LMFDB - Embedded newform 3234.2.e.c.2155.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.14
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.c.2155.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -3.45711i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -3.45711i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +3.45711 q^{10} +(3.07598 - 1.24029i) q^{11} -1.00000i q^{12} -5.39143 q^{13} +3.45711 q^{15} +1.00000 q^{16} +0.0457263 q^{17} -1.00000i q^{18} -6.95062 q^{19} +3.45711i q^{20} +(1.24029 + 3.07598i) q^{22} +1.19252 q^{23} +1.00000 q^{24} -6.95158 q^{25} -5.39143i q^{26} -1.00000i q^{27} -7.78271i q^{29} +3.45711i q^{30} +6.61846i q^{31} +1.00000i q^{32} +(1.24029 + 3.07598i) q^{33} +0.0457263i q^{34} +1.00000 q^{36} -1.51053 q^{37} -6.95062i q^{38} -5.39143i q^{39} -3.45711 q^{40} +4.87368 q^{41} +3.27873i q^{43} +(-3.07598 + 1.24029i) q^{44} +3.45711i q^{45} +1.19252i q^{46} +12.1060i q^{47} +1.00000i q^{48} -6.95158i q^{50} +0.0457263i q^{51} +5.39143 q^{52} -3.69054 q^{53} +1.00000 q^{54} +(-4.28781 - 10.6340i) q^{55} -6.95062i q^{57} +7.78271 q^{58} +14.8396i q^{59} -3.45711 q^{60} -3.63129 q^{61} -6.61846 q^{62} -1.00000 q^{64} +18.6387i q^{65} +(-3.07598 + 1.24029i) q^{66} +6.66903 q^{67} -0.0457263 q^{68} +1.19252i q^{69} +6.89741 q^{71} +1.00000i q^{72} -3.04272 q^{73} -1.51053i q^{74} -6.95158i q^{75} +6.95062 q^{76} +5.39143 q^{78} +12.9709i q^{79} -3.45711i q^{80} +1.00000 q^{81} +4.87368i q^{82} -8.48330 q^{83} -0.158081i q^{85} -3.27873 q^{86} +7.78271 q^{87} +(-1.24029 - 3.07598i) q^{88} +4.20562i q^{89} -3.45711 q^{90} -1.19252 q^{92} -6.61846 q^{93} -12.1060 q^{94} +24.0290i q^{95} -1.00000 q^{96} -6.64551i q^{97} +(-3.07598 + 1.24029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9} + 24 q^{16} + 16 q^{17} - 32 q^{19} - 8 q^{22} + 24 q^{24} - 8 q^{25} - 8 q^{33} + 24 q^{36} + 16 q^{37} - 16 q^{41} + 24 q^{54} + 16 q^{55} - 16 q^{62} - 24 q^{64} - 64 q^{67} - 16 q^{68} + 64 q^{71} + 32 q^{76} + 24 q^{81} - 16 q^{83} + 8 q^{88} - 16 q^{93} + 64 q^{94} - 24 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9 + 24 * q^16 + 16 * q^17 - 32 * q^19 - 8 * q^22 + 24 * q^24 - 8 * q^25 - 8 * q^33 + 24 * q^36 + 16 * q^37 - 16 * q^41 + 24 * q^54 + 16 * q^55 - 16 * q^62 - 24 * q^64 - 64 * q^67 - 16 * q^68 + 64 * q^71 + 32 * q^76 + 24 * q^81 - 16 * q^83 + 8 * q^88 - 16 * q^93 + 64 * q^94 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$		−	3.45711i		−	1.54606i	−0.634366	−	0.773032i	$-0.718739\pi$
$5$		−	3.45711i		−	1.54606i	0.634366	−	0.773032i	$-0.281261\pi$
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	3.45711			1.09323
$11$	3.07598	−	1.24029i	0.927444	−	0.373961i
$11$	3.07598	−	1.24029i	0.927444	−	0.373961i
$12$		−	1.00000i		−	0.288675i
$13$	−5.39143			−1.49531			−0.747656	−	0.664086i	$-0.768821\pi$
$13$	−5.39143			−1.49531			−0.747656	+	0.664086i	$0.768821\pi$
$14$		0			0
$15$	3.45711			0.892621
$16$	1.00000			0.250000
$17$	0.0457263			0.0110903			0.00554513	−	0.999985i	$-0.498235\pi$
$17$	0.0457263			0.0110903			0.00554513	+	0.999985i	$0.498235\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−6.95062			−1.59458			−0.797291	−	0.603595i	$-0.793734\pi$
$19$	−6.95062			−1.59458			−0.797291	+	0.603595i	$0.793734\pi$
$20$			3.45711i			0.773032i
$21$		0			0
$22$	1.24029	+	3.07598i	0.264431	+	0.655802i
$23$	1.19252			0.248657			0.124329	−	0.992241i	$-0.460322\pi$
$23$	1.19252			0.248657			0.124329	+	0.992241i	$0.460322\pi$
$24$	1.00000			0.204124
$25$	−6.95158			−1.39032
$26$		−	5.39143i		−	1.05735i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	7.78271i		−	1.44521i	−0.691259	−	0.722607i	$-0.742944\pi$
$29$		−	7.78271i		−	1.44521i	0.691259	−	0.722607i	$-0.257056\pi$
$30$			3.45711i			0.631178i
$31$			6.61846i			1.18871i	0.804203	+	0.594355i	$0.202593\pi$
$31$			6.61846i			1.18871i	−0.804203	+	0.594355i	$0.797407\pi$
$32$			1.00000i			0.176777i
$33$	1.24029	+	3.07598i	0.215907	+	0.535460i
$34$			0.0457263i			0.00784200i
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.51053			−0.248330			−0.124165	−	0.992262i	$-0.539625\pi$
$37$	−1.51053			−0.248330			−0.124165	+	0.992262i	$0.539625\pi$
$38$		−	6.95062i		−	1.12754i
$39$		−	5.39143i		−	0.863319i
$40$	−3.45711			−0.546617
$41$	4.87368			0.761140			0.380570	−	0.924752i	$-0.375728\pi$
$41$	4.87368			0.761140			0.380570	+	0.924752i	$0.375728\pi$
$42$		0			0
$43$			3.27873i			0.500001i	0.968246	+	0.250001i	$0.0804308\pi$
$43$			3.27873i			0.500001i	−0.968246	+	0.250001i	$0.919569\pi$
$44$	−3.07598	+	1.24029i	−0.463722	+	0.186981i
$45$			3.45711i			0.515355i
$46$			1.19252i			0.175827i
$47$			12.1060i			1.76584i	0.469524	+	0.882920i	$0.344426\pi$
$47$			12.1060i			1.76584i	−0.469524	+	0.882920i	$0.655574\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$		−	6.95158i		−	0.983102i
$51$			0.0457263i			0.00640297i
$52$	5.39143			0.747656
$53$	−3.69054			−0.506935			−0.253467	−	0.967344i	$-0.581571\pi$
$53$	−3.69054			−0.506935			−0.253467	+	0.967344i	$0.581571\pi$
$54$	1.00000			0.136083
$55$	−4.28781	−	10.6340i	−0.578169	−	1.43389i
$56$		0			0
$57$		−	6.95062i		−	0.920632i
$58$	7.78271			1.02192
$59$			14.8396i			1.93195i	0.258638	+	0.965974i	$0.416726\pi$
$59$			14.8396i			1.93195i	−0.258638	+	0.965974i	$0.583274\pi$
$60$	−3.45711			−0.446311
$61$	−3.63129			−0.464939			−0.232469	−	0.972604i	$-0.574681\pi$
$61$	−3.63129			−0.464939			−0.232469	+	0.972604i	$0.574681\pi$
$62$	−6.61846			−0.840545
$63$		0			0
$64$	−1.00000			−0.125000
$65$			18.6387i			2.31185i
$66$	−3.07598	+	1.24029i	−0.378628	+	0.152669i
$67$	6.66903			0.814751			0.407376	−	0.913261i	$-0.366444\pi$
$67$	6.66903			0.814751			0.407376	+	0.913261i	$0.366444\pi$
$68$	−0.0457263			−0.00554513
$69$			1.19252i			0.143562i
$70$		0			0
$71$	6.89741			0.818572			0.409286	−	0.912406i	$-0.365778\pi$
$71$	6.89741			0.818572			0.409286	+	0.912406i	$0.365778\pi$
$72$			1.00000i			0.117851i
$73$	−3.04272			−0.356123			−0.178062	−	0.984019i	$-0.556983\pi$
$73$	−3.04272			−0.356123			−0.178062	+	0.984019i	$0.556983\pi$
$74$		−	1.51053i		−	0.175596i
$75$		−	6.95158i		−	0.802700i
$76$	6.95062			0.797291
$77$		0			0
$78$	5.39143			0.610459
$79$			12.9709i			1.45935i	0.683796	+	0.729673i	$0.260328\pi$
$79$			12.9709i			1.45935i	−0.683796	+	0.729673i	$0.739672\pi$
$80$		−	3.45711i		−	0.386516i
$81$	1.00000			0.111111
$82$			4.87368i			0.538207i
$83$	−8.48330			−0.931163			−0.465582	−	0.885005i	$-0.654155\pi$
$83$	−8.48330			−0.931163			−0.465582	+	0.885005i	$0.654155\pi$
$84$		0			0
$85$		−	0.158081i		−	0.0171463i
$86$	−3.27873			−0.353554
$87$	7.78271			0.834395
$88$	−1.24029	−	3.07598i	−0.132215	−	0.327901i
$89$			4.20562i			0.445795i	0.974842	+	0.222897i	$0.0715515\pi$
$89$			4.20562i			0.445795i	−0.974842	+	0.222897i	$0.928448\pi$
$90$	−3.45711			−0.364411
$91$		0			0
$92$	−1.19252			−0.124329
$93$	−6.61846			−0.686302
$94$	−12.1060			−1.24864
$95$			24.0290i			2.46533i
$96$	−1.00000			−0.102062
$97$		−	6.64551i		−	0.674749i	−0.941370	−	0.337375i	$-0.890461\pi$
$97$		−	6.64551i		−	0.674749i	0.941370	−	0.337375i	$-0.109539\pi$
$98$		0			0
$99$	−3.07598	+	1.24029i	−0.309148	+	0.124654i
$100$	6.95158			0.695158
$101$	−14.1963			−1.41258			−0.706290	−	0.707922i	$-0.749633\pi$
$101$	−14.1963			−1.41258			−0.706290	+	0.707922i	$0.749633\pi$
$102$	−0.0457263			−0.00452758
$103$		−	1.26090i		−	0.124240i	−0.998069	−	0.0621200i	$-0.980214\pi$
$103$		−	1.26090i		−	0.124240i	0.998069	−	0.0621200i	$-0.0197861\pi$
$104$			5.39143i			0.528673i
$105$		0			0
$106$		−	3.69054i		−	0.358457i
$107$		−	0.676179i		−	0.0653687i	−0.999466	−	0.0326843i	$-0.989594\pi$
$107$		−	0.676179i		−	0.0653687i	0.999466	−	0.0326843i	$-0.0104056\pi$
$108$			1.00000i			0.0962250i
$109$			19.6069i			1.87800i	0.343913	+	0.939002i	$0.388248\pi$
$109$			19.6069i			1.87800i	−0.343913	+	0.939002i	$0.611752\pi$
$110$	10.6340	−	4.28781i	1.01391	−	0.408827i
$111$		−	1.51053i		−	0.143373i
$112$		0			0
$113$	−2.24860			−0.211531			−0.105765	−	0.994391i	$-0.533729\pi$
$113$	−2.24860			−0.211531			−0.105765	+	0.994391i	$0.533729\pi$
$114$	6.95062			0.650985
$115$		−	4.12266i		−	0.384440i
$116$			7.78271i			0.722607i
$117$	5.39143			0.498438
$118$	−14.8396			−1.36609
$119$		0			0
$120$		−	3.45711i		−	0.315589i
$121$	7.92336	−	7.63022i	0.720306	−	0.693657i
$122$		−	3.63129i		−	0.328761i
$123$			4.87368i			0.439444i
$124$		−	6.61846i		−	0.594355i
$125$			6.74683i			0.603455i
$126$		0			0
$127$			2.24140i			0.198892i	0.995043	+	0.0994461i	$0.0317071\pi$
$127$			2.24140i			0.198892i	−0.995043	+	0.0994461i	$0.968293\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−3.27873			−0.288676
$130$	−18.6387			−1.63473
$131$	−2.65048			−0.231573			−0.115787	−	0.993274i	$-0.536939\pi$
$131$	−2.65048			−0.231573			−0.115787	+	0.993274i	$0.536939\pi$
$132$	−1.24029	−	3.07598i	−0.107953	−	0.267730i
$133$		0			0
$134$			6.66903i			0.576116i
$135$	−3.45711			−0.297540
$136$		−	0.0457263i		−	0.00392100i
$137$	−14.9046			−1.27339			−0.636694	−	0.771117i	$-0.719698\pi$
$137$	−14.9046			−1.27339			−0.636694	+	0.771117i	$0.719698\pi$
$138$	−1.19252			−0.101514
$139$	−17.4420			−1.47941			−0.739707	−	0.672929i	$-0.765036\pi$
$139$	−17.4420			−1.47941			−0.739707	+	0.672929i	$0.765036\pi$
$140$		0			0
$141$	−12.1060			−1.01951
$142$			6.89741i			0.578818i
$143$	−16.5839	+	6.68693i	−1.38682	+	0.559189i
$144$	−1.00000			−0.0833333
$145$	−26.9057			−2.23439
$146$		−	3.04272i		−	0.251817i
$147$		0			0
$148$	1.51053			0.124165
$149$		−	11.1458i		−	0.913098i	−0.889698	−	0.456549i	$-0.849085\pi$
$149$		−	11.1458i		−	0.913098i	0.889698	−	0.456549i	$-0.150915\pi$
$150$	6.95158			0.567594
$151$			13.7210i			1.11660i	0.829639	+	0.558300i	$0.188546\pi$
$151$			13.7210i			1.11660i	−0.829639	+	0.558300i	$0.811454\pi$
$152$			6.95062i			0.563770i
$153$	−0.0457263			−0.00369676
$154$		0			0
$155$	22.8807			1.83782
$156$			5.39143i			0.431660i
$157$		−	20.5517i		−	1.64021i	−0.572215	−	0.820104i	$-0.693916\pi$
$157$		−	20.5517i		−	1.64021i	0.572215	−	0.820104i	$-0.306084\pi$
$158$	−12.9709			−1.03191
$159$		−	3.69054i		−	0.292679i
$160$	3.45711			0.273308
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	−10.3412			−0.809986			−0.404993	−	0.914320i	$-0.632726\pi$
$163$	−10.3412			−0.809986			−0.404993	+	0.914320i	$0.632726\pi$
$164$	−4.87368			−0.380570
$165$	10.6340	−	4.28781i	0.827856	−	0.333806i
$166$		−	8.48330i		−	0.658432i
$167$	23.7721			1.83954			0.919769	−	0.392460i	$-0.128376\pi$
$167$	23.7721			1.83954			0.919769	+	0.392460i	$0.128376\pi$
$168$		0			0
$169$	16.0675			1.23596
$170$	0.158081			0.0121242
$171$	6.95062			0.531527
$172$		−	3.27873i		−	0.250001i
$173$	13.5605			1.03099			0.515494	−	0.856893i	$-0.327608\pi$
$173$	13.5605			1.03099			0.515494	+	0.856893i	$0.327608\pi$
$174$			7.78271i			0.590006i
$175$		0			0
$176$	3.07598	−	1.24029i	0.231861	−	0.0934903i
$177$	−14.8396			−1.11541
$178$	−4.20562			−0.315225
$179$	−16.1833			−1.20960			−0.604799	−	0.796378i	$-0.706747\pi$
$179$	−16.1833			−1.20960			−0.604799	+	0.796378i	$0.706747\pi$
$180$		−	3.45711i		−	0.257677i
$181$			15.6283i			1.16164i	0.814031	+	0.580821i	$0.197268\pi$
$181$			15.6283i			1.16164i	−0.814031	+	0.580821i	$0.802732\pi$
$182$		0			0
$183$		−	3.63129i		−	0.268433i
$184$		−	1.19252i		−	0.0879135i
$185$			5.22206i			0.383934i
$186$		−	6.61846i		−	0.485289i
$187$	0.140654	−	0.0567139i	0.0102856	−	0.00414733i
$188$		−	12.1060i		−	0.882920i
$189$		0			0
$190$	−24.0290			−1.74325
$191$	−8.42409			−0.609546			−0.304773	−	0.952425i	$-0.598581\pi$
$191$	−8.42409			−0.609546			−0.304773	+	0.952425i	$0.598581\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			9.14795i			0.658484i	0.944246	+	0.329242i	$0.106793\pi$
$193$			9.14795i			0.658484i	−0.944246	+	0.329242i	$0.893207\pi$
$194$	6.64551			0.477120
$195$	−18.6387			−1.33475
$196$		0			0
$197$		−	13.7101i		−	0.976806i	−0.872618	−	0.488403i	$-0.837580\pi$
$197$		−	13.7101i		−	0.976806i	0.872618	−	0.488403i	$-0.162420\pi$
$198$	−1.24029	−	3.07598i	−0.0881435	−	0.218601i
$199$		−	5.92036i		−	0.419683i	−0.977735	−	0.209842i	$-0.932705\pi$
$199$		−	5.92036i		−	0.419683i	0.977735	−	0.209842i	$-0.0672948\pi$
$200$			6.95158i			0.491551i
$201$			6.66903i			0.470397i
$202$		−	14.1963i		−	0.998845i
$203$		0			0
$204$		−	0.0457263i		−	0.00320148i
$205$		−	16.8488i		−	1.17677i
$206$	1.26090			0.0878509
$207$	−1.19252			−0.0828857
$208$	−5.39143			−0.373828
$209$	−21.3800	+	8.62078i	−1.47889	+	0.596312i
$210$		0			0
$211$		−	6.27732i		−	0.432148i	−0.976377	−	0.216074i	$-0.930675\pi$
$211$		−	6.27732i		−	0.432148i	0.976377	−	0.216074i	$-0.0693253\pi$
$212$	3.69054			0.253467
$213$			6.89741i			0.472603i
$214$	0.676179			0.0462226
$215$	11.3349			0.773034
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−19.6069			−1.32795
$219$		−	3.04272i		−	0.205608i
$220$	4.28781	+	10.6340i	0.289084	+	0.716945i
$221$	−0.246530			−0.0165834
$222$	1.51053			0.101380
$223$		−	23.9882i		−	1.60637i	−0.595730	−	0.803185i	$-0.703137\pi$
$223$		−	23.9882i		−	1.60637i	0.595730	−	0.803185i	$-0.296863\pi$
$224$		0			0
$225$	6.95158			0.463439
$226$		−	2.24860i		−	0.149575i
$227$	−27.9605			−1.85581			−0.927903	−	0.372823i	$-0.878390\pi$
$227$	−27.9605			−1.85581			−0.927903	+	0.372823i	$0.878390\pi$
$228$			6.95062i			0.460316i
$229$			22.8477i			1.50982i	0.655830	+	0.754908i	$0.272319\pi$
$229$			22.8477i			1.50982i	−0.655830	+	0.754908i	$0.727681\pi$
$230$	4.12266			0.271840
$231$		0			0
$232$	−7.78271			−0.510960
$233$			5.11552i			0.335129i	0.985861	+	0.167564i	$0.0535902\pi$
$233$			5.11552i			0.335129i	−0.985861	+	0.167564i	$0.946410\pi$
$234$			5.39143i			0.352449i
$235$	41.8517			2.73010
$236$		−	14.8396i		−	0.965974i
$237$	−12.9709			−0.842554
$238$		0			0
$239$			11.3940i			0.737016i	0.929625	+	0.368508i	$0.120131\pi$
$239$			11.3940i			0.737016i	−0.929625	+	0.368508i	$0.879869\pi$
$240$	3.45711			0.223155
$241$	20.6584			1.33072			0.665361	−	0.746521i	$-0.268277\pi$
$241$	20.6584			1.33072			0.665361	+	0.746521i	$0.268277\pi$
$242$	7.63022	+	7.92336i	0.490489	+	0.509333i
$243$			1.00000i			0.0641500i
$244$	3.63129			0.232469
$245$		0			0
$246$	−4.87368			−0.310734
$247$	37.4738			2.38440
$248$	6.61846			0.420273
$249$		−	8.48330i		−	0.537607i
$250$	−6.74683			−0.426707
$251$		−	15.9325i		−	1.00565i	−0.864389	−	0.502824i	$-0.832294\pi$
$251$		−	15.9325i		−	1.00565i	0.864389	−	0.502824i	$-0.167706\pi$
$252$		0			0
$253$	3.66816	−	1.47907i	0.230616	−	0.0929881i
$254$	−2.24140			−0.140638
$255$	0.158081			0.00989941
$256$	1.00000			0.0625000
$257$			2.50401i			0.156196i	0.996946	+	0.0780979i	$0.0248847\pi$
$257$			2.50401i			0.156196i	−0.996946	+	0.0780979i	$0.975115\pi$
$258$		−	3.27873i		−	0.204125i
$259$		0			0
$260$		−	18.6387i		−	1.15593i
$261$			7.78271i			0.481738i
$262$		−	2.65048i		−	0.163747i
$263$			21.6317i			1.33387i	0.745117	+	0.666934i	$0.232394\pi$
$263$			21.6317i			1.33387i	−0.745117	+	0.666934i	$0.767606\pi$
$264$	3.07598	−	1.24029i	0.189314	−	0.0763345i
$265$			12.7586i			0.783754i
$266$		0			0
$267$	−4.20562			−0.257380
$268$	−6.66903			−0.407376
$269$		−	6.05738i		−	0.369325i	−0.982802	−	0.184663i	$-0.940881\pi$
$269$		−	6.05738i		−	0.369325i	0.982802	−	0.184663i	$-0.0591192\pi$
$270$		−	3.45711i		−	0.210393i
$271$	17.7596			1.07882			0.539409	−	0.842044i	$-0.318648\pi$
$271$	17.7596			1.07882			0.539409	+	0.842044i	$0.318648\pi$
$272$	0.0457263			0.00277257
$273$		0			0
$274$		−	14.9046i		−	0.900421i
$275$	−21.3830	+	8.62198i	−1.28944	+	0.519925i
$276$		−	1.19252i		−	0.0717811i
$277$		−	28.8259i		−	1.73198i	−0.500059	−	0.865992i	$-0.666688\pi$
$277$		−	28.8259i		−	1.73198i	0.500059	−	0.865992i	$-0.333312\pi$
$278$		−	17.4420i		−	1.04610i
$279$		−	6.61846i		−	0.396237i
$280$		0			0
$281$			21.1314i			1.26060i	0.776354	+	0.630298i	$0.217067\pi$
$281$			21.1314i			1.26060i	−0.776354	+	0.630298i	$0.782933\pi$
$282$		−	12.1060i		−	0.720901i
$283$	−3.10856			−0.184785			−0.0923924	−	0.995723i	$-0.529451\pi$
$283$	−3.10856			−0.184785			−0.0923924	+	0.995723i	$0.529451\pi$
$284$	−6.89741			−0.409286
$285$	−24.0290			−1.42336
$286$	−6.68693	−	16.5839i	−0.395407	−	0.980629i
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−16.9979			−0.999877
$290$		−	26.9057i		−	1.57996i
$291$	6.64551			0.389567
$292$	3.04272			0.178062
$293$	−24.9692			−1.45872			−0.729358	−	0.684132i	$-0.760181\pi$
$293$	−24.9692			−1.45872			−0.729358	+	0.684132i	$0.760181\pi$
$294$		0			0
$295$	51.3020			2.98692
$296$			1.51053i			0.0877978i
$297$	−1.24029	−	3.07598i	−0.0719689	−	0.178487i
$298$	11.1458			0.645658
$299$	−6.42937			−0.371820
$300$			6.95158i			0.401350i
$301$		0			0
$302$	−13.7210			−0.789556
$303$		−	14.1963i		−	0.815554i
$304$	−6.95062			−0.398646
$305$			12.5538i			0.718826i
$306$		−	0.0457263i		−	0.00261400i
$307$	13.6795			0.780732			0.390366	−	0.920660i	$-0.372348\pi$
$307$	13.6795			0.780732			0.390366	+	0.920660i	$0.372348\pi$
$308$		0			0
$309$	1.26090			0.0717300
$310$			22.8807i			1.29954i
$311$		−	10.5374i		−	0.597521i	−0.954328	−	0.298760i	$-0.903427\pi$
$311$		−	10.5374i		−	0.597521i	0.954328	−	0.298760i	$-0.0965731\pi$
$312$	−5.39143			−0.305229
$313$		−	9.21844i		−	0.521057i	−0.965466	−	0.260528i	$-0.916103\pi$
$313$		−	9.21844i		−	0.521057i	0.965466	−	0.260528i	$-0.0838968\pi$
$314$	20.5517			1.15980
$315$		0			0
$316$		−	12.9709i		−	0.729673i
$317$	9.13510			0.513078			0.256539	−	0.966534i	$-0.417418\pi$
$317$	9.13510			0.513078			0.256539	+	0.966534i	$0.417418\pi$
$318$	3.69054			0.206955
$319$	−9.65282	−	23.9395i	−0.540454	−	1.34036i
$320$			3.45711i			0.193258i
$321$	0.676179			0.0377406
$322$		0			0
$323$	−0.317827			−0.0176843
$324$	−1.00000			−0.0555556
$325$	37.4790			2.07896
$326$		−	10.3412i		−	0.572746i
$327$	−19.6069			−1.08427
$328$		−	4.87368i		−	0.269104i
$329$		0			0
$330$	4.28781	+	10.6340i	0.236036	+	0.585383i
$331$	−9.48566			−0.521379			−0.260690	−	0.965423i	$-0.583950\pi$
$331$	−9.48566			−0.521379			−0.260690	+	0.965423i	$0.583950\pi$
$332$	8.48330			0.465582
$333$	1.51053			0.0827765
$334$			23.7721i			1.30075i
$335$		−	23.0555i		−	1.25966i
$336$		0			0
$337$		−	21.0197i		−	1.14501i	−0.819900	−	0.572507i	$-0.805971\pi$
$337$		−	21.0197i		−	1.14501i	0.819900	−	0.572507i	$-0.194029\pi$
$338$			16.0675i			0.873956i
$339$		−	2.24860i		−	0.122127i
$340$			0.158081i			0.00857314i
$341$	8.20881	+	20.3583i	0.444532	+	1.10246i
$342$			6.95062i			0.375847i
$343$		0			0
$344$	3.27873			0.176777
$345$	4.12266			0.221957
$346$			13.5605i			0.729019i
$347$			1.87391i			0.100597i	0.998734	+	0.0502984i	$0.0160172\pi$
$347$			1.87391i			0.100597i	−0.998734	+	0.0502984i	$0.983983\pi$
$348$	−7.78271			−0.417197
$349$	−32.8189			−1.75675			−0.878377	−	0.477969i	$-0.841373\pi$
$349$	−32.8189			−1.75675			−0.878377	+	0.477969i	$0.841373\pi$
$350$		0			0
$351$			5.39143i			0.287773i
$352$	1.24029	+	3.07598i	0.0661077	+	0.163951i
$353$		−	19.8071i		−	1.05422i	−0.849796	−	0.527112i	$-0.823275\pi$
$353$		−	19.8071i		−	1.05422i	0.849796	−	0.527112i	$-0.176725\pi$
$354$		−	14.8396i		−	0.788715i
$355$		−	23.8451i		−	1.26557i
$356$		−	4.20562i		−	0.222897i
$357$		0			0
$358$		−	16.1833i		−	0.855316i
$359$		−	27.4211i		−	1.44723i	−0.690203	−	0.723616i	$-0.742479\pi$
$359$		−	27.4211i		−	1.44723i	0.690203	−	0.723616i	$-0.257521\pi$
$360$	3.45711			0.182206
$361$	29.3112			1.54269
$362$	−15.6283			−0.821405
$363$	7.63022	+	7.92336i	0.400483	+	0.415869i
$364$		0			0
$365$			10.5190i			0.550590i
$366$	3.63129			0.189811
$367$		−	17.2117i		−	0.898444i	−0.893420	−	0.449222i	$-0.851701\pi$
$367$		−	17.2117i		−	0.898444i	0.893420	−	0.449222i	$-0.148299\pi$
$368$	1.19252			0.0621643
$369$	−4.87368			−0.253713
$370$	−5.22206			−0.271482
$371$		0			0
$372$	6.61846			0.343151
$373$			23.5811i			1.22099i	0.792022	+	0.610493i	$0.209029\pi$
$373$			23.5811i			1.22099i	−0.792022	+	0.610493i	$0.790971\pi$
$374$	0.0567139	+	0.140654i	0.00293261	+	0.00727302i
$375$	−6.74683			−0.348405
$376$	12.1060			0.624319
$377$			41.9599i			2.16105i
$378$		0			0
$379$	6.82325			0.350487			0.175243	−	0.984525i	$-0.443929\pi$
$379$	6.82325			0.350487			0.175243	+	0.984525i	$0.443929\pi$
$380$		−	24.0290i		−	1.23266i
$381$	−2.24140			−0.114830
$382$		−	8.42409i		−	0.431014i
$383$		−	10.0655i		−	0.514321i	−0.966369	−	0.257160i	$-0.917213\pi$
$383$		−	10.0655i		−	0.514321i	0.966369	−	0.257160i	$-0.0827869\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−9.14795			−0.465618
$387$		−	3.27873i		−	0.166667i
$388$			6.64551i			0.337375i
$389$	11.3167			0.573778			0.286889	−	0.957964i	$-0.407379\pi$
$389$	11.3167			0.573778			0.286889	+	0.957964i	$0.407379\pi$
$390$		−	18.6387i		−	0.943809i
$391$	0.0545295			0.00275767
$392$		0			0
$393$		−	2.65048i		−	0.133699i
$394$	13.7101			0.690706
$395$	44.8419			2.25624
$396$	3.07598	−	1.24029i	0.154574	−	0.0623269i
$397$			26.8201i			1.34606i	0.739614	+	0.673031i	$0.235008\pi$
$397$			26.8201i			1.34606i	−0.739614	+	0.673031i	$0.764992\pi$
$398$	5.92036			0.296761
$399$		0			0
$400$	−6.95158			−0.347579
$401$	−14.0066			−0.699457			−0.349728	−	0.936851i	$-0.613726\pi$
$401$	−14.0066			−0.699457			−0.349728	+	0.936851i	$0.613726\pi$
$402$	−6.66903			−0.332621
$403$		−	35.6829i		−	1.77749i
$404$	14.1963			0.706290
$405$		−	3.45711i		−	0.171785i
$406$		0			0
$407$	−4.64637	+	1.87349i	−0.230312	+	0.0928657i
$408$	0.0457263			0.00226379
$409$	−6.38532			−0.315734			−0.157867	−	0.987460i	$-0.550462\pi$
$409$	−6.38532			−0.315734			−0.157867	+	0.987460i	$0.550462\pi$
$410$	16.8488			0.832104
$411$		−	14.9046i		−	0.735190i
$412$			1.26090i			0.0621200i
$413$		0			0
$414$		−	1.19252i		−	0.0586090i
$415$			29.3277i			1.43964i
$416$		−	5.39143i		−	0.264336i
$417$		−	17.4420i		−	0.854140i
$418$	−8.62078	−	21.3800i	−0.421656	−	1.04573i
$419$			18.9490i			0.925718i	0.886432	+	0.462859i	$0.153176\pi$
$419$			18.9490i			0.925718i	−0.886432	+	0.462859i	$0.846824\pi$
$420$		0			0
$421$	−21.8148			−1.06319			−0.531595	−	0.846999i	$-0.678407\pi$
$421$	−21.8148			−1.06319			−0.531595	+	0.846999i	$0.678407\pi$
$422$	6.27732			0.305575
$423$		−	12.1060i		−	0.588613i
$424$			3.69054i			0.179229i
$425$	−0.317871			−0.0154190
$426$	−6.89741			−0.334181
$427$		0			0
$428$			0.676179i			0.0326843i
$429$	−6.68693	−	16.5839i	−0.322848	−	0.800680i
$430$			11.3349i			0.546618i
$431$			6.96363i			0.335426i	0.985836	+	0.167713i	$0.0536383\pi$
$431$			6.96363i			0.335426i	−0.985836	+	0.167713i	$0.946362\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			4.32631i			0.207909i	0.994582	+	0.103955i	$0.0331496\pi$
$433$			4.32631i			0.207909i	−0.994582	+	0.103955i	$0.966850\pi$
$434$		0			0
$435$		−	26.9057i		−	1.29003i
$436$		−	19.6069i		−	0.939002i
$437$	−8.28874			−0.396504
$438$	3.04272			0.145387
$439$	−1.95568			−0.0933395			−0.0466698	−	0.998910i	$-0.514861\pi$
$439$	−1.95568			−0.0933395			−0.0466698	+	0.998910i	$0.514861\pi$
$440$	−10.6340	+	4.28781i	−0.506956	+	0.204413i
$441$		0			0
$442$		−	0.246530i		−	0.0117262i
$443$	−13.8098			−0.656122			−0.328061	−	0.944656i	$-0.606395\pi$
$443$	−13.8098			−0.656122			−0.328061	+	0.944656i	$0.606395\pi$
$444$			1.51053i			0.0716866i
$445$	14.5393			0.689228
$446$	23.9882			1.13588
$447$	11.1458			0.527178
$448$		0			0
$449$	−34.4653			−1.62652			−0.813259	−	0.581901i	$-0.802309\pi$
$449$	−34.4653			−1.62652			−0.813259	+	0.581901i	$0.802309\pi$
$450$			6.95158i			0.327701i
$451$	14.9913	−	6.04477i	0.705915	−	0.284637i
$452$	2.24860			0.105765
$453$	−13.7210			−0.644670
$454$		−	27.9605i		−	1.31225i
$455$		0			0
$456$	−6.95062			−0.325493
$457$		−	24.0756i		−	1.12621i	−0.826386	−	0.563104i	$-0.809607\pi$
$457$		−	24.0756i		−	1.12621i	0.826386	−	0.563104i	$-0.190393\pi$
$458$	−22.8477			−1.06760
$459$		−	0.0457263i		−	0.00213432i
$460$			4.12266i			0.192220i
$461$	6.27016			0.292030			0.146015	−	0.989282i	$-0.453355\pi$
$461$	6.27016			0.292030			0.146015	+	0.989282i	$0.453355\pi$
$462$		0			0
$463$	−0.766178			−0.0356073			−0.0178036	−	0.999842i	$-0.505667\pi$
$463$	−0.766178			−0.0356073			−0.0178036	+	0.999842i	$0.505667\pi$
$464$		−	7.78271i		−	0.361303i
$465$			22.8807i			1.06107i
$466$	−5.11552			−0.236972
$467$			27.5152i			1.27325i	0.771172	+	0.636626i	$0.219671\pi$
$467$			27.5152i			1.27325i	−0.771172	+	0.636626i	$0.780329\pi$
$468$	−5.39143			−0.249219
$469$		0			0
$470$			41.8517i			1.93047i
$471$	20.5517			0.946974
$472$	14.8396			0.683047
$473$	4.06657	+	10.0853i	0.186981	+	0.463723i
$474$		−	12.9709i		−	0.595775i
$475$	48.3178			2.21697
$476$		0			0
$477$	3.69054			0.168978
$478$	−11.3940			−0.521149
$479$	−14.3917			−0.657575			−0.328788	−	0.944404i	$-0.606640\pi$
$479$	−14.3917			−0.657575			−0.328788	+	0.944404i	$0.606640\pi$
$480$			3.45711i			0.157795i
$481$	8.14391			0.371330
$482$			20.6584i			0.940963i
$483$		0			0
$484$	−7.92336	+	7.63022i	−0.360153	+	0.346828i
$485$	−22.9742			−1.04321
$486$	−1.00000			−0.0453609
$487$	−15.4033			−0.697988			−0.348994	−	0.937125i	$-0.613477\pi$
$487$	−15.4033			−0.697988			−0.348994	+	0.937125i	$0.613477\pi$
$488$			3.63129i			0.164381i
$489$		−	10.3412i		−	0.467646i
$490$		0			0
$491$			5.09884i			0.230107i	0.993359	+	0.115054i	$0.0367040\pi$
$491$			5.09884i			0.230107i	−0.993359	+	0.115054i	$0.963296\pi$
$492$		−	4.87368i		−	0.219722i
$493$		−	0.355875i		−	0.0160278i
$494$			37.4738i			1.68602i
$495$	4.28781	+	10.6340i	0.192723	+	0.477963i
$496$			6.61846i			0.297178i
$497$		0			0
$498$	8.48330			0.380146
$499$	−23.7056			−1.06121			−0.530605	−	0.847619i	$-0.678035\pi$
$499$	−23.7056			−1.06121			−0.530605	+	0.847619i	$0.678035\pi$
$500$		−	6.74683i		−	0.301728i
$501$			23.7721i			1.06206i
$502$	15.9325			0.711101
$503$	38.3613			1.71045			0.855223	−	0.518260i	$-0.173420\pi$
$503$	38.3613			1.71045			0.855223	+	0.518260i	$0.173420\pi$
$504$		0			0
$505$			49.0780i			2.18394i
$506$	1.47907	+	3.66816i	0.0657525	+	0.163070i
$507$			16.0675i			0.713582i
$508$		−	2.24140i		−	0.0994461i
$509$		−	30.6547i		−	1.35874i	−0.733794	−	0.679372i	$-0.762252\pi$
$509$		−	30.6547i		−	1.35874i	0.733794	−	0.679372i	$-0.237748\pi$
$510$			0.158081i			0.00699994i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			6.95062i			0.306877i
$514$	−2.50401			−0.110447
$515$	−4.35906			−0.192083
$516$	3.27873			0.144338
$517$	15.0149	+	37.2378i	0.660356	+	1.63772i
$518$		0			0
$519$			13.5605i			0.595242i
$520$	18.6387			0.817363
$521$			41.7976i			1.83119i	0.402106	+	0.915593i	$0.368278\pi$
$521$			41.7976i			1.83119i	−0.402106	+	0.915593i	$0.631722\pi$
$522$	−7.78271			−0.340640
$523$	13.0947			0.572591			0.286296	−	0.958141i	$-0.407576\pi$
$523$	13.0947			0.572591			0.286296	+	0.958141i	$0.407576\pi$
$524$	2.65048			0.115787
$525$		0			0
$526$	−21.6317			−0.943187
$527$			0.302638i			0.0131831i
$528$	1.24029	+	3.07598i	0.0539767	+	0.133865i
$529$	−21.5779			−0.938170
$530$	−12.7586			−0.554198
$531$		−	14.8396i		−	0.643983i
$532$		0			0
$533$	−26.2761			−1.13814
$534$		−	4.20562i		−	0.181995i
$535$	−2.33762			−0.101064
$536$		−	6.66903i		−	0.288058i
$537$		−	16.1833i		−	0.698362i
$538$	6.05738			0.261152
$539$		0			0
$540$	3.45711			0.148770
$541$			9.85167i			0.423556i	0.977318	+	0.211778i	$0.0679254\pi$
$541$			9.85167i			0.423556i	−0.977318	+	0.211778i	$0.932075\pi$
$542$			17.7596i			0.762840i
$543$	−15.6283			−0.670675
$544$			0.0457263i			0.00196050i
$545$	67.7832			2.90352
$546$		0			0
$547$			7.17541i			0.306798i	0.988164	+	0.153399i	$0.0490220\pi$
$547$			7.17541i			0.306798i	−0.988164	+	0.153399i	$0.950978\pi$
$548$	14.9046			0.636694
$549$	3.63129			0.154980
$550$	−8.62198	−	21.3830i	−0.367642	−	0.911773i
$551$			54.0947i			2.30451i
$552$	1.19252			0.0507569
$553$		0			0
$554$	28.8259			1.22470
$555$	−5.22206			−0.221664
$556$	17.4420			0.739707
$557$			38.2620i			1.62121i	0.585590	+	0.810607i	$0.300863\pi$
$557$			38.2620i			1.62121i	−0.585590	+	0.810607i	$0.699137\pi$
$558$	6.61846			0.280182
$559$		−	17.6770i		−	0.747658i
$560$		0			0
$561$	0.0567139	+	0.140654i	0.00239446	+	0.00593840i
$562$	−21.1314			−0.891375
$563$	−39.6058			−1.66918			−0.834592	−	0.550868i	$-0.814297\pi$
$563$	−39.6058			−1.66918			−0.834592	+	0.550868i	$0.814297\pi$
$564$	12.1060			0.509754
$565$			7.77366i			0.327040i
$566$		−	3.10856i		−	0.130663i
$567$		0			0
$568$		−	6.89741i		−	0.289409i
$569$			9.08146i			0.380715i	0.981715	+	0.190357i	$0.0609646\pi$
$569$			9.08146i			0.380715i	−0.981715	+	0.190357i	$0.939035\pi$
$570$		−	24.0290i		−	1.00647i
$571$		−	18.5109i		−	0.774659i	−0.921941	−	0.387329i	$-0.873398\pi$
$571$		−	18.5109i		−	0.774659i	0.921941	−	0.387329i	$-0.126602\pi$
$572$	16.5839	−	6.68693i	0.693410	−	0.279595i
$573$		−	8.42409i		−	0.351921i
$574$		0			0
$575$	−8.28988			−0.345712
$576$	1.00000			0.0416667
$577$			35.6857i			1.48562i	0.669505	+	0.742808i	$0.266506\pi$
$577$			35.6857i			1.48562i	−0.669505	+	0.742808i	$0.733494\pi$
$578$		−	16.9979i		−	0.707020i
$579$	−9.14795			−0.380176
$580$	26.9057			1.11720
$581$		0			0
$582$			6.64551i			0.275465i
$583$	−11.3520	+	4.57734i	−0.470154	+	0.189574i
$584$			3.04272i			0.125909i
$585$		−	18.6387i		−	0.770617i
$586$		−	24.9692i		−	1.03147i
$587$		−	11.3534i		−	0.468606i	−0.972164	−	0.234303i	$-0.924719\pi$
$587$		−	11.3534i		−	0.468606i	0.972164	−	0.234303i	$-0.0752808\pi$
$588$		0			0
$589$		−	46.0024i		−	1.89550i
$590$			51.3020i			2.11207i
$591$	13.7101			0.563959
$592$	−1.51053			−0.0620824
$593$	18.1657			0.745974			0.372987	−	0.927837i	$-0.378334\pi$
$593$	18.1657			0.745974			0.372987	+	0.927837i	$0.378334\pi$
$594$	3.07598	−	1.24029i	0.126209	−	0.0508897i
$595$		0			0
$596$			11.1458i			0.456549i
$597$	5.92036			0.242304
$598$		−	6.42937i		−	0.262916i
$599$	34.4805			1.40884			0.704419	−	0.709785i	$-0.251208\pi$
$599$	34.4805			1.40884			0.704419	+	0.709785i	$0.251208\pi$
$600$	−6.95158			−0.283797
$601$	−19.6808			−0.802797			−0.401398	−	0.915904i	$-0.631476\pi$
$601$	−19.6808			−0.802797			−0.401398	+	0.915904i	$0.631476\pi$
$602$		0			0
$603$	−6.66903			−0.271584
$604$		−	13.7210i		−	0.558300i
$605$	−26.3785	−	27.3919i	−1.07244	−	1.11364i
$606$	14.1963			0.576684
$607$	−16.2385			−0.659102			−0.329551	−	0.944138i	$-0.606897\pi$
$607$	−16.2385			−0.659102			−0.329551	+	0.944138i	$0.606897\pi$
$608$		−	6.95062i		−	0.281885i
$609$		0			0
$610$	−12.5538			−0.508287
$611$		−	65.2685i		−	2.64048i
$612$	0.0457263			0.00184838
$613$		−	15.9340i		−	0.643567i	−0.946813	−	0.321783i	$-0.895718\pi$
$613$		−	15.9340i		−	0.643567i	0.946813	−	0.321783i	$-0.104282\pi$
$614$			13.6795i			0.552061i
$615$	16.8488			0.679410
$616$		0			0
$617$	8.30634			0.334401			0.167200	−	0.985923i	$-0.446527\pi$
$617$	8.30634			0.334401			0.167200	+	0.985923i	$0.446527\pi$
$618$			1.26090i			0.0507207i
$619$		−	13.0920i		−	0.526212i	−0.964767	−	0.263106i	$-0.915253\pi$
$619$		−	13.0920i		−	0.526212i	0.964767	−	0.263106i	$-0.0847468\pi$
$620$	−22.8807			−0.918912
$621$		−	1.19252i		−	0.0478541i
$622$	10.5374			0.422511
$623$		0			0
$624$		−	5.39143i		−	0.215830i
$625$	−11.4334			−0.457336
$626$	9.21844			0.368443
$627$	−8.62078	−	21.3800i	−0.344281	−	0.853835i
$628$			20.5517i			0.820104i
$629$	−0.0690710			−0.00275404
$630$		0			0
$631$	4.60081			0.183155			0.0915776	−	0.995798i	$-0.470809\pi$
$631$	4.60081			0.183155			0.0915776	+	0.995798i	$0.470809\pi$
$632$	12.9709			0.515957
$633$	6.27732			0.249501
$634$			9.13510i			0.362801i
$635$	7.74876			0.307500
$636$			3.69054i			0.146339i
$637$		0			0
$638$	23.9395	−	9.65282i	0.947774	−	0.382159i
$639$	−6.89741			−0.272857
$640$	−3.45711			−0.136654
$641$	−20.5868			−0.813131			−0.406565	−	0.913622i	$-0.633274\pi$
$641$	−20.5868			−0.813131			−0.406565	+	0.913622i	$0.633274\pi$
$642$			0.676179i			0.0266866i
$643$		−	3.20879i		−	0.126542i	−0.997996	−	0.0632712i	$-0.979847\pi$
$643$		−	3.20879i		−	0.126542i	0.997996	−	0.0632712i	$-0.0201533\pi$
$644$		0			0
$645$			11.3349i			0.446312i
$646$		−	0.317827i		−	0.0125047i
$647$		−	3.22975i		−	0.126974i	−0.997983	−	0.0634872i	$-0.979778\pi$
$647$		−	3.22975i		−	0.126974i	0.997983	−	0.0634872i	$-0.0202222\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	18.4054	+	45.6463i	0.722474	+	1.79177i
$650$			37.4790i			1.47005i
$651$		0			0
$652$	10.3412			0.404993
$653$	38.6968			1.51432			0.757162	−	0.653227i	$-0.226585\pi$
$653$	38.6968			1.51432			0.757162	+	0.653227i	$0.226585\pi$
$654$		−	19.6069i		−	0.766692i
$655$			9.16298i			0.358027i
$656$	4.87368			0.190285
$657$	3.04272			0.118708
$658$		0			0
$659$		−	15.9199i		−	0.620150i	−0.950712	−	0.310075i	$-0.899646\pi$
$659$		−	15.9199i		−	0.620150i	0.950712	−	0.310075i	$-0.100354\pi$
$660$	−10.6340	+	4.28781i	−0.413928	+	0.166903i
$661$		−	13.1465i		−	0.511338i	−0.966764	−	0.255669i	$-0.917704\pi$
$661$		−	13.1465i		−	0.511338i	0.966764	−	0.255669i	$-0.0822958\pi$
$662$		−	9.48566i		−	0.368671i
$663$		−	0.246530i		−	0.00957444i
$664$			8.48330i			0.329216i
$665$		0			0
$666$			1.51053i			0.0585319i
$667$		−	9.28102i		−	0.359363i
$668$	−23.7721			−0.919769
$669$	23.9882			0.927438
$670$	23.0555			0.890713
$671$	−11.1698	+	4.50385i	−0.431205	+	0.173869i
$672$		0			0
$673$			3.87040i			0.149193i	0.997214	+	0.0745965i	$0.0237669\pi$
$673$			3.87040i			0.149193i	−0.997214	+	0.0745965i	$0.976233\pi$
$674$	21.0197			0.809647
$675$			6.95158i			0.267567i
$676$	−16.0675			−0.617980
$677$	39.9138			1.53401			0.767006	−	0.641640i	$-0.221746\pi$
$677$	39.9138			1.53401			0.767006	+	0.641640i	$0.221746\pi$
$678$	2.24860			0.0863571
$679$		0			0
$680$	−0.158081			−0.00606212
$681$		−	27.9605i		−	1.07145i
$682$	−20.3583	+	8.20881i	−0.779559	+	0.314331i
$683$	−30.6358			−1.17225			−0.586124	−	0.810222i	$-0.699347\pi$
$683$	−30.6358			−1.17225			−0.586124	+	0.810222i	$0.699347\pi$
$684$	−6.95062			−0.265764
$685$			51.5268i			1.96874i
$686$		0			0
$687$	−22.8477			−0.871693
$688$			3.27873i			0.125000i
$689$	19.8973			0.758026
$690$			4.12266i			0.156947i
$691$		−	14.2288i		−	0.541290i	−0.962679	−	0.270645i	$-0.912763\pi$
$691$		−	14.2288i		−	0.541290i	0.962679	−	0.270645i	$-0.0872369\pi$
$692$	−13.5605			−0.515494
$693$		0			0
$694$	−1.87391			−0.0711326
$695$			60.2989i			2.28727i
$696$		−	7.78271i		−	0.295003i
$697$	0.222855			0.00844125
$698$		−	32.8189i		−	1.24221i
$699$	−5.11552			−0.193487
$700$		0			0
$701$			44.8935i			1.69560i	0.530312	+	0.847802i	$0.322075\pi$
$701$			44.8935i			1.69560i	−0.530312	+	0.847802i	$0.677925\pi$
$702$	−5.39143			−0.203486
$703$	10.4991			0.395982
$704$	−3.07598	+	1.24029i	−0.115931	+	0.0467452i
$705$			41.8517i			1.57623i
$706$	19.8071			0.745449
$707$		0			0
$708$	14.8396			0.557706
$709$	19.5243			0.733252			0.366626	−	0.930368i	$-0.380513\pi$
$709$	19.5243			0.733252			0.366626	+	0.930368i	$0.380513\pi$
$710$	23.8451			0.894890
$711$		−	12.9709i		−	0.486449i
$712$	4.20562			0.157612
$713$			7.89263i			0.295581i
$714$		0			0
$715$	23.1174	+	57.3325i	0.864543	+	2.14411i
$716$	16.1833			0.604799
$717$	−11.3940			−0.425516
$718$	27.4211			1.02335
$719$			34.6102i			1.29074i	0.763870	+	0.645371i	$0.223297\pi$
$719$			34.6102i			1.29074i	−0.763870	+	0.645371i	$0.776703\pi$
$720$			3.45711i			0.128839i
$721$		0			0
$722$			29.3112i			1.09085i
$723$			20.6584i			0.768293i
$724$		−	15.6283i		−	0.580821i
$725$			54.1022i			2.00930i
$726$	−7.92336	+	7.63022i	−0.294064	+	0.283184i
$727$		−	17.5486i		−	0.650840i	−0.945570	−	0.325420i	$-0.894494\pi$
$727$		−	17.5486i		−	0.650840i	0.945570	−	0.325420i	$-0.105506\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−10.5190			−0.389326
$731$			0.149924i			0.00554515i
$732$			3.63129i			0.134216i
$733$	−39.1221			−1.44501			−0.722504	−	0.691367i	$-0.757009\pi$
$733$	−39.1221			−1.44501			−0.722504	+	0.691367i	$0.757009\pi$
$734$	17.2117			0.635296
$735$		0			0
$736$			1.19252i			0.0439568i
$737$	20.5138	−	8.27153i	0.755637	−	0.304686i
$738$		−	4.87368i		−	0.179402i
$739$			33.6557i			1.23804i	0.785374	+	0.619022i	$0.212471\pi$
$739$			33.6557i			1.23804i	−0.785374	+	0.619022i	$0.787529\pi$
$740$		−	5.22206i		−	0.191967i
$741$			37.4738i			1.37663i
$742$		0			0
$743$			32.1198i			1.17836i	0.808001	+	0.589181i	$0.200550\pi$
$743$			32.1198i			1.17836i	−0.808001	+	0.589181i	$0.799450\pi$
$744$			6.61846i			0.242644i
$745$	−38.5322			−1.41171
$746$	−23.5811			−0.863367
$747$	8.48330			0.310388
$748$	−0.140654	+	0.0567139i	−0.00514280	+	0.00207367i
$749$		0			0
$750$		−	6.74683i		−	0.246360i
$751$	51.6804			1.88584			0.942922	−	0.333014i	$-0.108065\pi$
$751$	51.6804			1.88584			0.942922	+	0.333014i	$0.108065\pi$
$752$			12.1060i			0.441460i
$753$	15.9325			0.580611
$754$	−41.9599			−1.52809
$755$	47.4350			1.72634
$756$		0			0
$757$	43.1042			1.56665			0.783324	−	0.621614i	$-0.213523\pi$
$757$	43.1042			1.56665			0.783324	+	0.621614i	$0.213523\pi$
$758$			6.82325i			0.247831i
$759$	1.47907	+	3.66816i	0.0536867	+	0.133146i
$760$	24.0290			0.871625
$761$	6.05142			0.219364			0.109682	−	0.993967i	$-0.465017\pi$
$761$	6.05142			0.219364			0.109682	+	0.993967i	$0.465017\pi$
$762$		−	2.24140i		−	0.0811974i
$763$		0			0
$764$	8.42409			0.304773
$765$			0.158081i			0.00571543i
$766$	10.0655			0.363680
$767$		−	80.0065i		−	2.88887i
$768$			1.00000i			0.0360844i
$769$	44.3139			1.59800			0.799000	−	0.601331i	$-0.205363\pi$
$769$	44.3139			1.59800			0.799000	+	0.601331i	$0.205363\pi$
$770$		0			0
$771$	−2.50401			−0.0901797
$772$		−	9.14795i		−	0.329242i
$773$		−	0.830514i		−	0.0298715i	−0.999888	−	0.0149358i	$-0.995246\pi$
$773$		−	0.830514i		−	0.0298715i	0.999888	−	0.0149358i	$-0.00475437\pi$
$774$	3.27873			0.117851
$775$		−	46.0088i		−	1.65268i
$776$	−6.64551			−0.238560
$777$		0			0
$778$			11.3167i			0.405722i
$779$	−33.8751			−1.21370
$780$	18.6387			0.667374
$781$	21.2163	−	8.55479i	0.759180	−	0.306114i
$782$			0.0545295i			0.00194997i
$783$	−7.78271			−0.278132
$784$		0			0
$785$	−71.0496			−2.53587
$786$	2.65048			0.0945394
$787$	41.5963			1.48275			0.741374	−	0.671092i	$-0.234174\pi$
$787$	41.5963			1.48275			0.741374	+	0.671092i	$0.234174\pi$
$788$			13.7101i			0.488403i
$789$	−21.6317			−0.770109
$790$			44.8419i			1.59540i
$791$		0			0
$792$	1.24029	+	3.07598i	0.0440718	+	0.109300i
$793$	19.5778			0.695229
$794$	−26.8201			−0.951810
$795$	−12.7586			−0.452501
$796$			5.92036i			0.209842i
$797$		−	13.1136i		−	0.464507i	−0.972655	−	0.232254i	$-0.925390\pi$
$797$		−	13.1136i		−	0.464507i	0.972655	−	0.232254i	$-0.0746099\pi$
$798$		0			0
$799$			0.553563i			0.0195836i
$800$		−	6.95158i		−	0.245776i
$801$		−	4.20562i		−	0.148598i
$802$		−	14.0066i		−	0.494591i
$803$	−9.35936	+	3.77385i	−0.330285	+	0.133176i
$804$		−	6.66903i		−	0.235198i
$805$		0			0
$806$	35.6829			1.25688
$807$	6.05738			0.213230
$808$			14.1963i			0.499423i
$809$		−	11.7322i		−	0.412481i	−0.978501	−	0.206240i	$-0.933877\pi$
$809$		−	11.7322i		−	0.412481i	0.978501	−	0.206240i	$-0.0661229\pi$
$810$	3.45711			0.121470
$811$	−45.2773			−1.58990			−0.794950	−	0.606675i	$-0.792503\pi$
$811$	−45.2773			−1.58990			−0.794950	+	0.606675i	$0.792503\pi$
$812$		0			0
$813$			17.7596i			0.622856i
$814$	−1.87349	−	4.64637i	−0.0656660	−	0.162855i
$815$			35.7506i			1.25229i
$816$			0.0457263i			0.00160074i
$817$		−	22.7892i		−	0.797293i
$818$		−	6.38532i		−	0.223258i
$819$		0			0
$820$			16.8488i			0.588386i
$821$			4.57149i			0.159546i	0.996813	+	0.0797730i	$0.0254195\pi$
$821$			4.57149i			0.159546i	−0.996813	+	0.0797730i	$0.974580\pi$
$822$	14.9046			0.519858
$823$	3.85368			0.134331			0.0671655	−	0.997742i	$-0.478604\pi$
$823$	3.85368			0.134331			0.0671655	+	0.997742i	$0.478604\pi$
$824$	−1.26090			−0.0439255
$825$	−8.62198	−	21.3830i	−0.300179	−	0.744459i
$826$		0			0
$827$		−	0.321085i		−	0.0111652i	−0.999984	−	0.00558261i	$-0.998223\pi$
$827$		−	0.321085i		−	0.0111652i	0.999984	−	0.00558261i	$-0.00177701\pi$
$828$	1.19252			0.0414428
$829$			9.89076i			0.343520i	0.985139	+	0.171760i	$0.0549454\pi$
$829$			9.89076i			0.343520i	−0.985139	+	0.171760i	$0.945055\pi$
$830$	−29.3277			−1.01798
$831$	28.8259			0.999961
$832$	5.39143			0.186914
$833$		0			0
$834$	17.4420			0.603968
$835$		−	82.1826i		−	2.84404i
$836$	21.3800	−	8.62078i	0.739443	−	0.298156i
$837$	6.61846			0.228767
$838$	−18.9490			−0.654581
$839$		−	19.1031i		−	0.659512i	−0.944066	−	0.329756i	$-0.893033\pi$
$839$		−	19.1031i		−	0.659512i	0.944066	−	0.329756i	$-0.106967\pi$
$840$		0			0
$841$	−31.5706			−1.08864
$842$		−	21.8148i		−	0.751789i
$843$	−21.1314			−0.727805
$844$			6.27732i			0.216074i
$845$		−	55.5470i		−	1.91087i
$846$	12.1060			0.416212
$847$		0			0
$848$	−3.69054			−0.126734
$849$		−	3.10856i		−	0.106686i
$850$		−	0.317871i		−	0.0109029i
$851$	−1.80133			−0.0617489
$852$		−	6.89741i		−	0.236301i
$853$	−6.65956			−0.228019			−0.114009	−	0.993480i	$-0.536369\pi$
$853$	−6.65956			−0.228019			−0.114009	+	0.993480i	$0.536369\pi$
$854$		0			0
$855$		−	24.0290i		−	0.821776i
$856$	−0.676179			−0.0231113
$857$	−18.2342			−0.622867			−0.311434	−	0.950268i	$-0.600809\pi$
$857$	−18.2342			−0.622867			−0.311434	+	0.950268i	$0.600809\pi$
$858$	16.5839	−	6.68693i	0.566167	−	0.228288i
$859$		−	47.3128i		−	1.61429i	−0.590352	−	0.807146i	$-0.701011\pi$
$859$		−	47.3128i		−	1.61429i	0.590352	−	0.807146i	$-0.298989\pi$
$860$	−11.3349			−0.386517
$861$		0			0
$862$	−6.96363			−0.237182
$863$	47.4281			1.61447			0.807236	−	0.590228i	$-0.200962\pi$
$863$	47.4281			1.61447			0.807236	+	0.590228i	$0.200962\pi$
$864$	1.00000			0.0340207
$865$		−	46.8802i		−	1.59398i
$866$	−4.32631			−0.147014
$867$		−	16.9979i		−	0.577279i
$868$		0			0
$869$	16.0877	+	39.8984i	0.545739	+	1.35346i
$870$	26.9057			0.912188
$871$	−35.9556			−1.21831
$872$	19.6069			0.663974
$873$			6.64551i			0.224916i
$874$		−	8.28874i		−	0.280371i
$875$		0			0
$876$			3.04272i			0.102804i
$877$		−	16.9463i		−	0.572236i	−0.958194	−	0.286118i	$-0.907635\pi$
$877$		−	16.9463i		−	0.572236i	0.958194	−	0.286118i	$-0.0923649\pi$
$878$		−	1.95568i		−	0.0660010i
$879$		−	24.9692i		−	0.842190i
$880$	−4.28781	−	10.6340i	−0.144542	−	0.358472i
$881$		−	34.5802i		−	1.16504i	−0.812817	−	0.582518i	$-0.802067\pi$
$881$		−	34.5802i		−	1.16504i	0.812817	−	0.582518i	$-0.197933\pi$
$882$		0			0
$883$	−15.6051			−0.525154			−0.262577	−	0.964911i	$-0.584572\pi$
$883$	−15.6051			−0.525154			−0.262577	+	0.964911i	$0.584572\pi$
$884$	0.246530			0.00829171
$885$			51.3020i			1.72450i
$886$		−	13.8098i		−	0.463949i
$887$	1.12794			0.0378727			0.0189363	−	0.999821i	$-0.493972\pi$
$887$	1.12794			0.0378727			0.0189363	+	0.999821i	$0.493972\pi$
$888$	−1.51053			−0.0506901
$889$		0			0
$890$			14.5393i			0.487358i
$891$	3.07598	−	1.24029i	0.103049	−	0.0415513i
$892$			23.9882i			0.803185i
$893$		−	84.1441i		−	2.81578i
$894$			11.1458i			0.372771i
$895$			55.9475i			1.87012i
$896$		0			0
$897$		−	6.42937i		−	0.214670i
$898$		−	34.4653i		−	1.15012i
$899$	51.5096			1.71794
$900$	−6.95158			−0.231719
$901$	−0.168755			−0.00562204
$902$	6.04477	+	14.9913i	0.201269	+	0.499157i
$903$		0			0
$904$			2.24860i			0.0747875i
$905$	54.0287			1.79597
$906$		−	13.7210i		−	0.455850i
$907$	−43.2193			−1.43507			−0.717537	−	0.696521i	$-0.754730\pi$
$907$	−43.2193			−1.43507			−0.717537	+	0.696521i	$0.754730\pi$
$908$	27.9605			0.927903
$909$	14.1963			0.470860
$910$		0			0
$911$	13.2783			0.439928			0.219964	−	0.975508i	$-0.429406\pi$
$911$	13.2783			0.439928			0.219964	+	0.975508i	$0.429406\pi$
$912$		−	6.95062i		−	0.230158i
$913$	−26.0945	+	10.5217i	−0.863602	+	0.348219i
$914$	24.0756			0.796349
$915$	−12.5538			−0.415014
$916$		−	22.8477i		−	0.754908i
$917$		0			0
$918$	0.0457263			0.00150919
$919$		−	15.5661i		−	0.513478i	−0.966481	−	0.256739i	$-0.917352\pi$
$919$		−	15.5661i		−	0.513478i	0.966481	−	0.256739i	$-0.0826481\pi$
$920$	−4.12266			−0.135920
$921$			13.6795i			0.450756i
$922$			6.27016i			0.206497i
$923$	−37.1869			−1.22402
$924$		0			0
$925$	10.5006			0.345257
$926$		−	0.766178i		−	0.0251782i
$927$			1.26090i			0.0414133i
$928$	7.78271			0.255480
$929$			21.8356i			0.716403i	0.933644	+	0.358201i	$0.116610\pi$
$929$			21.8356i			0.716403i	−0.933644	+	0.358201i	$0.883390\pi$
$930$	−22.8807			−0.750288
$931$		0			0
$932$		−	5.11552i		−	0.167564i
$933$	10.5374			0.344979
$934$	−27.5152			−0.900326
$935$	−0.196066	−	0.486254i	−0.00641205	−	0.0159022i
$936$		−	5.39143i		−	0.176224i
$937$	−40.9973			−1.33932			−0.669661	−	0.742667i	$-0.733561\pi$
$937$	−40.9973			−1.33932			−0.669661	+	0.742667i	$0.733561\pi$
$938$		0			0
$939$	9.21844			0.300832
$940$	−41.8517			−1.36505
$941$	30.0564			0.979811			0.489905	−	0.871776i	$-0.337031\pi$
$941$	30.0564			0.979811			0.489905	+	0.871776i	$0.337031\pi$
$942$			20.5517i			0.669612i
$943$	5.81194			0.189263
$944$			14.8396i			0.482987i
$945$		0			0
$946$	−10.0853	+	4.06657i	−0.327902	+	0.132216i
$947$	−49.6856			−1.61457			−0.807283	−	0.590165i	$-0.799063\pi$
$947$	−49.6856			−1.61457			−0.807283	+	0.590165i	$0.799063\pi$
$948$	12.9709			0.421277
$949$	16.4046			0.532516
$950$			48.3178i			1.56764i
$951$			9.13510i			0.296226i
$952$		0			0
$953$		−	55.8496i		−	1.80915i	−0.426319	−	0.904573i	$-0.640190\pi$
$953$		−	55.8496i		−	1.80915i	0.426319	−	0.904573i	$-0.359810\pi$
$954$			3.69054i			0.119486i
$955$			29.1230i			0.942397i
$956$		−	11.3940i		−	0.368508i
$957$	23.9395	−	9.65282i	0.773854	−	0.312031i
$958$		−	14.3917i		−	0.464976i
$959$		0			0
$960$	−3.45711			−0.111578
$961$	−12.8040			−0.413032
$962$			8.14391i			0.262570i
$963$			0.676179i			0.0217896i
$964$	−20.6584			−0.665361
$965$	31.6254			1.01806
$966$		0			0
$967$		−	38.2830i		−	1.23110i	−0.788098	−	0.615549i	$-0.788934\pi$
$967$		−	38.2830i		−	1.23110i	0.788098	−	0.615549i	$-0.211066\pi$
$968$	−7.63022	−	7.92336i	−0.245245	−	0.254667i
$969$		−	0.317827i		−	0.0102101i
$970$		−	22.9742i		−	0.737658i
$971$			16.1758i			0.519107i	0.965729	+	0.259554i	$0.0835754\pi$
$971$			16.1758i			0.519107i	−0.965729	+	0.259554i	$0.916425\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$		−	15.4033i		−	0.493552i
$975$			37.4790i			1.20029i
$976$	−3.63129			−0.116235
$977$	29.2417			0.935525			0.467763	−	0.883854i	$-0.345060\pi$
$977$	29.2417			0.935525			0.467763	+	0.883854i	$0.345060\pi$
$978$	10.3412			0.330675
$979$	5.21619	+	12.9364i	0.166710	+	0.413450i
$980$		0			0
$981$		−	19.6069i		−	0.626001i
$982$	−5.09884			−0.162710
$983$		−	23.6960i		−	0.755784i	−0.925850	−	0.377892i	$-0.876649\pi$
$983$		−	23.6960i		−	0.755784i	0.925850	−	0.377892i	$-0.123351\pi$
$984$	4.87368			0.155367
$985$	−47.3974			−1.51021
$986$	0.355875			0.0113334
$987$		0			0
$988$	−37.4738			−1.19220
$989$			3.90994i			0.124329i
$990$	−10.6340	+	4.28781i	−0.337971	+	0.136276i
$991$	−56.4659			−1.79370			−0.896849	−	0.442337i	$-0.854150\pi$
$991$	−56.4659			−1.79370			−0.896849	+	0.442337i	$0.854150\pi$
$992$	−6.61846			−0.210136
$993$		−	9.48566i		−	0.301018i
$994$		0			0
$995$	−20.4673			−0.648858
$996$			8.48330i			0.268804i
$997$	9.69675			0.307099			0.153550	−	0.988141i	$-0.450930\pi$
$997$	9.69675			0.307099			0.153550	+	0.988141i	$0.450930\pi$
$998$		−	23.7056i		−	0.750388i
$999$			1.51053i			0.0477911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.c.2155.14	yes	24
7.6	odd	2		3234.2.e.d.2155.23	yes	24
11.10	odd	2		3234.2.e.d.2155.2	yes	24
77.76	even	2	inner	3234.2.e.c.2155.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.e.c.2155.11	✓	24	77.76	even	2	inner
3234.2.e.c.2155.14	yes	24	1.1	even	1	trivial
3234.2.e.d.2155.2	yes	24	11.10	odd	2
3234.2.e.d.2155.23	yes	24	7.6	odd	2

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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -3.45711i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -3.45711i q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +3.45711 q^{10} +(3.07598 - 1.24029i) q^{11} -1.00000i q^{12} -5.39143 q^{13} +3.45711 q^{15} +1.00000 q^{16} +0.0457263 q^{17} -1.00000i q^{18} -6.95062 q^{19} +3.45711i q^{20} +(1.24029 + 3.07598i) q^{22} +1.19252 q^{23} +1.00000 q^{24} -6.95158 q^{25} -5.39143i q^{26} -1.00000i q^{27} -7.78271i q^{29} +3.45711i q^{30} +6.61846i q^{31} +1.00000i q^{32} +(1.24029 + 3.07598i) q^{33} +0.0457263i q^{34} +1.00000 q^{36} -1.51053 q^{37} -6.95062i q^{38} -5.39143i q^{39} -3.45711 q^{40} +4.87368 q^{41} +3.27873i q^{43} +(-3.07598 + 1.24029i) q^{44} +3.45711i q^{45} +1.19252i q^{46} +12.1060i q^{47} +1.00000i q^{48} -6.95158i q^{50} +0.0457263i q^{51} +5.39143 q^{52} -3.69054 q^{53} +1.00000 q^{54} +(-4.28781 - 10.6340i) q^{55} -6.95062i q^{57} +7.78271 q^{58} +14.8396i q^{59} -3.45711 q^{60} -3.63129 q^{61} -6.61846 q^{62} -1.00000 q^{64} +18.6387i q^{65} +(-3.07598 + 1.24029i) q^{66} +6.66903 q^{67} -0.0457263 q^{68} +1.19252i q^{69} +6.89741 q^{71} +1.00000i q^{72} -3.04272 q^{73} -1.51053i q^{74} -6.95158i q^{75} +6.95062 q^{76} +5.39143 q^{78} +12.9709i q^{79} -3.45711i q^{80} +1.00000 q^{81} +4.87368i q^{82} -8.48330 q^{83} -0.158081i q^{85} -3.27873 q^{86} +7.78271 q^{87} +(-1.24029 - 3.07598i) q^{88} +4.20562i q^{89} -3.45711 q^{90} -1.19252 q^{92} -6.61846 q^{93} -12.1060 q^{94} +24.0290i q^{95} -1.00000 q^{96} -6.64551i q^{97} +(-3.07598 + 1.24029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 24 q^{6} - 24 q^{9} + 24 q^{16} + 16 q^{17} - 32 q^{19} - 8 q^{22} + 24 q^{24} - 8 q^{25} - 8 q^{33} + 24 q^{36} + 16 q^{37} - 16 q^{41} + 24 q^{54} + 16 q^{55} - 16 q^{62} - 24 q^{64} - 64 q^{67} - 16 q^{68} + 64 q^{71} + 32 q^{76} + 24 q^{81} - 16 q^{83} + 8 q^{88} - 16 q^{93} + 64 q^{94} - 24 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 24 * q^6 - 24 * q^9 + 24 * q^16 + 16 * q^17 - 32 * q^19 - 8 * q^22 + 24 * q^24 - 8 * q^25 - 8 * q^33 + 24 * q^36 + 16 * q^37 - 16 * q^41 + 24 * q^54 + 16 * q^55 - 16 * q^62 - 24 * q^64 - 64 * q^67 - 16 * q^68 + 64 * q^71 + 32 * q^76 + 24 * q^81 - 16 * q^83 + 8 * q^88 - 16 * q^93 + 64 * q^94 - 24 * q^96

Introduction

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