LMFDB - Embedded newform 495.2.c.e.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(199,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, 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("495.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.c (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:	$3.95259490005$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.6
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	495.199
Dual form			495.2.c.e.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17009i q^{2} -2.70928 q^{4} +(-2.17009 - 0.539189i) q^{5} -3.70928i q^{7} -1.53919i q^{8} +O(q^{10})$	\(q+2.17009i q^{2} -2.70928 q^{4} +(-2.17009 - 0.539189i) q^{5} -3.70928i q^{7} -1.53919i q^{8} +(1.17009 - 4.70928i) q^{10} -1.00000 q^{11} -1.70928i q^{13} +8.04945 q^{14} -2.07838 q^{16} -6.04945i q^{17} +3.07838 q^{19} +(5.87936 + 1.46081i) q^{20} -2.17009i q^{22} -4.00000i q^{23} +(4.41855 + 2.34017i) q^{25} +3.70928 q^{26} +10.0494i q^{28} +5.26180 q^{29} -6.34017 q^{31} -7.58864i q^{32} +13.1278 q^{34} +(-2.00000 + 8.04945i) q^{35} +3.41855i q^{37} +6.68035i q^{38} +(-0.829914 + 3.34017i) q^{40} -9.57531 q^{41} -3.12783i q^{43} +2.70928 q^{44} +8.68035 q^{46} +2.73820i q^{47} -6.75872 q^{49} +(-5.07838 + 9.58864i) q^{50} +4.63090i q^{52} -13.7587i q^{53} +(2.17009 + 0.539189i) q^{55} -5.70928 q^{56} +11.4186i q^{58} -3.60197 q^{59} -14.6803 q^{61} -13.7587i q^{62} +12.3112 q^{64} +(-0.921622 + 3.70928i) q^{65} -1.84324i q^{67} +16.3896i q^{68} +(-17.4680 - 4.34017i) q^{70} +7.23513 q^{71} +6.38962i q^{73} -7.41855 q^{74} -8.34017 q^{76} +3.70928i q^{77} +7.44521 q^{79} +(4.51026 + 1.12064i) q^{80} -20.7792i q^{82} +7.86603i q^{83} +(-3.26180 + 13.1278i) q^{85} +6.78765 q^{86} +1.53919i q^{88} -5.02052 q^{89} -6.34017 q^{91} +10.8371i q^{92} -5.94214 q^{94} +(-6.68035 - 1.65983i) q^{95} -16.9939i q^{97} -14.6670i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} - 2 q^{5}+O(q^{10}) $ 6 * q - 2 * q^4 - 2 * q^5	$ 6 q - 2 q^{4} - 2 q^{5} - 4 q^{10} - 6 q^{11} + 12 q^{14} - 6 q^{16} + 12 q^{19} + 10 q^{20} - 2 q^{25} + 8 q^{26} + 16 q^{29} - 16 q^{31} + 36 q^{34} - 12 q^{35} - 16 q^{40} - 16 q^{41} + 2 q^{44} + 8 q^{46} + 10 q^{49} - 24 q^{50} + 2 q^{55} - 20 q^{56} + 16 q^{59} - 44 q^{61} + 22 q^{64} - 12 q^{65} - 40 q^{70} + 24 q^{71} - 16 q^{74} - 28 q^{76} + 20 q^{79} - 6 q^{80} - 4 q^{85} + 20 q^{86} + 36 q^{89} - 16 q^{91} + 24 q^{94} + 4 q^{95}+O(q^{100}) $ 6 * q - 2 * q^4 - 2 * q^5 - 4 * q^10 - 6 * q^11 + 12 * q^14 - 6 * q^16 + 12 * q^19 + 10 * q^20 - 2 * q^25 + 8 * q^26 + 16 * q^29 - 16 * q^31 + 36 * q^34 - 12 * q^35 - 16 * q^40 - 16 * q^41 + 2 * q^44 + 8 * q^46 + 10 * q^49 - 24 * q^50 + 2 * q^55 - 20 * q^56 + 16 * q^59 - 44 * q^61 + 22 * q^64 - 12 * q^65 - 40 * q^70 + 24 * q^71 - 16 * q^74 - 28 * q^76 + 20 * q^79 - 6 * q^80 - 4 * q^85 + 20 * q^86 + 36 * q^89 - 16 * q^91 + 24 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			2.17009i			1.53448i	0.641358	+	0.767241i	$0.278371\pi$
$2$			2.17009i			1.53448i	−0.641358	+	0.767241i	$0.721629\pi$
$3$		0			0
$3$		0			0
$4$	−2.70928			−1.35464
$5$	−2.17009	−	0.539189i	−0.970492	−	0.241133i
$5$	−2.17009	−	0.539189i	−0.970492	−	0.241133i
$6$		0			0
$7$		−	3.70928i		−	1.40197i	−0.713174	−	0.700987i	$-0.752743\pi$
$7$		−	3.70928i		−	1.40197i	0.713174	−	0.700987i	$-0.247257\pi$
$8$		−	1.53919i		−	0.544185i
$9$		0			0
$10$	1.17009	−	4.70928i	0.370014	−	1.48920i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		0			0
$13$		−	1.70928i		−	0.474068i	−0.971501	−	0.237034i	$-0.923825\pi$
$13$		−	1.70928i		−	0.474068i	0.971501	−	0.237034i	$-0.0761752\pi$
$14$	8.04945			2.15131
$15$		0			0
$16$	−2.07838			−0.519594
$17$		−	6.04945i		−	1.46721i	−0.679578	−	0.733603i	$-0.737837\pi$
$17$		−	6.04945i		−	1.46721i	0.679578	−	0.733603i	$-0.262163\pi$
$18$		0			0
$19$	3.07838			0.706228			0.353114	−	0.935580i	$-0.385123\pi$
$19$	3.07838			0.706228			0.353114	+	0.935580i	$0.385123\pi$
$20$	5.87936	+	1.46081i	1.31467	+	0.326647i
$21$		0			0
$22$		−	2.17009i		−	0.462664i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$	3.70928			0.727449
$27$		0			0
$28$			10.0494i			1.89917i
$29$	5.26180			0.977091			0.488545	−	0.872538i	$-0.337528\pi$
$29$	5.26180			0.977091			0.488545	+	0.872538i	$0.337528\pi$
$30$		0			0
$31$	−6.34017			−1.13873			−0.569364	−	0.822085i	$-0.692811\pi$
$31$	−6.34017			−1.13873			−0.569364	+	0.822085i	$0.692811\pi$
$32$		−	7.58864i		−	1.34149i
$33$		0			0
$34$	13.1278			2.25140
$35$	−2.00000	+	8.04945i	−0.338062	+	1.36061i
$36$		0			0
$37$			3.41855i			0.562006i	0.959707	+	0.281003i	$0.0906671\pi$
$37$			3.41855i			0.562006i	−0.959707	+	0.281003i	$0.909333\pi$
$38$			6.68035i			1.08370i
$39$		0			0
$40$	−0.829914	+	3.34017i	−0.131221	+	0.528128i
$41$	−9.57531			−1.49541			−0.747706	−	0.664030i	$-0.768845\pi$
$41$	−9.57531			−1.49541			−0.747706	+	0.664030i	$0.768845\pi$
$42$		0			0
$43$		−	3.12783i		−	0.476989i	−0.971144	−	0.238495i	$-0.923346\pi$
$43$		−	3.12783i		−	0.476989i	0.971144	−	0.238495i	$-0.0766539\pi$
$44$	2.70928			0.408439
$45$		0			0
$46$	8.68035			1.27985
$47$			2.73820i			0.399408i	0.979856	+	0.199704i	$0.0639981\pi$
$47$			2.73820i			0.399408i	−0.979856	+	0.199704i	$0.936002\pi$
$48$		0			0
$49$	−6.75872			−0.965532
$50$	−5.07838	+	9.58864i	−0.718191	+	1.35604i
$51$		0			0
$52$			4.63090i			0.642190i
$53$		−	13.7587i		−	1.88991i	−0.327206	−	0.944953i	$-0.606107\pi$
$53$		−	13.7587i		−	1.88991i	0.327206	−	0.944953i	$-0.393893\pi$
$54$		0			0
$55$	2.17009	+	0.539189i	0.292614	+	0.0727042i
$56$	−5.70928			−0.762934
$57$		0			0
$58$			11.4186i			1.49933i
$59$	−3.60197			−0.468936			−0.234468	−	0.972124i	$-0.575335\pi$
$59$	−3.60197			−0.468936			−0.234468	+	0.972124i	$0.575335\pi$
$60$		0			0
$61$	−14.6803			−1.87963			−0.939813	−	0.341690i	$-0.889001\pi$
$61$	−14.6803			−1.87963			−0.939813	+	0.341690i	$0.889001\pi$
$62$		−	13.7587i		−	1.74736i
$63$		0			0
$64$	12.3112			1.53891
$65$	−0.921622	+	3.70928i	−0.114313	+	0.460079i
$66$		0			0
$67$		−	1.84324i		−	0.225188i	−0.993641	−	0.112594i	$-0.964084\pi$
$67$		−	1.84324i		−	0.225188i	0.993641	−	0.112594i	$-0.0359160\pi$
$68$			16.3896i			1.98753i
$69$		0			0
$70$	−17.4680	−	4.34017i	−2.08783	−	0.518750i
$71$	7.23513			0.858652			0.429326	−	0.903150i	$-0.358751\pi$
$71$	7.23513			0.858652			0.429326	+	0.903150i	$0.358751\pi$
$72$		0			0
$73$			6.38962i			0.747849i	0.927459	+	0.373924i	$0.121988\pi$
$73$			6.38962i			0.747849i	−0.927459	+	0.373924i	$0.878012\pi$
$74$	−7.41855			−0.862389
$75$		0			0
$76$	−8.34017			−0.956683
$77$			3.70928i			0.422711i
$78$		0			0
$79$	7.44521			0.837652			0.418826	−	0.908067i	$-0.362442\pi$
$79$	7.44521			0.837652			0.418826	+	0.908067i	$0.362442\pi$
$80$	4.51026	+	1.12064i	0.504262	+	0.125291i
$81$		0			0
$82$		−	20.7792i		−	2.29468i
$83$			7.86603i			0.863409i	0.902015	+	0.431705i	$0.142088\pi$
$83$			7.86603i			0.863409i	−0.902015	+	0.431705i	$0.857912\pi$
$84$		0			0
$85$	−3.26180	+	13.1278i	−0.353791	+	1.42391i
$86$	6.78765			0.731931
$87$		0			0
$88$			1.53919i			0.164078i
$89$	−5.02052			−0.532174			−0.266087	−	0.963949i	$-0.585731\pi$
$89$	−5.02052			−0.532174			−0.266087	+	0.963949i	$0.585731\pi$
$90$		0			0
$91$	−6.34017			−0.664631
$92$			10.8371i			1.12985i
$93$		0			0
$94$	−5.94214			−0.612885
$95$	−6.68035	−	1.65983i	−0.685389	−	0.170295i
$96$		0			0
$97$		−	16.9939i		−	1.72546i	−0.505661	−	0.862732i	$-0.668751\pi$
$97$		−	16.9939i		−	1.72546i	0.505661	−	0.862732i	$-0.331249\pi$
$98$		−	14.6670i		−	1.48159i
$99$		0			0
$100$	−11.9711	−	6.34017i	−1.19711	−	0.634017i
$101$	18.9360			1.88420			0.942101	−	0.335329i	$-0.108847\pi$
$101$	18.9360			1.88420			0.942101	+	0.335329i	$0.108847\pi$
$102$		0			0
$103$		−	11.7854i		−	1.16125i	−0.814172	−	0.580624i	$-0.802809\pi$
$103$		−	11.7854i		−	1.16125i	0.814172	−	0.580624i	$-0.197191\pi$
$104$	−2.63090			−0.257981
$105$		0			0
$106$	29.8576			2.90003
$107$			11.2846i			1.09092i	0.838136	+	0.545461i	$0.183645\pi$
$107$			11.2846i			1.09092i	−0.838136	+	0.545461i	$0.816355\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	−1.17009	+	4.70928i	−0.111563	+	0.449012i
$111$		0			0
$112$			7.70928i			0.728458i
$113$			0.496928i			0.0467471i	0.999727	+	0.0233735i	$0.00744071\pi$
$113$			0.496928i			0.0467471i	−0.999727	+	0.0233735i	$0.992559\pi$
$114$		0			0
$115$	−2.15676	+	8.68035i	−0.201118	+	0.809446i
$116$	−14.2557			−1.32360
$117$		0			0
$118$		−	7.81658i		−	0.719575i
$119$	−22.4391			−2.05699
$120$		0			0
$121$	1.00000			0.0909091
$122$		−	31.8576i		−	2.88425i
$123$		0			0
$124$	17.1773			1.54256
$125$	−8.32684	−	7.46081i	−0.744775	−	0.667315i
$126$		0			0
$127$		−	2.81432i		−	0.249730i	−0.992174	−	0.124865i	$-0.960150\pi$
$127$		−	2.81432i		−	0.249730i	0.992174	−	0.124865i	$-0.0398498\pi$
$128$			11.5392i			1.01993i
$129$		0			0
$130$	−8.04945	−	2.00000i	−0.705983	−	0.175412i
$131$	−8.68035			−0.758405			−0.379203	−	0.925314i	$-0.623802\pi$
$131$	−8.68035			−0.758405			−0.379203	+	0.925314i	$0.623802\pi$
$132$		0			0
$133$		−	11.4186i		−	0.990114i
$134$	4.00000			0.345547
$135$		0			0
$136$	−9.31124			−0.798433
$137$			1.07838i			0.0921320i	0.998938	+	0.0460660i	$0.0146685\pi$
$137$			1.07838i			0.0921320i	−0.998938	+	0.0460660i	$0.985332\pi$
$138$		0			0
$139$	−10.2823			−0.872135			−0.436067	−	0.899914i	$-0.643629\pi$
$139$	−10.2823			−0.872135			−0.436067	+	0.899914i	$0.643629\pi$
$140$	5.41855	−	21.8082i	0.457951	−	1.84313i
$141$		0			0
$142$			15.7009i			1.31759i
$143$			1.70928i			0.142937i
$144$		0			0
$145$	−11.4186	−	2.83710i	−0.948259	−	0.235608i
$146$	−13.8660			−1.14756
$147$		0			0
$148$		−	9.26180i		−	0.761315i
$149$	11.4186			0.935444			0.467722	−	0.883876i	$-0.345075\pi$
$149$	11.4186			0.935444			0.467722	+	0.883876i	$0.345075\pi$
$150$		0			0
$151$	−4.92162			−0.400516			−0.200258	−	0.979743i	$-0.564178\pi$
$151$	−4.92162			−0.400516			−0.200258	+	0.979743i	$0.564178\pi$
$152$		−	4.73820i		−	0.384319i
$153$		0			0
$154$	−8.04945			−0.648643
$155$	13.7587	+	3.41855i	1.10513	+	0.274585i
$156$		0			0
$157$			3.41855i			0.272830i	0.990652	+	0.136415i	$0.0435581\pi$
$157$			3.41855i			0.272830i	−0.990652	+	0.136415i	$0.956442\pi$
$158$			16.1568i			1.28536i
$159$		0			0
$160$	−4.09171	+	16.4680i	−0.323478	+	1.30191i
$161$	−14.8371			−1.16933
$162$		0			0
$163$			9.26180i			0.725440i	0.931898	+	0.362720i	$0.118152\pi$
$163$			9.26180i			0.725440i	−0.931898	+	0.362720i	$0.881848\pi$
$164$	25.9421			2.02574
$165$		0			0
$166$	−17.0700			−1.32489
$167$			7.55252i			0.584432i	0.956352	+	0.292216i	$0.0943925\pi$
$167$			7.55252i			0.584432i	−0.956352	+	0.292216i	$0.905607\pi$
$168$		0			0
$169$	10.0784			0.775260
$170$	−28.4885	−	7.07838i	−2.18497	−	0.542887i
$171$		0			0
$172$			8.47414i			0.646147i
$173$		−	6.14834i		−	0.467450i	−0.972303	−	0.233725i	$-0.924908\pi$
$173$		−	6.14834i		−	0.467450i	0.972303	−	0.233725i	$-0.0750915\pi$
$174$		0			0
$175$	8.68035	−	16.3896i	0.656172	−	1.23894i
$176$	2.07838			0.156664
$177$		0			0
$178$		−	10.8950i		−	0.816612i
$179$	−6.15676			−0.460178			−0.230089	−	0.973170i	$-0.573902\pi$
$179$	−6.15676			−0.460178			−0.230089	+	0.973170i	$0.573902\pi$
$180$		0			0
$181$	14.5958			1.08490			0.542450	−	0.840088i	$-0.317497\pi$
$181$	14.5958			1.08490			0.542450	+	0.840088i	$0.317497\pi$
$182$		−	13.7587i		−	1.01986i
$183$		0			0
$184$	−6.15676			−0.453882
$185$	1.84324	−	7.41855i	0.135518	−	0.545423i
$186$		0			0
$187$			6.04945i			0.442379i
$188$		−	7.41855i		−	0.541053i
$189$		0			0
$190$	3.60197	−	14.4969i	0.261314	−	1.05172i
$191$	−5.84324			−0.422802			−0.211401	−	0.977399i	$-0.567803\pi$
$191$	−5.84324			−0.422802			−0.211401	+	0.977399i	$0.567803\pi$
$192$		0			0
$193$			2.02279i			0.145603i	0.997346	+	0.0728017i	$0.0231940\pi$
$193$			2.02279i			0.145603i	−0.997346	+	0.0728017i	$0.976806\pi$
$194$	36.8781			2.64770
$195$		0			0
$196$	18.3112			1.30795
$197$			17.8348i			1.27068i	0.772233	+	0.635340i	$0.219140\pi$
$197$			17.8348i			1.27068i	−0.772233	+	0.635340i	$0.780860\pi$
$198$		0			0
$199$	−25.6742			−1.82000			−0.909998	−	0.414613i	$-0.863917\pi$
$199$	−25.6742			−1.82000			−0.909998	+	0.414613i	$0.863917\pi$
$200$	3.60197	−	6.80098i	0.254698	−	0.480902i
$201$		0			0
$202$			41.0928i			2.89128i
$203$		−	19.5174i		−	1.36986i
$204$		0			0
$205$	20.7792	+	5.16290i	1.45129	+	0.360592i
$206$	25.5753			1.78192
$207$		0			0
$208$			3.55252i			0.246323i
$209$	−3.07838			−0.212936
$210$		0			0
$211$	8.43907			0.580970			0.290485	−	0.956880i	$-0.406183\pi$
$211$	8.43907			0.580970			0.290485	+	0.956880i	$0.406183\pi$
$212$			37.2762i			2.56014i
$213$		0			0
$214$	−24.4885			−1.67400
$215$	−1.68649	+	6.78765i	−0.115018	+	0.462914i
$216$		0			0
$217$			23.5174i			1.59647i
$218$			21.7009i			1.46977i
$219$		0			0
$220$	−5.87936	−	1.46081i	−0.396386	−	0.0984879i
$221$	−10.3402			−0.695555
$222$		0			0
$223$			12.5814i			0.842516i	0.906941	+	0.421258i	$0.138411\pi$
$223$			12.5814i			0.842516i	−0.906941	+	0.421258i	$0.861589\pi$
$224$	−28.1483			−1.88074
$225$		0			0
$226$	−1.07838			−0.0717326
$227$			4.23287i			0.280945i	0.990085	+	0.140473i	$0.0448622\pi$
$227$			4.23287i			0.280945i	−0.990085	+	0.140473i	$0.955138\pi$
$228$		0			0
$229$	26.1978			1.73120			0.865599	−	0.500737i	$-0.166938\pi$
$229$	26.1978			1.73120			0.865599	+	0.500737i	$0.166938\pi$
$230$	−18.8371	−	4.68035i	−1.24208	−	0.308613i
$231$		0			0
$232$		−	8.09890i		−	0.531719i
$233$			18.6309i			1.22055i	0.792189	+	0.610275i	$0.208941\pi$
$233$			18.6309i			1.22055i	−0.792189	+	0.610275i	$0.791059\pi$
$234$		0			0
$235$	1.47641	−	5.94214i	0.0963103	−	0.387623i
$236$	9.75872			0.635239
$237$		0			0
$238$		−	48.6947i		−	3.15641i
$239$	22.3545			1.44600			0.722998	−	0.690850i	$-0.242764\pi$
$239$	22.3545			1.44600			0.722998	+	0.690850i	$0.242764\pi$
$240$		0			0
$241$	9.20394			0.592878			0.296439	−	0.955052i	$-0.404201\pi$
$241$	9.20394			0.592878			0.296439	+	0.955052i	$0.404201\pi$
$242$			2.17009i			0.139498i
$243$		0			0
$244$	39.7731			2.54621
$245$	14.6670	+	3.64423i	0.937041	+	0.232821i
$246$		0			0
$247$		−	5.26180i		−	0.334800i
$248$			9.75872i			0.619680i
$249$		0			0
$250$	16.1906	−	18.0700i	1.02398	−	1.14285i
$251$	22.1256			1.39655			0.698276	−	0.715828i	$-0.253951\pi$
$251$	22.1256			1.39655			0.698276	+	0.715828i	$0.253951\pi$
$252$		0			0
$253$			4.00000i			0.251478i
$254$	6.10731			0.383207
$255$		0			0
$256$	−0.418551			−0.0261594
$257$			3.02052i			0.188415i	0.995553	+	0.0942074i	$0.0300317\pi$
$257$			3.02052i			0.188415i	−0.995553	+	0.0942074i	$0.969968\pi$
$258$		0			0
$259$	12.6803			0.787918
$260$	2.49693	−	10.0494i	0.154853	−	0.623240i
$261$		0			0
$262$		−	18.8371i		−	1.16376i
$263$		−	18.2907i		−	1.12785i	−0.825825	−	0.563927i	$-0.809290\pi$
$263$		−	18.2907i		−	1.12785i	0.825825	−	0.563927i	$-0.190710\pi$
$264$		0			0
$265$	−7.41855	+	29.8576i	−0.455718	+	1.83414i
$266$	24.7792			1.51931
$267$		0			0
$268$			4.99386i			0.305048i
$269$	30.5646			1.86356			0.931779	−	0.363026i	$-0.118256\pi$
$269$	30.5646			1.86356			0.931779	+	0.363026i	$0.118256\pi$
$270$		0			0
$271$	−20.0722			−1.21930			−0.609651	−	0.792670i	$-0.708690\pi$
$271$	−20.0722			−1.21930			−0.609651	+	0.792670i	$0.708690\pi$
$272$			12.5730i			0.762352i
$273$		0			0
$274$	−2.34017			−0.141375
$275$	−4.41855	−	2.34017i	−0.266449	−	0.141118i
$276$		0			0
$277$		−	0.760991i		−	0.0457235i	−0.999739	−	0.0228618i	$-0.992722\pi$
$277$		−	0.760991i		−	0.0457235i	0.999739	−	0.0228618i	$-0.00727776\pi$
$278$		−	22.3135i		−	1.33828i
$279$		0			0
$280$	12.3896	+	3.07838i	0.740421	+	0.183968i
$281$	−0.581449			−0.0346864			−0.0173432	−	0.999850i	$-0.505521\pi$
$281$	−0.581449			−0.0346864			−0.0173432	+	0.999850i	$0.505521\pi$
$282$		0			0
$283$		−	10.8143i		−	0.642844i	−0.946936	−	0.321422i	$-0.895839\pi$
$283$		−	10.8143i		−	0.642844i	0.946936	−	0.321422i	$-0.104161\pi$
$284$	−19.6020			−1.16316
$285$		0			0
$286$	−3.70928			−0.219334
$287$			35.5174i			2.09653i
$288$		0			0
$289$	−19.5958			−1.15270
$290$	6.15676	−	24.7792i	0.361537	−	1.45509i
$291$		0			0
$292$		−	17.3112i		−	1.01306i
$293$		−	7.04331i		−	0.411474i	−0.978607	−	0.205737i	$-0.934041\pi$
$293$		−	7.04331i		−	0.411474i	0.978607	−	0.205737i	$-0.0659592\pi$
$294$		0			0
$295$	7.81658	+	1.94214i	0.455099	+	0.113076i
$296$	5.26180			0.305836
$297$		0			0
$298$			24.7792i			1.43542i
$299$	−6.83710			−0.395400
$300$		0			0
$301$	−11.6020			−0.668726
$302$		−	10.6803i		−	0.614585i
$303$		0			0
$304$	−6.39803			−0.366952
$305$	31.8576	+	7.91548i	1.82416	+	0.453239i
$306$		0			0
$307$			20.1750i			1.15145i	0.817644	+	0.575724i	$0.195280\pi$
$307$			20.1750i			1.15145i	−0.817644	+	0.575724i	$0.804720\pi$
$308$		−	10.0494i		−	0.572620i
$309$		0			0
$310$	−7.41855	+	29.8576i	−0.421345	+	1.69580i
$311$	−21.2762			−1.20646			−0.603230	−	0.797567i	$-0.706120\pi$
$311$	−21.2762			−1.20646			−0.603230	+	0.797567i	$0.706120\pi$
$312$		0			0
$313$			16.4657i			0.930698i	0.885127	+	0.465349i	$0.154071\pi$
$313$			16.4657i			0.930698i	−0.885127	+	0.465349i	$0.845929\pi$
$314$	−7.41855			−0.418653
$315$		0			0
$316$	−20.1711			−1.13471
$317$		−	22.1711i		−	1.24525i	−0.782518	−	0.622627i	$-0.786065\pi$
$317$		−	22.1711i		−	1.24525i	0.782518	−	0.622627i	$-0.213935\pi$
$318$		0			0
$319$	−5.26180			−0.294604
$320$	−26.7165	−	6.63809i	−1.49350	−	0.371080i
$321$		0			0
$322$		−	32.1978i		−	1.79431i
$323$		−	18.6225i		−	1.03618i
$324$		0			0
$325$	4.00000	−	7.55252i	0.221880	−	0.418938i
$326$	−20.0989			−1.11317
$327$		0			0
$328$			14.7382i			0.813781i
$329$	10.1568			0.559960
$330$		0			0
$331$	−6.34017			−0.348487			−0.174244	−	0.984703i	$-0.555748\pi$
$331$	−6.34017			−0.348487			−0.174244	+	0.984703i	$0.555748\pi$
$332$		−	21.3112i		−	1.16961i
$333$		0			0
$334$	−16.3896			−0.896800
$335$	−0.993857	+	4.00000i	−0.0543002	+	0.218543i
$336$		0			0
$337$		−	3.18568i		−	0.173535i	−0.996229	−	0.0867677i	$-0.972346\pi$
$337$		−	3.18568i		−	0.173535i	0.996229	−	0.0867677i	$-0.0276538\pi$
$338$			21.8710i			1.18962i
$339$		0			0
$340$	8.83710	−	35.5669i	0.479259	−	1.92889i
$341$	6.34017			0.343340
$342$		0			0
$343$		−	0.894960i		−	0.0483233i
$344$	−4.81432			−0.259570
$345$		0			0
$346$	13.3424			0.717294
$347$		−	5.39576i		−	0.289660i	−0.989457	−	0.144830i	$-0.953737\pi$
$347$		−	5.39576i		−	0.289660i	0.989457	−	0.144830i	$-0.0462635\pi$
$348$		0			0
$349$	15.6742			0.839021			0.419510	−	0.907751i	$-0.362202\pi$
$349$	15.6742			0.839021			0.419510	+	0.907751i	$0.362202\pi$
$350$	35.5669	+	18.8371i	1.90113	+	1.00689i
$351$		0			0
$352$			7.58864i			0.404476i
$353$			5.75872i			0.306506i	0.988187	+	0.153253i	$0.0489749\pi$
$353$			5.75872i			0.306506i	−0.988187	+	0.153253i	$0.951025\pi$
$354$		0			0
$355$	−15.7009	−	3.90110i	−0.833315	−	0.207049i
$356$	13.6020			0.720903
$357$		0			0
$358$		−	13.3607i		−	0.706135i
$359$	−10.5236			−0.555414			−0.277707	−	0.960666i	$-0.589574\pi$
$359$	−10.5236			−0.555414			−0.277707	+	0.960666i	$0.589574\pi$
$360$		0			0
$361$	−9.52359			−0.501242
$362$			31.6742i			1.66476i
$363$		0			0
$364$	17.1773			0.900334
$365$	3.44521	−	13.8660i	0.180331	−	0.725781i
$366$		0			0
$367$		−	8.89496i		−	0.464313i	−0.972678	−	0.232157i	$-0.925422\pi$
$367$		−	8.89496i		−	0.464313i	0.972678	−	0.232157i	$-0.0745782\pi$
$368$			8.31351i			0.433372i
$369$		0			0
$370$	16.0989	+	4.00000i	0.836942	+	0.207950i
$371$	−51.0349			−2.64960
$372$		0			0
$373$		−	23.1689i		−	1.19964i	−0.800136	−	0.599819i	$-0.795239\pi$
$373$		−	23.1689i		−	1.19964i	0.800136	−	0.599819i	$-0.204761\pi$
$374$	−13.1278			−0.678824
$375$		0			0
$376$	4.21461			0.217352
$377$		−	8.99386i		−	0.463207i
$378$		0			0
$379$	11.8310			0.607716			0.303858	−	0.952717i	$-0.401725\pi$
$379$	11.8310			0.607716			0.303858	+	0.952717i	$0.401725\pi$
$380$	18.0989	+	4.49693i	0.928454	+	0.230688i
$381$		0			0
$382$		−	12.6803i		−	0.648783i
$383$		−	25.9421i		−	1.32558i	−0.748805	−	0.662791i	$-0.769372\pi$
$383$		−	25.9421i		−	1.32558i	0.748805	−	0.662791i	$-0.230628\pi$
$384$		0			0
$385$	2.00000	−	8.04945i	0.101929	−	0.410238i
$386$	−4.38962			−0.223426
$387$		0			0
$388$			46.0410i			2.33738i
$389$	1.00614			0.0510135			0.0255067	−	0.999675i	$-0.491880\pi$
$389$	1.00614			0.0510135			0.0255067	+	0.999675i	$0.491880\pi$
$390$		0			0
$391$	−24.1978			−1.22374
$392$			10.4030i			0.525428i
$393$		0			0
$394$	−38.7031			−1.94984
$395$	−16.1568	−	4.01438i	−0.812935	−	0.201985i
$396$		0			0
$397$		−	34.7214i		−	1.74262i	−0.490736	−	0.871308i	$-0.663272\pi$
$397$		−	34.7214i		−	1.74262i	0.490736	−	0.871308i	$-0.336728\pi$
$398$		−	55.7152i		−	2.79275i
$399$		0			0
$400$	−9.18342	−	4.86376i	−0.459171	−	0.243188i
$401$	13.0205			0.650214			0.325107	−	0.945677i	$-0.394600\pi$
$401$	13.0205			0.650214			0.325107	+	0.945677i	$0.394600\pi$
$402$		0			0
$403$			10.8371i			0.539834i
$404$	−51.3028			−2.55241
$405$		0			0
$406$	42.3545			2.10202
$407$		−	3.41855i		−	0.169451i
$408$		0			0
$409$	29.5174			1.45954			0.729772	−	0.683691i	$-0.239626\pi$
$409$	29.5174			1.45954			0.729772	+	0.683691i	$0.239626\pi$
$410$	−11.2039	+	45.0928i	−0.553323	+	2.22697i
$411$		0			0
$412$			31.9299i			1.57307i
$413$			13.3607i			0.657437i
$414$		0			0
$415$	4.24128	−	17.0700i	0.208196	−	0.837932i
$416$	−12.9711			−0.635959
$417$		0			0
$418$		−	6.68035i		−	0.326746i
$419$	−6.15676			−0.300777			−0.150389	−	0.988627i	$-0.548052\pi$
$419$	−6.15676			−0.300777			−0.150389	+	0.988627i	$0.548052\pi$
$420$		0			0
$421$	9.96880			0.485850			0.242925	−	0.970045i	$-0.421893\pi$
$421$	9.96880			0.485850			0.242925	+	0.970045i	$0.421893\pi$
$422$			18.3135i			0.891488i
$423$		0			0
$424$	−21.1773			−1.02846
$425$	14.1568	−	26.7298i	0.686704	−	1.29659i
$426$		0			0
$427$			54.4534i			2.63519i
$428$		−	30.5730i		−	1.47780i
$429$		0			0
$430$	−14.7298	−	3.65983i	−0.710334	−	0.176493i
$431$	−8.68035			−0.418118			−0.209059	−	0.977903i	$-0.567040\pi$
$431$	−8.68035			−0.418118			−0.209059	+	0.977903i	$0.567040\pi$
$432$		0			0
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	−51.0349			−2.44975
$435$		0			0
$436$	−27.0928			−1.29751
$437$		−	12.3135i		−	0.589035i
$438$		0			0
$439$	−3.07838			−0.146923			−0.0734615	−	0.997298i	$-0.523405\pi$
$439$	−3.07838			−0.146923			−0.0734615	+	0.997298i	$0.523405\pi$
$440$	0.829914	−	3.34017i	0.0395646	−	0.159236i
$441$		0			0
$442$		−	22.4391i		−	1.06732i
$443$		−	29.2618i		−	1.39027i	−0.718879	−	0.695135i	$-0.755345\pi$
$443$		−	29.2618i		−	1.39027i	0.718879	−	0.695135i	$-0.244655\pi$
$444$		0			0
$445$	10.8950	+	2.70701i	0.516471	+	0.128324i
$446$	−27.3028			−1.29283
$447$		0			0
$448$		−	45.6658i		−	2.15751i
$449$	10.6947			0.504715			0.252358	−	0.967634i	$-0.418794\pi$
$449$	10.6947			0.504715			0.252358	+	0.967634i	$0.418794\pi$
$450$		0			0
$451$	9.57531			0.450884
$452$		−	1.34632i		−	0.0633254i
$453$		0			0
$454$	−9.18568			−0.431106
$455$	13.7587	+	3.41855i	0.645019	+	0.160264i
$456$		0			0
$457$		−	22.8554i		−	1.06913i	−0.845128	−	0.534564i	$-0.820476\pi$
$457$		−	22.8554i		−	1.06913i	0.845128	−	0.534564i	$-0.179524\pi$
$458$			56.8515i			2.65650i
$459$		0			0
$460$	5.84324	−	23.5174i	0.272443	−	1.09651i
$461$	21.7731			1.01407			0.507037	−	0.861924i	$-0.330741\pi$
$461$	21.7731			1.01407			0.507037	+	0.861924i	$0.330741\pi$
$462$		0			0
$463$			24.8950i			1.15697i	0.815694	+	0.578483i	$0.196355\pi$
$463$			24.8950i			1.15697i	−0.815694	+	0.578483i	$0.803645\pi$
$464$	−10.9360			−0.507691
$465$		0			0
$466$	−40.4307			−1.87291
$467$		−	19.2039i		−	0.888652i	−0.895865	−	0.444326i	$-0.853443\pi$
$467$		−	19.2039i		−	0.888652i	0.895865	−	0.444326i	$-0.146557\pi$
$468$		0			0
$469$	−6.83710			−0.315708
$470$	12.8950	+	3.20394i	0.594800	+	0.147787i
$471$		0			0
$472$			5.54411i			0.255188i
$473$			3.12783i			0.143818i
$474$		0			0
$475$	13.6020	+	7.20394i	0.624101	+	0.330539i
$476$	60.7936			2.78647
$477$		0			0
$478$			48.5113i			2.21886i
$479$	9.47641			0.432988			0.216494	−	0.976284i	$-0.430538\pi$
$479$	9.47641			0.432988			0.216494	+	0.976284i	$0.430538\pi$
$480$		0			0
$481$	5.84324			0.266429
$482$			19.9733i			0.909761i
$483$		0			0
$484$	−2.70928			−0.123149
$485$	−9.16290	+	36.8781i	−0.416066	+	1.67455i
$486$		0			0
$487$		−	35.2039i		−	1.59524i	−0.603159	−	0.797621i	$-0.706091\pi$
$487$		−	35.2039i		−	1.59524i	0.603159	−	0.797621i	$-0.293909\pi$
$488$			22.5958i			1.02286i
$489$		0			0
$490$	−7.90829	+	31.8287i	−0.357260	+	1.43787i
$491$	8.00000			0.361035			0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000			0.361035			0.180517	+	0.983572i	$0.442223\pi$
$492$		0			0
$493$		−	31.8310i		−	1.43359i
$494$	11.4186			0.513745
$495$		0			0
$496$	13.1773			0.591677
$497$		−	26.8371i		−	1.20381i
$498$		0			0
$499$	−26.1568			−1.17094			−0.585469	−	0.810695i	$-0.699089\pi$
$499$	−26.1568			−1.17094			−0.585469	+	0.810695i	$0.699089\pi$
$500$	22.5597	+	20.2134i	1.00890	+	0.903970i
$501$		0			0
$502$			48.0144i			2.14299i
$503$			28.2784i			1.26087i	0.776241	+	0.630437i	$0.217124\pi$
$503$			28.2784i			1.26087i	−0.776241	+	0.630437i	$0.782876\pi$
$504$		0			0
$505$	−41.0928	−	10.2101i	−1.82860	−	0.454343i
$506$	−8.68035			−0.385888
$507$		0			0
$508$			7.62475i			0.338294i
$509$	8.47027			0.375438			0.187719	−	0.982223i	$-0.439891\pi$
$509$	8.47027			0.375438			0.187719	+	0.982223i	$0.439891\pi$
$510$		0			0
$511$	23.7009			1.04846
$512$			22.1701i			0.979789i
$513$		0			0
$514$	−6.55479			−0.289119
$515$	−6.35455	+	25.5753i	−0.280015	+	1.12698i
$516$		0			0
$517$		−	2.73820i		−	0.120426i
$518$			27.5174i			1.20905i
$519$		0			0
$520$	5.70928	+	1.41855i	0.250368	+	0.0622076i
$521$	−13.7009			−0.600246			−0.300123	−	0.953901i	$-0.597028\pi$
$521$	−13.7009			−0.600246			−0.300123	+	0.953901i	$0.597028\pi$
$522$		0			0
$523$			24.4885i			1.07081i	0.844596	+	0.535404i	$0.179841\pi$
$523$			24.4885i			1.07081i	−0.844596	+	0.535404i	$0.820159\pi$
$524$	23.5174			1.02736
$525$		0			0
$526$	39.6925			1.73067
$527$			38.3545i			1.67075i
$528$		0			0
$529$	7.00000			0.304348
$530$	−64.7936	−	16.0989i	−2.81445	−	0.699291i
$531$		0			0
$532$			30.9360i			1.34125i
$533$			16.3668i			0.708926i
$534$		0			0
$535$	6.08452	−	24.4885i	0.263057	−	1.05873i
$536$	−2.83710			−0.122544
$537$		0			0
$538$			66.3279i			2.85960i
$539$	6.75872			0.291119
$540$		0			0
$541$	4.83710			0.207963			0.103982	−	0.994579i	$-0.466842\pi$
$541$	4.83710			0.207963			0.103982	+	0.994579i	$0.466842\pi$
$542$		−	43.5585i		−	1.87100i
$543$		0			0
$544$	−45.9071			−1.96825
$545$	−21.7009	−	5.39189i	−0.929563	−	0.230963i
$546$		0			0
$547$			30.5464i			1.30607i	0.757328	+	0.653034i	$0.226504\pi$
$547$			30.5464i			1.30607i	−0.757328	+	0.653034i	$0.773496\pi$
$548$		−	2.92162i		−	0.124806i
$549$		0			0
$550$	5.07838	−	9.58864i	0.216543	−	0.408861i
$551$	16.1978			0.690049
$552$		0			0
$553$		−	27.6163i		−	1.17437i
$554$	1.65142			0.0701620
$555$		0			0
$556$	27.8576			1.18143
$557$		−	7.57918i		−	0.321140i	−0.987024	−	0.160570i	$-0.948667\pi$
$557$		−	7.57918i		−	0.321140i	0.987024	−	0.160570i	$-0.0513333\pi$
$558$		0			0
$559$	−5.34632			−0.226125
$560$	4.15676	−	16.7298i	0.175655	−	0.706963i
$561$		0			0
$562$		−	1.26180i		−	0.0532256i
$563$			14.1750i			0.597405i	0.954346	+	0.298703i	$0.0965539\pi$
$563$			14.1750i			0.597405i	−0.954346	+	0.298703i	$0.903446\pi$
$564$		0			0
$565$	0.267938	−	1.07838i	0.0112722	−	0.0453677i
$566$	23.4680			0.986434
$567$		0			0
$568$		−	11.1362i		−	0.467266i
$569$	−14.7382			−0.617858			−0.308929	−	0.951085i	$-0.599970\pi$
$569$	−14.7382			−0.617858			−0.308929	+	0.951085i	$0.599970\pi$
$570$		0			0
$571$	1.23513			0.0516887			0.0258444	−	0.999666i	$-0.491773\pi$
$571$	1.23513			0.0516887			0.0258444	+	0.999666i	$0.491773\pi$
$572$		−	4.63090i		−	0.193628i
$573$		0			0
$574$	−77.0759			−3.21709
$575$	9.36069	−	17.6742i	0.390368	−	0.737065i
$576$		0			0
$577$		−	28.9770i		−	1.20633i	−0.797617	−	0.603165i	$-0.793906\pi$
$577$		−	28.9770i		−	1.20633i	0.797617	−	0.603165i	$-0.206094\pi$
$578$		−	42.5246i		−	1.76879i
$579$		0			0
$580$	30.9360	+	7.68649i	1.28455	+	0.319164i
$581$	29.1773			1.21048
$582$		0			0
$583$			13.7587i			0.569828i
$584$	9.83483			0.406968
$585$		0			0
$586$	15.2846			0.631400
$587$		−	20.9939i		−	0.866509i	−0.901272	−	0.433255i	$-0.857365\pi$
$587$		−	20.9939i		−	0.866509i	0.901272	−	0.433255i	$-0.142635\pi$
$588$		0			0
$589$	−19.5174			−0.804202
$590$	−4.21461	+	16.9627i	−0.173513	+	0.698342i
$591$		0			0
$592$		−	7.10504i		−	0.292015i
$593$			23.8927i			0.981155i	0.871397	+	0.490578i	$0.163214\pi$
$593$			23.8927i			0.981155i	−0.871397	+	0.490578i	$0.836786\pi$
$594$		0			0
$595$	48.6947	+	12.0989i	1.99629	+	0.496006i
$596$	−30.9360			−1.26719
$597$		0			0
$598$		−	14.8371i		−	0.606734i
$599$	−45.6742			−1.86620			−0.933099	−	0.359620i	$-0.882906\pi$
$599$	−45.6742			−1.86620			−0.933099	+	0.359620i	$0.882906\pi$
$600$		0			0
$601$	−16.2101			−0.661223			−0.330611	−	0.943767i	$-0.607255\pi$
$601$	−16.2101			−0.661223			−0.330611	+	0.943767i	$0.607255\pi$
$602$		−	25.1773i		−	1.02615i
$603$		0			0
$604$	13.3340			0.542554
$605$	−2.17009	−	0.539189i	−0.0882266	−	0.0219211i
$606$		0			0
$607$		−	20.8020i		−	0.844328i	−0.906519	−	0.422164i	$-0.861271\pi$
$607$		−	20.8020i		−	0.844328i	0.906519	−	0.422164i	$-0.138729\pi$
$608$		−	23.3607i		−	0.947401i
$609$		0			0
$610$	−17.1773	+	69.1338i	−0.695488	+	2.79915i
$611$	4.68035			0.189347
$612$		0			0
$613$			15.3835i			0.621333i	0.950519	+	0.310666i	$0.100552\pi$
$613$			15.3835i			0.621333i	−0.950519	+	0.310666i	$0.899448\pi$
$614$	−43.7815			−1.76688
$615$		0			0
$616$	5.70928			0.230033
$617$			21.9733i			0.884613i	0.896864	+	0.442307i	$0.145840\pi$
$617$			21.9733i			0.884613i	−0.896864	+	0.442307i	$0.854160\pi$
$618$		0			0
$619$	−10.3935			−0.417750			−0.208875	−	0.977942i	$-0.566980\pi$
$619$	−10.3935			−0.417750			−0.208875	+	0.977942i	$0.566980\pi$
$620$	−37.2762	−	9.26180i	−1.49705	−	0.371963i
$621$		0			0
$622$		−	46.1711i		−	1.85129i
$623$			18.6225i			0.746094i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	−35.7321			−1.42814
$627$		0			0
$628$		−	9.26180i		−	0.369586i
$629$	20.6803			0.824579
$630$		0			0
$631$	38.7214			1.54147			0.770737	−	0.637153i	$-0.219888\pi$
$631$	38.7214			1.54147			0.770737	+	0.637153i	$0.219888\pi$
$632$		−	11.4596i		−	0.455838i
$633$		0			0
$634$	48.1133			1.91082
$635$	−1.51745	+	6.10731i	−0.0602181	+	0.242361i
$636$		0			0
$637$			11.5525i			0.457728i
$638$		−	11.4186i		−	0.452065i
$639$		0			0
$640$	6.22180	−	25.0410i	0.245938	−	0.989834i
$641$	−24.2245			−0.956808			−0.478404	−	0.878140i	$-0.658785\pi$
$641$	−24.2245			−0.956808			−0.478404	+	0.878140i	$0.658785\pi$
$642$		0			0
$643$		−	25.8888i		−	1.02096i	−0.859891	−	0.510478i	$-0.829469\pi$
$643$		−	25.8888i		−	1.02096i	0.859891	−	0.510478i	$-0.170531\pi$
$644$	40.1978			1.58401
$645$		0			0
$646$	40.4124			1.59000
$647$		−	0.581449i		−	0.0228591i	−0.999935	−	0.0114296i	$-0.996362\pi$
$647$		−	0.581449i		−	0.0228591i	0.999935	−	0.0114296i	$-0.00363822\pi$
$648$		0			0
$649$	3.60197			0.141390
$650$	16.3896	+	8.68035i	0.642854	+	0.340471i
$651$		0			0
$652$		−	25.0928i		−	0.982708i
$653$		−	37.0082i		−	1.44824i	−0.689672	−	0.724122i	$-0.742245\pi$
$653$		−	37.0082i		−	1.44824i	0.689672	−	0.724122i	$-0.257755\pi$
$654$		0			0
$655$	18.8371	+	4.68035i	0.736026	+	0.182876i
$656$	19.9011			0.777008
$657$		0			0
$658$			22.0410i			0.859249i
$659$	30.5236			1.18903			0.594515	−	0.804084i	$-0.297344\pi$
$659$	30.5236			1.18903			0.594515	+	0.804084i	$0.297344\pi$
$660$		0			0
$661$	5.88428			0.228872			0.114436	−	0.993431i	$-0.463494\pi$
$661$	5.88428			0.228872			0.114436	+	0.993431i	$0.463494\pi$
$662$		−	13.7587i		−	0.534748i
$663$		0			0
$664$	12.1073			0.469855
$665$	−6.15676	+	24.7792i	−0.238749	+	0.960898i
$666$		0			0
$667$		−	21.0472i		−	0.814950i
$668$		−	20.4619i		−	0.791693i
$669$		0			0
$670$	−8.68035	−	2.15676i	−0.335351	−	0.0833227i
$671$	14.6803			0.566728
$672$		0			0
$673$		−	26.9711i		−	1.03966i	−0.854270	−	0.519829i	$-0.825996\pi$
$673$		−	26.9711i		−	1.03966i	0.854270	−	0.519829i	$-0.174004\pi$
$674$	6.91321			0.266287
$675$		0			0
$676$	−27.3051			−1.05020
$677$		−	17.9506i		−	0.689896i	−0.938622	−	0.344948i	$-0.887897\pi$
$677$		−	17.9506i		−	0.689896i	0.938622	−	0.344948i	$-0.112103\pi$
$678$		0			0
$679$	−63.0349			−2.41906
$680$	20.2062	+	5.02052i	0.774873	+	0.192528i
$681$		0			0
$682$			13.7587i			0.526849i
$683$		−	8.77924i		−	0.335928i	−0.985793	−	0.167964i	$-0.946281\pi$
$683$		−	8.77924i		−	0.335928i	0.985793	−	0.167964i	$-0.0537193\pi$
$684$		0			0
$685$	0.581449	−	2.34017i	0.0222160	−	0.0894134i
$686$	1.94214			0.0741513
$687$		0			0
$688$			6.50080i			0.247841i
$689$	−23.5174			−0.895943
$690$		0			0
$691$	−14.7214			−0.560028			−0.280014	−	0.959996i	$-0.590339\pi$
$691$	−14.7214			−0.560028			−0.280014	+	0.959996i	$0.590339\pi$
$692$			16.6576i			0.633225i
$693$		0			0
$694$	11.7093			0.444478
$695$	22.3135	+	5.54411i	0.846400	+	0.210300i
$696$		0			0
$697$			57.9253i			2.19408i
$698$			34.0144i			1.28746i
$699$		0			0
$700$	−23.5174	+	44.4040i	−0.888876	+	1.67831i
$701$	7.10504			0.268354			0.134177	−	0.990957i	$-0.457161\pi$
$701$	7.10504			0.268354			0.134177	+	0.990957i	$0.457161\pi$
$702$		0			0
$703$			10.5236i			0.396905i
$704$	−12.3112			−0.463997
$705$		0			0
$706$	−12.4969			−0.470328
$707$		−	70.2388i		−	2.64160i
$708$		0			0
$709$	34.1666			1.28315			0.641577	−	0.767059i	$-0.278281\pi$
$709$	34.1666			1.28315			0.641577	+	0.767059i	$0.278281\pi$
$710$	8.46573	−	34.0722i	0.317713	−	1.27871i
$711$		0			0
$712$			7.72753i			0.289601i
$713$			25.3607i			0.949765i
$714$		0			0
$715$	0.921622	−	3.70928i	0.0344667	−	0.138719i
$716$	16.6803			0.623374
$717$		0			0
$718$		−	22.8371i		−	0.852273i
$719$	31.8310			1.18709			0.593547	−	0.804799i	$-0.297727\pi$
$719$	31.8310			1.18709			0.593547	+	0.804799i	$0.297727\pi$
$720$		0			0
$721$	−43.7152			−1.62804
$722$		−	20.6670i		−	0.769147i
$723$		0			0
$724$	−39.5441			−1.46965
$725$	23.2495	+	12.3135i	0.863465	+	0.457312i
$726$		0			0
$727$		−	5.16290i		−	0.191481i	−0.995406	−	0.0957407i	$-0.969478\pi$
$727$		−	5.16290i		−	0.191481i	0.995406	−	0.0957407i	$-0.0305219\pi$
$728$			9.75872i			0.361682i
$729$		0			0
$730$	30.0905	+	7.47641i	1.11370	+	0.276714i
$731$	−18.9216			−0.699841
$732$		0			0
$733$		−	36.4475i		−	1.34622i	−0.739543	−	0.673109i	$-0.764958\pi$
$733$		−	36.4475i		−	1.34622i	0.739543	−	0.673109i	$-0.235042\pi$
$734$	19.3028			0.712481
$735$		0			0
$736$	−30.3545			−1.11888
$737$			1.84324i			0.0678968i
$738$		0			0
$739$	−25.4329			−0.935565			−0.467783	−	0.883844i	$-0.654947\pi$
$739$	−25.4329			−0.935565			−0.467783	+	0.883844i	$0.654947\pi$
$740$	−4.99386	+	20.0989i	−0.183578	+	0.738850i
$741$		0			0
$742$		−	110.750i		−	4.06577i
$743$		−	10.1217i		−	0.371329i	−0.982613	−	0.185664i	$-0.940556\pi$
$743$		−	10.1217i		−	0.371329i	0.982613	−	0.185664i	$-0.0594437\pi$
$744$		0			0
$745$	−24.7792	−	6.15676i	−0.907841	−	0.225566i
$746$	50.2784			1.84082
$747$		0			0
$748$		−	16.3896i		−	0.599264i
$749$	41.8576			1.52944
$750$		0			0
$751$	10.4703			0.382065			0.191033	−	0.981584i	$-0.438816\pi$
$751$	10.4703			0.382065			0.191033	+	0.981584i	$0.438816\pi$
$752$		−	5.69102i		−	0.207530i
$753$		0			0
$754$	19.5174			0.710784
$755$	10.6803	+	2.65368i	0.388698	+	0.0965774i
$756$		0			0
$757$			6.73820i			0.244904i	0.992474	+	0.122452i	$0.0390758\pi$
$757$			6.73820i			0.244904i	−0.992474	+	0.122452i	$0.960924\pi$
$758$			25.6742i			0.932529i
$759$		0			0
$760$	−2.55479	+	10.2823i	−0.0926719	+	0.372979i
$761$	5.57531			0.202105			0.101052	−	0.994881i	$-0.467779\pi$
$761$	5.57531			0.202105			0.101052	+	0.994881i	$0.467779\pi$
$762$		0			0
$763$		−	37.0928i		−	1.34285i
$764$	15.8310			0.572744
$765$		0			0
$766$	56.2967			2.03408
$767$			6.15676i			0.222308i
$768$		0			0
$769$	11.5297			0.415773			0.207886	−	0.978153i	$-0.433342\pi$
$769$	11.5297			0.415773			0.207886	+	0.978153i	$0.433342\pi$
$770$	17.4680	+	4.34017i	0.629503	+	0.156409i
$771$		0			0
$772$		−	5.48029i		−	0.197240i
$773$			28.7480i			1.03400i	0.855987	+	0.516998i	$0.172950\pi$
$773$			28.7480i			1.03400i	−0.855987	+	0.516998i	$0.827050\pi$
$774$		0			0
$775$	−28.0144	−	14.8371i	−1.00631	−	0.532964i
$776$	−26.1568			−0.938973
$777$		0			0
$778$			2.18342i			0.0782793i
$779$	−29.4764			−1.05610
$780$		0			0
$781$	−7.23513			−0.258893
$782$		−	52.5113i		−	1.87780i
$783$		0			0
$784$	14.0472			0.501685
$785$	1.84324	−	7.41855i	0.0657882	−	0.264779i
$786$		0			0
$787$			13.4536i			0.479570i	0.970826	+	0.239785i	$0.0770769\pi$
$787$			13.4536i			0.479570i	−0.970826	+	0.239785i	$0.922923\pi$
$788$		−	48.3195i		−	1.72131i
$789$		0			0
$790$	8.71154	−	35.0616i	0.309943	−	1.24743i
$791$	1.84324			0.0655382
$792$		0			0
$793$			25.0928i			0.891070i
$794$	75.3484			2.67401
$795$		0			0
$796$	69.5585			2.46544
$797$		−	48.3279i		−	1.71186i	−0.517090	−	0.855931i	$-0.672985\pi$
$797$		−	48.3279i		−	1.71186i	0.517090	−	0.855931i	$-0.327015\pi$
$798$		0			0
$799$	16.5646			0.586014
$800$	17.7587	−	33.5308i	0.627866	−	1.18549i
$801$		0			0
$802$			28.2557i			0.997742i
$803$		−	6.38962i		−	0.225485i
$804$		0			0
$805$	32.1978	+	8.00000i	1.13482	+	0.281963i
$806$	−23.5174			−0.828367
$807$		0			0
$808$		−	29.1461i		−	1.02536i
$809$	−43.8141			−1.54042			−0.770212	−	0.637789i	$-0.779849\pi$
$809$	−43.8141			−1.54042			−0.770212	+	0.637789i	$0.779849\pi$
$810$		0			0
$811$	−47.2762			−1.66009			−0.830045	−	0.557696i	$-0.811686\pi$
$811$	−47.2762			−1.66009			−0.830045	+	0.557696i	$0.811686\pi$
$812$			52.8781i			1.85566i
$813$		0			0
$814$	7.41855			0.260020
$815$	4.99386	−	20.0989i	0.174927	−	0.704034i
$816$		0			0
$817$		−	9.62863i		−	0.336863i
$818$			64.0554i			2.23965i
$819$		0			0
$820$	−56.2967	−	13.9877i	−1.96597	−	0.488472i
$821$	3.30283			0.115270			0.0576348	−	0.998338i	$-0.481644\pi$
$821$	3.30283			0.115270			0.0576348	+	0.998338i	$0.481644\pi$
$822$		0			0
$823$			11.0517i			0.385239i	0.981274	+	0.192619i	$0.0616982\pi$
$823$			11.0517i			0.385239i	−0.981274	+	0.192619i	$0.938302\pi$
$824$	−18.1399			−0.631935
$825$		0			0
$826$	−28.9939			−1.00883
$827$			5.12783i			0.178312i	0.996018	+	0.0891560i	$0.0284170\pi$
$827$			5.12783i			0.178312i	−0.996018	+	0.0891560i	$0.971583\pi$
$828$		0			0
$829$	6.39803			0.222213			0.111106	−	0.993809i	$-0.464561\pi$
$829$	6.39803			0.222213			0.111106	+	0.993809i	$0.464561\pi$
$830$	37.0433	+	9.20394i	1.28579	+	0.319473i
$831$		0			0
$832$		−	21.0433i		−	0.729545i
$833$			40.8865i			1.41663i
$834$		0			0
$835$	4.07223	−	16.3896i	0.140925	−	0.567186i
$836$	8.34017			0.288451
$837$		0			0
$838$		−	13.3607i		−	0.461537i
$839$	−22.0722			−0.762018			−0.381009	−	0.924571i	$-0.624423\pi$
$839$	−22.0722			−0.762018			−0.381009	+	0.924571i	$0.624423\pi$
$840$		0			0
$841$	−1.31351			−0.0452935
$842$			21.6332i			0.745528i
$843$		0			0
$844$	−22.8638			−0.787003
$845$	−21.8710	−	5.43415i	−0.752384	−	0.186940i
$846$		0			0
$847$		−	3.70928i		−	0.127452i
$848$			28.5958i			0.981985i
$849$		0			0
$850$	58.0060	+	30.7214i	1.98959	+	1.05373i
$851$	13.6742			0.468746
$852$		0			0
$853$		−	8.76099i		−	0.299971i	−0.988688	−	0.149985i	$-0.952077\pi$
$853$		−	8.76099i		−	0.299971i	0.988688	−	0.149985i	$-0.0479226\pi$
$854$	−118.169			−4.04365
$855$		0			0
$856$	17.3691			0.593664
$857$		−	36.5730i		−	1.24931i	−0.780900	−	0.624656i	$-0.785239\pi$
$857$		−	36.5730i		−	1.24931i	0.780900	−	0.624656i	$-0.214761\pi$
$858$		0			0
$859$	49.6886			1.69535			0.847676	−	0.530514i	$-0.178001\pi$
$859$	49.6886			1.69535			0.847676	+	0.530514i	$0.178001\pi$
$860$	4.56916	−	18.3896i	0.155807	−	0.627081i
$861$		0			0
$862$		−	18.8371i		−	0.641594i
$863$			34.1399i			1.16214i	0.813855	+	0.581068i	$0.197365\pi$
$863$			34.1399i			1.16214i	−0.813855	+	0.581068i	$0.802635\pi$
$864$		0			0
$865$	−3.31512	+	13.3424i	−0.112717	+	0.453657i
$866$	34.7214			1.17988
$867$		0			0
$868$		−	63.7152i		−	2.16264i
$869$	−7.44521			−0.252562
$870$		0			0
$871$	−3.15061			−0.106754
$872$		−	15.3919i		−	0.521235i
$873$		0			0
$874$	26.7214			0.903864
$875$	−27.6742	+	30.8865i	−0.935559	+	1.04416i
$876$		0			0
$877$			43.5357i			1.47010i	0.678015	+	0.735048i	$0.262840\pi$
$877$			43.5357i			1.47010i	−0.678015	+	0.735048i	$0.737160\pi$
$878$		−	6.68035i		−	0.225451i
$879$		0			0
$880$	−4.51026	−	1.12064i	−0.152041	−	0.0377767i
$881$	8.52359			0.287167			0.143584	−	0.989638i	$-0.454137\pi$
$881$	8.52359			0.287167			0.143584	+	0.989638i	$0.454137\pi$
$882$		0			0
$883$			43.0349i			1.44824i	0.689674	+	0.724120i	$0.257754\pi$
$883$			43.0349i			1.44824i	−0.689674	+	0.724120i	$0.742246\pi$
$884$	28.0144			0.942225
$885$		0			0
$886$	63.5006			2.13335
$887$			17.0289i			0.571775i	0.958263	+	0.285888i	$0.0922884\pi$
$887$			17.0289i			0.571775i	−0.958263	+	0.285888i	$0.907712\pi$
$888$		0			0
$889$	−10.4391			−0.350115
$890$	−5.87444	+	23.6430i	−0.196912	+	0.792515i
$891$		0			0
$892$		−	34.0866i		−	1.14130i
$893$			8.42923i			0.282073i
$894$		0			0
$895$	13.3607	+	3.31965i	0.446599	+	0.110964i
$896$	42.8020			1.42992
$897$		0			0
$898$			23.2085i			0.774477i
$899$	−33.3607			−1.11264
$900$		0			0
$901$	−83.2327			−2.77288
$902$			20.7792i			0.691873i
$903$		0			0
$904$	0.764867			0.0254391
$905$	−31.6742	−	7.86991i	−1.05289	−	0.261605i
$906$		0			0
$907$		−	6.13993i		−	0.203873i	−0.994791	−	0.101937i	$-0.967496\pi$
$907$		−	6.13993i		−	0.203873i	0.994791	−	0.101937i	$-0.0325039\pi$
$908$		−	11.4680i		−	0.380579i
$909$		0			0
$910$	−7.41855	+	29.8576i	−0.245923	+	0.989770i
$911$	−53.8720			−1.78486			−0.892429	−	0.451187i	$-0.851001\pi$
$911$	−53.8720			−1.78486			−0.892429	+	0.451187i	$0.851001\pi$
$912$		0			0
$913$		−	7.86603i		−	0.260328i
$914$	49.5981			1.64056
$915$		0			0
$916$	−70.9770			−2.34515
$917$			32.1978i			1.06326i
$918$		0			0
$919$	48.2700			1.59228			0.796141	−	0.605112i	$-0.206872\pi$
$919$	48.2700			1.59228			0.796141	+	0.605112i	$0.206872\pi$
$920$	13.3607	+	3.31965i	0.440489	+	0.109446i
$921$		0			0
$922$			47.2495i			1.55608i
$923$		−	12.3668i		−	0.407059i
$924$		0			0
$925$	−8.00000	+	15.1050i	−0.263038	+	0.496651i
$926$	−54.0242			−1.77535
$927$		0			0
$928$		−	39.9299i		−	1.31076i
$929$	4.10343			0.134629			0.0673146	−	0.997732i	$-0.478557\pi$
$929$	4.10343			0.134629			0.0673146	+	0.997732i	$0.478557\pi$
$930$		0			0
$931$	−20.8059			−0.681886
$932$		−	50.4762i		−	1.65340i
$933$		0			0
$934$	41.6742			1.36362
$935$	3.26180	−	13.1278i	0.106672	−	0.429326i
$936$		0			0
$937$			38.5341i			1.25885i	0.777060	+	0.629427i	$0.216710\pi$
$937$			38.5341i			1.25885i	−0.777060	+	0.629427i	$0.783290\pi$
$938$		−	14.8371i		−	0.484449i
$939$		0			0
$940$	−4.00000	+	16.0989i	−0.130466	+	0.525088i
$941$	−14.6849			−0.478713			−0.239357	−	0.970932i	$-0.576937\pi$
$941$	−14.6849			−0.478713			−0.239357	+	0.970932i	$0.576937\pi$
$942$		0			0
$943$			38.3012i			1.24726i
$944$	7.48625			0.243657
$945$		0			0
$946$	−6.78765			−0.220686
$947$			6.05786i			0.196854i	0.995144	+	0.0984270i	$0.0313811\pi$
$947$			6.05786i			0.196854i	−0.995144	+	0.0984270i	$0.968619\pi$
$948$		0			0
$949$	10.9216			0.354531
$950$	−15.6332	+	29.5174i	−0.507207	+	0.957672i
$951$		0			0
$952$			34.5380i			1.11938i
$953$		−	40.1438i		−	1.30039i	−0.759769	−	0.650193i	$-0.774688\pi$
$953$		−	40.1438i		−	1.30039i	0.759769	−	0.650193i	$-0.225312\pi$
$954$		0			0
$955$	12.6803	+	3.15061i	0.410326	+	0.101951i
$956$	−60.5646			−1.95880
$957$		0			0
$958$			20.5646i			0.664413i
$959$	4.00000			0.129167
$960$		0			0
$961$	9.19779			0.296703
$962$			12.6803i			0.408831i
$963$		0			0
$964$	−24.9360			−0.803134
$965$	1.09066	−	4.38962i	0.0351097	−	0.141307i
$966$		0			0
$967$			50.6285i			1.62810i	0.580794	+	0.814051i	$0.302742\pi$
$967$			50.6285i			1.62810i	−0.580794	+	0.814051i	$0.697258\pi$
$968$		−	1.53919i		−	0.0494714i
$969$		0			0
$970$	−80.0288	−	19.8843i	−2.56957	−	0.638446i
$971$	6.69263			0.214777			0.107388	−	0.994217i	$-0.465751\pi$
$971$	6.69263			0.214777			0.107388	+	0.994217i	$0.465751\pi$
$972$		0			0
$973$			38.1399i			1.22271i
$974$	76.3956			2.44787
$975$		0			0
$976$	30.5113			0.976643
$977$			38.5835i			1.23440i	0.786808	+	0.617198i	$0.211732\pi$
$977$			38.5835i			1.23440i	−0.786808	+	0.617198i	$0.788268\pi$
$978$		0			0
$979$	5.02052			0.160456
$980$	−39.7370	−	9.87322i	−1.26935	−	0.315388i
$981$		0			0
$982$			17.3607i			0.554002i
$983$			28.4657i			0.907916i	0.891023	+	0.453958i	$0.149988\pi$
$983$			28.4657i			0.907916i	−0.891023	+	0.453958i	$0.850012\pi$
$984$		0			0
$985$	9.61634	−	38.7031i	0.306402	−	1.23318i
$986$	69.0759			2.19983
$987$		0			0
$988$			14.2557i			0.453533i
$989$	−12.5113			−0.397836
$990$		0			0
$991$	2.65368			0.0842970			0.0421485	−	0.999111i	$-0.486580\pi$
$991$	2.65368			0.0842970			0.0421485	+	0.999111i	$0.486580\pi$
$992$			48.1133i			1.52760i
$993$		0			0
$994$	58.2388			1.84722
$995$	55.7152	+	13.8432i	1.76629	+	0.438860i
$996$		0			0
$997$			8.08065i			0.255917i	0.991780	+	0.127958i	$0.0408424\pi$
$997$			8.08065i			0.255917i	−0.991780	+	0.127958i	$0.959158\pi$
$998$		−	56.7624i		−	1.79678i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.c.e.199.6		6
3.2	odd	2		165.2.c.b.34.1	✓	6
5.2	odd	4		2475.2.a.ba.1.1		3
5.3	odd	4		2475.2.a.bc.1.3		3
5.4	even	2	inner	495.2.c.e.199.1		6
12.11	even	2		2640.2.d.h.529.3		6
15.2	even	4		825.2.a.l.1.3		3
15.8	even	4		825.2.a.j.1.1		3
15.14	odd	2		165.2.c.b.34.6	yes	6
33.32	even	2		1815.2.c.e.364.6		6
60.59	even	2		2640.2.d.h.529.6		6
165.32	odd	4		9075.2.a.cg.1.1		3
165.98	odd	4		9075.2.a.ch.1.3		3
165.164	even	2		1815.2.c.e.364.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.c.b.34.1	✓	6	3.2	odd	2
165.2.c.b.34.6	yes	6	15.14	odd	2
495.2.c.e.199.1		6	5.4	even	2	inner
495.2.c.e.199.6		6	1.1	even	1	trivial
825.2.a.j.1.1		3	15.8	even	4
825.2.a.l.1.3		3	15.2	even	4
1815.2.c.e.364.1		6	165.164	even	2
1815.2.c.e.364.6		6	33.32	even	2
2475.2.a.ba.1.1		3	5.2	odd	4
2475.2.a.bc.1.3		3	5.3	odd	4
2640.2.d.h.529.3		6	12.11	even	2
2640.2.d.h.529.6		6	60.59	even	2
9075.2.a.cg.1.1		3	165.32	odd	4
9075.2.a.ch.1.3		3	165.98	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.17009i q^{2} -2.70928 q^{4} +(-2.17009 - 0.539189i) q^{5} -3.70928i q^{7} -1.53919i q^{8} +O(q^{10})\)	\(q+2.17009i q^{2} -2.70928 q^{4} +(-2.17009 - 0.539189i) q^{5} -3.70928i q^{7} -1.53919i q^{8} +(1.17009 - 4.70928i) q^{10} -1.00000 q^{11} -1.70928i q^{13} +8.04945 q^{14} -2.07838 q^{16} -6.04945i q^{17} +3.07838 q^{19} +(5.87936 + 1.46081i) q^{20} -2.17009i q^{22} -4.00000i q^{23} +(4.41855 + 2.34017i) q^{25} +3.70928 q^{26} +10.0494i q^{28} +5.26180 q^{29} -6.34017 q^{31} -7.58864i q^{32} +13.1278 q^{34} +(-2.00000 + 8.04945i) q^{35} +3.41855i q^{37} +6.68035i q^{38} +(-0.829914 + 3.34017i) q^{40} -9.57531 q^{41} -3.12783i q^{43} +2.70928 q^{44} +8.68035 q^{46} +2.73820i q^{47} -6.75872 q^{49} +(-5.07838 + 9.58864i) q^{50} +4.63090i q^{52} -13.7587i q^{53} +(2.17009 + 0.539189i) q^{55} -5.70928 q^{56} +11.4186i q^{58} -3.60197 q^{59} -14.6803 q^{61} -13.7587i q^{62} +12.3112 q^{64} +(-0.921622 + 3.70928i) q^{65} -1.84324i q^{67} +16.3896i q^{68} +(-17.4680 - 4.34017i) q^{70} +7.23513 q^{71} +6.38962i q^{73} -7.41855 q^{74} -8.34017 q^{76} +3.70928i q^{77} +7.44521 q^{79} +(4.51026 + 1.12064i) q^{80} -20.7792i q^{82} +7.86603i q^{83} +(-3.26180 + 13.1278i) q^{85} +6.78765 q^{86} +1.53919i q^{88} -5.02052 q^{89} -6.34017 q^{91} +10.8371i q^{92} -5.94214 q^{94} +(-6.68035 - 1.65983i) q^{95} -16.9939i q^{97} -14.6670i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} - 2 q^{5}+O(q^{10}) \) 6 * q - 2 * q^4 - 2 * q^5	\( 6 q - 2 q^{4} - 2 q^{5} - 4 q^{10} - 6 q^{11} + 12 q^{14} - 6 q^{16} + 12 q^{19} + 10 q^{20} - 2 q^{25} + 8 q^{26} + 16 q^{29} - 16 q^{31} + 36 q^{34} - 12 q^{35} - 16 q^{40} - 16 q^{41} + 2 q^{44} + 8 q^{46} + 10 q^{49} - 24 q^{50} + 2 q^{55} - 20 q^{56} + 16 q^{59} - 44 q^{61} + 22 q^{64} - 12 q^{65} - 40 q^{70} + 24 q^{71} - 16 q^{74} - 28 q^{76} + 20 q^{79} - 6 q^{80} - 4 q^{85} + 20 q^{86} + 36 q^{89} - 16 q^{91} + 24 q^{94} + 4 q^{95}+O(q^{100}) \) 6 * q - 2 * q^4 - 2 * q^5 - 4 * q^10 - 6 * q^11 + 12 * q^14 - 6 * q^16 + 12 * q^19 + 10 * q^20 - 2 * q^25 + 8 * q^26 + 16 * q^29 - 16 * q^31 + 36 * q^34 - 12 * q^35 - 16 * q^40 - 16 * q^41 + 2 * q^44 + 8 * q^46 + 10 * q^49 - 24 * q^50 + 2 * q^55 - 20 * q^56 + 16 * q^59 - 44 * q^61 + 22 * q^64 - 12 * q^65 - 40 * q^70 + 24 * q^71 - 16 * q^74 - 28 * q^76 + 20 * q^79 - 6 * q^80 - 4 * q^85 + 20 * q^86 + 36 * q^89 - 16 * q^91 + 24 * q^94 + 4 * q^95

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