LMFDB - Embedded newform 1275.2.d.i.424.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1275,2,Mod(424,1275)] 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("1275.424"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1275 = 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1275.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-12,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1809262577$
Analytic rank:	$0$
Dimension:	$12$
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} + 20x^{10} + 144x^{8} + 452x^{6} + 604x^{4} + 268x^{2} + 36 $ x^12 + 20x^10 + 144x^8 + 452x^6 + 604x^4 + 268*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			424.6
Root			$-0.505687i$ of defining polynomial
Character	$\chi$	$=$	1275.424
Dual form			1275.2.d.i.424.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.505687i q^{2} -1.00000 q^{3} +1.74428 q^{4} +0.505687i q^{6} +2.32475 q^{7} -1.89343i q^{8} +1.00000 q^{9} +3.83044i q^{11} -1.74428 q^{12} +1.37414i q^{13} -1.17560i q^{14} +2.53108 q^{16} +(-3.54700 + 2.10209i) q^{17} -0.505687i q^{18} +6.12980 q^{19} -2.32475 q^{21} +1.93700 q^{22} +1.89121 q^{23} +1.89343i q^{24} +0.694887 q^{26} -1.00000 q^{27} +4.05502 q^{28} +4.87983i q^{29} +1.84404i q^{31} -5.06680i q^{32} -3.83044i q^{33} +(1.06300 + 1.79367i) q^{34} +1.74428 q^{36} -3.82266 q^{37} -3.09976i q^{38} -1.37414i q^{39} +4.24219i q^{41} +1.17560i q^{42} -6.76392i q^{43} +6.68136i q^{44} -0.956358i q^{46} +6.98287i q^{47} -2.53108 q^{48} -1.59554 q^{49} +(3.54700 - 2.10209i) q^{51} +2.39689i q^{52} -10.3558i q^{53} +0.505687i q^{54} -4.40176i q^{56} -6.12980 q^{57} +2.46767 q^{58} +6.24463 q^{59} -2.08944i q^{61} +0.932508 q^{62} +2.32475 q^{63} +2.49994 q^{64} -1.93700 q^{66} +11.4165i q^{67} +(-6.18697 + 3.66663i) q^{68} -1.89121 q^{69} -0.485278i q^{71} -1.89343i q^{72} +15.0256 q^{73} +1.93307i q^{74} +10.6921 q^{76} +8.90481i q^{77} -0.694887 q^{78} -16.0715i q^{79} +1.00000 q^{81} +2.14522 q^{82} -2.21770i q^{83} -4.05502 q^{84} -3.42043 q^{86} -4.87983i q^{87} +7.25268 q^{88} -0.0376087 q^{89} +3.19454i q^{91} +3.29879 q^{92} -1.84404i q^{93} +3.53115 q^{94} +5.06680i q^{96} +8.19523 q^{97} +0.806843i q^{98} +3.83044i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} - 16 q^{4} + 12 q^{9} + 16 q^{12} + 32 q^{16} - 6 q^{17} + 4 q^{19} + 12 q^{22} - 16 q^{23} - 36 q^{26} - 12 q^{27} - 36 q^{28} + 24 q^{34} - 16 q^{36} - 4 q^{37} - 32 q^{48} + 16 q^{49}+ \cdots - 16 q^{97}+O(q^{100}) $ 12 * q - 12 * q^3 - 16 * q^4 + 12 * q^9 + 16 * q^12 + 32 * q^16 - 6 * q^17 + 4 * q^19 + 12 * q^22 - 16 * q^23 - 36 * q^26 - 12 * q^27 - 36 * q^28 + 24 * q^34 - 16 * q^36 - 4 * q^37 - 32 * q^48 + 16 * q^49 + 6 * q^51 - 4 * q^57 + 4 * q^58 - 32 * q^59 - 56 * q^62 - 56 * q^64 - 12 * q^66 - 20 * q^68 + 16 * q^69 + 44 * q^73 + 64 * q^76 + 36 * q^78 + 12 * q^81 - 40 * q^82 + 36 * q^84 + 20 * q^86 - 8 * q^88 - 4 * q^89 - 40 * q^94 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1275\mathbb{Z}\right)^\times$.

$n$	$52$	$751$	$851$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	0.505687i		−	0.357575i	−0.983888	−	0.178787i	$-0.942783\pi$
$2$		−	0.505687i		−	0.357575i	0.983888	−	0.178787i	$-0.0572174\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.74428			0.872140
$5$		0			0
$5$		0			0
$6$			0.505687i			0.206446i
$7$	2.32475			0.878673			0.439336	−	0.898323i	$-0.355214\pi$
$7$	2.32475			0.878673			0.439336	+	0.898323i	$0.355214\pi$
$8$		−	1.89343i		−	0.669430i
$9$	1.00000			0.333333
$10$		0			0
$11$			3.83044i			1.15492i	0.816419	+	0.577460i	$0.195956\pi$
$11$			3.83044i			1.15492i	−0.816419	+	0.577460i	$0.804044\pi$
$12$	−1.74428			−0.503530
$13$			1.37414i			0.381119i	0.981676	+	0.190559i	$0.0610302\pi$
$13$			1.37414i			0.381119i	−0.981676	+	0.190559i	$0.938970\pi$
$14$		−	1.17560i		−	0.314191i
$15$		0			0
$16$	2.53108			0.632769
$17$	−3.54700	+	2.10209i	−0.860275	+	0.509831i
$17$	−3.54700	+	2.10209i	−0.860275	+	0.509831i
$18$		−	0.505687i		−	0.119192i
$19$	6.12980			1.40627			0.703136	−	0.711055i	$-0.251782\pi$
$19$	6.12980			1.40627			0.703136	+	0.711055i	$0.251782\pi$
$20$		0			0
$21$	−2.32475			−0.507302
$22$	1.93700			0.412970
$23$	1.89121			0.394344			0.197172	−	0.980369i	$-0.436824\pi$
$23$	1.89121			0.394344			0.197172	+	0.980369i	$0.436824\pi$
$24$			1.89343i			0.386496i
$25$		0			0
$26$	0.694887			0.136279
$27$	−1.00000			−0.192450
$28$	4.05502			0.766326
$29$			4.87983i			0.906162i	0.891469	+	0.453081i	$0.149675\pi$
$29$			4.87983i			0.906162i	−0.891469	+	0.453081i	$0.850325\pi$
$30$		0			0
$31$			1.84404i			0.331199i	0.986193	+	0.165600i	$0.0529560\pi$
$31$			1.84404i			0.331199i	−0.986193	+	0.165600i	$0.947044\pi$
$32$		−	5.06680i		−	0.895692i
$33$		−	3.83044i		−	0.666794i
$34$	1.06300	+	1.79367i	0.182303	+	0.307613i
$35$		0			0
$36$	1.74428			0.290713
$37$	−3.82266			−0.628441			−0.314221	−	0.949350i	$-0.601743\pi$
$37$	−3.82266			−0.628441			−0.314221	+	0.949350i	$0.601743\pi$
$38$		−	3.09976i		−	0.502847i
$39$		−	1.37414i		−	0.220039i
$40$		0			0
$41$			4.24219i			0.662519i	0.943540	+	0.331259i	$0.107474\pi$
$41$			4.24219i			0.662519i	−0.943540	+	0.331259i	$0.892526\pi$
$42$			1.17560i			0.181398i
$43$		−	6.76392i		−	1.03149i	−0.856743	−	0.515744i	$-0.827516\pi$
$43$		−	6.76392i		−	1.03149i	0.856743	−	0.515744i	$-0.172484\pi$
$44$			6.68136i			1.00725i
$45$		0			0
$46$		−	0.956358i		−	0.141007i
$47$			6.98287i			1.01856i	0.860602	+	0.509278i	$0.170088\pi$
$47$			6.98287i			1.01856i	−0.860602	+	0.509278i	$0.829912\pi$
$48$	−2.53108			−0.365329
$49$	−1.59554			−0.227934
$50$		0			0
$51$	3.54700	−	2.10209i	0.496680	−	0.294351i
$52$			2.39689i			0.332389i
$53$		−	10.3558i		−	1.42247i	−0.702953	−	0.711237i	$-0.748135\pi$
$53$		−	10.3558i		−	1.42247i	0.702953	−	0.711237i	$-0.251865\pi$
$54$			0.505687i			0.0688153i
$55$		0			0
$56$		−	4.40176i		−	0.588210i
$57$	−6.12980			−0.811912
$58$	2.46767			0.324021
$59$	6.24463			0.812981			0.406491	−	0.913655i	$-0.366752\pi$
$59$	6.24463			0.812981			0.406491	+	0.913655i	$0.366752\pi$
$60$		0			0
$61$		−	2.08944i		−	0.267525i	−0.991013	−	0.133763i	$-0.957294\pi$
$61$		−	2.08944i		−	0.267525i	0.991013	−	0.133763i	$-0.0427060\pi$
$62$	0.932508			0.118429
$63$	2.32475			0.292891
$64$	2.49994			0.312492
$65$		0			0
$66$	−1.93700			−0.238429
$67$			11.4165i			1.39475i	0.716706	+	0.697376i	$0.245649\pi$
$67$			11.4165i			1.39475i	−0.716706	+	0.697376i	$0.754351\pi$
$68$	−6.18697	+	3.66663i	−0.750280	+	0.444644i
$69$	−1.89121			−0.227674
$70$		0			0
$71$		−	0.485278i		−	0.0575919i	−0.999585	−	0.0287960i	$-0.990833\pi$
$71$		−	0.485278i		−	0.0575919i	0.999585	−	0.0287960i	$-0.00916731\pi$
$72$		−	1.89343i		−	0.223143i
$73$	15.0256			1.75861			0.879305	−	0.476259i	$-0.158007\pi$
$73$	15.0256			1.75861			0.879305	+	0.476259i	$0.158007\pi$
$74$			1.93307i			0.224715i
$75$		0			0
$76$	10.6921			1.22647
$77$			8.90481i			1.01480i
$78$	−0.694887			−0.0786804
$79$		−	16.0715i		−	1.80819i	−0.427332	−	0.904095i	$-0.640546\pi$
$79$		−	16.0715i		−	1.80819i	0.427332	−	0.904095i	$-0.359454\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	2.14522			0.236900
$83$		−	2.21770i		−	0.243424i	−0.992565	−	0.121712i	$-0.961162\pi$
$83$		−	2.21770i		−	0.243424i	0.992565	−	0.121712i	$-0.0388385\pi$
$84$	−4.05502			−0.442439
$85$		0			0
$86$	−3.42043			−0.368834
$87$		−	4.87983i		−	0.523173i
$88$	7.25268			0.773138
$89$	−0.0376087			−0.00398652			−0.00199326	−	0.999998i	$-0.500634\pi$
$89$	−0.0376087			−0.00398652			−0.00199326	+	0.999998i	$0.500634\pi$
$90$		0			0
$91$			3.19454i			0.334879i
$92$	3.29879			0.343923
$93$		−	1.84404i		−	0.191218i
$94$	3.53115			0.364210
$95$		0			0
$96$			5.06680i			0.517128i
$97$	8.19523			0.832100			0.416050	−	0.909342i	$-0.363414\pi$
$97$	8.19523			0.832100			0.416050	+	0.909342i	$0.363414\pi$
$98$			0.806843i			0.0815034i
$99$			3.83044i			0.384973i
$100$		0			0
$101$	13.7028			1.36348			0.681738	−	0.731596i	$-0.261224\pi$
$101$	13.7028			1.36348			0.681738	+	0.731596i	$0.261224\pi$
$102$	−1.06300	−	1.79367i	−0.105252	−	0.177600i
$103$			8.53495i			0.840974i	0.907299	+	0.420487i	$0.138141\pi$
$103$			8.53495i			0.840974i	−0.907299	+	0.420487i	$0.861859\pi$
$104$	2.60185			0.255132
$105$		0			0
$106$	−5.23677			−0.508641
$107$	−8.99707			−0.869780			−0.434890	−	0.900484i	$-0.643213\pi$
$107$	−8.99707			−0.869780			−0.434890	+	0.900484i	$0.643213\pi$
$108$	−1.74428			−0.167843
$109$			0.529331i			0.0507007i	0.999679	+	0.0253504i	$0.00807013\pi$
$109$			0.529331i			0.0507007i	−0.999679	+	0.0253504i	$0.991930\pi$
$110$		0			0
$111$	3.82266			0.362831
$112$	5.88412			0.555997
$113$	5.59928			0.526736			0.263368	−	0.964695i	$-0.415167\pi$
$113$	5.59928			0.526736			0.263368	+	0.964695i	$0.415167\pi$
$114$			3.09976i			0.290319i
$115$		0			0
$116$			8.51179i			0.790300i
$117$			1.37414i			0.127040i
$118$		−	3.15783i		−	0.290702i
$119$	−8.24590	+	4.88682i	−0.755900	+	0.447974i
$120$		0			0
$121$	−3.67225			−0.333841
$122$	−1.05660			−0.0956603
$123$		−	4.24219i		−	0.382505i
$124$			3.21652i			0.288852i
$125$		0			0
$126$		−	1.17560i		−	0.104730i
$127$			6.18065i			0.548444i	0.961666	+	0.274222i	$0.0884203\pi$
$127$			6.18065i			0.548444i	−0.961666	+	0.274222i	$0.911580\pi$
$128$		−	11.3978i		−	1.00743i
$129$			6.76392i			0.595530i
$130$		0			0
$131$		−	12.3531i		−	1.07930i	−0.841890	−	0.539649i	$-0.818557\pi$
$131$		−	12.3531i		−	1.07930i	0.841890	−	0.539649i	$-0.181443\pi$
$132$		−	6.68136i		−	0.581537i
$133$	14.2502			1.23565
$134$	5.77319			0.498728
$135$		0			0
$136$	3.98016	+	6.71602i	0.341296	+	0.575894i
$137$		−	10.2200i		−	0.873150i	−0.899668	−	0.436575i	$-0.856191\pi$
$137$		−	10.2200i		−	0.873150i	0.899668	−	0.436575i	$-0.143809\pi$
$138$			0.956358i			0.0814106i
$139$		−	22.5106i		−	1.90933i	−0.297690	−	0.954663i	$-0.596216\pi$
$139$		−	22.5106i		−	1.90933i	0.297690	−	0.954663i	$-0.403784\pi$
$140$		0			0
$141$		−	6.98287i		−	0.588064i
$142$	−0.245399			−0.0205934
$143$	−5.26357			−0.440162
$144$	2.53108			0.210923
$145$		0			0
$146$		−	7.59824i		−	0.628835i
$147$	1.59554			0.131598
$148$	−6.66779			−0.548089
$149$	−19.1867			−1.57183			−0.785917	−	0.618332i	$-0.787809\pi$
$149$	−19.1867			−1.57183			−0.785917	+	0.618332i	$0.787809\pi$
$150$		0			0
$151$	−19.2687			−1.56807			−0.784034	−	0.620718i	$-0.786841\pi$
$151$	−19.2687			−1.56807			−0.784034	+	0.620718i	$0.786841\pi$
$152$		−	11.6064i		−	0.941401i
$153$	−3.54700	+	2.10209i	−0.286758	+	0.169944i
$154$	4.50305			0.362866
$155$		0			0
$156$		−	2.39689i		−	0.191905i
$157$			7.64868i			0.610431i	0.952283	+	0.305215i	$0.0987285\pi$
$157$			7.64868i			0.610431i	−0.952283	+	0.305215i	$0.901272\pi$
$158$	−8.12717			−0.646563
$159$			10.3558i			0.821265i
$160$		0			0
$161$	4.39658			0.346499
$162$		−	0.505687i		−	0.0397305i
$163$	−5.11501			−0.400639			−0.200319	−	0.979731i	$-0.564198\pi$
$163$	−5.11501			−0.400639			−0.200319	+	0.979731i	$0.564198\pi$
$164$			7.39957i			0.577809i
$165$		0			0
$166$	−1.12146			−0.0870424
$167$	17.9196			1.38666			0.693330	−	0.720621i	$-0.256143\pi$
$167$	17.9196			1.38666			0.693330	+	0.720621i	$0.256143\pi$
$168$			4.40176i			0.339603i
$169$	11.1117			0.854748
$170$		0			0
$171$	6.12980			0.468757
$172$		−	11.7982i		−	0.899602i
$173$	−6.63957			−0.504797			−0.252399	−	0.967623i	$-0.581219\pi$
$173$	−6.63957			−0.504797			−0.252399	+	0.967623i	$0.581219\pi$
$174$	−2.46767			−0.187073
$175$		0			0
$176$			9.69513i			0.730798i
$177$	−6.24463			−0.469375
$178$			0.0190183i			0.00142548i
$179$	−7.04898			−0.526866			−0.263433	−	0.964678i	$-0.584855\pi$
$179$	−7.04898			−0.526866			−0.263433	+	0.964678i	$0.584855\pi$
$180$		0			0
$181$			1.48990i			0.110743i	0.998466	+	0.0553715i	$0.0176343\pi$
$181$			1.48990i			0.110743i	−0.998466	+	0.0553715i	$0.982366\pi$
$182$	1.61544			0.119744
$183$			2.08944i			0.154456i
$184$		−	3.58087i		−	0.263985i
$185$		0			0
$186$	−0.932508			−0.0683748
$187$	−8.05190	−	13.5866i	−0.588814	−	0.993549i
$188$			12.1801i			0.888324i
$189$	−2.32475			−0.169101
$190$		0			0
$191$	−3.85489			−0.278930			−0.139465	−	0.990227i	$-0.544538\pi$
$191$	−3.85489			−0.278930			−0.139465	+	0.990227i	$0.544538\pi$
$192$	−2.49994			−0.180417
$193$	−24.4093			−1.75702			−0.878511	−	0.477722i	$-0.841463\pi$
$193$	−24.4093			−1.75702			−0.878511	+	0.477722i	$0.841463\pi$
$194$		−	4.14422i		−	0.297538i
$195$		0			0
$196$	−2.78306			−0.198790
$197$	7.22171			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$197$	7.22171			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$198$	1.93700			0.137657
$199$		−	23.3923i		−	1.65824i	−0.559074	−	0.829118i	$-0.688843\pi$
$199$		−	23.3923i		−	1.65824i	0.559074	−	0.829118i	$-0.311157\pi$
$200$		0			0
$201$		−	11.4165i		−	0.805260i
$202$		−	6.92931i		−	0.487545i
$203$			11.3444i			0.796220i
$204$	6.18697	−	3.66663i	0.433175	−	0.256715i
$205$		0			0
$206$	4.31602			0.300711
$207$	1.89121			0.131448
$208$			3.47806i			0.241160i
$209$			23.4798i			1.62413i
$210$		0			0
$211$			25.3754i			1.74691i	0.486901	+	0.873457i	$0.338127\pi$
$211$			25.3754i			1.74691i	−0.486901	+	0.873457i	$0.661873\pi$
$212$		−	18.0634i		−	1.24060i
$213$			0.485278i			0.0332507i
$214$			4.54970i			0.311011i
$215$		0			0
$216$			1.89343i			0.128832i
$217$			4.28693i			0.291016i
$218$	0.267676			0.0181293
$219$	−15.0256			−1.01533
$220$		0			0
$221$	−2.88857	−	4.87409i	−0.194306	−	0.327867i
$222$		−	1.93307i		−	0.129739i
$223$			7.63412i			0.511218i	0.966780	+	0.255609i	$0.0822760\pi$
$223$			7.63412i			0.511218i	−0.966780	+	0.255609i	$0.917724\pi$
$224$		−	11.7790i		−	0.787021i
$225$		0			0
$226$		−	2.83149i		−	0.188348i
$227$	−21.5939			−1.43324			−0.716620	−	0.697464i	$-0.754312\pi$
$227$	−21.5939			−1.43324			−0.716620	+	0.697464i	$0.754312\pi$
$228$	−10.6921			−0.708101
$229$	4.89696			0.323600			0.161800	−	0.986824i	$-0.448270\pi$
$229$	4.89696			0.323600			0.161800	+	0.986824i	$0.448270\pi$
$230$		0			0
$231$		−	8.90481i		−	0.585893i
$232$	9.23964			0.606612
$233$	10.7349			0.703264			0.351632	−	0.936138i	$-0.385627\pi$
$233$	10.7349			0.703264			0.351632	+	0.936138i	$0.385627\pi$
$234$	0.694887			0.0454262
$235$		0			0
$236$	10.8924			0.709034
$237$			16.0715i			1.04396i
$238$	2.47120	+	4.16984i	0.160184	+	0.270291i
$239$	−16.3116			−1.05511			−0.527554	−	0.849521i	$-0.676891\pi$
$239$	−16.3116			−1.05511			−0.527554	+	0.849521i	$0.676891\pi$
$240$		0			0
$241$			15.1531i			0.976099i	0.872816	+	0.488049i	$0.162291\pi$
$241$			15.1531i			0.976099i	−0.872816	+	0.488049i	$0.837709\pi$
$242$			1.85701i			0.119373i
$243$	−1.00000			−0.0641500
$244$		−	3.64457i		−	0.233320i
$245$		0			0
$246$	−2.14522			−0.136774
$247$			8.42322i			0.535957i
$248$	3.49157			0.221715
$249$			2.21770i			0.140541i
$250$		0			0
$251$	−27.5040			−1.73604			−0.868019	−	0.496531i	$-0.834607\pi$
$251$	−27.5040			−1.73604			−0.868019	+	0.496531i	$0.834607\pi$
$252$	4.05502			0.255442
$253$			7.24414i			0.455435i
$254$	3.12547			0.196110
$255$		0			0
$256$	−0.763844			−0.0477402
$257$			4.83678i			0.301710i	0.988556	+	0.150855i	$0.0482027\pi$
$257$			4.83678i			0.301710i	−0.988556	+	0.150855i	$0.951797\pi$
$258$	3.42043			0.212946
$259$	−8.88673			−0.552194
$260$		0			0
$261$			4.87983i			0.302054i
$262$	−6.24681			−0.385929
$263$		−	0.614515i		−	0.0378926i	−0.999821	−	0.0189463i	$-0.993969\pi$
$263$		−	0.614515i		−	0.0378926i	0.999821	−	0.0189463i	$-0.00603116\pi$
$264$	−7.25268			−0.446372
$265$		0			0
$266$		−	7.20617i		−	0.441838i
$267$	0.0376087			0.00230162
$268$			19.9136i			1.21642i
$269$		−	24.1847i		−	1.47457i	−0.675582	−	0.737285i	$-0.736108\pi$
$269$		−	24.1847i		−	1.47457i	0.675582	−	0.737285i	$-0.263892\pi$
$270$		0			0
$271$	−25.6004			−1.55511			−0.777556	−	0.628814i	$-0.783541\pi$
$271$	−25.6004			−1.55511			−0.777556	+	0.628814i	$0.783541\pi$
$272$	−8.97774	+	5.32054i	−0.544355	+	0.322605i
$273$		−	3.19454i		−	0.193342i
$274$	−5.16810			−0.312217
$275$		0			0
$276$	−3.29879			−0.198564
$277$	1.53603			0.0922909			0.0461454	−	0.998935i	$-0.485306\pi$
$277$	1.53603			0.0922909			0.0461454	+	0.998935i	$0.485306\pi$
$278$	−11.3833			−0.682727
$279$			1.84404i			0.110400i
$280$		0			0
$281$	−17.0111			−1.01480			−0.507398	−	0.861712i	$-0.669393\pi$
$281$	−17.0111			−1.01480			−0.507398	+	0.861712i	$0.669393\pi$
$282$	−3.53115			−0.210277
$283$	9.57549			0.569204			0.284602	−	0.958646i	$-0.408139\pi$
$283$	9.57549			0.569204			0.284602	+	0.958646i	$0.408139\pi$
$284$		−	0.846461i		−	0.0502282i
$285$		0			0
$286$			2.66172i			0.157391i
$287$			9.86203i			0.582137i
$288$		−	5.06680i		−	0.298564i
$289$	8.16248	−	14.9122i	0.480146	−	0.877189i
$290$		0			0
$291$	−8.19523			−0.480413
$292$	26.2088			1.53375
$293$			12.5909i			0.735571i	0.929911	+	0.367785i	$0.119884\pi$
$293$			12.5909i			0.735571i	−0.929911	+	0.367785i	$0.880116\pi$
$294$		−	0.806843i		−	0.0470560i
$295$		0			0
$296$			7.23795i			0.420698i
$297$		−	3.83044i		−	0.222265i
$298$			9.70246i			0.562048i
$299$			2.59879i			0.150292i
$300$		0			0
$301$		−	15.7244i		−	0.906340i
$302$			9.74395i			0.560701i
$303$	−13.7028			−0.787204
$304$	15.5150			0.889845
$305$		0			0
$306$	1.06300	+	1.79367i	0.0607675	+	0.102538i
$307$		−	4.24103i		−	0.242048i	−0.992650	−	0.121024i	$-0.961382\pi$
$307$		−	4.24103i		−	0.242048i	0.992650	−	0.121024i	$-0.0386179\pi$
$308$			15.5325i			0.885045i
$309$		−	8.53495i		−	0.485537i
$310$		0			0
$311$		−	27.6793i		−	1.56955i	−0.619781	−	0.784775i	$-0.712779\pi$
$311$		−	27.6793i		−	1.56955i	0.619781	−	0.784775i	$-0.287221\pi$
$312$	−2.60185			−0.147301
$313$	−7.92765			−0.448098			−0.224049	−	0.974578i	$-0.571927\pi$
$313$	−7.92765			−0.448098			−0.224049	+	0.974578i	$0.571927\pi$
$314$	3.86784			0.218275
$315$		0			0
$316$		−	28.0333i		−	1.57700i
$317$	−6.63483			−0.372649			−0.186324	−	0.982488i	$-0.559658\pi$
$317$	−6.63483			−0.372649			−0.186324	+	0.982488i	$0.559658\pi$
$318$	5.23677			0.293664
$319$	−18.6919			−1.04654
$320$		0			0
$321$	8.99707			0.502168
$322$		−	2.22329i		−	0.123899i
$323$	−21.7424	+	12.8854i	−1.20978	+	0.716960i
$324$	1.74428			0.0969045
$325$		0			0
$326$			2.58660i			0.143258i
$327$		−	0.529331i		−	0.0292721i
$328$	8.03231			0.443510
$329$			16.2334i			0.894978i
$330$		0			0
$331$	−9.36993			−0.515018			−0.257509	−	0.966276i	$-0.582902\pi$
$331$	−9.36993			−0.515018			−0.257509	+	0.966276i	$0.582902\pi$
$332$		−	3.86829i		−	0.212300i
$333$	−3.82266			−0.209480
$334$		−	9.06171i		−	0.495834i
$335$		0			0
$336$	−5.88412			−0.321005
$337$	3.14459			0.171296			0.0856482	−	0.996325i	$-0.472704\pi$
$337$	3.14459			0.171296			0.0856482	+	0.996325i	$0.472704\pi$
$338$		−	5.61906i		−	0.305636i
$339$	−5.59928			−0.304111
$340$		0			0
$341$	−7.06348			−0.382509
$342$		−	3.09976i		−	0.167616i
$343$	−19.9825			−1.07895
$344$	−12.8070			−0.690509
$345$		0			0
$346$			3.35754i			0.180503i
$347$	−18.0617			−0.969605			−0.484802	−	0.874624i	$-0.661108\pi$
$347$	−18.0617			−0.969605			−0.484802	+	0.874624i	$0.661108\pi$
$348$		−	8.51179i		−	0.456280i
$349$	−7.72131			−0.413312			−0.206656	−	0.978414i	$-0.566258\pi$
$349$	−7.72131			−0.413312			−0.206656	+	0.978414i	$0.566258\pi$
$350$		0			0
$351$		−	1.37414i		−	0.0733464i
$352$	19.4081			1.03445
$353$		−	28.5719i		−	1.52073i	−0.649497	−	0.760364i	$-0.725021\pi$
$353$		−	28.5719i		−	1.52073i	0.649497	−	0.760364i	$-0.274979\pi$
$354$			3.15783i			0.167837i
$355$		0			0
$356$	−0.0656002			−0.00347680
$357$	8.24590	−	4.88682i	0.436419	−	0.258638i
$358$			3.56458i			0.188394i
$359$	16.7892			0.886101			0.443050	−	0.896497i	$-0.353896\pi$
$359$	16.7892			0.886101			0.443050	+	0.896497i	$0.353896\pi$
$360$		0			0
$361$	18.5744			0.977602
$362$	0.753421			0.0395989
$363$	3.67225			0.192743
$364$			5.57218i			0.292061i
$365$		0			0
$366$	1.05660			0.0552295
$367$	4.94971			0.258373			0.129186	−	0.991620i	$-0.458763\pi$
$367$	4.94971			0.258373			0.129186	+	0.991620i	$0.458763\pi$
$368$	4.78678			0.249528
$369$			4.24219i			0.220840i
$370$		0			0
$371$		−	24.0746i		−	1.24989i
$372$		−	3.21652i		−	0.166769i
$373$		−	20.3711i		−	1.05478i	−0.849625	−	0.527388i	$-0.823171\pi$
$373$		−	20.3711i		−	1.05478i	0.849625	−	0.527388i	$-0.176829\pi$
$374$	−6.87056	+	4.07174i	−0.355268	+	0.210545i
$375$		0			0
$376$	13.2216			0.681853
$377$	−6.70559			−0.345355
$378$			1.17560i			0.0604661i
$379$			14.5285i			0.746279i	0.927775	+	0.373140i	$0.121719\pi$
$379$			14.5285i			0.746279i	−0.927775	+	0.373140i	$0.878281\pi$
$380$		0			0
$381$		−	6.18065i		−	0.316644i
$382$			1.94937i			0.0997385i
$383$			30.1233i			1.53923i	0.638508	+	0.769616i	$0.279552\pi$
$383$			30.1233i			1.53923i	−0.638508	+	0.769616i	$0.720448\pi$
$384$			11.3978i			0.581641i
$385$		0			0
$386$			12.3435i			0.628267i
$387$		−	6.76392i		−	0.343829i
$388$	14.2948			0.725708
$389$	−12.1939			−0.618254			−0.309127	−	0.951021i	$-0.600037\pi$
$389$	−12.1939			−0.618254			−0.309127	+	0.951021i	$0.600037\pi$
$390$		0			0
$391$	−6.70811	+	3.97547i	−0.339244	+	0.201048i
$392$			3.02105i			0.152586i
$393$			12.3531i			0.623133i
$394$		−	3.65192i		−	0.183981i
$395$		0			0
$396$			6.68136i			0.335751i
$397$	−23.1700			−1.16287			−0.581434	−	0.813593i	$-0.697508\pi$
$397$	−23.1700			−1.16287			−0.581434	+	0.813593i	$0.697508\pi$
$398$	−11.8292			−0.592943
$399$	−14.2502			−0.713405
$400$		0			0
$401$		−	33.8852i		−	1.69215i	−0.533067	−	0.846073i	$-0.678961\pi$
$401$		−	33.8852i		−	1.69215i	0.533067	−	0.846073i	$-0.321039\pi$
$402$	−5.77319			−0.287941
$403$	−2.53398			−0.126226
$404$	23.9015			1.18914
$405$		0			0
$406$	5.73671			0.284708
$407$		−	14.6425i		−	0.725800i
$408$	−3.98016	−	6.71602i	−0.197047	−	0.332493i
$409$	16.7600			0.828728			0.414364	−	0.910111i	$-0.364004\pi$
$409$	16.7600			0.828728			0.414364	+	0.910111i	$0.364004\pi$
$410$		0			0
$411$			10.2200i			0.504114i
$412$			14.8874i			0.733447i
$413$	14.5172			0.714345
$414$		−	0.956358i		−	0.0470024i
$415$		0			0
$416$	6.96251			0.341365
$417$			22.5106i			1.10235i
$418$	11.8734			0.580749
$419$		−	7.77239i		−	0.379706i	−0.981813	−	0.189853i	$-0.939199\pi$
$419$		−	7.77239i		−	0.379706i	0.981813	−	0.189853i	$-0.0608012\pi$
$420$		0			0
$421$	−0.392213			−0.0191153			−0.00955765	−	0.999954i	$-0.503042\pi$
$421$	−0.392213			−0.0191153			−0.00955765	+	0.999954i	$0.503042\pi$
$422$	12.8320			0.624653
$423$			6.98287i			0.339519i
$424$	−19.6080			−0.952246
$425$		0			0
$426$	0.245399			0.0118896
$427$		−	4.85742i		−	0.235067i
$428$	−15.6934			−0.758570
$429$	5.26357			0.254128
$430$		0			0
$431$			33.3511i			1.60646i	0.595666	+	0.803232i	$0.296888\pi$
$431$			33.3511i			1.60646i	−0.595666	+	0.803232i	$0.703112\pi$
$432$	−2.53108			−0.121776
$433$			23.0430i			1.10738i	0.832724	+	0.553689i	$0.186780\pi$
$433$			23.0430i			1.10738i	−0.832724	+	0.553689i	$0.813220\pi$
$434$	2.16785			0.104060
$435$		0			0
$436$			0.923302i			0.0442181i
$437$	11.5927			0.554554
$438$			7.59824i			0.363058i
$439$			15.4050i			0.735241i	0.929976	+	0.367620i	$0.119827\pi$
$439$			15.4050i			0.735241i	−0.929976	+	0.367620i	$0.880173\pi$
$440$		0			0
$441$	−1.59554			−0.0759780
$442$	−2.46477	+	1.46071i	−0.117237	+	0.0694789i
$443$		−	9.39992i		−	0.446604i	−0.974749	−	0.223302i	$-0.928316\pi$
$443$		−	9.39992i		−	0.446604i	0.974749	−	0.223302i	$-0.0716836\pi$
$444$	6.66779			0.316439
$445$		0			0
$446$	3.86048			0.182799
$447$	19.1867			0.907499
$448$	5.81172			0.274578
$449$		−	34.8548i		−	1.64490i	−0.568836	−	0.822451i	$-0.692606\pi$
$449$		−	34.8548i		−	1.64490i	0.568836	−	0.822451i	$-0.307394\pi$
$450$		0			0
$451$	−16.2494			−0.765156
$452$	9.76672			0.459388
$453$	19.2687			0.905324
$454$			10.9198i			0.512491i
$455$		0			0
$456$			11.6064i			0.543518i
$457$			5.59302i			0.261631i	0.991407	+	0.130815i	$0.0417595\pi$
$457$			5.59302i			0.261631i	−0.991407	+	0.130815i	$0.958241\pi$
$458$		−	2.47633i		−	0.115711i
$459$	3.54700	−	2.10209i	0.165560	−	0.0981169i
$460$		0			0
$461$	37.6643			1.75420			0.877102	−	0.480305i	$-0.159474\pi$
$461$	37.6643			1.75420			0.877102	+	0.480305i	$0.159474\pi$
$462$	−4.50305			−0.209501
$463$			4.49005i			0.208671i	0.994542	+	0.104335i	$0.0332715\pi$
$463$			4.49005i			0.208671i	−0.994542	+	0.104335i	$0.966729\pi$
$464$			12.3512i			0.573391i
$465$		0			0
$466$		−	5.42848i		−	0.251469i
$467$		−	24.4972i		−	1.13359i	−0.823857	−	0.566797i	$-0.808182\pi$
$467$		−	24.4972i		−	1.13359i	0.823857	−	0.566797i	$-0.191818\pi$
$468$			2.39689i			0.110796i
$469$			26.5406i			1.22553i
$470$		0			0
$471$		−	7.64868i		−	0.352432i
$472$		−	11.8238i		−	0.544234i
$473$	25.9088			1.19129
$474$	8.12717			0.373293
$475$		0			0
$476$	−14.3832	+	8.52399i	−0.659251	+	0.390696i
$477$		−	10.3558i		−	0.474158i
$478$			8.24856i			0.377280i
$479$			23.7462i			1.08499i	0.840059	+	0.542495i	$0.182520\pi$
$479$			23.7462i			1.08499i	−0.840059	+	0.542495i	$0.817480\pi$
$480$		0			0
$481$		−	5.25288i		−	0.239511i
$482$	7.66274			0.349028
$483$	−4.39658			−0.200051
$484$	−6.40543			−0.291156
$485$		0			0
$486$			0.505687i			0.0229384i
$487$	9.54322			0.432445			0.216222	−	0.976344i	$-0.430626\pi$
$487$	9.54322			0.432445			0.216222	+	0.976344i	$0.430626\pi$
$488$	−3.95622			−0.179090
$489$	5.11501			0.231309
$490$		0			0
$491$	15.6317			0.705447			0.352724	−	0.935728i	$-0.385256\pi$
$491$	15.6317			0.705447			0.352724	+	0.935728i	$0.385256\pi$
$492$		−	7.39957i		−	0.333598i
$493$	−10.2578	−	17.3088i	−0.461989	−	0.779548i
$494$	4.25952			0.191645
$495$		0			0
$496$			4.66741i			0.209573i
$497$		−	1.12815i		−	0.0506045i
$498$	1.12146			0.0502539
$499$		−	13.9399i		−	0.624036i	−0.950076	−	0.312018i	$-0.898995\pi$
$499$		−	13.9399i		−	0.624036i	0.950076	−	0.312018i	$-0.101005\pi$
$500$		0			0
$501$	−17.9196			−0.800588
$502$			13.9084i			0.620763i
$503$	19.4642			0.867868			0.433934	−	0.900945i	$-0.357125\pi$
$503$	19.4642			0.867868			0.433934	+	0.900945i	$0.357125\pi$
$504$		−	4.40176i		−	0.196070i
$505$		0			0
$506$	3.66327			0.162852
$507$	−11.1117			−0.493489
$508$			10.7808i			0.478320i
$509$	10.3056			0.456786			0.228393	−	0.973569i	$-0.426653\pi$
$509$	10.3056			0.456786			0.228393	+	0.973569i	$0.426653\pi$
$510$		0			0
$511$	34.9307			1.54524
$512$		−	22.4093i		−	0.990361i
$513$	−6.12980			−0.270637
$514$	2.44590			0.107884
$515$		0			0
$516$			11.7982i			0.519385i
$517$	−26.7475			−1.17635
$518$			4.49390i			0.197451i
$519$	6.63957			0.291445
$520$		0			0
$521$			36.6047i			1.60368i	0.597539	+	0.801840i	$0.296145\pi$
$521$			36.6047i			1.60368i	−0.597539	+	0.801840i	$0.703855\pi$
$522$	2.46767			0.108007
$523$		−	23.6841i		−	1.03564i	−0.855491	−	0.517818i	$-0.826745\pi$
$523$		−	23.6841i		−	1.03564i	0.855491	−	0.517818i	$-0.173255\pi$
$524$		−	21.5473i		−	0.941299i
$525$		0			0
$526$	−0.310752			−0.0135494
$527$	−3.87633	−	6.54082i	−0.168856	−	0.284923i
$528$		−	9.69513i		−	0.421926i
$529$	−19.4233			−0.844493
$530$		0			0
$531$	6.24463			0.270994
$532$	24.8564			1.07766
$533$	−5.82938			−0.252498
$534$		−	0.0190183i		−	0.000823000i
$535$		0			0
$536$	21.6164			0.933688
$537$	7.04898			0.304186
$538$	−12.2299			−0.527269
$539$		−	6.11161i		−	0.263246i
$540$		0			0
$541$			7.82890i			0.336591i	0.985737	+	0.168295i	$0.0538262\pi$
$541$			7.82890i			0.336591i	−0.985737	+	0.168295i	$0.946174\pi$
$542$			12.9458i			0.556069i
$543$		−	1.48990i		−	0.0639375i
$544$	10.6508	+	17.9720i	0.456651	+	0.770542i
$545$		0			0
$546$	−1.61544			−0.0691344
$547$	−15.9716			−0.682896			−0.341448	−	0.939901i	$-0.610917\pi$
$547$	−15.9716			−0.682896			−0.341448	+	0.939901i	$0.610917\pi$
$548$		−	17.8265i		−	0.761510i
$549$		−	2.08944i		−	0.0891751i
$550$		0			0
$551$			29.9124i			1.27431i
$552$			3.58087i			0.152412i
$553$		−	37.3623i		−	1.58881i
$554$		−	0.776749i		−	0.0330009i
$555$		0			0
$556$		−	39.2648i		−	1.66520i
$557$			37.8410i			1.60337i	0.597745	+	0.801687i	$0.296064\pi$
$557$			37.8410i			1.60337i	−0.597745	+	0.801687i	$0.703936\pi$
$558$	0.932508			0.0394762
$559$	9.29459			0.393119
$560$		0			0
$561$	8.05190	+	13.5866i	0.339952	+	0.573626i
$562$			8.60229i			0.362866i
$563$		−	4.01350i		−	0.169149i	−0.996417	−	0.0845744i	$-0.973047\pi$
$563$		−	4.01350i		−	0.169149i	0.996417	−	0.0845744i	$-0.0269531\pi$
$564$		−	12.1801i		−	0.512874i
$565$		0			0
$566$		−	4.84220i		−	0.203533i
$567$	2.32475			0.0976303
$568$	−0.918842			−0.0385538
$569$	22.9552			0.962333			0.481166	−	0.876629i	$-0.340213\pi$
$569$	22.9552			0.962333			0.481166	+	0.876629i	$0.340213\pi$
$570$		0			0
$571$		−	45.8971i		−	1.92073i	−0.278738	−	0.960367i	$-0.589916\pi$
$571$		−	45.8971i		−	1.92073i	0.278738	−	0.960367i	$-0.410084\pi$
$572$	−9.18114			−0.383883
$573$	3.85489			0.161041
$574$	4.98710			0.208158
$575$		0			0
$576$	2.49994			0.104164
$577$			5.62185i			0.234041i	0.993130	+	0.117020i	$0.0373343\pi$
$577$			5.62185i			0.234041i	−0.993130	+	0.117020i	$0.962666\pi$
$578$	−7.54091	−	4.12766i	−0.313661	−	0.171688i
$579$	24.4093			1.01442
$580$		0			0
$581$		−	5.15560i		−	0.213890i
$582$			4.14422i			0.171784i
$583$	39.6671			1.64284
$584$		−	28.4499i		−	1.17727i
$585$		0			0
$586$	6.36708			0.263022
$587$		−	26.5389i		−	1.09538i	−0.836682	−	0.547689i	$-0.815508\pi$
$587$		−	26.5389i		−	1.09538i	0.836682	−	0.547689i	$-0.184492\pi$
$588$	2.78306			0.114772
$589$			11.3036i			0.465757i
$590$		0			0
$591$	−7.22171			−0.297061
$592$	−9.67544			−0.397658
$593$		−	37.9304i		−	1.55762i	−0.627263	−	0.778808i	$-0.715825\pi$
$593$		−	37.9304i		−	1.55762i	0.627263	−	0.778808i	$-0.284175\pi$
$594$	−1.93700			−0.0794762
$595$		0			0
$596$	−33.4670			−1.37086
$597$			23.3923i			0.957383i
$598$	1.31417			0.0537405
$599$	−16.2424			−0.663645			−0.331823	−	0.943342i	$-0.607664\pi$
$599$	−16.2424			−0.663645			−0.331823	+	0.943342i	$0.607664\pi$
$600$		0			0
$601$			36.2489i			1.47862i	0.673364	+	0.739311i	$0.264849\pi$
$601$			36.2489i			1.47862i	−0.673364	+	0.739311i	$0.735151\pi$
$602$	−7.95163			−0.324084
$603$			11.4165i			0.464917i
$604$	−33.6101			−1.36757
$605$		0			0
$606$			6.92931i			0.281484i
$607$	3.39794			0.137918			0.0689591	−	0.997619i	$-0.478032\pi$
$607$	3.39794			0.137918			0.0689591	+	0.997619i	$0.478032\pi$
$608$		−	31.0585i		−	1.25959i
$609$		−	11.3444i		−	0.459698i
$610$		0			0
$611$	−9.59547			−0.388191
$612$	−6.18697	+	3.66663i	−0.250093	+	0.148215i
$613$		−	39.3248i		−	1.58831i	−0.607713	−	0.794157i	$-0.707913\pi$
$613$		−	39.3248i		−	1.58831i	0.607713	−	0.794157i	$-0.292087\pi$
$614$	−2.14463			−0.0865504
$615$		0			0
$616$	16.8607			0.679336
$617$	38.7378			1.55953			0.779763	−	0.626075i	$-0.215339\pi$
$617$	38.7378			1.55953			0.779763	+	0.626075i	$0.215339\pi$
$618$	−4.31602			−0.173616
$619$			0.0346436i			0.00139244i	1.00000		0.000696222i	$0.000221614\pi$
$619$			0.0346436i			0.00139244i	−1.00000		0.000696222i	$0.999778\pi$
$620$		0			0
$621$	−1.89121			−0.0758914
$622$	−13.9971			−0.561231
$623$	−0.0874309			−0.00350284
$624$		−	3.47806i		−	0.139234i
$625$		0			0
$626$			4.00891i			0.160228i
$627$		−	23.4798i		−	0.937693i
$628$			13.3414i			0.532381i
$629$	13.5590	−	8.03555i	0.540632	−	0.320399i
$630$		0			0
$631$	−8.34701			−0.332289			−0.166145	−	0.986101i	$-0.553132\pi$
$631$	−8.34701			−0.332289			−0.166145	+	0.986101i	$0.553132\pi$
$632$	−30.4304			−1.21046
$633$		−	25.3754i		−	1.00858i
$634$			3.35515i			0.133250i
$635$		0			0
$636$			18.0634i			0.716259i
$637$		−	2.19250i		−	0.0868699i
$638$			9.45225i			0.374218i
$639$		−	0.485278i		−	0.0191973i
$640$		0			0
$641$		−	30.5955i		−	1.20845i	−0.796813	−	0.604225i	$-0.793483\pi$
$641$		−	30.5955i		−	1.20845i	0.796813	−	0.604225i	$-0.206517\pi$
$642$		−	4.54970i		−	0.179562i
$643$	−15.2754			−0.602404			−0.301202	−	0.953560i	$-0.597388\pi$
$643$	−15.2754			−0.602404			−0.301202	+	0.953560i	$0.597388\pi$
$644$	7.66887			0.302196
$645$		0			0
$646$	6.51596	+	10.9949i	0.256367	+	0.432587i
$647$			29.0753i			1.14307i	0.820579	+	0.571533i	$0.193651\pi$
$647$			29.0753i			1.14307i	−0.820579	+	0.571533i	$0.806349\pi$
$648$		−	1.89343i		−	0.0743811i
$649$			23.9196i			0.938928i
$650$		0			0
$651$		−	4.28693i		−	0.168018i
$652$	−8.92202			−0.349413
$653$	46.6691			1.82630			0.913152	−	0.407618i	$-0.133641\pi$
$653$	46.6691			1.82630			0.913152	+	0.407618i	$0.133641\pi$
$654$	−0.267676			−0.0104670
$655$		0			0
$656$			10.7373i			0.419221i
$657$	15.0256			0.586203
$658$	8.20904			0.320022
$659$	7.46941			0.290967			0.145483	−	0.989361i	$-0.453526\pi$
$659$	7.46941			0.290967			0.145483	+	0.989361i	$0.453526\pi$
$660$		0			0
$661$	5.29492			0.205948			0.102974	−	0.994684i	$-0.467164\pi$
$661$	5.29492			0.205948			0.102974	+	0.994684i	$0.467164\pi$
$662$			4.73825i			0.184158i
$663$	2.88857	+	4.87409i	0.112183	+	0.189294i
$664$	−4.19907			−0.162955
$665$		0			0
$666$			1.93307i			0.0749049i
$667$			9.22876i			0.357339i
$668$	31.2568			1.20936
$669$		−	7.63412i		−	0.295152i
$670$		0			0
$671$	8.00347			0.308970
$672$			11.7790i			0.454387i
$673$	2.55338			0.0984256			0.0492128	−	0.998788i	$-0.484329\pi$
$673$	2.55338			0.0984256			0.0492128	+	0.998788i	$0.484329\pi$
$674$		−	1.59018i		−	0.0612513i
$675$		0			0
$676$	19.3820			0.745460
$677$	−18.6769			−0.717810			−0.358905	−	0.933374i	$-0.616850\pi$
$677$	−18.6769			−0.717810			−0.358905	+	0.933374i	$0.616850\pi$
$678$			2.83149i			0.108743i
$679$	19.0519			0.731144
$680$		0			0
$681$	21.5939			0.827482
$682$			3.57191i			0.136776i
$683$	−34.7600			−1.33005			−0.665027	−	0.746820i	$-0.731580\pi$
$683$	−34.7600			−1.33005			−0.665027	+	0.746820i	$0.731580\pi$
$684$	10.6921			0.408822
$685$		0			0
$686$			10.1049i			0.385806i
$687$	−4.89696			−0.186831
$688$		−	17.1200i		−	0.652693i
$689$	14.2303			0.542131
$690$		0			0
$691$			34.9888i			1.33104i	0.746381	+	0.665519i	$0.231790\pi$
$691$			34.9888i			1.33104i	−0.746381	+	0.665519i	$0.768210\pi$
$692$	−11.5813			−0.440254
$693$			8.90481i			0.338266i
$694$			9.13359i			0.346706i
$695$		0			0
$696$	−9.23964			−0.350228
$697$	−8.91744	−	15.0471i	−0.337772	−	0.569948i
$698$			3.90457i			0.147790i
$699$	−10.7349			−0.406030
$700$		0			0
$701$	−38.1963			−1.44266			−0.721328	−	0.692594i	$-0.756468\pi$
$701$	−38.1963			−1.44266			−0.721328	+	0.692594i	$0.756468\pi$
$702$	−0.694887			−0.0262268
$703$	−23.4321			−0.883760
$704$			9.57584i			0.360903i
$705$		0			0
$706$	−14.4484			−0.543774
$707$	31.8555			1.19805
$708$	−10.8924			−0.409361
$709$			29.6717i			1.11434i	0.830397	+	0.557172i	$0.188114\pi$
$709$			29.6717i			1.11434i	−0.830397	+	0.557172i	$0.811886\pi$
$710$		0			0
$711$		−	16.0715i		−	0.602730i
$712$			0.0712097i			0.00266869i
$713$			3.48746i			0.130606i
$714$	−2.47120	−	4.16984i	−0.0924824	−	0.156053i
$715$		0			0
$716$	−12.2954			−0.459501
$717$	16.3116			0.609167
$718$		−	8.49009i		−	0.316847i
$719$			27.4951i			1.02539i	0.858570	+	0.512697i	$0.171354\pi$
$719$			27.4951i			1.02539i	−0.858570	+	0.512697i	$0.828646\pi$
$720$		0			0
$721$			19.8416i			0.738941i
$722$		−	9.39285i		−	0.349566i
$723$		−	15.1531i		−	0.563551i
$724$			2.59880i			0.0965835i
$725$		0			0
$726$		−	1.85701i		−	0.0689201i
$727$		−	6.27499i		−	0.232726i	−0.993207	−	0.116363i	$-0.962876\pi$
$727$		−	6.27499i		−	0.232726i	0.993207	−	0.116363i	$-0.0371237\pi$
$728$	6.04865			0.224178
$729$	1.00000			0.0370370
$730$		0			0
$731$	14.2183	+	23.9916i	0.525884	+	0.887363i
$732$			3.64457i			0.134707i
$733$		−	34.9909i		−	1.29242i	−0.763160	−	0.646210i	$-0.776353\pi$
$733$		−	34.9909i		−	1.29242i	0.763160	−	0.646210i	$-0.223647\pi$
$734$		−	2.50301i		−	0.0923876i
$735$		0			0
$736$		−	9.58236i		−	0.353210i
$737$	−43.7303			−1.61083
$738$	2.14522			0.0789667
$739$	−33.5129			−1.23279			−0.616396	−	0.787437i	$-0.711408\pi$
$739$	−33.5129			−1.23279			−0.616396	+	0.787437i	$0.711408\pi$
$740$		0			0
$741$		−	8.42322i		−	0.309435i
$742$	−12.1742			−0.446929
$743$	20.6043			0.755898			0.377949	−	0.925826i	$-0.376629\pi$
$743$	20.6043			0.755898			0.377949	+	0.925826i	$0.376629\pi$
$744$	−3.49157			−0.128007
$745$		0			0
$746$	−10.3014			−0.377161
$747$		−	2.21770i		−	0.0811414i
$748$	−14.0448	−	23.6988i	−0.513528	−	0.866514i
$749$	−20.9159			−0.764252
$750$		0			0
$751$		−	0.215296i		−	0.00785625i	−0.999992	−	0.00392812i	$-0.998750\pi$
$751$		−	0.215296i		−	0.00785625i	0.999992	−	0.00392812i	$-0.00125036\pi$
$752$			17.6742i			0.644511i
$753$	27.5040			1.00230
$754$			3.39093i			0.123490i
$755$		0			0
$756$	−4.05502			−0.147480
$757$		−	29.8753i		−	1.08584i	−0.839786	−	0.542918i	$-0.817320\pi$
$757$		−	29.8753i		−	1.08584i	0.839786	−	0.542918i	$-0.182680\pi$
$758$	7.34688			0.266851
$759$		−	7.24414i		−	0.262946i
$760$		0			0
$761$	54.5427			1.97717			0.988586	−	0.150659i	$-0.0481396\pi$
$761$	54.5427			1.97717			0.988586	+	0.150659i	$0.0481396\pi$
$762$	−3.12547			−0.113224
$763$			1.23056i			0.0445493i
$764$	−6.72402			−0.243266
$765$		0			0
$766$	15.2330			0.550390
$767$			8.58101i			0.309842i
$768$	0.763844			0.0275628
$769$	33.8727			1.22148			0.610741	−	0.791831i	$-0.290872\pi$
$769$	33.8727			1.22148			0.610741	+	0.791831i	$0.290872\pi$
$770$		0			0
$771$		−	4.83678i		−	0.174193i
$772$	−42.5767			−1.53237
$773$			6.63104i			0.238502i	0.992864	+	0.119251i	$0.0380493\pi$
$773$			6.63104i			0.238502i	−0.992864	+	0.119251i	$0.961951\pi$
$774$	−3.42043			−0.122945
$775$		0			0
$776$		−	15.5171i		−	0.557033i
$777$	8.88673			0.318810
$778$			6.16629i			0.221072i
$779$			26.0038i			0.931682i
$780$		0			0
$781$	1.85883			0.0665141
$782$	2.01035	+	3.39221i	0.0718898	+	0.121305i
$783$		−	4.87983i		−	0.174391i
$784$	−4.03843			−0.144230
$785$		0			0
$786$	6.24681			0.222816
$787$	−6.09846			−0.217387			−0.108693	−	0.994075i	$-0.534667\pi$
$787$	−6.09846			−0.217387			−0.108693	+	0.994075i	$0.534667\pi$
$788$	12.5967			0.448738
$789$			0.614515i			0.0218773i
$790$		0			0
$791$	13.0169			0.462829
$792$	7.25268			0.257713
$793$	2.87119			0.101959
$794$			11.7168i			0.415813i
$795$		0			0
$796$		−	40.8027i		−	1.44621i
$797$			56.0490i			1.98536i	0.120787	+	0.992678i	$0.461458\pi$
$797$			56.0490i			1.98536i	−0.120787	+	0.992678i	$0.538542\pi$
$798$			7.20617i			0.255096i
$799$	−14.6786	−	24.7683i	−0.519291	−	0.876239i
$800$		0			0
$801$	−0.0376087			−0.00132884
$802$	−17.1353			−0.605069
$803$			57.5545i			2.03105i
$804$		−	19.9136i		−	0.702300i
$805$		0			0
$806$			1.28140i			0.0451354i
$807$			24.1847i			0.851343i
$808$		−	25.9453i		−	0.912752i
$809$		−	1.98666i		−	0.0698473i	−0.999390	−	0.0349237i	$-0.988881\pi$
$809$		−	1.98666i		−	0.0698473i	0.999390	−	0.0349237i	$-0.0111188\pi$
$810$		0			0
$811$			4.99801i			0.175504i	0.996142	+	0.0877519i	$0.0279683\pi$
$811$			4.99801i			0.175504i	−0.996142	+	0.0877519i	$0.972032\pi$
$812$			19.7878i			0.694415i
$813$	25.6004			0.897844
$814$	−7.40450			−0.259528
$815$		0			0
$816$	8.97774	−	5.32054i	0.314284	−	0.186256i
$817$		−	41.4615i		−	1.45055i
$818$		−	8.47531i		−	0.296332i
$819$			3.19454i			0.111626i
$820$		0			0
$821$		−	12.0615i		−	0.420950i	−0.977599	−	0.210475i	$-0.932499\pi$
$821$		−	12.0615i		−	0.420950i	0.977599	−	0.210475i	$-0.0675010\pi$
$822$	5.16810			0.180258
$823$	−50.2102			−1.75022			−0.875108	−	0.483927i	$-0.839210\pi$
$823$	−50.2102			−1.75022			−0.875108	+	0.483927i	$0.839210\pi$
$824$	16.1604			0.562973
$825$		0			0
$826$		−	7.34116i		−	0.255432i
$827$	7.32302			0.254646			0.127323	−	0.991861i	$-0.459361\pi$
$827$	7.32302			0.254646			0.127323	+	0.991861i	$0.459361\pi$
$828$	3.29879			0.114641
$829$	5.98889			0.208003			0.104001	−	0.994577i	$-0.466835\pi$
$829$	5.98889			0.208003			0.104001	+	0.994577i	$0.466835\pi$
$830$		0			0
$831$	−1.53603			−0.0532842
$832$			3.43527i			0.119097i
$833$	5.65938	−	3.35396i	0.196086	−	0.116208i
$834$	11.3833			0.394172
$835$		0			0
$836$			40.9554i			1.41647i
$837$		−	1.84404i		−	0.0637394i
$838$	−3.93040			−0.135773
$839$		−	43.0621i		−	1.48667i	−0.668920	−	0.743335i	$-0.733243\pi$
$839$		−	43.0621i		−	1.48667i	0.668920	−	0.743335i	$-0.266757\pi$
$840$		0			0
$841$	5.18725			0.178871
$842$			0.198337i			0.00683515i
$843$	17.0111			0.585893
$844$			44.2618i			1.52355i
$845$		0			0
$846$	3.53115			0.121403
$847$	−8.53706			−0.293337
$848$		−	26.2112i		−	0.900097i
$849$	−9.57549			−0.328630
$850$		0			0
$851$	−7.22943			−0.247822
$852$			0.846461i			0.0289993i
$853$	−25.6869			−0.879503			−0.439751	−	0.898120i	$-0.644933\pi$
$853$	−25.6869			−0.879503			−0.439751	+	0.898120i	$0.644933\pi$
$854$	−2.45634			−0.0840541
$855$		0			0
$856$			17.0354i			0.582257i
$857$	40.9919			1.40026			0.700128	−	0.714017i	$-0.253126\pi$
$857$	40.9919			1.40026			0.700128	+	0.714017i	$0.253126\pi$
$858$		−	2.66172i		−	0.0908696i
$859$	−4.27475			−0.145853			−0.0729264	−	0.997337i	$-0.523234\pi$
$859$	−4.27475			−0.145853			−0.0729264	+	0.997337i	$0.523234\pi$
$860$		0			0
$861$		−	9.86203i		−	0.336097i
$862$	16.8652			0.574431
$863$		−	34.0512i		−	1.15912i	−0.814931	−	0.579559i	$-0.803225\pi$
$863$		−	34.0512i		−	1.15912i	0.814931	−	0.579559i	$-0.196775\pi$
$864$			5.06680i			0.172376i
$865$		0			0
$866$	11.6526			0.395970
$867$	−8.16248	+	14.9122i	−0.277212	+	0.506445i
$868$			7.47761i			0.253807i
$869$	61.5610			2.08831
$870$		0			0
$871$	−15.6880			−0.531566
$872$	1.00225			0.0339406
$873$	8.19523			0.277367
$874$		−	5.86228i		−	0.198295i
$875$		0			0
$876$	−26.2088			−0.885514
$877$	39.9948			1.35053			0.675264	−	0.737576i	$-0.264030\pi$
$877$	39.9948			1.35053			0.675264	+	0.737576i	$0.264030\pi$
$878$	7.79011			0.262904
$879$		−	12.5909i		−	0.424682i
$880$		0			0
$881$		−	0.223269i		−	0.00752212i	−0.999993	−	0.00376106i	$-0.998803\pi$
$881$		−	0.223269i		−	0.00752212i	0.999993	−	0.00376106i	$-0.00119719\pi$
$882$			0.806843i			0.0271678i
$883$			57.6604i			1.94043i	0.242252	+	0.970213i	$0.422114\pi$
$883$			57.6604i			1.94043i	−0.242252	+	0.970213i	$0.577886\pi$
$884$	−5.03847	−	8.50179i	−0.169462	−	0.285946i
$885$		0			0
$886$	−4.75342			−0.159694
$887$	38.8898			1.30579			0.652895	−	0.757448i	$-0.273554\pi$
$887$	38.8898			1.30579			0.652895	+	0.757448i	$0.273554\pi$
$888$		−	7.23795i		−	0.242890i
$889$			14.3685i			0.481903i
$890$		0			0
$891$			3.83044i			0.128324i
$892$			13.3160i			0.445854i
$893$			42.8036i			1.43237i
$894$		−	9.70246i		−	0.324499i
$895$		0			0
$896$		−	26.4970i		−	0.885203i
$897$		−	2.59879i		−	0.0867710i
$898$	−17.6256			−0.588175
$899$	−8.99861			−0.300120
$900$		0			0
$901$	21.7687	+	36.7319i	0.725220	+	1.22372i
$902$			8.21713i			0.273601i
$903$			15.7244i			0.523276i
$904$		−	10.6019i		−	0.352613i
$905$		0			0
$906$		−	9.74395i		−	0.323721i
$907$	−35.5315			−1.17981			−0.589903	−	0.807474i	$-0.700834\pi$
$907$	−35.5315			−1.17981			−0.589903	+	0.807474i	$0.700834\pi$
$908$	−37.6659			−1.24999
$909$	13.7028			0.454492
$910$		0			0
$911$		−	45.6538i		−	1.51258i	−0.654239	−	0.756288i	$-0.727011\pi$
$911$		−	45.6538i		−	1.51258i	0.654239	−	0.756288i	$-0.272989\pi$
$912$	−15.5150			−0.513752
$913$	8.49476			0.281136
$914$	2.82832			0.0935525
$915$		0			0
$916$	8.54167			0.282225
$917$		−	28.7179i		−	0.948349i
$918$	−1.06300	−	1.79367i	−0.0350841	−	0.0592001i
$919$	50.6856			1.67196			0.835981	−	0.548758i	$-0.184899\pi$
$919$	50.6856			1.67196			0.835981	+	0.548758i	$0.184899\pi$
$920$		0			0
$921$			4.24103i			0.139747i
$922$		−	19.0464i		−	0.627259i
$923$	0.666842			0.0219494
$924$		−	15.5325i		−	0.510981i
$925$		0			0
$926$	2.27056			0.0746153
$927$			8.53495i			0.280325i
$928$	24.7251			0.811642
$929$			25.8365i			0.847668i	0.905740	+	0.423834i	$0.139316\pi$
$929$			25.8365i			0.847668i	−0.905740	+	0.423834i	$0.860684\pi$
$930$		0			0
$931$	−9.78032			−0.320537
$932$	18.7246			0.613345
$933$			27.6793i			0.906180i
$934$	−12.3879			−0.405345
$935$		0			0
$936$	2.60185			0.0850442
$937$		−	8.65692i		−	0.282809i	−0.989952	−	0.141405i	$-0.954838\pi$
$937$		−	8.65692i		−	0.282809i	0.989952	−	0.141405i	$-0.0451619\pi$
$938$	13.4212			0.438219
$939$	7.92765			0.258709
$940$		0			0
$941$			44.7978i			1.46037i	0.683251	+	0.730184i	$0.260566\pi$
$941$			44.7978i			1.46037i	−0.683251	+	0.730184i	$0.739434\pi$
$942$	−3.86784			−0.126021
$943$			8.02285i			0.261260i
$944$	15.8056			0.514429
$945$		0			0
$946$		−	13.1017i		−	0.425974i
$947$	53.4086			1.73555			0.867774	−	0.496960i	$-0.165550\pi$
$947$	53.4086			1.73555			0.867774	+	0.496960i	$0.165550\pi$
$948$			28.0333i			0.910479i
$949$			20.6473i			0.670240i
$950$		0			0
$951$	6.63483			0.215149
$952$	9.25288	+	15.6131i	0.299887	+	0.506022i
$953$			25.4821i			0.825445i	0.910857	+	0.412722i	$0.135422\pi$
$953$			25.4821i			0.825445i	−0.910857	+	0.412722i	$0.864578\pi$
$954$	−5.23677			−0.169547
$955$		0			0
$956$	−28.4520			−0.920202
$957$	18.6919			0.604223
$958$	12.0081			0.387965
$959$		−	23.7589i		−	0.767213i
$960$		0			0
$961$	27.5995			0.890307
$962$	−2.65632			−0.0856430
$963$	−8.99707			−0.289927
$964$			26.4313i			0.851295i
$965$		0			0
$966$			2.22329i			0.0715333i
$967$		−	57.1051i		−	1.83638i	−0.396144	−	0.918188i	$-0.629652\pi$
$967$		−	57.1051i		−	1.83638i	0.396144	−	0.918188i	$-0.370348\pi$
$968$			6.95316i			0.223483i
$969$	21.7424	−	12.8854i	0.698467	−	0.413937i
$970$		0			0
$971$	−10.9022			−0.349867			−0.174934	−	0.984580i	$-0.555971\pi$
$971$	−10.9022			−0.349867			−0.174934	+	0.984580i	$0.555971\pi$
$972$	−1.74428			−0.0559478
$973$		−	52.3315i		−	1.67767i
$974$		−	4.82588i		−	0.154631i
$975$		0			0
$976$		−	5.28853i		−	0.169282i
$977$			14.8498i			0.475087i	0.971377	+	0.237544i	$0.0763423\pi$
$977$			14.8498i			0.475087i	−0.971377	+	0.237544i	$0.923658\pi$
$978$		−	2.58660i		−	0.0827102i
$979$		−	0.144058i		−	0.00460411i
$980$		0			0
$981$			0.529331i			0.0169002i
$982$		−	7.90473i		−	0.252250i
$983$	−2.90236			−0.0925707			−0.0462854	−	0.998928i	$-0.514738\pi$
$983$	−2.90236			−0.0925707			−0.0462854	+	0.998928i	$0.514738\pi$
$984$	−8.03231			−0.256061
$985$		0			0
$986$	−8.75283	+	5.18725i	−0.278747	+	0.165196i
$987$		−	16.2334i		−	0.516716i
$988$			14.6925i			0.467430i
$989$		−	12.7920i		−	0.406761i
$990$		0			0
$991$		−	56.8848i		−	1.80700i	−0.428583	−	0.903502i	$-0.640987\pi$
$991$		−	56.8848i		−	1.80700i	0.428583	−	0.903502i	$-0.359013\pi$
$992$	9.34339			0.296653
$993$	9.36993			0.297346
$994$	−0.570491			−0.0180949
$995$		0			0
$996$			3.86829i			0.122571i
$997$	−52.0909			−1.64974			−0.824868	−	0.565325i	$-0.808751\pi$
$997$	−52.0909			−1.64974			−0.824868	+	0.565325i	$0.808751\pi$
$998$	−7.04923			−0.223140
$999$	3.82266			0.120944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1275.2.d.i.424.6		12
5.2	odd	4		1275.2.g.e.526.8	yes	12
5.3	odd	4		1275.2.g.f.526.5	yes	12
5.4	even	2		1275.2.d.j.424.7		12
17.16	even	2		1275.2.d.j.424.6		12
85.33	odd	4		1275.2.g.f.526.6	yes	12
85.67	odd	4		1275.2.g.e.526.7	✓	12
85.84	even	2	inner	1275.2.d.i.424.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1275.2.d.i.424.6		12	1.1	even	1	trivial
1275.2.d.i.424.7		12	85.84	even	2	inner
1275.2.d.j.424.6		12	17.16	even	2
1275.2.d.j.424.7		12	5.4	even	2
1275.2.g.e.526.7	✓	12	85.67	odd	4
1275.2.g.e.526.8	yes	12	5.2	odd	4
1275.2.g.f.526.5	yes	12	5.3	odd	4
1275.2.g.f.526.6	yes	12	85.33	odd	4

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:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1275.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.505687i q^{2} -1.00000 q^{3} +1.74428 q^{4} +0.505687i q^{6} +2.32475 q^{7} -1.89343i q^{8} +1.00000 q^{9} +3.83044i q^{11} -1.74428 q^{12} +1.37414i q^{13} -1.17560i q^{14} +2.53108 q^{16} +(-3.54700 + 2.10209i) q^{17} -0.505687i q^{18} +6.12980 q^{19} -2.32475 q^{21} +1.93700 q^{22} +1.89121 q^{23} +1.89343i q^{24} +0.694887 q^{26} -1.00000 q^{27} +4.05502 q^{28} +4.87983i q^{29} +1.84404i q^{31} -5.06680i q^{32} -3.83044i q^{33} +(1.06300 + 1.79367i) q^{34} +1.74428 q^{36} -3.82266 q^{37} -3.09976i q^{38} -1.37414i q^{39} +4.24219i q^{41} +1.17560i q^{42} -6.76392i q^{43} +6.68136i q^{44} -0.956358i q^{46} +6.98287i q^{47} -2.53108 q^{48} -1.59554 q^{49} +(3.54700 - 2.10209i) q^{51} +2.39689i q^{52} -10.3558i q^{53} +0.505687i q^{54} -4.40176i q^{56} -6.12980 q^{57} +2.46767 q^{58} +6.24463 q^{59} -2.08944i q^{61} +0.932508 q^{62} +2.32475 q^{63} +2.49994 q^{64} -1.93700 q^{66} +11.4165i q^{67} +(-6.18697 + 3.66663i) q^{68} -1.89121 q^{69} -0.485278i q^{71} -1.89343i q^{72} +15.0256 q^{73} +1.93307i q^{74} +10.6921 q^{76} +8.90481i q^{77} -0.694887 q^{78} -16.0715i q^{79} +1.00000 q^{81} +2.14522 q^{82} -2.21770i q^{83} -4.05502 q^{84} -3.42043 q^{86} -4.87983i q^{87} +7.25268 q^{88} -0.0376087 q^{89} +3.19454i q^{91} +3.29879 q^{92} -1.84404i q^{93} +3.53115 q^{94} +5.06680i q^{96} +8.19523 q^{97} +0.806843i q^{98} +3.83044i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} - 16 q^{4} + 12 q^{9} + 16 q^{12} + 32 q^{16} - 6 q^{17} + 4 q^{19} + 12 q^{22} - 16 q^{23} - 36 q^{26} - 12 q^{27} - 36 q^{28} + 24 q^{34} - 16 q^{36} - 4 q^{37} - 32 q^{48} + 16 q^{49}+ \cdots - 16 q^{97}+O(q^{100}) \) 12 * q - 12 * q^3 - 16 * q^4 + 12 * q^9 + 16 * q^12 + 32 * q^16 - 6 * q^17 + 4 * q^19 + 12 * q^22 - 16 * q^23 - 36 * q^26 - 12 * q^27 - 36 * q^28 + 24 * q^34 - 16 * q^36 - 4 * q^37 - 32 * q^48 + 16 * q^49 + 6 * q^51 - 4 * q^57 + 4 * q^58 - 32 * q^59 - 56 * q^62 - 56 * q^64 - 12 * q^66 - 20 * q^68 + 16 * q^69 + 44 * q^73 + 64 * q^76 + 36 * q^78 + 12 * q^81 - 40 * q^82 + 36 * q^84 + 20 * q^86 - 8 * q^88 - 4 * q^89 - 40 * q^94 - 16 * q^97

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