273878i	$-0.911694\pi$
$709$	−9.17734	−	28.2449i	−0.344662	−	1.06076i	0.617102	−	0.786883i	$-0.288306\pi$
$710$		0			0
$711$	45.7649	+	33.2502i	1.71632	+	1.24698i
$712$	−21.2132			−0.794998
$713$		0			0
$714$	−16.0000			−0.598785
$715$		0			0
$716$	−20.5942	+	14.9626i	−0.769642	+	0.559177i
$717$	−19.7771	−	60.8676i	−0.738589	−	2.27314i
$718$	−12.0000			−0.447836
$719$	5.65685			0.210965			0.105483	−	0.994421i	$-0.466361\pi$
$719$	5.65685			0.210965			0.105483	+	0.994421i	$0.466361\pi$
$720$		0			0
$721$	−19.7771	+	60.8676i	−0.736537	+	2.26683i
$722$	0.927051	−	2.85317i	0.0345013	−	0.106184i
$723$	22.6525	+	16.4580i	0.842455	+	0.612079i
$724$	−1.31105	−	4.03499i	−0.0487247	−	0.149959i
$725$	−5.72061	−	4.15627i	−0.212458	−	0.154360i
$726$	−6.86474	+	4.98752i	−0.254774	+	0.185104i
$727$	2.47214	−	7.60845i	0.0916864	−	0.282182i	−0.894690	−	0.446689i	$-0.852603\pi$
$727$	2.47214	−	7.60845i	0.0916864	−	0.282182i	0.986376	+	0.164507i	$0.0526032\pi$
$728$	−13.7295	+	9.97505i	−0.508848	+	0.369700i
$729$	34.7877	−	25.2748i	1.28843	−	0.936102i
$730$		0			0
$731$	−9.70820	+	7.05342i	−0.359071	+	0.260880i
$732$	3.23607	+	2.35114i	0.119609	+	0.0869007i
$733$	−4.94427	−	15.2169i	−0.182621	−	0.562049i	0.817278	−	0.576243i	$-0.195482\pi$
$733$	−4.94427	−	15.2169i	−0.182621	−	0.562049i	−0.999899	+	0.0141938i	$0.995482\pi$
$734$	13.7295	+	9.97505i	0.506764	+	0.368186i
$735$		0			0
$736$	8.74032	−	26.8999i	0.322172	−	0.991545i
$737$	−3.49613	−	10.7600i	−0.128782	−	0.396349i
$738$	10.0000			0.368105
$739$	−8.48528			−0.312136			−0.156068	−	0.987746i	$-0.549882\pi$
$739$	−8.48528			−0.312136			−0.156068	+	0.987746i	$0.549882\pi$
$740$		0			0
$741$	12.9443	−	9.40456i	0.475520	−	0.345485i
$742$	13.7295	+	9.97505i	0.504025	+	0.366195i
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$		0			0
$745$		0			0
$746$	−4.85410	−	3.52671i	−0.177721	−	0.129122i
$747$	57.2061	−	41.5627i	2.09306	−	1.52070i
$748$	−1.23607	−	3.80423i	−0.0451951	−	0.139096i
$749$	−32.0000			−1.16925
$750$		0			0
$751$	−1.23607	−	3.80423i	−0.0451048	−	0.138818i	0.925968	−	0.377602i	$-0.123251\pi$
$751$	−1.23607	−	3.80423i	−0.0451048	−	0.138818i	−0.971073	+	0.238784i	$0.923251\pi$
$752$	−3.70820	+	11.4127i	−0.135224	+	0.416178i
$753$	2.47214	−	7.60845i	0.0900896	−	0.277267i
$754$	−1.61803	−	1.17557i	−0.0589253	−	0.0428118i
$755$		0			0
$756$	18.3060	+	13.3001i	0.665782	+	0.483719i
$757$	−12.5854	+	9.14379i	−0.457422	+	0.332337i	−0.792519	−	0.609847i	$-0.791231\pi$
$757$	−12.5854	+	9.14379i	−0.457422	+	0.332337i	0.335097	+	0.942184i	$0.391231\pi$
$758$	4.94427	−	15.2169i	0.179584	−	0.552703i
$759$	36.6119	−	26.6001i	1.32893	−	0.965523i
$760$		0			0
$761$	−15.2956	+	47.0749i	−0.554464	+	1.70646i	0.142892	+	0.989738i	$0.454360\pi$
$761$	−15.2956	+	47.0749i	−0.554464	+	1.70646i	−0.697356	+	0.716725i	$0.745640\pi$
$762$		0			0
$763$	−6.47214	−	4.70228i	−0.234307	−	0.170234i
$764$	−3.70820	−	11.4127i	−0.134158	−	0.412896i
$765$		0			0
$766$	−1.74806	+	5.37999i	−0.0631601	+	0.194387i
$767$	3.49613	−	10.7600i	0.126238	−	0.388520i
$768$	−14.8585	−	45.7299i	−0.536162	−	1.65014i
$769$	24.0000			0.865462			0.432731	−	0.901523i	$-0.357550\pi$
$769$	24.0000			0.865462			0.432731	+	0.901523i	$0.357550\pi$
$770$		0			0
$771$		0			0
$772$	12.9443	−	9.40456i	0.465875	−	0.338478i
$773$	−24.0266	−	17.4563i	−0.864176	−	0.627861i	0.0648419	−	0.997896i	$-0.479346\pi$
$773$	−24.0266	−	17.4563i	−0.864176	−	0.627861i	−0.929018	+	0.370035i	$0.879346\pi$
$774$	−42.4264			−1.52499
$775$		0			0
$776$	24.0000			0.861550
$777$	38.8328	+	28.2137i	1.39312	+	1.01216i
$778$	−12.5854	+	9.14379i	−0.451207	+	0.327821i
$779$	2.47214	+	7.60845i	0.0885735	+	0.272601i
$780$		0			0
$781$	22.6274			0.809673
$782$	2.47214	+	7.60845i	0.0884034	+	0.272078i
$783$	−2.47214	+	7.60845i	−0.0883469	+	0.271904i
$784$	−2.78115	+	8.55951i	−0.0993269	+	0.305697i
$785$		0			0
$786$	−3.49613	−	10.7600i	−0.124703	−	0.383796i
$787$	6.86474	+	4.98752i	0.244701	+	0.177786i	0.703375	−	0.710819i	$-0.251675\pi$
$787$	6.86474	+	4.98752i	0.244701	+	0.177786i	−0.458674	+	0.888605i	$0.651675\pi$
$788$	14.8736	−	10.8063i	0.529850	−	0.384959i
$789$	24.7214	−	76.0845i	0.880104	−	2.70868i
$790$		0			0
$791$	−25.8885	+	18.8091i	−0.920491	+	0.668776i
$792$	13.1105	−	40.3499i	0.465861	−	1.43377i
$793$	−1.61803	+	1.17557i	−0.0574581	+	0.0417457i
$794$	−25.8885	−	18.8091i	−0.918750	−	0.667511i
$795$		0			0
$796$	−9.15298	−	6.65003i	−0.324419	−	0.235704i
$797$	−7.42927	+	22.8649i	−0.263158	+	0.809918i	0.728954	+	0.684563i	$0.240007\pi$
$797$	−7.42927	+	22.8649i	−0.263158	+	0.809918i	−0.992112	+	0.125355i	$0.959993\pi$
$798$	13.9845	−	43.0399i	0.495046	−	1.52360i
$799$	5.24419	+	16.1400i	0.185526	+	0.570991i
$800$	25.0000			0.883883
$801$	−35.3553			−1.24922
$802$	0.437016	+	1.34500i	0.0154316	+	0.0474935i
$803$	9.70820	−	7.05342i	0.342595	−	0.248910i
$804$	−9.15298	−	6.65003i	−0.322801	−	0.234529i
$805$		0			0
$806$		0			0
$807$	−4.00000			−0.140807
$808$		0			0
$809$	−24.0266	+	17.4563i	−0.844730	+	0.613732i	−0.923688	−	0.383146i	$-0.874841\pi$
$809$	−24.0266	+	17.4563i	−0.844730	+	0.613732i	0.0789583	+	0.996878i	$0.474841\pi$
$810$		0			0
$811$	40.0000			1.40459			0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000			1.40459			0.702295	+	0.711886i	$0.252159\pi$
$812$	5.65685			0.198517
$813$	4.94427	+	15.2169i	0.173403	+	0.533680i
$814$	3.70820	−	11.4127i	0.129972	−	0.400014i
$815$		0			0
$816$	3.23607	+	2.35114i	0.113285	+	0.0823064i
$817$	−10.4884	−	32.2799i	−0.366942	−	1.12933i
$818$	3.43237	+	2.49376i	0.120010	+	0.0871923i
$819$	−22.8825	+	16.6251i	−0.799578	+	0.580927i
$820$		0			0
$821$	24.0266	−	17.4563i	0.838533	−	0.609230i	−0.0834272	−	0.996514i	$-0.526587\pi$
$821$	24.0266	−	17.4563i	0.838533	−	0.609230i	0.921961	+	0.387284i	$0.126587\pi$
$822$	35.5967	−	25.8626i	1.24158	−	0.902060i
$823$	13.9845	−	43.0399i	0.487469	−	1.50028i	−0.340903	−	0.940099i	$-0.610733\pi$
$823$	13.9845	−	43.0399i	0.487469	−	1.50028i	0.828372	−	0.560178i	$-0.189267\pi$
$824$	38.8328	−	28.2137i	1.35281	−	0.982871i
$825$	32.3607	+	23.5114i	1.12665	+	0.818562i
$826$	−9.88854	−	30.4338i	−0.344066	−	1.05893i
$827$	20.5942	+	14.9626i	0.716131	+	0.520300i	0.885146	−	0.465314i	$-0.154059\pi$
$827$	20.5942	+	14.9626i	0.716131	+	0.520300i	−0.169015	+	0.985614i	$0.554059\pi$
$828$	8.74032	−	26.8999i	0.303747	−	0.934838i
$829$	17.0436	−	52.4549i	0.591950	−	1.82183i	0.0225900	−	0.999745i	$-0.492809\pi$
$829$	17.0436	−	52.4549i	0.591950	−	1.82183i	0.569360	−	0.822089i	$-0.307191\pi$
$830$		0			0
$831$	−12.0000			−0.416275
$832$	9.89949			0.343203
$833$	3.93314	+	12.1050i	0.136275	+	0.419412i
$834$	−45.3050	+	32.9160i	−1.56878	+	1.13979i
$835$		0			0
$836$	11.3137			0.391293
$837$		0			0
$838$	−16.0000			−0.552711
$839$	29.1246	+	21.1603i	1.00549	+	0.730534i	0.963259	−	0.268574i	$-0.0865524\pi$
$839$	29.1246	+	21.1603i	1.00549	+	0.730534i	0.0422342	+	0.999108i	$0.486552\pi$
$840$		0			0
$841$	−8.34346	−	25.6785i	−0.287705	−	0.885466i
$842$	32.0000			1.10279
$843$	45.2548			1.55866
$844$		0			0
$845$		0			0
$846$	−18.5410	+	57.0634i	−0.637453	+	1.96188i
$847$	9.70820	+	7.05342i	0.333578	+	0.242358i
$848$	−1.31105	−	4.03499i	−0.0450216	−	0.138562i
$849$	36.6119	+	26.6001i	1.25652	+	0.912914i
$850$	−5.72061	+	4.15627i	−0.196215	+	0.142559i
$851$	7.41641	−	22.8254i	0.254231	−	0.782443i
$852$	18.3060	−	13.3001i	0.627152	−	0.455653i
$853$	−12.9443	+	9.40456i	−0.443203	+	0.322006i	−0.786907	−	0.617072i	$-0.788319\pi$
$853$	−12.9443	+	9.40456i	−0.443203	+	0.322006i	0.343703	+	0.939078i	$0.388319\pi$
$854$	−1.74806	+	5.37999i	−0.0598175	+	0.184099i
$855$		0			0
$856$	19.4164	+	14.1068i	0.663639	+	0.482162i
$857$	−4.94427	−	15.2169i	−0.168893	−	0.519800i	0.830409	−	0.557154i	$-0.188107\pi$
$857$	−4.94427	−	15.2169i	−0.168893	−	0.519800i	−0.999302	+	0.0373548i	$0.988107\pi$
$858$	9.15298	+	6.65003i	0.312478	+	0.227028i
$859$	11.3624	−	34.9699i	0.387681	−	1.19316i	−0.546836	−	0.837240i	$-0.684168\pi$
$859$	11.3624	−	34.9699i	0.387681	−	1.19316i	0.934517	−	0.355919i	$-0.115832\pi$
$860$		0			0
$861$	−6.99226	−	21.5200i	−0.238295	−	0.733398i
$862$	−12.0000			−0.408722
$863$	22.6274			0.770246			0.385123	−	0.922865i	$-0.374159\pi$
$863$	22.6274			0.770246			0.385123	+	0.922865i	$0.374159\pi$
$864$	−8.74032	−	26.8999i	−0.297352	−	0.915155i
$865$		0			0
$866$	10.2971	+	7.48128i	0.349910	+	0.254224i
$867$	−42.4264			−1.44088
$868$		0			0
$869$	−32.0000			−1.08553
$870$		0			0
$871$	4.57649	−	3.32502i	0.155068	−	0.112664i
$872$	1.85410	+	5.70634i	0.0627878	+	0.193241i
$873$	40.0000			1.35379
$874$	−22.6274			−0.765384
$875$		0			0
$876$	3.70820	−	11.4127i	0.125289	−	0.385599i
$877$	14.8328	−	45.6507i	0.500869	−	1.54152i	−0.306738	−	0.951794i	$-0.599238\pi$
$877$	14.8328	−	45.6507i	0.500869	−	1.54152i	0.807607	−	0.589721i	$-0.200762\pi$
$878$	16.1803	+	11.7557i	0.546060	+	0.396736i
$879$	22.7248	+	69.9398i	0.766490	+	2.35901i
$880$		0			0
$881$	−28.6031	+	20.7813i	−0.963662	+	0.700141i	−0.953998	−	0.299812i	$-0.903076\pi$
$881$	−28.6031	+	20.7813i	−0.963662	+	0.700141i	−0.00966359	+	0.999953i	$0.503076\pi$
$882$	−13.9058	+	42.7975i	−0.468231	+	1.44107i
$883$	6.86474	−	4.98752i	0.231017	−	0.167844i	−0.466255	−	0.884650i	$-0.654397\pi$
$883$	6.86474	−	4.98752i	0.231017	−	0.167844i	0.697272	+	0.716807i	$0.254397\pi$
$884$	1.61803	−	1.17557i	0.0544204	−	0.0395387i
$885$		0			0
$886$	16.1803	−	11.7557i	0.543589	−	0.394941i
$887$	9.70820	+	7.05342i	0.325970	+	0.236831i	0.738718	−	0.674014i	$-0.235431\pi$
$887$	9.70820	+	7.05342i	0.325970	+	0.236831i	−0.412749	+	0.910845i	$0.635431\pi$
$888$	−11.1246	−	34.2380i	−0.373318	−	1.14895i
$889$		0			0
$890$		0			0
$891$	0.874032	−	2.68999i	0.0292812	−	0.0901182i
$892$	−5.24419	−	16.1400i	−0.175589	−	0.540406i
$893$	−48.0000			−1.60626
$894$		0			0
$895$		0			0
$896$	−9.70820	+	7.05342i	−0.324328	+	0.235638i
$897$	18.3060	+	13.3001i	0.611218	+	0.444076i
$898$	24.0416			0.802280
$899$		0			0
$900$	25.0000			0.833333
$901$	−4.85410	−	3.52671i	−0.161714	−	0.117492i
$902$	−4.57649	+	3.32502i	−0.152380	+	0.110711i
$903$	29.6656	+	91.3014i	0.987210	+	3.03832i
$904$	24.0000			0.798228
$905$		0			0
$906$	9.88854	+	30.4338i	0.328525	+	1.01110i
$907$	2.47214	−	7.60845i	0.0820859	−	0.252635i	−0.901588	−	0.432597i	$-0.857597\pi$
$907$	2.47214	−	7.60845i	0.0820859	−	0.252635i	0.983674	+	0.179962i	$0.0575975\pi$
$908$	−7.41641	+	22.8254i	−0.246122	+	0.757486i
$909$		0			0
$910$		0			0
$911$	−36.6119	−	26.6001i	−1.21301	−	0.881301i	−0.217507	−	0.976059i	$-0.569792\pi$
$911$	−36.6119	−	26.6001i	−1.21301	−	0.881301i	−0.995500	+	0.0947573i	$0.969792\pi$
$912$	−9.15298	+	6.65003i	−0.303086	+	0.220205i
$913$	−12.3607	+	38.0423i	−0.409079	+	1.25902i
$914$	−3.43237	+	2.49376i	−0.113533	+	0.0824863i
$915$		0			0
$916$	5.68121	−	17.4850i	0.187712	−	0.577719i
$917$	−12.9443	+	9.40456i	−0.427458	+	0.310566i
$918$	6.47214	+	4.70228i	0.213612	+	0.155198i
$919$	17.3050	+	53.2592i	0.570838	+	1.75686i	0.649934	+	0.759991i	$0.274797\pi$
$919$	17.3050	+	53.2592i	0.570838	+	1.75686i	−0.0790962	+	0.996867i	$0.525203\pi$
$920$		0			0
$921$	−13.9845	+	43.0399i	−0.460805	+	1.41821i
$922$	−7.42927	+	22.8649i	−0.244670	+	0.753017i
$923$	3.49613	+	10.7600i	0.115076	+	0.354169i
$924$	−32.0000			−1.05272
$925$	21.2132			0.697486
$926$	−6.99226	−	21.5200i	−0.229780	−	0.707190i
$927$	64.7214	−	47.0228i	2.12573	−	1.54443i
$928$	−5.72061	−	4.15627i	−0.187788	−	0.136436i
$929$	−9.89949			−0.324792			−0.162396	−	0.986726i	$-0.551922\pi$
$929$	−9.89949			−0.324792			−0.162396	+	0.986726i	$0.551922\pi$
$930$		0			0
$931$	−36.0000			−1.17985
$932$	−19.4164	−	14.1068i	−0.636006	−	0.462085i
$933$	−36.6119	+	26.6001i	−1.19862	+	0.870849i
$934$	12.3607	+	38.0423i	0.404454	+	1.24478i
$935$		0			0
$936$	21.2132			0.693375
$937$	−4.94427	−	15.2169i	−0.161522	−	0.497115i	0.837241	−	0.546834i	$-0.184167\pi$
$937$	−4.94427	−	15.2169i	−0.161522	−	0.497115i	−0.998763	+	0.0497197i	$0.984167\pi$
$938$	4.94427	−	15.2169i	0.161436	−	0.496850i
$939$	−25.9574	+	79.8887i	−0.847089	+	2.60707i
$940$		0			0
$941$	14.4215	+	44.3849i	0.470128	+	1.44691i	0.852417	+	0.522863i	$0.175136\pi$
$941$	14.4215	+	44.3849i	0.470128	+	1.44691i	−0.382288	+	0.924043i	$0.624864\pi$
$942$	4.57649	+	3.32502i	0.149110	+	0.108335i
$943$	−9.15298	+	6.65003i	−0.298062	+	0.216555i
$944$	−2.47214	+	7.60845i	−0.0804612	+	0.247634i
$945$		0			0
$946$	19.4164	−	14.1068i	0.631282	−	0.458653i
$947$	13.1105	−	40.3499i	0.426033	−	1.31120i	−0.475968	−	0.879463i	$-0.657902\pi$
$947$	13.1105	−	40.3499i	0.426033	−	1.31120i	0.902001	−	0.431733i	$-0.142098\pi$
$948$	−25.8885	+	18.8091i	−0.840821	+	0.610892i
$949$	4.85410	+	3.52671i	0.157571	+	0.114482i
$950$	−6.18034	−	19.0211i	−0.200517	−	0.617127i
$951$	36.6119	+	26.6001i	1.18722	+	0.862568i
$952$	5.24419	−	16.1400i	0.169965	−	0.523099i
$953$	11.7994	−	36.3149i	0.382221	−	1.17636i	−0.556255	−	0.831012i	$-0.687762\pi$
$953$	11.7994	−	36.3149i	0.382221	−	1.17636i	0.938476	−	0.345344i	$-0.112238\pi$
$954$	−6.55524	−	20.1750i	−0.212234	−	0.653188i
$955$		0			0
$956$	22.6274			0.731823
$957$	−3.49613	−	10.7600i	−0.113014	−	0.347821i
$958$	−19.4164	+	14.1068i	−0.627316	+	0.455772i
$959$	−50.3414	−	36.5752i	−1.62561	−	1.18107i
$960$		0			0
$961$		0			0
$962$	6.00000			0.193448
$963$	32.3607	+	23.5114i	1.04281	+	0.757645i
$964$	−8.00886	+	5.81878i	−0.257948	+	0.187410i
$965$		0			0
$966$	64.0000			2.05917
$967$	5.65685			0.181912			0.0909561	−	0.995855i	$-0.471008\pi$
$967$	5.65685			0.181912			0.0909561	+	0.995855i	$0.471008\pi$
$968$	−2.78115	−	8.55951i	−0.0893896	−	0.275113i
$969$	−4.94427	+	15.2169i	−0.158833	+	0.488837i
$970$		0			0
$971$	−29.1246	−	21.1603i	−0.934653	−	0.679065i	0.0124744	−	0.999922i	$-0.496029\pi$
$971$	−29.1246	−	21.1603i	−0.934653	−	0.679065i	−0.947128	+	0.320857i	$0.896029\pi$
$972$	4.37016	+	13.4500i	0.140173	+	0.431408i
$973$	64.0709	+	46.5502i	2.05402	+	1.49233i
$974$	−27.4589	+	19.9501i	−0.879841	+	0.639242i
$975$	−6.18034	+	19.0211i	−0.197929	+	0.609164i
$976$	1.14412	−	0.831254i	0.0366225	−	0.0266078i
$977$	24.2705	−	17.6336i	0.776482	−	0.564147i	−0.127439	−	0.991846i	$-0.540676\pi$
$977$	24.2705	−	17.6336i	0.776482	−	0.564147i	0.903921	+	0.427699i	$0.140676\pi$
$978$	−13.9845	+	43.0399i	−0.447175	+	1.37626i
$979$	16.1803	−	11.7557i	0.517126	−	0.375714i
$980$		0			0
$981$	3.09017	+	9.51057i	0.0986615	+	0.303649i
$982$	16.0177	+	11.6376i	0.511146	+	0.371369i
$983$	−3.49613	+	10.7600i	−0.111509	+	0.343190i	−0.991203	−	0.132351i	$-0.957748\pi$
$983$	−3.49613	+	10.7600i	−0.111509	+	0.343190i	0.879694	+	0.475541i	$0.157748\pi$
$984$	−5.24419	+	16.1400i	−0.167179	+	0.514523i
$985$		0			0
$986$	2.00000			0.0636930
$987$	135.765			4.32143
$988$	1.74806	+	5.37999i	0.0556133	+	0.171160i
$989$	38.8328	−	28.2137i	1.23481	−	0.897143i
$990$		0			0
$991$	33.9411			1.07818			0.539088	−	0.842250i	$-0.318769\pi$
$991$	33.9411			1.07818			0.539088	+	0.842250i	$0.318769\pi$
$992$		0			0
$993$	−8.00000			−0.253872
$994$	25.8885	+	18.8091i	0.821135	+	0.596589i
$995$		0			0
$996$	12.3607	+	38.0423i	0.391663	+	1.20542i
$997$	−10.0000			−0.316703			−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000			−0.316703			−0.158352	+	0.987383i	$0.550618\pi$
$998$	−2.82843			−0.0895323
$999$	−7.41641	−	22.8254i	−0.234645	−	0.722162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.k.374.1		8
31.2	even	5	inner	961.2.d.k.628.2		8
31.3	odd	30		961.2.g.q.235.1		16
31.4	even	5		961.2.a.b.1.2	yes	2
31.5	even	3		961.2.g.q.732.2		16
31.6	odd	6		961.2.g.q.816.2		16
31.7	even	15		961.2.c.b.439.1		4
31.8	even	5	inner	961.2.d.k.531.2		8
31.9	even	15		961.2.g.q.844.1		16
31.10	even	15		961.2.g.q.448.2		16
31.11	odd	30		961.2.c.b.521.2		4
31.12	odd	30		961.2.g.q.846.2		16
31.13	odd	30		961.2.g.q.338.2		16
31.14	even	15		961.2.g.q.547.2		16
31.15	odd	10	inner	961.2.d.k.388.2		8
31.16	even	5	inner	961.2.d.k.388.1		8
31.17	odd	30		961.2.g.q.547.1		16
31.18	even	15		961.2.g.q.338.1		16
31.19	even	15		961.2.g.q.846.1		16
31.20	even	15		961.2.c.b.521.1		4
31.21	odd	30		961.2.g.q.448.1		16
31.22	odd	30		961.2.g.q.844.2		16
31.23	odd	10	inner	961.2.d.k.531.1		8
31.24	odd	30		961.2.c.b.439.2		4
31.25	even	3		961.2.g.q.816.1		16
31.26	odd	6		961.2.g.q.732.1		16
31.27	odd	10		961.2.a.b.1.1	✓	2
31.28	even	15		961.2.g.q.235.2		16
31.29	odd	10	inner	961.2.d.k.628.1		8
31.30	odd	2	inner	961.2.d.k.374.2		8
93.35	odd	10		8649.2.a.j.1.1		2
93.89	even	10		8649.2.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.b.1.1	✓	2	31.27	odd	10
961.2.a.b.1.2	yes	2	31.4	even	5
961.2.c.b.439.1		4	31.7	even	15
961.2.c.b.439.2		4	31.24	odd	30
961.2.c.b.521.1		4	31.20	even	15
961.2.c.b.521.2		4	31.11	odd	30
961.2.d.k.374.1		8	1.1	even	1	trivial
961.2.d.k.374.2		8	31.30	odd	2	inner
961.2.d.k.388.1		8	31.16	even	5	inner
961.2.d.k.388.2		8	31.15	odd	10	inner
961.2.d.k.531.1		8	31.23	odd	10	inner
961.2.d.k.531.2		8	31.8	even	5	inner
961.2.d.k.628.1		8	31.29	odd	10	inner
961.2.d.k.628.2		8	31.2	even	5	inner
961.2.g.q.235.1		16	31.3	odd	30
961.2.g.q.235.2		16	31.28	even	15
961.2.g.q.338.1		16	31.18	even	15
961.2.g.q.338.2		16	31.13	odd	30
961.2.g.q.448.1		16	31.21	odd	30
961.2.g.q.448.2		16	31.10	even	15
961.2.g.q.547.1		16	31.17	odd	30
961.2.g.q.547.2		16	31.14	even	15
961.2.g.q.732.1		16	31.26	odd	6
961.2.g.q.732.2		16	31.5	even	3
961.2.g.q.816.1		16	31.25	even	3
961.2.g.q.816.2		16	31.6	odd	6
961.2.g.q.844.1		16	31.9	even	15
961.2.g.q.844.2		16	31.22	odd	30
961.2.g.q.846.1		16	31.19	even	15
961.2.g.q.846.2		16	31.12	odd	30
8649.2.a.j.1.1		2	93.35	odd	10
8649.2.a.j.1.2		2	93.89	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-2.28825 + 1.66251i) q^{3} +(-0.309017 - 0.951057i) q^{4} -2.82843 q^{6} +(1.23607 + 3.80423i) q^{7} +(0.927051 - 2.85317i) q^{8} +(1.54508 - 4.75528i) q^{9} +(0.874032 + 2.68999i) q^{11} +(2.28825 + 1.66251i) q^{12} +(-1.14412 + 0.831254i) q^{13} +(-1.23607 + 3.80423i) q^{14} +(0.809017 - 0.587785i) q^{16} +(0.437016 - 1.34500i) q^{17} +(4.04508 - 2.93893i) q^{18} +(3.23607 + 2.35114i) q^{19} +(-9.15298 - 6.65003i) q^{21} +(-0.874032 + 2.68999i) q^{22} +(-1.74806 + 5.37999i) q^{23} +(2.62210 + 8.06998i) q^{24} -5.00000 q^{25} -1.41421 q^{26} +(1.74806 + 5.37999i) q^{27} +(3.23607 - 2.35114i) q^{28} +(1.14412 + 0.831254i) q^{29} -5.00000 q^{32} +(-6.47214 - 4.70228i) q^{33} +(1.14412 - 0.831254i) q^{34} -5.00000 q^{36} -4.24264 q^{37} +(1.23607 + 3.80423i) q^{38} +(1.23607 - 3.80423i) q^{39} +(1.61803 + 1.17557i) q^{41} +(-3.49613 - 10.7600i) q^{42} +(-6.86474 - 4.98752i) q^{43} +(2.28825 - 1.66251i) q^{44} +(-4.57649 + 3.32502i) q^{46} +(-9.70820 + 7.05342i) q^{47} +(-0.874032 + 2.68999i) q^{48} +(-7.28115 + 5.29007i) q^{49} +(-4.04508 - 2.93893i) q^{50} +(1.23607 + 3.80423i) q^{51} +(1.14412 + 0.831254i) q^{52} +(1.31105 - 4.03499i) q^{53} +(-1.74806 + 5.37999i) q^{54} +12.0000 q^{56} -11.3137 q^{57} +(0.437016 + 1.34500i) q^{58} +(-6.47214 + 4.70228i) q^{59} +1.41421 q^{61} +20.0000 q^{63} +(-5.66312 - 4.11450i) q^{64} +(-2.47214 - 7.60845i) q^{66} -4.00000 q^{67} -1.41421 q^{68} +(-4.94427 - 15.2169i) q^{69} +(2.47214 - 7.60845i) q^{71} +(-12.1353 - 8.81678i) q^{72} +(-1.31105 - 4.03499i) q^{73} +(-3.43237 - 2.49376i) q^{74} +(11.4412 - 8.31254i) q^{75} +(1.23607 - 3.80423i) q^{76} +(-9.15298 + 6.65003i) q^{77} +(3.23607 - 2.35114i) q^{78} +(-3.49613 + 10.7600i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.618034 + 1.90211i) q^{82} +(11.4412 + 8.31254i) q^{83} +(-3.49613 + 10.7600i) q^{84} +(-2.62210 - 8.06998i) q^{86} -4.00000 q^{87} +8.48528 q^{88} +(-2.18508 - 6.72499i) q^{89} +(-4.57649 - 3.32502i) q^{91} +5.65685 q^{92} -12.0000 q^{94} +(11.4412 - 8.31254i) q^{96} +(2.47214 + 7.60845i) q^{97} -9.00000 q^{98} +14.1421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{4} - 8 q^{7} - 6 q^{8} - 10 q^{9} + 8 q^{14} + 2 q^{16} + 10 q^{18} + 8 q^{19} - 40 q^{25} + 8 q^{28} - 40 q^{32} - 16 q^{33} - 40 q^{36} - 8 q^{38} - 8 q^{39} + 4 q^{41} - 24 q^{47}+ \cdots - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^4 - 8 * q^7 - 6 * q^8 - 10 * q^9 + 8 * q^14 + 2 * q^16 + 10 * q^18 + 8 * q^19 - 40 * q^25 + 8 * q^28 - 40 * q^32 - 16 * q^33 - 40 * q^36 - 8 * q^38 - 8 * q^39 + 4 * q^41 - 24 * q^47 - 18 * q^49 - 10 * q^50 - 8 * q^51 + 96 * q^56 - 16 * q^59 + 160 * q^63 - 14 * q^64 + 16 * q^66 - 32 * q^67 + 32 * q^69 - 16 * q^71 - 30 * q^72 - 8 * q^76 + 8 * q^78 - 2 * q^81 - 4 * q^82 - 32 * q^87 - 96 * q^94 - 16 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more