LMFDB - Embedded newform 855.2.c.g.514.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(514,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.514"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-22,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 25x^{12} + 242x^{10} + 1134x^{8} + 2605x^{6} + 2545x^{4} + 552x^{2} + 16 $ x^14 + 25x^12 + 242x^10 + 1134x^8 + 2605x^6 + 2545x^4 + 552x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			514.8
Root			$0.184902i$ of defining polynomial
Character	$\chi$	$=$	855.514
Dual form			855.2.c.g.514.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.184902i q^{2} +1.96581 q^{4} +(-1.94200 + 1.10844i) q^{5} -1.90997i q^{7} +0.733287i q^{8} +(-0.204953 - 0.359080i) q^{10} +3.94075 q^{11} +4.53675i q^{13} +0.353158 q^{14} +3.79604 q^{16} -4.68488i q^{17} -1.00000 q^{19} +(-3.81761 + 2.17898i) q^{20} +0.728653i q^{22} +6.18360i q^{23} +(2.54273 - 4.30517i) q^{25} -0.838856 q^{26} -3.75465i q^{28} +5.98837 q^{29} +7.31166 q^{31} +2.16847i q^{32} +0.866244 q^{34} +(2.11709 + 3.70917i) q^{35} +8.07490i q^{37} -0.184902i q^{38} +(-0.812803 - 1.42404i) q^{40} -0.0567471 q^{41} +0.822008i q^{43} +7.74677 q^{44} -1.14336 q^{46} -7.50487i q^{47} +3.35200 q^{49} +(0.796036 + 0.470156i) q^{50} +8.91840i q^{52} -1.28799i q^{53} +(-7.65293 + 4.36808i) q^{55} +1.40056 q^{56} +1.10726i q^{58} -8.28180 q^{59} -11.3330 q^{61} +1.35194i q^{62} +7.19112 q^{64} +(-5.02871 - 8.81038i) q^{65} +10.3415i q^{67} -9.20959i q^{68} +(-0.685833 + 0.391454i) q^{70} +10.3415 q^{71} -10.0984i q^{73} -1.49307 q^{74} -1.96581 q^{76} -7.52672i q^{77} -4.12580 q^{79} +(-7.37190 + 4.20767i) q^{80} -0.0104927i q^{82} +11.6295i q^{83} +(5.19290 + 9.09804i) q^{85} -0.151991 q^{86} +2.88970i q^{88} +7.17054 q^{89} +8.66508 q^{91} +12.1558i q^{92} +1.38767 q^{94} +(1.94200 - 1.10844i) q^{95} -2.70038i q^{97} +0.619793i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 22 q^{4} - 2 q^{5} + 2 q^{10} + 8 q^{11} - 8 q^{14} + 38 q^{16} - 14 q^{19} - 12 q^{20} - 4 q^{25} + 40 q^{26} - 12 q^{29} + 8 q^{31} - 4 q^{34} + 14 q^{35} + 18 q^{40} - 4 q^{41} - 64 q^{44} - 8 q^{46}+ \cdots + 2 q^{95}+O(q^{100}) $ 14 * q - 22 * q^4 - 2 * q^5 + 2 * q^10 + 8 * q^11 - 8 * q^14 + 38 * q^16 - 14 * q^19 - 12 * q^20 - 4 * q^25 + 40 * q^26 - 12 * q^29 + 8 * q^31 - 4 * q^34 + 14 * q^35 + 18 * q^40 - 4 * q^41 - 64 * q^44 - 8 * q^46 - 34 * q^49 - 4 * q^50 - 2 * q^55 + 44 * q^56 - 36 * q^59 + 24 * q^61 - 22 * q^64 + 12 * q^65 - 60 * q^70 + 36 * q^71 + 12 * q^74 + 22 * q^76 + 8 * q^79 - 36 * q^80 - 18 * q^85 + 92 * q^86 - 16 * q^89 + 24 * q^91 + 40 * q^94 + 2 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			0.184902i			0.130746i	0.997861	+	0.0653728i	$0.0208237\pi$
$2$			0.184902i			0.130746i	−0.997861	+	0.0653728i	$0.979176\pi$
$3$		0			0
$3$		0			0
$4$	1.96581			0.982906
$5$	−1.94200	+	1.10844i	−0.868489	+	0.495709i
$5$	−1.94200	+	1.10844i	−0.868489	+	0.495709i
$6$		0			0
$7$		−	1.90997i		−	0.721902i	−0.932585	−	0.360951i	$-0.882452\pi$
$7$		−	1.90997i		−	0.721902i	0.932585	−	0.360951i	$-0.117548\pi$
$8$			0.733287i			0.259256i
$9$		0			0
$10$	−0.204953	−	0.359080i	−0.0648117	−	0.113551i
$11$	3.94075			1.18818			0.594090	−	0.804399i	$-0.297512\pi$
$11$	3.94075			1.18818			0.594090	+	0.804399i	$0.297512\pi$
$12$		0			0
$13$			4.53675i			1.25827i	0.777296	+	0.629135i	$0.216591\pi$
$13$			4.53675i			1.25827i	−0.777296	+	0.629135i	$0.783409\pi$
$14$	0.353158			0.0943855
$15$		0			0
$16$	3.79604			0.949009
$17$		−	4.68488i		−	1.13625i	−0.822942	−	0.568125i	$-0.807669\pi$
$17$		−	4.68488i		−	1.13625i	0.822942	−	0.568125i	$-0.192331\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−3.81761	+	2.17898i	−0.853643	+	0.487235i
$21$		0			0
$22$			0.728653i			0.155349i
$23$			6.18360i			1.28937i	0.764449	+	0.644684i	$0.223011\pi$
$23$			6.18360i			1.28937i	−0.764449	+	0.644684i	$0.776989\pi$
$24$		0			0
$25$	2.54273	−	4.30517i	0.508546	−	0.861035i
$26$	−0.838856			−0.164513
$27$		0			0
$28$		−	3.75465i		−	0.709561i
$29$	5.98837			1.11201			0.556006	−	0.831178i	$-0.312333\pi$
$29$	5.98837			1.11201			0.556006	+	0.831178i	$0.312333\pi$
$30$		0			0
$31$	7.31166			1.31321			0.656607	−	0.754233i	$-0.271991\pi$
$31$	7.31166			1.31321			0.656607	+	0.754233i	$0.271991\pi$
$32$			2.16847i			0.383335i
$33$		0			0
$34$	0.866244			0.148560
$35$	2.11709	+	3.70917i	0.357853	+	0.626964i
$36$		0			0
$37$			8.07490i			1.32751i	0.747952	+	0.663753i	$0.231037\pi$
$37$			8.07490i			1.32751i	−0.747952	+	0.663753i	$0.768963\pi$
$38$		−	0.184902i		−	0.0299951i
$39$		0			0
$40$	−0.812803	−	1.42404i	−0.128515	−	0.225161i
$41$	−0.0567471			−0.00886241			−0.00443121	−	0.999990i	$-0.501411\pi$
$41$	−0.0567471			−0.00886241			−0.00443121	+	0.999990i	$0.501411\pi$
$42$		0			0
$43$			0.822008i			0.125355i	0.998034	+	0.0626776i	$0.0199640\pi$
$43$			0.822008i			0.125355i	−0.998034	+	0.0626776i	$0.980036\pi$
$44$	7.74677			1.16787
$45$		0			0
$46$	−1.14336			−0.168579
$47$		−	7.50487i		−	1.09470i	−0.836905	−	0.547349i	$-0.815637\pi$
$47$		−	7.50487i		−	1.09470i	0.836905	−	0.547349i	$-0.184363\pi$
$48$		0			0
$49$	3.35200			0.478858
$50$	0.796036	+	0.470156i	0.112576	+	0.0664901i
$51$		0			0
$52$			8.91840i			1.23676i
$53$		−	1.28799i		−	0.176920i	−0.996080	−	0.0884598i	$-0.971806\pi$
$53$		−	1.28799i		−	0.176920i	0.996080	−	0.0884598i	$-0.0281945\pi$
$54$		0			0
$55$	−7.65293	+	4.36808i	−1.03192	+	0.588991i
$56$	1.40056			0.187157
$57$		0			0
$58$			1.10726i			0.145391i
$59$	−8.28180			−1.07820			−0.539099	−	0.842242i	$-0.681235\pi$
$59$	−8.28180			−1.07820			−0.539099	+	0.842242i	$0.681235\pi$
$60$		0			0
$61$	−11.3330			−1.45104			−0.725521	−	0.688200i	$-0.758401\pi$
$61$	−11.3330			−1.45104			−0.725521	+	0.688200i	$0.758401\pi$
$62$			1.35194i			0.171697i
$63$		0			0
$64$	7.19112			0.898890
$65$	−5.02871	−	8.81038i	−0.623735	−	1.09279i
$66$		0			0
$67$			10.3415i			1.26342i	0.775205	+	0.631709i	$0.217646\pi$
$67$			10.3415i			1.26342i	−0.775205	+	0.631709i	$0.782354\pi$
$68$		−	9.20959i		−	1.11683i
$69$		0			0
$70$	−0.685833	+	0.391454i	−0.0819727	+	0.0467877i
$71$	10.3415			1.22731			0.613657	−	0.789573i	$-0.289698\pi$
$71$	10.3415			1.22731			0.613657	+	0.789573i	$0.289698\pi$
$72$		0			0
$73$		−	10.0984i		−	1.18192i	−0.806699	−	0.590962i	$-0.798748\pi$
$73$		−	10.0984i		−	1.18192i	0.806699	−	0.590962i	$-0.201252\pi$
$74$	−1.49307			−0.173566
$75$		0			0
$76$	−1.96581			−0.225494
$77$		−	7.52672i		−	0.857749i
$78$		0			0
$79$	−4.12580			−0.464189			−0.232094	−	0.972693i	$-0.574558\pi$
$79$	−4.12580			−0.464189			−0.232094	+	0.972693i	$0.574558\pi$
$80$	−7.37190	+	4.20767i	−0.824204	+	0.470432i
$81$		0			0
$82$		−	0.0104927i		−	0.00115872i
$83$			11.6295i			1.27651i	0.769827	+	0.638253i	$0.220343\pi$
$83$			11.6295i			1.27651i	−0.769827	+	0.638253i	$0.779657\pi$
$84$		0			0
$85$	5.19290	+	9.09804i	0.563249	+	0.986821i
$86$	−0.151991			−0.0163896
$87$		0			0
$88$			2.88970i			0.308043i
$89$	7.17054			0.760075			0.380038	−	0.924971i	$-0.375911\pi$
$89$	7.17054			0.760075			0.380038	+	0.924971i	$0.375911\pi$
$90$		0			0
$91$	8.66508			0.908347
$92$			12.1558i			1.26733i
$93$		0			0
$94$	1.38767			0.143127
$95$	1.94200	−	1.10844i	0.199245	−	0.113723i
$96$		0			0
$97$		−	2.70038i		−	0.274182i	−0.990558	−	0.137091i	$-0.956225\pi$
$97$		−	2.70038i		−	0.274182i	0.990558	−	0.137091i	$-0.0437752\pi$
$98$			0.619793i			0.0626085i
$99$		0			0
$100$	4.99853	−	8.46316i	0.499853	−	0.846316i
$101$	−2.17791			−0.216710			−0.108355	−	0.994112i	$-0.534558\pi$
$101$	−2.17791			−0.216710			−0.108355	+	0.994112i	$0.534558\pi$
$102$		0			0
$103$		−	10.2701i		−	1.01195i	−0.862549	−	0.505973i	$-0.831134\pi$
$103$		−	10.2701i		−	1.01195i	0.862549	−	0.505973i	$-0.168866\pi$
$104$	−3.32674			−0.326214
$105$		0			0
$106$	0.238153			0.0231314
$107$		−	7.81995i		−	0.755983i	−0.925809	−	0.377991i	$-0.876615\pi$
$107$		−	7.81995i		−	0.755983i	0.925809	−	0.377991i	$-0.123385\pi$
$108$		0			0
$109$	−7.93162			−0.759712			−0.379856	−	0.925046i	$-0.624026\pi$
$109$	−7.93162			−0.759712			−0.379856	+	0.925046i	$0.624026\pi$
$110$	−0.807667	−	1.41504i	−0.0770080	−	0.134919i
$111$		0			0
$112$		−	7.25033i		−	0.685091i
$113$		−	9.54169i		−	0.897607i	−0.893631	−	0.448803i	$-0.851850\pi$
$113$		−	9.54169i		−	0.897607i	0.893631	−	0.448803i	$-0.148150\pi$
$114$		0			0
$115$	−6.85413	−	12.0085i	−0.639151	−	1.11980i
$116$	11.7720			1.09300
$117$		0			0
$118$		−	1.53132i		−	0.140970i
$119$	−8.94799			−0.820261
$120$		0			0
$121$	4.52949			0.411772
$122$		−	2.09550i		−	0.189717i
$123$		0			0
$124$	14.3733			1.29076
$125$	−0.165961	+	11.1791i	−0.0148440	+	0.999890i
$126$		0			0
$127$			7.84804i			0.696401i	0.937420	+	0.348201i	$0.113207\pi$
$127$			7.84804i			0.696401i	−0.937420	+	0.348201i	$0.886793\pi$
$128$			5.66659i			0.500861i
$129$		0			0
$130$	1.62906	−	0.929820i	0.142878	−	0.0815506i
$131$	−1.36722			−0.119455			−0.0597273	−	0.998215i	$-0.519023\pi$
$131$	−1.36722			−0.119455			−0.0597273	+	0.998215i	$0.519023\pi$
$132$		0			0
$133$			1.90997i			0.165616i
$134$	−1.91217			−0.165186
$135$		0			0
$136$	3.43536			0.294580
$137$		−	12.0300i		−	1.02779i	−0.857853	−	0.513896i	$-0.828202\pi$
$137$		−	12.0300i		−	1.02779i	0.857853	−	0.513896i	$-0.171798\pi$
$138$		0			0
$139$	−12.6898			−1.07634			−0.538169	−	0.842837i	$-0.680884\pi$
$139$	−12.6898			−1.07634			−0.538169	+	0.842837i	$0.680884\pi$
$140$	4.16179	+	7.29152i	0.351736	+	0.616246i
$141$		0			0
$142$			1.91217i			0.160466i
$143$			17.8782i			1.49505i
$144$		0			0
$145$	−11.6294	+	6.63774i	−0.965770	+	0.551234i
$146$	1.86721			0.154531
$147$		0			0
$148$			15.8737i			1.30481i
$149$	−21.0429			−1.72390			−0.861951	−	0.506992i	$-0.830758\pi$
$149$	−21.0429			−1.72390			−0.861951	+	0.506992i	$0.830758\pi$
$150$		0			0
$151$	−3.32628			−0.270689			−0.135344	−	0.990799i	$-0.543214\pi$
$151$	−3.32628			−0.270689			−0.135344	+	0.990799i	$0.543214\pi$
$152$		−	0.733287i		−	0.0594774i
$153$		0			0
$154$	1.39171			0.112147
$155$	−14.1992	+	8.10453i	−1.14051	+	0.650971i
$156$		0			0
$157$		−	16.3037i		−	1.30118i	−0.759430	−	0.650589i	$-0.774522\pi$
$157$		−	16.3037i		−	1.30118i	0.759430	−	0.650589i	$-0.225478\pi$
$158$		−	0.762870i		−	0.0606906i
$159$		0			0
$160$	−2.40361	−	4.21117i	−0.190022	−	0.332922i
$161$	11.8105			0.930798
$162$		0			0
$163$		−	10.3731i		−	0.812486i	−0.913765	−	0.406243i	$-0.866839\pi$
$163$		−	10.3731i		−	0.812486i	0.913765	−	0.406243i	$-0.133161\pi$
$164$	−0.111554			−0.00871092
$165$		0			0
$166$	−2.15032			−0.166897
$167$			24.4309i			1.89052i	0.326315	+	0.945261i	$0.394193\pi$
$167$			24.4309i			1.89052i	−0.326315	+	0.945261i	$0.605807\pi$
$168$		0			0
$169$	−7.58214			−0.583242
$170$	−1.68225	+	0.960178i	−0.129022	+	0.0736423i
$171$		0			0
$172$			1.61591i			0.123212i
$173$		−	21.4851i		−	1.63348i	−0.577002	−	0.816742i	$-0.695778\pi$
$173$		−	21.4851i		−	1.63348i	0.577002	−	0.816742i	$-0.304222\pi$
$174$		0			0
$175$	−8.22277	−	4.85654i	−0.621583	−	0.367120i
$176$	14.9592			1.12759
$177$		0			0
$178$			1.32585i			0.0993765i
$179$	−14.7939			−1.10575			−0.552875	−	0.833264i	$-0.686469\pi$
$179$	−14.7939			−1.10575			−0.552875	+	0.833264i	$0.686469\pi$
$180$		0			0
$181$	17.8632			1.32776			0.663882	−	0.747837i	$-0.268908\pi$
$181$	17.8632			1.32776			0.663882	+	0.747837i	$0.268908\pi$
$182$			1.60219i			0.118762i
$183$		0			0
$184$	−4.53435			−0.334277
$185$	−8.95053	−	15.6815i	−0.658056	−	1.15292i
$186$		0			0
$187$		−	18.4619i		−	1.35007i
$188$		−	14.7532i		−	1.07598i
$189$		0			0
$190$	0.204953	+	0.359080i	0.0148688	+	0.0260504i
$191$	−12.8206			−0.927663			−0.463832	−	0.885923i	$-0.653526\pi$
$191$	−12.8206			−0.927663			−0.463832	+	0.885923i	$0.653526\pi$
$192$		0			0
$193$		−	15.8737i		−	1.14262i	−0.820736	−	0.571308i	$-0.806436\pi$
$193$		−	15.8737i		−	1.14262i	0.820736	−	0.571308i	$-0.193564\pi$
$194$	0.499305			0.0358480
$195$		0			0
$196$	6.58941			0.470672
$197$			13.8571i			0.987277i	0.869667	+	0.493638i	$0.164333\pi$
$197$			13.8571i			0.987277i	−0.869667	+	0.493638i	$0.835667\pi$
$198$		0			0
$199$	−26.5763			−1.88394			−0.941972	−	0.335693i	$-0.891030\pi$
$199$	−26.5763			−1.88394			−0.941972	+	0.335693i	$0.891030\pi$
$200$	3.15693	+	1.86455i	0.223229	+	0.131844i
$201$		0			0
$202$		−	0.402700i		−	0.0283338i
$203$		−	11.4376i		−	0.802764i
$204$		0			0
$205$	0.110203	−	0.0629007i	0.00769691	−	0.00439318i
$206$	1.89897			0.132307
$207$		0			0
$208$			17.2217i			1.19411i
$209$	−3.94075			−0.272587
$210$		0			0
$211$	−12.3339			−0.849101			−0.424550	−	0.905404i	$-0.639568\pi$
$211$	−12.3339			−0.849101			−0.424550	+	0.905404i	$0.639568\pi$
$212$		−	2.53195i		−	0.173895i
$213$		0			0
$214$	1.44592			0.0988414
$215$	−0.911146	−	1.59634i	−0.0621396	−	0.108870i
$216$		0			0
$217$		−	13.9651i		−	0.948011i
$218$		−	1.46657i		−	0.0993289i
$219$		0			0
$220$	−15.0442	+	8.58681i	−1.01428	+	0.578923i
$221$	21.2541			1.42971
$222$		0			0
$223$		−	25.8035i		−	1.72793i	−0.503551	−	0.863966i	$-0.667973\pi$
$223$		−	25.8035i		−	1.72793i	0.503551	−	0.863966i	$-0.332027\pi$
$224$	4.14172			0.276730
$225$		0			0
$226$	1.76428			0.117358
$227$		−	14.1348i		−	0.938163i	−0.883155	−	0.469081i	$-0.844585\pi$
$227$		−	14.1348i		−	0.938163i	0.883155	−	0.469081i	$-0.155415\pi$
$228$		0			0
$229$	−14.7671			−0.975838			−0.487919	−	0.872889i	$-0.662244\pi$
$229$	−14.7671			−0.975838			−0.487919	+	0.872889i	$0.662244\pi$
$230$	2.22041	−	1.26734i	0.146409	−	0.0835662i
$231$		0			0
$232$			4.39119i			0.288296i
$233$			15.5104i			1.01612i	0.861322	+	0.508060i	$0.169637\pi$
$233$			15.5104i			1.01612i	−0.861322	+	0.508060i	$0.830363\pi$
$234$		0			0
$235$	8.31868	+	14.5745i	0.542651	+	0.950733i
$236$	−16.2804			−1.05977
$237$		0			0
$238$		−	1.65450i		−	0.107246i
$239$	1.16086			0.0750897			0.0375448	−	0.999295i	$-0.488046\pi$
$239$	1.16086			0.0750897			0.0375448	+	0.999295i	$0.488046\pi$
$240$		0			0
$241$	−14.7586			−0.950685			−0.475343	−	0.879801i	$-0.657676\pi$
$241$	−14.7586			−0.950685			−0.475343	+	0.879801i	$0.657676\pi$
$242$			0.837513i			0.0538374i
$243$		0			0
$244$	−22.2785			−1.42624
$245$	−6.50959	+	3.71549i	−0.415883	+	0.237374i
$246$		0			0
$247$		−	4.53675i		−	0.288667i
$248$			5.36155i			0.340459i
$249$		0			0
$250$	−2.06704	−	0.0306866i	−0.130731	−	0.00194079i
$251$	5.83488			0.368294			0.184147	−	0.982899i	$-0.441048\pi$
$251$	5.83488			0.368294			0.184147	+	0.982899i	$0.441048\pi$
$252$		0			0
$253$			24.3680i			1.53200i
$254$	−1.45112			−0.0910514
$255$		0			0
$256$	13.3345			0.833404
$257$			2.19805i			0.137111i	0.997647	+	0.0685554i	$0.0218390\pi$
$257$			2.19805i			0.137111i	−0.997647	+	0.0685554i	$0.978161\pi$
$258$		0			0
$259$	15.4228			0.958329
$260$	−9.88550	−	17.3195i	−0.613073	−	1.07411i
$261$		0			0
$262$		−	0.252802i		−	0.0156182i
$263$		−	21.4529i		−	1.32284i	−0.750015	−	0.661420i	$-0.769954\pi$
$263$		−	21.4529i		−	1.32284i	0.750015	−	0.661420i	$-0.230046\pi$
$264$		0			0
$265$	1.42766	+	2.50128i	0.0877005	+	0.153653i
$266$	−0.353158			−0.0216535
$267$		0			0
$268$			20.3295i			1.24182i
$269$	−0.680401			−0.0414848			−0.0207424	−	0.999785i	$-0.506603\pi$
$269$	−0.680401			−0.0414848			−0.0207424	+	0.999785i	$0.506603\pi$
$270$		0			0
$271$	17.3272			1.05255			0.526276	−	0.850314i	$-0.323588\pi$
$271$	17.3272			1.05255			0.526276	+	0.850314i	$0.323588\pi$
$272$		−	17.7840i		−	1.07831i
$273$		0			0
$274$	2.22437			0.134379
$275$	10.0203	−	16.9656i	0.604244	−	1.02306i
$276$		0			0
$277$			25.8337i			1.55219i	0.630613	+	0.776097i	$0.282803\pi$
$277$			25.8337i			1.55219i	−0.630613	+	0.776097i	$0.717197\pi$
$278$		−	2.34638i		−	0.140726i
$279$		0			0
$280$	−2.71988	+	1.55243i	−0.162544	+	0.0927756i
$281$	6.31534			0.376741			0.188371	−	0.982098i	$-0.439679\pi$
$281$	6.31534			0.376741			0.188371	+	0.982098i	$0.439679\pi$
$282$		0			0
$283$		−	7.03773i		−	0.418350i	−0.977878	−	0.209175i	$-0.932922\pi$
$283$		−	7.03773i		−	0.418350i	0.977878	−	0.209175i	$-0.0670778\pi$
$284$	20.3295			1.20633
$285$		0			0
$286$	−3.30572			−0.195471
$287$			0.108385i			0.00639779i
$288$		0			0
$289$	−4.94810			−0.291065
$290$	−1.22733	−	2.15030i	−0.0720714	−	0.126270i
$291$		0			0
$292$		−	19.8515i		−	1.16172i
$293$			16.3174i			0.953274i	0.879100	+	0.476637i	$0.158144\pi$
$293$			16.3174i			0.953274i	−0.879100	+	0.476637i	$0.841856\pi$
$294$		0			0
$295$	16.0832	−	9.17986i	0.936403	−	0.534472i
$296$	−5.92122			−0.344164
$297$		0			0
$298$		−	3.89088i		−	0.225393i
$299$	−28.0535			−1.62237
$300$		0			0
$301$	1.57001			0.0904941
$302$		−	0.615036i		−	0.0353913i
$303$		0			0
$304$	−3.79604			−0.217718
$305$	22.0087	−	12.5619i	1.26021	−	0.719294i
$306$		0			0
$307$		−	18.3294i		−	1.04611i	−0.852298	−	0.523056i	$-0.824792\pi$
$307$		−	18.3294i		−	1.04611i	0.852298	−	0.523056i	$-0.175208\pi$
$308$		−	14.7961i		−	0.843087i
$309$		0			0
$310$	−1.49854	−	2.62547i	−0.0851116	−	0.149117i
$311$	11.7605			0.666879			0.333439	−	0.942772i	$-0.391791\pi$
$311$	11.7605			0.666879			0.333439	+	0.942772i	$0.391791\pi$
$312$		0			0
$313$			17.1712i			0.970574i	0.874355	+	0.485287i	$0.161285\pi$
$313$			17.1712i			0.970574i	−0.874355	+	0.485287i	$0.838715\pi$
$314$	3.01459			0.170123
$315$		0			0
$316$	−8.11055			−0.456254
$317$			11.8192i			0.663833i	0.943309	+	0.331916i	$0.107695\pi$
$317$			11.8192i			0.663833i	−0.943309	+	0.331916i	$0.892305\pi$
$318$		0			0
$319$	23.5987			1.32127
$320$	−13.9652	+	7.97091i	−0.780676	+	0.445587i
$321$		0			0
$322$			2.18379i			0.121698i
$323$			4.68488i			0.260674i
$324$		0			0
$325$	19.5315	+	11.5357i	1.08341	+	0.639888i
$326$	1.91801			0.106229
$327$		0			0
$328$		−	0.0416119i		−	0.00229764i
$329$	−14.3341			−0.790264
$330$		0			0
$331$	−25.0090			−1.37462			−0.687309	−	0.726365i	$-0.741208\pi$
$331$	−25.0090			−1.37462			−0.687309	+	0.726365i	$0.741208\pi$
$332$			22.8614i			1.25468i
$333$		0			0
$334$	−4.51733			−0.247177
$335$	−11.4629	−	20.0832i	−0.626288	−	1.09727i
$336$		0			0
$337$			0.451357i			0.0245870i	0.999924	+	0.0122935i	$0.00391324\pi$
$337$			0.451357i			0.0245870i	−0.999924	+	0.0122935i	$0.996087\pi$
$338$		−	1.40195i		−	0.0762563i
$339$		0			0
$340$	10.2083	+	17.8850i	0.553621	+	0.969952i
$341$	28.8134			1.56033
$342$		0			0
$343$		−	19.7720i		−	1.06759i
$344$	−0.602768			−0.0324991
$345$		0			0
$346$	3.97265			0.213571
$347$			8.93849i			0.479843i	0.970792	+	0.239922i	$0.0771217\pi$
$347$			8.93849i			0.479843i	−0.970792	+	0.239922i	$0.922878\pi$
$348$		0			0
$349$	15.9394			0.853215			0.426607	−	0.904437i	$-0.359709\pi$
$349$	15.9394			0.853215			0.426607	+	0.904437i	$0.359709\pi$
$350$	0.897985	−	1.52041i	0.0479993	−	0.0812692i
$351$		0			0
$352$			8.54539i			0.455471i
$353$			8.53844i			0.454455i	0.973842	+	0.227228i	$0.0729662\pi$
$353$			8.53844i			0.454455i	−0.973842	+	0.227228i	$0.927034\pi$
$354$		0			0
$355$	−20.0832	+	11.4629i	−1.06591	+	0.608390i
$356$	14.0959			0.747082
$357$		0			0
$358$		−	2.73543i		−	0.144572i
$359$	16.7400			0.883503			0.441752	−	0.897137i	$-0.354357\pi$
$359$	16.7400			0.883503			0.441752	+	0.897137i	$0.354357\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$			3.30295i			0.173599i
$363$		0			0
$364$	17.0339			0.892819
$365$	11.1934	+	19.6110i	0.585890	+	1.02649i
$366$		0			0
$367$		−	0.300558i		−	0.0156890i	−0.999969	−	0.00784451i	$-0.997503\pi$
$367$		−	0.300558i		−	0.0156890i	0.999969	−	0.00784451i	$-0.00249701\pi$
$368$			23.4732i			1.22362i
$369$		0			0
$370$	2.89954	−	1.65497i	0.150740	−	0.0860379i
$371$	−2.46003			−0.127719
$372$		0			0
$373$			25.3500i			1.31257i	0.754512	+	0.656287i	$0.227874\pi$
$373$			25.3500i			1.31257i	−0.754512	+	0.656287i	$0.772126\pi$
$374$	3.41365			0.176516
$375$		0			0
$376$	5.50322			0.283807
$377$			27.1678i			1.39921i
$378$		0			0
$379$	−16.3050			−0.837530			−0.418765	−	0.908095i	$-0.637537\pi$
$379$	−16.3050			−0.837530			−0.418765	+	0.908095i	$0.637537\pi$
$380$	3.81761	−	2.17898i	0.195839	−	0.111779i
$381$		0			0
$382$		−	2.37055i		−	0.121288i
$383$			30.4652i			1.55670i	0.627832	+	0.778349i	$0.283943\pi$
$383$			30.4652i			1.55670i	−0.627832	+	0.778349i	$0.716057\pi$
$384$		0			0
$385$	8.34290	+	14.6169i	0.425194	+	0.744946i
$386$	2.93509			0.149392
$387$		0			0
$388$		−	5.30843i		−	0.269495i
$389$	−1.28401			−0.0651017			−0.0325508	−	0.999470i	$-0.510363\pi$
$389$	−1.28401			−0.0651017			−0.0325508	+	0.999470i	$0.510363\pi$
$390$		0			0
$391$	28.9694			1.46505
$392$			2.45798i			0.124147i
$393$		0			0
$394$	−2.56221			−0.129082
$395$	8.01231	−	4.57320i	0.403143	−	0.230102i
$396$		0			0
$397$		−	12.5188i		−	0.628299i	−0.949374	−	0.314149i	$-0.898281\pi$
$397$		−	12.5188i		−	0.628299i	0.949374	−	0.314149i	$-0.101719\pi$
$398$		−	4.91401i		−	0.246317i
$399$		0			0
$400$	9.65229	−	16.3426i	0.482615	−	0.817130i
$401$	−1.22276			−0.0610620			−0.0305310	−	0.999534i	$-0.509720\pi$
$401$	−1.22276			−0.0610620			−0.0305310	+	0.999534i	$0.509720\pi$
$402$		0			0
$403$			33.1712i			1.65238i
$404$	−4.28135			−0.213005
$405$		0			0
$406$	2.11484			0.104958
$407$			31.8212i			1.57732i
$408$		0			0
$409$	27.7692			1.37310			0.686550	−	0.727083i	$-0.259124\pi$
$409$	27.7692			1.37310			0.686550	+	0.727083i	$0.259124\pi$
$410$	0.0116305	+	0.0203768i	0.000574388	+	0.00100634i
$411$		0			0
$412$		−	20.1891i		−	0.994647i
$413$			15.8180i			0.778353i
$414$		0			0
$415$	−12.8906	−	22.5845i	−0.632775	−	1.10863i
$416$	−9.83781			−0.482338
$417$		0			0
$418$		−	0.728653i		−	0.0356396i
$419$	−14.4570			−0.706273			−0.353136	−	0.935572i	$-0.614885\pi$
$419$	−14.4570			−0.706273			−0.353136	+	0.935572i	$0.614885\pi$
$420$		0			0
$421$	35.5761			1.73387			0.866937	−	0.498418i	$-0.166086\pi$
$421$	35.5761			1.73387			0.866937	+	0.498418i	$0.166086\pi$
$422$		−	2.28056i		−	0.111016i
$423$		0			0
$424$	0.944469			0.0458675
$425$	−20.1692	−	11.9124i	−0.978351	−	0.577835i
$426$		0			0
$427$			21.6457i			1.04751i
$428$		−	15.3725i		−	0.743060i
$429$		0			0
$430$	0.295167	−	0.168473i	0.0142342	−	0.00812448i
$431$	−11.1892			−0.538966			−0.269483	−	0.963005i	$-0.586853\pi$
$431$	−11.1892			−0.538966			−0.269483	+	0.963005i	$0.586853\pi$
$432$		0			0
$433$			10.2174i			0.491018i	0.969394	+	0.245509i	$0.0789550\pi$
$433$			10.2174i			0.491018i	−0.969394	+	0.245509i	$0.921045\pi$
$434$	2.58217			0.123948
$435$		0			0
$436$	−15.5921			−0.746725
$437$		−	6.18360i		−	0.295802i
$438$		0			0
$439$	4.79196			0.228708			0.114354	−	0.993440i	$-0.463520\pi$
$439$	4.79196			0.228708			0.114354	+	0.993440i	$0.463520\pi$
$440$	−3.20305	−	5.61180i	−0.152700	−	0.267532i
$441$		0			0
$442$			3.92994i			0.186928i
$443$		−	13.3293i		−	0.633296i	−0.948543	−	0.316648i	$-0.897443\pi$
$443$		−	13.3293i		−	0.633296i	0.948543	−	0.316648i	$-0.102557\pi$
$444$		0			0
$445$	−13.9252	+	7.94810i	−0.660117	+	0.376776i
$446$	4.77113			0.225919
$447$		0			0
$448$		−	13.7348i		−	0.648910i
$449$	20.0362			0.945566			0.472783	−	0.881179i	$-0.343249\pi$
$449$	20.0362			0.945566			0.472783	+	0.881179i	$0.343249\pi$
$450$		0			0
$451$	−0.223626			−0.0105301
$452$		−	18.7572i		−	0.882263i
$453$		0			0
$454$	2.61356			0.122661
$455$	−16.8276	+	9.60470i	−0.788889	+	0.450275i
$456$		0			0
$457$			14.4875i			0.677696i	0.940841	+	0.338848i	$0.110037\pi$
$457$			14.4875i			0.677696i	−0.940841	+	0.338848i	$0.889963\pi$
$458$		−	2.73047i		−	0.127586i
$459$		0			0
$460$	−13.4739	−	23.6065i	−0.628225	−	1.10066i
$461$	−14.7512			−0.687031			−0.343515	−	0.939147i	$-0.611618\pi$
$461$	−14.7512			−0.687031			−0.343515	+	0.939147i	$0.611618\pi$
$462$		0			0
$463$		−	30.8315i		−	1.43286i	−0.697658	−	0.716431i	$-0.745774\pi$
$463$		−	30.8315i		−	1.43286i	0.697658	−	0.716431i	$-0.254226\pi$
$464$	22.7321			1.05531
$465$		0			0
$466$	−2.86790			−0.132853
$467$		−	20.0644i		−	0.928471i	−0.885712	−	0.464235i	$-0.846329\pi$
$467$		−	20.0644i		−	0.928471i	0.885712	−	0.464235i	$-0.153671\pi$
$468$		0			0
$469$	19.7520			0.912064
$470$	−2.69485	+	1.53814i	−0.124304	+	0.0709492i
$471$		0			0
$472$		−	6.07293i		−	0.279529i
$473$			3.23933i			0.148944i
$474$		0			0
$475$	−2.54273	+	4.30517i	−0.116668	+	0.197535i
$476$	−17.5901			−0.806239
$477$		0			0
$478$			0.214645i			0.00981764i
$479$	−21.4676			−0.980879			−0.490440	−	0.871475i	$-0.663164\pi$
$479$	−21.4676			−0.980879			−0.490440	+	0.871475i	$0.663164\pi$
$480$		0			0
$481$	−36.6339			−1.67036
$482$		−	2.72890i		−	0.124298i
$483$		0			0
$484$	8.90412			0.404733
$485$	2.99320	+	5.24413i	0.135914	+	0.238124i
$486$		0			0
$487$		−	0.118331i		−	0.00536207i	−0.999996	−	0.00268103i	$-0.999147\pi$
$487$		−	0.118331i		−	0.00536207i	0.999996	−	0.00268103i	$-0.000853401\pi$
$488$		−	8.31034i		−	0.376192i
$489$		0			0
$490$	−0.687002	−	1.20364i	−0.0310356	−	0.0543748i
$491$	−6.96487			−0.314320			−0.157160	−	0.987573i	$-0.550234\pi$
$491$	−6.96487			−0.314320			−0.157160	+	0.987573i	$0.550234\pi$
$492$		0			0
$493$		−	28.0548i		−	1.26352i
$494$	0.838856			0.0377419
$495$		0			0
$496$	27.7553			1.24625
$497$		−	19.7520i		−	0.886000i
$498$		0			0
$499$	15.3967			0.689250			0.344625	−	0.938741i	$-0.388006\pi$
$499$	15.3967			0.689250			0.344625	+	0.938741i	$0.388006\pi$
$500$	−0.326249	+	21.9760i	−0.0145903	+	0.982797i
$501$		0			0
$502$			1.07888i			0.0481529i
$503$		−	5.79980i		−	0.258600i	−0.991606	−	0.129300i	$-0.958727\pi$
$503$		−	5.79980i		−	0.258600i	0.991606	−	0.129300i	$-0.0412731\pi$
$504$		0			0
$505$	4.22949	−	2.41407i	0.188210	−	0.107425i
$506$	−4.50569			−0.200303
$507$		0			0
$508$			15.4278i			0.684497i
$509$	33.9293			1.50389			0.751945	−	0.659226i	$-0.229116\pi$
$509$	33.9293			1.50389			0.751945	+	0.659226i	$0.229116\pi$
$510$		0			0
$511$	−19.2876			−0.853234
$512$			13.7988i			0.609825i
$513$		0			0
$514$	−0.406425			−0.0179266
$515$	11.3838	+	19.9446i	0.501630	+	0.878864i
$516$		0			0
$517$		−	29.5748i		−	1.30070i
$518$			2.85172i			0.125297i
$519$		0			0
$520$	6.46054	−	3.68749i	0.283313	−	0.161707i
$521$	8.82716			0.386725			0.193362	−	0.981127i	$-0.438061\pi$
$521$	8.82716			0.386725			0.193362	+	0.981127i	$0.438061\pi$
$522$		0			0
$523$			20.7651i			0.907995i	0.891003	+	0.453997i	$0.150002\pi$
$523$			20.7651i			0.907995i	−0.891003	+	0.453997i	$0.849998\pi$
$524$	−2.68770			−0.117413
$525$		0			0
$526$	3.96668			0.172956
$527$		−	34.2543i		−	1.49214i
$528$		0			0
$529$	−15.2369			−0.662472
$530$	−0.462493	+	0.263978i	−0.0200894	+	0.0114665i
$531$		0			0
$532$			3.75465i			0.162785i
$533$		−	0.257448i		−	0.0111513i
$534$		0			0
$535$	8.66793	+	15.1863i	0.374747	+	0.656563i
$536$	−7.58331			−0.327549
$537$		0			0
$538$		−	0.125808i		−	0.00542395i
$539$	13.2094			0.568969
$540$		0			0
$541$	44.2527			1.90257			0.951286	−	0.308309i	$-0.0997631\pi$
$541$	44.2527			1.90257			0.951286	+	0.308309i	$0.0997631\pi$
$542$			3.20384i			0.137617i
$543$		0			0
$544$	10.1590			0.435564
$545$	15.4032	−	8.79171i	0.659801	−	0.376596i
$546$		0			0
$547$		−	18.6666i		−	0.798127i	−0.916923	−	0.399064i	$-0.869335\pi$
$547$		−	18.6666i		−	0.798127i	0.916923	−	0.399064i	$-0.130665\pi$
$548$		−	23.6487i		−	1.01022i
$549$		0			0
$550$	3.13698	+	1.85277i	0.133761	+	0.0790022i
$551$	−5.98837			−0.255113
$552$		0			0
$553$			7.88017i			0.335099i
$554$	−4.77670			−0.202943
$555$		0			0
$556$	−24.9458			−1.05794
$557$		−	4.34816i		−	0.184237i	−0.995748	−	0.0921187i	$-0.970636\pi$
$557$		−	4.34816i		−	0.184237i	0.995748	−	0.0921187i	$-0.0293639\pi$
$558$		0			0
$559$	−3.72925			−0.157730
$560$	8.03654	+	14.0801i	0.339606	+	0.594994i
$561$		0			0
$562$			1.16772i			0.0492573i
$563$			9.70917i			0.409193i	0.978846	+	0.204596i	$0.0655882\pi$
$563$			9.70917i			0.409193i	−0.978846	+	0.204596i	$0.934412\pi$
$564$		0			0
$565$	10.5764	+	18.5300i	0.444951	+	0.779562i
$566$	1.30129			0.0546974
$567$		0			0
$568$			7.58331i			0.318189i
$569$	−36.6849			−1.53791			−0.768956	−	0.639301i	$-0.779224\pi$
$569$	−36.6849			−1.53791			−0.768956	+	0.639301i	$0.779224\pi$
$570$		0			0
$571$	−33.6378			−1.40770			−0.703849	−	0.710350i	$-0.748537\pi$
$571$	−33.6378			−1.40770			−0.703849	+	0.710350i	$0.748537\pi$
$572$			35.1452i			1.46949i
$573$		0			0
$574$	−0.0200407			−0.000836483
$575$	26.6215	+	15.7232i	1.11019	+	0.655703i
$576$		0			0
$577$			31.9286i			1.32920i	0.747197	+	0.664602i	$0.231399\pi$
$577$			31.9286i			1.32920i	−0.747197	+	0.664602i	$0.768601\pi$
$578$		−	0.914914i		−	0.0380554i
$579$		0			0
$580$	−22.8612	+	13.0485i	−0.949261	+	0.541811i
$581$	22.2121			0.921512
$582$		0			0
$583$		−	5.07566i		−	0.210212i
$584$	7.40500			0.306421
$585$		0			0
$586$	−3.01713			−0.124636
$587$		−	16.0973i		−	0.664406i	−0.943208	−	0.332203i	$-0.892208\pi$
$587$		−	16.0973i		−	0.664406i	0.943208	−	0.332203i	$-0.107792\pi$
$588$		0			0
$589$	−7.31166			−0.301272
$590$	1.69738	+	2.97383i	0.0698798	+	0.122431i
$591$		0			0
$592$			30.6526i			1.25982i
$593$		−	30.3210i		−	1.24513i	−0.782567	−	0.622566i	$-0.786090\pi$
$593$		−	30.3210i		−	1.24513i	0.782567	−	0.622566i	$-0.213910\pi$
$594$		0			0
$595$	17.3770	−	9.91830i	0.712388	−	0.406611i
$596$	−41.3664			−1.69443
$597$		0			0
$598$		−	5.18714i		−	0.212118i
$599$	27.5881			1.12722			0.563610	−	0.826041i	$-0.309412\pi$
$599$	27.5881			1.12722			0.563610	+	0.826041i	$0.309412\pi$
$600$		0			0
$601$	−7.71122			−0.314547			−0.157274	−	0.987555i	$-0.550270\pi$
$601$	−7.71122			−0.314547			−0.157274	+	0.987555i	$0.550270\pi$
$602$			0.290299i			0.0118317i
$603$		0			0
$604$	−6.53883			−0.266061
$605$	−8.79627	+	5.02066i	−0.357619	+	0.204119i
$606$		0			0
$607$			30.1322i			1.22303i	0.791233	+	0.611515i	$0.209440\pi$
$607$			30.1322i			1.22303i	−0.791233	+	0.611515i	$0.790560\pi$
$608$		−	2.16847i		−	0.0879430i
$609$		0			0
$610$	2.32273	+	4.06946i	0.0940445	+	0.164767i
$611$	34.0478			1.37742
$612$		0			0
$613$			28.2790i			1.14218i	0.820888	+	0.571089i	$0.193479\pi$
$613$			28.2790i			1.14218i	−0.820888	+	0.571089i	$0.806521\pi$
$614$	3.38914			0.136775
$615$		0			0
$616$	5.51925			0.222377
$617$		−	1.58263i		−	0.0637143i	−0.999492	−	0.0318572i	$-0.989858\pi$
$617$		−	1.58263i		−	0.0637143i	0.999492	−	0.0318572i	$-0.0101422\pi$
$618$		0			0
$619$	6.99796			0.281272			0.140636	−	0.990061i	$-0.455085\pi$
$619$	6.99796			0.281272			0.140636	+	0.990061i	$0.455085\pi$
$620$	−27.9130	+	15.9320i	−1.12101	+	0.639843i
$621$		0			0
$622$			2.17455i			0.0871914i
$623$		−	13.6955i		−	0.548700i
$624$		0			0
$625$	−12.0691	−	21.8938i	−0.482762	−	0.875752i
$626$	−3.17499			−0.126898
$627$		0			0
$628$		−	32.0500i		−	1.27893i
$629$	37.8300			1.50838
$630$		0			0
$631$	23.8697			0.950238			0.475119	−	0.879922i	$-0.342405\pi$
$631$	23.8697			0.950238			0.475119	+	0.879922i	$0.342405\pi$
$632$		−	3.02540i		−	0.120344i
$633$		0			0
$634$	−2.18540			−0.0867932
$635$	−8.69907	−	15.2409i	−0.345212	−	0.604817i
$636$		0			0
$637$			15.2072i			0.602532i
$638$			4.36344i			0.172750i
$639$		0			0
$640$	−6.28107	−	11.0045i	−0.248281	−	0.434992i
$641$	24.5476			0.969572			0.484786	−	0.874633i	$-0.338897\pi$
$641$	24.5476			0.969572			0.484786	+	0.874633i	$0.338897\pi$
$642$		0			0
$643$			36.1097i			1.42403i	0.702165	+	0.712014i	$0.252217\pi$
$643$			36.1097i			1.42403i	−0.702165	+	0.712014i	$0.747783\pi$
$644$	23.2172			0.914886
$645$		0			0
$646$	−0.866244			−0.0340819
$647$		−	7.25157i		−	0.285089i	−0.989788	−	0.142544i	$-0.954472\pi$
$647$		−	7.25157i		−	0.285089i	0.989788	−	0.142544i	$-0.0455284\pi$
$648$		0			0
$649$	−32.6365			−1.28109
$650$	−2.13298	+	3.61142i	−0.0836625	+	0.141652i
$651$		0			0
$652$		−	20.3916i		−	0.798597i
$653$		−	40.4550i		−	1.58312i	−0.611088	−	0.791562i	$-0.709268\pi$
$653$		−	40.4550i		−	1.58312i	0.611088	−	0.791562i	$-0.290732\pi$
$654$		0			0
$655$	2.65514	−	1.51548i	0.103745	−	0.0592147i
$656$	−0.215414			−0.00841051
$657$		0			0
$658$		−	2.65041i		−	0.103324i
$659$	6.41486			0.249887			0.124944	−	0.992164i	$-0.460125\pi$
$659$	6.41486			0.249887			0.124944	+	0.992164i	$0.460125\pi$
$660$		0			0
$661$	30.1068			1.17102			0.585510	−	0.810665i	$-0.300894\pi$
$661$	30.1068			1.17102			0.585510	+	0.810665i	$0.300894\pi$
$662$		−	4.62421i		−	0.179725i
$663$		0			0
$664$	−8.52778			−0.330942
$665$	−2.11709	−	3.70917i	−0.0820971	−	0.143835i
$666$		0			0
$667$			37.0297i			1.43379i
$668$			48.0266i			1.85820i
$669$		0			0
$670$	3.71344	−	2.11952i	0.143463	−	0.0818843i
$671$	−44.6605			−1.72410
$672$		0			0
$673$		−	32.5367i		−	1.25420i	−0.778940	−	0.627099i	$-0.784242\pi$
$673$		−	32.5367i		−	1.25420i	0.778940	−	0.627099i	$-0.215758\pi$
$674$	−0.0834569			−0.00321464
$675$		0			0
$676$	−14.9051			−0.573271
$677$			7.19269i			0.276438i	0.990402	+	0.138219i	$0.0441377\pi$
$677$			7.19269i			0.276438i	−0.990402	+	0.138219i	$0.955862\pi$
$678$		0			0
$679$	−5.15764			−0.197932
$680$	−6.67147	+	3.80789i	−0.255839	+	0.146026i
$681$		0			0
$682$			5.32766i			0.204007i
$683$		−	11.7394i		−	0.449195i	−0.974452	−	0.224598i	$-0.927893\pi$
$683$		−	11.7394i		−	0.449195i	0.974452	−	0.224598i	$-0.0721067\pi$
$684$		0			0
$685$	13.3345	+	23.3623i	0.509485	+	0.892626i
$686$	3.65589			0.139583
$687$		0			0
$688$			3.12037i			0.118963i
$689$	5.84331			0.222612
$690$		0			0
$691$	−26.8706			−1.02221			−0.511103	−	0.859520i	$-0.670763\pi$
$691$	−26.8706			−1.02221			−0.511103	+	0.859520i	$0.670763\pi$
$692$		−	42.2357i		−	1.60556i
$693$		0			0
$694$	−1.65275			−0.0627374
$695$	24.6437	−	14.0659i	0.934788	−	0.533550i
$696$		0			0
$697$			0.265854i			0.0100699i
$698$			2.94722i			0.111554i
$699$		0			0
$700$	−16.1644	−	9.54705i	−0.610957	−	0.360845i
$701$	−36.2813			−1.37033			−0.685163	−	0.728390i	$-0.740269\pi$
$701$	−36.2813			−1.37033			−0.685163	+	0.728390i	$0.740269\pi$
$702$		0			0
$703$		−	8.07490i		−	0.304551i
$704$	28.3384			1.06804
$705$		0			0
$706$	−1.57878			−0.0594180
$707$			4.15974i			0.156443i
$708$		0			0
$709$	9.09197			0.341456			0.170728	−	0.985318i	$-0.445388\pi$
$709$	9.09197			0.341456			0.170728	+	0.985318i	$0.445388\pi$
$710$	−2.11952	−	3.71344i	−0.0795443	−	0.139363i
$711$		0			0
$712$			5.25806i			0.197054i
$713$			45.2124i			1.69322i
$714$		0			0
$715$	−19.8169	−	34.7195i	−0.741109	−	1.29843i
$716$	−29.0821			−1.08685
$717$		0			0
$718$			3.09526i			0.115514i
$719$	−26.9986			−1.00688			−0.503439	−	0.864031i	$-0.667932\pi$
$719$	−26.9986			−1.00688			−0.503439	+	0.864031i	$0.667932\pi$
$720$		0			0
$721$	−19.6157			−0.730526
$722$			0.184902i			0.00688135i
$723$		0			0
$724$	35.1158			1.30507
$725$	15.2268	−	25.7810i	0.565509	−	0.957481i
$726$		0			0
$727$			6.30378i			0.233794i	0.993144	+	0.116897i	$0.0372948\pi$
$727$			6.30378i			0.233794i	−0.993144	+	0.116897i	$0.962705\pi$
$728$			6.35399i			0.235495i
$729$		0			0
$730$	−3.62612	+	2.06969i	−0.134209	+	0.0766026i
$731$	3.85101			0.142435
$732$		0			0
$733$			6.84548i			0.252843i	0.991977	+	0.126422i	$0.0403492\pi$
$733$			6.84548i			0.252843i	−0.991977	+	0.126422i	$0.959651\pi$
$734$	0.0555739			0.00205127
$735$		0			0
$736$	−13.4089			−0.494260
$737$			40.7533i			1.50117i
$738$		0			0
$739$	−18.4720			−0.679504			−0.339752	−	0.940515i	$-0.610343\pi$
$739$	−18.4720			−0.679504			−0.339752	+	0.940515i	$0.610343\pi$
$740$	−17.5951	−	30.8268i	−0.646807	−	1.13322i
$741$		0			0
$742$		−	0.454865i		−	0.0166986i
$743$			18.7512i			0.687916i	0.938985	+	0.343958i	$0.111768\pi$
$743$			18.7512i			0.687916i	−0.938985	+	0.343958i	$0.888232\pi$
$744$		0			0
$745$	40.8653	−	23.3248i	1.49719	−	0.854553i
$746$	−4.68727			−0.171613
$747$		0			0
$748$		−	36.2927i		−	1.32699i
$749$	−14.9359			−0.545745
$750$		0			0
$751$	−3.19610			−0.116628			−0.0583138	−	0.998298i	$-0.518572\pi$
$751$	−3.19610			−0.116628			−0.0583138	+	0.998298i	$0.518572\pi$
$752$		−	28.4888i		−	1.03888i
$753$		0			0
$754$	−5.02338			−0.182941
$755$	6.45963	−	3.68697i	0.235090	−	0.134183i
$756$		0			0
$757$		−	30.6268i		−	1.11315i	−0.830798	−	0.556575i	$-0.812115\pi$
$757$		−	30.6268i		−	1.11315i	0.830798	−	0.556575i	$-0.187885\pi$
$758$		−	3.01482i		−	0.109503i
$759$		0			0
$760$	0.812803	+	1.42404i	0.0294835	+	0.0516555i
$761$	−32.4024			−1.17458			−0.587292	−	0.809375i	$-0.699806\pi$
$761$	−32.4024			−1.17458			−0.587292	+	0.809375i	$0.699806\pi$
$762$		0			0
$763$			15.1492i			0.548437i
$764$	−25.2028			−0.911805
$765$		0			0
$766$	−5.63308			−0.203531
$767$		−	37.5725i		−	1.35666i
$768$		0			0
$769$	38.2846			1.38058			0.690288	−	0.723535i	$-0.257484\pi$
$769$	38.2846			1.38058			0.690288	+	0.723535i	$0.257484\pi$
$770$	−2.70269	+	1.54262i	−0.0973984	+	0.0555922i
$771$		0			0
$772$		−	31.2048i		−	1.12308i
$773$			33.4716i			1.20389i	0.798538	+	0.601944i	$0.205607\pi$
$773$			33.4716i			1.20389i	−0.798538	+	0.601944i	$0.794393\pi$
$774$		0			0
$775$	18.5916	−	31.4780i	0.667829	−	1.13072i
$776$	1.98015			0.0710833
$777$		0			0
$778$		−	0.237415i		−	0.00851176i
$779$	0.0567471			0.00203318
$780$		0			0
$781$	40.7533			1.45827
$782$			5.35651i			0.191548i
$783$		0			0
$784$	12.7243			0.454440
$785$	18.0717	+	31.6618i	0.645005	+	1.13006i
$786$		0			0
$787$			33.9153i			1.20895i	0.796625	+	0.604474i	$0.206617\pi$
$787$			33.9153i			1.20895i	−0.796625	+	0.604474i	$0.793383\pi$
$788$			27.2404i			0.970400i
$789$		0			0
$790$	0.845594	+	1.48149i	0.0300849	+	0.0527092i
$791$	−18.2244			−0.647984
$792$		0			0
$793$		−	51.4151i		−	1.82580i
$794$	2.31475			0.0821473
$795$		0			0
$796$	−52.2440			−1.85174
$797$			17.4970i			0.619777i	0.950773	+	0.309889i	$0.100292\pi$
$797$			17.4970i			0.619777i	−0.950773	+	0.309889i	$0.899708\pi$
$798$		0			0
$799$	−35.1594			−1.24385
$800$	9.33564	+	5.51383i	0.330065	+	0.194943i
$801$		0			0
$802$		−	0.226092i		−	0.00798358i
$803$		−	39.7951i		−	1.40434i
$804$		0			0
$805$	−22.9360	+	13.0912i	−0.808388	+	0.461405i
$806$	−6.13343			−0.216041
$807$		0			0
$808$		−	1.59703i		−	0.0561833i
$809$	−24.8019			−0.871990			−0.435995	−	0.899949i	$-0.643603\pi$
$809$	−24.8019			−0.871990			−0.435995	+	0.899949i	$0.643603\pi$
$810$		0			0
$811$	−33.9010			−1.19043			−0.595213	−	0.803568i	$-0.702932\pi$
$811$	−33.9010			−1.19043			−0.595213	+	0.803568i	$0.702932\pi$
$812$		−	22.4842i		−	0.789041i
$813$		0			0
$814$	−5.88380			−0.206227
$815$	11.4980	+	20.1446i	0.402757	+	0.705635i
$816$		0			0
$817$		−	0.822008i		−	0.0287584i
$818$			5.13459i			0.179527i
$819$		0			0
$820$	0.216638	−	0.123651i	0.00756533	−	0.00431808i
$821$	27.2965			0.952654			0.476327	−	0.879268i	$-0.341968\pi$
$821$	27.2965			0.952654			0.476327	+	0.879268i	$0.341968\pi$
$822$		0			0
$823$		−	36.2799i		−	1.26464i	−0.774708	−	0.632319i	$-0.782103\pi$
$823$		−	36.2799i		−	1.26464i	0.774708	−	0.632319i	$-0.217897\pi$
$824$	7.53095			0.262353
$825$		0			0
$826$	−2.92478			−0.101766
$827$		−	20.8780i		−	0.725998i	−0.931789	−	0.362999i	$-0.881753\pi$
$827$		−	20.8780i		−	0.725998i	0.931789	−	0.362999i	$-0.118247\pi$
$828$		0			0
$829$	−45.3011			−1.57337			−0.786687	−	0.617353i	$-0.788205\pi$
$829$	−45.3011			−1.57337			−0.786687	+	0.617353i	$0.788205\pi$
$830$	4.17593	−	2.38350i	0.144949	−	0.0827325i
$831$		0			0
$832$			32.6243i			1.13105i
$833$		−	15.7037i		−	0.544102i
$834$		0			0
$835$	−27.0802	−	47.4449i	−0.937148	−	1.64190i
$836$	−7.74677			−0.267927
$837$		0			0
$838$		−	2.67314i		−	0.0923421i
$839$	−18.9618			−0.654633			−0.327317	−	0.944915i	$-0.606144\pi$
$839$	−18.9618			−0.654633			−0.327317	+	0.944915i	$0.606144\pi$
$840$		0			0
$841$	6.86057			0.236571
$842$			6.57810i			0.226696i
$843$		0			0
$844$	−24.2461			−0.834586
$845$	14.7245	−	8.40433i	0.506539	−	0.289118i
$846$		0			0
$847$		−	8.65120i		−	0.297259i
$848$		−	4.88927i		−	0.167898i
$849$		0			0
$850$	2.20263	−	3.72933i	0.0755494	−	0.127915i
$851$	−49.9319			−1.71165
$852$		0			0
$853$		−	37.9971i		−	1.30100i	−0.759507	−	0.650499i	$-0.774560\pi$
$853$		−	37.9971i		−	1.30100i	0.759507	−	0.650499i	$-0.225440\pi$
$854$	−4.00234			−0.136957
$855$		0			0
$856$	5.73426			0.195993
$857$			11.0179i			0.376363i	0.982134	+	0.188182i	$0.0602593\pi$
$857$			11.0179i			0.376363i	−0.982134	+	0.188182i	$0.939741\pi$
$858$		0			0
$859$	−26.2271			−0.894858			−0.447429	−	0.894319i	$-0.647660\pi$
$859$	−26.2271			−0.894858			−0.447429	+	0.894319i	$0.647660\pi$
$860$	−1.79114	−	3.13810i	−0.0610774	−	0.107008i
$861$		0			0
$862$		−	2.06891i		−	0.0704674i
$863$			21.0735i			0.717351i	0.933462	+	0.358675i	$0.116771\pi$
$863$			21.0735i			0.717351i	−0.933462	+	0.358675i	$0.883229\pi$
$864$		0			0
$865$	23.8149	+	41.7241i	0.809733	+	1.41866i
$866$	−1.88922			−0.0641984
$867$		0			0
$868$		−	27.4527i		−	0.931805i
$869$	−16.2587			−0.551540
$870$		0			0
$871$	−46.9170			−1.58972
$872$		−	5.81616i		−	0.196960i
$873$		0			0
$874$	1.14336			0.0386747
$875$	21.3518	+	0.316982i	0.721822	+	0.0107159i
$876$		0			0
$877$			2.20753i			0.0745431i	0.999305	+	0.0372716i	$0.0118667\pi$
$877$			2.20753i			0.0745431i	−0.999305	+	0.0372716i	$0.988133\pi$
$878$			0.886043i			0.0299025i
$879$		0			0
$880$	−29.0508	+	16.5814i	−0.979303	+	0.558958i
$881$	−17.6683			−0.595262			−0.297631	−	0.954681i	$-0.596196\pi$
$881$	−17.6683			−0.595262			−0.297631	+	0.954681i	$0.596196\pi$
$882$		0			0
$883$			19.7314i			0.664013i	0.943277	+	0.332007i	$0.107726\pi$
$883$			19.7314i			0.664013i	−0.943277	+	0.332007i	$0.892274\pi$
$884$	41.7816			1.40527
$885$		0			0
$886$	2.46462			0.0828007
$887$		−	42.4935i		−	1.42679i	−0.700762	−	0.713396i	$-0.747156\pi$
$887$		−	42.4935i		−	1.42679i	0.700762	−	0.713396i	$-0.252844\pi$
$888$		0			0
$889$	14.9895			0.502733
$890$	−1.46962	−	2.57480i	−0.0492618	−	0.0863074i
$891$		0			0
$892$		−	50.7248i		−	1.69839i
$893$			7.50487i			0.251141i
$894$		0			0
$895$	28.7298	−	16.3982i	0.960332	−	0.548130i
$896$	10.8230			0.361572
$897$		0			0
$898$			3.70473i			0.123629i
$899$	43.7849			1.46031
$900$		0			0
$901$	−6.03410			−0.201025
$902$		−	0.0413490i		−	0.00137677i
$903$		0			0
$904$	6.99680			0.232710
$905$	−34.6904	+	19.8003i	−1.15315	+	0.658184i
$906$		0			0
$907$			3.21385i			0.106714i	0.998575	+	0.0533571i	$0.0169922\pi$
$907$			3.21385i			0.106714i	−0.998575	+	0.0533571i	$0.983008\pi$
$908$		−	27.7864i		−	0.922126i
$909$		0			0
$910$	−1.77593	−	3.11146i	−0.0588715	−	0.103144i
$911$	−50.5059			−1.67334			−0.836668	−	0.547710i	$-0.815500\pi$
$911$	−50.5059			−1.67334			−0.836668	+	0.547710i	$0.815500\pi$
$912$		0			0
$913$			45.8290i			1.51672i
$914$	−2.67877			−0.0886057
$915$		0			0
$916$	−29.0293			−0.959156
$917$			2.61135i			0.0862345i
$918$		0			0
$919$	−15.9521			−0.526212			−0.263106	−	0.964767i	$-0.584747\pi$
$919$	−15.9521			−0.526212			−0.263106	+	0.964767i	$0.584747\pi$
$920$	8.80571	−	5.02605i	0.290316	−	0.165704i
$921$		0			0
$922$		−	2.72752i		−	0.0898262i
$923$			46.9170i			1.54429i
$924$		0			0
$925$	34.7639	+	20.5323i	1.14303	+	0.675098i
$926$	5.70082			0.187340
$927$		0			0
$928$			12.9856i			0.426273i
$929$	−57.3866			−1.88279			−0.941396	−	0.337304i	$-0.890485\pi$
$929$	−57.3866			−1.88279			−0.941396	+	0.337304i	$0.890485\pi$
$930$		0			0
$931$	−3.35200			−0.109857
$932$			30.4905i			0.998749i
$933$		0			0
$934$	3.70996			0.121393
$935$	20.4639	+	35.8531i	0.669241	+	1.17252i
$936$		0			0
$937$		−	43.8839i		−	1.43363i	−0.697266	−	0.716813i	$-0.745600\pi$
$937$		−	43.8839i		−	1.43363i	0.697266	−	0.716813i	$-0.254400\pi$
$938$			3.65219i			0.119248i
$939$		0			0
$940$	16.3530	+	28.6506i	0.533375	+	0.934481i
$941$	−56.0765			−1.82804			−0.914021	−	0.405667i	$-0.867039\pi$
$941$	−56.0765			−1.82804			−0.914021	+	0.405667i	$0.867039\pi$
$942$		0			0
$943$		−	0.350901i		−	0.0114269i
$944$	−31.4380			−1.02322
$945$		0			0
$946$	−0.598959			−0.0194738
$947$		−	46.3239i		−	1.50532i	−0.658407	−	0.752662i	$-0.728769\pi$
$947$		−	46.3239i		−	1.50532i	0.658407	−	0.752662i	$-0.271231\pi$
$948$		0			0
$949$	45.8138			1.48718
$950$	−0.796036	−	0.470156i	−0.0258268	−	0.0152539i
$951$		0			0
$952$		−	6.56145i		−	0.212658i
$953$		−	40.2270i		−	1.30308i	−0.758615	−	0.651540i	$-0.774123\pi$
$953$		−	40.2270i		−	1.30308i	0.758615	−	0.651540i	$-0.225877\pi$
$954$		0			0
$955$	24.8975	−	14.2108i	0.805665	−	0.459851i
$956$	2.28203			0.0738061
$957$		0			0
$958$		−	3.96940i		−	0.128246i
$959$	−22.9770			−0.741965
$960$		0			0
$961$	22.4604			0.724529
$962$		−	6.77368i		−	0.218392i
$963$		0			0
$964$	−29.0126			−0.934434
$965$	17.5951	+	30.8268i	0.566405	+	0.992350i
$966$		0			0
$967$		−	5.60792i		−	0.180339i	−0.995926	−	0.0901693i	$-0.971259\pi$
$967$		−	5.60792i		−	0.180339i	0.995926	−	0.0901693i	$-0.0287408\pi$
$968$			3.32142i			0.106754i
$969$		0			0
$970$	−0.969651	+	0.553449i	−0.0311336	+	0.0177702i
$971$	18.2825			0.586712			0.293356	−	0.956003i	$-0.405228\pi$
$971$	18.2825			0.586712			0.293356	+	0.956003i	$0.405228\pi$
$972$		0			0
$973$			24.2372i			0.777010i
$974$	0.0218796			0.000701067
$975$		0			0
$976$	−43.0205			−1.37705
$977$			4.99368i			0.159762i	0.996804	+	0.0798810i	$0.0254540\pi$
$977$			4.99368i			0.159762i	−0.996804	+	0.0798810i	$0.974546\pi$
$978$		0			0
$979$	28.2573			0.903106
$980$	−12.7966	+	7.30395i	−0.408773	+	0.233316i
$981$		0			0
$982$		−	1.28782i		−	0.0410960i
$983$			40.9361i			1.30566i	0.757505	+	0.652830i	$0.226418\pi$
$983$			40.9361i			1.30566i	−0.757505	+	0.652830i	$0.773582\pi$
$984$		0			0
$985$	−15.3597	−	26.9105i	−0.489402	−	0.857439i
$986$	5.18739			0.165200
$987$		0			0
$988$		−	8.91840i		−	0.283732i
$989$	−5.08297			−0.161629
$990$		0			0
$991$	−14.3877			−0.457039			−0.228520	−	0.973539i	$-0.573388\pi$
$991$	−14.3877			−0.457039			−0.228520	+	0.973539i	$0.573388\pi$
$992$			15.8551i			0.503400i
$993$		0			0
$994$	3.65219			0.115841
$995$	51.6112	−	29.4582i	1.63618	−	0.933887i
$996$		0			0
$997$		−	17.9495i		−	0.568467i	−0.958755	−	0.284233i	$-0.908261\pi$
$997$		−	17.9495i		−	0.568467i	0.958755	−	0.284233i	$-0.0917391\pi$
$998$			2.84688i			0.0901163i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.c.g.514.8		14
3.2	odd	2		285.2.c.b.229.7	✓	14
5.2	odd	4		4275.2.a.bw.1.3		7
5.3	odd	4		4275.2.a.bv.1.5		7
5.4	even	2	inner	855.2.c.g.514.7		14
15.2	even	4		1425.2.a.y.1.5		7
15.8	even	4		1425.2.a.z.1.3		7
15.14	odd	2		285.2.c.b.229.8	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.c.b.229.7	✓	14	3.2	odd	2
285.2.c.b.229.8	yes	14	15.14	odd	2
855.2.c.g.514.7		14	5.4	even	2	inner
855.2.c.g.514.8		14	1.1	even	1	trivial
1425.2.a.y.1.5		7	15.2	even	4
1425.2.a.z.1.3		7	15.8	even	4
4275.2.a.bv.1.5		7	5.3	odd	4
4275.2.a.bw.1.3		7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.184902i q^{2} +1.96581 q^{4} +(-1.94200 + 1.10844i) q^{5} -1.90997i q^{7} +0.733287i q^{8} +(-0.204953 - 0.359080i) q^{10} +3.94075 q^{11} +4.53675i q^{13} +0.353158 q^{14} +3.79604 q^{16} -4.68488i q^{17} -1.00000 q^{19} +(-3.81761 + 2.17898i) q^{20} +0.728653i q^{22} +6.18360i q^{23} +(2.54273 - 4.30517i) q^{25} -0.838856 q^{26} -3.75465i q^{28} +5.98837 q^{29} +7.31166 q^{31} +2.16847i q^{32} +0.866244 q^{34} +(2.11709 + 3.70917i) q^{35} +8.07490i q^{37} -0.184902i q^{38} +(-0.812803 - 1.42404i) q^{40} -0.0567471 q^{41} +0.822008i q^{43} +7.74677 q^{44} -1.14336 q^{46} -7.50487i q^{47} +3.35200 q^{49} +(0.796036 + 0.470156i) q^{50} +8.91840i q^{52} -1.28799i q^{53} +(-7.65293 + 4.36808i) q^{55} +1.40056 q^{56} +1.10726i q^{58} -8.28180 q^{59} -11.3330 q^{61} +1.35194i q^{62} +7.19112 q^{64} +(-5.02871 - 8.81038i) q^{65} +10.3415i q^{67} -9.20959i q^{68} +(-0.685833 + 0.391454i) q^{70} +10.3415 q^{71} -10.0984i q^{73} -1.49307 q^{74} -1.96581 q^{76} -7.52672i q^{77} -4.12580 q^{79} +(-7.37190 + 4.20767i) q^{80} -0.0104927i q^{82} +11.6295i q^{83} +(5.19290 + 9.09804i) q^{85} -0.151991 q^{86} +2.88970i q^{88} +7.17054 q^{89} +8.66508 q^{91} +12.1558i q^{92} +1.38767 q^{94} +(1.94200 - 1.10844i) q^{95} -2.70038i q^{97} +0.619793i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 22 q^{4} - 2 q^{5} + 2 q^{10} + 8 q^{11} - 8 q^{14} + 38 q^{16} - 14 q^{19} - 12 q^{20} - 4 q^{25} + 40 q^{26} - 12 q^{29} + 8 q^{31} - 4 q^{34} + 14 q^{35} + 18 q^{40} - 4 q^{41} - 64 q^{44} - 8 q^{46}+ \cdots + 2 q^{95}+O(q^{100}) \) 14 * q - 22 * q^4 - 2 * q^5 + 2 * q^10 + 8 * q^11 - 8 * q^14 + 38 * q^16 - 14 * q^19 - 12 * q^20 - 4 * q^25 + 40 * q^26 - 12 * q^29 + 8 * q^31 - 4 * q^34 + 14 * q^35 + 18 * q^40 - 4 * q^41 - 64 * q^44 - 8 * q^46 - 34 * q^49 - 4 * q^50 - 2 * q^55 + 44 * q^56 - 36 * q^59 + 24 * q^61 - 22 * q^64 + 12 * q^65 - 60 * q^70 + 36 * q^71 + 12 * q^74 + 22 * q^76 + 8 * q^79 - 36 * q^80 - 18 * q^85 + 92 * q^86 - 16 * q^89 + 24 * q^91 + 40 * q^94 + 2 * q^95

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