LMFDB - Embedded newform 1600.2.j.d.143.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(143,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("1600.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.j (of order $4$, degree $2$, not 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.9
Root			$-0.480367 + 1.33013i$ of defining polynomial
Character	$\chi$	$=$	1600.143
Dual form			1600.2.j.d.1007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.85601i q^{3} +(-0.458895 + 0.458895i) q^{7} -5.15678 q^{9} +O(q^{10})$	$q+2.85601i q^{3} +(-0.458895 + 0.458895i) q^{7} -5.15678 q^{9} +(0.492763 - 0.492763i) q^{11} -4.52109 q^{13} +(3.12823 - 3.12823i) q^{17} +(-4.04508 + 4.04508i) q^{19} +(-1.31061 - 1.31061i) q^{21} +(-1.80660 - 1.80660i) q^{23} -6.15978i q^{27} +(-3.83926 - 3.83926i) q^{29} +0.139949i q^{31} +(1.40733 + 1.40733i) q^{33} -5.84330 q^{37} -12.9123i q^{39} -4.55648i q^{41} -7.49928 q^{43} +(-4.14073 - 4.14073i) q^{47} +6.57883i q^{49} +(8.93426 + 8.93426i) q^{51} -2.75773i q^{53} +(-11.5528 - 11.5528i) q^{57} +(3.62521 + 3.62521i) q^{59} +(3.72781 - 3.72781i) q^{61} +(2.36642 - 2.36642i) q^{63} +3.32677 q^{67} +(5.15965 - 5.15965i) q^{69} -1.37056 q^{71} +(2.55028 - 2.55028i) q^{73} +0.452252i q^{77} +3.86426 q^{79} +2.12204 q^{81} +14.4698i q^{83} +(10.9650 - 10.9650i) q^{87} -3.35011 q^{89} +(2.07470 - 2.07470i) q^{91} -0.399696 q^{93} +(4.95582 - 4.95582i) q^{97} +(-2.54107 + 2.54107i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{7} - 10 q^{9}+O(q^{10}) $ 18 * q + 2 * q^7 - 10 * q^9	$ 18 q + 2 q^{7} - 10 q^{9} + 2 q^{11} + 6 q^{17} - 2 q^{19} - 16 q^{21} - 2 q^{23} - 14 q^{29} + 8 q^{33} - 8 q^{37} - 44 q^{43} - 38 q^{47} - 8 q^{51} - 24 q^{57} + 10 q^{59} + 14 q^{61} + 6 q^{63} + 12 q^{67} + 32 q^{69} - 24 q^{71} - 14 q^{73} - 16 q^{79} + 2 q^{81} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 18 q^{97} + 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^7 - 10 * q^9 + 2 * q^11 + 6 * q^17 - 2 * q^19 - 16 * q^21 - 2 * q^23 - 14 * q^29 + 8 * q^33 - 8 * q^37 - 44 * q^43 - 38 * q^47 - 8 * q^51 - 24 * q^57 + 10 * q^59 + 14 * q^61 + 6 * q^63 + 12 * q^67 + 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^79 + 2 * q^81 + 24 * q^87 - 12 * q^89 - 16 * q^93 - 18 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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			0
$2$		0			0
$3$			2.85601i			1.64892i	0.565923	+	0.824458i	$0.308520\pi$
$3$			2.85601i			1.64892i	−0.565923	+	0.824458i	$0.691480\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.458895	+	0.458895i	−0.173446	+	0.173446i	−0.788491	−	0.615046i	$-0.789138\pi$
$7$	−0.458895	+	0.458895i	−0.173446	+	0.173446i	0.615046	+	0.788491i	$0.289138\pi$
$8$		0			0
$9$	−5.15678			−1.71893
$10$		0			0
$11$	0.492763	−	0.492763i	0.148574	−	0.148574i	−0.628907	−	0.777481i	$-0.716497\pi$
$11$	0.492763	−	0.492763i	0.148574	−	0.148574i	0.777481	+	0.628907i	$0.216497\pi$
$12$		0			0
$13$	−4.52109			−1.25393			−0.626963	−	0.779049i	$-0.715702\pi$
$13$	−4.52109			−1.25393			−0.626963	+	0.779049i	$0.715702\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.12823	−	3.12823i	0.758708	−	0.758708i	−0.217379	−	0.976087i	$-0.569751\pi$
$17$	3.12823	−	3.12823i	0.758708	−	0.758708i	0.976087	+	0.217379i	$0.0697508\pi$
$18$		0			0
$19$	−4.04508	+	4.04508i	−0.928005	+	0.928005i	−0.997577	−	0.0695721i	$-0.977837\pi$
$19$	−4.04508	+	4.04508i	−0.928005	+	0.928005i	0.0695721	+	0.997577i	$0.477837\pi$
$20$		0			0
$21$	−1.31061	−	1.31061i	−0.285998	−	0.285998i
$22$		0			0
$23$	−1.80660	−	1.80660i	−0.376701	−	0.376701i	0.493209	−	0.869911i	$-0.335824\pi$
$23$	−1.80660	−	1.80660i	−0.376701	−	0.376701i	−0.869911	+	0.493209i	$0.835824\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	6.15978i		−	1.18545i
$28$		0			0
$29$	−3.83926	−	3.83926i	−0.712932	−	0.712932i	0.254215	−	0.967148i	$-0.418183\pi$
$29$	−3.83926	−	3.83926i	−0.712932	−	0.712932i	−0.967148	+	0.254215i	$0.918183\pi$
$30$		0			0
$31$			0.139949i			0.0251356i	0.999921	+	0.0125678i	$0.00400057\pi$
$31$			0.139949i			0.0251356i	−0.999921	+	0.0125678i	$0.995999\pi$
$32$		0			0
$33$	1.40733	+	1.40733i	0.244985	+	0.244985i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.84330			−0.960633			−0.480317	−	0.877095i	$-0.659478\pi$
$37$	−5.84330			−0.960633			−0.480317	+	0.877095i	$0.659478\pi$
$38$		0			0
$39$		−	12.9123i		−	2.06762i
$40$		0			0
$41$		−	4.55648i		−	0.711602i	−0.934562	−	0.355801i	$-0.884208\pi$
$41$		−	4.55648i		−	0.711602i	0.934562	−	0.355801i	$-0.115792\pi$
$42$		0			0
$43$	−7.49928			−1.14363			−0.571815	−	0.820383i	$-0.693760\pi$
$43$	−7.49928			−1.14363			−0.571815	+	0.820383i	$0.693760\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.14073	−	4.14073i	−0.603987	−	0.603987i	0.337381	−	0.941368i	$-0.390459\pi$
$47$	−4.14073	−	4.14073i	−0.603987	−	0.603987i	−0.941368	+	0.337381i	$0.890459\pi$
$48$		0			0
$49$			6.57883i			0.939833i
$50$		0			0
$51$	8.93426	+	8.93426i	1.25105	+	1.25105i
$52$		0			0
$53$		−	2.75773i		−	0.378803i	−0.981900	−	0.189402i	$-0.939345\pi$
$53$		−	2.75773i		−	0.378803i	0.981900	−	0.189402i	$-0.0606548\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−11.5528	−	11.5528i	−1.53020	−	1.53020i
$58$		0			0
$59$	3.62521	+	3.62521i	0.471962	+	0.471962i	0.902549	−	0.430587i	$-0.141694\pi$
$59$	3.62521	+	3.62521i	0.471962	+	0.471962i	−0.430587	+	0.902549i	$0.641694\pi$
$60$		0			0
$61$	3.72781	−	3.72781i	0.477298	−	0.477298i	−0.426969	−	0.904266i	$-0.640419\pi$
$61$	3.72781	−	3.72781i	0.477298	−	0.477298i	0.904266	+	0.426969i	$0.140419\pi$
$62$		0			0
$63$	2.36642	−	2.36642i	0.298141	−	0.298141i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.32677			0.406430			0.203215	−	0.979134i	$-0.434861\pi$
$67$	3.32677			0.406430			0.203215	+	0.979134i	$0.434861\pi$
$68$		0			0
$69$	5.15965	−	5.15965i	0.621149	−	0.621149i
$70$		0			0
$71$	−1.37056			−0.162655			−0.0813275	−	0.996687i	$-0.525916\pi$
$71$	−1.37056			−0.162655			−0.0813275	+	0.996687i	$0.525916\pi$
$72$		0			0
$73$	2.55028	−	2.55028i	0.298488	−	0.298488i	−0.541933	−	0.840422i	$-0.682307\pi$
$73$	2.55028	−	2.55028i	0.298488	−	0.298488i	0.840422	+	0.541933i	$0.182307\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			0.452252i			0.0515389i
$78$		0			0
$79$	3.86426			0.434763			0.217382	−	0.976087i	$-0.430248\pi$
$79$	3.86426			0.434763			0.217382	+	0.976087i	$0.430248\pi$
$80$		0			0
$81$	2.12204			0.235782
$82$		0			0
$83$			14.4698i			1.58827i	0.607744	+	0.794133i	$0.292075\pi$
$83$			14.4698i			1.58827i	−0.607744	+	0.794133i	$0.707925\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	10.9650	−	10.9650i	1.17557	−	1.17557i
$88$		0			0
$89$	−3.35011			−0.355111			−0.177556	−	0.984111i	$-0.556819\pi$
$89$	−3.35011			−0.355111			−0.177556	+	0.984111i	$0.556819\pi$
$90$		0			0
$91$	2.07470	−	2.07470i	0.217488	−	0.217488i
$92$		0			0
$93$	−0.399696			−0.0414466
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.95582	−	4.95582i	0.503187	−	0.503187i	−0.409240	−	0.912427i	$-0.634206\pi$
$97$	4.95582	−	4.95582i	0.503187	−	0.503187i	0.912427	+	0.409240i	$0.134206\pi$
$98$		0			0
$99$	−2.54107	+	2.54107i	−0.255387	+	0.255387i
$100$		0			0
$101$	−1.84536	−	1.84536i	−0.183621	−	0.183621i	0.609311	−	0.792931i	$-0.291446\pi$
$101$	−1.84536	−	1.84536i	−0.183621	−	0.183621i	−0.792931	+	0.609311i	$0.791446\pi$
$102$		0			0
$103$	−11.6655	−	11.6655i	−1.14944	−	1.14944i	−0.986664	−	0.162773i	$-0.947956\pi$
$103$	−11.6655	−	11.6655i	−1.14944	−	1.14944i	−0.162773	−	0.986664i	$-0.552044\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			15.3106i			1.48013i	0.672534	+	0.740067i	$0.265206\pi$
$107$			15.3106i			1.48013i	−0.672534	+	0.740067i	$0.734794\pi$
$108$		0			0
$109$	12.4798	+	12.4798i	1.19535	+	1.19535i	0.975544	+	0.219803i	$0.0705416\pi$
$109$	12.4798	+	12.4798i	1.19535	+	1.19535i	0.219803	+	0.975544i	$0.429458\pi$
$110$		0			0
$111$		−	16.6885i		−	1.58400i
$112$		0			0
$113$	−2.53557	−	2.53557i	−0.238526	−	0.238526i	0.577713	−	0.816240i	$-0.303945\pi$
$113$	−2.53557	−	2.53557i	−0.238526	−	0.238526i	−0.816240	+	0.577713i	$0.803945\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	23.3143			2.15541
$118$		0			0
$119$			2.87106i			0.263189i
$120$		0			0
$121$			10.5144i			0.955852i
$122$		0			0
$123$	13.0133			1.17337
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−0.615790	−	0.615790i	−0.0546426	−	0.0546426i	0.679257	−	0.733900i	$-0.262302\pi$
$127$	−0.615790	−	0.615790i	−0.0546426	−	0.0546426i	−0.733900	+	0.679257i	$0.762302\pi$
$128$		0			0
$129$		−	21.4180i		−	1.88575i
$130$		0			0
$131$	−9.55413	−	9.55413i	−0.834748	−	0.834748i	0.153414	−	0.988162i	$-0.450973\pi$
$131$	−9.55413	−	9.55413i	−0.834748	−	0.834748i	−0.988162	+	0.153414i	$0.950973\pi$
$132$		0			0
$133$		−	3.71253i		−	0.321917i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.70277	+	3.70277i	0.316349	+	0.316349i	0.847363	−	0.531014i	$-0.178189\pi$
$137$	3.70277	+	3.70277i	0.316349	+	0.316349i	−0.531014	+	0.847363i	$0.678189\pi$
$138$		0			0
$139$	−5.46761	−	5.46761i	−0.463756	−	0.463756i	0.436128	−	0.899885i	$-0.356349\pi$
$139$	−5.46761	−	5.46761i	−0.463756	−	0.463756i	−0.899885	+	0.436128i	$0.856349\pi$
$140$		0			0
$141$	11.8260	−	11.8260i	0.995925	−	0.995925i
$142$		0			0
$143$	−2.22783	+	2.22783i	−0.186300	+	0.186300i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−18.7892			−1.54971
$148$		0			0
$149$	4.21561	−	4.21561i	0.345356	−	0.345356i	−0.513021	−	0.858376i	$-0.671474\pi$
$149$	4.21561	−	4.21561i	0.345356	−	0.345356i	0.858376	+	0.513021i	$0.171474\pi$
$150$		0			0
$151$	−12.4417			−1.01249			−0.506244	−	0.862390i	$-0.668966\pi$
$151$	−12.4417			−1.01249			−0.506244	+	0.862390i	$0.668966\pi$
$152$		0			0
$153$	−16.1316	+	16.1316i	−1.30416	+	1.30416i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			7.50500i			0.598964i	0.954102	+	0.299482i	$0.0968138\pi$
$157$			7.50500i			0.598964i	−0.954102	+	0.299482i	$0.903186\pi$
$158$		0			0
$159$	7.87609			0.624615
$160$		0			0
$161$	1.65807			0.130675
$162$		0			0
$163$		−	23.7284i		−	1.85855i	−0.369383	−	0.929277i	$-0.620431\pi$
$163$		−	23.7284i		−	1.85855i	0.369383	−	0.929277i	$-0.379569\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.402976	+	0.402976i	−0.0311832	+	0.0311832i	−0.722526	−	0.691343i	$-0.757019\pi$
$167$	−0.402976	+	0.402976i	−0.0311832	+	0.0311832i	0.691343	+	0.722526i	$0.257019\pi$
$168$		0			0
$169$	7.44028			0.572330
$170$		0			0
$171$	20.8596	−	20.8596i	1.59517	−	1.59517i
$172$		0			0
$173$	15.4500			1.17464			0.587320	−	0.809355i	$-0.300183\pi$
$173$	15.4500			1.17464			0.587320	+	0.809355i	$0.300183\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.3536	+	10.3536i	−0.778225	+	0.778225i
$178$		0			0
$179$	−5.20444	+	5.20444i	−0.388998	+	0.388998i	−0.874330	−	0.485332i	$-0.838699\pi$
$179$	−5.20444	+	5.20444i	−0.388998	+	0.388998i	0.485332	+	0.874330i	$0.338699\pi$
$180$		0			0
$181$	−9.08925	−	9.08925i	−0.675599	−	0.675599i	0.283402	−	0.959001i	$-0.408537\pi$
$181$	−9.08925	−	9.08925i	−0.675599	−	0.675599i	−0.959001	+	0.283402i	$0.908537\pi$
$182$		0			0
$183$	10.6467	+	10.6467i	0.787024	+	0.787024i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	3.08295i		−	0.225448i
$188$		0			0
$189$	2.82669	+	2.82669i	0.205611	+	0.205611i
$190$		0			0
$191$			15.1075i			1.09314i	0.837413	+	0.546571i	$0.184067\pi$
$191$			15.1075i			1.09314i	−0.837413	+	0.546571i	$0.815933\pi$
$192$		0			0
$193$	−4.19166	−	4.19166i	−0.301722	−	0.301722i	0.539965	−	0.841687i	$-0.318437\pi$
$193$	−4.19166	−	4.19166i	−0.301722	−	0.301722i	−0.841687	+	0.539965i	$0.818437\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.03184			0.287256			0.143628	−	0.989632i	$-0.454123\pi$
$197$	4.03184			0.287256			0.143628	+	0.989632i	$0.454123\pi$
$198$		0			0
$199$		−	5.43055i		−	0.384961i	−0.981301	−	0.192481i	$-0.938347\pi$
$199$		−	5.43055i		−	0.384961i	0.981301	−	0.192481i	$-0.0616533\pi$
$200$		0			0
$201$			9.50129i			0.670169i
$202$		0			0
$203$	3.52363			0.247310
$204$		0			0
$205$		0			0
$206$		0			0
$207$	9.31622	+	9.31622i	0.647522	+	0.647522i
$208$		0			0
$209$			3.98653i			0.275754i
$210$		0			0
$211$	−3.23020	−	3.23020i	−0.222376	−	0.222376i	0.587122	−	0.809498i	$-0.300261\pi$
$211$	−3.23020	−	3.23020i	−0.222376	−	0.222376i	−0.809498	+	0.587122i	$0.800261\pi$
$212$		0			0
$213$		−	3.91432i		−	0.268205i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.0642220	−	0.0642220i	−0.00435967	−	0.00435967i
$218$		0			0
$219$	7.28363	+	7.28363i	0.492182	+	0.492182i
$220$		0			0
$221$	−14.1430	+	14.1430i	−0.951363	+	0.951363i
$222$		0			0
$223$	−8.17319	+	8.17319i	−0.547317	+	0.547317i	−0.925664	−	0.378347i	$-0.876493\pi$
$223$	−8.17319	+	8.17319i	−0.547317	+	0.547317i	0.378347	+	0.925664i	$0.376493\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.54068			−0.102258			−0.0511292	−	0.998692i	$-0.516282\pi$
$227$	−1.54068			−0.102258			−0.0511292	+	0.998692i	$0.516282\pi$
$228$		0			0
$229$	−17.5646	+	17.5646i	−1.16070	+	1.16070i	−0.176378	+	0.984322i	$0.556438\pi$
$229$	−17.5646	+	17.5646i	−1.16070	+	1.16070i	−0.984322	+	0.176378i	$0.943562\pi$
$230$		0			0
$231$	−1.29164			−0.0849834
$232$		0			0
$233$	−9.99018	+	9.99018i	−0.654479	+	0.654479i	−0.954068	−	0.299590i	$-0.903150\pi$
$233$	−9.99018	+	9.99018i	−0.654479	+	0.654479i	0.299590	+	0.954068i	$0.403150\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			11.0364i			0.716889i
$238$		0			0
$239$	−26.2762			−1.69967			−0.849833	−	0.527052i	$-0.823297\pi$
$239$	−26.2762			−1.69967			−0.849833	+	0.527052i	$0.823297\pi$
$240$		0			0
$241$	−0.113242			−0.00729456			−0.00364728	−	0.999993i	$-0.501161\pi$
$241$	−0.113242			−0.00729456			−0.00364728	+	0.999993i	$0.501161\pi$
$242$		0			0
$243$		−	12.4188i		−	0.796665i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	18.2882	−	18.2882i	1.16365	−	1.16365i
$248$		0			0
$249$	−41.3258			−2.61892
$250$		0			0
$251$	−19.2220	+	19.2220i	−1.21328	+	1.21328i	−0.243339	+	0.969941i	$0.578243\pi$
$251$	−19.2220	+	19.2220i	−1.21328	+	1.21328i	−0.969941	+	0.243339i	$0.921757\pi$
$252$		0			0
$253$	−1.78045			−0.111936
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.757800	−	0.757800i	0.0472703	−	0.0472703i	−0.683077	−	0.730347i	$-0.739358\pi$
$257$	0.757800	−	0.757800i	0.0472703	−	0.0472703i	0.730347	+	0.683077i	$0.239358\pi$
$258$		0			0
$259$	2.68146	−	2.68146i	0.166618	−	0.166618i
$260$		0			0
$261$	19.7982	+	19.7982i	1.22548	+	1.22548i
$262$		0			0
$263$	5.73017	+	5.73017i	0.353338	+	0.353338i	0.861350	−	0.508012i	$-0.169620\pi$
$263$	5.73017	+	5.73017i	0.353338	+	0.353338i	−0.508012	+	0.861350i	$0.669620\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	9.56795i		−	0.585549i
$268$		0			0
$269$	9.78879	+	9.78879i	0.596833	+	0.596833i	0.939468	−	0.342635i	$-0.111320\pi$
$269$	9.78879	+	9.78879i	0.596833	+	0.596833i	−0.342635	+	0.939468i	$0.611320\pi$
$270$		0			0
$271$			4.10159i			0.249154i	0.992210	+	0.124577i	$0.0397574\pi$
$271$			4.10159i			0.249154i	−0.992210	+	0.124577i	$0.960243\pi$
$272$		0			0
$273$	5.92537	+	5.92537i	0.358620	+	0.358620i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−24.6755			−1.48261			−0.741305	−	0.671169i	$-0.765793\pi$
$277$	−24.6755			−1.48261			−0.741305	+	0.671169i	$0.765793\pi$
$278$		0			0
$279$		−	0.721688i		−	0.0432063i
$280$		0			0
$281$			23.6688i			1.41196i	0.708230	+	0.705981i	$0.249494\pi$
$281$			23.6688i			1.41196i	−0.708230	+	0.705981i	$0.750506\pi$
$282$		0			0
$283$	13.0492			0.775694			0.387847	−	0.921724i	$-0.373219\pi$
$283$	13.0492			0.775694			0.387847	+	0.921724i	$0.373219\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.09094	+	2.09094i	0.123424	+	0.123424i
$288$		0			0
$289$		−	2.57168i		−	0.151275i
$290$		0			0
$291$	14.1539	+	14.1539i	0.829714	+	0.829714i
$292$		0			0
$293$			31.6731i			1.85036i	0.379526	+	0.925181i	$0.376087\pi$
$293$			31.6731i			1.85036i	−0.379526	+	0.925181i	$0.623913\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.03531	−	3.03531i	−0.176127	−	0.176127i
$298$		0			0
$299$	8.16779	+	8.16779i	0.472355	+	0.472355i
$300$		0			0
$301$	3.44138	−	3.44138i	0.198358	−	0.198358i
$302$		0			0
$303$	5.27037	−	5.27037i	0.302775	−	0.302775i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−27.3597			−1.56150			−0.780751	−	0.624843i	$-0.785163\pi$
$307$	−27.3597			−1.56150			−0.780751	+	0.624843i	$0.785163\pi$
$308$		0			0
$309$	33.3168	−	33.3168i	1.89532	−	1.89532i
$310$		0			0
$311$	15.8076			0.896368			0.448184	−	0.893941i	$-0.352071\pi$
$311$	15.8076			0.896368			0.448184	+	0.893941i	$0.352071\pi$
$312$		0			0
$313$	13.8388	−	13.8388i	0.782217	−	0.782217i	−0.197988	−	0.980205i	$-0.563441\pi$
$313$	13.8388	−	13.8388i	0.782217	−	0.782217i	0.980205	+	0.197988i	$0.0634406\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	35.0092i		−	1.96631i	−0.182766	−	0.983156i	$-0.558505\pi$
$317$		−	35.0092i		−	1.96631i	0.182766	−	0.983156i	$-0.441495\pi$
$318$		0			0
$319$	−3.78369			−0.211846
$320$		0			0
$321$	−43.7272			−2.44062
$322$		0			0
$323$			25.3079i			1.40817i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−35.6424	+	35.6424i	−1.97103	+	1.97103i
$328$		0			0
$329$	3.80032			0.209518
$330$		0			0
$331$	−16.8212	+	16.8212i	−0.924578	+	0.924578i	−0.997349	−	0.0727709i	$-0.976816\pi$
$331$	−16.8212	+	16.8212i	−0.924578	+	0.924578i	0.0727709	+	0.997349i	$0.476816\pi$
$332$		0			0
$333$	30.1326			1.65126
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−14.4984	+	14.4984i	−0.789777	+	0.789777i	−0.981457	−	0.191680i	$-0.938606\pi$
$337$	−14.4984	+	14.4984i	−0.789777	+	0.789777i	0.191680	+	0.981457i	$0.438606\pi$
$338$		0			0
$339$	7.24160	−	7.24160i	0.393310	−	0.393310i
$340$		0			0
$341$	0.0689618	+	0.0689618i	0.00373449	+	0.00373449i
$342$		0			0
$343$	−6.23125	−	6.23125i	−0.336456	−	0.336456i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			16.7705i			0.900286i	0.892956	+	0.450143i	$0.148627\pi$
$347$			16.7705i			0.900286i	−0.892956	+	0.450143i	$0.851373\pi$
$348$		0			0
$349$	1.86337	+	1.86337i	0.0997439	+	0.0997439i	0.755218	−	0.655474i	$-0.227531\pi$
$349$	1.86337	+	1.86337i	0.0997439	+	0.0997439i	−0.655474	+	0.755218i	$0.727531\pi$
$350$		0			0
$351$			27.8489i			1.48647i
$352$		0			0
$353$	−24.1362	−	24.1362i	−1.28464	−	1.28464i	−0.937998	−	0.346642i	$-0.887322\pi$
$353$	−24.1362	−	24.1362i	−1.28464	−	1.28464i	−0.346642	−	0.937998i	$-0.612678\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−8.19976			−0.433978
$358$		0			0
$359$			12.2500i			0.646532i	0.946308	+	0.323266i	$0.104781\pi$
$359$			12.2500i			0.646532i	−0.946308	+	0.323266i	$0.895219\pi$
$360$		0			0
$361$		−	13.7253i		−	0.722386i
$362$		0			0
$363$	−30.0291			−1.57612
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.71307	+	2.71307i	0.141621	+	0.141621i	0.774363	−	0.632742i	$-0.218071\pi$
$367$	2.71307	+	2.71307i	0.141621	+	0.141621i	−0.632742	+	0.774363i	$0.718071\pi$
$368$		0			0
$369$			23.4967i			1.22319i
$370$		0			0
$371$	1.26551	+	1.26551i	0.0657018	+	0.0657018i
$372$		0			0
$373$		−	16.4846i		−	0.853541i	−0.904360	−	0.426771i	$-0.859651\pi$
$373$		−	16.4846i		−	0.853541i	0.904360	−	0.426771i	$-0.140349\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.3576	+	17.3576i	0.893964	+	0.893964i
$378$		0			0
$379$	13.7716	+	13.7716i	0.707401	+	0.707401i	0.965988	−	0.258587i	$-0.0832568\pi$
$379$	13.7716	+	13.7716i	0.707401	+	0.707401i	−0.258587	+	0.965988i	$0.583257\pi$
$380$		0			0
$381$	1.75870	−	1.75870i	0.0901011	−	0.0901011i
$382$		0			0
$383$	11.5530	−	11.5530i	0.590332	−	0.590332i	−0.347389	−	0.937721i	$-0.612932\pi$
$383$	11.5530	−	11.5530i	0.590332	−	0.590332i	0.937721	+	0.347389i	$0.112932\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	38.6722			1.96582
$388$		0			0
$389$	−15.7728	+	15.7728i	−0.799712	+	0.799712i	−0.983050	−	0.183338i	$-0.941310\pi$
$389$	−15.7728	+	15.7728i	−0.799712	+	0.799712i	0.183338	+	0.983050i	$0.441310\pi$
$390$		0			0
$391$	−11.3029			−0.571612
$392$		0			0
$393$	27.2867	−	27.2867i	1.37643	−	1.37643i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			29.9558i			1.50344i	0.659483	+	0.751720i	$0.270775\pi$
$397$			29.9558i			1.50344i	−0.659483	+	0.751720i	$0.729225\pi$
$398$		0			0
$399$	10.6030			0.530815
$400$		0			0
$401$	19.9241			0.994963			0.497481	−	0.867475i	$-0.334258\pi$
$401$	19.9241			0.994963			0.497481	+	0.867475i	$0.334258\pi$
$402$		0			0
$403$		−	0.632724i		−	0.0315182i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.87936	+	2.87936i	−0.142725	+	0.142725i
$408$		0			0
$409$	5.89856			0.291665			0.145832	−	0.989309i	$-0.453414\pi$
$409$	5.89856			0.291665			0.145832	+	0.989309i	$0.453414\pi$
$410$		0			0
$411$	−10.5751	+	10.5751i	−0.521634	+	0.521634i
$412$		0			0
$413$	−3.32717			−0.163720
$414$		0			0
$415$		0			0
$416$		0			0
$417$	15.6155	−	15.6155i	0.764696	−	0.764696i
$418$		0			0
$419$	−8.24430	+	8.24430i	−0.402760	+	0.402760i	−0.879205	−	0.476444i	$-0.841925\pi$
$419$	−8.24430	+	8.24430i	−0.402760	+	0.402760i	0.476444	+	0.879205i	$0.341925\pi$
$420$		0			0
$421$	−17.1776	−	17.1776i	−0.837184	−	0.837184i	0.151304	−	0.988487i	$-0.451653\pi$
$421$	−17.1776	−	17.1776i	−0.837184	−	0.837184i	−0.988487	+	0.151304i	$0.951653\pi$
$422$		0			0
$423$	21.3528	+	21.3528i	1.03821	+	1.03821i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			3.42135i			0.165571i
$428$		0			0
$429$	−6.36269	−	6.36269i	−0.307194	−	0.307194i
$430$		0			0
$431$		−	32.1769i		−	1.54990i	−0.632020	−	0.774952i	$-0.717774\pi$
$431$		−	32.1769i		−	1.54990i	0.632020	−	0.774952i	$-0.282226\pi$
$432$		0			0
$433$	20.3383	+	20.3383i	0.977396	+	0.977396i	0.999750	−	0.0223540i	$-0.00711609\pi$
$433$	20.3383	+	20.3383i	0.977396	+	0.977396i	−0.0223540	+	0.999750i	$0.507116\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	14.6156			0.699161
$438$		0			0
$439$		−	35.4180i		−	1.69041i	−0.534444	−	0.845204i	$-0.679479\pi$
$439$		−	35.4180i		−	1.69041i	0.534444	−	0.845204i	$-0.320521\pi$
$440$		0			0
$441$		−	33.9256i		−	1.61550i
$442$		0			0
$443$	−3.03787			−0.144333			−0.0721667	−	0.997393i	$-0.522991\pi$
$443$	−3.03787			−0.144333			−0.0721667	+	0.997393i	$0.522991\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.0398	+	12.0398i	0.569463	+	0.569463i
$448$		0			0
$449$			8.65559i			0.408483i	0.978921	+	0.204241i	$0.0654727\pi$
$449$			8.65559i			0.408483i	−0.978921	+	0.204241i	$0.934527\pi$
$450$		0			0
$451$	−2.24526	−	2.24526i	−0.105725	−	0.105725i
$452$		0			0
$453$		−	35.5335i		−	1.66951i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	13.5575	+	13.5575i	0.634193	+	0.634193i	0.949117	−	0.314924i	$-0.101979\pi$
$457$	13.5575	+	13.5575i	0.634193	+	0.634193i	−0.314924	+	0.949117i	$0.601979\pi$
$458$		0			0
$459$	−19.2692	−	19.2692i	−0.899411	−	0.899411i
$460$		0			0
$461$	−1.19682	+	1.19682i	−0.0557416	+	0.0557416i	−0.734428	−	0.678687i	$-0.762550\pi$
$461$	−1.19682	+	1.19682i	−0.0557416	+	0.0557416i	0.678687	+	0.734428i	$0.262550\pi$
$462$		0			0
$463$	−21.1815	+	21.1815i	−0.984390	+	0.984390i	−0.999880	−	0.0154904i	$-0.995069\pi$
$463$	−21.1815	+	21.1815i	−0.984390	+	0.984390i	0.0154904	+	0.999880i	$0.495069\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	24.8448			1.14968			0.574840	−	0.818266i	$-0.305064\pi$
$467$	24.8448			1.14968			0.574840	+	0.818266i	$0.305064\pi$
$468$		0			0
$469$	−1.52664	+	1.52664i	−0.0704936	+	0.0704936i
$470$		0			0
$471$	−21.4343			−0.987642
$472$		0			0
$473$	−3.69537	+	3.69537i	−0.169913	+	0.169913i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			14.2210i			0.651135i
$478$		0			0
$479$	23.5766			1.07724			0.538621	−	0.842548i	$-0.318946\pi$
$479$	23.5766			1.07724			0.538621	+	0.842548i	$0.318946\pi$
$480$		0			0
$481$	26.4181			1.20456
$482$		0			0
$483$			4.73547i			0.215471i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.63011	+	2.63011i	−0.119182	+	0.119182i	−0.764182	−	0.645001i	$-0.776857\pi$
$487$	−2.63011	+	2.63011i	−0.119182	+	0.119182i	0.645001	+	0.764182i	$0.276857\pi$
$488$		0			0
$489$	67.7686			3.06460
$490$		0			0
$491$	18.6899	−	18.6899i	0.843465	−	0.843465i	−0.145843	−	0.989308i	$-0.546589\pi$
$491$	18.6899	−	18.6899i	0.843465	−	0.843465i	0.989308	+	0.145843i	$0.0465894\pi$
$492$		0			0
$493$	−24.0202			−1.08182
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.628940	−	0.628940i	0.0282118	−	0.0282118i
$498$		0			0
$499$	9.69342	−	9.69342i	0.433937	−	0.433937i	−0.456028	−	0.889965i	$-0.650728\pi$
$499$	9.69342	−	9.69342i	0.433937	−	0.433937i	0.889965	+	0.456028i	$0.150728\pi$
$500$		0			0
$501$	−1.15090	−	1.15090i	−0.0514185	−	0.0514185i
$502$		0			0
$503$	−13.0434	−	13.0434i	−0.581577	−	0.581577i	0.353759	−	0.935336i	$-0.384903\pi$
$503$	−13.0434	−	13.0434i	−0.581577	−	0.581577i	−0.935336	+	0.353759i	$0.884903\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			21.2495i			0.943724i
$508$		0			0
$509$	−25.8539	−	25.8539i	−1.14595	−	1.14595i	−0.987341	−	0.158611i	$-0.949298\pi$
$509$	−25.8539	−	25.8539i	−1.14595	−	1.14595i	−0.158611	−	0.987341i	$-0.550702\pi$
$510$		0			0
$511$			2.34062i			0.103543i
$512$		0			0
$513$	24.9168	+	24.9168i	1.10010	+	1.10010i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−4.08080			−0.179473
$518$		0			0
$519$			44.1252i			1.93688i
$520$		0			0
$521$		−	25.0528i		−	1.09758i	−0.835959	−	0.548792i	$-0.815088\pi$
$521$		−	25.0528i		−	1.09758i	0.835959	−	0.548792i	$-0.184912\pi$
$522$		0			0
$523$	40.3434			1.76410			0.882048	−	0.471160i	$-0.156165\pi$
$523$	40.3434			1.76410			0.882048	+	0.471160i	$0.156165\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.437794	+	0.437794i	0.0190706	+	0.0190706i
$528$		0			0
$529$		−	16.4724i		−	0.716192i
$530$		0			0
$531$	−18.6944	−	18.6944i	−0.811267	−	0.811267i
$532$		0			0
$533$			20.6003i			0.892296i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−14.8639	−	14.8639i	−0.641425	−	0.641425i
$538$		0			0
$539$	3.24180	+	3.24180i	0.139634	+	0.139634i
$540$		0			0
$541$	−24.7446	+	24.7446i	−1.06385	+	1.06385i	−0.0660360	+	0.997817i	$0.521035\pi$
$541$	−24.7446	+	24.7446i	−1.06385	+	1.06385i	−0.997817	+	0.0660360i	$0.978965\pi$
$542$		0			0
$543$	25.9590	−	25.9590i	1.11401	−	1.11401i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	19.0254			0.813465			0.406733	−	0.913547i	$-0.366668\pi$
$547$	19.0254			0.813465			0.406733	+	0.913547i	$0.366668\pi$
$548$		0			0
$549$	−19.2235	+	19.2235i	−0.820440	+	0.820440i
$550$		0			0
$551$	31.0602			1.32321
$552$		0			0
$553$	−1.77329	+	1.77329i	−0.0754079	+	0.0754079i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			30.9517i			1.31146i	0.754993	+	0.655732i	$0.227640\pi$
$557$			30.9517i			1.31146i	−0.754993	+	0.655732i	$0.772360\pi$
$558$		0			0
$559$	33.9050			1.43403
$560$		0			0
$561$	8.80494			0.371745
$562$		0			0
$563$			3.50238i			0.147608i	0.997273	+	0.0738039i	$0.0235139\pi$
$563$			3.50238i			0.147608i	−0.997273	+	0.0738039i	$0.976486\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.973793	+	0.973793i	−0.0408955	+	0.0408955i
$568$		0			0
$569$	−0.525780			−0.0220418			−0.0110209	−	0.999939i	$-0.503508\pi$
$569$	−0.525780			−0.0220418			−0.0110209	+	0.999939i	$0.503508\pi$
$570$		0			0
$571$	11.2487	−	11.2487i	0.470743	−	0.470743i	−0.431412	−	0.902155i	$-0.641984\pi$
$571$	11.2487	−	11.2487i	0.470743	−	0.470743i	0.902155	+	0.431412i	$0.141984\pi$
$572$		0			0
$573$	−43.1472			−1.80250
$574$		0			0
$575$		0			0
$576$		0			0
$577$	2.92884	−	2.92884i	0.121929	−	0.121929i	−0.643509	−	0.765438i	$-0.722522\pi$
$577$	2.92884	−	2.92884i	0.121929	−	0.121929i	0.765438	+	0.643509i	$0.222522\pi$
$578$		0			0
$579$	11.9714	−	11.9714i	0.497515	−	0.497515i
$580$		0			0
$581$	−6.64011	−	6.64011i	−0.275478	−	0.275478i
$582$		0			0
$583$	−1.35891	−	1.35891i	−0.0562801	−	0.0562801i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	23.1574i		−	0.955809i	−0.878412	−	0.477905i	$-0.841396\pi$
$587$		−	23.1574i		−	0.955809i	0.878412	−	0.477905i	$-0.158604\pi$
$588$		0			0
$589$	−0.566106	−	0.566106i	−0.0233260	−	0.0233260i
$590$		0			0
$591$			11.5150i			0.473662i
$592$		0			0
$593$	13.9325	+	13.9325i	0.572141	+	0.572141i	0.932726	−	0.360585i	$-0.117423\pi$
$593$	13.9325	+	13.9325i	0.572141	+	0.572141i	−0.360585	+	0.932726i	$0.617423\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	15.5097			0.634769
$598$		0			0
$599$			33.5311i			1.37004i	0.728523	+	0.685021i	$0.240207\pi$
$599$			33.5311i			1.37004i	−0.728523	+	0.685021i	$0.759793\pi$
$600$		0			0
$601$			19.4164i			0.792011i	0.918248	+	0.396005i	$0.129604\pi$
$601$			19.4164i			0.792011i	−0.918248	+	0.396005i	$0.870396\pi$
$602$		0			0
$603$	−17.1554			−0.698623
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−9.51495	−	9.51495i	−0.386200	−	0.386200i	0.487130	−	0.873330i	$-0.338044\pi$
$607$	−9.51495	−	9.51495i	−0.386200	−	0.386200i	−0.873330	+	0.487130i	$0.838044\pi$
$608$		0			0
$609$			10.0635i			0.407794i
$610$		0			0
$611$	18.7206	+	18.7206i	0.757355	+	0.757355i
$612$		0			0
$613$			9.37947i			0.378833i	0.981897	+	0.189417i	$0.0606597\pi$
$613$			9.37947i			0.378833i	−0.981897	+	0.189417i	$0.939340\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.54768	+	3.54768i	0.142824	+	0.142824i	0.774904	−	0.632079i	$-0.217798\pi$
$617$	3.54768	+	3.54768i	0.142824	+	0.142824i	−0.632079	+	0.774904i	$0.717798\pi$
$618$		0			0
$619$	−24.6158	−	24.6158i	−0.989392	−	0.989392i	0.0105527	−	0.999944i	$-0.496641\pi$
$619$	−24.6158	−	24.6158i	−0.989392	−	0.989392i	−0.999944	+	0.0105527i	$0.996641\pi$
$620$		0			0
$621$	−11.1282	+	11.1282i	−0.446561	+	0.446561i
$622$		0			0
$623$	1.53735	−	1.53735i	0.0615926	−	0.0615926i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−11.3856			−0.454695
$628$		0			0
$629$	−18.2792	+	18.2792i	−0.728840	+	0.728840i
$630$		0			0
$631$	28.8921			1.15018			0.575088	−	0.818092i	$-0.304968\pi$
$631$	28.8921			1.15018			0.575088	+	0.818092i	$0.304968\pi$
$632$		0			0
$633$	9.22547	−	9.22547i	0.366679	−	0.366679i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	29.7435i		−	1.17848i
$638$		0			0
$639$	7.06765			0.279592
$640$		0			0
$641$	−16.6914			−0.659271			−0.329636	−	0.944108i	$-0.606926\pi$
$641$	−16.6914			−0.659271			−0.329636	+	0.944108i	$0.606926\pi$
$642$		0			0
$643$		−	5.22468i		−	0.206041i	−0.994679	−	0.103021i	$-0.967149\pi$
$643$		−	5.22468i		−	0.206041i	0.994679	−	0.103021i	$-0.0328507\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.6797	−	21.6797i	0.852318	−	0.852318i	−0.138100	−	0.990418i	$-0.544100\pi$
$647$	21.6797	−	21.6797i	0.852318	−	0.852318i	0.990418	+	0.138100i	$0.0440996\pi$
$648$		0			0
$649$	3.57273			0.140242
$650$		0			0
$651$	0.183418	−	0.183418i	0.00718874	−	0.00718874i
$652$		0			0
$653$	−22.7642			−0.890833			−0.445417	−	0.895323i	$-0.646944\pi$
$653$	−22.7642			−0.890833			−0.445417	+	0.895323i	$0.646944\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−13.1513	+	13.1513i	−0.513079	+	0.513079i
$658$		0			0
$659$	1.66201	−	1.66201i	0.0647427	−	0.0647427i	−0.673994	−	0.738737i	$-0.735423\pi$
$659$	1.66201	−	1.66201i	0.0647427	−	0.0647427i	0.738737	+	0.673994i	$0.235423\pi$
$660$		0			0
$661$	−5.62818	−	5.62818i	−0.218911	−	0.218911i	0.589129	−	0.808039i	$-0.299471\pi$
$661$	−5.62818	−	5.62818i	−0.218911	−	0.218911i	−0.808039	+	0.589129i	$0.799471\pi$
$662$		0			0
$663$	−40.3926	−	40.3926i	−1.56872	−	1.56872i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			13.8720i			0.537125i
$668$		0			0
$669$	−23.3427	−	23.3427i	−0.902481	−	0.902481i
$670$		0			0
$671$		−	3.67386i		−	0.141828i
$672$		0			0
$673$	−0.278251	−	0.278251i	−0.0107258	−	0.0107258i	0.701724	−	0.712449i	$-0.252414\pi$
$673$	−0.278251	−	0.278251i	−0.0107258	−	0.0107258i	−0.712449	+	0.701724i	$0.752414\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−26.3591			−1.01306			−0.506531	−	0.862222i	$-0.669072\pi$
$677$	−26.3591			−1.01306			−0.506531	+	0.862222i	$0.669072\pi$
$678$		0			0
$679$			4.54840i			0.174551i
$680$		0			0
$681$		−	4.40019i		−	0.168616i
$682$		0			0
$683$	−2.83023			−0.108296			−0.0541479	−	0.998533i	$-0.517244\pi$
$683$	−2.83023			−0.108296			−0.0541479	+	0.998533i	$0.517244\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−50.1646	−	50.1646i	−1.91390	−	1.91390i
$688$		0			0
$689$			12.4679i			0.474991i
$690$		0			0
$691$	−22.1815	−	22.1815i	−0.843825	−	0.843825i	0.145529	−	0.989354i	$-0.453512\pi$
$691$	−22.1815	−	22.1815i	−0.843825	−	0.843825i	−0.989354	+	0.145529i	$0.953512\pi$
$692$		0			0
$693$		−	2.33217i		−	0.0885917i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−14.2537	−	14.2537i	−0.539898	−	0.539898i
$698$		0			0
$699$	−28.5320	−	28.5320i	−1.07918	−	1.07918i
$700$		0			0
$701$	16.2264	−	16.2264i	0.612864	−	0.612864i	−0.330828	−	0.943691i	$-0.607328\pi$
$701$	16.2264	−	16.2264i	0.612864	−	0.612864i	0.943691	+	0.330828i	$0.107328\pi$
$702$		0			0
$703$	23.6366	−	23.6366i	0.891472	−	0.891472i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.69365			0.0636965
$708$		0			0
$709$	25.3577	−	25.3577i	0.952329	−	0.952329i	−0.0465856	−	0.998914i	$-0.514834\pi$
$709$	25.3577	−	25.3577i	0.952329	−	0.952329i	0.998914	+	0.0465856i	$0.0148340\pi$
$710$		0			0
$711$	−19.9271			−0.747326
$712$		0			0
$713$	0.252832	−	0.252832i	0.00946863	−	0.00946863i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	75.0450i		−	2.80261i
$718$		0			0
$719$	−41.3374			−1.54163			−0.770813	−	0.637061i	$-0.780150\pi$
$719$	−41.3374			−1.54163			−0.770813	+	0.637061i	$0.780150\pi$
$720$		0			0
$721$	10.7065			0.398730
$722$		0			0
$723$		−	0.323420i		−	0.0120281i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−23.4630	+	23.4630i	−0.870193	+	0.870193i	−0.992493	−	0.122300i	$-0.960973\pi$
$727$	−23.4630	+	23.4630i	−0.870193	+	0.870193i	0.122300	+	0.992493i	$0.460973\pi$
$728$		0			0
$729$	41.8342			1.54942
$730$		0			0
$731$	−23.4595	+	23.4595i	−0.867681	+	0.867681i
$732$		0			0
$733$	15.1628			0.560051			0.280025	−	0.959993i	$-0.409657\pi$
$733$	15.1628			0.560051			0.280025	+	0.959993i	$0.409657\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.63931	−	1.63931i	0.0603848	−	0.0603848i
$738$		0			0
$739$	0.974343	−	0.974343i	0.0358418	−	0.0358418i	−0.688959	−	0.724801i	$-0.741932\pi$
$739$	0.974343	−	0.974343i	0.0358418	−	0.0358418i	0.724801	+	0.688959i	$0.241932\pi$
$740$		0			0
$741$	52.2312	+	52.2312i	1.91876	+	1.91876i
$742$		0			0
$743$	29.0897	+	29.0897i	1.06720	+	1.06720i	0.997573	+	0.0696259i	$0.0221806\pi$
$743$	29.0897	+	29.0897i	1.06720	+	1.06720i	0.0696259	+	0.997573i	$0.477819\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	74.6176i		−	2.73011i
$748$		0			0
$749$	−7.02596	−	7.02596i	−0.256723	−	0.256723i
$750$		0			0
$751$		−	7.77705i		−	0.283789i	−0.989882	−	0.141894i	$-0.954681\pi$
$751$		−	7.77705i		−	0.283789i	0.989882	−	0.141894i	$-0.0453193\pi$
$752$		0			0
$753$	−54.8981	−	54.8981i	−2.00060	−	2.00060i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.42073			−0.0516372			−0.0258186	−	0.999667i	$-0.508219\pi$
$757$	−1.42073			−0.0516372			−0.0258186	+	0.999667i	$0.508219\pi$
$758$		0			0
$759$		−	5.08497i		−	0.184573i
$760$		0			0
$761$			26.6737i			0.966921i	0.875366	+	0.483460i	$0.160620\pi$
$761$			26.6737i			0.966921i	−0.875366	+	0.483460i	$0.839380\pi$
$762$		0			0
$763$	−11.4538			−0.414656
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.3899	−	16.3899i	−0.591805	−	0.591805i
$768$		0			0
$769$		−	45.8210i		−	1.65235i	−0.563415	−	0.826174i	$-0.690513\pi$
$769$		−	45.8210i		−	1.65235i	0.563415	−	0.826174i	$-0.309487\pi$
$770$		0			0
$771$	2.16428	+	2.16428i	0.0779447	+	0.0779447i
$772$		0			0
$773$			18.5473i			0.667101i	0.942732	+	0.333550i	$0.108247\pi$
$773$			18.5473i			0.667101i	−0.942732	+	0.333550i	$0.891753\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	7.65827	+	7.65827i	0.274739	+	0.274739i
$778$		0			0
$779$	18.4313	+	18.4313i	0.660370	+	0.660370i
$780$		0			0
$781$	−0.675359	+	0.675359i	−0.0241662	+	0.0241662i
$782$		0			0
$783$	−23.6490	+	23.6490i	−0.845146	+	0.845146i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−21.3016			−0.759319			−0.379659	−	0.925126i	$-0.623959\pi$
$787$	−21.3016			−0.759319			−0.379659	+	0.925126i	$0.623959\pi$
$788$		0			0
$789$	−16.3654	+	16.3654i	−0.582624	+	0.582624i
$790$		0			0
$791$	2.32712			0.0827427
$792$		0			0
$793$	−16.8538	+	16.8538i	−0.598496	+	0.598496i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	2.35457i		−	0.0834033i	−0.999130	−	0.0417016i	$-0.986722\pi$
$797$		−	2.35457i		−	0.0834033i	0.999130	−	0.0417016i	$-0.0132779\pi$
$798$		0			0
$799$	−25.9063			−0.916500
$800$		0			0
$801$	17.2758			0.610410
$802$		0			0
$803$		−	2.51337i		−	0.0886949i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−27.9569	+	27.9569i	−0.984128	+	0.984128i
$808$		0			0
$809$	−23.9476			−0.841952			−0.420976	−	0.907072i	$-0.638312\pi$
$809$	−23.9476			−0.841952			−0.420976	+	0.907072i	$0.638312\pi$
$810$		0			0
$811$	1.33006	−	1.33006i	0.0467048	−	0.0467048i	−0.683369	−	0.730073i	$-0.739486\pi$
$811$	1.33006	−	1.33006i	0.0467048	−	0.0467048i	0.730073	+	0.683369i	$0.239486\pi$
$812$		0			0
$813$	−11.7142			−0.410834
$814$		0			0
$815$		0			0
$816$		0			0
$817$	30.3352	−	30.3352i	1.06129	−	1.06129i
$818$		0			0
$819$	−10.6988	+	10.6988i	−0.373846	+	0.373846i
$820$		0			0
$821$	36.4676	+	36.4676i	1.27273	+	1.27273i	0.944651	+	0.328076i	$0.106400\pi$
$821$	36.4676	+	36.4676i	1.27273	+	1.27273i	0.328076	+	0.944651i	$0.393600\pi$
$822$		0			0
$823$	26.3978	+	26.3978i	0.920170	+	0.920170i	0.997041	−	0.0768712i	$-0.0244930\pi$
$823$	26.3978	+	26.3978i	0.920170	+	0.920170i	−0.0768712	+	0.997041i	$0.524493\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1.99830i			0.0694878i	0.999396	+	0.0347439i	$0.0110616\pi$
$827$			1.99830i			0.0694878i	−0.999396	+	0.0347439i	$0.988938\pi$
$828$		0			0
$829$	−13.0376	−	13.0376i	−0.452813	−	0.452813i	0.443474	−	0.896287i	$-0.353746\pi$
$829$	−13.0376	−	13.0376i	−0.452813	−	0.452813i	−0.896287	+	0.443474i	$0.853746\pi$
$830$		0			0
$831$		−	70.4735i		−	2.44470i
$832$		0			0
$833$	20.5801	+	20.5801i	0.713059	+	0.713059i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.862057			0.0297971
$838$		0			0
$839$		−	15.4102i		−	0.532018i	−0.963971	−	0.266009i	$-0.914295\pi$
$839$		−	15.4102i		−	0.532018i	0.963971	−	0.266009i	$-0.0857050\pi$
$840$		0			0
$841$			0.479815i			0.0165453i
$842$		0			0
$843$	−67.5983			−2.32821
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−4.82499	−	4.82499i	−0.165789	−	0.165789i
$848$		0			0
$849$			37.2686i			1.27906i
$850$		0			0
$851$	10.5565	+	10.5565i	0.361872	+	0.361872i
$852$		0			0
$853$		−	7.96419i		−	0.272689i	−0.990662	−	0.136344i	$-0.956465\pi$
$853$		−	7.96419i		−	0.272689i	0.990662	−	0.136344i	$-0.0435353\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.35407	−	5.35407i	−0.182891	−	0.182891i	0.609723	−	0.792615i	$-0.291281\pi$
$857$	−5.35407	−	5.35407i	−0.182891	−	0.182891i	−0.792615	+	0.609723i	$0.791281\pi$
$858$		0			0
$859$	−35.0058	−	35.0058i	−1.19438	−	1.19438i	−0.975824	−	0.218559i	$-0.929864\pi$
$859$	−35.0058	−	35.0058i	−1.19438	−	1.19438i	−0.218559	−	0.975824i	$-0.570136\pi$
$860$		0			0
$861$	−5.97175	+	5.97175i	−0.203517	+	0.203517i
$862$		0			0
$863$	−36.7138	+	36.7138i	−1.24975	+	1.24975i	−0.293923	+	0.955829i	$0.594961\pi$
$863$	−36.7138	+	36.7138i	−1.24975	+	1.24975i	−0.955829	+	0.293923i	$0.905039\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	7.34475			0.249441
$868$		0			0
$869$	1.90416	−	1.90416i	0.0645943	−	0.0645943i
$870$		0			0
$871$	−15.0406			−0.509633
$872$		0			0
$873$	−25.5561	+	25.5561i	−0.864942	+	0.864942i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	14.3410i		−	0.484262i	−0.970244	−	0.242131i	$-0.922154\pi$
$877$		−	14.3410i		−	0.484262i	0.970244	−	0.242131i	$-0.0778463\pi$
$878$		0			0
$879$	−90.4586			−3.05109
$880$		0			0
$881$	−13.6397			−0.459533			−0.229767	−	0.973246i	$-0.573796\pi$
$881$	−13.6397			−0.459533			−0.229767	+	0.973246i	$0.573796\pi$
$882$		0			0
$883$			6.12563i			0.206144i	0.994674	+	0.103072i	$0.0328672\pi$
$883$			6.12563i			0.206144i	−0.994674	+	0.103072i	$0.967133\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	25.5187	−	25.5187i	0.856834	−	0.856834i	−0.134130	−	0.990964i	$-0.542824\pi$
$887$	25.5187	−	25.5187i	0.856834	−	0.856834i	0.990964	+	0.134130i	$0.0428239\pi$
$888$		0			0
$889$	0.565166			0.0189551
$890$		0			0
$891$	1.04566	−	1.04566i	0.0350310	−	0.0350310i
$892$		0			0
$893$	33.4992			1.12101
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−23.3273	+	23.3273i	−0.778875	+	0.778875i
$898$		0			0
$899$	0.537302	−	0.537302i	0.0179200	−	0.0179200i
$900$		0			0
$901$	−8.62682	−	8.62682i	−0.287401	−	0.287401i
$902$		0			0
$903$	9.82861	+	9.82861i	0.327076	+	0.327076i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	32.1815i		−	1.06857i	−0.845305	−	0.534284i	$-0.820581\pi$
$907$		−	32.1815i		−	1.06857i	0.845305	−	0.534284i	$-0.179419\pi$
$908$		0			0
$909$	9.51614	+	9.51614i	0.315630	+	0.315630i
$910$		0			0
$911$			38.6282i			1.27981i	0.768455	+	0.639904i	$0.221026\pi$
$911$			38.6282i			1.27981i	−0.768455	+	0.639904i	$0.778974\pi$
$912$		0			0
$913$	7.13018	+	7.13018i	0.235974	+	0.235974i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.76867			0.289567
$918$		0			0
$919$			19.1924i			0.633099i	0.948576	+	0.316550i	$0.102524\pi$
$919$			19.1924i			0.633099i	−0.948576	+	0.316550i	$0.897476\pi$
$920$		0			0
$921$		−	78.1395i		−	2.57479i
$922$		0			0
$923$	6.19641			0.203957
$924$		0			0
$925$		0			0
$926$		0			0
$927$	60.1564	+	60.1564i	1.97580	+	1.97580i
$928$		0			0
$929$			16.8576i			0.553081i	0.961002	+	0.276541i	$0.0891880\pi$
$929$			16.8576i			0.553081i	−0.961002	+	0.276541i	$0.910812\pi$
$930$		0			0
$931$	−26.6119	−	26.6119i	−0.872170	−	0.872170i
$932$		0			0
$933$			45.1467i			1.47804i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	23.9511	+	23.9511i	0.782449	+	0.782449i	0.980243	−	0.197795i	$-0.0633779\pi$
$937$	23.9511	+	23.9511i	0.782449	+	0.782449i	−0.197795	+	0.980243i	$0.563378\pi$
$938$		0			0
$939$	39.5238	+	39.5238i	1.28981	+	1.28981i
$940$		0			0
$941$	14.2496	−	14.2496i	0.464525	−	0.464525i	−0.435610	−	0.900135i	$-0.643467\pi$
$941$	14.2496	−	14.2496i	0.464525	−	0.464525i	0.900135	+	0.435610i	$0.143467\pi$
$942$		0			0
$943$	−8.23171	+	8.23171i	−0.268061	+	0.268061i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.2943			0.659477			0.329738	−	0.944072i	$-0.393039\pi$
$947$	20.2943			0.659477			0.329738	+	0.944072i	$0.393039\pi$
$948$		0			0
$949$	−11.5301	+	11.5301i	−0.374282	+	0.374282i
$950$		0			0
$951$	99.9866			3.24229
$952$		0			0
$953$	10.9257	−	10.9257i	0.353919	−	0.353919i	−0.507647	−	0.861565i	$-0.669484\pi$
$953$	10.9257	−	10.9257i	0.353919	−	0.353919i	0.861565	+	0.507647i	$0.169484\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	10.8062i		−	0.349316i
$958$		0			0
$959$	−3.39836			−0.109739
$960$		0			0
$961$	30.9804			0.999368
$962$		0			0
$963$		−	78.9535i		−	2.54424i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	10.7569	−	10.7569i	0.345918	−	0.345918i	−0.512669	−	0.858586i	$-0.671343\pi$
$967$	10.7569	−	10.7569i	0.345918	−	0.345918i	0.858586	+	0.512669i	$0.171343\pi$
$968$		0			0
$969$	−72.2796			−2.32195
$970$		0			0
$971$	18.7456	−	18.7456i	0.601574	−	0.601574i	−0.339156	−	0.940730i	$-0.610142\pi$
$971$	18.7456	−	18.7456i	0.601574	−	0.601574i	0.940730	+	0.339156i	$0.110142\pi$
$972$		0			0
$973$	5.01811			0.160873
$974$		0			0
$975$		0			0
$976$		0			0
$977$	26.3906	−	26.3906i	0.844309	−	0.844309i	−0.145107	−	0.989416i	$-0.546353\pi$
$977$	26.3906	−	26.3906i	0.844309	−	0.844309i	0.989416	+	0.145107i	$0.0463526\pi$
$978$		0			0
$979$	−1.65081	+	1.65081i	−0.0527602	+	0.0527602i
$980$		0			0
$981$	−64.3556	−	64.3556i	−2.05472	−	2.05472i
$982$		0			0
$983$	−4.87875	−	4.87875i	−0.155608	−	0.155608i	0.625009	−	0.780617i	$-0.285095\pi$
$983$	−4.87875	−	4.87875i	−0.155608	−	0.155608i	−0.780617	+	0.625009i	$0.785095\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			10.8537i			0.345478i
$988$		0			0
$989$	13.5482	+	13.5482i	0.430807	+	0.430807i
$990$		0			0
$991$			61.2103i			1.94441i	0.234130	+	0.972205i	$0.424776\pi$
$991$			61.2103i			1.94441i	−0.234130	+	0.972205i	$0.575224\pi$
$992$		0			0
$993$	−48.0415	−	48.0415i	−1.52455	−	1.52455i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−39.1082			−1.23857			−0.619284	−	0.785167i	$-0.712577\pi$
$997$	−39.1082			−1.23857			−0.619284	+	0.785167i	$0.712577\pi$
$998$		0			0
$999$			35.9935i			1.13878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.j.d.143.9		18
4.3	odd	2		400.2.j.d.43.5		18
5.2	odd	4		1600.2.s.d.207.9		18
5.3	odd	4		320.2.s.b.207.1		18
5.4	even	2		320.2.j.b.143.1		18
16.3	odd	4		1600.2.s.d.943.9		18
16.13	even	4		400.2.s.d.243.9		18
20.3	even	4		80.2.s.b.27.1	yes	18
20.7	even	4		400.2.s.d.107.9		18
20.19	odd	2		80.2.j.b.43.5	✓	18
40.3	even	4		640.2.s.d.287.1		18
40.13	odd	4		640.2.s.c.287.9		18
40.19	odd	2		640.2.j.d.543.1		18
40.29	even	2		640.2.j.c.543.9		18
60.23	odd	4		720.2.z.g.667.9		18
60.59	even	2		720.2.bd.g.523.5		18
80.3	even	4		320.2.j.b.47.9		18
80.13	odd	4		80.2.j.b.67.5	yes	18
80.19	odd	4		320.2.s.b.303.1		18
80.29	even	4		80.2.s.b.3.1	yes	18
80.43	even	4		640.2.j.c.607.1		18
80.53	odd	4		640.2.j.d.607.9		18
80.59	odd	4		640.2.s.c.223.9		18
80.67	even	4	inner	1600.2.j.d.1007.1		18
80.69	even	4		640.2.s.d.223.1		18
80.77	odd	4		400.2.j.d.307.5		18
240.29	odd	4		720.2.z.g.163.9		18
240.173	even	4		720.2.bd.g.307.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	20.19	odd	2
80.2.j.b.67.5	yes	18	80.13	odd	4
80.2.s.b.3.1	yes	18	80.29	even	4
80.2.s.b.27.1	yes	18	20.3	even	4
320.2.j.b.47.9		18	80.3	even	4
320.2.j.b.143.1		18	5.4	even	2
320.2.s.b.207.1		18	5.3	odd	4
320.2.s.b.303.1		18	80.19	odd	4
400.2.j.d.43.5		18	4.3	odd	2
400.2.j.d.307.5		18	80.77	odd	4
400.2.s.d.107.9		18	20.7	even	4
400.2.s.d.243.9		18	16.13	even	4
640.2.j.c.543.9		18	40.29	even	2
640.2.j.c.607.1		18	80.43	even	4
640.2.j.d.543.1		18	40.19	odd	2
640.2.j.d.607.9		18	80.53	odd	4
640.2.s.c.223.9		18	80.59	odd	4
640.2.s.c.287.9		18	40.13	odd	4
640.2.s.d.223.1		18	80.69	even	4
640.2.s.d.287.1		18	40.3	even	4
720.2.z.g.163.9		18	240.29	odd	4
720.2.z.g.667.9		18	60.23	odd	4
720.2.bd.g.307.5		18	240.173	even	4
720.2.bd.g.523.5		18	60.59	even	2
1600.2.j.d.143.9		18	1.1	even	1	trivial
1600.2.j.d.1007.1		18	80.67	even	4	inner
1600.2.s.d.207.9		18	5.2	odd	4
1600.2.s.d.943.9		18	16.3	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.85601i q^{3} +(-0.458895 + 0.458895i) q^{7} -5.15678 q^{9} +O(q^{10})\)	\(q+2.85601i q^{3} +(-0.458895 + 0.458895i) q^{7} -5.15678 q^{9} +(0.492763 - 0.492763i) q^{11} -4.52109 q^{13} +(3.12823 - 3.12823i) q^{17} +(-4.04508 + 4.04508i) q^{19} +(-1.31061 - 1.31061i) q^{21} +(-1.80660 - 1.80660i) q^{23} -6.15978i q^{27} +(-3.83926 - 3.83926i) q^{29} +0.139949i q^{31} +(1.40733 + 1.40733i) q^{33} -5.84330 q^{37} -12.9123i q^{39} -4.55648i q^{41} -7.49928 q^{43} +(-4.14073 - 4.14073i) q^{47} +6.57883i q^{49} +(8.93426 + 8.93426i) q^{51} -2.75773i q^{53} +(-11.5528 - 11.5528i) q^{57} +(3.62521 + 3.62521i) q^{59} +(3.72781 - 3.72781i) q^{61} +(2.36642 - 2.36642i) q^{63} +3.32677 q^{67} +(5.15965 - 5.15965i) q^{69} -1.37056 q^{71} +(2.55028 - 2.55028i) q^{73} +0.452252i q^{77} +3.86426 q^{79} +2.12204 q^{81} +14.4698i q^{83} +(10.9650 - 10.9650i) q^{87} -3.35011 q^{89} +(2.07470 - 2.07470i) q^{91} -0.399696 q^{93} +(4.95582 - 4.95582i) q^{97} +(-2.54107 + 2.54107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} - 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^7 - 10 * q^9	\( 18 q + 2 q^{7} - 10 q^{9} + 2 q^{11} + 6 q^{17} - 2 q^{19} - 16 q^{21} - 2 q^{23} - 14 q^{29} + 8 q^{33} - 8 q^{37} - 44 q^{43} - 38 q^{47} - 8 q^{51} - 24 q^{57} + 10 q^{59} + 14 q^{61} + 6 q^{63} + 12 q^{67} + 32 q^{69} - 24 q^{71} - 14 q^{73} - 16 q^{79} + 2 q^{81} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 18 q^{97} + 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 - 10 * q^9 + 2 * q^11 + 6 * q^17 - 2 * q^19 - 16 * q^21 - 2 * q^23 - 14 * q^29 + 8 * q^33 - 8 * q^37 - 44 * q^43 - 38 * q^47 - 8 * q^51 - 24 * q^57 + 10 * q^59 + 14 * q^61 + 6 * q^63 + 12 * q^67 + 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^79 + 2 * q^81 + 24 * q^87 - 12 * q^89 - 16 * q^93 - 18 * q^97 + 22 * q^99

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