LMFDB - Embedded newform 975.2.bb.k.874.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(724,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("975.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			874.4
Root			$1.75780 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.874
Dual form			975.2.bb.k.724.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.294342 - 0.169938i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.942242 + 1.63201i) q^{4} +(-0.169938 + 0.294342i) q^{6} +(0.571683 + 0.330062i) q^{7} +1.32025i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.294342 - 0.169938i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.942242 + 1.63201i) q^{4} +(-0.169938 + 0.294342i) q^{6} +(0.571683 + 0.330062i) q^{7} +1.32025i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.339877 - 0.588684i) q^{11} -1.88448i q^{12} +(3.04397 + 1.93243i) q^{13} +0.224361 q^{14} +(-1.66012 - 2.87542i) q^{16} +(6.43378 + 3.71455i) q^{17} -0.339877i q^{18} +(0.0577581 - 0.100040i) q^{19} -0.660123 q^{21} +(-0.200080 - 0.115516i) q^{22} +(-6.72812 + 3.88448i) q^{23} +(-0.660123 - 1.14337i) q^{24} +(1.22436 + 0.0515075i) q^{26} +1.00000i q^{27} +(-1.07733 + 0.621996i) q^{28} +(2.77230 + 4.80177i) q^{29} -9.97370 q^{31} +(-3.26402 - 1.88448i) q^{32} +(0.588684 + 0.339877i) q^{33} +2.52498 q^{34} +(0.942242 + 1.63201i) q^{36} +(-8.46017 + 4.88448i) q^{37} -0.0392613i q^{38} +(-3.60236 - 0.151548i) q^{39} +(-2.11218 - 3.65840i) q^{41} +(-0.194302 + 0.112180i) q^{42} +(0.471643 + 0.272303i) q^{43} +1.28098 q^{44} +(-1.32025 + 2.28673i) q^{46} +5.01963i q^{47} +(2.87542 + 1.66012i) q^{48} +(-3.28212 - 5.68480i) q^{49} -7.42909 q^{51} +(-6.02189 + 3.14697i) q^{52} +0.679754i q^{53} +(0.169938 + 0.294342i) q^{54} +(-0.435763 + 0.754763i) q^{56} +0.115516i q^{57} +(1.63201 + 0.942242i) q^{58} +(1.11218 - 1.92635i) q^{59} +(2.10236 - 3.64140i) q^{61} +(-2.93568 + 1.69491i) q^{62} +(0.571683 - 0.330062i) q^{63} +5.35951 q^{64} +0.231033 q^{66} +(6.61108 - 3.81691i) q^{67} +(-12.1244 + 7.00000i) q^{68} +(3.88448 - 6.72812i) q^{69} +(-3.65679 + 6.33374i) q^{71} +(1.14337 + 0.660123i) q^{72} +8.01963i q^{73} +(-1.66012 + 2.87542i) q^{74} +(0.108844 + 0.188524i) q^{76} -0.448721i q^{77} +(-1.08608 + 0.567573i) q^{78} -9.97370 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.24341 - 0.717881i) q^{82} +1.76897i q^{83} +(0.621996 - 1.07733i) q^{84} +0.185099 q^{86} +(-4.80177 - 2.77230i) q^{87} +(0.777208 - 0.448721i) q^{88} +(6.77230 + 11.7300i) q^{89} +(1.10236 + 2.10943i) q^{91} -14.6405i q^{92} +(8.63748 - 4.98685i) q^{93} +(0.853028 + 1.47749i) q^{94} +3.76897 q^{96} +(8.57721 + 4.95206i) q^{97} +(-1.93213 - 1.11552i) q^{98} -0.679754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} + 6 q^{9}+O(q^{10}) $ 12 * q + 12 * q^4 + 6 * q^9	$ 12 q + 12 q^{4} + 6 q^{9} - 48 q^{14} - 24 q^{16} + 24 q^{19} - 12 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} + 12 q^{31} - 12 q^{36} - 24 q^{39} + 48 q^{44} - 24 q^{46} - 12 q^{49} - 60 q^{56} - 12 q^{59} + 6 q^{61} + 48 q^{64} + 96 q^{66} + 24 q^{71} - 24 q^{74} - 96 q^{76} + 12 q^{79} - 6 q^{81} - 24 q^{84} - 24 q^{86} + 60 q^{89} - 6 q^{91} + 72 q^{94} - 48 q^{96}+O(q^{100}) $ 12 * q + 12 * q^4 + 6 * q^9 - 48 * q^14 - 24 * q^16 + 24 * q^19 - 12 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 + 12 * q^31 - 12 * q^36 - 24 * q^39 + 48 * q^44 - 24 * q^46 - 12 * q^49 - 60 * q^56 - 12 * q^59 + 6 * q^61 + 48 * q^64 + 96 * q^66 + 24 * q^71 - 24 * q^74 - 96 * q^76 + 12 * q^79 - 6 * q^81 - 24 * q^84 - 24 * q^86 + 60 * q^89 - 6 * q^91 + 72 * q^94 - 48 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.294342	−	0.169938i	0.208131	−	0.120165i	−0.392311	−	0.919832i	$-0.628324\pi$
$2$	0.294342	−	0.169938i	0.208131	−	0.120165i	0.600443	+	0.799668i	$0.294991\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.942242	+	1.63201i	−0.471121	+	0.816005i
$5$		0			0
$5$		0			0
$6$	−0.169938	+	0.294342i	−0.0693771	+	0.120165i
$7$	0.571683	+	0.330062i	0.216076	+	0.124752i	0.604132	−	0.796884i	$-0.293520\pi$
$7$	0.571683	+	0.330062i	0.216076	+	0.124752i	−0.388056	+	0.921636i	$0.626853\pi$
$8$			1.32025i			0.466778i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−0.339877	−	0.588684i	−0.102477	−	0.177495i	0.810228	−	0.586115i	$-0.199343\pi$
$11$	−0.339877	−	0.588684i	−0.102477	−	0.177495i	−0.912704	+	0.408620i	$0.866010\pi$
$12$		−	1.88448i		−	0.544004i
$13$	3.04397	+	1.93243i	0.844244	+	0.535959i
$13$	3.04397	+	1.93243i	0.844244	+	0.535959i
$14$	0.224361			0.0599629
$15$		0			0
$16$	−1.66012	−	2.87542i	−0.415031	−	0.718854i
$17$	6.43378	+	3.71455i	1.56042	+	0.900910i	0.997214	+	0.0745938i	$0.0237660\pi$
$17$	6.43378	+	3.71455i	1.56042	+	0.900910i	0.563207	+	0.826316i	$0.309567\pi$
$18$		−	0.339877i		−	0.0801098i
$19$	0.0577581	−	0.100040i	0.0132506	−	0.0229508i	−0.859324	−	0.511431i	$-0.829115\pi$
$19$	0.0577581	−	0.100040i	0.0132506	−	0.0229508i	0.872575	+	0.488481i	$0.162449\pi$
$20$		0			0
$21$	−0.660123			−0.144051
$22$	−0.200080	−	0.115516i	−0.0426572	−	0.0246282i
$23$	−6.72812	+	3.88448i	−1.40291	+	0.809971i	−0.994690	−	0.102913i	$-0.967184\pi$
$23$	−6.72812	+	3.88448i	−1.40291	+	0.809971i	−0.408220	+	0.912883i	$0.633850\pi$
$24$	−0.660123	−	1.14337i	−0.134747	−	0.233389i
$25$		0			0
$26$	1.22436	+	0.0515075i	0.240117	+	0.0101015i
$27$			1.00000i			0.192450i
$28$	−1.07733	+	0.621996i	−0.203596	+	0.117546i
$29$	2.77230	+	4.80177i	0.514804	+	0.891666i	0.999852	+	0.0171792i	$0.00546857\pi$
$29$	2.77230	+	4.80177i	0.514804	+	0.891666i	−0.485049	+	0.874487i	$0.661198\pi$
$30$		0			0
$31$	−9.97370			−1.79133			−0.895664	−	0.444730i	$-0.853299\pi$
$31$	−9.97370			−1.79133			−0.895664	+	0.444730i	$0.853299\pi$
$32$	−3.26402	−	1.88448i	−0.577003	−	0.333133i
$33$	0.588684	+	0.339877i	0.102477	+	0.0591650i
$34$	2.52498			0.433030
$35$		0			0
$36$	0.942242	+	1.63201i	0.157040	+	0.272002i
$37$	−8.46017	+	4.88448i	−1.39084	+	0.803004i	−0.993409	−	0.114626i	$-0.963433\pi$
$37$	−8.46017	+	4.88448i	−1.39084	+	0.803004i	−0.397435	+	0.917630i	$0.630100\pi$
$38$		−	0.0392613i		−	0.00636903i
$39$	−3.60236	−	0.151548i	−0.576840	−	0.0242670i
$40$		0			0
$41$	−2.11218	−	3.65840i	−0.329867	−	0.571347i	0.652618	−	0.757687i	$-0.273671\pi$
$41$	−2.11218	−	3.65840i	−0.329867	−	0.571347i	−0.982485	+	0.186340i	$0.940337\pi$
$42$	−0.194302	+	0.112180i	−0.0299814	+	0.0173098i
$43$	0.471643	+	0.272303i	0.0719249	+	0.0415259i	0.535531	−	0.844515i	$-0.320111\pi$
$43$	0.471643	+	0.272303i	0.0719249	+	0.0415259i	−0.463606	+	0.886041i	$0.653445\pi$
$44$	1.28098			0.193116
$45$		0			0
$46$	−1.32025	+	2.28673i	−0.194660	+	0.337160i
$47$			5.01963i			0.732188i	0.930578	+	0.366094i	$0.119305\pi$
$47$			5.01963i			0.732188i	−0.930578	+	0.366094i	$0.880695\pi$
$48$	2.87542	+	1.66012i	0.415031	+	0.239618i
$49$	−3.28212	−	5.68480i	−0.468874	−	0.812114i
$50$		0			0
$51$	−7.42909			−1.04028
$52$	−6.02189	+	3.14697i	−0.835086	+	0.436406i
$53$			0.679754i			0.0933714i	0.998910	+	0.0466857i	$0.0148659\pi$
$53$			0.679754i			0.0933714i	−0.998910	+	0.0466857i	$0.985134\pi$
$54$	0.169938	+	0.294342i	0.0231257	+	0.0400549i
$55$		0			0
$56$	−0.435763	+	0.754763i	−0.0582312	+	0.100859i
$57$			0.115516i			0.0153005i
$58$	1.63201	+	0.942242i	0.214294	+	0.123722i
$59$	1.11218	−	1.92635i	0.144794	−	0.250790i	−0.784502	−	0.620126i	$-0.787082\pi$
$59$	1.11218	−	1.92635i	0.144794	−	0.250790i	0.929296	+	0.369336i	$0.120415\pi$
$60$		0			0
$61$	2.10236	−	3.64140i	0.269180	−	0.466234i	−0.699470	−	0.714662i	$-0.746581\pi$
$61$	2.10236	−	3.64140i	0.269180	−	0.466234i	0.968650	+	0.248428i	$0.0799139\pi$
$62$	−2.93568	+	1.69491i	−0.372832	+	0.215254i
$63$	0.571683	−	0.330062i	0.0720253	−	0.0415838i
$64$	5.35951			0.669938
$65$		0			0
$66$	0.231033			0.0284381
$67$	6.61108	−	3.81691i	0.807672	−	0.466310i	−0.0384746	−	0.999260i	$-0.512250\pi$
$67$	6.61108	−	3.81691i	0.807672	−	0.466310i	0.846147	+	0.532950i	$0.178917\pi$
$68$	−12.1244	+	7.00000i	−1.47029	+	0.848875i
$69$	3.88448	−	6.72812i	0.467637	−	0.809971i
$70$		0			0
$71$	−3.65679	+	6.33374i	−0.433981	+	0.751677i	−0.997212	−	0.0746227i	$-0.976225\pi$
$71$	−3.65679	+	6.33374i	−0.433981	+	0.751677i	0.563231	+	0.826299i	$0.309558\pi$
$72$	1.14337	+	0.660123i	0.134747	+	0.0777963i
$73$			8.01963i			0.938627i	0.883032	+	0.469313i	$0.155499\pi$
$73$			8.01963i			0.938627i	−0.883032	+	0.469313i	$0.844501\pi$
$74$	−1.66012	+	2.87542i	−0.192985	+	0.334261i
$75$		0			0
$76$	0.108844	+	0.188524i	0.0124853	+	0.0216252i
$77$		−	0.448721i		−	0.0511365i
$78$	−1.08608	+	0.567573i	−0.122974	+	0.0642650i
$79$	−9.97370			−1.12213			−0.561064	−	0.827772i	$-0.689608\pi$
$79$	−9.97370			−1.12213			−0.561064	+	0.827772i	$0.689608\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.24341	−	0.717881i	−0.137311	−	0.0792767i
$83$			1.76897i			0.194169i	0.995276	+	0.0970847i	$0.0309518\pi$
$83$			1.76897i			0.194169i	−0.995276	+	0.0970847i	$0.969048\pi$
$84$	0.621996	−	1.07733i	0.0678653	−	0.117546i
$85$		0			0
$86$	0.185099			0.0199598
$87$	−4.80177	−	2.77230i	−0.514804	−	0.297222i
$88$	0.777208	−	0.448721i	0.0828506	−	0.0478338i
$89$	6.77230	+	11.7300i	0.717863	+	1.24337i	0.961845	+	0.273595i	$0.0882128\pi$
$89$	6.77230	+	11.7300i	0.717863	+	1.24337i	−0.243982	+	0.969780i	$0.578454\pi$
$90$		0			0
$91$	1.10236	+	2.10943i	0.115559	+	0.221129i
$92$		−	14.6405i		−	1.52638i
$93$	8.63748	−	4.98685i	0.895664	−	0.517112i
$94$	0.853028	+	1.47749i	0.0879831	+	0.152391i
$95$		0			0
$96$	3.76897			0.384669
$97$	8.57721	+	4.95206i	0.870884	+	0.502805i	0.867642	−	0.497190i	$-0.165635\pi$
$97$	8.57721	+	4.95206i	0.870884	+	0.502805i	0.00324223	+	0.999995i	$0.498968\pi$
$98$	−1.93213	−	1.11552i	−0.195175	−	0.112684i
$99$	−0.679754			−0.0683178
$100$		0			0
$101$	4.67975	+	8.10557i	0.465653	+	0.806534i	0.999231	−	0.0392165i	$-0.0124862\pi$
$101$	4.67975	+	8.10557i	0.465653	+	0.806534i	−0.533578	+	0.845751i	$0.679153\pi$
$102$	−2.18669	+	1.26249i	−0.216515	+	0.125005i
$103$			4.50535i			0.443925i	0.975055	+	0.221962i	$0.0712462\pi$
$103$			4.50535i			0.443925i	−0.975055	+	0.221962i	$0.928754\pi$
$104$	−2.55128	+	4.01878i	−0.250173	+	0.394074i
$105$		0			0
$106$	0.115516	+	0.200080i	0.0112199	+	0.0194335i
$107$	−0.494422	+	0.285455i	−0.0477976	+	0.0275960i	−0.523708	−	0.851898i	$-0.675452\pi$
$107$	−0.494422	+	0.285455i	−0.0477976	+	0.0275960i	0.475911	+	0.879494i	$0.342119\pi$
$108$	−1.63201	−	0.942242i	−0.157040	−	0.0906673i
$109$	−15.4095			−1.47596			−0.737979	−	0.674823i	$-0.764220\pi$
$109$	−15.4095			−1.47596			−0.737979	+	0.674823i	$0.764220\pi$
$110$		0			0
$111$	4.88448	−	8.46017i	0.463615	−	0.803004i
$112$		−	2.19177i		−	0.207103i
$113$	4.60747	+	2.66012i	0.433434	+	0.250243i	0.700809	−	0.713349i	$-0.252823\pi$
$113$	4.60747	+	2.66012i	0.433434	+	0.250243i	−0.267374	+	0.963593i	$0.586156\pi$
$114$	0.0196307	+	0.0340013i	0.00183858	+	0.00318451i
$115$		0			0
$116$	−10.4487			−0.970139
$117$	3.19551	−	1.66994i	0.295425	−	0.154386i
$118$		−	0.756009i		−	0.0695962i
$119$	2.45206	+	4.24709i	0.224780	+	0.389330i
$120$		0			0
$121$	5.26897	−	9.12612i	0.478997	−	0.829647i
$122$		−	1.42909i		−	0.129384i
$123$	3.65840	+	2.11218i	0.329867	+	0.190449i
$124$	9.39764	−	16.2772i	0.843933	−	1.46173i
$125$		0			0
$126$	0.112180	−	0.194302i	0.00999381	−	0.0173098i
$127$	10.4093	−	6.00982i	0.923676	−	0.533285i	0.0388704	−	0.999244i	$-0.487624\pi$
$127$	10.4093	−	6.00982i	0.923676	−	0.533285i	0.884806	+	0.465959i	$0.154291\pi$
$128$	8.10557	−	4.67975i	0.716438	−	0.413636i
$129$	−0.544607			−0.0479500
$130$		0			0
$131$	10.9041			0.952697			0.476348	−	0.879257i	$-0.341960\pi$
$131$	10.9041			0.952697			0.476348	+	0.879257i	$0.341960\pi$
$132$	−1.10937	+	0.640492i	−0.0965579	+	0.0557477i
$133$	0.0660387	−	0.0381275i	0.00572629	−	0.00330607i
$134$	1.29728	−	2.24695i	0.112068	−	0.194107i
$135$		0			0
$136$	−4.90411	+	8.49418i	−0.420524	+	0.728370i
$137$	2.93568	+	1.69491i	0.250812	+	0.144806i	0.620136	−	0.784494i	$-0.287077\pi$
$137$	2.93568	+	1.69491i	0.250812	+	0.144806i	−0.369324	+	0.929301i	$0.620411\pi$
$138$		−	2.64049i		−	0.224774i
$139$	7.40411	−	12.8243i	0.628009	−	1.08774i	−0.359942	−	0.932975i	$-0.617204\pi$
$139$	7.40411	−	12.8243i	0.628009	−	1.08774i	0.987951	−	0.154768i	$-0.0494631\pi$
$140$		0			0
$141$	−2.50982	−	4.34713i	−0.211365	−	0.366094i
$142$			2.48571i			0.208597i
$143$	0.103015	−	2.44872i	0.00861455	−	0.204772i
$144$	−3.32025			−0.276687
$145$		0			0
$146$	1.36284	+	2.36051i	0.112790	+	0.195358i
$147$	5.68480	+	3.28212i	0.468874	+	0.270705i
$148$		−	18.4095i		−	1.51325i
$149$	−8.54461	+	14.7997i	−0.700001	+	1.21244i	0.268464	+	0.963290i	$0.413484\pi$
$149$	−8.54461	+	14.7997i	−0.700001	+	1.21244i	−0.968465	+	0.249148i	$0.919849\pi$
$150$		0			0
$151$	13.0130			1.05898			0.529490	−	0.848316i	$-0.322383\pi$
$151$	13.0130			1.05898			0.529490	+	0.848316i	$0.322383\pi$
$152$	0.132077	+	0.0762550i	0.0107129	+	0.00618510i
$153$	6.43378	−	3.71455i	0.520140	−	0.300303i
$154$	−0.0762550	−	0.132077i	−0.00614480	−	0.0106431i
$155$		0			0
$156$	3.64163	−	5.73630i	0.291563	−	0.459272i
$157$			0.775639i			0.0619028i	0.999521	+	0.0309514i	$0.00985370\pi$
$157$			0.775639i			0.0619028i	−0.999521	+	0.0309514i	$0.990146\pi$
$158$	−2.93568	+	1.69491i	−0.233550	+	0.134840i
$159$	−0.339877	−	0.588684i	−0.0269540	−	0.0466857i
$160$		0			0
$161$	−5.12847			−0.404180
$162$	−0.294342	−	0.169938i	−0.0231257	−	0.0133516i
$163$	−10.5638	−	6.09903i	−0.827423	−	0.477713i	0.0255466	−	0.999674i	$-0.491867\pi$
$163$	−10.5638	−	6.09903i	−0.827423	−	0.477713i	−0.852969	+	0.521961i	$0.825201\pi$
$164$	7.96074			0.621629
$165$		0			0
$166$	0.300616	+	0.520681i	0.0233323	+	0.0404127i
$167$	1.37745	−	0.795270i	0.106590	−	0.0615398i	−0.445757	−	0.895154i	$-0.647066\pi$
$167$	1.37745	−	0.795270i	0.106590	−	0.0615398i	0.552347	+	0.833614i	$0.313732\pi$
$168$		−	0.871525i		−	0.0672396i
$169$	5.53146	+	11.7645i	0.425497	+	0.904960i
$170$		0			0
$171$	−0.0577581	−	0.100040i	−0.00441688	−	0.00765025i
$172$	−0.888804	+	0.513151i	−0.0677707	+	0.0391274i
$173$	−11.0412	−	6.37467i	−0.839451	−	0.484657i	0.0176268	−	0.999845i	$-0.494389\pi$
$173$	−11.0412	−	6.37467i	−0.839451	−	0.484657i	−0.857077	+	0.515188i	$0.827722\pi$
$174$	−1.88448			−0.142862
$175$		0			0
$176$	−1.12847	+	1.95458i	−0.0850620	+	0.147332i
$177$			2.22436i			0.167193i
$178$	3.98675	+	2.30175i	0.298819	+	0.172523i
$179$	8.88115	+	15.3826i	0.663808	+	1.14975i	0.979607	+	0.200923i	$0.0643942\pi$
$179$	8.88115	+	15.3826i	0.663808	+	1.14975i	−0.315799	+	0.948826i	$0.602272\pi$
$180$		0			0
$181$	7.02630			0.522261			0.261130	−	0.965304i	$-0.415905\pi$
$181$	7.02630			0.522261			0.261130	+	0.965304i	$0.415905\pi$
$182$	0.682946	+	0.433560i	0.0506233	+	0.0321376i
$183$			4.20473i			0.310823i
$184$	−5.12847	−	8.88278i	−0.378076	−	0.654847i
$185$		0			0
$186$	1.69491	−	2.93568i	0.124277	−	0.215254i
$187$		−	5.04995i		−	0.369289i
$188$	−8.19209	−	4.72971i	−0.597470	−	0.344949i
$189$	−0.330062	+	0.571683i	−0.0240084	+	0.0415838i
$190$		0			0
$191$	6.97703	−	12.0846i	0.504840	−	0.874409i	−0.495144	−	0.868811i	$-0.664885\pi$
$191$	6.97703	−	12.0846i	0.504840	−	0.874409i	0.999984	−	0.00559828i	$-0.00178200\pi$
$192$	−4.64147	+	2.67975i	−0.334969	+	0.193395i
$193$	20.5675	−	11.8747i	1.48048	−	0.854757i	0.480728	−	0.876870i	$-0.340373\pi$
$193$	20.5675	−	11.8747i	1.48048	−	0.854757i	0.999755	+	0.0221126i	$0.00703924\pi$
$194$	3.36618			0.241678
$195$		0			0
$196$	12.3702			0.883586
$197$	−13.6903	+	7.90411i	−0.975395	+	0.563145i	−0.900877	−	0.434075i	$-0.857075\pi$
$197$	−13.6903	+	7.90411i	−0.975395	+	0.563145i	−0.0745186	+	0.997220i	$0.523742\pi$
$198$	−0.200080	+	0.115516i	−0.0142191	+	0.00820939i
$199$	4.38448	−	7.59415i	0.310808	−	0.538335i	−0.667730	−	0.744404i	$-0.732734\pi$
$199$	4.38448	−	7.59415i	0.310808	−	0.538335i	0.978537	+	0.206069i	$0.0660671\pi$
$200$		0			0
$201$	−3.81691	+	6.61108i	−0.269224	+	0.466310i
$202$	2.75490	+	1.59054i	0.193834	+	0.111910i
$203$			3.66012i			0.256890i
$204$	7.00000	−	12.1244i	0.490098	−	0.848875i
$205$		0			0
$206$	0.765631	+	1.32611i	0.0533441	+	0.0923946i
$207$			7.76897i			0.539981i
$208$	0.503175	−	11.9607i	0.0348889	−	0.829328i
$209$	−0.0785226			−0.00543152
$210$		0			0
$211$	−4.40411	−	7.62815i	−0.303192	−	0.525143i	0.673665	−	0.739037i	$-0.264719\pi$
$211$	−4.40411	−	7.62815i	−0.303192	−	0.525143i	−0.976857	+	0.213893i	$0.931386\pi$
$212$	−1.10937	−	0.640492i	−0.0761915	−	0.0439892i
$213$		−	7.31357i		−	0.501118i
$214$	−0.0970195	+	0.168043i	−0.00663211	+	0.0114872i
$215$		0			0
$216$	−1.32025			−0.0898314
$217$	−5.70180	−	3.29193i	−0.387063	−	0.223471i
$218$	−4.53565	+	2.61866i	−0.307193	+	0.177358i
$219$	−4.00982	−	6.94520i	−0.270958	−	0.469313i
$220$		0			0
$221$	12.4061	+	23.7398i	0.834526	+	1.59691i
$222$		−	3.32025i		−	0.222840i
$223$	8.69426	−	5.01963i	0.582210	−	0.336139i	−0.179801	−	0.983703i	$-0.557545\pi$
$223$	8.69426	−	5.01963i	0.582210	−	0.336139i	0.762011	+	0.647564i	$0.224212\pi$
$224$	−1.24399	−	2.15466i	−0.0831177	−	0.143964i
$225$		0			0
$226$	1.80823			0.120282
$227$	1.04910	+	0.605701i	0.0696315	+	0.0402018i	0.534412	−	0.845224i	$-0.320533\pi$
$227$	1.04910	+	0.605701i	0.0696315	+	0.0402018i	−0.464780	+	0.885426i	$0.653867\pi$
$228$	−0.188524	−	0.108844i	−0.0124853	−	0.00720839i
$229$	−19.2440			−1.27168			−0.635839	−	0.771821i	$-0.719346\pi$
$229$	−19.2440			−1.27168			−0.635839	+	0.771821i	$0.719346\pi$
$230$		0			0
$231$	0.224361	+	0.388604i	0.0147618	+	0.0255683i
$232$	−6.33952	+	3.66012i	−0.416210	+	0.240299i
$233$		−	23.9081i		−	1.56627i	−0.621849	−	0.783137i	$-0.713618\pi$
$233$		−	23.9081i		−	1.56627i	0.621849	−	0.783137i	$-0.286382\pi$
$234$	0.656787	−	1.03457i	0.0429355	−	0.0676322i
$235$		0			0
$236$	2.09589	+	3.63018i	0.136431	+	0.236305i
$237$	8.63748	−	4.98685i	0.561064	−	0.323931i
$238$	1.44349	+	0.833398i	0.0935674	+	0.0540211i
$239$	−18.6798			−1.20829			−0.604146	−	0.796873i	$-0.706486\pi$
$239$	−18.6798			−1.20829			−0.604146	+	0.796873i	$0.706486\pi$
$240$		0			0
$241$	−3.05776	+	5.29619i	−0.196968	+	0.341158i	−0.947544	−	0.319626i	$-0.896443\pi$
$241$	−3.05776	+	5.29619i	−0.196968	+	0.341158i	0.750576	+	0.660784i	$0.229776\pi$
$242$		−	3.58160i		−	0.230234i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	3.96187	+	6.86216i	0.253633	+	0.439305i
$245$		0			0
$246$	1.43576			0.0915409
$247$	0.369134	−	0.192905i	0.0234874	−	0.0122743i
$248$		−	13.1677i		−	0.836152i
$249$	−0.884484	−	1.53197i	−0.0560519	−	0.0970847i
$250$		0			0
$251$	−1.67975	+	2.90942i	−0.106025	+	0.183641i	−0.914157	−	0.405361i	$-0.867146\pi$
$251$	−1.67975	+	2.90942i	−0.106025	+	0.183641i	0.808131	+	0.589002i	$0.200479\pi$
$252$			1.24399i			0.0783641i
$253$	4.57347	+	2.64049i	0.287531	+	0.166006i
$254$	2.04260	−	3.53788i	0.128164	−	0.221986i
$255$		0			0
$256$	−3.76897	+	6.52804i	−0.235560	+	0.408003i
$257$	8.75452	−	5.05442i	0.546092	−	0.315286i	−0.201452	−	0.979498i	$-0.564566\pi$
$257$	8.75452	−	5.05442i	0.546092	−	0.315286i	0.747544	+	0.664212i	$0.231233\pi$
$258$	−0.160301	+	0.0925496i	−0.00997988	+	0.00576189i
$259$	−6.44872			−0.400704
$260$		0			0
$261$	5.54461			0.343203
$262$	3.20954	−	1.85303i	0.198286	−	0.114480i
$263$	−19.5014	+	11.2592i	−1.20251	+	0.694269i	−0.961112	−	0.276157i	$-0.910939\pi$
$263$	−19.5014	+	11.2592i	−1.20251	+	0.694269i	−0.241397	+	0.970426i	$0.577606\pi$
$264$	−0.448721	+	0.777208i	−0.0276169	+	0.0478338i
$265$		0			0
$266$	0.0129587	−	0.0224450i	0.000794546	−	0.00137619i
$267$	−11.7300	−	6.77230i	−0.717863	−	0.414458i
$268$			14.3858i			0.878753i
$269$	4.24733	−	7.35659i	0.258964	−	0.448539i	−0.707001	−	0.707213i	$-0.749952\pi$
$269$	4.24733	−	7.35659i	0.258964	−	0.448539i	0.965965	+	0.258674i	$0.0832855\pi$
$270$		0			0
$271$	−4.68510	−	8.11483i	−0.284600	−	0.492941i	0.687912	−	0.725794i	$-0.258527\pi$
$271$	−4.68510	−	8.11483i	−0.284600	−	0.492941i	−0.972512	+	0.232853i	$0.925194\pi$
$272$		−	24.6664i		−	1.49562i
$273$	−2.00939	−	1.27564i	−0.121614	−	0.0772052i
$274$	1.15212			0.0696024
$275$		0			0
$276$	7.32025	+	12.6790i	0.440627	+	0.763188i
$277$	0.622685	+	0.359508i	0.0374135	+	0.0216007i	0.518590	−	0.855023i	$-0.326457\pi$
$277$	0.622685	+	0.359508i	0.0374135	+	0.0216007i	−0.481177	+	0.876624i	$0.659790\pi$
$278$		−	5.03297i		−	0.301858i
$279$	−4.98685	+	8.63748i	−0.298555	+	0.517112i
$280$		0			0
$281$	1.54461			0.0921435			0.0460718	−	0.998938i	$-0.485330\pi$
$281$	1.54461			0.0921435			0.0460718	+	0.998938i	$0.485330\pi$
$282$	−1.47749	−	0.853028i	−0.0879831	−	0.0507971i
$283$	−15.6920	+	9.05977i	−0.932791	+	0.538547i	−0.887693	−	0.460435i	$-0.847693\pi$
$283$	−15.6920	+	9.05977i	−0.932791	+	0.538547i	−0.0450980	+	0.998983i	$0.514360\pi$
$284$	−6.89116	−	11.9358i	−0.408915	−	0.708261i
$285$		0			0
$286$	−0.385810	−	0.738268i	−0.0228134	−	0.0436547i
$287$		−	2.78860i		−	0.164606i
$288$	−3.26402	+	1.88448i	−0.192334	+	0.111044i
$289$	19.0957	+	33.0747i	1.12328	+	1.94557i
$290$		0			0
$291$	−9.90411			−0.580589
$292$	−13.0881	−	7.55643i	−0.765924	−	0.442207i
$293$	26.4181	+	15.2525i	1.54336	+	0.891059i	0.998623	+	0.0524523i	$0.0167037\pi$
$293$	26.4181	+	15.2525i	1.54336	+	0.891059i	0.544737	+	0.838607i	$0.316630\pi$
$294$	2.23103			0.130116
$295$		0			0
$296$	−6.44872	−	11.1695i	−0.374824	−	0.649215i
$297$	0.588684	−	0.339877i	0.0341589	−	0.0197217i
$298$			5.80823i			0.336462i
$299$	−27.9867	−	1.17737i	−1.61851	−	0.0680890i
$300$		0			0
$301$	0.179754	+	0.311343i	0.0103608	+	0.0179455i
$302$	3.83026	−	2.21140i	0.220407	−	0.127252i
$303$	−8.10557	−	4.67975i	−0.465653	−	0.268845i
$304$	−0.383543			−0.0219977
$305$		0			0
$306$	1.26249	−	2.18669i	0.0721716	−	0.125005i
$307$			4.77564i			0.272560i	0.990670	+	0.136280i	$0.0435147\pi$
$307$			4.77564i			0.272560i	−0.990670	+	0.136280i	$0.956485\pi$
$308$	0.732318	+	0.422804i	0.0417277	+	0.0240915i
$309$	−2.25267	−	3.90174i	−0.128150	−	0.221962i
$310$		0			0
$311$	30.5812			1.73410			0.867051	−	0.498220i	$-0.166013\pi$
$311$	30.5812			1.73410			0.867051	+	0.498220i	$0.166013\pi$
$312$	0.200080	−	4.75601i	0.0113273	−	0.269256i
$313$		−	26.7230i		−	1.51048i	−0.655451	−	0.755238i	$-0.727521\pi$
$313$		−	26.7230i		−	1.51048i	0.655451	−	0.755238i	$-0.272479\pi$
$314$	0.131811	+	0.228303i	0.00743852	+	0.0128839i
$315$		0			0
$316$	9.39764	−	16.2772i	0.528658	−	0.915663i
$317$			20.6271i			1.15854i	0.815137	+	0.579268i	$0.196662\pi$
$317$			20.6271i			1.15854i	−0.815137	+	0.579268i	$0.803338\pi$
$318$	−0.200080	−	0.115516i	−0.0112199	−	0.00647783i
$319$	1.88448	−	3.26402i	0.105511	−	0.182750i
$320$		0			0
$321$	0.285455	−	0.494422i	0.0159325	−	0.0275960i
$322$	−1.50953	+	0.871525i	−0.0841226	+	0.0485682i
$323$	0.743207	−	0.429091i	0.0413531	−	0.0238752i
$324$	1.88448			0.104694
$325$		0			0
$326$	−4.14584			−0.229617
$327$	13.3450	−	7.70473i	0.737979	−	0.426073i
$328$	4.82999	−	2.78860i	0.266692	−	0.153975i
$329$	−1.65679	+	2.86964i	−0.0913416	+	0.158208i
$330$		0			0
$331$	−2.68510	+	4.65073i	−0.147586	+	0.255627i	−0.930335	−	0.366711i	$-0.880484\pi$
$331$	−2.68510	+	4.65073i	−0.147586	+	0.255627i	0.782749	+	0.622338i	$0.213817\pi$
$332$	−2.88697	−	1.66680i	−0.158443	−	0.0914773i
$333$			9.76897i			0.535336i
$334$	0.270294	−	0.468163i	0.0147898	−	0.0256167i
$335$		0			0
$336$	1.09589	+	1.89813i	0.0597855	+	0.103551i
$337$		−	28.7623i		−	1.56678i	−0.621529	−	0.783391i	$-0.713488\pi$
$337$		−	28.7623i		−	1.56678i	0.621529	−	0.783391i	$-0.286512\pi$
$338$	3.62738	+	2.52277i	0.197303	+	0.137221i
$339$	−5.32025			−0.288956
$340$		0			0
$341$	3.38983	+	5.87136i	0.183570	+	0.317952i
$342$	−0.0340013	−	0.0196307i	−0.00183858	−	0.00106150i
$343$		−	8.95407i		−	0.483474i
$344$	−0.359508	+	0.622685i	−0.0193833	+	0.0335729i
$345$		0			0
$346$	−4.33320			−0.232955
$347$	19.3956	+	11.1981i	1.04121	+	0.601143i	0.920176	−	0.391505i	$-0.128045\pi$
$347$	19.3956	+	11.1981i	1.04121	+	0.601143i	0.121035	+	0.992648i	$0.461379\pi$
$348$	9.04886	−	5.22436i	0.485070	−	0.280055i
$349$	−5.98685	−	10.3695i	−0.320469	−	0.555068i	0.660116	−	0.751164i	$-0.270507\pi$
$349$	−5.98685	−	10.3695i	−0.320469	−	0.555068i	−0.980585	+	0.196096i	$0.937174\pi$
$350$		0			0
$351$	−1.93243	+	3.04397i	−0.103145	+	0.162475i
$352$			2.56197i			0.136553i
$353$	−14.7541	+	8.51830i	−0.785283	+	0.453384i	−0.838299	−	0.545210i	$-0.816450\pi$
$353$	−14.7541	+	8.51830i	−0.785283	+	0.453384i	0.0530161	+	0.998594i	$0.483117\pi$
$354$	0.378004	+	0.654723i	0.0200907	+	0.0347981i
$355$		0			0
$356$	−25.5246			−1.35280
$357$	−4.24709	−	2.45206i	−0.224780	−	0.129777i
$358$	5.22819	+	3.01850i	0.276318	+	0.159533i
$359$	35.0825			1.85159			0.925793	−	0.378031i	$-0.123399\pi$
$359$	35.0825			1.85159			0.925793	+	0.378031i	$0.123399\pi$
$360$		0			0
$361$	9.49333	+	16.4429i	0.499649	+	0.865417i
$362$	2.06814	−	1.19404i	0.108699	−	0.0627573i
$363$			10.5379i			0.553098i
$364$	−4.48131	−	0.188524i	−0.234884	−	0.00988133i
$365$		0			0
$366$	0.714545	+	1.23763i	0.0373499	+	0.0646919i
$367$	−17.3920	+	10.0413i	−0.907855	+	0.524150i	−0.879740	−	0.475455i	$-0.842284\pi$
$367$	−17.3920	+	10.0413i	−0.907855	+	0.524150i	−0.0281143	+	0.999605i	$0.508950\pi$
$368$	22.3390	+	12.8974i	1.16450	+	0.672326i
$369$	−4.22436			−0.219911
$370$		0			0
$371$	−0.224361	+	0.388604i	−0.0116482	+	0.0201753i
$372$			18.7953i			0.974489i
$373$	20.3334	+	11.7395i	1.05283	+	0.607849i	0.923439	−	0.383745i	$-0.125366\pi$
$373$	20.3334	+	11.7395i	1.05283	+	0.607849i	0.129387	+	0.991594i	$0.458699\pi$
$374$	−0.858181	−	1.48641i	−0.0443755	−	0.0768606i
$375$		0			0
$376$	−6.62715			−0.341769
$377$	−0.840272	+	19.9737i	−0.0432762	+	1.02870i
$378$			0.224361i			0.0115399i
$379$	10.5707	+	18.3090i	0.542981	+	0.940471i	0.998731	+	0.0503631i	$0.0160379\pi$
$379$	10.5707	+	18.3090i	0.542981	+	0.940471i	−0.455750	+	0.890108i	$0.650629\pi$
$380$		0			0
$381$	−6.00982	+	10.4093i	−0.307892	+	0.533285i
$382$		−	4.74266i		−	0.242656i
$383$	−1.50571	−	0.869323i	−0.0769383	−	0.0444203i	0.461037	−	0.887381i	$-0.347477\pi$
$383$	−1.50571	−	0.869323i	−0.0769383	−	0.0444203i	−0.537976	+	0.842960i	$0.680811\pi$
$384$	−4.67975	+	8.10557i	−0.238813	+	0.413636i
$385$		0			0
$386$	4.03593	−	6.99043i	0.205423	−	0.355803i
$387$	0.471643	−	0.272303i	0.0239750	−	0.0138420i
$388$	−16.1636	+	9.33207i	−0.820584	+	0.473764i
$389$	26.6664			1.35204			0.676020	−	0.736883i	$-0.263703\pi$
$389$	26.6664			1.35204			0.676020	+	0.736883i	$0.263703\pi$
$390$		0			0
$391$	−57.7164			−2.91884
$392$	7.50533	−	4.33320i	0.379076	−	0.218860i
$393$	−9.44324	+	5.45206i	−0.476348	+	0.275020i
$394$	−2.68643	+	4.65303i	−0.135340	+	0.234416i
$395$		0			0
$396$	0.640492	−	1.10937i	0.0321860	−	0.0557477i
$397$	12.5960	+	7.27230i	0.632175	+	0.364986i	0.781594	−	0.623788i	$-0.214407\pi$
$397$	12.5960	+	7.27230i	0.632175	+	0.364986i	−0.149419	+	0.988774i	$0.547740\pi$
$398$		−	2.98037i		−	0.149392i
$399$	−0.0381275	+	0.0660387i	−0.00190876	+	0.00330607i
$400$		0			0
$401$	4.18510	+	7.24880i	0.208994	+	0.361988i	0.951398	−	0.307964i	$-0.0996478\pi$
$401$	4.18510	+	7.24880i	0.208994	+	0.361988i	−0.742404	+	0.669952i	$0.766314\pi$
$402$			2.59456i			0.129405i
$403$	−30.3596	−	19.2734i	−1.51232	−	0.960078i
$404$	−17.6378			−0.877515
$405$		0			0
$406$	0.621996	+	1.07733i	0.0308691	+	0.0534669i
$407$	5.75084	+	3.32025i	0.285058	+	0.164578i
$408$		−	9.80823i		−	0.485580i
$409$	8.62734	−	14.9430i	0.426595	−	0.738883i	−0.569973	−	0.821663i	$-0.693046\pi$
$409$	8.62734	−	14.9430i	0.426595	−	0.738883i	0.996568	+	0.0827798i	$0.0263798\pi$
$410$		0			0
$411$	−3.38983			−0.167208
$412$	−7.35277	−	4.24513i	−0.362245	−	0.209142i
$413$	1.27163	−	0.734176i	0.0625728	−	0.0361264i
$414$	1.32025	+	2.28673i	0.0648866	+	0.112387i
$415$		0			0
$416$	−6.29394	−	12.0438i	−0.308586	−	0.590495i
$417$			14.8082i			0.725162i
$418$	−0.0231125	+	0.0133440i	−0.00113047	+	0.000652677i
$419$	6.43243	+	11.1413i	0.314245	+	0.544288i	0.979277	−	0.202527i	$-0.0649155\pi$
$419$	6.43243	+	11.1413i	0.314245	+	0.544288i	−0.665032	+	0.746815i	$0.731582\pi$
$420$		0			0
$421$	24.5616			1.19706			0.598529	−	0.801101i	$-0.295752\pi$
$421$	24.5616			1.19706			0.598529	+	0.801101i	$0.295752\pi$
$422$	−2.59263	−	1.49686i	−0.126207	−	0.0728658i
$423$	4.34713	+	2.50982i	0.211365	+	0.122031i
$424$	−0.897442			−0.0435837
$425$		0			0
$426$	−1.24286	−	2.15269i	−0.0602166	−	0.104298i
$427$	2.40377	−	1.38782i	0.116327	−	0.0671613i
$428$		−	1.07587i		−	0.0520041i
$429$	1.13515	+	2.17216i	0.0548054	+	0.104873i
$430$		0			0
$431$	−12.3898	−	21.4598i	−0.596797	−	1.03368i	−0.993291	−	0.115645i	$-0.963106\pi$
$431$	−12.3898	−	21.4598i	−0.596797	−	1.03368i	0.396493	−	0.918038i	$-0.370227\pi$
$432$	2.87542	−	1.66012i	0.138344	−	0.0798727i
$433$	12.1754	+	7.02945i	0.585110	+	0.337814i	0.763162	−	0.646208i	$-0.223646\pi$
$433$	12.1754	+	7.02945i	0.585110	+	0.337814i	−0.178051	+	0.984021i	$0.556979\pi$
$434$	−2.23770			−0.107413
$435$		0			0
$436$	14.5194	−	25.1484i	0.695355	−	1.20439i
$437$			0.897442i			0.0429305i
$438$	−2.36051	−	1.36284i	−0.112790	−	0.0651192i
$439$	10.4226	+	18.0525i	0.497444	+	0.861598i	0.999996	−	0.00294880i	$-0.000938633\pi$
$439$	10.4226	+	18.0525i	0.497444	+	0.861598i	−0.502552	+	0.864547i	$0.667605\pi$
$440$		0			0
$441$	−6.56424			−0.312583
$442$	7.68594	+	4.87933i	0.365583	+	0.232086i
$443$		−	11.4291i		−	0.543012i	−0.962437	−	0.271506i	$-0.912478\pi$
$443$		−	11.4291i		−	0.543012i	0.962437	−	0.271506i	$-0.0875218\pi$
$444$	9.20473	+	15.9431i	0.436837	+	0.756624i
$445$		0			0
$446$	1.70606	−	2.95498i	0.0807841	−	0.139922i
$447$		−	17.0892i		−	0.808292i
$448$	3.06394	+	1.76897i	0.144758	+	0.0835759i
$449$	12.9541	−	22.4371i	0.611340	−	1.05887i	−0.379675	−	0.925120i	$-0.623964\pi$
$449$	12.9541	−	22.4371i	0.611340	−	1.05887i	0.991015	−	0.133752i	$-0.0427026\pi$
$450$		0			0
$451$	−1.43576	+	2.48681i	−0.0676074	+	0.117099i
$452$	−8.68270	+	5.01296i	−0.408400	+	0.235790i
$453$	−11.2696	+	6.50648i	−0.529490	+	0.305701i
$454$	0.411728			0.0193233
$455$		0			0
$456$	−0.152510			−0.00714193
$457$	−5.11311	+	2.95206i	−0.239181	+	0.138091i	−0.614800	−	0.788683i	$-0.710763\pi$
$457$	−5.11311	+	2.95206i	−0.239181	+	0.138091i	0.375619	+	0.926774i	$0.377430\pi$
$458$	−5.66432	+	3.27029i	−0.264676	+	0.152811i
$459$	−3.71455	+	6.43378i	−0.173380	+	0.300303i
$460$		0			0
$461$	7.74600	−	13.4165i	0.360767	−	0.624867i	−0.627320	−	0.778762i	$-0.715848\pi$
$461$	7.74600	−	13.4165i	0.360767	−	0.624867i	0.988087	+	0.153894i	$0.0491815\pi$
$462$	0.132077	+	0.0762550i	0.00614480	+	0.00354770i
$463$			17.4420i			0.810601i	0.914184	+	0.405300i	$0.132833\pi$
$463$			17.4420i			0.810601i	−0.914184	+	0.405300i	$0.867167\pi$
$464$	9.20473	−	15.9431i	0.427319	−	0.740138i
$465$		0			0
$466$	−4.06291	−	7.03717i	−0.188211	−	0.325991i
$467$			20.4790i			0.947657i	0.880617	+	0.473829i	$0.157128\pi$
$467$			20.4790i			0.947657i	−0.880617	+	0.473829i	$0.842872\pi$
$468$	−0.285589	+	6.78860i	−0.0132014	+	0.313803i
$469$	5.03926			0.232691
$470$		0			0
$471$	−0.387820	−	0.671723i	−0.0178698	−	0.0309514i
$472$	2.54326	+	1.46835i	0.117063	+	0.0675864i
$473$		−	0.370199i		−	0.0170217i
$474$	1.69491	−	2.93568i	0.0778500	−	0.134840i
$475$		0			0
$476$	−9.24172			−0.423594
$477$	0.588684	+	0.339877i	0.0269540	+	0.0155619i
$478$	−5.49824	+	3.17441i	−0.251483	+	0.145194i
$479$	−20.4953	−	35.4990i	−0.936456	−	1.62199i	−0.772017	−	0.635602i	$-0.780752\pi$
$479$	−20.4953	−	35.4990i	−0.936456	−	1.62199i	−0.164439	−	0.986387i	$-0.552581\pi$
$480$		0			0
$481$	−35.1914	−	1.48046i	−1.60459	−	0.0675033i
$482$			2.07852i			0.0946741i
$483$	4.44139	−	2.56424i	0.202090	−	0.116677i
$484$	9.92928	+	17.1980i	0.451331	+	0.781728i
$485$		0			0
$486$	0.339877			0.0154171
$487$	20.8391	+	12.0315i	0.944309	+	0.545197i	0.891309	−	0.453397i	$-0.149788\pi$
$487$	20.8391	+	12.0315i	0.944309	+	0.545197i	0.0530008	+	0.998594i	$0.483121\pi$
$488$	4.80755	+	2.77564i	0.217627	+	0.125647i
$489$	12.1981			0.551615
$490$		0			0
$491$	−18.3865	−	31.8463i	−0.829771	−	1.43721i	−0.898218	−	0.439550i	$-0.855138\pi$
$491$	−18.3865	−	31.8463i	−0.829771	−	1.43721i	0.0684471	−	0.997655i	$-0.478196\pi$
$492$	−6.89420	+	3.98037i	−0.310815	+	0.179449i
$493$			41.1914i			1.85517i
$494$	0.0758696	−	0.119510i	0.00341354	−	0.00537701i
$495$		0			0
$496$	16.5576	+	28.6785i	0.743457	+	1.28770i
$497$	−4.18105	+	2.41393i	−0.187546	+	0.108280i
$498$	−0.520681	−	0.300616i	−0.0233323	−	0.0134709i
$499$	−34.8212			−1.55881			−0.779405	−	0.626520i	$-0.784479\pi$
$499$	−34.8212			−1.55881			−0.779405	+	0.626520i	$0.784479\pi$
$500$		0			0
$501$	−0.795270	+	1.37745i	−0.0355300	+	0.0615398i
$502$			1.14182i			0.0509619i
$503$	27.7353	+	16.0130i	1.23665	+	0.713983i	0.968409	−	0.249368i	$-0.0802229\pi$
$503$	27.7353	+	16.0130i	1.23665	+	0.713983i	0.268245	+	0.963351i	$0.413556\pi$
$504$	0.435763	+	0.754763i	0.0194104	+	0.0336198i
$505$		0			0
$506$	1.79488			0.0797924
$507$	−10.6726	−	7.42261i	−0.473988	−	0.329650i
$508$			22.6508i			1.00497i
$509$	−20.6731	−	35.8068i	−0.916318	−	1.58711i	−0.804960	−	0.593329i	$-0.797813\pi$
$509$	−20.6731	−	35.8068i	−0.916318	−	1.58711i	−0.111359	−	0.993780i	$-0.535520\pi$
$510$		0			0
$511$	−2.64697	+	4.58469i	−0.117095	+	0.202815i
$512$			21.2810i			0.940496i
$513$	0.100040	+	0.0577581i	0.00441688	+	0.00255008i
$514$	1.71788	−	2.97546i	0.0757725	−	0.131242i
$515$		0			0
$516$	0.513151	−	0.888804i	0.0225902	−	0.0391274i
$517$	2.95498	−	1.70606i	0.129960	−	0.0750323i
$518$	−1.89813	+	1.09589i	−0.0833990	+	0.0481505i
$519$	12.7493			0.559634
$520$		0			0
$521$	4.40279			0.192890			0.0964448	−	0.995338i	$-0.469253\pi$
$521$	4.40279			0.192890			0.0964448	+	0.995338i	$0.469253\pi$
$522$	1.63201	−	0.942242i	0.0714312	−	0.0412408i
$523$	−28.1014	+	16.2244i	−1.22879	+	0.709442i	−0.966777	−	0.255623i	$-0.917720\pi$
$523$	−28.1014	+	16.2244i	−1.22879	+	0.709442i	−0.262013	+	0.965064i	$0.584386\pi$
$524$	−10.2743	+	17.7956i	−0.448835	+	0.777406i
$525$		0			0
$526$	−3.82673	+	6.62808i	−0.166853	+	0.288998i
$527$	−64.1686	−	37.0478i	−2.79523	−	1.61383i
$528$		−	2.25695i		−	0.0982211i
$529$	18.6784	−	32.3520i	0.812106	−	1.40661i
$530$		0			0
$531$	−1.11218	−	1.92635i	−0.0482645	−	0.0835966i
$532$			0.143701i			0.00623024i
$533$	0.640192	−	15.2177i	0.0277298	−	0.659151i
$534$	−4.60350			−0.199213
$535$		0			0
$536$	5.03926	+	8.72826i	0.217663	+	0.377003i
$537$	−15.3826	−	8.88115i	−0.663808	−	0.383250i
$538$		−	2.88714i		−	0.124473i
$539$	−2.23103	+	3.86426i	−0.0960974	+	0.166446i
$540$		0			0
$541$	−8.57720			−0.368762			−0.184381	−	0.982855i	$-0.559028\pi$
$541$	−8.57720			−0.368762			−0.184381	+	0.982855i	$0.559028\pi$
$542$	−2.75804	−	1.59236i	−0.118468	−	0.0683976i
$543$	−6.08496	+	3.51315i	−0.261130	+	0.150764i
$544$	−14.0000	−	24.2487i	−0.600245	−	1.03965i
$545$		0			0
$546$	−0.808229	−	0.0340013i	−0.0345890	−	0.00145512i
$547$			32.4920i			1.38926i	0.719368	+	0.694629i	$0.244431\pi$
$547$			32.4920i			1.38926i	−0.719368	+	0.694629i	$0.755569\pi$
$548$	−5.53224	+	3.19404i	−0.236325	+	0.136443i
$549$	−2.10236	−	3.64140i	−0.0897268	−	0.155411i
$550$		0			0
$551$	0.640492			0.0272859
$552$	8.88278	+	5.12847i	0.378076	+	0.218282i
$553$	−5.70180	−	3.29193i	−0.242465	−	0.139987i
$554$	0.244377			0.0103826
$555$		0			0
$556$	13.9529	+	24.1672i	0.591736	+	1.02492i
$557$	35.6933	−	20.6075i	1.51237	−	0.873169i	0.512477	−	0.858701i	$-0.328728\pi$
$557$	35.6933	−	20.6075i	1.51237	−	0.873169i	0.999895	−	0.0144676i	$-0.00460533\pi$
$558$			3.38983i			0.143503i
$559$	0.909460	+	1.74030i	0.0384661	+	0.0736068i
$560$		0			0
$561$	2.52498	+	4.37339i	0.106605	+	0.184645i
$562$	0.454643	−	0.262488i	0.0191779	−	0.0110724i
$563$	10.5468	+	6.08921i	0.444496	+	0.256630i	0.705503	−	0.708707i	$-0.250721\pi$
$563$	10.5468	+	6.08921i	0.444496	+	0.256630i	−0.261007	+	0.965337i	$0.584055\pi$
$564$	9.45941			0.398313
$565$		0			0
$566$	−3.07921	+	5.33334i	−0.129429	+	0.224177i
$567$		−	0.660123i		−	0.0277226i
$568$	−8.36210	−	4.82786i	−0.350866	−	0.202572i
$569$	3.47169	+	6.01314i	0.145541	+	0.252084i	0.929575	−	0.368634i	$-0.120174\pi$
$569$	3.47169	+	6.01314i	0.145541	+	0.252084i	−0.784034	+	0.620718i	$0.786841\pi$
$570$		0			0
$571$	3.51429			0.147068			0.0735341	−	0.997293i	$-0.476572\pi$
$571$	3.51429			0.147068			0.0735341	+	0.997293i	$0.476572\pi$
$572$	3.89927	+	2.47541i	0.163037	+	0.103502i
$573$			13.9541i			0.582939i
$574$	−0.473890	−	0.820802i	−0.0197798	−	0.0342596i
$575$		0			0
$576$	2.67975	−	4.64147i	0.111656	−	0.193395i
$577$		−	3.14182i		−	0.130796i	−0.997859	−	0.0653978i	$-0.979168\pi$
$577$		−	3.14182i		−	0.130796i	0.997859	−	0.0653978i	$-0.0208316\pi$
$578$	11.2413	+	6.49018i	0.467578	+	0.269956i
$579$	−11.8747	+	20.5675i	−0.493494	+	0.854757i
$580$		0			0
$581$	−0.583868	+	1.01129i	−0.0242229	+	0.0419553i
$582$	−2.91520	+	1.68309i	−0.120839	+	0.0697663i
$583$	0.400160	−	0.231033i	0.0165729	−	0.00956839i
$584$	−10.5879			−0.438130
$585$		0			0
$586$	10.3679			0.428295
$587$	−32.8897	+	18.9889i	−1.35750	+	0.783754i	−0.989287	−	0.145987i	$-0.953364\pi$
$587$	−32.8897	+	18.9889i	−1.35750	+	0.783754i	−0.368215	+	0.929741i	$0.620031\pi$
$588$	−10.7129	+	6.18510i	−0.441793	+	0.255069i
$589$	−0.576062	+	0.997769i	−0.0237362	+	0.0411124i
$590$		0			0
$591$	7.90411	−	13.6903i	0.325132	−	0.563145i
$592$	28.0899	+	16.2177i	1.15449	+	0.666543i
$593$			10.4487i			0.429078i	0.976715	+	0.214539i	$0.0688248\pi$
$593$			10.4487i			0.429078i	−0.976715	+	0.214539i	$0.931175\pi$
$594$	0.115516	−	0.200080i	0.00473969	−	0.00820939i
$595$		0			0
$596$	−16.1022	−	27.8898i	−0.659571	−	1.14241i
$597$			8.76897i			0.358890i
$598$	−8.43773	+	4.40946i	−0.345044	+	0.180316i
$599$	45.5705			1.86196			0.930981	−	0.365069i	$-0.118955\pi$
$599$	45.5705			1.86196			0.930981	+	0.365069i	$0.118955\pi$
$600$		0			0
$601$	7.39096	+	12.8015i	0.301484	+	0.522185i	0.976472	−	0.215643i	$-0.0691848\pi$
$601$	7.39096	+	12.8015i	0.301484	+	0.522185i	−0.674989	+	0.737828i	$0.735851\pi$
$602$	0.105818	+	0.0610942i	0.00431283	+	0.00249001i
$603$		−	7.63382i		−	0.310873i
$604$	−12.2614	+	21.2373i	−0.498907	+	0.864133i
$605$		0			0
$606$	−3.18108			−0.129223
$607$	−16.3977	−	9.46722i	−0.665562	−	0.384263i	0.128831	−	0.991667i	$-0.458878\pi$
$607$	−16.3977	−	9.46722i	−0.665562	−	0.384263i	−0.794393	+	0.607404i	$0.792211\pi$
$608$	−0.377048	+	0.217689i	−0.0152913	+	0.00882844i
$609$	−1.83006	−	3.16976i	−0.0741578	−	0.128445i
$610$		0			0
$611$	−9.70007	+	15.2796i	−0.392423	+	0.618146i
$612$			14.0000i			0.565916i
$613$	−2.23770	+	1.29193i	−0.0903797	+	0.0521807i	−0.544509	−	0.838755i	$-0.683284\pi$
$613$	−2.23770	+	1.29193i	−0.0903797	+	0.0521807i	0.454129	+	0.890936i	$0.349951\pi$
$614$	0.811565	+	1.40567i	0.0327521	+	0.0567283i
$615$		0			0
$616$	0.592422			0.0238694
$617$	12.1584	+	7.01963i	0.489477	+	0.282600i	0.724357	−	0.689425i	$-0.242137\pi$
$617$	12.1584	+	7.01963i	0.489477	+	0.282600i	−0.234880	+	0.972024i	$0.575470\pi$
$618$	−1.32611	−	0.765631i	−0.0533441	−	0.0307982i
$619$	17.8582			0.717781			0.358890	−	0.933380i	$-0.383155\pi$
$619$	17.8582			0.717781			0.358890	+	0.933380i	$0.383155\pi$
$620$		0			0
$621$	−3.88448	−	6.72812i	−0.155879	−	0.269990i
$622$	9.00134	−	5.19692i	0.360921	−	0.208378i
$623$			8.94111i			0.358218i
$624$	5.54461	+	10.6099i	0.221962	+	0.424736i
$625$		0			0
$626$	−4.54127	−	7.86571i	−0.181506	−	0.314377i
$627$	0.0680026	−	0.0392613i	0.00271576	−	0.00156795i
$628$	−1.26585	−	0.730840i	−0.0505130	−	0.0291637i
$629$	−72.5745			−2.89374
$630$		0			0
$631$	12.4815	−	21.6186i	0.496881	−	0.860623i	−0.503113	−	0.864221i	$-0.667812\pi$
$631$	12.4815	−	21.6186i	0.496881	−	0.860623i	0.999994	+	0.00359801i	$0.00114528\pi$
$632$		−	13.1677i		−	0.523784i
$633$	7.62815	+	4.40411i	0.303192	+	0.175048i
$634$	3.50535	+	6.07144i	0.139215	+	0.241128i
$635$		0			0
$636$	1.28098			0.0507944
$637$	0.994794	−	23.6468i	0.0394152	−	0.936920i
$638$		−	1.28098i		−	0.0507147i
$639$	3.65679	+	6.33374i	0.144660	+	0.250559i
$640$		0			0
$641$	−11.6535	+	20.1844i	−0.460284	+	0.797235i	−0.998975	−	0.0452686i	$-0.985586\pi$
$641$	−11.6535	+	20.1844i	−0.460284	+	0.797235i	0.538691	+	0.842503i	$0.318919\pi$
$642$		−	0.194039i		−	0.00765811i
$643$	−39.3860	−	22.7395i	−1.55323	−	0.896759i	−0.997876	−	0.0651470i	$-0.979248\pi$
$643$	−39.3860	−	22.7395i	−1.55323	−	0.896759i	−0.555357	−	0.831612i	$-0.687418\pi$
$644$	4.83226	−	8.36973i	0.190418	−	0.329813i
$645$		0			0
$646$	0.145838	−	0.252599i	0.00573792	−	0.00993836i
$647$	−5.55076	+	3.20473i	−0.218223	+	0.125991i	−0.605127	−	0.796129i	$-0.706878\pi$
$647$	−5.55076	+	3.20473i	−0.218223	+	0.125991i	0.386904	+	0.922120i	$0.373544\pi$
$648$	1.14337	−	0.660123i	0.0449157	−	0.0259321i
$649$	−1.51202			−0.0593519
$650$		0			0
$651$	6.58387			0.258042
$652$	19.9074	−	11.4935i	0.779632	−	0.450121i
$653$	1.28319	−	0.740848i	0.0502150	−	0.0289916i	−0.474682	−	0.880157i	$-0.657437\pi$
$653$	1.28319	−	0.740848i	0.0502150	−	0.0289916i	0.524897	+	0.851166i	$0.324104\pi$
$654$	2.61866	−	4.53565i	0.102398	−	0.177358i
$655$		0			0
$656$	−7.01296	+	12.1468i	−0.273810	+	0.474253i
$657$	6.94520	+	4.00982i	0.270958	+	0.156438i
$658$			1.12621i			0.0439041i
$659$	−3.54461	+	6.13944i	−0.138078	+	0.239159i	−0.926769	−	0.375631i	$-0.877426\pi$
$659$	−3.54461	+	6.13944i	−0.138078	+	0.239159i	0.788691	+	0.614790i	$0.210759\pi$
$660$		0			0
$661$	−0.589214	−	1.02055i	−0.0229178	−	0.0396947i	0.854339	−	0.519716i	$-0.173962\pi$
$661$	−0.589214	−	1.02055i	−0.0229178	−	0.0396947i	−0.877257	+	0.480021i	$0.840629\pi$
$662$			1.82521i			0.0709387i
$663$	−22.6139	−	14.3562i	−0.878251	−	0.557548i
$664$	−2.33547			−0.0906339
$665$		0			0
$666$	1.66012	+	2.87542i	0.0643285	+	0.111420i
$667$	−37.3048	−	21.5379i	−1.44445	−	0.833952i
$668$			2.99735i			0.115971i
$669$	−5.01963	+	8.69426i	−0.194070	+	0.336139i
$670$		0			0
$671$	−2.85818			−0.110339
$672$	2.15466	+	1.24399i	0.0831177	+	0.0479880i
$673$	11.7412	−	6.77878i	0.452590	−	0.261303i	−0.256334	−	0.966588i	$-0.582515\pi$
$673$	11.7412	−	6.77878i	0.452590	−	0.261303i	0.708923	+	0.705286i	$0.249181\pi$
$674$	−4.88782	−	8.46595i	−0.188272	−	0.326096i
$675$		0			0
$676$	−24.4117	−	2.05759i	−0.938913	−	0.0791381i
$677$		−	9.53793i		−	0.366573i	−0.983060	−	0.183286i	$-0.941326\pi$
$677$		−	9.53793i		−	0.366573i	0.983060	−	0.183286i	$-0.0586735\pi$
$678$	−1.56597	+	0.904114i	−0.0601408	+	0.0347223i
$679$	3.26897	+	5.66202i	0.125451	+	0.217288i
$680$		0			0
$681$	−1.21140			−0.0464210
$682$	1.99554	+	1.15212i	0.0764131	+	0.0441171i
$683$	38.5540	+	22.2592i	1.47523	+	0.851723i	0.999610	−	0.0279296i	$-0.00889141\pi$
$683$	38.5540	+	22.2592i	1.47523	+	0.851723i	0.475617	+	0.879652i	$0.342225\pi$
$684$	0.217689			0.00832353
$685$		0			0
$686$	−1.52164	−	2.63556i	−0.0580965	−	0.100626i
$687$	16.6658	−	9.62200i	0.635839	−	0.367102i
$688$		−	1.80823i		−	0.0689381i
$689$	−1.31357	+	2.06915i	−0.0500432	+	0.0788282i
$690$		0			0
$691$	2.64030	+	4.57313i	0.100442	+	0.173970i	0.911867	−	0.410486i	$-0.134641\pi$
$691$	2.64030	+	4.57313i	0.100442	+	0.173970i	−0.811425	+	0.584457i	$0.801308\pi$
$692$	20.8071	−	12.0130i	0.790966	−	0.456664i
$693$	−0.388604	−	0.224361i	−0.0147618	−	0.00852275i
$694$	7.61192			0.288945
$695$		0			0
$696$	3.66012	−	6.33952i	0.138737	−	0.240299i
$697$		−	31.3832i		−	1.18872i
$698$	−3.52436	−	2.03479i	−0.133399	−	0.0770180i
$699$	11.9541	+	20.7051i	0.452144	+	0.783137i
$700$		0			0
$701$	20.1392			0.760646			0.380323	−	0.924854i	$-0.375813\pi$
$701$	20.1392			0.760646			0.380323	+	0.924854i	$0.375813\pi$
$702$	−0.0515075	+	1.22436i	−0.00194403	+	0.0462105i
$703$			1.12847i			0.0425612i
$704$	−1.82157	−	3.15506i	−0.0686531	−	0.118911i
$705$		0			0
$706$	−2.89517	+	5.01459i	−0.108961	+	0.188727i
$707$			6.17843i			0.232364i
$708$	−3.63018	−	2.09589i	−0.136431	−	0.0787682i
$709$	0.770294	−	1.33419i	0.0289290	−	0.0501065i	−0.851198	−	0.524844i	$-0.824124\pi$
$709$	0.770294	−	1.33419i	0.0289290	−	0.0501065i	0.880127	+	0.474737i	$0.157457\pi$
$710$		0			0
$711$	−4.98685	+	8.63748i	−0.187021	+	0.323931i
$712$	−15.4865	+	8.94111i	−0.580379	+	0.335082i
$713$	67.1043	−	38.7427i	2.51307	−	1.45092i
$714$	−1.66680			−0.0623782
$715$		0			0
$716$	−33.4728			−1.25094
$717$	16.1771	−	9.33988i	0.604146	−	0.348804i
$718$	10.3263	−	5.96187i	0.385373	−	0.222495i
$719$	18.5020	−	32.0464i	0.690009	−	1.19513i	−0.281826	−	0.959466i	$-0.590940\pi$
$719$	18.5020	−	32.0464i	0.690009	−	1.19513i	0.971835	−	0.235664i	$-0.0757266\pi$
$720$		0			0
$721$	−1.48704	+	2.57563i	−0.0553803	+	0.0959215i
$722$	5.58857	+	3.22656i	0.207985	+	0.120080i
$723$		−	6.11552i		−	0.227438i
$724$	−6.62048	+	11.4670i	−0.246048	+	0.426168i
$725$		0			0
$726$	1.79080	+	3.10176i	0.0664628	+	0.115117i
$727$			44.9015i			1.66530i	0.553797	+	0.832652i	$0.313178\pi$
$727$			44.9015i			1.66530i	−0.553797	+	0.832652i	$0.686822\pi$
$728$	−2.78497	+	1.45539i	−0.103218	+	0.0539405i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	2.02297	+	3.50388i	0.0748221	+	0.129596i
$732$	−6.86216	−	3.96187i	−0.253633	−	0.146435i
$733$		−	4.94072i		−	0.182490i	−0.995828	−	0.0912449i	$-0.970915\pi$
$733$		−	4.94072i		−	0.182490i	0.995828	−	0.0912449i	$-0.0290846\pi$
$734$	−3.41280	+	5.91114i	−0.125969	+	0.218184i
$735$		0			0
$736$	29.2810			1.07931
$737$	−4.49391	−	2.59456i	−0.165535	−	0.0955718i
$738$	−1.24341	+	0.717881i	−0.0457704	+	0.0264256i
$739$	3.01963	+	5.23015i	0.111079	+	0.192394i	0.916206	−	0.400709i	$-0.131236\pi$
$739$	3.01963	+	5.23015i	0.111079	+	0.192394i	−0.805127	+	0.593103i	$0.797903\pi$
$740$		0			0
$741$	−0.223227	+	0.351628i	−0.00820044	+	0.0129174i
$742$			0.152510i			0.00559882i
$743$	−11.3093	+	6.52945i	−0.414899	+	0.239542i	−0.692893	−	0.721041i	$-0.743664\pi$
$743$	−11.3093	+	6.52945i	−0.414899	+	0.239542i	0.277993	+	0.960583i	$0.410331\pi$
$744$	6.58387	+	11.4036i	0.241376	+	0.418076i
$745$		0			0
$746$	7.97998			0.292168
$747$	1.53197	+	0.884484i	0.0560519	+	0.0323616i
$748$	8.24158	+	4.75828i	0.301342	+	0.173980i
$749$	−0.376871			−0.0137706
$750$		0			0
$751$	−24.0118	−	41.5897i	−0.876204	−	1.51763i	−0.855475	−	0.517845i	$-0.826735\pi$
$751$	−24.0118	−	41.5897i	−0.876204	−	1.51763i	−0.0207292	−	0.999785i	$-0.506599\pi$
$752$	14.4335	−	8.33320i	0.526337	−	0.303881i
$753$		−	3.35951i		−	0.122427i
$754$	3.14697	+	6.02189i	0.114606	+	0.219304i
$755$		0			0
$756$	−0.621996	−	1.07733i	−0.0226218	−	0.0391820i
$757$	3.95275	−	2.28212i	0.143665	−	0.0829450i	−0.426445	−	0.904514i	$-0.640234\pi$
$757$	3.95275	−	2.28212i	0.143665	−	0.0829450i	0.570110	+	0.821569i	$0.306901\pi$
$758$	6.22281	+	3.59274i	0.226023	+	0.130494i
$759$	−5.28098			−0.191688
$760$		0			0
$761$	−10.5446	+	18.2638i	−0.382242	+	0.662062i	−0.991382	−	0.131000i	$-0.958181\pi$
$761$	−10.5446	+	18.2638i	−0.382242	+	0.662062i	0.609141	+	0.793062i	$0.291514\pi$
$762$			4.08519i			0.147991i
$763$	−8.80933	−	5.08607i	−0.318919	−	0.184128i
$764$	13.1481	+	22.7732i	0.475682	+	0.823905i
$765$		0			0
$766$	−0.590926			−0.0213510
$767$	7.10797	−	3.71455i	0.256654	−	0.134124i
$768$		−	7.53793i		−	0.272002i
$769$	21.1666	+	36.6616i	0.763287	+	1.32205i	0.941147	+	0.337996i	$0.109749\pi$
$769$	21.1666	+	36.6616i	0.763287	+	1.32205i	−0.177860	+	0.984056i	$0.556917\pi$
$770$		0			0
$771$	−5.05442	+	8.75452i	−0.182031	+	0.315286i
$772$			44.7552i			1.61078i
$773$	−43.5122	−	25.1218i	−1.56503	−	0.903568i	−0.996735	−	0.0807410i	$-0.974271\pi$
$773$	−43.5122	−	25.1218i	−1.56503	−	0.903568i	−0.568291	−	0.822827i	$-0.692395\pi$
$774$	0.0925496	−	0.160301i	0.00332663	−	0.00576189i
$775$		0			0
$776$	−6.53793

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.294342 - 0.169938i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.942242 + 1.63201i) q^{4} +(-0.169938 + 0.294342i) q^{6} +(0.571683 + 0.330062i) q^{7} +1.32025i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.294342 - 0.169938i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.942242 + 1.63201i) q^{4} +(-0.169938 + 0.294342i) q^{6} +(0.571683 + 0.330062i) q^{7} +1.32025i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.339877 - 0.588684i) q^{11} -1.88448i q^{12} +(3.04397 + 1.93243i) q^{13} +0.224361 q^{14} +(-1.66012 - 2.87542i) q^{16} +(6.43378 + 3.71455i) q^{17} -0.339877i q^{18} +(0.0577581 - 0.100040i) q^{19} -0.660123 q^{21} +(-0.200080 - 0.115516i) q^{22} +(-6.72812 + 3.88448i) q^{23} +(-0.660123 - 1.14337i) q^{24} +(1.22436 + 0.0515075i) q^{26} +1.00000i q^{27} +(-1.07733 + 0.621996i) q^{28} +(2.77230 + 4.80177i) q^{29} -9.97370 q^{31} +(-3.26402 - 1.88448i) q^{32} +(0.588684 + 0.339877i) q^{33} +2.52498 q^{34} +(0.942242 + 1.63201i) q^{36} +(-8.46017 + 4.88448i) q^{37} -0.0392613i q^{38} +(-3.60236 - 0.151548i) q^{39} +(-2.11218 - 3.65840i) q^{41} +(-0.194302 + 0.112180i) q^{42} +(0.471643 + 0.272303i) q^{43} +1.28098 q^{44} +(-1.32025 + 2.28673i) q^{46} +5.01963i q^{47} +(2.87542 + 1.66012i) q^{48} +(-3.28212 - 5.68480i) q^{49} -7.42909 q^{51} +(-6.02189 + 3.14697i) q^{52} +0.679754i q^{53} +(0.169938 + 0.294342i) q^{54} +(-0.435763 + 0.754763i) q^{56} +0.115516i q^{57} +(1.63201 + 0.942242i) q^{58} +(1.11218 - 1.92635i) q^{59} +(2.10236 - 3.64140i) q^{61} +(-2.93568 + 1.69491i) q^{62} +(0.571683 - 0.330062i) q^{63} +5.35951 q^{64} +0.231033 q^{66} +(6.61108 - 3.81691i) q^{67} +(-12.1244 + 7.00000i) q^{68} +(3.88448 - 6.72812i) q^{69} +(-3.65679 + 6.33374i) q^{71} +(1.14337 + 0.660123i) q^{72} +8.01963i q^{73} +(-1.66012 + 2.87542i) q^{74} +(0.108844 + 0.188524i) q^{76} -0.448721i q^{77} +(-1.08608 + 0.567573i) q^{78} -9.97370 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.24341 - 0.717881i) q^{82} +1.76897i q^{83} +(0.621996 - 1.07733i) q^{84} +0.185099 q^{86} +(-4.80177 - 2.77230i) q^{87} +(0.777208 - 0.448721i) q^{88} +(6.77230 + 11.7300i) q^{89} +(1.10236 + 2.10943i) q^{91} -14.6405i q^{92} +(8.63748 - 4.98685i) q^{93} +(0.853028 + 1.47749i) q^{94} +3.76897 q^{96} +(8.57721 + 4.95206i) q^{97} +(-1.93213 - 1.11552i) q^{98} -0.679754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) 12 * q + 12 * q^4 + 6 * q^9	\( 12 q + 12 q^{4} + 6 q^{9} - 48 q^{14} - 24 q^{16} + 24 q^{19} - 12 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} + 12 q^{31} - 12 q^{36} - 24 q^{39} + 48 q^{44} - 24 q^{46} - 12 q^{49} - 60 q^{56} - 12 q^{59} + 6 q^{61} + 48 q^{64} + 96 q^{66} + 24 q^{71} - 24 q^{74} - 96 q^{76} + 12 q^{79} - 6 q^{81} - 24 q^{84} - 24 q^{86} + 60 q^{89} - 6 q^{91} + 72 q^{94} - 48 q^{96}+O(q^{100}) \) 12 * q + 12 * q^4 + 6 * q^9 - 48 * q^14 - 24 * q^16 + 24 * q^19 - 12 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 + 12 * q^31 - 12 * q^36 - 24 * q^39 + 48 * q^44 - 24 * q^46 - 12 * q^49 - 60 * q^56 - 12 * q^59 + 6 * q^61 + 48 * q^64 + 96 * q^66 + 24 * q^71 - 24 * q^74 - 96 * q^76 + 12 * q^79 - 6 * q^81 - 24 * q^84 - 24 * q^86 + 60 * q^89 - 6 * q^91 + 72 * q^94 - 48 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more