LMFDB - Embedded newform 975.2.bb.k.724.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(724,975)] 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("975.724"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [12,0,0,12,0,0,0,0,6,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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:	12.0.752609431977984.1
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			724.3
Root			$-1.75780 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.724
Dual form			975.2.bb.k.874.3

$q$-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} +(-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} - 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}+ \cdots - 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

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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	$-0.371676\pi$
$2$	−0.294342	−	0.169938i	−0.208131	−	0.120165i	−0.600443	+	0.799668i	$0.705009\pi$
$3$	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	$-0.706480\pi$
$7$	−0.571683	+	0.330062i	−0.216076	+	0.124752i	0.388056	+	0.921636i	$0.373147\pi$
$8$			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	−0.912704	−	0.408620i	$-0.866010\pi$
$11$	−0.339877	+	0.588684i	−0.102477	+	0.177495i	0.810228	+	0.586115i	$0.199343\pi$
$12$		−	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	−0.563207	+	0.826316i	$0.690433\pi$
$17$	−6.43378	+	3.71455i	−1.56042	+	0.900910i	−0.997214	+	0.0745938i	$0.976234\pi$
$18$		−	0.339877i		−	0.0801098i
$19$	0.0577581	+	0.100040i	0.0132506	+	0.0229508i	0.872575	−	0.488481i	$-0.162449\pi$
$19$	0.0577581	+	0.100040i	0.0132506	+	0.0229508i	−0.859324	+	0.511431i	$0.829115\pi$
$20$		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	$-0.0328162\pi$
$23$	6.72812	+	3.88448i	1.40291	+	0.809971i	0.408220	+	0.912883i	$0.366150\pi$
$24$	−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	−0.485049	−	0.874487i	$-0.661198\pi$
$29$	2.77230	−	4.80177i	0.514804	−	0.891666i	0.999852	−	0.0171792i	$-0.00546857\pi$
$30$		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	$-0.0365670\pi$
$37$	8.46017	+	4.88448i	1.39084	+	0.803004i	0.397435	+	0.917630i	$0.369900\pi$
$38$		−	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	−0.982485	−	0.186340i	$-0.940337\pi$
$41$	−2.11218	+	3.65840i	−0.329867	+	0.571347i	0.652618	+	0.757687i	$0.273671\pi$
$42$	0.194302	+	0.112180i	0.0299814	+	0.0173098i
$43$	−0.471643	+	0.272303i	−0.0719249	+	0.0415259i	−0.535531	−	0.844515i	$-0.679889\pi$
$43$	−0.471643	+	0.272303i	−0.0719249	+	0.0415259i	0.463606	+	0.886041i	$0.346555\pi$
$44$	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	0.929296	−	0.369336i	$-0.120415\pi$
$59$	1.11218	+	1.92635i	0.144794	+	0.250790i	−0.784502	+	0.620126i	$0.787082\pi$
$60$		0			0
$61$	2.10236	+	3.64140i	0.269180	+	0.466234i	0.968650	−	0.248428i	$-0.0799139\pi$
$61$	2.10236	+	3.64140i	0.269180	+	0.466234i	−0.699470	+	0.714662i	$0.746581\pi$
$62$	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	$-0.487750\pi$
$67$	−6.61108	−	3.81691i	−0.807672	−	0.466310i	−0.846147	+	0.532950i	$0.821083\pi$
$68$	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	0.563231	−	0.826299i	$-0.309558\pi$
$71$	−3.65679	−	6.33374i	−0.433981	−	0.751677i	−0.997212	+	0.0746227i	$0.976225\pi$
$72$	−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	−0.243982	−	0.969780i	$-0.578454\pi$
$89$	6.77230	−	11.7300i	0.717863	−	1.24337i	0.961845	−	0.273595i	$-0.0882128\pi$
$90$		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	$-0.834365\pi$
$97$	−8.57721	+	4.95206i	−0.870884	+	0.502805i	−0.00324223	+	0.999995i	$0.501032\pi$
$98$	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	−0.533578	−	0.845751i	$-0.679153\pi$
$101$	4.67975	−	8.10557i	0.465653	−	0.806534i	0.999231	+	0.0392165i	$0.0124862\pi$
$102$	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	$-0.324548\pi$
$107$	0.494422	+	0.285455i	0.0477976	+	0.0275960i	−0.475911	+	0.879494i	$0.657881\pi$
$108$	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	$-0.747177\pi$
$113$	−4.60747	+	2.66012i	−0.433434	+	0.250243i	0.267374	+	0.963593i	$0.413844\pi$
$114$	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	$-0.512376\pi$
$127$	−10.4093	−	6.00982i	−0.923676	−	0.533285i	−0.884806	+	0.465959i	$0.845709\pi$
$128$	−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	$-0.712923\pi$
$137$	−2.93568	+	1.69491i	−0.250812	+	0.144806i	0.369324	+	0.929301i	$0.379589\pi$
$138$		−	2.64049i		−	0.224774i
$139$	7.40411	+	12.8243i	0.628009	+	1.08774i	0.987951	+	0.154768i	$0.0494631\pi$
$139$	7.40411	+	12.8243i	0.628009	+	1.08774i	−0.359942	+	0.932975i	$0.617204\pi$
$140$		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	−0.968465	−	0.249148i	$-0.919849\pi$
$149$	−8.54461	−	14.7997i	−0.700001	−	1.21244i	0.268464	−	0.963290i	$-0.413484\pi$
$150$		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	$-0.508133\pi$
$163$	10.5638	−	6.09903i	0.827423	−	0.477713i	0.852969	+	0.521961i	$0.174799\pi$
$164$	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	$-0.352934\pi$
$167$	−1.37745	−	0.795270i	−0.106590	−	0.0615398i	−0.552347	+	0.833614i	$0.686268\pi$
$168$		−	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	$-0.505611\pi$
$173$	11.0412	−	6.37467i	0.839451	−	0.484657i	0.857077	+	0.515188i	$0.172278\pi$
$174$	−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	−0.315799	−	0.948826i	$-0.602272\pi$
$179$	8.88115	−	15.3826i	0.663808	−	1.14975i	0.979607	−	0.200923i	$-0.0643942\pi$
$180$		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	0.999984	+	0.00559828i	$0.00178200\pi$
$191$	6.97703	+	12.0846i	0.504840	+	0.874409i	−0.495144	+	0.868811i	$0.664885\pi$
$192$	4.64147	+	2.67975i	0.334969	+	0.193395i
$193$	−20.5675	−	11.8747i	−1.48048	−	0.854757i	−0.480728	−	0.876870i	$-0.659627\pi$
$193$	−20.5675	−	11.8747i	−1.48048	−	0.854757i	−0.999755	+	0.0221126i	$0.992961\pi$
$194$	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	$-0.142925\pi$
$197$	13.6903	+	7.90411i	0.975395	+	0.563145i	0.0745186	+	0.997220i	$0.476258\pi$
$198$	0.200080	+	0.115516i	0.0142191	+	0.00820939i
$199$	4.38448	+	7.59415i	0.310808	+	0.538335i	0.978537	−	0.206069i	$-0.0660671\pi$
$199$	4.38448	+	7.59415i	0.310808	+	0.538335i	−0.667730	+	0.744404i	$0.732734\pi$
$200$		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	−0.976857	−	0.213893i	$-0.931386\pi$
$211$	−4.40411	+	7.62815i	−0.303192	+	0.525143i	0.673665	+	0.739037i	$0.264719\pi$
$212$	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	$-0.442455\pi$
$223$	−8.69426	−	5.01963i	−0.582210	−	0.336139i	−0.762011	+	0.647564i	$0.775788\pi$
$224$	−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	$-0.679467\pi$
$227$	−1.04910	+	0.605701i	−0.0696315	+	0.0402018i	0.464780	+	0.885426i	$0.346133\pi$
$228$	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	0.750576	−	0.660784i	$-0.229776\pi$
$241$	−3.05776	−	5.29619i	−0.196968	−	0.341158i	−0.947544	+	0.319626i	$0.896443\pi$
$242$		−	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	0.808131	−	0.589002i	$-0.200479\pi$
$251$	−1.67975	−	2.90942i	−0.106025	−	0.183641i	−0.914157	+	0.405361i	$0.867146\pi$
$252$			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	$-0.435434\pi$
$257$	−8.75452	−	5.05442i	−0.546092	−	0.315286i	−0.747544	+	0.664212i	$0.768767\pi$
$258$	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	$-0.0890611\pi$
$263$	19.5014	+	11.2592i	1.20251	+	0.694269i	0.241397	+	0.970426i	$0.422394\pi$
$264$	−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	0.965965	−	0.258674i	$-0.0832855\pi$
$269$	4.24733	+	7.35659i	0.258964	+	0.448539i	−0.707001	+	0.707213i	$0.749952\pi$
$270$		0			0
$271$	−4.68510	+	8.11483i	−0.284600	+	0.492941i	−0.972512	−	0.232853i	$-0.925194\pi$
$271$	−4.68510	+	8.11483i	−0.284600	+	0.492941i	0.687912	+	0.725794i	$0.258527\pi$
$272$		−	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	$-0.673543\pi$
$277$	−0.622685	+	0.359508i	−0.0374135	+	0.0216007i	0.481177	+	0.876624i	$0.340210\pi$
$278$		−	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	$-0.152307\pi$
$283$	15.6920	+	9.05977i	0.932791	+	0.538547i	0.0450980	+	0.998983i	$0.485640\pi$
$284$	−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	−0.544737	+	0.838607i	$0.683370\pi$
$293$	−26.4181	+	15.2525i	−1.54336	+	0.891059i	−0.998623	+	0.0524523i	$0.983296\pi$
$294$	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	0.782749	−	0.622338i	$-0.213817\pi$
$331$	−2.68510	−	4.65073i	−0.147586	−	0.255627i	−0.930335	+	0.366711i	$0.880484\pi$
$332$	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	$-0.871955\pi$
$347$	−19.3956	+	11.1981i	−1.04121	+	0.601143i	−0.121035	+	0.992648i	$0.538621\pi$
$348$	−9.04886	−	5.22436i	−0.485070	−	0.280055i
$349$	−5.98685	+	10.3695i	−0.320469	+	0.555068i	−0.980585	−	0.196096i	$-0.937174\pi$
$349$	−5.98685	+	10.3695i	−0.320469	+	0.555068i	0.660116	+	0.751164i	$0.270507\pi$
$350$		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	$-0.183550\pi$
$353$	14.7541	+	8.51830i	0.785283	+	0.453384i	−0.0530161	+	0.998594i	$0.516883\pi$
$354$	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	$-0.157716\pi$
$367$	17.3920	+	10.0413i	0.907855	+	0.524150i	0.0281143	+	0.999605i	$0.491050\pi$
$368$	−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	$-0.874634\pi$
$373$	−20.3334	+	11.7395i	−1.05283	+	0.607849i	−0.129387	+	0.991594i	$0.541301\pi$
$374$	−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	−0.455750	−	0.890108i	$-0.650629\pi$
$379$	10.5707	−	18.3090i	0.542981	−	0.940471i	0.998731	−	0.0503631i	$-0.0160379\pi$
$380$		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	$-0.652523\pi$
$383$	1.50571	−	0.869323i	0.0769383	−	0.0444203i	0.537976	+	0.842960i	$0.319189\pi$
$384$	−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	$-0.785593\pi$
$397$	−12.5960	+	7.27230i	−0.632175	+	0.364986i	0.149419	+	0.988774i	$0.452260\pi$
$398$		−	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	−0.742404	−	0.669952i	$-0.766314\pi$
$401$	4.18510	−	7.24880i	0.208994	−	0.361988i	0.951398	+	0.307964i	$0.0996478\pi$
$402$			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	0.996568	−	0.0827798i	$-0.0263798\pi$
$409$	8.62734	+	14.9430i	0.426595	+	0.738883i	−0.569973	+	0.821663i	$0.693046\pi$
$410$		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	−0.665032	−	0.746815i	$-0.731582\pi$
$419$	6.43243	−	11.1413i	0.314245	−	0.544288i	0.979277	+	0.202527i	$0.0649155\pi$
$420$		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	0.396493	+	0.918038i	$0.370227\pi$
$431$	−12.3898	+	21.4598i	−0.596797	+	1.03368i	−0.993291	+	0.115645i	$0.963106\pi$
$432$	−2.87542	−	1.66012i	−0.138344	−	0.0798727i
$433$	−12.1754	+	7.02945i	−0.585110	+	0.337814i	−0.763162	−	0.646208i	$-0.776354\pi$
$433$	−12.1754	+	7.02945i	−0.585110	+	0.337814i	0.178051	+	0.984021i	$0.443021\pi$
$434$	−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	−0.502552	−	0.864547i	$-0.667605\pi$
$439$	10.4226	−	18.0525i	0.497444	−	0.861598i	0.999996	+	0.00294880i	$0.000938633\pi$
$440$		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	0.991015	+	0.133752i	$0.0427026\pi$
$449$	12.9541	+	22.4371i	0.611340	+	1.05887i	−0.379675	+	0.925120i	$0.623964\pi$
$450$		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	$-0.289237\pi$
$457$	5.11311	+	2.95206i	0.239181	+	0.138091i	−0.375619	+	0.926774i	$0.622570\pi$
$458$	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	0.988087	−	0.153894i	$-0.0491815\pi$
$461$	7.74600	+	13.4165i	0.360767	+	0.624867i	−0.627320	+	0.778762i	$0.715848\pi$
$462$	−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	−0.164439	+	0.986387i	$0.552581\pi$
$479$	−20.4953	+	35.4990i	−0.936456	+	1.62199i	−0.772017	+	0.635602i	$0.780752\pi$
$480$		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	$-0.850212\pi$
$487$	−20.8391	+	12.0315i	−0.944309	+	0.545197i	−0.0530008	+	0.998594i	$0.516879\pi$
$488$	−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	0.0684471	+	0.997655i	$0.478196\pi$
$491$	−18.3865	+	31.8463i	−0.829771	+	1.43721i	−0.898218	+	0.439550i	$0.855138\pi$
$492$	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	$-0.919777\pi$
$503$	−27.7353	+	16.0130i	−1.23665	+	0.713983i	−0.268245	+	0.963351i	$0.586444\pi$
$504$	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	−0.111359	+	0.993780i	$0.535520\pi$
$509$	−20.6731	+	35.8068i	−0.916318	+	1.58711i	−0.804960	+	0.593329i	$0.797813\pi$
$510$		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	$-0.0822805\pi$
$523$	28.1014	+	16.2244i	1.22879	+	0.709442i	0.262013	+	0.965064i	$0.415614\pi$
$524$	−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	−0.999895	−	0.0144676i	$-0.995395\pi$
$557$	−35.6933	−	20.6075i	−1.51237	−	0.873169i	−0.512477	−	0.858701i	$-0.671272\pi$
$558$			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	$-0.749279\pi$
$563$	−10.5468	+	6.08921i	−0.444496	+	0.256630i	0.261007	+	0.965337i	$0.415945\pi$
$564$	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	−0.784034	−	0.620718i	$-0.786841\pi$
$569$	3.47169	−	6.01314i	0.145541	−	0.252084i	0.929575	+	0.368634i	$0.120174\pi$
$570$		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	$-0.0466356\pi$
$587$	32.8897	+	18.9889i	1.35750	+	0.783754i	0.368215	+	0.929741i	$0.379969\pi$
$588$	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	−0.674989	−	0.737828i	$-0.735851\pi$
$601$	7.39096	−	12.8015i	0.301484	−	0.522185i	0.976472	+	0.215643i	$0.0691848\pi$
$602$	−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	$-0.541122\pi$
$607$	16.3977	−	9.46722i	0.665562	−	0.384263i	0.794393	+	0.607404i	$0.207789\pi$
$608$	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	$-0.316716\pi$
$613$	2.23770	+	1.29193i	0.0903797	+	0.0521807i	−0.454129	+	0.890936i	$0.650049\pi$
$614$	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	$-0.757863\pi$
$617$	−12.1584	+	7.01963i	−0.489477	+	0.282600i	0.234880	+	0.972024i	$0.424530\pi$
$618$	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	0.999994	−	0.00359801i	$-0.00114528\pi$
$631$	12.4815	+	21.6186i	0.496881	+	0.860623i	−0.503113	+	0.864221i	$0.667812\pi$
$632$		−	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	0.538691	−	0.842503i	$-0.318919\pi$
$641$	−11.6535	−	20.1844i	−0.460284	−	0.797235i	−0.998975	+	0.0452686i	$0.985586\pi$
$642$		−	0.194039i		−	0.00765811i
$643$	39.3860	−	22.7395i	1.55323	−	0.896759i	0.555357	−	0.831612i	$-0.312582\pi$
$643$	39.3860	−	22.7395i	1.55323	−	0.896759i	0.997876	−	0.0651470i	$-0.0207516\pi$
$644$	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	$-0.293122\pi$
$647$	5.55076	+	3.20473i	0.218223	+	0.125991i	−0.386904	+	0.922120i	$0.626456\pi$
$648$	−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	$-0.342563\pi$
$653$	−1.28319	−	0.740848i	−0.0502150	−	0.0289916i	−0.524897	+	0.851166i	$0.675896\pi$
$654$	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	0.788691	−	0.614790i	$-0.210759\pi$
$659$	−3.54461	−	6.13944i	−0.138078	−	0.239159i	−0.926769	+	0.375631i	$0.877426\pi$
$660$		0			0
$661$	−0.589214	+	1.02055i	−0.0229178	+	0.0396947i	−0.877257	−	0.480021i	$-0.840629\pi$
$661$	−0.589214	+	1.02055i	−0.0229178	+	0.0396947i	0.854339	+	0.519716i	$0.173962\pi$
$662$			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	$-0.417485\pi$
$673$	−11.7412	−	6.77878i	−0.452590	−	0.261303i	−0.708923	+	0.705286i	$0.750819\pi$
$674$	−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	$-0.991109\pi$
$683$	−38.5540	+	22.2592i	−1.47523	+	0.851723i	−0.475617	+	0.879652i	$0.657775\pi$
$684$	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	−0.811425	−	0.584457i	$-0.801308\pi$
$691$	2.64030	−	4.57313i	0.100442	−	0.173970i	0.911867	+	0.410486i	$0.134641\pi$
$692$	−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	0.880127	−	0.474737i	$-0.157457\pi$
$709$	0.770294	+	1.33419i	0.0289290	+	0.0501065i	−0.851198	+	0.524844i	$0.824124\pi$
$710$		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	0.971835	+	0.235664i	$0.0757266\pi$
$719$	18.5020	+	32.0464i	0.690009	+	1.19513i	−0.281826	+	0.959466i	$0.590940\pi$
$720$		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	−0.805127	−	0.593103i	$-0.797903\pi$
$739$	3.01963	−	5.23015i	0.111079	−	0.192394i	0.916206	+	0.400709i	$0.131236\pi$
$740$		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	$-0.256336\pi$
$743$	11.3093	+	6.52945i	0.414899	+	0.239542i	−0.277993	+	0.960583i	$0.589669\pi$
$744$	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	−0.0207292	+	0.999785i	$0.506599\pi$
$751$	−24.0118	+	41.5897i	−0.876204	+	1.51763i	−0.855475	+	0.517845i	$0.826735\pi$
$752$	−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	$-0.359766\pi$
$757$	−3.95275	−	2.28212i	−0.143665	−	0.0829450i	−0.570110	+	0.821569i	$0.693099\pi$
$758$	−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	0.609141	−	0.793062i	$-0.291514\pi$
$761$	−10.5446	−	18.2638i	−0.382242	−	0.662062i	−0.991382	+	0.131000i	$0.958181\pi$
$762$			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	−0.177860	−	0.984056i	$-0.556917\pi$
$769$	21.1666	−	36.6616i	0.763287	−	1.32205i	0.941147	−	0.337996i	$-0.109749\pi$
$770$		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	0.568291	−	0.822827i	$-0.307605\pi$
$773$	43.5122	−	25.1218i	1.56503	−	0.903568i	0.996735	−	0.0807410i	$-0.0257287\pi$
$774$	0.0925496	+	0.160301i	0.00332663	+	0.00576189i
$775$		0			0
$776$	−6.53793	−	11.3240i	−0.234698	−	0.406509i
$777$	−5.58476	−	3.22436i	−0.200352	−	0.115673i
$778$	−7.84904	−	4.53165i	−0.281402	−	0.162467i
$779$	−0.487982			−0.0174838
$780$		0			0
$781$	4.97143			0.177892
$782$	16.9884	+	9.80823i	0.607502	+	0.350742i
$783$	4.80177	+	2.77230i	0.171601	+	0.0990740i
$784$	−10.8974	−	18.8749i	−0.389194	−	0.674104i
$785$		0			0
$786$	−1.85303	−	3.20954i	−0.0660953	−	0.114480i
$787$	9.16393	−	5.29080i	0.326659	−	0.188597i	−0.327698	−	0.944783i	$-0.606273\pi$
$787$	9.16393	−	5.29080i	0.326659	−	0.188597i	0.654357	+	0.756186i	$0.272939\pi$
$788$		−	29.7903i		−	1.06124i
$789$	11.2592	+	19.5014i	0.400836	+	0.694269i
$790$		0			0
$791$	1.75601	−	3.04150i	0.0624365	−	0.108143i
$792$		−	0.897442i		−	0.0318892i
$793$	−13.4363	−	7.02164i	−0.477136	−	0.249346i
$794$	4.94338			0.175434
$795$		0			0
$796$	8.26249	−	14.3110i	0.292856	−	0.507242i
$797$	17.4488	−	10.0741i	0.618067	−	0.356841i	−0.158049	−	0.987431i	$-0.550520\pi$
$797$	17.4488	−	10.0741i	0.618067	−	0.356841i	0.776116	+	0.630590i	$0.217187\pi$
$798$			0.0259173i			0.000917463i
$799$	−18.6456	−	32.2952i	−0.659636	−	1.14252i
$800$		0			0
$801$	13.5446			0.478575
$802$	−2.46370	+	1.42242i	−0.0869963	+	0.0502273i
$803$	−4.72103	−	2.72569i	−0.166601	−	0.0961874i
$804$	−7.19291	+	12.4585i	−0.253674	+	0.439377i
$805$		0			0
$806$	−12.2114	+	0.513720i	−0.430128	+	0.0180950i
$807$			8.49465i			0.299026i
$808$	10.7013	+	6.17843i	0.376472	+	0.217356i
$809$	6.45539	−	11.1811i	0.226960	−	0.393105i	−0.729946	−	0.683505i	$-0.760455\pi$
$809$	6.45539	−	11.1811i	0.226960	−	0.393105i	0.956906	+	0.290399i	$0.0937882\pi$
$810$		0			0
$811$	−15.8974			−0.558235			−0.279117	−	0.960257i	$-0.590042\pi$
$811$	−15.8974			−0.558235			−0.279117	+	0.960257i	$0.590042\pi$
$812$	5.97336	−	3.44872i	0.209624	−	0.121026i
$813$	−8.11483	+	4.68510i	−0.284600	+	0.164314i
$814$	2.25695			0.0791061
$815$		0			0
$816$	12.3332	−	21.3617i	0.431749	−	0.747810i
$817$	−0.0544825	−	0.0314555i	−0.00190610	−	0.00110049i
$818$		−	5.86447i		−	0.205046i
$819$	2.37800	−	0.100040i	0.0830942	−	0.00349568i
$820$		0			0
$821$	18.6142	−	32.2407i	0.649640	−	1.12521i	−0.333569	−	0.942726i	$-0.608253\pi$
$821$	18.6142	−	32.2407i	0.649640	−	1.12521i	0.983209	−	0.182483i	$-0.0584136\pi$
$822$	0.997769	+	0.576062i	0.0348012	+	0.0200925i
$823$	−4.24131	+	2.44872i	−0.147843	+	0.0853571i	−0.572097	−	0.820186i	$-0.693870\pi$
$823$	−4.24131	+	2.44872i	−0.147843	+	0.0853571i	0.424254	+	0.905543i	$0.360536\pi$
$824$	−5.94817			−0.207214
$825$		0			0
$826$	0.249529	+	0.432198i	0.00868224	+	0.0150381i
$827$		−	37.6334i		−	1.30864i	−0.756217	−	0.654321i	$-0.772954\pi$
$827$		−	37.6334i		−	1.30864i	0.756217	−	0.654321i	$-0.227046\pi$
$828$	12.6790	−	7.32025i	0.440627	−	0.254396i
$829$	−24.4552	+	42.3576i	−0.849364	+	1.47114i	0.0324123	+	0.999475i	$0.489681\pi$
$829$	−24.4552	+	42.3576i	−0.849364	+	1.47114i	−0.881777	+	0.471667i	$0.843652\pi$
$830$		0			0
$831$	−0.719015			−0.0249424
$832$	−16.3142	+	10.3569i	−0.565592	+	0.359059i
$833$		−	48.7663i		−	1.68965i
$834$	2.51649	−	4.35868i	0.0871388	−	0.150929i
$835$		0			0
$836$	0.0739873	+	0.128150i	0.00255890	+	0.00443215i
$837$		−	9.97370i		−	0.344741i
$838$	−3.78667	+	2.18623i	−0.130808	+	0.0755222i
$839$	24.1392	+	41.8103i	0.833377	+	1.44345i	0.895345	+	0.445372i	$0.146929\pi$
$839$	24.1392	+	41.8103i	0.833377	+	1.44345i	−0.0619688	+	0.998078i	$0.519738\pi$
$840$		0			0
$841$	−0.871332	−	1.50919i	−0.0300459	−	0.0520411i
$842$	−7.22951	−	4.17396i	−0.249145	−	0.143844i
$843$	1.33767	+	0.772303i	0.0460718	+	0.0265995i
$844$	16.5990			0.571360
$845$		0			0
$846$	1.70606			0.0586554
$847$	−6.02436	−	3.47817i	−0.207000	−	0.119511i
$848$	−1.95458	−	1.12847i	−0.0671204	−	0.0387520i
$849$	9.05977	+	15.6920i	0.310930	+	0.538547i
$850$		0			0
$851$	37.9474	+	65.7268i	1.30082	+	2.25309i
$852$	−11.9358	+	6.89116i	−0.408915	+	0.236087i
$853$		−	14.4291i		−	0.494043i	−0.969010	−	0.247021i	$-0.920548\pi$
$853$		−	14.4291i		−	0.494043i	0.969010	−	0.247021i	$-0.0794518\pi$
$854$	0.471688	+	0.816987i	0.0161408	+	0.0279567i
$855$		0			0
$856$	−0.376871	+	0.652759i	−0.0128812	+	0.0223108i
$857$		−	3.64678i		−	0.124572i	−0.998058	−	0.0622858i	$-0.980161\pi$
$857$		−	3.64678i		−	0.124572i	0.998058	−	0.0622858i	$-0.0198390\pi$
$858$	−0.703255	+	0.446454i	−0.0240087	+	0.0152417i
$859$	−21.7427			−0.741850			−0.370925	−	0.928663i	$-0.620959\pi$
$859$	−21.7427			−0.741850			−0.370925	+	0.928663i	$0.620959\pi$
$860$		0			0
$861$	1.39430	−	2.41500i	0.0475176	−	0.0823029i
$862$	7.29369	−	4.21102i	0.248424	−	0.143428i
$863$		−	17.0892i		−	0.581724i	−0.956765	−	0.290862i	$-0.906058\pi$
$863$		−	17.0892i		−	0.581724i	0.956765	−	0.290862i	$-0.0939420\pi$
$864$	1.88448	+	3.26402i	0.0641114	+	0.111044i
$865$		0			0
$866$	4.77829			0.162373
$867$	33.0747	−	19.0957i	1.12328	−	0.648524i
$868$	−10.7449	−	6.20360i	−0.364707	−	0.210564i
$869$	3.38983	−	5.87136i	0.114992	−	0.199172i
$870$		0			0
$871$	27.4998	−	1.15689i	0.931795	−	0.0391996i
$872$		−	20.3443i		−	0.688944i
$873$	−8.57721	−	4.95206i	−0.290295	−	0.167602i
$874$	0.152510	−	0.264155i	0.00515873	−	0.00893518i
$875$		0			0
$876$	15.1129			0.510616
$877$	4.20731	−	2.42909i	0.142071	−	0.0820246i	−0.427280	−	0.904119i	$-0.640528\pi$
$877$	4.20731	−	2.42909i	0.142071	−	0.0820246i	0.569351	+	0.822095i	$0.307195\pi$
$878$	−6.13562	+	3.54240i	−0.207067	+	0.119550i
$879$	−30.5050			−1.02891
$880$		0			0
$881$	11.6601	−	20.1959i	0.392840	−	0.680418i	−0.599983	−	0.800013i	$-0.704826\pi$
$881$	11.6601	−	20.1959i	0.392840	−	0.680418i	0.992823	+	0.119595i	$0.0381595\pi$
$882$	1.93213	+	1.11552i	0.0650582	+	0.0375614i
$883$		−	12.8934i		−	0.433898i	−0.976183	−	0.216949i	$-0.930389\pi$
$883$		−	12.8934i		−	0.433898i	0.976183	−	0.216949i	$-0.0696106\pi$
$884$	−50.4331	+	2.12167i	−1.69625	+	0.0713593i
$885$		0			0
$886$	−1.94224	+	3.36406i	−0.0652509	+	0.113018i
$887$	26.7842	+	15.4639i	0.899326	+	0.519226i	0.876982	−	0.480524i	$-0.159553\pi$
$887$	26.7842	+	15.4639i	0.899326	+	0.519226i	0.0223448	+	0.999750i	$0.492887\pi$
$888$	−11.1695	+	6.44872i	−0.374824	+	0.216405i
$889$	7.93444			0.266112
$890$		0			0
$891$	−0.339877	−	0.588684i	−0.0113863	−	0.0197217i
$892$			18.9188i			0.633449i
$893$	−0.502164	+	0.289925i	−0.0168043	+	0.00970196i
$894$	−2.90411	+	5.03007i	−0.0971281	+	0.168231i
$895$		0			0
$896$	6.17843			0.206407
$897$	−24.8258	−	12.9737i	−0.828911	−	0.433179i
$898$		−	8.80558i		−	0.293846i
$899$	−27.6501	+	47.8914i	−0.922183	+	1.59727i
$900$		0			0
$901$	−2.52498	−	4.37339i	−0.0841192	−	0.145699i
$902$			0.975965i			0.0324961i
$903$	0.311343	−	0.179754i	0.0103608	−	0.00598183i
$904$	−3.51202	−	6.08299i	−0.116808	−	0.202317i
$905$		0			0
$906$	−2.21140	−	3.83026i	−0.0734689	−	0.127252i
$907$	−14.6881	−	8.48018i	−0.487710	−	0.281580i	0.235914	−	0.971774i	$-0.424192\pi$
$907$	−14.6881	−	8.48018i	−0.487710	−	0.281580i	−0.723624	+	0.690194i	$0.757525\pi$
$908$	1.97702	+	1.14143i	0.0656097	+	0.0378798i
$909$	9.35951			0.310435
$910$		0			0
$911$	37.7297			1.25004			0.625020	−	0.780608i	$-0.285091\pi$
$911$	37.7297			1.25004			0.625020	+	0.780608i	$0.285091\pi$
$912$	−0.332158	−	0.191771i	−0.0109988	−	0.00635018i
$913$	−1.04136	−	0.601231i	−0.0344641	−	0.0198978i
$914$	−1.00334	−	1.73783i	−0.0331874	−	0.0574823i
$915$		0			0
$916$	18.1325	+	31.4064i	0.599114	+	1.03770i
$917$	−6.23370	+	3.59903i	−0.205855	+	0.118850i
$918$			2.52498i			0.0833366i
$919$	20.0814	+	34.7820i	0.662425	+	1.14735i	0.979977	+	0.199112i	$0.0638058\pi$
$919$	20.0814	+	34.7820i	0.662425	+	1.14735i	−0.317552	+	0.948241i	$0.602861\pi$
$920$		0			0
$921$	−2.38782	+	4.13583i	−0.0786813	+	0.136280i
$922$		−	5.26537i		−	0.173406i
$923$	23.3706	+	12.2132i	0.769253	+	0.402003i
$924$	−0.845608			−0.0278185
$925$		0			0
$926$	2.96407	−	5.13393i	0.0974055	−	0.168711i
$927$	−3.90174	+	2.25267i	−0.128150	+	0.0739875i
$928$		−	20.8974i		−	0.685992i
$929$	11.8845	+	20.5845i	0.389917	+	0.675357i	0.992438	−	0.122747i	$-0.0391703\pi$
$929$	11.8845	+	20.5845i	0.389917	+	0.675357i	−0.602521	+	0.798103i	$0.705837\pi$
$930$		0			0
$931$	−0.758276			−0.0248515
$932$	−39.0183	+	22.5272i	−1.27809	+	0.737904i
$933$	26.4841	+	15.2906i	0.867051	+	0.500592i
$934$	3.48018	−	6.02784i	0.113875	−	0.197237i
$935$		0			0
$936$	2.20473	−	4.21886i	0.0720639	−	0.137898i
$937$			7.43803i			0.242990i	0.992592	+	0.121495i	$0.0387688\pi$
$937$			7.43803i			0.242990i	−0.992592	+	0.121495i	$0.961231\pi$
$938$	−1.48327	−	0.856364i	−0.0484304	−	0.0279613i
$939$	13.3615	−	23.1428i	0.436037	−	0.755238i
$940$		0			0
$941$	−19.3528			−0.630884			−0.315442	−	0.948945i	$-0.602153\pi$
$941$	−19.3528			−0.630884			−0.315442	+	0.948945i	$0.602153\pi$
$942$	0.228303	−	0.131811i	0.00743852	−	0.00429463i
$943$	−28.4220	+	16.4095i	−0.925548	+	0.534366i
$944$	−7.38542			−0.240375
$945$		0			0
$946$	−0.0629110	+	0.108965i	−0.00204541	+	0.00354276i
$947$	12.0525	+	6.95854i	0.391655	+	0.226122i	0.682877	−	0.730533i	$-0.260729\pi$
$947$	12.0525	+	6.95854i	0.391655	+	0.226122i	−0.291222	+	0.956655i	$0.594062\pi$
$948$			18.7953i			0.610442i
$949$	−15.4973	−	24.4115i	−0.503065	−	0.792430i
$950$		0			0
$951$	−10.3136	+	17.8636i	−0.334441	+	0.579268i
$952$	5.60720	+	3.23732i	0.181730	+	0.104922i
$953$	−9.20338	+	5.31357i	−0.298127	+	0.172124i	−0.641601	−	0.767039i	$-0.721729\pi$
$953$	−9.20338	+	5.31357i	−0.298127	+	0.172124i	0.343474	+	0.939162i	$0.388396\pi$
$954$	0.231033			0.00747996
$955$		0			0
$956$	17.6008	+	30.4856i	0.569252	+	0.985973i
$957$			3.76897i			0.121833i
$958$	12.0653	−	6.96589i	0.389811	−	0.225058i
$959$	1.11885	−	1.93791i	0.0361296	−	0.0625783i
$960$		0			0
$961$	68.4746			2.20886
$962$	10.6099	+	5.54461i	0.342077	+	0.178765i
$963$			0.570909i			0.0183973i
$964$	−5.76230	+	9.98059i	−0.185591	+	0.321453i
$965$		0			0
$966$	0.871525	+	1.50953i	0.0280409	+	0.0485682i
$967$		−	51.6771i		−	1.66182i	−0.556404	−	0.830912i	$-0.687819\pi$
$967$		−	51.6771i		−	1.66182i	0.556404	−	0.830912i	$-0.312181\pi$
$968$	−12.0487	+	6.95633i	−0.387261	+	0.223585i
$969$	−0.429091	−	0.743207i	−0.0137844	−	0.0238752i
$970$		0			0
$971$	21.4487	+	37.1503i	0.688322	+	1.19221i	0.972380	+	0.233402i	$0.0749858\pi$
$971$	21.4487	+	37.1503i	0.688322	+	1.19221i	−0.284058	+	0.958807i	$0.591681\pi$
$972$	1.63201	+	0.942242i	0.0523468	+	0.0302224i
$973$	−8.46562	−	4.88763i	−0.271395	−	0.156690i
$974$	8.17843			0.262054
$975$		0			0
$976$	−13.9607			−0.446872
$977$	15.7314	+	9.08254i	0.503293	+	0.290576i	0.730072	−	0.683370i	$-0.239486\pi$
$977$	15.7314	+	9.08254i	0.503293	+	0.290576i	−0.226780	+	0.973946i	$0.572820\pi$
$978$	−3.59040	−	2.07292i	−0.114808	−	0.0662846i
$979$	4.60350	+	7.97349i	0.147128	+	0.254834i
$980$		0			0
$981$	−7.70473	−	13.3450i	−0.245993	−	0.426073i
$982$	10.8238	−	6.24914i	0.345402	−	0.199418i
$983$		−	10.8582i		−	0.346322i	−0.984894	−	0.173161i	$-0.944602\pi$
$983$		−	10.8582i		−	0.346322i	0.984894	−	0.173161i	$-0.0553981\pi$
$984$	−2.78860	−	4.82999i	−0.0888973	−	0.153975i
$985$		0			0
$986$	7.00000	−	12.1244i	0.222925	−	0.386118i
$987$		−	3.31357i		−	0.105472i
$988$	0.0329902	+	0.784194i	0.00104956	+	0.0249485i
$989$	−4.23103			−0.134539
$990$		0			0
$991$	11.1862	−	19.3751i	0.355342	−	0.615471i	−0.631834	−	0.775104i	$-0.717698\pi$
$991$	11.1862	−	19.3751i	0.355342	−	0.615471i	0.987177	+	0.159633i	$0.0510309\pi$
$992$	−32.5544	+	18.7953i	−1.03360	+	0.596750i
$993$		−	5.37020i		−	0.170418i
$994$	−0.820439	−	1.42104i	−0.0260227	−	0.0450727i
$995$		0			0
$996$	3.33359			0.105629
$997$	20.9901	−	12.1187i	0.664764	−	0.383802i	−0.129326	−	0.991602i	$-0.541281\pi$
$997$	20.9901	−	12.1187i	0.664764	−	0.383802i	0.794090	+	0.607800i	$0.207948\pi$
$998$	10.2493	+	5.91746i	0.324437	+	0.187314i
$999$	−4.88448	+	8.46017i	−0.154538	+	0.267668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bb.k.724.3		12
5.2	odd	4		195.2.i.d.61.2	yes	6
5.3	odd	4		975.2.i.l.451.2		6
5.4	even	2	inner	975.2.bb.k.724.4		12
13.3	even	3	inner	975.2.bb.k.874.4		12
15.2	even	4		585.2.j.f.451.2		6
65.3	odd	12		975.2.i.l.601.2		6
65.17	odd	12		2535.2.a.ba.1.2		3
65.22	odd	12		2535.2.a.bb.1.2		3
65.29	even	6	inner	975.2.bb.k.874.3		12
65.42	odd	12		195.2.i.d.16.2	✓	6
195.17	even	12		7605.2.a.bw.1.2		3
195.107	even	12		585.2.j.f.406.2		6
195.152	even	12		7605.2.a.bv.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.2	✓	6	65.42	odd	12
195.2.i.d.61.2	yes	6	5.2	odd	4
585.2.j.f.406.2		6	195.107	even	12
585.2.j.f.451.2		6	15.2	even	4
975.2.i.l.451.2		6	5.3	odd	4
975.2.i.l.601.2		6	65.3	odd	12
975.2.bb.k.724.3		12	1.1	even	1	trivial
975.2.bb.k.724.4		12	5.4	even	2	inner
975.2.bb.k.874.3		12	65.29	even	6	inner
975.2.bb.k.874.4		12	13.3	even	3	inner
2535.2.a.ba.1.2		3	65.17	odd	12
2535.2.a.bb.1.2		3	65.22	odd	12
7605.2.a.bv.1.2		3	195.152	even	12
7605.2.a.bw.1.2		3	195.17	even	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} + 6 q^{9} - 48 q^{14} - 24 q^{16} + 24 q^{19} - 12 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} + 12 q^{31} - 12 q^{36} - 24 q^{39} + 48 q^{44} - 24 q^{46} - 12 q^{49} - 60 q^{56} - 12 q^{59}+ \cdots - 48 q^{96}+O(q^{100}) \) 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

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Representations

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Database

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