LMFDB - Embedded newform 1890.2.d.e.1889.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1889,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1890.1889");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 3 x^{14} + 5 x^{12} + 15 x^{11} - 12 x^{10} + 381 x^{9} - 1356 x^{8} + 1905 x^{7} + \cdots + 390625 $ x^16 - 3x^15 + 3x^14 + 5x^12 + 15x^11 - 12x^10 + 381x^9 - 1356x^8 + 1905x^7 - 300x^6 + 1875x^5 + 3125x^4 + 46875x^2 - 234375*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1889.2
Root			$-1.56583 - 1.59630i$ of defining polynomial
Character	$\chi$	$=$	1890.1889
Dual form			1890.2.d.e.1889.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-2.16535 + 0.557894i) q^{5} +(1.39492 - 2.24815i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.16535 + 0.557894i) q^{5} +(1.39492 - 2.24815i) q^{7} -1.00000 q^{8} +(2.16535 - 0.557894i) q^{10} -3.69641i q^{11} -0.958131 q^{13} +(-1.39492 + 2.24815i) q^{14} +1.00000 q^{16} +1.53776i q^{17} +1.31008i q^{19} +(-2.16535 + 0.557894i) q^{20} +3.69641i q^{22} -7.48590 q^{23} +(4.37751 - 2.41607i) q^{25} +0.958131 q^{26} +(1.39492 - 2.24815i) q^{28} -3.86433i q^{29} -3.04213i q^{31} -1.00000 q^{32} -1.53776i q^{34} +(-1.76627 + 5.64626i) q^{35} +3.00470i q^{37} -1.31008i q^{38} +(2.16535 - 0.557894i) q^{40} +2.07167 q^{41} +4.66423i q^{43} -3.69641i q^{44} +7.48590 q^{46} +12.3497i q^{47} +(-3.10839 - 6.27199i) q^{49} +(-4.37751 + 2.41607i) q^{50} -0.958131 q^{52} -7.82242 q^{53} +(2.06221 + 8.00404i) q^{55} +(-1.39492 + 2.24815i) q^{56} +3.86433i q^{58} +10.1504 q^{59} +3.04213i q^{62} +1.00000 q^{64} +(2.07469 - 0.534535i) q^{65} -1.34516i q^{67} +1.53776i q^{68} +(1.76627 - 5.64626i) q^{70} +5.46412i q^{71} -7.94324 q^{73} -3.00470i q^{74} +1.31008i q^{76} +(-8.31011 - 5.15621i) q^{77} -12.6876 q^{79} +(-2.16535 + 0.557894i) q^{80} -2.07167 q^{82} -0.194288i q^{83} +(-0.857908 - 3.32980i) q^{85} -4.66423i q^{86} +3.69641i q^{88} -1.16442 q^{89} +(-1.33652 + 2.15403i) q^{91} -7.48590 q^{92} -12.3497i q^{94} +(-0.730883 - 2.83678i) q^{95} -9.91039 q^{97} +(3.10839 + 6.27199i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} + 8 q^{23} - 6 q^{25} - 16 q^{32} - q^{35} - 8 q^{46} + 2 q^{49} + 6 q^{50} - 16 q^{53} + 16 q^{64} - 40 q^{65} + q^{70} - 14 q^{77} - 8 q^{79} - 44 q^{85} - 40 q^{91} + 8 q^{92} - 36 q^{95} - 2 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 + 8 * q^23 - 6 * q^25 - 16 * q^32 - q^35 - 8 * q^46 + 2 * q^49 + 6 * q^50 - 16 * q^53 + 16 * q^64 - 40 * q^65 + q^70 - 14 * q^77 - 8 * q^79 - 44 * q^85 - 40 * q^91 + 8 * q^92 - 36 * q^95 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−2.16535	+	0.557894i	−0.968375	+	0.249498i
$5$	−2.16535	+	0.557894i	−0.968375	+	0.249498i
$6$		0			0
$7$	1.39492	−	2.24815i	0.527230	−	0.849722i
$7$	1.39492	−	2.24815i	0.527230	−	0.849722i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.16535	−	0.557894i	0.684745	−	0.176421i
$11$		−	3.69641i		−	1.11451i	−0.830341	−	0.557256i	$-0.811854\pi$
$11$		−	3.69641i		−	1.11451i	0.830341	−	0.557256i	$-0.188146\pi$
$12$		0			0
$13$	−0.958131			−0.265738			−0.132869	−	0.991134i	$-0.542419\pi$
$13$	−0.958131			−0.265738			−0.132869	+	0.991134i	$0.542419\pi$
$14$	−1.39492	+	2.24815i	−0.372808	+	0.600844i
$15$		0			0
$16$	1.00000			0.250000
$17$			1.53776i			0.372962i	0.982459	+	0.186481i	$0.0597083\pi$
$17$			1.53776i			0.372962i	−0.982459	+	0.186481i	$0.940292\pi$
$18$		0			0
$19$			1.31008i			0.300552i	0.988644	+	0.150276i	$0.0480162\pi$
$19$			1.31008i			0.300552i	−0.988644	+	0.150276i	$0.951984\pi$
$20$	−2.16535	+	0.557894i	−0.484188	+	0.124749i
$21$		0			0
$22$			3.69641i			0.788078i
$23$	−7.48590			−1.56092			−0.780459	−	0.625207i	$-0.785015\pi$
$23$	−7.48590			−1.56092			−0.780459	+	0.625207i	$0.785015\pi$
$24$		0			0
$25$	4.37751	−	2.41607i	0.875502	−	0.483215i
$26$	0.958131			0.187905
$27$		0			0
$28$	1.39492	−	2.24815i	0.263615	−	0.424861i
$29$		−	3.86433i		−	0.717589i	−0.933417	−	0.358794i	$-0.883188\pi$
$29$		−	3.86433i		−	0.717589i	0.933417	−	0.358794i	$-0.116812\pi$
$30$		0			0
$31$		−	3.04213i		−	0.546382i	−0.961960	−	0.273191i	$-0.911921\pi$
$31$		−	3.04213i		−	0.546382i	0.961960	−	0.273191i	$-0.0880791\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		−	1.53776i		−	0.263724i
$35$	−1.76627	+	5.64626i	−0.298553	+	0.954393i
$36$		0			0
$37$			3.00470i			0.493969i	0.969019	+	0.246984i	$0.0794397\pi$
$37$			3.00470i			0.493969i	−0.969019	+	0.246984i	$0.920560\pi$
$38$		−	1.31008i		−	0.212522i
$39$		0			0
$40$	2.16535	−	0.557894i	0.342372	−	0.0882107i
$41$	2.07167			0.323541			0.161770	−	0.986828i	$-0.448280\pi$
$41$	2.07167			0.323541			0.161770	+	0.986828i	$0.448280\pi$
$42$		0			0
$43$			4.66423i			0.711288i	0.934621	+	0.355644i	$0.115738\pi$
$43$			4.66423i			0.711288i	−0.934621	+	0.355644i	$0.884262\pi$
$44$		−	3.69641i		−	0.557256i
$45$		0			0
$46$	7.48590			1.10374
$47$			12.3497i			1.80139i	0.434453	+	0.900694i	$0.356942\pi$
$47$			12.3497i			1.80139i	−0.434453	+	0.900694i	$0.643058\pi$
$48$		0			0
$49$	−3.10839	−	6.27199i	−0.444056	−	0.895999i
$50$	−4.37751	+	2.41607i	−0.619073	+	0.341684i
$51$		0			0
$52$	−0.958131			−0.132869
$53$	−7.82242			−1.07449			−0.537246	−	0.843426i	$-0.680535\pi$
$53$	−7.82242			−1.07449			−0.537246	+	0.843426i	$0.680535\pi$
$54$		0			0
$55$	2.06221	+	8.00404i	0.278068	+	1.07927i
$56$	−1.39492	+	2.24815i	−0.186404	+	0.300422i
$57$		0			0
$58$			3.86433i			0.507412i
$59$	10.1504			1.32146			0.660732	−	0.750622i	$-0.270246\pi$
$59$	10.1504			1.32146			0.660732	+	0.750622i	$0.270246\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$			3.04213i			0.386350i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.07469	−	0.534535i	0.257334	−	0.0663009i
$66$		0			0
$67$		−	1.34516i		−	0.164338i	−0.996618	−	0.0821690i	$-0.973815\pi$
$67$		−	1.34516i		−	0.164338i	0.996618	−	0.0821690i	$-0.0261847\pi$
$68$			1.53776i			0.186481i
$69$		0			0
$70$	1.76627	−	5.64626i	0.211109	−	0.674858i
$71$			5.46412i			0.648472i	0.945976	+	0.324236i	$0.105107\pi$
$71$			5.46412i			0.648472i	−0.945976	+	0.324236i	$0.894893\pi$
$72$		0			0
$73$	−7.94324			−0.929686			−0.464843	−	0.885393i	$-0.653889\pi$
$73$	−7.94324			−0.929686			−0.464843	+	0.885393i	$0.653889\pi$
$74$		−	3.00470i		−	0.349289i
$75$		0			0
$76$			1.31008i			0.150276i
$77$	−8.31011	−	5.15621i	−0.947025	−	0.587604i
$78$		0			0
$79$	−12.6876			−1.42747			−0.713734	−	0.700417i	$-0.752998\pi$
$79$	−12.6876			−1.42747			−0.713734	+	0.700417i	$0.752998\pi$
$80$	−2.16535	+	0.557894i	−0.242094	+	0.0623744i
$81$		0			0
$82$	−2.07167			−0.228778
$83$		−	0.194288i		−	0.0213259i	−0.999943	−	0.0106629i	$-0.996606\pi$
$83$		−	0.194288i		−	0.0213259i	0.999943	−	0.0106629i	$-0.00339419\pi$
$84$		0			0
$85$	−0.857908	−	3.32980i	−0.0930532	−	0.361167i
$86$		−	4.66423i		−	0.502957i
$87$		0			0
$88$			3.69641i			0.394039i
$89$	−1.16442			−0.123429			−0.0617144	−	0.998094i	$-0.519657\pi$
$89$	−1.16442			−0.123429			−0.0617144	+	0.998094i	$0.519657\pi$
$90$		0			0
$91$	−1.33652	+	2.15403i	−0.140105	+	0.225803i
$92$	−7.48590			−0.780459
$93$		0			0
$94$		−	12.3497i		−	1.27377i
$95$	−0.730883	−	2.83678i	−0.0749870	−	0.291047i
$96$		0			0
$97$	−9.91039			−1.00625			−0.503124	−	0.864214i	$-0.667816\pi$
$97$	−9.91039			−1.00625			−0.503124	+	0.864214i	$0.667816\pi$
$98$	3.10839	+	6.27199i	0.313995	+	0.633567i
$99$		0			0
$100$	4.37751	−	2.41607i	0.437751	−	0.241607i
$101$	−15.0638			−1.49890			−0.749452	−	0.662059i	$-0.769683\pi$
$101$	−15.0638			−1.49890			−0.749452	+	0.662059i	$0.769683\pi$
$102$		0			0
$103$	−7.54787			−0.743714			−0.371857	−	0.928290i	$-0.621279\pi$
$103$	−7.54787			−0.743714			−0.371857	+	0.928290i	$0.621279\pi$
$104$	0.958131			0.0939525
$105$		0			0
$106$	7.82242			0.759780
$107$	1.93260			0.186832			0.0934158	−	0.995627i	$-0.470221\pi$
$107$	1.93260			0.186832			0.0934158	+	0.995627i	$0.470221\pi$
$108$		0			0
$109$	3.59608			0.344442			0.172221	−	0.985058i	$-0.444906\pi$
$109$	3.59608			0.344442			0.172221	+	0.985058i	$0.444906\pi$
$110$	−2.06221	−	8.00404i	−0.196624	−	0.763156i
$111$		0			0
$112$	1.39492	−	2.24815i	0.131808	−	0.212431i
$113$	−7.59608			−0.714579			−0.357290	−	0.933994i	$-0.616299\pi$
$113$	−7.59608			−0.714579			−0.357290	+	0.933994i	$0.616299\pi$
$114$		0			0
$115$	16.2096	−	4.17634i	1.51155	−	0.389445i
$116$		−	3.86433i		−	0.358794i
$117$		0			0
$118$	−10.1504			−0.934416
$119$	3.45713	+	2.14506i	0.316914	+	0.196637i
$120$		0			0
$121$	−2.66348			−0.242135
$122$		0			0
$123$		0			0
$124$		−	3.04213i		−	0.273191i
$125$	−8.13094	+	7.67384i	−0.727254	+	0.686369i
$126$		0			0
$127$			0.908067i			0.0805779i	0.999188	+	0.0402890i	$0.0128278\pi$
$127$			0.908067i			0.0805779i	−0.999188	+	0.0402890i	$0.987172\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−2.07469	+	0.534535i	−0.181963	+	0.0468818i
$131$	−5.13343			−0.448510			−0.224255	−	0.974531i	$-0.571995\pi$
$131$	−5.13343			−0.448510			−0.224255	+	0.974531i	$0.571995\pi$
$132$		0			0
$133$	2.94525	+	1.82745i	0.255386	+	0.158460i
$134$			1.34516i			0.116204i
$135$		0			0
$136$		−	1.53776i		−	0.131862i
$137$	−8.55330			−0.730758			−0.365379	−	0.930859i	$-0.619061\pi$
$137$	−8.55330			−0.730758			−0.365379	+	0.930859i	$0.619061\pi$
$138$		0			0
$139$			12.4272i			1.05407i	0.849845	+	0.527033i	$0.176695\pi$
$139$			12.4272i			1.05407i	−0.849845	+	0.527033i	$0.823305\pi$
$140$	−1.76627	+	5.64626i	−0.149277	+	0.477196i
$141$		0			0
$142$		−	5.46412i		−	0.458539i
$143$			3.54165i			0.296168i
$144$		0			0
$145$	2.15589	+	8.36765i	0.179037	+	0.694895i
$146$	7.94324			0.657387
$147$		0			0
$148$			3.00470i			0.246984i
$149$		−	14.7059i		−	1.20475i	−0.798212	−	0.602376i	$-0.794221\pi$
$149$		−	14.7059i		−	1.20475i	0.798212	−	0.602376i	$-0.205779\pi$
$150$		0			0
$151$	−17.0392			−1.38663			−0.693315	−	0.720634i	$-0.743851\pi$
$151$	−17.0392			−1.38663			−0.693315	+	0.720634i	$0.743851\pi$
$152$		−	1.31008i		−	0.106261i
$153$		0			0
$154$	8.31011	+	5.15621i	0.669648	+	0.415499i
$155$	1.69718	+	6.58728i	0.136321	+	0.529103i
$156$		0			0
$157$	8.60949			0.687112			0.343556	−	0.939132i	$-0.388369\pi$
$157$	8.60949			0.687112			0.343556	+	0.939132i	$0.388369\pi$
$158$	12.6876			1.00937
$159$		0			0
$160$	2.16535	−	0.557894i	0.171186	−	0.0441054i
$161$	−10.4422	+	16.8295i	−0.822964	+	1.32635i
$162$		0			0
$163$			10.4044i			0.814939i	0.913219	+	0.407469i	$0.133589\pi$
$163$			10.4044i			0.814939i	−0.913219	+	0.407469i	$0.866411\pi$
$164$	2.07167			0.161770
$165$		0			0
$166$			0.194288i			0.0150797i
$167$		−	14.0483i		−	1.08709i	−0.839379	−	0.543547i	$-0.817081\pi$
$167$		−	14.0483i		−	1.08709i	0.839379	−	0.543547i	$-0.182919\pi$
$168$		0			0
$169$	−12.0820			−0.929383
$170$	0.857908	+	3.32980i	0.0657985	+	0.255384i
$171$		0			0
$172$			4.66423i			0.355644i
$173$			14.1282i			1.07415i	0.843534	+	0.537075i	$0.180471\pi$
$173$			14.1282i			1.07415i	−0.843534	+	0.537075i	$0.819529\pi$
$174$		0			0
$175$	0.674573	−	13.2115i	0.0509929	−	0.998699i
$176$		−	3.69641i		−	0.278628i
$177$		0			0
$178$	1.16442			0.0872773
$179$		−	25.3580i		−	1.89535i	−0.319240	−	0.947674i	$-0.603428\pi$
$179$		−	25.3580i		−	1.89535i	0.319240	−	0.947674i	$-0.396572\pi$
$180$		0			0
$181$			19.0502i			1.41599i	0.706217	+	0.707996i	$0.250400\pi$
$181$			19.0502i			1.41599i	−0.706217	+	0.707996i	$0.749600\pi$
$182$	1.33652	−	2.15403i	0.0990692	−	0.159667i
$183$		0			0
$184$	7.48590			0.551868
$185$	−1.67630	−	6.50623i	−0.123244	−	0.478347i
$186$		0			0
$187$	5.68421			0.415671
$188$			12.3497i			0.900694i
$189$		0			0
$190$	0.730883	+	2.83678i	0.0530238	+	0.205801i
$191$		−	10.8616i		−	0.785916i	−0.919556	−	0.392958i	$-0.871452\pi$
$191$		−	10.8616i		−	0.785916i	0.919556	−	0.392958i	$-0.128548\pi$
$192$		0			0
$193$		−	18.0865i		−	1.30189i	−0.759123	−	0.650947i	$-0.774372\pi$
$193$		−	18.0865i		−	1.30189i	0.759123	−	0.650947i	$-0.225628\pi$
$194$	9.91039			0.711525
$195$		0			0
$196$	−3.10839	−	6.27199i	−0.222028	−	0.448000i
$197$	−4.20172			−0.299360			−0.149680	−	0.988734i	$-0.547824\pi$
$197$	−4.20172			−0.299360			−0.149680	+	0.988734i	$0.547824\pi$
$198$		0			0
$199$			26.2395i			1.86007i	0.367472	+	0.930035i	$0.380223\pi$
$199$			26.2395i			1.86007i	−0.367472	+	0.930035i	$0.619777\pi$
$200$	−4.37751	+	2.41607i	−0.309537	+	0.170842i
$201$		0			0
$202$	15.0638			1.05988
$203$	−8.68762	−	5.39044i	−0.609751	−	0.378335i
$204$		0			0
$205$	−4.48590	+	1.15577i	−0.313309	+	0.0807227i
$206$	7.54787			0.525885
$207$		0			0
$208$	−0.958131			−0.0664344
$209$	4.84258			0.334968
$210$		0			0
$211$	−20.1735			−1.38880			−0.694401	−	0.719588i	$-0.744331\pi$
$211$	−20.1735			−1.38880			−0.694401	+	0.719588i	$0.744331\pi$
$212$	−7.82242			−0.537246
$213$		0			0
$214$	−1.93260			−0.132110
$215$	−2.60214	−	10.0997i	−0.177465	−	0.688794i
$216$		0			0
$217$	−6.83917	−	4.24353i	−0.464273	−	0.288069i
$218$	−3.59608			−0.243557
$219$		0			0
$220$	2.06221	+	8.00404i	0.139034	+	0.539633i
$221$		−	1.47338i		−	0.0991101i
$222$		0			0
$223$	−18.1775			−1.21725			−0.608627	−	0.793457i	$-0.708279\pi$
$223$	−18.1775			−1.21725			−0.608627	+	0.793457i	$0.708279\pi$
$224$	−1.39492	+	2.24815i	−0.0932021	+	0.150211i
$225$		0			0
$226$	7.59608			0.505284
$227$			21.5928i			1.43317i	0.697502	+	0.716583i	$0.254295\pi$
$227$			21.5928i			1.43317i	−0.697502	+	0.716583i	$0.745705\pi$
$228$		0			0
$229$		−	6.08425i		−	0.402059i	−0.979585	−	0.201029i	$-0.935571\pi$
$229$		−	6.08425i		−	0.402059i	0.979585	−	0.201029i	$-0.0644287\pi$
$230$	−16.2096	+	4.17634i	−1.06883	+	0.275379i
$231$		0			0
$232$			3.86433i			0.253706i
$233$	15.1061			0.989635			0.494817	−	0.868997i	$-0.335235\pi$
$233$	15.1061			0.989635			0.494817	+	0.868997i	$0.335235\pi$
$234$		0			0
$235$	−6.88982	−	26.7415i	−0.449442	−	1.74442i
$236$	10.1504			0.660732
$237$		0			0
$238$	−3.45713	−	2.14506i	−0.224092	−	0.139043i
$239$			25.3781i			1.64157i	0.571237	+	0.820785i	$0.306464\pi$
$239$			25.3781i			1.64157i	−0.571237	+	0.820785i	$0.693536\pi$
$240$		0			0
$241$		−	23.0530i		−	1.48498i	−0.669859	−	0.742488i	$-0.733646\pi$
$241$		−	23.0530i		−	1.48498i	0.669859	−	0.742488i	$-0.266354\pi$
$242$	2.66348			0.171215
$243$		0			0
$244$		0			0
$245$	10.2299	+	11.8469i	0.653563	+	0.756873i
$246$		0			0
$247$		−	1.25522i		−	0.0798680i
$248$			3.04213i			0.193175i
$249$		0			0
$250$	8.13094	−	7.67384i	0.514246	−	0.485336i
$251$	13.3864			0.844945			0.422473	−	0.906376i	$-0.361162\pi$
$251$	13.3864			0.844945			0.422473	+	0.906376i	$0.361162\pi$
$252$		0			0
$253$			27.6710i			1.73966i
$254$		−	0.908067i		−	0.0569772i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	10.0037i		−	0.624015i	−0.950080	−	0.312008i	$-0.898999\pi$
$257$		−	10.0037i		−	0.624015i	0.950080	−	0.312008i	$-0.101001\pi$
$258$		0			0
$259$	6.75502	+	4.19131i	0.419736	+	0.260435i
$260$	2.07469	−	0.534535i	0.128667	−	0.0331505i
$261$		0			0
$262$	5.13343			0.317144
$263$	12.8129			0.790075			0.395038	−	0.918665i	$-0.370732\pi$
$263$	12.8129			0.790075			0.395038	+	0.918665i	$0.370732\pi$
$264$		0			0
$265$	16.9383	−	4.36408i	1.04051	−	0.268083i
$266$	−2.94525	−	1.82745i	−0.180585	−	0.112048i
$267$		0			0
$268$		−	1.34516i		−	0.0821690i
$269$	16.7411			1.02073			0.510363	−	0.859959i	$-0.329511\pi$
$269$	16.7411			1.02073			0.510363	+	0.859959i	$0.329511\pi$
$270$		0			0
$271$			25.3956i			1.54267i	0.636429	+	0.771335i	$0.280411\pi$
$271$			25.3956i			1.54267i	−0.636429	+	0.771335i	$0.719589\pi$
$272$			1.53776i			0.0932406i
$273$		0			0
$274$	8.55330			0.516724
$275$	−8.93081	−	16.1811i	−0.538548	−	0.975756i
$276$		0			0
$277$		−	30.0040i		−	1.80277i	−0.433022	−	0.901383i	$-0.642553\pi$
$277$		−	30.0040i		−	1.80277i	0.433022	−	0.901383i	$-0.357447\pi$
$278$		−	12.4272i		−	0.745337i
$279$		0			0
$280$	1.76627	−	5.64626i	0.105555	−	0.337429i
$281$			25.7354i			1.53524i	0.640903	+	0.767622i	$0.278560\pi$
$281$			25.7354i			1.53524i	−0.640903	+	0.767622i	$0.721440\pi$
$282$		0			0
$283$	−33.2739			−1.97793			−0.988964	−	0.148158i	$-0.952666\pi$
$283$	−33.2739			−1.97793			−0.988964	+	0.148158i	$0.952666\pi$
$284$			5.46412i			0.324236i
$285$		0			0
$286$		−	3.54165i		−	0.209422i
$287$	2.88982	−	4.65744i	0.170581	−	0.274920i
$288$		0			0
$289$	14.6353			0.860899
$290$	−2.15589	−	8.36765i	−0.126598	−	0.491365i
$291$		0			0
$292$	−7.94324			−0.464843
$293$		−	10.0037i		−	0.584424i	−0.956354	−	0.292212i	$-0.905609\pi$
$293$		−	10.0037i		−	0.584424i	0.956354	−	0.292212i	$-0.0943913\pi$
$294$		0			0
$295$	−21.9791	+	5.66282i	−1.27967	+	0.329702i
$296$		−	3.00470i		−	0.174644i
$297$		0			0
$298$			14.7059i			0.851888i
$299$	7.17247			0.414795
$300$		0			0
$301$	10.4859	+	6.50623i	0.604397	+	0.375013i
$302$	17.0392			0.980496
$303$		0			0
$304$			1.31008i			0.0751380i
$305$		0			0
$306$		0			0
$307$	1.23005			0.0702024			0.0351012	−	0.999384i	$-0.488825\pi$
$307$	1.23005			0.0702024			0.0351012	+	0.999384i	$0.488825\pi$
$308$	−8.31011	−	5.15621i	−0.473512	−	0.293802i
$309$		0			0
$310$	−1.69718	−	6.58728i	−0.0963935	−	0.374132i
$311$	−32.4192			−1.83833			−0.919163	−	0.393877i	$-0.871134\pi$
$311$	−32.4192			−1.83833			−0.919163	+	0.393877i	$0.871134\pi$
$312$		0			0
$313$	−18.3146			−1.03520			−0.517602	−	0.855622i	$-0.673175\pi$
$313$	−18.3146			−1.03520			−0.517602	+	0.855622i	$0.673175\pi$
$314$	−8.60949			−0.485861
$315$		0			0
$316$	−12.6876			−0.713734
$317$	14.0669			0.790077			0.395038	−	0.918665i	$-0.370731\pi$
$317$	14.0669			0.790077			0.395038	+	0.918665i	$0.370731\pi$
$318$		0			0
$319$	−14.2842			−0.799761
$320$	−2.16535	+	0.557894i	−0.121047	+	0.0311872i
$321$		0			0
$322$	10.4422	−	16.8295i	0.581923	−	0.937869i
$323$	−2.01459			−0.112095
$324$		0			0
$325$	−4.19423	+	2.31492i	−0.232654	+	0.128408i
$326$		−	10.4044i		−	0.576249i
$327$		0			0
$328$	−2.07167			−0.114389
$329$	27.7640	+	17.2269i	1.53068	+	0.949747i
$330$		0			0
$331$	−10.5287			−0.578709			−0.289354	−	0.957222i	$-0.593441\pi$
$331$	−10.5287			−0.578709			−0.289354	+	0.957222i	$0.593441\pi$
$332$		−	0.194288i		−	0.0106629i
$333$		0			0
$334$			14.0483i			0.768692i
$335$	0.750459	+	2.91276i	0.0410019	+	0.159141i
$336$		0			0
$337$			22.9186i			1.24846i	0.781242	+	0.624229i	$0.214587\pi$
$337$			22.9186i			1.24846i	−0.781242	+	0.624229i	$0.785413\pi$
$338$	12.0820			0.657173
$339$		0			0
$340$	−0.857908	−	3.32980i	−0.0465266	−	0.180584i
$341$	−11.2450			−0.608949
$342$		0			0
$343$	−18.4364	−	1.76079i	−0.995470	−	0.0950737i
$344$		−	4.66423i		−	0.251478i
$345$		0			0
$346$		−	14.1282i		−	0.759539i
$347$	32.2651			1.73208			0.866039	−	0.499976i	$-0.166658\pi$
$347$	32.2651			1.73208			0.866039	+	0.499976i	$0.166658\pi$
$348$		0			0
$349$		−	32.6731i		−	1.74895i	−0.485068	−	0.874477i	$-0.661205\pi$
$349$		−	32.6731i		−	1.74895i	0.485068	−	0.874477i	$-0.338795\pi$
$350$	−0.674573	+	13.2115i	−0.0360575	+	0.706187i
$351$		0			0
$352$			3.69641i			0.197020i
$353$		−	12.0852i		−	0.643228i	−0.946871	−	0.321614i	$-0.895775\pi$
$353$		−	12.0852i		−	0.643228i	0.946871	−	0.321614i	$-0.104225\pi$
$354$		0			0
$355$	−3.04840	−	11.8318i	−0.161792	−	0.627964i
$356$	−1.16442			−0.0617144
$357$		0			0
$358$			25.3580i			1.34021i
$359$		−	32.9275i		−	1.73785i	−0.494947	−	0.868923i	$-0.664812\pi$
$359$		−	32.9275i		−	1.73785i	0.494947	−	0.868923i	$-0.335188\pi$
$360$		0			0
$361$	17.2837			0.909669
$362$		−	19.0502i		−	1.00126i
$363$		0			0
$364$	−1.33652	+	2.15403i	−0.0700525	+	0.112902i
$365$	17.1999	−	4.43149i	0.900285	−	0.231955i
$366$		0			0
$367$	16.9811			0.886406			0.443203	−	0.896421i	$-0.353842\pi$
$367$	16.9811			0.886406			0.443203	+	0.896421i	$0.353842\pi$
$368$	−7.48590			−0.390230
$369$		0			0
$370$	1.67630	+	6.50623i	0.0871467	+	0.338243i
$371$	−10.9117	+	17.5860i	−0.566505	+	0.913020i
$372$		0			0
$373$			29.1739i			1.51057i	0.655397	+	0.755284i	$0.272501\pi$
$373$			29.1739i			1.51057i	−0.655397	+	0.755284i	$0.727499\pi$
$374$	−5.68421			−0.293923
$375$		0			0
$376$		−	12.3497i		−	0.636887i
$377$			3.70254i			0.190690i
$378$		0			0
$379$	10.9718			0.563584			0.281792	−	0.959476i	$-0.409071\pi$
$379$	10.9718			0.563584			0.281792	+	0.959476i	$0.409071\pi$
$380$	−0.730883	−	2.83678i	−0.0374935	−	0.145524i
$381$		0			0
$382$			10.8616i			0.555727i
$383$			8.16073i			0.416994i	0.978023	+	0.208497i	$0.0668571\pi$
$383$			8.16073i			0.416994i	−0.978023	+	0.208497i	$0.933143\pi$
$384$		0			0
$385$	20.8709	+	6.52885i	1.06368	+	0.332741i
$386$			18.0865i			0.920578i
$387$		0			0
$388$	−9.91039			−0.503124
$389$		−	9.75100i		−	0.494395i	−0.968965	−	0.247198i	$-0.920490\pi$
$389$		−	9.75100i		−	0.494395i	0.968965	−	0.247198i	$-0.0795097\pi$
$390$		0			0
$391$		−	11.5115i		−	0.582164i
$392$	3.10839	+	6.27199i	0.156998	+	0.316783i
$393$		0			0
$394$	4.20172			0.211679
$395$	27.4732	−	7.07834i	1.38233	−	0.356150i
$396$		0			0
$397$	26.1533			1.31260			0.656299	−	0.754501i	$-0.272121\pi$
$397$	26.1533			1.31260			0.656299	+	0.754501i	$0.272121\pi$
$398$		−	26.2395i		−	1.31527i
$399$		0			0
$400$	4.37751	−	2.41607i	0.218875	−	0.120804i
$401$		−	22.2753i		−	1.11238i	−0.831056	−	0.556189i	$-0.812263\pi$
$401$		−	22.2753i		−	1.11238i	0.831056	−	0.556189i	$-0.187737\pi$
$402$		0			0
$403$			2.91476i			0.145194i
$404$	−15.0638			−0.749452
$405$		0			0
$406$	8.68762	+	5.39044i	0.431159	+	0.267523i
$407$	11.1066			0.550534
$408$		0			0
$409$			18.8617i			0.932652i	0.884613	+	0.466326i	$0.154423\pi$
$409$			18.8617i			0.932652i	−0.884613	+	0.466326i	$0.845577\pi$
$410$	4.48590	−	1.15577i	0.221543	−	0.0570795i
$411$		0			0
$412$	−7.54787			−0.371857
$413$	14.1589	−	22.8196i	0.696716	−	1.12288i
$414$		0			0
$415$	0.108392	+	0.420702i	0.00532076	+	0.0206515i
$416$	0.958131			0.0469762
$417$		0			0
$418$	−4.84258			−0.236858
$419$	15.2501			0.745017			0.372508	−	0.928029i	$-0.378498\pi$
$419$	15.2501			0.745017			0.372508	+	0.928029i	$0.378498\pi$
$420$		0			0
$421$	20.9869			1.02284			0.511419	−	0.859332i	$-0.329120\pi$
$421$	20.9869			1.02284			0.511419	+	0.859332i	$0.329120\pi$
$422$	20.1735			0.982032
$423$		0			0
$424$	7.82242			0.379890
$425$	3.71535	+	6.73157i	0.180221	+	0.326529i
$426$		0			0
$427$		0			0
$428$	1.93260			0.0934158
$429$		0			0
$430$	2.60214	+	10.0997i	0.125486	+	0.487051i
$431$			19.9737i			0.962099i	0.876694	+	0.481049i	$0.159744\pi$
$431$			19.9737i			0.962099i	−0.876694	+	0.481049i	$0.840256\pi$
$432$		0			0
$433$	−13.1103			−0.630043			−0.315021	−	0.949085i	$-0.602012\pi$
$433$	−13.1103			−0.630043			−0.315021	+	0.949085i	$0.602012\pi$
$434$	6.83917	+	4.24353i	0.328291	+	0.203696i
$435$		0			0
$436$	3.59608			0.172221
$437$		−	9.80710i		−	0.469137i
$438$		0			0
$439$		−	14.3928i		−	0.686930i	−0.939166	−	0.343465i	$-0.888399\pi$
$439$		−	14.3928i		−	0.686930i	0.939166	−	0.343465i	$-0.111601\pi$
$440$	−2.06221	−	8.00404i	−0.0983118	−	0.381578i
$441$		0			0
$442$			1.47338i			0.0700815i
$443$	28.4180			1.35018			0.675090	−	0.737735i	$-0.264105\pi$
$443$	28.4180			1.35018			0.675090	+	0.737735i	$0.264105\pi$
$444$		0			0
$445$	2.52139	−	0.649625i	0.119525	−	0.0307952i
$446$	18.1775			0.860728
$447$		0			0
$448$	1.39492	−	2.24815i	0.0659038	−	0.106215i
$449$			4.07377i			0.192253i	0.995369	+	0.0961265i	$0.0306453\pi$
$449$			4.07377i			0.192253i	−0.995369	+	0.0961265i	$0.969355\pi$
$450$		0			0
$451$		−	7.65776i		−	0.360590i
$452$	−7.59608			−0.357290
$453$		0			0
$454$		−	21.5928i		−	1.01340i
$455$	1.69231	−	5.40986i	0.0793369	−	0.253618i
$456$		0			0
$457$		−	8.89136i		−	0.415920i	−0.978137	−	0.207960i	$-0.933318\pi$
$457$		−	8.89136i		−	0.415920i	0.978137	−	0.207960i	$-0.0666824\pi$
$458$			6.08425i			0.284298i
$459$		0			0
$460$	16.2096	−	4.17634i	0.755777	−	0.194723i
$461$	−11.4649			−0.533976			−0.266988	−	0.963700i	$-0.586028\pi$
$461$	−11.4649			−0.533976			−0.266988	+	0.963700i	$0.586028\pi$
$462$		0			0
$463$		−	1.42495i		−	0.0662230i	−0.999452	−	0.0331115i	$-0.989458\pi$
$463$		−	1.42495i		−	0.0662230i	0.999452	−	0.0331115i	$-0.0105417\pi$
$464$		−	3.86433i		−	0.179397i
$465$		0			0
$466$	−15.1061			−0.699778
$467$		−	26.0118i		−	1.20368i	−0.798615	−	0.601842i	$-0.794434\pi$
$467$		−	26.0118i		−	1.20368i	0.798615	−	0.601842i	$-0.205566\pi$
$468$		0			0
$469$	−3.02414	−	1.87640i	−0.139642	−	0.0866440i
$470$	6.88982	+	26.7415i	0.317804	+	1.23349i
$471$		0			0
$472$	−10.1504			−0.467208
$473$	17.2409			0.792738
$474$		0			0
$475$	3.16524	+	5.73487i	0.145231	+	0.263134i
$476$	3.45713	+	2.14506i	0.158457	+	0.0983185i
$477$		0			0
$478$		−	25.3781i		−	1.16077i
$479$	−22.0479			−1.00739			−0.503696	−	0.863881i	$-0.668027\pi$
$479$	−22.0479			−1.00739			−0.503696	+	0.863881i	$0.668027\pi$
$480$		0			0
$481$		−	2.87889i		−	0.131266i
$482$			23.0530i			1.05004i
$483$		0			0
$484$	−2.66348			−0.121067
$485$	21.4595	−	5.52894i	0.974425	−	0.251056i
$486$		0			0
$487$		−	24.9355i		−	1.12993i	−0.825113	−	0.564967i	$-0.808889\pi$
$487$		−	24.9355i		−	1.12993i	0.825113	−	0.564967i	$-0.191111\pi$
$488$		0			0
$489$		0			0
$490$	−10.2299	−	11.8469i	−0.462139	−	0.535190i
$491$			15.2511i			0.688275i	0.938919	+	0.344137i	$0.111829\pi$
$491$			15.2511i			0.688275i	−0.938919	+	0.344137i	$0.888171\pi$
$492$		0			0
$493$	5.94243			0.267634
$494$			1.25522i			0.0564752i
$495$		0			0
$496$		−	3.04213i		−	0.136596i
$497$	12.2842	+	7.62202i	0.551021	+	0.341894i
$498$		0			0
$499$	−10.8370			−0.485131			−0.242565	−	0.970135i	$-0.577989\pi$
$499$	−10.8370			−0.485131			−0.242565	+	0.970135i	$0.577989\pi$
$500$	−8.13094	+	7.67384i	−0.363627	+	0.343184i
$501$		0			0
$502$	−13.3864			−0.597466
$503$		−	42.4860i		−	1.89436i	−0.320705	−	0.947179i	$-0.603920\pi$
$503$		−	42.4860i		−	1.89436i	0.320705	−	0.947179i	$-0.396080\pi$
$504$		0			0
$505$	32.6184	−	8.40399i	1.45150	−	0.373973i
$506$		−	27.6710i		−	1.23013i
$507$		0			0
$508$			0.908067i			0.0402890i
$509$	19.3226			0.856459			0.428230	−	0.903670i	$-0.359137\pi$
$509$	19.3226			0.856459			0.428230	+	0.903670i	$0.359137\pi$
$510$		0			0
$511$	−11.0802	+	17.8576i	−0.490159	+	0.789975i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			10.0037i			0.441246i
$515$	16.3438	−	4.21091i	0.720194	−	0.185555i
$516$		0			0
$517$	45.6496			2.00767
$518$	−6.75502	−	4.19131i	−0.296798	−	0.184156i
$519$		0			0
$520$	−2.07469	+	0.534535i	−0.0909813	+	0.0234409i
$521$	19.0689			0.835426			0.417713	−	0.908579i	$-0.362832\pi$
$521$	19.0689			0.835426			0.417713	+	0.908579i	$0.362832\pi$
$522$		0			0
$523$	−16.0556			−0.702062			−0.351031	−	0.936364i	$-0.614169\pi$
$523$	−16.0556			−0.702062			−0.351031	+	0.936364i	$0.614169\pi$
$524$	−5.13343			−0.224255
$525$		0			0
$526$	−12.8129			−0.558668
$527$	4.67807			0.203780
$528$		0			0
$529$	33.0387			1.43647
$530$	−16.9383	+	4.36408i	−0.735753	+	0.189563i
$531$		0			0
$532$	2.94525	+	1.82745i	0.127693	+	0.0792301i
$533$	−1.98493			−0.0859770
$534$		0			0
$535$	−4.18476	+	1.07819i	−0.180923	+	0.0466140i
$536$			1.34516i			0.0581022i
$537$		0			0
$538$	−16.7411			−0.721762
$539$	−23.1839	+	11.4899i	−0.998601	+	0.494905i
$540$		0			0
$541$	6.40392			0.275326			0.137663	−	0.990479i	$-0.456041\pi$
$541$	6.40392			0.275326			0.137663	+	0.990479i	$0.456041\pi$
$542$		−	25.3956i		−	1.09083i
$543$		0			0
$544$		−	1.53776i		−	0.0659310i
$545$	−7.78679	+	2.00623i	−0.333549	+	0.0859375i
$546$		0			0
$547$		−	27.9854i		−	1.19657i	−0.801284	−	0.598284i	$-0.795849\pi$
$547$		−	27.9854i		−	1.19657i	0.801284	−	0.598284i	$-0.204151\pi$
$548$	−8.55330			−0.365379
$549$		0			0
$550$	8.93081	+	16.1811i	0.380811	+	0.689964i
$551$	5.06257			0.215673
$552$		0			0
$553$	−17.6982	+	28.5237i	−0.752605	+	1.21295i
$554$			30.0040i			1.27475i
$555$		0			0
$556$			12.4272i			0.527033i
$557$	−8.24092			−0.349179			−0.174589	−	0.984641i	$-0.555860\pi$
$557$	−8.24092			−0.349179			−0.174589	+	0.984641i	$0.555860\pi$
$558$		0			0
$559$		−	4.46894i		−	0.189016i
$560$	−1.76627	+	5.64626i	−0.0746383	+	0.238598i
$561$		0			0
$562$		−	25.7354i		−	1.08558i
$563$			2.96458i			0.124942i	0.998047	+	0.0624710i	$0.0198981\pi$
$563$			2.96458i			0.124942i	−0.998047	+	0.0624710i	$0.980102\pi$
$564$		0			0
$565$	16.4482	−	4.23781i	0.691981	−	0.178286i
$566$	33.2739			1.39861
$567$		0			0
$568$		−	5.46412i		−	0.229269i
$569$		−	34.9443i		−	1.46494i	−0.680798	−	0.732471i	$-0.738367\pi$
$569$		−	34.9443i		−	1.46494i	0.680798	−	0.732471i	$-0.261633\pi$
$570$		0			0
$571$	43.0105			1.79993			0.899967	−	0.435958i	$-0.143590\pi$
$571$	43.0105			1.79993			0.899967	+	0.435958i	$0.143590\pi$
$572$			3.54165i			0.148084i
$573$		0			0
$574$	−2.88982	+	4.65744i	−0.120619	+	0.194398i
$575$	−32.7696	+	18.0865i	−1.36659	+	0.754259i
$576$		0			0
$577$	−2.44707			−0.101873			−0.0509364	−	0.998702i	$-0.516221\pi$
$577$	−2.44707			−0.101873			−0.0509364	+	0.998702i	$0.516221\pi$
$578$	−14.6353			−0.608748
$579$		0			0
$580$	2.15589	+	8.36765i	0.0895184	+	0.347448i
$581$	−0.436790	−	0.271017i	−0.0181211	−	0.0112437i
$582$		0			0
$583$			28.9149i			1.19753i
$584$	7.94324			0.328694
$585$		0			0
$586$			10.0037i			0.413250i
$587$			4.76687i			0.196750i	0.995149	+	0.0983750i	$0.0313645\pi$
$587$			4.76687i			0.196750i	−0.995149	+	0.0983750i	$0.968636\pi$
$588$		0			0
$589$	3.98541			0.164216
$590$	21.9791	−	5.66282i	0.904865	−	0.233134i
$591$		0			0
$592$			3.00470i			0.123492i
$593$			44.4850i			1.82678i	0.407088	+	0.913389i	$0.366544\pi$
$593$			44.4850i			1.82678i	−0.407088	+	0.913389i	$0.633456\pi$
$594$		0			0
$595$	−8.68262	−	2.71610i	−0.355953	−	0.111349i
$596$		−	14.7059i		−	0.602376i
$597$		0			0
$598$	−7.17247			−0.293304
$599$			45.6945i			1.86703i	0.358543	+	0.933513i	$0.383274\pi$
$599$			45.6945i			1.86703i	−0.358543	+	0.933513i	$0.616726\pi$
$600$		0			0
$601$		−	26.7774i		−	1.09227i	−0.837696	−	0.546136i	$-0.816098\pi$
$601$		−	26.7774i		−	1.09227i	0.837696	−	0.546136i	$-0.183902\pi$
$602$	−10.4859	−	6.50623i	−0.427373	−	0.265174i
$603$		0			0
$604$	−17.0392			−0.693315
$605$	5.76738	−	1.48594i	0.234477	−	0.0604121i
$606$		0			0
$607$	30.0757			1.22073			0.610367	−	0.792119i	$-0.291022\pi$
$607$	30.0757			1.22073			0.610367	+	0.792119i	$0.291022\pi$
$608$		−	1.31008i		−	0.0531306i
$609$		0			0
$610$		0			0
$611$		−	11.8326i		−	0.478697i
$612$		0			0
$613$			13.5002i			0.545270i	0.962118	+	0.272635i	$0.0878951\pi$
$613$			13.5002i			0.545270i	−0.962118	+	0.272635i	$0.912105\pi$
$614$	−1.23005			−0.0496406
$615$		0			0
$616$	8.31011	+	5.15621i	0.334824	+	0.207749i
$617$	−31.6740			−1.27515			−0.637574	−	0.770389i	$-0.720062\pi$
$617$	−31.6740			−1.27515			−0.637574	+	0.770389i	$0.720062\pi$
$618$		0			0
$619$			10.3662i			0.416653i	0.978059	+	0.208327i	$0.0668017\pi$
$619$			10.3662i			0.416653i	−0.978059	+	0.208327i	$0.933198\pi$
$620$	1.69718	+	6.58728i	0.0681605	+	0.264551i
$621$		0			0
$622$	32.4192			1.29989
$623$	−1.62428	+	2.61781i	−0.0650754	+	0.104880i
$624$		0			0
$625$	13.3252	−	21.1528i	0.533007	−	0.846111i
$626$	18.3146			0.732000
$627$		0			0
$628$	8.60949			0.343556
$629$	−4.62051			−0.184232
$630$		0			0
$631$	6.62022			0.263547			0.131773	−	0.991280i	$-0.457933\pi$
$631$	6.62022			0.263547			0.131773	+	0.991280i	$0.457933\pi$
$632$	12.6876			0.504686
$633$		0			0
$634$	−14.0669			−0.558669
$635$	−0.506605	−	1.96629i	−0.0201040	−	0.0780297i
$636$		0			0
$637$	2.97825	+	6.00939i	0.118002	+	0.238101i
$638$	14.2842			0.565516
$639$		0			0
$640$	2.16535	−	0.557894i	0.0855931	−	0.0220527i
$641$			0.866555i			0.0342269i	0.999854	+	0.0171134i	$0.00544764\pi$
$641$			0.866555i			0.0342269i	−0.999854	+	0.0171134i	$0.994552\pi$
$642$		0			0
$643$	30.3339			1.19625			0.598126	−	0.801402i	$-0.295912\pi$
$643$	30.3339			1.19625			0.598126	+	0.801402i	$0.295912\pi$
$644$	−10.4422	+	16.8295i	−0.411482	+	0.663174i
$645$		0			0
$646$	2.01459			0.0792628
$647$		−	5.19960i		−	0.204417i	−0.994763	−	0.102209i	$-0.967409\pi$
$647$		−	5.19960i		−	0.204417i	0.994763	−	0.102209i	$-0.0325909\pi$
$648$		0			0
$649$		−	37.5199i		−	1.47279i
$650$	4.19423	−	2.31492i	0.164511	−	0.0907984i
$651$		0			0
$652$			10.4044i			0.407469i
$653$	−0.510519			−0.0199782			−0.00998908	−	0.999950i	$-0.503180\pi$
$653$	−0.510519			−0.0199782			−0.00998908	+	0.999950i	$0.503180\pi$
$654$		0			0
$655$	11.1157	−	2.86391i	0.434326	−	0.111902i
$656$	2.07167			0.0808852
$657$		0			0
$658$	−27.7640	−	17.2269i	−1.08235	−	0.671573i
$659$			8.38903i			0.326790i	0.986561	+	0.163395i	$0.0522445\pi$
$659$			8.38903i			0.326790i	−0.986561	+	0.163395i	$0.947755\pi$
$660$		0			0
$661$		−	29.1672i		−	1.13447i	−0.823555	−	0.567237i	$-0.808012\pi$
$661$		−	29.1672i		−	1.13447i	0.823555	−	0.567237i	$-0.191988\pi$
$662$	10.5287			0.409209
$663$		0			0
$664$			0.194288i			0.00753984i
$665$	−7.39703	−	2.31394i	−0.286845	−	0.0897308i
$666$		0			0
$667$			28.9280i			1.12010i
$668$		−	14.0483i		−	0.543547i
$669$		0			0
$670$	−0.750459	−	2.91276i	−0.0289927	−	0.112530i
$671$		0			0
$672$		0			0
$673$			3.75616i			0.144789i	0.997376	+	0.0723947i	$0.0230641\pi$
$673$			3.75616i			0.144789i	−0.997376	+	0.0723947i	$0.976936\pi$
$674$		−	22.9186i		−	0.882793i
$675$		0			0
$676$	−12.0820			−0.464692
$677$		−	35.3252i		−	1.35766i	−0.734297	−	0.678828i	$-0.762488\pi$
$677$		−	35.3252i		−	1.35766i	0.734297	−	0.678828i	$-0.237512\pi$
$678$		0			0
$679$	−13.8242	+	22.2801i	−0.530524	+	0.855031i
$680$	0.857908	+	3.32980i	0.0328993	+	0.127692i
$681$		0			0
$682$	11.2450			0.430592
$683$	−11.0428			−0.422540			−0.211270	−	0.977428i	$-0.567760\pi$
$683$	−11.0428			−0.422540			−0.211270	+	0.977428i	$0.567760\pi$
$684$		0			0
$685$	18.5209	−	4.77183i	0.707648	−	0.182322i
$686$	18.4364	+	1.76079i	0.703904	+	0.0672273i
$687$		0			0
$688$			4.66423i			0.177822i
$689$	7.49490			0.285533
$690$		0			0
$691$			32.1353i			1.22248i	0.791444	+	0.611241i	$0.209330\pi$
$691$			32.1353i			1.22248i	−0.791444	+	0.611241i	$0.790670\pi$
$692$			14.1282i			0.537075i
$693$		0			0
$694$	−32.2651			−1.22476
$695$	−6.93308	−	26.9094i	−0.262987	−	1.02073i
$696$		0			0
$697$			3.18574i			0.120668i
$698$			32.6731i			1.23670i
$699$		0			0
$700$	0.674573	−	13.2115i	0.0254965	−	0.499350i
$701$			20.0505i			0.757297i	0.925541	+	0.378649i	$0.123611\pi$
$701$			20.0505i			0.757297i	−0.925541	+	0.378649i	$0.876389\pi$
$702$		0			0
$703$	−3.93638			−0.148463
$704$		−	3.69641i		−	0.139314i
$705$		0			0
$706$			12.0852i			0.454831i
$707$	−21.0128	+	33.8657i	−0.790268	+	1.27365i
$708$		0			0
$709$	23.7792			0.893045			0.446522	−	0.894772i	$-0.352662\pi$
$709$	23.7792			0.893045			0.446522	+	0.894772i	$0.352662\pi$
$710$	3.04840	+	11.8318i	0.114404	+	0.444038i
$711$		0			0
$712$	1.16442			0.0436387
$713$			22.7731i			0.852858i
$714$		0			0
$715$	−1.97586	−	7.66892i	−0.0738931	−	0.286801i
$716$		−	25.3580i		−	0.947674i
$717$		0			0
$718$			32.9275i			1.22884i
$719$	−22.3854			−0.834834			−0.417417	−	0.908715i	$-0.637065\pi$
$719$	−22.3854			−0.834834			−0.417417	+	0.908715i	$0.637065\pi$
$720$		0			0
$721$	−10.5287	+	16.9688i	−0.392109	+	0.631950i
$722$	−17.2837			−0.643233
$723$		0			0
$724$			19.0502i			0.707996i
$725$	−9.33652	−	16.9162i	−0.346750	−	0.628250i
$726$		0			0
$727$	−47.2104			−1.75094			−0.875469	−	0.483274i	$-0.839448\pi$
$727$	−47.2104			−1.75094			−0.875469	+	0.483274i	$0.839448\pi$
$728$	1.33652	−	2.15403i	0.0495346	−	0.0798335i
$729$		0			0
$730$	−17.1999	+	4.43149i	−0.636598	+	0.164017i
$731$	−7.17247			−0.265284
$732$		0			0
$733$	−35.2291			−1.30121			−0.650607	−	0.759414i	$-0.725486\pi$
$733$	−35.2291			−1.30121			−0.650607	+	0.759414i	$0.725486\pi$
$734$	−16.9811			−0.626784
$735$		0			0
$736$	7.48590			0.275934
$737$	−4.97228			−0.183156
$738$		0			0
$739$	−6.97180			−0.256462			−0.128231	−	0.991744i	$-0.540930\pi$
$739$	−6.97180			−0.256462			−0.128231	+	0.991744i	$0.540930\pi$
$740$	−1.67630	−	6.50623i	−0.0616220	−	0.239174i
$741$		0			0
$742$	10.9117	−	17.5860i	0.400579	−	0.645602i
$743$	11.9195			0.437283			0.218641	−	0.975805i	$-0.429837\pi$
$743$	11.9195			0.437283			0.218641	+	0.975805i	$0.429837\pi$
$744$		0			0
$745$	8.20431	+	31.8434i	0.300583	+	1.16665i
$746$		−	29.1739i		−	1.06813i
$747$		0			0
$748$	5.68421			0.207835
$749$	2.69582	−	4.34478i	0.0985033	−	0.158755i
$750$		0			0
$751$	−35.3078			−1.28840			−0.644201	−	0.764857i	$-0.722810\pi$
$751$	−35.3078			−1.28840			−0.644201	+	0.764857i	$0.722810\pi$
$752$			12.3497i			0.450347i
$753$		0			0
$754$		−	3.70254i		−	0.134839i
$755$	36.8959	−	9.50606i	1.34278	−	0.345961i
$756$		0			0
$757$			7.51232i			0.273040i	0.990637	+	0.136520i	$0.0435918\pi$
$757$			7.51232i			0.273040i	−0.990637	+	0.136520i	$0.956408\pi$
$758$	−10.9718			−0.398514
$759$		0			0
$760$	0.730883	+	2.83678i	0.0265119	+	0.102901i
$761$	−45.2360			−1.63980			−0.819901	−	0.572505i	$-0.805972\pi$
$761$	−45.2360			−1.63980			−0.819901	+	0.572505i	$0.805972\pi$
$762$		0			0
$763$	5.01625	−	8.08455i	0.181600	−	0.292680i
$764$		−	10.8616i		−	0.392958i
$765$		0			0
$766$		−	8.16073i		−	0.294859i
$767$	−9.72537			−0.351163
$768$		0			0
$769$		−	24.2725i		−	0.875287i	−0.899148	−	0.437644i	$-0.855813\pi$
$769$		−	24.2725i		−	0.875287i	0.899148	−	0.437644i	$-0.144187\pi$
$770$	−20.8709	−	6.52885i	−0.752136	−	0.235283i
$771$		0			0
$772$		−	18.0865i		−	0.650947i
$773$			12.0018i			0.431676i	0.976429	+	0.215838i	$0.0692482\pi$
$773$			12.0018i			0.431676i	−0.976429	+	0.215838i	$0.930752\pi$
$774$		0			0
$775$	−7.35000	−	13.3169i	−0.264020	−	0.478358i
$776$	9.91039			0.355762
$777$		0			0
$778$			9.75100i			0.349590i
$779$			2.71405i			0.0972408i
$780$		0			0
$781$	20.1977			0.722729
$782$			11.5115i			0.411652i
$783$		0			0
$784$	−3.10839	−	6.27199i	−0.111014	−	0.224000i
$785$	−18.6426	+	4.80318i	−0.665382	+	0.171433i
$786$		0			0
$787$	−29.9585			−1.06790			−0.533952	−	0.845515i	$-0.679294\pi$
$787$	−29.9585			−1.06790			−0.533952	+	0.845515i	$0.679294\pi$
$788$	−4.20172			−0.149680
$789$		0			0
$790$	−27.4732	+	7.07834i	−0.977452	+	0.251836i
$791$	−10.5959	+	17.0772i	−0.376748	+	0.607194i
$792$		0			0
$793$		0			0
$794$	−26.1533			−0.928147
$795$		0			0
$796$			26.2395i			0.930035i
$797$			36.0109i			1.27557i	0.770214	+	0.637785i	$0.220149\pi$
$797$			36.0109i			1.27557i	−0.770214	+	0.637785i	$0.779851\pi$
$798$		0			0
$799$	−18.9909			−0.671850
$800$	−4.37751	+	2.41607i	−0.154768	+	0.0854211i
$801$		0			0
$802$			22.2753i			0.786570i
$803$			29.3615i			1.03615i
$804$		0			0
$805$	13.2221	−	42.2674i	0.466017	−	1.48973i
$806$		−	2.91476i		−	0.102668i
$807$		0			0
$808$	15.0638			0.529942
$809$		−	36.4258i		−	1.28066i	−0.768099	−	0.640331i	$-0.778797\pi$
$809$		−	36.4258i		−	1.28066i	0.768099	−	0.640331i	$-0.221203\pi$
$810$		0			0
$811$		−	45.9870i		−	1.61482i	−0.589990	−	0.807411i	$-0.700868\pi$
$811$		−	45.9870i		−	1.61482i	0.589990	−	0.807411i	$-0.299132\pi$
$812$	−8.68762	−	5.39044i	−0.304876	−	0.189167i
$813$		0			0
$814$	−11.1066			−0.389286
$815$	−5.80457	−	22.5293i	−0.203325	−	0.789167i
$816$		0			0
$817$	−6.11049			−0.213779
$818$		−	18.8617i		−	0.659485i
$819$		0			0
$820$	−4.48590	+	1.15577i	−0.156654	+	0.0403613i
$821$		−	9.20205i		−	0.321154i	−0.987023	−	0.160577i	$-0.948665\pi$
$821$		−	9.20205i		−	0.321154i	0.987023	−	0.160577i	$-0.0513354\pi$
$822$		0			0
$823$		−	47.9339i		−	1.67087i	−0.549589	−	0.835435i	$-0.685216\pi$
$823$		−	47.9339i		−	1.67087i	0.549589	−	0.835435i	$-0.314784\pi$
$824$	7.54787			0.262943
$825$		0			0
$826$	−14.1589	+	22.8196i	−0.492652	+	0.793994i
$827$	−10.6539			−0.370474			−0.185237	−	0.982694i	$-0.559305\pi$
$827$	−10.6539			−0.370474			−0.185237	+	0.982694i	$0.559305\pi$
$828$		0			0
$829$		−	4.30336i		−	0.149462i	−0.997204	−	0.0747310i	$-0.976190\pi$
$829$		−	4.30336i		−	0.149462i	0.997204	−	0.0747310i	$-0.0238098\pi$
$830$	−0.108392	−	0.420702i	−0.00376235	−	0.0146028i
$831$		0			0
$832$	−0.958131			−0.0332172
$833$	9.64484	−	4.77997i	0.334174	−	0.165616i
$834$		0			0
$835$	7.83749	+	30.4196i	0.271227	+	1.05272i
$836$	4.84258			0.167484
$837$		0			0
$838$	−15.2501			−0.526806
$839$	−38.1028			−1.31545			−0.657727	−	0.753256i	$-0.728482\pi$
$839$	−38.1028			−1.31545			−0.657727	+	0.753256i	$0.728482\pi$
$840$		0			0
$841$	14.0669			0.485066
$842$	−20.9869			−0.723255
$843$		0			0
$844$	−20.1735			−0.694401
$845$	26.1618	−	6.74046i	0.899992	−	0.231879i
$846$		0			0
$847$	−3.71535	+	5.98792i	−0.127661	+	0.205747i
$848$	−7.82242			−0.268623
$849$		0			0
$850$	−3.71535	−	6.73157i	−0.127435	−	0.230891i
$851$		−	22.4929i		−	0.771045i
$852$		0			0
$853$	−56.3707			−1.93010			−0.965048	−	0.262072i	$-0.915594\pi$
$853$	−56.3707			−1.93010			−0.965048	+	0.262072i	$0.915594\pi$
$854$		0			0
$855$		0			0
$856$	−1.93260			−0.0660549
$857$		−	15.7781i		−	0.538968i	−0.963005	−	0.269484i	$-0.913147\pi$
$857$		−	15.7781i		−	0.538968i	0.963005	−	0.269484i	$-0.0868532\pi$
$858$		0			0
$859$		−	11.7024i		−	0.399280i	−0.979869	−	0.199640i	$-0.936023\pi$
$859$		−	11.7024i		−	0.399280i	0.979869	−	0.199640i	$-0.0639773\pi$
$860$	−2.60214	−	10.0997i	−0.0887323	−	0.344397i
$861$		0			0
$862$		−	19.9737i		−	0.680306i
$863$	−42.5925			−1.44987			−0.724933	−	0.688820i	$-0.758129\pi$
$863$	−42.5925			−1.44987			−0.724933	+	0.688820i	$0.758129\pi$
$864$		0			0
$865$	−7.88206	−	30.5926i	−0.267998	−	1.04018i
$866$	13.1103			0.445507
$867$		0			0
$868$	−6.83917	−	4.24353i	−0.232136	−	0.144035i
$869$			46.8987i			1.59093i
$870$		0			0
$871$			1.28884i			0.0436708i
$872$	−3.59608			−0.121779
$873$		0			0
$874$			9.80710i			0.331730i
$875$	5.90995	+	28.9840i	0.199793	+	0.979838i
$876$		0			0
$877$			21.6401i			0.730735i	0.930863	+	0.365368i	$0.119057\pi$
$877$			21.6401i			0.730735i	−0.930863	+	0.365368i	$0.880943\pi$
$878$			14.3928i			0.485733i
$879$		0			0
$880$	2.06221	+	8.00404i	0.0695170	+	0.269816i
$881$	−42.0251			−1.41586			−0.707931	−	0.706282i	$-0.750371\pi$
$881$	−42.0251			−1.41586			−0.707931	+	0.706282i	$0.750371\pi$
$882$		0			0
$883$			5.89798i			0.198483i	0.995063	+	0.0992414i	$0.0316416\pi$
$883$			5.89798i			0.198483i	−0.995063	+	0.0992414i	$0.968358\pi$
$884$		−	1.47338i		−	0.0495551i
$885$		0			0
$886$	−28.4180			−0.954722
$887$		−	24.9068i		−	0.836288i	−0.908381	−	0.418144i	$-0.862681\pi$
$887$		−	24.9068i		−	0.836288i	0.908381	−	0.418144i	$-0.137319\pi$
$888$		0			0
$889$	2.04147	+	1.26668i	0.0684688	+	0.0424831i
$890$	−2.52139	+	0.649625i	−0.0845172	+	0.0217755i
$891$		0			0
$892$	−18.1775			−0.608627
$893$	−16.1790			−0.541411
$894$		0			0
$895$	14.1471	+	54.9091i	0.472885	+	1.83541i
$896$	−1.39492	+	2.24815i	−0.0466010	+	0.0751056i
$897$		0			0
$898$		−	4.07377i		−	0.135943i
$899$	−11.7558			−0.392078
$900$		0			0
$901$		−	12.0290i		−	0.400745i
$902$			7.65776i			0.254975i
$903$		0			0
$904$	7.59608			0.252642
$905$	−10.6280	−	41.2504i	−0.353286	−	1.37121i
$906$		0			0
$907$		−	18.8831i		−	0.627005i	−0.949587	−	0.313502i	$-0.898498\pi$
$907$		−	18.8831i		−	0.627005i	0.949587	−	0.313502i	$-0.101502\pi$
$908$			21.5928i			0.716583i
$909$		0			0
$910$	−1.69231	+	5.40986i	−0.0560997	+	0.179335i
$911$			27.4634i			0.909902i	0.890516	+	0.454951i	$0.150343\pi$
$911$			27.4634i			0.909902i	−0.890516	+	0.454951i	$0.849657\pi$
$912$		0			0
$913$	−0.718170			−0.0237679
$914$			8.89136i			0.294100i
$915$		0			0
$916$		−	6.08425i		−	0.201029i
$917$	−7.16073	+	11.5407i	−0.236468	+	0.381109i
$918$		0			0
$919$	−40.2460			−1.32759			−0.663796	−	0.747914i	$-0.731056\pi$
$919$	−40.2460			−1.32759			−0.663796	+	0.747914i	$0.731056\pi$
$920$	−16.2096	+	4.17634i	−0.534415	+	0.137690i
$921$		0			0
$922$	11.4649			0.377578
$923$		−	5.23534i		−	0.172323i
$924$		0			0
$925$	7.25957	+	13.1531i	0.238693	+	0.432471i
$926$			1.42495i			0.0468268i
$927$		0			0
$928$			3.86433i			0.126853i
$929$	9.56970			0.313972			0.156986	−	0.987601i	$-0.449822\pi$
$929$	9.56970			0.313972			0.156986	+	0.987601i	$0.449822\pi$
$930$		0			0
$931$	8.21678	−	4.07223i	0.269294	−	0.133462i
$932$	15.1061			0.494817
$933$		0			0
$934$			26.0118i			0.851133i
$935$	−12.3083	+	3.17118i	−0.402525	+	0.103709i
$936$		0			0
$937$	4.31701			0.141031			0.0705153	−	0.997511i	$-0.477536\pi$
$937$	4.31701			0.141031			0.0705153	+	0.997511i	$0.477536\pi$
$938$	3.02414	+	1.87640i	0.0987415	+	0.0612665i
$939$		0			0
$940$	−6.88982	−	26.7415i	−0.224721	−	0.872210i
$941$	−1.57282			−0.0512724			−0.0256362	−	0.999671i	$-0.508161\pi$
$941$	−1.57282			−0.0512724			−0.0256362	+	0.999671i	$0.508161\pi$
$942$		0			0
$943$	−15.5083			−0.505021
$944$	10.1504			0.330366
$945$		0			0
$946$	−17.2409			−0.560551
$947$	−3.27867			−0.106542			−0.0532712	−	0.998580i	$-0.516965\pi$
$947$	−3.27867			−0.106542			−0.0532712	+	0.998580i	$0.516965\pi$
$948$		0			0
$949$	7.61067			0.247053
$950$	−3.16524	−	5.73487i	−0.102694	−	0.186064i
$951$		0			0
$952$	−3.45713	−	2.14506i	−0.112046	−	0.0695217i
$953$	12.7887			0.414268			0.207134	−	0.978313i	$-0.433586\pi$
$953$	12.7887			0.414268			0.207134	+	0.978313i	$0.433586\pi$
$954$		0			0
$955$	6.05961	+	23.5192i	0.196084	+	0.761062i
$956$			25.3781i			0.820785i
$957$		0			0
$958$	22.0479			0.712334
$959$	−11.9312	+	19.2291i	−0.385278	+	0.620941i
$960$		0			0
$961$	21.7455			0.701467
$962$			2.87889i			0.0928192i
$963$		0			0
$964$		−	23.0530i		−	0.742488i
$965$	10.0903	+	39.1636i	0.324819	+	1.26072i
$966$		0			0
$967$		−	35.1053i		−	1.12891i	−0.825463	−	0.564456i	$-0.809086\pi$
$967$		−	35.1053i		−	1.12891i	0.825463	−	0.564456i	$-0.190914\pi$
$968$	2.66348			0.0856076
$969$		0			0
$970$	−21.4595	+	5.52894i	−0.689023	+	0.177524i
$971$	−3.97005			−0.127405			−0.0637024	−	0.997969i	$-0.520291\pi$
$971$	−3.97005			−0.127405			−0.0637024	+	0.997969i	$0.520291\pi$
$972$		0			0
$973$	27.9384	+	17.3350i	0.895663	+	0.555735i
$974$			24.9355i			0.798984i
$975$		0			0
$976$		0			0
$977$	−25.9285			−0.829527			−0.414764	−	0.909929i	$-0.636136\pi$
$977$	−25.9285			−0.829527			−0.414764	+	0.909929i	$0.636136\pi$
$978$		0			0
$979$			4.30420i			0.137563i
$980$	10.2299	+	11.8469i	0.326781	+	0.378436i
$981$		0			0
$982$		−	15.2511i		−	0.486684i
$983$			45.4172i			1.44858i	0.689493	+	0.724292i	$0.257833\pi$
$983$			45.4172i			1.44858i	−0.689493	+	0.724292i	$0.742167\pi$
$984$		0			0
$985$	9.09820	−	2.34411i	0.289893	−	0.0746896i
$986$	−5.94243			−0.189246
$987$		0			0
$988$		−	1.25522i		−	0.0399340i
$989$		−	34.9159i		−	1.11026i
$990$		0			0
$991$	−49.7751			−1.58116			−0.790579	−	0.612360i	$-0.790220\pi$
$991$	−49.7751			−1.58116			−0.790579	+	0.612360i	$0.790220\pi$
$992$			3.04213i			0.0965876i
$993$		0			0
$994$	−12.2842	−	7.62202i	−0.389631	−	0.241756i
$995$	−14.6389	−	56.8178i	−0.464083	−	1.80125i
$996$		0			0
$997$	33.3630			1.05662			0.528309	−	0.849052i	$-0.322826\pi$
$997$	33.3630			1.05662			0.528309	+	0.849052i	$0.322826\pi$
$998$	10.8370			0.343039
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.d.e.1889.2	yes	16
3.2	odd	2		1890.2.d.f.1889.15	yes	16
5.4	even	2		1890.2.d.f.1889.1	yes	16
7.6	odd	2	inner	1890.2.d.e.1889.15	yes	16
15.14	odd	2	inner	1890.2.d.e.1889.16	yes	16
21.20	even	2		1890.2.d.f.1889.2	yes	16
35.34	odd	2		1890.2.d.f.1889.16	yes	16
105.104	even	2	inner	1890.2.d.e.1889.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.d.e.1889.1	✓	16	105.104	even	2	inner
1890.2.d.e.1889.2	yes	16	1.1	even	1	trivial
1890.2.d.e.1889.15	yes	16	7.6	odd	2	inner
1890.2.d.e.1889.16	yes	16	15.14	odd	2	inner
1890.2.d.f.1889.1	yes	16	5.4	even	2
1890.2.d.f.1889.2	yes	16	21.20	even	2
1890.2.d.f.1889.15	yes	16	3.2	odd	2
1890.2.d.f.1889.16	yes	16	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.16535 + 0.557894i) q^{5} +(1.39492 - 2.24815i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.16535 + 0.557894i) q^{5} +(1.39492 - 2.24815i) q^{7} -1.00000 q^{8} +(2.16535 - 0.557894i) q^{10} -3.69641i q^{11} -0.958131 q^{13} +(-1.39492 + 2.24815i) q^{14} +1.00000 q^{16} +1.53776i q^{17} +1.31008i q^{19} +(-2.16535 + 0.557894i) q^{20} +3.69641i q^{22} -7.48590 q^{23} +(4.37751 - 2.41607i) q^{25} +0.958131 q^{26} +(1.39492 - 2.24815i) q^{28} -3.86433i q^{29} -3.04213i q^{31} -1.00000 q^{32} -1.53776i q^{34} +(-1.76627 + 5.64626i) q^{35} +3.00470i q^{37} -1.31008i q^{38} +(2.16535 - 0.557894i) q^{40} +2.07167 q^{41} +4.66423i q^{43} -3.69641i q^{44} +7.48590 q^{46} +12.3497i q^{47} +(-3.10839 - 6.27199i) q^{49} +(-4.37751 + 2.41607i) q^{50} -0.958131 q^{52} -7.82242 q^{53} +(2.06221 + 8.00404i) q^{55} +(-1.39492 + 2.24815i) q^{56} +3.86433i q^{58} +10.1504 q^{59} +3.04213i q^{62} +1.00000 q^{64} +(2.07469 - 0.534535i) q^{65} -1.34516i q^{67} +1.53776i q^{68} +(1.76627 - 5.64626i) q^{70} +5.46412i q^{71} -7.94324 q^{73} -3.00470i q^{74} +1.31008i q^{76} +(-8.31011 - 5.15621i) q^{77} -12.6876 q^{79} +(-2.16535 + 0.557894i) q^{80} -2.07167 q^{82} -0.194288i q^{83} +(-0.857908 - 3.32980i) q^{85} -4.66423i q^{86} +3.69641i q^{88} -1.16442 q^{89} +(-1.33652 + 2.15403i) q^{91} -7.48590 q^{92} -12.3497i q^{94} +(-0.730883 - 2.83678i) q^{95} -9.91039 q^{97} +(3.10839 + 6.27199i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} + 8 q^{23} - 6 q^{25} - 16 q^{32} - q^{35} - 8 q^{46} + 2 q^{49} + 6 q^{50} - 16 q^{53} + 16 q^{64} - 40 q^{65} + q^{70} - 14 q^{77} - 8 q^{79} - 44 q^{85} - 40 q^{91} + 8 q^{92} - 36 q^{95} - 2 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 + 8 * q^23 - 6 * q^25 - 16 * q^32 - q^35 - 8 * q^46 + 2 * q^49 + 6 * q^50 - 16 * q^53 + 16 * q^64 - 40 * q^65 + q^70 - 14 * q^77 - 8 * q^79 - 44 * q^85 - 40 * q^91 + 8 * q^92 - 36 * q^95 - 2 * q^98

Introduction

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