LMFDB - Embedded newform 1710.2.d.f.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:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.2
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.f.1369.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +1.07838i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +1.07838i q^{7} +1.00000i q^{8} +(2.17009 - 0.539189i) q^{10} -6.34017 q^{11} +3.41855i q^{13} +1.07838 q^{14} +1.00000 q^{16} -5.41855i q^{17} -1.00000 q^{19} +(-0.539189 - 2.17009i) q^{20} +6.34017i q^{22} -6.34017i q^{23} +(-4.41855 + 2.34017i) q^{25} +3.41855 q^{26} -1.07838i q^{28} -0.340173 q^{29} +1.07838 q^{31} -1.00000i q^{32} -5.41855 q^{34} +(-2.34017 + 0.581449i) q^{35} -3.41855i q^{37} +1.00000i q^{38} +(-2.17009 + 0.539189i) q^{40} -7.60197 q^{41} -11.1773i q^{43} +6.34017 q^{44} -6.34017 q^{46} -6.34017i q^{47} +5.83710 q^{49} +(2.34017 + 4.41855i) q^{50} -3.41855i q^{52} -6.00000i q^{53} +(-3.41855 - 13.7587i) q^{55} -1.07838 q^{56} +0.340173i q^{58} +0.738205 q^{59} -2.68035 q^{61} -1.07838i q^{62} -1.00000 q^{64} +(-7.41855 + 1.84324i) q^{65} -2.83710i q^{67} +5.41855i q^{68} +(0.581449 + 2.34017i) q^{70} +2.83710 q^{71} +6.83710i q^{73} -3.41855 q^{74} +1.00000 q^{76} -6.83710i q^{77} +1.07838 q^{79} +(0.539189 + 2.17009i) q^{80} +7.60197i q^{82} -0.894960i q^{83} +(11.7587 - 2.92162i) q^{85} -11.1773 q^{86} -6.34017i q^{88} +6.92162 q^{89} -3.68649 q^{91} +6.34017i q^{92} -6.34017 q^{94} +(-0.539189 - 2.17009i) q^{95} +3.65983i q^{97} -5.83710i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4}+O(q^{10}) $ 6 * q - 6 * q^4	$ 6 q - 6 q^{4} + 2 q^{10} - 16 q^{11} + 6 q^{16} - 6 q^{19} + 2 q^{25} - 8 q^{26} + 20 q^{29} - 4 q^{34} + 8 q^{35} - 2 q^{40} - 8 q^{41} + 16 q^{44} - 16 q^{46} - 22 q^{49} - 8 q^{50} + 8 q^{55} + 20 q^{59} + 28 q^{61} - 6 q^{64} - 16 q^{65} + 32 q^{70} - 40 q^{71} + 8 q^{74} + 6 q^{76} + 20 q^{85} + 12 q^{86} + 48 q^{89} - 48 q^{91} - 16 q^{94}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^10 - 16 * q^11 + 6 * q^16 - 6 * q^19 + 2 * q^25 - 8 * q^26 + 20 * q^29 - 4 * q^34 + 8 * q^35 - 2 * q^40 - 8 * q^41 + 16 * q^44 - 16 * q^46 - 22 * q^49 - 8 * q^50 + 8 * q^55 + 20 * q^59 + 28 * q^61 - 6 * q^64 - 16 * q^65 + 32 * q^70 - 40 * q^71 + 8 * q^74 + 6 * q^76 + 20 * q^85 + 12 * q^86 + 48 * q^89 - 48 * q^91 - 16 * q^94

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
$5$	0.539189	+	2.17009i	0.241133	+	0.970492i
$5$	0.539189	+	2.17009i	0.241133	+	0.970492i
$6$		0			0
$7$			1.07838i			0.407588i	0.979014	+	0.203794i	$0.0653274\pi$
$7$			1.07838i			0.407588i	−0.979014	+	0.203794i	$0.934673\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.17009	−	0.539189i	0.686242	−	0.170506i
$11$	−6.34017			−1.91163			−0.955817	−	0.293962i	$-0.905026\pi$
$11$	−6.34017			−1.91163			−0.955817	+	0.293962i	$0.905026\pi$
$12$		0			0
$13$			3.41855i			0.948135i	0.880488	+	0.474068i	$0.157215\pi$
$13$			3.41855i			0.948135i	−0.880488	+	0.474068i	$0.842785\pi$
$14$	1.07838			0.288209
$15$		0			0
$16$	1.00000			0.250000
$17$		−	5.41855i		−	1.31419i	−0.753807	−	0.657096i	$-0.771785\pi$
$17$		−	5.41855i		−	1.31419i	0.753807	−	0.657096i	$-0.228215\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−0.539189	−	2.17009i	−0.120566	−	0.485246i
$21$		0			0
$22$			6.34017i			1.35173i
$23$		−	6.34017i		−	1.32202i	−0.750378	−	0.661009i	$-0.770129\pi$
$23$		−	6.34017i		−	1.32202i	0.750378	−	0.661009i	$-0.229871\pi$
$24$		0			0
$25$	−4.41855	+	2.34017i	−0.883710	+	0.468035i
$26$	3.41855			0.670433
$27$		0			0
$28$		−	1.07838i		−	0.203794i
$29$	−0.340173			−0.0631685			−0.0315843	−	0.999501i	$-0.510055\pi$
$29$	−0.340173			−0.0631685			−0.0315843	+	0.999501i	$0.510055\pi$
$30$		0			0
$31$	1.07838			0.193682			0.0968412	−	0.995300i	$-0.469126\pi$
$31$	1.07838			0.193682			0.0968412	+	0.995300i	$0.469126\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−5.41855			−0.929274
$35$	−2.34017	+	0.581449i	−0.395561	+	0.0982829i
$36$		0			0
$37$		−	3.41855i		−	0.562006i	−0.959707	−	0.281003i	$-0.909333\pi$
$37$		−	3.41855i		−	0.562006i	0.959707	−	0.281003i	$-0.0906671\pi$
$38$			1.00000i			0.162221i
$39$		0			0
$40$	−2.17009	+	0.539189i	−0.343121	+	0.0852532i
$41$	−7.60197			−1.18723			−0.593614	−	0.804750i	$-0.702299\pi$
$41$	−7.60197			−1.18723			−0.593614	+	0.804750i	$0.702299\pi$
$42$		0			0
$43$		−	11.1773i		−	1.70452i	−0.523120	−	0.852259i	$-0.675232\pi$
$43$		−	11.1773i		−	1.70452i	0.523120	−	0.852259i	$-0.324768\pi$
$44$	6.34017			0.955817
$45$		0			0
$46$	−6.34017			−0.934808
$47$		−	6.34017i		−	0.924809i	−0.886669	−	0.462405i	$-0.846987\pi$
$47$		−	6.34017i		−	0.924809i	0.886669	−	0.462405i	$-0.153013\pi$
$48$		0			0
$49$	5.83710			0.833872
$50$	2.34017	+	4.41855i	0.330950	+	0.624877i
$51$		0			0
$52$		−	3.41855i		−	0.474068i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		0			0
$55$	−3.41855	−	13.7587i	−0.460957	−	1.85523i
$56$	−1.07838			−0.144104
$57$		0			0
$58$			0.340173i			0.0446669i
$59$	0.738205			0.0961061			0.0480530	−	0.998845i	$-0.484698\pi$
$59$	0.738205			0.0961061			0.0480530	+	0.998845i	$0.484698\pi$
$60$		0			0
$61$	−2.68035			−0.343183			−0.171592	−	0.985168i	$-0.554891\pi$
$61$	−2.68035			−0.343183			−0.171592	+	0.985168i	$0.554891\pi$
$62$		−	1.07838i		−	0.136954i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.41855	+	1.84324i	−0.920158	+	0.228626i
$66$		0			0
$67$		−	2.83710i		−	0.346607i	−0.984868	−	0.173304i	$-0.944556\pi$
$67$		−	2.83710i		−	0.346607i	0.984868	−	0.173304i	$-0.0554442\pi$
$68$			5.41855i			0.657096i
$69$		0			0
$70$	0.581449	+	2.34017i	0.0694965	+	0.279704i
$71$	2.83710			0.336702			0.168351	−	0.985727i	$-0.446156\pi$
$71$	2.83710			0.336702			0.168351	+	0.985727i	$0.446156\pi$
$72$		0			0
$73$			6.83710i			0.800222i	0.916467	+	0.400111i	$0.131028\pi$
$73$			6.83710i			0.800222i	−0.916467	+	0.400111i	$0.868972\pi$
$74$	−3.41855			−0.397398
$75$		0			0
$76$	1.00000			0.114708
$77$		−	6.83710i		−	0.779160i
$78$		0			0
$79$	1.07838			0.121327			0.0606635	−	0.998158i	$-0.480678\pi$
$79$	1.07838			0.121327			0.0606635	+	0.998158i	$0.480678\pi$
$80$	0.539189	+	2.17009i	0.0602831	+	0.242623i
$81$		0			0
$82$			7.60197i			0.839497i
$83$		−	0.894960i		−	0.0982347i	−0.998793	−	0.0491173i	$-0.984359\pi$
$83$		−	0.894960i		−	0.0982347i	0.998793	−	0.0491173i	$-0.0156408\pi$
$84$		0			0
$85$	11.7587	−	2.92162i	1.27541	−	0.316894i
$86$	−11.1773			−1.20528
$87$		0			0
$88$		−	6.34017i		−	0.675865i
$89$	6.92162			0.733690			0.366845	−	0.930282i	$-0.380438\pi$
$89$	6.92162			0.733690			0.366845	+	0.930282i	$0.380438\pi$
$90$		0			0
$91$	−3.68649			−0.386449
$92$			6.34017i			0.661009i
$93$		0			0
$94$	−6.34017			−0.653939
$95$	−0.539189	−	2.17009i	−0.0553196	−	0.222646i
$96$		0			0
$97$			3.65983i			0.371599i	0.982588	+	0.185800i	$0.0594875\pi$
$97$			3.65983i			0.371599i	−0.982588	+	0.185800i	$0.940512\pi$
$98$		−	5.83710i		−	0.589636i
$99$		0			0
$100$	4.41855	−	2.34017i	0.441855	−	0.234017i
$101$	−19.6020			−1.95047			−0.975234	−	0.221174i	$-0.929011\pi$
$101$	−19.6020			−1.95047			−0.975234	+	0.221174i	$0.929011\pi$
$102$		0			0
$103$		−	11.7587i		−	1.15862i	−0.815107	−	0.579311i	$-0.803322\pi$
$103$		−	11.7587i		−	1.15862i	0.815107	−	0.579311i	$-0.196678\pi$
$104$	−3.41855			−0.335216
$105$		0			0
$106$	−6.00000			−0.582772
$107$			6.15676i			0.595196i	0.954691	+	0.297598i	$0.0961855\pi$
$107$			6.15676i			0.595196i	−0.954691	+	0.297598i	$0.903814\pi$
$108$		0			0
$109$	−17.9155			−1.71599			−0.857996	−	0.513657i	$-0.828291\pi$
$109$	−17.9155			−1.71599			−0.857996	+	0.513657i	$0.828291\pi$
$110$	−13.7587	+	3.41855i	−1.31184	+	0.325946i
$111$		0			0
$112$			1.07838i			0.101897i
$113$			13.2039i			1.24212i	0.783762	+	0.621061i	$0.213298\pi$
$113$			13.2039i			1.24212i	−0.783762	+	0.621061i	$0.786702\pi$
$114$		0			0
$115$	13.7587	−	3.41855i	1.28301	−	0.318781i
$116$	0.340173			0.0315843
$117$		0			0
$118$		−	0.738205i		−	0.0679573i
$119$	5.84324			0.535649
$120$		0			0
$121$	29.1978			2.65434
$122$			2.68035i			0.242667i
$123$		0			0
$124$	−1.07838			−0.0968412
$125$	−7.46081	−	8.32684i	−0.667315	−	0.744775i
$126$		0			0
$127$			0.921622i			0.0817808i	0.999164	+	0.0408904i	$0.0130194\pi$
$127$			0.921622i			0.0817808i	−0.999164	+	0.0408904i	$0.986981\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	1.84324	+	7.41855i	0.161663	+	0.650650i
$131$	−10.6537			−0.930817			−0.465408	−	0.885096i	$-0.654093\pi$
$131$	−10.6537			−0.930817			−0.465408	+	0.885096i	$0.654093\pi$
$132$		0			0
$133$		−	1.07838i		−	0.0935072i
$134$	−2.83710			−0.245088
$135$		0			0
$136$	5.41855			0.464637
$137$			20.6225i			1.76190i	0.473211	+	0.880949i	$0.343095\pi$
$137$			20.6225i			1.76190i	−0.473211	+	0.880949i	$0.656905\pi$
$138$		0			0
$139$	−18.8371			−1.59774			−0.798871	−	0.601502i	$-0.794569\pi$
$139$	−18.8371			−1.59774			−0.798871	+	0.601502i	$0.794569\pi$
$140$	2.34017	−	0.581449i	0.197781	−	0.0491414i
$141$		0			0
$142$		−	2.83710i		−	0.238084i
$143$		−	21.6742i		−	1.81249i
$144$		0			0
$145$	−0.183417	−	0.738205i	−0.0152320	−	0.0613046i
$146$	6.83710			0.565843
$147$		0			0
$148$			3.41855i			0.281003i
$149$	−5.44521			−0.446089			−0.223045	−	0.974808i	$-0.571600\pi$
$149$	−5.44521			−0.446089			−0.223045	+	0.974808i	$0.571600\pi$
$150$		0			0
$151$	−23.1194			−1.88143			−0.940716	−	0.339196i	$-0.889845\pi$
$151$	−23.1194			−1.88143			−0.940716	+	0.339196i	$0.889845\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		0			0
$154$	−6.83710			−0.550949
$155$	0.581449	+	2.34017i	0.0467031	+	0.187967i
$156$		0			0
$157$			9.73206i			0.776703i	0.921511	+	0.388352i	$0.126955\pi$
$157$			9.73206i			0.776703i	−0.921511	+	0.388352i	$0.873045\pi$
$158$		−	1.07838i		−	0.0857911i
$159$		0			0
$160$	2.17009	−	0.539189i	0.171560	−	0.0426266i
$161$	6.83710			0.538839
$162$		0			0
$163$		−	6.49693i		−	0.508879i	−0.967089	−	0.254439i	$-0.918109\pi$
$163$		−	6.49693i		−	0.508879i	0.967089	−	0.254439i	$-0.0818909\pi$
$164$	7.60197			0.593614
$165$		0			0
$166$	−0.894960			−0.0694624
$167$			20.9939i			1.62455i	0.583272	+	0.812277i	$0.301772\pi$
$167$			20.9939i			1.62455i	−0.583272	+	0.812277i	$0.698228\pi$
$168$		0			0
$169$	1.31351			0.101039
$170$	−2.92162	−	11.7587i	−0.224078	−	0.901853i
$171$		0			0
$172$			11.1773i			0.852259i
$173$			6.99386i			0.531733i	0.964010	+	0.265867i	$0.0856581\pi$
$173$			6.99386i			0.531733i	−0.964010	+	0.265867i	$0.914342\pi$
$174$		0			0
$175$	−2.52359	−	4.76487i	−0.190766	−	0.360190i
$176$	−6.34017			−0.477909
$177$		0			0
$178$		−	6.92162i		−	0.518798i
$179$	−4.73820			−0.354150			−0.177075	−	0.984197i	$-0.556664\pi$
$179$	−4.73820			−0.354150			−0.177075	+	0.984197i	$0.556664\pi$
$180$		0			0
$181$	−12.0722			−0.897322			−0.448661	−	0.893702i	$-0.648099\pi$
$181$	−12.0722			−0.897322			−0.448661	+	0.893702i	$0.648099\pi$
$182$			3.68649i			0.273261i
$183$		0			0
$184$	6.34017			0.467404
$185$	7.41855	−	1.84324i	0.545423	−	0.135518i
$186$		0			0
$187$			34.3545i			2.51225i
$188$			6.34017i			0.462405i
$189$		0			0
$190$	−2.17009	+	0.539189i	−0.157435	+	0.0391169i
$191$	7.26180			0.525445			0.262723	−	0.964871i	$-0.415380\pi$
$191$	7.26180			0.525445			0.262723	+	0.964871i	$0.415380\pi$
$192$		0			0
$193$		−	18.8638i		−	1.35784i	−0.734211	−	0.678922i	$-0.762448\pi$
$193$		−	18.8638i		−	1.35784i	0.734211	−	0.678922i	$-0.237552\pi$
$194$	3.65983			0.262760
$195$		0			0
$196$	−5.83710			−0.416936
$197$			17.7009i			1.26113i	0.776135	+	0.630567i	$0.217178\pi$
$197$			17.7009i			1.26113i	−0.776135	+	0.630567i	$0.782822\pi$
$198$		0			0
$199$	0.313511			0.0222242			0.0111121	−	0.999938i	$-0.496463\pi$
$199$	0.313511			0.0222242			0.0111121	+	0.999938i	$0.496463\pi$
$200$	−2.34017	−	4.41855i	−0.165475	−	0.312439i
$201$		0			0
$202$			19.6020i			1.37919i
$203$		−	0.366835i		−	0.0257468i
$204$		0			0
$205$	−4.09890	−	16.4969i	−0.286279	−	1.15220i
$206$	−11.7587			−0.819269
$207$		0			0
$208$			3.41855i			0.237034i
$209$	6.34017			0.438559
$210$		0			0
$211$	14.8371			1.02143			0.510714	−	0.859751i	$-0.329381\pi$
$211$	14.8371			1.02143			0.510714	+	0.859751i	$0.329381\pi$
$212$			6.00000i			0.412082i
$213$		0			0
$214$	6.15676			0.420867
$215$	24.2557	−	6.02666i	1.65422	−	0.411015i
$216$		0			0
$217$			1.16290i			0.0789427i
$218$			17.9155i			1.21339i
$219$		0			0
$220$	3.41855	+	13.7587i	0.230479	+	0.927613i
$221$	18.5236			1.24603
$222$		0			0
$223$			1.28846i			0.0862815i	0.999069	+	0.0431407i	$0.0137364\pi$
$223$			1.28846i			0.0862815i	−0.999069	+	0.0431407i	$0.986264\pi$
$224$	1.07838			0.0720521
$225$		0			0
$226$	13.2039			0.878313
$227$			20.9939i			1.39341i	0.717357	+	0.696706i	$0.245352\pi$
$227$			20.9939i			1.39341i	−0.717357	+	0.696706i	$0.754648\pi$
$228$		0			0
$229$	2.36683			0.156405			0.0782024	−	0.996938i	$-0.475082\pi$
$229$	2.36683			0.156405			0.0782024	+	0.996938i	$0.475082\pi$
$230$	−3.41855	−	13.7587i	−0.225413	−	0.907223i
$231$		0			0
$232$		−	0.340173i		−	0.0223334i
$233$		−	5.10504i		−	0.334442i	−0.985919	−	0.167221i	$-0.946521\pi$
$233$		−	5.10504i		−	0.334442i	0.985919	−	0.167221i	$-0.0534794\pi$
$234$		0			0
$235$	13.7587	−	3.41855i	0.897520	−	0.223002i
$236$	−0.738205			−0.0480530
$237$		0			0
$238$		−	5.84324i		−	0.378761i
$239$	10.4124			0.673523			0.336761	−	0.941590i	$-0.390668\pi$
$239$	10.4124			0.673523			0.336761	+	0.941590i	$0.390668\pi$
$240$		0			0
$241$	3.36069			0.216481			0.108241	−	0.994125i	$-0.465478\pi$
$241$	3.36069			0.216481			0.108241	+	0.994125i	$0.465478\pi$
$242$		−	29.1978i		−	1.87691i
$243$		0			0
$244$	2.68035			0.171592
$245$	3.14730	+	12.6670i	0.201074	+	0.809266i
$246$		0			0
$247$		−	3.41855i		−	0.217517i
$248$			1.07838i			0.0684771i
$249$		0			0
$250$	−8.32684	+	7.46081i	−0.526636	+	0.471863i
$251$	−21.8576			−1.37964			−0.689820	−	0.723981i	$-0.742311\pi$
$251$	−21.8576			−1.37964			−0.689820	+	0.723981i	$0.742311\pi$
$252$		0			0
$253$			40.1978i			2.52721i
$254$	0.921622			0.0578277
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	26.8781i		−	1.67661i	−0.545200	−	0.838306i	$-0.683546\pi$
$257$		−	26.8781i		−	1.67661i	0.545200	−	0.838306i	$-0.316454\pi$
$258$		0			0
$259$	3.68649			0.229067
$260$	7.41855	−	1.84324i	0.460079	−	0.114313i
$261$		0			0
$262$			10.6537i			0.658187i
$263$		−	22.3402i		−	1.37755i	−0.724973	−	0.688777i	$-0.758148\pi$
$263$		−	22.3402i		−	1.37755i	0.724973	−	0.688777i	$-0.241852\pi$
$264$		0			0
$265$	13.0205	−	3.23513i	0.799844	−	0.198733i
$266$	−1.07838			−0.0661196
$267$		0			0
$268$			2.83710i			0.173304i
$269$	−17.3340			−1.05687			−0.528437	−	0.848972i	$-0.677222\pi$
$269$	−17.3340			−1.05687			−0.528437	+	0.848972i	$0.677222\pi$
$270$		0			0
$271$	−13.3607			−0.811604			−0.405802	−	0.913961i	$-0.633008\pi$
$271$	−13.3607			−0.811604			−0.405802	+	0.913961i	$0.633008\pi$
$272$		−	5.41855i		−	0.328548i
$273$		0			0
$274$	20.6225			1.24585
$275$	28.0144	−	14.8371i	1.68933	−	0.894711i
$276$		0			0
$277$		−	0.738205i		−	0.0443544i	−0.999754	−	0.0221772i	$-0.992940\pi$
$277$		−	0.738205i		−	0.0443544i	0.999754	−	0.0221772i	$-0.00705980\pi$
$278$			18.8371i			1.12977i
$279$		0			0
$280$	−0.581449	−	2.34017i	−0.0347482	−	0.139852i
$281$	31.7998			1.89701			0.948507	−	0.316755i	$-0.102593\pi$
$281$	31.7998			1.89701			0.948507	+	0.316755i	$0.102593\pi$
$282$		0			0
$283$		−	4.70701i		−	0.279803i	−0.990165	−	0.139901i	$-0.955321\pi$
$283$		−	4.70701i		−	0.279803i	0.990165	−	0.139901i	$-0.0446785\pi$
$284$	−2.83710			−0.168351
$285$		0			0
$286$	−21.6742			−1.28162
$287$		−	8.19779i		−	0.483900i
$288$		0			0
$289$	−12.3607			−0.727100
$290$	−0.738205	+	0.183417i	−0.0433489	+	0.0107706i
$291$		0			0
$292$		−	6.83710i		−	0.400111i
$293$		−	26.1978i		−	1.53049i	−0.643738	−	0.765246i	$-0.722617\pi$
$293$		−	26.1978i		−	1.53049i	0.643738	−	0.765246i	$-0.277383\pi$
$294$		0			0
$295$	0.398032	+	1.60197i	0.0231743	+	0.0932702i
$296$	3.41855			0.198699
$297$		0			0
$298$			5.44521i			0.315433i
$299$	21.6742			1.25345
$300$		0			0
$301$	12.0533			0.694742
$302$			23.1194i			1.33037i
$303$		0			0
$304$	−1.00000			−0.0573539
$305$	−1.44521	−	5.81658i	−0.0827526	−	0.333057i
$306$		0			0
$307$		−	32.1978i		−	1.83763i	−0.394694	−	0.918813i	$-0.629149\pi$
$307$		−	32.1978i		−	1.83763i	0.394694	−	0.918813i	$-0.370851\pi$
$308$			6.83710i			0.389580i
$309$		0			0
$310$	2.34017	−	0.581449i	0.132913	−	0.0330241i
$311$	−16.7382			−0.949137			−0.474568	−	0.880219i	$-0.657396\pi$
$311$	−16.7382			−0.949137			−0.474568	+	0.880219i	$0.657396\pi$
$312$		0			0
$313$		−	14.1568i		−	0.800187i	−0.916474	−	0.400094i	$-0.868978\pi$
$313$		−	14.1568i		−	0.800187i	0.916474	−	0.400094i	$-0.131022\pi$
$314$	9.73206			0.549212
$315$		0			0
$316$	−1.07838			−0.0606635
$317$		−	21.8843i		−	1.22914i	−0.788861	−	0.614572i	$-0.789329\pi$
$317$		−	21.8843i		−	1.22914i	0.788861	−	0.614572i	$-0.210671\pi$
$318$		0			0
$319$	2.15676			0.120755
$320$	−0.539189	−	2.17009i	−0.0301416	−	0.121312i
$321$		0			0
$322$		−	6.83710i		−	0.381017i
$323$			5.41855i			0.301496i
$324$		0			0
$325$	−8.00000	−	15.1050i	−0.443760	−	0.837877i
$326$	−6.49693			−0.359832
$327$		0			0
$328$		−	7.60197i		−	0.419748i
$329$	6.83710			0.376942
$330$		0			0
$331$	−26.1568			−1.43771			−0.718853	−	0.695162i	$-0.755332\pi$
$331$	−26.1568			−1.43771			−0.718853	+	0.695162i	$0.755332\pi$
$332$			0.894960i			0.0491173i
$333$		0			0
$334$	20.9939			1.14873
$335$	6.15676	−	1.52973i	0.336379	−	0.0835783i
$336$		0			0
$337$			29.7009i			1.61791i	0.587871	+	0.808955i	$0.299966\pi$
$337$			29.7009i			1.61791i	−0.587871	+	0.808955i	$0.700034\pi$
$338$		−	1.31351i		−	0.0714456i
$339$		0			0
$340$	−11.7587	+	2.92162i	−0.637706	+	0.158447i
$341$	−6.83710			−0.370250
$342$		0			0
$343$			13.8432i			0.747465i
$344$	11.1773			0.602638
$345$		0			0
$346$	6.99386			0.375992
$347$			23.4186i			1.25717i	0.777739	+	0.628587i	$0.216366\pi$
$347$			23.4186i			1.25717i	−0.777739	+	0.628587i	$0.783634\pi$
$348$		0			0
$349$	−6.48255			−0.347003			−0.173502	−	0.984834i	$-0.555508\pi$
$349$	−6.48255			−0.347003			−0.173502	+	0.984834i	$0.555508\pi$
$350$	−4.76487	+	2.52359i	−0.254693	+	0.134892i
$351$		0			0
$352$			6.34017i			0.337932i
$353$		−	2.58145i		−	0.137397i	−0.997637	−	0.0686983i	$-0.978115\pi$
$353$		−	2.58145i		−	0.137397i	0.997637	−	0.0686983i	$-0.0218846\pi$
$354$		0			0
$355$	1.52973	+	6.15676i	0.0811898	+	0.326767i
$356$	−6.92162			−0.366845
$357$		0			0
$358$			4.73820i			0.250422i
$359$	28.1399			1.48517			0.742584	−	0.669752i	$-0.233600\pi$
$359$	28.1399			1.48517			0.742584	+	0.669752i	$0.233600\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$			12.0722i			0.634503i
$363$		0			0
$364$	3.68649			0.193225
$365$	−14.8371	+	3.68649i	−0.776609	+	0.192960i
$366$		0			0
$367$		−	10.5548i		−	0.550955i	−0.961307	−	0.275478i	$-0.911164\pi$
$367$		−	10.5548i		−	0.550955i	0.961307	−	0.275478i	$-0.0888360\pi$
$368$		−	6.34017i		−	0.330504i
$369$		0			0
$370$	−1.84324	−	7.41855i	−0.0958257	−	0.385672i
$371$	6.47027			0.335919
$372$		0			0
$373$			17.8888i			0.926248i	0.886294	+	0.463124i	$0.153272\pi$
$373$			17.8888i			0.926248i	−0.886294	+	0.463124i	$0.846728\pi$
$374$	34.3545			1.77643
$375$		0			0
$376$	6.34017			0.326969
$377$		−	1.16290i		−	0.0598923i
$378$		0			0
$379$	−4.36683			−0.224309			−0.112155	−	0.993691i	$-0.535775\pi$
$379$	−4.36683			−0.224309			−0.112155	+	0.993691i	$0.535775\pi$
$380$	0.539189	+	2.17009i	0.0276598	+	0.111323i
$381$		0			0
$382$		−	7.26180i		−	0.371546i
$383$		−	22.5236i		−	1.15090i	−0.817836	−	0.575451i	$-0.804827\pi$
$383$		−	22.5236i		−	1.15090i	0.817836	−	0.575451i	$-0.195173\pi$
$384$		0			0
$385$	14.8371	−	3.68649i	0.756169	−	0.187881i
$386$	−18.8638			−0.960140
$387$		0			0
$388$		−	3.65983i		−	0.185800i
$389$	−9.07838			−0.460292			−0.230146	−	0.973156i	$-0.573920\pi$
$389$	−9.07838			−0.460292			−0.230146	+	0.973156i	$0.573920\pi$
$390$		0			0
$391$	−34.3545			−1.73738
$392$			5.83710i			0.294818i
$393$		0			0
$394$	17.7009			0.891757
$395$	0.581449	+	2.34017i	0.0292559	+	0.117747i
$396$		0			0
$397$			3.74435i			0.187923i	0.995576	+	0.0939617i	$0.0299531\pi$
$397$			3.74435i			0.187923i	−0.995576	+	0.0939617i	$0.970047\pi$
$398$		−	0.313511i		−	0.0157149i
$399$		0			0
$400$	−4.41855	+	2.34017i	−0.220928	+	0.117009i
$401$	11.9155			0.595031			0.297515	−	0.954717i	$-0.403842\pi$
$401$	11.9155			0.595031			0.297515	+	0.954717i	$0.403842\pi$
$402$		0			0
$403$			3.68649i			0.183637i
$404$	19.6020			0.975234
$405$		0			0
$406$	−0.366835			−0.0182057
$407$			21.6742i			1.07435i
$408$		0			0
$409$	2.99386			0.148037			0.0740183	−	0.997257i	$-0.476418\pi$
$409$	2.99386			0.148037			0.0740183	+	0.997257i	$0.476418\pi$
$410$	−16.4969	+	4.09890i	−0.814725	+	0.202430i
$411$		0			0
$412$			11.7587i			0.579311i
$413$			0.796064i			0.0391717i
$414$		0			0
$415$	1.94214	−	0.482553i	0.0953360	−	0.0236876i
$416$	3.41855			0.167608
$417$		0			0
$418$		−	6.34017i		−	0.310108i
$419$	−33.5441			−1.63874			−0.819368	−	0.573267i	$-0.805676\pi$
$419$	−33.5441			−1.63874			−0.819368	+	0.573267i	$0.805676\pi$
$420$		0			0
$421$	31.5897			1.53959			0.769793	−	0.638293i	$-0.220359\pi$
$421$	31.5897			1.53959			0.769793	+	0.638293i	$0.220359\pi$
$422$		−	14.8371i		−	0.722259i
$423$		0			0
$424$	6.00000			0.291386
$425$	12.6803	+	23.9421i	0.615087	+	1.16136i
$426$		0			0
$427$		−	2.89043i		−	0.139877i
$428$		−	6.15676i		−	0.297598i
$429$		0			0
$430$	−6.02666	−	24.2557i	−0.290631	−	1.16971i
$431$	40.5113			1.95136			0.975680	−	0.219198i	$-0.0703440\pi$
$431$	40.5113			1.95136			0.975680	+	0.219198i	$0.0703440\pi$
$432$		0			0
$433$			5.13624i			0.246832i	0.992355	+	0.123416i	$0.0393849\pi$
$433$			5.13624i			0.246832i	−0.992355	+	0.123416i	$0.960615\pi$
$434$	1.16290			0.0558209
$435$		0			0
$436$	17.9155			0.857996
$437$			6.34017i			0.303292i
$438$		0			0
$439$	17.7054			0.845033			0.422516	−	0.906355i	$-0.361147\pi$
$439$	17.7054			0.845033			0.422516	+	0.906355i	$0.361147\pi$
$440$	13.7587	−	3.41855i	0.655921	−	0.162973i
$441$		0			0
$442$		−	18.5236i		−	0.881077i
$443$		−	6.73820i		−	0.320142i	−0.987106	−	0.160071i	$-0.948828\pi$
$443$		−	6.73820i		−	0.320142i	0.987106	−	0.160071i	$-0.0511723\pi$
$444$		0			0
$445$	3.73206	+	15.0205i	0.176917	+	0.712041i
$446$	1.28846			0.0610102
$447$		0			0
$448$		−	1.07838i		−	0.0509486i
$449$	−36.2290			−1.70975			−0.854876	−	0.518833i	$-0.826367\pi$
$449$	−36.2290			−1.70975			−0.854876	+	0.518833i	$0.826367\pi$
$450$		0			0
$451$	48.1978			2.26955
$452$		−	13.2039i		−	0.621061i
$453$		0			0
$454$	20.9939			0.985291
$455$	−1.98771	−	8.00000i	−0.0931855	−	0.375046i
$456$		0			0
$457$			8.00000i			0.374224i	0.982339	+	0.187112i	$0.0599128\pi$
$457$			8.00000i			0.374224i	−0.982339	+	0.187112i	$0.940087\pi$
$458$		−	2.36683i		−	0.110595i
$459$		0			0
$460$	−13.7587	+	3.41855i	−0.641504	+	0.159391i
$461$	−35.7464			−1.66488			−0.832439	−	0.554117i	$-0.813056\pi$
$461$	−35.7464			−1.66488			−0.832439	+	0.554117i	$0.813056\pi$
$462$		0			0
$463$		−	37.3295i		−	1.73485i	−0.497569	−	0.867424i	$-0.665774\pi$
$463$		−	37.3295i		−	1.73485i	0.497569	−	0.867424i	$-0.334226\pi$
$464$	−0.340173			−0.0157921
$465$		0			0
$466$	−5.10504			−0.236486
$467$		−	12.0989i		−	0.559870i	−0.960019	−	0.279935i	$-0.909687\pi$
$467$		−	12.0989i		−	0.559870i	0.960019	−	0.279935i	$-0.0903129\pi$
$468$		0			0
$469$	3.05947			0.141273
$470$	−3.41855	−	13.7587i	−0.157686	−	0.634643i
$471$		0			0
$472$			0.738205i			0.0339786i
$473$			70.8659i			3.25842i
$474$		0			0
$475$	4.41855	−	2.34017i	0.202737	−	0.107375i
$476$	−5.84324			−0.267825
$477$		0			0
$478$		−	10.4124i		−	0.476252i
$479$	−34.6102			−1.58138			−0.790690	−	0.612216i	$-0.790278\pi$
$479$	−34.6102			−1.58138			−0.790690	+	0.612216i	$0.790278\pi$
$480$		0			0
$481$	11.6865			0.532858
$482$		−	3.36069i		−	0.153075i
$483$		0			0
$484$	−29.1978			−1.32717
$485$	−7.94214	+	1.97334i	−0.360634	+	0.0896047i
$486$		0			0
$487$		−	30.2823i		−	1.37222i	−0.727497	−	0.686111i	$-0.759316\pi$
$487$		−	30.2823i		−	1.37222i	0.727497	−	0.686111i	$-0.240684\pi$
$488$		−	2.68035i		−	0.121334i
$489$		0			0
$490$	12.6670	−	3.14730i	0.572237	−	0.142181i
$491$	27.0205			1.21942			0.609709	−	0.792625i	$-0.291286\pi$
$491$	27.0205			1.21942			0.609709	+	0.792625i	$0.291286\pi$
$492$		0			0
$493$			1.84324i			0.0830156i
$494$	−3.41855			−0.153808
$495$		0			0
$496$	1.07838			0.0484206
$497$			3.05947i			0.137236i
$498$		0			0
$499$	35.0349			1.56838			0.784189	−	0.620522i	$-0.213079\pi$
$499$	35.0349			1.56838			0.784189	+	0.620522i	$0.213079\pi$
$500$	7.46081	+	8.32684i	0.333658	+	0.372388i
$501$		0			0
$502$			21.8576i			0.975553i
$503$			29.5441i			1.31731i	0.752447	+	0.658653i	$0.228874\pi$
$503$			29.5441i			1.31731i	−0.752447	+	0.658653i	$0.771126\pi$
$504$		0			0
$505$	−10.5692	−	42.5380i	−0.470322	−	1.89291i
$506$	40.1978			1.78701
$507$		0			0
$508$		−	0.921622i		−	0.0408904i
$509$	29.2183			1.29508			0.647539	−	0.762032i	$-0.275798\pi$
$509$	29.2183			1.29508			0.647539	+	0.762032i	$0.275798\pi$
$510$		0			0
$511$	−7.37298			−0.326161
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−26.8781			−1.18554
$515$	25.5174	−	6.34017i	1.12443	−	0.279381i
$516$		0			0
$517$			40.1978i			1.76790i
$518$		−	3.68649i		−	0.161975i
$519$		0			0
$520$	−1.84324	−	7.41855i	−0.0808316	−	0.325325i
$521$	16.3980			0.718411			0.359205	−	0.933259i	$-0.383048\pi$
$521$	16.3980			0.718411			0.359205	+	0.933259i	$0.383048\pi$
$522$		0			0
$523$		−	13.8432i		−	0.605323i	−0.953098	−	0.302661i	$-0.902125\pi$
$523$		−	13.8432i		−	0.605323i	0.953098	−	0.302661i	$-0.0978751\pi$
$524$	10.6537			0.465408
$525$		0			0
$526$	−22.3402			−0.974078
$527$		−	5.84324i		−	0.254536i
$528$		0			0
$529$	−17.1978			−0.747730
$530$	−3.23513	−	13.0205i	−0.140525	−	0.565575i
$531$		0			0
$532$			1.07838i			0.0467536i
$533$		−	25.9877i		−	1.12565i
$534$		0			0
$535$	−13.3607	+	3.31965i	−0.577633	+	0.143521i
$536$	2.83710			0.122544
$537$		0			0
$538$			17.3340i			0.747323i
$539$	−37.0082			−1.59406
$540$		0			0
$541$	−5.20394			−0.223735			−0.111867	−	0.993723i	$-0.535683\pi$
$541$	−5.20394			−0.223735			−0.111867	+	0.993723i	$0.535683\pi$
$542$			13.3607i			0.573891i
$543$		0			0
$544$	−5.41855			−0.232318
$545$	−9.65983	−	38.8781i	−0.413782	−	1.66536i
$546$		0			0
$547$		−	19.8843i		−	0.850191i	−0.905149	−	0.425095i	$-0.860241\pi$
$547$		−	19.8843i		−	0.850191i	0.905149	−	0.425095i	$-0.139759\pi$
$548$		−	20.6225i		−	0.880949i
$549$		0			0
$550$	−14.8371	−	28.0144i	−0.632656	−	1.19454i
$551$	0.340173			0.0144919
$552$		0			0
$553$			1.16290i			0.0494515i
$554$	−0.738205			−0.0313633
$555$		0			0
$556$	18.8371			0.798871
$557$			17.0205i			0.721183i	0.932724	+	0.360591i	$0.117425\pi$
$557$			17.0205i			0.721183i	−0.932724	+	0.360591i	$0.882575\pi$
$558$		0			0
$559$	38.2101			1.61611
$560$	−2.34017	+	0.581449i	−0.0988904	+	0.0245707i
$561$		0			0
$562$		−	31.7998i		−	1.34139i
$563$		−	12.6270i		−	0.532166i	−0.963950	−	0.266083i	$-0.914271\pi$
$563$		−	12.6270i		−	0.532166i	0.963950	−	0.266083i	$-0.0857294\pi$
$564$		0			0
$565$	−28.6537	+	7.11942i	−1.20547	+	0.299516i
$566$	−4.70701			−0.197850
$567$		0			0
$568$			2.83710i			0.119042i
$569$	−31.9155			−1.33797			−0.668983	−	0.743277i	$-0.733270\pi$
$569$	−31.9155			−1.33797			−0.668983	+	0.743277i	$0.733270\pi$
$570$		0			0
$571$	24.5113			1.02577			0.512883	−	0.858458i	$-0.328577\pi$
$571$	24.5113			1.02577			0.512883	+	0.858458i	$0.328577\pi$
$572$			21.6742i			0.906244i
$573$		0			0
$574$	−8.19779			−0.342169
$575$	14.8371	+	28.0144i	0.618750	+	1.16828i
$576$		0			0
$577$			32.0000i			1.33218i	0.745873	+	0.666089i	$0.232033\pi$
$577$			32.0000i			1.33218i	−0.745873	+	0.666089i	$0.767967\pi$
$578$			12.3607i			0.514137i
$579$		0			0
$580$	0.183417	+	0.738205i	0.00761600	+	0.0306523i
$581$	0.965105			0.0400393
$582$		0			0
$583$			38.0410i			1.57550i
$584$	−6.83710			−0.282921
$585$		0			0
$586$	−26.1978			−1.08222
$587$		−	8.58145i		−	0.354194i	−0.984193	−	0.177097i	$-0.943329\pi$
$587$		−	8.58145i		−	0.354194i	0.984193	−	0.177097i	$-0.0566707\pi$
$588$		0			0
$589$	−1.07838			−0.0444338
$590$	1.60197	−	0.398032i	0.0659520	−	0.0163867i
$591$		0			0
$592$		−	3.41855i		−	0.140502i
$593$			10.7792i			0.442650i	0.975200	+	0.221325i	$0.0710382\pi$
$593$			10.7792i			0.442650i	−0.975200	+	0.221325i	$0.928962\pi$
$594$		0			0
$595$	3.15061	+	12.6803i	0.129163	+	0.519844i
$596$	5.44521			0.223045
$597$		0			0
$598$		−	21.6742i		−	0.886324i
$599$	−18.2101			−0.744044			−0.372022	−	0.928224i	$-0.621335\pi$
$599$	−18.2101			−0.744044			−0.372022	+	0.928224i	$0.621335\pi$
$600$		0			0
$601$	−32.0410			−1.30698			−0.653491	−	0.756935i	$-0.726696\pi$
$601$	−32.0410			−1.30698			−0.653491	+	0.756935i	$0.726696\pi$
$602$		−	12.0533i		−	0.491257i
$603$		0			0
$604$	23.1194			0.940716
$605$	15.7431	+	63.3617i	0.640049	+	2.57602i
$606$		0			0
$607$		−	11.5609i		−	0.469244i	−0.972087	−	0.234622i	$-0.924615\pi$
$607$		−	11.5609i		−	0.469244i	0.972087	−	0.234622i	$-0.0753852\pi$
$608$			1.00000i			0.0405554i
$609$		0			0
$610$	−5.81658	+	1.44521i	−0.235507	+	0.0585150i
$611$	21.6742			0.876844
$612$		0			0
$613$		−	2.58145i		−	0.104264i	−0.998640	−	0.0521319i	$-0.983398\pi$
$613$		−	2.58145i		−	0.104264i	0.998640	−	0.0521319i	$-0.0166016\pi$
$614$	−32.1978			−1.29940
$615$		0			0
$616$	6.83710			0.275475
$617$		−	9.90110i		−	0.398603i	−0.979938	−	0.199302i	$-0.936133\pi$
$617$		−	9.90110i		−	0.398603i	0.979938	−	0.199302i	$-0.0638674\pi$
$618$		0			0
$619$	−11.2039			−0.450324			−0.225162	−	0.974321i	$-0.572291\pi$
$619$	−11.2039			−0.450324			−0.225162	+	0.974321i	$0.572291\pi$
$620$	−0.581449	−	2.34017i	−0.0233516	−	0.0939836i
$621$		0			0
$622$			16.7382i			0.671141i
$623$			7.46412i			0.299044i
$624$		0			0
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$	−14.1568			−0.565818
$627$		0			0
$628$		−	9.73206i		−	0.388352i
$629$	−18.5236			−0.738584
$630$		0			0
$631$	−23.3197			−0.928341			−0.464170	−	0.885746i	$-0.653647\pi$
$631$	−23.3197			−0.928341			−0.464170	+	0.885746i	$0.653647\pi$
$632$			1.07838i			0.0428956i
$633$		0			0
$634$	−21.8843			−0.869136
$635$	−2.00000	+	0.496928i	−0.0793676	+	0.0197200i
$636$		0			0
$637$			19.9544i			0.790623i
$638$		−	2.15676i		−	0.0853868i
$639$		0			0
$640$	−2.17009	+	0.539189i	−0.0857802	+	0.0213133i
$641$	19.2885			0.761848			0.380924	−	0.924606i	$-0.375606\pi$
$641$	19.2885			0.761848			0.380924	+	0.924606i	$0.375606\pi$
$642$		0			0
$643$			31.3751i			1.23731i	0.785662	+	0.618656i	$0.212323\pi$
$643$			31.3751i			1.23731i	−0.785662	+	0.618656i	$0.787677\pi$
$644$	−6.83710			−0.269420
$645$		0			0
$646$	5.41855			0.213190
$647$			33.2306i			1.30643i	0.757173	+	0.653215i	$0.226580\pi$
$647$			33.2306i			1.30643i	−0.757173	+	0.653215i	$0.773420\pi$
$648$		0			0
$649$	−4.68035			−0.183720
$650$	−15.1050	+	8.00000i	−0.592468	+	0.313786i
$651$		0			0
$652$			6.49693i			0.254439i
$653$		−	7.85762i		−	0.307492i	−0.988110	−	0.153746i	$-0.950866\pi$
$653$		−	7.85762i		−	0.307492i	0.988110	−	0.153746i	$-0.0491338\pi$
$654$		0			0
$655$	−5.74435	−	23.1194i	−0.224450	−	0.903350i
$656$	−7.60197			−0.296807
$657$		0			0
$658$		−	6.83710i		−	0.266538i
$659$	−25.4186			−0.990166			−0.495083	−	0.868846i	$-0.664862\pi$
$659$	−25.4186			−0.990166			−0.495083	+	0.868846i	$0.664862\pi$
$660$		0			0
$661$	30.9093			1.20223			0.601117	−	0.799161i	$-0.294723\pi$
$661$	30.9093			1.20223			0.601117	+	0.799161i	$0.294723\pi$
$662$			26.1568i			1.01661i
$663$		0			0
$664$	0.894960			0.0347312
$665$	2.34017	−	0.581449i	0.0907480	−	0.0225476i
$666$		0			0
$667$			2.15676i			0.0835099i
$668$		−	20.9939i		−	0.812277i
$669$		0			0
$670$	−1.52973	−	6.15676i	−0.0590988	−	0.237856i
$671$	16.9939			0.656041
$672$		0			0
$673$		−	27.9733i		−	1.07829i	−0.842212	−	0.539146i	$-0.818747\pi$
$673$		−	27.9733i		−	1.07829i	0.842212	−	0.539146i	$-0.181253\pi$
$674$	29.7009			1.14403
$675$		0			0
$676$	−1.31351			−0.0505197
$677$		−	4.15676i		−	0.159757i	−0.996805	−	0.0798785i	$-0.974547\pi$
$677$		−	4.15676i		−	0.159757i	0.996805	−	0.0798785i	$-0.0254532\pi$
$678$		0			0
$679$	−3.94668			−0.151460
$680$	2.92162	+	11.7587i	0.112039	+	0.450926i
$681$		0			0
$682$			6.83710i			0.261806i
$683$			19.5708i			0.748855i	0.927256	+	0.374427i	$0.122161\pi$
$683$			19.5708i			0.748855i	−0.927256	+	0.374427i	$0.877839\pi$
$684$		0			0
$685$	−44.7526	+	11.1194i	−1.70991	+	0.424851i
$686$	13.8432			0.528538
$687$		0			0
$688$		−	11.1773i		−	0.426130i
$689$	20.5113			0.781418
$690$		0			0
$691$	−10.8371			−0.412263			−0.206131	−	0.978524i	$-0.566087\pi$
$691$	−10.8371			−0.412263			−0.206131	+	0.978524i	$0.566087\pi$
$692$		−	6.99386i		−	0.265867i
$693$		0			0
$694$	23.4186			0.888956
$695$	−10.1568	−	40.8781i	−0.385268	−	1.55060i
$696$		0			0
$697$			41.1917i			1.56025i
$698$			6.48255i			0.245368i
$699$		0			0
$700$	2.52359	+	4.76487i	0.0953828	+	0.180095i
$701$	42.0098			1.58669			0.793345	−	0.608772i	$-0.208338\pi$
$701$	42.0098			1.58669			0.793345	+	0.608772i	$0.208338\pi$
$702$		0			0
$703$			3.41855i			0.128933i
$704$	6.34017			0.238954
$705$		0			0
$706$	−2.58145			−0.0971541
$707$		−	21.1383i		−	0.794989i
$708$		0			0
$709$	−23.6209			−0.887101			−0.443550	−	0.896249i	$-0.646281\pi$
$709$	−23.6209			−0.887101			−0.443550	+	0.896249i	$0.646281\pi$
$710$	6.15676	−	1.52973i	0.231059	−	0.0574099i
$711$		0			0
$712$			6.92162i			0.259399i
$713$		−	6.83710i		−	0.256051i
$714$		0			0
$715$	47.0349	−	11.6865i	1.75901	−	0.437050i
$716$	4.73820			0.177075
$717$		0			0
$718$		−	28.1399i		−	1.05017i
$719$	30.9770			1.15525			0.577624	−	0.816303i	$-0.303980\pi$
$719$	30.9770			1.15525			0.577624	+	0.816303i	$0.303980\pi$
$720$		0			0
$721$	12.6803			0.472241
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$	12.0722			0.448661
$725$	1.50307	−	0.796064i	0.0558227	−	0.0295651i
$726$		0			0
$727$		−	23.7464i		−	0.880707i	−0.897825	−	0.440353i	$-0.854853\pi$
$727$		−	23.7464i		−	0.880707i	0.897825	−	0.440353i	$-0.145147\pi$
$728$		−	3.68649i		−	0.136630i
$729$		0			0
$730$	3.68649	+	14.8371i	0.136443	+	0.549146i
$731$	−60.5646			−2.24006
$732$		0			0
$733$			41.9832i			1.55068i	0.631542	+	0.775342i	$0.282423\pi$
$733$			41.9832i			1.55068i	−0.631542	+	0.775342i	$0.717577\pi$
$734$	−10.5548			−0.389584
$735$		0			0
$736$	−6.34017			−0.233702
$737$			17.9877i			0.662586i
$738$		0			0
$739$	41.3074			1.51952			0.759758	−	0.650206i	$-0.225317\pi$
$739$	41.3074			1.51952			0.759758	+	0.650206i	$0.225317\pi$
$740$	−7.41855	+	1.84324i	−0.272711	+	0.0677590i
$741$		0			0
$742$		−	6.47027i		−	0.237531i
$743$		−	28.3668i		−	1.04068i	−0.853960	−	0.520339i	$-0.825806\pi$
$743$		−	28.3668i		−	1.04068i	0.853960	−	0.520339i	$-0.174194\pi$
$744$		0			0
$745$	−2.93600	−	11.8166i	−0.107567	−	0.432926i
$746$	17.8888			0.654956
$747$		0			0
$748$		−	34.3545i		−	1.25613i
$749$	−6.63931			−0.242595
$750$		0			0
$751$	5.75872			0.210139			0.105069	−	0.994465i	$-0.466494\pi$
$751$	5.75872			0.210139			0.105069	+	0.994465i	$0.466494\pi$
$752$		−	6.34017i		−	0.231202i
$753$		0			0
$754$	−1.16290			−0.0423503
$755$	−12.4657	−	50.1711i	−0.453674	−	1.82591i
$756$		0			0
$757$			32.3090i			1.17429i	0.809482	+	0.587145i	$0.199748\pi$
$757$			32.3090i			1.17429i	−0.809482	+	0.587145i	$0.800252\pi$
$758$			4.36683i			0.158611i
$759$		0			0
$760$	2.17009	−	0.539189i	0.0787173	−	0.0195584i
$761$	−33.5708			−1.21694			−0.608470	−	0.793577i	$-0.708216\pi$
$761$	−33.5708			−1.21694			−0.608470	+	0.793577i	$0.708216\pi$
$762$		0			0
$763$		−	19.3197i		−	0.699418i
$764$	−7.26180			−0.262723
$765$		0			0
$766$	−22.5236			−0.813810
$767$			2.52359i			0.0911216i
$768$		0			0
$769$	17.8843			0.644924			0.322462	−	0.946582i	$-0.395490\pi$
$769$	17.8843			0.644924			0.322462	+	0.946582i	$0.395490\pi$
$770$	−3.68649	−	14.8371i	−0.132852	−	0.534692i
$771$		0			0
$772$			18.8638i			0.678922i
$773$			46.5113i			1.67290i	0.548047	+	0.836448i	$0.315372\pi$
$773$			46.5113i			1.67290i	−0.548047	+	0.836448i	$0.684628\pi$
$774$		0			0
$775$	−4.76487	+	2.52359i	−0.171159	+	0.0906500i
$776$	−3.65983			−0.131380
$777$		0			0
$778$			9.07838i			0.325476i
$779$	7.60197			0.272369
$780$		0			0
$781$	−17.9877			−0.643651
$782$			34.3545i			1.22852i
$783$		0			0
$784$	5.83710			0.208468
$785$	−21.1194	+	5.24742i	−0.753784	+	0.187288i
$786$		0			0
$787$			41.9877i			1.49670i	0.663304	+	0.748350i	$0.269154\pi$
$787$			41.9877i			1.49670i	−0.663304	+	0.748350i	$0.730846\pi$
$788$		−	17.7009i		−	0.630567i
$789$		0			0
$790$	2.34017	−	0.581449i	0.0832596	−	0.0206870i
$791$	−14.2388			−0.506275
$792$		0			0
$793$		−	9.16290i		−	0.325384i
$794$	3.74435			0.132882
$795$		0			0
$796$	−0.313511			−0.0111121
$797$		−	11.3074i		−	0.400528i	−0.979742	−	0.200264i	$-0.935820\pi$
$797$		−	11.3074i		−	0.400528i	0.979742	−	0.200264i	$-0.0641799\pi$
$798$		0			0
$799$	−34.3545			−1.21538
$800$	2.34017	+	4.41855i	0.0827376	+	0.156219i
$801$		0			0
$802$		−	11.9155i		−	0.420750i
$803$		−	43.3484i		−	1.52973i
$804$		0			0
$805$	3.68649	+	14.8371i	0.129932	+	0.522939i
$806$	3.68649			0.129851
$807$		0			0
$808$		−	19.6020i		−	0.689595i
$809$	−48.5523			−1.70701			−0.853505	−	0.521085i	$-0.825527\pi$
$809$	−48.5523			−1.70701			−0.853505	+	0.521085i	$0.825527\pi$
$810$		0			0
$811$	−1.42309			−0.0499713			−0.0249856	−	0.999688i	$-0.507954\pi$
$811$	−1.42309			−0.0499713			−0.0249856	+	0.999688i	$0.507954\pi$
$812$			0.366835i			0.0128734i
$813$		0			0
$814$	21.6742			0.759680
$815$	14.0989	−	3.50307i	0.493863	−	0.122707i
$816$		0			0
$817$			11.1773i			0.391043i
$818$		−	2.99386i		−	0.104678i
$819$		0			0
$820$	4.09890	+	16.4969i	0.143140	+	0.576098i
$821$	6.55479			0.228764			0.114382	−	0.993437i	$-0.463511\pi$
$821$	6.55479			0.228764			0.114382	+	0.993437i	$0.463511\pi$
$822$		0			0
$823$			0.0845208i			0.00294621i	0.999999	+	0.00147311i	$0.000468904\pi$
$823$			0.0845208i			0.00294621i	−0.999999	+	0.00147311i	$0.999531\pi$
$824$	11.7587			0.409635
$825$		0			0
$826$	0.796064			0.0276986
$827$		−	26.4703i		−	0.920461i	−0.887799	−	0.460231i	$-0.847767\pi$
$827$		−	26.4703i		−	0.920461i	0.887799	−	0.460231i	$-0.152233\pi$
$828$		0			0
$829$	12.4924			0.433879			0.216939	−	0.976185i	$-0.430393\pi$
$829$	12.4924			0.433879			0.216939	+	0.976185i	$0.430393\pi$
$830$	−0.482553	−	1.94214i	−0.0167496	−	0.0674127i
$831$		0			0
$832$		−	3.41855i		−	0.118517i
$833$		−	31.6286i		−	1.09587i
$834$		0			0
$835$	−45.5585	+	11.3197i	−1.57662	+	0.391733i
$836$	−6.34017			−0.219279
$837$		0			0
$838$			33.5441i			1.15876i
$839$	−17.5297			−0.605194			−0.302597	−	0.953119i	$-0.597854\pi$
$839$	−17.5297			−0.605194			−0.302597	+	0.953119i	$0.597854\pi$
$840$		0			0
$841$	−28.8843			−0.996010
$842$		−	31.5897i		−	1.08865i
$843$		0			0
$844$	−14.8371			−0.510714
$845$	0.708231	+	2.85043i	0.0243639	+	0.0980579i
$846$		0			0
$847$			31.4863i			1.08188i
$848$		−	6.00000i		−	0.206041i
$849$		0			0
$850$	23.9421	−	12.6803i	0.821209	−	0.434932i
$851$	−21.6742			−0.742982
$852$		0			0
$853$		−	22.0456i		−	0.754826i	−0.926045	−	0.377413i	$-0.876814\pi$
$853$		−	22.0456i		−	0.754826i	0.926045	−	0.377413i	$-0.123186\pi$
$854$	−2.89043			−0.0989083
$855$		0			0
$856$	−6.15676			−0.210434
$857$			13.1506i			0.449216i	0.974449	+	0.224608i	$0.0721102\pi$
$857$			13.1506i			0.449216i	−0.974449	+	0.224608i	$0.927890\pi$
$858$		0			0
$859$	−5.42309			−0.185033			−0.0925166	−	0.995711i	$-0.529491\pi$
$859$	−5.42309			−0.185033			−0.0925166	+	0.995711i	$0.529491\pi$
$860$	−24.2557	+	6.02666i	−0.827111	+	0.205507i
$861$		0			0
$862$		−	40.5113i		−	1.37982i
$863$			28.6803i			0.976290i	0.872762	+	0.488145i	$0.162326\pi$
$863$			28.6803i			0.976290i	−0.872762	+	0.488145i	$0.837674\pi$
$864$		0			0
$865$	−15.1773	+	3.77101i	−0.516043	+	0.128218i
$866$	5.13624			0.174536
$867$		0			0
$868$		−	1.16290i		−	0.0394713i
$869$	−6.83710			−0.231933
$870$		0			0
$871$	9.69878			0.328630
$872$		−	17.9155i		−	0.606695i
$873$		0			0
$874$	6.34017			0.214460
$875$	8.97948	−	8.04557i	0.303562	−	0.271990i
$876$		0			0
$877$			24.4657i			0.826149i	0.910697	+	0.413075i	$0.135545\pi$
$877$			24.4657i			0.826149i	−0.910697	+	0.413075i	$0.864455\pi$
$878$		−	17.7054i		−	0.597528i
$879$		0			0
$880$	−3.41855	−	13.7587i	−0.115239	−	0.463806i
$881$	−5.51745			−0.185888			−0.0929438	−	0.995671i	$-0.529628\pi$
$881$	−5.51745			−0.185888			−0.0929438	+	0.995671i	$0.529628\pi$
$882$		0			0
$883$		−	7.23060i		−	0.243329i	−0.992571	−	0.121665i	$-0.961177\pi$
$883$		−	7.23060i		−	0.243329i	0.992571	−	0.121665i	$-0.0388232\pi$
$884$	−18.5236			−0.623016
$885$		0			0
$886$	−6.73820			−0.226374
$887$			18.1568i			0.609644i	0.952409	+	0.304822i	$0.0985970\pi$
$887$			18.1568i			0.609644i	−0.952409	+	0.304822i	$0.901403\pi$
$888$		0			0
$889$	−0.993857			−0.0333329
$890$	15.0205	−	3.73206i	0.503489	−	0.125099i
$891$		0			0
$892$		−	1.28846i		−	0.0431407i
$893$			6.34017i			0.212166i
$894$		0			0
$895$	−2.55479	−	10.2823i	−0.0853971	−	0.343700i
$896$	−1.07838			−0.0360261
$897$		0			0
$898$			36.2290i			1.20898i
$899$	−0.366835			−0.0122346
$900$		0			0
$901$	−32.5113			−1.08311
$902$		−	48.1978i		−	1.60481i
$903$		0			0
$904$	−13.2039			−0.439156
$905$	−6.50921	−	26.1978i	−0.216374	−	0.870844i
$906$		0			0
$907$			19.2039i			0.637656i	0.947813	+	0.318828i	$0.103289\pi$
$907$			19.2039i			0.637656i	−0.947813	+	0.318828i	$0.896711\pi$
$908$		−	20.9939i		−	0.696706i
$909$		0			0
$910$	−8.00000	+	1.98771i	−0.265197	+	0.0658921i
$911$	−52.8781			−1.75193			−0.875965	−	0.482374i	$-0.839775\pi$
$911$	−52.8781			−1.75193			−0.875965	+	0.482374i	$0.839775\pi$
$912$		0			0
$913$			5.67420i			0.187789i
$914$	8.00000			0.264616
$915$		0			0
$916$	−2.36683			−0.0782024
$917$		−	11.4887i		−	0.379390i
$918$		0			0
$919$	−10.0410			−0.331223			−0.165612	−	0.986191i	$-0.552960\pi$
$919$	−10.0410			−0.331223			−0.165612	+	0.986191i	$0.552960\pi$
$920$	3.41855	+	13.7587i	0.112706	+	0.453612i
$921$		0			0
$922$			35.7464i			1.17725i
$923$			9.69878i			0.319239i
$924$		0			0
$925$	8.00000	+	15.1050i	0.263038	+	0.496651i
$926$	−37.3295			−1.22672
$927$		0			0
$928$			0.340173i			0.0111667i
$929$	11.3074			0.370983			0.185491	−	0.982646i	$-0.440612\pi$
$929$	11.3074			0.370983			0.185491	+	0.982646i	$0.440612\pi$
$930$		0			0
$931$	−5.83710			−0.191303
$932$			5.10504i			0.167221i
$933$		0			0
$934$	−12.0989			−0.395888
$935$	−74.5523	+	18.5236i	−2.43812	+	0.605786i
$936$		0			0
$937$			27.0349i			0.883192i	0.897214	+	0.441596i	$0.145587\pi$
$937$			27.0349i			0.883192i	−0.897214	+	0.441596i	$0.854413\pi$
$938$		−	3.05947i		−	0.0998951i
$939$		0			0
$940$	−13.7587	+	3.41855i	−0.448760	+	0.111501i
$941$	19.9733			0.651112			0.325556	−	0.945523i	$-0.394449\pi$
$941$	19.9733			0.651112			0.325556	+	0.945523i	$0.394449\pi$
$942$		0			0
$943$			48.1978i			1.56954i
$944$	0.738205			0.0240265
$945$		0			0
$946$	70.8659			2.30405
$947$			12.5281i			0.407109i	0.979064	+	0.203555i	$0.0652495\pi$
$947$			12.5281i			0.407109i	−0.979064	+	0.203555i	$0.934751\pi$
$948$		0			0
$949$	−23.3730			−0.758719
$950$	−2.34017	−	4.41855i	−0.0759252	−	0.143357i
$951$		0			0
$952$			5.84324i			0.189381i
$953$			46.5113i			1.50665i	0.657649	+	0.753324i	$0.271551\pi$
$953$			46.5113i			1.50665i	−0.657649	+	0.753324i	$0.728449\pi$
$954$		0			0
$955$	3.91548	+	15.7587i	0.126702	+	0.509940i
$956$	−10.4124			−0.336761
$957$		0			0
$958$			34.6102i			1.11820i
$959$	−22.2388			−0.718129
$960$		0			0
$961$	−29.8371			−0.962487
$962$		−	11.6865i		−	0.376788i
$963$		0			0
$964$	−3.36069			−0.108241
$965$	40.9360	−	10.1711i	1.31778	−	0.327420i
$966$		0			0
$967$		−	37.2762i		−	1.19872i	−0.800479	−	0.599360i	$-0.795422\pi$
$967$		−	37.2762i		−	1.19872i	0.800479	−	0.599360i	$-0.204578\pi$
$968$			29.1978i			0.938453i
$969$		0			0
$970$	1.97334	+	7.94214i	0.0633601	+	0.255007i
$971$	16.4534			0.528016			0.264008	−	0.964520i	$-0.414955\pi$
$971$	16.4534			0.528016			0.264008	+	0.964520i	$0.414955\pi$
$972$		0			0
$973$		−	20.3135i		−	0.651221i
$974$	−30.2823			−0.970308
$975$		0			0
$976$	−2.68035			−0.0857958
$977$		−	34.5646i		−	1.10582i	−0.833241	−	0.552910i	$-0.813517\pi$
$977$		−	34.5646i		−	1.10582i	0.833241	−	0.552910i	$-0.186483\pi$
$978$		0			0
$979$	−43.8843			−1.40255
$980$	−3.14730	−	12.6670i	−0.100537	−	0.404633i
$981$		0			0
$982$		−	27.0205i		−	0.862259i
$983$			40.1978i			1.28211i	0.767495	+	0.641055i	$0.221503\pi$
$983$			40.1978i			1.28211i	−0.767495	+	0.641055i	$0.778497\pi$
$984$		0			0
$985$	−38.4124	+	9.54411i	−1.22392	+	0.304101i
$986$	1.84324			0.0587009
$987$		0			0
$988$			3.41855i			0.108759i
$989$	−70.8659			−2.25340
$990$		0			0
$991$	−24.6491			−0.783006			−0.391503	−	0.920177i	$-0.628045\pi$
$991$	−24.6491			−0.783006			−0.391503	+	0.920177i	$0.628045\pi$
$992$		−	1.07838i		−	0.0342385i
$993$		0			0
$994$	3.05947			0.0970404
$995$	0.169042	+	0.680346i	0.00535898	+	0.0215684i
$996$		0			0
$997$		−	6.89496i		−	0.218366i	−0.994022	−	0.109183i	$-0.965177\pi$
$997$		−	6.89496i		−	0.218366i	0.994022	−	0.109183i	$-0.0348234\pi$
$998$		−	35.0349i		−	1.10901i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.f.1369.2		6
3.2	odd	2		570.2.d.c.229.5	yes	6
5.2	odd	4		8550.2.a.cq.1.2		3
5.3	odd	4		8550.2.a.ce.1.2		3
5.4	even	2	inner	1710.2.d.f.1369.5		6
15.2	even	4		2850.2.a.bl.1.2		3
15.8	even	4		2850.2.a.bm.1.2		3
15.14	odd	2		570.2.d.c.229.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.c.229.2	✓	6	15.14	odd	2
570.2.d.c.229.5	yes	6	3.2	odd	2
1710.2.d.f.1369.2		6	1.1	even	1	trivial
1710.2.d.f.1369.5		6	5.4	even	2	inner
2850.2.a.bl.1.2		3	15.2	even	4
2850.2.a.bm.1.2		3	15.8	even	4
8550.2.a.ce.1.2		3	5.3	odd	4
8550.2.a.cq.1.2		3	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +1.07838i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +1.07838i q^{7} +1.00000i q^{8} +(2.17009 - 0.539189i) q^{10} -6.34017 q^{11} +3.41855i q^{13} +1.07838 q^{14} +1.00000 q^{16} -5.41855i q^{17} -1.00000 q^{19} +(-0.539189 - 2.17009i) q^{20} +6.34017i q^{22} -6.34017i q^{23} +(-4.41855 + 2.34017i) q^{25} +3.41855 q^{26} -1.07838i q^{28} -0.340173 q^{29} +1.07838 q^{31} -1.00000i q^{32} -5.41855 q^{34} +(-2.34017 + 0.581449i) q^{35} -3.41855i q^{37} +1.00000i q^{38} +(-2.17009 + 0.539189i) q^{40} -7.60197 q^{41} -11.1773i q^{43} +6.34017 q^{44} -6.34017 q^{46} -6.34017i q^{47} +5.83710 q^{49} +(2.34017 + 4.41855i) q^{50} -3.41855i q^{52} -6.00000i q^{53} +(-3.41855 - 13.7587i) q^{55} -1.07838 q^{56} +0.340173i q^{58} +0.738205 q^{59} -2.68035 q^{61} -1.07838i q^{62} -1.00000 q^{64} +(-7.41855 + 1.84324i) q^{65} -2.83710i q^{67} +5.41855i q^{68} +(0.581449 + 2.34017i) q^{70} +2.83710 q^{71} +6.83710i q^{73} -3.41855 q^{74} +1.00000 q^{76} -6.83710i q^{77} +1.07838 q^{79} +(0.539189 + 2.17009i) q^{80} +7.60197i q^{82} -0.894960i q^{83} +(11.7587 - 2.92162i) q^{85} -11.1773 q^{86} -6.34017i q^{88} +6.92162 q^{89} -3.68649 q^{91} +6.34017i q^{92} -6.34017 q^{94} +(-0.539189 - 2.17009i) q^{95} +3.65983i q^{97} -5.83710i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4}+O(q^{10}) \) 6 * q - 6 * q^4	\( 6 q - 6 q^{4} + 2 q^{10} - 16 q^{11} + 6 q^{16} - 6 q^{19} + 2 q^{25} - 8 q^{26} + 20 q^{29} - 4 q^{34} + 8 q^{35} - 2 q^{40} - 8 q^{41} + 16 q^{44} - 16 q^{46} - 22 q^{49} - 8 q^{50} + 8 q^{55} + 20 q^{59} + 28 q^{61} - 6 q^{64} - 16 q^{65} + 32 q^{70} - 40 q^{71} + 8 q^{74} + 6 q^{76} + 20 q^{85} + 12 q^{86} + 48 q^{89} - 48 q^{91} - 16 q^{94}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^10 - 16 * q^11 + 6 * q^16 - 6 * q^19 + 2 * q^25 - 8 * q^26 + 20 * q^29 - 4 * q^34 + 8 * q^35 - 2 * q^40 - 8 * q^41 + 16 * q^44 - 16 * q^46 - 22 * q^49 - 8 * q^50 + 8 * q^55 + 20 * q^59 + 28 * q^61 - 6 * q^64 - 16 * q^65 + 32 * q^70 - 40 * q^71 + 8 * q^74 + 6 * q^76 + 20 * q^85 + 12 * q^86 + 48 * q^89 - 48 * q^91 - 16 * q^94

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