LMFDB - Embedded newform 1710.2.d.c.1369.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1369,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1710.1369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.c.1369.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} -1.58579i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} -1.58579i q^{7} +1.00000i q^{8} +(-2.12132 - 0.707107i) q^{10} -1.41421 q^{11} +0.171573i q^{13} -1.58579 q^{14} +1.00000 q^{16} +1.00000i q^{17} +1.00000 q^{19} +(-0.707107 + 2.12132i) q^{20} +1.41421i q^{22} -9.24264i q^{23} +(-4.00000 - 3.00000i) q^{25} +0.171573 q^{26} +1.58579i q^{28} -5.82843 q^{29} -2.24264 q^{31} -1.00000i q^{32} +1.00000 q^{34} +(-3.36396 - 1.12132i) q^{35} -8.48528i q^{37} -1.00000i q^{38} +(2.12132 + 0.707107i) q^{40} -4.24264 q^{41} +10.2426i q^{43} +1.41421 q^{44} -9.24264 q^{46} +4.48528 q^{49} +(-3.00000 + 4.00000i) q^{50} -0.171573i q^{52} +11.4853i q^{53} +(-1.00000 + 3.00000i) q^{55} +1.58579 q^{56} +5.82843i q^{58} -12.8995 q^{59} +5.75736 q^{61} +2.24264i q^{62} -1.00000 q^{64} +(0.363961 + 0.121320i) q^{65} -13.2426i q^{67} -1.00000i q^{68} +(-1.12132 + 3.36396i) q^{70} +10.5858 q^{71} -5.48528i q^{73} -8.48528 q^{74} -1.00000 q^{76} +2.24264i q^{77} -10.4853 q^{79} +(0.707107 - 2.12132i) q^{80} +4.24264i q^{82} +2.48528i q^{83} +(2.12132 + 0.707107i) q^{85} +10.2426 q^{86} -1.41421i q^{88} -7.07107 q^{89} +0.272078 q^{91} +9.24264i q^{92} +(0.707107 - 2.12132i) q^{95} +11.6569i q^{97} -4.48528i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4}+O(q^{10}) $ 4 * q - 4 * q^4	$ 4 q - 4 q^{4} - 12 q^{14} + 4 q^{16} + 4 q^{19} - 16 q^{25} + 12 q^{26} - 12 q^{29} + 8 q^{31} + 4 q^{34} + 12 q^{35} - 20 q^{46} - 16 q^{49} - 12 q^{50} - 4 q^{55} + 12 q^{56} - 12 q^{59} + 40 q^{61} - 4 q^{64} - 24 q^{65} + 4 q^{70} + 48 q^{71} - 4 q^{76} - 8 q^{79} + 24 q^{86} + 52 q^{91}+O(q^{100}) $ 4 * q - 4 * q^4 - 12 * q^14 + 4 * q^16 + 4 * q^19 - 16 * q^25 + 12 * q^26 - 12 * q^29 + 8 * q^31 + 4 * q^34 + 12 * q^35 - 20 * q^46 - 16 * q^49 - 12 * q^50 - 4 * q^55 + 12 * q^56 - 12 * q^59 + 40 * q^61 - 4 * q^64 - 24 * q^65 + 4 * q^70 + 48 * q^71 - 4 * q^76 - 8 * q^79 + 24 * q^86 + 52 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$6$		0			0
$7$		−	1.58579i		−	0.599371i	−0.954038	−	0.299685i	$-0.903118\pi$
$7$		−	1.58579i		−	0.599371i	0.954038	−	0.299685i	$-0.0968817\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.12132	−	0.707107i	−0.670820	−	0.223607i
$11$	−1.41421			−0.426401			−0.213201	−	0.977008i	$-0.568389\pi$
$11$	−1.41421			−0.426401			−0.213201	+	0.977008i	$0.568389\pi$
$12$		0			0
$13$			0.171573i			0.0475858i	0.999717	+	0.0237929i	$0.00757422\pi$
$13$			0.171573i			0.0475858i	−0.999717	+	0.0237929i	$0.992426\pi$
$14$	−1.58579			−0.423819
$15$		0			0
$16$	1.00000			0.250000
$17$			1.00000i			0.242536i	0.992620	+	0.121268i	$0.0386960\pi$
$17$			1.00000i			0.242536i	−0.992620	+	0.121268i	$0.961304\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−0.707107	+	2.12132i	−0.158114	+	0.474342i
$21$		0			0
$22$			1.41421i			0.301511i
$23$		−	9.24264i		−	1.92722i	−0.267305	−	0.963612i	$-0.586133\pi$
$23$		−	9.24264i		−	1.92722i	0.267305	−	0.963612i	$-0.413867\pi$
$24$		0			0
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$	0.171573			0.0336482
$27$		0			0
$28$			1.58579i			0.299685i
$29$	−5.82843			−1.08231			−0.541156	−	0.840922i	$-0.682013\pi$
$29$	−5.82843			−1.08231			−0.541156	+	0.840922i	$0.682013\pi$
$30$		0			0
$31$	−2.24264			−0.402790			−0.201395	−	0.979510i	$-0.564548\pi$
$31$	−2.24264			−0.402790			−0.201395	+	0.979510i	$0.564548\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	1.00000			0.171499
$35$	−3.36396	−	1.12132i	−0.568613	−	0.189538i
$36$		0			0
$37$		−	8.48528i		−	1.39497i	−0.716599	−	0.697486i	$-0.754302\pi$
$37$		−	8.48528i		−	1.39497i	0.716599	−	0.697486i	$-0.245698\pi$
$38$		−	1.00000i		−	0.162221i
$39$		0			0
$40$	2.12132	+	0.707107i	0.335410	+	0.111803i
$41$	−4.24264			−0.662589			−0.331295	−	0.943527i	$-0.607485\pi$
$41$	−4.24264			−0.662589			−0.331295	+	0.943527i	$0.607485\pi$
$42$		0			0
$43$			10.2426i			1.56199i	0.624538	+	0.780994i	$0.285287\pi$
$43$			10.2426i			1.56199i	−0.624538	+	0.780994i	$0.714713\pi$
$44$	1.41421			0.213201
$45$		0			0
$46$	−9.24264			−1.36275
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$	4.48528			0.640754
$50$	−3.00000	+	4.00000i	−0.424264	+	0.565685i
$51$		0			0
$52$		−	0.171573i		−	0.0237929i
$53$			11.4853i			1.57762i	0.614634	+	0.788812i	$0.289304\pi$
$53$			11.4853i			1.57762i	−0.614634	+	0.788812i	$0.710696\pi$
$54$		0			0
$55$	−1.00000	+	3.00000i	−0.134840	+	0.404520i
$56$	1.58579			0.211910
$57$		0			0
$58$			5.82843i			0.765310i
$59$	−12.8995			−1.67937			−0.839686	−	0.543073i	$-0.817261\pi$
$59$	−12.8995			−1.67937			−0.839686	+	0.543073i	$0.817261\pi$
$60$		0			0
$61$	5.75736			0.737154			0.368577	−	0.929597i	$-0.379845\pi$
$61$	5.75736			0.737154			0.368577	+	0.929597i	$0.379845\pi$
$62$			2.24264i			0.284816i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.363961	+	0.121320i	0.0451438	+	0.0150479i
$66$		0			0
$67$		−	13.2426i		−	1.61785i	−0.587915	−	0.808923i	$-0.700051\pi$
$67$		−	13.2426i		−	1.61785i	0.587915	−	0.808923i	$-0.299949\pi$
$68$		−	1.00000i		−	0.121268i
$69$		0			0
$70$	−1.12132	+	3.36396i	−0.134023	+	0.402070i
$71$	10.5858			1.25630			0.628151	−	0.778092i	$-0.283812\pi$
$71$	10.5858			1.25630			0.628151	+	0.778092i	$0.283812\pi$
$72$		0			0
$73$		−	5.48528i		−	0.642004i	−0.947079	−	0.321002i	$-0.895980\pi$
$73$		−	5.48528i		−	0.642004i	0.947079	−	0.321002i	$-0.104020\pi$
$74$	−8.48528			−0.986394
$75$		0			0
$76$	−1.00000			−0.114708
$77$			2.24264i			0.255573i
$78$		0			0
$79$	−10.4853			−1.17969			−0.589843	−	0.807518i	$-0.700810\pi$
$79$	−10.4853			−1.17969			−0.589843	+	0.807518i	$0.700810\pi$
$80$	0.707107	−	2.12132i	0.0790569	−	0.237171i
$81$		0			0
$82$			4.24264i			0.468521i
$83$			2.48528i			0.272795i	0.990654	+	0.136398i	$0.0435524\pi$
$83$			2.48528i			0.272795i	−0.990654	+	0.136398i	$0.956448\pi$
$84$		0			0
$85$	2.12132	+	0.707107i	0.230089	+	0.0766965i
$86$	10.2426			1.10449
$87$		0			0
$88$		−	1.41421i		−	0.150756i
$89$	−7.07107			−0.749532			−0.374766	−	0.927119i	$-0.622277\pi$
$89$	−7.07107			−0.749532			−0.374766	+	0.927119i	$0.622277\pi$
$90$		0			0
$91$	0.272078			0.0285215
$92$			9.24264i			0.963612i
$93$		0			0
$94$		0			0
$95$	0.707107	−	2.12132i	0.0725476	−	0.217643i
$96$		0			0
$97$			11.6569i			1.18357i	0.806094	+	0.591787i	$0.201577\pi$
$97$			11.6569i			1.18357i	−0.806094	+	0.591787i	$0.798423\pi$
$98$		−	4.48528i		−	0.453082i
$99$		0			0
$100$	4.00000	+	3.00000i	0.400000	+	0.300000i
$101$	1.07107			0.106575			0.0532876	−	0.998579i	$-0.483030\pi$
$101$	1.07107			0.106575			0.0532876	+	0.998579i	$0.483030\pi$
$102$		0			0
$103$		−	4.24264i		−	0.418040i	−0.977911	−	0.209020i	$-0.932973\pi$
$103$		−	4.24264i		−	0.418040i	0.977911	−	0.209020i	$-0.0670273\pi$
$104$	−0.171573			−0.0168241
$105$		0			0
$106$	11.4853			1.11555
$107$		−	5.72792i		−	0.553739i	−0.960908	−	0.276870i	$-0.910703\pi$
$107$		−	5.72792i		−	0.553739i	0.960908	−	0.276870i	$-0.0892970\pi$
$108$		0			0
$109$	−15.9706			−1.52970			−0.764851	−	0.644207i	$-0.777188\pi$
$109$	−15.9706			−1.52970			−0.764851	+	0.644207i	$0.777188\pi$
$110$	3.00000	+	1.00000i	0.286039	+	0.0953463i
$111$		0			0
$112$		−	1.58579i		−	0.149843i
$113$			1.75736i			0.165318i	0.996578	+	0.0826592i	$0.0263413\pi$
$113$			1.75736i			0.165318i	−0.996578	+	0.0826592i	$0.973659\pi$
$114$		0			0
$115$	−19.6066	−	6.53553i	−1.82833	−	0.609442i
$116$	5.82843			0.541156
$117$		0			0
$118$			12.8995i			1.18749i
$119$	1.58579			0.145369
$120$		0			0
$121$	−9.00000			−0.818182
$122$		−	5.75736i		−	0.521247i
$123$		0			0
$124$	2.24264			0.201395
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$		0			0
$127$		−	14.4853i		−	1.28536i	−0.766134	−	0.642680i	$-0.777822\pi$
$127$		−	14.4853i		−	1.28536i	0.766134	−	0.642680i	$-0.222178\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	0.121320	−	0.363961i	0.0106405	−	0.0319215i
$131$	−16.9706			−1.48272			−0.741362	−	0.671105i	$-0.765820\pi$
$131$	−16.9706			−1.48272			−0.741362	+	0.671105i	$0.765820\pi$
$132$		0			0
$133$		−	1.58579i		−	0.137505i
$134$	−13.2426			−1.14399
$135$		0			0
$136$	−1.00000			−0.0857493
$137$			13.0000i			1.11066i	0.831628	+	0.555332i	$0.187409\pi$
$137$			13.0000i			1.11066i	−0.831628	+	0.555332i	$0.812591\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$	3.36396	+	1.12132i	0.284307	+	0.0947689i
$141$		0			0
$142$		−	10.5858i		−	0.888339i
$143$		−	0.242641i		−	0.0202906i
$144$		0			0
$145$	−4.12132	+	12.3640i	−0.342257	+	1.02677i
$146$	−5.48528			−0.453965
$147$		0			0
$148$			8.48528i			0.697486i
$149$	6.34315			0.519651			0.259825	−	0.965656i	$-0.416335\pi$
$149$	6.34315			0.519651			0.259825	+	0.965656i	$0.416335\pi$
$150$		0			0
$151$	6.48528			0.527765			0.263882	−	0.964555i	$-0.414997\pi$
$151$	6.48528			0.527765			0.263882	+	0.964555i	$0.414997\pi$
$152$			1.00000i			0.0811107i
$153$		0			0
$154$	2.24264			0.180717
$155$	−1.58579	+	4.75736i	−0.127373	+	0.382120i
$156$		0			0
$157$		−	0.343146i		−	0.0273860i	−0.999906	−	0.0136930i	$-0.995641\pi$
$157$		−	0.343146i		−	0.0273860i	0.999906	−	0.0136930i	$-0.00435876\pi$
$158$			10.4853i			0.834164i
$159$		0			0
$160$	−2.12132	−	0.707107i	−0.167705	−	0.0559017i
$161$	−14.6569			−1.15512
$162$		0			0
$163$		−	1.75736i		−	0.137647i	−0.997629	−	0.0688235i	$-0.978075\pi$
$163$		−	1.75736i		−	0.137647i	0.997629	−	0.0688235i	$-0.0219245\pi$
$164$	4.24264			0.331295
$165$		0			0
$166$	2.48528			0.192895
$167$		−	9.75736i		−	0.755047i	−0.926000	−	0.377524i	$-0.876776\pi$
$167$		−	9.75736i		−	0.755047i	0.926000	−	0.377524i	$-0.123224\pi$
$168$		0			0
$169$	12.9706			0.997736
$170$	0.707107	−	2.12132i	0.0542326	−	0.162698i
$171$		0			0
$172$		−	10.2426i		−	0.780994i
$173$			16.4853i			1.25335i	0.779280	+	0.626676i	$0.215585\pi$
$173$			16.4853i			1.25335i	−0.779280	+	0.626676i	$0.784415\pi$
$174$		0			0
$175$	−4.75736	+	6.34315i	−0.359623	+	0.479497i
$176$	−1.41421			−0.106600
$177$		0			0
$178$			7.07107i			0.529999i
$179$	−0.343146			−0.0256479			−0.0128240	−	0.999918i	$-0.504082\pi$
$179$	−0.343146			−0.0256479			−0.0128240	+	0.999918i	$0.504082\pi$
$180$		0			0
$181$	8.48528			0.630706			0.315353	−	0.948974i	$-0.397877\pi$
$181$	8.48528			0.630706			0.315353	+	0.948974i	$0.397877\pi$
$182$		−	0.272078i		−	0.0201678i
$183$		0			0
$184$	9.24264			0.681377
$185$	−18.0000	−	6.00000i	−1.32339	−	0.441129i
$186$		0			0
$187$		−	1.41421i		−	0.103418i
$188$		0			0
$189$		0			0
$190$	−2.12132	−	0.707107i	−0.153897	−	0.0512989i
$191$	18.5563			1.34269			0.671345	−	0.741145i	$-0.265717\pi$
$191$	18.5563			1.34269			0.671345	+	0.741145i	$0.265717\pi$
$192$		0			0
$193$		−	11.6569i		−	0.839079i	−0.907737	−	0.419539i	$-0.862192\pi$
$193$		−	11.6569i		−	0.839079i	0.907737	−	0.419539i	$-0.137808\pi$
$194$	11.6569			0.836913
$195$		0			0
$196$	−4.48528			−0.320377
$197$		−	20.2426i		−	1.44223i	−0.692816	−	0.721114i	$-0.743630\pi$
$197$		−	20.2426i		−	1.44223i	0.692816	−	0.721114i	$-0.256370\pi$
$198$		0			0
$199$	−0.757359			−0.0536878			−0.0268439	−	0.999640i	$-0.508546\pi$
$199$	−0.757359			−0.0536878			−0.0268439	+	0.999640i	$0.508546\pi$
$200$	3.00000	−	4.00000i	0.212132	−	0.282843i
$201$		0			0
$202$		−	1.07107i		−	0.0753601i
$203$			9.24264i			0.648706i
$204$		0			0
$205$	−3.00000	+	9.00000i	−0.209529	+	0.628587i
$206$	−4.24264			−0.295599
$207$		0			0
$208$			0.171573i			0.0118964i
$209$	−1.41421			−0.0978232
$210$		0			0
$211$	5.72792			0.394326			0.197163	−	0.980371i	$-0.436827\pi$
$211$	5.72792			0.394326			0.197163	+	0.980371i	$0.436827\pi$
$212$		−	11.4853i		−	0.788812i
$213$		0			0
$214$	−5.72792			−0.391553
$215$	21.7279	+	7.24264i	1.48183	+	0.493944i
$216$		0			0
$217$			3.55635i			0.241421i
$218$			15.9706i			1.08166i
$219$		0			0
$220$	1.00000	−	3.00000i	0.0674200	−	0.202260i
$221$	−0.171573			−0.0115412
$222$		0			0
$223$		−	20.8284i		−	1.39477i	−0.716694	−	0.697387i	$-0.754346\pi$
$223$		−	20.8284i		−	1.39477i	0.716694	−	0.697387i	$-0.245654\pi$
$224$	−1.58579			−0.105955
$225$		0			0
$226$	1.75736			0.116898
$227$		−	25.2426i		−	1.67541i	−0.546121	−	0.837706i	$-0.683896\pi$
$227$		−	25.2426i		−	1.67541i	0.546121	−	0.837706i	$-0.316104\pi$
$228$		0			0
$229$	18.9706			1.25361			0.626805	−	0.779176i	$-0.284362\pi$
$229$	18.9706			1.25361			0.626805	+	0.779176i	$0.284362\pi$
$230$	−6.53553	+	19.6066i	−0.430940	+	1.29282i
$231$		0			0
$232$		−	5.82843i		−	0.382655i
$233$		−	8.97056i		−	0.587681i	−0.955854	−	0.293841i	$-0.905067\pi$
$233$		−	8.97056i		−	0.587681i	0.955854	−	0.293841i	$-0.0949335\pi$
$234$		0			0
$235$		0			0
$236$	12.8995			0.839686
$237$		0			0
$238$		−	1.58579i		−	0.102791i
$239$	12.8995			0.834399			0.417199	−	0.908815i	$-0.363012\pi$
$239$	12.8995			0.834399			0.417199	+	0.908815i	$0.363012\pi$
$240$		0			0
$241$	−24.9706			−1.60850			−0.804248	−	0.594294i	$-0.797431\pi$
$241$	−24.9706			−1.60850			−0.804248	+	0.594294i	$0.797431\pi$
$242$			9.00000i			0.578542i
$243$		0			0
$244$	−5.75736			−0.368577
$245$	3.17157	−	9.51472i	0.202624	−	0.607873i
$246$		0			0
$247$			0.171573i			0.0109169i
$248$		−	2.24264i		−	0.142408i
$249$		0			0
$250$	6.36396	+	9.19239i	0.402492	+	0.581378i
$251$	27.5563			1.73934			0.869671	−	0.493632i	$-0.164331\pi$
$251$	27.5563			1.73934			0.869671	+	0.493632i	$0.164331\pi$
$252$		0			0
$253$			13.0711i			0.821771i
$254$	−14.4853			−0.908887
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	4.72792i		−	0.294920i	−0.989068	−	0.147460i	$-0.952890\pi$
$257$		−	4.72792i		−	0.294920i	0.989068	−	0.147460i	$-0.0471097\pi$
$258$		0			0
$259$	−13.4558			−0.836105
$260$	−0.363961	−	0.121320i	−0.0225719	−	0.00752397i
$261$		0			0
$262$			16.9706i			1.04844i
$263$		−	6.97056i		−	0.429823i	−0.976633	−	0.214912i	$-0.931054\pi$
$263$		−	6.97056i		−	0.429823i	0.976633	−	0.214912i	$-0.0689464\pi$
$264$		0			0
$265$	24.3640	+	8.12132i	1.49667	+	0.498889i
$266$	−1.58579			−0.0972308
$267$		0			0
$268$			13.2426i			0.808923i
$269$	28.6274			1.74544			0.872722	−	0.488217i	$-0.162353\pi$
$269$	28.6274			1.74544			0.872722	+	0.488217i	$0.162353\pi$
$270$		0			0
$271$	−18.7574			−1.13943			−0.569714	−	0.821843i	$-0.692946\pi$
$271$	−18.7574			−1.13943			−0.569714	+	0.821843i	$0.692946\pi$
$272$			1.00000i			0.0606339i
$273$		0			0
$274$	13.0000			0.785359
$275$	5.65685	+	4.24264i	0.341121	+	0.255841i
$276$		0			0
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		−	12.0000i		−	0.719712i
$279$		0			0
$280$	1.12132	−	3.36396i	0.0670117	−	0.201035i
$281$	4.24264			0.253095			0.126547	−	0.991961i	$-0.459610\pi$
$281$	4.24264			0.253095			0.126547	+	0.991961i	$0.459610\pi$
$282$		0			0
$283$			3.85786i			0.229326i	0.993404	+	0.114663i	$0.0365789\pi$
$283$			3.85786i			0.229326i	−0.993404	+	0.114663i	$0.963421\pi$
$284$	−10.5858			−0.628151
$285$		0			0
$286$	−0.242641			−0.0143476
$287$			6.72792i			0.397137i
$288$		0			0
$289$	16.0000			0.941176
$290$	12.3640	+	4.12132i	0.726037	+	0.242012i
$291$		0			0
$292$			5.48528i			0.321002i
$293$		−	11.4853i		−	0.670977i	−0.942044	−	0.335489i	$-0.891099\pi$
$293$		−	11.4853i		−	0.670977i	0.942044	−	0.335489i	$-0.108901\pi$
$294$		0			0
$295$	−9.12132	+	27.3640i	−0.531064	+	1.59319i
$296$	8.48528			0.493197
$297$		0			0
$298$		−	6.34315i		−	0.367449i
$299$	1.58579			0.0917084
$300$		0			0
$301$	16.2426			0.936210
$302$		−	6.48528i		−	0.373186i
$303$		0			0
$304$	1.00000			0.0573539
$305$	4.07107	−	12.2132i	0.233109	−	0.699326i
$306$		0			0
$307$			6.34315i			0.362022i	0.983481	+	0.181011i	$0.0579370\pi$
$307$			6.34315i			0.362022i	−0.983481	+	0.181011i	$0.942063\pi$
$308$		−	2.24264i		−	0.127786i
$309$		0			0
$310$	4.75736	+	1.58579i	0.270200	+	0.0900666i
$311$	13.2426			0.750921			0.375461	−	0.926838i	$-0.377485\pi$
$311$	13.2426			0.750921			0.375461	+	0.926838i	$0.377485\pi$
$312$		0			0
$313$			25.9706i			1.46794i	0.679180	+	0.733971i	$0.262335\pi$
$313$			25.9706i			1.46794i	−0.679180	+	0.733971i	$0.737665\pi$
$314$	−0.343146			−0.0193648
$315$		0			0
$316$	10.4853			0.589843
$317$			7.48528i			0.420415i	0.977657	+	0.210208i	$0.0674140\pi$
$317$			7.48528i			0.420415i	−0.977657	+	0.210208i	$0.932586\pi$
$318$		0			0
$319$	8.24264			0.461499
$320$	−0.707107	+	2.12132i	−0.0395285	+	0.118585i
$321$		0			0
$322$			14.6569i			0.816795i
$323$			1.00000i			0.0556415i
$324$		0			0
$325$	0.514719	−	0.686292i	0.0285515	−	0.0380686i
$326$	−1.75736			−0.0973311
$327$		0			0
$328$		−	4.24264i		−	0.234261i
$329$		0			0
$330$		0			0
$331$	−10.7574			−0.591278			−0.295639	−	0.955300i	$-0.595533\pi$
$331$	−10.7574			−0.591278			−0.295639	+	0.955300i	$0.595533\pi$
$332$		−	2.48528i		−	0.136398i
$333$		0			0
$334$	−9.75736			−0.533899
$335$	−28.0919	−	9.36396i	−1.53482	−	0.511608i
$336$		0			0
$337$		−	33.8995i		−	1.84662i	−0.384052	−	0.923312i	$-0.625472\pi$
$337$		−	33.8995i		−	1.84662i	0.384052	−	0.923312i	$-0.374528\pi$
$338$		−	12.9706i		−	0.705506i
$339$		0			0
$340$	−2.12132	−	0.707107i	−0.115045	−	0.0383482i
$341$	3.17157			0.171750
$342$		0			0
$343$		−	18.2132i		−	0.983421i
$344$	−10.2426			−0.552246
$345$		0			0
$346$	16.4853			0.886254
$347$		−	22.4853i		−	1.20707i	−0.797335	−	0.603537i	$-0.793758\pi$
$347$		−	22.4853i		−	1.20707i	0.797335	−	0.603537i	$-0.206242\pi$
$348$		0			0
$349$	−6.00000			−0.321173			−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000			−0.321173			−0.160586	+	0.987022i	$0.551338\pi$
$350$	6.34315	+	4.75736i	0.339055	+	0.254292i
$351$		0			0
$352$			1.41421i			0.0753778i
$353$			19.4853i			1.03710i	0.855048	+	0.518548i	$0.173527\pi$
$353$			19.4853i			1.03710i	−0.855048	+	0.518548i	$0.826473\pi$
$354$		0			0
$355$	7.48528	−	22.4558i	0.397277	−	1.19183i
$356$	7.07107			0.374766
$357$		0			0
$358$			0.343146i			0.0181358i
$359$	−31.2426			−1.64892			−0.824462	−	0.565918i	$-0.808522\pi$
$359$	−31.2426			−1.64892			−0.824462	+	0.565918i	$0.808522\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	8.48528i		−	0.445976i
$363$		0			0
$364$	−0.272078			−0.0142608
$365$	−11.6360	−	3.87868i	−0.609058	−	0.203019i
$366$		0			0
$367$		−	25.4558i		−	1.32878i	−0.747384	−	0.664392i	$-0.768691\pi$
$367$		−	25.4558i		−	1.32878i	0.747384	−	0.664392i	$-0.231309\pi$
$368$		−	9.24264i		−	0.481806i
$369$		0			0
$370$	−6.00000	+	18.0000i	−0.311925	+	0.935775i
$371$	18.2132			0.945582
$372$		0			0
$373$			9.00000i			0.466002i	0.972476	+	0.233001i	$0.0748546\pi$
$373$			9.00000i			0.466002i	−0.972476	+	0.233001i	$0.925145\pi$
$374$	−1.41421			−0.0731272
$375$		0			0
$376$		0			0
$377$		−	1.00000i		−	0.0515026i
$378$		0			0
$379$	−2.75736			−0.141636			−0.0708180	−	0.997489i	$-0.522561\pi$
$379$	−2.75736			−0.141636			−0.0708180	+	0.997489i	$0.522561\pi$
$380$	−0.707107	+	2.12132i	−0.0362738	+	0.108821i
$381$		0			0
$382$		−	18.5563i		−	0.949425i
$383$		−	3.75736i		−	0.191992i	−0.995382	−	0.0959960i	$-0.969396\pi$
$383$		−	3.75736i		−	0.191992i	0.995382	−	0.0959960i	$-0.0306036\pi$
$384$		0			0
$385$	4.75736	+	1.58579i	0.242457	+	0.0808192i
$386$	−11.6569			−0.593318
$387$		0			0
$388$		−	11.6569i		−	0.591787i
$389$	37.0711			1.87958			0.939789	−	0.341756i	$-0.111021\pi$
$389$	37.0711			1.87958			0.939789	+	0.341756i	$0.111021\pi$
$390$		0			0
$391$	9.24264			0.467420
$392$			4.48528i			0.226541i
$393$		0			0
$394$	−20.2426			−1.01981
$395$	−7.41421	+	22.2426i	−0.373050	+	1.11915i
$396$		0			0
$397$		−	24.0000i		−	1.20453i	−0.798298	−	0.602263i	$-0.794266\pi$
$397$		−	24.0000i		−	1.20453i	0.798298	−	0.602263i	$-0.205734\pi$
$398$			0.757359i			0.0379630i
$399$		0			0
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$	22.5858			1.12788			0.563940	−	0.825816i	$-0.309285\pi$
$401$	22.5858			1.12788			0.563940	+	0.825816i	$0.309285\pi$
$402$		0			0
$403$		−	0.384776i		−	0.0191671i
$404$	−1.07107			−0.0532876
$405$		0			0
$406$	9.24264			0.458705
$407$			12.0000i			0.594818i
$408$		0			0
$409$	17.2132			0.851138			0.425569	−	0.904926i	$-0.360074\pi$
$409$	17.2132			0.851138			0.425569	+	0.904926i	$0.360074\pi$
$410$	9.00000	+	3.00000i	0.444478	+	0.148159i
$411$		0			0
$412$			4.24264i			0.209020i
$413$			20.4558i			1.00657i
$414$		0			0
$415$	5.27208	+	1.75736i	0.258796	+	0.0862654i
$416$	0.171573			0.00841205
$417$		0			0
$418$			1.41421i			0.0691714i
$419$	16.5858			0.810269			0.405134	−	0.914257i	$-0.367225\pi$
$419$	16.5858			0.810269			0.405134	+	0.914257i	$0.367225\pi$
$420$		0			0
$421$	2.51472			0.122560			0.0612799	−	0.998121i	$-0.480482\pi$
$421$	2.51472			0.122560			0.0612799	+	0.998121i	$0.480482\pi$
$422$		−	5.72792i		−	0.278831i
$423$		0			0
$424$	−11.4853			−0.557775
$425$	3.00000	−	4.00000i	0.145521	−	0.194029i
$426$		0			0
$427$		−	9.12994i		−	0.441829i
$428$			5.72792i			0.276870i
$429$		0			0
$430$	7.24264	−	21.7279i	0.349271	−	1.04781i
$431$	−30.3848			−1.46358			−0.731792	−	0.681528i	$-0.761316\pi$
$431$	−30.3848			−1.46358			−0.731792	+	0.681528i	$0.761316\pi$
$432$		0			0
$433$			21.5563i			1.03593i	0.855401	+	0.517966i	$0.173311\pi$
$433$			21.5563i			1.03593i	−0.855401	+	0.517966i	$0.826689\pi$
$434$	3.55635			0.170710
$435$		0			0
$436$	15.9706			0.764851
$437$		−	9.24264i		−	0.442135i
$438$		0			0
$439$	14.2426			0.679764			0.339882	−	0.940468i	$-0.389613\pi$
$439$	14.2426			0.679764			0.339882	+	0.940468i	$0.389613\pi$
$440$	−3.00000	−	1.00000i	−0.143019	−	0.0476731i
$441$		0			0
$442$			0.171573i			0.00816089i
$443$			4.24264i			0.201574i	0.994908	+	0.100787i	$0.0321361\pi$
$443$			4.24264i			0.201574i	−0.994908	+	0.100787i	$0.967864\pi$
$444$		0			0
$445$	−5.00000	+	15.0000i	−0.237023	+	0.711068i
$446$	−20.8284			−0.986255
$447$		0			0
$448$			1.58579i			0.0749214i
$449$	−5.31371			−0.250769			−0.125385	−	0.992108i	$-0.540017\pi$
$449$	−5.31371			−0.250769			−0.125385	+	0.992108i	$0.540017\pi$
$450$		0			0
$451$	6.00000			0.282529
$452$		−	1.75736i		−	0.0826592i
$453$		0			0
$454$	−25.2426			−1.18470
$455$	0.192388	−	0.577164i	0.00901930	−	0.0270579i
$456$		0			0
$457$			3.00000i			0.140334i	0.997535	+	0.0701670i	$0.0223532\pi$
$457$			3.00000i			0.140334i	−0.997535	+	0.0701670i	$0.977647\pi$
$458$		−	18.9706i		−	0.886436i
$459$		0			0
$460$	19.6066	+	6.53553i	0.914163	+	0.304721i
$461$	−27.5563			−1.28343			−0.641714	−	0.766944i	$-0.721776\pi$
$461$	−27.5563			−1.28343			−0.641714	+	0.766944i	$0.721776\pi$
$462$		0			0
$463$		−	14.1421i		−	0.657241i	−0.944462	−	0.328620i	$-0.893416\pi$
$463$		−	14.1421i		−	0.657241i	0.944462	−	0.328620i	$-0.106584\pi$
$464$	−5.82843			−0.270578
$465$		0			0
$466$	−8.97056			−0.415553
$467$		−	24.7279i		−	1.14427i	−0.820159	−	0.572136i	$-0.806115\pi$
$467$		−	24.7279i		−	1.14427i	0.820159	−	0.572136i	$-0.193885\pi$
$468$		0			0
$469$	−21.0000			−0.969690
$470$		0			0
$471$		0			0
$472$		−	12.8995i		−	0.593747i
$473$		−	14.4853i		−	0.666034i
$474$		0			0
$475$	−4.00000	−	3.00000i	−0.183533	−	0.137649i
$476$	−1.58579			−0.0726844
$477$		0			0
$478$		−	12.8995i		−	0.590009i
$479$	31.1127			1.42158			0.710788	−	0.703407i	$-0.248339\pi$
$479$	31.1127			1.42158			0.710788	+	0.703407i	$0.248339\pi$
$480$		0			0
$481$	1.45584			0.0663808
$482$			24.9706i			1.13738i
$483$		0			0
$484$	9.00000			0.409091
$485$	24.7279	+	8.24264i	1.12284	+	0.374279i
$486$		0			0
$487$			1.79899i			0.0815200i	0.999169	+	0.0407600i	$0.0129779\pi$
$487$			1.79899i			0.0815200i	−0.999169	+	0.0407600i	$0.987022\pi$
$488$			5.75736i			0.260623i
$489$		0			0
$490$	−9.51472	−	3.17157i	−0.429831	−	0.143277i
$491$	2.44365			0.110280			0.0551402	−	0.998479i	$-0.482439\pi$
$491$	2.44365			0.110280			0.0551402	+	0.998479i	$0.482439\pi$
$492$		0			0
$493$		−	5.82843i		−	0.262499i
$494$	0.171573			0.00771943
$495$		0			0
$496$	−2.24264			−0.100698
$497$		−	16.7868i		−	0.752991i
$498$		0			0
$499$	34.2426			1.53291			0.766456	−	0.642297i	$-0.222019\pi$
$499$	34.2426			1.53291			0.766456	+	0.642297i	$0.222019\pi$
$500$	9.19239	−	6.36396i	0.411096	−	0.284605i
$501$		0			0
$502$		−	27.5563i		−	1.22990i
$503$		−	39.7279i		−	1.77138i	−0.464277	−	0.885690i	$-0.653686\pi$
$503$		−	39.7279i		−	1.77138i	0.464277	−	0.885690i	$-0.346314\pi$
$504$		0			0
$505$	0.757359	−	2.27208i	0.0337020	−	0.101106i
$506$	13.0711			0.581080
$507$		0			0
$508$			14.4853i			0.642680i
$509$	−4.97056			−0.220316			−0.110158	−	0.993914i	$-0.535136\pi$
$509$	−4.97056			−0.220316			−0.110158	+	0.993914i	$0.535136\pi$
$510$		0			0
$511$	−8.69848			−0.384798
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−4.72792			−0.208540
$515$	−9.00000	−	3.00000i	−0.396587	−	0.132196i
$516$		0			0
$517$		0			0
$518$			13.4558i			0.591216i
$519$		0			0
$520$	−0.121320	+	0.363961i	−0.00532025	+	0.0159607i
$521$	−0.686292			−0.0300670			−0.0150335	−	0.999887i	$-0.504785\pi$
$521$	−0.686292			−0.0300670			−0.0150335	+	0.999887i	$0.504785\pi$
$522$		0			0
$523$		−	27.7279i		−	1.21246i	−0.795290	−	0.606229i	$-0.792682\pi$
$523$		−	27.7279i		−	1.21246i	0.795290	−	0.606229i	$-0.207318\pi$
$524$	16.9706			0.741362
$525$		0			0
$526$	−6.97056			−0.303931
$527$		−	2.24264i		−	0.0976910i
$528$		0			0
$529$	−62.4264			−2.71419
$530$	8.12132	−	24.3640i	0.352768	−	1.05830i
$531$		0			0
$532$			1.58579i			0.0687526i
$533$		−	0.727922i		−	0.0315298i
$534$		0			0
$535$	−12.1508	−	4.05025i	−0.525323	−	0.175108i
$536$	13.2426			0.571995
$537$		0			0
$538$		−	28.6274i		−	1.23422i
$539$	−6.34315			−0.273219
$540$		0			0
$541$	18.2426			0.784312			0.392156	−	0.919899i	$-0.371729\pi$
$541$	18.2426			0.784312			0.392156	+	0.919899i	$0.371729\pi$
$542$			18.7574i			0.805698i
$543$		0			0
$544$	1.00000			0.0428746
$545$	−11.2929	+	33.8787i	−0.483734	+	1.45120i
$546$		0			0
$547$		−	5.31371i		−	0.227198i	−0.993527	−	0.113599i	$-0.963762\pi$
$547$		−	5.31371i		−	0.227198i	0.993527	−	0.113599i	$-0.0362379\pi$
$548$		−	13.0000i		−	0.555332i
$549$		0			0
$550$	4.24264	−	5.65685i	0.180907	−	0.241209i
$551$	−5.82843			−0.248299
$552$		0			0
$553$			16.6274i			0.707070i
$554$		0			0
$555$		0			0
$556$	−12.0000			−0.508913
$557$			16.0000i			0.677942i	0.940797	+	0.338971i	$0.110079\pi$
$557$			16.0000i			0.677942i	−0.940797	+	0.338971i	$0.889921\pi$
$558$		0			0
$559$	−1.75736			−0.0743284
$560$	−3.36396	−	1.12132i	−0.142153	−	0.0473844i
$561$		0			0
$562$		−	4.24264i		−	0.178965i
$563$			28.9706i			1.22096i	0.792030	+	0.610482i	$0.209024\pi$
$563$			28.9706i			1.22096i	−0.792030	+	0.610482i	$0.790976\pi$
$564$		0			0
$565$	3.72792	+	1.24264i	0.156835	+	0.0522783i
$566$	3.85786			0.162158
$567$		0			0
$568$			10.5858i			0.444170i
$569$	28.2843			1.18574			0.592869	−	0.805299i	$-0.297995\pi$
$569$	28.2843			1.18574			0.592869	+	0.805299i	$0.297995\pi$
$570$		0			0
$571$	6.24264			0.261246			0.130623	−	0.991432i	$-0.458302\pi$
$571$	6.24264			0.261246			0.130623	+	0.991432i	$0.458302\pi$
$572$			0.242641i			0.0101453i
$573$		0			0
$574$	6.72792			0.280818
$575$	−27.7279	+	36.9706i	−1.15633	+	1.54178i
$576$		0			0
$577$		−	2.31371i		−	0.0963209i	−0.998840	−	0.0481605i	$-0.984664\pi$
$577$		−	2.31371i		−	0.0963209i	0.998840	−	0.0481605i	$-0.0153359\pi$
$578$		−	16.0000i		−	0.665512i
$579$		0			0
$580$	4.12132	−	12.3640i	0.171129	−	0.513386i
$581$	3.94113			0.163505
$582$		0			0
$583$		−	16.2426i		−	0.672701i
$584$	5.48528			0.226983
$585$		0			0
$586$	−11.4853			−0.474453
$587$			21.7574i			0.898022i	0.893526	+	0.449011i	$0.148224\pi$
$587$			21.7574i			0.898022i	−0.893526	+	0.449011i	$0.851776\pi$
$588$		0			0
$589$	−2.24264			−0.0924064
$590$	27.3640	+	9.12132i	1.12656	+	0.375519i
$591$		0			0
$592$		−	8.48528i		−	0.348743i
$593$		−	22.0000i		−	0.903432i	−0.892162	−	0.451716i	$-0.850812\pi$
$593$		−	22.0000i		−	0.903432i	0.892162	−	0.451716i	$-0.149188\pi$
$594$		0			0
$595$	1.12132	−	3.36396i	0.0459697	−	0.137909i
$596$	−6.34315			−0.259825
$597$		0			0
$598$		−	1.58579i		−	0.0648476i
$599$	27.2132			1.11190			0.555951	−	0.831215i	$-0.312354\pi$
$599$	27.2132			1.11190			0.555951	+	0.831215i	$0.312354\pi$
$600$		0			0
$601$	−11.7574			−0.479593			−0.239796	−	0.970823i	$-0.577081\pi$
$601$	−11.7574			−0.479593			−0.239796	+	0.970823i	$0.577081\pi$
$602$		−	16.2426i		−	0.662001i
$603$		0			0
$604$	−6.48528			−0.263882
$605$	−6.36396	+	19.0919i	−0.258732	+	0.776195i
$606$		0			0
$607$		−	8.82843i		−	0.358335i	−0.983819	−	0.179167i	$-0.942660\pi$
$607$		−	8.82843i		−	0.358335i	0.983819	−	0.179167i	$-0.0573404\pi$
$608$		−	1.00000i		−	0.0405554i
$609$		0			0
$610$	−12.2132	−	4.07107i	−0.494498	−	0.164833i
$611$		0			0
$612$		0			0
$613$			47.6985i			1.92652i	0.268564	+	0.963262i	$0.413451\pi$
$613$			47.6985i			1.92652i	−0.268564	+	0.963262i	$0.586549\pi$
$614$	6.34315			0.255989
$615$		0			0
$616$	−2.24264			−0.0903586
$617$			12.4853i			0.502639i	0.967904	+	0.251319i	$0.0808644\pi$
$617$			12.4853i			0.502639i	−0.967904	+	0.251319i	$0.919136\pi$
$618$		0			0
$619$	−16.2426			−0.652847			−0.326423	−	0.945224i	$-0.605844\pi$
$619$	−16.2426			−0.652847			−0.326423	+	0.945224i	$0.605844\pi$
$620$	1.58579	−	4.75736i	0.0636867	−	0.191060i
$621$		0			0
$622$		−	13.2426i		−	0.530982i
$623$			11.2132i			0.449248i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	25.9706			1.03799
$627$		0			0
$628$			0.343146i			0.0136930i
$629$	8.48528			0.338330
$630$		0			0
$631$	−5.02944			−0.200219			−0.100109	−	0.994976i	$-0.531919\pi$
$631$	−5.02944			−0.200219			−0.100109	+	0.994976i	$0.531919\pi$
$632$		−	10.4853i		−	0.417082i
$633$		0			0
$634$	7.48528			0.297279
$635$	−30.7279	−	10.2426i	−1.21940	−	0.406467i
$636$		0			0
$637$			0.769553i			0.0304908i
$638$		−	8.24264i		−	0.326329i
$639$		0			0
$640$	2.12132	+	0.707107i	0.0838525	+	0.0279508i
$641$	−30.0416			−1.18657			−0.593287	−	0.804991i	$-0.702170\pi$
$641$	−30.0416			−1.18657			−0.593287	+	0.804991i	$0.702170\pi$
$642$		0			0
$643$			2.48528i			0.0980099i	0.998799	+	0.0490050i	$0.0156050\pi$
$643$			2.48528i			0.0980099i	−0.998799	+	0.0490050i	$0.984395\pi$
$644$	14.6569			0.577561
$645$		0			0
$646$	1.00000			0.0393445
$647$		−	27.2426i		−	1.07102i	−0.844529	−	0.535509i	$-0.820120\pi$
$647$		−	27.2426i		−	1.07102i	0.844529	−	0.535509i	$-0.179880\pi$
$648$		0			0
$649$	18.2426			0.716086
$650$	−0.686292	−	0.514719i	−0.0269186	−	0.0201889i
$651$		0			0
$652$			1.75736i			0.0688235i
$653$		−	4.97056i		−	0.194513i	−0.995259	−	0.0972566i	$-0.968993\pi$
$653$		−	4.97056i		−	0.194513i	0.995259	−	0.0972566i	$-0.0310067\pi$
$654$		0			0
$655$	−12.0000	+	36.0000i	−0.468879	+	1.40664i
$656$	−4.24264			−0.165647
$657$		0			0
$658$		0			0
$659$	−0.899495			−0.0350393			−0.0175197	−	0.999847i	$-0.505577\pi$
$659$	−0.899495			−0.0350393			−0.0175197	+	0.999847i	$0.505577\pi$
$660$		0			0
$661$	32.4558			1.26239			0.631193	−	0.775626i	$-0.282566\pi$
$661$	32.4558			1.26239			0.631193	+	0.775626i	$0.282566\pi$
$662$			10.7574i			0.418097i
$663$		0			0
$664$	−2.48528			−0.0964476
$665$	−3.36396	−	1.12132i	−0.130449	−	0.0434829i
$666$		0			0
$667$			53.8701i			2.08586i
$668$			9.75736i			0.377524i
$669$		0			0
$670$	−9.36396	+	28.0919i	−0.361761	+	1.08528i
$671$	−8.14214			−0.314324
$672$		0			0
$673$		−	12.0000i		−	0.462566i	−0.972887	−	0.231283i	$-0.925708\pi$
$673$		−	12.0000i		−	0.462566i	0.972887	−	0.231283i	$-0.0742923\pi$
$674$	−33.8995			−1.30576
$675$		0			0
$676$	−12.9706			−0.498868
$677$			26.9411i			1.03543i	0.855553	+	0.517716i	$0.173218\pi$
$677$			26.9411i			1.03543i	−0.855553	+	0.517716i	$0.826782\pi$
$678$		0			0
$679$	18.4853			0.709400
$680$	−0.707107	+	2.12132i	−0.0271163	+	0.0813489i
$681$		0			0
$682$		−	3.17157i		−	0.121446i
$683$		−	12.0000i		−	0.459167i	−0.973289	−	0.229584i	$-0.926264\pi$
$683$		−	12.0000i		−	0.459167i	0.973289	−	0.229584i	$-0.0737364\pi$
$684$		0			0
$685$	27.5772	+	9.19239i	1.05367	+	0.351223i
$686$	−18.2132			−0.695383
$687$		0			0
$688$			10.2426i			0.390497i
$689$	−1.97056			−0.0750725
$690$		0			0
$691$	5.51472			0.209790			0.104895	−	0.994483i	$-0.466549\pi$
$691$	5.51472			0.209790			0.104895	+	0.994483i	$0.466549\pi$
$692$		−	16.4853i		−	0.626676i
$693$		0			0
$694$	−22.4853			−0.853530
$695$	8.48528	−	25.4558i	0.321865	−	0.965595i
$696$		0			0
$697$		−	4.24264i		−	0.160701i
$698$			6.00000i			0.227103i
$699$		0			0
$700$	4.75736	−	6.34315i	0.179811	−	0.239748i
$701$	16.9706			0.640969			0.320485	−	0.947254i	$-0.396154\pi$
$701$	16.9706			0.640969			0.320485	+	0.947254i	$0.396154\pi$
$702$		0			0
$703$		−	8.48528i		−	0.320028i
$704$	1.41421			0.0533002
$705$		0			0
$706$	19.4853			0.733338
$707$		−	1.69848i		−	0.0638781i
$708$		0			0
$709$	34.0000			1.27690			0.638448	−	0.769665i	$-0.279577\pi$
$709$	34.0000			1.27690			0.638448	+	0.769665i	$0.279577\pi$
$710$	−22.4558	−	7.48528i	−0.842753	−	0.280918i
$711$		0			0
$712$		−	7.07107i		−	0.264999i
$713$			20.7279i			0.776267i
$714$		0			0
$715$	−0.514719	−	0.171573i	−0.0192494	−	0.00641646i
$716$	0.343146			0.0128240
$717$		0			0
$718$			31.2426i			1.16596i
$719$	−24.8995			−0.928594			−0.464297	−	0.885679i	$-0.653693\pi$
$719$	−24.8995			−0.928594			−0.464297	+	0.885679i	$0.653693\pi$
$720$		0			0
$721$	−6.72792			−0.250561
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$	−8.48528			−0.315353
$725$	23.3137	+	17.4853i	0.865849	+	0.649387i
$726$		0			0
$727$			15.7279i			0.583316i	0.956523	+	0.291658i	$0.0942070\pi$
$727$			15.7279i			0.583316i	−0.956523	+	0.291658i	$0.905793\pi$
$728$			0.272078i			0.0100839i
$729$		0			0
$730$	−3.87868	+	11.6360i	−0.143556	+	0.430669i
$731$	−10.2426			−0.378838
$732$		0			0
$733$			12.0000i			0.443230i	0.975134	+	0.221615i	$0.0711328\pi$
$733$			12.0000i			0.443230i	−0.975134	+	0.221615i	$0.928867\pi$
$734$	−25.4558			−0.939592
$735$		0			0
$736$	−9.24264			−0.340688
$737$			18.7279i			0.689852i
$738$		0			0
$739$	−26.7279			−0.983203			−0.491601	−	0.870820i	$-0.663588\pi$
$739$	−26.7279			−0.983203			−0.491601	+	0.870820i	$0.663588\pi$
$740$	18.0000	+	6.00000i	0.661693	+	0.220564i
$741$		0			0
$742$		−	18.2132i		−	0.668628i
$743$			18.7279i			0.687061i	0.939142	+	0.343530i	$0.111623\pi$
$743$			18.7279i			0.687061i	−0.939142	+	0.343530i	$0.888377\pi$
$744$		0			0
$745$	4.48528	−	13.4558i	0.164328	−	0.492984i
$746$	9.00000			0.329513
$747$		0			0
$748$			1.41421i			0.0517088i
$749$	−9.08326			−0.331895
$750$		0			0
$751$	−1.27208			−0.0464188			−0.0232094	−	0.999731i	$-0.507388\pi$
$751$	−1.27208			−0.0464188			−0.0232094	+	0.999731i	$0.507388\pi$
$752$		0			0
$753$		0			0
$754$	−1.00000			−0.0364179
$755$	4.58579	−	13.7574i	0.166894	−	0.500682i
$756$		0			0
$757$		−	23.6569i		−	0.859823i	−0.902871	−	0.429911i	$-0.858545\pi$
$757$		−	23.6569i		−	0.859823i	0.902871	−	0.429911i	$-0.141455\pi$
$758$			2.75736i			0.100152i
$759$		0			0
$760$	2.12132	+	0.707107i	0.0769484	+	0.0256495i
$761$	−10.0294			−0.363567			−0.181783	−	0.983339i	$-0.558187\pi$
$761$	−10.0294			−0.363567			−0.181783	+	0.983339i	$0.558187\pi$
$762$		0			0
$763$			25.3259i			0.916859i
$764$	−18.5563			−0.671345
$765$		0			0
$766$	−3.75736			−0.135759
$767$		−	2.21320i		−	0.0799141i
$768$		0			0
$769$	−14.4558			−0.521291			−0.260646	−	0.965435i	$-0.583935\pi$
$769$	−14.4558			−0.521291			−0.260646	+	0.965435i	$0.583935\pi$
$770$	1.58579	−	4.75736i	0.0571478	−	0.171443i
$771$		0			0
$772$			11.6569i			0.419539i
$773$			19.9706i			0.718291i	0.933282	+	0.359146i	$0.116932\pi$
$773$			19.9706i			0.718291i	−0.933282	+	0.359146i	$0.883068\pi$
$774$		0			0
$775$	8.97056	+	6.72792i	0.322232	+	0.241674i
$776$	−11.6569			−0.418457
$777$		0			0
$778$		−	37.0711i		−	1.32906i
$779$	−4.24264			−0.152008
$780$		0			0
$781$	−14.9706			−0.535689
$782$		−	9.24264i		−	0.330516i
$783$		0			0
$784$	4.48528			0.160189
$785$	−0.727922	−	0.242641i	−0.0259807	−	0.00866022i
$786$		0			0
$787$		−	35.1838i		−	1.25417i	−0.778953	−	0.627083i	$-0.784249\pi$
$787$		−	35.1838i		−	1.25417i	0.778953	−	0.627083i	$-0.215751\pi$
$788$			20.2426i			0.721114i
$789$		0			0
$790$	22.2426	+	7.41421i	0.791358	+	0.263786i
$791$	2.78680			0.0990871
$792$		0			0
$793$			0.987807i			0.0350780i
$794$	−24.0000			−0.851728
$795$		0			0
$796$	0.757359			0.0268439
$797$		−	30.5147i		−	1.08089i	−0.841380	−	0.540443i	$-0.818257\pi$
$797$		−	30.5147i		−	1.08089i	0.841380	−	0.540443i	$-0.181743\pi$
$798$		0			0
$799$		0			0
$800$	−3.00000	+	4.00000i	−0.106066	+	0.141421i
$801$		0			0
$802$		−	22.5858i		−	0.797532i
$803$			7.75736i			0.273751i
$804$		0			0
$805$	−10.3640	+	31.0919i	−0.365282	+	1.09584i
$806$	−0.384776			−0.0135532
$807$		0			0
$808$			1.07107i			0.0376800i
$809$	10.7990			0.379672			0.189836	−	0.981816i	$-0.439204\pi$
$809$	10.7990			0.379672			0.189836	+	0.981816i	$0.439204\pi$
$810$		0			0
$811$	−6.69848			−0.235216			−0.117608	−	0.993060i	$-0.537523\pi$
$811$	−6.69848			−0.235216			−0.117608	+	0.993060i	$0.537523\pi$
$812$		−	9.24264i		−	0.324353i
$813$		0			0
$814$	12.0000			0.420600
$815$	−3.72792	−	1.24264i	−0.130583	−	0.0435278i
$816$		0			0
$817$			10.2426i			0.358345i
$818$		−	17.2132i		−	0.601846i
$819$		0			0
$820$	3.00000	−	9.00000i	0.104765	−	0.314294i
$821$	−17.6569			−0.616228			−0.308114	−	0.951349i	$-0.599698\pi$
$821$	−17.6569			−0.616228			−0.308114	+	0.951349i	$0.599698\pi$
$822$		0			0
$823$			9.72792i			0.339094i	0.985522	+	0.169547i	$0.0542305\pi$
$823$			9.72792i			0.339094i	−0.985522	+	0.169547i	$0.945770\pi$
$824$	4.24264			0.147799
$825$		0			0
$826$	20.4558			0.711750
$827$			38.6985i			1.34568i	0.739789	+	0.672839i	$0.234925\pi$
$827$			38.6985i			1.34568i	−0.739789	+	0.672839i	$0.765075\pi$
$828$		0			0
$829$	40.4558			1.40509			0.702545	−	0.711640i	$-0.252047\pi$
$829$	40.4558			1.40509			0.702545	+	0.711640i	$0.252047\pi$
$830$	1.75736	−	5.27208i	0.0609988	−	0.182996i
$831$		0			0
$832$		−	0.171573i		−	0.00594822i
$833$			4.48528i			0.155406i
$834$		0			0
$835$	−20.6985	−	6.89949i	−0.716301	−	0.238767i
$836$	1.41421			0.0489116
$837$		0			0
$838$		−	16.5858i		−	0.572946i
$839$	−22.6274			−0.781185			−0.390593	−	0.920564i	$-0.627730\pi$
$839$	−22.6274			−0.781185			−0.390593	+	0.920564i	$0.627730\pi$
$840$		0			0
$841$	4.97056			0.171399
$842$		−	2.51472i		−	0.0866629i
$843$		0			0
$844$	−5.72792			−0.197163
$845$	9.17157	−	27.5147i	0.315512	−	0.946535i
$846$		0			0
$847$			14.2721i			0.490394i
$848$			11.4853i			0.394406i
$849$		0			0
$850$	−4.00000	−	3.00000i	−0.137199	−	0.102899i
$851$	−78.4264			−2.68842
$852$		0			0
$853$			39.9411i			1.36756i	0.729689	+	0.683779i	$0.239665\pi$
$853$			39.9411i			1.36756i	−0.729689	+	0.683779i	$0.760335\pi$
$854$	−9.12994			−0.312420
$855$		0			0
$856$	5.72792			0.195776
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	20.7279			0.707228			0.353614	−	0.935392i	$-0.384953\pi$
$859$	20.7279			0.707228			0.353614	+	0.935392i	$0.384953\pi$
$860$	−21.7279	−	7.24264i	−0.740916	−	0.246972i
$861$		0			0
$862$			30.3848i			1.03491i
$863$			24.7279i			0.841748i	0.907119	+	0.420874i	$0.138277\pi$
$863$			24.7279i			0.841748i	−0.907119	+	0.420874i	$0.861723\pi$
$864$		0			0
$865$	34.9706	+	11.6569i	1.18903	+	0.396345i
$866$	21.5563			0.732515
$867$		0			0
$868$		−	3.55635i		−	0.120710i
$869$	14.8284			0.503020
$870$		0			0
$871$	2.27208			0.0769864
$872$		−	15.9706i		−	0.540831i
$873$		0			0
$874$	−9.24264			−0.312637
$875$	10.0919	+	14.5772i	0.341168	+	0.492798i
$876$		0			0
$877$			47.1421i			1.59188i	0.605378	+	0.795938i	$0.293022\pi$
$877$			47.1421i			1.59188i	−0.605378	+	0.795938i	$0.706978\pi$
$878$		−	14.2426i		−	0.480666i
$879$		0			0
$880$	−1.00000	+	3.00000i	−0.0337100	+	0.101130i
$881$	−39.5980			−1.33409			−0.667045	−	0.745018i	$-0.732441\pi$
$881$	−39.5980			−1.33409			−0.667045	+	0.745018i	$0.732441\pi$
$882$		0			0
$883$		−	2.48528i		−	0.0836364i	−0.999125	−	0.0418182i	$-0.986685\pi$
$883$		−	2.48528i		−	0.0836364i	0.999125	−	0.0418182i	$-0.0133150\pi$
$884$	0.171573			0.00577062
$885$		0			0
$886$	4.24264			0.142534
$887$		−	2.78680i		−	0.0935715i	−0.998905	−	0.0467857i	$-0.985102\pi$
$887$		−	2.78680i		−	0.0935715i	0.998905	−	0.0467857i	$-0.0148978\pi$
$888$		0			0
$889$	−22.9706			−0.770408
$890$	15.0000	+	5.00000i	0.502801	+	0.167600i
$891$		0			0
$892$			20.8284i			0.697387i
$893$		0			0
$894$		0			0
$895$	−0.242641	+	0.727922i	−0.00811058	+	0.0243318i
$896$	1.58579			0.0529774
$897$		0			0
$898$			5.31371i			0.177321i
$899$	13.0711			0.435945
$900$		0			0
$901$	−11.4853			−0.382630
$902$		−	6.00000i		−	0.199778i
$903$		0			0
$904$	−1.75736			−0.0584489
$905$	6.00000	−	18.0000i	0.199447	−	0.598340i
$906$		0			0
$907$			20.6985i			0.687282i	0.939101	+	0.343641i	$0.111660\pi$
$907$			20.6985i			0.687282i	−0.939101	+	0.343641i	$0.888340\pi$
$908$			25.2426i			0.837706i
$909$		0			0
$910$	−0.577164	−	0.192388i	−0.0191328	−	0.00637761i
$911$	16.2843			0.539522			0.269761	−	0.962927i	$-0.413055\pi$
$911$	16.2843			0.539522			0.269761	+	0.962927i	$0.413055\pi$
$912$		0			0
$913$		−	3.51472i		−	0.116320i
$914$	3.00000			0.0992312
$915$		0			0
$916$	−18.9706			−0.626805
$917$			26.9117i			0.888702i
$918$		0			0
$919$	−36.2132			−1.19456			−0.597282	−	0.802032i	$-0.703753\pi$
$919$	−36.2132			−1.19456			−0.597282	+	0.802032i	$0.703753\pi$
$920$	6.53553	−	19.6066i	0.215470	−	0.646411i
$921$		0			0
$922$			27.5563i			0.907520i
$923$			1.81623i			0.0597821i
$924$		0			0
$925$	−25.4558	+	33.9411i	−0.836983	+	1.11598i
$926$	−14.1421			−0.464739
$927$		0			0
$928$			5.82843i			0.191327i
$929$	−17.8284			−0.584932			−0.292466	−	0.956276i	$-0.594476\pi$
$929$	−17.8284			−0.584932			−0.292466	+	0.956276i	$0.594476\pi$
$930$		0			0
$931$	4.48528			0.146999
$932$			8.97056i			0.293841i
$933$		0			0
$934$	−24.7279			−0.809122
$935$	−3.00000	−	1.00000i	−0.0981105	−	0.0327035i
$936$		0			0
$937$		−	27.0000i		−	0.882052i	−0.897494	−	0.441026i	$-0.854615\pi$
$937$		−	27.0000i		−	0.882052i	0.897494	−	0.441026i	$-0.145385\pi$
$938$			21.0000i			0.685674i
$939$		0			0
$940$		0			0
$941$	−24.8579			−0.810343			−0.405172	−	0.914241i	$-0.632788\pi$
$941$	−24.8579			−0.810343			−0.405172	+	0.914241i	$0.632788\pi$
$942$		0			0
$943$			39.2132i			1.27696i
$944$	−12.8995			−0.419843
$945$		0			0
$946$	−14.4853			−0.470957
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$		0			0
$949$	0.941125			0.0305502
$950$	−3.00000	+	4.00000i	−0.0973329	+	0.129777i
$951$		0			0
$952$			1.58579i			0.0513956i
$953$			6.72792i			0.217939i	0.994045	+	0.108969i	$0.0347550\pi$
$953$			6.72792i			0.217939i	−0.994045	+	0.108969i	$0.965245\pi$
$954$		0			0
$955$	13.1213	−	39.3640i	0.424596	−	1.27379i
$956$	−12.8995			−0.417199
$957$		0			0
$958$		−	31.1127i		−	1.00521i
$959$	20.6152			0.665700
$960$		0			0
$961$	−25.9706			−0.837760
$962$		−	1.45584i		−	0.0469383i
$963$		0			0
$964$	24.9706			0.804248
$965$	−24.7279	−	8.24264i	−0.796020	−	0.265340i
$966$		0			0
$967$			19.1127i			0.614623i	0.951609	+	0.307311i	$0.0994293\pi$
$967$			19.1127i			0.614623i	−0.951609	+	0.307311i	$0.900571\pi$
$968$		−	9.00000i		−	0.289271i
$969$		0			0
$970$	8.24264	−	24.7279i	0.264655	−	0.793966i
$971$	−30.3431			−0.973758			−0.486879	−	0.873469i	$-0.661865\pi$
$971$	−30.3431			−0.973758			−0.486879	+	0.873469i	$0.661865\pi$
$972$		0			0
$973$		−	19.0294i		−	0.610056i
$974$	1.79899			0.0576434
$975$		0			0
$976$	5.75736			0.184289
$977$		−	8.24264i		−	0.263705i	−0.991269	−	0.131853i	$-0.957907\pi$
$977$		−	8.24264i		−	0.263705i	0.991269	−	0.131853i	$-0.0420926\pi$
$978$		0			0
$979$	10.0000			0.319601
$980$	−3.17157	+	9.51472i	−0.101312	+	0.303937i
$981$		0			0
$982$		−	2.44365i		−	0.0779800i
$983$			0.544156i			0.0173559i	0.999962	+	0.00867794i	$0.00276231\pi$
$983$			0.544156i			0.0173559i	−0.999962	+	0.00867794i	$0.997238\pi$
$984$		0			0
$985$	−42.9411	−	14.3137i	−1.36822	−	0.456073i
$986$	−5.82843			−0.185615
$987$		0			0
$988$		−	0.171573i		−	0.00545846i
$989$	94.6690			3.01030
$990$		0			0
$991$	22.2426			0.706561			0.353280	−	0.935517i	$-0.385066\pi$
$991$	22.2426			0.706561			0.353280	+	0.935517i	$0.385066\pi$
$992$			2.24264i			0.0712039i
$993$		0			0
$994$	−16.7868			−0.532445
$995$	−0.535534	+	1.60660i	−0.0169776	+	0.0509327i
$996$		0			0
$997$		−	23.2721i		−	0.737034i	−0.929621	−	0.368517i	$-0.879866\pi$
$997$		−	23.2721i		−	0.737034i	0.929621	−	0.368517i	$-0.120134\pi$
$998$		−	34.2426i		−	1.08393i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.c.1369.2		4
3.2	odd	2		190.2.b.a.39.4	yes	4
5.2	odd	4		8550.2.a.cb.1.1		2
5.3	odd	4		8550.2.a.bn.1.2		2
5.4	even	2	inner	1710.2.d.c.1369.4		4
12.11	even	2		1520.2.d.e.609.1		4
15.2	even	4		950.2.a.f.1.2		2
15.8	even	4		950.2.a.g.1.1		2
15.14	odd	2		190.2.b.a.39.1	✓	4
60.23	odd	4		7600.2.a.bg.1.2		2
60.47	odd	4		7600.2.a.v.1.1		2
60.59	even	2		1520.2.d.e.609.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.b.a.39.1	✓	4	15.14	odd	2
190.2.b.a.39.4	yes	4	3.2	odd	2
950.2.a.f.1.2		2	15.2	even	4
950.2.a.g.1.1		2	15.8	even	4
1520.2.d.e.609.1		4	12.11	even	2
1520.2.d.e.609.4		4	60.59	even	2
1710.2.d.c.1369.2		4	1.1	even	1	trivial
1710.2.d.c.1369.4		4	5.4	even	2	inner
7600.2.a.v.1.1		2	60.47	odd	4
7600.2.a.bg.1.2		2	60.23	odd	4
8550.2.a.bn.1.2		2	5.3	odd	4
8550.2.a.cb.1.1		2	5.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} -1.58579i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} -1.58579i q^{7} +1.00000i q^{8} +(-2.12132 - 0.707107i) q^{10} -1.41421 q^{11} +0.171573i q^{13} -1.58579 q^{14} +1.00000 q^{16} +1.00000i q^{17} +1.00000 q^{19} +(-0.707107 + 2.12132i) q^{20} +1.41421i q^{22} -9.24264i q^{23} +(-4.00000 - 3.00000i) q^{25} +0.171573 q^{26} +1.58579i q^{28} -5.82843 q^{29} -2.24264 q^{31} -1.00000i q^{32} +1.00000 q^{34} +(-3.36396 - 1.12132i) q^{35} -8.48528i q^{37} -1.00000i q^{38} +(2.12132 + 0.707107i) q^{40} -4.24264 q^{41} +10.2426i q^{43} +1.41421 q^{44} -9.24264 q^{46} +4.48528 q^{49} +(-3.00000 + 4.00000i) q^{50} -0.171573i q^{52} +11.4853i q^{53} +(-1.00000 + 3.00000i) q^{55} +1.58579 q^{56} +5.82843i q^{58} -12.8995 q^{59} +5.75736 q^{61} +2.24264i q^{62} -1.00000 q^{64} +(0.363961 + 0.121320i) q^{65} -13.2426i q^{67} -1.00000i q^{68} +(-1.12132 + 3.36396i) q^{70} +10.5858 q^{71} -5.48528i q^{73} -8.48528 q^{74} -1.00000 q^{76} +2.24264i q^{77} -10.4853 q^{79} +(0.707107 - 2.12132i) q^{80} +4.24264i q^{82} +2.48528i q^{83} +(2.12132 + 0.707107i) q^{85} +10.2426 q^{86} -1.41421i q^{88} -7.07107 q^{89} +0.272078 q^{91} +9.24264i q^{92} +(0.707107 - 2.12132i) q^{95} +11.6569i q^{97} -4.48528i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4}+O(q^{10}) \) 4 * q - 4 * q^4	\( 4 q - 4 q^{4} - 12 q^{14} + 4 q^{16} + 4 q^{19} - 16 q^{25} + 12 q^{26} - 12 q^{29} + 8 q^{31} + 4 q^{34} + 12 q^{35} - 20 q^{46} - 16 q^{49} - 12 q^{50} - 4 q^{55} + 12 q^{56} - 12 q^{59} + 40 q^{61} - 4 q^{64} - 24 q^{65} + 4 q^{70} + 48 q^{71} - 4 q^{76} - 8 q^{79} + 24 q^{86} + 52 q^{91}+O(q^{100}) \) 4 * q - 4 * q^4 - 12 * q^14 + 4 * q^16 + 4 * q^19 - 16 * q^25 + 12 * q^26 - 12 * q^29 + 8 * q^31 + 4 * q^34 + 12 * q^35 - 20 * q^46 - 16 * q^49 - 12 * q^50 - 4 * q^55 + 12 * q^56 - 12 * q^59 + 40 * q^61 - 4 * q^64 - 24 * q^65 + 4 * q^70 + 48 * q^71 - 4 * q^76 - 8 * q^79 + 24 * q^86 + 52 * q^91

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